LMFDB - Embedded newform 1470.2.d.g.1469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.2
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.71521 + 0.240923i) q^{3} +1.00000 q^{4} +(0.263182 - 2.22053i) q^{5} +(1.71521 - 0.240923i) q^{6} -1.00000 q^{8} +(2.88391 - 0.826470i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.71521 + 0.240923i) q^{3} +1.00000 q^{4} +(0.263182 - 2.22053i) q^{5} +(1.71521 - 0.240923i) q^{6} -1.00000 q^{8} +(2.88391 - 0.826470i) q^{9} +(-0.263182 + 2.22053i) q^{10} -4.81031i q^{11} +(-1.71521 + 0.240923i) q^{12} -4.56331 q^{13} +(0.0835634 + 3.87208i) q^{15} +1.00000 q^{16} -1.16632i q^{17} +(-2.88391 + 0.826470i) q^{18} -4.61409i q^{19} +(0.263182 - 2.22053i) q^{20} +4.81031i q^{22} +3.85238 q^{23} +(1.71521 - 0.240923i) q^{24} +(-4.86147 - 1.16881i) q^{25} +4.56331 q^{26} +(-4.74741 + 2.11237i) q^{27} +1.96431i q^{29} +(-0.0835634 - 3.87208i) q^{30} +5.57387i q^{31} -1.00000 q^{32} +(1.15892 + 8.25071i) q^{33} +1.16632i q^{34} +(2.88391 - 0.826470i) q^{36} -8.98759i q^{37} +4.61409i q^{38} +(7.82704 - 1.09941i) q^{39} +(-0.263182 + 2.22053i) q^{40} -3.76181 q^{41} +4.02444i q^{43} -4.81031i q^{44} +(-1.07620 - 6.62131i) q^{45} -3.85238 q^{46} -6.36970i q^{47} +(-1.71521 + 0.240923i) q^{48} +(4.86147 + 1.16881i) q^{50} +(0.280995 + 2.00050i) q^{51} -4.56331 q^{52} +10.0081 q^{53} +(4.74741 - 2.11237i) q^{54} +(-10.6814 - 1.26599i) q^{55} +(1.11164 + 7.91414i) q^{57} -1.96431i q^{58} +12.7078 q^{59} +(0.0835634 + 3.87208i) q^{60} +4.96802i q^{61} -5.57387i q^{62} +1.00000 q^{64} +(-1.20098 + 10.1329i) q^{65} +(-1.15892 - 8.25071i) q^{66} +12.5244i q^{67} -1.16632i q^{68} +(-6.60766 + 0.928130i) q^{69} +2.74047i q^{71} +(-2.88391 + 0.826470i) q^{72} -13.9852 q^{73} +8.98759i q^{74} +(8.62005 + 0.833508i) q^{75} -4.61409i q^{76} +(-7.82704 + 1.09941i) q^{78} -10.5162 q^{79} +(0.263182 - 2.22053i) q^{80} +(7.63389 - 4.76693i) q^{81} +3.76181 q^{82} -3.54903i q^{83} +(-2.58985 - 0.306956i) q^{85} -4.02444i q^{86} +(-0.473250 - 3.36922i) q^{87} +4.81031i q^{88} -16.0060 q^{89} +(1.07620 + 6.62131i) q^{90} +3.85238 q^{92} +(-1.34288 - 9.56038i) q^{93} +6.36970i q^{94} +(-10.2457 - 1.21435i) q^{95} +(1.71521 - 0.240923i) q^{96} +1.30193 q^{97} +(-3.97558 - 13.8725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.71521	+	0.240923i	−0.990279	+	0.139097i
$3$	−1.71521	+	0.240923i	−0.990279	+	0.139097i
$4$	1.00000			0.500000
$5$	0.263182	−	2.22053i	0.117699	−	0.993049i
$5$	0.263182	−	2.22053i	0.117699	−	0.993049i
$6$	1.71521	−	0.240923i	0.700233	−	0.0983566i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.88391	−	0.826470i	0.961304	−	0.275490i
$10$	−0.263182	+	2.22053i	−0.0832255	+	0.702192i
$11$		−	4.81031i		−	1.45036i	−0.688557	−	0.725182i	$-0.741756\pi$
$11$		−	4.81031i		−	1.45036i	0.688557	−	0.725182i	$-0.258244\pi$
$12$	−1.71521	+	0.240923i	−0.495139	+	0.0695486i
$13$	−4.56331			−1.26563			−0.632817	−	0.774302i	$-0.718101\pi$
$13$	−4.56331			−1.26563			−0.632817	+	0.774302i	$0.718101\pi$
$14$		0			0
$15$	0.0835634	+	3.87208i	0.0215760	+	0.999767i
$16$	1.00000			0.250000
$17$		−	1.16632i		−	0.282875i	−0.989947	−	0.141438i	$-0.954828\pi$
$17$		−	1.16632i		−	0.282875i	0.989947	−	0.141438i	$-0.0451725\pi$
$18$	−2.88391	+	0.826470i	−0.679745	+	0.194801i
$19$		−	4.61409i		−	1.05854i	−0.848452	−	0.529272i	$-0.822465\pi$
$19$		−	4.61409i		−	1.05854i	0.848452	−	0.529272i	$-0.177535\pi$
$20$	0.263182	−	2.22053i	0.0588493	−	0.496525i
$21$		0			0
$22$			4.81031i			1.02556i
$23$	3.85238			0.803278			0.401639	−	0.915798i	$-0.368441\pi$
$23$	3.85238			0.803278			0.401639	+	0.915798i	$0.368441\pi$
$24$	1.71521	−	0.240923i	0.350116	−	0.0491783i
$25$	−4.86147	−	1.16881i	−0.972294	−	0.233761i
$26$	4.56331			0.894938
$27$	−4.74741	+	2.11237i	−0.913639	+	0.406527i
$28$		0			0
$29$			1.96431i			0.364764i	0.983228	+	0.182382i	$0.0583808\pi$
$29$			1.96431i			0.364764i	−0.983228	+	0.182382i	$0.941619\pi$
$30$	−0.0835634	−	3.87208i	−0.0152565	−	0.706942i
$31$			5.57387i			1.00110i	0.865709	+	0.500548i	$0.166868\pi$
$31$			5.57387i			1.00110i	−0.865709	+	0.500548i	$0.833132\pi$
$32$	−1.00000			−0.176777
$33$	1.15892	+	8.25071i	0.201742	+	1.43626i
$34$			1.16632i			0.200023i
$35$		0			0
$36$	2.88391	−	0.826470i	0.480652	−	0.137745i
$37$		−	8.98759i		−	1.47755i	−0.673952	−	0.738775i	$-0.735405\pi$
$37$		−	8.98759i		−	1.47755i	0.673952	−	0.738775i	$-0.264595\pi$
$38$			4.61409i			0.748504i
$39$	7.82704	−	1.09941i	1.25333	−	0.176046i
$40$	−0.263182	+	2.22053i	−0.0416127	+	0.351096i
$41$	−3.76181			−0.587495			−0.293748	−	0.955883i	$-0.594903\pi$
$41$	−3.76181			−0.587495			−0.293748	+	0.955883i	$0.594903\pi$
$42$		0			0
$43$			4.02444i			0.613722i	0.951754	+	0.306861i	$0.0992786\pi$
$43$			4.02444i			0.613722i	−0.951754	+	0.306861i	$0.900721\pi$
$44$		−	4.81031i		−	0.725182i
$45$	−1.07620	−	6.62131i	−0.160431	−	0.987047i
$46$	−3.85238			−0.568003
$47$		−	6.36970i		−	0.929116i	−0.885543	−	0.464558i	$-0.846213\pi$
$47$		−	6.36970i		−	0.929116i	0.885543	−	0.464558i	$-0.153787\pi$
$48$	−1.71521	+	0.240923i	−0.247570	+	0.0347743i
$49$		0			0
$50$	4.86147	+	1.16881i	0.687516	+	0.165294i
$51$	0.280995	+	2.00050i	0.0393472	+	0.280125i
$52$	−4.56331			−0.632817
$53$	10.0081			1.37472			0.687362	−	0.726315i	$-0.258769\pi$
$53$	10.0081			1.37472			0.687362	+	0.726315i	$0.258769\pi$
$54$	4.74741	−	2.11237i	0.646040	−	0.287458i
$55$	−10.6814	−	1.26599i	−1.44028	−	0.170706i
$56$		0			0
$57$	1.11164	+	7.91414i	0.147241	+	1.04825i
$58$		−	1.96431i		−	0.257927i
$59$	12.7078			1.65442			0.827209	−	0.561894i	$-0.189927\pi$
$59$	12.7078			1.65442			0.827209	+	0.561894i	$0.189927\pi$
$60$	0.0835634	+	3.87208i	0.0107880	+	0.499884i
$61$			4.96802i			0.636090i	0.948076	+	0.318045i	$0.103026\pi$
$61$			4.96802i			0.636090i	−0.948076	+	0.318045i	$0.896974\pi$
$62$		−	5.57387i		−	0.707882i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.20098	+	10.1329i	−0.148963	+	1.25684i
$66$	−1.15892	−	8.25071i	−0.142653	−	1.01559i
$67$			12.5244i			1.53010i	0.643974	+	0.765048i	$0.277285\pi$
$67$			12.5244i			1.53010i	−0.643974	+	0.765048i	$0.722715\pi$
$68$		−	1.16632i		−	0.141438i
$69$	−6.60766	+	0.928130i	−0.795469	+	0.111734i
$70$		0			0
$71$			2.74047i			0.325234i	0.986689	+	0.162617i	$0.0519935\pi$
$71$			2.74047i			0.325234i	−0.986689	+	0.162617i	$0.948006\pi$
$72$	−2.88391	+	0.826470i	−0.339872	+	0.0974004i
$73$	−13.9852			−1.63685			−0.818424	−	0.574615i	$-0.805152\pi$
$73$	−13.9852			−1.63685			−0.818424	+	0.574615i	$0.805152\pi$
$74$			8.98759i			1.04479i
$75$	8.62005	+	0.833508i	0.995358	+	0.0962452i
$76$		−	4.61409i		−	0.529272i
$77$		0			0
$78$	−7.82704	+	1.09941i	−0.886238	+	0.124483i
$79$	−10.5162			−1.18316			−0.591581	−	0.806246i	$-0.701496\pi$
$79$	−10.5162			−1.18316			−0.591581	+	0.806246i	$0.701496\pi$
$80$	0.263182	−	2.22053i	0.0294247	−	0.248262i
$81$	7.63389	−	4.76693i	0.848210	−	0.529659i
$82$	3.76181			0.415422
$83$		−	3.54903i		−	0.389557i	−0.980847	−	0.194778i	$-0.937601\pi$
$83$		−	3.54903i		−	0.389557i	0.980847	−	0.194778i	$-0.0623988\pi$
$84$		0			0
$85$	−2.58985	−	0.306956i	−0.280909	−	0.0332940i
$86$		−	4.02444i		−	0.433967i
$87$	−0.473250	−	3.36922i	−0.0507377	−	0.361218i
$88$			4.81031i			0.512781i
$89$	−16.0060			−1.69664			−0.848318	−	0.529487i	$-0.822384\pi$
$89$	−16.0060			−1.69664			−0.848318	+	0.529487i	$0.822384\pi$
$90$	1.07620	+	6.62131i	0.113442	+	0.697948i
$91$		0			0
$92$	3.85238			0.401639
$93$	−1.34288	−	9.56038i	−0.139250	−	0.991365i
$94$			6.36970i			0.656984i
$95$	−10.2457	−	1.21435i	−1.05119	−	0.124589i
$96$	1.71521	−	0.240923i	0.175058	−	0.0245891i
$97$	1.30193			0.132191			0.0660953	−	0.997813i	$-0.478946\pi$
$97$	1.30193			0.132191			0.0660953	+	0.997813i	$0.478946\pi$
$98$		0			0
$99$	−3.97558	−	13.8725i	−0.399561	−	1.39424i
$100$	−4.86147	−	1.16881i	−0.486147	−	0.116881i
$101$	−12.4689			−1.24070			−0.620351	−	0.784324i	$-0.713010\pi$
$101$	−12.4689			−1.24070			−0.620351	+	0.784324i	$0.713010\pi$
$102$	−0.280995	−	2.00050i	−0.0278226	−	0.198079i
$103$	−0.300347			−0.0295941			−0.0147970	−	0.999891i	$-0.504710\pi$
$103$	−0.300347			−0.0295941			−0.0147970	+	0.999891i	$0.504710\pi$
$104$	4.56331			0.447469
$105$		0			0
$106$	−10.0081			−0.972076
$107$	13.5389			1.30886			0.654429	−	0.756123i	$-0.272909\pi$
$107$	13.5389			1.30886			0.654429	+	0.756123i	$0.272909\pi$
$108$	−4.74741	+	2.11237i	−0.456819	+	0.203263i
$109$	−14.8845			−1.42567			−0.712837	−	0.701330i	$-0.752590\pi$
$109$	−14.8845			−1.42567			−0.712837	+	0.701330i	$0.752590\pi$
$110$	10.6814	+	1.26599i	1.01843	+	0.120707i
$111$	2.16532	+	15.4156i	0.205523	+	1.46319i
$112$		0			0
$113$	−9.49406			−0.893126			−0.446563	−	0.894752i	$-0.647352\pi$
$113$	−9.49406			−0.893126			−0.446563	+	0.894752i	$0.647352\pi$
$114$	−1.11164	−	7.91414i	−0.104115	−	0.741228i
$115$	1.01388	−	8.55432i	0.0945446	−	0.797694i
$116$			1.96431i			0.182382i
$117$	−13.1602	+	3.77144i	−1.21666	+	0.348669i
$118$	−12.7078			−1.16985
$119$		0			0
$120$	−0.0835634	−	3.87208i	−0.00762826	−	0.353471i
$121$	−12.1391			−1.10355
$122$		−	4.96802i		−	0.449784i
$123$	6.45230	−	0.906307i	0.581784	−	0.0817190i
$124$			5.57387i			0.500548i
$125$	−3.87481	+	10.4874i	−0.346574	+	0.938023i
$126$		0			0
$127$			14.0483i			1.24659i	0.781988	+	0.623294i	$0.214206\pi$
$127$			14.0483i			1.24659i	−0.781988	+	0.623294i	$0.785794\pi$
$128$	−1.00000			−0.0883883
$129$	−0.969582	−	6.90277i	−0.0853670	−	0.607755i
$130$	1.20098	−	10.1329i	0.105333	−	0.888718i
$131$	−10.1222			−0.884384			−0.442192	−	0.896921i	$-0.645799\pi$
$131$	−10.1222			−0.884384			−0.442192	+	0.896921i	$0.645799\pi$
$132$	1.15892	+	8.25071i	0.100871	+	0.718132i
$133$		0			0
$134$		−	12.5244i		−	1.08194i
$135$	3.44115	+	11.0977i	0.296167	+	0.955136i
$136$			1.16632i			0.100012i
$137$	−17.8156			−1.52209			−0.761046	−	0.648698i	$-0.775314\pi$
$137$	−17.8156			−1.52209			−0.761046	+	0.648698i	$0.775314\pi$
$138$	6.60766	−	0.928130i	0.562481	−	0.0790076i
$139$		−	16.7252i		−	1.41861i	−0.704902	−	0.709305i	$-0.749009\pi$
$139$		−	16.7252i		−	1.41861i	0.704902	−	0.709305i	$-0.250991\pi$
$140$		0			0
$141$	1.53461	+	10.9254i	0.129237	+	0.920084i
$142$		−	2.74047i		−	0.229975i
$143$			21.9509i			1.83563i
$144$	2.88391	−	0.826470i	0.240326	−	0.0688725i
$145$	4.36181	+	0.516973i	0.362229	+	0.0429322i
$146$	13.9852			1.15743
$147$		0			0
$148$		−	8.98759i		−	0.738775i
$149$		−	20.0263i		−	1.64062i	−0.571921	−	0.820309i	$-0.693802\pi$
$149$		−	20.0263i		−	1.64062i	0.571921	−	0.820309i	$-0.306198\pi$
$150$	−8.62005	−	0.833508i	−0.703824	−	0.0680556i
$151$	−3.80170			−0.309378			−0.154689	−	0.987963i	$-0.549438\pi$
$151$	−3.80170			−0.309378			−0.154689	+	0.987963i	$0.549438\pi$
$152$			4.61409i			0.374252i
$153$	−0.963932	−	3.36358i	−0.0779293	−	0.271929i
$154$		0			0
$155$	12.3769	+	1.46694i	0.994139	+	0.117828i
$156$	7.82704	−	1.09941i	0.626665	−	0.0880231i
$157$	10.2291			0.816369			0.408185	−	0.912899i	$-0.366162\pi$
$157$	10.2291			0.816369			0.408185	+	0.912899i	$0.366162\pi$
$158$	10.5162			0.836621
$159$	−17.1661	+	2.41119i	−1.36136	+	0.191220i
$160$	−0.263182	+	2.22053i	−0.0208064	+	0.175548i
$161$		0			0
$162$	−7.63389	+	4.76693i	−0.599775	+	0.374526i
$163$			1.05739i			0.0828212i	0.999142	+	0.0414106i	$0.0131852\pi$
$163$			1.05739i			0.0828212i	−0.999142	+	0.0414106i	$0.986815\pi$
$164$	−3.76181			−0.293748
$165$	18.6259	−	0.401966i	1.45003	−	0.0312930i
$166$			3.54903i			0.275458i
$167$		−	1.75194i		−	0.135569i	−0.997700	−	0.0677845i	$-0.978407\pi$
$167$		−	1.75194i		−	0.135569i	0.997700	−	0.0677845i	$-0.0215930\pi$
$168$		0			0
$169$	7.82377			0.601828
$170$	2.58985	+	0.306956i	0.198633	+	0.0235424i
$171$	−3.81341	−	13.3066i	−0.291618	−	1.01758i
$172$			4.02444i			0.306861i
$173$		−	0.127913i		−	0.00972507i	−0.999988	−	0.00486254i	$-0.998452\pi$
$173$		−	0.127913i		−	0.00972507i	0.999988	−	0.00486254i	$-0.00154780\pi$
$174$	0.473250	+	3.36922i	0.0358770	+	0.255420i
$175$		0			0
$176$		−	4.81031i		−	0.362591i
$177$	−21.7966	+	3.06161i	−1.63834	+	0.230125i
$178$	16.0060			1.19970
$179$		−	6.24279i		−	0.466608i	−0.972404	−	0.233304i	$-0.925046\pi$
$179$		−	6.24279i		−	0.466608i	0.972404	−	0.233304i	$-0.0749537\pi$
$180$	−1.07620	−	6.62131i	−0.0802155	−	0.493524i
$181$		−	1.20138i		−	0.0892975i	−0.999003	−	0.0446488i	$-0.985783\pi$
$181$		−	1.20138i		−	0.0892975i	0.999003	−	0.0446488i	$-0.0142169\pi$
$182$		0			0
$183$	−1.19691	−	8.52122i	−0.0884784	−	0.629906i
$184$	−3.85238			−0.284001
$185$	−19.9572	−	2.36537i	−1.46728	−	0.173906i
$186$	1.34288	+	9.56038i	0.0984645	+	0.701001i
$187$	−5.61039			−0.410272
$188$		−	6.36970i		−	0.464558i
$189$		0			0
$190$	10.2457	+	1.21435i	0.743301	+	0.0880979i
$191$			21.8612i			1.58182i	0.611931	+	0.790911i	$0.290393\pi$
$191$			21.8612i			1.58182i	−0.611931	+	0.790911i	$0.709607\pi$
$192$	−1.71521	+	0.240923i	−0.123785	+	0.0173872i
$193$		−	16.1261i		−	1.16078i	−0.814338	−	0.580391i	$-0.802900\pi$
$193$		−	16.1261i		−	1.16078i	0.814338	−	0.580391i	$-0.197100\pi$
$194$	−1.30193			−0.0934729
$195$	−0.381326	−	17.6695i	−0.0273073	−	1.26534i
$196$		0			0
$197$	−10.4115			−0.741786			−0.370893	−	0.928676i	$-0.620948\pi$
$197$	−10.4115			−0.741786			−0.370893	+	0.928676i	$0.620948\pi$
$198$	3.97558	+	13.8725i	0.282532	+	0.985877i
$199$			17.7968i			1.26158i	0.775953	+	0.630791i	$0.217270\pi$
$199$			17.7968i			1.26158i	−0.775953	+	0.630791i	$0.782730\pi$
$200$	4.86147	+	1.16881i	0.343758	+	0.0826470i
$201$	−3.01741	−	21.4820i	−0.212832	−	1.51522i
$202$	12.4689			0.877309
$203$		0			0
$204$	0.280995	+	2.00050i	0.0196736	+	0.140063i
$205$	−0.990040	+	8.35319i	−0.0691474	+	0.583412i
$206$	0.300347			0.0209262
$207$	11.1099	−	3.18388i	0.772194	−	0.221295i
$208$	−4.56331			−0.316408
$209$	−22.1952			−1.53527
$210$		0			0
$211$	7.89044			0.543200			0.271600	−	0.962410i	$-0.412447\pi$
$211$	7.89044			0.543200			0.271600	+	0.962410i	$0.412447\pi$
$212$	10.0081			0.687362
$213$	−0.660244	−	4.70049i	−0.0452392	−	0.322073i
$214$	−13.5389			−0.925503
$215$	8.93638	+	1.05916i	0.609456	+	0.0722342i
$216$	4.74741	−	2.11237i	0.323020	−	0.143729i
$217$		0			0
$218$	14.8845			1.00810
$219$	23.9877	−	3.36937i	1.62094	−	0.227681i
$220$	−10.6814	−	1.26599i	−0.720141	−	0.0853529i
$221$			5.32230i			0.358016i
$222$	−2.16532	−	15.4156i	−0.145327	−	1.03463i
$223$	17.9707			1.20341			0.601704	−	0.798719i	$-0.294489\pi$
$223$	17.9707			1.20341			0.601704	+	0.798719i	$0.294489\pi$
$224$		0			0
$225$	−14.9860	+	0.647129i	−0.999069	+	0.0431419i
$226$	9.49406			0.631535
$227$		−	5.34178i		−	0.354547i	−0.984162	−	0.177273i	$-0.943272\pi$
$227$		−	5.34178i		−	0.354547i	0.984162	−	0.177273i	$-0.0567277\pi$
$228$	1.11164	+	7.91414i	0.0736203	+	0.524127i
$229$			3.53602i			0.233667i	0.993152	+	0.116834i	$0.0372744\pi$
$229$			3.53602i			0.233667i	−0.993152	+	0.116834i	$0.962726\pi$
$230$	−1.01388	+	8.55432i	−0.0668532	+	0.564055i
$231$		0			0
$232$		−	1.96431i		−	0.128964i
$233$	−5.24366			−0.343524			−0.171762	−	0.985138i	$-0.554946\pi$
$233$	−5.24366			−0.343524			−0.171762	+	0.985138i	$0.554946\pi$
$234$	13.1602	−	3.77144i	0.860307	−	0.246547i
$235$	−14.1441	−	1.67639i	−0.922658	−	0.109356i
$236$	12.7078			0.827209
$237$	18.0375	−	2.53359i	1.17166	−	0.164574i
$238$		0			0
$239$		−	24.3376i		−	1.57427i	−0.616780	−	0.787135i	$-0.711563\pi$
$239$		−	24.3376i		−	1.57427i	0.616780	−	0.787135i	$-0.288437\pi$
$240$	0.0835634	+	3.87208i	0.00539400	+	0.249942i
$241$			24.9383i			1.60642i	0.595698	+	0.803209i	$0.296876\pi$
$241$			24.9383i			1.60642i	−0.595698	+	0.803209i	$0.703124\pi$
$242$	12.1391			0.780331
$243$	−11.9453	+	10.0155i	−0.766291	+	0.642494i
$244$			4.96802i			0.318045i
$245$		0			0
$246$	−6.45230	+	0.906307i	−0.411384	+	0.0577840i
$247$			21.0555i			1.33973i
$248$		−	5.57387i		−	0.353941i
$249$	0.855045	+	6.08735i	0.0541863	+	0.385770i
$250$	3.87481	−	10.4874i	0.245065	−	0.663282i
$251$	8.21145			0.518302			0.259151	−	0.965837i	$-0.416557\pi$
$251$	8.21145			0.518302			0.259151	+	0.965837i	$0.416557\pi$
$252$		0			0
$253$		−	18.5312i		−	1.16504i
$254$		−	14.0483i		−	0.881471i
$255$	4.51610	−	0.0974621i	0.282809	−	0.00610331i
$256$	1.00000			0.0625000
$257$			2.18021i			0.135998i	0.997685	+	0.0679990i	$0.0216615\pi$
$257$			2.18021i			0.135998i	−0.997685	+	0.0679990i	$0.978339\pi$
$258$	0.969582	+	6.90277i	0.0603636	+	0.429748i
$259$		0			0
$260$	−1.20098	+	10.1329i	−0.0744817	+	0.628418i
$261$	1.62345	+	5.66491i	0.100489	+	0.350649i
$262$	10.1222			0.625354
$263$	−21.9316			−1.35236			−0.676179	−	0.736737i	$-0.736366\pi$
$263$	−21.9316			−1.35236			−0.676179	+	0.736737i	$0.736366\pi$
$264$	−1.15892	−	8.25071i	−0.0713264	−	0.507796i
$265$	2.63396	−	22.2233i	0.161803	−	1.36517i
$266$		0			0
$267$	27.4537	−	3.85623i	1.68014	−	0.235997i
$268$			12.5244i			0.765048i
$269$	25.5632			1.55861			0.779307	−	0.626642i	$-0.215571\pi$
$269$	25.5632			1.55861			0.779307	+	0.626642i	$0.215571\pi$
$270$	−3.44115	−	11.0977i	−0.209422	−	0.675383i
$271$			5.09869i			0.309724i	0.987936	+	0.154862i	$0.0494932\pi$
$271$			5.09869i			0.309724i	−0.987936	+	0.154862i	$0.950507\pi$
$272$		−	1.16632i		−	0.0707188i
$273$		0			0
$274$	17.8156			1.07628
$275$	−5.62232	+	23.3852i	−0.339039	+	1.41018i
$276$	−6.60766	+	0.928130i	−0.397734	+	0.0558668i
$277$			4.98773i			0.299684i	0.988710	+	0.149842i	$0.0478764\pi$
$277$			4.98773i			0.299684i	−0.988710	+	0.149842i	$0.952124\pi$
$278$			16.7252i			1.00311i
$279$	4.60664	+	16.0746i	0.275792	+	0.962358i
$280$		0			0
$281$			18.3073i			1.09212i	0.837746	+	0.546060i	$0.183873\pi$
$281$			18.3073i			1.09212i	−0.837746	+	0.546060i	$0.816127\pi$
$282$	−1.53461	−	10.9254i	−0.0913847	−	0.650598i
$283$	5.04720			0.300025			0.150012	−	0.988684i	$-0.452069\pi$
$283$	5.04720			0.300025			0.150012	+	0.988684i	$0.452069\pi$
$284$			2.74047i			0.162617i
$285$	17.8661	−	0.385569i	1.05830	−	0.0228391i
$286$		−	21.9509i		−	1.29799i
$287$		0			0
$288$	−2.88391	+	0.826470i	−0.169936	+	0.0487002i
$289$	15.6397			0.919982
$290$	−4.36181	−	0.516973i	−0.256134	−	0.0303577i
$291$	−2.23308	+	0.313665i	−0.130906	+	0.0183874i
$292$	−13.9852			−0.818424
$293$			24.4169i			1.42645i	0.700934	+	0.713226i	$0.252767\pi$
$293$			24.4169i			1.42645i	−0.700934	+	0.713226i	$0.747233\pi$
$294$		0			0
$295$	3.34447	−	28.2181i	0.194723	−	1.64292i
$296$			8.98759i			0.522393i
$297$	10.1612	+	22.8365i	0.589611	+	1.32511i
$298$			20.0263i			1.16009i
$299$	−17.5796			−1.01666
$300$	8.62005	+	0.833508i	0.497679	+	0.0481226i
$301$		0			0
$302$	3.80170			0.218763
$303$	21.3868	−	3.00405i	1.22864	−	0.172578i
$304$		−	4.61409i		−	0.264636i
$305$	11.0316	+	1.30749i	0.631669	+	0.0748669i
$306$	0.963932	+	3.36358i	0.0551044	+	0.192283i
$307$	15.1857			0.866691			0.433346	−	0.901228i	$-0.357333\pi$
$307$	15.1857			0.866691			0.433346	+	0.901228i	$0.357333\pi$
$308$		0			0
$309$	0.515159	−	0.0723606i	0.0293064	−	0.00411645i
$310$	−12.3769	−	1.46694i	−0.702962	−	0.0833168i
$311$	11.0840			0.628518			0.314259	−	0.949337i	$-0.398244\pi$
$311$	11.0840			0.628518			0.314259	+	0.949337i	$0.398244\pi$
$312$	−7.82704	+	1.09941i	−0.443119	+	0.0622417i
$313$	7.05798			0.398940			0.199470	−	0.979904i	$-0.436078\pi$
$313$	7.05798			0.398940			0.199470	+	0.979904i	$0.436078\pi$
$314$	−10.2291			−0.577260
$315$		0			0
$316$	−10.5162			−0.591581
$317$	−1.09383			−0.0614354			−0.0307177	−	0.999528i	$-0.509779\pi$
$317$	−1.09383			−0.0614354			−0.0307177	+	0.999528i	$0.509779\pi$
$318$	17.1661	−	2.41119i	0.962626	−	0.135213i
$319$	9.44897			0.529041
$320$	0.263182	−	2.22053i	0.0147123	−	0.124131i
$321$	−23.2222	+	3.26185i	−1.29614	+	0.182059i
$322$		0			0
$323$	−5.38152			−0.299436
$324$	7.63389	−	4.76693i	0.424105	−	0.264830i
$325$	22.1844	+	5.33362i	1.23057	+	0.295856i
$326$		−	1.05739i		−	0.0585635i
$327$	25.5300	−	3.58602i	1.41181	−	0.198307i
$328$	3.76181			0.207711
$329$		0			0
$330$	−18.6259	+	0.401966i	−1.02532	+	0.0221275i
$331$	−13.3568			−0.734154			−0.367077	−	0.930191i	$-0.619641\pi$
$331$	−13.3568			−0.734154			−0.367077	+	0.930191i	$0.619641\pi$
$332$		−	3.54903i		−	0.194778i
$333$	−7.42797	−	25.9194i	−0.407050	−	1.42037i
$334$			1.75194i			0.0958617i
$335$	27.8107	+	3.29619i	1.51946	+	0.180090i
$336$		0			0
$337$		−	12.3715i		−	0.673921i	−0.941519	−	0.336960i	$-0.890601\pi$
$337$		−	12.3715i		−	0.673921i	0.941519	−	0.336960i	$-0.109399\pi$
$338$	−7.82377			−0.425557
$339$	16.2843	−	2.28734i	0.884444	−	0.124231i
$340$	−2.58985	−	0.306956i	−0.140455	−	0.0166470i
$341$	26.8121			1.45195
$342$	3.81341	+	13.3066i	0.206205	+	0.719540i
$343$		0			0
$344$		−	4.02444i		−	0.216983i
$345$	0.321918	+	14.9167i	0.0173315	+	0.803091i
$346$			0.127913i			0.00687666i
$347$	2.96861			0.159363			0.0796817	−	0.996820i	$-0.474610\pi$
$347$	2.96861			0.159363			0.0796817	+	0.996820i	$0.474610\pi$
$348$	−0.473250	−	3.36922i	−0.0253688	−	0.180609i
$349$			1.03511i			0.0554080i	0.999616	+	0.0277040i	$0.00881959\pi$
$349$			1.03511i			0.0554080i	−0.999616	+	0.0277040i	$0.991180\pi$
$350$		0			0
$351$	21.6639	−	9.63941i	1.15633	−	0.514514i
$352$			4.81031i			0.256390i
$353$		−	13.4155i		−	0.714037i	−0.934097	−	0.357018i	$-0.883793\pi$
$353$		−	13.4155i		−	0.714037i	0.934097	−	0.357018i	$-0.116207\pi$
$354$	21.7966	−	3.06161i	1.15848	−	0.162723i
$355$	6.08529	+	0.721243i	0.322974	+	0.0382796i
$356$	−16.0060			−0.848318
$357$		0			0
$358$			6.24279i			0.329942i
$359$		−	24.8666i		−	1.31241i	−0.754584	−	0.656204i	$-0.772161\pi$
$359$		−	24.8666i		−	1.31241i	0.754584	−	0.656204i	$-0.227839\pi$
$360$	1.07620	+	6.62131i	0.0567210	+	0.348974i
$361$	−2.28981			−0.120516
$362$			1.20138i			0.0631429i
$363$	20.8211	−	2.92459i	1.09283	−	0.153501i
$364$		0			0
$365$	−3.68066	+	31.0546i	−0.192655	+	1.62547i
$366$	1.19691	+	8.52122i	0.0625637	+	0.445411i
$367$	5.54367			0.289377			0.144689	−	0.989477i	$-0.453782\pi$
$367$	5.54367			0.289377			0.144689	+	0.989477i	$0.453782\pi$
$368$	3.85238			0.200819
$369$	−10.8487	+	3.10902i	−0.564762	+	0.161849i
$370$	19.9572	+	2.36537i	1.03752	+	0.122970i
$371$		0			0
$372$	−1.34288	−	9.56038i	−0.0696249	−	0.495682i
$373$		−	3.87531i		−	0.200656i	−0.994954	−	0.100328i	$-0.968011\pi$
$373$		−	3.87531i		−	0.200656i	0.994954	−	0.100328i	$-0.0319892\pi$
$374$	5.61039			0.290106
$375$	4.11947	−	18.9217i	0.212728	−	0.977111i
$376$			6.36970i			0.328492i
$377$		−	8.96377i		−	0.461658i
$378$		0			0
$379$	−16.5126			−0.848195			−0.424098	−	0.905616i	$-0.639409\pi$
$379$	−16.5126			−0.848195			−0.424098	+	0.905616i	$0.639409\pi$
$380$	−10.2457	−	1.21435i	−0.525593	−	0.0622946i
$381$	−3.38457	−	24.0959i	−0.173397	−	1.23447i
$382$		−	21.8612i		−	1.11852i
$383$		−	38.1711i		−	1.95045i	−0.221214	−	0.975225i	$-0.571002\pi$
$383$		−	38.1711i		−	1.95045i	0.221214	−	0.975225i	$-0.428998\pi$
$384$	1.71521	−	0.240923i	0.0875291	−	0.0122946i
$385$		0			0
$386$			16.1261i			0.820797i
$387$	3.32608	+	11.6061i	0.169074	+	0.589973i
$388$	1.30193			0.0660953
$389$		−	10.2990i		−	0.522181i	−0.965314	−	0.261090i	$-0.915918\pi$
$389$		−	10.2990i		−	0.522181i	0.965314	−	0.261090i	$-0.0840820\pi$
$390$	0.381326	+	17.6695i	0.0193092	+	0.894730i
$391$		−	4.49313i		−	0.227227i
$392$		0			0
$393$	17.3618	−	2.43868i	0.875786	−	0.123015i
$394$	10.4115			0.524522
$395$	−2.76767	+	23.3514i	−0.139256	+	1.17494i
$396$	−3.97558	−	13.8725i	−0.199780	−	0.697120i
$397$	−9.95455			−0.499605			−0.249802	−	0.968297i	$-0.580366\pi$
$397$	−9.95455			−0.499605			−0.249802	+	0.968297i	$0.580366\pi$
$398$		−	17.7968i		−	0.892074i
$399$		0			0
$400$	−4.86147	−	1.16881i	−0.243074	−	0.0584403i
$401$		−	14.6489i		−	0.731529i	−0.930707	−	0.365765i	$-0.880807\pi$
$401$		−	14.6489i		−	0.731529i	0.930707	−	0.365765i	$-0.119193\pi$
$402$	3.01741	+	21.4820i	0.150495	+	1.07142i
$403$		−	25.4353i		−	1.26702i
$404$	−12.4689			−0.620351
$405$	−8.57600	−	18.2058i	−0.426145	−	0.904655i
$406$		0			0
$407$	−43.2331			−2.14298
$408$	−0.280995	−	2.00050i	−0.0139113	−	0.0990393i
$409$		−	32.8807i		−	1.62585i	−0.582371	−	0.812923i	$-0.697875\pi$
$409$		−	32.8807i		−	1.62585i	0.582371	−	0.812923i	$-0.302125\pi$
$410$	0.990040	−	8.35319i	0.0488946	−	0.412535i
$411$	30.5576	−	4.29220i	1.50730	−	0.211719i
$412$	−0.300347			−0.0147970
$413$		0			0
$414$	−11.1099	+	3.18388i	−0.546023	+	0.156479i
$415$	−7.88072	−	0.934042i	−0.386849	−	0.0458503i
$416$	4.56331			0.223735
$417$	4.02948	+	28.6872i	0.197325	+	1.40482i
$418$	22.1952			1.08560
$419$	18.3939			0.898599			0.449299	−	0.893381i	$-0.351674\pi$
$419$	18.3939			0.898599			0.449299	+	0.893381i	$0.351674\pi$
$420$		0			0
$421$	−25.4508			−1.24040			−0.620199	−	0.784444i	$-0.712948\pi$
$421$	−25.4508			−1.24040			−0.620199	+	0.784444i	$0.712948\pi$
$422$	−7.89044			−0.384101
$423$	−5.26437	−	18.3697i	−0.255962	−	0.893163i
$424$	−10.0081			−0.486038
$425$	−1.36321	+	5.67005i	−0.0661252	+	0.275038i
$426$	0.660244	+	4.70049i	0.0319889	+	0.227740i
$427$		0			0
$428$	13.5389			0.654429
$429$	−5.28849	−	37.6505i	−0.255331	−	1.81778i
$430$	−8.93638	−	1.05916i	−0.430950	−	0.0510773i
$431$		−	1.04891i		−	0.0505243i	−0.999681	−	0.0252621i	$-0.991958\pi$
$431$		−	1.04891i		−	0.0505243i	0.999681	−	0.0252621i	$-0.00804204\pi$
$432$	−4.74741	+	2.11237i	−0.228410	+	0.101632i
$433$	27.5424			1.32360			0.661801	−	0.749679i	$-0.269792\pi$
$433$	27.5424			1.32360			0.661801	+	0.749679i	$0.269792\pi$
$434$		0			0
$435$	−7.60599	+	0.164145i	−0.364679	+	0.00787014i
$436$	−14.8845			−0.712837
$437$		−	17.7752i		−	0.850305i
$438$	−23.9877	+	3.36937i	−1.14617	+	0.160995i
$439$		−	11.2089i		−	0.534972i	−0.963562	−	0.267486i	$-0.913807\pi$
$439$		−	11.2089i		−	0.534972i	0.963562	−	0.267486i	$-0.0861929\pi$
$440$	10.6814	+	1.26599i	0.509217	+	0.0603536i
$441$		0			0
$442$		−	5.32230i		−	0.253156i
$443$	−33.2580			−1.58013			−0.790067	−	0.613021i	$-0.789954\pi$
$443$	−33.2580			−1.58013			−0.790067	+	0.613021i	$0.789954\pi$
$444$	2.16532	+	15.4156i	0.102762	+	0.731593i
$445$	−4.21250	+	35.5418i	−0.199692	+	1.68484i
$446$	−17.9707			−0.850938
$447$	4.82480	+	34.3494i	0.228205	+	1.62467i
$448$		0			0
$449$		−	9.45808i		−	0.446354i	−0.974778	−	0.223177i	$-0.928357\pi$
$449$		−	9.45808i		−	0.446354i	0.974778	−	0.223177i	$-0.0716428\pi$
$450$	14.9860	−	0.647129i	0.706448	−	0.0305059i
$451$			18.0955i			0.852082i
$452$	−9.49406			−0.446563
$453$	6.52073	−	0.915920i	0.306371	−	0.0430337i
$454$			5.34178i			0.250702i
$455$		0			0
$456$	−1.11164	−	7.91414i	−0.0520574	−	0.370614i
$457$			14.7842i			0.691577i	0.938312	+	0.345789i	$0.112389\pi$
$457$			14.7842i			0.691577i	−0.938312	+	0.345789i	$0.887611\pi$
$458$		−	3.53602i		−	0.165228i
$459$	2.46371	+	5.53702i	0.114996	+	0.258446i
$460$	1.01388	−	8.55432i	0.0472723	−	0.398847i
$461$	−14.8821			−0.693130			−0.346565	−	0.938026i	$-0.612652\pi$
$461$	−14.8821			−0.693130			−0.346565	+	0.938026i	$0.612652\pi$
$462$		0			0
$463$			6.24696i			0.290321i	0.989408	+	0.145161i	$0.0463699\pi$
$463$			6.24696i			0.290321i	−0.989408	+	0.145161i	$0.953630\pi$
$464$			1.96431i			0.0911910i
$465$	−21.5825	+	0.465772i	−1.00086	+	0.0215996i
$466$	5.24366			0.242908
$467$			16.4666i			0.761985i	0.924578	+	0.380993i	$0.124418\pi$
$467$			16.4666i			0.761985i	−0.924578	+	0.380993i	$0.875582\pi$
$468$	−13.1602	+	3.77144i	−0.608329	+	0.174335i
$469$		0			0
$470$	14.1441	+	1.67639i	0.652418	+	0.0773262i
$471$	−17.5450	+	2.46442i	−0.808433	+	0.113555i
$472$	−12.7078			−0.584925
$473$	19.3588			0.890119
$474$	−18.0375	+	2.53359i	−0.828488	+	0.116372i
$475$	−5.39297	+	22.4313i	−0.247446	+	1.02922i
$476$		0			0
$477$	28.8626	−	8.27142i	1.32153	−	0.378723i
$478$			24.3376i			1.11318i
$479$	20.0178			0.914635			0.457317	−	0.889304i	$-0.348810\pi$
$479$	20.0178			0.914635			0.457317	+	0.889304i	$0.348810\pi$
$480$	−0.0835634	−	3.87208i	−0.00381413	−	0.176736i
$481$			41.0131i			1.87004i
$482$		−	24.9383i		−	1.13591i
$483$		0			0
$484$	−12.1391			−0.551777
$485$	0.342644	−	2.89096i	0.0155587	−	0.131272i
$486$	11.9453	−	10.0155i	0.541849	−	0.454312i
$487$		−	16.5821i		−	0.751406i	−0.926740	−	0.375703i	$-0.877401\pi$
$487$		−	16.5821i		−	0.751406i	0.926740	−	0.375703i	$-0.122599\pi$
$488$		−	4.96802i		−	0.224892i
$489$	−0.254750	−	1.81365i	−0.0115202	−	0.0820161i
$490$		0			0
$491$		−	11.5268i		−	0.520197i	−0.965582	−	0.260098i	$-0.916245\pi$
$491$		−	11.5268i		−	0.520197i	0.965582	−	0.260098i	$-0.0837550\pi$
$492$	6.45230	−	0.906307i	0.290892	−	0.0408595i
$493$	2.29103			0.103183
$494$		−	21.0555i		−	0.947332i
$495$	−31.8506	+	5.17688i	−1.43158	+	0.232683i
$496$			5.57387i			0.250274i
$497$		0			0
$498$	−0.855045	−	6.08735i	−0.0383155	−	0.272781i
$499$	−16.9811			−0.760180			−0.380090	−	0.924950i	$-0.624107\pi$
$499$	−16.9811			−0.760180			−0.380090	+	0.924950i	$0.624107\pi$
$500$	−3.87481	+	10.4874i	−0.173287	+	0.469011i
$501$	0.422083	+	3.00495i	0.0188573	+	0.134251i
$502$	−8.21145			−0.366495
$503$			15.3592i			0.684833i	0.939548	+	0.342416i	$0.111245\pi$
$503$			15.3592i			0.684833i	−0.939548	+	0.342416i	$0.888755\pi$
$504$		0			0
$505$	−3.28159	+	27.6875i	−0.146029	+	1.23208i
$506$			18.5312i			0.823811i
$507$	−13.4194	+	1.88493i	−0.595978	+	0.0837127i
$508$			14.0483i			0.623294i
$509$	11.6509			0.516415			0.258208	−	0.966089i	$-0.416868\pi$
$509$	11.6509			0.516415			0.258208	+	0.966089i	$0.416868\pi$
$510$	−4.51610	+	0.0974621i	−0.199976	+	0.00431569i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	9.74668	+	21.9050i	0.430327	+	0.967127i
$514$		−	2.18021i		−	0.0961652i
$515$	−0.0790459	+	0.666928i	−0.00348318	+	0.0293884i
$516$	−0.969582	−	6.90277i	−0.0426835	−	0.303878i
$517$	−30.6402			−1.34756
$518$		0			0
$519$	0.0308173	+	0.219399i	0.00135273	+	0.00963053i
$520$	1.20098	−	10.1329i	0.0526665	−	0.444359i
$521$	−28.6635			−1.25577			−0.627886	−	0.778306i	$-0.716079\pi$
$521$	−28.6635			−1.25577			−0.627886	+	0.778306i	$0.716079\pi$
$522$	−1.62345	−	5.66491i	−0.0710564	−	0.247946i
$523$	−19.6604			−0.859689			−0.429844	−	0.902903i	$-0.641432\pi$
$523$	−19.6604			−0.859689			−0.429844	+	0.902903i	$0.641432\pi$
$524$	−10.1222			−0.442192
$525$		0			0
$526$	21.9316			0.956262
$527$	6.50094			0.283186
$528$	1.15892	+	8.25071i	0.0504354	+	0.359066i
$529$	−8.15914			−0.354745
$530$	−2.63396	+	22.2233i	−0.114412	+	0.965319i
$531$	36.6482	−	10.5026i	1.59040	−	0.455776i
$532$		0			0
$533$	17.1663			0.743554
$534$	−27.4537	+	3.85623i	−1.18804	+	0.166875i
$535$	3.56321	−	30.0636i	0.154051	−	1.29976i
$536$		−	12.5244i		−	0.540970i
$537$	1.50403	+	10.7077i	0.0649039	+	0.462072i
$538$	−25.5632			−1.10211
$539$		0			0
$540$	3.44115	+	11.0977i	0.148083	+	0.477568i
$541$	25.9929			1.11752			0.558762	−	0.829328i	$-0.311277\pi$
$541$	25.9929			1.11752			0.558762	+	0.829328i	$0.311277\pi$
$542$		−	5.09869i		−	0.219008i
$543$	0.289440	+	2.06062i	0.0124210	+	0.0884295i
$544$			1.16632i			0.0500058i
$545$	−3.91733	+	33.0514i	−0.167800	+	1.41576i
$546$		0			0
$547$			2.66375i			0.113894i	0.998377	+	0.0569468i	$0.0181366\pi$
$547$			2.66375i			0.113894i	−0.998377	+	0.0569468i	$0.981863\pi$
$548$	−17.8156			−0.761046
$549$	4.10592	+	14.3273i	0.175236	+	0.611476i
$550$	5.62232	−	23.3852i	0.239736	−	0.997148i
$551$	9.06352			0.386119
$552$	6.60766	−	0.928130i	0.281241	−	0.0395038i
$553$		0			0
$554$		−	4.98773i		−	0.211908i
$555$	34.8007	−	0.751033i	1.47721	−	0.0318796i
$556$		−	16.7252i		−	0.709305i
$557$	3.35036			0.141959			0.0709796	−	0.997478i	$-0.477387\pi$
$557$	3.35036			0.141959			0.0709796	+	0.997478i	$0.477387\pi$
$558$	−4.60664	−	16.0746i	−0.195015	−	0.680490i
$559$		−	18.3648i		−	0.776747i
$560$		0			0
$561$	9.62301	−	1.35167i	0.406284	−	0.0570677i
$562$		−	18.3073i		−	0.772246i
$563$		−	36.7092i		−	1.54711i	−0.633730	−	0.773554i	$-0.718477\pi$
$563$		−	36.7092i		−	1.54711i	0.633730	−	0.773554i	$-0.281523\pi$
$564$	1.53461	+	10.9254i	0.0646187	+	0.460042i
$565$	−2.49867	+	21.0818i	−0.105120	+	0.886918i
$566$	−5.04720			−0.212150
$567$		0			0
$568$		−	2.74047i		−	0.114988i
$569$		−	33.4105i		−	1.40064i	−0.713829	−	0.700320i	$-0.753041\pi$
$569$		−	33.4105i		−	1.40064i	0.713829	−	0.700320i	$-0.246959\pi$
$570$	−17.8661	+	0.385569i	−0.748330	+	0.0161497i
$571$	25.3007			1.05880			0.529401	−	0.848372i	$-0.322417\pi$
$571$	25.3007			1.05880			0.529401	+	0.848372i	$0.322417\pi$
$572$			21.9509i			0.917814i
$573$	−5.26688	−	37.4967i	−0.220027	−	1.56645i
$574$		0			0
$575$	−18.7282	−	4.50269i	−0.781022	−	0.187775i
$576$	2.88391	−	0.826470i	0.120163	−	0.0344363i
$577$	5.59667			0.232992			0.116496	−	0.993191i	$-0.462834\pi$
$577$	5.59667			0.232992			0.116496	+	0.993191i	$0.462834\pi$
$578$	−15.6397			−0.650525
$579$	3.88515	+	27.6597i	0.161462	+	1.14950i
$580$	4.36181	+	0.516973i	0.181114	+	0.0214661i
$581$		0			0
$582$	2.23308	−	0.313665i	0.0925642	−	0.0130018i
$583$		−	48.1423i		−	1.99385i
$584$	13.9852			0.578713
$585$	4.91105	+	30.2151i	0.203047	+	1.24924i
$586$		−	24.4169i		−	1.00865i
$587$		−	39.5032i		−	1.63047i	−0.579129	−	0.815236i	$-0.696607\pi$
$587$		−	39.5032i		−	1.63047i	0.579129	−	0.815236i	$-0.303393\pi$
$588$		0			0
$589$	25.7183			1.05971
$590$	−3.34447	+	28.2181i	−0.137690	+	1.16172i
$591$	17.8579	−	2.50837i	0.734575	−	0.103180i
$592$		−	8.98759i		−	0.369388i
$593$		−	21.9019i		−	0.899403i	−0.893179	−	0.449701i	$-0.851530\pi$
$593$		−	21.9019i		−	0.899403i	0.893179	−	0.449701i	$-0.148470\pi$
$594$	−10.1612	−	22.8365i	−0.416918	−	0.936993i
$595$		0			0
$596$		−	20.0263i		−	0.820309i
$597$	−4.28767	−	30.5253i	−0.175483	−	1.24932i
$598$	17.5796			0.718884
$599$			32.9458i			1.34613i	0.739584	+	0.673065i	$0.235022\pi$
$599$			32.9458i			1.34613i	−0.739584	+	0.673065i	$0.764978\pi$
$600$	−8.62005	−	0.833508i	−0.351912	−	0.0340278i
$601$			32.4903i			1.32531i	0.748927	+	0.662653i	$0.230570\pi$
$601$			32.4903i			1.32531i	−0.748927	+	0.662653i	$0.769430\pi$
$602$		0			0
$603$	10.3510	+	36.1192i	0.421526	+	1.47089i
$604$	−3.80170			−0.154689
$605$	−3.19479	+	26.9552i	−0.129887	+	1.09588i
$606$	−21.3868	+	3.00405i	−0.868780	+	0.122031i
$607$	17.6501			0.716396			0.358198	−	0.933646i	$-0.383391\pi$
$607$	17.6501			0.716396			0.358198	+	0.933646i	$0.383391\pi$
$608$			4.61409i			0.187126i
$609$		0			0
$610$	−11.0316	−	1.30749i	−0.446657	−	0.0529389i
$611$			29.0669i			1.17592i
$612$	−0.963932	−	3.36358i	−0.0389647	−	0.135965i
$613$			7.21302i			0.291331i	0.989334	+	0.145666i	$0.0465323\pi$
$613$			7.21302i			0.291331i	−0.989334	+	0.145666i	$0.953468\pi$
$614$	−15.1857			−0.612843
$615$	−0.314349	−	14.5660i	−0.0126758	−	0.587359i
$616$		0			0
$617$	−27.1108			−1.09144			−0.545720	−	0.837968i	$-0.683744\pi$
$617$	−27.1108			−1.09144			−0.545720	+	0.837968i	$0.683744\pi$
$618$	−0.515159	+	0.0723606i	−0.0207227	+	0.00291077i
$619$			32.0212i			1.28704i	0.765430	+	0.643520i	$0.222527\pi$
$619$			32.0212i			1.28704i	−0.765430	+	0.643520i	$0.777473\pi$
$620$	12.3769	+	1.46694i	0.497069	+	0.0589138i
$621$	−18.2888	+	8.13768i	−0.733906	+	0.326554i
$622$	−11.0840			−0.444429
$623$		0			0
$624$	7.82704	−	1.09941i	0.313333	−	0.0440115i
$625$	22.2678	+	11.3642i	0.890712	+	0.454569i
$626$	−7.05798			−0.282094
$627$	38.0695	−	5.34735i	1.52035	−	0.213552i
$628$	10.2291			0.408185
$629$	−10.4824			−0.417962
$630$		0			0
$631$	−26.6088			−1.05928			−0.529641	−	0.848222i	$-0.677673\pi$
$631$	−26.6088			−1.05928			−0.529641	+	0.848222i	$0.677673\pi$
$632$	10.5162			0.418311
$633$	−13.5338	+	1.90099i	−0.537920	+	0.0755577i
$634$	1.09383			0.0434414
$635$	31.1947	+	3.69727i	1.23792	+	0.146722i
$636$	−17.1661	+	2.41119i	−0.680680	+	0.0956101i
$637$		0			0
$638$	−9.44897			−0.374088
$639$	2.26492	+	7.90328i	0.0895988	+	0.312649i
$640$	−0.263182	+	2.22053i	−0.0104032	+	0.0877740i
$641$			41.5662i			1.64177i	0.571096	+	0.820883i	$0.306518\pi$
$641$			41.5662i			1.64177i	−0.571096	+	0.820883i	$0.693482\pi$
$642$	23.2222	−	3.26185i	0.916506	−	0.128735i
$643$	−13.9242			−0.549116			−0.274558	−	0.961571i	$-0.588531\pi$
$643$	−13.9242			−0.549116			−0.274558	+	0.961571i	$0.588531\pi$
$644$		0			0
$645$	−15.5830	+	0.336296i	−0.613579	+	0.0132416i
$646$	5.38152			0.211733
$647$		−	4.60509i		−	0.181045i	−0.995894	−	0.0905223i	$-0.971146\pi$
$647$		−	4.60509i		−	0.181045i	0.995894	−	0.0905223i	$-0.0288536\pi$
$648$	−7.63389	+	4.76693i	−0.299888	+	0.187263i
$649$		−	61.1286i		−	2.39951i
$650$	−22.1844	−	5.33362i	−0.870143	−	0.209202i
$651$		0			0
$652$			1.05739i			0.0414106i
$653$	2.75937			0.107982			0.0539912	−	0.998541i	$-0.482806\pi$
$653$	2.75937			0.107982			0.0539912	+	0.998541i	$0.482806\pi$
$654$	−25.5300	+	3.58602i	−0.998304	+	0.140224i
$655$	−2.66399	+	22.4767i	−0.104091	+	0.878237i
$656$	−3.76181			−0.146874
$657$	−40.3322	+	11.5584i	−1.57351	+	0.450935i
$658$		0			0
$659$		−	36.2287i		−	1.41127i	−0.708576	−	0.705635i	$-0.750662\pi$
$659$		−	36.2287i		−	1.41127i	0.708576	−	0.705635i	$-0.249338\pi$
$660$	18.6259	−	0.401966i	0.725013	−	0.0156465i
$661$			9.32762i			0.362803i	0.983409	+	0.181401i	$0.0580633\pi$
$661$			9.32762i			0.362803i	−0.983409	+	0.181401i	$0.941937\pi$
$662$	13.3568			0.519125
$663$	−1.28227	−	9.12887i	−0.0497991	−	0.354536i
$664$			3.54903i			0.137729i
$665$		0			0
$666$	7.42797	+	25.9194i	0.287828	+	1.00436i
$667$			7.56729i			0.293007i
$668$		−	1.75194i		−	0.0677845i
$669$	−30.8236	+	4.32957i	−1.19171	+	0.167391i
$670$	−27.8107	−	3.29619i	−1.07442	−	0.127343i
$671$	23.8977			0.922562
$672$		0			0
$673$			50.4977i			1.94654i	0.229661	+	0.973271i	$0.426238\pi$
$673$			50.4977i			1.94654i	−0.229661	+	0.973271i	$0.573762\pi$
$674$			12.3715i			0.476534i
$675$	25.5483	−	4.72045i	0.983356	−	0.181690i
$676$	7.82377			0.300914
$677$		−	26.8241i		−	1.03093i	−0.856910	−	0.515467i	$-0.827619\pi$
$677$		−	26.8241i		−	1.03093i	0.856910	−	0.515467i	$-0.172381\pi$
$678$	−16.2843	+	2.28734i	−0.625396	+	0.0878448i
$679$		0			0
$680$	2.58985	+	0.306956i	0.0993164	+	0.0117712i
$681$	1.28696	+	9.16230i	0.0493165	+	0.351100i
$682$	−26.8121			−1.02669
$683$	2.00337			0.0766570			0.0383285	−	0.999265i	$-0.487797\pi$
$683$	2.00337			0.0766570			0.0383285	+	0.999265i	$0.487797\pi$
$684$	−3.81341	−	13.3066i	−0.145809	−	0.508791i
$685$	−4.68876	+	39.5601i	−0.179148	+	1.51151i
$686$		0			0
$687$	−0.851911	−	6.06504i	−0.0325024	−	0.231396i
$688$			4.02444i			0.153430i
$689$	−45.6702			−1.73990
$690$	−0.321918	−	14.9167i	−0.0122552	−	0.567871i
$691$		−	26.4071i		−	1.00457i	−0.864702	−	0.502286i	$-0.832492\pi$
$691$		−	26.4071i		−	1.00457i	0.864702	−	0.502286i	$-0.167508\pi$
$692$		−	0.127913i		−	0.00486254i
$693$		0			0
$694$	−2.96861			−0.112687
$695$	−37.1386	−	4.40176i	−1.40875	−	0.166968i
$696$	0.473250	+	3.36922i	0.0179385	+	0.127710i
$697$			4.38749i			0.166188i
$698$		−	1.03511i		−	0.0391794i
$699$	8.99400	−	1.26332i	0.340184	−	0.0477832i
$700$		0			0
$701$			14.6209i			0.552222i	0.961126	+	0.276111i	$0.0890457\pi$
$701$			14.6209i			0.552222i	−0.961126	+	0.276111i	$0.910954\pi$
$702$	−21.6639	+	9.63941i	−0.817650	+	0.363816i
$703$	−41.4695			−1.56405
$704$		−	4.81031i		−	0.181295i
$705$	24.6640	−	0.532274i	0.928900	−	0.0200466i
$706$			13.4155i			0.504900i
$707$		0			0
$708$	−21.7966	+	3.06161i	−0.819168	+	0.115062i
$709$	−20.7963			−0.781022			−0.390511	−	0.920598i	$-0.627702\pi$
$709$	−20.7963			−0.781022			−0.390511	+	0.920598i	$0.627702\pi$
$710$	−6.08529	−	0.721243i	−0.228377	−	0.0270678i
$711$	−30.3277	+	8.69130i	−1.13738	+	0.325949i
$712$	16.0060			0.599851
$713$			21.4727i			0.804159i
$714$		0			0
$715$	48.7426	+	5.77709i	1.82287	+	0.216051i
$716$		−	6.24279i		−	0.233304i
$717$	5.86351	+	41.7442i	0.218977	+	1.55897i
$718$			24.8666i			0.928012i
$719$	−5.57749			−0.208005			−0.104003	−	0.994577i	$-0.533165\pi$
$719$	−5.57749			−0.208005			−0.104003	+	0.994577i	$0.533165\pi$
$720$	−1.07620	−	6.62131i	−0.0401078	−	0.246762i
$721$		0			0
$722$	2.28981			0.0852180
$723$	−6.00822	−	42.7745i	−0.223448	−	1.59080i
$724$		−	1.20138i		−	0.0446488i
$725$	2.29590	−	9.54946i	0.0852676	−	0.354658i
$726$	−20.8211	+	2.92459i	−0.772745	+	0.108542i
$727$	−37.0725			−1.37494			−0.687471	−	0.726212i	$-0.741279\pi$
$727$	−37.0725			−1.37494			−0.687471	+	0.726212i	$0.741279\pi$
$728$		0			0
$729$	18.0757	−	20.0566i	0.669472	−	0.742837i
$730$	3.68066	−	31.0546i	0.136227	−	1.14938i
$731$	4.69380			0.173607
$732$	−1.19691	−	8.52122i	−0.0442392	−	0.314953i
$733$	−1.87554			−0.0692748			−0.0346374	−	0.999400i	$-0.511028\pi$
$733$	−1.87554			−0.0692748			−0.0346374	+	0.999400i	$0.511028\pi$
$734$	−5.54367			−0.204621
$735$		0			0
$736$	−3.85238			−0.142001
$737$	60.2461			2.21919
$738$	10.8487	−	3.10902i	0.399347	−	0.114445i
$739$	21.1942			0.779642			0.389821	−	0.920891i	$-0.372537\pi$
$739$	21.1942			0.779642			0.389821	+	0.920891i	$0.372537\pi$
$740$	−19.9572	−	2.36537i	−0.733640	−	0.0869528i
$741$	−5.07276	−	36.1147i	−0.186353	−	1.32671i
$742$		0			0
$743$	11.1477			0.408969			0.204484	−	0.978870i	$-0.434448\pi$
$743$	11.1477			0.408969			0.204484	+	0.978870i	$0.434448\pi$
$744$	1.34288	+	9.56038i	0.0492322	+	0.350500i
$745$	−44.4689	−	5.27056i	−1.62921	−	0.193098i
$746$			3.87531i			0.141885i
$747$	−2.93317	−	10.2351i	−0.107319	−	0.374483i
$748$	−5.61039			−0.205136
$749$		0			0
$750$	−4.11947	+	18.9217i	−0.150422	+	0.690922i
$751$	48.0203			1.75229			0.876143	−	0.482052i	$-0.160108\pi$
$751$	48.0203			1.75229			0.876143	+	0.482052i	$0.160108\pi$
$752$		−	6.36970i		−	0.232279i
$753$	−14.0844	+	1.97833i	−0.513263	+	0.0720944i
$754$			8.96377i			0.326441i
$755$	−1.00054	+	8.44178i	−0.0364134	+	0.307228i
$756$		0			0
$757$		−	26.1445i		−	0.950239i	−0.879921	−	0.475120i	$-0.842405\pi$
$757$		−	26.1445i		−	0.950239i	0.879921	−	0.475120i	$-0.157595\pi$
$758$	16.5126			0.599765
$759$	4.46459	+	31.7849i	0.162054	+	1.15372i
$760$	10.2457	+	1.21435i	0.371651	+	0.0440489i
$761$	0.650185			0.0235692			0.0117846	−	0.999931i	$-0.496249\pi$
$761$	0.650185			0.0235692			0.0117846	+	0.999931i	$0.496249\pi$
$762$	3.38457	+	24.0959i	0.122610	+	0.872902i
$763$		0			0
$764$			21.8612i			0.790911i
$765$	−7.72260	+	1.25520i	−0.279211	+	0.0453820i
$766$			38.1711i			1.37918i
$767$	−57.9897			−2.09389
$768$	−1.71521	+	0.240923i	−0.0618924	+	0.00869358i
$769$		−	14.2303i		−	0.513159i	−0.966523	−	0.256580i	$-0.917404\pi$
$769$		−	14.2303i		−	0.513159i	0.966523	−	0.256580i	$-0.0825956\pi$
$770$		0			0
$771$	−0.525265	−	3.73953i	−0.0189170	−	0.134676i
$772$		−	16.1261i		−	0.580391i
$773$			4.49715i			0.161751i	0.996724	+	0.0808756i	$0.0257716\pi$
$773$			4.49715i			0.161751i	−0.996724	+	0.0808756i	$0.974228\pi$
$774$	−3.32608	−	11.6061i	−0.119553	−	0.417174i
$775$	6.51477	−	27.0972i	0.234017	−	0.973360i
$776$	−1.30193			−0.0467364
$777$		0			0
$778$			10.2990i			0.369237i
$779$			17.3573i			0.621890i
$780$	−0.381326	−	17.6695i	−0.0136536	−	0.632669i
$781$	13.1825			0.471708
$782$			4.49313i			0.160674i
$783$	−4.14937	−	9.32540i	−0.148286	−	0.333263i
$784$		0			0
$785$	2.69211	−	22.7139i	0.0960855	−	0.810695i
$786$	−17.3618	+	2.43868i	−0.619274	+	0.0869850i
$787$	−39.8904			−1.42194			−0.710970	−	0.703223i	$-0.751744\pi$
$787$	−39.8904			−1.42194			−0.710970	+	0.703223i	$0.751744\pi$
$788$	−10.4115			−0.370893
$789$	37.6173	−	5.28383i	1.33921	−	0.188109i
$790$	2.76767	−	23.3514i	0.0984692	−	0.830806i
$791$		0			0
$792$	3.97558	+	13.8725i	0.141266	+	0.492938i
$793$		−	22.6706i		−	0.805057i
$794$	9.95455			0.353274
$795$	0.836314	+	38.7523i	0.0296610	+	1.37440i
$796$			17.7968i			0.630791i
$797$		−	10.5614i		−	0.374105i	−0.982350	−	0.187052i	$-0.940107\pi$
$797$		−	10.5614i		−	0.374105i	0.982350	−	0.187052i	$-0.0598934\pi$
$798$		0			0
$799$	−7.42914			−0.262824
$800$	4.86147	+	1.16881i	0.171879	+	0.0413235i
$801$	−46.1600	+	13.2285i	−1.63098	+	0.467406i
$802$			14.6489i			0.517269i
$803$			67.2733i			2.37402i
$804$	−3.01741	−	21.4820i	−0.106416	−	0.757610i
$805$		0			0
$806$			25.4353i			0.895920i
$807$	−43.8463	+	6.15877i	−1.54346	+	0.216799i
$808$	12.4689			0.438654
$809$			31.1336i			1.09460i	0.836936	+	0.547300i	$0.184344\pi$
$809$			31.1336i			1.09460i	−0.836936	+	0.547300i	$0.815656\pi$
$810$	8.57600	+	18.2058i	0.301330	+	0.639688i
$811$			15.1367i			0.531521i	0.964039	+	0.265761i	$0.0856231\pi$
$811$			15.1367i			0.531521i	−0.964039	+	0.265761i	$0.914377\pi$
$812$		0			0
$813$	−1.22839	−	8.74535i	−0.0430817	−	0.306713i
$814$	43.2331			1.51532
$815$	2.34796	+	0.278286i	0.0822456	+	0.00974794i
$816$	0.280995	+	2.00050i	0.00983679	+	0.0700313i
$817$	18.5691			0.649652
$818$			32.8807i			1.14965i
$819$		0			0
$820$	−0.990040	+	8.35319i	−0.0345737	+	0.291706i
$821$		−	48.4610i		−	1.69130i	−0.533738	−	0.845650i	$-0.679213\pi$
$821$		−	48.4610i		−	1.69130i	0.533738	−	0.845650i	$-0.320787\pi$
$822$	−30.5576	+	4.29220i	−1.06582	+	0.149708i
$823$		−	28.3716i		−	0.988971i	−0.869186	−	0.494486i	$-0.835356\pi$
$823$		−	28.3716i		−	0.988971i	0.869186	−	0.494486i	$-0.164644\pi$
$824$	0.300347			0.0104631
$825$	4.00943	−	41.4651i	0.139591	−	1.44363i
$826$		0			0
$827$	−2.09153			−0.0727296			−0.0363648	−	0.999339i	$-0.511578\pi$
$827$	−2.09153			−0.0727296			−0.0363648	+	0.999339i	$0.511578\pi$
$828$	11.1099	−	3.18388i	0.386097	−	0.110647i
$829$		−	45.5410i		−	1.58170i	−0.612008	−	0.790852i	$-0.709638\pi$
$829$		−	45.5410i		−	1.58170i	0.612008	−	0.790852i	$-0.290362\pi$
$830$	7.88072	+	0.934042i	0.273544	+	0.0324211i
$831$	−1.20166	−	8.55502i	−0.0416852	−	0.296770i
$832$	−4.56331			−0.158204
$833$		0			0
$834$	−4.02948	−	28.6872i	−0.139530	−	0.993357i
$835$	−3.89022	−	0.461078i	−0.134627	−	0.0159563i
$836$	−22.1952			−0.767637
$837$	−11.7741	−	26.4614i	−0.406973	−	0.914641i
$838$	−18.3939			−0.635405
$839$	41.3972			1.42919			0.714595	−	0.699538i	$-0.246611\pi$
$839$	41.3972			1.42919			0.714595	+	0.699538i	$0.246611\pi$
$840$		0			0
$841$	25.1415			0.866947
$842$	25.4508			0.877094
$843$	−4.41065	−	31.4009i	−0.151911	−	1.08150i
$844$	7.89044			0.271600
$845$	2.05908	−	17.3729i	0.0708344	−	0.597645i
$846$	5.26437	+	18.3697i	0.180993	+	0.631562i
$847$		0			0
$848$	10.0081			0.343681
$849$	−8.65702	+	1.21599i	−0.297108	+	0.0417326i
$850$	1.36321	−	5.67005i	0.0467576	−	0.194481i
$851$		−	34.6236i		−	1.18688i
$852$	−0.660244	−	4.70049i	−0.0226196	−	0.161036i
$853$	9.62551			0.329571			0.164786	−	0.986329i	$-0.447307\pi$
$853$	9.62551			0.329571			0.164786	+	0.986329i	$0.447307\pi$
$854$		0			0
$855$	−30.5513	+	4.96570i	−1.04483	+	0.169823i
$856$	−13.5389			−0.462751
$857$		−	11.8071i		−	0.403321i	−0.979455	−	0.201661i	$-0.935366\pi$
$857$		−	11.8071i		−	0.403321i	0.979455	−	0.201661i	$-0.0646338\pi$
$858$	5.28849	+	37.6505i	0.180546	+	1.28537i
$859$			37.9641i			1.29532i	0.761930	+	0.647659i	$0.224252\pi$
$859$			37.9641i			1.29532i	−0.761930	+	0.647659i	$0.775748\pi$
$860$	8.93638	+	1.05916i	0.304728	+	0.0361171i
$861$		0			0
$862$			1.04891i			0.0357260i
$863$	26.7170			0.909456			0.454728	−	0.890630i	$-0.349736\pi$
$863$	26.7170			0.909456			0.454728	+	0.890630i	$0.349736\pi$
$864$	4.74741	−	2.11237i	0.161510	−	0.0718644i
$865$	−0.284035	−	0.0336645i	−0.00965748	−	0.00114463i
$866$	−27.5424			−0.935928
$867$	−26.8254	+	3.76797i	−0.911038	+	0.127967i
$868$		0			0
$869$			50.5860i			1.71601i
$870$	7.60599	−	0.164145i	0.257867	−	0.00556503i
$871$		−	57.1525i		−	1.93654i
$872$	14.8845			0.504052
$873$	3.75464	−	1.07600i	0.127075	−	0.0364172i
$874$			17.7752i			0.601256i
$875$		0			0
$876$	23.9877	−	3.36937i	0.810468	−	0.113840i
$877$		−	52.4373i		−	1.77068i	−0.464942	−	0.885341i	$-0.653925\pi$
$877$		−	52.4373i		−	1.77068i	0.464942	−	0.885341i	$-0.346075\pi$
$878$			11.2089i			0.378282i
$879$	−5.88261	−	41.8802i	−0.198415	−	1.41258i
$880$	−10.6814	−	1.26599i	−0.360071	−	0.0426764i
$881$	33.9634			1.14426			0.572129	−	0.820164i	$-0.306118\pi$
$881$	33.9634			1.14426			0.572129	+	0.820164i	$0.306118\pi$
$882$		0			0
$883$		−	25.6542i		−	0.863333i	−0.902033	−	0.431666i	$-0.857926\pi$
$883$		−	25.6542i		−	0.863333i	0.902033	−	0.431666i	$-0.142074\pi$
$884$			5.32230i			0.179008i
$885$	1.06191	+	49.2057i	0.0356957	+	1.65403i
$886$	33.2580			1.11732
$887$			26.8939i			0.903008i	0.892269	+	0.451504i	$0.149112\pi$
$887$			26.8939i			0.903008i	−0.892269	+	0.451504i	$0.850888\pi$
$888$	−2.16532	−	15.4156i	−0.0726634	−	0.517315i
$889$		0			0
$890$	4.21250	−	35.5418i	0.141203	−	1.19136i
$891$	−22.9304	−	36.7214i	−0.768199	−	1.23021i
$892$	17.9707			0.601704
$893$	−29.3904			−0.983511
$894$	−4.82480	−	34.3494i	−0.161366	−	1.14881i
$895$	−13.8623	−	1.64299i	−0.463365	−	0.0549191i
$896$		0			0
$897$	30.1528	−	4.23534i	1.00677	−	0.141414i
$898$			9.45808i			0.315620i
$899$	−10.9488			−0.365164
$900$	−14.9860	+	0.647129i	−0.499534	+	0.0215710i
$901$		−	11.6727i		−	0.388875i
$902$		−	18.0955i		−	0.602513i
$903$		0			0
$904$	9.49406			0.315768
$905$	−2.66769	−	0.316181i	−0.0886769	−	0.0105102i
$906$	−6.52073	+	0.915920i	−0.216637	+	0.0304294i
$907$			26.5074i			0.880165i	0.897957	+	0.440082i	$0.145051\pi$
$907$			26.5074i			0.880165i	−0.897957	+	0.440082i	$0.854949\pi$
$908$		−	5.34178i		−	0.177273i
$909$	−35.9592	+	10.3052i	−1.19269	+	0.341801i
$910$		0			0
$911$		−	2.71732i		−	0.0900289i	−0.998986	−	0.0450145i	$-0.985667\pi$
$911$		−	2.71732i		−	0.0900289i	0.998986	−	0.0450145i	$-0.0143334\pi$
$912$	1.11164	+	7.91414i	0.0368102	+	0.262064i
$913$	−17.0720			−0.564999
$914$		−	14.7842i		−	0.489019i
$915$	−19.2366	+	0.415145i	−0.635942	+	0.0137243i
$916$			3.53602i			0.116834i
$917$		0			0
$918$	−2.46371	−	5.53702i	−0.0813147	−	0.182749i
$919$	36.4031			1.20083			0.600414	−	0.799689i	$-0.295002\pi$
$919$	36.4031			1.20083			0.600414	+	0.799689i	$0.295002\pi$
$920$	−1.01388	+	8.55432i	−0.0334266	+	0.282028i
$921$	−26.0466	+	3.65858i	−0.858266	+	0.120554i
$922$	14.8821			0.490117
$923$		−	12.5056i		−	0.411627i
$924$		0			0
$925$	−10.5047	+	43.6929i	−0.345394	+	1.43661i
$926$		−	6.24696i		−	0.205288i
$927$	−0.866174	+	0.248228i	−0.0284489	+	0.00815287i
$928$		−	1.96431i		−	0.0644818i
$929$	−1.92528			−0.0631665			−0.0315833	−	0.999501i	$-0.510055\pi$
$929$	−1.92528			−0.0631665			−0.0315833	+	0.999501i	$0.510055\pi$
$930$	21.5825	−	0.465772i	0.707718	−	0.0152733i
$931$		0			0
$932$	−5.24366			−0.171762
$933$	−19.0115	+	2.67040i	−0.622408	+	0.0874251i
$934$		−	16.4666i		−	0.538805i
$935$	−1.47655	+	12.4580i	−0.0482884	+	0.407420i
$936$	13.1602	−	3.77144i	0.430154	−	0.123273i
$937$	−28.5051			−0.931220			−0.465610	−	0.884990i	$-0.654165\pi$
$937$	−28.5051			−0.931220			−0.465610	+	0.884990i	$0.654165\pi$
$938$		0			0
$939$	−12.1059	+	1.70043i	−0.395062	+	0.0554915i
$940$	−14.1441	−	1.67639i	−0.461329	−	0.0546778i
$941$	37.8130			1.23267			0.616334	−	0.787485i	$-0.288617\pi$
$941$	37.8130			1.23267			0.616334	+	0.787485i	$0.288617\pi$
$942$	17.5450	−	2.46442i	0.571648	−	0.0802953i
$943$	−14.4919			−0.471922
$944$	12.7078			0.413605
$945$		0			0
$946$	−19.3588			−0.629409
$947$	−43.7379			−1.42129			−0.710645	−	0.703551i	$-0.751597\pi$
$947$	−43.7379			−1.42129			−0.710645	+	0.703551i	$0.751597\pi$
$948$	18.0375	−	2.53359i	0.585830	−	0.0822872i
$949$	63.8189			2.07165
$950$	5.39297	−	22.4313i	0.174971	−	0.727766i
$951$	1.87615	−	0.263529i	0.0608382	−	0.00854550i
$952$		0			0
$953$	7.44666			0.241221			0.120611	−	0.992700i	$-0.461515\pi$
$953$	7.44666			0.241221			0.120611	+	0.992700i	$0.461515\pi$
$954$	−28.8626	+	8.27142i	−0.934460	+	0.267797i
$955$	48.5434	+	5.75348i	1.57083	+	0.186178i
$956$		−	24.3376i		−	0.787135i
$957$	−16.2070	+	2.27648i	−0.523898	+	0.0735881i
$958$	−20.0178			−0.646744
$959$		0			0
$960$	0.0835634	+	3.87208i	0.00269700	+	0.124971i
$961$	−0.0680375			−0.00219476
$962$		−	41.0131i		−	1.32232i
$963$	39.0451	−	11.1895i	1.25821	−	0.360578i
$964$			24.9383i			0.803209i
$965$	−35.8084	−	4.24410i	−1.15271	−	0.136622i
$966$		0			0
$967$			7.99874i			0.257222i	0.991695	+	0.128611i	$0.0410519\pi$
$967$			7.99874i			0.257222i	−0.991695	+	0.128611i	$0.958948\pi$
$968$	12.1391			0.390166
$969$	9.23046	−	1.29654i	0.296525	−	0.0416507i
$970$	−0.342644	+	2.89096i	−0.0110016	+	0.0928232i
$971$	−4.32616			−0.138833			−0.0694165	−	0.997588i	$-0.522114\pi$
$971$	−4.32616			−0.138833			−0.0694165	+	0.997588i	$0.522114\pi$
$972$	−11.9453	+	10.0155i	−0.383145	+	0.321247i
$973$		0			0
$974$			16.5821i			0.531324i
$975$	−39.3359	−	3.80355i	−1.25976	−	0.121811i
$976$			4.96802i			0.159023i
$977$	50.2866			1.60881			0.804405	−	0.594081i	$-0.202484\pi$
$977$	50.2866			1.60881			0.804405	+	0.594081i	$0.202484\pi$
$978$	0.254750	+	1.81365i	0.00814601	+	0.0579941i
$979$			76.9940i			2.46074i
$980$		0			0
$981$	−42.9255	+	12.3016i	−1.37051	+	0.392759i
$982$			11.5268i			0.367834i
$983$			60.7315i			1.93703i	0.248948	+	0.968517i	$0.419915\pi$
$983$			60.7315i			1.93703i	−0.248948	+	0.968517i	$0.580085\pi$
$984$	−6.45230	+	0.906307i	−0.205692	+	0.0288920i
$985$	−2.74011	+	23.1189i	−0.0873072	+	0.736630i
$986$	−2.29103			−0.0729612
$987$		0			0
$988$			21.0555i			0.669865i
$989$			15.5037i			0.492989i
$990$	31.8506	−	5.17688i	1.01228	−	0.164532i
$991$	−25.5740			−0.812384			−0.406192	−	0.913788i	$-0.633144\pi$
$991$	−25.5740			−0.812384			−0.406192	+	0.913788i	$0.633144\pi$
$992$		−	5.57387i		−	0.176971i
$993$	22.9097	−	3.21796i	0.727017	−	0.102119i
$994$		0			0
$995$	39.5183	+	4.68380i	1.25281	+	0.148487i
$996$	0.855045	+	6.08735i	0.0270931	+	0.192885i
$997$	9.46618			0.299797			0.149898	−	0.988701i	$-0.452105\pi$
$997$	9.46618			0.299797			0.149898	+	0.988701i	$0.452105\pi$
$998$	16.9811			0.537528
$999$	18.9851	+	42.6677i	0.600663	+	1.34995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.2	yes	24
3.2	odd	2		1470.2.d.h.1469.1	yes	24
5.4	even	2		1470.2.d.h.1469.23	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.23	yes	24
15.14	odd	2	inner	1470.2.d.g.1469.24	yes	24
21.20	even	2		1470.2.d.h.1469.24	yes	24
35.34	odd	2		1470.2.d.h.1469.2	yes	24
105.104	even	2	inner	1470.2.d.g.1469.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.1	✓	24	105.104	even	2	inner
1470.2.d.g.1469.2	yes	24	1.1	even	1	trivial
1470.2.d.g.1469.23	yes	24	7.6	odd	2	inner
1470.2.d.g.1469.24	yes	24	15.14	odd	2	inner
1470.2.d.h.1469.1	yes	24	3.2	odd	2
1470.2.d.h.1469.2	yes	24	35.34	odd	2
1470.2.d.h.1469.23	yes	24	5.4	even	2
1470.2.d.h.1469.24	yes	24	21.20	even	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.71521 + 0.240923i) q^{3} +1.00000 q^{4} +(0.263182 - 2.22053i) q^{5} +(1.71521 - 0.240923i) q^{6} -1.00000 q^{8} +(2.88391 - 0.826470i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.71521 + 0.240923i) q^{3} +1.00000 q^{4} +(0.263182 - 2.22053i) q^{5} +(1.71521 - 0.240923i) q^{6} -1.00000 q^{8} +(2.88391 - 0.826470i) q^{9} +(-0.263182 + 2.22053i) q^{10} -4.81031i q^{11} +(-1.71521 + 0.240923i) q^{12} -4.56331 q^{13} +(0.0835634 + 3.87208i) q^{15} +1.00000 q^{16} -1.16632i q^{17} +(-2.88391 + 0.826470i) q^{18} -4.61409i q^{19} +(0.263182 - 2.22053i) q^{20} +4.81031i q^{22} +3.85238 q^{23} +(1.71521 - 0.240923i) q^{24} +(-4.86147 - 1.16881i) q^{25} +4.56331 q^{26} +(-4.74741 + 2.11237i) q^{27} +1.96431i q^{29} +(-0.0835634 - 3.87208i) q^{30} +5.57387i q^{31} -1.00000 q^{32} +(1.15892 + 8.25071i) q^{33} +1.16632i q^{34} +(2.88391 - 0.826470i) q^{36} -8.98759i q^{37} +4.61409i q^{38} +(7.82704 - 1.09941i) q^{39} +(-0.263182 + 2.22053i) q^{40} -3.76181 q^{41} +4.02444i q^{43} -4.81031i q^{44} +(-1.07620 - 6.62131i) q^{45} -3.85238 q^{46} -6.36970i q^{47} +(-1.71521 + 0.240923i) q^{48} +(4.86147 + 1.16881i) q^{50} +(0.280995 + 2.00050i) q^{51} -4.56331 q^{52} +10.0081 q^{53} +(4.74741 - 2.11237i) q^{54} +(-10.6814 - 1.26599i) q^{55} +(1.11164 + 7.91414i) q^{57} -1.96431i q^{58} +12.7078 q^{59} +(0.0835634 + 3.87208i) q^{60} +4.96802i q^{61} -5.57387i q^{62} +1.00000 q^{64} +(-1.20098 + 10.1329i) q^{65} +(-1.15892 - 8.25071i) q^{66} +12.5244i q^{67} -1.16632i q^{68} +(-6.60766 + 0.928130i) q^{69} +2.74047i q^{71} +(-2.88391 + 0.826470i) q^{72} -13.9852 q^{73} +8.98759i q^{74} +(8.62005 + 0.833508i) q^{75} -4.61409i q^{76} +(-7.82704 + 1.09941i) q^{78} -10.5162 q^{79} +(0.263182 - 2.22053i) q^{80} +(7.63389 - 4.76693i) q^{81} +3.76181 q^{82} -3.54903i q^{83} +(-2.58985 - 0.306956i) q^{85} -4.02444i q^{86} +(-0.473250 - 3.36922i) q^{87} +4.81031i q^{88} -16.0060 q^{89} +(1.07620 + 6.62131i) q^{90} +3.85238 q^{92} +(-1.34288 - 9.56038i) q^{93} +6.36970i q^{94} +(-10.2457 - 1.21435i) q^{95} +(1.71521 - 0.240923i) q^{96} +1.30193 q^{97} +(-3.97558 - 13.8725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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