LMFDB - Embedded newform 1530.2.m.h.647.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1530.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.17364600040304039428096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 20 x^{14} - 40 x^{13} + 104 x^{12} - 180 x^{11} + 242 x^{10} - 132 x^{9} - 302 x^{8} + \cdots + 1 $ x^16 - 4x^15 + 20x^14 - 40x^13 + 104x^12 - 180x^11 + 242x^10 - 132x^9 - 302x^8 + 416x^7 + 296x^6 - 416x^5 + 2x^4 + 32x^3 + 46x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.5
Root			$-0.890827 - 0.368993i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.h.953.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.75703 - 1.38306i) q^{5} +(-2.78165 - 2.78165i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.75703 - 1.38306i) q^{5} +(-2.78165 - 2.78165i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.22038 + 0.264435i) q^{10} -0.747934i q^{11} +(0.296842 - 0.296842i) q^{13} -3.93385 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +2.34858i q^{19} +(-1.38306 + 1.75703i) q^{20} +(-0.528869 - 0.528869i) q^{22} +(1.04025 + 1.04025i) q^{23} +(1.17429 + 4.86015i) q^{25} -0.419798i q^{26} +(-2.78165 + 2.78165i) q^{28} -10.6338 q^{29} +0.685860 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(1.04025 + 8.73463i) q^{35} +(5.51925 + 5.51925i) q^{37} +(1.66070 + 1.66070i) q^{38} +(0.264435 + 2.22038i) q^{40} -5.23706i q^{41} +(0.767973 - 0.767973i) q^{43} -0.747934 q^{44} +1.47113 q^{46} +(-7.94087 + 7.94087i) q^{47} +8.47519i q^{49} +(4.26699 + 2.60630i) q^{50} +(-0.296842 - 0.296842i) q^{52} +(1.83401 + 1.83401i) q^{53} +(-1.03444 + 1.31414i) q^{55} +3.93385i q^{56} +(-7.51925 + 7.51925i) q^{58} -13.4244 q^{59} -3.27954 q^{61} +(0.484976 - 0.484976i) q^{62} +1.00000i q^{64} +(-0.932109 + 0.111009i) q^{65} +(6.77203 + 6.77203i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(6.91188 + 5.44075i) q^{70} -4.05847i q^{71} +(4.73760 - 4.73760i) q^{73} +7.80540 q^{74} +2.34858 q^{76} +(-2.08049 + 2.08049i) q^{77} -9.88858i q^{79} +(1.75703 + 1.38306i) q^{80} +(-3.70316 - 3.70316i) q^{82} +(2.25381 + 2.25381i) q^{83} +(-2.22038 + 0.264435i) q^{85} -1.08608i q^{86} +(-0.528869 + 0.528869i) q^{88} -5.21259 q^{89} -1.65142 q^{91} +(1.04025 - 1.04025i) q^{92} +11.2301i q^{94} +(3.24822 - 4.12652i) q^{95} +(-3.76797 - 3.76797i) q^{97} +(5.99287 + 5.99287i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.75703	−	1.38306i	−0.785766	−	0.618523i
$5$	−1.75703	−	1.38306i	−0.785766	−	0.618523i
$6$		0			0
$7$	−2.78165	−	2.78165i	−1.05137	−	1.05137i	−0.998607	−	0.0527589i	$-0.983199\pi$
$7$	−2.78165	−	2.78165i	−1.05137	−	1.05137i	−0.0527589	−	0.998607i	$-0.516801\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.22038	+	0.264435i	−0.702145	+	0.0836216i
$11$		−	0.747934i		−	0.225511i	−0.993623	−	0.112755i	$-0.964032\pi$
$11$		−	0.747934i		−	0.225511i	0.993623	−	0.112755i	$-0.0359676\pi$
$12$		0			0
$13$	0.296842	−	0.296842i	0.0823291	−	0.0823291i	−0.664743	−	0.747072i	$-0.731459\pi$
$13$	0.296842	−	0.296842i	0.0823291	−	0.0823291i	0.747072	+	0.664743i	$0.231459\pi$
$14$	−3.93385			−1.05137
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$			2.34858i			0.538801i	0.963028	+	0.269400i	$0.0868255\pi$
$19$			2.34858i			0.538801i	−0.963028	+	0.269400i	$0.913175\pi$
$20$	−1.38306	+	1.75703i	−0.309262	+	0.392883i
$21$		0			0
$22$	−0.528869	−	0.528869i	−0.112755	−	0.112755i
$23$	1.04025	+	1.04025i	0.216906	+	0.216906i	0.807193	−	0.590287i	$-0.200985\pi$
$23$	1.04025	+	1.04025i	0.216906	+	0.216906i	−0.590287	+	0.807193i	$0.700985\pi$
$24$		0			0
$25$	1.17429	+	4.86015i	0.234858	+	0.972030i
$26$		−	0.419798i		−	0.0823291i
$27$		0			0
$28$	−2.78165	+	2.78165i	−0.525683	+	0.525683i
$29$	−10.6338			−1.97465			−0.987326	−	0.158706i	$-0.949268\pi$
$29$	−10.6338			−1.97465			−0.987326	+	0.158706i	$0.949268\pi$
$30$		0			0
$31$	0.685860			0.123184			0.0615920	−	0.998101i	$-0.480382\pi$
$31$	0.685860			0.123184			0.0615920	+	0.998101i	$0.480382\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.00000i		−	0.171499i
$35$	1.04025	+	8.73463i	0.175834	+	1.47642i
$36$		0			0
$37$	5.51925	+	5.51925i	0.907359	+	0.907359i	0.996058	−	0.0886994i	$-0.0282711\pi$
$37$	5.51925	+	5.51925i	0.907359	+	0.907359i	−0.0886994	+	0.996058i	$0.528271\pi$
$38$	1.66070	+	1.66070i	0.269400	+	0.269400i
$39$		0			0
$40$	0.264435	+	2.22038i	0.0418108	+	0.351072i
$41$		−	5.23706i		−	0.817891i	−0.912559	−	0.408945i	$-0.865897\pi$
$41$		−	5.23706i		−	0.817891i	0.912559	−	0.408945i	$-0.134103\pi$
$42$		0			0
$43$	0.767973	−	0.767973i	0.117115	−	0.117115i	−0.646121	−	0.763235i	$-0.723610\pi$
$43$	0.767973	−	0.767973i	0.117115	−	0.117115i	0.763235	+	0.646121i	$0.223610\pi$
$44$	−0.747934			−0.112755
$45$		0			0
$46$	1.47113			0.216906
$47$	−7.94087	+	7.94087i	−1.15829	+	1.15829i	−0.173453	+	0.984842i	$0.555492\pi$
$47$	−7.94087	+	7.94087i	−1.15829	+	1.15829i	−0.984842	+	0.173453i	$0.944508\pi$
$48$		0			0
$49$			8.47519i			1.21074i
$50$	4.26699	+	2.60630i	0.603444	+	0.368586i
$51$		0			0
$52$	−0.296842	−	0.296842i	−0.0411645	−	0.0411645i
$53$	1.83401	+	1.83401i	0.251921	+	0.251921i	0.821758	−	0.569837i	$-0.192994\pi$
$53$	1.83401	+	1.83401i	0.251921	+	0.251921i	−0.569837	+	0.821758i	$0.692994\pi$
$54$		0			0
$55$	−1.03444	+	1.31414i	−0.139484	+	0.177199i
$56$			3.93385i			0.525683i
$57$		0			0
$58$	−7.51925	+	7.51925i	−0.987326	+	0.987326i
$59$	−13.4244			−1.74771			−0.873855	−	0.486187i	$-0.838387\pi$
$59$	−13.4244			−1.74771			−0.873855	+	0.486187i	$0.838387\pi$
$60$		0			0
$61$	−3.27954			−0.419902			−0.209951	−	0.977712i	$-0.567331\pi$
$61$	−3.27954			−0.419902			−0.209951	+	0.977712i	$0.567331\pi$
$62$	0.484976	−	0.484976i	0.0615920	−	0.0615920i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.932109	+	0.111009i	−0.115614	+	0.0137690i
$66$		0			0
$67$	6.77203	+	6.77203i	0.827336	+	0.827336i	0.987147	−	0.159812i	$-0.0510888\pi$
$67$	6.77203	+	6.77203i	0.827336	+	0.827336i	−0.159812	+	0.987147i	$0.551089\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	6.91188	+	5.44075i	0.826128	+	0.650295i
$71$		−	4.05847i		−	0.481651i	−0.970568	−	0.240826i	$-0.922582\pi$
$71$		−	4.05847i		−	0.481651i	0.970568	−	0.240826i	$-0.0774182\pi$
$72$		0			0
$73$	4.73760	−	4.73760i	0.554494	−	0.554494i	−0.373241	−	0.927734i	$-0.621753\pi$
$73$	4.73760	−	4.73760i	0.554494	−	0.554494i	0.927734	+	0.373241i	$0.121753\pi$
$74$	7.80540			0.907359
$75$		0			0
$76$	2.34858			0.269400
$77$	−2.08049	+	2.08049i	−0.237094	+	0.237094i
$78$		0			0
$79$		−	9.88858i		−	1.11255i	−0.830997	−	0.556276i	$-0.812230\pi$
$79$		−	9.88858i		−	1.11255i	0.830997	−	0.556276i	$-0.187770\pi$
$80$	1.75703	+	1.38306i	0.196442	+	0.154631i
$81$		0			0
$82$	−3.70316	−	3.70316i	−0.408945	−	0.408945i
$83$	2.25381	+	2.25381i	0.247388	+	0.247388i	0.819898	−	0.572510i	$-0.194030\pi$
$83$	2.25381	+	2.25381i	0.247388	+	0.247388i	−0.572510	+	0.819898i	$0.694030\pi$
$84$		0			0
$85$	−2.22038	+	0.264435i	−0.240834	+	0.0286820i
$86$		−	1.08608i		−	0.117115i
$87$		0			0
$88$	−0.528869	+	0.528869i	−0.0563776	+	0.0563776i
$89$	−5.21259			−0.552534			−0.276267	−	0.961081i	$-0.589097\pi$
$89$	−5.21259			−0.552534			−0.276267	+	0.961081i	$0.589097\pi$
$90$		0			0
$91$	−1.65142			−0.173116
$92$	1.04025	−	1.04025i	0.108453	−	0.108453i
$93$		0			0
$94$			11.2301i			1.15829i
$95$	3.24822	−	4.12652i	0.333261	−	0.423372i
$96$		0			0
$97$	−3.76797	−	3.76797i	−0.382580	−	0.382580i	0.489451	−	0.872031i	$-0.337197\pi$
$97$	−3.76797	−	3.76797i	−0.382580	−	0.382580i	−0.872031	+	0.489451i	$0.837197\pi$
$98$	5.99287	+	5.99287i	0.605371	+	0.605371i
$99$		0			0
$100$	4.86015	−	1.17429i	0.486015	−	0.117429i
$101$		−	11.0243i		−	1.09696i	−0.836165	−	0.548478i	$-0.815208\pi$
$101$		−	11.0243i		−	1.09696i	0.836165	−	0.548478i	$-0.184792\pi$
$102$		0			0
$103$	−8.24917	+	8.24917i	−0.812815	+	0.812815i	−0.985055	−	0.172240i	$-0.944899\pi$
$103$	−8.24917	+	8.24917i	−0.812815	+	0.812815i	0.172240	+	0.985055i	$0.444899\pi$
$104$	−0.419798			−0.0411645
$105$		0			0
$106$	2.59368			0.251921
$107$	−10.2763	+	10.2763i	−0.993451	+	0.993451i	−0.999979	−	0.00652803i	$-0.997922\pi$
$107$	−10.2763	+	10.2763i	−0.993451	+	0.993451i	0.00652803	+	0.999979i	$0.497922\pi$
$108$		0			0
$109$		−	3.57460i		−	0.342385i	−0.985238	−	0.171192i	$-0.945238\pi$
$109$		−	3.57460i		−	0.342385i	0.985238	−	0.171192i	$-0.0547620\pi$
$110$	0.197780	+	1.66070i	0.0188575	+	0.158341i
$111$		0			0
$112$	2.78165	+	2.78165i	0.262842	+	0.262842i
$113$	−2.95030	−	2.95030i	−0.277540	−	0.277540i	0.554586	−	0.832126i	$-0.312877\pi$
$113$	−2.95030	−	2.95030i	−0.277540	−	0.277540i	−0.832126	+	0.554586i	$0.812877\pi$
$114$		0			0
$115$	−0.389018	−	3.26647i	−0.0362761	−	0.304599i
$116$			10.6338i			0.987326i
$117$		0			0
$118$	−9.49249	+	9.49249i	−0.873855	+	0.873855i
$119$	−3.93385			−0.360616
$120$		0			0
$121$	10.4406			0.949145
$122$	−2.31899	+	2.31899i	−0.209951	+	0.209951i
$123$		0			0
$124$		−	0.685860i		−	0.0615920i
$125$	4.65862	−	10.1635i	0.416680	−	0.909053i
$126$		0			0
$127$	−9.97670	−	9.97670i	−0.885289	−	0.885289i	0.108777	−	0.994066i	$-0.465306\pi$
$127$	−9.97670	−	9.97670i	−0.885289	−	0.885289i	−0.994066	+	0.108777i	$0.965306\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−0.580605	+	0.737596i	−0.0509225	+	0.0646914i
$131$		−	21.1373i		−	1.84677i	−0.383871	−	0.923387i	$-0.625409\pi$
$131$		−	21.1373i		−	1.84677i	0.383871	−	0.923387i	$-0.374591\pi$
$132$		0			0
$133$	6.53293	−	6.53293i	0.566477	−	0.566477i
$134$	9.57710			0.827336
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	10.1517	−	10.1517i	0.867320	−	0.867320i	−0.124855	−	0.992175i	$-0.539847\pi$
$137$	10.1517	−	10.1517i	0.867320	−	0.867320i	0.992175	+	0.124855i	$0.0398466\pi$
$138$		0			0
$139$			12.2878i			1.04224i	0.853484	+	0.521120i	$0.174486\pi$
$139$			12.2878i			1.04224i	−0.853484	+	0.521120i	$0.825514\pi$
$140$	8.73463	−	1.04025i	0.738211	−	0.0879169i
$141$		0			0
$142$	−2.86977	−	2.86977i	−0.240826	−	0.240826i
$143$	−0.222018	−	0.222018i	−0.0185661	−	0.0185661i
$144$		0			0
$145$	18.6839	+	14.7072i	1.55161	+	1.22137i
$146$		−	6.69997i		−	0.554494i
$147$		0			0
$148$	5.51925	−	5.51925i	0.453680	−	0.453680i
$149$	−19.3849			−1.58808			−0.794038	−	0.607868i	$-0.792025\pi$
$149$	−19.3849			−1.58808			−0.794038	+	0.607868i	$0.792025\pi$
$150$		0			0
$151$	−17.6595			−1.43711			−0.718557	−	0.695468i	$-0.755197\pi$
$151$	−17.6595			−1.43711			−0.718557	+	0.695468i	$0.755197\pi$
$152$	1.66070	−	1.66070i	0.134700	−	0.134700i
$153$		0			0
$154$			2.94226i			0.237094i
$155$	−1.20507	−	0.948585i	−0.0967939	−	0.0761922i
$156$		0			0
$157$	0.139851	+	0.139851i	0.0111613	+	0.0111613i	0.712665	−	0.701504i	$-0.247488\pi$
$157$	0.139851	+	0.139851i	0.0111613	+	0.0111613i	−0.701504	+	0.712665i	$0.747488\pi$
$158$	−6.99229	−	6.99229i	−0.556276	−	0.556276i
$159$		0			0
$160$	2.22038	−	0.264435i	0.175536	−	0.0209054i
$161$		−	5.78721i		−	0.456096i
$162$		0			0
$163$	11.9392	−	11.9392i	0.935154	−	0.935154i	−0.0628679	−	0.998022i	$-0.520025\pi$
$163$	11.9392	−	11.9392i	0.935154	−	0.935154i	0.998022	+	0.0628679i	$0.0200247\pi$
$164$	−5.23706			−0.408945
$165$		0			0
$166$	3.18737			0.247388
$167$	−2.14567	+	2.14567i	−0.166037	+	0.166037i	−0.785235	−	0.619198i	$-0.787458\pi$
$167$	−2.14567	+	2.14567i	−0.166037	+	0.166037i	0.619198	+	0.785235i	$0.287458\pi$
$168$		0			0
$169$			12.8238i			0.986444i
$170$	−1.38306	+	1.75703i	−0.106076	+	0.134758i
$171$		0			0
$172$	−0.767973	−	0.767973i	−0.0585574	−	0.0585574i
$173$	−4.60300	−	4.60300i	−0.349960	−	0.349960i	0.510135	−	0.860095i	$-0.329596\pi$
$173$	−4.60300	−	4.60300i	−0.349960	−	0.349960i	−0.860095	+	0.510135i	$0.829596\pi$
$174$		0			0
$175$	10.2528	−	16.7857i	0.775038	−	1.26888i
$176$			0.747934i			0.0563776i
$177$		0			0
$178$	−3.68586	+	3.68586i	−0.276267	+	0.276267i
$179$	4.53782			0.339173			0.169586	−	0.985515i	$-0.445757\pi$
$179$	4.53782			0.339173			0.169586	+	0.985515i	$0.445757\pi$
$180$		0			0
$181$	20.4561			1.52049			0.760245	−	0.649636i	$-0.225079\pi$
$181$	20.4561			1.52049			0.760245	+	0.649636i	$0.225079\pi$
$182$	−1.16773	+	1.16773i	−0.0865580	+	0.0865580i
$183$		0			0
$184$		−	1.47113i		−	0.108453i
$185$	−2.06402	−	17.3309i	−0.151750	−	1.27419i
$186$		0			0
$187$	−0.528869	−	0.528869i	−0.0386747	−	0.0386747i
$188$	7.94087	+	7.94087i	0.579147	+	0.579147i
$189$		0			0
$190$	−0.621045	−	5.21473i	−0.0450554	−	0.378316i
$191$		−	12.6850i		−	0.917852i	−0.888475	−	0.458926i	$-0.848234\pi$
$191$		−	12.6850i		−	0.917852i	0.888475	−	0.458926i	$-0.151766\pi$
$192$		0			0
$193$	−13.1135	+	13.1135i	−0.943933	+	0.943933i	−0.998510	−	0.0545766i	$-0.982619\pi$
$193$	−13.1135	+	13.1135i	−0.943933	+	0.943933i	0.0545766	+	0.998510i	$0.482619\pi$
$194$	−5.32872			−0.382580
$195$		0			0
$196$	8.47519			0.605371
$197$	−6.80811	+	6.80811i	−0.485058	+	0.485058i	−0.906743	−	0.421685i	$-0.861439\pi$
$197$	−6.80811	+	6.80811i	−0.485058	+	0.485058i	0.421685	+	0.906743i	$0.361439\pi$
$198$		0			0
$199$		−	4.19565i		−	0.297422i	−0.988881	−	0.148711i	$-0.952488\pi$
$199$		−	4.19565i		−	0.297422i	0.988881	−	0.148711i	$-0.0475124\pi$
$200$	2.60630	−	4.26699i	0.184293	−	0.301722i
$201$		0			0
$202$	−7.79533	−	7.79533i	−0.548478	−	0.548478i
$203$	29.5796	+	29.5796i	2.07608	+	2.07608i
$204$		0			0
$205$	−7.24316	+	9.20165i	−0.505885	+	0.642671i
$206$			11.6661i			0.812815i
$207$		0			0
$208$	−0.296842	+	0.296842i	−0.0205823	+	0.0205823i
$209$	1.75658			0.121505
$210$		0			0
$211$	−13.0111			−0.895724			−0.447862	−	0.894103i	$-0.647814\pi$
$211$	−13.0111			−0.895724			−0.447862	+	0.894103i	$0.647814\pi$
$212$	1.83401	−	1.83401i	0.125960	−	0.125960i
$213$		0			0
$214$			14.5329i			0.993451i
$215$	−2.41150	+	0.287196i	−0.164463	+	0.0195866i
$216$		0			0
$217$	−1.90782	−	1.90782i	−0.129512	−	0.129512i
$218$	−2.52763	−	2.52763i	−0.171192	−	0.171192i
$219$		0			0
$220$	1.31414	+	1.03444i	0.0885993	+	0.0697418i
$221$		−	0.419798i		−	0.0282386i
$222$		0			0
$223$	3.23803	−	3.23803i	0.216834	−	0.216834i	−0.590329	−	0.807163i	$-0.701002\pi$
$223$	3.23803	−	3.23803i	0.216834	−	0.216834i	0.807163	+	0.590329i	$0.201002\pi$
$224$	3.93385			0.262842
$225$		0			0
$226$	−4.17235			−0.277540
$227$	−1.91567	+	1.91567i	−0.127147	+	0.127147i	−0.767817	−	0.640670i	$-0.778657\pi$
$227$	−1.91567	+	1.91567i	−0.127147	+	0.127147i	0.640670	+	0.767817i	$0.278657\pi$
$228$		0			0
$229$		−	6.88151i		−	0.454743i	−0.973808	−	0.227371i	$-0.926987\pi$
$229$		−	6.88151i		−	0.454743i	0.973808	−	0.227371i	$-0.0730131\pi$
$230$	−2.58482	−	2.03466i	−0.170438	−	0.134162i
$231$		0			0
$232$	7.51925	+	7.51925i	0.493663	+	0.493663i
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	0.899716	−	0.436475i	$-0.143773\pi$
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	−0.436475	+	0.899716i	$0.643773\pi$
$234$		0			0
$235$	24.9350	−	2.96962i	1.62658	−	0.193717i
$236$			13.4244i			0.873855i
$237$		0			0
$238$	−2.78165	+	2.78165i	−0.180308	+	0.180308i
$239$	15.2642			0.987357			0.493678	−	0.869645i	$-0.335652\pi$
$239$	15.2642			0.987357			0.493678	+	0.869645i	$0.335652\pi$
$240$		0			0
$241$	−11.8845			−0.765549			−0.382775	−	0.923842i	$-0.625031\pi$
$241$	−11.8845			−0.765549			−0.382775	+	0.923842i	$0.625031\pi$
$242$	7.38262	−	7.38262i	0.474572	−	0.474572i
$243$		0			0
$244$			3.27954i			0.209951i
$245$	11.7217	−	14.8911i	0.748872	−	0.951360i
$246$		0			0
$247$	0.697156	+	0.697156i	0.0443590	+	0.0443590i
$248$	−0.484976	−	0.484976i	−0.0307960	−	0.0307960i
$249$		0			0
$250$	−3.89256	−	10.4808i	−0.246187	−	0.662867i
$251$			13.2838i			0.838467i	0.907878	+	0.419234i	$0.137701\pi$
$251$			13.2838i			0.838467i	−0.907878	+	0.419234i	$0.862299\pi$
$252$		0			0
$253$	0.778036	−	0.778036i	0.0489147	−	0.0489147i
$254$	−14.1092			−0.885289
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.7187	−	18.7187i	1.16764	−	1.16764i	0.184876	−	0.982762i	$-0.440812\pi$
$257$	18.7187	−	18.7187i	1.16764	−	1.16764i	0.982762	−	0.184876i	$-0.0591883\pi$
$258$		0			0
$259$		−	30.7053i		−	1.90793i
$260$	0.111009	+	0.932109i	0.00688449	+	0.0578070i
$261$		0			0
$262$	−14.9463	−	14.9463i	−0.923387	−	0.923387i
$263$	−19.9351	−	19.9351i	−1.22925	−	1.22925i	−0.964248	−	0.265003i	$-0.914627\pi$
$263$	−19.9351	−	19.9351i	−1.22925	−	1.22925i	−0.265003	−	0.964248i	$-0.585373\pi$
$264$		0			0
$265$	−0.685860	−	5.75896i	−0.0421320	−	0.353770i
$266$		−	9.23896i		−	0.566477i
$267$		0			0
$268$	6.77203	−	6.77203i	0.413668	−	0.413668i
$269$	4.70602			0.286931			0.143466	−	0.989655i	$-0.454175\pi$
$269$	4.70602			0.286931			0.143466	+	0.989655i	$0.454175\pi$
$270$		0			0
$271$	−5.29084			−0.321396			−0.160698	−	0.987004i	$-0.551374\pi$
$271$	−5.29084			−0.321396			−0.160698	+	0.987004i	$0.551374\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$		0			0
$274$		−	14.3567i		−	0.867320i
$275$	3.63507	−	0.878291i	0.219203	−	0.0529629i
$276$		0			0
$277$	−9.55791	−	9.55791i	−0.574279	−	0.574279i	0.359042	−	0.933321i	$-0.383103\pi$
$277$	−9.55791	−	9.55791i	−0.574279	−	0.574279i	−0.933321	+	0.359042i	$0.883103\pi$
$278$	8.68880	+	8.68880i	0.521120	+	0.521120i
$279$		0			0
$280$	5.44075	−	6.91188i	0.325147	−	0.413064i
$281$			18.9592i			1.13101i	0.824745	+	0.565505i	$0.191319\pi$
$281$			18.9592i			1.13101i	−0.824745	+	0.565505i	$0.808681\pi$
$282$		0			0
$283$	−4.43669	+	4.43669i	−0.263734	+	0.263734i	−0.826569	−	0.562835i	$-0.809711\pi$
$283$	−4.43669	+	4.43669i	−0.263734	+	0.263734i	0.562835	+	0.826569i	$0.309711\pi$
$284$	−4.05847			−0.240826
$285$		0			0
$286$	−0.313981			−0.0185661
$287$	−14.5677	+	14.5677i	−0.859903	+	0.859903i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	23.6111	−	2.81195i	1.38649	−	0.165123i
$291$		0			0
$292$	−4.73760	−	4.73760i	−0.277247	−	0.277247i
$293$	15.1937	+	15.1937i	0.887628	+	0.887628i	0.994295	−	0.106667i	$-0.0340179\pi$
$293$	15.1937	+	15.1937i	0.887628	+	0.887628i	−0.106667	+	0.994295i	$0.534018\pi$
$294$		0			0
$295$	23.5871	+	18.5668i	1.37329	+	1.08100i
$296$		−	7.80540i		−	0.453680i
$297$		0			0
$298$	−13.7072	+	13.7072i	−0.794038	+	0.794038i
$299$	0.617577			0.0357154
$300$		0			0
$301$	−4.27247			−0.246261
$302$	−12.4872	+	12.4872i	−0.718557	+	0.718557i
$303$		0			0
$304$		−	2.34858i		−	0.134700i
$305$	5.76225	+	4.53581i	0.329945	+	0.259719i
$306$		0			0
$307$	−15.5199	−	15.5199i	−0.885765	−	0.885765i	0.108348	−	0.994113i	$-0.465444\pi$
$307$	−15.5199	−	15.5199i	−0.885765	−	0.885765i	−0.994113	+	0.108348i	$0.965444\pi$
$308$	2.08049	+	2.08049i	0.118547	+	0.118547i
$309$		0			0
$310$	−1.52287	+	0.181365i	−0.0864930	+	0.0103008i
$311$			5.42972i			0.307891i	0.988079	+	0.153946i	$0.0491980\pi$
$311$			5.42972i			0.307891i	−0.988079	+	0.153946i	$0.950802\pi$
$312$		0			0
$313$	11.4621	−	11.4621i	0.647877	−	0.647877i	−0.304603	−	0.952480i	$-0.598524\pi$
$313$	11.4621	−	11.4621i	0.647877	−	0.647877i	0.952480	+	0.304603i	$0.0985236\pi$
$314$	0.197780			0.0111613
$315$		0			0
$316$	−9.88858			−0.556276
$317$	−11.6547	+	11.6547i	−0.654594	+	0.654594i	−0.954096	−	0.299501i	$-0.903180\pi$
$317$	−11.6547	+	11.6547i	−0.654594	+	0.654594i	0.299501	+	0.954096i	$0.403180\pi$
$318$		0			0
$319$			7.95340i			0.445305i
$320$	1.38306	−	1.75703i	0.0773154	−	0.0982208i
$321$		0			0
$322$	−4.09218	−	4.09218i	−0.228048	−	0.228048i
$323$	1.66070	+	1.66070i	0.0924036	+	0.0924036i
$324$		0			0
$325$	1.79127	+	1.09412i	0.0993620	+	0.0606907i
$326$		−	16.8846i		−	0.935154i
$327$		0			0
$328$	−3.70316	+	3.70316i	−0.204473	+	0.204473i
$329$	44.1775			2.43558
$330$		0			0
$331$	−12.1723			−0.669053			−0.334526	−	0.942386i	$-0.608576\pi$
$331$	−12.1723			−0.669053			−0.334526	+	0.942386i	$0.608576\pi$
$332$	2.25381	−	2.25381i	0.123694	−	0.123694i
$333$		0			0
$334$			3.03444i			0.166037i
$335$	−2.53252	−	21.2648i	−0.138366	−	1.16182i
$336$		0			0
$337$	−10.2128	−	10.2128i	−0.556326	−	0.556326i	0.371933	−	0.928259i	$-0.378695\pi$
$337$	−10.2128	−	10.2128i	−0.556326	−	0.556326i	−0.928259	+	0.371933i	$0.878695\pi$
$338$	9.06777	+	9.06777i	0.493222	+	0.493222i
$339$		0			0
$340$	0.264435	+	2.22038i	0.0143410	+	0.120417i
$341$		−	0.512978i		−	0.0277793i
$342$		0			0
$343$	4.10347	−	4.10347i	0.221567	−	0.221567i
$344$	−1.08608			−0.0585574
$345$		0			0
$346$	−6.50963			−0.349960
$347$	4.84150	−	4.84150i	0.259905	−	0.259905i	−0.565110	−	0.825015i	$-0.691166\pi$
$347$	4.84150	−	4.84150i	0.259905	−	0.259905i	0.825015	+	0.565110i	$0.191166\pi$
$348$		0			0
$349$		−	13.8965i		−	0.743864i	−0.928260	−	0.371932i	$-0.878695\pi$
$349$		−	13.8965i		−	0.743864i	0.928260	−	0.371932i	$-0.121305\pi$
$350$	−4.61948	−	19.1191i	−0.246922	−	1.02196i
$351$		0			0
$352$	0.528869	+	0.528869i	0.0281888	+	0.0281888i
$353$	10.7878	+	10.7878i	0.574176	+	0.574176i	0.933293	−	0.359116i	$-0.116922\pi$
$353$	10.7878	+	10.7878i	0.574176	+	0.574176i	−0.359116	+	0.933293i	$0.616922\pi$
$354$		0			0
$355$	−5.61310	+	7.13083i	−0.297913	+	0.378465i
$356$			5.21259i			0.276267i
$357$		0			0
$358$	3.20873	−	3.20873i	0.169586	−	0.169586i
$359$	−15.7843			−0.833065			−0.416533	−	0.909121i	$-0.636755\pi$
$359$	−15.7843			−0.833065			−0.416533	+	0.909121i	$0.636755\pi$
$360$		0			0
$361$	13.4842			0.709694
$362$	14.4647	−	14.4647i	0.760245	−	0.760245i
$363$		0			0
$364$			1.65142i			0.0865580i
$365$	−14.8765	+	1.77170i	−0.778670	+	0.0927353i
$366$		0			0
$367$	−19.2145	−	19.2145i	−1.00299	−	1.00299i	−0.999996	−	0.00299135i	$-0.999048\pi$
$367$	−19.2145	−	19.2145i	−1.00299	−	1.00299i	−0.00299135	−	0.999996i	$-0.500952\pi$
$368$	−1.04025	−	1.04025i	−0.0542266	−	0.0542266i
$369$		0			0
$370$	−13.7143	−	10.7953i	−0.712972	−	0.561223i
$371$		−	10.2032i		−	0.529722i
$372$		0			0
$373$	17.6566	−	17.6566i	0.914222	−	0.914222i	−0.0823792	−	0.996601i	$-0.526252\pi$
$373$	17.6566	−	17.6566i	0.914222	−	0.914222i	0.996601	+	0.0823792i	$0.0262519\pi$
$374$	−0.747934			−0.0386747
$375$		0			0
$376$	11.2301			0.579147
$377$	−3.15656	+	3.15656i	−0.162571	+	0.162571i
$378$		0			0
$379$		−	10.5329i		−	0.541040i	−0.962714	−	0.270520i	$-0.912804\pi$
$379$		−	10.5329i		−	0.541040i	0.962714	−	0.270520i	$-0.0871957\pi$
$380$	−4.12652	−	3.24822i	−0.211686	−	0.166630i
$381$		0			0
$382$	−8.96962	−	8.96962i	−0.458926	−	0.458926i
$383$	−0.130357	−	0.130357i	−0.00666092	−	0.00666092i	0.703768	−	0.710429i	$-0.251499\pi$
$383$	−0.130357	−	0.130357i	−0.00666092	−	0.00666092i	−0.710429	+	0.703768i	$0.751499\pi$
$384$		0			0
$385$	6.53293	−	0.778036i	0.332949	−	0.0396524i
$386$			18.5453i			0.943933i
$387$		0			0
$388$	−3.76797	+	3.76797i	−0.191290	+	0.191290i
$389$	−16.0635			−0.814454			−0.407227	−	0.913327i	$-0.633504\pi$
$389$	−16.0635			−0.814454			−0.407227	+	0.913327i	$0.633504\pi$
$390$		0			0
$391$	1.47113			0.0743983
$392$	5.99287	−	5.99287i	0.302685	−	0.302685i
$393$		0			0
$394$			9.62812i			0.485058i
$395$	−13.6765	+	17.3745i	−0.688140	+	0.874207i
$396$		0			0
$397$	−14.3621	−	14.3621i	−0.720813	−	0.720813i	0.247958	−	0.968771i	$-0.420241\pi$
$397$	−14.3621	−	14.3621i	−0.720813	−	0.720813i	−0.968771	+	0.247958i	$0.920241\pi$
$398$	−2.96677	−	2.96677i	−0.148711	−	0.148711i
$399$		0			0
$400$	−1.17429	−	4.86015i	−0.0587145	−	0.243007i
$401$		−	15.2182i		−	0.759961i	−0.924995	−	0.379980i	$-0.875931\pi$
$401$		−	15.2182i		−	0.759961i	0.924995	−	0.379980i	$-0.124069\pi$
$402$		0			0
$403$	0.203592	−	0.203592i	0.0101416	−	0.0101416i
$404$	−11.0243			−0.548478
$405$		0			0
$406$	41.8319			2.07608
$407$	4.12803	−	4.12803i	0.204619	−	0.204619i
$408$		0			0
$409$		−	16.0120i		−	0.791743i	−0.918306	−	0.395871i	$-0.870443\pi$
$409$		−	16.0120i		−	0.791743i	0.918306	−	0.395871i	$-0.129557\pi$
$410$	1.38486	+	11.6282i	0.0683933	+	0.574278i
$411$		0			0
$412$	8.24917	+	8.24917i	0.406407	+	0.406407i
$413$	37.3421	+	37.3421i	1.83748	+	1.83748i
$414$		0			0
$415$	−0.842850	−	7.07716i	−0.0413739	−	0.347404i
$416$			0.419798i			0.0205823i
$417$		0			0
$418$	1.24209	−	1.24209i	0.0607526	−	0.0607526i
$419$	−34.7593			−1.69810			−0.849050	−	0.528312i	$-0.822825\pi$
$419$	−34.7593			−1.69810			−0.849050	+	0.528312i	$0.822825\pi$
$420$		0			0
$421$	−2.75188			−0.134118			−0.0670592	−	0.997749i	$-0.521362\pi$
$421$	−2.75188			−0.134118			−0.0670592	+	0.997749i	$0.521362\pi$
$422$	−9.20026	+	9.20026i	−0.447862	+	0.447862i
$423$		0			0
$424$		−	2.59368i		−	0.125960i
$425$	4.26699	+	2.60630i	0.206980	+	0.126424i
$426$		0			0
$427$	9.12255	+	9.12255i	0.441471	+	0.441471i
$428$	10.2763	+	10.2763i	0.496725	+	0.496725i
$429$		0			0
$430$	−1.50211	+	1.90827i	−0.0724382	+	0.0920248i
$431$			22.5581i			1.08659i	0.839543	+	0.543293i	$0.182823\pi$
$431$			22.5581i			1.08659i	−0.839543	+	0.543293i	$0.817177\pi$
$432$		0			0
$433$	−19.8702	+	19.8702i	−0.954901	+	0.954901i	−0.999026	−	0.0441246i	$-0.985950\pi$
$433$	−19.8702	+	19.8702i	−0.954901	+	0.954901i	0.0441246	+	0.999026i	$0.485950\pi$
$434$	−2.69807			−0.129512
$435$		0			0
$436$	−3.57460			−0.171192
$437$	−2.44310	+	2.44310i	−0.116869	+	0.116869i
$438$		0			0
$439$		−	40.7175i		−	1.94334i	−0.236345	−	0.971669i	$-0.575950\pi$
$439$		−	40.7175i		−	1.94334i	0.236345	−	0.971669i	$-0.424050\pi$
$440$	1.66070	−	0.197780i	0.0791705	−	0.00942877i
$441$		0			0
$442$	−0.296842	−	0.296842i	−0.0141193	−	0.0141193i
$443$	17.7544	+	17.7544i	0.843539	+	0.843539i	0.989317	−	0.145778i	$-0.0465685\pi$
$443$	17.7544	+	17.7544i	0.843539	+	0.843539i	−0.145778	+	0.989317i	$0.546569\pi$
$444$		0			0
$445$	9.15867	+	7.20933i	0.434162	+	0.341755i
$446$		−	4.57927i		−	0.216834i
$447$		0			0
$448$	2.78165	−	2.78165i	0.131421	−	0.131421i
$449$	0.219498			0.0103588			0.00517938	−	0.999987i	$-0.498351\pi$
$449$	0.219498			0.0103588			0.00517938	+	0.999987i	$0.498351\pi$
$450$		0			0
$451$	−3.91697			−0.184443
$452$	−2.95030	+	2.95030i	−0.138770	+	0.138770i
$453$		0			0
$454$			2.70916i			0.127147i
$455$	2.90159	+	2.28402i	0.136029	+	0.107076i
$456$		0			0
$457$	20.2068	+	20.2068i	0.945234	+	0.945234i	0.998576	−	0.0533427i	$-0.0169876\pi$
$457$	20.2068	+	20.2068i	0.945234	+	0.945234i	−0.0533427	+	0.998576i	$0.516988\pi$
$458$	−4.86596	−	4.86596i	−0.227371	−	0.227371i
$459$		0			0
$460$	−3.26647	+	0.389018i	−0.152300	+	0.0181381i
$461$		−	38.9075i		−	1.81210i	−0.423168	−	0.906051i	$-0.639082\pi$
$461$		−	38.9075i		−	1.81210i	0.423168	−	0.906051i	$-0.360918\pi$
$462$		0			0
$463$	−15.7851	+	15.7851i	−0.733596	+	0.733596i	−0.971330	−	0.237734i	$-0.923595\pi$
$463$	−15.7851	+	15.7851i	−0.733596	+	0.733596i	0.237734	+	0.971330i	$0.423595\pi$
$464$	10.6338			0.493663
$465$		0			0
$466$	10.0000			0.463241
$467$	−6.41053	+	6.41053i	−0.296644	+	0.296644i	−0.839698	−	0.543054i	$-0.817268\pi$
$467$	−6.41053	+	6.41053i	−0.296644	+	0.296644i	0.543054	+	0.839698i	$0.317268\pi$
$468$		0			0
$469$		−	37.6749i		−	1.73967i
$470$	15.5319	−	19.7316i	0.716432	−	0.910149i
$471$		0			0
$472$	9.49249	+	9.49249i	0.436927	+	0.436927i
$473$	−0.574393	−	0.574393i	−0.0264106	−	0.0264106i
$474$		0			0
$475$	−11.4144	+	2.75791i	−0.523730	+	0.126542i
$476$			3.93385i			0.180308i
$477$		0			0
$478$	10.7934	−	10.7934i	0.493678	−	0.493678i
$479$	−41.0832			−1.87714			−0.938571	−	0.345087i	$-0.887849\pi$
$479$	−41.0832			−1.87714			−0.938571	+	0.345087i	$0.887849\pi$
$480$		0			0
$481$	3.27669			0.149404
$482$	−8.40363	+	8.40363i	−0.382775	+	0.382775i
$483$		0			0
$484$		−	10.4406i		−	0.474572i
$485$	1.40910	+	11.8318i	0.0639838	+	0.537253i
$486$		0			0
$487$	10.8892	+	10.8892i	0.493436	+	0.493436i	0.909387	−	0.415951i	$-0.136551\pi$
$487$	10.8892	+	10.8892i	0.493436	+	0.493436i	−0.415951	+	0.909387i	$0.636551\pi$
$488$	2.31899	+	2.31899i	0.104976	+	0.104976i
$489$		0			0
$490$	−2.24113	−	18.8181i	−0.101244	−	0.850116i
$491$			9.12283i			0.411708i	0.978583	+	0.205854i	$0.0659972\pi$
$491$			9.12283i			0.411708i	−0.978583	+	0.205854i	$0.934003\pi$
$492$		0			0
$493$	−7.51925	+	7.51925i	−0.338650	+	0.338650i
$494$	0.985928			0.0443590
$495$		0			0
$496$	−0.685860			−0.0307960
$497$	−11.2892	+	11.2892i	−0.506392	+	0.506392i
$498$		0			0
$499$			5.40243i			0.241846i	0.992662	+	0.120923i	$0.0385854\pi$
$499$			5.40243i			0.241846i	−0.992662	+	0.120923i	$0.961415\pi$
$500$	−10.1635	−	4.65862i	−0.454527	−	0.208340i
$501$		0			0
$502$	9.39308	+	9.39308i	0.419234	+	0.419234i
$503$	−10.6805	−	10.6805i	−0.476220	−	0.476220i	0.427700	−	0.903921i	$-0.359324\pi$
$503$	−10.6805	−	10.6805i	−0.476220	−	0.476220i	−0.903921	+	0.427700i	$0.859324\pi$
$504$		0			0
$505$	−15.2472	+	19.3699i	−0.678493	+	0.861951i
$506$		−	1.10031i		−	0.0489147i
$507$		0			0
$508$	−9.97670	+	9.97670i	−0.442644	+	0.442644i
$509$	14.7140			0.652187			0.326093	−	0.945338i	$-0.394268\pi$
$509$	14.7140			0.652187			0.326093	+	0.945338i	$0.394268\pi$
$510$		0			0
$511$	−26.3567			−1.16595
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	26.4722i		−	1.16764i
$515$	25.9031	−	3.08492i	1.14143	−	0.135938i
$516$		0			0
$517$	5.93925	+	5.93925i	0.261208	+	0.261208i
$518$	−21.7119	−	21.7119i	−0.953967	−	0.953967i
$519$		0			0
$520$	0.737596	+	0.580605i	0.0323457	+	0.0254612i
$521$		−	11.0572i		−	0.484426i	−0.970223	−	0.242213i	$-0.922127\pi$
$521$		−	11.0572i		−	0.484426i	0.970223	−	0.242213i	$-0.0778732\pi$
$522$		0			0
$523$	−6.21295	+	6.21295i	−0.271673	+	0.271673i	−0.829774	−	0.558100i	$-0.811530\pi$
$523$	−6.21295	+	6.21295i	−0.271673	+	0.271673i	0.558100	+	0.829774i	$0.311530\pi$
$524$	−21.1373			−0.923387
$525$		0			0
$526$	−28.1925			−1.22925
$527$	0.484976	−	0.484976i	0.0211259	−	0.0211259i
$528$		0			0
$529$		−	20.8358i		−	0.905903i
$530$	−4.55717	−	3.58722i	−0.197951	−	0.155819i
$531$		0			0
$532$	−6.53293	−	6.53293i	−0.283238	−	0.283238i
$533$	−1.55458	−	1.55458i	−0.0673362	−	0.0673362i
$534$		0			0
$535$	32.2686	−	3.84301i	1.39509	−	0.166148i
$536$		−	9.57710i		−	0.413668i
$537$		0			0
$538$	3.32766	−	3.32766i	0.143466	−	0.143466i
$539$	6.33888			0.273035
$540$		0			0
$541$	37.9707			1.63249			0.816243	−	0.577708i	$-0.196053\pi$
$541$	37.9707			1.63249			0.816243	+	0.577708i	$0.196053\pi$
$542$	−3.74119	+	3.74119i	−0.160698	+	0.160698i
$543$		0			0
$544$			1.00000i			0.0428746i
$545$	−4.94389	+	6.28068i	−0.211773	+	0.269035i
$546$		0			0
$547$	16.4710	+	16.4710i	0.704248	+	0.704248i	0.965319	−	0.261072i	$-0.0840759\pi$
$547$	16.4710	+	16.4710i	0.704248	+	0.704248i	−0.261072	+	0.965319i	$0.584076\pi$
$548$	−10.1517	−	10.1517i	−0.433660	−	0.433660i
$549$		0			0
$550$	1.94934	−	3.19143i	0.0831200	−	0.136083i
$551$		−	24.9744i		−	1.06394i
$552$		0			0
$553$	−27.5066	+	27.5066i	−1.16970	+	1.16970i
$554$	−13.5169			−0.574279
$555$		0			0
$556$	12.2878			0.521120
$557$	20.2732	−	20.2732i	0.859004	−	0.859004i	−0.132216	−	0.991221i	$-0.542209\pi$
$557$	20.2732	−	20.2732i	0.859004	−	0.859004i	0.991221	+	0.132216i	$0.0422094\pi$
$558$		0			0
$559$		−	0.455933i		−	0.0192839i
$560$	−1.04025	−	8.73463i	−0.0439584	−	0.369106i
$561$		0			0
$562$	13.4062	+	13.4062i	0.565505	+	0.565505i
$563$	−6.86054	−	6.86054i	−0.289137	−	0.289137i	0.547602	−	0.836739i	$-0.315541\pi$
$563$	−6.86054	−	6.86054i	−0.289137	−	0.289137i	−0.836739	+	0.547602i	$0.815541\pi$
$564$		0			0
$565$	1.10331	+	9.26419i	0.0464167	+	0.389747i
$566$			6.27443i			0.263734i
$567$		0			0
$568$	−2.86977	+	2.86977i	−0.120413	+	0.120413i
$569$	32.2947			1.35386			0.676931	−	0.736046i	$-0.263309\pi$
$569$	32.2947			1.35386			0.676931	+	0.736046i	$0.263309\pi$
$570$		0			0
$571$	−12.4641			−0.521604			−0.260802	−	0.965392i	$-0.583987\pi$
$571$	−12.4641			−0.521604			−0.260802	+	0.965392i	$0.583987\pi$
$572$	−0.222018	+	0.222018i	−0.00928304	+	0.00928304i
$573$		0			0
$574$			20.6018i			0.859903i
$575$	−3.83420	+	6.27730i	−0.159897	+	0.261782i
$576$		0			0
$577$	13.6364	+	13.6364i	0.567691	+	0.567691i	0.931481	−	0.363790i	$-0.118517\pi$
$577$	13.6364	+	13.6364i	0.567691	+	0.567691i	−0.363790	+	0.931481i	$0.618517\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	14.7072	−	18.6839i	0.610684	−	0.775807i
$581$		−	12.5386i		−	0.520190i
$582$		0			0
$583$	1.37172	−	1.37172i	0.0568108	−	0.0568108i
$584$	−6.69997			−0.277247
$585$		0			0
$586$	21.4872			0.887628
$587$	0.994416	−	0.994416i	0.0410439	−	0.0410439i	−0.686287	−	0.727331i	$-0.740761\pi$
$587$	0.994416	−	0.994416i	0.0410439	−	0.0410439i	0.727331	+	0.686287i	$0.240761\pi$
$588$		0			0
$589$			1.61079i			0.0663716i
$590$	29.8072	−	3.54988i	1.22715	−	0.146146i
$591$		0			0
$592$	−5.51925	−	5.51925i	−0.226840	−	0.226840i
$593$	9.13307	+	9.13307i	0.375050	+	0.375050i	0.869313	−	0.494263i	$-0.164562\pi$
$593$	9.13307	+	9.13307i	0.375050	+	0.375050i	−0.494263	+	0.869313i	$0.664562\pi$
$594$		0			0
$595$	6.91188	+	5.44075i	0.283360	+	0.223049i
$596$			19.3849i			0.794038i
$597$		0			0
$598$	0.436693	−	0.436693i	0.0178577	−	0.0178577i
$599$	−2.13516			−0.0872404			−0.0436202	−	0.999048i	$-0.513889\pi$
$599$	−2.13516			−0.0872404			−0.0436202	+	0.999048i	$0.513889\pi$
$600$		0			0
$601$	−28.0974			−1.14612			−0.573059	−	0.819514i	$-0.694244\pi$
$601$	−28.0974			−1.14612			−0.573059	+	0.819514i	$0.694244\pi$
$602$	−3.02109	+	3.02109i	−0.123130	+	0.123130i
$603$		0			0
$604$			17.6595i			0.718557i
$605$	−18.3444	−	14.4400i	−0.745806	−	0.587068i
$606$		0			0
$607$	−0.356257	−	0.356257i	−0.0144600	−	0.0144600i	0.699840	−	0.714300i	$-0.253255\pi$
$607$	−0.356257	−	0.356257i	−0.0144600	−	0.0144600i	−0.714300	+	0.699840i	$0.753255\pi$
$608$	−1.66070	−	1.66070i	−0.0673501	−	0.0673501i
$609$		0			0
$610$	7.28182	−	0.867225i	0.294832	−	0.0351129i
$611$			4.71436i			0.190723i
$612$		0			0
$613$	−26.6689	+	26.6689i	−1.07715	+	1.07715i	−0.0803826	+	0.996764i	$0.525614\pi$
$613$	−26.6689	+	26.6689i	−1.07715	+	1.07715i	−0.996764	+	0.0803826i	$0.974386\pi$
$614$	−21.9484			−0.885765
$615$		0			0
$616$	2.94226			0.118547
$617$	25.0003	−	25.0003i	1.00648	−	1.00648i	0.00649727	−	0.999979i	$-0.497932\pi$
$617$	25.0003	−	25.0003i	1.00648	−	1.00648i	0.999979	−	0.00649727i	$-0.00206816\pi$
$618$		0			0
$619$		−	11.3110i		−	0.454626i	−0.973822	−	0.227313i	$-0.927006\pi$
$619$		−	11.3110i		−	0.454626i	0.973822	−	0.227313i	$-0.0729941\pi$
$620$	−0.948585	+	1.20507i	−0.0380961	+	0.0483969i
$621$		0			0
$622$	3.83939	+	3.83939i	0.153946	+	0.153946i
$623$	14.4996	+	14.4996i	0.580915	+	0.580915i
$624$		0			0
$625$	−22.2421	+	11.4144i	−0.889684	+	0.456578i
$626$		−	16.2099i		−	0.647877i
$627$		0			0
$628$	0.139851	−	0.139851i	0.00558067	−	0.00558067i
$629$	7.80540			0.311222
$630$		0			0
$631$	−33.3798			−1.32883			−0.664415	−	0.747364i	$-0.731319\pi$
$631$	−33.3798			−1.32883			−0.664415	+	0.747364i	$0.731319\pi$
$632$	−6.99229	+	6.99229i	−0.278138	+	0.278138i
$633$		0			0
$634$			16.4823i			0.654594i
$635$	3.73096	+	31.3277i	0.148058	+	1.24320i
$636$		0			0
$637$	2.51579	+	2.51579i	0.0996793	+	0.0996793i
$638$	5.62390	+	5.62390i	0.222652	+	0.222652i
$639$		0			0
$640$	−0.264435	−	2.22038i	−0.0104527	−	0.0877681i
$641$		−	2.15940i		−	0.0852913i	−0.999090	−	0.0426456i	$-0.986421\pi$
$641$		−	2.15940i		−	0.0852913i	0.999090	−	0.0426456i	$-0.0135786\pi$
$642$		0			0
$643$	−33.7284	+	33.7284i	−1.33012	+	1.33012i	−0.424860	+	0.905259i	$0.639677\pi$
$643$	−33.7284	+	33.7284i	−1.33012	+	1.33012i	−0.905259	+	0.424860i	$0.860323\pi$
$644$	−5.78721			−0.228048
$645$		0			0
$646$	2.34858			0.0924036
$647$	−14.0015	+	14.0015i	−0.550458	+	0.550458i	−0.926573	−	0.376115i	$-0.877260\pi$
$647$	−14.0015	+	14.0015i	−0.550458	+	0.550458i	0.376115	+	0.926573i	$0.377260\pi$
$648$		0			0
$649$			10.0406i			0.394127i
$650$	2.04028	−	0.492964i	0.0800263	−	0.0193356i
$651$		0			0
$652$	−11.9392	−	11.9392i	−0.467577	−	0.467577i
$653$	9.49595	+	9.49595i	0.371605	+	0.371605i	0.868062	−	0.496456i	$-0.165366\pi$
$653$	9.49595	+	9.49595i	0.371605	+	0.371605i	−0.496456	+	0.868062i	$0.665366\pi$
$654$		0			0
$655$	−29.2341	+	37.1388i	−1.14227	+	1.45113i
$656$			5.23706i			0.204473i
$657$		0			0
$658$	31.2382	−	31.2382i	1.21779	−	1.21779i
$659$	−5.22534			−0.203551			−0.101775	−	0.994807i	$-0.532452\pi$
$659$	−5.22534			−0.203551			−0.101775	+	0.994807i	$0.532452\pi$
$660$		0			0
$661$	−34.6484			−1.34767			−0.673833	−	0.738883i	$-0.735353\pi$
$661$	−34.6484			−1.34767			−0.673833	+	0.738883i	$0.735353\pi$
$662$	−8.60715	+	8.60715i	−0.334526	+	0.334526i
$663$		0			0
$664$		−	3.18737i		−	0.123694i
$665$	−20.5140	+	2.44310i	−0.795498	+	0.0947394i
$666$		0			0
$667$	−11.0618	−	11.0618i	−0.428315	−	0.428315i
$668$	2.14567	+	2.14567i	0.0830185	+	0.0830185i
$669$		0			0
$670$	−16.8272	−	13.2457i	−0.650093	−	0.511726i
$671$			2.45288i			0.0946925i
$672$		0			0
$673$	30.4044	−	30.4044i	1.17200	−	1.17200i	0.190271	−	0.981732i	$-0.439063\pi$
$673$	30.4044	−	30.4044i	1.17200	−	1.17200i	0.981732	−	0.190271i	$-0.0609366\pi$
$674$	−14.4431			−0.556326
$675$		0			0
$676$	12.8238			0.493222
$677$	23.3595	−	23.3595i	0.897779	−	0.897779i	−0.0974608	−	0.995239i	$-0.531072\pi$
$677$	23.3595	−	23.3595i	0.897779	−	0.897779i	0.995239	+	0.0974608i	$0.0310721\pi$
$678$		0			0
$679$			20.9624i			0.804463i
$680$	1.75703	+	1.38306i	0.0673789	+	0.0530379i
$681$		0			0
$682$	−0.362730	−	0.362730i	−0.0138897	−	0.0138897i
$683$	18.5696	+	18.5696i	0.710545	+	0.710545i	0.966649	−	0.256104i	$-0.0824390\pi$
$683$	18.5696	+	18.5696i	0.710545	+	0.710545i	−0.256104	+	0.966649i	$0.582439\pi$
$684$		0			0
$685$	−31.8773	+	3.79641i	−1.21797	+	0.145053i
$686$		−	5.80319i		−	0.221567i
$687$		0			0
$688$	−0.767973	+	0.767973i	−0.0292787	+	0.0292787i
$689$	1.08882			0.0414808
$690$		0			0
$691$	39.1347			1.48876			0.744378	−	0.667759i	$-0.232746\pi$
$691$	39.1347			1.48876			0.744378	+	0.667759i	$0.232746\pi$
$692$	−4.60300	+	4.60300i	−0.174980	+	0.174980i
$693$		0			0
$694$		−	6.84691i		−	0.259905i
$695$	16.9948	−	21.5900i	0.644650	−	0.818957i
$696$		0			0
$697$	−3.70316	−	3.70316i	−0.140267	−	0.140267i
$698$	−9.82633	−	9.82633i	−0.371932	−	0.371932i
$699$		0			0
$700$	−16.7857	−	10.2528i	−0.634440	−	0.387519i
$701$			1.04312i			0.0393980i	0.999806	+	0.0196990i	$0.00627080\pi$
$701$			1.04312i			0.0393980i	−0.999806	+	0.0196990i	$0.993729\pi$
$702$		0			0
$703$	−12.9624	+	12.9624i	−0.488886	+	0.488886i
$704$	0.747934			0.0281888
$705$		0			0
$706$	15.2562			0.574176
$707$	−30.6657	+	30.6657i	−1.15330	+	1.15330i
$708$		0			0
$709$			44.0345i			1.65375i	0.562387	+	0.826874i	$0.309883\pi$
$709$			44.0345i			1.65375i	−0.562387	+	0.826874i	$0.690117\pi$
$710$	1.07320	+	9.01132i	0.0402764	+	0.338189i
$711$		0			0
$712$	3.68586	+	3.68586i	0.138133	+	0.138133i
$713$	0.713463	+	0.713463i	0.0267194	+	0.0267194i
$714$		0			0
$715$	0.0830274	+	0.697156i	0.00310505	+	0.0260722i
$716$		−	4.53782i		−	0.169586i
$717$		0			0
$718$	−11.1612	+	11.1612i	−0.416533	+	0.416533i
$719$	37.5229			1.39937			0.699683	−	0.714453i	$-0.253324\pi$
$719$	37.5229			1.39937			0.699683	+	0.714453i	$0.253324\pi$
$720$		0			0
$721$	45.8926			1.70913
$722$	9.53476	−	9.53476i	0.354847	−	0.354847i
$723$		0			0
$724$		−	20.4561i		−	0.760245i
$725$	−12.4872	−	51.6820i	−0.463762	−	1.91942i
$726$		0			0
$727$	10.0802	+	10.0802i	0.373853	+	0.373853i	0.868878	−	0.495026i	$-0.164841\pi$
$727$	10.0802	+	10.0802i	0.373853	+	0.373853i	−0.495026	+	0.868878i	$0.664841\pi$
$728$	1.16773	+	1.16773i	0.0432790	+	0.0432790i
$729$		0			0
$730$	−9.26647	+	11.7720i	−0.342967	+	0.435703i
$731$		−	1.08608i		−	0.0401700i
$732$		0			0
$733$	12.3396	−	12.3396i	0.455772	−	0.455772i	−0.441493	−	0.897265i	$-0.645551\pi$
$733$	12.3396	−	12.3396i	0.455772	−	0.455772i	0.897265	+	0.441493i	$0.145551\pi$
$734$	−27.1734			−1.00299
$735$		0			0
$736$	−1.47113			−0.0542266
$737$	5.06503	−	5.06503i	0.186573	−	0.186573i
$738$		0			0
$739$			23.6334i			0.869368i	0.900583	+	0.434684i	$0.143140\pi$
$739$			23.6334i			0.869368i	−0.900583	+	0.434684i	$0.856860\pi$
$740$	−17.3309	+	2.06402i	−0.637097	+	0.0758748i
$741$		0			0
$742$	−7.21473	−	7.21473i	−0.264861	−	0.264861i
$743$	8.86414	+	8.86414i	0.325194	+	0.325194i	0.850755	−	0.525562i	$-0.176145\pi$
$743$	8.86414	+	8.86414i	0.325194	+	0.325194i	−0.525562	+	0.850755i	$0.676145\pi$
$744$		0			0
$745$	34.0599	+	26.8105i	1.24786	+	0.982262i
$746$		−	24.9701i		−	0.914222i
$747$		0			0
$748$	−0.528869	+	0.528869i	−0.0193374	+	0.0193374i
$749$	57.1704			2.08896
$750$		0			0
$751$	15.2080			0.554947			0.277474	−	0.960733i	$-0.410503\pi$
$751$	15.2080			0.554947			0.277474	+	0.960733i	$0.410503\pi$
$752$	7.94087	−	7.94087i	0.289574	−	0.289574i
$753$		0			0
$754$			4.46405i			0.162571i
$755$	31.0283	+	24.4242i	1.12924	+	0.888888i
$756$		0			0
$757$	35.7955	+	35.7955i	1.30101	+	1.30101i	0.927711	+	0.373299i	$0.121773\pi$
$757$	35.7955	+	35.7955i	1.30101	+	1.30101i	0.373299	+	0.927711i	$0.378227\pi$
$758$	−7.44791	−	7.44791i	−0.270520	−	0.270520i
$759$		0			0
$760$	−5.21473	+	0.621045i	−0.189158	+	0.0225277i
$761$			6.48070i			0.234925i	0.993077	+	0.117463i	$0.0374760\pi$
$761$			6.48070i			0.234925i	−0.993077	+	0.117463i	$0.962524\pi$
$762$		0			0
$763$	−9.94331	+	9.94331i	−0.359972	+	0.359972i
$764$	−12.6850			−0.458926
$765$		0			0
$766$	−0.184352			−0.00666092
$767$	−3.98493	+	3.98493i	−0.143887	+	0.143887i
$768$		0			0
$769$		−	55.1489i		−	1.98872i	−0.106059	−	0.994360i	$-0.533823\pi$
$769$		−	55.1489i		−	1.98872i	0.106059	−	0.994360i	$-0.466177\pi$
$770$	4.06932	−	5.16963i	0.146648	−	0.186301i
$771$		0			0
$772$	13.1135	+	13.1135i	0.471966	+	0.471966i
$773$	−31.6256	−	31.6256i	−1.13750	−	1.13750i	−0.988898	−	0.148597i	$-0.952524\pi$
$773$	−31.6256	−	31.6256i	−1.13750	−	1.13750i	−0.148597	−	0.988898i	$-0.547476\pi$
$774$		0			0
$775$	0.805397	+	3.33338i	0.0289307	+	0.119739i
$776$			5.32872i			0.191290i
$777$		0			0
$778$	−11.3586	+	11.3586i	−0.407227	+	0.407227i
$779$	12.2996			0.440680
$780$		0			0
$781$	−3.03546			−0.108617
$782$	1.04025	−	1.04025i	0.0371991	−	0.0371991i
$783$		0			0
$784$		−	8.47519i		−	0.302685i
$785$	−0.0522998	−	0.439145i	−0.00186666	−	0.0156738i
$786$		0			0
$787$	32.4875	+	32.4875i	1.15806	+	1.15806i	0.984893	+	0.173162i	$0.0553985\pi$
$787$	32.4875	+	32.4875i	1.15806	+	1.15806i	0.173162	+	0.984893i	$0.444602\pi$
$788$	6.80811	+	6.80811i	0.242529	+	0.242529i
$789$		0			0
$790$	2.61488	+	21.9564i	0.0930334	+	0.781173i
$791$			16.4134i			0.583593i
$792$		0			0
$793$	−0.973505	+	0.973505i	−0.0345702	+	0.0345702i
$794$	−20.3111			−0.720813
$795$		0			0
$796$	−4.19565			−0.148711
$797$	−5.95478	+	5.95478i	−0.210929	+	0.210929i	−0.804662	−	0.593733i	$-0.797654\pi$
$797$	−5.95478	+	5.95478i	−0.210929	+	0.210929i	0.593733	+	0.804662i	$0.297654\pi$
$798$		0			0
$799$			11.2301i			0.397292i
$800$	−4.26699	−	2.60630i	−0.150861	−	0.0921465i
$801$		0			0
$802$	−10.7609	−	10.7609i	−0.379980	−	0.379980i
$803$	−3.54341	−	3.54341i	−0.125044	−	0.125044i
$804$		0			0
$805$	−8.00406	+	10.1683i	−0.282106	+	0.358385i
$806$		−	0.287922i		−	0.0101416i
$807$		0			0
$808$	−7.79533	+	7.79533i	−0.274239	+	0.274239i
$809$	−37.1953			−1.30772			−0.653859	−	0.756616i	$-0.726851\pi$
$809$	−37.1953			−1.30772			−0.653859	+	0.756616i	$0.726851\pi$
$810$		0			0
$811$	−42.9323			−1.50756			−0.753779	−	0.657128i	$-0.771771\pi$
$811$	−42.9323			−1.50756			−0.753779	+	0.657128i	$0.771771\pi$
$812$	29.5796	−	29.5796i	1.03804	−	1.03804i
$813$		0			0
$814$		−	5.83792i		−	0.204619i
$815$	−37.4903	+	4.46488i	−1.31323	+	0.156398i
$816$		0			0
$817$	1.80364	+	1.80364i	0.0631015	+	0.0631015i
$818$	−11.3222	−	11.3222i	−0.395871	−	0.395871i
$819$		0			0
$820$	9.20165	+	7.24316i	0.321336	+	0.252942i
$821$			55.9918i			1.95413i	0.212947	+	0.977064i	$0.431694\pi$
$821$			55.9918i			1.95413i	−0.212947	+	0.977064i	$0.568306\pi$
$822$		0			0
$823$	23.6821	−	23.6821i	0.825506	−	0.825506i	−0.161386	−	0.986891i	$-0.551596\pi$
$823$	23.6821	−	23.6821i	0.825506	−	0.825506i	0.986891	+	0.161386i	$0.0515964\pi$
$824$	11.6661			0.406407
$825$		0			0
$826$	52.8096			1.83748
$827$	−29.4393	+	29.4393i	−1.02370	+	1.02370i	−0.0239909	+	0.999712i	$0.507637\pi$
$827$	−29.4393	+	29.4393i	−1.02370	+	1.02370i	−0.999712	+	0.0239909i	$0.992363\pi$
$828$		0			0
$829$			24.7946i			0.861152i	0.902554	+	0.430576i	$0.141690\pi$
$829$			24.7946i			0.861152i	−0.902554	+	0.430576i	$0.858310\pi$
$830$	−5.60029	−	4.40832i	−0.194389	−	0.153015i
$831$		0			0
$832$	0.296842	+	0.296842i	0.0102911	+	0.0102911i
$833$	5.99287	+	5.99287i	0.207640	+	0.207640i
$834$		0			0
$835$	6.73760	−	0.802410i	0.233164	−	0.0277686i
$836$		−	1.75658i		−	0.0607526i
$837$		0			0
$838$	−24.5785	+	24.5785i	−0.849050	+	0.849050i
$839$	−14.8463			−0.512550			−0.256275	−	0.966604i	$-0.582495\pi$
$839$	−14.8463			−0.512550			−0.256275	+	0.966604i	$0.582495\pi$
$840$		0			0
$841$	84.0782			2.89925
$842$	−1.94587	+	1.94587i	−0.0670592	+	0.0670592i
$843$		0			0
$844$			13.0111i			0.447862i
$845$	17.7360	−	22.5317i	0.610139	−	0.775114i
$846$		0			0
$847$	−29.0421	−	29.0421i	−0.997899	−	0.997899i
$848$	−1.83401	−	1.83401i	−0.0629802	−	0.0629802i
$849$		0			0
$850$	4.86015	−	1.17429i	0.166702	−	0.0402778i
$851$			11.4828i			0.393624i
$852$		0			0
$853$	21.6416	−	21.6416i	0.740996	−	0.740996i	−0.231774	−	0.972770i	$-0.574453\pi$
$853$	21.6416	−	21.6416i	0.740996	−	0.740996i	0.972770	+	0.231774i	$0.0744530\pi$
$854$	12.9012			0.441471
$855$		0			0
$856$	14.5329			0.496725
$857$	−9.86654	+	9.86654i	−0.337035	+	0.337035i	−0.855250	−	0.518215i	$-0.826597\pi$
$857$	−9.86654	+	9.86654i	−0.337035	+	0.337035i	0.518215	+	0.855250i	$0.326597\pi$
$858$		0			0
$859$			3.29896i			0.112559i	0.998415	+	0.0562796i	$0.0179238\pi$
$859$			3.29896i			0.112559i	−0.998415	+	0.0562796i	$0.982076\pi$
$860$	0.287196	+	2.41150i	0.00979332	+	0.0822315i
$861$		0			0
$862$	15.9510	+	15.9510i	0.543293	+	0.543293i
$863$	−5.58369	−	5.58369i	−0.190071	−	0.190071i	0.605656	−	0.795727i	$-0.292911\pi$
$863$	−5.58369	−	5.58369i	−0.190071	−	0.190071i	−0.795727	+	0.605656i	$0.792911\pi$
$864$		0			0
$865$	1.72137	+	14.4538i	0.0585284	+	0.491445i
$866$			28.1007i			0.954901i
$867$		0			0
$868$	−1.90782	+	1.90782i	−0.0647558	+	0.0647558i
$869$	−7.39601			−0.250892
$870$		0			0
$871$	4.02045			0.136228
$872$	−2.52763	+	2.52763i	−0.0855962	+	0.0855962i
$873$		0			0
$874$			3.45507i			0.116869i
$875$	−41.2301	+	15.3127i	−1.39383	+	0.517665i
$876$		0			0
$877$	34.6805	+	34.6805i	1.17108	+	1.17108i	0.981954	+	0.189122i	$0.0605643\pi$
$877$	34.6805	+	34.6805i	1.17108	+	1.17108i	0.189122	+	0.981954i	$0.439436\pi$
$878$	−28.7916	−	28.7916i	−0.971669	−	0.971669i
$879$		0			0
$880$	1.03444	−	1.31414i	0.0348709	−	0.0442997i
$881$		−	11.4256i		−	0.384937i	−0.981303	−	0.192469i	$-0.938351\pi$
$881$		−	11.4256i		−	0.384937i	0.981303	−	0.192469i	$-0.0616494\pi$
$882$		0			0
$883$	20.8328	−	20.8328i	0.701079	−	0.701079i	−0.263563	−	0.964642i	$-0.584898\pi$
$883$	20.8328	−	20.8328i	0.701079	−	0.701079i	0.964642	+	0.263563i	$0.0848977\pi$
$884$	−0.419798			−0.0141193
$885$		0			0
$886$	25.1086			0.843539
$887$	0.926866	−	0.926866i	0.0311211	−	0.0311211i	−0.691375	−	0.722496i	$-0.742995\pi$
$887$	0.926866	−	0.926866i	0.0311211	−	0.0311211i	0.722496	+	0.691375i	$0.242995\pi$
$888$		0			0
$889$			55.5034i			1.86153i
$890$	11.5739	−	1.37839i	0.387959	−	0.0462037i
$891$		0			0
$892$	−3.23803	−	3.23803i	−0.108417	−	0.108417i
$893$	−18.6498	−	18.6498i	−0.624090	−	0.624090i
$894$		0			0
$895$	−7.97308	−	6.27608i	−0.266511	−	0.209786i
$896$		−	3.93385i		−	0.131421i
$897$		0			0
$898$	0.155209	−	0.155209i	0.00517938	−	0.00517938i
$899$	−7.29331			−0.243246
$900$		0			0
$901$	2.59368			0.0864081
$902$	−2.76972	+	2.76972i	−0.0922215	+	0.0922215i
$903$		0			0
$904$			4.17235i			0.138770i
$905$	−35.9419	−	28.2920i	−1.19475	−	0.940459i
$906$		0			0
$907$	18.3982	+	18.3982i	0.610903	+	0.610903i	0.943181	−	0.332279i	$-0.107817\pi$
$907$	18.3982	+	18.3982i	0.610903	+	0.610903i	−0.332279	+	0.943181i	$0.607817\pi$
$908$	1.91567	+	1.91567i	0.0635736	+	0.0635736i
$909$		0			0
$910$	3.66678	−	0.436693i	0.121553	−	0.0144762i
$911$		−	19.5077i		−	0.646317i	−0.946345	−	0.323159i	$-0.895255\pi$
$911$		−	19.5077i		−	0.646317i	0.946345	−	0.323159i	$-0.104745\pi$
$912$		0			0
$913$	1.68570	−	1.68570i	0.0557885	−	0.0557885i
$914$	28.5767			0.945234
$915$		0			0
$916$	−6.88151			−0.227371
$917$	−58.7966	+	58.7966i	−1.94164	+	1.94164i
$918$		0			0
$919$			21.9961i			0.725585i	0.931870	+	0.362792i	$0.118177\pi$
$919$			21.9961i			0.725585i	−0.931870	+	0.362792i	$0.881823\pi$
$920$	−2.03466	+	2.58482i	−0.0670808	+	0.0852189i
$921$		0			0
$922$	−27.5117	−	27.5117i	−0.906051	−	0.906051i
$923$	−1.20472	−	1.20472i	−0.0396539	−	0.0396539i
$924$		0			0
$925$	−20.3432	+	33.3056i	−0.668880	+	1.09508i
$926$			22.3235i			0.733596i
$927$		0			0
$928$	7.51925	−	7.51925i	0.246831	−	0.246831i
$929$	35.5097			1.16504			0.582518	−	0.812818i	$-0.302068\pi$
$929$	35.5097			1.16504			0.582518	+	0.812818i	$0.302068\pi$
$930$		0			0
$931$	−19.9046			−0.652349
$932$	7.07107	−	7.07107i	0.231621	−	0.231621i
$933$		0			0
$934$			9.06586i			0.296644i
$935$	0.197780	+	1.66070i	0.00646809	+	0.0543105i
$936$		0			0
$937$	−36.0853	−	36.0853i	−1.17885	−	1.17885i	−0.980036	−	0.198818i	$-0.936290\pi$
$937$	−36.0853	−	36.0853i	−1.17885	−	1.17885i	−0.198818	−	0.980036i	$-0.563710\pi$
$938$	−26.6402	−	26.6402i	−0.869833	−	0.869833i
$939$		0			0
$940$	−2.96962	−	24.9350i	−0.0968584	−	0.813291i
$941$		−	12.1070i		−	0.394676i	−0.980336	−	0.197338i	$-0.936770\pi$
$941$		−	12.1070i		−	0.394676i	0.980336	−	0.197338i	$-0.0632296\pi$
$942$		0			0
$943$	5.44783	−	5.44783i	0.177406	−	0.177406i
$944$	13.4244			0.436927
$945$		0			0
$946$	−0.812314			−0.0264106
$947$	−7.61525	+	7.61525i	−0.247462	+	0.247462i	−0.819928	−	0.572466i	$-0.805987\pi$
$947$	−7.61525	+	7.61525i	−0.247462	+	0.247462i	0.572466	+	0.819928i	$0.305987\pi$
$948$		0			0
$949$		−	2.81263i		−	0.0913019i
$950$	−6.12109	+	10.0214i	−0.198594	+	0.325136i
$951$		0			0
$952$	2.78165	+	2.78165i	0.0901539	+	0.0901539i
$953$	30.0683	+	30.0683i	0.974008	+	0.974008i	0.999671	−	0.0256624i	$-0.00816950\pi$
$953$	30.0683	+	30.0683i	0.974008	+	0.974008i	−0.0256624	+	0.999671i	$0.508169\pi$
$954$		0			0
$955$	−17.5441	+	22.2878i	−0.567713	+	0.721217i
$956$		−	15.2642i		−	0.493678i
$957$		0			0
$958$	−29.0502	+	29.0502i	−0.938571	+	0.938571i
$959$	−56.4771			−1.82374
$960$		0			0
$961$	−30.5296			−0.984826
$962$	2.31697	−	2.31697i	0.0747020	−	0.0747020i
$963$		0			0
$964$			11.8845i			0.382775i
$965$	41.1776	−	4.90403i	1.32556	−	0.157866i
$966$		0			0
$967$	−21.8158	−	21.8158i	−0.701550	−	0.701550i	0.263193	−	0.964743i	$-0.415224\pi$
$967$	−21.8158	−	21.8158i	−0.701550	−	0.701550i	−0.964743	+	0.263193i	$0.915224\pi$
$968$	−7.38262	−	7.38262i	−0.237286	−	0.237286i
$969$		0			0
$970$	9.36270	+	7.36994i	0.300618	+	0.236634i
$971$		−	0.966954i		−	0.0310310i	−0.999880	−	0.0155155i	$-0.995061\pi$
$971$		−	0.966954i		−	0.0310310i	0.999880	−	0.0155155i	$-0.00493894\pi$
$972$		0			0
$973$	34.1805	−	34.1805i	1.09578	−	1.09578i
$974$	15.3996			0.493436
$975$		0			0
$976$	3.27954			0.104976
$977$	−2.73828	+	2.73828i	−0.0876055	+	0.0876055i	−0.749552	−	0.661946i	$-0.769731\pi$
$977$	−2.73828	+	2.73828i	−0.0876055	+	0.0876055i	0.661946	+	0.749552i	$0.269731\pi$
$978$		0			0
$979$			3.89868i			0.124602i
$980$	−14.8911	−	11.7217i	−0.475680	−	0.374436i
$981$		0			0
$982$	6.45082	+	6.45082i	0.205854	+	0.205854i
$983$	−40.0759	−	40.0759i	−1.27822	−	1.27822i	−0.941661	−	0.336563i	$-0.890735\pi$
$983$	−40.0759	−	40.0759i	−1.27822	−	1.27822i	−0.336563	−	0.941661i	$-0.609265\pi$
$984$		0			0
$985$	21.3781	−	2.54601i	0.681162	−	0.0811226i
$986$			10.6338i			0.338650i
$987$		0			0
$988$	0.697156	−	0.697156i	0.0221795	−	0.0221795i
$989$	1.59776			0.0508059
$990$		0			0
$991$	0.983596			0.0312450			0.0156225	−	0.999878i	$-0.495027\pi$
$991$	0.983596			0.0312450			0.0156225	+	0.999878i	$0.495027\pi$
$992$	−0.484976	+	0.484976i	−0.0153980	+	0.0153980i
$993$		0			0
$994$			15.9654i			0.506392i
$995$	−5.80283	+	7.37187i	−0.183962	+	0.233704i
$996$		0			0
$997$	−15.3543	−	15.3543i	−0.486276	−	0.486276i	0.420853	−	0.907129i	$-0.361731\pi$
$997$	−15.3543	−	15.3543i	−0.486276	−	0.486276i	−0.907129	+	0.420853i	$0.861731\pi$
$998$	3.82010	+	3.82010i	0.120923	+	0.120923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.h.647.5	yes	16
3.2	odd	2	inner	1530.2.m.h.647.4	✓	16
5.3	odd	4	inner	1530.2.m.h.953.4	yes	16
15.8	even	4	inner	1530.2.m.h.953.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.h.647.4	✓	16	3.2	odd	2	inner
1530.2.m.h.647.5	yes	16	1.1	even	1	trivial
1530.2.m.h.953.4	yes	16	5.3	odd	4	inner
1530.2.m.h.953.5	yes	16	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.75703 - 1.38306i) q^{5} +(-2.78165 - 2.78165i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.75703 - 1.38306i) q^{5} +(-2.78165 - 2.78165i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.22038 + 0.264435i) q^{10} -0.747934i q^{11} +(0.296842 - 0.296842i) q^{13} -3.93385 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +2.34858i q^{19} +(-1.38306 + 1.75703i) q^{20} +(-0.528869 - 0.528869i) q^{22} +(1.04025 + 1.04025i) q^{23} +(1.17429 + 4.86015i) q^{25} -0.419798i q^{26} +(-2.78165 + 2.78165i) q^{28} -10.6338 q^{29} +0.685860 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(1.04025 + 8.73463i) q^{35} +(5.51925 + 5.51925i) q^{37} +(1.66070 + 1.66070i) q^{38} +(0.264435 + 2.22038i) q^{40} -5.23706i q^{41} +(0.767973 - 0.767973i) q^{43} -0.747934 q^{44} +1.47113 q^{46} +(-7.94087 + 7.94087i) q^{47} +8.47519i q^{49} +(4.26699 + 2.60630i) q^{50} +(-0.296842 - 0.296842i) q^{52} +(1.83401 + 1.83401i) q^{53} +(-1.03444 + 1.31414i) q^{55} +3.93385i q^{56} +(-7.51925 + 7.51925i) q^{58} -13.4244 q^{59} -3.27954 q^{61} +(0.484976 - 0.484976i) q^{62} +1.00000i q^{64} +(-0.932109 + 0.111009i) q^{65} +(6.77203 + 6.77203i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(6.91188 + 5.44075i) q^{70} -4.05847i q^{71} +(4.73760 - 4.73760i) q^{73} +7.80540 q^{74} +2.34858 q^{76} +(-2.08049 + 2.08049i) q^{77} -9.88858i q^{79} +(1.75703 + 1.38306i) q^{80} +(-3.70316 - 3.70316i) q^{82} +(2.25381 + 2.25381i) q^{83} +(-2.22038 + 0.264435i) q^{85} -1.08608i q^{86} +(-0.528869 + 0.528869i) q^{88} -5.21259 q^{89} -1.65142 q^{91} +(1.04025 - 1.04025i) q^{92} +11.2301i q^{94} +(3.24822 - 4.12652i) q^{95} +(-3.76797 - 3.76797i) q^{97} +(5.99287 + 5.99287i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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