LMFDB - Embedded newform 675.2.q.a.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(143,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("675.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.q (of order $12$, degree $4$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	675.557
Dual form			675.2.q.a.143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29724 + 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(0.530190 - 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +O(q^{10})$	\(q+(1.29724 + 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(0.530190 - 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.762281 - 0.440103i) q^{11} +(-1.43820 - 5.36743i) q^{13} +(1.37557 - 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(1.13610 - 1.13610i) q^{17} +1.52456i q^{19} +(1.14184 - 0.305956i) q^{22} +(1.53331 - 0.410850i) q^{23} -7.46278i q^{26} +(-0.284392 + 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(0.286379 + 1.06878i) q^{32} +(1.86870 - 1.07889i) q^{34} +(4.25746 + 4.25746i) q^{37} +(-0.529931 + 1.97773i) q^{38} +(-3.11546 - 1.79871i) q^{41} +(1.85841 + 0.497959i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(-7.99942 - 2.14344i) q^{47} +(2.42805 + 1.40183i) q^{49} +(-0.282368 + 1.05381i) q^{52} +(-4.65601 - 4.65601i) q^{53} +(-5.23290 + 3.02121i) q^{56} +(0.553777 + 2.06672i) q^{58} +(3.81780 - 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(6.63838 - 6.63838i) q^{62} +8.62358i q^{64} +(-3.20857 + 0.859733i) q^{67} +(-0.304699 + 0.0816439i) q^{68} +5.89798i q^{71} +(-1.58900 + 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(-0.466676 - 1.74166i) q^{77} +(6.69401 - 3.86479i) q^{79} +(-3.41628 - 3.41628i) q^{82} +(-2.57170 + 9.59770i) q^{83} +(2.23772 + 1.29195i) q^{86} +(-2.50787 - 0.671981i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(-0.301043 - 0.0806641i) q^{92} +(-9.63215 - 5.56112i) q^{94} +(1.02621 - 3.82988i) q^{97} +(2.66250 + 2.66250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 + 2 * q^7	$ 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.29724	+	0.347596i	0.917290	+	0.245787i	0.686427	−	0.727199i	$-0.259178\pi$
$2$	1.29724	+	0.347596i	0.917290	+	0.245787i	0.230863	+	0.972986i	$0.425845\pi$
$3$		0			0
$3$		0			0
$4$	−0.170031	−	0.0981673i	−0.0850154	−	0.0490837i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.530190	−	1.97869i	0.200393	−	0.747876i	−0.790412	−	0.612576i	$-0.790133\pi$
$7$	0.530190	−	1.97869i	0.200393	−	0.747876i	0.990805	−	0.135300i	$-0.0432000\pi$
$8$	−2.08575	−	2.08575i	−0.737423	−	0.737423i
$9$		0			0
$10$		0			0
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	−0.380660	−	0.924715i	$-0.624303\pi$
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	0.610497	+	0.792019i	$0.290970\pi$
$12$		0			0
$13$	−1.43820	−	5.36743i	−0.398885	−	1.48866i	−0.815062	−	0.579374i	$-0.803297\pi$
$13$	−1.43820	−	5.36743i	−0.398885	−	1.48866i	0.416177	−	0.909283i	$-0.363370\pi$
$14$	1.37557	−	2.38256i	0.367637	−	0.636766i
$15$		0			0
$16$	−1.78439	−	3.09066i	−0.446098	−	0.772664i
$17$	1.13610	−	1.13610i	0.275544	−	0.275544i	−0.555783	−	0.831327i	$-0.687582\pi$
$17$	1.13610	−	1.13610i	0.275544	−	0.275544i	0.831327	+	0.555783i	$0.187582\pi$
$18$		0			0
$19$			1.52456i			0.349758i	0.984590	+	0.174879i	$0.0559535\pi$
$19$			1.52456i			0.349758i	−0.984590	+	0.174879i	$0.944047\pi$
$20$		0			0
$21$		0			0
$22$	1.14184	−	0.305956i	0.243442	−	0.0652300i
$23$	1.53331	−	0.410850i	0.319718	−	0.0856682i	−0.0953909	−	0.995440i	$-0.530410\pi$
$23$	1.53331	−	0.410850i	0.319718	−	0.0856682i	0.415109	+	0.909772i	$0.363743\pi$
$24$		0			0
$25$		0			0
$26$		−	7.46278i		−	1.46357i
$27$		0			0
$28$	−0.284392	+	0.284392i	−0.0537450	+	0.0537450i
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	0.930459	−	0.366396i	$-0.119408\pi$
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	−0.782537	+	0.622603i	$0.786075\pi$
$30$		0			0
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	−0.360249	−	0.932856i	$-0.617308\pi$
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	0.988002	−	0.154443i	$-0.0493583\pi$
$32$	0.286379	+	1.06878i	0.0506251	+	0.188936i
$33$		0			0
$34$	1.86870	−	1.07889i	0.320479	−	0.185029i
$35$		0			0
$36$		0			0
$37$	4.25746	+	4.25746i	0.699922	+	0.699922i	0.964393	−	0.264472i	$-0.0851975\pi$
$37$	4.25746	+	4.25746i	0.699922	+	0.699922i	−0.264472	+	0.964393i	$0.585198\pi$
$38$	−0.529931	+	1.97773i	−0.0859661	+	0.320830i
$39$		0			0
$40$		0			0
$41$	−3.11546	−	1.79871i	−0.486552	−	0.280911i	0.236591	−	0.971609i	$-0.423970\pi$
$41$	−3.11546	−	1.79871i	−0.486552	−	0.280911i	−0.723143	+	0.690698i	$0.757303\pi$
$42$		0			0
$43$	1.85841	+	0.497959i	0.283404	+	0.0759380i	0.397721	−	0.917506i	$-0.369801\pi$
$43$	1.85841	+	0.497959i	0.283404	+	0.0759380i	−0.114317	+	0.993444i	$0.536468\pi$
$44$	−0.172815			−0.0260528
$45$		0			0
$46$	2.13189			0.314330
$47$	−7.99942	−	2.14344i	−1.16683	−	0.312652i	−0.377142	−	0.926155i	$-0.623093\pi$
$47$	−7.99942	−	2.14344i	−1.16683	−	0.312652i	−0.789693	+	0.613503i	$0.789760\pi$
$48$		0			0
$49$	2.42805	+	1.40183i	0.346864	+	0.200262i
$50$		0			0
$51$		0			0
$52$	−0.282368	+	1.05381i	−0.0391574	+	0.146137i
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	0.310893	−	0.950445i	$-0.399372\pi$
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	−0.950445	+	0.310893i	$0.899372\pi$
$54$		0			0
$55$		0			0
$56$	−5.23290	+	3.02121i	−0.699275	+	0.403727i
$57$		0			0
$58$	0.553777	+	2.06672i	0.0727145	+	0.271374i
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	−0.502959	−	0.864310i	$-0.667755\pi$
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	0.999994	+	0.00342048i	$0.00108877\pi$
$60$		0			0
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	−0.0308900	+	0.999523i	$0.509834\pi$
$62$	6.63838	−	6.63838i	0.843075	−	0.843075i
$63$		0			0
$64$			8.62358i			1.07795i
$65$		0			0
$66$		0			0
$67$	−3.20857	+	0.859733i	−0.391989	+	0.105033i	−0.449429	−	0.893316i	$-0.648373\pi$
$67$	−3.20857	+	0.859733i	−0.391989	+	0.105033i	0.0574406	+	0.998349i	$0.481706\pi$
$68$	−0.304699	+	0.0816439i	−0.0369502	+	0.00990078i
$69$		0			0
$70$		0			0
$71$			5.89798i			0.699961i	0.936757	+	0.349980i	$0.113812\pi$
$71$			5.89798i			0.699961i	−0.936757	+	0.349980i	$0.886188\pi$
$72$		0			0
$73$	−1.58900	+	1.58900i	−0.185979	+	0.185979i	−0.793955	−	0.607976i	$-0.791982\pi$
$73$	−1.58900	+	1.58900i	−0.185979	+	0.185979i	0.607976	+	0.793955i	$0.291982\pi$
$74$	4.04309	+	7.00284i	0.470000	+	0.814063i
$75$		0			0
$76$	0.149662	−	0.259222i	0.0171674	−	0.0297348i
$77$	−0.466676	−	1.74166i	−0.0531827	−	0.198480i
$78$		0			0
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	−0.0736905	−	0.997281i	$-0.523478\pi$
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	0.826826	+	0.562458i	$0.190144\pi$
$80$		0			0
$81$		0			0
$82$	−3.41628	−	3.41628i	−0.377265	−	0.377265i
$83$	−2.57170	+	9.59770i	−0.282280	+	1.05348i	0.668523	+	0.743691i	$0.266927\pi$
$83$	−2.57170	+	9.59770i	−0.282280	+	1.05348i	−0.950804	+	0.309794i	$0.899740\pi$
$84$		0			0
$85$		0			0
$86$	2.23772	+	1.29195i	0.241299	+	0.139314i
$87$		0			0
$88$	−2.50787	−	0.671981i	−0.267340	−	0.0716334i
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$		0			0
$91$	−11.3830			−1.19327
$92$	−0.301043	−	0.0806641i	−0.0313859	−	0.00840982i
$93$		0			0
$94$	−9.63215	−	5.56112i	−0.993480	−	0.573586i
$95$		0			0
$96$		0			0
$97$	1.02621	−	3.82988i	0.104196	−	0.388865i	−0.894057	−	0.447954i	$-0.852153\pi$
$97$	1.02621	−	3.82988i	0.104196	−	0.388865i	0.998253	+	0.0590888i	$0.0188195\pi$
$98$	2.66250	+	2.66250i	0.268953	+	0.268953i
$99$		0			0
$100$		0			0
$101$	2.23195	−	1.28862i	0.222087	−	0.128222i	−0.384829	−	0.922988i	$-0.625740\pi$
$101$	2.23195	−	1.28862i	0.222087	−	0.128222i	0.606916	+	0.794766i	$0.292406\pi$
$102$		0			0
$103$	3.38106	+	12.6183i	0.333146	+	1.24332i	0.905865	+	0.423566i	$0.139222\pi$
$103$	3.38106	+	12.6183i	0.333146	+	1.24332i	−0.572719	+	0.819752i	$0.694111\pi$
$104$	−8.19538	+	14.1948i	−0.803623	+	1.39192i
$105$		0			0
$106$	−4.42157	−	7.65839i	−0.429461	−	0.743848i
$107$	−9.23034	+	9.23034i	−0.892331	+	0.892331i	−0.994742	−	0.102411i	$-0.967344\pi$
$107$	−9.23034	+	9.23034i	−0.892331	+	0.892331i	0.102411	+	0.994742i	$0.467344\pi$
$108$		0			0
$109$		−	8.05480i		−	0.771510i	−0.922601	−	0.385755i	$-0.873941\pi$
$109$		−	8.05480i		−	0.771510i	0.922601	−	0.385755i	$-0.126059\pi$
$110$		0			0
$111$		0			0
$112$	−7.06153	+	1.89213i	−0.667252	+	0.178790i
$113$	11.5941	−	3.10662i	1.09068	−	0.292246i	0.331714	−	0.943380i	$-0.392373\pi$
$113$	11.5941	−	3.10662i	1.09068	−	0.292246i	0.758963	+	0.651134i	$0.225706\pi$
$114$		0			0
$115$		0			0
$116$		−	0.312794i		−	0.0290422i
$117$		0			0
$118$	7.25113	−	7.25113i	0.667521	−	0.667521i
$119$	−1.64564	−	2.85034i	−0.150856	−	0.261290i
$120$		0			0
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$	4.61608	+	17.2274i	0.417920	+	1.55970i
$123$		0			0
$124$	−1.18858	+	0.686224i	−0.106737	+	0.0616248i
$125$		0			0
$126$		0			0
$127$	−1.90230	−	1.90230i	−0.168802	−	0.168802i	0.617651	−	0.786452i	$-0.288085\pi$
$127$	−1.90230	−	1.90230i	−0.168802	−	0.168802i	−0.786452	+	0.617651i	$0.788085\pi$
$128$	−2.42476	+	9.04933i	−0.214321	+	0.799855i
$129$		0			0
$130$		0			0
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.987613	+	0.156912i	$0.0501541\pi$
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.629696	+	0.776841i	$0.283179\pi$
$132$		0			0
$133$	3.01664	+	0.808307i	0.261576	+	0.0700891i
$134$	−4.46113			−0.385383
$135$		0			0
$136$	−4.73922			−0.406385
$137$	6.62594	+	1.77541i	0.566092	+	0.151684i	0.530504	−	0.847683i	$-0.322003\pi$
$137$	6.62594	+	1.77541i	0.566092	+	0.151684i	0.0355883	+	0.999367i	$0.488669\pi$
$138$		0			0
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	0.552018	−	0.833832i	$-0.313858\pi$
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	−0.446111	+	0.894978i	$0.647191\pi$
$140$		0			0
$141$		0			0
$142$	−2.05011	+	7.65111i	−0.172041	+	0.642067i
$143$	−3.45853	−	3.45853i	−0.289217	−	0.289217i
$144$		0			0
$145$		0			0
$146$	−2.61366	+	1.50900i	−0.216308	+	0.124885i
$147$		0			0
$148$	−0.305956	−	1.14184i	−0.0251494	−	0.0938589i
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	−0.296674	−	0.954979i	$-0.595878\pi$
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	0.975373	−	0.220562i	$-0.0707891\pi$
$150$		0			0
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	0.866141	−	0.499800i	$-0.166593\pi$
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	−0.865910	+	0.500200i	$0.833260\pi$
$152$	3.17985	−	3.17985i	0.257920	−	0.257920i
$153$		0			0
$154$		−	2.42157i		−	0.195136i
$155$		0			0
$156$		0			0
$157$	8.17112	−	2.18944i	0.652126	−	0.174737i	0.0824362	−	0.996596i	$-0.473730\pi$
$157$	8.17112	−	2.18944i	0.652126	−	0.174737i	0.569690	+	0.821860i	$0.307063\pi$
$158$	10.0272	−	2.68677i	0.797717	−	0.213748i
$159$		0			0
$160$		0			0
$161$		−	3.25179i		−	0.256277i
$162$		0			0
$163$	−4.19302	+	4.19302i	−0.328422	+	0.328422i	−0.851986	−	0.523564i	$-0.824602\pi$
$163$	−4.19302	+	4.19302i	−0.328422	+	0.328422i	0.523564	+	0.851986i	$0.324602\pi$
$164$	0.353149	+	0.611672i	0.0275763	+	0.0477635i
$165$		0			0
$166$	−6.67224	+	11.5567i	−0.517866	+	0.896970i
$167$	−1.54428	−	5.76334i	−0.119500	−	0.445980i	0.880084	−	0.474818i	$-0.157486\pi$
$167$	−1.54428	−	5.76334i	−0.119500	−	0.445980i	−0.999584	+	0.0288375i	$0.990819\pi$
$168$		0			0
$169$	−15.4826	+	8.93886i	−1.19097	+	0.687605i
$170$		0			0
$171$		0			0
$172$	−0.267103	−	0.267103i	−0.0203664	−	0.0203664i
$173$	3.53677	−	13.1994i	0.268896	−	1.00353i	−0.690927	−	0.722925i	$-0.742797\pi$
$173$	3.53677	−	13.1994i	0.268896	−	1.00353i	0.959822	−	0.280608i	$-0.0905361\pi$
$174$		0			0
$175$		0			0
$176$	−2.72042	−	1.57063i	−0.205059	−	0.118391i
$177$		0			0
$178$	−6.00319	−	1.60855i	−0.449958	−	0.120566i
$179$	−17.2370			−1.28836			−0.644178	−	0.764875i	$-0.722801\pi$
$179$	−17.2370			−1.28836			−0.644178	+	0.764875i	$0.722801\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	−14.7666	−	3.95669i	−1.09457	−	0.293289i
$183$		0			0
$184$	−4.05503	−	2.34117i	−0.298941	−	0.172594i
$185$		0			0
$186$		0			0
$187$	0.366025	−	1.36603i	0.0267664	−	0.0998937i
$188$	1.14973	+	1.14973i	0.0838528	+	0.0838528i
$189$		0			0
$190$		0			0
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	−0.656073	−	0.754697i	$-0.727784\pi$
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	0.325550	+	0.945525i	$0.394450\pi$
$192$		0			0
$193$	−2.40873	−	8.98952i	−0.173384	−	0.647080i	−0.996821	−	0.0796715i	$-0.974613\pi$
$193$	−2.40873	−	8.98952i	−0.173384	−	0.647080i	0.823437	−	0.567408i	$-0.192054\pi$
$194$	2.66250	−	4.61158i	0.191156	−	0.331092i
$195$		0			0
$196$	−0.275228	−	0.476709i	−0.0196592	−	0.0340507i
$197$	9.49539	−	9.49539i	0.676519	−	0.676519i	−0.282692	−	0.959211i	$-0.591227\pi$
$197$	9.49539	−	9.49539i	0.676519	−	0.676519i	0.959211	+	0.282692i	$0.0912274\pi$
$198$		0			0
$199$		−	17.6342i		−	1.25005i	−0.780604	−	0.625026i	$-0.785088\pi$
$199$		−	17.6342i		−	1.25005i	0.780604	−	0.625026i	$-0.214912\pi$
$200$		0			0
$201$		0			0
$202$	3.34330	−	0.895835i	0.235234	−	0.0630307i
$203$	3.15239	−	0.844680i	0.221254	−	0.0592849i
$204$		0			0
$205$		0			0
$206$			17.5443i			1.22237i
$207$		0			0
$208$	−14.0226	+	14.0226i	−0.972291	+	0.972291i
$209$	0.670964	+	1.16214i	0.0464116	+	0.0803872i
$210$		0			0
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	−0.863897	−	0.503668i	$-0.831983\pi$
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	0.868138	+	0.496323i	$0.165317\pi$
$212$	0.334597	+	1.24873i	0.0229802	+	0.0857633i
$213$		0			0
$214$	−15.1824	+	8.76558i	−1.03785	+	0.599203i
$215$		0			0
$216$		0			0
$217$	−10.1256	−	10.1256i	−0.687368	−	0.687368i
$218$	2.79981	−	10.4490i	0.189627	−	0.707698i
$219$		0			0
$220$		0			0
$221$	−7.73186	−	4.46399i	−0.520101	−	0.300281i
$222$		0			0
$223$	2.41842	+	0.648014i	0.161949	+	0.0433942i	0.338883	−	0.940829i	$-0.389951\pi$
$223$	2.41842	+	0.648014i	0.161949	+	0.0433942i	−0.176933	+	0.984223i	$0.556618\pi$
$224$	2.26663			0.151445
$225$		0			0
$226$	16.1202			1.07230
$227$	14.7293	+	3.94671i	0.977619	+	0.261952i	0.712042	−	0.702137i	$-0.247771\pi$
$227$	14.7293	+	3.94671i	0.977619	+	0.261952i	0.265577	+	0.964090i	$0.414437\pi$
$228$		0			0
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.973599	−	0.228265i	$-0.0733054\pi$
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.289116	+	0.957294i	$0.406639\pi$
$230$		0			0
$231$		0			0
$232$	1.21628	−	4.53922i	0.0798527	−	0.298014i
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	0.831740	−	0.555165i	$-0.187345\pi$
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	−0.555165	+	0.831740i	$0.687345\pi$
$234$		0			0
$235$		0			0
$236$	−1.29829	+	0.749566i	−0.0845112	+	0.0487926i
$237$		0			0
$238$	−1.14404	−	4.26960i	−0.0741569	−	0.276757i
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	−0.997639	−	0.0686835i	$-0.978120\pi$
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	0.558301	+	0.829639i	$0.311453\pi$
$240$		0			0
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	0.771415	−	0.636333i	$-0.219549\pi$
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	−0.936788	+	0.349898i	$0.886216\pi$
$242$	−9.71038	+	9.71038i	−0.624207	+	0.624207i
$243$		0			0
$244$		−	2.60733i		−	0.166917i
$245$		0			0
$246$		0			0
$247$	8.18298	−	2.19262i	0.520670	−	0.139513i
$248$	−19.9168	+	5.33669i	−1.26472	+	0.338880i
$249$		0			0
$250$		0			0
$251$		−	2.60221i		−	0.164250i	−0.996622	−	0.0821251i	$-0.973829\pi$
$251$		−	2.60221i		−	0.164250i	0.996622	−	0.0821251i	$-0.0261707\pi$
$252$		0			0
$253$	0.987999	−	0.987999i	0.0621150	−	0.0621150i
$254$	−1.80652	−	3.12898i	−0.113351	−	0.196329i
$255$		0			0
$256$	2.33257	−	4.04013i	0.145786	−	0.252508i
$257$	−2.73197	−	10.1958i	−0.170415	−	0.635999i	−0.997287	−	0.0736085i	$-0.976548\pi$
$257$	−2.73197	−	10.1958i	−0.170415	−	0.635999i	0.826872	−	0.562390i	$-0.190118\pi$
$258$		0			0
$259$	10.6815	−	6.16695i	0.663714	−	0.383196i
$260$		0			0
$261$		0			0
$262$	20.2984	+	20.2984i	1.25404	+	1.25404i
$263$	−2.17720	+	8.12541i	−0.134252	+	0.501034i	0.865748	+	0.500480i	$0.166843\pi$
$263$	−2.17720	+	8.12541i	−0.134252	+	0.501034i	−1.00000		0.000554412i	$0.999824\pi$
$264$		0			0
$265$		0			0
$266$	3.63236	+	2.09714i	0.222714	+	0.128584i
$267$		0			0
$268$	0.629953	+	0.168795i	0.0384805	+	0.0103108i
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$		0			0
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	−5.53853	−	1.48405i	−0.335823	−	0.0899834i
$273$		0			0
$274$	7.97833	+	4.60629i	0.481989	+	0.278276i
$275$		0			0
$276$		0			0
$277$	−7.05259	+	26.3206i	−0.423749	+	1.58145i	0.342891	+	0.939375i	$0.388594\pi$
$277$	−7.05259	+	26.3206i	−0.423749	+	1.58145i	−0.766640	+	0.642078i	$0.778073\pi$
$278$	1.36920	+	1.36920i	0.0821189	+	0.0821189i
$279$		0			0
$280$		0			0
$281$	22.7050	−	13.1087i	1.35447	−	0.782002i	0.365595	−	0.930774i	$-0.380865\pi$
$281$	22.7050	−	13.1087i	1.35447	−	0.782002i	0.988872	+	0.148772i	$0.0475320\pi$
$282$		0			0
$283$	0.921880	+	3.44050i	0.0548001	+	0.204517i	0.987898	−	0.155106i	$-0.0495720\pi$
$283$	0.921880	+	3.44050i	0.0548001	+	0.204517i	−0.933098	+	0.359623i	$0.882905\pi$
$284$	0.578988	−	1.00284i	0.0343566	−	0.0595074i
$285$		0			0
$286$	−3.28439	−	5.68873i	−0.194210	−	0.336382i
$287$	−5.21088	+	5.21088i	−0.307589	+	0.307589i
$288$		0			0
$289$			14.4186i			0.848151i
$290$		0			0
$291$		0			0
$292$	0.426168	−	0.114191i	0.0249396	−	0.00668254i
$293$	2.87816	−	0.771199i	0.168144	−	0.0450539i	−0.173765	−	0.984787i	$-0.555593\pi$
$293$	2.87816	−	0.771199i	0.168144	−	0.0450539i	0.341909	+	0.939733i	$0.388927\pi$
$294$		0			0
$295$		0			0
$296$		−	17.7600i		−	1.03228i
$297$		0			0
$298$	15.7349	−	15.7349i	0.911496	−	0.911496i
$299$	−4.41042	−	7.63907i	−0.255061	−	0.441779i
$300$		0			0
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$	0.00197247	+	0.00736135i	0.000113503	+	0.000423598i
$303$		0			0
$304$	4.71190	−	2.72042i	0.270246	−	0.156027i
$305$		0			0
$306$		0			0
$307$	−21.8017	−	21.8017i	−1.24429	−	1.24429i	−0.958205	−	0.286081i	$-0.907647\pi$
$307$	−21.8017	−	21.8017i	−1.24429	−	1.24429i	−0.286081	−	0.958205i	$-0.592353\pi$
$308$	−0.0916247	+	0.341948i	−0.00522080	+	0.0194843i
$309$		0			0
$310$		0			0
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.969539	−	0.244939i	$-0.921232\pi$
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.696892	−	0.717176i	$-0.745435\pi$
$312$		0			0
$313$	22.4027	+	6.00279i	1.26628	+	0.339298i	0.828603	−	0.559836i	$-0.189136\pi$
$313$	22.4027	+	6.00279i	1.26628	+	0.339298i	0.437673	+	0.899134i	$0.355803\pi$
$314$	11.3610			0.641137
$315$		0			0
$316$	−1.51758			−0.0853708
$317$	−3.86401	−	1.03536i	−0.217024	−	0.0581515i	0.148669	−	0.988887i	$-0.452501\pi$
$317$	−3.86401	−	1.03536i	−0.217024	−	0.0581515i	−0.365693	+	0.930736i	$0.619168\pi$
$318$		0			0
$319$	1.21444	+	0.701157i	0.0679956	+	0.0392573i
$320$		0			0
$321$		0			0
$322$	1.13031	−	4.21836i	0.0629896	−	0.235080i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$		0			0
$325$		0			0
$326$	−6.89684	+	3.98189i	−0.381981	+	0.220537i
$327$		0			0
$328$	2.74640	+	10.2497i	0.151645	+	0.565945i
$329$	−8.48242	+	14.6920i	−0.467651	+	0.809995i
$330$		0			0
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	0.772369	−	0.635174i	$-0.219071\pi$
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	−0.936261	+	0.351305i	$0.885738\pi$
$332$	1.37945	−	1.37945i	0.0757071	−	0.0757071i
$333$		0			0
$334$		−	8.01324i		−	0.438465i
$335$		0			0
$336$		0			0
$337$	−9.56887	+	2.56397i	−0.521250	+	0.139668i	−0.509845	−	0.860267i	$-0.670297\pi$
$337$	−9.56887	+	2.56397i	−0.521250	+	0.139668i	−0.0114051	+	0.999935i	$0.503630\pi$
$338$	−23.1918	+	6.21422i	−1.26147	+	0.338009i
$339$		0			0
$340$		0			0
$341$		−	6.15295i		−	0.333201i
$342$		0			0
$343$	14.2007	−	14.2007i	0.766764	−	0.766764i
$344$	−2.83755	−	4.91478i	−0.152990	−	0.264987i
$345$		0			0
$346$	9.17611	−	15.8935i	0.493311	−	0.854440i
$347$	−2.74569	−	10.2471i	−0.147396	−	0.550091i	−0.999637	−	0.0269407i	$-0.991423\pi$
$347$	−2.74569	−	10.2471i	−0.147396	−	0.550091i	0.852241	−	0.523150i	$-0.175243\pi$
$348$		0			0
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	−0.267648	−	0.963517i	$-0.586247\pi$
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	0.700606	+	0.713549i	$0.252913\pi$
$350$		0			0
$351$		0			0
$352$	0.688675	+	0.688675i	0.0367065	+	0.0367065i
$353$	−4.96965	+	18.5470i	−0.264508	+	0.987156i	0.698043	+	0.716055i	$0.254054\pi$
$353$	−4.96965	+	18.5470i	−0.264508	+	0.987156i	−0.962551	+	0.271100i	$0.912612\pi$
$354$		0			0
$355$		0			0
$356$	0.786842	+	0.454284i	0.0417026	+	0.0240770i
$357$		0			0
$358$	−22.3606	−	5.99152i	−1.18180	−	0.316662i
$359$	12.5944			0.664705			0.332352	−	0.943155i	$-0.392158\pi$
$359$	12.5944			0.664705			0.332352	+	0.943155i	$0.392158\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$	19.1613	+	5.13426i	1.00710	+	0.269851i
$363$		0			0
$364$	1.93546	+	1.11744i	0.101446	+	0.0585698i
$365$		0			0
$366$		0			0
$367$	7.32206	−	27.3263i	0.382209	−	1.42642i	−0.460312	−	0.887757i	$-0.652262\pi$
$367$	7.32206	−	27.3263i	0.382209	−	1.42642i	0.842520	−	0.538665i	$-0.181071\pi$
$368$	−4.00583	−	4.00583i	−0.208818	−	0.208818i
$369$		0			0
$370$		0			0
$371$	−11.6814	+	6.74425i	−0.606467	+	0.350144i
$372$		0			0
$373$	−0.604851	−	2.25734i	−0.0313180	−	0.116880i	0.948497	−	0.316785i	$-0.102603\pi$
$373$	−0.604851	−	2.25734i	−0.0313180	−	0.116880i	−0.979815	+	0.199905i	$0.935937\pi$
$374$	0.949649	−	1.64484i	0.0491052	−	0.0850526i
$375$		0			0
$376$	12.2141	+	21.1554i	0.629894	+	1.09101i
$377$	6.25992	−	6.25992i	0.322402	−	0.322402i
$378$		0			0
$379$			18.4618i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$379$			18.4618i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$380$		0			0
$381$		0			0
$382$	−6.84241	+	1.83342i	−0.350088	+	0.0938059i
$383$	−23.3806	+	6.26481i	−1.19469	+	0.320117i	−0.800739	−	0.599014i	$-0.795559\pi$
$383$	−23.3806	+	6.26481i	−1.19469	+	0.320117i	−0.393953	+	0.919131i	$0.628893\pi$
$384$		0			0
$385$		0			0
$386$		−	12.4989i		−	0.636176i
$387$		0			0
$388$	−0.550457	+	0.550457i	−0.0279452	+	0.0279452i
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	0.972890	+	0.231268i	$0.0742876\pi$
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	−0.286161	+	0.958182i	$0.592379\pi$
$390$		0			0
$391$	1.27523	−	2.20876i	0.0644911	−	0.111702i
$392$	−2.14042	−	7.98815i	−0.108108	−	0.403463i
$393$		0			0
$394$	15.6184	−	9.01729i	0.786844	−	0.454284i
$395$		0			0
$396$		0			0
$397$	18.2252	+	18.2252i	0.914698	+	0.914698i	0.996637	−	0.0819389i	$-0.0261112\pi$
$397$	18.2252	+	18.2252i	0.914698	+	0.914698i	−0.0819389	+	0.996637i	$0.526111\pi$
$398$	6.12955	−	22.8758i	0.307247	−	1.14666i
$399$		0			0
$400$		0			0
$401$	11.1294	+	6.42558i	0.555777	+	0.320878i	0.751449	−	0.659791i	$-0.229355\pi$
$401$	11.1294	+	6.42558i	0.555777	+	0.320878i	−0.195672	+	0.980669i	$0.562689\pi$
$402$		0			0
$403$	−37.5202	−	10.0535i	−1.86902	−	0.500801i
$404$	−0.506000			−0.0251745
$405$		0			0
$406$	4.38302			0.217526
$407$	5.11910	+	1.37166i	0.253744	+	0.0679906i
$408$		0			0
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.163737	−	0.986504i	$-0.552355\pi$
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.936206	+	0.351451i	$0.885688\pi$
$410$		0			0
$411$		0			0
$412$	0.663820	−	2.47741i	0.0327041	−	0.122053i
$413$	−11.0602	−	11.0602i	−0.544237	−	0.544237i
$414$		0			0
$415$		0			0
$416$	5.32474	−	3.07424i	0.261067	−	0.150727i
$417$		0			0
$418$	0.466448	+	1.74081i	0.0228147	+	0.0851457i
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	−0.676453	−	0.736486i	$-0.736484\pi$
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	0.976042	+	0.217583i	$0.0698172\pi$
$420$		0			0
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	0.633870	−	0.773439i	$-0.281465\pi$
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	−0.986753	+	0.162228i	$0.948132\pi$
$422$	0.117006	−	0.117006i	0.00569577	−	0.00569577i
$423$		0			0
$424$			19.4225i			0.943240i
$425$		0			0
$426$		0			0
$427$	26.2771	−	7.04094i	1.27164	−	0.340735i
$428$	2.47556	−	0.663324i	0.119661	−	0.0320630i
$429$		0			0
$430$		0			0
$431$			35.9660i			1.73242i	0.499678	+	0.866211i	$0.333452\pi$
$431$			35.9660i			1.73242i	−0.499678	+	0.866211i	$0.666548\pi$
$432$		0			0
$433$	0.331545	−	0.331545i	0.0159331	−	0.0159331i	−0.699095	−	0.715028i	$-0.746414\pi$
$433$	0.331545	−	0.331545i	0.0159331	−	0.0159331i	0.715028	+	0.699095i	$0.246414\pi$
$434$	−9.61573	−	16.6549i	−0.461570	−	0.799462i
$435$		0			0
$436$	−0.790718	+	1.36956i	−0.0378685	+	0.0655902i
$437$	0.626366	+	2.33763i	0.0299632	+	0.111824i
$438$		0			0
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	0.530457	+	0.847712i	$0.322020\pi$
$440$		0			0
$441$		0			0
$442$	−8.47845	−	8.47845i	−0.403279	−	0.403279i
$443$	8.29218	−	30.9468i	0.393973	−	1.47033i	−0.429548	−	0.903044i	$-0.641327\pi$
$443$	8.29218	−	30.9468i	0.393973	−	1.47033i	0.823522	−	0.567285i	$-0.192006\pi$
$444$		0			0
$445$		0			0
$446$	2.91203	+	1.68126i	0.137889	+	0.0796101i
$447$		0			0
$448$	17.0634	+	4.57213i	0.806172	+	0.216013i
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$		0			0
$451$	−3.16647			−0.149103
$452$	−2.27631	−	0.609937i	−0.107069	−	0.0286890i
$453$		0			0
$454$	17.7357	+	10.2397i	0.832376	+	0.480572i
$455$		0			0
$456$		0			0
$457$	0.235886	−	0.880339i	0.0110343	−	0.0411805i	−0.960189	−	0.279351i	$-0.909881\pi$
$457$	0.235886	−	0.880339i	0.0110343	−	0.0411805i	0.971223	+	0.238170i	$0.0765475\pi$
$458$	20.9534	+	20.9534i	0.979090	+	0.979090i
$459$		0			0
$460$		0			0
$461$	18.7320	−	10.8149i	0.872434	−	0.503700i	0.00427761	−	0.999991i	$-0.498638\pi$
$461$	18.7320	−	10.8149i	0.872434	−	0.503700i	0.868156	+	0.496291i	$0.165305\pi$
$462$		0			0
$463$	−4.85644	−	18.1245i	−0.225698	−	0.842316i	−0.982124	−	0.188236i	$-0.939723\pi$
$463$	−4.85644	−	18.1245i	−0.225698	−	0.842316i	0.756426	−	0.654079i	$-0.226944\pi$
$464$	2.84283	−	4.92393i	0.131975	−	0.228588i
$465$		0			0
$466$	4.00916	+	6.94407i	0.185721	+	0.321678i
$467$	−16.8295	+	16.8295i	−0.778777	+	0.778777i	−0.979623	−	0.200846i	$-0.935631\pi$
$467$	−16.8295	+	16.8295i	−0.778777	+	0.778777i	0.200846	+	0.979623i	$0.435631\pi$
$468$		0			0
$469$			6.80460i			0.314207i
$470$		0			0
$471$		0			0
$472$	−21.7552	+	5.82929i	−1.00136	+	0.268315i
$473$	1.63578	−	0.438306i	0.0752133	−	0.0201533i
$474$		0			0
$475$		0			0
$476$			0.646194i			0.0296182i
$477$		0			0
$478$	−12.9000	+	12.9000i	−0.590033	+	0.590033i
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	0.587163	−	0.809469i	$-0.300245\pi$
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	−0.994602	+	0.103764i	$0.966911\pi$
$480$		0			0
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$	−1.78475	−	6.66078i	−0.0812931	−	0.303390i
$483$		0			0
$484$	1.73861	−	1.00378i	0.0790275	−	0.0456265i
$485$		0			0
$486$		0			0
$487$	21.8232	+	21.8232i	0.988904	+	0.988904i	0.999939	−	0.0110354i	$-0.00351274\pi$
$487$	21.8232	+	21.8232i	0.988904	+	0.988904i	−0.0110354	+	0.999939i	$0.503513\pi$
$488$	10.1385	−	37.8372i	0.458946	−	1.71281i
$489$		0			0
$490$		0			0
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.993787	−	0.111295i	$-0.964500\pi$
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.593278	−	0.804998i	$-0.702166\pi$
$492$		0			0
$493$	2.47249	+	0.662503i	0.111356	+	0.0298376i
$494$	11.3775			0.511896
$495$		0			0
$496$	−24.9471			−1.12016
$497$	11.6703	+	3.12705i	0.523484	+	0.140267i
$498$		0			0
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.966768	−	0.255655i	$-0.917709\pi$
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.704788	−	0.709418i	$-0.748958\pi$
$500$		0			0
$501$		0			0
$502$	0.904518	−	3.37571i	0.0403706	−	0.150665i
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.954537	+	0.298093i	$0.0963506\pi$
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.298093	+	0.954537i	$0.403649\pi$
$504$		0			0
$505$		0			0
$506$	1.62510	−	0.938252i	0.0722445	−	0.0417104i
$507$		0			0
$508$	0.136706	+	0.510193i	0.00606534	+	0.0226361i
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	−0.654404	−	0.756145i	$-0.727080\pi$
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	0.982043	+	0.188658i	$0.0604136\pi$
$510$		0			0
$511$	2.30168	+	3.98663i	0.101820	+	0.176358i
$512$	17.6794	−	17.6794i	0.781325	−	0.781325i
$513$		0			0
$514$		−	14.1761i		−	0.625282i
$515$		0			0
$516$		0			0
$517$	−7.04114	+	1.88667i	−0.309669	+	0.0829755i
$518$	16.0001	−	4.28721i	0.703003	−	0.188369i
$519$		0			0
$520$		0			0
$521$		−	28.4812i		−	1.24778i	−0.781511	−	0.623892i	$-0.785551\pi$
$521$		−	28.4812i		−	1.24778i	0.781511	−	0.623892i	$-0.214449\pi$
$522$		0			0
$523$	−15.4076	+	15.4076i	−0.673726	+	0.673726i	−0.958573	−	0.284847i	$-0.908057\pi$
$523$	−15.4076	+	15.4076i	−0.673726	+	0.673726i	0.284847	+	0.958573i	$0.408057\pi$
$524$	−2.09829	−	3.63434i	−0.0916641	−	0.158767i
$525$		0			0
$526$	−5.64872	+	9.78386i	−0.246296	+	0.426597i
$527$	−2.90687	−	10.8486i	−0.126625	−	0.472572i
$528$		0			0
$529$	−17.7363	+	10.2401i	−0.771145	+	0.445221i
$530$		0			0
$531$		0			0
$532$	−0.433573	−	0.433573i	−0.0187978	−	0.0187978i
$533$	−5.17380	+	19.3089i	−0.224102	+	0.836361i
$534$		0			0
$535$		0			0
$536$	8.48544	+	4.89907i	0.366515	+	0.211608i
$537$		0			0
$538$	34.7283	+	9.30542i	1.49724	+	0.401185i
$539$	2.46780			0.106296
$540$		0			0
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	−24.1093	−	6.46008i	−1.03558	−	0.277484i
$543$		0			0
$544$	1.53959	+	0.888885i	0.0660096	+	0.0381106i
$545$		0			0
$546$		0			0
$547$	−8.33894	+	31.1213i	−0.356547	+	1.33065i	0.521979	+	0.852958i	$0.325194\pi$
$547$	−8.33894	+	31.1213i	−0.356547	+	1.33065i	−0.878526	+	0.477694i	$0.841473\pi$
$548$	−0.952326	−	0.952326i	−0.0406813	−	0.0406813i
$549$		0			0
$550$		0			0
$551$	−2.10347	+	1.21444i	−0.0896109	+	0.0517369i
$552$		0			0
$553$	−4.09814	−	15.2945i	−0.174271	−	0.650387i
$554$	−18.2979	+	31.6928i	−0.777402	+	1.34650i
$555$		0			0
$556$	−0.141537	−	0.245149i	−0.00600250	−	0.0103966i
$557$	−30.4033	+	30.4033i	−1.28823	+	1.28823i	−0.352366	+	0.935862i	$0.614623\pi$
$557$	−30.4033	+	30.4033i	−1.28823	+	1.28823i	−0.935862	+	0.352366i	$0.885377\pi$
$558$		0			0
$559$		−	10.6910i		−	0.452182i
$560$		0			0
$561$		0			0
$562$	34.0105	−	9.11308i	1.43465	−	0.384412i
$563$	1.12220	−	0.300692i	0.0472950	−	0.0126727i	−0.235094	−	0.971973i	$-0.575540\pi$
$563$	1.12220	−	0.300692i	0.0472950	−	0.0126727i	0.282389	+	0.959300i	$0.408873\pi$
$564$		0			0
$565$		0			0
$566$			4.78361i			0.201070i
$567$		0			0
$568$	12.3017	−	12.3017i	0.516167	−	0.516167i
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	0.862962	−	0.505268i	$-0.168606\pi$
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	−0.869056	+	0.494713i	$0.835273\pi$
$570$		0			0
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	−0.998593	+	0.0530223i	$0.983115\pi$
$572$	0.248542	+	0.927572i	0.0103921	+	0.0387837i
$573$		0			0
$574$	−8.57106	+	4.94851i	−0.357749	+	0.206547i
$575$		0			0
$576$		0			0
$577$	2.52834	+	2.52834i	0.105256	+	0.105256i	0.757774	−	0.652517i	$-0.226287\pi$
$577$	2.52834	+	2.52834i	0.105256	+	0.105256i	−0.652517	+	0.757774i	$0.726287\pi$
$578$	−5.01183	+	18.7044i	−0.208465	+	0.778000i
$579$		0			0
$580$		0			0
$581$	17.6274	+	10.1772i	0.731309	+	0.422222i
$582$		0			0
$583$	−5.59831	−	1.50006i	−0.231858	−	0.0621262i
$584$	6.62852			0.274290
$585$		0			0
$586$	4.00174			0.165310
$587$	40.0121	+	10.7212i	1.65147	+	0.442511i	0.960025	−	0.279914i	$-0.0903059\pi$
$587$	40.0121	+	10.7212i	1.65147	+	0.442511i	0.691449	+	0.722425i	$0.256973\pi$
$588$		0			0
$589$	9.22943	+	5.32861i	0.380292	+	0.219562i
$590$		0			0
$591$		0			0
$592$	5.56137	−	20.7553i	0.228571	−	0.853038i
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.995017	−	0.0997087i	$-0.968209\pi$
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.0997087	−	0.995017i	$-0.531791\pi$
$594$		0			0
$595$		0			0
$596$	−2.81726	+	1.62655i	−0.115400	+	0.0666260i
$597$		0			0
$598$	−3.06608	−	11.4428i	−0.125382	−	0.467930i
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	0.457762	+	0.889075i	$0.348651\pi$
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	−0.998842	+	0.0481037i	$0.984682\pi$
$600$		0			0
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	0.939835	−	0.341628i	$-0.110978\pi$
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	−0.765776	+	0.643107i	$0.777645\pi$
$602$	3.74279	−	3.74279i	0.152545	−	0.152545i
$603$		0			0
$604$		−	0.00111412i		−	4.53329e-5i
$605$		0			0
$606$		0			0
$607$	−44.4113	+	11.9000i	−1.80260	+	0.483005i	−0.994379	−	0.105876i	$-0.966235\pi$
$607$	−44.4113	+	11.9000i	−1.80260	+	0.483005i	−0.808220	+	0.588881i	$0.799569\pi$
$608$	−1.62942	+	0.436602i	−0.0660818	+	0.0177066i
$609$		0			0
$610$		0			0
$611$			46.0190i			1.86173i
$612$		0			0
$613$	−17.3219	+	17.3219i	−0.699625	+	0.699625i	−0.964330	−	0.264705i	$-0.914726\pi$
$613$	−17.3219	+	17.3219i	−0.699625	+	0.699625i	0.264705	+	0.964330i	$0.414726\pi$
$614$	−20.7039	−	35.8602i	−0.835542	−	1.44720i
$615$		0			0
$616$	−2.65929	+	4.60603i	−0.107146	+	0.185582i
$617$	9.74553	+	36.3708i	0.392340	+	1.46423i	0.826263	+	0.563284i	$0.190462\pi$
$617$	9.74553	+	36.3708i	0.392340	+	1.46423i	−0.433923	+	0.900950i	$0.642871\pi$
$618$		0			0
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	−0.662318	−	0.749223i	$-0.730427\pi$
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	0.317687	+	0.948196i	$0.397094\pi$
$620$		0			0
$621$		0			0
$622$	−32.2255	−	32.2255i	−1.29213	−	1.29213i
$623$	−2.45353	+	9.15670i	−0.0982986	+	0.366855i
$624$		0			0
$625$		0			0
$626$	26.9753	+	15.5742i	1.07815	+	0.622469i
$627$		0			0
$628$	−1.60427	−	0.429864i	−0.0640175	−	0.0171534i
$629$	9.67378			0.385719
$630$		0			0
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	−22.0230	−	5.90104i	−0.876027	−	0.234731i
$633$		0			0
$634$	−4.65268	−	2.68622i	−0.184781	−	0.106684i
$635$		0			0
$636$		0			0
$637$	4.03223	−	15.0485i	0.159763	−	0.596242i
$638$	1.33171	+	1.33171i	0.0527227	+	0.0527227i
$639$		0			0
$640$		0			0
$641$	−21.8054	+	12.5894i	−0.861263	+	0.497251i	−0.864435	−	0.502744i	$-0.832324\pi$
$641$	−21.8054	+	12.5894i	−0.861263	+	0.497251i	0.00317173	+	0.999995i	$0.498990\pi$
$642$		0			0
$643$	8.05166	+	30.0492i	0.317526	+	1.18502i	0.921614	+	0.388107i	$0.126871\pi$
$643$	8.05166	+	30.0492i	0.317526	+	1.18502i	−0.604088	+	0.796918i	$0.706462\pi$
$644$	−0.319219	+	0.552904i	−0.0125790	+	0.0217875i
$645$		0			0
$646$	1.64484	+	2.84895i	0.0647154	+	0.112090i
$647$	7.86580	−	7.86580i	0.309237	−	0.309237i	−0.535377	−	0.844613i	$-0.679830\pi$
$647$	7.86580	−	7.86580i	0.309237	−	0.309237i	0.844613	+	0.535377i	$0.179830\pi$
$648$		0			0
$649$		−	6.72090i		−	0.263818i
$650$		0			0
$651$		0			0
$652$	1.12456	−	0.301325i	0.0440411	−	0.0118008i
$653$	0.279676	−	0.0749391i	0.0109446	−	0.00293259i	−0.253343	−	0.967377i	$-0.581530\pi$
$653$	0.279676	−	0.0749391i	0.0109446	−	0.00293259i	0.264287	+	0.964444i	$0.414863\pi$
$654$		0			0
$655$		0			0
$656$			12.8384i			0.501256i
$657$		0			0
$658$	−16.1106	+	16.1106i	−0.628058	+	0.628058i
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	0.999672	+	0.0256228i	$0.00815688\pi$
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	−0.477646	+	0.878552i	$0.658510\pi$
$660$		0			0
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	−0.999955	−	0.00945786i	$-0.996989\pi$
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	0.508168	+	0.861258i	$0.330323\pi$
$662$	−2.07289	−	7.73611i	−0.0805650	−	0.300673i
$663$		0			0
$664$	25.3823	−	14.6545i	0.985024	−	0.568704i
$665$		0			0
$666$		0			0
$667$	1.78827	+	1.78827i	0.0692421	+	0.0692421i
$668$	−0.303196	+	1.13154i	−0.0117310	+	0.0437807i
$669$		0			0
$670$		0			0
$671$	10.1231	+	5.84458i	0.390799	+	0.225628i
$672$		0			0
$673$	23.5227	+	6.30290i	0.906735	+	0.242959i	0.681906	−	0.731439i	$-0.261151\pi$
$673$	23.5227	+	6.30290i	0.906735	+	0.242959i	0.224829	+	0.974398i	$0.427818\pi$
$674$	−13.3044			−0.512466
$675$		0			0
$676$	3.51002			0.135001
$677$	−0.896681	−	0.240265i	−0.0344623	−	0.00923414i	0.241547	−	0.970389i	$-0.422345\pi$
$677$	−0.896681	−	0.240265i	−0.0344623	−	0.00923414i	−0.276009	+	0.961155i	$0.589012\pi$
$678$		0			0
$679$	−7.03407	−	4.06112i	−0.269943	−	0.155852i
$680$		0			0
$681$		0			0
$682$	2.13874	−	7.98188i	0.0818966	−	0.305642i
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	0.990077	−	0.140526i	$-0.0448795\pi$
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	−0.140526	+	0.990077i	$0.544880\pi$
$684$		0			0
$685$		0			0
$686$	23.3578	−	13.4856i	0.891805	−	0.514884i
$687$		0			0
$688$	−1.77711	−	6.63225i	−0.0677515	−	0.252852i
$689$	−18.2945	+	31.6871i	−0.696966	+	1.20718i
$690$		0			0
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	0.778439	−	0.627721i	$-0.216012\pi$
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	−0.932841	+	0.360287i	$0.882679\pi$
$692$	−1.89711	+	1.89711i	−0.0721173	+	0.0721173i
$693$		0			0
$694$		−	14.2473i		−	0.540821i
$695$		0			0
$696$		0			0
$697$	−5.58297	+	1.49595i	−0.211470	+	0.0566633i
$698$	12.1157	−	3.24640i	0.458586	−	0.122878i
$699$		0			0
$700$		0			0
$701$			19.6359i			0.741637i	0.928705	+	0.370819i	$0.120923\pi$
$701$			19.6359i			0.741637i	−0.928705	+	0.370819i	$0.879077\pi$
$702$		0			0
$703$	−6.49076	+	6.49076i	−0.244804	+	0.244804i
$704$	3.79526	+	6.57359i	0.143039	+	0.247752i
$705$		0			0
$706$	−12.8937	+	22.3325i	−0.485260	+	0.840496i
$707$	−1.36642	−	5.09956i	−0.0513896	−	0.191789i
$708$		0			0
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	−0.448756	−	0.893654i	$-0.648133\pi$
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	0.549549	+	0.835461i	$0.314799\pi$
$710$		0			0
$711$		0			0
$712$	9.65210	+	9.65210i	0.361728	+	0.361728i
$713$	2.87199	−	10.7184i	0.107557	−	0.401408i
$714$		0			0
$715$		0			0
$716$	2.93083	+	1.69211i	0.109530	+	0.0632373i
$717$		0			0
$718$	16.3380	+	4.37774i	0.609727	+	0.163376i
$719$	−20.3126			−0.757533			−0.378767	−	0.925492i	$-0.623652\pi$
$719$	−20.3126			−0.757533			−0.378767	+	0.925492i	$0.623652\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$	21.6325	+	5.79640i	0.805077	+	0.215720i
$723$		0			0
$724$	−2.51149	−	1.45001i	−0.0933388	−	0.0538892i
$725$		0			0
$726$		0			0
$727$	−4.57247	+	17.0647i	−0.169584	+	0.632895i	0.827827	+	0.560983i	$0.189577\pi$
$727$	−4.57247	+	17.0647i	−0.169584	+	0.632895i	−0.997411	+	0.0719119i	$0.977090\pi$
$728$	23.7421	+	23.7421i	0.879941	+	0.879941i
$729$		0			0
$730$		0			0
$731$	2.67706	−	1.54560i	0.0990147	−	0.0571662i
$732$		0			0
$733$	6.82693	+	25.4785i	0.252158	+	0.941068i	0.969649	+	0.244500i	$0.0786239\pi$
$733$	6.82693	+	25.4785i	0.252158	+	0.941068i	−0.717491	+	0.696568i	$0.754709\pi$
$734$	18.9970	−	32.9038i	0.701192	−	1.21450i
$735$		0			0
$736$	0.878218	+	1.52112i	0.0323715	+	0.0560692i
$737$	−2.06746	+	2.06746i	−0.0761558	+	0.0761558i
$738$		0			0
$739$			6.41459i			0.235965i	0.993016	+	0.117982i	$0.0376426\pi$
$739$			6.41459i			0.235965i	−0.993016	+	0.117982i	$0.962357\pi$
$740$		0			0
$741$		0			0
$742$	−17.4979	+	4.68854i	−0.642368	+	0.172122i
$743$	−18.4970	+	4.95625i	−0.678588	+	0.181827i	−0.581620	−	0.813460i	$-0.697581\pi$
$743$	−18.4970	+	4.95625i	−0.678588	+	0.181827i	−0.0969677	+	0.995288i	$0.530914\pi$
$744$		0			0
$745$		0			0
$746$		−	3.13856i		−	0.114911i
$747$		0			0
$748$	−0.196335	+	0.196335i	−0.00717870	+	0.00717870i
$749$	13.3702	+	23.1579i	0.488536	+	0.846170i
$750$		0			0
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	−0.899721	−	0.436465i	$-0.856230\pi$
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	0.827850	+	0.560949i	$0.189564\pi$
$752$	7.64946	+	28.5482i	0.278947	+	1.04105i
$753$		0			0
$754$	10.2966	−	5.94472i	0.374979	−	0.216494i
$755$		0			0
$756$		0			0
$757$	−17.3710	−	17.3710i	−0.631361	−	0.631361i	0.317049	−	0.948409i	$-0.397308\pi$
$757$	−17.3710	−	17.3710i	−0.631361	−	0.631361i	−0.948409	+	0.317049i	$0.897308\pi$
$758$	−6.41725	+	23.9495i	−0.233085	+	0.869885i
$759$		0			0
$760$		0			0
$761$	−7.11860	−	4.10993i	−0.258049	−	0.148985i	0.365395	−	0.930853i	$-0.380934\pi$
$761$	−7.11860	−	4.10993i	−0.258049	−	0.148985i	−0.623444	+	0.781868i	$0.714267\pi$
$762$		0			0
$763$	−15.9380	−	4.27057i	−0.576994	−	0.154605i
$764$	1.03558			0.0374660
$765$		0			0
$766$	−32.5079			−1.17456
$767$	−40.9835	−	10.9815i	−1.47983	−	0.396519i
$768$		0			0
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	0.534151	−	0.845389i	$-0.320631\pi$
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	−0.465053	+	0.885283i	$0.653965\pi$
$770$		0			0
$771$		0			0
$772$	−0.472918	+	1.76495i	−0.0170207	+	0.0635221i
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	0.543400	−	0.839474i	$-0.317137\pi$
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	−0.839474	+	0.543400i	$0.817137\pi$
$774$		0			0
$775$		0			0
$776$	−10.1286	+	5.84773i	−0.363595	+	0.209921i
$777$		0			0
$778$	9.41596	+	35.1408i	0.337579	+	1.25986i
$779$	2.74224	−	4.74970i	0.0982511	−	0.170176i
$780$		0			0
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$	2.42204	−	2.42204i	0.0866119	−	0.0866119i
$783$		0			0
$784$		−	10.0057i		−	0.357346i
$785$		0			0
$786$		0			0
$787$	−33.8541	+	9.07119i	−1.20677	+	0.323353i	−0.805494	−	0.592604i	$-0.798100\pi$
$787$	−33.8541	+	9.07119i	−1.20677	+	0.323353i	−0.401276	+	0.915957i	$0.631433\pi$
$788$	−2.54665	+	0.682372i	−0.0907205	+	0.0243085i
$789$		0			0
$790$		0			0
$791$		−	24.5882i		−	0.874256i
$792$		0			0
$793$	52.1803	−	52.1803i	1.85298	−	1.85298i
$794$	17.3076	+	29.9776i	0.614223	+	1.06387i
$795$		0			0
$796$	−1.73110	+	2.99835i	−0.0613571	+	0.106274i
$797$	−6.77343	−	25.2788i	−0.239927	−	0.895421i	−0.975866	−	0.218372i	$-0.929925\pi$
$797$	−6.77343	−	25.2788i	−0.239927	−	0.895421i	0.735938	−	0.677049i	$-0.236741\pi$
$798$		0			0
$799$	−11.5233	+	6.65297i	−0.407664	+	0.235365i
$800$		0			0
$801$		0			0
$802$	12.2041	+	12.2041i	0.430941	+	0.430941i
$803$	−0.511942	+	1.91059i	−0.0180660	+	0.0674233i
$804$		0			0
$805$		0			0
$806$	−45.1784	−	26.0837i	−1.59134	−	0.918761i
$807$		0			0
$808$	−7.34301	−	1.96755i	−0.258326	−	0.0692183i
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$		0			0
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	−0.618923	−	0.165840i	−0.0217199	−	0.00581984i
$813$		0			0
$814$	6.16394	+	3.55875i	0.216046	+	0.124734i
$815$		0			0
$816$		0			0
$817$	−0.759168	+	2.83326i	−0.0265599	+	0.0991231i
$818$	−24.3930	−	24.3930i	−0.852880	−	0.852880i
$819$		0			0
$820$		0			0
$821$	−13.3109	+	7.68503i	−0.464552	+	0.268209i	−0.713956	−	0.700190i	$-0.753099\pi$
$821$	−13.3109	+	7.68503i	−0.464552	+	0.268209i	0.249404	+	0.968399i	$0.419765\pi$
$822$		0			0
$823$	−3.77065	−	14.0723i	−0.131437	−	0.490528i	0.868551	−	0.495601i	$-0.165052\pi$
$823$	−3.77065	−	14.0723i	−0.131437	−	0.490528i	−0.999987	+	0.00507263i	$0.998385\pi$
$824$	19.2665	−	33.3706i	0.671182	−	1.16252i
$825$		0			0
$826$	−10.5033	−	18.1923i	−0.365457	−	0.632989i
$827$	−3.31824	+	3.31824i	−0.115387	+	0.115387i	−0.762443	−	0.647056i	$-0.776000\pi$
$827$	−3.31824	+	3.31824i	−0.115387	+	0.115387i	0.647056	+	0.762443i	$0.276000\pi$
$828$		0			0
$829$			33.9539i			1.17927i	0.807671	+	0.589633i	$0.200728\pi$
$829$			33.9539i			1.17927i	−0.807671	+	0.589633i	$0.799272\pi$
$830$		0			0
$831$		0			0
$832$	46.2865	−	12.4024i	1.60469	−	0.429977i
$833$	4.35112	−	1.16588i	0.150757	−	0.0403953i
$834$		0			0
$835$		0			0
$836$		−	0.263467i		−	0.00911220i
$837$		0			0
$838$	11.6473	−	11.6473i	0.402349	−	0.402349i
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	0.750274	−	0.661127i	$-0.229921\pi$
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	−0.947690	+	0.319193i	$0.896588\pi$
$840$		0			0
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$	−5.03357	−	18.7855i	−0.173468	−	0.647392i
$843$		0			0
$844$	−0.0209495	+	0.0120952i	−0.000721111	+	0.000416334i
$845$		0			0
$846$		0			0
$847$	14.8113	+	14.8113i	0.508923	+	0.508923i
$848$	−6.08198	+	22.6983i	−0.208856	+	0.779462i
$849$		0			0
$850$		0			0
$851$	8.27720	+	4.77884i	0.283739	+	0.163817i
$852$		0			0
$853$	−23.0994	−	6.18947i	−0.790909	−	0.211923i	−0.159320	−	0.987227i	$-0.550930\pi$
$853$	−23.0994	−	6.18947i	−0.790909	−	0.211923i	−0.631589	+	0.775304i	$0.717597\pi$
$854$	36.5353			1.25021
$855$		0			0
$856$	38.5043			1.31605
$857$	−14.4874	−	3.88189i	−0.494881	−	0.132603i	0.00274224	−	0.999996i	$-0.499127\pi$
$857$	−14.4874	−	3.88189i	−0.494881	−	0.132603i	−0.497623	+	0.867393i	$0.665794\pi$
$858$		0			0
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.977366	−	0.211555i	$-0.0678529\pi$
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.305471	+	0.952201i	$0.401186\pi$
$860$		0			0
$861$		0			0
$862$	−12.5016	+	46.6567i	−0.425807	+	1.58913i
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	0.658088	−	0.752941i	$-0.271365\pi$
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	−0.752941	+	0.658088i	$0.771365\pi$
$864$		0			0
$865$		0			0
$866$	0.545339	−	0.314852i	0.0185314	−	0.0106991i
$867$		0			0
$868$	0.727658	+	2.71566i	0.0246983	+	0.0921754i
$869$	3.40181	−	5.89211i	0.115399	−	0.199876i
$870$		0			0
$871$	9.22911	+	15.9853i	0.312717	+	0.541641i
$872$	−16.8003	+	16.8003i	−0.568929	+	0.568929i
$873$		0			0
$874$			3.25020i			0.109940i
$875$		0			0
$876$		0			0
$877$	41.5598	−	11.1359i	1.40338	−	0.376033i	0.523820	−	0.851829i	$-0.324507\pi$
$877$	41.5598	−	11.1359i	1.40338	−	0.376033i	0.879556	+	0.475796i	$0.157840\pi$
$878$	1.93163	−	0.517577i	0.0651892	−	0.0174674i
$879$		0			0
$880$		0			0
$881$		−	47.0487i		−	1.58511i	−0.609801	−	0.792555i	$-0.708751\pi$
$881$		−	47.0487i		−	1.58511i	0.609801	−	0.792555i	$-0.291249\pi$
$882$		0			0
$883$	−21.0669	+	21.0669i	−0.708957	+	0.708957i	−0.966316	−	0.257359i	$-0.917148\pi$
$883$	−21.0669	+	21.0669i	−0.708957	+	0.708957i	0.257359	+	0.966316i	$0.417148\pi$
$884$	0.876436	+	1.51803i	0.0294777	+	0.0510569i
$885$		0			0
$886$	21.5140	−	37.2633i	0.722776	−	1.25188i
$887$	0.939801	+	3.50739i	0.0315554	+	0.117766i	0.979907	−	0.199454i	$-0.0639170\pi$
$887$	0.939801	+	3.50739i	0.0315554	+	0.117766i	−0.948352	+	0.317221i	$0.897250\pi$
$888$		0			0
$889$	−4.77265	+	2.75549i	−0.160069	+	0.0924161i
$890$		0			0
$891$		0			0
$892$	−0.347592	−	0.347592i	−0.0116382	−	0.0116382i
$893$	3.26780	−	12.1956i	0.109353	−	0.408110i
$894$		0			0
$895$		0			0
$896$	16.6203	+	9.59572i	0.555245	+	0.320571i
$897$		0			0
$898$	−28.3167	−	7.58743i	−0.944939	−	0.253196i
$899$	11.1368			0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$	−4.10768	−	1.10065i	−0.136771	−	0.0366477i
$903$		0			0
$904$	−30.6619	−	17.7026i	−1.01980	−	0.588781i
$905$		0			0
$906$		0			0
$907$	2.71600	−	10.1363i	0.0901833	−	0.336569i	−0.906062	−	0.423145i	$-0.860926\pi$
$907$	2.71600	−	10.1363i	0.0901833	−	0.336569i	0.996245	+	0.0865764i	$0.0275927\pi$
$908$	−2.11700	−	2.11700i	−0.0702551	−	0.0702551i
$909$		0			0
$910$		0			0
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	−0.608018	−	0.793923i	$-0.708035\pi$
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	0.383548	+	0.923521i	$0.374702\pi$
$912$		0			0
$913$	2.26362	+	8.44796i	0.0749150	+	0.279587i
$914$	0.612004	−	1.06002i	0.0202433	−	0.0350624i
$915$		0			0
$916$	−2.16600	−	3.75163i	−0.0715668	−	0.123957i
$917$	30.9612	−	30.9612i	1.02243	−	1.02243i
$918$		0			0
$919$		−	4.61000i		−	0.152070i	−0.997105	−	0.0760349i	$-0.975774\pi$
$919$		−	4.61000i		−	0.152070i	0.997105	−	0.0760349i	$-0.0242260\pi$
$920$		0			0
$921$		0			0
$922$	28.0591	−	7.51842i	0.924078	−	0.247606i
$923$	31.6570	−	8.48246i	1.04200	−	0.279204i
$924$		0			0
$925$		0			0
$926$		−	25.1999i		−	0.828122i
$927$		0			0
$928$	−1.24650	+	1.24650i	−0.0409182	+	0.0409182i
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	−0.999842	−	0.0177609i	$-0.994346\pi$
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	0.484540	−	0.874769i	$-0.338987\pi$
$930$		0			0
$931$	−2.13718	+	3.70170i	−0.0700433	+	0.121318i
$932$	−0.303388	−	1.13226i	−0.00993782	−	0.0370884i
$933$		0			0
$934$	−27.6818	+	15.9821i	−0.905778	+	0.522951i
$935$		0			0
$936$		0			0
$937$	21.3617	+	21.3617i	0.697856	+	0.697856i	0.963948	−	0.266092i	$-0.0857324\pi$
$937$	21.3617	+	21.3617i	0.697856	+	0.697856i	−0.266092	+	0.963948i	$0.585732\pi$
$938$	−2.36525	+	8.82722i	−0.0772281	+	0.288219i
$939$		0			0
$940$		0			0
$941$	5.77035	+	3.33151i	0.188108	+	0.108604i	0.591096	−	0.806601i	$-0.298695\pi$
$941$	5.77035	+	3.33151i	0.188108	+	0.108604i	−0.402989	+	0.915205i	$0.632029\pi$
$942$		0			0
$943$	−5.51597	−	1.47800i	−0.179625	−	0.0481303i
$944$	−27.2498			−0.886905
$945$		0			0
$946$	2.27436			0.0739458
$947$	3.23873	+	0.867814i	0.105245	+	0.0282002i	0.311057	−	0.950391i	$-0.399317\pi$
$947$	3.23873	+	0.867814i	0.105245	+	0.0282002i	−0.205812	+	0.978591i	$0.565984\pi$
$948$		0			0
$949$	10.8142	+	6.24356i	0.351043	+	0.202675i
$950$		0			0
$951$		0			0
$952$	−2.51269	+	9.37748i	−0.0814367	+	0.303926i
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	0.00499525	−	0.999988i	$-0.498410\pi$
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	−0.999988	+	0.00499525i	$0.998410\pi$
$954$		0			0
$955$		0			0
$956$	2.30970	−	1.33350i	0.0747009	−	0.0431286i
$957$		0			0
$958$	−6.19919	−	23.1357i	−0.200287	−	0.747480i
$959$	7.02601	−	12.1694i	0.226882	−	0.392970i
$960$		0			0
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$	31.7725	−	31.7725i	1.02439	−	1.02439i
$963$		0			0
$964$			1.00809i			0.0324684i
$965$		0			0
$966$		0			0
$967$	−5.53906	+	1.48419i	−0.178124	+	0.0477282i	−0.346779	−	0.937947i	$-0.612724\pi$
$967$	−5.53906	+	1.48419i	−0.178124	+	0.0477282i	0.168654	+	0.985675i	$0.446058\pi$
$968$	29.1336	−	7.80632i	0.936388	−	0.250904i
$969$		0			0
$970$		0			0
$971$		−	14.2248i		−	0.456496i	−0.973603	−	0.228248i	$-0.926700\pi$
$971$		−	14.2248i		−	0.456496i	0.973603	−	0.228248i	$-0.0732998\pi$
$972$		0			0
$973$	2.08844	−	2.08844i	0.0669524	−	0.0669524i
$974$	20.7244	+	35.8957i	0.664052	+	1.15017i
$975$		0			0
$976$	23.6968	−	41.0440i	0.758516	−	1.31379i
$977$	8.07944	+	30.1529i	0.258484	+	0.964676i	0.966119	+	0.258097i	$0.0830956\pi$
$977$	8.07944	+	30.1529i	0.258484	+	0.964676i	−0.707635	+	0.706578i	$0.750238\pi$
$978$		0			0
$979$	−3.52757	+	2.03664i	−0.112742	+	0.0650913i
$980$		0			0
$981$		0			0
$982$	−38.5627	−	38.5627i	−1.23059	−	1.23059i
$983$	2.66543	−	9.94750i	0.0850139	−	0.317276i	−0.910303	−	0.413943i	$-0.864151\pi$
$983$	2.66543	−	9.94750i	0.0850139	−	0.317276i	0.995317	+	0.0966666i	$0.0308181\pi$
$984$		0			0
$985$		0			0
$986$	2.97715	+	1.71886i	0.0948116	+	0.0547395i
$987$		0			0
$988$	−1.60660	−	0.430488i	−0.0511128	−	0.0136956i
$989$	3.05411			0.0971150
$990$		0			0
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	7.47116	+	2.00189i	0.237210	+	0.0635601i
$993$		0			0
$994$	14.0523	+	8.11308i	0.445711	+	0.257331i
$995$		0			0
$996$		0			0
$997$	8.06937	−	30.1153i	0.255559	−	0.953761i	−0.712219	−	0.701957i	$-0.752310\pi$
$997$	8.06937	−	30.1153i	0.255559	−	0.953761i	0.967778	−	0.251804i	$-0.0810237\pi$
$998$	−40.9452	−	40.9452i	−1.29610	−	1.29610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.q.a.557.4		16
3.2	odd	2		225.2.p.b.32.1		16
5.2	odd	4		135.2.m.a.98.1		16
5.3	odd	4	inner	675.2.q.a.368.4		16
5.4	even	2		135.2.m.a.17.1		16
9.2	odd	6	inner	675.2.q.a.332.4		16
9.7	even	3		225.2.p.b.182.1		16
15.2	even	4		45.2.l.a.23.4	yes	16
15.8	even	4		225.2.p.b.68.1		16
15.14	odd	2		45.2.l.a.32.4	yes	16
45.2	even	12		135.2.m.a.8.1		16
45.4	even	6		405.2.f.a.242.6		16
45.7	odd	12		45.2.l.a.38.4	yes	16
45.14	odd	6		405.2.f.a.242.3		16
45.22	odd	12		405.2.f.a.323.3		16
45.29	odd	6		135.2.m.a.62.1		16
45.32	even	12		405.2.f.a.323.6		16
45.34	even	6		45.2.l.a.2.4	✓	16
45.38	even	12	inner	675.2.q.a.143.4		16
45.43	odd	12		225.2.p.b.218.1		16
60.47	odd	4		720.2.cu.c.113.3		16
60.59	even	2		720.2.cu.c.257.4		16
180.7	even	12		720.2.cu.c.353.4		16
180.79	odd	6		720.2.cu.c.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	45.34	even	6
45.2.l.a.23.4	yes	16	15.2	even	4
45.2.l.a.32.4	yes	16	15.14	odd	2
45.2.l.a.38.4	yes	16	45.7	odd	12
135.2.m.a.8.1		16	45.2	even	12
135.2.m.a.17.1		16	5.4	even	2
135.2.m.a.62.1		16	45.29	odd	6
135.2.m.a.98.1		16	5.2	odd	4
225.2.p.b.32.1		16	3.2	odd	2
225.2.p.b.68.1		16	15.8	even	4
225.2.p.b.182.1		16	9.7	even	3
225.2.p.b.218.1		16	45.43	odd	12
405.2.f.a.242.3		16	45.14	odd	6
405.2.f.a.242.6		16	45.4	even	6
405.2.f.a.323.3		16	45.22	odd	12
405.2.f.a.323.6		16	45.32	even	12
675.2.q.a.143.4		16	45.38	even	12	inner
675.2.q.a.332.4		16	9.2	odd	6	inner
675.2.q.a.368.4		16	5.3	odd	4	inner
675.2.q.a.557.4		16	1.1	even	1	trivial
720.2.cu.c.113.3		16	60.47	odd	4
720.2.cu.c.257.4		16	60.59	even	2
720.2.cu.c.353.4		16	180.7	even	12
720.2.cu.c.497.3		16	180.79	odd	6

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29724 + 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(0.530190 - 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +O(q^{10})\)	\(q+(1.29724 + 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(0.530190 - 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.762281 - 0.440103i) q^{11} +(-1.43820 - 5.36743i) q^{13} +(1.37557 - 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(1.13610 - 1.13610i) q^{17} +1.52456i q^{19} +(1.14184 - 0.305956i) q^{22} +(1.53331 - 0.410850i) q^{23} -7.46278i q^{26} +(-0.284392 + 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(0.286379 + 1.06878i) q^{32} +(1.86870 - 1.07889i) q^{34} +(4.25746 + 4.25746i) q^{37} +(-0.529931 + 1.97773i) q^{38} +(-3.11546 - 1.79871i) q^{41} +(1.85841 + 0.497959i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(-7.99942 - 2.14344i) q^{47} +(2.42805 + 1.40183i) q^{49} +(-0.282368 + 1.05381i) q^{52} +(-4.65601 - 4.65601i) q^{53} +(-5.23290 + 3.02121i) q^{56} +(0.553777 + 2.06672i) q^{58} +(3.81780 - 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(6.63838 - 6.63838i) q^{62} +8.62358i q^{64} +(-3.20857 + 0.859733i) q^{67} +(-0.304699 + 0.0816439i) q^{68} +5.89798i q^{71} +(-1.58900 + 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(-0.466676 - 1.74166i) q^{77} +(6.69401 - 3.86479i) q^{79} +(-3.41628 - 3.41628i) q^{82} +(-2.57170 + 9.59770i) q^{83} +(2.23772 + 1.29195i) q^{86} +(-2.50787 - 0.671981i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(-0.301043 - 0.0806641i) q^{92} +(-9.63215 - 5.56112i) q^{94} +(1.02621 - 3.82988i) q^{97} +(2.66250 + 2.66250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 + 2 * q^7	\( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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