LMFDB - Embedded newform 775.2.f.f.557.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(557,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("775.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.f (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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 42 x^{13} + 66 x^{12} - 24 x^{11} - 162 x^{10} + 612 x^{9} - 1349 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 18x^14 - 42x^13 + 66x^12 - 24x^11 - 162x^10 + 612x^9 - 1349x^8 + 1836x^7 - 1458x^6 - 648x^5 + 5346x^4 - 10206x^3 + 13122x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.7
Root			$1.70486 - 0.305721i$ of defining polynomial
Character	$\chi$	$=$	775.557
Dual form			775.2.f.f.743.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72585 + 1.72585i) q^{2} +(-2.01058 - 2.01058i) q^{3} +3.95712i q^{4} -6.93991i q^{6} +(-0.725850 - 0.725850i) q^{7} +(-3.37769 + 3.37769i) q^{8} +5.08484i q^{9} +O(q^{10})$	\(q+(1.72585 + 1.72585i) q^{2} +(-2.01058 - 2.01058i) q^{3} +3.95712i q^{4} -6.93991i q^{6} +(-0.725850 - 0.725850i) q^{7} +(-3.37769 + 3.37769i) q^{8} +5.08484i q^{9} +4.60996i q^{11} +(7.95609 - 7.95609i) q^{12} +(-1.16498 - 1.16498i) q^{13} -2.50542i q^{14} -3.74455 q^{16} +(-3.76436 + 3.76436i) q^{17} +(-8.77568 + 8.77568i) q^{18} +3.87228i q^{19} +2.91876i q^{21} +(-7.95609 + 7.95609i) q^{22} +(5.77493 + 5.77493i) q^{23} +13.5822 q^{24} -4.02115i q^{26} +(4.19174 - 4.19174i) q^{27} +(2.87228 - 2.87228i) q^{28} +4.95112 q^{29} +(-5.53654 - 0.588801i) q^{31} +(0.292852 + 0.292852i) q^{32} +(9.26867 - 9.26867i) q^{33} -12.9934 q^{34} -20.1213 q^{36} +(-4.78054 + 4.78054i) q^{37} +(-6.68297 + 6.68297i) q^{38} +4.68456i q^{39} -3.44086 q^{41} +(-5.03734 + 5.03734i) q^{42} +(-2.15937 - 2.15937i) q^{43} -18.2421 q^{44} +19.9333i q^{46} +(-1.45170 - 1.45170i) q^{47} +(7.52871 + 7.52871i) q^{48} -5.94628i q^{49} +15.1371 q^{51} +(4.60996 - 4.60996i) q^{52} +(-3.61556 - 3.61556i) q^{53} +14.4686 q^{54} +4.90340 q^{56} +(7.78551 - 7.78551i) q^{57} +(8.54489 + 8.54489i) q^{58} +4.09112i q^{59} -8.38348i q^{61} +(-8.53906 - 10.5714i) q^{62} +(3.69083 - 3.69083i) q^{63} +8.49994i q^{64} +31.9927 q^{66} +(7.01778 + 7.01778i) q^{67} +(-14.8960 - 14.8960i) q^{68} -23.2219i q^{69} +1.76714 q^{71} +(-17.1750 - 17.1750i) q^{72} +(-1.92436 - 1.92436i) q^{73} -16.5010 q^{74} -15.3231 q^{76} +(3.34614 - 3.34614i) q^{77} +(-8.08484 + 8.08484i) q^{78} +2.57759 q^{79} -1.60110 q^{81} +(-5.93842 - 5.93842i) q^{82} +(1.48436 + 1.48436i) q^{83} -11.5499 q^{84} -7.45351i q^{86} +(-9.95461 - 9.95461i) q^{87} +(-15.5710 - 15.5710i) q^{88} +17.3122 q^{89} +1.69120i q^{91} +(-22.8521 + 22.8521i) q^{92} +(9.94782 + 12.3155i) q^{93} -5.01084i q^{94} -1.17760i q^{96} +(4.21257 + 4.21257i) q^{97} +(10.2624 - 10.2624i) q^{98} -23.4409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 12 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 + 12 * q^7 - 16 * q^8	$ 16 q + 4 q^{2} + 12 q^{7} - 16 q^{8} - 16 q^{18} + 16 q^{28} - 16 q^{31} - 8 q^{32} + 44 q^{33} - 88 q^{36} - 28 q^{38} - 24 q^{41} + 24 q^{47} - 32 q^{51} - 16 q^{56} - 44 q^{62} - 40 q^{63} + 112 q^{66} - 60 q^{67} + 72 q^{71} - 80 q^{72} - 32 q^{76} - 104 q^{78} + 24 q^{81} - 76 q^{82} + 20 q^{87} + 60 q^{93} + 72 q^{97} + 68 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 + 12 * q^7 - 16 * q^8 - 16 * q^18 + 16 * q^28 - 16 * q^31 - 8 * q^32 + 44 * q^33 - 88 * q^36 - 28 * q^38 - 24 * q^41 + 24 * q^47 - 32 * q^51 - 16 * q^56 - 44 * q^62 - 40 * q^63 + 112 * q^66 - 60 * q^67 + 72 * q^71 - 80 * q^72 - 32 * q^76 - 104 * q^78 + 24 * q^81 - 76 * q^82 + 20 * q^87 + 60 * q^93 + 72 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.72585	+	1.72585i	1.22036	+	1.22036i	0.967504	+	0.252857i	$0.0813701\pi$
$2$	1.72585	+	1.72585i	1.22036	+	1.22036i	0.252857	+	0.967504i	$0.418630\pi$
$3$	−2.01058	−	2.01058i	−1.16081	−	1.16081i	−0.984299	−	0.176508i	$-0.943520\pi$
$3$	−2.01058	−	2.01058i	−1.16081	−	1.16081i	−0.176508	−	0.984299i	$-0.556480\pi$
$4$			3.95712i			1.97856i
$5$		0			0
$5$		0			0
$6$		−	6.93991i		−	2.83321i
$7$	−0.725850	−	0.725850i	−0.274346	−	0.274346i	0.556501	−	0.830847i	$-0.312143\pi$
$7$	−0.725850	−	0.725850i	−0.274346	−	0.274346i	−0.830847	+	0.556501i	$0.812143\pi$
$8$	−3.37769	+	3.37769i	−1.19420	+	1.19420i
$9$			5.08484i			1.69495i
$10$		0			0
$11$			4.60996i			1.38995i	0.719032	+	0.694977i	$0.244585\pi$
$11$			4.60996i			1.38995i	−0.719032	+	0.694977i	$0.755415\pi$
$12$	7.95609	−	7.95609i	2.29673	−	2.29673i
$13$	−1.16498	−	1.16498i	−0.323107	−	0.323107i	0.526851	−	0.849958i	$-0.323373\pi$
$13$	−1.16498	−	1.16498i	−0.323107	−	0.323107i	−0.849958	+	0.526851i	$0.823373\pi$
$14$		−	2.50542i		−	0.669601i
$15$		0			0
$16$	−3.74455			−0.936138
$17$	−3.76436	+	3.76436i	−0.912990	+	0.912990i	−0.996506	−	0.0835160i	$-0.973385\pi$
$17$	−3.76436	+	3.76436i	−0.912990	+	0.912990i	0.0835160	+	0.996506i	$0.473385\pi$
$18$	−8.77568	+	8.77568i	−2.06845	+	2.06845i
$19$			3.87228i			0.888361i	0.895937	+	0.444181i	$0.146505\pi$
$19$			3.87228i			0.888361i	−0.895937	+	0.444181i	$0.853495\pi$
$20$		0			0
$21$			2.91876i			0.636925i
$22$	−7.95609	+	7.95609i	−1.69624	+	1.69624i
$23$	5.77493	+	5.77493i	1.20416	+	1.20416i	0.972890	+	0.231266i	$0.0742869\pi$
$23$	5.77493	+	5.77493i	1.20416	+	1.20416i	0.231266	+	0.972890i	$0.425713\pi$
$24$	13.5822			2.77246
$25$		0			0
$26$		−	4.02115i		−	0.788613i
$27$	4.19174	−	4.19174i	0.806700	−	0.806700i
$28$	2.87228	−	2.87228i	0.542809	−	0.542809i
$29$	4.95112			0.919400			0.459700	−	0.888074i	$-0.347957\pi$
$29$	4.95112			0.919400			0.459700	+	0.888074i	$0.347957\pi$
$30$		0			0
$31$	−5.53654	−	0.588801i	−0.994393	−	0.105752i
$31$	−5.53654	−	0.588801i	−0.994393	−	0.105752i
$32$	0.292852	+	0.292852i	0.0517694	+	0.0517694i
$33$	9.26867	−	9.26867i	1.61347	−	1.61347i
$34$	−12.9934			−2.22836
$35$		0			0
$36$	−20.1213			−3.35355
$37$	−4.78054	+	4.78054i	−0.785916	+	0.785916i	−0.980822	−	0.194906i	$-0.937560\pi$
$37$	−4.78054	+	4.78054i	−0.785916	+	0.785916i	0.194906	+	0.980822i	$0.437560\pi$
$38$	−6.68297	+	6.68297i	−1.08412	+	1.08412i
$39$			4.68456i			0.750129i
$40$		0			0
$41$	−3.44086			−0.537373			−0.268686	−	0.963228i	$-0.586590\pi$
$41$	−3.44086			−0.537373			−0.268686	+	0.963228i	$0.586590\pi$
$42$	−5.03734	+	5.03734i	−0.777278	+	0.777278i
$43$	−2.15937	−	2.15937i	−0.329301	−	0.329301i	0.523019	−	0.852321i	$-0.324805\pi$
$43$	−2.15937	−	2.15937i	−0.329301	−	0.329301i	−0.852321	+	0.523019i	$0.824805\pi$
$44$	−18.2421			−2.75011
$45$		0			0
$46$			19.9333i			2.93901i
$47$	−1.45170	−	1.45170i	−0.211752	−	0.211752i	0.593259	−	0.805012i	$-0.297841\pi$
$47$	−1.45170	−	1.45170i	−0.211752	−	0.211752i	−0.805012	+	0.593259i	$0.797841\pi$
$48$	7.52871	+	7.52871i	1.08668	+	1.08668i
$49$		−	5.94628i		−	0.849469i
$50$		0			0
$51$	15.1371			2.11961
$52$	4.60996	−	4.60996i	0.639286	−	0.639286i
$53$	−3.61556	−	3.61556i	−0.496635	−	0.496635i	0.413753	−	0.910389i	$-0.364218\pi$
$53$	−3.61556	−	3.61556i	−0.496635	−	0.496635i	−0.910389	+	0.413753i	$0.864218\pi$
$54$	14.4686			1.96893
$55$		0			0
$56$	4.90340			0.655245
$57$	7.78551	−	7.78551i	1.03122	−	1.03122i
$58$	8.54489	+	8.54489i	1.12200	+	1.12200i
$59$			4.09112i			0.532619i	0.963888	+	0.266309i	$0.0858043\pi$
$59$			4.09112i			0.532619i	−0.963888	+	0.266309i	$0.914196\pi$
$60$		0			0
$61$		−	8.38348i		−	1.07339i	−0.843775	−	0.536697i	$-0.819672\pi$
$61$		−	8.38348i		−	1.07339i	0.843775	−	0.536697i	$-0.180328\pi$
$62$	−8.53906	−	10.5714i	−1.08446	−	1.34257i
$63$	3.69083	−	3.69083i	0.465001	−	0.465001i
$64$			8.49994i			1.06249i
$65$		0			0
$66$	31.9927			3.93803
$67$	7.01778	+	7.01778i	0.857359	+	0.857359i	0.991026	−	0.133668i	$-0.0426755\pi$
$67$	7.01778	+	7.01778i	0.857359	+	0.857359i	−0.133668	+	0.991026i	$0.542675\pi$
$68$	−14.8960	−	14.8960i	−1.80641	−	1.80641i
$69$		−	23.2219i		−	2.79559i
$70$		0			0
$71$	1.76714			0.209721			0.104861	−	0.994487i	$-0.466560\pi$
$71$	1.76714			0.209721			0.104861	+	0.994487i	$0.466560\pi$
$72$	−17.1750	−	17.1750i	−2.02410	−	2.02410i
$73$	−1.92436	−	1.92436i	−0.225229	−	0.225229i	0.585467	−	0.810696i	$-0.300911\pi$
$73$	−1.92436	−	1.92436i	−0.225229	−	0.225229i	−0.810696	+	0.585467i	$0.800911\pi$
$74$	−16.5010			−1.91820
$75$		0			0
$76$	−15.3231			−1.75768
$77$	3.34614	−	3.34614i	0.381328	−	0.381328i
$78$	−8.08484	+	8.08484i	−0.915428	+	0.915428i
$79$	2.57759			0.290002			0.145001	−	0.989432i	$-0.453682\pi$
$79$	2.57759			0.290002			0.145001	+	0.989432i	$0.453682\pi$
$80$		0			0
$81$	−1.60110			−0.177900
$82$	−5.93842	−	5.93842i	−0.655788	−	0.655788i
$83$	1.48436	+	1.48436i	0.162929	+	0.162929i	0.783863	−	0.620934i	$-0.213246\pi$
$83$	1.48436	+	1.48436i	0.162929	+	0.162929i	−0.620934	+	0.783863i	$0.713246\pi$
$84$	−11.5499			−1.26019
$85$		0			0
$86$		−	7.45351i		−	0.803732i
$87$	−9.95461	−	9.95461i	−1.06725	−	1.06725i
$88$	−15.5710	−	15.5710i	−1.65988	−	1.65988i
$89$	17.3122			1.83509			0.917544	−	0.397635i	$-0.130169\pi$
$89$	17.3122			1.83509			0.917544	+	0.397635i	$0.130169\pi$
$90$		0			0
$91$			1.69120i			0.177286i
$92$	−22.8521	+	22.8521i	−2.38250	+	2.38250i
$93$	9.94782	+	12.3155i	1.03154	+	1.27706i
$94$		−	5.01084i		−	0.516828i
$95$		0			0
$96$		−	1.17760i		−	0.120189i
$97$	4.21257	+	4.21257i	0.427721	+	0.427721i	0.887851	−	0.460130i	$-0.152197\pi$
$97$	4.21257	+	4.21257i	0.427721	+	0.427721i	−0.460130	+	0.887851i	$0.652197\pi$
$98$	10.2624	−	10.2624i	1.03666	−	1.03666i
$99$	−23.4409			−2.35590
$100$		0			0
$101$	−3.13308			−0.311753			−0.155877	−	0.987777i	$-0.549820\pi$
$101$	−3.13308			−0.311753			−0.155877	+	0.987777i	$0.549820\pi$
$102$	26.1243	+	26.1243i	2.58669	+	2.58669i
$103$	−5.10513	+	5.10513i	−0.503024	+	0.503024i	−0.912376	−	0.409353i	$-0.865755\pi$
$103$	−5.10513	+	5.10513i	−0.503024	+	0.503024i	0.409353	+	0.912376i	$0.365755\pi$
$104$	7.86988			0.771705
$105$		0			0
$106$		−	12.4798i		−	1.21215i
$107$	−5.44542	−	5.44542i	−0.526429	−	0.526429i	0.393077	−	0.919506i	$-0.371411\pi$
$107$	−5.44542	−	5.44542i	−0.526429	−	0.526429i	−0.919506	+	0.393077i	$0.871411\pi$
$108$	16.5872	+	16.5872i	1.59610	+	1.59610i
$109$		−	3.78651i		−	0.362682i	−0.983420	−	0.181341i	$-0.941956\pi$
$109$		−	3.78651i		−	0.362682i	0.983420	−	0.181341i	$-0.0580438\pi$
$110$		0			0
$111$	19.2233			1.82459
$112$	2.71798	+	2.71798i	0.256825	+	0.256825i
$113$	7.60268	−	7.60268i	0.715200	−	0.715200i	−0.252418	−	0.967618i	$-0.581226\pi$
$113$	7.60268	−	7.60268i	0.715200	−	0.715200i	0.967618	+	0.252418i	$0.0812258\pi$
$114$	26.8733			2.51691
$115$		0			0
$116$			19.5922i			1.81909i
$117$	5.92373	−	5.92373i	0.547649	−	0.547649i
$118$	−7.06066	+	7.06066i	−0.649987	+	0.649987i
$119$	5.46472			0.500950
$120$		0			0
$121$	−10.2517			−0.931972
$122$	14.4686	−	14.4686i	1.30993	−	1.30993i
$123$	6.91812	+	6.91812i	0.623786	+	0.623786i
$124$	2.32996	−	21.9088i	0.209236	−	1.96746i
$125$		0			0
$126$	12.7397			1.13494
$127$	6.79112	−	6.79112i	0.602614	−	0.602614i	−0.338391	−	0.941005i	$-0.609883\pi$
$127$	6.79112	−	6.79112i	0.602614	−	0.602614i	0.941005	+	0.338391i	$0.109883\pi$
$128$	−14.0839	+	14.0839i	−1.24485	+	1.24485i
$129$			8.68317i			0.764511i
$130$		0			0
$131$	6.38087			0.557499			0.278750	−	0.960364i	$-0.410080\pi$
$131$	6.38087			0.557499			0.278750	+	0.960364i	$0.410080\pi$
$132$	36.6772	+	36.6772i	3.19234	+	3.19234i
$133$	2.81069	−	2.81069i	0.243718	−	0.243718i
$134$			24.2233i			2.09257i
$135$		0			0
$136$		−	25.4297i		−	2.18058i
$137$	0.319378	−	0.319378i	0.0272863	−	0.0272863i	−0.693332	−	0.720618i	$-0.743858\pi$
$137$	0.319378	−	0.319378i	0.0272863	−	0.0272863i	0.720618	+	0.693332i	$0.243858\pi$
$138$	40.0775	−	40.0775i	3.41163	−	3.41163i
$139$	12.4798			1.05853			0.529263	−	0.848458i	$-0.322469\pi$
$139$	12.4798			1.05853			0.529263	+	0.848458i	$0.322469\pi$
$140$		0			0
$141$			5.83751i			0.491607i
$142$	3.04983	+	3.04983i	0.255936	+	0.255936i
$143$	5.37050	−	5.37050i	0.449103	−	0.449103i
$144$		−	19.0405i		−	1.58671i
$145$		0			0
$146$		−	6.64232i		−	0.549722i
$147$	−11.9555	+	11.9555i	−0.986070	+	0.986070i
$148$	−18.9172	−	18.9172i	−1.55498	−	1.55498i
$149$			6.44622i			0.528095i	0.964510	+	0.264048i	$0.0850576\pi$
$149$			6.44622i			0.528095i	−0.964510	+	0.264048i	$0.914942\pi$
$150$		0			0
$151$			12.8210i			1.04336i	0.853142	+	0.521679i	$0.174694\pi$
$151$			12.8210i			1.04336i	−0.853142	+	0.521679i	$0.825306\pi$
$152$	−13.0794	−	13.0794i	−1.06088	−	1.06088i
$153$	−19.1412	−	19.1412i	−1.54747	−	1.54747i
$154$	11.5499			0.930715
$155$		0			0
$156$	−18.5373			−1.48418
$157$	−4.40095	−	4.40095i	−0.351234	−	0.351234i	0.509334	−	0.860569i	$-0.329892\pi$
$157$	−4.40095	−	4.40095i	−0.351234	−	0.351234i	−0.860569	+	0.509334i	$0.829892\pi$
$158$	4.44854	+	4.44854i	0.353907	+	0.353907i
$159$			14.5387i			1.15300i
$160$		0			0
$161$		−	8.38348i		−	0.660710i
$162$	−2.76325	−	2.76325i	−0.217102	−	0.217102i
$163$	−6.48283	+	6.48283i	−0.507774	+	0.507774i	−0.913843	−	0.406069i	$-0.866899\pi$
$163$	−6.48283	+	6.48283i	−0.507774	+	0.507774i	0.406069	+	0.913843i	$0.366899\pi$
$164$		−	13.6159i		−	1.06322i
$165$		0			0
$166$			5.12355i			0.397665i
$167$	−9.73166	+	9.73166i	−0.753058	+	0.753058i	−0.975049	−	0.221990i	$-0.928745\pi$
$167$	−9.73166	+	9.73166i	−0.753058	+	0.753058i	0.221990	+	0.975049i	$0.428745\pi$
$168$	−9.85867	−	9.85867i	−0.760613	−	0.760613i
$169$		−	10.2857i		−	0.791204i
$170$		0			0
$171$	−19.6899			−1.50573
$172$	8.54489	−	8.54489i	0.651542	−	0.651542i
$173$	−2.48124	+	2.48124i	−0.188645	+	0.188645i	−0.795110	−	0.606465i	$-0.792587\pi$
$173$	−2.48124	+	2.48124i	−0.188645	+	0.188645i	0.606465	+	0.795110i	$0.292587\pi$
$174$		−	34.3603i		−	2.60485i
$175$		0			0
$176$		−	17.2622i		−	1.30119i
$177$	8.22552	−	8.22552i	0.618268	−	0.618268i
$178$	29.8782	+	29.8782i	2.23947	+	2.23947i
$179$	−10.7886			−0.806380			−0.403190	−	0.915116i	$-0.632099\pi$
$179$	−10.7886			−0.806380			−0.403190	+	0.915116i	$0.632099\pi$
$180$		0			0
$181$		−	21.5810i		−	1.60410i	−0.597256	−	0.802050i	$-0.703743\pi$
$181$		−	21.5810i		−	1.60410i	0.597256	−	0.802050i	$-0.296257\pi$
$182$	−2.91876	+	2.91876i	−0.216353	+	0.216353i
$183$	−16.8556	+	16.8556i	−1.24600	+	1.24600i
$184$	−39.0119			−2.87600
$185$		0			0
$186$	−4.08623	+	38.4231i	−0.299617	+	2.81732i
$187$	−17.3535	−	17.3535i	−1.26901	−	1.26901i
$188$	5.74455	−	5.74455i	0.418965	−	0.418965i
$189$	−6.08515			−0.442629
$190$		0			0
$191$	−14.4445			−1.04517			−0.522584	−	0.852588i	$-0.675032\pi$
$191$	−14.4445			−1.04517			−0.522584	+	0.852588i	$0.675032\pi$
$192$	17.0898	−	17.0898i	1.23335	−	1.23335i
$193$	6.88629	−	6.88629i	0.495686	−	0.495686i	−0.414406	−	0.910092i	$-0.636011\pi$
$193$	6.88629	−	6.88629i	0.495686	−	0.495686i	0.910092	+	0.414406i	$0.136011\pi$
$194$			14.5405i			1.04395i
$195$		0			0
$196$	23.5301			1.68072
$197$	4.88854	−	4.88854i	0.348294	−	0.348294i	−0.511180	−	0.859474i	$-0.670791\pi$
$197$	4.88854	−	4.88854i	0.348294	−	0.348294i	0.859474	+	0.511180i	$0.170791\pi$
$198$	−40.4555	−	40.4555i	−2.87505	−	2.87505i
$199$	−6.59875			−0.467773			−0.233886	−	0.972264i	$-0.575144\pi$
$199$	−6.59875			−0.467773			−0.233886	+	0.972264i	$0.575144\pi$
$200$		0			0
$201$		−	28.2196i		−	1.99046i
$202$	−5.40723	−	5.40723i	−0.380452	−	0.380452i
$203$	−3.59377	−	3.59377i	−0.252233	−	0.252233i
$204$			59.8991i			4.19378i
$205$		0			0
$206$	−17.6214			−1.22774
$207$	−29.3646	+	29.3646i	−2.04098	+	2.04098i
$208$	4.36232	+	4.36232i	0.302473	+	0.302473i
$209$	−17.8510			−1.23478
$210$		0			0
$211$	−13.5942			−0.935866			−0.467933	−	0.883764i	$-0.655001\pi$
$211$	−13.5942			−0.935866			−0.467933	+	0.883764i	$0.655001\pi$
$212$	14.3072	−	14.3072i	0.982623	−	0.982623i
$213$	−3.55298	−	3.55298i	−0.243446	−	0.243446i
$214$		−	18.7960i		−	1.28487i
$215$		0			0
$216$			28.3168i			1.92672i
$217$	3.59132	+	4.44608i	0.243795	+	0.301820i
$218$	6.53496	−	6.53496i	0.442603	−	0.442603i
$219$			7.73816i			0.522896i
$220$		0			0
$221$	8.77078			0.589987
$222$	33.1765	+	33.1765i	2.22666	+	2.22666i
$223$	14.9178	+	14.9178i	0.998969	+	0.998969i	0.999999	−	0.00103019i	$-0.000327918\pi$
$223$	14.9178	+	14.9178i	0.998969	+	0.998969i	−0.00103019	+	0.999999i	$0.500328\pi$
$224$		−	0.425133i		−	0.0284054i
$225$		0			0
$226$	26.2422			1.74560
$227$	9.90043	+	9.90043i	0.657115	+	0.657115i	0.954696	−	0.297582i	$-0.0961801\pi$
$227$	9.90043	+	9.90043i	0.657115	+	0.657115i	−0.297582	+	0.954696i	$0.596180\pi$
$228$	30.8082	+	30.8082i	2.04032	+	2.04032i
$229$	−15.6210			−1.03226			−0.516132	−	0.856509i	$-0.672628\pi$
$229$	−15.6210			−1.03226			−0.516132	+	0.856509i	$0.672628\pi$
$230$		0			0
$231$	−13.4553			−0.885296
$232$	−16.7234	+	16.7234i	−1.09794	+	1.09794i
$233$	20.1820	−	20.1820i	1.32217	−	1.32217i	0.410147	−	0.912020i	$-0.365478\pi$
$233$	20.1820	−	20.1820i	1.32217	−	1.32217i	0.912020	−	0.410147i	$-0.134522\pi$
$234$	20.4469			1.33666
$235$		0			0
$236$	−16.1891			−1.05382
$237$	−5.18245	−	5.18245i	−0.336636	−	0.336636i
$238$	9.43129	+	9.43129i	0.611340	+	0.611340i
$239$	9.51750			0.615636			0.307818	−	0.951445i	$-0.400401\pi$
$239$	9.51750			0.615636			0.307818	+	0.951445i	$0.400401\pi$
$240$		0			0
$241$			3.25992i			0.209990i	0.994473	+	0.104995i	$0.0334827\pi$
$241$			3.25992i			0.209990i	−0.994473	+	0.104995i	$0.966517\pi$
$242$	−17.6929	−	17.6929i	−1.13734	−	1.13734i
$243$	−9.35608	−	9.35608i	−0.600193	−	0.600193i
$244$	33.1744			2.12377
$245$		0			0
$246$			23.8793i			1.52249i
$247$	4.51112	−	4.51112i	0.287035	−	0.287035i
$248$	20.6895	−	16.7120i	1.31379	−	1.06121i
$249$		−	5.96883i		−	0.378259i
$250$		0			0
$251$			14.9323i			0.942516i	0.881995	+	0.471258i	$0.156200\pi$
$251$			14.9323i			0.942516i	−0.881995	+	0.471258i	$0.843800\pi$
$252$	14.6051	+	14.6051i	0.920033	+	0.920033i
$253$	−26.6222	+	26.6222i	−1.67372	+	1.67372i
$254$	23.4409			1.47081
$255$		0			0
$256$	−31.6136			−1.97585
$257$	18.0863	+	18.0863i	1.12819	+	1.12819i	0.990471	+	0.137722i	$0.0439781\pi$
$257$	18.0863	+	18.0863i	1.12819	+	1.12819i	0.137722	+	0.990471i	$0.456022\pi$
$258$	−14.9859	+	14.9859i	−0.932979	+	0.932979i
$259$	6.93991			0.431225
$260$		0			0
$261$			25.1757i			1.55834i
$262$	11.0124	+	11.0124i	0.680350	+	0.680350i
$263$	1.50799	+	1.50799i	0.0929868	+	0.0929868i	0.752070	−	0.659083i	$-0.229056\pi$
$263$	1.50799	+	1.50799i	0.0929868	+	0.0929868i	−0.659083	+	0.752070i	$0.729056\pi$
$264$			62.6135i			3.85359i
$265$		0			0
$266$	9.70167			0.594848
$267$	−34.8075	−	34.8075i	−2.13018	−	2.13018i
$268$	−27.7702	+	27.7702i	−1.69633	+	1.69633i
$269$	−14.5122			−0.884824			−0.442412	−	0.896812i	$-0.645877\pi$
$269$	−14.5122			−0.884824			−0.442412	+	0.896812i	$0.645877\pi$
$270$		0			0
$271$			21.3333i			1.29591i	0.761680	+	0.647954i	$0.224375\pi$
$271$			21.3333i			1.29591i	−0.761680	+	0.647954i	$0.775625\pi$
$272$	14.0958	−	14.0958i	0.854685	−	0.854685i
$273$	3.40029	−	3.40029i	0.205795	−	0.205795i
$274$	1.10240			0.0665983
$275$		0			0
$276$	91.8918			5.53124
$277$	−12.3329	+	12.3329i	−0.741011	+	0.741011i	−0.972773	−	0.231761i	$-0.925551\pi$
$277$	−12.3329	+	12.3329i	−0.741011	+	0.741011i	0.231761	+	0.972773i	$0.425551\pi$
$278$	21.5383	+	21.5383i	1.29178	+	1.29178i
$279$	2.99396	−	28.1525i	0.179244	−	1.68544i
$280$		0			0
$281$	8.75995			0.522575			0.261287	−	0.965261i	$-0.415853\pi$
$281$	8.75995			0.522575			0.261287	+	0.965261i	$0.415853\pi$
$282$	−10.0747	+	10.0747i	−0.599938	+	0.599938i
$283$	16.7833	−	16.7833i	0.997666	−	0.997666i	−0.00233124	−	0.999997i	$-0.500742\pi$
$283$	16.7833	−	16.7833i	0.997666	−	0.997666i	0.999997	+	0.00233124i	$0.000742057\pi$
$284$			6.99280i			0.414946i
$285$		0			0
$286$	18.5373			1.09614
$287$	2.49755	+	2.49755i	0.147426	+	0.147426i
$288$	−1.48910	+	1.48910i	−0.0877463	+	0.0877463i
$289$		−	11.3408i		−	0.667103i
$290$		0			0
$291$		−	16.9394i		−	0.993004i
$292$	7.61493	−	7.61493i	0.445630	−	0.445630i
$293$	−6.73577	+	6.73577i	−0.393508	+	0.393508i	−0.875936	−	0.482428i	$-0.839755\pi$
$293$	−6.73577	+	6.73577i	−0.393508	+	0.393508i	0.482428	+	0.875936i	$0.339755\pi$
$294$	−41.2667			−2.40672
$295$		0			0
$296$		−	32.2944i		−	1.87707i
$297$	19.3237	+	19.3237i	1.12128	+	1.12128i
$298$	−11.1252	+	11.1252i	−0.644467	+	0.644467i
$299$		−	13.4553i		−	0.778142i
$300$		0			0
$301$			3.13476i			0.180685i
$302$	−22.1271	+	22.1271i	−1.27327	+	1.27327i
$303$	6.29931	+	6.29931i	0.361886	+	0.361886i
$304$		−	14.4999i		−	0.831629i
$305$		0			0
$306$		−	66.0696i		−	3.77694i
$307$	19.4446	+	19.4446i	1.10976	+	1.10976i	0.993181	+	0.116583i	$0.0371941\pi$
$307$	19.4446	+	19.4446i	1.10976	+	1.10976i	0.116583	+	0.993181i	$0.462806\pi$
$308$	13.2411	+	13.2411i	0.754480	+	0.754480i
$309$	20.5285			1.16783
$310$		0			0
$311$	0.637117			0.0361276			0.0180638	−	0.999837i	$-0.494250\pi$
$311$	0.637117			0.0361276			0.0180638	+	0.999837i	$0.494250\pi$
$312$	−15.8230	−	15.8230i	−0.895801	−	0.895801i
$313$	−9.20544	−	9.20544i	−0.520322	−	0.520322i	0.397346	−	0.917669i	$-0.369931\pi$
$313$	−9.20544	−	9.20544i	−0.520322	−	0.520322i	−0.917669	+	0.397346i	$0.869931\pi$
$314$		−	15.1908i		−	0.857265i
$315$		0			0
$316$			10.1998i			0.573785i
$317$	−5.71568	−	5.71568i	−0.321025	−	0.321025i	0.528135	−	0.849160i	$-0.322891\pi$
$317$	−5.71568	−	5.71568i	−0.321025	−	0.321025i	−0.849160	+	0.528135i	$0.822891\pi$
$318$	−25.0917	+	25.0917i	−1.40707	+	1.40707i
$319$			22.8245i			1.27792i
$320$		0			0
$321$			21.8969i			1.22216i
$322$	14.4686	−	14.4686i	0.806305	−	0.806305i
$323$	−14.5766	−	14.5766i	−0.811065	−	0.811065i
$324$		−	6.33573i		−	0.351985i
$325$		0			0
$326$	−22.3768			−1.23933
$327$	−7.61308	+	7.61308i	−0.421004	+	0.421004i
$328$	11.6222	−	11.6222i	0.641728	−	0.641728i
$329$			2.10743i			0.116187i
$330$		0			0
$331$			8.70631i			0.478542i	0.970953	+	0.239271i	$0.0769085\pi$
$331$			8.70631i			0.478542i	−0.970953	+	0.239271i	$0.923092\pi$
$332$	−5.87377	+	5.87377i	−0.322365	+	0.322365i
$333$	−24.3083	−	24.3083i	−1.33209	−	1.33209i
$334$	−33.5908			−1.83801
$335$		0			0
$336$		−	10.9294i		−	0.596250i
$337$	0.0770524	−	0.0770524i	0.00419731	−	0.00419731i	−0.705005	−	0.709202i	$-0.749055\pi$
$337$	0.0770524	−	0.0770524i	0.00419731	−	0.00419731i	0.709202	+	0.705005i	$0.249055\pi$
$338$	17.7515	−	17.7515i	0.965554	−	0.965554i
$339$	−30.5716			−1.66042
$340$		0			0
$341$	2.71435	−	25.5232i	0.146990	−	1.38216i
$342$	−33.9818	−	33.9818i	−1.83753	−	1.83753i
$343$	−9.39706	+	9.39706i	−0.507394	+	0.507394i
$344$	14.5874			0.786500
$345$		0			0
$346$	−8.56450			−0.460430
$347$	8.02969	−	8.02969i	0.431056	−	0.431056i	−0.457931	−	0.888988i	$-0.651409\pi$
$347$	8.02969	−	8.02969i	0.431056	−	0.431056i	0.888988	+	0.457931i	$0.151409\pi$
$348$	39.3916	−	39.3916i	2.11161	−	2.11161i
$349$			17.5339i			0.938568i	0.883047	+	0.469284i	$0.155488\pi$
$349$			17.5339i			0.938568i	−0.883047	+	0.469284i	$0.844512\pi$
$350$		0			0
$351$	−9.76656			−0.521301
$352$	−1.35003	+	1.35003i	−0.0719570	+	0.0719570i
$353$	19.1095	+	19.1095i	1.01710	+	1.01710i	0.999851	+	0.0172464i	$0.00548997\pi$
$353$	19.1095	+	19.1095i	1.01710	+	1.01710i	0.0172464	+	0.999851i	$0.494510\pi$
$354$	28.3920			1.50902
$355$		0			0
$356$			68.5063i			3.63083i
$357$	−10.9872	−	10.9872i	−0.581506	−	0.581506i
$358$	−18.6196	−	18.6196i	−0.984075	−	0.984075i
$359$		−	28.6429i		−	1.51172i	−0.654735	−	0.755858i	$-0.727220\pi$
$359$		−	28.6429i		−	1.51172i	0.654735	−	0.755858i	$-0.272780\pi$
$360$		0			0
$361$	4.00548			0.210815
$362$	37.2455	−	37.2455i	1.95758	−	1.95758i
$363$	20.6118	+	20.6118i	1.08184	+	1.08184i
$364$	−6.69228			−0.350771
$365$		0			0
$366$	−58.1806			−3.04115
$367$	12.3955	−	12.3955i	0.647038	−	0.647038i	−0.305238	−	0.952276i	$-0.598736\pi$
$367$	12.3955	−	12.3955i	0.647038	−	0.647038i	0.952276	+	0.305238i	$0.0987360\pi$
$368$	−21.6245	−	21.6245i	−1.12726	−	1.12726i
$369$		−	17.4963i		−	0.910819i
$370$		0			0
$371$			5.24871i			0.272500i
$372$	−48.7338	+	39.3647i	−2.52673	+	2.04096i
$373$	−5.20014	+	5.20014i	−0.269253	+	0.269253i	−0.828799	−	0.559546i	$-0.810976\pi$
$373$	−5.20014	+	5.20014i	−0.269253	+	0.269253i	0.559546	+	0.828799i	$0.310976\pi$
$374$		−	59.8991i		−	3.09731i
$375$		0			0
$376$	9.80680			0.505747
$377$	−5.76795	−	5.76795i	−0.297064	−	0.297064i
$378$	−10.5021	−	10.5021i	−0.540167	−	0.540167i
$379$			11.0807i			0.569180i	0.958649	+	0.284590i	$0.0918574\pi$
$379$			11.0807i			0.569180i	−0.958649	+	0.284590i	$0.908143\pi$
$380$		0			0
$381$	−27.3081			−1.39904
$382$	−24.9290	−	24.9290i	−1.27548	−	1.27548i
$383$	−4.25432	−	4.25432i	−0.217385	−	0.217385i	0.590010	−	0.807396i	$-0.299124\pi$
$383$	−4.25432	−	4.25432i	−0.217385	−	0.217385i	−0.807396	+	0.590010i	$0.799124\pi$
$384$	56.6336			2.89007
$385$		0			0
$386$	23.7694			1.20983
$387$	10.9801	−	10.9801i	0.558148	−	0.558148i
$388$	−16.6696	+	16.6696i	−0.846272	+	0.846272i
$389$	26.3280			1.33488			0.667442	−	0.744662i	$-0.267389\pi$
$389$	26.3280			1.33488			0.667442	+	0.744662i	$0.267389\pi$
$390$		0			0
$391$	−43.4778			−2.19877
$392$	20.0847	+	20.0847i	1.01443	+	1.01443i
$393$	−12.8292	−	12.8292i	−0.647149	−	0.647149i
$394$	16.8738			0.850089
$395$		0			0
$396$		−	92.7584i		−	4.66129i
$397$	17.5303	+	17.5303i	0.879819	+	0.879819i	0.993516	−	0.113697i	$-0.0362692\pi$
$397$	17.5303	+	17.5303i	0.879819	+	0.879819i	−0.113697	+	0.993516i	$0.536269\pi$
$398$	−11.3884	−	11.3884i	−0.570851	−	0.570851i
$399$	−11.3022			−0.565819
$400$		0			0
$401$		−	30.2084i		−	1.50853i	−0.656568	−	0.754267i	$-0.727992\pi$
$401$		−	30.2084i		−	1.50853i	0.656568	−	0.754267i	$-0.272008\pi$
$402$	48.7028	−	48.7028i	2.42907	−	2.42907i
$403$	5.76401	+	7.13589i	0.287126	+	0.355464i
$404$		−	12.3980i		−	0.616823i
$405$		0			0
$406$		−	12.4046i		−	0.615631i
$407$	−22.0381	−	22.0381i	−1.09239	−	1.09239i
$408$	−51.1284	+	51.1284i	−2.53123	+	2.53123i
$409$	35.7956			1.76998			0.884989	−	0.465613i	$-0.154166\pi$
$409$	35.7956			1.76998			0.884989	+	0.465613i	$0.154166\pi$
$410$		0			0
$411$	−1.28427			−0.0633483
$412$	−20.2016	−	20.2016i	−0.995262	−	0.995262i
$413$	2.96954	−	2.96954i	0.146122	−	0.146122i
$414$	−101.358			−4.98147
$415$		0			0
$416$		−	0.682331i		−	0.0334541i
$417$	−25.0917	−	25.0917i	−1.22874	−	1.22874i
$418$	−30.8082	−	30.8082i	−1.50688	−	1.50688i
$419$		−	22.4624i		−	1.09736i	−0.836032	−	0.548681i	$-0.815130\pi$
$419$		−	22.4624i		−	1.09736i	0.836032	−	0.548681i	$-0.184870\pi$
$420$		0			0
$421$	−31.0910			−1.51528			−0.757641	−	0.652671i	$-0.773648\pi$
$421$	−31.0910			−1.51528			−0.757641	+	0.652671i	$0.773648\pi$
$422$	−23.4616	−	23.4616i	−1.14209	−	1.14209i
$423$	7.38167	−	7.38167i	0.358909	−	0.358909i
$424$	24.4245			1.18616
$425$		0			0
$426$		−	12.2638i		−	0.594184i
$427$	−6.08515	+	6.08515i	−0.294481	+	0.294481i
$428$	21.5482	−	21.5482i	1.04157	−	1.04157i
$429$	−21.5956			−1.04265
$430$		0			0
$431$	31.3721			1.51114			0.755570	−	0.655067i	$-0.227360\pi$
$431$	31.3721			1.51114			0.755570	+	0.655067i	$0.227360\pi$
$432$	−15.6962	+	15.6962i	−0.755183	+	0.755183i
$433$	9.96482	+	9.96482i	0.478879	+	0.478879i	0.904773	−	0.425894i	$-0.140040\pi$
$433$	9.96482	+	9.96482i	0.478879	+	0.478879i	−0.425894	+	0.904773i	$0.640040\pi$
$434$	−1.47519	+	13.8714i	−0.0708115	+	0.665846i
$435$		0			0
$436$	14.9837			0.717588
$437$	−22.3621	+	22.3621i	−1.06973	+	1.06973i
$438$	−13.3549	+	13.3549i	−0.638122	+	0.638122i
$439$			32.9765i			1.57388i	0.617028	+	0.786941i	$0.288336\pi$
$439$			32.9765i			1.57388i	−0.617028	+	0.786941i	$0.711664\pi$
$440$		0			0
$441$	30.2359			1.43981
$442$	15.1371	+	15.1371i	0.719996	+	0.719996i
$443$	−9.94617	+	9.94617i	−0.472557	+	0.472557i	−0.902741	−	0.430184i	$-0.858449\pi$
$443$	−9.94617	+	9.94617i	−0.472557	+	0.472557i	0.430184	+	0.902741i	$0.358449\pi$
$444$			76.0688i			3.61007i
$445$		0			0
$446$			51.4918i			2.43821i
$447$	12.9606	−	12.9606i	0.613017	−	0.613017i
$448$	6.16969	−	6.16969i	0.291490	−	0.291490i
$449$	−20.1746			−0.952098			−0.476049	−	0.879419i	$-0.657932\pi$
$449$	−20.1746			−0.952098			−0.476049	+	0.879419i	$0.657932\pi$
$450$		0			0
$451$		−	15.8622i		−	0.746923i
$452$	30.0847	+	30.0847i	1.41507	+	1.41507i
$453$	25.7776	−	25.7776i	1.21114	−	1.21114i
$454$			34.1733i			1.60383i
$455$		0			0
$456$			52.5942i			2.46295i
$457$	−9.25724	+	9.25724i	−0.433036	+	0.433036i	−0.889660	−	0.456624i	$-0.849058\pi$
$457$	−9.25724	+	9.25724i	−0.433036	+	0.433036i	0.456624	+	0.889660i	$0.349058\pi$
$458$	−26.9595	−	26.9595i	−1.25973	−	1.25973i
$459$			31.5584i			1.47302i
$460$		0			0
$461$			0.118779i			0.00553208i	0.999996	+	0.00276604i	$0.000880460\pi$
$461$			0.118779i			0.00553208i	−0.999996	+	0.00276604i	$0.999120\pi$
$462$	−23.2219	−	23.2219i	−1.08038	−	1.08038i
$463$	16.8112	+	16.8112i	0.781283	+	0.781283i	0.980047	−	0.198764i	$-0.0636929\pi$
$463$	16.8112	+	16.8112i	0.781283	+	0.781283i	−0.198764	+	0.980047i	$0.563693\pi$
$464$	−18.5397			−0.860686
$465$		0			0
$466$	69.6622			3.22704
$467$	−1.44225	−	1.44225i	−0.0667393	−	0.0667393i	0.672949	−	0.739689i	$-0.265027\pi$
$467$	−1.44225	−	1.44225i	−0.0667393	−	0.0667393i	−0.739689	+	0.672949i	$0.765027\pi$
$468$	23.4409	+	23.4409i	1.08356	+	1.08356i
$469$		−	10.1877i		−	0.470425i
$470$		0			0
$471$			17.6969i			0.815431i
$472$	−13.8186	−	13.8186i	−0.636051	−	0.636051i
$473$	9.95461	−	9.95461i	0.457714	−	0.457714i
$474$		−	17.8883i		−	0.821635i
$475$		0			0
$476$			21.6245i			0.991159i
$477$	18.3846	−	18.3846i	0.841771	−	0.841771i
$478$	16.4258	+	16.4258i	0.751298	+	0.751298i
$479$		−	27.3888i		−	1.25142i	−0.780054	−	0.625712i	$-0.784809\pi$
$479$		−	27.3888i		−	1.25142i	0.780054	−	0.625712i	$-0.215191\pi$
$480$		0			0
$481$	11.1384			0.507869
$482$	−5.62614	+	5.62614i	−0.256264	+	0.256264i
$483$	−16.8556	+	16.8556i	−0.766958	+	0.766958i
$484$		−	40.5672i		−	1.84396i
$485$		0			0
$486$		−	32.2944i		−	1.46490i
$487$	25.5876	−	25.5876i	1.15949	−	1.15949i	0.174901	−	0.984586i	$-0.444039\pi$
$487$	25.5876	−	25.5876i	1.15949	−	1.15949i	0.984586	−	0.174901i	$-0.0559605\pi$
$488$	28.3168	+	28.3168i	1.28184	+	1.28184i
$489$	26.0684			1.17886
$490$		0			0
$491$		−	22.0946i		−	0.997114i	−0.866857	−	0.498557i	$-0.833864\pi$
$491$		−	22.0946i		−	0.997114i	0.866857	−	0.498557i	$-0.166136\pi$
$492$	−27.3758	+	27.3758i	−1.23420	+	1.23420i
$493$	−18.6378	+	18.6378i	−0.839404	+	0.839404i
$494$	15.5710			0.700573
$495$		0			0
$496$	20.7319	+	2.20480i	0.930889	+	0.0989983i
$497$	−1.28268	−	1.28268i	−0.0575362	−	0.0575362i
$498$	10.3013	−	10.3013i	0.461612	−	0.461612i
$499$	32.0720			1.43574			0.717870	−	0.696177i	$-0.245117\pi$
$499$	32.0720			1.43574			0.717870	+	0.696177i	$0.245117\pi$
$500$		0			0
$501$	39.1325			1.74831
$502$	−25.7709	+	25.7709i	−1.15021	+	1.15021i
$503$	4.71184	−	4.71184i	0.210091	−	0.210091i	−0.594215	−	0.804306i	$-0.702537\pi$
$503$	4.71184	−	4.71184i	0.210091	−	0.210091i	0.804306	+	0.594215i	$0.202537\pi$
$504$			24.9330i			1.11061i
$505$		0			0
$506$	−91.8918			−4.08509
$507$	−20.6801	+	20.6801i	−0.918436	+	0.918436i
$508$	26.8733	+	26.8733i	1.19231	+	1.19231i
$509$	−10.2724			−0.455314			−0.227657	−	0.973741i	$-0.573107\pi$
$509$	−10.2724			−0.455314			−0.227657	+	0.973741i	$0.573107\pi$
$510$		0			0
$511$			2.79360i			0.123581i
$512$	−26.3925	−	26.3925i	−1.16640	−	1.16640i
$513$	16.2316	+	16.2316i	0.716641	+	0.716641i
$514$			62.4285i			2.75360i
$515$		0			0
$516$	−34.3603			−1.51263
$517$	6.69228	−	6.69228i	0.294326	−	0.294326i
$518$	11.9772	+	11.9772i	0.526250	+	0.526250i
$519$	9.97745			0.437961
$520$		0			0
$521$	12.0112			0.526219			0.263110	−	0.964766i	$-0.415252\pi$
$521$	12.0112			0.526219			0.263110	+	0.964766i	$0.415252\pi$
$522$	−43.4494	+	43.4494i	−1.90173	+	1.90173i
$523$	0.332002	+	0.332002i	0.0145175	+	0.0145175i	0.714328	−	0.699811i	$-0.246732\pi$
$523$	0.332002	+	0.332002i	0.0145175	+	0.0145175i	−0.699811	+	0.714328i	$0.746732\pi$
$524$			25.2499i			1.10304i
$525$		0			0
$526$			5.20514i			0.226955i
$527$	23.0580	−	18.6251i	1.00442	−	0.811321i
$528$	−34.7070	+	34.7070i	−1.51043	+	1.51043i
$529$			43.6997i			1.89999i
$530$		0			0
$531$	−20.8027			−0.902761
$532$	11.1222	+	11.1222i	0.482211	+	0.482211i
$533$	4.00853	+	4.00853i	0.173629	+	0.173629i
$534$		−	120.145i		−	5.19918i
$535$		0			0
$536$	−47.4079			−2.04771
$537$	21.6914	+	21.6914i	0.936052	+	0.936052i
$538$	−25.0459	−	25.0459i	−1.07980	−	1.07980i
$539$	27.4121			1.18072
$540$		0			0
$541$	6.49677			0.279318			0.139659	−	0.990200i	$-0.455399\pi$
$541$	6.49677			0.279318			0.139659	+	0.990200i	$0.455399\pi$
$542$	−36.8181	+	36.8181i	−1.58147	+	1.58147i
$543$	−43.3902	+	43.3902i	−1.86205	+	1.86205i
$544$	−2.20480			−0.0945299
$545$		0			0
$546$	11.7368			0.502287
$547$	−4.59357	−	4.59357i	−0.196407	−	0.196407i	0.602051	−	0.798458i	$-0.294350\pi$
$547$	−4.59357	−	4.59357i	−0.196407	−	0.196407i	−0.798458	+	0.602051i	$0.794350\pi$
$548$	1.26382	+	1.26382i	0.0539876	+	0.0539876i
$549$	42.6287			1.81935
$550$		0			0
$551$			19.1721i			0.816759i
$552$	78.4365	+	78.4365i	3.33848	+	3.33848i
$553$	−1.87095	−	1.87095i	−0.0795607	−	0.0795607i
$554$	−42.5694			−1.80860
$555$		0			0
$556$			49.3842i			2.09436i
$557$	20.6709	−	20.6709i	0.875856	−	0.875856i	−0.117247	−	0.993103i	$-0.537407\pi$
$557$	20.6709	−	20.6709i	0.875856	−	0.875856i	0.993103	+	0.117247i	$0.0374069\pi$
$558$	53.7540	−	43.4198i	2.27559	−	1.83811i
$559$			5.03124i			0.212799i
$560$		0			0
$561$			69.7812i			2.94616i
$562$	15.1184	+	15.1184i	0.637729	+	0.637729i
$563$	1.61068	−	1.61068i	0.0678823	−	0.0678823i	−0.672351	−	0.740233i	$-0.734715\pi$
$563$	1.61068	−	1.61068i	0.0678823	−	0.0678823i	0.740233	+	0.672351i	$0.234715\pi$
$564$	−23.0997			−0.972674
$565$		0			0
$566$	57.9311			2.43502
$567$	1.16216	+	1.16216i	0.0488060	+	0.0488060i
$568$	−5.96887	+	5.96887i	−0.250448	+	0.250448i
$569$	1.56604			0.0656518			0.0328259	−	0.999461i	$-0.489549\pi$
$569$	1.56604			0.0656518			0.0328259	+	0.999461i	$0.489549\pi$
$570$		0			0
$571$		−	33.8068i		−	1.41477i	−0.706829	−	0.707385i	$-0.749875\pi$
$571$		−	33.8068i		−	1.41477i	0.706829	−	0.707385i	$-0.250125\pi$
$572$	21.2517	+	21.2517i	0.888578	+	0.888578i
$573$	29.0418	+	29.0418i	1.21324	+	1.21324i
$574$			8.62080i			0.359825i
$575$		0			0
$576$	−43.2209			−1.80087
$577$	17.7303	+	17.7303i	0.738122	+	0.738122i	0.972214	−	0.234093i	$-0.0752119\pi$
$577$	17.7303	+	17.7303i	0.738122	+	0.738122i	−0.234093	+	0.972214i	$0.575212\pi$
$578$	19.5724	−	19.5724i	0.814106	−	0.814106i
$579$	−27.6908			−1.15079
$580$		0			0
$581$		−	2.15484i		−	0.0893979i
$582$	29.2348	−	29.2348i	1.21182	−	1.21182i
$583$	16.6676	−	16.6676i	0.690300	−	0.690300i
$584$	12.9998			0.537936
$585$		0			0
$586$	−23.2499			−0.960443
$587$	−0.235011	+	0.235011i	−0.00969994	+	0.00969994i	−0.711940	−	0.702240i	$-0.752183\pi$
$587$	−0.235011	+	0.235011i	−0.00969994	+	0.00969994i	0.702240	+	0.711940i	$0.252183\pi$
$588$	−47.3092	−	47.3092i	−1.95100	−	1.95100i
$589$	2.28000	−	21.4390i	0.0939458	−	0.883380i
$590$		0			0
$591$	−19.6576			−0.808605
$592$	17.9010	−	17.9010i	0.735726	−	0.735726i
$593$	−10.3736	+	10.3736i	−0.425993	+	0.425993i	−0.887261	−	0.461268i	$-0.847395\pi$
$593$	−10.3736	+	10.3736i	−0.425993	+	0.425993i	0.461268	+	0.887261i	$0.347395\pi$
$594$			66.6997i			2.73672i
$595$		0			0
$596$	−25.5085			−1.04487
$597$	13.2673	+	13.2673i	0.542994	+	0.542994i
$598$	23.2219	−	23.2219i	0.949614	−	0.949614i
$599$			12.8092i			0.523371i	0.965153	+	0.261685i	$0.0842783\pi$
$599$			12.8092i			0.523371i	−0.965153	+	0.261685i	$0.915722\pi$
$600$		0			0
$601$			0.0247071i			0.00100782i	1.00000		0.000503911i	$0.000160400\pi$
$601$			0.0247071i			0.00100782i	−1.00000		0.000503911i	$0.999840\pi$
$602$	−5.41013	+	5.41013i	−0.220501	+	0.220501i
$603$	−35.6843	+	35.6843i	−1.45318	+	1.45318i
$604$	−50.7342			−2.06435
$605$		0			0
$606$			21.7433i			0.883262i
$607$	20.1563	+	20.1563i	0.818121	+	0.818121i	0.985836	−	0.167715i	$-0.0536388\pi$
$607$	20.1563	+	20.1563i	0.818121	+	0.818121i	−0.167715	+	0.985836i	$0.553639\pi$
$608$	−1.13400	+	1.13400i	−0.0459899	+	0.0459899i
$609$			14.4511i			0.585589i
$610$		0			0
$611$			3.38240i			0.136837i
$612$	75.7438	−	75.7438i	3.06176	−	3.06176i
$613$	−24.8253	−	24.8253i	−1.00269	−	1.00269i	−0.999996	−	0.00268986i	$-0.999144\pi$
$613$	−24.8253	−	24.8253i	−1.00269	−	1.00269i	−0.00268986	−	0.999996i	$-0.500856\pi$
$614$			67.1171i			2.70862i
$615$		0			0
$616$			22.6045i			0.910760i
$617$	−23.5989	−	23.5989i	−0.950057	−	0.950057i	0.0487537	−	0.998811i	$-0.484475\pi$
$617$	−23.5989	−	23.5989i	−0.950057	−	0.950057i	−0.998811	+	0.0487537i	$0.984475\pi$
$618$	35.4292	+	35.4292i	1.42517	+	1.42517i
$619$	−17.3911			−0.699006			−0.349503	−	0.936935i	$-0.613650\pi$
$619$	−17.3911			−0.699006			−0.349503	+	0.936935i	$0.613650\pi$
$620$		0			0
$621$	48.4140			1.94279
$622$	1.09957	+	1.09957i	0.0440887	+	0.0440887i
$623$	−12.5660	−	12.5660i	−0.503448	−	0.503448i
$624$		−	17.5416i		−	0.702225i
$625$		0			0
$626$		−	31.7744i		−	1.26996i
$627$	35.8909	+	35.8909i	1.43334	+	1.43334i
$628$	17.4151	−	17.4151i	0.694938	−	0.694938i
$629$		−	35.9913i		−	1.43507i
$630$		0			0
$631$			2.70007i			0.107488i	0.998555	+	0.0537440i	$0.0171155\pi$
$631$			2.70007i			0.107488i	−0.998555	+	0.0537440i	$0.982885\pi$
$632$	−8.70631	+	8.70631i	−0.346319	+	0.346319i
$633$	27.3323	+	27.3323i	1.08636	+	1.08636i
$634$		−	19.7288i		−	0.783532i
$635$		0			0
$636$	−57.5315			−2.28127
$637$	−6.92729	+	6.92729i	−0.274469	+	0.274469i
$638$	−39.3916	+	39.3916i	−1.55953	+	1.55953i
$639$			8.98565i			0.355467i
$640$		0			0
$641$			2.03236i			0.0802736i	0.999194	+	0.0401368i	$0.0127794\pi$
$641$			2.03236i			0.0802736i	−0.999194	+	0.0401368i	$0.987221\pi$
$642$	−37.7907	+	37.7907i	−1.49148	+	1.49148i
$643$	−20.6991	−	20.6991i	−0.816293	−	0.816293i	0.169276	−	0.985569i	$-0.445857\pi$
$643$	−20.6991	−	20.6991i	−0.816293	−	0.816293i	−0.985569	+	0.169276i	$0.945857\pi$
$644$	33.1744			1.30725
$645$		0			0
$646$		−	50.3142i		−	1.97958i
$647$	20.3153	−	20.3153i	0.798677	−	0.798677i	−0.184210	−	0.982887i	$-0.558973\pi$
$647$	20.3153	−	20.3153i	0.798677	−	0.798677i	0.982887	+	0.184210i	$0.0589727\pi$
$648$	5.40802	−	5.40802i	0.212447	−	0.212447i
$649$	−18.8599			−0.740315
$650$		0			0
$651$	1.71857	−	16.1598i	0.0673559	−	0.633353i
$652$	−25.6533	−	25.6533i	−1.00466	−	1.00466i
$653$	19.1877	−	19.1877i	0.750872	−	0.750872i	−0.223770	−	0.974642i	$-0.571837\pi$
$653$	19.1877	−	19.1877i	0.750872	−	0.750872i	0.974642	+	0.223770i	$0.0718366\pi$
$654$	−26.2781			−1.02755
$655$		0			0
$656$	12.8845			0.503055
$657$	9.78508	−	9.78508i	0.381752	−	0.381752i
$658$	−3.63712	+	3.63712i	−0.141790	+	0.141790i
$659$			43.2592i			1.68514i	0.538588	+	0.842569i	$0.318958\pi$
$659$			43.2592i			1.68514i	−0.538588	+	0.842569i	$0.681042\pi$
$660$		0			0
$661$	−17.3091			−0.673247			−0.336623	−	0.941639i	$-0.609285\pi$
$661$	−17.3091			−0.673247			−0.336623	+	0.941639i	$0.609285\pi$
$662$	−15.0258	+	15.0258i	−0.583994	+	0.583994i
$663$	−17.6343	−	17.6343i	−0.684861	−	0.684861i
$664$	−10.0274			−0.389139
$665$		0			0
$666$		−	83.9049i		−	3.25125i
$667$	28.5924	+	28.5924i	1.10710	+	1.10710i
$668$	−38.5093	−	38.5093i	−1.48997	−	1.48997i
$669$		−	59.9868i		−	2.31922i
$670$		0			0
$671$	38.6474			1.49197
$672$	−0.854763	+	0.854763i	−0.0329732	+	0.0329732i
$673$	18.3375	+	18.3375i	0.706860	+	0.706860i	0.965874	−	0.259014i	$-0.0833976\pi$
$673$	18.3375	+	18.3375i	0.706860	+	0.706860i	−0.259014	+	0.965874i	$0.583398\pi$
$674$	0.265962			0.0102445
$675$		0			0
$676$	40.7016			1.56544
$677$	−14.5640	+	14.5640i	−0.559740	+	0.559740i	−0.929233	−	0.369493i	$-0.879531\pi$
$677$	−14.5640	+	14.5640i	−0.559740	+	0.559740i	0.369493	+	0.929233i	$0.379531\pi$
$678$	−52.7620	−	52.7620i	−2.02631	−	2.02631i
$679$		−	6.11539i		−	0.234687i
$680$		0			0
$681$		−	39.8112i		−	1.52557i
$682$	48.7338	−	39.3647i	1.86611	−	1.50735i
$683$	−25.6152	+	25.6152i	−0.980140	+	0.980140i	−0.999807	−	0.0196666i	$-0.993740\pi$
$683$	−25.6152	+	25.6152i	−0.980140	+	0.980140i	0.0196666	+	0.999807i	$0.493740\pi$
$684$		−	77.9153i		−	2.97917i
$685$		0			0
$686$	−32.4359			−1.23841
$687$	31.4072	+	31.4072i	1.19826	+	1.19826i
$688$	8.08588	+	8.08588i	0.308271	+	0.308271i
$689$			8.42410i			0.320933i
$690$		0			0
$691$	0.422947			0.0160897			0.00804483	−	0.999968i	$-0.497439\pi$
$691$	0.422947			0.0160897			0.00804483	+	0.999968i	$0.497439\pi$
$692$	−9.81856	−	9.81856i	−0.373246	−	0.373246i
$693$	17.0146	+	17.0146i	0.646331	+	0.646331i
$694$	27.7161			1.05209
$695$		0			0
$696$	67.2473			2.54900
$697$	12.9526	−	12.9526i	0.490616	−	0.490616i
$698$	−30.2609	+	30.2609i	−1.14539	+	1.14539i
$699$	−81.1549			−3.06956
$700$		0			0
$701$	34.0152			1.28474			0.642369	−	0.766396i	$-0.277952\pi$
$701$	34.0152			1.28474			0.642369	+	0.766396i	$0.277952\pi$
$702$	−16.8556	−	16.8556i	−0.636175	−	0.636175i
$703$	−18.5116	−	18.5116i	−0.698177	−	0.698177i
$704$	−39.1844			−1.47682
$705$		0			0
$706$			65.9604i			2.48245i
$707$	2.27415	+	2.27415i	0.0855282	+	0.0855282i
$708$	32.5493	+	32.5493i	1.22328	+	1.22328i
$709$	−17.7538			−0.666758			−0.333379	−	0.942793i	$-0.608189\pi$
$709$	−17.7538			−0.666758			−0.333379	+	0.942793i	$0.608189\pi$
$710$		0			0
$711$			13.1066i			0.491538i
$712$	−58.4752	+	58.4752i	−2.19145	+	2.19145i
$713$	−28.5729	−	35.3735i	−1.07006	−	1.32475i
$714$		−	37.9247i		−	1.41929i
$715$		0			0
$716$		−	42.6919i		−	1.59547i
$717$	−19.1357	−	19.1357i	−0.714635	−	0.714635i
$718$	49.4334	−	49.4334i	1.84484	−	1.84484i
$719$	34.5808			1.28965			0.644823	−	0.764332i	$-0.276931\pi$
$719$	34.5808			1.28965			0.644823	+	0.764332i	$0.276931\pi$
$720$		0			0
$721$	7.41112			0.276005
$722$	6.91285	+	6.91285i	0.257270	+	0.257270i
$723$	6.55433	−	6.55433i	0.243758	−	0.243758i
$724$	85.3985			3.17381
$725$		0			0
$726$			71.1458i			2.64047i
$727$	−15.5070	−	15.5070i	−0.575124	−	0.575124i	0.358432	−	0.933556i	$-0.383311\pi$
$727$	−15.5070	−	15.5070i	−0.575124	−	0.575124i	−0.933556	+	0.358432i	$0.883311\pi$
$728$	−5.71235	−	5.71235i	−0.211714	−	0.211714i
$729$			42.4255i			1.57132i
$730$		0			0
$731$	16.2573			0.601298
$732$	−66.6997	−	66.6997i	−2.46529	−	2.46529i
$733$	17.9493	−	17.9493i	0.662974	−	0.662974i	−0.293106	−	0.956080i	$-0.594689\pi$
$733$	17.9493	−	17.9493i	0.662974	−	0.662974i	0.956080	+	0.293106i	$0.0946889\pi$
$734$	42.7854			1.57924
$735$		0			0
$736$			3.38240i			0.124677i
$737$	−32.3517	+	32.3517i	−1.19169	+	1.19169i
$738$	30.1959	−	30.1959i	1.11153	−	1.11153i
$739$	36.3119			1.33575			0.667877	−	0.744272i	$-0.267203\pi$
$739$	36.3119			1.33575			0.667877	+	0.744272i	$0.267203\pi$
$740$		0			0
$741$	−18.1399			−0.666386
$742$	−9.05849	+	9.05849i	−0.332548	+	0.332548i
$743$	−14.8006	−	14.8006i	−0.542982	−	0.542982i	0.381420	−	0.924402i	$-0.375435\pi$
$743$	−14.8006	−	14.8006i	−0.542982	−	0.542982i	−0.924402	+	0.381420i	$0.875435\pi$
$744$	−75.1986	−	7.99723i	−2.75692	−	0.293193i
$745$		0			0
$746$	−17.9493			−0.657172
$747$	−7.54772	+	7.54772i	−0.276157	+	0.276157i
$748$	68.6699	−	68.6699i	2.51082	−	2.51082i
$749$			7.90512i			0.288847i
$750$		0			0
$751$	15.2911			0.557981			0.278991	−	0.960294i	$-0.410000\pi$
$751$	15.2911			0.557981			0.278991	+	0.960294i	$0.410000\pi$
$752$	5.43597	+	5.43597i	0.198229	+	0.198229i
$753$	30.0225	−	30.0225i	1.09408	−	1.09408i
$754$		−	19.9092i		−	0.725051i
$755$		0			0
$756$		−	24.0797i		−	0.875769i
$757$	−23.7167	+	23.7167i	−0.861998	+	0.861998i	−0.991570	−	0.129572i	$-0.958640\pi$
$757$	−23.7167	+	23.7167i	−0.861998	+	0.861998i	0.129572	+	0.991570i	$0.458640\pi$
$758$	−19.1237	+	19.1237i	−0.694605	+	0.694605i
$759$	107.052			3.88574
$760$		0			0
$761$			28.8937i			1.04739i	0.851904	+	0.523697i	$0.175448\pi$
$761$			28.8937i			1.04739i	−0.851904	+	0.523697i	$0.824552\pi$
$762$	−47.1297	−	47.1297i	−1.70733	−	1.70733i
$763$	−2.74844	+	2.74844i	−0.0995003	+	0.0995003i
$764$		−	57.1586i		−	2.06793i
$765$		0			0
$766$		−	14.6846i		−	0.530577i
$767$	4.76607	−	4.76607i	0.172093	−	0.172093i
$768$	63.5616	+	63.5616i	2.29358	+	2.29358i
$769$			19.1831i			0.691761i	0.938279	+	0.345880i	$0.112420\pi$
$769$			19.1831i			0.691761i	−0.938279	+	0.345880i	$0.887580\pi$
$770$		0			0
$771$		−	72.7279i		−	2.61923i
$772$	27.2499	+	27.2499i	0.980744	+	0.980744i
$773$	6.79750	+	6.79750i	0.244489	+	0.244489i	0.818704	−	0.574215i	$-0.194693\pi$
$773$	6.79750	+	6.79750i	0.244489	+	0.244489i	−0.574215	+	0.818704i	$0.694693\pi$
$774$	37.8999			1.36228
$775$		0			0
$776$	−28.4575			−1.02157
$777$	−13.9532	−	13.9532i	−0.500569	−	0.500569i
$778$	45.4382	+	45.4382i	1.62904	+	1.62904i
$779$		−	13.3240i		−	0.477381i
$780$		0			0
$781$			8.14646i			0.291503i
$782$	−75.0362	−	75.0362i	−2.68329	−	2.68329i
$783$	20.7538	−	20.7538i	0.741680	−	0.741680i
$784$			22.2662i			0.795220i
$785$		0			0
$786$		−	44.2827i		−	1.57951i
$787$	−32.9894	+	32.9894i	−1.17594	+	1.17594i	−0.195175	+	0.980768i	$0.562527\pi$
$787$	−32.9894	+	32.9894i	−1.17594	+	1.17594i	−0.980768	+	0.195175i	$0.937473\pi$
$788$	19.3445	+	19.3445i	0.689121	+	0.689121i
$789$		−	6.06387i		−	0.215879i
$790$		0			0
$791$	−11.0368			−0.392424
$792$	79.1762	−	79.1762i	2.81340	−	2.81340i
$793$	−9.76656	+	9.76656i	−0.346821	+	0.346821i
$794$			60.5092i			2.14739i
$795$		0			0
$796$		−	26.1120i		−	0.925516i
$797$	34.1161	−	34.1161i	1.20845	−	1.20845i	0.236925	−	0.971528i	$-0.423860\pi$
$797$	34.1161	−	34.1161i	1.20845	−	1.20845i	0.971528	−	0.236925i	$-0.0761396\pi$
$798$	−19.5060	−	19.5060i	−0.690504	−	0.690504i
$799$	10.9294			0.386656
$800$		0			0
$801$			88.0297i			3.11038i
$802$	52.1351	−	52.1351i	1.84096	−	1.84096i
$803$	8.87122	−	8.87122i	0.313059	−	0.313059i
$804$	111.668			3.93824
$805$		0			0
$806$	−2.36766	+	22.2633i	−0.0833973	+	0.784191i
$807$	29.1779	+	29.1779i	1.02711	+	1.02711i
$808$	10.5826	−	10.5826i	0.372294	−	0.372294i
$809$	−26.7444			−0.940283			−0.470141	−	0.882591i	$-0.655797\pi$
$809$	−26.7444			−0.940283			−0.470141	+	0.882591i	$0.655797\pi$
$810$		0			0
$811$	24.4227			0.857597			0.428799	−	0.903400i	$-0.358937\pi$
$811$	24.4227			0.857597			0.428799	+	0.903400i	$0.358937\pi$
$812$	14.2210	−	14.2210i	0.499059	−	0.499059i
$813$	42.8923	−	42.8923i	1.50430	−	1.50430i
$814$		−	76.0688i		−	2.66621i
$815$		0			0
$816$	−56.6815			−1.98425
$817$	8.36169	−	8.36169i	0.292538	−	0.292538i
$818$	61.7778	+	61.7778i	2.16001	+	2.16001i
$819$	−8.59948			−0.300490
$820$		0			0
$821$			51.1437i			1.78493i	0.451120	+	0.892463i	$0.351025\pi$
$821$			51.1437i			1.78493i	−0.451120	+	0.892463i	$0.648975\pi$
$822$	−2.21646	−	2.21646i	−0.0773078	−	0.0773078i
$823$	−12.7304	−	12.7304i	−0.443753	−	0.443753i	0.449518	−	0.893271i	$-0.351596\pi$
$823$	−12.7304	−	12.7304i	−0.443753	−	0.443753i	−0.893271	+	0.449518i	$0.851596\pi$
$824$		−	34.4871i		−	1.20142i
$825$		0			0
$826$	10.2500			0.356642
$827$	−38.0359	+	38.0359i	−1.32264	+	1.32264i	−0.411002	+	0.911635i	$0.634821\pi$
$827$	−38.0359	+	38.0359i	−1.32264	+	1.32264i	−0.911635	+	0.411002i	$0.865179\pi$
$828$	−116.199	−	116.199i	−4.03821	−	4.03821i
$829$	−38.9867			−1.35406			−0.677032	−	0.735954i	$-0.736734\pi$
$829$	−38.9867			−1.35406			−0.677032	+	0.735954i	$0.736734\pi$
$830$		0			0
$831$	49.5924			1.72034
$832$	9.90224	−	9.90224i	0.343299	−	0.343299i
$833$	22.3839	+	22.3839i	0.775557	+	0.775557i
$834$		−	86.6089i		−	2.99902i
$835$		0			0
$836$		−	70.6386i		−	2.44309i
$837$	−25.6758	+	20.7396i	−0.887487	+	0.716867i
$838$	38.7668	−	38.7668i	1.33918	−	1.33918i
$839$		−	35.2740i		−	1.21780i	−0.793249	−	0.608898i	$-0.791612\pi$
$839$		−	35.2740i		−	1.21780i	0.793249	−	0.608898i	$-0.208388\pi$
$840$		0			0
$841$	−4.48640			−0.154703
$842$	−53.6584	−	53.6584i	−1.84919	−	1.84919i
$843$	−17.6125	−	17.6125i	−0.606608	−	0.606608i
$844$		−	53.7940i		−	1.85167i
$845$		0			0
$846$	25.4793			0.875997
$847$	7.44119	+	7.44119i	0.255682	+	0.255682i
$848$	13.5387	+	13.5387i	0.464919	+	0.464919i
$849$	−67.4884			−2.31620
$850$		0			0
$851$	−55.2146			−1.89273
$852$	14.0596	−	14.0596i	0.481673	−	0.481673i
$853$	−0.443168	+	0.443168i	−0.0151738	+	0.0151738i	−0.714653	−	0.699479i	$-0.753415\pi$
$853$	−0.443168	+	0.443168i	−0.0151738	+	0.0151738i	0.699479	+	0.714653i	$0.253415\pi$
$854$	−21.0041			−0.718746
$855$		0			0
$856$	36.7859			1.25732
$857$	37.9536	+	37.9536i	1.29647	+	1.29647i	0.930708	+	0.365764i	$0.119192\pi$
$857$	37.9536	+	37.9536i	1.29647	+	1.29647i	0.365764	+	0.930708i	$0.380808\pi$
$858$	−37.2708	−	37.2708i	−1.27240	−	1.27240i
$859$	−31.5767			−1.07738			−0.538692	−	0.842503i	$-0.681081\pi$
$859$	−31.5767			−1.07738			−0.538692	+	0.842503i	$0.681081\pi$
$860$		0			0
$861$		−	10.0430i		−	0.342266i
$862$	54.1436	+	54.1436i	1.84414	+	1.84414i
$863$	16.0029	+	16.0029i	0.544746	+	0.544746i	0.924917	−	0.380170i	$-0.124135\pi$
$863$	16.0029	+	16.0029i	0.544746	+	0.544746i	−0.380170	+	0.924917i	$0.624135\pi$
$864$	2.45511			0.0835247
$865$		0			0
$866$			34.3956i			1.16881i
$867$	−22.8015	+	22.8015i	−0.774378	+	0.774378i
$868$	−17.5937	+	14.2113i	−0.597168	+	0.482362i
$869$			11.8826i			0.403089i
$870$		0			0
$871$		−	16.3511i		−	0.554037i
$872$	12.7897	+	12.7897i	0.433113	+	0.433113i
$873$	−21.4202	+	21.4202i	−0.724965	+	0.724965i
$874$	−77.1874			−2.61090
$875$		0			0
$876$	−30.6208			−1.03458
$877$	−33.4411	−	33.4411i	−1.12922	−	1.12922i	−0.990303	−	0.138922i	$-0.955636\pi$
$877$	−33.4411	−	33.4411i	−1.12922	−	1.12922i	−0.138922	−	0.990303i	$-0.544364\pi$
$878$	−56.9125	+	56.9125i	−1.92070	+	1.92070i
$879$	27.0856			0.913573
$880$		0			0
$881$		−	9.04110i		−	0.304602i	−0.988334	−	0.152301i	$-0.951332\pi$
$881$		−	9.04110i		−	0.304602i	0.988334	−	0.152301i	$-0.0486684\pi$
$882$	52.1827	+	52.1827i	1.75708	+	1.75708i
$883$	24.0442	+	24.0442i	0.809151	+	0.809151i	0.984505	−	0.175354i	$-0.0561072\pi$
$883$	24.0442	+	24.0442i	0.809151	+	0.809151i	−0.175354	+	0.984505i	$0.556107\pi$
$884$			34.7070i			1.16732i
$885$		0			0
$886$	−34.3312			−1.15338
$887$	−22.6555	−	22.6555i	−0.760697	−	0.760697i	0.215752	−	0.976448i	$-0.430780\pi$
$887$	−22.6555	−	22.6555i	−0.760697	−	0.760697i	−0.976448	+	0.215752i	$0.930780\pi$
$888$	−64.9304	+	64.9304i	−2.17892	+	2.17892i
$889$	−9.85867			−0.330649
$890$		0			0
$891$		−	7.38099i		−	0.247272i
$892$	−59.0315	+	59.0315i	−1.97652	+	1.97652i
$893$	5.62139	−	5.62139i	0.188113	−	0.188113i
$894$	44.7362			1.49620
$895$		0			0
$896$	20.4456			0.683041
$897$	−27.0530	+	27.0530i	−0.903273	+	0.903273i
$898$	−34.8183	−	34.8183i	−1.16190	−	1.16190i
$899$	−27.4121	−	2.91523i	−0.914245	−	0.0972282i
$900$		0			0
$901$	27.2205			0.906847
$902$	27.3758	−	27.3758i	0.911516	−	0.911516i
$903$	6.30268	−	6.30268i	0.209740	−	0.209740i
$904$			51.3591i			1.70818i
$905$		0			0
$906$	88.9766			2.95605
$907$	−34.3272	−	34.3272i	−1.13981	−	1.13981i	−0.988483	−	0.151332i	$-0.951644\pi$
$907$	−34.3272	−	34.3272i	−1.13981	−	1.13981i	−0.151332	−	0.988483i	$-0.548356\pi$
$908$	−39.1772	+	39.1772i	−1.30014	+	1.30014i
$909$		−	15.9312i		−	0.528406i
$910$		0			0
$911$		−	26.2908i		−	0.871054i	−0.900176	−	0.435527i	$-0.856562\pi$
$911$		−	26.2908i		−	0.871054i	0.900176	−	0.435527i	$-0.143438\pi$
$912$	−29.1533	+	29.1533i	−0.965361	+	0.965361i
$913$	−6.84282	+	6.84282i	−0.226464	+	0.226464i
$914$	−31.9532			−1.05692
$915$		0			0
$916$		−	61.8141i		−	2.04239i
$917$	−4.63156	−	4.63156i	−0.152947	−	0.152947i
$918$	−54.4651	+	54.4651i	−1.79761	+	1.79761i
$919$			24.7367i			0.815989i	0.912984	+	0.407994i	$0.133772\pi$
$919$			24.7367i			0.815989i	−0.912984	+	0.407994i	$0.866228\pi$
$920$		0			0
$921$		−	78.1899i		−	2.57644i
$922$	−0.204995	+	0.204995i	−0.00675114	+	0.00675114i
$923$	−2.05868	−	2.05868i	−0.0677624	−	0.0677624i
$924$		−	53.2444i		−	1.75161i
$925$		0			0
$926$			58.0272i			1.90689i
$927$	−25.9588	−	25.9588i	−0.852599	−	0.852599i
$928$	1.44994	+	1.44994i	0.0475968	+	0.0475968i
$929$	−58.3812			−1.91542			−0.957712	−	0.287728i	$-0.907100\pi$
$929$	−58.3812			−1.91542			−0.957712	+	0.287728i	$0.907100\pi$
$930$		0			0
$931$	23.0256			0.754635
$932$	79.8625	+	79.8625i	2.61598	+	2.61598i
$933$	−1.28097	−	1.28097i	−0.0419372	−	0.0419372i
$934$		−	4.97821i		−	0.162892i
$935$		0			0
$936$			40.0171i			1.30800i
$937$	29.8420	+	29.8420i	0.974897	+	0.974897i	0.999693	−	0.0247956i	$-0.00789351\pi$
$937$	29.8420	+	29.8420i	0.974897	+	0.974897i	−0.0247956	+	0.999693i	$0.507894\pi$
$938$	17.5825	−	17.5825i	0.574088	−	0.574088i
$939$			37.0165i			1.20799i
$940$		0			0
$941$		−	11.0363i		−	0.359772i	−0.983687	−	0.179886i	$-0.942427\pi$
$941$		−	11.0363i		−	0.359772i	0.983687	−	0.179886i	$-0.0575729\pi$
$942$	−30.5422	+	30.5422i	−0.995120	+	0.995120i
$943$	−19.8708	−	19.8708i	−0.647081	−	0.647081i
$944$		−	15.3194i		−	0.498605i
$945$		0			0
$946$	34.3603			1.11715
$947$	11.2378	−	11.2378i	0.365180	−	0.365180i	−0.500536	−	0.865716i	$-0.666864\pi$
$947$	11.2378	−	11.2378i	0.365180	−	0.365180i	0.865716	+	0.500536i	$0.166864\pi$
$948$	20.5076	−	20.5076i	0.666054	−	0.666054i
$949$			4.48368i			0.145546i
$950$		0			0
$951$			22.9836i			0.745296i
$952$	−18.4581	+	18.4581i	−0.598232	+	0.598232i
$953$	−38.4875	−	38.4875i	−1.24673	−	1.24673i	−0.957154	−	0.289580i	$-0.906484\pi$
$953$	−38.4875	−	38.4875i	−1.24673	−	1.24673i	−0.289580	−	0.957154i	$-0.593516\pi$
$954$	63.4580			2.05453
$955$		0			0
$956$			37.6619i			1.21807i
$957$	45.8903	−	45.8903i	1.48342	−	1.48342i
$958$	47.2689	−	47.2689i	1.52719	−	1.52719i
$959$	−0.463642			−0.0149718
$960$		0			0
$961$	30.3066	+	6.51984i	0.977633	+	0.210318i
$962$	19.2233	+	19.2233i	0.619784	+	0.619784i
$963$	27.6891	−	27.6891i	0.892269	−	0.892269i
$964$	−12.8999			−0.415478
$965$		0			0
$966$	−58.1806			−1.87193
$967$	20.2981	−	20.2981i	0.652744	−	0.652744i	−0.300909	−	0.953653i	$-0.597290\pi$
$967$	20.2981	−	20.2981i	0.652744	−	0.652744i	0.953653	+	0.300909i	$0.0972899\pi$
$968$	34.6271	−	34.6271i	1.11296	−	1.11296i
$969$			58.6149i			1.88298i
$970$		0			0
$971$	47.7296			1.53171			0.765857	−	0.643010i	$-0.222315\pi$
$971$	47.7296			1.53171			0.765857	+	0.643010i	$0.222315\pi$
$972$	37.0231	−	37.0231i	1.18752	−	1.18752i
$973$	−9.05849	−	9.05849i	−0.290402	−	0.290402i
$974$	88.3209			2.82998
$975$		0			0
$976$			31.3924i			1.00485i
$977$	0.0611284	+	0.0611284i	0.00195567	+	0.00195567i	0.708084	−	0.706128i	$-0.249560\pi$
$977$	0.0611284	+	0.0611284i	0.00195567	+	0.00195567i	−0.706128	+	0.708084i	$0.749560\pi$
$978$	44.9902	+	44.9902i	1.43863	+	1.43863i
$979$			79.8084i			2.55069i
$980$		0			0
$981$	19.2538			0.614727
$982$	38.1319	−	38.1319i	1.21684	−	1.21684i
$983$	33.5782	+	33.5782i	1.07098	+	1.07098i	0.997281	+	0.0736960i	$0.0234795\pi$
$983$	33.5782	+	33.5782i	1.07098	+	1.07098i	0.0736960	+	0.997281i	$0.476521\pi$
$984$	−46.7346			−1.48985
$985$		0			0
$986$	−64.3321			−2.04875
$987$	4.23716	−	4.23716i	0.134870	−	0.134870i
$988$	17.8510	+	17.8510i	0.567917	+	0.567917i
$989$		−	24.9405i		−	0.793061i
$990$		0			0
$991$			5.98524i			0.190127i	0.995471	+	0.0950637i	$0.0303055\pi$
$991$			5.98524i			0.190127i	−0.995471	+	0.0950637i	$0.969695\pi$
$992$	−1.44895	−	1.79382i	−0.0460044	−	0.0569538i
$993$	17.5047	−	17.5047i	0.555495	−	0.555495i
$994$		−	4.42744i		−	0.140430i
$995$		0			0
$996$	23.6194			0.748408
$997$	−2.00284	−	2.00284i	−0.0634305	−	0.0634305i	0.674680	−	0.738110i	$-0.264282\pi$
$997$	−2.00284	−	2.00284i	−0.0634305	−	0.0634305i	−0.738110	+	0.674680i	$0.764282\pi$
$998$	55.3515	+	55.3515i	1.75212	+	1.75212i
$999$			40.0775i			1.26800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.f.f.557.7		16
5.2	odd	4		155.2.f.b.123.1	yes	16
5.3	odd	4	inner	775.2.f.f.743.8		16
5.4	even	2		155.2.f.b.92.2	yes	16
31.30	odd	2	inner	775.2.f.f.557.8		16
155.92	even	4		155.2.f.b.123.2	yes	16
155.123	even	4	inner	775.2.f.f.743.7		16
155.154	odd	2		155.2.f.b.92.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.f.b.92.1	✓	16	155.154	odd	2
155.2.f.b.92.2	yes	16	5.4	even	2
155.2.f.b.123.1	yes	16	5.2	odd	4
155.2.f.b.123.2	yes	16	155.92	even	4
775.2.f.f.557.7		16	1.1	even	1	trivial
775.2.f.f.557.8		16	31.30	odd	2	inner
775.2.f.f.743.7		16	155.123	even	4	inner
775.2.f.f.743.8		16	5.3	odd	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72585 + 1.72585i) q^{2} +(-2.01058 - 2.01058i) q^{3} +3.95712i q^{4} -6.93991i q^{6} +(-0.725850 - 0.725850i) q^{7} +(-3.37769 + 3.37769i) q^{8} +5.08484i q^{9} +O(q^{10})\)	\(q+(1.72585 + 1.72585i) q^{2} +(-2.01058 - 2.01058i) q^{3} +3.95712i q^{4} -6.93991i q^{6} +(-0.725850 - 0.725850i) q^{7} +(-3.37769 + 3.37769i) q^{8} +5.08484i q^{9} +4.60996i q^{11} +(7.95609 - 7.95609i) q^{12} +(-1.16498 - 1.16498i) q^{13} -2.50542i q^{14} -3.74455 q^{16} +(-3.76436 + 3.76436i) q^{17} +(-8.77568 + 8.77568i) q^{18} +3.87228i q^{19} +2.91876i q^{21} +(-7.95609 + 7.95609i) q^{22} +(5.77493 + 5.77493i) q^{23} +13.5822 q^{24} -4.02115i q^{26} +(4.19174 - 4.19174i) q^{27} +(2.87228 - 2.87228i) q^{28} +4.95112 q^{29} +(-5.53654 - 0.588801i) q^{31} +(0.292852 + 0.292852i) q^{32} +(9.26867 - 9.26867i) q^{33} -12.9934 q^{34} -20.1213 q^{36} +(-4.78054 + 4.78054i) q^{37} +(-6.68297 + 6.68297i) q^{38} +4.68456i q^{39} -3.44086 q^{41} +(-5.03734 + 5.03734i) q^{42} +(-2.15937 - 2.15937i) q^{43} -18.2421 q^{44} +19.9333i q^{46} +(-1.45170 - 1.45170i) q^{47} +(7.52871 + 7.52871i) q^{48} -5.94628i q^{49} +15.1371 q^{51} +(4.60996 - 4.60996i) q^{52} +(-3.61556 - 3.61556i) q^{53} +14.4686 q^{54} +4.90340 q^{56} +(7.78551 - 7.78551i) q^{57} +(8.54489 + 8.54489i) q^{58} +4.09112i q^{59} -8.38348i q^{61} +(-8.53906 - 10.5714i) q^{62} +(3.69083 - 3.69083i) q^{63} +8.49994i q^{64} +31.9927 q^{66} +(7.01778 + 7.01778i) q^{67} +(-14.8960 - 14.8960i) q^{68} -23.2219i q^{69} +1.76714 q^{71} +(-17.1750 - 17.1750i) q^{72} +(-1.92436 - 1.92436i) q^{73} -16.5010 q^{74} -15.3231 q^{76} +(3.34614 - 3.34614i) q^{77} +(-8.08484 + 8.08484i) q^{78} +2.57759 q^{79} -1.60110 q^{81} +(-5.93842 - 5.93842i) q^{82} +(1.48436 + 1.48436i) q^{83} -11.5499 q^{84} -7.45351i q^{86} +(-9.95461 - 9.95461i) q^{87} +(-15.5710 - 15.5710i) q^{88} +17.3122 q^{89} +1.69120i q^{91} +(-22.8521 + 22.8521i) q^{92} +(9.94782 + 12.3155i) q^{93} -5.01084i q^{94} -1.17760i q^{96} +(4.21257 + 4.21257i) q^{97} +(10.2624 - 10.2624i) q^{98} -23.4409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 12 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 + 12 * q^7 - 16 * q^8	\( 16 q + 4 q^{2} + 12 q^{7} - 16 q^{8} - 16 q^{18} + 16 q^{28} - 16 q^{31} - 8 q^{32} + 44 q^{33} - 88 q^{36} - 28 q^{38} - 24 q^{41} + 24 q^{47} - 32 q^{51} - 16 q^{56} - 44 q^{62} - 40 q^{63} + 112 q^{66} - 60 q^{67} + 72 q^{71} - 80 q^{72} - 32 q^{76} - 104 q^{78} + 24 q^{81} - 76 q^{82} + 20 q^{87} + 60 q^{93} + 72 q^{97} + 68 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 + 12 * q^7 - 16 * q^8 - 16 * q^18 + 16 * q^28 - 16 * q^31 - 8 * q^32 + 44 * q^33 - 88 * q^36 - 28 * q^38 - 24 * q^41 + 24 * q^47 - 32 * q^51 - 16 * q^56 - 44 * q^62 - 40 * q^63 + 112 * q^66 - 60 * q^67 + 72 * q^71 - 80 * q^72 - 32 * q^76 - 104 * q^78 + 24 * q^81 - 76 * q^82 + 20 * q^87 + 60 * q^93 + 72 * q^97 + 68 * q^98

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