LMFDB - Embedded newform 76.2.i.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Root			$2.25236 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	76.25
Dual form			76.2.i.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456991 + 0.166331i) q^{3} +(0.485063 + 2.75093i) q^{5} +(1.68285 - 2.91479i) q^{7} +(-2.11696 - 1.77634i) q^{9} +O(q^{10})$	\(q+(0.456991 + 0.166331i) q^{3} +(0.485063 + 2.75093i) q^{5} +(1.68285 - 2.91479i) q^{7} +(-2.11696 - 1.77634i) q^{9} +(0.258097 + 0.447037i) q^{11} +(-4.37365 + 1.59188i) q^{13} +(-0.235896 + 1.33783i) q^{15} +(-0.735881 + 0.617477i) q^{17} +(-3.12016 - 3.04379i) q^{19} +(1.25387 - 1.05212i) q^{21} +(0.629673 - 3.57105i) q^{23} +(-2.63386 + 0.958648i) q^{25} +(-1.40145 - 2.42738i) q^{27} +(6.21450 + 5.21459i) q^{29} +(-2.38969 + 4.13907i) q^{31} +(0.0435918 + 0.247221i) q^{33} +(8.83466 + 3.21555i) q^{35} +9.13084 q^{37} -2.26350 q^{39} +(-6.54978 - 2.38392i) q^{41} +(-0.817138 - 4.63422i) q^{43} +(3.85973 - 6.68524i) q^{45} +(10.4172 + 8.74111i) q^{47} +(-2.16398 - 3.74813i) q^{49} +(-0.438996 + 0.159782i) q^{51} +(-1.20127 + 6.81274i) q^{53} +(-1.10457 + 0.926847i) q^{55} +(-0.919606 - 1.90996i) q^{57} +(-10.9602 + 9.19667i) q^{59} +(1.05803 - 6.00040i) q^{61} +(-8.74018 + 3.18116i) q^{63} +(-6.50065 - 11.2594i) q^{65} +(3.38541 + 2.84069i) q^{67} +(0.881732 - 1.52720i) q^{69} +(-1.66206 - 9.42601i) q^{71} +(5.65102 + 2.05680i) q^{73} -1.36310 q^{75} +1.73735 q^{77} +(-9.85305 - 3.58622i) q^{79} +(1.20293 + 6.82213i) q^{81} +(2.39066 - 4.14075i) q^{83} +(-2.05558 - 1.72484i) q^{85} +(1.97262 + 3.41669i) q^{87} +(-8.30245 + 3.02185i) q^{89} +(-2.72022 + 15.4272i) q^{91} +(-1.78053 + 1.49404i) q^{93} +(6.85977 - 10.0598i) q^{95} +(8.46492 - 7.10291i) q^{97} +(0.247709 - 1.40483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.456991	+	0.166331i	0.263844	+	0.0960313i	0.470555	−	0.882371i	$-0.344054\pi$
$3$	0.456991	+	0.166331i	0.263844	+	0.0960313i	−0.206711	+	0.978402i	$0.566276\pi$
$4$		0			0
$5$	0.485063	+	2.75093i	0.216927	+	1.23025i	0.877531	+	0.479519i	$0.159189\pi$
$5$	0.485063	+	2.75093i	0.216927	+	1.23025i	−0.660605	+	0.750734i	$0.729700\pi$
$6$		0			0
$7$	1.68285	−	2.91479i	0.636058	−	1.10169i	−0.350231	−	0.936663i	$-0.613897\pi$
$7$	1.68285	−	2.91479i	0.636058	−	1.10169i	0.986290	−	0.165022i	$-0.0527696\pi$
$8$		0			0
$9$	−2.11696	−	1.77634i	−0.705653	−	0.592113i
$10$		0			0
$11$	0.258097	+	0.447037i	0.0778191	+	0.134787i	0.902309	−	0.431090i	$-0.141871\pi$
$11$	0.258097	+	0.447037i	0.0778191	+	0.134787i	−0.824490	+	0.565877i	$0.808538\pi$
$12$		0			0
$13$	−4.37365	+	1.59188i	−1.21303	+	0.441508i	−0.867755	−	0.496993i	$-0.834438\pi$
$13$	−4.37365	+	1.59188i	−1.21303	+	0.441508i	−0.345278	+	0.938500i	$0.612215\pi$
$14$		0			0
$15$	−0.235896	+	1.33783i	−0.0609080	+	0.345426i
$16$		0			0
$17$	−0.735881	+	0.617477i	−0.178477	+	0.149760i	−0.727650	−	0.685949i	$-0.759387\pi$
$17$	−0.735881	+	0.617477i	−0.178477	+	0.149760i	0.549173	+	0.835709i	$0.314943\pi$
$18$		0			0
$19$	−3.12016	−	3.04379i	−0.715813	−	0.698292i
$19$	−3.12016	−	3.04379i	−0.715813	−	0.698292i
$20$		0			0
$21$	1.25387	−	1.05212i	0.273616	−	0.229591i
$22$		0			0
$23$	0.629673	−	3.57105i	0.131296	−	0.744616i	−0.846072	−	0.533069i	$-0.821039\pi$
$23$	0.629673	−	3.57105i	0.131296	−	0.744616i	0.977368	−	0.211547i	$-0.0678501\pi$
$24$		0			0
$25$	−2.63386	+	0.958648i	−0.526773	+	0.191730i
$26$		0			0
$27$	−1.40145	−	2.42738i	−0.269709	−	0.467150i
$28$		0			0
$29$	6.21450	+	5.21459i	1.15400	+	0.968325i	0.999806	−	0.0197150i	$-0.00627588\pi$
$29$	6.21450	+	5.21459i	1.15400	+	0.968325i	0.154199	+	0.988040i	$0.450720\pi$
$30$		0			0
$31$	−2.38969	+	4.13907i	−0.429202	+	0.743399i	−0.996803	−	0.0799047i	$-0.974538\pi$
$31$	−2.38969	+	4.13907i	−0.429202	+	0.743399i	0.567601	+	0.823304i	$0.307872\pi$
$32$		0			0
$33$	0.0435918	+	0.247221i	0.00758835	+	0.0430357i
$34$		0			0
$35$	8.83466	+	3.21555i	1.49333	+	0.543528i
$36$		0			0
$37$	9.13084			1.50110			0.750550	−	0.660813i	$-0.229789\pi$
$37$	9.13084			1.50110			0.750550	+	0.660813i	$0.229789\pi$
$38$		0			0
$39$	−2.26350			−0.362450
$40$		0			0
$41$	−6.54978	−	2.38392i	−1.02290	−	0.372306i	−0.224529	−	0.974467i	$-0.572084\pi$
$41$	−6.54978	−	2.38392i	−1.02290	−	0.372306i	−0.798375	+	0.602161i	$0.794306\pi$
$42$		0			0
$43$	−0.817138	−	4.63422i	−0.124612	−	0.706712i	−0.981537	−	0.191271i	$-0.938739\pi$
$43$	−0.817138	−	4.63422i	−0.124612	−	0.706712i	0.856925	−	0.515441i	$-0.172372\pi$
$44$		0			0
$45$	3.85973	−	6.68524i	0.575374	−	0.996577i
$46$		0			0
$47$	10.4172	+	8.74111i	1.51951	+	1.27502i	0.841950	+	0.539555i	$0.181408\pi$
$47$	10.4172	+	8.74111i	1.51951	+	1.27502i	0.677562	+	0.735466i	$0.263037\pi$
$48$		0			0
$49$	−2.16398	−	3.74813i	−0.309141	−	0.535447i
$50$		0			0
$51$	−0.438996	+	0.159782i	−0.0614718	+	0.0223739i
$52$		0			0
$53$	−1.20127	+	6.81274i	−0.165007	+	0.935802i	0.784050	+	0.620698i	$0.213151\pi$
$53$	−1.20127	+	6.81274i	−0.165007	+	0.935802i	−0.949057	+	0.315104i	$0.897960\pi$
$54$		0			0
$55$	−1.10457	+	0.926847i	−0.148941	+	0.124976i
$56$		0			0
$57$	−0.919606	−	1.90996i	−0.121805	−	0.252981i
$58$		0			0
$59$	−10.9602	+	9.19667i	−1.42689	+	1.19730i	−0.479370	+	0.877613i	$0.659135\pi$
$59$	−10.9602	+	9.19667i	−1.42689	+	1.19730i	−0.947522	+	0.319691i	$0.896421\pi$
$60$		0			0
$61$	1.05803	−	6.00040i	0.135467	−	0.768272i	−0.839066	−	0.544029i	$-0.816898\pi$
$61$	1.05803	−	6.00040i	0.135467	−	0.768272i	0.974533	−	0.224243i	$-0.0719908\pi$
$62$		0			0
$63$	−8.74018	+	3.18116i	−1.10116	+	0.400789i
$64$		0			0
$65$	−6.50065	−	11.2594i	−0.806306	−	1.39656i
$66$		0			0
$67$	3.38541	+	2.84069i	0.413593	+	0.347046i	0.825720	−	0.564081i	$-0.190769\pi$
$67$	3.38541	+	2.84069i	0.413593	+	0.347046i	−0.412126	+	0.911127i	$0.635214\pi$
$68$		0			0
$69$	0.881732	−	1.52720i	0.106148	−	0.183854i
$70$		0			0
$71$	−1.66206	−	9.42601i	−0.197250	−	1.11866i	−0.909178	−	0.416408i	$-0.863289\pi$
$71$	−1.66206	−	9.42601i	−0.197250	−	1.11866i	0.711928	−	0.702253i	$-0.247822\pi$
$72$		0			0
$73$	5.65102	+	2.05680i	0.661401	+	0.240730i	0.650841	−	0.759214i	$-0.274416\pi$
$73$	5.65102	+	2.05680i	0.661401	+	0.240730i	0.0105601	+	0.999944i	$0.496639\pi$
$74$		0			0
$75$	−1.36310			−0.157398
$76$		0			0
$77$	1.73735			0.197990
$78$		0			0
$79$	−9.85305	−	3.58622i	−1.10856	−	0.403481i	−0.278092	−	0.960554i	$-0.589702\pi$
$79$	−9.85305	−	3.58622i	−1.10856	−	0.403481i	−0.830463	+	0.557073i	$0.811924\pi$
$80$		0			0
$81$	1.20293	+	6.82213i	0.133658	+	0.758015i
$82$		0			0
$83$	2.39066	−	4.14075i	0.262409	−	0.454506i	−0.704472	−	0.709731i	$-0.748816\pi$
$83$	2.39066	−	4.14075i	0.262409	−	0.454506i	0.966882	+	0.255225i	$0.0821497\pi$
$84$		0			0
$85$	−2.05558	−	1.72484i	−0.222959	−	0.187085i
$86$		0			0
$87$	1.97262	+	3.41669i	0.211487	+	0.366307i
$88$		0			0
$89$	−8.30245	+	3.02185i	−0.880058	+	0.320315i	−0.742233	−	0.670142i	$-0.766233\pi$
$89$	−8.30245	+	3.02185i	−0.880058	+	0.320315i	−0.137825	+	0.990457i	$0.544011\pi$
$90$		0			0
$91$	−2.72022	+	15.4272i	−0.285157	+	1.61721i
$92$		0			0
$93$	−1.78053	+	1.49404i	−0.184632	+	0.154925i
$94$		0			0
$95$	6.85977	−	10.0598i	0.703797	−	1.03211i
$96$		0			0
$97$	8.46492	−	7.10291i	0.859482	−	0.721191i	−0.102374	−	0.994746i	$-0.532644\pi$
$97$	8.46492	−	7.10291i	0.859482	−	0.721191i	0.961856	+	0.273555i	$0.0881994\pi$
$98$		0			0
$99$	0.247709	−	1.40483i	0.0248956	−	0.141190i
$100$		0			0
$101$	−0.382988	+	0.139396i	−0.0381087	+	0.0138704i	−0.361004	−	0.932564i	$-0.617566\pi$
$101$	−0.382988	+	0.139396i	−0.0381087	+	0.0138704i	0.322895	+	0.946435i	$0.395344\pi$
$102$		0			0
$103$	2.40104	+	4.15872i	0.236581	+	0.409770i	0.959731	−	0.280921i	$-0.0906398\pi$
$103$	2.40104	+	4.15872i	0.236581	+	0.409770i	−0.723150	+	0.690691i	$0.757306\pi$
$104$		0			0
$105$	3.50251	+	2.93896i	0.341810	+	0.286813i
$106$		0			0
$107$	4.53236	−	7.85028i	0.438160	−	0.758916i	−0.559387	−	0.828906i	$-0.688964\pi$
$107$	4.53236	−	7.85028i	0.438160	−	0.758916i	0.997548	+	0.0699906i	$0.0222969\pi$
$108$		0			0
$109$	1.35374	+	7.67741i	0.129664	+	0.735363i	0.978428	+	0.206590i	$0.0662366\pi$
$109$	1.35374	+	7.67741i	0.129664	+	0.735363i	−0.848763	+	0.528773i	$0.822652\pi$
$110$		0			0
$111$	4.17271	+	1.51874i	0.396056	+	0.144153i
$112$		0			0
$113$	−3.07308			−0.289091			−0.144546	−	0.989498i	$-0.546172\pi$
$113$	−3.07308			−0.289091			−0.144546	+	0.989498i	$0.546172\pi$
$114$		0			0
$115$	10.1291			0.944547
$116$		0			0
$117$	12.0866	+	4.39915i	1.11740	+	0.406701i
$118$		0			0
$119$	0.561435	+	3.18406i	0.0514667	+	0.291882i
$120$		0			0
$121$	5.36677	−	9.29552i	0.487888	−	0.845047i
$122$		0			0
$123$	−2.59667	−	2.17886i	−0.234134	−	0.196461i
$124$		0			0
$125$	3.06865	+	5.31506i	0.274469	+	0.475394i
$126$		0			0
$127$	−9.77012	+	3.55603i	−0.866958	+	0.315547i	−0.736935	−	0.675964i	$-0.763727\pi$
$127$	−9.77012	+	3.55603i	−0.866958	+	0.315547i	−0.130023	+	0.991511i	$0.541505\pi$
$128$		0			0
$129$	0.397390	−	2.25371i	0.0349882	−	0.198428i
$130$		0			0
$131$	2.54356	−	2.13430i	0.222232	−	0.186475i	−0.524874	−	0.851180i	$-0.675887\pi$
$131$	2.54356	−	2.13430i	0.222232	−	0.186475i	0.747106	+	0.664705i	$0.231443\pi$
$132$		0			0
$133$	−14.1227	+	3.97234i	−1.22460	+	0.344446i
$134$		0			0
$135$	5.99777	−	5.03272i	0.516206	−	0.433148i
$136$		0			0
$137$	0.738982	−	4.19097i	0.0631355	−	0.358059i	−0.936830	−	0.349784i	$-0.886255\pi$
$137$	0.738982	−	4.19097i	0.0631355	−	0.358059i	0.999966	−	0.00827481i	$-0.00263398\pi$
$138$		0			0
$139$	4.85603	−	1.76745i	0.411883	−	0.149913i	−0.127764	−	0.991805i	$-0.540780\pi$
$139$	4.85603	−	1.76745i	0.411883	−	0.149913i	0.539647	+	0.841892i	$0.318558\pi$
$140$		0			0
$141$	3.30667	+	5.72732i	0.278472	+	0.482327i
$142$		0			0
$143$	−1.84045	−	1.54432i	−0.153906	−	0.129143i
$144$		0			0
$145$	−11.3305	+	19.6251i	−0.940950	+	1.62977i
$146$		0			0
$147$	−0.365491	−	2.07280i	−0.0301451	−	0.170962i
$148$		0			0
$149$	−17.5930	−	6.40331i	−1.44127	−	0.524580i	−0.501132	−	0.865371i	$-0.667083\pi$
$149$	−17.5930	−	6.40331i	−1.44127	−	0.524580i	−0.940139	+	0.340791i	$0.889305\pi$
$150$		0			0
$151$	9.08388			0.739235			0.369618	−	0.929184i	$-0.379489\pi$
$151$	9.08388			0.739235			0.369618	+	0.929184i	$0.379489\pi$
$152$		0			0
$153$	2.65468			0.214618
$154$		0			0
$155$	−12.5454	−	4.56617i	−1.00767	−	0.366764i
$156$		0			0
$157$	−0.531125	−	3.01216i	−0.0423884	−	0.240397i	0.956251	−	0.292548i	$-0.0945032\pi$
$157$	−0.531125	−	3.01216i	−0.0423884	−	0.240397i	−0.998639	+	0.0521517i	$0.983392\pi$
$158$		0			0
$159$	−1.68214	+	2.91355i	−0.133402	+	0.231060i
$160$		0			0
$161$	−9.34920	−	7.84491i	−0.736820	−	0.618266i
$162$		0			0
$163$	−7.64442	−	13.2405i	−0.598757	−	1.03708i	−0.993005	−	0.118074i	$-0.962328\pi$
$163$	−7.64442	−	13.2405i	−0.598757	−	1.03708i	0.394248	−	0.919004i	$-0.371005\pi$
$164$		0			0
$165$	−0.658943	+	0.239836i	−0.0512987	+	0.0186712i
$166$		0			0
$167$	2.57778	−	14.6193i	0.199475	−	1.13128i	−0.706426	−	0.707787i	$-0.749694\pi$
$167$	2.57778	−	14.6193i	0.199475	−	1.13128i	0.905901	−	0.423491i	$-0.139195\pi$
$168$		0			0
$169$	6.63618	−	5.56842i	0.510475	−	0.428340i
$170$		0			0
$171$	1.19844	+	11.9860i	0.0916473	+	0.916594i
$172$		0			0
$173$	−4.06288	+	3.40916i	−0.308895	+	0.259194i	−0.784035	−	0.620716i	$-0.786842\pi$
$173$	−4.06288	+	3.40916i	−0.308895	+	0.259194i	0.475140	+	0.879910i	$0.342397\pi$
$174$		0			0
$175$	−1.63815	+	9.29041i	−0.123833	+	0.702289i
$176$		0			0
$177$	−6.53839	+	2.37978i	−0.491455	+	0.178875i
$178$		0			0
$179$	−5.46494	−	9.46556i	−0.408469	−	0.707489i	0.586249	−	0.810131i	$-0.300604\pi$
$179$	−5.46494	−	9.46556i	−0.408469	−	0.707489i	−0.994718	+	0.102641i	$0.967271\pi$
$180$		0			0
$181$	−2.57271	−	2.15876i	−0.191228	−	0.160460i	0.542147	−	0.840284i	$-0.317612\pi$
$181$	−2.57271	−	2.15876i	−0.191228	−	0.160460i	−0.733375	+	0.679824i	$0.762056\pi$
$182$		0			0
$183$	1.48156	−	2.56614i	0.109520	−	0.189695i
$184$		0			0
$185$	4.42903	+	25.1183i	0.325629	+	1.84673i
$186$		0			0
$187$	−0.465963	−	0.169597i	−0.0340746	−	0.0124021i
$188$		0			0
$189$	−9.43373			−0.686203
$190$		0			0
$191$	−17.6763			−1.27902			−0.639508	−	0.768785i	$-0.720862\pi$
$191$	−17.6763			−1.27902			−0.639508	+	0.768785i	$0.720862\pi$
$192$		0			0
$193$	23.3296	+	8.49127i	1.67930	+	0.611215i	0.993213	−	0.116306i	$-0.0371053\pi$
$193$	23.3296	+	8.49127i	1.67930	+	0.611215i	0.686086	+	0.727521i	$0.259328\pi$
$194$		0			0
$195$	−1.09794	−	6.22672i	−0.0786251	−	0.445905i
$196$		0			0
$197$	−0.599101	+	1.03767i	−0.0426842	+	0.0739311i	−0.886578	−	0.462579i	$-0.846924\pi$
$197$	−0.599101	+	1.03767i	−0.0426842	+	0.0739311i	0.843894	+	0.536510i	$0.180258\pi$
$198$		0			0
$199$	10.0334	+	8.41899i	0.711246	+	0.596806i	0.924948	−	0.380093i	$-0.124108\pi$
$199$	10.0334	+	8.41899i	0.711246	+	0.596806i	−0.213703	+	0.976899i	$0.568552\pi$
$200$		0			0
$201$	1.07460	+	1.86127i	0.0757968	+	0.131284i
$202$		0			0
$203$	25.6575	−	9.33857i	1.80080	−	0.655439i
$204$		0			0
$205$	3.38095	−	19.1743i	0.236136	−	1.33919i
$206$		0			0
$207$	−7.67639	+	6.44126i	−0.533546	+	0.447698i
$208$		0			0
$209$	0.555382	−	2.18041i	0.0384166	−	0.150822i
$210$		0			0
$211$	0.362133	−	0.303866i	0.0249303	−	0.0209190i	−0.630237	−	0.776403i	$-0.717042\pi$
$211$	0.362133	−	0.303866i	0.0249303	−	0.0209190i	0.655168	+	0.755484i	$0.272598\pi$
$212$		0			0
$213$	0.808292	−	4.58405i	0.0553833	−	0.314094i
$214$		0			0
$215$	12.3520	−	4.49578i	0.842402	−	0.306609i
$216$		0			0
$217$	8.04301	+	13.9309i	0.545995	+	0.945691i
$218$		0			0
$219$	2.24035	+	1.87988i	0.151389	+	0.127030i
$220$		0			0
$221$	2.23554	−	3.87206i	0.150378	−	0.260463i
$222$		0			0
$223$	−3.40576	−	19.3150i	−0.228066	−	1.29343i	−0.856736	−	0.515756i	$-0.827511\pi$
$223$	−3.40576	−	19.3150i	−0.228066	−	1.29343i	0.628669	−	0.777673i	$-0.283600\pi$
$224$		0			0
$225$	7.27867	+	2.64922i	0.485244	+	0.176615i
$226$		0			0
$227$	0.929069			0.0616645			0.0308322	−	0.999525i	$-0.490184\pi$
$227$	0.929069			0.0616645			0.0308322	+	0.999525i	$0.490184\pi$
$228$		0			0
$229$	−7.58741			−0.501390			−0.250695	−	0.968066i	$-0.580659\pi$
$229$	−7.58741			−0.501390			−0.250695	+	0.968066i	$0.580659\pi$
$230$		0			0
$231$	0.793955	+	0.288976i	0.0522384	+	0.0190132i
$232$		0			0
$233$	0.646394	+	3.66588i	0.0423467	+	0.240160i	0.998633	−	0.0522725i	$-0.0166464\pi$
$233$	0.646394	+	3.66588i	0.0423467	+	0.240160i	−0.956286	+	0.292433i	$0.905535\pi$
$234$		0			0
$235$	−18.9931	+	32.8971i	−1.23898	+	2.14597i
$236$		0			0
$237$	−3.90626	−	3.27774i	−0.253739	−	0.212912i
$238$		0			0
$239$	9.65144	+	16.7168i	0.624300	+	1.08132i	0.988676	+	0.150067i	$0.0479490\pi$
$239$	9.65144	+	16.7168i	0.624300	+	1.08132i	−0.364376	+	0.931252i	$0.618718\pi$
$240$		0			0
$241$	12.8080	−	4.66174i	0.825037	−	0.300289i	0.105217	−	0.994449i	$-0.466446\pi$
$241$	12.8080	−	4.66174i	0.825037	−	0.300289i	0.719821	+	0.694160i	$0.244224\pi$
$242$		0			0
$243$	−2.04516	+	11.5987i	−0.131197	+	0.744056i
$244$		0			0
$245$	9.26118	−	7.77105i	0.591675	−	0.496474i
$246$		0			0
$247$	18.4918	+	8.34555i	1.17661	+	0.531015i
$248$		0			0
$249$	1.78125	−	1.49464i	0.112882	−	0.0947191i
$250$		0			0
$251$	−2.99329	+	16.9758i	−0.188935	+	1.07150i	0.731859	+	0.681456i	$0.238653\pi$
$251$	−2.99329	+	16.9758i	−0.188935	+	1.07150i	−0.920794	+	0.390048i	$0.872458\pi$
$252$		0			0
$253$	1.75891	−	0.640190i	0.110582	−	0.0402484i
$254$		0			0
$255$	−0.652489	−	1.13014i	−0.0408604	−	0.0707724i
$256$		0			0
$257$	−10.4154	−	8.73957i	−0.649695	−	0.545159i	0.257283	−	0.966336i	$-0.417173\pi$
$257$	−10.4154	−	8.73957i	−0.649695	−	0.545159i	−0.906979	+	0.421177i	$0.861617\pi$
$258$		0			0
$259$	15.3659	−	26.6144i	0.954788	−	1.65374i
$260$		0			0
$261$	−3.89297	−	22.0781i	−0.240969	−	1.36660i
$262$		0			0
$263$	−7.53896	−	2.74396i	−0.464872	−	0.169200i	0.0989559	−	0.995092i	$-0.468450\pi$
$263$	−7.53896	−	2.74396i	−0.464872	−	0.169200i	−0.563828	+	0.825892i	$0.690672\pi$
$264$		0			0
$265$	−19.3241			−1.18707
$266$		0			0
$267$	−4.29677			−0.262958
$268$		0			0
$269$	0.158312	+	0.0576210i	0.00965248	+	0.00351322i	0.346842	−	0.937924i	$-0.387254\pi$
$269$	0.158312	+	0.0576210i	0.00965248	+	0.00351322i	−0.337189	+	0.941437i	$0.609476\pi$
$270$		0			0
$271$	−2.06021	−	11.6841i	−0.125149	−	0.709756i	−0.981219	−	0.192896i	$-0.938212\pi$
$271$	−2.06021	−	11.6841i	−0.125149	−	0.709756i	0.856070	−	0.516860i	$-0.172899\pi$
$272$		0			0
$273$	−3.80913	+	6.59761i	−0.230539	+	0.399306i
$274$		0			0
$275$	−1.10834	−	0.930010i	−0.0668356	−	0.0560817i
$276$		0			0
$277$	−1.34766	−	2.33422i	−0.0809733	−	0.140250i	0.822695	−	0.568483i	$-0.192470\pi$
$277$	−1.34766	−	2.33422i	−0.0809733	−	0.140250i	−0.903668	+	0.428233i	$0.859136\pi$
$278$		0			0
$279$	12.4113	−	4.51734i	0.743044	−	0.270446i
$280$		0			0
$281$	3.33967	−	18.9402i	0.199228	−	1.12988i	−0.707039	−	0.707174i	$-0.749970\pi$
$281$	3.33967	−	18.9402i	0.199228	−	1.12988i	0.906267	−	0.422705i	$-0.138919\pi$
$282$		0			0
$283$	−21.2293	+	17.8135i	−1.26195	+	1.05890i	−0.266478	+	0.963841i	$0.585860\pi$
$283$	−21.2293	+	17.8135i	−1.26195	+	1.05890i	−0.995471	+	0.0950608i	$0.969695\pi$
$284$		0			0
$285$	4.80810	−	3.45622i	0.284807	−	0.204729i
$286$		0			0
$287$	−17.9709	+	15.0794i	−1.06079	+	0.890109i
$288$		0			0
$289$	−2.79178	+	15.8330i	−0.164222	+	0.931350i
$290$		0			0
$291$	5.04983	−	1.83799i	0.296026	−	0.107745i
$292$		0			0
$293$	8.84253	+	15.3157i	0.516586	+	0.894754i	0.999815	+	0.0192592i	$0.00613078\pi$
$293$	8.84253	+	15.3157i	0.516586	+	0.894754i	−0.483228	+	0.875494i	$0.660536\pi$
$294$		0			0
$295$	−30.6158	−	25.6897i	−1.78252	−	1.49571i
$296$		0			0
$297$	0.723419	−	1.25300i	0.0419770	−	0.0727064i
$298$		0			0
$299$	2.93071	+	16.6209i	0.169488	+	0.961211i
$300$		0			0
$301$	−14.8829	−	5.41692i	−0.857835	−	0.312226i
$302$		0			0
$303$	−0.198208			−0.0113868
$304$		0			0
$305$	17.0199			0.974555
$306$		0			0
$307$	−9.96657	−	3.62753i	−0.568822	−	0.207034i	0.0415675	−	0.999136i	$-0.486765\pi$
$307$	−9.96657	−	3.62753i	−0.568822	−	0.207034i	−0.610389	+	0.792101i	$0.708987\pi$
$308$		0			0
$309$	0.405528	+	2.29986i	0.0230697	+	0.130835i
$310$		0			0
$311$	−13.1081	+	22.7039i	−0.743292	+	1.28742i	0.207697	+	0.978193i	$0.433403\pi$
$311$	−13.1081	+	22.7039i	−0.743292	+	1.28742i	−0.950989	+	0.309226i	$0.899930\pi$
$312$		0			0
$313$	−6.73987	−	5.65542i	−0.380960	−	0.319663i	0.432119	−	0.901817i	$-0.357766\pi$
$313$	−6.73987	−	5.65542i	−0.380960	−	0.319663i	−0.813079	+	0.582153i	$0.802210\pi$
$314$		0			0
$315$	−12.9907	−	22.5005i	−0.731943	−	1.26776i
$316$		0			0
$317$	−15.5280	+	5.65174i	−0.872140	+	0.317433i	−0.739034	−	0.673669i	$-0.764718\pi$
$317$	−15.5280	+	5.65174i	−0.872140	+	0.317433i	−0.133107	+	0.991102i	$0.542495\pi$
$318$		0			0
$319$	−0.727169	+	4.12398i	−0.0407136	+	0.230898i
$320$		0			0
$321$	3.37700	−	2.83364i	0.188486	−	0.158158i
$322$		0			0
$323$	4.17553	+	0.313238i	0.232333	+	0.0174290i
$324$		0			0
$325$	9.99355	−	8.38559i	0.554343	−	0.465149i
$326$		0			0
$327$	−0.658348	+	3.73368i	−0.0364067	+	0.206473i
$328$		0			0
$329$	43.0091	−	15.6540i	2.37117	−	0.863036i
$330$		0			0
$331$	3.22922	+	5.59317i	0.177494	+	0.307429i	0.941022	−	0.338347i	$-0.109868\pi$
$331$	3.22922	+	5.59317i	0.177494	+	0.307429i	−0.763528	+	0.645775i	$0.776534\pi$
$332$		0			0
$333$	−19.3296	−	16.2195i	−1.05926	−	0.888821i
$334$		0			0
$335$	−6.17241	+	10.6909i	−0.337235	+	0.584108i
$336$		0			0
$337$	−1.92728	−	10.9302i	−0.104986	−	0.595404i	−0.991226	−	0.132178i	$-0.957803\pi$
$337$	−1.92728	−	10.9302i	−0.104986	−	0.595404i	0.886240	−	0.463226i	$-0.153308\pi$
$338$		0			0
$339$	−1.40437	−	0.511149i	−0.0762750	−	0.0277618i
$340$		0			0
$341$	−2.46709			−0.133600
$342$		0			0
$343$	8.99327			0.485591
$344$		0			0
$345$	4.62893	+	1.68479i	0.249213	+	0.0907061i
$346$		0			0
$347$	0.526344	+	2.98505i	0.0282556	+	0.160246i	0.995671	−	0.0929497i	$-0.0296296\pi$
$347$	0.526344	+	2.98505i	0.0282556	+	0.160246i	−0.967415	+	0.253195i	$0.918518\pi$
$348$		0			0
$349$	2.04290	−	3.53842i	0.109354	−	0.189407i	−0.806155	−	0.591705i	$-0.798455\pi$
$349$	2.04290	−	3.53842i	0.109354	−	0.189407i	0.915509	+	0.402298i	$0.131788\pi$
$350$		0			0
$351$	9.99355	+	8.38559i	0.533416	+	0.447590i
$352$		0			0
$353$	8.04626	+	13.9365i	0.428259	+	0.741767i	0.996719	−	0.0809447i	$-0.0257937\pi$
$353$	8.04626	+	13.9365i	0.428259	+	0.741767i	−0.568459	+	0.822711i	$0.692460\pi$
$354$		0			0
$355$	25.1241	−	9.14442i	1.33345	−	0.485335i
$356$		0			0
$357$	−0.273037	+	1.54847i	−0.0144506	+	0.0819537i
$358$		0			0
$359$	22.4035	−	18.7988i	1.18241	−	0.992160i	0.182451	−	0.983215i	$-0.441597\pi$
$359$	22.4035	−	18.7988i	1.18241	−	0.992160i	0.999960	−	0.00894547i	$-0.00284747\pi$
$360$		0			0
$361$	0.470738	+	18.9942i	0.0247757	+	0.999693i
$362$		0			0
$363$	3.99870	−	3.35531i	0.209877	−	0.176108i
$364$		0			0
$365$	−2.91702	+	16.5432i	−0.152684	+	0.865912i
$366$		0			0
$367$	−7.57969	+	2.75878i	−0.395657	+	0.144007i	−0.532183	−	0.846629i	$-0.678628\pi$
$367$	−7.57969	+	2.75878i	−0.395657	+	0.144007i	0.136527	+	0.990636i	$0.456406\pi$
$368$		0			0
$369$	9.63095	+	16.6813i	0.501367	+	0.868393i
$370$		0			0
$371$	17.8361	+	14.9663i	0.926006	+	0.777011i
$372$		0			0
$373$	0.0909149	−	0.157469i	0.00470740	−	0.00815345i	−0.863662	−	0.504071i	$-0.831835\pi$
$373$	0.0909149	−	0.157469i	0.00470740	−	0.00815345i	0.868370	+	0.495918i	$0.165168\pi$
$374$		0			0
$375$	0.518286	+	2.93935i	0.0267642	+	0.151787i
$376$		0			0
$377$	−35.4811	−	12.9141i	−1.82737	−	0.665108i
$378$		0			0
$379$	2.82977			0.145355			0.0726777	−	0.997355i	$-0.476846\pi$
$379$	2.82977			0.145355			0.0726777	+	0.997355i	$0.476846\pi$
$380$		0			0
$381$	−5.05633			−0.259044
$382$		0			0
$383$	24.5927	+	8.95103i	1.25663	+	0.457376i	0.882637	−	0.470055i	$-0.155766\pi$
$383$	24.5927	+	8.95103i	1.25663	+	0.457376i	0.373994	+	0.927431i	$0.377988\pi$
$384$		0			0
$385$	0.842727	+	4.77934i	0.0429493	+	0.243578i
$386$		0			0
$387$	−6.50210	+	11.2620i	−0.330520	+	0.572478i
$388$		0			0
$389$	−13.7179	−	11.5107i	−0.695528	−	0.583617i	0.224970	−	0.974366i	$-0.427772\pi$
$389$	−13.7179	−	11.5107i	−0.695528	−	0.583617i	−0.920497	+	0.390749i	$0.872216\pi$
$390$		0			0
$391$	1.74168	+	3.01668i	0.0880805	+	0.152560i
$392$		0			0
$393$	1.51739	−	0.552283i	0.0765420	−	0.0278590i
$394$		0			0
$395$	5.08608	−	28.8446i	0.255909	−	1.45133i
$396$		0			0
$397$	2.05186	−	1.72171i	0.102980	−	0.0864103i	−0.589844	−	0.807517i	$-0.700811\pi$
$397$	2.05186	−	1.72171i	0.102980	−	0.0864103i	0.692824	+	0.721107i	$0.256366\pi$
$398$		0			0
$399$	−7.11469	−	0.533727i	−0.356180	−	0.0267198i
$400$		0			0
$401$	23.8632	−	20.0236i	1.19167	−	0.999929i	0.191840	−	0.981426i	$-0.438554\pi$
$401$	23.8632	−	20.0236i	1.19167	−	0.999929i	0.999829	−	0.0185028i	$-0.00588995\pi$
$402$		0			0
$403$	3.86279	−	21.9070i	0.192419	−	1.09126i
$404$		0			0
$405$	−18.1837	+	6.61833i	−0.903556	+	0.328867i
$406$		0			0
$407$	2.35664	+	4.08182i	0.116814	+	0.202328i
$408$		0			0
$409$	8.46492	+	7.10291i	0.418563	+	0.351216i	0.827616	−	0.561294i	$-0.189696\pi$
$409$	8.46492	+	7.10291i	0.418563	+	0.351216i	−0.409053	+	0.912511i	$0.634141\pi$
$410$		0			0
$411$	1.03480	−	1.79232i	0.0510428	−	0.0884087i
$412$		0			0
$413$	8.36198	+	47.4232i	0.411466	+	2.33354i
$414$		0			0
$415$	12.5505	+	4.56802i	0.616081	+	0.224235i
$416$		0			0
$417$	2.51314			0.123069
$418$		0			0
$419$	−8.02242			−0.391921			−0.195960	−	0.980612i	$-0.562782\pi$
$419$	−8.02242			−0.391921			−0.195960	+	0.980612i	$0.562782\pi$
$420$		0			0
$421$	17.7095	+	6.44572i	0.863107	+	0.314145i	0.735372	−	0.677663i	$-0.237007\pi$
$421$	17.7095	+	6.44572i	0.863107	+	0.314145i	0.127734	+	0.991808i	$0.459230\pi$
$422$		0			0
$423$	−6.52571	−	37.0091i	−0.317291	−	1.79945i
$424$		0			0
$425$	1.34627	−	2.33180i	0.0653035	−	0.113109i
$426$		0			0
$427$	−15.7094	−	13.1817i	−0.760229	−	0.637908i
$428$		0			0
$429$	−0.584201	−	1.01187i	−0.0282055	−	0.0488534i
$430$		0			0
$431$	−14.3859	+	5.23604i	−0.692945	+	0.252211i	−0.664395	−	0.747381i	$-0.731311\pi$
$431$	−14.3859	+	5.23604i	−0.692945	+	0.252211i	−0.0285491	+	0.999592i	$0.509089\pi$
$432$		0			0
$433$	0.647150	−	3.67017i	0.0311000	−	0.176377i	−0.965301	−	0.261139i	$-0.915902\pi$
$433$	0.647150	−	3.67017i	0.0311000	−	0.176377i	0.996401	+	0.0847620i	$0.0270130\pi$
$434$		0			0
$435$	−8.44221	+	7.08386i	−0.404773	+	0.339645i
$436$		0			0
$437$	−12.8342	+	9.22565i	−0.613943	+	0.441322i
$438$		0			0
$439$	−6.52228	+	5.47284i	−0.311292	+	0.261205i	−0.785026	−	0.619463i	$-0.787350\pi$
$439$	−6.52228	+	5.47284i	−0.311292	+	0.261205i	0.473734	+	0.880668i	$0.342906\pi$
$440$		0			0
$441$	−2.07689	+	11.7786i	−0.0988994	+	0.560886i
$442$		0			0
$443$	10.2321	−	3.72417i	0.486141	−	0.176941i	−0.0873095	−	0.996181i	$-0.527827\pi$
$443$	10.2321	−	3.72417i	0.486141	−	0.176941i	0.573450	+	0.819241i	$0.305605\pi$
$444$		0			0
$445$	−12.3401	−	21.3737i	−0.584977	−	1.01321i
$446$		0			0
$447$	−6.97475	−	5.85251i	−0.329894	−	0.276814i
$448$		0			0
$449$	−3.42967	+	5.94036i	−0.161856	+	0.280343i	−0.935534	−	0.353236i	$-0.885081\pi$
$449$	−3.42967	+	5.94036i	−0.161856	+	0.280343i	0.773678	+	0.633579i	$0.218415\pi$
$450$		0			0
$451$	−0.624774	−	3.54327i	−0.0294195	−	0.166846i
$452$		0			0
$453$	4.15125	+	1.51093i	0.195043	+	0.0709897i
$454$		0			0
$455$	−43.7585			−2.05143
$456$		0			0
$457$	−32.5371			−1.52202			−0.761010	−	0.648740i	$-0.775296\pi$
$457$	−32.5371			−1.52202			−0.761010	+	0.648740i	$0.775296\pi$
$458$		0			0
$459$	2.53015	+	0.920900i	0.118097	+	0.0429839i
$460$		0			0
$461$	3.42346	+	19.4154i	0.159446	+	0.904265i	0.954608	+	0.297867i	$0.0962751\pi$
$461$	3.42346	+	19.4154i	0.159446	+	0.904265i	−0.795161	+	0.606398i	$0.792614\pi$
$462$		0			0
$463$	10.5884	−	18.3396i	0.492084	−	0.852314i	−0.507875	−	0.861431i	$-0.669569\pi$
$463$	10.5884	−	18.3396i	0.492084	−	0.852314i	0.999958	+	0.00911693i	$0.00290205\pi$
$464$		0			0
$465$	−4.97366	−	4.17340i	−0.230648	−	0.193537i
$466$		0			0
$467$	5.61175	+	9.71984i	0.259681	+	0.449781i	0.966156	−	0.257957i	$-0.0830492\pi$
$467$	5.61175	+	9.71984i	0.259681	+	0.449781i	−0.706475	+	0.707738i	$0.749716\pi$
$468$		0			0
$469$	13.9772	−	5.08727i	0.645405	−	0.234908i
$470$		0			0
$471$	0.258296	−	1.46487i	0.0119017	−	0.0674977i
$472$		0			0
$473$	1.86076	−	1.56137i	0.0855580	−	0.0717917i
$474$		0			0
$475$	11.1360	+	5.02579i	0.510954	+	0.230599i
$476$		0			0
$477$	14.6448	−	12.2884i	0.670539	−	0.562649i
$478$		0			0
$479$	3.86409	−	21.9143i	0.176555	−	1.00129i	−0.759779	−	0.650181i	$-0.774693\pi$
$479$	3.86409	−	21.9143i	0.176555	−	1.00129i	0.936334	−	0.351110i	$-0.114196\pi$
$480$		0			0
$481$	−39.9351	+	14.5352i	−1.82088	+	0.662748i
$482$		0			0
$483$	−2.96765	−	5.14012i	−0.135033	−	0.233883i
$484$		0			0
$485$	23.6456	+	19.8410i	1.07369	+	0.900935i
$486$		0			0
$487$	−2.74337	+	4.75166i	−0.124314	+	0.215318i	−0.921465	−	0.388462i	$-0.873006\pi$
$487$	−2.74337	+	4.75166i	−0.124314	+	0.215318i	0.797151	+	0.603781i	$0.206340\pi$
$488$		0			0
$489$	−1.29112	−	7.32230i	−0.0583865	−	0.331126i
$490$		0			0
$491$	−25.4961	−	9.27982i	−1.15062	−	0.418792i	−0.304884	−	0.952390i	$-0.598618\pi$
$491$	−25.4961	−	9.27982i	−1.15062	−	0.418792i	−0.845739	+	0.533597i	$0.820840\pi$
$492$		0			0
$493$	−7.79302			−0.350980
$494$		0			0
$495$	3.98473			0.179100
$496$		0			0
$497$	−30.2718	−	11.0180i	−1.35788	−	0.494226i
$498$		0			0
$499$	2.79671	+	15.8609i	0.125198	+	0.710032i	0.981190	+	0.193044i	$0.0618359\pi$
$499$	2.79671	+	15.8609i	0.125198	+	0.710032i	−0.855992	+	0.516988i	$0.827053\pi$
$500$		0			0
$501$	3.60967	−	6.25214i	0.161268	−	0.279325i
$502$		0			0
$503$	17.2137	+	14.4440i	0.767523	+	0.644028i	0.940073	−	0.340973i	$-0.110756\pi$
$503$	17.2137	+	14.4440i	0.767523	+	0.644028i	−0.172550	+	0.985001i	$0.555201\pi$
$504$		0			0
$505$	−0.569243	−	0.985957i	−0.0253310	−	0.0438745i
$506$		0			0
$507$	3.95887	−	1.44091i	0.175820	−	0.0639932i
$508$		0			0
$509$	3.46194	−	19.6336i	0.153448	−	0.870246i	−0.806743	−	0.590902i	$-0.798772\pi$
$509$	3.46194	−	19.6336i	0.153448	−	0.870246i	0.960191	−	0.279344i	$-0.0901169\pi$
$510$		0			0
$511$	15.5050	−	13.0102i	0.685899	−	0.575538i
$512$		0			0
$513$	−3.01569	+	11.8395i	−0.133146	+	0.522728i
$514$		0			0
$515$	−10.2757	+	8.62232i	−0.452801	+	0.379945i
$516$		0			0
$517$	−1.21894	+	6.91294i	−0.0536088	+	0.304031i
$518$		0			0
$519$	−2.42375	+	0.882173i	−0.106391	+	0.0387231i
$520$		0			0
$521$	−8.39608	−	14.5424i	−0.367839	−	0.637116i	0.621388	−	0.783503i	$-0.286569\pi$
$521$	−8.39608	−	14.5424i	−0.367839	−	0.637116i	−0.989227	+	0.146387i	$0.953236\pi$
$522$		0			0
$523$	−11.8256	−	9.92282i	−0.517096	−	0.433895i	0.346522	−	0.938042i	$-0.387363\pi$
$523$	−11.8256	−	9.92282i	−0.517096	−	0.433895i	−0.863618	+	0.504147i	$0.831807\pi$
$524$		0			0
$525$	−2.29390	+	3.97316i	−0.100114	+	0.173403i
$526$		0			0
$527$	−0.797253	−	4.52144i	−0.0347289	−	0.196957i
$528$		0			0
$529$	9.25701	+	3.36928i	0.402479	+	0.146490i
$530$		0			0
$531$	39.5386			1.71583
$532$		0			0
$533$	32.4414			1.40519
$534$		0			0
$535$	23.7941	+	8.66033i	1.02871	+	0.374419i
$536$		0			0
$537$	−0.923013	−	5.23467i	−0.0398309	−	0.225892i
$538$		0			0
$539$	1.11703	−	1.93476i	0.0481141	−	0.0833360i
$540$		0			0
$541$	10.5437	+	8.84722i	0.453309	+	0.380372i	0.840662	−	0.541560i	$-0.182166\pi$
$541$	10.5437	+	8.84722i	0.453309	+	0.380372i	−0.387353	+	0.921932i	$0.626610\pi$
$542$		0			0
$543$	−0.816637	−	1.41446i	−0.0350453	−	0.0607002i
$544$		0			0
$545$	−20.4634	+	7.44806i	−0.876555	+	0.319040i
$546$		0			0
$547$	−6.60558	+	37.4621i	−0.282434	+	1.60176i	0.431875	+	0.901933i	$0.357852\pi$
$547$	−6.60558	+	37.4621i	−0.282434	+	1.60176i	−0.714310	+	0.699830i	$0.753259\pi$
$548$		0			0
$549$	−12.8985	+	10.8232i	−0.550497	+	0.461921i
$550$		0			0
$551$	−3.51813	−	35.1859i	−0.149877	−	1.49897i
$552$		0			0
$553$	−27.0343	+	22.6845i	−1.14962	+	0.964642i
$554$		0			0
$555$	−2.15393	+	12.2155i	−0.0914290	+	0.518520i
$556$		0			0
$557$	35.8744	−	13.0572i	1.52005	−	0.553251i	0.558886	−	0.829245i	$-0.311229\pi$
$557$	35.8744	−	13.0572i	1.52005	−	0.553251i	0.961160	+	0.275993i	$0.0890068\pi$
$558$		0			0
$559$	10.9510	+	18.9677i	0.463178	+	0.802247i
$560$		0			0
$561$	−0.184732	−	0.155008i	−0.00779938	−	0.00654446i
$562$		0			0
$563$	1.24788	−	2.16139i	0.0525919	−	0.0910919i	−0.838531	−	0.544854i	$-0.816585\pi$
$563$	1.24788	−	2.16139i	0.0525919	−	0.0910919i	0.891123	+	0.453762i	$0.149918\pi$
$564$		0			0
$565$	−1.49064	−	8.45384i	−0.0627117	−	0.355656i
$566$		0			0
$567$	21.9094	+	7.97437i	0.920108	+	0.334892i
$568$		0			0
$569$	36.7113			1.53902			0.769509	−	0.638636i	$-0.220501\pi$
$569$	36.7113			1.53902			0.769509	+	0.638636i	$0.220501\pi$
$570$		0			0
$571$	17.9010			0.749133			0.374567	−	0.927200i	$-0.377792\pi$
$571$	17.9010			0.749133			0.374567	+	0.927200i	$0.377792\pi$
$572$		0			0
$573$	−8.07793	−	2.94012i	−0.337460	−	0.122825i
$574$		0			0
$575$	1.76491	+	10.0093i	0.0736018	+	0.417417i
$576$		0			0
$577$	6.61207	−	11.4524i	0.275264	−	0.476771i	−0.694938	−	0.719070i	$-0.744568\pi$
$577$	6.61207	−	11.4524i	0.275264	−	0.476771i	0.970202	+	0.242299i	$0.0779014\pi$
$578$		0			0
$579$	9.24904	+	7.76087i	0.384377	+	0.322531i
$580$		0			0
$581$	−8.04626	−	13.9365i	−0.333815	−	0.578185i
$582$		0			0
$583$	−3.35559	+	1.22133i	−0.138974	+	0.0505825i
$584$		0			0
$585$	−6.23900	+	35.3831i	−0.257951	+	1.46291i
$586$		0			0
$587$	1.65952	−	1.39250i	0.0684957	−	0.0574747i	−0.607897	−	0.794016i	$-0.707987\pi$
$587$	1.65952	−	1.39250i	0.0684957	−	0.0574747i	0.676393	+	0.736541i	$0.263542\pi$
$588$		0			0
$589$	20.0547	−	5.64083i	0.826338	−	0.232426i
$590$		0			0
$591$	−0.446381	+	0.374558i	−0.0183617	+	0.0154073i
$592$		0			0
$593$	7.84333	−	44.4818i	0.322087	−	1.82665i	−0.207313	−	0.978275i	$-0.566472\pi$
$593$	7.84333	−	44.4818i	0.322087	−	1.82665i	0.529400	−	0.848372i	$-0.322417\pi$
$594$		0			0
$595$	−8.48679	+	3.08894i	−0.347924	+	0.126634i
$596$		0			0
$597$	3.18481	+	5.51626i	0.130346	+	0.225766i
$598$		0			0
$599$	−7.79340	−	6.53944i	−0.318430	−	0.267194i	0.469536	−	0.882913i	$-0.344421\pi$
$599$	−7.79340	−	6.53944i	−0.318430	−	0.267194i	−0.787966	+	0.615719i	$0.788866\pi$
$600$		0			0
$601$	16.7570	−	29.0241i	0.683534	−	1.18392i	−0.290361	−	0.956917i	$-0.593775\pi$
$601$	16.7570	−	29.0241i	0.683534	−	1.18392i	0.973895	−	0.226999i	$-0.0728914\pi$
$602$		0			0
$603$	−2.12073	−	12.0273i	−0.0863629	−	0.489788i
$604$		0			0
$605$	28.1745	+	10.2547i	1.14546	+	0.416913i
$606$		0			0
$607$	−17.0948			−0.693856			−0.346928	−	0.937892i	$-0.612775\pi$
$607$	−17.0948			−0.693856			−0.346928	+	0.937892i	$0.612775\pi$
$608$		0			0
$609$	13.2785			0.538074
$610$		0			0
$611$	−59.4762	−	21.6476i	−2.40615	−	0.875767i
$612$		0			0
$613$	−1.92635	−	10.9248i	−0.0778043	−	0.441250i	−0.998679	−	0.0513907i	$-0.983635\pi$
$613$	−1.92635	−	10.9248i	−0.0778043	−	0.441250i	0.920874	−	0.389860i	$-0.127476\pi$
$614$		0			0
$615$	4.73435	−	8.20014i	0.190907	−	0.330661i
$616$		0			0
$617$	2.39215	+	2.00725i	0.0963042	+	0.0808088i	0.689669	−	0.724125i	$-0.257756\pi$
$617$	2.39215	+	2.00725i	0.0963042	+	0.0808088i	−0.593364	+	0.804934i	$0.702201\pi$
$618$		0			0
$619$	0.214658	+	0.371798i	0.00862783	+	0.0149438i	0.870307	−	0.492509i	$-0.163920\pi$
$619$	0.214658	+	0.371798i	0.00862783	+	0.0149438i	−0.861679	+	0.507453i	$0.830587\pi$
$620$		0			0
$621$	−9.55076	+	3.47619i	−0.383259	+	0.139495i
$622$		0			0
$623$	−5.16377	+	29.2852i	−0.206882	+	1.17329i
$624$		0			0
$625$	−23.8686	+	20.0281i	−0.954744	+	0.801126i
$626$		0			0
$627$	0.616475	−	0.904052i	0.0246196	−	0.0361044i
$628$		0			0
$629$	−6.71921	+	5.63808i	−0.267912	+	0.224805i
$630$		0			0
$631$	−5.64012	+	31.9867i	−0.224530	+	1.27337i	0.639052	+	0.769163i	$0.279327\pi$
$631$	−5.64012	+	31.9867i	−0.224530	+	1.27337i	−0.863582	+	0.504208i	$0.831784\pi$
$632$		0			0
$633$	0.216034	−	0.0786299i	0.00858658	−	0.00312526i
$634$		0			0
$635$	−14.5215	−	25.1520i	−0.576269	−	0.998127i
$636$		0			0
$637$	15.4311	+	12.9482i	0.611402	+	0.513027i
$638$		0			0
$639$	−13.2253	+	22.9068i	−0.523184	+	0.906181i
$640$		0			0
$641$	−3.22929	−	18.3142i	−0.127549	−	0.723368i	−0.979761	−	0.200171i	$-0.935850\pi$
$641$	−3.22929	−	18.3142i	−0.127549	−	0.723368i	0.852212	−	0.523197i	$-0.175261\pi$
$642$		0			0
$643$	27.0472	+	9.84439i	1.06664	+	0.388225i	0.814919	−	0.579575i	$-0.196782\pi$
$643$	27.0472	+	9.84439i	1.06664	+	0.388225i	0.251720	+	0.967800i	$0.419004\pi$
$644$		0			0
$645$	6.39256			0.251707
$646$		0			0
$647$	−36.0213			−1.41614			−0.708071	−	0.706141i	$-0.750435\pi$
$647$	−36.0213			−1.41614			−0.708071	+	0.706141i	$0.750435\pi$
$648$		0			0
$649$	−6.94003	−	2.52596i	−0.272420	−	0.0991528i
$650$		0			0
$651$	1.35844	+	7.70409i	0.0532414	+	0.301947i
$652$		0			0
$653$	−14.4702	+	25.0631i	−0.566262	+	0.980795i	0.430669	+	0.902510i	$0.358278\pi$
$653$	−14.4702	+	25.0631i	−0.566262	+	0.980795i	−0.996931	+	0.0782852i	$0.975056\pi$
$654$		0			0
$655$	7.10510	+	5.96189i	0.277619	+	0.232950i
$656$		0			0
$657$	−8.30939	−	14.3923i	−0.324180	−	0.561497i
$658$		0			0
$659$	−45.1158	+	16.4208i	−1.75746	+	0.639664i	−0.999914	−	0.0131131i	$-0.995826\pi$
$659$	−45.1158	+	16.4208i	−1.75746	+	0.639664i	−0.757550	+	0.652778i	$0.773604\pi$
$660$		0			0
$661$	−1.64069	+	9.30480i	−0.0638154	+	0.361915i	0.936132	+	0.351649i	$0.114379\pi$
$661$	−1.64069	+	9.30480i	−0.0638154	+	0.361915i	−0.999947	+	0.0102659i	$0.996732\pi$
$662$		0			0
$663$	1.66566	−	1.39766i	0.0646891	−	0.0542806i
$664$		0			0
$665$	−17.7781	−	36.9238i	−0.689403	−	1.43185i
$666$		0			0
$667$	22.5347	−	18.9088i	0.872546	−	0.732153i
$668$		0			0
$669$	1.65629	−	9.39327i	0.0640357	−	0.363165i
$670$		0			0
$671$	2.95547	−	1.07570i	0.114095	−	0.0415271i
$672$		0			0
$673$	−9.60353	−	16.6338i	−0.370189	−	0.641186i	0.619406	−	0.785071i	$-0.287374\pi$
$673$	−9.60353	−	16.6338i	−0.370189	−	0.641186i	−0.989594	+	0.143885i	$0.954040\pi$
$674$		0			0
$675$	6.01823	+	5.04990i	0.231642	+	0.194371i
$676$		0			0
$677$	−0.226932	+	0.393058i	−0.00872171	+	0.0151064i	−0.870353	−	0.492428i	$-0.836110\pi$
$677$	−0.226932	+	0.393058i	−0.00872171	+	0.0151064i	0.861632	+	0.507534i	$0.169443\pi$
$678$		0			0
$679$	−6.45825	−	36.6266i	−0.247845	−	1.40560i
$680$		0			0
$681$	0.424576	+	0.154533i	0.0162698	+	0.00592172i
$682$		0			0
$683$	6.53688			0.250127			0.125063	−	0.992149i	$-0.460087\pi$
$683$	6.53688			0.250127			0.125063	+	0.992149i	$0.460087\pi$
$684$		0			0
$685$	11.8875			0.454199
$686$		0			0
$687$	−3.46738	−	1.26202i	−0.132289	−	0.0481491i
$688$		0			0
$689$	−5.59113	−	31.7089i	−0.213005	−	1.20801i
$690$		0			0
$691$	10.9350	−	18.9400i	0.415987	−	0.720510i	−0.579545	−	0.814941i	$-0.696770\pi$
$691$	10.9350	−	18.9400i	0.415987	−	0.720510i	0.995531	+	0.0944301i	$0.0301029\pi$
$692$		0			0
$693$	−3.67791	−	3.08613i	−0.139712	−	0.117232i
$694$		0			0
$695$	7.21761	+	12.5013i	0.273779	+	0.474200i
$696$		0			0
$697$	6.29187	−	2.29005i	0.238322	−	0.0867420i
$698$		0			0
$699$	−0.314354	+	1.78279i	−0.0118900	+	0.0674314i
$700$		0			0
$701$	3.84736	−	3.22832i	0.145313	−	0.121932i	−0.567233	−	0.823557i	$-0.691986\pi$
$701$	3.84736	−	3.22832i	0.145313	−	0.121932i	0.712546	+	0.701625i	$0.247542\pi$
$702$		0			0
$703$	−28.4896	−	27.7923i	−1.07451	−	1.04821i
$704$		0			0
$705$	−14.1515	+	11.8745i	−0.532977	+	0.447220i
$706$		0			0
$707$	−0.238202	+	1.35091i	−0.00895851	+	0.0508062i
$708$		0			0
$709$	−47.1948	+	17.1775i	−1.77244	+	0.645115i	−0.772489	+	0.635028i	$0.780989\pi$
$709$	−47.1948	+	17.1775i	−1.77244	+	0.645115i	−0.999949	+	0.0100871i	$0.996789\pi$
$710$		0			0
$711$	14.4882	+	25.0942i	0.543349	+	0.941108i
$712$		0			0
$713$	13.2761	+	11.1400i	0.497194	+	0.417196i
$714$		0			0
$715$	3.35559	−	5.81205i	0.125492	−	0.217358i
$716$		0			0
$717$	1.63010	+	9.24476i	0.0608772	+	0.345252i
$718$		0			0
$719$	10.9561	+	3.98770i	0.408594	+	0.148716i	0.538136	−	0.842858i	$-0.319129\pi$
$719$	10.9561	+	3.98770i	0.408594	+	0.148716i	−0.129542	+	0.991574i	$0.541351\pi$
$720$		0			0
$721$	16.1624			0.601918
$722$		0			0
$723$	6.62854			0.246518
$724$		0			0
$725$	−21.3671	−	7.77699i	−0.793555	−	0.288830i
$726$		0			0
$727$	6.57741	+	37.3023i	0.243942	+	1.38347i	0.822936	+	0.568134i	$0.192335\pi$
$727$	6.57741	+	37.3023i	0.243942	+	1.38347i	−0.578993	+	0.815332i	$0.696554\pi$
$728$		0			0
$729$	7.52722	−	13.0375i	0.278786	−	0.482871i
$730$		0			0
$731$	3.46284	+	2.90567i	0.128078	+	0.107470i
$732$		0			0
$733$	8.45973	+	14.6527i	0.312467	+	0.541209i	0.978896	−	0.204360i	$-0.0655112\pi$
$733$	8.45973	+	14.6527i	0.312467	+	0.541209i	−0.666429	+	0.745569i	$0.732178\pi$
$734$		0			0
$735$	5.52484	−	2.01088i	0.203787	−	0.0741723i
$736$		0			0
$737$	−0.396132	+	2.24658i	−0.0145917	+	0.0827537i
$738$		0			0
$739$	−26.7418	+	22.4390i	−0.983712	+	0.825432i	−0.984645	−	0.174567i	$-0.944147\pi$
$739$	−26.7418	+	22.4390i	−0.983712	+	0.825432i	0.000933516		1.00000i	$0.499703\pi$
$740$		0			0
$741$	7.06247	+	6.88960i	0.259446	+	0.253096i
$742$		0			0
$743$	−31.8275	+	26.7064i	−1.16764	+	0.979765i	−0.999982	−	0.00608086i	$-0.998064\pi$
$743$	−31.8275	+	26.7064i	−1.16764	+	0.979765i	−0.167656	+	0.985845i	$0.553620\pi$
$744$		0			0
$745$	9.08137	−	51.5030i	0.332716	−	1.88692i
$746$		0			0
$747$	−12.4163	+	4.51916i	−0.454289	+	0.165348i
$748$		0			0
$749$	−15.2546	−	26.4217i	−0.557391	−	0.965429i
$750$		0			0
$751$	38.7302	+	32.4985i	1.41328	+	1.18589i	0.954824	+	0.297172i	$0.0960435\pi$
$751$	38.7302	+	32.4985i	1.41328	+	1.18589i	0.458461	+	0.888715i	$0.348401\pi$
$752$		0			0
$753$	−4.19151	+	7.25991i	−0.152747	+	0.264566i
$754$		0			0
$755$	4.40625	+	24.9891i	0.160360	+	0.909447i
$756$		0			0
$757$	36.3326	+	13.2240i	1.32053	+	0.480634i	0.903628	−	0.428318i	$-0.140894\pi$
$757$	36.3326	+	13.2240i	1.32053	+	0.480634i	0.416902	+	0.908951i	$0.363116\pi$
$758$		0			0
$759$	0.910288			0.0330414
$760$		0			0
$761$	−22.8058			−0.826711			−0.413355	−	0.910570i	$-0.635643\pi$
$761$	−22.8058			−0.826711			−0.413355	+	0.910570i	$0.635643\pi$
$762$		0			0
$763$	24.6562	+	8.97411i	0.892613	+	0.324884i
$764$		0			0
$765$	1.28769	+	7.30283i	0.0465564	+	0.264034i
$766$		0			0
$767$	33.2960	−	57.6703i	1.20225	−	2.08235i
$768$		0			0
$769$	5.37493	+	4.51010i	0.193825	+	0.162638i	0.734535	−	0.678570i	$-0.237400\pi$
$769$	5.37493	+	4.51010i	0.193825	+	0.162638i	−0.540711	+	0.841209i	$0.681845\pi$
$770$		0			0
$771$	−3.30609	−	5.72631i	−0.119066	−	0.206228i
$772$		0			0
$773$	20.2329	−	7.36419i	0.727728	−	0.264871i	0.0485254	−	0.998822i	$-0.484548\pi$
$773$	20.2329	−	7.36419i	0.727728	−	0.264871i	0.679203	+	0.733950i	$0.262326\pi$
$774$		0			0
$775$	2.32622	−	13.1926i	0.0835602	−	0.473893i
$776$		0			0
$777$	11.4489	−	9.60674i	0.410726	−	0.344640i
$778$		0			0
$779$	13.1802	+	27.3743i	0.472228	+	0.980787i
$780$		0			0
$781$	3.78480	−	3.17582i	0.135431	−	0.113640i
$782$		0			0
$783$	3.94848	−	22.3930i	0.141107	−	0.800259i
$784$		0			0
$785$	8.02861	−	2.92218i	0.286553	−	0.104297i
$786$		0			0
$787$	−20.7212	−	35.8901i	−0.738630	−	1.27934i	−0.953112	−	0.302616i	$-0.902140\pi$
$787$	−20.7212	−	35.8901i	−0.738630	−	1.27934i	0.214483	−	0.976728i	$-0.431193\pi$
$788$		0			0
$789$	−2.98883	−	2.50793i	−0.106405	−	0.0892846i
$790$		0			0
$791$	−5.17155	+	8.95738i	−0.183879	+	0.318488i
$792$		0			0
$793$	4.92444	+	27.9279i	0.174872	+	0.991749i
$794$		0			0
$795$	−8.83093	−	3.21419i	−0.313201	−	0.113996i
$796$		0			0
$797$	18.8182			0.666574			0.333287	−	0.942825i	$-0.391842\pi$
$797$	18.8182			0.666574			0.333287	+	0.942825i	$0.391842\pi$
$798$		0			0
$799$	−13.0633			−0.462146
$800$		0			0
$801$	22.9438	+	8.35085i	0.810678	+	0.295063i
$802$		0			0
$803$	0.539043	+	3.05706i	0.0190224	+	0.107881i
$804$		0			0
$805$	17.0458	−	29.5243i	0.600787	−	1.04059i
$806$		0			0
$807$	0.0627632	+	0.0526646i	0.00220937	+	0.00185388i
$808$		0			0
$809$	6.63505	+	11.4922i	0.233276	+	0.404046i	0.958770	−	0.284183i	$-0.0917222\pi$
$809$	6.63505	+	11.4922i	0.233276	+	0.404046i	−0.725494	+	0.688228i	$0.758389\pi$
$810$		0			0
$811$	−46.9744	+	17.0973i	−1.64949	+	0.600367i	−0.988661	−	0.150166i	$-0.952019\pi$
$811$	−46.9744	+	17.0973i	−1.64949	+	0.600367i	−0.660833	+	0.750533i	$0.729797\pi$
$812$		0			0
$813$	1.00192	−	5.68218i	0.0351389	−	0.199283i
$814$		0			0
$815$	32.7157	−	27.4517i	1.14598	−	0.961593i
$816$		0			0
$817$	−11.5560	+	16.9467i	−0.404292	+	0.592889i
$818$		0			0
$819$	33.1625	−	27.8266i	1.15879	−	0.972341i
$820$		0			0
$821$	−4.94472	+	28.0429i	−0.172572	+	0.978704i	0.768337	+	0.640045i	$0.221084\pi$
$821$	−4.94472	+	28.0429i	−0.172572	+	0.978704i	−0.940909	+	0.338659i	$0.890027\pi$
$822$		0			0
$823$	−14.2257	+	5.17773i	−0.495877	+	0.180484i	−0.577838	−	0.816151i	$-0.696104\pi$
$823$	−14.2257	+	5.17773i	−0.495877	+	0.180484i	0.0819619	+	0.996635i	$0.473881\pi$
$824$		0			0
$825$	−0.351813	−	0.609358i	−0.0122486	−	0.0212151i
$826$		0			0
$827$	37.8843	+	31.7887i	1.31737	+	1.10540i	0.986856	+	0.161600i	$0.0516654\pi$
$827$	37.8843	+	31.7887i	1.31737	+	1.10540i	0.330511	+	0.943802i	$0.392779\pi$
$828$		0			0
$829$	−21.9838	+	38.0771i	−0.763529	+	1.32247i	0.177492	+	0.984122i	$0.443202\pi$
$829$	−21.9838	+	38.0771i	−0.763529	+	1.32247i	−0.941021	+	0.338349i	$0.890132\pi$
$830$		0			0
$831$	−0.227617	−	1.29088i	−0.00789593	−	0.0447801i
$832$		0			0
$833$	3.90682	+	1.42197i	0.135363	+	0.0492682i
$834$		0			0
$835$	41.4671			1.43503
$836$		0			0
$837$	13.3961			0.463039
$838$		0			0
$839$	0.514663	+	0.187322i	0.0177681	+	0.00646708i	0.350889	−	0.936417i	$-0.385879\pi$
$839$	0.514663	+	0.187322i	0.0177681	+	0.00646708i	−0.333121	+	0.942884i	$0.608102\pi$
$840$		0			0
$841$	6.39234	+	36.2528i	0.220425	+	1.25009i
$842$		0			0
$843$	4.67655	−	8.10002i	0.161069	−	0.278980i
$844$		0			0
$845$	18.5373	+	15.5546i	0.637702	+	0.535095i
$846$		0			0
$847$	−18.0630	−	31.2860i	−0.620651	−	1.07500i
$848$		0			0
$849$	−12.6645	+	4.60951i	−0.434645	+	0.158198i
$850$		0			0
$851$	5.74944	−	32.6067i	0.197088	−	1.11774i
$852$		0			0
$853$	−11.8253	+	9.92258i	−0.404890	+	0.339743i	−0.822380	−	0.568939i	$-0.807354\pi$
$853$	−11.8253	+	9.92258i	−0.404890	+	0.339743i	0.417490	+	0.908681i	$0.362910\pi$
$854$		0			0
$855$	−32.3914	+	9.11081i	−1.10776	+	0.311583i
$856$		0			0
$857$	−25.5748	+	21.4598i	−0.873619	+	0.733054i	−0.964857	−	0.262776i	$-0.915362\pi$
$857$	−25.5748	+	21.4598i	−0.873619	+	0.733054i	0.0912378	+	0.995829i	$0.470918\pi$
$858$		0			0
$859$	4.69049	−	26.6011i	0.160037	−	0.907617i	−0.793997	−	0.607921i	$-0.792004\pi$
$859$	4.69049	−	26.6011i	0.160037	−	0.907617i	0.954035	−	0.299696i	$-0.0968852\pi$
$860$		0			0
$861$	−10.7207	+	3.90203i	−0.365361	+	0.132981i
$862$		0			0
$863$	−5.50763	−	9.53949i	−0.187482	−	0.324728i	0.756928	−	0.653498i	$-0.226699\pi$
$863$	−5.50763	−	9.53949i	−0.187482	−	0.324728i	−0.944410	+	0.328770i	$0.893366\pi$
$864$		0			0
$865$	−11.3491	−	9.52305i	−0.385882	−	0.323793i
$866$		0			0
$867$	−3.90933	+	6.77116i	−0.132768	+	0.229961i
$868$		0			0
$869$	−0.939870	−	5.33027i	−0.0318829	−	0.180817i
$870$		0			0
$871$	−19.3286	−	7.03505i	−0.654926	−	0.238374i
$872$		0			0
$873$	−30.5371			−1.03352
$874$		0			0
$875$	20.6564			0.698313
$876$		0			0
$877$	−5.08935	−	1.85237i	−0.171855	−	0.0625502i	0.254660	−	0.967031i	$-0.418037\pi$
$877$	−5.08935	−	1.85237i	−0.171855	−	0.0625502i	−0.426515	+	0.904481i	$0.640259\pi$
$878$		0			0
$879$	1.49348	+	8.46993i	0.0503737	+	0.285684i
$880$		0			0
$881$	−2.50935	+	4.34631i	−0.0845420	+	0.146431i	−0.905196	−	0.424994i	$-0.860276\pi$
$881$	−2.50935	+	4.34631i	−0.0845420	+	0.146431i	0.820654	+	0.571425i	$0.193609\pi$
$882$		0			0
$883$	−40.3981	−	33.8980i	−1.35950	−	1.14076i	−0.976135	−	0.217165i	$-0.930319\pi$
$883$	−40.3981	−	33.8980i	−1.35950	−	1.14076i	−0.383370	−	0.923595i	$-0.625237\pi$
$884$		0			0
$885$	−9.71813	−	16.8323i	−0.326671	−	0.565812i
$886$		0			0
$887$	15.9355	−	5.80006i	0.535063	−	0.194747i	−0.0603347	−	0.998178i	$-0.519217\pi$
$887$	15.9355	−	5.80006i	0.535063	−	0.194747i	0.595398	+	0.803431i	$0.296995\pi$
$888$		0			0
$889$	−6.07659	+	34.4621i	−0.203802	+	1.15582i
$890$		0			0
$891$	−2.73927	+	2.29852i	−0.0917690	+	0.0770034i
$892$		0			0
$893$	−5.89737	−	58.9815i	−0.197348	−	1.97374i
$894$		0			0
$895$	23.3882	−	19.6251i	0.781783	−	0.655994i
$896$		0			0
$897$	−1.42526	+	8.08307i	−0.0475882	+	0.269886i
$898$		0			0
$899$	−36.4343	+	13.2610i	−1.21515	+	0.442279i
$900$		0			0
$901$	−3.32272	−	5.75512i	−0.110696	−	0.191731i
$902$		0			0
$903$	−5.90034	−	4.95097i	−0.196351	−	0.164758i
$904$		0			0
$905$	4.69068	−	8.12449i	0.155923	−	0.270067i
$906$		0			0
$907$	2.93064	+	16.6205i	0.0973104	+	0.551875i	0.994015	+	0.109245i	$0.0348433\pi$
$907$	2.93064	+	16.6205i	0.0973104	+	0.551875i	−0.896704	+	0.442630i	$0.854046\pi$
$908$		0			0
$909$	1.05838	+	0.385221i	0.0351044	+	0.0127770i
$910$		0			0
$911$	−9.57339			−0.317181			−0.158590	−	0.987344i	$-0.550695\pi$
$911$	−9.57339			−0.317181			−0.158590	+	0.987344i	$0.550695\pi$
$912$		0			0
$913$	2.46809			0.0816817
$914$		0			0
$915$	7.77793	+	2.83093i	0.257130	+	0.0935878i
$916$		0			0
$917$	−1.94059	−	11.0057i	−0.0640840	−	0.363439i
$918$		0			0
$919$	10.2796	−	17.8047i	0.339091	−	0.587323i	−0.645171	−	0.764038i	$-0.723214\pi$
$919$	10.2796	−	17.8047i	0.339091	−	0.587323i	0.984262	+	0.176715i	$0.0565472\pi$
$920$		0			0
$921$	−3.95126	−	3.31550i	−0.130198	−	0.109249i
$922$		0			0
$923$	22.2743	+	38.5803i	0.733169	+	1.26989i
$924$		0			0
$925$	−24.0494	+	8.75326i	−0.790739	+	0.287805i
$926$		0			0
$927$	2.30440	−	13.0689i	0.0756863	−	0.429238i
$928$		0			0
$929$	−15.4080	+	12.9288i	−0.505519	+	0.424181i	−0.859549	−	0.511053i	$-0.829255\pi$
$929$	−15.4080	+	12.9288i	−0.505519	+	0.424181i	0.354030	+	0.935234i	$0.384811\pi$
$930$		0			0
$931$	−4.65654	+	18.2815i	−0.152612	+	0.599151i
$932$		0			0
$933$	−9.76664	+	8.19519i	−0.319746	+	0.268298i
$934$		0			0
$935$	0.240527	−	1.36410i	0.00786608	−	0.0446107i
$936$		0			0
$937$	20.2898	−	7.38487i	0.662838	−	0.241253i	0.0113766	−	0.999935i	$-0.496379\pi$
$937$	20.2898	−	7.38487i	0.662838	−	0.241253i	0.651461	+	0.758682i	$0.274156\pi$
$938$		0			0
$939$	−2.13939	−	3.70553i	−0.0698163	−	0.120925i
$940$		0			0
$941$	−4.36721	−	3.66452i	−0.142367	−	0.119460i	0.568823	−	0.822460i	$-0.307399\pi$
$941$	−4.36721	−	3.66452i	−0.142367	−	0.119460i	−0.711190	+	0.703000i	$0.751843\pi$
$942$		0			0
$943$	−12.6373	+	21.8885i	−0.411528	+	0.712787i
$944$		0			0
$945$	−4.57596	−	25.9515i	−0.148856	−	0.844203i
$946$		0			0
$947$	−2.71384	−	0.987756i	−0.0881879	−	0.0320978i	0.297549	−	0.954706i	$-0.403831\pi$
$947$	−2.71384	−	0.987756i	−0.0881879	−	0.0320978i	−0.385737	+	0.922609i	$0.626053\pi$
$948$		0			0
$949$	−27.9898			−0.908586
$950$		0			0
$951$	−8.03622			−0.260592
$952$		0			0
$953$	−15.8902	−	5.78355i	−0.514733	−	0.187348i	0.0715755	−	0.997435i	$-0.477197\pi$
$953$	−15.8902	−	5.78355i	−0.514733	−	0.187348i	−0.586309	+	0.810088i	$0.699420\pi$
$954$		0			0
$955$	−8.57414	−	48.6264i	−0.277453	−	1.57351i
$956$		0			0
$957$	−1.01826	+	1.76367i	−0.0329155	+	0.0570114i
$958$		0			0
$959$	−10.9722	−	9.20676i	−0.354311	−	0.297302i
$960$		0			0
$961$	4.07872	+	7.06455i	0.131572	+	0.227889i
$962$		0			0
$963$	−23.5396	+	8.56771i	−0.758553	+	0.276091i
$964$		0			0
$965$	−12.0426	+	68.2968i	−0.387664	+	2.19855i
$966$		0			0
$967$	31.8032	−	26.6860i	1.02272	−	0.858165i	0.0327538	−	0.999463i	$-0.489572\pi$
$967$	31.8032	−	26.6860i	1.02272	−	0.858165i	0.989967	+	0.141299i	$0.0451278\pi$
$968$		0			0
$969$	1.85608	+	0.837667i	0.0596258	+	0.0269098i
$970$		0			0
$971$	16.7074	−	14.0192i	0.536166	−	0.449896i	−0.334059	−	0.942552i	$-0.608418\pi$
$971$	16.7074	−	14.0192i	0.536166	−	0.449896i	0.870224	+	0.492656i	$0.163974\pi$
$972$		0			0
$973$	3.02024	−	17.1286i	0.0968244	−	0.549119i
$974$		0			0
$975$	5.96175	−	2.16990i	0.190929	−	0.0694924i
$976$		0			0
$977$	22.8843	+	39.6367i	0.732132	+	1.26809i	0.955970	+	0.293464i	$0.0948082\pi$
$977$	22.8843	+	39.6367i	0.732132	+	1.26809i	−0.223838	+	0.974626i	$0.571859\pi$
$978$		0			0
$979$	−3.49371	−	2.93157i	−0.111659	−	0.0936934i
$980$		0			0
$981$	10.7719	−	18.6575i	0.343920	−	0.595687i
$982$		0			0
$983$	8.63229	+	48.9562i	0.275327	+	1.56146i	0.737920	+	0.674888i	$0.235808\pi$
$983$	8.63229	+	48.9562i	0.275327	+	1.56146i	−0.462593	+	0.886571i	$0.653081\pi$
$984$		0			0
$985$	−3.14517	−	1.14475i	−0.100213	−	0.0364747i
$986$		0			0
$987$	22.2585			0.708497
$988$		0			0
$989$	−17.0636			−0.542590
$990$		0			0
$991$	−36.8537	−	13.4137i	−1.17070	−	0.426099i	−0.317790	−	0.948161i	$-0.602941\pi$
$991$	−36.8537	−	13.4137i	−1.17070	−	0.426099i	−0.852908	+	0.522062i	$0.825163\pi$
$992$		0			0
$993$	0.545406	+	3.09315i	0.0173079	+	0.0981581i
$994$		0			0
$995$	−18.2932	+	31.6848i	−0.579934	+	1.00448i
$996$		0			0
$997$	17.4326	+	14.6277i	0.552096	+	0.463263i	0.875650	−	0.482946i	$-0.160433\pi$
$997$	17.4326	+	14.6277i	0.552096	+	0.463263i	−0.323554	+	0.946210i	$0.604878\pi$
$998$		0			0
$999$	−12.7964	−	22.1640i	−0.404861	−	0.701239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.i.a.25.2	✓	12
3.2	odd	2		684.2.bo.c.253.1		12
4.3	odd	2		304.2.u.e.177.1		12
19.4	even	9		1444.2.a.h.1.3		6
19.6	even	9		1444.2.e.g.653.4		12
19.9	even	9		1444.2.e.g.429.4		12
19.10	odd	18		1444.2.e.h.429.3		12
19.13	odd	18		1444.2.e.h.653.3		12
19.15	odd	18		1444.2.a.g.1.4		6
19.16	even	9	inner	76.2.i.a.73.2	yes	12
57.35	odd	18		684.2.bo.c.73.1		12
76.15	even	18		5776.2.a.by.1.3		6
76.23	odd	18		5776.2.a.bw.1.4		6
76.35	odd	18		304.2.u.e.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.25.2	✓	12	1.1	even	1	trivial
76.2.i.a.73.2	yes	12	19.16	even	9	inner
304.2.u.e.177.1		12	4.3	odd	2
304.2.u.e.225.1		12	76.35	odd	18
684.2.bo.c.73.1		12	57.35	odd	18
684.2.bo.c.253.1		12	3.2	odd	2
1444.2.a.g.1.4		6	19.15	odd	18
1444.2.a.h.1.3		6	19.4	even	9
1444.2.e.g.429.4		12	19.9	even	9
1444.2.e.g.653.4		12	19.6	even	9
1444.2.e.h.429.3		12	19.10	odd	18
1444.2.e.h.653.3		12	19.13	odd	18
5776.2.a.bw.1.4		6	76.23	odd	18
5776.2.a.by.1.3		6	76.15	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456991 + 0.166331i) q^{3} +(0.485063 + 2.75093i) q^{5} +(1.68285 - 2.91479i) q^{7} +(-2.11696 - 1.77634i) q^{9} +O(q^{10})\)	\(q+(0.456991 + 0.166331i) q^{3} +(0.485063 + 2.75093i) q^{5} +(1.68285 - 2.91479i) q^{7} +(-2.11696 - 1.77634i) q^{9} +(0.258097 + 0.447037i) q^{11} +(-4.37365 + 1.59188i) q^{13} +(-0.235896 + 1.33783i) q^{15} +(-0.735881 + 0.617477i) q^{17} +(-3.12016 - 3.04379i) q^{19} +(1.25387 - 1.05212i) q^{21} +(0.629673 - 3.57105i) q^{23} +(-2.63386 + 0.958648i) q^{25} +(-1.40145 - 2.42738i) q^{27} +(6.21450 + 5.21459i) q^{29} +(-2.38969 + 4.13907i) q^{31} +(0.0435918 + 0.247221i) q^{33} +(8.83466 + 3.21555i) q^{35} +9.13084 q^{37} -2.26350 q^{39} +(-6.54978 - 2.38392i) q^{41} +(-0.817138 - 4.63422i) q^{43} +(3.85973 - 6.68524i) q^{45} +(10.4172 + 8.74111i) q^{47} +(-2.16398 - 3.74813i) q^{49} +(-0.438996 + 0.159782i) q^{51} +(-1.20127 + 6.81274i) q^{53} +(-1.10457 + 0.926847i) q^{55} +(-0.919606 - 1.90996i) q^{57} +(-10.9602 + 9.19667i) q^{59} +(1.05803 - 6.00040i) q^{61} +(-8.74018 + 3.18116i) q^{63} +(-6.50065 - 11.2594i) q^{65} +(3.38541 + 2.84069i) q^{67} +(0.881732 - 1.52720i) q^{69} +(-1.66206 - 9.42601i) q^{71} +(5.65102 + 2.05680i) q^{73} -1.36310 q^{75} +1.73735 q^{77} +(-9.85305 - 3.58622i) q^{79} +(1.20293 + 6.82213i) q^{81} +(2.39066 - 4.14075i) q^{83} +(-2.05558 - 1.72484i) q^{85} +(1.97262 + 3.41669i) q^{87} +(-8.30245 + 3.02185i) q^{89} +(-2.72022 + 15.4272i) q^{91} +(-1.78053 + 1.49404i) q^{93} +(6.85977 - 10.0598i) q^{95} +(8.46492 - 7.10291i) q^{97} +(0.247709 - 1.40483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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Database

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