LMFDB - Embedded newform 180.2.k.d.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(127,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("180.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.k (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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.157351936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{4} + 16 $ x^8 + x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$1.28897 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	180.127
Dual form			180.2.k.d.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28897 - 0.581861i) q^{2} +(1.32288 - 1.50000i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-2.64575 + 2.64575i) q^{7} +(0.832353 - 2.70318i) q^{8} +O(q^{10})$	\(q+(1.28897 - 0.581861i) q^{2} +(1.32288 - 1.50000i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-2.64575 + 2.64575i) q^{7} +(0.832353 - 2.70318i) q^{8} +(3.14575 - 0.322876i) q^{10} -3.74166i q^{11} +(-2.00000 + 2.00000i) q^{13} +(-1.87083 + 4.94975i) q^{14} +(-0.500000 - 3.96863i) q^{16} +(-1.41421 - 1.41421i) q^{17} -5.29150 q^{19} +(3.86690 - 2.24657i) q^{20} +(-2.17712 - 4.82288i) q^{22} +(3.74166 + 3.74166i) q^{23} +(4.00000 + 3.00000i) q^{25} +(-1.41421 + 3.74166i) q^{26} +(0.468627 + 7.46863i) q^{28} +1.41421i q^{29} +(-2.95367 - 4.82450i) q^{32} +(-2.64575 - 1.00000i) q^{34} +(-7.48331 + 3.74166i) q^{35} +(-2.00000 - 2.00000i) q^{37} +(-6.82058 + 3.07892i) q^{38} +(3.67712 - 5.14575i) q^{40} -8.48528 q^{41} +(5.29150 + 5.29150i) q^{43} +(-5.61249 - 4.94975i) q^{44} +(7.00000 + 2.64575i) q^{46} +(-3.74166 + 3.74166i) q^{47} -7.00000i q^{49} +(6.90145 + 1.53946i) q^{50} +(0.354249 + 5.64575i) q^{52} +(5.65685 - 5.65685i) q^{53} +(2.64575 - 7.93725i) q^{55} +(4.94975 + 9.35414i) q^{56} +(0.822876 + 1.82288i) q^{58} +11.2250 q^{59} +2.00000 q^{61} +(-6.61438 - 4.50000i) q^{64} +(-5.65685 + 2.82843i) q^{65} +(5.29150 - 5.29150i) q^{67} +(-3.99215 + 0.250492i) q^{68} +(-7.46863 + 9.17712i) q^{70} -14.9666i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-3.74166 - 1.41421i) q^{74} +(-7.00000 + 7.93725i) q^{76} +(9.89949 + 9.89949i) q^{77} +10.5830 q^{79} +(1.74558 - 8.77228i) q^{80} +(-10.9373 + 4.93725i) q^{82} +(3.74166 + 3.74166i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(9.89949 + 3.74166i) q^{86} +(-10.1144 - 3.11438i) q^{88} -11.3137i q^{89} -10.5830i q^{91} +(10.5622 - 0.662739i) q^{92} +(-2.64575 + 7.00000i) q^{94} +(-11.2250 - 3.74166i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(-4.07303 - 9.02277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{10} - 16 q^{13} - 4 q^{16} - 28 q^{22} + 32 q^{25} - 28 q^{28} - 16 q^{37} + 40 q^{40} + 56 q^{46} + 24 q^{52} - 4 q^{58} + 16 q^{61} - 28 q^{70} - 40 q^{73} - 56 q^{76} - 24 q^{82} - 16 q^{85} - 28 q^{88} - 40 q^{97}+O(q^{100}) $ 8 * q + 4 * q^10 - 16 * q^13 - 4 * q^16 - 28 * q^22 + 32 * q^25 - 28 * q^28 - 16 * q^37 + 40 * q^40 + 56 * q^46 + 24 * q^52 - 4 * q^58 + 16 * q^61 - 28 * q^70 - 40 * q^73 - 56 * q^76 - 24 * q^82 - 16 * q^85 - 28 * q^88 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.28897	−	0.581861i	0.911438	−	0.411438i
$2$	1.28897	−	0.581861i	0.911438	−	0.411438i
$3$		0			0
$3$		0			0
$4$	1.32288	−	1.50000i	0.661438	−	0.750000i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$		0			0
$7$	−2.64575	+	2.64575i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$7$	−2.64575	+	2.64575i	−1.00000	+	1.00000i	−1.00000			$\pi$
$8$	0.832353	−	2.70318i	0.294281	−	0.955719i
$9$		0			0
$10$	3.14575	−	0.322876i	0.994774	−	0.102102i
$11$		−	3.74166i		−	1.12815i	−0.825723	−	0.564076i	$-0.809232\pi$
$11$		−	3.74166i		−	1.12815i	0.825723	−	0.564076i	$-0.190768\pi$
$12$		0			0
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$	−1.87083	+	4.94975i	−0.500000	+	1.32288i
$15$		0			0
$16$	−0.500000	−	3.96863i	−0.125000	−	0.992157i
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$	−5.29150			−1.21395			−0.606977	−	0.794719i	$-0.707618\pi$
$19$	−5.29150			−1.21395			−0.606977	+	0.794719i	$0.707618\pi$
$20$	3.86690	−	2.24657i	0.864666	−	0.502347i
$21$		0			0
$22$	−2.17712	−	4.82288i	−0.464164	−	1.02824i
$23$	3.74166	+	3.74166i	0.780189	+	0.780189i	0.979863	−	0.199673i	$-0.0639880\pi$
$23$	3.74166	+	3.74166i	0.780189	+	0.780189i	−0.199673	+	0.979863i	$0.563988\pi$
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$	−1.41421	+	3.74166i	−0.277350	+	0.733799i
$27$		0			0
$28$	0.468627	+	7.46863i	0.0885622	+	1.41144i
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−2.95367	−	4.82450i	−0.522141	−	0.852859i
$33$		0			0
$34$	−2.64575	−	1.00000i	−0.453743	−	0.171499i
$35$	−7.48331	+	3.74166i	−1.26491	+	0.632456i
$36$		0			0
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	−6.82058	+	3.07892i	−1.10644	+	0.499467i
$39$		0			0
$40$	3.67712	−	5.14575i	0.581404	−	0.813615i
$41$	−8.48528			−1.32518			−0.662589	−	0.748983i	$-0.730542\pi$
$41$	−8.48528			−1.32518			−0.662589	+	0.748983i	$0.730542\pi$
$42$		0			0
$43$	5.29150	+	5.29150i	0.806947	+	0.806947i	0.984171	−	0.177224i	$-0.0567117\pi$
$43$	5.29150	+	5.29150i	0.806947	+	0.806947i	−0.177224	+	0.984171i	$0.556712\pi$
$44$	−5.61249	−	4.94975i	−0.846114	−	0.746203i
$45$		0			0
$46$	7.00000	+	2.64575i	1.03209	+	0.390095i
$47$	−3.74166	+	3.74166i	−0.545777	+	0.545777i	−0.925216	−	0.379440i	$-0.876117\pi$
$47$	−3.74166	+	3.74166i	−0.545777	+	0.545777i	0.379440	+	0.925216i	$0.376117\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$	6.90145	+	1.53946i	0.976013	+	0.217712i
$51$		0			0
$52$	0.354249	+	5.64575i	0.0491255	+	0.782925i
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	−0.202296	−	0.979324i	$-0.564840\pi$
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	0.979324	+	0.202296i	$0.0648402\pi$
$54$		0			0
$55$	2.64575	−	7.93725i	0.356753	−	1.07026i
$56$	4.94975	+	9.35414i	0.661438	+	1.25000i
$57$		0			0
$58$	0.822876	+	1.82288i	0.108049	+	0.239355i
$59$	11.2250			1.46137			0.730683	−	0.682716i	$-0.239202\pi$
$59$	11.2250			1.46137			0.730683	+	0.682716i	$0.239202\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$		0			0
$64$	−6.61438	−	4.50000i	−0.826797	−	0.562500i
$65$	−5.65685	+	2.82843i	−0.701646	+	0.350823i
$66$		0			0
$67$	5.29150	−	5.29150i	0.646460	−	0.646460i	−0.305676	−	0.952136i	$-0.598882\pi$
$67$	5.29150	−	5.29150i	0.646460	−	0.646460i	0.952136	+	0.305676i	$0.0988823\pi$
$68$	−3.99215	+	0.250492i	−0.484119	+	0.0303766i
$69$		0			0
$70$	−7.46863	+	9.17712i	−0.892672	+	1.09688i
$71$		−	14.9666i		−	1.77621i	−0.459639	−	0.888106i	$-0.652021\pi$
$71$		−	14.9666i		−	1.77621i	0.459639	−	0.888106i	$-0.347979\pi$
$72$		0			0
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$	−3.74166	−	1.41421i	−0.434959	−	0.164399i
$75$		0			0
$76$	−7.00000	+	7.93725i	−0.802955	+	0.910465i
$77$	9.89949	+	9.89949i	1.12815	+	1.12815i
$78$		0			0
$79$	10.5830			1.19068			0.595341	−	0.803473i	$-0.297017\pi$
$79$	10.5830			1.19068			0.595341	+	0.803473i	$0.297017\pi$
$80$	1.74558	−	8.77228i	0.195162	−	0.980771i
$81$		0			0
$82$	−10.9373	+	4.93725i	−1.20782	+	0.545228i
$83$	3.74166	+	3.74166i	0.410700	+	0.410700i	0.881982	−	0.471282i	$-0.156209\pi$
$83$	3.74166	+	3.74166i	0.410700	+	0.410700i	−0.471282	+	0.881982i	$0.656209\pi$
$84$		0			0
$85$	−2.00000	−	4.00000i	−0.216930	−	0.433861i
$86$	9.89949	+	3.74166i	1.06749	+	0.403473i
$87$		0			0
$88$	−10.1144	−	3.11438i	−1.07820	−	0.331994i
$89$		−	11.3137i		−	1.19925i	−0.800281	−	0.599625i	$-0.795316\pi$
$89$		−	11.3137i		−	1.19925i	0.800281	−	0.599625i	$-0.204684\pi$
$90$		0			0
$91$		−	10.5830i		−	1.10940i
$92$	10.5622	−	0.662739i	1.10119	−	0.0690953i
$93$		0			0
$94$	−2.64575	+	7.00000i	−0.272888	+	0.721995i
$95$	−11.2250	−	3.74166i	−1.15166	−	0.383886i
$96$		0			0
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	0.406138	−	0.913812i	$-0.366875\pi$
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	−4.07303	−	9.02277i	−0.411438	−	0.911438i
$99$		0			0
$100$	9.79150	−	2.03137i	0.979150	−	0.203137i
$101$	12.7279			1.26648			0.633238	−	0.773957i	$-0.281726\pi$
$101$	12.7279			1.26648			0.633238	+	0.773957i	$0.281726\pi$
$102$		0			0
$103$	−2.64575	−	2.64575i	−0.260694	−	0.260694i	0.564642	−	0.825336i	$-0.309014\pi$
$103$	−2.64575	−	2.64575i	−0.260694	−	0.260694i	−0.825336	+	0.564642i	$0.809014\pi$
$104$	3.74166	+	7.07107i	0.366900	+	0.693375i
$105$		0			0
$106$	4.00000	−	10.5830i	0.388514	−	1.02791i
$107$	−3.74166	+	3.74166i	−0.361720	+	0.361720i	−0.864446	−	0.502726i	$-0.832330\pi$
$107$	−3.74166	+	3.74166i	−0.361720	+	0.361720i	0.502726	+	0.864446i	$0.332330\pi$
$108$		0			0
$109$			6.00000i			0.574696i	0.957826	+	0.287348i	$0.0927736\pi$
$109$			6.00000i			0.574696i	−0.957826	+	0.287348i	$0.907226\pi$
$110$	−1.20809	−	11.7703i	−0.115187	−	1.12226i
$111$		0			0
$112$	11.8229	+	9.17712i	1.11716	+	0.867157i
$113$	−7.07107	+	7.07107i	−0.665190	+	0.665190i	−0.956599	−	0.291409i	$-0.905876\pi$
$113$	−7.07107	+	7.07107i	−0.665190	+	0.665190i	0.291409	+	0.956599i	$0.405876\pi$
$114$		0			0
$115$	5.29150	+	10.5830i	0.493435	+	0.986870i
$116$	2.12132	+	1.87083i	0.196960	+	0.173702i
$117$		0			0
$118$	14.4686	−	6.53137i	1.33195	−	0.601262i
$119$	7.48331			0.685994
$120$		0			0
$121$	−3.00000			−0.272727
$122$	2.57794	−	1.16372i	0.233395	−	0.105358i
$123$		0			0
$124$		0			0
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$		0			0
$127$	−2.64575	+	2.64575i	−0.234772	+	0.234772i	−0.814681	−	0.579909i	$-0.803088\pi$
$127$	−2.64575	+	2.64575i	−0.234772	+	0.234772i	0.579909	+	0.814681i	$0.303088\pi$
$128$	−11.1441	−	1.95171i	−0.985008	−	0.172508i
$129$		0			0
$130$	−5.64575	+	6.93725i	−0.495165	+	0.608437i
$131$		−	3.74166i		−	0.326910i	−0.986551	−	0.163455i	$-0.947736\pi$
$131$		−	3.74166i		−	0.326910i	0.986551	−	0.163455i	$-0.0522639\pi$
$132$		0			0
$133$	14.0000	−	14.0000i	1.21395	−	1.21395i
$134$	3.74166	−	9.89949i	0.323230	−	0.855186i
$135$		0			0
$136$	−5.00000	+	2.64575i	−0.428746	+	0.226871i
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	0.143831	−	0.989602i	$-0.454058\pi$
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	−0.989602	+	0.143831i	$0.954058\pi$
$138$		0			0
$139$	−5.29150			−0.448819			−0.224410	−	0.974495i	$-0.572045\pi$
$139$	−5.29150			−0.448819			−0.224410	+	0.974495i	$0.572045\pi$
$140$	−4.28701	+	16.1747i	−0.362318	+	1.36701i
$141$		0			0
$142$	−8.70850	−	19.2915i	−0.730801	−	1.61891i
$143$	7.48331	+	7.48331i	0.625786	+	0.625786i
$144$		0			0
$145$	−1.00000	+	3.00000i	−0.0830455	+	0.249136i
$146$	−3.53553	+	9.35414i	−0.292603	+	0.774154i
$147$		0			0
$148$	−5.64575	+	0.354249i	−0.464078	+	0.0291191i
$149$		−	7.07107i		−	0.579284i	−0.957135	−	0.289642i	$-0.906464\pi$
$149$		−	7.07107i		−	0.579284i	0.957135	−	0.289642i	$-0.0935363\pi$
$150$		0			0
$151$			15.8745i			1.29185i	0.763401	+	0.645925i	$0.223528\pi$
$151$			15.8745i			1.29185i	−0.763401	+	0.645925i	$0.776472\pi$
$152$	−4.40440	+	14.3039i	−0.357244	+	1.16020i
$153$		0			0
$154$	18.5203	+	7.00000i	1.49241	+	0.564076i
$155$		0			0
$156$		0			0
$157$	16.0000	+	16.0000i	1.27694	+	1.27694i	0.942372	+	0.334567i	$0.108590\pi$
$157$	16.0000	+	16.0000i	1.27694	+	1.27694i	0.334567	+	0.942372i	$0.391410\pi$
$158$	13.6412	−	6.15784i	1.08523	−	0.489891i
$159$		0			0
$160$	−2.85425	−	12.3229i	−0.225648	−	0.974209i
$161$	−19.7990			−1.56038
$162$		0			0
$163$	−10.5830	−	10.5830i	−0.828925	−	0.828925i	0.158443	−	0.987368i	$-0.449353\pi$
$163$	−10.5830	−	10.5830i	−0.828925	−	0.828925i	−0.987368	+	0.158443i	$0.949353\pi$
$164$	−11.2250	+	12.7279i	−0.876523	+	0.993884i
$165$		0			0
$166$	7.00000	+	2.64575i	0.543305	+	0.205350i
$167$	−3.74166	+	3.74166i	−0.289538	+	0.289538i	−0.836898	−	0.547359i	$-0.815633\pi$
$167$	−3.74166	+	3.74166i	−0.289538	+	0.289538i	0.547359	+	0.836898i	$0.315633\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−4.90538	−	3.99215i	−0.376225	−	0.306184i
$171$		0			0
$172$	14.9373	−	0.937254i	1.13895	−	0.0714649i
$173$	1.41421	−	1.41421i	0.107521	−	0.107521i	−0.651300	−	0.758820i	$-0.725776\pi$
$173$	1.41421	−	1.41421i	0.107521	−	0.107521i	0.758820	+	0.651300i	$0.225776\pi$
$174$		0			0
$175$	−18.5203	+	2.64575i	−1.40000	+	0.200000i
$176$	−14.8492	+	1.87083i	−1.11930	+	0.141019i
$177$		0			0
$178$	−6.58301	−	14.5830i	−0.493417	−	1.09304i
$179$	−11.2250			−0.838994			−0.419497	−	0.907757i	$-0.637793\pi$
$179$	−11.2250			−0.838994			−0.419497	+	0.907757i	$0.637793\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−6.15784	−	13.6412i	−0.456449	−	1.01115i
$183$		0			0
$184$	13.2288	−	7.00000i	0.975237	−	0.516047i
$185$	−2.82843	−	5.65685i	−0.207950	−	0.415900i
$186$		0			0
$187$	−5.29150	+	5.29150i	−0.386953	+	0.386953i
$188$	0.662739	+	10.5622i	0.0483352	+	0.770330i
$189$		0			0
$190$	−16.6458	+	1.70850i	−1.20761	+	0.123947i
$191$			7.48331i			0.541474i	0.962653	+	0.270737i	$0.0872673\pi$
$191$			7.48331i			0.541474i	−0.962653	+	0.270737i	$0.912733\pi$
$192$		0			0
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	0.503871	+	0.863779i	$0.331909\pi$
$194$	−9.35414	−	3.53553i	−0.671588	−	0.253837i
$195$		0			0
$196$	−10.5000	−	9.26013i	−0.750000	−	0.661438i
$197$	2.82843	+	2.82843i	0.201517	+	0.201517i	0.800650	−	0.599133i	$-0.204488\pi$
$197$	2.82843	+	2.82843i	0.201517	+	0.201517i	−0.599133	+	0.800650i	$0.704488\pi$
$198$		0			0
$199$	−5.29150			−0.375105			−0.187552	−	0.982255i	$-0.560055\pi$
$199$	−5.29150			−0.375105			−0.187552	+	0.982255i	$0.560055\pi$
$200$	11.4390	−	8.31567i	0.808856	−	0.588006i
$201$		0			0
$202$	16.4059	−	7.40588i	1.15431	−	0.521076i
$203$	−3.74166	−	3.74166i	−0.262613	−	0.262613i
$204$		0			0
$205$	−18.0000	−	6.00000i	−1.25717	−	0.419058i
$206$	−4.94975	−	1.87083i	−0.344865	−	0.130347i
$207$		0			0
$208$	8.93725	+	6.93725i	0.619687	+	0.481012i
$209$			19.7990i			1.36952i
$210$		0			0
$211$			15.8745i			1.09285i	0.837509	+	0.546423i	$0.184011\pi$
$211$			15.8745i			1.09285i	−0.837509	+	0.546423i	$0.815989\pi$
$212$	−1.00197	−	15.9686i	−0.0688153	−	1.09673i
$213$		0			0
$214$	−2.64575	+	7.00000i	−0.180860	+	0.478510i
$215$	7.48331	+	14.9666i	0.510358	+	1.02072i
$216$		0			0
$217$		0			0
$218$	3.49117	+	7.73381i	0.236452	+	0.523799i
$219$		0			0
$220$	−8.40588	−	14.4686i	−0.566724	−	0.975475i
$221$	5.65685			0.380521
$222$		0			0
$223$	−2.64575	−	2.64575i	−0.177173	−	0.177173i	0.612949	−	0.790122i	$-0.289983\pi$
$223$	−2.64575	−	2.64575i	−0.177173	−	0.177173i	−0.790122	+	0.612949i	$0.789983\pi$
$224$	20.5791	+	4.94975i	1.37500	+	0.330719i
$225$		0			0
$226$	−5.00000	+	13.2288i	−0.332595	+	0.879964i
$227$	7.48331	−	7.48331i	0.496685	−	0.496685i	−0.413719	−	0.910404i	$-0.635771\pi$
$227$	7.48331	−	7.48331i	0.496685	−	0.496685i	0.910404	+	0.413719i	$0.135771\pi$
$228$		0			0
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$	12.9784	+	10.5622i	0.855771	+	0.696453i
$231$		0			0
$232$	3.82288	+	1.17712i	0.250984	+	0.0772820i
$233$	9.89949	−	9.89949i	0.648537	−	0.648537i	−0.304102	−	0.952639i	$-0.598356\pi$
$233$	9.89949	−	9.89949i	0.648537	−	0.648537i	0.952639	+	0.304102i	$0.0983564\pi$
$234$		0			0
$235$	−10.5830	+	5.29150i	−0.690359	+	0.345180i
$236$	14.8492	−	16.8375i	0.966603	−	1.09603i
$237$		0			0
$238$	9.64575	−	4.35425i	0.625241	−	0.282244i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	20.0000			1.28831			0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000			1.28831			0.644157	+	0.764894i	$0.277208\pi$
$242$	−3.86690	+	1.74558i	−0.248574	+	0.112210i
$243$		0			0
$244$	2.64575	−	3.00000i	0.169377	−	0.192055i
$245$	4.94975	−	14.8492i	0.316228	−	0.948683i
$246$		0			0
$247$	10.5830	−	10.5830i	0.673380	−	0.673380i
$248$		0			0
$249$		0			0
$250$	13.5516	+	8.14575i	0.857080	+	0.515183i
$251$		−	3.74166i		−	0.236171i	−0.993003	−	0.118086i	$-0.962324\pi$
$251$		−	3.74166i		−	0.236171i	0.993003	−	0.118086i	$-0.0376757\pi$
$252$		0			0
$253$	14.0000	−	14.0000i	0.880172	−	0.880172i
$254$	−1.87083	+	4.94975i	−0.117386	+	0.310575i
$255$		0			0
$256$	−15.5000	+	3.96863i	−0.968750	+	0.248039i
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	0.661622	−	0.749838i	$-0.269869\pi$
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	−0.749838	+	0.661622i	$0.769869\pi$
$258$		0			0
$259$	10.5830			0.657596
$260$	−3.24067	+	12.2269i	−0.200978	+	0.758283i
$261$		0			0
$262$	−2.17712	−	4.82288i	−0.134503	−	0.297958i
$263$	−18.7083	−	18.7083i	−1.15360	−	1.15360i	−0.985825	−	0.167778i	$-0.946341\pi$
$263$	−18.7083	−	18.7083i	−1.15360	−	1.15360i	−0.167778	−	0.985825i	$-0.553659\pi$
$264$		0			0
$265$	16.0000	−	8.00000i	0.982872	−	0.491436i
$266$	9.89949	−	26.1916i	0.606977	−	1.60591i
$267$		0			0
$268$	−0.937254	−	14.9373i	−0.0572519	−	0.912438i
$269$			26.8701i			1.63830i	0.573582	+	0.819148i	$0.305553\pi$
$269$			26.8701i			1.63830i	−0.573582	+	0.819148i	$0.694447\pi$
$270$		0			0
$271$		−	15.8745i		−	0.964308i	−0.876087	−	0.482154i	$-0.839855\pi$
$271$		−	15.8745i		−	0.964308i	0.876087	−	0.482154i	$-0.160145\pi$
$272$	−4.90538	+	6.31959i	−0.297432	+	0.383182i
$273$		0			0
$274$	−18.5203	−	7.00000i	−1.11885	−	0.422885i
$275$	11.2250	−	14.9666i	0.676891	−	0.902522i
$276$		0			0
$277$	−2.00000	−	2.00000i	−0.120168	−	0.120168i	0.644465	−	0.764634i	$-0.277080\pi$
$277$	−2.00000	−	2.00000i	−0.120168	−	0.120168i	−0.764634	+	0.644465i	$0.777080\pi$
$278$	−6.82058	+	3.07892i	−0.409071	+	0.184661i
$279$		0			0
$280$	3.88562	+	23.3431i	0.232210	+	1.39502i
$281$	8.48528			0.506189			0.253095	−	0.967442i	$-0.418552\pi$
$281$	8.48528			0.506189			0.253095	+	0.967442i	$0.418552\pi$
$282$		0			0
$283$	5.29150	+	5.29150i	0.314547	+	0.314547i	0.846668	−	0.532121i	$-0.178605\pi$
$283$	5.29150	+	5.29150i	0.314547	+	0.314547i	−0.532121	+	0.846668i	$0.678605\pi$
$284$	−22.4499	−	19.7990i	−1.33216	−	1.17485i
$285$		0			0
$286$	14.0000	+	5.29150i	0.827837	+	0.312893i
$287$	22.4499	−	22.4499i	1.32518	−	1.32518i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$	0.456615	+	4.44876i	0.0268134	+	0.261240i
$291$		0			0
$292$	0.885622	+	14.1144i	0.0518271	+	0.825982i
$293$	5.65685	−	5.65685i	0.330477	−	0.330477i	−0.522291	−	0.852768i	$-0.674922\pi$
$293$	5.65685	−	5.65685i	0.330477	−	0.330477i	0.852768	+	0.522291i	$0.174922\pi$
$294$		0			0
$295$	23.8118	+	7.93725i	1.38637	+	0.462125i
$296$	−7.07107	+	3.74166i	−0.410997	+	0.217479i
$297$		0			0
$298$	−4.11438	−	9.11438i	−0.238340	−	0.527982i
$299$	−14.9666			−0.865543
$300$		0			0
$301$	−28.0000			−1.61389
$302$	9.23676	+	20.4617i	0.531516	+	1.17744i
$303$		0			0
$304$	2.64575	+	21.0000i	0.151744	+	1.20443i
$305$	4.24264	+	1.41421i	0.242933	+	0.0809776i
$306$		0			0
$307$	5.29150	−	5.29150i	0.302002	−	0.302002i	−0.539795	−	0.841797i	$-0.681498\pi$
$307$	5.29150	−	5.29150i	0.302002	−	0.302002i	0.841797	+	0.539795i	$0.181498\pi$
$308$	27.9450	−	1.75344i	1.59232	−	0.0999116i
$309$		0			0
$310$		0			0
$311$			29.9333i			1.69736i	0.528907	+	0.848680i	$0.322602\pi$
$311$			29.9333i			1.69736i	−0.528907	+	0.848680i	$0.677398\pi$
$312$		0			0
$313$	−11.0000	+	11.0000i	−0.621757	+	0.621757i	−0.945980	−	0.324224i	$-0.894897\pi$
$313$	−11.0000	+	11.0000i	−0.621757	+	0.621757i	0.324224	+	0.945980i	$0.394897\pi$
$314$	29.9333	+	11.3137i	1.68923	+	0.638470i
$315$		0			0
$316$	14.0000	−	15.8745i	0.787562	−	0.893011i
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	0.666276	−	0.745706i	$-0.267887\pi$
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	−0.745706	+	0.666276i	$0.767887\pi$
$318$		0			0
$319$	5.29150			0.296267
$320$	−10.8492	−	14.2230i	−0.606491	−	0.795091i
$321$		0			0
$322$	−25.5203	+	11.5203i	−1.42219	+	0.641999i
$323$	7.48331	+	7.48331i	0.416383	+	0.416383i
$324$		0			0
$325$	−14.0000	+	2.00000i	−0.776580	+	0.110940i
$326$	−19.7990	−	7.48331i	−1.09656	−	0.414462i
$327$		0			0
$328$	−7.06275	+	22.9373i	−0.389975	+	1.26650i
$329$		−	19.7990i		−	1.09155i
$330$		0			0
$331$		−	15.8745i		−	0.872542i	−0.899815	−	0.436271i	$-0.856299\pi$
$331$		−	15.8745i		−	0.872542i	0.899815	−	0.436271i	$-0.143701\pi$
$332$	10.5622	−	0.662739i	0.579678	−	0.0363725i
$333$		0			0
$334$	−2.64575	+	7.00000i	−0.144769	+	0.383023i
$335$	14.9666	−	7.48331i	0.817714	−	0.408857i
$336$		0			0
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	0.340894	−	0.940102i	$-0.389270\pi$
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	−0.940102	+	0.340894i	$0.889270\pi$
$338$	2.90930	+	6.44484i	0.158245	+	0.350553i
$339$		0			0
$340$	−8.64575	−	2.29150i	−0.468882	−	0.124274i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	18.7083	−	9.89949i	1.00868	−	0.533745i
$345$		0			0
$346$	1.00000	−	2.64575i	0.0537603	−	0.142236i
$347$	−14.9666	+	14.9666i	−0.803451	+	0.803451i	−0.983633	−	0.180182i	$-0.942331\pi$
$347$	−14.9666	+	14.9666i	−0.803451	+	0.803451i	0.180182	+	0.983633i	$0.442331\pi$
$348$		0			0
$349$		−	6.00000i		−	0.321173i	−0.987022	−	0.160586i	$-0.948662\pi$
$349$		−	6.00000i		−	0.321173i	0.987022	−	0.160586i	$-0.0513385\pi$
$350$	−22.3326	+	14.1865i	−1.19373	+	0.758301i
$351$		0			0
$352$	−18.0516	+	11.0516i	−0.962155	+	0.589054i
$353$	−24.0416	+	24.0416i	−1.27961	+	1.27961i	−0.338719	+	0.940887i	$0.609994\pi$
$353$	−24.0416	+	24.0416i	−1.27961	+	1.27961i	−0.940887	+	0.338719i	$0.890006\pi$
$354$		0			0
$355$	10.5830	−	31.7490i	0.561688	−	1.68506i
$356$	−16.9706	−	14.9666i	−0.899438	−	0.793230i
$357$		0			0
$358$	−14.4686	+	6.53137i	−0.764691	+	0.345194i
$359$	−22.4499			−1.18486			−0.592431	−	0.805621i	$-0.701832\pi$
$359$	−22.4499			−1.18486			−0.592431	+	0.805621i	$0.701832\pi$
$360$		0			0
$361$	9.00000			0.473684
$362$	−12.8897	+	5.81861i	−0.677466	+	0.305819i
$363$		0			0
$364$	−15.8745	−	14.0000i	−0.832050	−	0.733799i
$365$	−14.1421	+	7.07107i	−0.740233	+	0.370117i
$366$		0			0
$367$	−2.64575	+	2.64575i	−0.138107	+	0.138107i	−0.772780	−	0.634673i	$-0.781135\pi$
$367$	−2.64575	+	2.64575i	−0.138107	+	0.138107i	0.634673	+	0.772780i	$0.281135\pi$
$368$	12.9784	−	16.7201i	0.676547	−	0.871594i
$369$		0			0
$370$	−6.93725	−	5.64575i	−0.360651	−	0.293509i
$371$			29.9333i			1.55406i
$372$		0			0
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	−0.595927	−	0.803039i	$-0.703215\pi$
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	0.803039	+	0.595927i	$0.203215\pi$
$374$	−3.74166	+	9.89949i	−0.193476	+	0.511891i
$375$		0			0
$376$	7.00000	+	13.2288i	0.360997	+	0.682221i
$377$	−2.82843	−	2.82843i	−0.145671	−	0.145671i
$378$		0			0
$379$	26.4575			1.35903			0.679516	−	0.733661i	$-0.262190\pi$
$379$	26.4575			1.35903			0.679516	+	0.733661i	$0.262190\pi$
$380$	−20.4617	+	11.8877i	−1.04966	+	0.609827i
$381$		0			0
$382$	4.35425	+	9.64575i	0.222783	+	0.493520i
$383$	−18.7083	−	18.7083i	−0.955949	−	0.955949i	0.0431210	−	0.999070i	$-0.486270\pi$
$383$	−18.7083	−	18.7083i	−0.955949	−	0.955949i	−0.999070	+	0.0431210i	$0.986270\pi$
$384$		0			0
$385$	14.0000	+	28.0000i	0.713506	+	1.42701i
$386$	−3.53553	+	9.35414i	−0.179954	+	0.476113i
$387$		0			0
$388$	−14.1144	+	0.885622i	−0.716549	+	0.0449606i
$389$		−	32.5269i		−	1.64918i	−0.565731	−	0.824590i	$-0.691406\pi$
$389$		−	32.5269i		−	1.64918i	0.565731	−	0.824590i	$-0.308594\pi$
$390$		0			0
$391$		−	10.5830i		−	0.535206i
$392$	−18.9223	−	5.82647i	−0.955719	−	0.294281i
$393$		0			0
$394$	5.29150	+	2.00000i	0.266582	+	0.100759i
$395$	22.4499	+	7.48331i	1.12958	+	0.376526i
$396$		0			0
$397$	4.00000	+	4.00000i	0.200754	+	0.200754i	0.800323	−	0.599569i	$-0.204661\pi$
$397$	4.00000	+	4.00000i	0.200754	+	0.200754i	−0.599569	+	0.800323i	$0.704661\pi$
$398$	−6.82058	+	3.07892i	−0.341885	+	0.154332i
$399$		0			0
$400$	9.90588	−	17.3745i	0.495294	−	0.868725i
$401$	33.9411			1.69494			0.847469	−	0.530844i	$-0.178125\pi$
$401$	33.9411			1.69494			0.847469	+	0.530844i	$0.178125\pi$
$402$		0			0
$403$		0			0
$404$	16.8375	−	19.0919i	0.837695	−	0.949857i
$405$		0			0
$406$	−7.00000	−	2.64575i	−0.347404	−	0.131306i
$407$	−7.48331	+	7.48331i	−0.370934	+	0.370934i
$408$		0			0
$409$		−	36.0000i		−	1.78009i	−0.455877	−	0.890043i	$-0.650674\pi$
$409$		−	36.0000i		−	1.78009i	0.455877	−	0.890043i	$-0.349326\pi$
$410$	−26.6926	+	2.73969i	−1.31825	+	0.135304i
$411$		0			0
$412$	−7.46863	+	0.468627i	−0.367953	+	0.0230876i
$413$	−29.6985	+	29.6985i	−1.46137	+	1.46137i
$414$		0			0
$415$	5.29150	+	10.5830i	0.259750	+	0.519499i
$416$	15.5563	+	3.74166i	0.762713	+	0.183450i
$417$		0			0
$418$	11.5203	+	25.5203i	0.563474	+	1.24824i
$419$	11.2250			0.548376			0.274188	−	0.961676i	$-0.411591\pi$
$419$	11.2250			0.548376			0.274188	+	0.961676i	$0.411591\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	9.23676	+	20.4617i	0.449638	+	0.996061i
$423$		0			0
$424$	−10.5830	−	20.0000i	−0.513956	−	0.971286i
$425$	−1.41421	−	9.89949i	−0.0685994	−	0.480196i
$426$		0			0
$427$	−5.29150	+	5.29150i	−0.256074	+	0.256074i
$428$	0.662739	+	10.5622i	0.0320347	+	0.510545i
$429$		0			0
$430$	18.3542	+	14.9373i	0.885120	+	0.720338i
$431$			7.48331i			0.360459i	0.983625	+	0.180229i	$0.0576840\pi$
$431$			7.48331i			0.360459i	−0.983625	+	0.180229i	$0.942316\pi$
$432$		0			0
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.111551	+	0.993759i	$0.535582\pi$
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.993759	+	0.111551i	$0.964418\pi$
$434$		0			0
$435$		0			0
$436$	9.00000	+	7.93725i	0.431022	+	0.380126i
$437$	−19.7990	−	19.7990i	−0.947114	−	0.947114i
$438$		0			0
$439$	−37.0405			−1.76785			−0.883924	−	0.467631i	$-0.845108\pi$
$439$	−37.0405			−1.76785			−0.883924	+	0.467631i	$0.845108\pi$
$440$	−19.2536	−	13.7585i	−0.917881	−	0.655913i
$441$		0			0
$442$	7.29150	−	3.29150i	0.346821	−	0.156561i
$443$	−7.48331	−	7.48331i	−0.355543	−	0.355543i	0.506624	−	0.862167i	$-0.330893\pi$
$443$	−7.48331	−	7.48331i	−0.355543	−	0.355543i	−0.862167	+	0.506624i	$0.830893\pi$
$444$		0			0
$445$	8.00000	−	24.0000i	0.379236	−	1.13771i
$446$	−4.94975	−	1.87083i	−0.234377	−	0.0885863i
$447$		0			0
$448$	29.4059	−	5.59412i	1.38930	−	0.264297i
$449$			14.1421i			0.667409i	0.942678	+	0.333704i	$0.108299\pi$
$449$			14.1421i			0.667409i	−0.942678	+	0.333704i	$0.891701\pi$
$450$		0			0
$451$			31.7490i			1.49500i
$452$	1.25246	+	19.9607i	0.0589107	+	0.938874i
$453$		0			0
$454$	5.29150	−	14.0000i	0.248343	−	0.657053i
$455$	7.48331	−	22.4499i	0.350823	−	1.05247i
$456$		0			0
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	0.187112	−	0.982339i	$-0.440087\pi$
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	−0.982339	+	0.187112i	$0.940087\pi$
$458$	10.4735	+	23.2014i	0.489394	+	1.08413i
$459$		0			0
$460$	22.8745	+	6.06275i	1.06653	+	0.282677i
$461$	−12.7279			−0.592798			−0.296399	−	0.955064i	$-0.595786\pi$
$461$	−12.7279			−0.592798			−0.296399	+	0.955064i	$0.595786\pi$
$462$		0			0
$463$	29.1033	+	29.1033i	1.35254	+	1.35254i	0.882806	+	0.469737i	$0.155651\pi$
$463$	29.1033	+	29.1033i	1.35254	+	1.35254i	0.469737	+	0.882806i	$0.344349\pi$
$464$	5.61249	−	0.707107i	0.260553	−	0.0328266i
$465$		0			0
$466$	7.00000	−	18.5203i	0.324269	−	0.857934i
$467$	18.7083	−	18.7083i	0.865716	−	0.865716i	−0.126279	−	0.991995i	$-0.540303\pi$
$467$	18.7083	−	18.7083i	0.865716	−	0.865716i	0.991995	+	0.126279i	$0.0403033\pi$
$468$		0			0
$469$			28.0000i			1.29292i
$470$	−10.5622	+	12.9784i	−0.487200	+	0.598650i
$471$		0			0
$472$	9.34313	−	30.3431i	0.430053	−	1.39666i
$473$	19.7990	−	19.7990i	0.910359	−	0.910359i
$474$		0			0
$475$	−21.1660	−	15.8745i	−0.971163	−	0.728372i
$476$	9.89949	−	11.2250i	0.453743	−	0.514496i
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$	8.00000			0.364769
$482$	25.7794	−	11.6372i	1.17422	−	0.530061i
$483$		0			0
$484$	−3.96863	+	4.50000i	−0.180392	+	0.204545i
$485$	−7.07107	−	14.1421i	−0.321081	−	0.642161i
$486$		0			0
$487$	−2.64575	+	2.64575i	−0.119890	+	0.119890i	−0.764506	−	0.644616i	$-0.777017\pi$
$487$	−2.64575	+	2.64575i	−0.119890	+	0.119890i	0.644616	+	0.764506i	$0.277017\pi$
$488$	1.66471	−	5.40636i	0.0753577	−	0.244735i
$489$		0			0
$490$	−2.26013	−	22.0203i	−0.102102	−	0.994774i
$491$			18.7083i			0.844293i	0.906528	+	0.422147i	$0.138723\pi$
$491$			18.7083i			0.844293i	−0.906528	+	0.422147i	$0.861277\pi$
$492$		0			0
$493$	2.00000	−	2.00000i	0.0900755	−	0.0900755i
$494$	7.48331	−	19.7990i	0.336690	−	0.890799i
$495$		0			0
$496$		0			0
$497$	39.5980	+	39.5980i	1.77621	+	1.77621i
$498$		0			0
$499$	−37.0405			−1.65816			−0.829081	−	0.559129i	$-0.811136\pi$
$499$	−37.0405			−1.65816			−0.829081	+	0.559129i	$0.811136\pi$
$500$	22.2073	+	2.61444i	0.993141	+	0.116922i
$501$		0			0
$502$	−2.17712	−	4.82288i	−0.0971698	−	0.215255i
$503$	3.74166	+	3.74166i	0.166832	+	0.166832i	0.785585	−	0.618753i	$-0.212362\pi$
$503$	3.74166	+	3.74166i	0.166832	+	0.166832i	−0.618753	+	0.785585i	$0.712362\pi$
$504$		0			0
$505$	27.0000	+	9.00000i	1.20148	+	0.400495i
$506$	9.89949	−	26.1916i	0.440086	−	1.16436i
$507$		0			0
$508$	0.468627	+	7.46863i	0.0207920	+	0.331367i
$509$			18.3848i			0.814891i	0.913230	+	0.407445i	$0.133580\pi$
$509$			18.3848i			0.814891i	−0.913230	+	0.407445i	$0.866420\pi$
$510$		0			0
$511$		−	26.4575i		−	1.17041i
$512$	−17.6698	+	14.1343i	−0.780903	+	0.624653i
$513$		0			0
$514$	−2.64575	−	1.00000i	−0.116699	−	0.0441081i
$515$	−3.74166	−	7.48331i	−0.164877	−	0.329754i
$516$		0			0
$517$	14.0000	+	14.0000i	0.615719	+	0.615719i
$518$	13.6412	−	6.15784i	0.599358	−	0.270560i
$519$		0			0
$520$	2.93725	+	17.6458i	0.128807	+	0.773817i
$521$	25.4558			1.11524			0.557620	−	0.830096i	$-0.311714\pi$
$521$	25.4558			1.11524			0.557620	+	0.830096i	$0.311714\pi$
$522$		0			0
$523$	5.29150	+	5.29150i	0.231381	+	0.231381i	0.813269	−	0.581888i	$-0.197686\pi$
$523$	5.29150	+	5.29150i	0.231381	+	0.231381i	−0.581888	+	0.813269i	$0.697686\pi$
$524$	−5.61249	−	4.94975i	−0.245183	−	0.216231i
$525$		0			0
$526$	−35.0000	−	13.2288i	−1.52607	−	0.576801i
$527$		0			0
$528$		0			0
$529$			5.00000i			0.217391i
$530$	15.9686	−	19.6215i	0.693631	−	0.852304i
$531$		0			0
$532$	−2.47974	−	39.5203i	−0.107510	−	1.71342i
$533$	16.9706	−	16.9706i	0.735077	−	0.735077i
$534$		0			0
$535$	−10.5830	+	5.29150i	−0.457543	+	0.228772i
$536$	−9.89949	−	18.7083i	−0.427593	−	0.808075i
$537$		0			0
$538$	15.6346	+	34.6346i	0.674057	+	1.49321i
$539$	−26.1916			−1.12815
$540$		0			0
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$	−9.23676	−	20.4617i	−0.396753	−	0.878906i
$543$		0			0
$544$	−2.64575	+	11.0000i	−0.113436	+	0.471621i
$545$	−4.24264	+	12.7279i	−0.181735	+	0.545204i
$546$		0			0
$547$	−26.4575	+	26.4575i	−1.13124	+	1.13124i	−0.141271	+	0.989971i	$0.545119\pi$
$547$	−26.4575	+	26.4575i	−1.13124	+	1.13124i	−0.989971	+	0.141271i	$0.954881\pi$
$548$	−27.9450	+	1.75344i	−1.19375	+	0.0749033i
$549$		0			0
$550$	5.76013	−	25.8229i	0.245613	−	1.10109i
$551$		−	7.48331i		−	0.318800i
$552$		0			0
$553$	−28.0000	+	28.0000i	−1.19068	+	1.19068i
$554$	−3.74166	−	1.41421i	−0.158968	−	0.0600842i
$555$		0			0
$556$	−7.00000	+	7.93725i	−0.296866	+	0.336615i
$557$	−5.65685	−	5.65685i	−0.239689	−	0.239689i	0.577033	−	0.816721i	$-0.304211\pi$
$557$	−5.65685	−	5.65685i	−0.239689	−	0.239689i	−0.816721	+	0.577033i	$0.804211\pi$
$558$		0			0
$559$	−21.1660			−0.895227
$560$	18.5909	+	27.8277i	0.785609	+	1.17593i
$561$		0			0
$562$	10.9373	−	4.93725i	0.461360	−	0.208265i
$563$	−29.9333	−	29.9333i	−1.26154	−	1.26154i	−0.950348	−	0.311188i	$-0.899273\pi$
$563$	−29.9333	−	29.9333i	−1.26154	−	1.26154i	−0.311188	−	0.950348i	$-0.600727\pi$
$564$		0			0
$565$	−20.0000	+	10.0000i	−0.841406	+	0.420703i
$566$	9.89949	+	3.74166i	0.416107	+	0.157274i
$567$		0			0
$568$	−40.4575	−	12.4575i	−1.69756	−	0.522706i
$569$			5.65685i			0.237148i	0.992945	+	0.118574i	$0.0378322\pi$
$569$			5.65685i			0.237148i	−0.992945	+	0.118574i	$0.962168\pi$
$570$		0			0
$571$			15.8745i			0.664327i	0.943222	+	0.332164i	$0.107779\pi$
$571$			15.8745i			0.664327i	−0.943222	+	0.332164i	$0.892221\pi$
$572$	21.1245	−	1.32548i	0.883258	−	0.0554210i
$573$		0			0
$574$	15.8745	−	42.0000i	0.662589	−	1.75305i
$575$	3.74166	+	26.1916i	0.156038	+	1.09227i
$576$		0			0
$577$	−11.0000	−	11.0000i	−0.457936	−	0.457936i	0.440041	−	0.897977i	$-0.354964\pi$
$577$	−11.0000	−	11.0000i	−0.457936	−	0.457936i	−0.897977	+	0.440041i	$0.854964\pi$
$578$	−7.56419	−	16.7566i	−0.314629	−	0.696982i
$579$		0			0
$580$	3.17712	+	5.46863i	0.131923	+	0.227072i
$581$	−19.7990			−0.821401
$582$		0			0
$583$	−21.1660	−	21.1660i	−0.876607	−	0.876607i
$584$	9.35414	+	17.6777i	0.387077	+	0.731507i
$585$		0			0
$586$	4.00000	−	10.5830i	0.165238	−	0.437180i
$587$	18.7083	−	18.7083i	0.772174	−	0.772174i	−0.206313	−	0.978486i	$-0.566146\pi$
$587$	18.7083	−	18.7083i	0.772174	−	0.772174i	0.978486	+	0.206313i	$0.0661464\pi$
$588$		0			0
$589$		0			0
$590$	35.3110	−	3.62427i	1.45373	−	0.149209i
$591$		0			0
$592$	−6.93725	+	8.93725i	−0.285119	+	0.367319i
$593$	18.3848	−	18.3848i	0.754972	−	0.754972i	−0.220430	−	0.975403i	$-0.570746\pi$
$593$	18.3848	−	18.3848i	0.754972	−	0.754972i	0.975403	+	0.220430i	$0.0707462\pi$
$594$		0			0
$595$	15.8745	+	5.29150i	0.650791	+	0.216930i
$596$	−10.6066	−	9.35414i	−0.434463	−	0.383161i
$597$		0			0
$598$	−19.2915	+	8.70850i	−0.788888	+	0.356117i
$599$	22.4499			0.917280			0.458640	−	0.888622i	$-0.348337\pi$
$599$	22.4499			0.917280			0.458640	+	0.888622i	$0.348337\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−36.0911	+	16.2921i	−1.47096	+	0.664017i
$603$		0			0
$604$	23.8118	+	21.0000i	0.968887	+	0.854478i
$605$	−6.36396	−	2.12132i	−0.258732	−	0.0862439i
$606$		0			0
$607$	−2.64575	+	2.64575i	−0.107388	+	0.107388i	−0.758759	−	0.651371i	$-0.774194\pi$
$607$	−2.64575	+	2.64575i	−0.107388	+	0.107388i	0.651371	+	0.758759i	$0.274194\pi$
$608$	15.6294	+	25.5289i	0.633855	+	1.03533i
$609$		0			0
$610$	6.29150	−	0.645751i	0.254735	−	0.0261457i
$611$		−	14.9666i		−	0.605485i
$612$		0			0
$613$	28.0000	−	28.0000i	1.13091	−	1.13091i	0.140883	−	0.990026i	$-0.455006\pi$
$613$	28.0000	−	28.0000i	1.13091	−	1.13091i	0.990026	−	0.140883i	$-0.0449942\pi$
$614$	3.74166	−	9.89949i	0.151001	−	0.399511i
$615$		0			0
$616$	35.0000	−	18.5203i	1.41019	−	0.746203i
$617$	−1.41421	−	1.41421i	−0.0569341	−	0.0569341i	0.678066	−	0.735001i	$-0.262818\pi$
$617$	−1.41421	−	1.41421i	−0.0569341	−	0.0569341i	−0.735001	+	0.678066i	$0.762818\pi$
$618$		0			0
$619$	26.4575			1.06342			0.531709	−	0.846927i	$-0.321550\pi$
$619$	26.4575			1.06342			0.531709	+	0.846927i	$0.321550\pi$
$620$		0			0
$621$		0			0
$622$	17.4170	+	38.5830i	0.698358	+	1.54704i
$623$	29.9333	+	29.9333i	1.19925	+	1.19925i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	−7.77817	+	20.5791i	−0.310878	+	0.822507i
$627$		0			0
$628$	45.1660	−	2.83399i	1.80232	−	0.113088i
$629$			5.65685i			0.225554i
$630$		0			0
$631$			31.7490i			1.26391i	0.775006	+	0.631954i	$0.217747\pi$
$631$			31.7490i			1.26391i	−0.775006	+	0.631954i	$0.782253\pi$
$632$	8.80879	−	28.6078i	0.350395	−	1.13796i
$633$		0			0
$634$	−2.64575	−	1.00000i	−0.105076	−	0.0397151i
$635$	−7.48331	+	3.74166i	−0.296966	+	0.148483i
$636$		0			0
$637$	14.0000	+	14.0000i	0.554700	+	0.554700i
$638$	6.82058	−	3.07892i	0.270029	−	0.121896i
$639$		0			0
$640$	−22.2601	−	12.0203i	−0.879909	−	0.475142i
$641$	−16.9706			−0.670297			−0.335148	−	0.942165i	$-0.608786\pi$
$641$	−16.9706			−0.670297			−0.335148	+	0.942165i	$0.608786\pi$
$642$		0			0
$643$	−10.5830	−	10.5830i	−0.417353	−	0.417353i	0.466937	−	0.884290i	$-0.345357\pi$
$643$	−10.5830	−	10.5830i	−0.417353	−	0.417353i	−0.884290	+	0.466937i	$0.845357\pi$
$644$	−26.1916	+	29.6985i	−1.03209	+	1.17028i
$645$		0			0
$646$	14.0000	+	5.29150i	0.550823	+	0.208191i
$647$	−3.74166	+	3.74166i	−0.147100	+	0.147100i	−0.776821	−	0.629721i	$-0.783169\pi$
$647$	−3.74166	+	3.74166i	−0.147100	+	0.147100i	0.629721	+	0.776821i	$0.283169\pi$
$648$		0			0
$649$		−	42.0000i		−	1.64864i
$650$	−16.8818	+	10.7240i	−0.662160	+	0.420629i
$651$		0			0
$652$	−29.8745	+	1.87451i	−1.16998	+	0.0734114i
$653$	−24.0416	+	24.0416i	−0.940822	+	0.940822i	−0.998344	−	0.0575225i	$-0.981680\pi$
$653$	−24.0416	+	24.0416i	−0.940822	+	0.940822i	0.0575225	+	0.998344i	$0.481680\pi$
$654$		0			0
$655$	2.64575	−	7.93725i	0.103378	−	0.310134i
$656$	4.24264	+	33.6749i	0.165647	+	1.31478i
$657$		0			0
$658$	−11.5203	−	25.5203i	−0.449106	−	0.994883i
$659$	11.2250			0.437263			0.218631	−	0.975808i	$-0.429841\pi$
$659$	11.2250			0.437263			0.218631	+	0.975808i	$0.429841\pi$
$660$		0			0
$661$	2.00000			0.0777910			0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000			0.0777910			0.0388955	+	0.999243i	$0.487616\pi$
$662$	−9.23676	−	20.4617i	−0.358997	−	0.795268i
$663$		0			0
$664$	13.2288	−	7.00000i	0.513375	−	0.271653i
$665$	39.5980	−	19.7990i	1.53554	−	0.767772i
$666$		0			0
$667$	−5.29150	+	5.29150i	−0.204888	+	0.204888i
$668$	0.662739	+	10.5622i	0.0256421	+	0.408665i
$669$		0			0
$670$	14.9373	−	18.3542i	0.577076	−	0.709086i
$671$		−	7.48331i		−	0.288890i
$672$		0			0
$673$	7.00000	−	7.00000i	0.269830	−	0.269830i	−0.559202	−	0.829032i	$-0.688892\pi$
$673$	7.00000	−	7.00000i	0.269830	−	0.269830i	0.829032	+	0.559202i	$0.188892\pi$
$674$	−20.5791	−	7.77817i	−0.792678	−	0.299604i
$675$		0			0
$676$	7.50000	+	6.61438i	0.288462	+	0.254399i
$677$	−26.8701	−	26.8701i	−1.03270	−	1.03270i	−0.999447	−	0.0332533i	$-0.989413\pi$
$677$	−26.8701	−	26.8701i	−1.03270	−	1.03270i	−0.0332533	−	0.999447i	$-0.510587\pi$
$678$		0			0
$679$	26.4575			1.01535
$680$	−12.4774	+	2.07695i	−0.478488	+	0.0796475i
$681$		0			0
$682$		0			0
$683$	3.74166	+	3.74166i	0.143171	+	0.143171i	0.775059	−	0.631889i	$-0.217720\pi$
$683$	3.74166	+	3.74166i	0.143171	+	0.143171i	−0.631889	+	0.775059i	$0.717720\pi$
$684$		0			0
$685$	−14.0000	−	28.0000i	−0.534913	−	1.06983i
$686$		0			0
$687$		0			0
$688$	18.3542	−	23.6458i	0.699749	−	0.901486i
$689$			22.6274i			0.862036i
$690$		0			0
$691$		−	47.6235i		−	1.81168i	−0.423615	−	0.905842i	$-0.639239\pi$
$691$		−	47.6235i		−	1.81168i	0.423615	−	0.905842i	$-0.360761\pi$
$692$	−0.250492	−	3.99215i	−0.00952226	−	0.151759i
$693$		0			0
$694$	−10.5830	+	28.0000i	−0.401725	+	1.06287i
$695$	−11.2250	−	3.74166i	−0.425787	−	0.141929i
$696$		0			0
$697$	12.0000	+	12.0000i	0.454532	+	0.454532i
$698$	−3.49117	−	7.73381i	−0.132143	−	0.292729i
$699$		0			0
$700$	−20.5314	+	31.2804i	−0.776013	+	1.18229i
$701$	−38.1838			−1.44218			−0.721090	−	0.692841i	$-0.756359\pi$
$701$	−38.1838			−1.44218			−0.721090	+	0.692841i	$0.756359\pi$
$702$		0			0
$703$	10.5830	+	10.5830i	0.399146	+	0.399146i
$704$	−16.8375	+	24.7487i	−0.634586	+	0.932753i
$705$		0			0
$706$	−17.0000	+	44.9778i	−0.639803	+	1.69276i
$707$	−33.6749	+	33.6749i	−1.26648	+	1.26648i
$708$		0			0
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$	−4.83236	−	47.0813i	−0.181355	−	1.76693i
$711$		0			0
$712$	−30.5830	−	9.41699i	−1.14615	−	0.352917i
$713$		0			0
$714$		0			0
$715$	10.5830	+	21.1660i	0.395782	+	0.791564i
$716$	−14.8492	+	16.8375i	−0.554942	+	0.629245i
$717$		0			0
$718$	−28.9373	+	13.0627i	−1.07993	+	0.487497i
$719$	−44.8999			−1.67448			−0.837242	−	0.546833i	$-0.815833\pi$
$719$	−44.8999			−1.67448			−0.837242	+	0.546833i	$0.815833\pi$
$720$		0			0
$721$	14.0000			0.521387
$722$	11.6007	−	5.23675i	0.431734	−	0.194892i
$723$		0			0
$724$	−13.2288	+	15.0000i	−0.491643	+	0.557471i
$725$	−4.24264	+	5.65685i	−0.157568	+	0.210090i
$726$		0			0
$727$	29.1033	−	29.1033i	1.07938	−	1.07938i	0.0828154	−	0.996565i	$-0.473609\pi$
$727$	29.1033	−	29.1033i	1.07938	−	1.07938i	0.996565	−	0.0828154i	$-0.0263912\pi$
$728$	−28.6078	−	8.80879i	−1.06027	−	0.326476i
$729$		0			0
$730$	−14.1144	+	17.3431i	−0.522397	+	0.641898i
$731$		−	14.9666i		−	0.553561i
$732$		0			0
$733$	10.0000	−	10.0000i	0.369358	−	0.369358i	−0.497885	−	0.867243i	$-0.665890\pi$
$733$	10.0000	−	10.0000i	0.369358	−	0.369358i	0.867243	+	0.497885i	$0.165890\pi$
$734$	−1.87083	+	4.94975i	−0.0690535	+	0.182699i
$735$		0			0
$736$	7.00000	−	29.1033i	0.258023	−	1.07276i
$737$	−19.7990	−	19.7990i	−0.729305	−	0.729305i
$738$		0			0
$739$	26.4575			0.973255			0.486628	−	0.873609i	$-0.338227\pi$
$739$	26.4575			0.973255			0.486628	+	0.873609i	$0.338227\pi$
$740$	−12.2269	−	3.24067i	−0.449471	−	0.119130i
$741$		0			0
$742$	17.4170	+	38.5830i	0.639398	+	1.41643i
$743$	26.1916	+	26.1916i	0.960877	+	0.960877i	0.999263	−	0.0383863i	$-0.0122217\pi$
$743$	26.1916	+	26.1916i	0.960877	+	0.960877i	−0.0383863	+	0.999263i	$0.512222\pi$
$744$		0			0
$745$	5.00000	−	15.0000i	0.183186	−	0.549557i
$746$	2.82843	−	7.48331i	0.103556	−	0.273984i
$747$		0			0
$748$	0.937254	+	14.9373i	0.0342694	+	0.546160i
$749$		−	19.7990i		−	0.723439i
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$	16.7201	+	12.9784i	0.609718	+	0.473274i
$753$		0			0
$754$	−5.29150	−	2.00000i	−0.192705	−	0.0728357i
$755$	−11.2250	+	33.6749i	−0.408519	+	1.22556i
$756$		0			0
$757$	−14.0000	−	14.0000i	−0.508839	−	0.508839i	0.405331	−	0.914170i	$-0.367156\pi$
$757$	−14.0000	−	14.0000i	−0.508839	−	0.508839i	−0.914170	+	0.405331i	$0.867156\pi$
$758$	34.1029	−	15.3946i	1.23867	−	0.559157i
$759$		0			0
$760$	−19.4575	+	27.2288i	−0.705798	+	0.987691i
$761$	25.4558			0.922774			0.461387	−	0.887199i	$-0.347352\pi$
$761$	25.4558			0.922774			0.461387	+	0.887199i	$0.347352\pi$
$762$		0			0
$763$	−15.8745	−	15.8745i	−0.574696	−	0.574696i
$764$	11.2250	+	9.89949i	0.406105	+	0.358151i
$765$		0			0
$766$	−35.0000	−	13.2288i	−1.26460	−	0.477974i
$767$	−22.4499	+	22.4499i	−0.810621	+	0.810621i
$768$		0			0
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$	34.3377	+	27.9450i	1.23744	+	1.00707i
$771$		0			0
$772$	0.885622	+	14.1144i	0.0318742	+	0.507988i
$773$	1.41421	−	1.41421i	0.0508657	−	0.0508657i	−0.681216	−	0.732082i	$-0.738549\pi$
$773$	1.41421	−	1.41421i	0.0508657	−	0.0508657i	0.732082	+	0.681216i	$0.238549\pi$
$774$		0			0
$775$		0			0
$776$	−17.6777	+	9.35414i	−0.634591	+	0.335794i
$777$		0			0
$778$	−18.9261	−	41.9261i	−0.678535	−	1.50312i
$779$	44.8999			1.60871
$780$		0			0
$781$	−56.0000			−2.00384
$782$	−6.15784	−	13.6412i	−0.220204	−	0.487807i
$783$		0			0
$784$	−27.7804	+	3.50000i	−0.992157	+	0.125000i
$785$	22.6274	+	45.2548i	0.807607	+	1.61521i
$786$		0			0
$787$	37.0405	−	37.0405i	1.32035	−	1.32035i	0.406862	−	0.913489i	$-0.366623\pi$
$787$	37.0405	−	37.0405i	1.32035	−	1.32035i	0.913489	−	0.406862i	$-0.133377\pi$
$788$	7.98430	−	0.500983i	0.284429	−	0.0178468i
$789$		0			0
$790$	33.2915	−	3.41699i	1.18446	−	0.121571i
$791$		−	37.4166i		−	1.33038i
$792$		0			0
$793$	−4.00000	+	4.00000i	−0.142044	+	0.142044i
$794$	7.48331	+	2.82843i	0.265573	+	0.100377i
$795$		0			0
$796$	−7.00000	+	7.93725i	−0.248108	+	0.281329i
$797$	15.5563	+	15.5563i	0.551034	+	0.551034i	0.926739	−	0.375705i	$-0.122599\pi$
$797$	15.5563	+	15.5563i	0.551034	+	0.551034i	−0.375705	+	0.926739i	$0.622599\pi$
$798$		0			0
$799$	10.5830			0.374400
$800$	2.65881	−	28.1590i	0.0940032	−	0.995572i
$801$		0			0
$802$	43.7490	−	19.7490i	1.54483	−	0.697362i
$803$	18.7083	+	18.7083i	0.660201	+	0.660201i
$804$		0			0
$805$	−42.0000	−	14.0000i	−1.48031	−	0.493435i
$806$		0			0
$807$		0			0
$808$	10.5941	−	34.4059i	0.372700	−	1.21039i
$809$		−	28.2843i		−	0.994422i	−0.867630	−	0.497211i	$-0.834357\pi$
$809$		−	28.2843i		−	0.994422i	0.867630	−	0.497211i	$-0.165643\pi$
$810$		0			0
$811$		−	15.8745i		−	0.557429i	−0.960374	−	0.278715i	$-0.910092\pi$
$811$		−	15.8745i		−	0.557429i	0.960374	−	0.278715i	$-0.0899084\pi$
$812$	−10.5622	+	0.662739i	−0.370662	+	0.0232576i
$813$		0			0
$814$	−5.29150	+	14.0000i	−0.185467	+	0.490700i
$815$	−14.9666	−	29.9333i	−0.524258	−	1.04852i
$816$		0			0
$817$	−28.0000	−	28.0000i	−0.979596	−	0.979596i
$818$	−20.9470	−	46.4028i	−0.732394	−	1.62244i
$819$		0			0
$820$	−32.8118	+	19.0627i	−1.14584	+	0.665700i
$821$	−12.7279			−0.444208			−0.222104	−	0.975023i	$-0.571292\pi$
$821$	−12.7279			−0.444208			−0.222104	+	0.975023i	$0.571292\pi$
$822$		0			0
$823$	−2.64575	−	2.64575i	−0.0922251	−	0.0922251i	0.659489	−	0.751714i	$-0.270773\pi$
$823$	−2.64575	−	2.64575i	−0.0922251	−	0.0922251i	−0.751714	+	0.659489i	$0.770773\pi$
$824$	−9.35414	+	4.94975i	−0.325867	+	0.172433i
$825$		0			0
$826$	−21.0000	+	55.5608i	−0.730683	+	1.93321i
$827$	29.9333	−	29.9333i	1.04088	−	1.04088i	0.0417535	−	0.999128i	$-0.486706\pi$
$827$	29.9333	−	29.9333i	1.04088	−	1.04088i	0.999128	−	0.0417535i	$-0.0132944\pi$
$828$		0			0
$829$			30.0000i			1.04194i	0.853574	+	0.520972i	$0.174430\pi$
$829$			30.0000i			1.04194i	−0.853574	+	0.520972i	$0.825570\pi$
$830$	12.9784	+	10.5622i	0.450487	+	0.366620i
$831$		0			0
$832$	22.2288	−	4.22876i	0.770643	−	0.146606i
$833$	−9.89949	+	9.89949i	−0.342997	+	0.342997i
$834$		0			0
$835$	−10.5830	+	5.29150i	−0.366240	+	0.183120i
$836$	29.6985	+	26.1916i	1.02714	+	0.905855i
$837$		0			0
$838$	14.4686	−	6.53137i	0.499810	−	0.225623i
$839$	22.4499			0.775058			0.387529	−	0.921857i	$-0.373329\pi$
$839$	22.4499			0.775058			0.387529	+	0.921857i	$0.373329\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	18.0455	−	8.14605i	0.621891	−	0.280732i
$843$		0			0
$844$	23.8118	+	21.0000i	0.819635	+	0.722850i
$845$	−3.53553	+	10.6066i	−0.121626	+	0.364878i
$846$		0			0
$847$	7.93725	−	7.93725i	0.272727	−	0.272727i
$848$	−25.2784	−	19.6215i	−0.868063	−	0.673806i
$849$		0			0
$850$	−7.58301	−	11.9373i	−0.260095	−	0.409444i
$851$		−	14.9666i		−	0.513049i
$852$		0			0
$853$	16.0000	−	16.0000i	0.547830	−	0.547830i	−0.377983	−	0.925813i	$-0.623382\pi$
$853$	16.0000	−	16.0000i	0.547830	−	0.547830i	0.925813	+	0.377983i	$0.123382\pi$
$854$	−3.74166	+	9.89949i	−0.128037	+	0.338754i
$855$		0			0
$856$	7.00000	+	13.2288i	0.239255	+	0.452150i
$857$	24.0416	+	24.0416i	0.821246	+	0.821246i	0.986287	−	0.165040i	$-0.0527754\pi$
$857$	24.0416	+	24.0416i	0.821246	+	0.821246i	−0.165040	+	0.986287i	$0.552775\pi$
$858$		0			0
$859$	−5.29150			−0.180544			−0.0902719	−	0.995917i	$-0.528774\pi$
$859$	−5.29150			−0.180544			−0.0902719	+	0.995917i	$0.528774\pi$
$860$	32.3494	+	8.57402i	1.10311	+	0.292372i
$861$		0			0
$862$	4.35425	+	9.64575i	0.148306	+	0.328536i
$863$	−18.7083	−	18.7083i	−0.636837	−	0.636837i	0.312937	−	0.949774i	$-0.398687\pi$
$863$	−18.7083	−	18.7083i	−0.636837	−	0.636837i	−0.949774	+	0.312937i	$0.898687\pi$
$864$		0			0
$865$	4.00000	−	2.00000i	0.136004	−	0.0680020i
$866$	−16.2635	+	43.0291i	−0.552655	+	1.46219i
$867$		0			0
$868$		0			0
$869$		−	39.5980i		−	1.34327i
$870$		0			0
$871$			21.1660i			0.717183i
$872$	16.2191	+	4.99412i	0.549248	+	0.169122i
$873$		0			0
$874$	−37.0405	−	14.0000i	−1.25291	−	0.473557i
$875$	−41.1582	−	7.48331i	−1.39140	−	0.252982i
$876$		0			0
$877$	28.0000	+	28.0000i	0.945493	+	0.945493i	0.998589	−	0.0530966i	$-0.0169091\pi$
$877$	28.0000	+	28.0000i	0.945493	+	0.945493i	−0.0530966	+	0.998589i	$0.516909\pi$
$878$	−47.7440	+	21.5524i	−1.61128	+	0.727359i
$879$		0			0
$880$	−32.8229	−	6.53137i	−1.10646	−	0.220173i
$881$	16.9706			0.571753			0.285876	−	0.958267i	$-0.407715\pi$
$881$	16.9706			0.571753			0.285876	+	0.958267i	$0.407715\pi$
$882$		0			0
$883$	21.1660	+	21.1660i	0.712293	+	0.712293i	0.967014	−	0.254721i	$-0.0819838\pi$
$883$	21.1660	+	21.1660i	0.712293	+	0.712293i	−0.254721	+	0.967014i	$0.581984\pi$
$884$	7.48331	−	8.48528i	0.251691	−	0.285391i
$885$		0			0
$886$	−14.0000	−	5.29150i	−0.470339	−	0.177772i
$887$	18.7083	−	18.7083i	0.628163	−	0.628163i	−0.319443	−	0.947606i	$-0.603496\pi$
$887$	18.7083	−	18.7083i	0.628163	−	0.628163i	0.947606	+	0.319443i	$0.103496\pi$
$888$		0			0
$889$		−	14.0000i		−	0.469545i
$890$	−3.65292	−	35.5901i	−0.122446	−	1.19298i
$891$		0			0
$892$	−7.46863	+	0.468627i	−0.250068	+	0.0156908i
$893$	19.7990	−	19.7990i	0.662548	−	0.662548i
$894$		0			0
$895$	−23.8118	−	7.93725i	−0.795939	−	0.265313i
$896$	34.6482	−	24.3208i	1.15752	−	0.812500i
$897$		0			0
$898$	8.22876	+	18.2288i	0.274597	+	0.608301i
$899$		0			0
$900$		0			0
$901$	−16.0000			−0.533037
$902$	18.4735	+	40.9235i	0.615101	+	1.36260i
$903$		0			0
$904$	13.2288	+	25.0000i	0.439982	+	0.831488i
$905$	−21.2132	−	7.07107i	−0.705151	−	0.235050i
$906$		0			0
$907$	21.1660	−	21.1660i	0.702806	−	0.702806i	−0.262206	−	0.965012i	$-0.584450\pi$
$907$	21.1660	−	21.1660i	0.702806	−	0.702806i	0.965012	+	0.262206i	$0.0844500\pi$
$908$	−1.32548	−	21.1245i	−0.0439875	−	0.701040i
$909$		0			0
$910$	−3.41699	−	33.2915i	−0.113272	−	1.10360i
$911$		−	37.4166i		−	1.23967i	−0.784734	−	0.619833i	$-0.787200\pi$
$911$		−	37.4166i		−	1.23967i	0.784734	−	0.619833i	$-0.212800\pi$
$912$		0			0
$913$	14.0000	−	14.0000i	0.463332	−	0.463332i
$914$	−31.8041	−	12.0208i	−1.05199	−	0.397613i
$915$		0			0
$916$	27.0000	+	23.8118i	0.892105	+	0.786763i
$917$	9.89949	+	9.89949i	0.326910	+	0.326910i
$918$		0			0
$919$	42.3320			1.39640			0.698202	−	0.715901i	$-0.253984\pi$
$919$	42.3320			1.39640			0.698202	+	0.715901i	$0.253984\pi$
$920$	33.0122	−	5.49510i	1.08838	−	0.181168i
$921$		0			0
$922$	−16.4059	+	7.40588i	−0.540299	+	0.243900i
$923$	29.9333	+	29.9333i	0.985265	+	0.985265i
$924$		0			0
$925$	−2.00000	−	14.0000i	−0.0657596	−	0.460317i
$926$	54.4472	+	20.5791i	1.78925	+	0.676272i
$927$		0			0
$928$	6.82288	−	4.17712i	0.223972	−	0.137121i
$929$			14.1421i			0.463988i	0.972717	+	0.231994i	$0.0745250\pi$
$929$			14.1421i			0.463988i	−0.972717	+	0.231994i	$0.925475\pi$
$930$		0			0
$931$			37.0405i			1.21395i
$932$	−1.75344	−	27.9450i	−0.0574359	−	0.915370i
$933$		0			0
$934$	13.2288	−	35.0000i	0.432858	−	1.14523i
$935$	−14.9666	+	7.48331i	−0.489461	+	0.244731i
$936$		0			0
$937$	37.0000	+	37.0000i	1.20874	+	1.20874i	0.971436	+	0.237301i	$0.0762628\pi$
$937$	37.0000	+	37.0000i	1.20874	+	1.20874i	0.237301	+	0.971436i	$0.423737\pi$
$938$	16.2921	+	36.0911i	0.531956	+	1.17842i
$939$		0			0
$940$	−6.06275	+	22.8745i	−0.197745	+	0.746084i
$941$	12.7279			0.414918			0.207459	−	0.978244i	$-0.433481\pi$
$941$	12.7279			0.414918			0.207459	+	0.978244i	$0.433481\pi$
$942$		0			0
$943$	−31.7490	−	31.7490i	−1.03389	−	1.03389i
$944$	−5.61249	−	44.5477i	−0.182671	−	1.44991i
$945$		0			0
$946$	14.0000	−	37.0405i	0.455179	−	1.20429i
$947$	−37.4166	+	37.4166i	−1.21588	+	1.21588i	−0.246812	+	0.969063i	$0.579383\pi$
$947$	−37.4166	+	37.4166i	−1.21588	+	1.21588i	−0.969063	+	0.246812i	$0.920617\pi$
$948$		0			0
$949$		−	20.0000i		−	0.649227i
$950$	−36.5191	−	8.14605i	−1.18483	−	0.264293i
$951$		0			0
$952$	6.22876	−	20.2288i	0.201875	−	0.655618i
$953$	26.8701	−	26.8701i	0.870407	−	0.870407i	−0.122110	−	0.992517i	$-0.538966\pi$
$953$	26.8701	−	26.8701i	0.870407	−	0.870407i	0.992517	+	0.122110i	$0.0389661\pi$
$954$		0			0
$955$	−5.29150	+	15.8745i	−0.171229	+	0.513687i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	52.3832			1.69154
$960$		0			0
$961$	31.0000			1.00000
$962$	10.3117	−	4.65489i	0.332464	−	0.150080i
$963$		0			0
$964$	26.4575	−	30.0000i	0.852139	−	0.966235i
$965$	−14.1421	+	7.07107i	−0.455251	+	0.227626i
$966$		0			0
$967$	−34.3948	+	34.3948i	−1.10606	+	1.10606i	−0.112398	+	0.993663i	$0.535853\pi$
$967$	−34.3948	+	34.3948i	−1.10606	+	1.10606i	−0.993663	+	0.112398i	$0.964147\pi$
$968$	−2.49706	+	8.10954i	−0.0802585	+	0.260651i
$969$		0			0
$970$	−17.3431	−	14.1144i	−0.556854	−	0.453185i
$971$		−	26.1916i		−	0.840528i	−0.907402	−	0.420264i	$-0.861937\pi$
$971$		−	26.1916i		−	0.840528i	0.907402	−	0.420264i	$-0.138063\pi$
$972$		0			0
$973$	14.0000	−	14.0000i	0.448819	−	0.448819i
$974$	−1.87083	+	4.94975i	−0.0599452	+	0.158600i
$975$		0			0
$976$	−1.00000	−	7.93725i	−0.0320092	−	0.254065i
$977$	32.5269	+	32.5269i	1.04063	+	1.04063i	0.999139	+	0.0414892i	$0.0132102\pi$
$977$	32.5269	+	32.5269i	1.04063	+	1.04063i	0.0414892	+	0.999139i	$0.486790\pi$
$978$		0			0
$979$	−42.3320			−1.35294
$980$	−15.7260	−	27.0683i	−0.502347	−	0.864666i
$981$		0			0
$982$	10.8856	+	24.1144i	0.347374	+	0.769521i
$983$	−18.7083	−	18.7083i	−0.596702	−	0.596702i	0.342732	−	0.939433i	$-0.388648\pi$
$983$	−18.7083	−	18.7083i	−0.596702	−	0.596702i	−0.939433	+	0.342732i	$0.888648\pi$
$984$		0			0
$985$	4.00000	+	8.00000i	0.127451	+	0.254901i
$986$	1.41421	−	3.74166i	0.0450377	−	0.119159i
$987$		0			0
$988$	−1.87451	−	29.8745i	−0.0596360	−	0.950435i
$989$			39.5980i			1.25914i
$990$		0			0
$991$			15.8745i			0.504270i	0.967692	+	0.252135i	$0.0811328\pi$
$991$			15.8745i			0.504270i	−0.967692	+	0.252135i	$0.918867\pi$
$992$		0			0
$993$		0			0
$994$	74.0810	+	28.0000i	2.34971	+	0.888106i
$995$	−11.2250	−	3.74166i	−0.355856	−	0.118619i
$996$		0			0
$997$	10.0000	+	10.0000i	0.316703	+	0.316703i	0.847499	−	0.530796i	$-0.178107\pi$
$997$	10.0000	+	10.0000i	0.316703	+	0.316703i	−0.530796	+	0.847499i	$0.678107\pi$
$998$	−47.7440	+	21.5524i	−1.51131	+	0.682230i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.k.d.127.4	yes	8
3.2	odd	2	inner	180.2.k.d.127.1	✓	8
4.3	odd	2	inner	180.2.k.d.127.2	yes	8
5.2	odd	4		900.2.k.k.343.3		8
5.3	odd	4	inner	180.2.k.d.163.2	yes	8
5.4	even	2		900.2.k.k.307.1		8
12.11	even	2	inner	180.2.k.d.127.3	yes	8
15.2	even	4		900.2.k.k.343.2		8
15.8	even	4	inner	180.2.k.d.163.3	yes	8
15.14	odd	2		900.2.k.k.307.4		8
20.3	even	4	inner	180.2.k.d.163.4	yes	8
20.7	even	4		900.2.k.k.343.1		8
20.19	odd	2		900.2.k.k.307.3		8
60.23	odd	4	inner	180.2.k.d.163.1	yes	8
60.47	odd	4		900.2.k.k.343.4		8
60.59	even	2		900.2.k.k.307.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.k.d.127.1	✓	8	3.2	odd	2	inner
180.2.k.d.127.2	yes	8	4.3	odd	2	inner
180.2.k.d.127.3	yes	8	12.11	even	2	inner
180.2.k.d.127.4	yes	8	1.1	even	1	trivial
180.2.k.d.163.1	yes	8	60.23	odd	4	inner
180.2.k.d.163.2	yes	8	5.3	odd	4	inner
180.2.k.d.163.3	yes	8	15.8	even	4	inner
180.2.k.d.163.4	yes	8	20.3	even	4	inner
900.2.k.k.307.1		8	5.4	even	2
900.2.k.k.307.2		8	60.59	even	2
900.2.k.k.307.3		8	20.19	odd	2
900.2.k.k.307.4		8	15.14	odd	2
900.2.k.k.343.1		8	20.7	even	4
900.2.k.k.343.2		8	15.2	even	4
900.2.k.k.343.3		8	5.2	odd	4
900.2.k.k.343.4		8	60.47	odd	4

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28897 - 0.581861i) q^{2} +(1.32288 - 1.50000i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-2.64575 + 2.64575i) q^{7} +(0.832353 - 2.70318i) q^{8} +O(q^{10})\)	\(q+(1.28897 - 0.581861i) q^{2} +(1.32288 - 1.50000i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-2.64575 + 2.64575i) q^{7} +(0.832353 - 2.70318i) q^{8} +(3.14575 - 0.322876i) q^{10} -3.74166i q^{11} +(-2.00000 + 2.00000i) q^{13} +(-1.87083 + 4.94975i) q^{14} +(-0.500000 - 3.96863i) q^{16} +(-1.41421 - 1.41421i) q^{17} -5.29150 q^{19} +(3.86690 - 2.24657i) q^{20} +(-2.17712 - 4.82288i) q^{22} +(3.74166 + 3.74166i) q^{23} +(4.00000 + 3.00000i) q^{25} +(-1.41421 + 3.74166i) q^{26} +(0.468627 + 7.46863i) q^{28} +1.41421i q^{29} +(-2.95367 - 4.82450i) q^{32} +(-2.64575 - 1.00000i) q^{34} +(-7.48331 + 3.74166i) q^{35} +(-2.00000 - 2.00000i) q^{37} +(-6.82058 + 3.07892i) q^{38} +(3.67712 - 5.14575i) q^{40} -8.48528 q^{41} +(5.29150 + 5.29150i) q^{43} +(-5.61249 - 4.94975i) q^{44} +(7.00000 + 2.64575i) q^{46} +(-3.74166 + 3.74166i) q^{47} -7.00000i q^{49} +(6.90145 + 1.53946i) q^{50} +(0.354249 + 5.64575i) q^{52} +(5.65685 - 5.65685i) q^{53} +(2.64575 - 7.93725i) q^{55} +(4.94975 + 9.35414i) q^{56} +(0.822876 + 1.82288i) q^{58} +11.2250 q^{59} +2.00000 q^{61} +(-6.61438 - 4.50000i) q^{64} +(-5.65685 + 2.82843i) q^{65} +(5.29150 - 5.29150i) q^{67} +(-3.99215 + 0.250492i) q^{68} +(-7.46863 + 9.17712i) q^{70} -14.9666i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-3.74166 - 1.41421i) q^{74} +(-7.00000 + 7.93725i) q^{76} +(9.89949 + 9.89949i) q^{77} +10.5830 q^{79} +(1.74558 - 8.77228i) q^{80} +(-10.9373 + 4.93725i) q^{82} +(3.74166 + 3.74166i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(9.89949 + 3.74166i) q^{86} +(-10.1144 - 3.11438i) q^{88} -11.3137i q^{89} -10.5830i q^{91} +(10.5622 - 0.662739i) q^{92} +(-2.64575 + 7.00000i) q^{94} +(-11.2250 - 3.74166i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(-4.07303 - 9.02277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{10} - 16 q^{13} - 4 q^{16} - 28 q^{22} + 32 q^{25} - 28 q^{28} - 16 q^{37} + 40 q^{40} + 56 q^{46} + 24 q^{52} - 4 q^{58} + 16 q^{61} - 28 q^{70} - 40 q^{73} - 56 q^{76} - 24 q^{82} - 16 q^{85} - 28 q^{88} - 40 q^{97}+O(q^{100}) \) 8 * q + 4 * q^10 - 16 * q^13 - 4 * q^16 - 28 * q^22 + 32 * q^25 - 28 * q^28 - 16 * q^37 + 40 * q^40 + 56 * q^46 + 24 * q^52 - 4 * q^58 + 16 * q^61 - 28 * q^70 - 40 * q^73 - 56 * q^76 - 24 * q^82 - 16 * q^85 - 28 * q^88 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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