LMFDB - Embedded newform 180.2.k.d.163.1

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			163.1
Root			$-1.28897 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	180.163
Dual form			180.2.k.d.127.1

$q$-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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$	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	$-0.672021\pi$
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	0.857493	+	0.514496i	$0.172021\pi$
$18$		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	$-0.936012\pi$
$23$	−3.74166	+	3.74166i	−0.780189	+	0.780189i	0.199673	+	0.979863i	$0.436012\pi$
$24$		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	−0.852129	−	0.523331i	$-0.824689\pi$
$37$	−2.00000	+	2.00000i	−0.328798	+	0.328798i	0.523331	+	0.852129i	$0.324689\pi$
$38$	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	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$	5.29150	−	5.29150i	0.806947	−	0.806947i	−0.177224	−	0.984171i	$-0.556712\pi$
$43$	5.29150	−	5.29150i	0.806947	−	0.806947i	0.984171	+	0.177224i	$0.0567117\pi$
$44$	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	$-0.123883\pi$
$47$	3.74166	+	3.74166i	0.545777	+	0.545777i	−0.379440	+	0.925216i	$0.623883\pi$
$48$		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	$-0.435160\pi$
$53$	−5.65685	−	5.65685i	−0.777029	−	0.777029i	−0.979324	+	0.202296i	$0.935160\pi$
$54$		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	$-0.760798\pi$
$59$	−11.2250			−1.46137			−0.730683	+	0.682716i	$0.760798\pi$
$60$		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	0.952136	−	0.305676i	$-0.0988823\pi$
$67$	5.29150	+	5.29150i	0.646460	+	0.646460i	−0.305676	+	0.952136i	$0.598882\pi$
$68$	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	0.351123	−	0.936329i	$-0.385800\pi$
$73$	−5.00000	−	5.00000i	−0.585206	−	0.585206i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	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	$-0.843791\pi$
$83$	−3.74166	+	3.74166i	−0.410700	+	0.410700i	0.471282	+	0.881982i	$0.343791\pi$
$84$		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	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−5.00000	+	5.00000i	−0.507673	+	0.507673i	0.406138	+	0.913812i	$0.366875\pi$
$98$	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	$-0.718274\pi$
$101$	−12.7279			−1.26648			−0.633238	+	0.773957i	$0.718274\pi$
$102$		0			0
$103$	−2.64575	+	2.64575i	−0.260694	+	0.260694i	−0.825336	−	0.564642i	$-0.809014\pi$
$103$	−2.64575	+	2.64575i	−0.260694	+	0.260694i	0.564642	+	0.825336i	$0.309014\pi$
$104$	−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	$-0.167670\pi$
$107$	3.74166	+	3.74166i	0.361720	+	0.361720i	−0.502726	+	0.864446i	$0.667670\pi$
$108$		0			0
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	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	$-0.0941239\pi$
$113$	7.07107	+	7.07107i	0.665190	+	0.665190i	−0.291409	+	0.956599i	$0.594124\pi$
$114$		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	0.579909	−	0.814681i	$-0.303088\pi$
$127$	−2.64575	−	2.64575i	−0.234772	−	0.234772i	−0.814681	+	0.579909i	$0.803088\pi$
$128$	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	$-0.545942\pi$
$137$	9.89949	−	9.89949i	0.845771	−	0.845771i	0.989602	+	0.143831i	$0.0459423\pi$
$138$		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	$-0.776472\pi$
$151$		−	15.8745i		−	1.29185i	0.763401	−	0.645925i	$-0.223528\pi$
$152$	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	0.334567	−	0.942372i	$-0.391410\pi$
$157$	16.0000	−	16.0000i	1.27694	−	1.27694i	0.942372	−	0.334567i	$-0.108590\pi$
$158$	−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	−0.987368	−	0.158443i	$-0.949353\pi$
$163$	−10.5830	+	10.5830i	−0.828925	+	0.828925i	0.158443	+	0.987368i	$0.449353\pi$
$164$	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	$-0.184367\pi$
$167$	3.74166	+	3.74166i	0.289538	+	0.289538i	−0.547359	+	0.836898i	$0.684367\pi$
$168$		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	$-0.274224\pi$
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	−0.758820	+	0.651300i	$0.774224\pi$
$174$		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	$-0.362207\pi$
$179$	11.2250			0.838994			0.419497	+	0.907757i	$0.362207\pi$
$180$		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	0.503871	−	0.863779i	$-0.331909\pi$
$193$	−5.00000	−	5.00000i	−0.359908	−	0.359908i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	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	$-0.795512\pi$
$197$	−2.82843	+	2.82843i	−0.201517	+	0.201517i	0.599133	+	0.800650i	$0.295512\pi$
$198$		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	$-0.815989\pi$
$211$		−	15.8745i		−	1.09285i	0.837509	−	0.546423i	$-0.184011\pi$
$212$	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	−0.790122	−	0.612949i	$-0.789983\pi$
$223$	−2.64575	+	2.64575i	−0.177173	+	0.177173i	0.612949	+	0.790122i	$0.289983\pi$
$224$	−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	$-0.364229\pi$
$227$	−7.48331	−	7.48331i	−0.496685	−	0.496685i	−0.910404	+	0.413719i	$0.864229\pi$
$228$		0			0
$229$		−	18.0000i		−	1.18947i	−0.803921	−	0.594737i	$-0.797256\pi$
$229$		−	18.0000i		−	1.18947i	0.803921	−	0.594737i	$-0.202744\pi$
$230$	−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	$-0.401644\pi$
$233$	−9.89949	−	9.89949i	−0.648537	−	0.648537i	−0.952639	+	0.304102i	$0.901644\pi$
$234$		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	$-0.730131\pi$
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	0.749838	+	0.661622i	$0.230131\pi$
$258$		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	0.167778	−	0.985825i	$-0.446341\pi$
$263$	18.7083	−	18.7083i	1.15360	−	1.15360i	0.985825	−	0.167778i	$-0.0536590\pi$
$264$		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	$0.160145\pi$
$271$			15.8745i			0.964308i	−0.876087	+	0.482154i	$0.839855\pi$
$272$	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	−0.764634	−	0.644465i	$-0.777080\pi$
$277$	−2.00000	+	2.00000i	−0.120168	+	0.120168i	0.644465	+	0.764634i	$0.277080\pi$
$278$	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	$-0.581448\pi$
$281$	−8.48528			−0.506189			−0.253095	+	0.967442i	$0.581448\pi$
$282$		0			0
$283$	5.29150	−	5.29150i	0.314547	−	0.314547i	−0.532121	−	0.846668i	$-0.678605\pi$
$283$	5.29150	−	5.29150i	0.314547	−	0.314547i	0.846668	+	0.532121i	$0.178605\pi$
$284$	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	$-0.325078\pi$
$293$	−5.65685	−	5.65685i	−0.330477	−	0.330477i	−0.852768	+	0.522291i	$0.825078\pi$
$294$		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	0.841797	−	0.539795i	$-0.181498\pi$
$307$	5.29150	+	5.29150i	0.302002	+	0.302002i	−0.539795	+	0.841797i	$0.681498\pi$
$308$	−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	0.324224	−	0.945980i	$-0.394897\pi$
$313$	−11.0000	−	11.0000i	−0.621757	−	0.621757i	−0.945980	+	0.324224i	$0.894897\pi$
$314$	−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	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$		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	$0.143701\pi$
$331$			15.8745i			0.872542i	−0.899815	+	0.436271i	$0.856299\pi$
$332$	−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	−0.940102	−	0.340894i	$-0.889270\pi$
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	0.340894	+	0.940102i	$0.389270\pi$
$338$	−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	$-0.0576688\pi$
$347$	14.9666	+	14.9666i	0.803451	+	0.803451i	−0.180182	+	0.983633i	$0.557669\pi$
$348$		0			0
$349$			6.00000i			0.321173i	0.987022	+	0.160586i	$0.0513385\pi$
$349$			6.00000i			0.321173i	−0.987022	+	0.160586i	$0.948662\pi$
$350$	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	0.940887	+	0.338719i	$0.109994\pi$
$353$	24.0416	+	24.0416i	1.27961	+	1.27961i	0.338719	+	0.940887i	$0.390006\pi$
$354$		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	$-0.298168\pi$
$359$	22.4499			1.18486			0.592431	+	0.805621i	$0.298168\pi$
$360$		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	0.634673	−	0.772780i	$-0.281135\pi$
$367$	−2.64575	−	2.64575i	−0.138107	−	0.138107i	−0.772780	+	0.634673i	$0.781135\pi$
$368$	−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	0.803039	−	0.595927i	$-0.203215\pi$
$373$	4.00000	+	4.00000i	0.207112	+	0.207112i	−0.595927	+	0.803039i	$0.703215\pi$
$374$	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	$-0.513730\pi$
$383$	18.7083	−	18.7083i	0.955949	−	0.955949i	0.999070	+	0.0431210i	$0.0137301\pi$
$384$		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	−0.599569	−	0.800323i	$-0.704661\pi$
$397$	4.00000	−	4.00000i	0.200754	−	0.200754i	0.800323	+	0.599569i	$0.204661\pi$
$398$	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	$-0.821875\pi$
$401$	−33.9411			−1.69494			−0.847469	+	0.530844i	$0.821875\pi$
$402$		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	$0.349326\pi$
$409$			36.0000i			1.78009i	−0.455877	+	0.890043i	$0.650674\pi$
$410$	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	$-0.588409\pi$
$419$	−11.2250			−0.548376			−0.274188	+	0.961676i	$0.588409\pi$
$420$		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	−0.993759	−	0.111551i	$-0.964418\pi$
$433$	−23.0000	−	23.0000i	−1.10531	−	1.10531i	−0.111551	−	0.993759i	$-0.535582\pi$
$434$		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	$-0.669107\pi$
$443$	7.48331	−	7.48331i	0.355543	−	0.355543i	0.862167	+	0.506624i	$0.169107\pi$
$444$		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	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	0.187112	+	0.982339i	$0.440087\pi$
$458$	−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	$-0.404214\pi$
$461$	12.7279			0.592798			0.296399	+	0.955064i	$0.404214\pi$
$462$		0			0
$463$	29.1033	−	29.1033i	1.35254	−	1.35254i	0.469737	−	0.882806i	$-0.344349\pi$
$463$	29.1033	−	29.1033i	1.35254	−	1.35254i	0.882806	−	0.469737i	$-0.155651\pi$
$464$	−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	$-0.459697\pi$
$467$	−18.7083	−	18.7083i	−0.865716	−	0.865716i	−0.991995	+	0.126279i	$0.959697\pi$
$468$		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	0.644616	−	0.764506i	$-0.277017\pi$
$487$	−2.64575	−	2.64575i	−0.119890	−	0.119890i	−0.764506	+	0.644616i	$0.777017\pi$
$488$	−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	$-0.787638\pi$
$503$	−3.74166	+	3.74166i	−0.166832	+	0.166832i	0.618753	+	0.785585i	$0.287638\pi$
$504$		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	$-0.688286\pi$
$521$	−25.4558			−1.11524			−0.557620	+	0.830096i	$0.688286\pi$
$522$		0			0
$523$	5.29150	−	5.29150i	0.231381	−	0.231381i	−0.581888	−	0.813269i	$-0.697686\pi$
$523$	5.29150	−	5.29150i	0.231381	−	0.231381i	0.813269	+	0.581888i	$0.197686\pi$
$524$	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	−0.989971	−	0.141271i	$-0.954881\pi$
$547$	−26.4575	−	26.4575i	−1.13124	−	1.13124i	−0.141271	−	0.989971i	$-0.545119\pi$
$548$	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	$-0.695789\pi$
$557$	5.65685	−	5.65685i	0.239689	−	0.239689i	0.816721	+	0.577033i	$0.195789\pi$
$558$		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	0.311188	−	0.950348i	$-0.399273\pi$
$563$	29.9333	−	29.9333i	1.26154	−	1.26154i	0.950348	−	0.311188i	$-0.100727\pi$
$564$		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	$-0.892221\pi$
$571$		−	15.8745i		−	0.664327i	0.943222	−	0.332164i	$-0.107779\pi$
$572$	−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	−0.897977	−	0.440041i	$-0.854964\pi$
$577$	−11.0000	+	11.0000i	−0.457936	+	0.457936i	0.440041	+	0.897977i	$0.354964\pi$
$578$	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	$-0.433854\pi$
$587$	−18.7083	−	18.7083i	−0.772174	−	0.772174i	−0.978486	+	0.206313i	$0.933854\pi$
$588$		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	$-0.429254\pi$
$593$	−18.3848	−	18.3848i	−0.754972	−	0.754972i	−0.975403	+	0.220430i	$0.929254\pi$
$594$		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	$-0.651663\pi$
$599$	−22.4499			−0.917280			−0.458640	+	0.888622i	$0.651663\pi$
$600$		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	0.651371	−	0.758759i	$-0.274194\pi$
$607$	−2.64575	−	2.64575i	−0.107388	−	0.107388i	−0.758759	+	0.651371i	$0.774194\pi$
$608$	−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	0.990026	+	0.140883i	$0.0449942\pi$
$613$	28.0000	+	28.0000i	1.13091	+	1.13091i	0.140883	+	0.990026i	$0.455006\pi$
$614$	−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	$-0.737182\pi$
$617$	1.41421	−	1.41421i	0.0569341	−	0.0569341i	0.735001	+	0.678066i	$0.237182\pi$
$618$		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	$-0.782253\pi$
$631$		−	31.7490i		−	1.26391i	0.775006	−	0.631954i	$-0.217747\pi$
$632$	−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	$-0.391214\pi$
$641$	16.9706			0.670297			0.335148	+	0.942165i	$0.391214\pi$
$642$		0			0
$643$	−10.5830	+	10.5830i	−0.417353	+	0.417353i	−0.884290	−	0.466937i	$-0.845357\pi$
$643$	−10.5830	+	10.5830i	−0.417353	+	0.417353i	0.466937	+	0.884290i	$0.345357\pi$
$644$	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	$-0.216831\pi$
$647$	3.74166	+	3.74166i	0.147100	+	0.147100i	−0.629721	+	0.776821i	$0.716831\pi$
$648$		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	$-0.0183201\pi$
$653$	24.0416	+	24.0416i	0.940822	+	0.940822i	−0.0575225	+	0.998344i	$0.518320\pi$
$654$		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	$-0.570159\pi$
$659$	−11.2250			−0.437263			−0.218631	+	0.975808i	$0.570159\pi$
$660$		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	0.829032	−	0.559202i	$-0.188892\pi$
$673$	7.00000	+	7.00000i	0.269830	+	0.269830i	−0.559202	+	0.829032i	$0.688892\pi$
$674$	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	0.0332533	−	0.999447i	$-0.489413\pi$
$677$	26.8701	−	26.8701i	1.03270	−	1.03270i	0.999447	−	0.0332533i	$-0.0105868\pi$
$678$		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	$-0.782280\pi$
$683$	−3.74166	+	3.74166i	−0.143171	+	0.143171i	0.631889	+	0.775059i	$0.282280\pi$
$684$		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	$0.360761\pi$
$691$			47.6235i			1.81168i	−0.423615	+	0.905842i	$0.639239\pi$
$692$	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	$-0.243641\pi$
$701$	38.1838			1.44218			0.721090	+	0.692841i	$0.243641\pi$
$702$		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	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	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	$-0.184167\pi$
$719$	44.8999			1.67448			0.837242	+	0.546833i	$0.184167\pi$
$720$		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	0.996565	+	0.0828154i	$0.0263912\pi$
$727$	29.1033	+	29.1033i	1.07938	+	1.07938i	0.0828154	+	0.996565i	$0.473609\pi$
$728$	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	0.867243	−	0.497885i	$-0.165890\pi$
$733$	10.0000	+	10.0000i	0.369358	+	0.369358i	−0.497885	+	0.867243i	$0.665890\pi$
$734$	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	$-0.987778\pi$
$743$	−26.1916	+	26.1916i	−0.960877	+	0.960877i	0.0383863	+	0.999263i	$0.487778\pi$
$744$		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	−0.914170	−	0.405331i	$-0.867156\pi$
$757$	−14.0000	+	14.0000i	−0.508839	+	0.508839i	0.405331	+	0.914170i	$0.367156\pi$
$758$	−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	$-0.652648\pi$
$761$	−25.4558			−0.922774			−0.461387	+	0.887199i	$0.652648\pi$
$762$		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	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$	−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	$-0.261451\pi$
$773$	−1.41421	−	1.41421i	−0.0508657	−	0.0508657i	−0.732082	+	0.681216i	$0.761451\pi$
$774$		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	0.913489	+	0.406862i	$0.133377\pi$
$787$	37.0405	+	37.0405i	1.32035	+	1.32035i	0.406862	+	0.913489i	$0.366623\pi$
$788$	−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	$-0.877401\pi$
$797$	−15.5563	+	15.5563i	−0.551034	+	0.551034i	0.375705	+	0.926739i	$0.377401\pi$
$798$		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	$0.0899084\pi$
$811$			15.8745i			0.557429i	−0.960374	+	0.278715i	$0.910092\pi$
$812$	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	$-0.428708\pi$
$821$	12.7279			0.444208			0.222104	+	0.975023i	$0.428708\pi$
$822$		0			0
$823$	−2.64575	+	2.64575i	−0.0922251	+	0.0922251i	−0.751714	−	0.659489i	$-0.770773\pi$
$823$	−2.64575	+	2.64575i	−0.0922251	+	0.0922251i	0.659489	+	0.751714i	$0.270773\pi$
$824$	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	−0.999128	−	0.0417535i	$-0.986706\pi$
$827$	−29.9333	−	29.9333i	−1.04088	−	1.04088i	−0.0417535	−	0.999128i	$-0.513294\pi$
$828$		0			0
$829$		−	30.0000i		−	1.04194i	−0.853574	−	0.520972i	$-0.825570\pi$
$829$		−	30.0000i		−	1.04194i	0.853574	−	0.520972i	$-0.174430\pi$
$830$	−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	$-0.626671\pi$
$839$	−22.4499			−0.775058			−0.387529	+	0.921857i	$0.626671\pi$
$840$		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	0.925813	−	0.377983i	$-0.123382\pi$
$853$	16.0000	+	16.0000i	0.547830	+	0.547830i	−0.377983	+	0.925813i	$0.623382\pi$
$854$	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	$-0.947225\pi$
$857$	−24.0416	+	24.0416i	−0.821246	+	0.821246i	0.165040	+	0.986287i	$0.447225\pi$
$858$		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	$-0.601313\pi$
$863$	18.7083	−	18.7083i	0.636837	−	0.636837i	0.949774	+	0.312937i	$0.101313\pi$
$864$		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	−0.0530966	−	0.998589i	$-0.516909\pi$
$877$	28.0000	−	28.0000i	0.945493	−	0.945493i	0.998589	+	0.0530966i	$0.0169091\pi$
$878$	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	$-0.592285\pi$
$881$	−16.9706			−0.571753			−0.285876	+	0.958267i	$0.592285\pi$
$882$		0			0
$883$	21.1660	−	21.1660i	0.712293	−	0.712293i	−0.254721	−	0.967014i	$-0.581984\pi$
$883$	21.1660	−	21.1660i	0.712293	−	0.712293i	0.967014	+	0.254721i	$0.0819838\pi$
$884$	−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	$-0.396504\pi$
$887$	−18.7083	−	18.7083i	−0.628163	−	0.628163i	−0.947606	+	0.319443i	$0.896504\pi$
$888$		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	0.965012	−	0.262206i	$-0.0844500\pi$
$907$	21.1660	+	21.1660i	0.702806	+	0.702806i	−0.262206	+	0.965012i	$0.584450\pi$
$908$	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	0.237301	−	0.971436i	$-0.423737\pi$
$937$	37.0000	−	37.0000i	1.20874	−	1.20874i	0.971436	−	0.237301i	$-0.0762628\pi$
$938$	−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	$-0.566519\pi$
$941$	−12.7279			−0.414918			−0.207459	+	0.978244i	$0.566519\pi$
$942$		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	0.969063	+	0.246812i	$0.0793830\pi$
$947$	37.4166	+	37.4166i	1.21588	+	1.21588i	0.246812	+	0.969063i	$0.420617\pi$
$948$		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	$-0.461034\pi$
$953$	−26.8701	−	26.8701i	−0.870407	−	0.870407i	−0.992517	+	0.122110i	$0.961034\pi$
$954$		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	−0.993663	−	0.112398i	$-0.964147\pi$
$967$	−34.3948	−	34.3948i	−1.10606	−	1.10606i	−0.112398	−	0.993663i	$-0.535853\pi$
$968$	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	−0.0414892	+	0.999139i	$0.513210\pi$
$977$	−32.5269	+	32.5269i	−1.04063	+	1.04063i	−0.999139	+	0.0414892i	$0.986790\pi$
$978$		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	$-0.611352\pi$
$983$	18.7083	−	18.7083i	0.596702	−	0.596702i	0.939433	+	0.342732i	$0.111352\pi$
$984$		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	$-0.918867\pi$
$991$		−	15.8745i		−	0.504270i	0.967692	−	0.252135i	$-0.0811328\pi$
$992$		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	−0.530796	−	0.847499i	$-0.678107\pi$
$997$	10.0000	−	10.0000i	0.316703	−	0.316703i	0.847499	+	0.530796i	$0.178107\pi$
$998$	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.163.1	yes	8
3.2	odd	2	inner	180.2.k.d.163.4	yes	8
4.3	odd	2	inner	180.2.k.d.163.3	yes	8
5.2	odd	4	inner	180.2.k.d.127.3	yes	8
5.3	odd	4		900.2.k.k.307.2		8
5.4	even	2		900.2.k.k.343.4		8
12.11	even	2	inner	180.2.k.d.163.2	yes	8
15.2	even	4	inner	180.2.k.d.127.2	yes	8
15.8	even	4		900.2.k.k.307.3		8
15.14	odd	2		900.2.k.k.343.1		8
20.3	even	4		900.2.k.k.307.4		8
20.7	even	4	inner	180.2.k.d.127.1	✓	8
20.19	odd	2		900.2.k.k.343.2		8
60.23	odd	4		900.2.k.k.307.1		8
60.47	odd	4	inner	180.2.k.d.127.4	yes	8
60.59	even	2		900.2.k.k.343.3		8

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

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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