LMFDB - Embedded newform 1088.2.o.w.769.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(769,1088)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1088, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1088.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.o (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.68772373992$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 544)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			769.4
Root			$1.27715 + 0.607364i$ of defining polynomial
Character	$\chi$	$=$	1088.769
Dual form			1088.2.o.w.897.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.431733 - 0.431733i) q^{3} +(-0.289169 + 0.289169i) q^{5} +(-2.55430 - 2.55430i) q^{7} +2.62721i q^{9} +O(q^{10})$	\(q+(0.431733 - 0.431733i) q^{3} +(-0.289169 + 0.289169i) q^{5} +(-2.55430 - 2.55430i) q^{7} +2.62721i q^{9} +(-2.86119 - 2.86119i) q^{11} -3.62721 q^{13} +0.249687i q^{15} +(3.91638 + 1.28917i) q^{17} +6.83553i q^{19} -2.20555 q^{21} +(5.84722 + 5.84722i) q^{23} +4.83276i q^{25} +(2.42945 + 2.42945i) q^{27} +(-5.91638 + 5.91638i) q^{29} +(0.124844 - 0.124844i) q^{31} -2.47054 q^{33} +1.47725 q^{35} +(-1.71083 + 1.71083i) q^{37} +(-1.56599 + 1.56599i) q^{39} +(1.00000 + 1.00000i) q^{41} -11.0807i q^{43} +(-0.759707 - 0.759707i) q^{45} -10.2172 q^{47} +6.04888i q^{49} +(2.24741 - 1.13425i) q^{51} -1.42166i q^{53} +1.65473 q^{55} +(2.95112 + 2.95112i) q^{57} +5.72237i q^{59} +(2.28917 + 2.28917i) q^{61} +(6.71068 - 6.71068i) q^{63} +(1.04888 - 1.04888i) q^{65} -12.5579 q^{67} +5.04888 q^{69} +(6.79943 - 6.79943i) q^{71} +(-4.83276 + 4.83276i) q^{73} +(2.08646 + 2.08646i) q^{75} +14.6167i q^{77} +(0.988310 + 0.988310i) q^{79} -5.78389 q^{81} -7.44931i q^{83} +(-1.50528 + 0.759707i) q^{85} +5.10860i q^{87} -13.0489 q^{89} +(9.26498 + 9.26498i) q^{91} -0.107798i q^{93} +(-1.97662 - 1.97662i) q^{95} +(5.20555 - 5.20555i) q^{97} +(7.51695 - 7.51695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) $ 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.431733	−	0.431733i	0.249261	−	0.249261i	−0.571406	−	0.820667i	$-0.693602\pi$
$3$	0.431733	−	0.431733i	0.249261	−	0.249261i	0.820667	+	0.571406i	$0.193602\pi$
$4$		0			0
$5$	−0.289169	+	0.289169i	−0.129320	+	0.129320i	−0.768804	−	0.639484i	$-0.779148\pi$
$5$	−0.289169	+	0.289169i	−0.129320	+	0.129320i	0.639484	+	0.768804i	$0.279148\pi$
$6$		0			0
$7$	−2.55430	−	2.55430i	−0.965434	−	0.965434i	0.0339884	−	0.999422i	$-0.489179\pi$
$7$	−2.55430	−	2.55430i	−0.965434	−	0.965434i	−0.999422	+	0.0339884i	$0.989179\pi$
$8$		0			0
$9$			2.62721i			0.875738i
$10$		0			0
$11$	−2.86119	−	2.86119i	−0.862680	−	0.862680i	0.128968	−	0.991649i	$-0.458833\pi$
$11$	−2.86119	−	2.86119i	−0.862680	−	0.862680i	−0.991649	+	0.128968i	$0.958833\pi$
$12$		0			0
$13$	−3.62721			−1.00601			−0.503004	−	0.864284i	$-0.667772\pi$
$13$	−3.62721			−1.00601			−0.503004	+	0.864284i	$0.667772\pi$
$14$		0			0
$15$			0.249687i			0.0644690i
$16$		0			0
$17$	3.91638	+	1.28917i	0.949862	+	0.312669i
$17$	3.91638	+	1.28917i	0.949862	+	0.312669i
$18$		0			0
$19$			6.83553i			1.56818i	0.620649	+	0.784089i	$0.286869\pi$
$19$			6.83553i			1.56818i	−0.620649	+	0.784089i	$0.713131\pi$
$20$		0			0
$21$	−2.20555			−0.481290
$22$		0			0
$23$	5.84722	+	5.84722i	1.21923	+	1.21923i	0.967902	+	0.251327i	$0.0808670\pi$
$23$	5.84722	+	5.84722i	1.21923	+	1.21923i	0.251327	+	0.967902i	$0.419133\pi$
$24$		0			0
$25$			4.83276i			0.966553i
$26$		0			0
$27$	2.42945	+	2.42945i	0.467549	+	0.467549i
$28$		0			0
$29$	−5.91638	+	5.91638i	−1.09864	+	1.09864i	−0.104075	+	0.994569i	$0.533188\pi$
$29$	−5.91638	+	5.91638i	−1.09864	+	1.09864i	−0.994569	+	0.104075i	$0.966812\pi$
$30$		0			0
$31$	0.124844	−	0.124844i	0.0224226	−	0.0224226i	−0.695807	−	0.718229i	$-0.744953\pi$
$31$	0.124844	−	0.124844i	0.0224226	−	0.0224226i	0.718229	+	0.695807i	$0.244953\pi$
$32$		0			0
$33$	−2.47054			−0.430066
$34$		0			0
$35$	1.47725			0.249700
$36$		0			0
$37$	−1.71083	+	1.71083i	−0.281259	+	0.281259i	−0.833611	−	0.552352i	$-0.813730\pi$
$37$	−1.71083	+	1.71083i	−0.281259	+	0.281259i	0.552352	+	0.833611i	$0.313730\pi$
$38$		0			0
$39$	−1.56599	+	1.56599i	−0.250759	+	0.250759i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$		−	11.0807i		−	1.68978i	−0.534937	−	0.844892i	$-0.679664\pi$
$43$		−	11.0807i		−	1.68978i	0.534937	−	0.844892i	$-0.320336\pi$
$44$		0			0
$45$	−0.759707	−	0.759707i	−0.113250	−	0.113250i
$46$		0			0
$47$	−10.2172			−1.49033			−0.745165	−	0.666880i	$-0.767629\pi$
$47$	−10.2172			−1.49033			−0.745165	+	0.666880i	$0.767629\pi$
$48$		0			0
$49$			6.04888i			0.864125i
$50$		0			0
$51$	2.24741	−	1.13425i	0.314700	−	0.158827i
$52$		0			0
$53$		−	1.42166i		−	0.195280i	−0.995222	−	0.0976402i	$-0.968871\pi$
$53$		−	1.42166i		−	0.195280i	0.995222	−	0.0976402i	$-0.0311294\pi$
$54$		0			0
$55$	1.65473			0.223124
$56$		0			0
$57$	2.95112	+	2.95112i	0.390886	+	0.390886i
$58$		0			0
$59$			5.72237i			0.744990i	0.928034	+	0.372495i	$0.121498\pi$
$59$			5.72237i			0.744990i	−0.928034	+	0.372495i	$0.878502\pi$
$60$		0			0
$61$	2.28917	+	2.28917i	0.293098	+	0.293098i	0.838303	−	0.545205i	$-0.183548\pi$
$61$	2.28917	+	2.28917i	0.293098	+	0.293098i	−0.545205	+	0.838303i	$0.683548\pi$
$62$		0			0
$63$	6.71068	−	6.71068i	0.845467	−	0.845467i
$64$		0			0
$65$	1.04888	−	1.04888i	0.130097	−	0.130097i
$66$		0			0
$67$	−12.5579			−1.53419			−0.767096	−	0.641532i	$-0.778299\pi$
$67$	−12.5579			−1.53419			−0.767096	+	0.641532i	$0.778299\pi$
$68$		0			0
$69$	5.04888			0.607813
$70$		0			0
$71$	6.79943	−	6.79943i	0.806944	−	0.806944i	−0.177227	−	0.984170i	$-0.556713\pi$
$71$	6.79943	−	6.79943i	0.806944	−	0.806944i	0.984170	+	0.177227i	$0.0567125\pi$
$72$		0			0
$73$	−4.83276	+	4.83276i	−0.565632	+	0.565632i	−0.930902	−	0.365270i	$-0.880977\pi$
$73$	−4.83276	+	4.83276i	−0.565632	+	0.565632i	0.365270	+	0.930902i	$0.380977\pi$
$74$		0			0
$75$	2.08646	+	2.08646i	0.240924	+	0.240924i
$76$		0			0
$77$			14.6167i			1.66572i
$78$		0			0
$79$	0.988310	+	0.988310i	0.111194	+	0.111194i	0.760515	−	0.649321i	$-0.224947\pi$
$79$	0.988310	+	0.988310i	0.111194	+	0.111194i	−0.649321	+	0.760515i	$0.724947\pi$
$80$		0			0
$81$	−5.78389			−0.642654
$82$		0			0
$83$		−	7.44931i		−	0.817668i	−0.912609	−	0.408834i	$-0.865936\pi$
$83$		−	7.44931i		−	0.817668i	0.912609	−	0.408834i	$-0.134064\pi$
$84$		0			0
$85$	−1.50528	+	0.759707i	−0.163271	+	0.0824018i
$86$		0			0
$87$			5.10860i			0.547699i
$88$		0			0
$89$	−13.0489			−1.38318			−0.691589	−	0.722291i	$-0.743089\pi$
$89$	−13.0489			−1.38318			−0.691589	+	0.722291i	$0.743089\pi$
$90$		0			0
$91$	9.26498	+	9.26498i	0.971234	+	0.971234i
$92$		0			0
$93$		−	0.107798i		−	0.0111782i
$94$		0			0
$95$	−1.97662	−	1.97662i	−0.202797	−	0.202797i
$96$		0			0
$97$	5.20555	−	5.20555i	0.528544	−	0.528544i	−0.391594	−	0.920138i	$-0.628076\pi$
$97$	5.20555	−	5.20555i	0.528544	−	0.528544i	0.920138	+	0.391594i	$0.128076\pi$
$98$		0			0
$99$	7.51695	−	7.51695i	0.755482	−	0.755482i
$100$		0			0
$101$	4.37279			0.435109			0.217554	−	0.976048i	$-0.430192\pi$
$101$	4.37279			0.435109			0.217554	+	0.976048i	$0.430192\pi$
$102$		0			0
$103$	−7.08522			−0.698127			−0.349064	−	0.937099i	$-0.613500\pi$
$103$	−7.08522			−0.698127			−0.349064	+	0.937099i	$0.613500\pi$
$104$		0			0
$105$	0.637776	−	0.637776i	0.0622405	−	0.0622405i
$106$		0			0
$107$	−1.29520	+	1.29520i	−0.125212	+	0.125212i	−0.766936	−	0.641724i	$-0.778219\pi$
$107$	−1.29520	+	1.29520i	−0.125212	+	0.125212i	0.641724	+	0.766936i	$0.278219\pi$
$108$		0			0
$109$	10.9653	+	10.9653i	1.05028	+	1.05028i	0.998667	+	0.0516141i	$0.0164366\pi$
$109$	10.9653	+	10.9653i	1.05028	+	1.05028i	0.0516141	+	0.998667i	$0.483563\pi$
$110$		0			0
$111$			1.47725i			0.140214i
$112$		0			0
$113$	−11.2056	−	11.2056i	−1.05413	−	1.05413i	−0.998449	−	0.0556809i	$-0.982267\pi$
$113$	−11.2056	−	11.2056i	−1.05413	−	1.05413i	−0.0556809	−	0.998449i	$-0.517733\pi$
$114$		0			0
$115$	−3.38166			−0.315342
$116$		0			0
$117$		−	9.52946i		−	0.880999i
$118$		0			0
$119$	−6.71068	−	13.2965i	−0.615167	−	1.21889i
$120$		0			0
$121$			5.37279i			0.488435i
$122$		0			0
$123$	0.863466			0.0778561
$124$		0			0
$125$	−2.84333	−	2.84333i	−0.254315	−	0.254315i
$126$		0			0
$127$			15.1483i			1.34419i	0.740463	+	0.672097i	$0.234606\pi$
$127$			15.1483i			1.34419i	−0.740463	+	0.672097i	$0.765394\pi$
$128$		0			0
$129$	−4.78389	−	4.78389i	−0.421198	−	0.421198i
$130$		0			0
$131$	−0.681420	+	0.681420i	−0.0595360	+	0.0595360i	−0.736248	−	0.676712i	$-0.763404\pi$
$131$	−0.681420	+	0.681420i	−0.0595360	+	0.0595360i	0.676712	+	0.736248i	$0.263404\pi$
$132$		0			0
$133$	17.4600	−	17.4600i	1.51397	−	1.51397i
$134$		0			0
$135$	−1.40504			−0.120927
$136$		0			0
$137$	2.47054			0.211072			0.105536	−	0.994415i	$-0.466344\pi$
$137$	2.47054			0.211072			0.105536	+	0.994415i	$0.466344\pi$
$138$		0			0
$139$	−3.11087	+	3.11087i	−0.263861	+	0.263861i	−0.826621	−	0.562760i	$-0.809740\pi$
$139$	−3.11087	+	3.11087i	−0.263861	+	0.263861i	0.562760	+	0.826621i	$0.309740\pi$
$140$		0			0
$141$	−4.41110	+	4.41110i	−0.371482	+	0.371482i
$142$		0			0
$143$	10.3781	+	10.3781i	0.867863	+	0.867863i
$144$		0			0
$145$		−	3.42166i		−	0.284154i
$146$		0			0
$147$	2.61150	+	2.61150i	0.215393	+	0.215393i
$148$		0			0
$149$	−8.84333			−0.724473			−0.362237	−	0.932086i	$-0.617987\pi$
$149$	−8.84333			−0.724473			−0.362237	+	0.932086i	$0.617987\pi$
$150$		0			0
$151$			4.60922i			0.375093i	0.982256	+	0.187547i	$0.0600535\pi$
$151$			4.60922i			0.375093i	−0.982256	+	0.187547i	$0.939946\pi$
$152$		0			0
$153$	−3.38692	+	10.2892i	−0.273816	+	0.831830i
$154$		0			0
$155$			0.0722017i			0.00579938i
$156$		0			0
$157$	17.2544			1.37705			0.688527	−	0.725211i	$-0.258258\pi$
$157$	17.2544			1.37705			0.688527	+	0.725211i	$0.258258\pi$
$158$		0			0
$159$	−0.613779	−	0.613779i	−0.0486758	−	0.0486758i
$160$		0			0
$161$		−	29.8711i		−	2.35417i
$162$		0			0
$163$	1.38394	+	1.38394i	0.108399	+	0.108399i	0.759226	−	0.650827i	$-0.225578\pi$
$163$	1.38394	+	1.38394i	0.108399	+	0.108399i	−0.650827	+	0.759226i	$0.725578\pi$
$164$		0			0
$165$	0.714402	−	0.714402i	0.0556161	−	0.0556161i
$166$		0			0
$167$	9.14014	−	9.14014i	0.707285	−	0.707285i	−0.258678	−	0.965964i	$-0.583287\pi$
$167$	9.14014	−	9.14014i	0.707285	−	0.707285i	0.965964	+	0.258678i	$0.0832870\pi$
$168$		0			0
$169$	0.156674			0.0120519
$170$		0			0
$171$	−17.9584			−1.37331
$172$		0			0
$173$	−5.91638	+	5.91638i	−0.449814	+	0.449814i	−0.895293	−	0.445478i	$-0.853034\pi$
$173$	−5.91638	+	5.91638i	−0.449814	+	0.449814i	0.445478	+	0.895293i	$0.353034\pi$
$174$		0			0
$175$	12.3443	−	12.3443i	0.933143	−	0.933143i
$176$		0			0
$177$	2.47054	+	2.47054i	0.185697	+	0.185697i
$178$		0			0
$179$			11.6944i			0.874083i	0.899441	+	0.437042i	$0.143974\pi$
$179$			11.6944i			0.874083i	−0.899441	+	0.437042i	$0.856026\pi$
$180$		0			0
$181$	5.54359	+	5.54359i	0.412052	+	0.412052i	0.882453	−	0.470401i	$-0.155891\pi$
$181$	5.54359	+	5.54359i	0.412052	+	0.412052i	−0.470401	+	0.882453i	$0.655891\pi$
$182$		0			0
$183$	1.97662			0.146116
$184$		0			0
$185$		−	0.989437i		−	0.0727449i
$186$		0			0
$187$	−7.51695	−	14.8941i	−0.549694	−	1.08916i
$188$		0			0
$189$		−	12.4111i		−	0.902775i
$190$		0			0
$191$	−10.0397			−0.726448			−0.363224	−	0.931702i	$-0.618324\pi$
$191$	−10.0397			−0.726448			−0.363224	+	0.931702i	$0.618324\pi$
$192$		0			0
$193$	17.4111	+	17.4111i	1.25328	+	1.25328i	0.954242	+	0.299037i	$0.0966654\pi$
$193$	17.4111	+	17.4111i	1.25328	+	1.25328i	0.299037	+	0.954242i	$0.403335\pi$
$194$		0			0
$195$		−	0.905669i		−	0.0648563i
$196$		0			0
$197$	−0.494719	−	0.494719i	−0.0352472	−	0.0352472i	0.689264	−	0.724511i	$-0.257934\pi$
$197$	−0.494719	−	0.494719i	−0.0352472	−	0.0352472i	−0.724511	+	0.689264i	$0.757934\pi$
$198$		0			0
$199$	−16.0644	+	16.0644i	−1.13878	+	1.13878i	−0.150106	+	0.988670i	$0.547961\pi$
$199$	−16.0644	+	16.0644i	−1.13878	+	1.13878i	−0.988670	+	0.150106i	$0.952039\pi$
$200$		0			0
$201$	−5.42166	+	5.42166i	−0.382415	+	0.382415i
$202$		0			0
$203$	30.2244			2.12134
$204$		0			0
$205$	−0.578337			−0.0403928
$206$		0			0
$207$	−15.3619	+	15.3619i	−1.06773	+	1.06773i
$208$		0			0
$209$	19.5577	−	19.5577i	1.35284	−	1.35284i
$210$		0			0
$211$	−6.40380	−	6.40380i	−0.440855	−	0.440855i	0.451444	−	0.892299i	$-0.350909\pi$
$211$	−6.40380	−	6.40380i	−0.440855	−	0.440855i	−0.892299	+	0.451444i	$0.850909\pi$
$212$		0			0
$213$		−	5.87108i		−	0.402280i
$214$		0			0
$215$	3.20418	+	3.20418i	0.218523	+	0.218523i
$216$		0			0
$217$	−0.637776			−0.0432950
$218$		0			0
$219$			4.17293i			0.281980i
$220$		0			0
$221$	−14.2056	−	4.67609i	−0.955569	−	0.314548i
$222$		0			0
$223$		−	18.7797i		−	1.25758i	−0.777576	−	0.628789i	$-0.783551\pi$
$223$		−	18.7797i		−	1.25758i	0.777576	−	0.628789i	$-0.216449\pi$
$224$		0			0
$225$	−12.6967			−0.846447
$226$		0			0
$227$	−4.58812	−	4.58812i	−0.304524	−	0.304524i	0.538257	−	0.842781i	$-0.319083\pi$
$227$	−4.58812	−	4.58812i	−0.304524	−	0.304524i	−0.842781	+	0.538257i	$0.819083\pi$
$228$		0			0
$229$		−	13.3622i		−	0.883001i	−0.897261	−	0.441500i	$-0.854446\pi$
$229$		−	13.3622i		−	0.883001i	0.897261	−	0.441500i	$-0.145554\pi$
$230$		0			0
$231$	6.31049	+	6.31049i	0.415200	+	0.415200i
$232$		0			0
$233$	3.37279	−	3.37279i	0.220959	−	0.220959i	−0.587943	−	0.808902i	$-0.700062\pi$
$233$	3.37279	−	3.37279i	0.220959	−	0.220959i	0.808902	+	0.587943i	$0.200062\pi$
$234$		0			0
$235$	2.95449	−	2.95449i	0.192730	−	0.192730i
$236$		0			0
$237$	0.853372			0.0554325
$238$		0			0
$239$	−3.13198			−0.202591			−0.101295	−	0.994856i	$-0.532299\pi$
$239$	−3.13198			−0.202591			−0.101295	+	0.994856i	$0.532299\pi$
$240$		0			0
$241$	19.9894	−	19.9894i	1.28763	−	1.28763i	0.351412	−	0.936221i	$-0.385702\pi$
$241$	19.9894	−	19.9894i	1.28763	−	1.28763i	0.936221	−	0.351412i	$-0.114298\pi$
$242$		0			0
$243$	−9.78546	+	9.78546i	−0.627737	+	0.627737i
$244$		0			0
$245$	−1.74914	−	1.74914i	−0.111749	−	0.111749i
$246$		0			0
$247$		−	24.7939i		−	1.57760i
$248$		0			0
$249$	−3.21611	−	3.21611i	−0.203813	−	0.203813i
$250$		0			0
$251$	−13.9629			−0.881333			−0.440667	−	0.897671i	$-0.645258\pi$
$251$	−13.9629			−0.881333			−0.440667	+	0.897671i	$0.645258\pi$
$252$		0			0
$253$		−	33.4600i		−	2.10361i
$254$		0			0
$255$	−0.321889	+	0.977871i	−0.0201575	+	0.0612366i
$256$		0			0
$257$			3.31386i			0.206713i	0.994644	+	0.103357i	$0.0329583\pi$
$257$			3.31386i			0.206713i	−0.994644	+	0.103357i	$0.967042\pi$
$258$		0			0
$259$	8.73995			0.543074
$260$		0			0
$261$	−15.5436	−	15.5436i	−0.962124	−	0.962124i
$262$		0			0
$263$		−	2.88229i		−	0.177730i	−0.996044	−	0.0888648i	$-0.971676\pi$
$263$		−	2.88229i		−	0.177730i	0.996044	−	0.0888648i	$-0.0283239\pi$
$264$		0			0
$265$	0.411100	+	0.411100i	0.0252537	+	0.0252537i
$266$		0			0
$267$	−5.63363	+	5.63363i	−0.344773	+	0.344773i
$268$		0			0
$269$	−10.7980	+	10.7980i	−0.658367	+	0.658367i	−0.954994	−	0.296627i	$-0.904138\pi$
$269$	−10.7980	+	10.7980i	−0.658367	+	0.658367i	0.296627	+	0.954994i	$0.404138\pi$
$270$		0			0
$271$	3.13198			0.190254			0.0951270	−	0.995465i	$-0.469674\pi$
$271$	3.13198			0.190254			0.0951270	+	0.995465i	$0.469674\pi$
$272$		0			0
$273$	8.00000			0.484182
$274$		0			0
$275$	13.8274	−	13.8274i	0.833826	−	0.833826i
$276$		0			0
$277$	12.5925	−	12.5925i	0.756608	−	0.756608i	−0.219095	−	0.975703i	$-0.570311\pi$
$277$	12.5925	−	12.5925i	0.756608	−	0.756608i	0.975703	+	0.219095i	$0.0703105\pi$
$278$		0			0
$279$	0.327991	+	0.327991i	0.0196363	+	0.0196363i
$280$		0			0
$281$		−	17.8328i		−	1.06381i	−0.846803	−	0.531907i	$-0.821476\pi$
$281$		−	17.8328i		−	1.06381i	0.846803	−	0.531907i	$-0.178524\pi$
$282$		0			0
$283$	9.08294	+	9.08294i	0.539925	+	0.539925i	0.923507	−	0.383582i	$-0.125310\pi$
$283$	9.08294	+	9.08294i	0.539925	+	0.539925i	−0.383582	+	0.923507i	$0.625310\pi$
$284$		0			0
$285$	−1.70674			−0.101099
$286$		0			0
$287$		−	5.10860i		−	0.301551i
$288$		0			0
$289$	13.6761	+	10.0978i	0.804476	+	0.593985i
$290$		0			0
$291$		−	4.49482i		−	0.263491i
$292$		0			0
$293$	8.09775			0.473076			0.236538	−	0.971622i	$-0.423987\pi$
$293$	8.09775			0.473076			0.236538	+	0.971622i	$0.423987\pi$
$294$		0			0
$295$	−1.65473	−	1.65473i	−0.0963422	−	0.0963422i
$296$		0			0
$297$		−	13.9022i		−	0.806690i
$298$		0			0
$299$	−21.2091	−	21.2091i	−1.22655	−	1.22655i
$300$		0			0
$301$	−28.3033	+	28.3033i	−1.63138	+	1.63138i
$302$		0			0
$303$	1.88788	−	1.88788i	0.108456	−	0.108456i
$304$		0			0
$305$	−1.32391			−0.0758069
$306$		0			0
$307$	28.2478			1.61219			0.806093	−	0.591789i	$-0.201578\pi$
$307$	28.2478			1.61219			0.806093	+	0.591789i	$0.201578\pi$
$308$		0			0
$309$	−3.05892	+	3.05892i	−0.174016	+	0.174016i
$310$		0			0
$311$	−14.2487	+	14.2487i	−0.807972	+	0.807972i	−0.984327	−	0.176355i	$-0.943569\pi$
$311$	−14.2487	+	14.2487i	−0.807972	+	0.807972i	0.176355	+	0.984327i	$0.443569\pi$
$312$		0			0
$313$	18.8328	+	18.8328i	1.06449	+	1.06449i	0.997772	+	0.0667189i	$0.0212531\pi$
$313$	18.8328	+	18.8328i	1.06449	+	1.06449i	0.0667189	+	0.997772i	$0.478747\pi$
$314$		0			0
$315$			3.88104i			0.218672i
$316$		0			0
$317$	3.50528	+	3.50528i	0.196876	+	0.196876i	0.798659	−	0.601783i	$-0.205543\pi$
$317$	3.50528	+	3.50528i	0.196876	+	0.196876i	−0.601783	+	0.798659i	$0.705543\pi$
$318$		0			0
$319$	33.8558			1.89556
$320$		0			0
$321$			1.11836i			0.0624208i
$322$		0			0
$323$	−8.81215	+	26.7705i	−0.490321	+	1.48955i
$324$		0			0
$325$		−	17.5295i		−	0.972360i
$326$		0			0
$327$	9.46813			0.523589
$328$		0			0
$329$	26.0978	+	26.0978i	1.43882	+	1.43882i
$330$		0			0
$331$			10.5813i			0.581600i	0.956784	+	0.290800i	$0.0939214\pi$
$331$			10.5813i			0.581600i	−0.956784	+	0.290800i	$0.906079\pi$
$332$		0			0
$333$	−4.49472	−	4.49472i	−0.246309	−	0.246309i
$334$		0			0
$335$	3.63135	−	3.63135i	0.198402	−	0.198402i
$336$		0			0
$337$	0.735011	−	0.735011i	0.0400386	−	0.0400386i	−0.686804	−	0.726843i	$-0.740987\pi$
$337$	0.735011	−	0.735011i	0.0400386	−	0.0400386i	0.726843	+	0.686804i	$0.240987\pi$
$338$		0			0
$339$	−9.67561			−0.525507
$340$		0			0
$341$	−0.714402			−0.0386870
$342$		0			0
$343$	−2.42945	+	2.42945i	−0.131178	+	0.131178i
$344$		0			0
$345$	−1.45998	+	1.45998i	−0.0786025	+	0.0786025i
$346$		0			0
$347$	−2.86119	−	2.86119i	−0.153597	−	0.153597i	0.626126	−	0.779722i	$-0.284640\pi$
$347$	−2.86119	−	2.86119i	−0.153597	−	0.153597i	−0.779722	+	0.626126i	$0.784640\pi$
$348$		0			0
$349$			6.57834i			0.352130i	0.984379	+	0.176065i	$0.0563369\pi$
$349$			6.57834i			0.352130i	−0.984379	+	0.176065i	$0.943663\pi$
$350$		0			0
$351$	−8.81215	−	8.81215i	−0.470358	−	0.470358i
$352$		0			0
$353$	−9.73501			−0.518142			−0.259071	−	0.965858i	$-0.583416\pi$
$353$	−9.73501			−0.518142			−0.259071	+	0.965858i	$0.583416\pi$
$354$		0			0
$355$			3.93236i			0.208708i
$356$		0			0
$357$	−8.63778	−	2.84333i	−0.457160	−	0.150485i
$358$		0			0
$359$			30.2244i			1.59518i	0.603198	+	0.797591i	$0.293893\pi$
$359$			30.2244i			1.59518i	−0.603198	+	0.797591i	$0.706107\pi$
$360$		0			0
$361$	−27.7244			−1.45918
$362$		0			0
$363$	2.31961	+	2.31961i	0.121748	+	0.121748i
$364$		0			0
$365$		−	2.79497i		−	0.146295i
$366$		0			0
$367$	−15.1122	−	15.1122i	−0.788850	−	0.788850i	0.192455	−	0.981306i	$-0.438355\pi$
$367$	−15.1122	−	15.1122i	−0.788850	−	0.788850i	−0.981306	+	0.192455i	$0.938355\pi$
$368$		0			0
$369$	−2.62721	+	2.62721i	−0.136767	+	0.136767i
$370$		0			0
$371$	−3.63135	+	3.63135i	−0.188530	+	0.188530i
$372$		0			0
$373$	30.5472			1.58167			0.790836	−	0.612028i	$-0.209646\pi$
$373$	30.5472			1.58167			0.790836	+	0.612028i	$0.209646\pi$
$374$		0			0
$375$	−2.45512			−0.126782
$376$		0			0
$377$	21.4600	−	21.4600i	1.10525	−	1.10525i
$378$		0			0
$379$	15.5078	−	15.5078i	0.796584	−	0.796584i	−0.185971	−	0.982555i	$-0.559543\pi$
$379$	15.5078	−	15.5078i	0.796584	−	0.796584i	0.982555	+	0.185971i	$0.0595431\pi$
$380$		0			0
$381$	6.54002	+	6.54002i	0.335056	+	0.335056i
$382$		0			0
$383$			25.0436i			1.27967i	0.768513	+	0.639834i	$0.220997\pi$
$383$			25.0436i			1.27967i	−0.768513	+	0.639834i	$0.779003\pi$
$384$		0			0
$385$	−4.22668	−	4.22668i	−0.215411	−	0.215411i
$386$		0			0
$387$	29.1112			1.47981
$388$		0			0
$389$		−	18.5189i		−	0.938945i	−0.882947	−	0.469473i	$-0.844444\pi$
$389$		−	18.5189i		−	0.938945i	0.882947	−	0.469473i	$-0.155556\pi$
$390$		0			0
$391$	15.3619	+	30.4380i	0.776884	+	1.53932i
$392$		0			0
$393$			0.588384i			0.0296800i
$394$		0			0
$395$	−0.571576			−0.0287591
$396$		0			0
$397$	16.7980	+	16.7980i	0.843068	+	0.843068i	0.989257	−	0.146188i	$-0.0467005\pi$
$397$	16.7980	+	16.7980i	0.843068	+	0.843068i	−0.146188	+	0.989257i	$0.546701\pi$
$398$		0			0
$399$		−	15.0761i		−	0.754749i
$400$		0			0
$401$	−7.67609	−	7.67609i	−0.383326	−	0.383326i	0.488973	−	0.872299i	$-0.337372\pi$
$401$	−7.67609	−	7.67609i	−0.383326	−	0.383326i	−0.872299	+	0.488973i	$0.837372\pi$
$402$		0			0
$403$	−0.452834	+	0.452834i	−0.0225573	+	0.0225573i
$404$		0			0
$405$	1.67252	−	1.67252i	0.0831081	−	0.0831081i
$406$		0			0
$407$	9.79002			0.485273
$408$		0			0
$409$	1.32391			0.0654632			0.0327316	−	0.999464i	$-0.489579\pi$
$409$	1.32391			0.0654632			0.0327316	+	0.999464i	$0.489579\pi$
$410$		0			0
$411$	1.06661	−	1.06661i	0.0526122	−	0.0526122i
$412$		0			0
$413$	14.6167	−	14.6167i	0.719238	−	0.719238i
$414$		0			0
$415$	2.15411	+	2.15411i	0.105741	+	0.105741i
$416$		0			0
$417$			2.68614i			0.131541i
$418$		0			0
$419$	−11.8765	−	11.8765i	−0.580204	−	0.580204i	0.354755	−	0.934959i	$-0.384564\pi$
$419$	−11.8765	−	11.8765i	−0.580204	−	0.580204i	−0.934959	+	0.354755i	$0.884564\pi$
$420$		0			0
$421$	−28.9794			−1.41237			−0.706185	−	0.708028i	$-0.749585\pi$
$421$	−28.9794			−1.41237			−0.706185	+	0.708028i	$0.749585\pi$
$422$		0			0
$423$		−	26.8427i		−	1.30514i
$424$		0			0
$425$	−6.23025	+	18.9269i	−0.302211	+	0.918092i
$426$		0			0
$427$		−	11.6944i		−	0.565933i
$428$		0			0
$429$	8.96117			0.432649
$430$		0			0
$431$	−12.6827	−	12.6827i	−0.610906	−	0.610906i	0.332276	−	0.943182i	$-0.392184\pi$
$431$	−12.6827	−	12.6827i	−0.610906	−	0.610906i	−0.943182	+	0.332276i	$0.892184\pi$
$432$		0			0
$433$		−	5.69670i		−	0.273766i	−0.990587	−	0.136883i	$-0.956292\pi$
$433$		−	5.69670i		−	0.273766i	0.990587	−	0.136883i	$-0.0437084\pi$
$434$		0			0
$435$	−1.47725	−	1.47725i	−0.0708285	−	0.0708285i
$436$		0			0
$437$	−39.9688	+	39.9688i	−1.91197	+	1.91197i
$438$		0			0
$439$	3.16808	−	3.16808i	0.151204	−	0.151204i	−0.627452	−	0.778656i	$-0.715902\pi$
$439$	3.16808	−	3.16808i	0.151204	−	0.151204i	0.778656	+	0.627452i	$0.215902\pi$
$440$		0			0
$441$	−15.8917			−0.756747
$442$		0			0
$443$	−7.52151			−0.357358			−0.178679	−	0.983907i	$-0.557182\pi$
$443$	−7.52151			−0.357358			−0.178679	+	0.983907i	$0.557182\pi$
$444$		0			0
$445$	3.77332	−	3.77332i	0.178873	−	0.178873i
$446$		0			0
$447$	−3.81796	+	3.81796i	−0.180583	+	0.180583i
$448$		0			0
$449$	−13.7144	−	13.7144i	−0.647223	−	0.647223i	0.305098	−	0.952321i	$-0.401311\pi$
$449$	−13.7144	−	13.7144i	−0.647223	−	0.647223i	−0.952321	+	0.305098i	$0.901311\pi$
$450$		0			0
$451$		−	5.72237i		−	0.269456i
$452$		0			0
$453$	1.98995	+	1.98995i	0.0934962	+	0.0934962i
$454$		0			0
$455$	−5.35828			−0.251200
$456$		0			0
$457$			7.45998i			0.348963i	0.984660	+	0.174481i	$0.0558249\pi$
$457$			7.45998i			0.348963i	−0.984660	+	0.174481i	$0.944175\pi$
$458$		0			0
$459$	6.38269	+	12.6466i	0.297919	+	0.590295i
$460$		0			0
$461$			18.2439i			0.849701i	0.905263	+	0.424851i	$0.139673\pi$
$461$			18.2439i			0.849701i	−0.905263	+	0.424851i	$0.860327\pi$
$462$		0			0
$463$	−25.2933			−1.17548			−0.587739	−	0.809050i	$-0.699982\pi$
$463$	−25.2933			−1.17548			−0.587739	+	0.809050i	$0.699982\pi$
$464$		0			0
$465$	0.0311719	+	0.0311719i	0.00144556	+	0.00144556i
$466$		0			0
$467$		−	5.28608i		−	0.244611i	−0.992493	−	0.122305i	$-0.960971\pi$
$467$		−	5.28608i		−	0.244611i	0.992493	−	0.122305i	$-0.0390287\pi$
$468$		0			0
$469$	32.0766	+	32.0766i	1.48116	+	1.48116i
$470$		0			0
$471$	7.44931	−	7.44931i	0.343246	−	0.343246i
$472$		0			0
$473$	−31.7038	+	31.7038i	−1.45774	+	1.45774i
$474$		0			0
$475$	−33.0345			−1.51573
$476$		0			0
$477$	3.73501			0.171014
$478$		0			0
$479$	16.1366	−	16.1366i	0.737301	−	0.737301i	−0.234754	−	0.972055i	$-0.575429\pi$
$479$	16.1366	−	16.1366i	0.737301	−	0.737301i	0.972055	+	0.234754i	$0.0754285\pi$
$480$		0			0
$481$	6.20555	−	6.20555i	0.282949	−	0.282949i
$482$		0			0
$483$	−12.8963	−	12.8963i	−0.586803	−	0.586803i
$484$		0			0
$485$			3.01056i			0.136703i
$486$		0			0
$487$	−6.30005	−	6.30005i	−0.285483	−	0.285483i	0.549808	−	0.835291i	$-0.314701\pi$
$487$	−6.30005	−	6.30005i	−0.285483	−	0.285483i	−0.835291	+	0.549808i	$0.814701\pi$
$488$		0			0
$489$	1.19499			0.0540392
$490$		0			0
$491$			27.2699i			1.23067i	0.788264	+	0.615337i	$0.210980\pi$
$491$			27.2699i			1.23067i	−0.788264	+	0.615337i	$0.789020\pi$
$492$		0			0
$493$	−30.7980	+	15.5436i	−1.38707	+	0.700048i
$494$		0			0
$495$			4.34733i			0.195398i
$496$		0			0
$497$	−34.7355			−1.55810
$498$		0			0
$499$	−16.7354	−	16.7354i	−0.749179	−	0.749179i	0.225146	−	0.974325i	$-0.427714\pi$
$499$	−16.7354	−	16.7354i	−0.749179	−	0.749179i	−0.974325	+	0.225146i	$0.927714\pi$
$500$		0			0
$501$		−	7.89220i		−	0.352598i
$502$		0			0
$503$	−11.9802	−	11.9802i	−0.534172	−	0.534172i	0.387639	−	0.921811i	$-0.373291\pi$
$503$	−11.9802	−	11.9802i	−0.534172	−	0.534172i	−0.921811	+	0.387639i	$0.873291\pi$
$504$		0			0
$505$	−1.26447	+	1.26447i	−0.0562683	+	0.0562683i
$506$		0			0
$507$	0.0676414	−	0.0676414i	0.00300406	−	0.00300406i
$508$		0			0
$509$	30.0766			1.33312			0.666562	−	0.745450i	$-0.267765\pi$
$509$	30.0766			1.33312			0.666562	+	0.745450i	$0.267765\pi$
$510$		0			0
$511$	24.6886			1.09216
$512$		0			0
$513$	−16.6066	+	16.6066i	−0.733199	+	0.733199i
$514$		0			0
$515$	2.04882	−	2.04882i	0.0902819	−	0.0902819i
$516$		0			0
$517$	29.2333	+	29.2333i	1.28568	+	1.28568i
$518$		0			0
$519$			5.10860i			0.224242i
$520$		0			0
$521$	−18.4005	−	18.4005i	−0.806142	−	0.806142i	0.177905	−	0.984048i	$-0.443068\pi$
$521$	−18.4005	−	18.4005i	−0.806142	−	0.806142i	−0.984048	+	0.177905i	$0.943068\pi$
$522$		0			0
$523$	17.4168			0.761584			0.380792	−	0.924661i	$-0.375651\pi$
$523$	17.4168			0.761584			0.380792	+	0.924661i	$0.375651\pi$
$524$		0			0
$525$		−	10.6589i		−	0.465193i
$526$		0			0
$527$	0.649880	−	0.327991i	0.0283092	−	0.0142875i
$528$		0			0
$529$			45.3799i			1.97304i
$530$		0			0
$531$	−15.0339			−0.652416
$532$		0			0
$533$	−3.62721	−	3.62721i	−0.157112	−	0.157112i
$534$		0			0
$535$		−	0.749062i		−	0.0323848i
$536$		0			0
$537$	5.04888	+	5.04888i	0.217875	+	0.217875i
$538$		0			0
$539$	17.3070	−	17.3070i	0.745464	−	0.745464i
$540$		0			0
$541$	13.1325	−	13.1325i	0.564610	−	0.564610i	−0.366003	−	0.930613i	$-0.619274\pi$
$541$	13.1325	−	13.1325i	0.564610	−	0.564610i	0.930613	+	0.366003i	$0.119274\pi$
$542$		0			0
$543$	4.78671			0.205417
$544$		0			0
$545$	−6.34162			−0.271645
$546$		0			0
$547$	−16.2569	+	16.2569i	−0.695095	+	0.695095i	−0.963348	−	0.268254i	$-0.913553\pi$
$547$	−16.2569	+	16.2569i	−0.695095	+	0.695095i	0.268254	+	0.963348i	$0.413553\pi$
$548$		0			0
$549$	−6.01413	+	6.01413i	−0.256677	+	0.256677i
$550$		0			0
$551$	−40.4416	−	40.4416i	−1.72287	−	1.72287i
$552$		0			0
$553$		−	5.04888i		−	0.214700i
$554$		0			0
$555$	−0.427173	−	0.427173i	−0.0181325	−	0.0181325i
$556$		0			0
$557$	−11.6272			−0.492661			−0.246330	−	0.969186i	$-0.579225\pi$
$557$	−11.6272			−0.492661			−0.246330	+	0.969186i	$0.579225\pi$
$558$		0			0
$559$			40.1919i			1.69994i
$560$		0			0
$561$	−9.67557	−	3.18494i	−0.408503	−	0.134468i
$562$		0			0
$563$			20.0703i			0.845862i	0.906162	+	0.422931i	$0.138999\pi$
$563$			20.0703i			0.845862i	−0.906162	+	0.422931i	$0.861001\pi$
$564$		0			0
$565$	6.48059			0.272640
$566$		0			0
$567$	14.7738	+	14.7738i	0.620440	+	0.620440i
$568$		0			0
$569$		−	31.2544i		−	1.31025i	−0.755519	−	0.655127i	$-0.772615\pi$
$569$		−	31.2544i		−	1.31025i	0.755519	−	0.655127i	$-0.227385\pi$
$570$		0			0
$571$	24.8616	+	24.8616i	1.04042	+	1.04042i	0.999148	+	0.0412761i	$0.0131423\pi$
$571$	24.8616	+	24.8616i	1.04042	+	1.04042i	0.0412761	+	0.999148i	$0.486858\pi$
$572$		0			0
$573$	−4.33447	+	4.33447i	−0.181075	+	0.181075i
$574$		0			0
$575$	−28.2582	+	28.2582i	−1.17845	+	1.17845i
$576$		0			0
$577$	21.3139			0.887308			0.443654	−	0.896198i	$-0.353682\pi$
$577$	21.3139			0.887308			0.443654	+	0.896198i	$0.353682\pi$
$578$		0			0
$579$	15.0339			0.624787
$580$		0			0
$581$	−19.0278	+	19.0278i	−0.789404	+	0.789404i
$582$		0			0
$583$	−4.06764	+	4.06764i	−0.168465	+	0.168465i
$584$		0			0
$585$	2.75562	+	2.75562i	0.113931	+	0.113931i
$586$		0			0
$587$			15.1483i			0.625237i	0.949879	+	0.312619i	$0.101206\pi$
$587$			15.1483i			0.625237i	−0.949879	+	0.312619i	$0.898794\pi$
$588$		0			0
$589$	0.853372	+	0.853372i	0.0351626	+	0.0351626i
$590$		0			0
$591$	−0.427173			−0.0175715
$592$		0			0
$593$			47.5466i			1.95251i	0.216632	+	0.976253i	$0.430493\pi$
$593$			47.5466i			1.95251i	−0.216632	+	0.976253i	$0.569507\pi$
$594$		0			0
$595$	5.78546	+	1.90442i	0.237181	+	0.0780735i
$596$		0			0
$597$			13.8711i			0.567705i
$598$		0			0
$599$	5.85766			0.239337			0.119669	−	0.992814i	$-0.461817\pi$
$599$	5.85766			0.239337			0.119669	+	0.992814i	$0.461817\pi$
$600$		0			0
$601$	9.67609	+	9.67609i	0.394696	+	0.394696i	0.876357	−	0.481661i	$-0.159967\pi$
$601$	9.67609	+	9.67609i	0.394696	+	0.394696i	−0.481661	+	0.876357i	$0.659967\pi$
$602$		0			0
$603$		−	32.9923i		−	1.34355i
$604$		0			0
$605$	−1.55364	−	1.55364i	−0.0631645	−	0.0631645i
$606$		0			0
$607$	−8.18793	+	8.18793i	−0.332338	+	0.332338i	−0.853474	−	0.521136i	$-0.825508\pi$
$607$	−8.18793	+	8.18793i	−0.332338	+	0.332338i	0.521136	+	0.853474i	$0.325508\pi$
$608$		0			0
$609$	13.0489	−	13.0489i	0.528767	−	0.528767i
$610$		0			0
$611$	37.0599			1.49928
$612$		0			0
$613$	36.1744			1.46107			0.730535	−	0.682876i	$-0.239271\pi$
$613$	36.1744			1.46107			0.730535	+	0.682876i	$0.239271\pi$
$614$		0			0
$615$	−0.249687	+	0.249687i	−0.0100684	+	0.0100684i
$616$		0			0
$617$	5.95112	−	5.95112i	0.239583	−	0.239583i	−0.577094	−	0.816678i	$-0.695813\pi$
$617$	5.95112	−	5.95112i	0.239583	−	0.239583i	0.816678	+	0.577094i	$0.195813\pi$
$618$		0			0
$619$	28.2267	+	28.2267i	1.13453	+	1.13453i	0.989415	+	0.145111i	$0.0463538\pi$
$619$	28.2267	+	28.2267i	1.13453	+	1.13453i	0.145111	+	0.989415i	$0.453646\pi$
$620$		0			0
$621$			28.4111i			1.14010i
$622$		0			0
$623$	33.3307	+	33.3307i	1.33537	+	1.33537i
$624$		0			0
$625$	−22.5194			−0.900777
$626$		0			0
$627$		−	16.8874i		−	0.674419i
$628$		0			0
$629$	−8.90582	+	4.49472i	−0.355098	+	0.179216i
$630$		0			0
$631$		−	24.8661i		−	0.989905i	−0.868920	−	0.494952i	$-0.835186\pi$
$631$		−	24.8661i		−	0.989905i	0.868920	−	0.494952i	$-0.164814\pi$
$632$		0			0
$633$	−5.52946			−0.219776
$634$		0			0
$635$	−4.38041	−	4.38041i	−0.173831	−	0.173831i
$636$		0			0
$637$		−	21.9406i		−	0.869317i
$638$		0			0
$639$	17.8635	+	17.8635i	0.706671	+	0.706671i
$640$		0			0
$641$	−11.8816	+	11.8816i	−0.469297	+	0.469297i	−0.901687	−	0.432390i	$-0.857670\pi$
$641$	−11.8816	+	11.8816i	−0.469297	+	0.469297i	0.432390	+	0.901687i	$0.357670\pi$
$642$		0			0
$643$	−18.7120	+	18.7120i	−0.737930	+	0.737930i	−0.972177	−	0.234247i	$-0.924737\pi$
$643$	−18.7120	+	18.7120i	−0.737930	+	0.737930i	0.234247	+	0.972177i	$0.424737\pi$
$644$		0			0
$645$	2.76670			0.108939
$646$		0			0
$647$	36.7380			1.44432			0.722161	−	0.691725i	$-0.243149\pi$
$647$	36.7380			1.44432			0.722161	+	0.691725i	$0.243149\pi$
$648$		0			0
$649$	16.3728	−	16.3728i	0.642688	−	0.642688i
$650$		0			0
$651$	−0.275349	+	0.275349i	−0.0107918	+	0.0107918i
$652$		0			0
$653$	20.1814	+	20.1814i	0.789758	+	0.789758i	0.981454	−	0.191696i	$-0.0613988\pi$
$653$	20.1814	+	20.1814i	0.789758	+	0.789758i	−0.191696	+	0.981454i	$0.561399\pi$
$654$		0			0
$655$		−	0.394091i		−	0.0153984i
$656$		0			0
$657$	−12.6967	−	12.6967i	−0.495345	−	0.495345i
$658$		0			0
$659$	6.76333			0.263462			0.131731	−	0.991286i	$-0.457947\pi$
$659$	6.76333			0.263462			0.131731	+	0.991286i	$0.457947\pi$
$660$		0			0
$661$			16.1461i			0.628011i	0.949421	+	0.314005i	$0.101671\pi$
$661$			16.1461i			0.628011i	−0.949421	+	0.314005i	$0.898329\pi$
$662$		0			0
$663$	−8.15183	+	4.11418i	−0.316591	+	0.159782i
$664$		0			0
$665$			10.0978i			0.391574i
$666$		0			0
$667$	−69.1888			−2.67900
$668$		0			0
$669$	−8.10780	−	8.10780i	−0.313466	−	0.313466i
$670$		0			0
$671$		−	13.0995i		−	0.505700i
$672$		0			0
$673$	9.88164	+	9.88164i	0.380909	+	0.380909i	0.871430	−	0.490520i	$-0.163193\pi$
$673$	9.88164	+	9.88164i	0.380909	+	0.380909i	−0.490520	+	0.871430i	$0.663193\pi$
$674$		0			0
$675$	−11.7410	+	11.7410i	−0.451910	+	0.451910i
$676$		0			0
$677$	13.4842	−	13.4842i	0.518238	−	0.518238i	−0.398800	−	0.917038i	$-0.630573\pi$
$677$	13.4842	−	13.4842i	0.518238	−	0.518238i	0.917038	+	0.398800i	$0.130573\pi$
$678$		0			0
$679$	−26.5931			−1.02055
$680$		0			0
$681$	−3.96169			−0.151812
$682$		0			0
$683$	−12.1262	+	12.1262i	−0.463995	+	0.463995i	−0.899962	−	0.435967i	$-0.856406\pi$
$683$	−12.1262	+	12.1262i	−0.463995	+	0.463995i	0.435967	+	0.899962i	$0.356406\pi$
$684$		0			0
$685$	−0.714402	+	0.714402i	−0.0272959	+	0.0272959i
$686$		0			0
$687$	−5.76891	−	5.76891i	−0.220098	−	0.220098i
$688$		0			0
$689$			5.15667i			0.196454i
$690$		0			0
$691$	−4.58812	−	4.58812i	−0.174540	−	0.174540i	0.614431	−	0.788971i	$-0.289386\pi$
$691$	−4.58812	−	4.58812i	−0.174540	−	0.174540i	−0.788971	+	0.614431i	$0.789386\pi$
$692$		0			0
$693$	−38.4011			−1.45874
$694$		0			0
$695$		−	1.79913i		−	0.0682451i
$696$		0			0
$697$	2.62721	+	5.20555i	0.0995128	+	0.197174i
$698$		0			0
$699$		−	2.91229i		−	0.110153i
$700$		0			0
$701$	−21.9406			−0.828684			−0.414342	−	0.910121i	$-0.635988\pi$
$701$	−21.9406			−0.828684			−0.414342	+	0.910121i	$0.635988\pi$
$702$		0			0
$703$	−11.6944	−	11.6944i	−0.441064	−	0.441064i
$704$		0			0
$705$		−	2.55110i		−	0.0960801i
$706$		0			0
$707$	−11.1694	−	11.1694i	−0.420069	−	0.420069i
$708$		0			0
$709$	−20.2297	+	20.2297i	−0.759743	+	0.759743i	−0.976276	−	0.216532i	$-0.930525\pi$
$709$	−20.2297	+	20.2297i	−0.759743	+	0.759743i	0.216532	+	0.976276i	$0.430525\pi$
$710$		0			0
$711$	−2.59650	+	2.59650i	−0.0973764	+	0.0973764i
$712$		0			0
$713$	1.45998			0.0546765
$714$		0			0
$715$	−6.00206			−0.224464
$716$		0			0
$717$	−1.35218	+	1.35218i	−0.0504980	+	0.0504980i
$718$		0			0
$719$	35.8685	−	35.8685i	1.33767	−	1.33767i	0.439355	−	0.898314i	$-0.355207\pi$
$719$	35.8685	−	35.8685i	1.33767	−	1.33767i	0.898314	−	0.439355i	$-0.144793\pi$
$720$		0			0
$721$	18.0978	+	18.0978i	0.673995	+	0.673995i
$722$		0			0
$723$		−	17.2602i		−	0.641914i
$724$		0			0
$725$	−28.5925	−	28.5925i	−1.06190	−	1.06190i
$726$		0			0
$727$	−6.40836			−0.237673			−0.118836	−	0.992914i	$-0.537916\pi$
$727$	−6.40836			−0.237673			−0.118836	+	0.992914i	$0.537916\pi$
$728$		0			0
$729$		−	8.90225i		−	0.329713i
$730$		0			0
$731$	14.2848	−	43.3961i	0.528344	−	1.60506i
$732$		0			0
$733$		−	41.4983i		−	1.53277i	−0.642379	−	0.766387i	$-0.722052\pi$
$733$		−	41.4983i		−	1.53277i	0.642379	−	0.766387i	$-0.277948\pi$
$734$		0			0
$735$	−1.51033			−0.0557093
$736$		0			0
$737$	35.9305	+	35.9305i	1.32352	+	1.32352i
$738$		0			0
$739$			11.6944i			0.430187i	0.976593	+	0.215093i	$0.0690056\pi$
$739$			11.6944i			0.430187i	−0.976593	+	0.215093i	$0.930994\pi$
$740$		0			0
$741$	−10.7044	−	10.7044i	−0.393234	−	0.393234i
$742$		0			0
$743$	23.6912	−	23.6912i	0.869146	−	0.869146i	−0.123232	−	0.992378i	$-0.539326\pi$
$743$	23.6912	−	23.6912i	0.869146	−	0.869146i	0.992378	+	0.123232i	$0.0393259\pi$
$744$		0			0
$745$	2.55721	−	2.55721i	0.0936890	−	0.0936890i
$746$		0			0
$747$	19.5709			0.716062
$748$		0			0
$749$	6.61665			0.241767
$750$		0			0
$751$	−5.14470	+	5.14470i	−0.187733	+	0.187733i	−0.794715	−	0.606983i	$-0.792380\pi$
$751$	−5.14470	+	5.14470i	−0.187733	+	0.187733i	0.606983	+	0.794715i	$0.292380\pi$
$752$		0			0
$753$	−6.02827	+	6.02827i	−0.219682	+	0.219682i
$754$		0			0
$755$	−1.33284	−	1.33284i	−0.0485071	−	0.0485071i
$756$		0			0
$757$			51.3210i			1.86529i	0.360791	+	0.932647i	$0.382507\pi$
$757$			51.3210i			1.86529i	−0.360791	+	0.932647i	$0.617493\pi$
$758$		0			0
$759$	−14.4458	−	14.4458i	−0.524349	−	0.524349i
$760$		0			0
$761$	−2.68614			−0.0973723			−0.0486862	−	0.998814i	$-0.515503\pi$
$761$	−2.68614			−0.0973723			−0.0486862	+	0.998814i	$0.515503\pi$
$762$		0			0
$763$		−	56.0171i		−	2.02795i
$764$		0			0
$765$	−1.99591	−	3.95469i	−0.0721624	−	0.142982i
$766$		0			0
$767$		−	20.7563i		−	0.749466i
$768$		0			0
$769$	−14.0594			−0.506996			−0.253498	−	0.967336i	$-0.581581\pi$
$769$	−14.0594			−0.506996			−0.253498	+	0.967336i	$0.581581\pi$
$770$		0			0
$771$	1.43071	+	1.43071i	0.0515256	+	0.0515256i
$772$		0			0
$773$		−	31.6555i		−	1.13857i	−0.822141	−	0.569284i	$-0.807220\pi$
$773$		−	31.6555i		−	1.13857i	0.822141	−	0.569284i	$-0.192780\pi$
$774$		0			0
$775$	0.603340	+	0.603340i	0.0216726	+	0.0216726i
$776$		0			0
$777$	3.77332	−	3.77332i	0.135367	−	0.135367i
$778$		0			0
$779$	−6.83553	+	6.83553i	−0.244908	+	0.244908i
$780$		0			0
$781$	−38.9089			−1.39227
$782$		0			0
$783$	−28.7472			−1.02734
$784$		0			0
$785$	−4.98944	+	4.98944i	−0.178081	+	0.178081i
$786$		0			0
$787$	28.2989	−	28.2989i	1.00875	−	1.00875i	0.00878482	−	0.999961i	$-0.497204\pi$
$787$	28.2989	−	28.2989i	1.00875	−	1.00875i	0.999961	−	0.00878482i	$-0.00279633\pi$
$788$		0			0
$789$	−1.24438	−	1.24438i	−0.0443011	−	0.0443011i
$790$		0			0
$791$			57.2446i			2.03538i
$792$		0			0
$793$	−8.30330	−	8.30330i	−0.294859	−	0.294859i
$794$		0			0
$795$	0.354971			0.0125895
$796$		0			0
$797$		−	32.6761i		−	1.15745i	−0.815524	−	0.578723i	$-0.803551\pi$
$797$		−	32.6761i		−	1.15745i	0.815524	−	0.578723i	$-0.196449\pi$
$798$		0			0
$799$	−40.0144	−	13.1717i	−1.41561	−	0.465981i
$800$		0			0
$801$		−	34.2822i		−	1.21130i
$802$		0			0
$803$	27.6549			0.975920
$804$		0			0
$805$	8.63778	+	8.63778i	0.304442	+	0.304442i
$806$		0			0
$807$			9.32373i			0.328211i
$808$		0			0
$809$	3.51890	+	3.51890i	0.123718	+	0.123718i	0.766255	−	0.642537i	$-0.222118\pi$
$809$	3.51890	+	3.51890i	0.123718	+	0.123718i	−0.642537	+	0.766255i	$0.722118\pi$
$810$		0			0
$811$	15.9185	−	15.9185i	0.558973	−	0.558973i	−0.370042	−	0.929015i	$-0.620657\pi$
$811$	15.9185	−	15.9185i	0.558973	−	0.558973i	0.929015	+	0.370042i	$0.120657\pi$
$812$		0			0
$813$	1.35218	−	1.35218i	0.0474229	−	0.0474229i
$814$		0			0
$815$	−0.800385			−0.0280363
$816$		0			0
$817$	75.7422			2.64988
$818$		0			0
$819$	−24.3411	+	24.3411i	−0.850546	+	0.850546i
$820$		0			0
$821$	8.32748	−	8.32748i	0.290631	−	0.290631i	−0.546698	−	0.837330i	$-0.684116\pi$
$821$	8.32748	−	8.32748i	0.290631	−	0.290631i	0.837330	+	0.546698i	$0.184116\pi$
$822$		0			0
$823$	34.0950	+	34.0950i	1.18848	+	1.18848i	0.977489	+	0.210988i	$0.0676683\pi$
$823$	34.0950	+	34.0950i	1.18848	+	1.18848i	0.210988	+	0.977489i	$0.432332\pi$
$824$		0			0
$825$		−	11.9395i		−	0.415681i
$826$		0			0
$827$	37.9188	+	37.9188i	1.31857	+	1.31857i	0.914911	+	0.403657i	$0.132261\pi$
$827$	37.9188	+	37.9188i	1.31857	+	1.31857i	0.403657	+	0.914911i	$0.367739\pi$
$828$		0			0
$829$	4.91995			0.170877			0.0854385	−	0.996343i	$-0.472771\pi$
$829$	4.91995			0.170877			0.0854385	+	0.996343i	$0.472771\pi$
$830$		0			0
$831$		−	10.8732i		−	0.377186i
$832$		0			0
$833$	−7.79802	+	23.6897i	−0.270185	+	0.820800i
$834$		0			0
$835$			5.28608i			0.182932i
$836$		0			0
$837$	0.606604			0.0209673
$838$		0			0
$839$	−9.14014	−	9.14014i	−0.315553	−	0.315553i	0.531503	−	0.847056i	$-0.321627\pi$
$839$	−9.14014	−	9.14014i	−0.315553	−	0.315553i	−0.847056	+	0.531503i	$0.821627\pi$
$840$		0			0
$841$		−	41.0071i		−	1.41404i
$842$		0			0
$843$	−7.69899	−	7.69899i	−0.265167	−	0.265167i
$844$		0			0
$845$	−0.0453052	+	0.0453052i	−0.00155855	+	0.00155855i
$846$		0			0
$847$	13.7237	−	13.7237i	0.471552	−	0.471552i
$848$		0			0
$849$	7.84281			0.269165
$850$		0			0
$851$	−20.0072			−0.685838
$852$		0			0
$853$	−21.2302	+	21.2302i	−0.726910	+	0.726910i	−0.970003	−	0.243093i	$-0.921838\pi$
$853$	−21.2302	+	21.2302i	−0.726910	+	0.726910i	0.243093	+	0.970003i	$0.421838\pi$
$854$		0			0
$855$	5.19300	−	5.19300i	0.177597	−	0.177597i
$856$		0			0
$857$	25.0766	+	25.0766i	0.856601	+	0.856601i	0.990936	−	0.134335i	$-0.0428897\pi$
$857$	25.0766	+	25.0766i	0.856601	+	0.856601i	−0.134335	+	0.990936i	$0.542890\pi$
$858$		0			0
$859$			39.9722i			1.36383i	0.731429	+	0.681917i	$0.238854\pi$
$859$			39.9722i			1.36383i	−0.731429	+	0.681917i	$0.761146\pi$
$860$		0			0
$861$	−2.20555	−	2.20555i	−0.0751649	−	0.0751649i
$862$		0			0
$863$	−28.7472			−0.978565			−0.489282	−	0.872125i	$-0.662741\pi$
$863$	−28.7472			−0.978565			−0.489282	+	0.872125i	$0.662741\pi$
$864$		0			0
$865$		−	3.42166i		−	0.116340i
$866$		0			0
$867$	10.2640	−	1.54489i	0.348582	−	0.0524671i
$868$		0			0
$869$		−	5.65548i		−	0.191849i
$870$		0			0
$871$	45.5502			1.54341
$872$		0			0
$873$	13.6761	+	13.6761i	0.462865	+	0.462865i
$874$		0			0
$875$			14.5254i			0.491048i
$876$		0			0
$877$	−4.07357	−	4.07357i	−0.137555	−	0.137555i	0.634977	−	0.772531i	$-0.281010\pi$
$877$	−4.07357	−	4.07357i	−0.137555	−	0.137555i	−0.772531	+	0.634977i	$0.781010\pi$
$878$		0			0
$879$	3.49607	−	3.49607i	0.117919	−	0.117919i
$880$		0			0
$881$	8.78440	−	8.78440i	0.295954	−	0.295954i	−0.543473	−	0.839427i	$-0.682891\pi$
$881$	8.78440	−	8.78440i	0.295954	−	0.295954i	0.839427	+	0.543473i	$0.182891\pi$
$882$		0			0
$883$	−23.4520			−0.789221			−0.394611	−	0.918848i	$-0.629120\pi$
$883$	−23.4520			−0.789221			−0.394611	+	0.918848i	$0.629120\pi$
$884$		0			0
$885$	−1.42880			−0.0480287
$886$		0			0
$887$	2.64304	−	2.64304i	0.0887446	−	0.0887446i	−0.661341	−	0.750085i	$-0.730012\pi$
$887$	2.64304	−	2.64304i	0.0887446	−	0.0887446i	0.750085	+	0.661341i	$0.230012\pi$
$888$		0			0
$889$	38.6933	−	38.6933i	1.29773	−	1.29773i
$890$		0			0
$891$	16.5488	+	16.5488i	0.554405	+	0.554405i
$892$		0			0
$893$		−	69.8399i		−	2.33710i
$894$		0			0
$895$	−3.38166	−	3.38166i	−0.113037	−	0.113037i
$896$		0			0
$897$	−18.3133			−0.611465
$898$		0			0
$899$			1.47725i			0.0492689i
$900$		0			0
$901$	1.83276	−	5.56777i	0.0610582	−	0.185489i
$902$		0			0
$903$			24.4389i			0.813277i
$904$		0			0
$905$	−3.20607			−0.106573
$906$		0			0
$907$	−5.81568	−	5.81568i	−0.193106	−	0.193106i	0.603931	−	0.797037i	$-0.293600\pi$
$907$	−5.81568	−	5.81568i	−0.193106	−	0.193106i	−0.797037	+	0.603931i	$0.793600\pi$
$908$		0			0
$909$			11.4882i			0.381041i
$910$		0			0
$911$	18.2020	+	18.2020i	0.603058	+	0.603058i	0.941123	−	0.338065i	$-0.109772\pi$
$911$	18.2020	+	18.2020i	0.603058	+	0.603058i	−0.338065	+	0.941123i	$0.609772\pi$
$912$		0			0
$913$	−21.3139	+	21.3139i	−0.705386	+	0.705386i
$914$		0			0
$915$	−0.571576	+	0.571576i	−0.0188957	+	0.0188957i
$916$		0			0
$917$	3.48110			0.114956
$918$		0			0
$919$	3.95324			0.130405			0.0652027	−	0.997872i	$-0.479231\pi$
$919$	3.95324			0.130405			0.0652027	+	0.997872i	$0.479231\pi$
$920$		0			0
$921$	12.1955	−	12.1955i	0.401856	−	0.401856i
$922$		0			0
$923$	−24.6630	+	24.6630i	−0.811792	+	0.811792i
$924$		0			0
$925$	−8.26804	−	8.26804i	−0.271852	−	0.271852i
$926$		0			0
$927$		−	18.6144i		−	0.611376i
$928$		0			0
$929$	−16.1567	−	16.1567i	−0.530083	−	0.530083i	0.390514	−	0.920597i	$-0.372297\pi$
$929$	−16.1567	−	16.1567i	−0.530083	−	0.530083i	−0.920597	+	0.390514i	$0.872297\pi$
$930$		0			0
$931$	−41.3473			−1.35510
$932$		0			0
$933$			12.3033i			0.402792i
$934$		0			0
$935$	6.48056	+	2.13323i	0.211937	+	0.0697640i
$936$		0			0
$937$		−	18.4394i		−	0.602388i	−0.953563	−	0.301194i	$-0.902615\pi$
$937$		−	18.4394i		−	0.602388i	0.953563	−	0.301194i	$-0.0973852\pi$
$938$		0			0
$939$	16.2615			0.530673
$940$		0			0
$941$	4.25086	+	4.25086i	0.138574	+	0.138574i	0.772991	−	0.634417i	$-0.218760\pi$
$941$	4.25086	+	4.25086i	0.138574	+	0.138574i	−0.634417	+	0.772991i	$0.718760\pi$
$942$		0			0
$943$			11.6944i			0.380823i
$944$		0			0
$945$	3.58890	+	3.58890i	0.116747	+	0.116747i
$946$		0			0
$947$	−1.49835	+	1.49835i	−0.0486897	+	0.0486897i	−0.731032	−	0.682343i	$-0.760961\pi$
$947$	−1.49835	+	1.49835i	−0.0486897	+	0.0486897i	0.682343	+	0.731032i	$0.260961\pi$
$948$		0			0
$949$	17.5295	−	17.5295i	0.569030	−	0.569030i
$950$		0			0
$951$	3.02669			0.0981472
$952$		0			0
$953$	13.1255			0.425177			0.212588	−	0.977142i	$-0.431811\pi$
$953$	13.1255			0.425177			0.212588	+	0.977142i	$0.431811\pi$
$954$		0			0
$955$	2.90317	−	2.90317i	0.0939443	−	0.0939443i
$956$		0			0
$957$	14.6167	−	14.6167i	0.472489	−	0.472489i
$958$		0			0
$959$	−6.31049	−	6.31049i	−0.203776	−	0.203776i
$960$		0			0
$961$			30.9688i			0.998994i
$962$		0			0
$963$	−3.40276	−	3.40276i	−0.109653	−	0.109653i
$964$		0			0
$965$	−10.0695			−0.324148
$966$		0			0
$967$		−	28.3200i		−	0.910709i	−0.890310	−	0.455355i	$-0.849512\pi$
$967$		−	28.3200i		−	0.910709i	0.890310	−	0.455355i	$-0.150488\pi$
$968$		0			0
$969$	7.75323	+	15.3622i	0.249070	+	0.493506i
$970$		0			0
$971$		−	57.6296i		−	1.84942i	−0.380670	−	0.924711i	$-0.624307\pi$
$971$		−	57.6296i		−	1.84942i	0.380670	−	0.924711i	$-0.375693\pi$
$972$		0			0
$973$	15.8922			0.509481
$974$		0			0
$975$	−7.56805	−	7.56805i	−0.242372	−	0.242372i
$976$		0			0
$977$		−	6.43223i		−	0.205785i	−0.994692	−	0.102893i	$-0.967190\pi$
$977$		−	6.43223i		−	0.205785i	0.994692	−	0.102893i	$-0.0328098\pi$
$978$		0			0
$979$	37.3353	+	37.3353i	1.19324	+	1.19324i
$980$		0			0
$981$	−28.8081	+	28.8081i	−0.919771	+	0.919771i
$982$		0			0
$983$	−13.4575	+	13.4575i	−0.429227	+	0.429227i	−0.888365	−	0.459138i	$-0.848158\pi$
$983$	−13.4575	+	13.4575i	−0.429227	+	0.429227i	0.459138	+	0.888365i	$0.348158\pi$
$984$		0			0
$985$	0.286114			0.00911635
$986$		0			0
$987$	22.5345			0.717282
$988$		0			0
$989$	64.7910	−	64.7910i	2.06023	−	2.06023i
$990$		0			0
$991$	−15.5394	+	15.5394i	−0.493624	+	0.493624i	−0.909446	−	0.415822i	$-0.863494\pi$
$991$	−15.5394	+	15.5394i	−0.493624	+	0.493624i	0.415822	+	0.909446i	$0.363494\pi$
$992$		0			0
$993$	4.56829	+	4.56829i	0.144970	+	0.144970i
$994$		0			0
$995$		−	9.29064i		−	0.294533i
$996$		0			0
$997$	−1.77027	−	1.77027i	−0.0560650	−	0.0560650i	0.678518	−	0.734583i	$-0.262622\pi$
$997$	−1.77027	−	1.77027i	−0.0560650	−	0.0560650i	−0.734583	+	0.678518i	$0.762622\pi$
$998$		0			0
$999$	−8.31277			−0.263005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.o.w.769.4		12
4.3	odd	2	inner	1088.2.o.w.769.3		12
8.3	odd	2		544.2.o.i.225.4	yes	12
8.5	even	2		544.2.o.i.225.3	✓	12
17.13	even	4	inner	1088.2.o.w.897.4		12
68.47	odd	4	inner	1088.2.o.w.897.3		12
136.13	even	4		544.2.o.i.353.3	yes	12
136.43	odd	8		9248.2.a.bv.1.7		12
136.59	odd	8		9248.2.a.bv.1.6		12
136.77	even	8		9248.2.a.bv.1.5		12
136.93	even	8		9248.2.a.bv.1.8		12
136.115	odd	4		544.2.o.i.353.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.o.i.225.3	✓	12	8.5	even	2
544.2.o.i.225.4	yes	12	8.3	odd	2
544.2.o.i.353.3	yes	12	136.13	even	4
544.2.o.i.353.4	yes	12	136.115	odd	4
1088.2.o.w.769.3		12	4.3	odd	2	inner
1088.2.o.w.769.4		12	1.1	even	1	trivial
1088.2.o.w.897.3		12	68.47	odd	4	inner
1088.2.o.w.897.4		12	17.13	even	4	inner
9248.2.a.bv.1.5		12	136.77	even	8
9248.2.a.bv.1.6		12	136.59	odd	8
9248.2.a.bv.1.7		12	136.43	odd	8
9248.2.a.bv.1.8		12	136.93	even	8

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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.431733 - 0.431733i) q^{3} +(-0.289169 + 0.289169i) q^{5} +(-2.55430 - 2.55430i) q^{7} +2.62721i q^{9} +O(q^{10})\)	\(q+(0.431733 - 0.431733i) q^{3} +(-0.289169 + 0.289169i) q^{5} +(-2.55430 - 2.55430i) q^{7} +2.62721i q^{9} +(-2.86119 - 2.86119i) q^{11} -3.62721 q^{13} +0.249687i q^{15} +(3.91638 + 1.28917i) q^{17} +6.83553i q^{19} -2.20555 q^{21} +(5.84722 + 5.84722i) q^{23} +4.83276i q^{25} +(2.42945 + 2.42945i) q^{27} +(-5.91638 + 5.91638i) q^{29} +(0.124844 - 0.124844i) q^{31} -2.47054 q^{33} +1.47725 q^{35} +(-1.71083 + 1.71083i) q^{37} +(-1.56599 + 1.56599i) q^{39} +(1.00000 + 1.00000i) q^{41} -11.0807i q^{43} +(-0.759707 - 0.759707i) q^{45} -10.2172 q^{47} +6.04888i q^{49} +(2.24741 - 1.13425i) q^{51} -1.42166i q^{53} +1.65473 q^{55} +(2.95112 + 2.95112i) q^{57} +5.72237i q^{59} +(2.28917 + 2.28917i) q^{61} +(6.71068 - 6.71068i) q^{63} +(1.04888 - 1.04888i) q^{65} -12.5579 q^{67} +5.04888 q^{69} +(6.79943 - 6.79943i) q^{71} +(-4.83276 + 4.83276i) q^{73} +(2.08646 + 2.08646i) q^{75} +14.6167i q^{77} +(0.988310 + 0.988310i) q^{79} -5.78389 q^{81} -7.44931i q^{83} +(-1.50528 + 0.759707i) q^{85} +5.10860i q^{87} -13.0489 q^{89} +(9.26498 + 9.26498i) q^{91} -0.107798i q^{93} +(-1.97662 - 1.97662i) q^{95} +(5.20555 - 5.20555i) q^{97} +(7.51695 - 7.51695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) \) 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Introduction

L-functions

Modular forms

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