LMFDB - Embedded newform 882.2.v.a.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(125,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("882.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.v (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.1
Character	$\chi$	$=$	882.251
Dual form			882.2.v.a.629.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 - 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-2.40184 - 1.15666i) q^{5} +(-0.0714045 - 2.64479i) q^{7} +(0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(-0.781831 - 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-2.40184 - 1.15666i) q^{5} +(-0.0714045 - 2.64479i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.15666 + 2.40184i) q^{10} +(-1.90670 - 1.52054i) q^{11} +(1.46732 + 1.17015i) q^{13} +(-1.59317 + 2.11230i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(-0.0538962 + 0.236135i) q^{17} -0.476570i q^{19} +(0.593205 - 2.59900i) q^{20} +(0.542676 + 2.37762i) q^{22} +(-6.02654 + 1.37552i) q^{23} +(1.31351 + 1.64709i) q^{25} +(-0.417622 - 1.82972i) q^{26} +(2.56259 - 0.658135i) q^{28} +(3.97962 + 0.908321i) q^{29} +4.23855i q^{31} +(0.974928 + 0.222521i) q^{32} +(0.189365 - 0.151014i) q^{34} +(-2.88763 + 6.43495i) q^{35} +(-1.24822 + 5.46883i) q^{37} +(-0.297136 + 0.372597i) q^{38} +(-2.08424 + 1.66212i) q^{40} +(-2.77328 - 1.33554i) q^{41} +(-0.992268 + 0.477851i) q^{43} +(1.05814 - 2.19725i) q^{44} +(5.56936 + 2.68206i) q^{46} +(-4.28679 + 5.37547i) q^{47} +(-6.98980 + 0.377699i) q^{49} -2.10671i q^{50} +(-0.814303 + 1.69092i) q^{52} +(1.18745 - 0.271028i) q^{53} +(2.82083 + 5.85752i) q^{55} +(-2.41385 - 1.08320i) q^{56} +(-2.54506 - 3.19140i) q^{58} +(-8.79410 + 4.23502i) q^{59} +(-8.96382 - 2.04593i) q^{61} +(2.64269 - 3.31383i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-2.17080 - 4.50771i) q^{65} -0.386179 q^{67} -0.242207 q^{68} +(6.26976 - 3.23063i) q^{70} +(9.30088 - 2.12287i) q^{71} +(-6.92698 + 5.52408i) q^{73} +(4.38566 - 3.49745i) q^{74} +(0.464621 - 0.106047i) q^{76} +(-3.88537 + 5.15139i) q^{77} -7.54903 q^{79} +2.66584 q^{80} +(1.33554 + 2.77328i) q^{82} +(0.608561 + 0.763112i) q^{83} +(0.402579 - 0.504818i) q^{85} +(1.07372 + 0.245070i) q^{86} +(-2.19725 + 1.05814i) q^{88} +(4.28981 + 5.37926i) q^{89} +(2.99003 - 3.96431i) q^{91} +(-2.68206 - 5.56936i) q^{92} +(6.70310 - 1.52994i) q^{94} +(-0.551231 + 1.14464i) q^{95} +16.9042i q^{97} +(5.70034 + 4.06277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 16 q^{4}+O(q^{10}) $ 96 * q + 16 * q^4	$ 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) $ 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$		0			0
$3$		0			0
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−2.40184	−	1.15666i	−1.07414	−	0.517276i	−0.188698	−	0.982035i	$-0.560427\pi$
$5$	−2.40184	−	1.15666i	−1.07414	−	0.517276i	−0.885437	+	0.464759i	$0.846141\pi$
$6$		0			0
$7$	−0.0714045	−	2.64479i	−0.0269883	−	0.999636i
$7$	−0.0714045	−	2.64479i	−0.0269883	−	0.999636i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$		0			0
$10$	1.15666	+	2.40184i	0.365770	+	0.759528i
$11$	−1.90670	−	1.52054i	−0.574892	−	0.458461i	0.292375	−	0.956304i	$-0.405554\pi$
$11$	−1.90670	−	1.52054i	−0.574892	−	0.458461i	−0.867267	+	0.497843i	$0.834126\pi$
$12$		0			0
$13$	1.46732	+	1.17015i	0.406962	+	0.324541i	0.805484	−	0.592617i	$-0.201905\pi$
$13$	1.46732	+	1.17015i	0.406962	+	0.324541i	−0.398522	+	0.917159i	$0.630477\pi$
$14$	−1.59317	+	2.11230i	−0.425793	+	0.564535i
$15$		0			0
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.0538962	+	0.236135i	−0.0130718	+	0.0572711i	−0.981043	−	0.193789i	$-0.937922\pi$
$17$	−0.0538962	+	0.236135i	−0.0130718	+	0.0572711i	0.967971	+	0.251060i	$0.0807793\pi$
$18$		0			0
$19$		−	0.476570i		−	0.109333i	−0.998505	−	0.0546663i	$-0.982591\pi$
$19$		−	0.476570i		−	0.109333i	0.998505	−	0.0546663i	$-0.0174095\pi$
$20$	0.593205	−	2.59900i	0.132645	−	0.581155i
$21$		0			0
$22$	0.542676	+	2.37762i	0.115699	+	0.506910i
$23$	−6.02654	+	1.37552i	−1.25662	+	0.286815i	−0.798457	−	0.602052i	$-0.794350\pi$
$23$	−6.02654	+	1.37552i	−1.25662	+	0.286815i	−0.458164	+	0.888868i	$0.651493\pi$
$24$		0			0
$25$	1.31351	+	1.64709i	0.262702	+	0.329418i
$26$	−0.417622	−	1.82972i	−0.0819024	−	0.358838i
$27$		0			0
$28$	2.56259	−	0.658135i	0.484284	−	0.124376i
$29$	3.97962	+	0.908321i	0.738996	+	0.168671i	0.575418	−	0.817859i	$-0.304839\pi$
$29$	3.97962	+	0.908321i	0.738996	+	0.168671i	0.163578	+	0.986530i	$0.447696\pi$
$30$		0			0
$31$			4.23855i			0.761265i	0.924726	+	0.380633i	$0.124294\pi$
$31$			4.23855i			0.761265i	−0.924726	+	0.380633i	$0.875706\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$		0			0
$34$	0.189365	−	0.151014i	0.0324759	−	0.0258987i
$35$	−2.88763	+	6.43495i	−0.488099	+	1.08770i
$36$		0			0
$37$	−1.24822	+	5.46883i	−0.205207	+	0.899070i	0.762499	+	0.646989i	$0.223972\pi$
$37$	−1.24822	+	5.46883i	−0.205207	+	0.899070i	−0.967706	+	0.252081i	$0.918885\pi$
$38$	−0.297136	+	0.372597i	−0.0482019	+	0.0604432i
$39$		0			0
$40$	−2.08424	+	1.66212i	−0.329547	+	0.262805i
$41$	−2.77328	−	1.33554i	−0.433113	−	0.208576i	0.204608	−	0.978844i	$-0.434408\pi$
$41$	−2.77328	−	1.33554i	−0.433113	−	0.208576i	−0.637720	+	0.770268i	$0.720122\pi$
$42$		0			0
$43$	−0.992268	+	0.477851i	−0.151319	+	0.0728716i	−0.508011	−	0.861351i	$-0.669619\pi$
$43$	−0.992268	+	0.477851i	−0.151319	+	0.0728716i	0.356691	+	0.934222i	$0.383905\pi$
$44$	1.05814	−	2.19725i	0.159521	−	0.331248i
$45$		0			0
$46$	5.56936	+	2.68206i	0.821158	+	0.395449i
$47$	−4.28679	+	5.37547i	−0.625293	+	0.784092i	−0.989078	−	0.147390i	$-0.952913\pi$
$47$	−4.28679	+	5.37547i	−0.625293	+	0.784092i	0.363786	+	0.931483i	$0.381484\pi$
$48$		0			0
$49$	−6.98980	+	0.377699i	−0.998543	+	0.0539570i
$50$		−	2.10671i		−	0.297933i
$51$		0			0
$52$	−0.814303	+	1.69092i	−0.112923	+	0.234488i
$53$	1.18745	−	0.271028i	0.163109	−	0.0372285i	−0.140187	−	0.990125i	$-0.544770\pi$
$53$	1.18745	−	0.271028i	0.163109	−	0.0372285i	0.303295	+	0.952897i	$0.401913\pi$
$54$		0			0
$55$	2.82083	+	5.85752i	0.380361	+	0.789827i
$56$	−2.41385	−	1.08320i	−0.322565	−	0.144748i
$57$		0			0
$58$	−2.54506	−	3.19140i	−0.334183	−	0.419052i
$59$	−8.79410	+	4.23502i	−1.14489	+	0.551352i	−0.907496	−	0.420060i	$-0.862009\pi$
$59$	−8.79410	+	4.23502i	−1.14489	+	0.551352i	−0.237398	+	0.971412i	$0.576295\pi$
$60$		0			0
$61$	−8.96382	−	2.04593i	−1.14770	−	0.261955i	−0.393960	−	0.919128i	$-0.628895\pi$
$61$	−8.96382	−	2.04593i	−1.14770	−	0.261955i	−0.753740	+	0.657173i	$0.771752\pi$
$62$	2.64269	−	3.31383i	0.335622	−	0.420857i
$63$		0			0
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−2.17080	−	4.50771i	−0.269255	−	0.559113i
$66$		0			0
$67$	−0.386179			−0.0471792			−0.0235896	−	0.999722i	$-0.507510\pi$
$67$	−0.386179			−0.0471792			−0.0235896	+	0.999722i	$0.507510\pi$
$68$	−0.242207			−0.0293720
$69$		0			0
$70$	6.26976	−	3.23063i	0.749380	−	0.386135i
$71$	9.30088	−	2.12287i	1.10381	−	0.251938i	0.368474	−	0.929638i	$-0.379880\pi$
$71$	9.30088	−	2.12287i	1.10381	−	0.251938i	0.735338	+	0.677700i	$0.237023\pi$
$72$		0			0
$73$	−6.92698	+	5.52408i	−0.810742	+	0.646545i	−0.938507	−	0.345259i	$-0.887791\pi$
$73$	−6.92698	+	5.52408i	−0.810742	+	0.646545i	0.127765	+	0.991804i	$0.459220\pi$
$74$	4.38566	−	3.49745i	0.509823	−	0.406570i
$75$		0			0
$76$	0.464621	−	0.106047i	0.0532957	−	0.0121644i
$77$	−3.88537	+	5.15139i	−0.442779	+	0.587056i
$78$		0			0
$79$	−7.54903			−0.849332			−0.424666	−	0.905350i	$-0.639608\pi$
$79$	−7.54903			−0.849332			−0.424666	+	0.905350i	$0.639608\pi$
$80$	2.66584			0.298050
$81$		0			0
$82$	1.33554	+	2.77328i	0.147486	+	0.306257i
$83$	0.608561	+	0.763112i	0.0667983	+	0.0837624i	0.814108	−	0.580713i	$-0.197226\pi$
$83$	0.608561	+	0.763112i	0.0667983	+	0.0837624i	−0.747310	+	0.664476i	$0.768655\pi$
$84$		0			0
$85$	0.402579	−	0.504818i	0.0436658	−	0.0547552i
$86$	1.07372	+	0.245070i	0.115782	+	0.0264266i
$87$		0			0
$88$	−2.19725	+	1.05814i	−0.234228	+	0.112798i
$89$	4.28981	+	5.37926i	0.454719	+	0.570200i	0.955356	−	0.295458i	$-0.0954721\pi$
$89$	4.28981	+	5.37926i	0.454719	+	0.570200i	−0.500636	+	0.865658i	$0.666901\pi$
$90$		0			0
$91$	2.99003	−	3.96431i	0.313440	−	0.415573i
$92$	−2.68206	−	5.56936i	−0.279624	−	0.580646i
$93$		0			0
$94$	6.70310	−	1.52994i	0.691372	−	0.157801i
$95$	−0.551231	+	1.14464i	−0.0565551	+	0.117438i
$96$		0			0
$97$			16.9042i			1.71636i	0.513349	+	0.858180i	$0.328405\pi$
$97$			16.9042i			1.71636i	−0.513349	+	0.858180i	$0.671595\pi$
$98$	5.70034	+	4.06277i	0.575821	+	0.410402i
$99$		0			0
$100$	−1.31351	+	1.64709i	−0.131351	+	0.164709i
$101$	−8.60894	−	4.14585i	−0.856622	−	0.412527i	−0.0465907	−	0.998914i	$-0.514836\pi$
$101$	−8.60894	−	4.14585i	−0.856622	−	0.412527i	−0.810031	+	0.586387i	$0.800550\pi$
$102$		0			0
$103$	5.29877	−	11.0030i	0.522104	−	1.08416i	−0.458597	−	0.888644i	$-0.651648\pi$
$103$	5.29877	−	11.0030i	0.522104	−	1.08416i	0.980701	−	0.195515i	$-0.0626378\pi$
$104$	1.69092	−	0.814303i	0.165808	−	0.0798489i
$105$		0			0
$106$	−1.09737	−	0.528465i	−0.106586	−	0.0513290i
$107$	−7.88034	+	6.28436i	−0.761822	+	0.607532i	−0.925397	−	0.378998i	$-0.876269\pi$
$107$	−7.88034	+	6.28436i	−0.761822	+	0.607532i	0.163576	+	0.986531i	$0.447697\pi$
$108$		0			0
$109$	7.35620	−	9.22438i	0.704596	−	0.883535i	−0.292762	−	0.956185i	$-0.594574\pi$
$109$	7.35620	−	9.22438i	0.704596	−	0.883535i	0.997357	+	0.0726502i	$0.0231457\pi$
$110$	1.44669	−	6.33835i	0.137936	−	0.604338i
$111$		0			0
$112$	1.21186	+	2.35189i	0.114510	+	0.222233i
$113$	12.6053	−	10.0524i	1.18581	−	0.945650i	0.186485	−	0.982458i	$-0.440291\pi$
$113$	12.6053	−	10.0524i	1.18581	−	0.945650i	0.999322	+	0.0368083i	$0.0117191\pi$
$114$		0			0
$115$	16.0658	+	3.66691i	1.49814	+	0.341941i
$116$			4.08196i			0.379000i
$117$		0			0
$118$	9.51600	+	2.17196i	0.876018	+	0.199945i
$119$	0.628375	+	0.125683i	0.0576030	+	0.0115213i
$120$		0			0
$121$	−1.12427	−	4.92576i	−0.102207	−	0.447797i
$122$	5.73258	+	7.18842i	0.519003	+	0.650809i
$123$		0			0
$124$	−4.13228	+	0.943165i	−0.371089	+	0.0846987i
$125$	1.71632	+	7.51968i	0.153512	+	0.672581i
$126$		0			0
$127$	3.18786	−	13.9669i	0.282877	−	1.23937i	−0.611208	−	0.791470i	$-0.709316\pi$
$127$	3.18786	−	13.9669i	0.282877	−	1.23937i	0.894085	−	0.447896i	$-0.147827\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−1.11331	+	4.87775i	−0.0976441	+	0.427807i
$131$	−8.81547	+	4.24531i	−0.770211	+	0.370914i	−0.777357	−	0.629060i	$-0.783440\pi$
$131$	−8.81547	+	4.24531i	−0.770211	+	0.370914i	0.00714514	+	0.999974i	$0.497726\pi$
$132$		0			0
$133$	−1.26043	+	0.0340292i	−0.109293	+	0.00295070i
$134$	0.301927	+	0.240778i	0.0260825	+	0.0208001i
$135$		0			0
$136$	0.189365	+	0.151014i	0.0162379	+	0.0129493i
$137$	9.29604	+	19.3034i	0.794214	+	1.64920i	0.760119	+	0.649783i	$0.225140\pi$
$137$	9.29604	+	19.3034i	0.794214	+	1.64920i	0.0340945	+	0.999419i	$0.489145\pi$
$138$		0			0
$139$	−2.81475	+	5.84488i	−0.238744	+	0.495757i	−0.985571	−	0.169261i	$-0.945862\pi$
$139$	−2.81475	+	5.84488i	−0.238744	+	0.495757i	0.746827	+	0.665018i	$0.231576\pi$
$140$	−6.91617	−	1.38332i	−0.584523	−	0.116912i
$141$		0			0
$142$	−8.59531	−	4.13928i	−0.721302	−	0.347361i
$143$	−1.01848	−	4.46226i	−0.0851696	−	0.373153i
$144$		0			0
$145$	−8.50777	−	6.78472i	−0.706532	−	0.563441i
$146$	8.85994			0.733254
$147$		0			0
$148$	−5.60947			−0.461096
$149$	1.55268	+	1.23822i	0.127201	+	0.101439i	0.685024	−	0.728521i	$-0.259792\pi$
$149$	1.55268	+	1.23822i	0.127201	+	0.101439i	−0.557823	+	0.829960i	$0.688363\pi$
$150$		0			0
$151$	−4.23695	−	18.5633i	−0.344798	−	1.51066i	−0.788809	−	0.614639i	$-0.789302\pi$
$151$	−4.23695	−	18.5633i	−0.344798	−	1.51066i	0.444011	−	0.896022i	$-0.353555\pi$
$152$	−0.429374	−	0.206776i	−0.0348269	−	0.0167717i
$153$		0			0
$154$	6.24954	−	1.60503i	0.503603	−	0.129337i
$155$	4.90258	−	10.1803i	0.393784	−	0.817702i
$156$		0			0
$157$	0.756550	+	1.57099i	0.0603793	+	0.125379i	0.928975	−	0.370143i	$-0.120691\pi$
$157$	0.756550	+	1.57099i	0.0603793	+	0.125379i	−0.868596	+	0.495522i	$0.834977\pi$
$158$	5.90207	+	4.70674i	0.469543	+	0.374448i
$159$		0			0
$160$	−2.08424	−	1.66212i	−0.164773	−	0.131402i
$161$	4.06828	+	15.8407i	0.320625	+	1.24842i
$162$		0			0
$163$	−16.7343	+	8.05881i	−1.31073	+	0.631214i	−0.953102	−	0.302650i	$-0.902129\pi$
$163$	−16.7343	+	8.05881i	−1.31073	+	0.631214i	−0.357628	+	0.933864i	$0.616415\pi$
$164$	0.684942	−	3.00093i	0.0534850	−	0.234333i
$165$		0			0
$166$		−	0.976056i		−	0.0757567i
$167$	0.0324603	−	0.142218i	0.00251185	−	0.0110051i	−0.973656	−	0.228020i	$-0.926775\pi$
$167$	0.0324603	−	0.142218i	0.00251185	−	0.0110051i	0.976168	+	0.217015i	$0.0696320\pi$
$168$		0			0
$169$	−2.10899	−	9.24009i	−0.162230	−	0.710776i
$170$	−0.629497	+	0.143679i	−0.0482803	+	0.0110197i
$171$		0			0
$172$	−0.686671	−	0.861058i	−0.0523581	−	0.0656550i
$173$	−1.93271	−	8.46776i	−0.146941	−	0.643792i	−0.993725	−	0.111854i	$-0.964321\pi$
$173$	−1.93271	−	8.46776i	−0.146941	−	0.643792i	0.846783	−	0.531938i	$-0.178536\pi$
$174$		0			0
$175$	4.26241	−	3.59156i	0.322208	−	0.271497i
$176$	2.37762	+	0.542676i	0.179220	+	0.0409057i
$177$		0			0
$178$		−	6.88033i		−	0.515702i
$179$	14.8942	+	3.39950i	1.11324	+	0.254090i	0.739310	−	0.673365i	$-0.235152\pi$
$179$	14.8942	+	3.39950i	1.11324	+	0.254090i	0.373933	+	0.927456i	$0.378009\pi$
$180$		0			0
$181$	−6.04982	+	4.82457i	−0.449679	+	0.358607i	−0.821991	−	0.569500i	$-0.807137\pi$
$181$	−6.04982	+	4.82457i	−0.449679	+	0.358607i	0.372312	+	0.928108i	$0.378565\pi$
$182$	−4.80940	+	1.23517i	−0.356497	+	0.0915570i
$183$		0			0
$184$	−1.37552	+	6.02654i	−0.101405	+	0.444282i
$185$	9.32364	−	11.6915i	0.685487	−	0.859574i
$186$		0			0
$187$	0.461817	−	0.368287i	0.0337714	−	0.0269318i
$188$	−6.19459	−	2.98316i	−0.451787	−	0.217569i
$189$		0			0
$190$	1.14464	−	0.551231i	0.0830412	−	0.0399905i
$191$	10.2825	−	21.3519i	0.744017	−	1.54497i	−0.0916872	−	0.995788i	$-0.529226\pi$
$191$	10.2825	−	21.3519i	0.744017	−	1.54497i	0.835704	−	0.549180i	$-0.185060\pi$
$192$		0			0
$193$	−13.3371	−	6.42282i	−0.960027	−	0.462325i	−0.112837	−	0.993614i	$-0.535994\pi$
$193$	−13.3371	−	6.42282i	−0.960027	−	0.462325i	−0.847191	+	0.531289i	$0.821708\pi$
$194$	10.5396	−	13.2162i	0.756698	−	0.948870i
$195$		0			0
$196$	−1.92361	−	6.73051i	−0.137400	−	0.480751i
$197$			8.31734i			0.592586i	0.955097	+	0.296293i	$0.0957505\pi$
$197$			8.31734i			0.592586i	−0.955097	+	0.296293i	$0.904250\pi$
$198$		0			0
$199$	8.66362	−	17.9902i	0.614148	−	1.27529i	−0.329443	−	0.944176i	$-0.606861\pi$
$199$	8.66362	−	17.9902i	0.614148	−	1.27529i	0.943590	−	0.331115i	$-0.107425\pi$
$200$	2.05389	−	0.468786i	0.145232	−	0.0331482i
$201$		0			0
$202$	4.14585	+	8.60894i	0.291701	+	0.605723i
$203$	2.11815	−	10.5901i	0.148665	−	0.743279i
$204$		0			0
$205$	5.11619	+	6.41550i	0.357330	+	0.448078i
$206$	−11.0030	+	5.29877i	−0.766616	+	0.369183i
$207$		0			0
$208$	−1.82972	−	0.417622i	−0.126868	−	0.0289569i
$209$	−0.724645	+	0.908676i	−0.0501247	+	0.0628544i
$210$		0			0
$211$	−13.8191	−	17.3286i	−0.951346	−	1.19295i	−0.981121	−	0.193393i	$-0.938051\pi$
$211$	−13.8191	−	17.3286i	−0.951346	−	1.19295i	0.0297754	−	0.999557i	$-0.490521\pi$
$212$	0.528465	+	1.09737i	0.0362951	+	0.0753676i
$213$		0			0
$214$	10.0793			0.689009
$215$	2.93598			0.200232
$216$		0			0
$217$	11.2101	−	0.302651i	0.760988	−	0.0205453i
$218$	−11.5026	+	2.62540i	−0.779055	+	0.177814i
$219$		0			0
$220$	−5.08296	+	4.05353i	−0.342693	+	0.273289i
$221$	−0.355396	+	0.283419i	−0.0239065	+	0.0190648i
$222$		0			0
$223$	−7.47552	+	1.70624i	−0.500598	+	0.114258i	−0.465361	−	0.885121i	$-0.654076\pi$
$223$	−7.47552	+	1.70624i	−0.500598	+	0.114258i	−0.0352366	+	0.999379i	$0.511218\pi$
$224$	0.518906	−	2.59437i	0.0346709	−	0.173343i
$225$		0			0
$226$	−16.1228			−1.07247
$227$	−26.7944			−1.77840			−0.889202	−	0.457515i	$-0.848740\pi$
$227$	−26.7944			−1.77840			−0.889202	+	0.457515i	$0.848740\pi$
$228$		0			0
$229$	−9.61190	−	19.9593i	−0.635172	−	1.31895i	−0.931458	−	0.363849i	$-0.881462\pi$
$229$	−9.61190	−	19.9593i	−0.635172	−	1.31895i	0.296286	−	0.955099i	$-0.404252\pi$
$230$	−10.2745	−	12.8838i	−0.677478	−	0.849531i
$231$		0			0
$232$	2.54506	−	3.19140i	0.167091	−	0.209526i
$233$	21.8409	+	4.98504i	1.43085	+	0.326581i	0.866591	−	0.499020i	$-0.166306\pi$
$233$	21.8409	+	4.98504i	1.43085	+	0.326581i	0.564255	+	0.825601i	$0.309164\pi$
$234$		0			0
$235$	16.5138	−	7.95263i	1.07724	−	0.518772i
$236$	−6.08571	−	7.63124i	−0.396146	−	0.496751i
$237$		0			0
$238$	−0.412921	−	0.490048i	−0.0267657	−	0.0317651i
$239$	−2.51899	−	5.23073i	−0.162940	−	0.338348i	0.803474	−	0.595340i	$-0.202983\pi$
$239$	−2.51899	−	5.23073i	−0.162940	−	0.338348i	−0.966413	+	0.256993i	$0.917268\pi$
$240$		0			0
$241$	16.1098	−	3.67695i	1.03772	−	0.236853i	0.330471	−	0.943816i	$-0.392792\pi$
$241$	16.1098	−	3.67695i	1.03772	−	0.236853i	0.707251	+	0.706963i	$0.249935\pi$
$242$	−2.19217	+	4.55209i	−0.140918	+	0.292619i
$243$		0			0
$244$		−	9.19434i		−	0.588607i
$245$	17.2253	+	7.17769i	1.10048	+	0.458566i
$246$		0			0
$247$	0.557658	−	0.699281i	0.0354829	−	0.0444942i
$248$	3.81880	+	1.83904i	0.242494	+	0.116779i
$249$		0			0
$250$	3.34657	−	6.94923i	0.211656	−	0.439508i
$251$	−11.6469	+	5.60883i	−0.735143	+	0.354026i	−0.763705	−	0.645566i	$-0.776622\pi$
$251$	−11.6469	+	5.60883i	−0.735143	+	0.354026i	0.0285614	+	0.999592i	$0.490907\pi$
$252$		0			0
$253$	13.5823	+	6.54091i	0.853915	+	0.411224i
$254$	−11.2006	+	8.93220i	−0.702790	+	0.560456i
$255$		0			0
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	5.57302	−	24.4170i	0.347635	−	1.52309i	−0.434897	−	0.900480i	$-0.643215\pi$
$257$	5.57302	−	24.4170i	0.347635	−	1.52309i	0.782533	−	0.622610i	$-0.213928\pi$
$258$		0			0
$259$	14.5530	+	2.91079i	0.904281	+	0.180868i
$260$	3.91165	−	3.11944i	0.242590	−	0.193459i
$261$		0			0
$262$	9.53912	+	2.17724i	0.589329	+	0.134510i
$263$		−	22.6069i		−	1.39400i	−0.717071	−	0.697000i	$-0.754518\pi$
$263$		−	22.6069i		−	1.39400i	0.717071	−	0.697000i	$-0.245482\pi$
$264$		0			0
$265$	−3.16555	−	0.722516i	−0.194458	−	0.0443838i
$266$	1.00666	+	0.759257i	0.0617221	+	0.0465530i
$267$		0			0
$268$	−0.0859328	−	0.376496i	−0.00524918	−	0.0229982i
$269$	0.883853	+	1.10832i	0.0538895	+	0.0675753i	0.808046	−	0.589120i	$-0.200525\pi$
$269$	0.883853	+	1.10832i	0.0538895	+	0.0675753i	−0.754156	+	0.656695i	$0.771954\pi$
$270$		0			0
$271$	−6.47959	+	1.47892i	−0.393607	+	0.0898382i	−0.414743	−	0.909938i	$-0.636129\pi$
$271$	−6.47959	+	1.47892i	−0.393607	+	0.0898382i	0.0211365	+	0.999777i	$0.493272\pi$
$272$	−0.0538962	−	0.236135i	−0.00326794	−	0.0143178i
$273$		0			0
$274$	4.76755	−	20.8880i	0.288018	−	1.26189i
$275$		−	5.13775i		−	0.309818i
$276$		0			0
$277$	−0.460017	+	2.01547i	−0.0276398	+	0.121098i	−0.986866	−	0.161543i	$-0.948353\pi$
$277$	−0.460017	+	2.01547i	−0.0276398	+	0.121098i	0.959226	+	0.282640i	$0.0912102\pi$
$278$	5.84488	−	2.81475i	0.350553	−	0.168817i
$279$		0			0
$280$	4.54479	+	5.39368i	0.271603	+	0.322334i
$281$	−1.54765	−	1.23421i	−0.0923252	−	0.0736269i	0.576239	−	0.817281i	$-0.304520\pi$
$281$	−1.54765	−	1.23421i	−0.0923252	−	0.0736269i	−0.668565	+	0.743654i	$0.733091\pi$
$282$		0			0
$283$	19.8683	+	15.8444i	1.18105	+	0.941853i	0.999140	−	0.0414631i	$-0.0132019\pi$
$283$	19.8683	+	15.8444i	1.18105	+	0.941853i	0.181906	+	0.983316i	$0.441773\pi$
$284$	4.13928	+	8.59531i	0.245621	+	0.510038i
$285$		0			0
$286$	−1.98589	+	4.12374i	−0.117428	+	0.243842i
$287$	−3.33419	+	7.43009i	−0.196811	+	0.438584i
$288$		0			0
$289$	15.2636	+	7.35057i	0.897860	+	0.432386i
$290$	2.42144	+	10.6090i	0.142192	+	0.622983i
$291$		0			0
$292$	−6.92698	−	5.52408i	−0.405371	−	0.323273i
$293$	−18.4148			−1.07580			−0.537902	−	0.843007i	$-0.680783\pi$
$293$	−18.4148			−1.07580			−0.537902	+	0.843007i	$0.680783\pi$
$294$		0			0
$295$	26.0205			1.51497
$296$	4.38566	+	3.49745i	0.254911	+	0.203285i
$297$		0			0
$298$	−0.441917	−	1.93617i	−0.0255996	−	0.112159i
$299$	−10.4524	−	5.03363i	−0.604480	−	0.291102i
$300$		0			0
$301$	1.33467	+	2.59022i	0.0769289	+	0.149298i
$302$	−8.26145	+	17.1551i	−0.475393	+	0.987163i
$303$		0			0
$304$	0.206776	+	0.429374i	0.0118594	+	0.0246263i
$305$	19.1632	+	15.2821i	1.09728	+	0.875053i
$306$		0			0
$307$	−25.2289	−	20.1194i	−1.43989	−	1.14827i	−0.963063	−	0.269276i	$-0.913216\pi$
$307$	−25.2289	−	20.1194i	−1.43989	−	1.14827i	−0.476826	−	0.878998i	$-0.658213\pi$
$308$	−5.88681	−	2.64166i	−0.335432	−	0.150523i
$309$		0			0
$310$	−10.1803	+	4.90258i	−0.578202	+	0.278448i
$311$	4.57909	−	20.0623i	0.259656	−	1.13763i	−0.661964	−	0.749536i	$-0.730277\pi$
$311$	4.57909	−	20.0623i	0.259656	−	1.13763i	0.921620	−	0.388093i	$-0.126866\pi$
$312$		0			0
$313$			18.8848i			1.06743i	0.845663	+	0.533717i	$0.179205\pi$
$313$			18.8848i			1.06743i	−0.845663	+	0.533717i	$0.820795\pi$
$314$	0.388003	−	1.69995i	0.0218963	−	0.0959339i
$315$		0			0
$316$	−1.67982	−	7.35976i	−0.0944971	−	0.414019i
$317$	−10.4147	+	2.37708i	−0.584946	+	0.133510i	−0.504745	−	0.863269i	$-0.668413\pi$
$317$	−10.4147	+	2.37708i	−0.584946	+	0.133510i	−0.0802010	+	0.996779i	$0.525556\pi$
$318$		0			0
$319$	−6.20680	−	7.78308i	−0.347514	−	0.435769i
$320$	0.593205	+	2.59900i	0.0331612	+	0.145289i
$321$		0			0
$322$	6.69581	−	14.9213i	0.373143	−	0.831531i
$323$	0.112535	+	0.0256853i	0.00626159	+	0.00142917i
$324$		0			0
$325$			3.95381i			0.219318i
$326$	18.1080	+	4.13303i	1.00291	+	0.228907i
$327$		0			0
$328$	−2.40656	+	1.91917i	−0.132880	+	0.105968i
$329$	14.5231	+	10.9538i	0.800682	+	0.603904i
$330$		0			0
$331$	−5.83744	+	25.5755i	−0.320855	+	1.40576i	0.515181	+	0.857081i	$0.327725\pi$
$331$	−5.83744	+	25.5755i	−0.320855	+	1.40576i	−0.836036	+	0.548675i	$0.815133\pi$
$332$	−0.608561	+	0.763112i	−0.0333991	+	0.0418812i
$333$		0			0
$334$	−0.114050	+	0.0909516i	−0.00624052	+	0.00497665i
$335$	0.927539	+	0.446679i	0.0506769	+	0.0244047i
$336$		0			0
$337$	−26.7238	+	12.8695i	−1.45574	+	0.701046i	−0.983581	−	0.180470i	$-0.942238\pi$
$337$	−26.7238	+	12.8695i	−1.45574	+	0.701046i	−0.472156	+	0.881515i	$0.656524\pi$
$338$	−4.11222	+	8.53912i	−0.223676	+	0.464467i
$339$		0			0
$340$	0.581743	+	0.280153i	0.0315495	+	0.0151934i
$341$	6.44489	−	8.08164i	0.349011	−	0.437645i
$342$		0			0
$343$	1.49804	+	18.4596i	0.0808864	+	0.996723i
$344$			1.10133i			0.0593800i
$345$		0			0
$346$	−3.76851	+	7.82539i	−0.202596	+	0.420695i
$347$	−21.8087	+	4.97769i	−1.17075	+	0.267216i	−0.763321	−	0.646020i	$-0.776432\pi$
$347$	−21.8087	+	4.97769i	−1.17075	+	0.267216i	−0.407431	+	0.913236i	$0.633575\pi$
$348$		0			0
$349$	11.9682	+	24.8523i	0.640645	+	1.33031i	0.928033	+	0.372499i	$0.121499\pi$
$349$	11.9682	+	24.8523i	0.640645	+	1.33031i	−0.287387	+	0.957814i	$0.592787\pi$
$350$	−5.57179	+	0.150428i	−0.297825	+	0.00804072i
$351$		0			0
$352$	−1.52054	−	1.90670i	−0.0810452	−	0.101628i
$353$	−30.9438	+	14.9017i	−1.64697	+	0.793139i	−0.647453	+	0.762106i	$0.724166\pi$
$353$	−30.9438	+	14.9017i	−1.64697	+	0.793139i	−0.999518	+	0.0310336i	$0.990120\pi$
$354$		0			0
$355$	−24.7947	−	5.65922i	−1.31596	−	0.300360i
$356$	−4.28981	+	5.37926i	−0.227360	+	0.285100i
$357$		0			0
$358$	−9.52518	−	11.9442i	−0.503421	−	0.631271i
$359$	−2.08224	−	4.32381i	−0.109896	−	0.228202i	0.838767	−	0.544491i	$-0.183277\pi$
$359$	−2.08224	−	4.32381i	−0.109896	−	0.228202i	−0.948663	+	0.316289i	$0.897563\pi$
$360$		0			0
$361$	18.7729			0.988046
$362$	7.73801			0.406701
$363$		0			0
$364$	4.53026	+	2.03292i	0.237450	+	0.106554i
$365$	23.0270	−	5.25576i	1.20529	−	0.275099i
$366$		0			0
$367$	−10.0336	+	8.00155i	−0.523751	+	0.417677i	−0.849350	−	0.527831i	$-0.823006\pi$
$367$	−10.0336	+	8.00155i	−0.523751	+	0.417677i	0.325599	+	0.945508i	$0.394434\pi$
$368$	4.83291	−	3.85412i	0.251933	−	0.200910i
$369$		0			0
$370$	−14.5790	+	3.32757i	−0.757927	+	0.172992i
$371$	−0.801600	−	3.12120i	−0.0416170	−	0.162045i
$372$		0			0
$373$	−4.70914			−0.243830			−0.121915	−	0.992541i	$-0.538904\pi$
$373$	−4.70914			−0.243830			−0.121915	+	0.992541i	$0.538904\pi$
$374$	−0.590686			−0.0305437
$375$		0			0
$376$	2.98316	+	6.19459i	0.153845	+	0.319462i
$377$	4.77651	+	5.98955i	0.246003	+	0.308478i
$378$		0			0
$379$	0.899680	−	1.12816i	0.0462135	−	0.0579499i	−0.758188	−	0.652036i	$-0.773915\pi$
$379$	0.899680	−	1.12816i	0.0462135	−	0.0579499i	0.804401	+	0.594087i	$0.202486\pi$
$380$	−1.23861	−	0.282704i	−0.0635391	−	0.0145024i
$381$		0			0
$382$	−21.3519	+	10.2825i	−1.09246	+	0.526100i
$383$	−14.5939	−	18.3002i	−0.745713	−	0.935095i	0.253769	−	0.967265i	$-0.418330\pi$
$383$	−14.5939	−	18.3002i	−0.745713	−	0.935095i	−0.999482	+	0.0321698i	$0.989758\pi$
$384$		0			0
$385$	15.2905	−	7.87875i	0.779274	−	0.401538i
$386$	6.42282	+	13.3371i	0.326913	+	0.678842i
$387$		0			0
$388$	−16.4804	+	3.76154i	−0.836664	+	0.190963i
$389$	−3.02451	+	6.28046i	−0.153349	+	0.318432i	−0.963464	−	0.267839i	$-0.913690\pi$
$389$	−3.02451	+	6.28046i	−0.153349	+	0.318432i	0.810115	+	0.586271i	$0.199405\pi$
$390$		0			0
$391$		−	1.49721i		−	0.0757172i
$392$	−2.69247	+	6.46147i	−0.135990	+	0.326354i
$393$		0			0
$394$	5.18578	−	6.50276i	0.261256	−	0.327604i
$395$	18.1315	+	8.73169i	0.912297	+	0.439339i
$396$		0			0
$397$	0.985031	−	2.04544i	0.0494373	−	0.102658i	−0.874787	−	0.484508i	$-0.838999\pi$
$397$	0.985031	−	2.04544i	0.0494373	−	0.102658i	0.924224	+	0.381850i	$0.124713\pi$
$398$	−17.9902	+	8.66362i	−0.901767	+	0.434268i
$399$		0			0
$400$	−1.89808	−	0.914065i	−0.0949038	−	0.0457033i
$401$	2.42423	−	1.93326i	0.121060	−	0.0965422i	−0.561088	−	0.827756i	$-0.689617\pi$
$401$	2.42423	−	1.93326i	0.121060	−	0.0965422i	0.682148	+	0.731214i	$0.261046\pi$
$402$		0			0
$403$	−4.95974	+	6.21931i	−0.247062	+	0.309806i
$404$	2.12623	−	9.31564i	0.105784	−	0.463470i
$405$		0			0
$406$	−8.25886	+	6.95902i	−0.409880	+	0.345371i
$407$	10.6956	−	8.52944i	0.530160	−	0.422789i
$408$		0			0
$409$	26.7705	+	6.11018i	1.32371	+	0.302129i	0.825243	−	0.564777i	$-0.191038\pi$
$409$	26.7705	+	6.11018i	1.32371	+	0.302129i	0.498471	+	0.866906i	$0.333895\pi$
$410$		−	8.20573i		−	0.405252i
$411$		0			0
$412$	11.9062	+	2.71752i	0.586578	+	0.133883i
$413$	11.8287	+	22.9561i	0.582050	+	1.12960i
$414$		0			0
$415$	−0.579002	−	2.53677i	−0.0284221	−	0.124525i
$416$	1.17015	+	1.46732i	0.0573714	+	0.0719414i
$417$		0			0
$418$	1.13310	−	0.258623i	0.0554217	−	0.0126496i
$419$	1.03441	+	4.53206i	0.0505344	+	0.221406i	0.993890	−	0.110379i	$-0.0352064\pi$
$419$	1.03441	+	4.53206i	0.0505344	+	0.221406i	−0.943355	+	0.331785i	$0.892349\pi$
$420$		0			0
$421$	−6.33069	+	27.7366i	−0.308539	+	1.35180i	0.548329	+	0.836263i	$0.315264\pi$
$421$	−6.33069	+	27.7366i	−0.308539	+	1.35180i	−0.856868	+	0.515536i	$0.827593\pi$
$422$			22.1641i			1.07893i
$423$		0			0
$424$	0.271028	−	1.18745i	0.0131623	−	0.0576676i
$425$	−0.459728	+	0.221393i	−0.0223001	+	0.0107392i
$426$		0			0
$427$	−4.77100	+	23.8535i	−0.230885	+	1.15435i
$428$	−7.88034	−	6.28436i	−0.380911	−	0.303766i
$429$		0			0
$430$	−2.29544	−	1.83055i	−0.110696	−	0.0882772i
$431$	−3.33228	−	6.91956i	−0.160510	−	0.333303i	0.805167	−	0.593048i	$-0.202076\pi$
$431$	−3.33228	−	6.91956i	−0.160510	−	0.333303i	−0.965677	+	0.259745i	$0.916361\pi$
$432$		0			0
$433$	−16.5347	+	34.3347i	−0.794608	+	1.65002i	−0.0352220	+	0.999380i	$0.511214\pi$
$433$	−16.5347	+	34.3347i	−0.794608	+	1.65002i	−0.759386	+	0.650641i	$0.774500\pi$
$434$	−8.95307	−	6.75273i	−0.429761	−	0.324141i
$435$		0			0
$436$	10.6300	+	5.11914i	0.509085	+	0.245163i
$437$	0.655530	+	2.87207i	0.0313583	+	0.137390i
$438$		0			0
$439$	4.01377	+	3.20087i	0.191567	+	0.152769i	0.714576	−	0.699557i	$-0.246619\pi$
$439$	4.01377	+	3.20087i	0.191567	+	0.152769i	−0.523010	+	0.852327i	$0.675191\pi$
$440$	6.50135			0.309940
$441$		0			0
$442$	0.454569			0.0216216
$443$	−26.0816	−	20.7994i	−1.23918	−	0.988210i	−0.999851	−	0.0172706i	$-0.994502\pi$
$443$	−26.0816	−	20.7994i	−1.23918	−	0.988210i	−0.239325	−	0.970939i	$-0.576926\pi$
$444$		0			0
$445$	−4.08145	−	17.8820i	−0.193479	−	0.847688i
$446$	6.90842	+	3.32692i	0.327123	+	0.157534i
$447$		0			0
$448$	−2.02326	+	1.70482i	−0.0955900	+	0.0805454i
$449$	1.43990	−	2.98997i	0.0679529	−	0.141106i	−0.864226	−	0.503104i	$-0.832191\pi$
$449$	1.43990	−	2.98997i	0.0679529	−	0.141106i	0.932179	+	0.361999i	$0.117905\pi$
$450$		0			0
$451$	3.25706	+	6.76336i	0.153369	+	0.318474i
$452$	12.6053	+	10.0524i	0.592904	+	0.472825i
$453$		0			0
$454$	20.9487	+	16.7060i	0.983170	+	0.784052i
$455$	−11.7669	+	6.06318i	−0.551643	+	0.284246i
$456$		0			0
$457$	−5.66992	+	2.73049i	−0.265228	+	0.127727i	−0.561772	−	0.827292i	$-0.689880\pi$
$457$	−5.66992	+	2.73049i	−0.265228	+	0.127727i	0.296544	+	0.955019i	$0.404166\pi$
$458$	−4.92954	+	21.5977i	−0.230342	+	1.00920i
$459$		0			0
$460$			16.4790i			0.768335i
$461$	−0.131740	+	0.577192i	−0.00613576	+	0.0268825i	−0.977903	−	0.209059i	$-0.932960\pi$
$461$	−0.131740	+	0.577192i	−0.00613576	+	0.0268825i	0.971767	+	0.235941i	$0.0758172\pi$
$462$		0			0
$463$	−5.73119	−	25.1100i	−0.266351	−	1.16696i	−0.914223	−	0.405211i	$-0.867198\pi$
$463$	−5.73119	−	25.1100i	−0.266351	−	1.16696i	0.647872	−	0.761749i	$-0.275659\pi$
$464$	−3.97962	+	0.908321i	−0.184749	+	0.0421678i
$465$		0			0
$466$	−13.9678	−	17.5150i	−0.647045	−	0.811369i
$467$	5.67546	+	24.8658i	0.262629	+	1.15065i	0.918388	+	0.395682i	$0.129492\pi$
$467$	5.67546	+	24.8658i	0.262629	+	1.15065i	−0.655759	+	0.754971i	$0.727651\pi$
$468$		0			0
$469$	0.0275749	+	1.02136i	0.00127329	+	0.0471621i
$470$	−17.8694	−	4.07857i	−0.824253	−	0.188130i
$471$		0			0
$472$			9.76072i			0.449273i
$473$	2.61855	+	0.597667i	0.120401	+	0.0274808i
$474$		0			0
$475$	0.784952	−	0.625979i	0.0360161	−	0.0287219i
$476$	0.0172947	+	0.640587i	0.000792701	+	0.0293613i
$477$		0			0
$478$	−1.29188	+	5.66011i	−0.0590894	+	0.258887i
$479$	0.727944	−	0.912813i	0.0332606	−	0.0417075i	−0.764923	−	0.644122i	$-0.777223\pi$
$479$	0.727944	−	0.912813i	0.0332606	−	0.0417075i	0.798184	+	0.602414i	$0.205794\pi$
$480$		0			0
$481$	−8.23090	+	6.56392i	−0.375297	+	0.299289i
$482$	−14.8877	−	7.16952i	−0.678115	−	0.326563i
$483$		0			0
$484$	4.55209	−	2.19217i	0.206913	−	0.0996441i
$485$	19.5525	−	40.6011i	0.887832	−	1.84360i
$486$		0			0
$487$	13.2145	+	6.36377i	0.598806	+	0.288370i	0.708629	−	0.705581i	$-0.249314\pi$
$487$	13.2145	+	6.36377i	0.598806	+	0.288370i	−0.109823	+	0.993951i	$0.535028\pi$
$488$	−5.73258	+	7.18842i	−0.259502	+	0.325405i
$489$		0			0
$490$	−8.99203	−	16.3515i	−0.406219	−	0.738686i
$491$			16.8058i			0.758435i	0.925308	+	0.379217i	$0.123807\pi$
$491$			16.8058i			0.758435i	−0.925308	+	0.379217i	$0.876193\pi$
$492$		0			0
$493$	−0.428972	+	0.890770i	−0.0193199	+	0.0401183i
$494$	−0.871989	+	0.199026i	−0.0392327	+	0.00895460i
$495$		0			0
$496$	−1.83904	−	3.81880i	−0.0825752	−	0.171469i
$497$	−6.27865	−	24.4473i	−0.281636	−	1.09661i
$498$		0			0
$499$	4.97925	+	6.24378i	0.222902	+	0.279510i	0.880690	−	0.473693i	$-0.157079\pi$
$499$	4.97925	+	6.24378i	0.222902	+	0.279510i	−0.657788	+	0.753203i	$0.728508\pi$
$500$	−6.94923	+	3.34657i	−0.310779	+	0.149663i
$501$		0			0
$502$	12.6029	+	2.87654i	0.562496	+	0.128386i
$503$	7.56611	−	9.48761i	0.337356	−	0.423031i	−0.583998	−	0.811755i	$-0.698512\pi$
$503$	7.56611	−	9.48761i	0.337356	−	0.423031i	0.921354	+	0.388724i	$0.127084\pi$
$504$		0			0
$505$	15.8819	+	19.9153i	0.706737	+	0.886220i
$506$	−6.54091	−	13.5823i	−0.290779	−	0.603809i
$507$		0			0
$508$	14.3261			0.635619
$509$	21.7050			0.962059			0.481030	−	0.876704i	$-0.340263\pi$
$509$	21.7050			0.962059			0.481030	+	0.876704i	$0.340263\pi$
$510$		0			0
$511$	15.1046	+	17.9260i	0.668190	+	0.792997i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$		0			0
$514$	−19.5809	+	15.6152i	−0.863677	+	0.688759i
$515$	−25.4536	+	20.2986i	−1.12162	+	0.894462i
$516$		0			0
$517$	16.3473	−	3.73116i	0.718952	−	0.164096i
$518$	−9.56316	−	11.3494i	−0.420181	−	0.498664i
$519$		0			0
$520$	−5.00319			−0.219404
$521$	−4.25159			−0.186266			−0.0931329	−	0.995654i	$-0.529688\pi$
$521$	−4.25159			−0.186266			−0.0931329	+	0.995654i	$0.529688\pi$
$522$		0			0
$523$	−12.5213	−	26.0008i	−0.547519	−	1.13693i	−0.972752	−	0.231850i	$-0.925522\pi$
$523$	−12.5213	−	26.0008i	−0.547519	−	1.13693i	0.425233	−	0.905084i	$-0.360192\pi$
$524$	−6.10050	−	7.64978i	−0.266501	−	0.334182i
$525$		0			0
$526$	−14.0952	+	17.6748i	−0.614578	+	0.770656i
$527$	−1.00087	−	0.228442i	−0.0435985	−	0.00995107i
$528$		0			0
$529$	13.7049	−	6.59991i	0.595864	−	0.286953i
$530$	2.02445	+	2.53857i	0.0879363	+	0.110269i
$531$		0			0
$532$	−0.313647	−	1.22125i	−0.0135983	−	0.0529480i
$533$	−2.50651	−	5.20482i	−0.108569	−	0.225446i
$534$		0			0
$535$	26.1962	−	5.97912i	1.13256	−	0.258500i
$536$	−0.167557	+	0.347935i	−0.00723735	+	0.0150285i
$537$		0			0
$538$		−	1.41759i		−	0.0611166i
$539$	13.9018	+	9.90814i	0.598792	+	0.426774i
$540$		0			0
$541$	10.8854	−	13.6498i	0.467999	−	0.586852i	−0.490681	−	0.871339i	$-0.663252\pi$
$541$	10.8854	−	13.6498i	0.467999	−	0.586852i	0.958680	+	0.284487i	$0.0918234\pi$
$542$	5.98804	+	2.88369i	0.257208	+	0.123865i
$543$		0			0
$544$	−0.105090	+	0.218221i	−0.00450569	+	0.00935616i
$545$	−28.3379	+	13.6468i	−1.21386	+	0.584566i
$546$		0			0
$547$	−3.87644	−	1.86679i	−0.165744	−	0.0798183i	0.349172	−	0.937059i	$-0.386463\pi$
$547$	−3.87644	−	1.86679i	−0.165744	−	0.0798183i	−0.514917	+	0.857240i	$0.672177\pi$
$548$	−16.7509	+	13.3584i	−0.715562	+	0.570642i
$549$		0			0
$550$	−3.20334	+	4.01686i	−0.136591	+	0.171279i
$551$	0.432878	−	1.89656i	0.0184412	−	0.0807963i
$552$		0			0
$553$	0.539034	+	19.9656i	0.0229221	+	0.849022i
$554$	1.61628	−	1.28894i	0.0686691	−	0.0547618i
$555$		0			0
$556$	−6.32468	−	1.44357i	−0.268226	−	0.0612209i
$557$		−	26.3988i		−	1.11855i	−0.828981	−	0.559277i	$-0.811079\pi$
$557$		−	26.3988i		−	1.11855i	0.828981	−	0.559277i	$-0.188921\pi$
$558$		0			0
$559$	−2.01513	−	0.459941i	−0.0852311	−	0.0194534i
$560$	−0.190353	−	7.05058i	−0.00804388	−	0.297941i
$561$		0			0
$562$	0.440485	+	1.92989i	0.0185807	+	0.0814076i
$563$	13.9669	+	17.5140i	0.588636	+	0.738127i	0.983559	−	0.180588i	$-0.0578000\pi$
$563$	13.9669	+	17.5140i	0.588636	+	0.738127i	−0.394922	+	0.918714i	$0.629229\pi$
$564$		0			0
$565$	−41.9032	+	9.56412i	−1.76288	+	0.402366i
$566$	−5.65481	−	24.7753i	−0.237689	−	1.04138i
$567$		0			0
$568$	2.12287	−	9.30088i	0.0890735	−	0.390256i
$569$		−	24.1699i		−	1.01325i	−0.862166	−	0.506627i	$-0.830892\pi$
$569$		−	24.1699i		−	1.01325i	0.862166	−	0.506627i	$-0.169108\pi$
$570$		0			0
$571$	6.07639	−	26.6224i	0.254289	−	1.11411i	−0.672964	−	0.739675i	$-0.734979\pi$
$571$	6.07639	−	26.6224i	0.254289	−	1.11411i	0.927253	−	0.374437i	$-0.122164\pi$
$572$	4.12374	−	1.98589i	0.172422	−	0.0830343i
$573$		0			0
$574$	7.23936	−	3.73024i	0.302165	−	0.155697i
$575$	−10.1815	−	8.11949i	−0.424599	−	0.338606i
$576$		0			0
$577$	−29.5417	−	23.5587i	−1.22984	−	0.980763i	−0.999972	−	0.00754048i	$-0.997600\pi$
$577$	−29.5417	−	23.5587i	−1.22984	−	0.980763i	−0.229866	−	0.973222i	$-0.573829\pi$
$578$	−7.35057	−	15.2636i	−0.305743	−	0.634883i
$579$		0			0
$580$	4.72146	−	9.80421i	0.196048	−	0.407098i
$581$	1.97481	−	1.66400i	0.0819291	−	0.0690345i
$582$		0			0
$583$	−2.67622	−	1.28880i	−0.110838	−	0.0533766i
$584$	1.97152	+	8.63780i	0.0815822	+	0.357435i
$585$		0			0
$586$	14.3973	+	11.4814i	0.594746	+	0.474294i
$587$	11.1853			0.461667			0.230833	−	0.972993i	$-0.425855\pi$
$587$	11.1853			0.461667			0.230833	+	0.972993i	$0.425855\pi$
$588$		0			0
$589$	2.01996			0.0832311
$590$	−20.3437	−	16.2235i	−0.837535	−	0.667912i
$591$		0			0
$592$	−1.24822	−	5.46883i	−0.0513017	−	0.224767i
$593$	−3.02983	−	1.45909i	−0.124420	−	0.0599177i	0.370638	−	0.928777i	$-0.379139\pi$
$593$	−3.02983	−	1.45909i	−0.124420	−	0.0599177i	−0.495058	+	0.868860i	$0.664853\pi$
$594$		0			0
$595$	−1.36388	−	1.02869i	−0.0559137	−	0.0421721i
$596$	−0.861675	+	1.78929i	−0.0352956	+	0.0732920i
$597$		0			0
$598$	5.03363	+	10.4524i	0.205841	+	0.427432i
$599$	−30.2192	−	24.0990i	−1.23472	−	0.984660i	−0.999920	−	0.0126174i	$-0.995984\pi$
$599$	−30.2192	−	24.0990i	−1.23472	−	0.984660i	−0.234804	−	0.972043i	$-0.575445\pi$
$600$		0			0
$601$	−13.4961	−	10.7628i	−0.550518	−	0.439023i	0.308311	−	0.951285i	$-0.400236\pi$
$601$	−13.4961	−	10.7628i	−0.550518	−	0.439023i	−0.858829	+	0.512262i	$0.828808\pi$
$602$	0.571489	−	2.85726i	0.0232922	−	0.116453i
$603$		0			0
$604$	17.1551	−	8.26145i	0.698030	−	0.336153i
$605$	−2.99713	+	13.1313i	−0.121851	+	0.533863i
$606$		0			0
$607$			3.86032i			0.156686i	0.996926	+	0.0783428i	$0.0249629\pi$
$607$			3.86032i			0.156686i	−0.996926	+	0.0783428i	$0.975037\pi$
$608$	0.106047	−	0.464621i	0.00430076	−	0.0188429i
$609$		0			0
$610$	−5.45413	−	23.8961i	−0.220831	−	0.967525i
$611$	−12.5802	+	2.87135i	−0.508941	+	0.116162i
$612$		0			0
$613$	23.3197	+	29.2419i	0.941873	+	1.18107i	0.983312	+	0.181930i	$0.0582344\pi$
$613$	23.3197	+	29.2419i	0.941873	+	1.18107i	−0.0414389	+	0.999141i	$0.513194\pi$
$614$	7.18052	+	31.4599i	0.289782	+	1.26962i
$615$		0			0
$616$	2.95545	+	5.73570i	0.119078	+	0.231098i
$617$	24.9959	+	5.70515i	1.00630	+	0.229681i	0.693745	−	0.720220i	$-0.255959\pi$
$617$	24.9959	+	5.70515i	1.00630	+	0.229681i	0.312551	+	0.949901i	$0.398816\pi$
$618$		0			0
$619$		−	14.5148i		−	0.583398i	−0.956510	−	0.291699i	$-0.905779\pi$
$619$		−	14.5148i		−	0.583398i	0.956510	−	0.291699i	$-0.0942206\pi$
$620$	11.0160	+	2.51433i	0.442413	+	0.100978i
$621$		0			0
$622$	−16.0887	+	12.8303i	−0.645099	+	0.514449i
$623$	13.9207	−	11.7298i	0.557720	−	0.469943i
$624$		0			0
$625$	6.91936	−	30.3157i	0.276774	−	1.21263i
$626$	11.7745	−	14.7648i	0.470604	−	0.590119i
$627$		0			0
$628$	−1.36326	+	1.08716i	−0.0543998	+	0.0433824i
$629$	−1.22411	−	0.589498i	−0.0488083	−	0.0235048i
$630$		0			0
$631$	−0.569682	+	0.274345i	−0.0226787	+	0.0109215i	−0.445189	−	0.895437i	$-0.646863\pi$
$631$	−0.569682	+	0.274345i	−0.0226787	+	0.0109215i	0.422510	+	0.906358i	$0.361149\pi$
$632$	−3.27540	+	6.80144i	−0.130288	+	0.270547i
$633$		0			0
$634$	9.62460	+	4.63496i	0.382242	+	0.184078i
$635$	−23.8118	+	29.8591i	−0.944943	+	1.18492i
$636$		0			0
$637$	−10.6983	−	7.62492i	−0.423881	−	0.302110i
$638$			9.95493i			0.394119i
$639$		0			0
$640$	1.15666	−	2.40184i	0.0457212	−	0.0949410i
$641$	−37.6533	+	8.59412i	−1.48722	+	0.339447i	−0.887515	−	0.460778i	$-0.847570\pi$
$641$	−37.6533	+	8.59412i	−1.48722	+	0.339447i	−0.599700	+	0.800225i	$0.704713\pi$
$642$		0			0
$643$	14.9936	+	31.1346i	0.591290	+	1.22783i	0.955081	+	0.296346i	$0.0957682\pi$
$643$	14.9936	+	31.1346i	0.591290	+	1.22783i	−0.363790	+	0.931481i	$0.618518\pi$
$644$	−14.5383	+	7.49116i	−0.572888	+	0.295193i
$645$		0			0
$646$	−0.0719686	−	0.0902457i	−0.00283157	−	0.00355067i
$647$	−1.04038	+	0.501020i	−0.0409015	+	0.0196971i	−0.454223	−	0.890888i	$-0.650083\pi$
$647$	−1.04038	+	0.501020i	−0.0409015	+	0.0196971i	0.413321	+	0.910585i	$0.364369\pi$
$648$		0			0
$649$	23.2073	+	5.29690i	0.910964	+	0.207922i
$650$	2.46516	−	3.09122i	0.0966917	−	0.121247i
$651$		0			0
$652$	−11.5805	−	14.5215i	−0.453527	−	0.568705i
$653$	−9.17950	−	19.0614i	−0.359221	−	0.745931i	0.640537	−	0.767928i	$-0.278712\pi$
$653$	−9.17950	−	19.0614i	−0.359221	−	0.745931i	−0.999758	+	0.0219966i	$0.992998\pi$
$654$		0			0
$655$	26.0837			1.01918
$656$	3.07810			0.120180
$657$		0			0
$658$	−4.52499	−	17.6190i	−0.176403	−	0.686861i
$659$	29.3898	−	6.70804i	1.14487	−	0.261308i	0.392307	−	0.919834i	$-0.371677\pi$
$659$	29.3898	−	6.70804i	1.14487	−	0.261308i	0.752558	+	0.658526i	$0.228820\pi$
$660$		0			0
$661$	−34.8777	+	27.8141i	−1.35659	+	1.08184i	−0.368222	+	0.929738i	$0.620033\pi$
$661$	−34.8777	+	27.8141i	−1.35659	+	1.08184i	−0.988365	+	0.152103i	$0.951395\pi$
$662$	20.5100	−	16.3561i	0.797142	−	0.635699i
$663$		0			0
$664$	0.951585	−	0.217193i	0.0369286	−	0.00842872i
$665$	3.06670	+	1.37616i	0.118921	+	0.0533651i
$666$		0			0
$667$	−25.2327			−0.977015
$668$	0.145875			0.00564408
$669$		0			0
$670$	−0.446679	−	0.927539i	−0.0172567	−	0.0358340i
$671$	13.9804	+	17.5309i	0.539707	+	0.676771i
$672$		0			0
$673$	−22.3438	+	28.0182i	−0.861290	+	1.08002i	0.134729	+	0.990882i	$0.456984\pi$
$673$	−22.3438	+	28.0182i	−0.861290	+	1.08002i	−0.996019	+	0.0891408i	$0.971588\pi$
$674$	28.9175	+	6.60023i	1.11386	+	0.254231i
$675$		0			0
$676$	8.53912	−	4.11222i	0.328428	−	0.158162i
$677$	19.7367	+	24.7491i	0.758544	+	0.951183i	0.999814	−	0.0192744i	$-0.00613561\pi$
$677$	19.7367	+	24.7491i	0.758544	+	0.951183i	−0.241271	+	0.970458i	$0.577564\pi$
$678$		0			0
$679$	44.7080	−	1.20703i	1.71573	−	0.0463217i
$680$	−0.280153	−	0.581743i	−0.0107434	−	0.0223088i
$681$		0			0
$682$	−10.0776	+	2.30016i	−0.385893	+	0.0880775i
$683$	9.77998	−	20.3083i	0.374221	−	0.777077i	−0.625775	−	0.780004i	$-0.715217\pi$
$683$	9.77998	−	20.3083i	0.374221	−	0.777077i	0.999996	+	0.00292632i	$0.000931479\pi$
$684$		0			0
$685$		−	57.1161i		−	2.18229i
$686$	10.3381	−	15.3663i	0.394712	−	0.586688i
$687$		0			0
$688$	0.686671	−	0.861058i	0.0261791	−	0.0328275i
$689$	2.05951	+	0.991810i	0.0784613	+	0.0377850i
$690$		0			0
$691$	−5.16618	+	10.7277i	−0.196531	+	0.408101i	−0.975824	−	0.218559i	$-0.929864\pi$
$691$	−5.16618	+	10.7277i	−0.196531	+	0.408101i	0.779293	+	0.626660i	$0.215579\pi$
$692$	7.82539	−	3.76851i	0.297477	−	0.143257i
$693$		0			0
$694$	20.1543	+	9.70578i	0.765045	+	0.368426i
$695$	13.5211	−	10.7828i	0.512886	−	0.409013i
$696$		0			0
$697$	0.464836	−	0.582886i	0.0176069	−	0.0220784i
$698$	6.13801	−	26.8924i	0.232327	−	1.01789i
$699$		0			0
$700$	4.44999	+	3.35634i	0.168194	+	0.126858i
$701$	−11.2689	+	8.98666i	−0.425621	+	0.339421i	−0.812759	−	0.582601i	$-0.802035\pi$
$701$	−11.2689	+	8.98666i	−0.425621	+	0.339421i	0.387138	+	0.922022i	$0.373464\pi$
$702$		0			0
$703$	2.60628	+	0.594866i	0.0982976	+	0.0224358i
$704$			2.43876i			0.0919143i
$705$		0			0
$706$	33.4839	+	7.64248i	1.26018	+	0.287629i
$707$	−10.3502	+	23.0649i	−0.389258	+	0.867443i
$708$		0			0
$709$	4.03120	+	17.6619i	0.151395	+	0.663305i	0.992481	+	0.122403i	$0.0390600\pi$
$709$	4.03120	+	17.6619i	0.151395	+	0.663305i	−0.841085	+	0.540902i	$0.818083\pi$
$710$	15.8568	+	19.8838i	0.595095	+	0.746225i
$711$		0			0
$712$	6.70782	−	1.53102i	0.251386	−	0.0573773i
$713$	−5.83020	−	25.5438i	−0.218343	−	0.956622i
$714$		0			0
$715$	−2.71511	+	11.8957i	−0.101539	+	0.444873i
$716$			15.2772i			0.570936i
$717$		0			0
$718$	−1.06789	+	4.67874i	−0.0398534	+	0.174609i
$719$	−19.6073	+	9.44235i	−0.731227	+	0.352140i	−0.762167	−	0.647381i	$-0.775864\pi$
$719$	−19.6073	+	9.44235i	−0.731227	+	0.352140i	0.0309396	+	0.999521i	$0.490150\pi$
$720$		0			0
$721$	−29.4790	−	13.2285i	−1.09786	−	0.492654i
$722$	−14.6772	−	11.7047i	−0.546230	−	0.435604i
$723$		0			0
$724$	−6.04982	−	4.82457i	−0.224840	−	0.179304i
$725$	3.73118	+	7.74787i	0.138572	+	0.287749i
$726$		0			0
$727$	6.91891	−	14.3673i	0.256608	−	0.532852i	−0.732371	−	0.680905i	$-0.761586\pi$
$727$	6.91891	−	14.3673i	0.256608	−	0.532852i	0.988979	+	0.148053i	$0.0473007\pi$
$728$	−2.27440	−	4.41397i	−0.0842947	−	0.163593i
$729$		0			0
$730$	−21.2802	−	10.2480i	−0.787614	−	0.379295i
$731$	−0.0593577	−	0.260063i	−0.00219543	−	0.00961879i
$732$		0			0
$733$	−3.13845	−	2.50283i	−0.115921	−	0.0924440i	0.563814	−	0.825902i	$-0.309334\pi$
$733$	−3.13845	−	2.50283i	−0.115921	−	0.0924440i	−0.679735	+	0.733458i	$0.737905\pi$
$734$	12.8335			0.473693
$735$		0			0
$736$	−6.18152			−0.227854
$737$	0.736327	+	0.587201i	0.0271230	+	0.0216298i
$738$		0			0
$739$	−7.09889	−	31.1023i	−0.261137	−	1.14412i	−0.920020	−	0.391871i	$-0.871828\pi$
$739$	−7.09889	−	31.1023i	−0.261137	−	1.14412i	0.658883	−	0.752245i	$-0.271029\pi$
$740$	13.4730	+	6.48828i	0.495279	+	0.238514i
$741$		0			0
$742$	−1.31932	+	2.94004i	−0.0484338	+	0.107932i
$743$	−14.3144	+	29.7242i	−0.525146	+	1.09048i	0.454686	+	0.890652i	$0.349752\pi$
$743$	−14.3144	+	29.7242i	−0.525146	+	1.09048i	−0.979832	+	0.199825i	$0.935963\pi$
$744$		0			0
$745$	−2.29709	−	4.76995i	−0.0841588	−	0.174758i
$746$	3.68176	+	2.93610i	0.134799	+	0.107498i
$747$		0			0
$748$	0.461817	+	0.368287i	0.0168857	+	0.0134659i
$749$	17.1835	+	20.3931i	0.627871	+	0.745148i
$750$		0			0
$751$	25.4017	−	12.2328i	0.926921	−	0.446381i	0.0913838	−	0.995816i	$-0.470871\pi$
$751$	25.4017	−	12.2328i	0.926921	−	0.446381i	0.835537	+	0.549434i	$0.185157\pi$
$752$	1.52994	−	6.70310i	0.0557911	−	0.244437i
$753$		0			0
$754$		−	7.66092i		−	0.278994i
$755$	−11.2950	+	49.4868i	−0.411069	+	1.80101i
$756$		0			0
$757$	−3.07509	−	13.4728i	−0.111766	−	0.489679i	−0.999566	−	0.0294500i	$-0.990624\pi$
$757$	−3.07509	−	13.4728i	−0.111766	−	0.489679i	0.887800	−	0.460229i	$-0.152233\pi$
$758$	−1.40680	+	0.321092i	−0.0510972	+	0.0116626i
$759$		0			0
$760$	0.792118	+	0.993284i	0.0287331	+	0.0360302i
$761$	−0.995001	−	4.35938i	−0.0360687	−	0.158027i	0.953686	−	0.300803i	$-0.0972546\pi$
$761$	−0.995001	−	4.35938i	−0.0360687	−	0.158027i	−0.989755	+	0.142775i	$0.954397\pi$
$762$		0			0
$763$	−24.9218	−	18.7969i	−0.902229	−	0.680494i
$764$	23.1046	+	5.27348i	0.835896	+	0.190788i
$765$		0			0
$766$			23.4068i			0.845722i
$767$	−17.8594	−	4.07629i	−0.644865	−	0.147186i
$768$		0			0
$769$	25.7211	−	20.5119i	0.927527	−	0.739678i	−0.0381916	−	0.999270i	$-0.512160\pi$
$769$	25.7211	−	20.5119i	0.927527	−	0.739678i	0.965718	+	0.259593i	$0.0835883\pi$
$770$	−16.8669	−	3.37359i	−0.607840	−	0.121576i
$771$		0			0
$772$	3.29400	−	14.4319i	0.118554	−	0.519417i
$773$	26.3896	−	33.0915i	0.949167	−	1.19022i	−0.0324728	−	0.999473i	$-0.510338\pi$
$773$	26.3896	−	33.0915i	0.949167	−	1.19022i	0.981640	−	0.190745i	$-0.0610904\pi$
$774$		0			0
$775$	−6.98126	+	5.56737i	−0.250774	+	0.199986i
$776$	15.2301	+	7.33445i	0.546730	+	0.263291i
$777$		0			0
$778$	6.28046	−	3.02451i	0.225165	−	0.108434i
$779$	−0.636477	+	1.32166i	−0.0228042	+	0.0473533i
$780$		0			0
$781$	−20.9619	−	10.0947i	−0.750076	−	0.361218i
$782$	−0.933496	+	1.17057i	−0.0333817	+	0.0418594i
$783$		0			0
$784$	6.13372	−	3.37306i	0.219061	−	0.120466i
$785$		−	4.64835i		−	0.165907i
$786$		0			0
$787$	14.3418	−	29.7811i	0.511230	−	1.06158i	−0.472401	−	0.881384i	$-0.656612\pi$
$787$	14.3418	−	29.7811i	0.511230	−	1.06158i	0.983631	−	0.180196i	$-0.0576733\pi$
$788$	−8.10881	+	1.85078i	−0.288864	+	0.0659314i
$789$		0			0
$790$	−8.73169	−	18.1315i	−0.310660	−	0.645092i
$791$	−27.4865	−	32.6206i	−0.977308	−	1.15985i
$792$		0			0
$793$	−10.7588	−	13.4911i	−0.382055	−	0.479082i
$794$	−2.04544	+	0.985031i	−0.0725899	+	0.0349574i
$795$		0			0
$796$	19.4670	+	4.44321i	0.689989	+	0.157485i
$797$	7.85087	−	9.84468i	0.278092	−	0.348717i	−0.623095	−	0.782146i	$-0.714125\pi$
$797$	7.85087	−	9.84468i	0.278092	−	0.348717i	0.901188	+	0.433429i	$0.142697\pi$
$798$		0			0
$799$	−1.03829	−	1.30198i	−0.0367321	−	0.0460607i
$800$	0.914065	+	1.89808i	0.0323171	+	0.0671071i
$801$		0			0
$802$	−3.10070			−0.109490
$803$	21.6073			0.762505
$804$		0			0
$805$	8.55104	−	42.7525i	0.301384	−	1.50683i
$806$	7.75536	−	1.77011i	0.273171	−	0.0623495i
$807$		0			0
$808$	−7.47056	+	5.95757i	−0.262813	+	0.209587i
$809$	−22.3818	+	17.8489i	−0.786902	+	0.627533i	−0.932237	−	0.361849i	$-0.882145\pi$
$809$	−22.3818	+	17.8489i	−0.786902	+	0.627533i	0.145335	+	0.989382i	$0.453574\pi$
$810$		0			0
$811$	−14.4533	+	3.29888i	−0.507525	+	0.115839i	−0.468613	−	0.883403i	$-0.655246\pi$
$811$	−14.4533	+	3.29888i	−0.507525	+	0.115839i	−0.0389115	+	0.999243i	$0.512389\pi$
$812$	10.7959	−	0.291470i	0.378862	−	0.0102286i
$813$		0			0
$814$	−13.6802			−0.479489
$815$	49.5144			1.73441
$816$		0			0
$817$	0.227729	+	0.472885i	0.00796724	+	0.0165441i
$818$	−17.1204	−	21.4682i	−0.598599	−	0.750620i
$819$		0			0
$820$	−5.11619	+	6.41550i	−0.178665	+	0.224039i
$821$	−17.0559	−	3.89290i	−0.595255	−	0.135863i	−0.0857290	−	0.996318i	$-0.527322\pi$
$821$	−17.0559	−	3.89290i	−0.595255	−	0.135863i	−0.509526	+	0.860456i	$0.670179\pi$
$822$		0			0
$823$	−10.8724	+	5.23587i	−0.378988	+	0.182511i	−0.613673	−	0.789561i	$-0.710308\pi$
$823$	−10.8724	+	5.23587i	−0.378988	+	0.182511i	0.234685	+	0.972072i	$0.424594\pi$
$824$	−7.61432	−	9.54806i	−0.265257	−	0.332622i
$825$		0			0
$826$	5.06490	−	25.3229i	0.176230	−	0.881095i
$827$	−3.26835	−	6.78679i	−0.113651	−	0.236000i	0.836382	−	0.548146i	$-0.184666\pi$
$827$	−3.26835	−	6.78679i	−0.113651	−	0.236000i	−0.950034	+	0.312147i	$0.898952\pi$
$828$		0			0
$829$	10.3118	−	2.35360i	0.358144	−	0.0817439i	−0.0396633	−	0.999213i	$-0.512629\pi$
$829$	10.3118	−	2.35360i	0.358144	−	0.0817439i	0.397807	+	0.917469i	$0.369771\pi$
$830$	−1.12897	+	2.34433i	−0.0391871	+	0.0813729i
$831$		0			0
$832$		−	1.87678i		−	0.0650655i
$833$	0.287536	−	1.67089i	0.00996253	−	0.0578930i
$834$		0			0
$835$	−0.242463	+	0.304038i	−0.00839076	+	0.0105217i
$836$	−1.04714	−	0.504277i	−0.0362162	−	0.0174408i
$837$		0			0
$838$	2.01696	−	4.18826i	0.0696747	−	0.144681i
$839$	25.9968	−	12.5194i	0.897509	−	0.432218i	0.0725207	−	0.997367i	$-0.476896\pi$
$839$	25.9968	−	12.5194i	0.897509	−	0.432218i	0.824989	+	0.565149i	$0.191181\pi$
$840$		0			0
$841$	−11.1158	−	5.35309i	−0.383304	−	0.184589i
$842$	22.2430	−	17.7382i	0.766545	−	0.611299i
$843$		0			0
$844$	13.8191	−	17.3286i	0.475673	−	0.596475i
$845$	−5.62223	+	24.6326i	−0.193411	+	0.847387i
$846$		0			0
$847$	−12.9473	+	3.32519i	−0.444875	+	0.114255i
$848$	−0.952261	+	0.759402i	−0.0327008	+	0.0260780i
$849$		0			0
$850$	0.497466	+	0.113543i	0.0170630	+	0.00389451i
$851$		−	34.6751i		−	1.18865i
$852$		0			0
$853$	−17.9137	−	4.08869i	−0.613354	−	0.139994i	−0.0954522	−	0.995434i	$-0.530430\pi$
$853$	−17.9137	−	4.08869i	−0.613354	−	0.139994i	−0.517902	+	0.855440i	$0.673287\pi$
$854$	18.6025	−	15.6747i	0.636565	−	0.536378i
$855$		0			0
$856$	2.24286	+	9.82663i	0.0766595	+	0.335867i
$857$	−16.9748	−	21.2857i	−0.579848	−	0.727106i	0.402239	−	0.915535i	$-0.368232\pi$
$857$	−16.9748	−	21.2857i	−0.579848	−	0.727106i	−0.982087	+	0.188428i	$0.939661\pi$
$858$		0			0
$859$	26.0724	−	5.95085i	0.889577	−	0.203040i	0.246775	−	0.969073i	$-0.420629\pi$
$859$	26.0724	−	5.95085i	0.889577	−	0.203040i	0.642802	+	0.766032i	$0.277772\pi$
$860$	0.653317	+	2.86237i	0.0222779	+	0.0976060i
$861$		0			0
$862$	−1.70899	+	7.48757i	−0.0582084	+	0.255028i
$863$		−	3.03773i		−	0.103406i	−0.998663	−	0.0517028i	$-0.983535\pi$
$863$		−	3.03773i		−	0.103406i	0.998663	−	0.0517028i	$-0.0164649\pi$
$864$		0			0
$865$	−5.15230	+	22.5737i	−0.175183	+	0.767529i
$866$	34.3347	−	16.5347i	1.16674	−	0.561873i
$867$		0			0
$868$	2.78953	+	10.8616i	0.0946830	+	0.368668i
$869$	14.3937	+	11.4786i	0.488274	+	0.389386i
$870$		0			0
$871$	−0.566649	−	0.451887i	−0.0192002	−	0.0153116i
$872$	−5.11914	−	10.6300i	−0.173356	−	0.359978i
$873$		0			0
$874$	1.27819	−	2.65419i	0.0432354	−	0.0897792i
$875$	19.7654	−	5.07623i	0.668193	−	0.171608i
$876$		0			0
$877$	46.9661	+	22.6177i	1.58593	+	0.763745i	0.998948	−	0.0458531i	$-0.0146006\pi$
$877$	46.9661	+	22.6177i	1.58593	+	0.763745i	0.586985	+	0.809598i	$0.300315\pi$
$878$	−1.14238	−	5.00509i	−0.0385534	−	0.168914i
$879$		0			0
$880$	−5.08296	−	4.05353i	−0.171347	−	0.136644i
$881$	−16.7216			−0.563365			−0.281682	−	0.959508i	$-0.590892\pi$
$881$	−16.7216			−0.563365			−0.281682	+	0.959508i	$0.590892\pi$
$882$		0			0
$883$	12.3311			0.414976			0.207488	−	0.978238i	$-0.433471\pi$
$883$	12.3311			0.414976			0.207488	+	0.978238i	$0.433471\pi$
$884$	−0.355396	−	0.283419i	−0.0119533	−	0.00953242i
$885$		0			0
$886$	7.42323	+	32.5233i	0.249388	+	1.09264i
$887$	−26.6805	−	12.8486i	−0.895843	−	0.431415i	−0.0714572	−	0.997444i	$-0.522765\pi$
$887$	−26.6805	−	12.8486i	−0.895843	−	0.431415i	−0.824386	+	0.566028i	$0.808479\pi$
$888$		0			0
$889$	−37.1672	−	7.43392i	−1.24655	−	0.249326i
$890$	−7.95823	+	16.5254i	−0.266761	+	0.553934i
$891$		0			0
$892$	−3.32692	−	6.90842i	−0.111394	−	0.231311i
$893$	2.56178	+	2.04295i	0.0857268	+	0.0683649i
$894$		0			0
$895$	−31.8413	−	25.3926i	−1.06434	−	0.848781i
$896$	2.64479	−	0.0714045i	0.0883562	−	0.00238546i
$897$		0			0
$898$	−2.98997	+	1.43990i	−0.0997767	+	0.0480499i
$899$	−3.84996	+	16.8678i	−0.128403	+	0.562572i
$900$		0			0
$901$			0.295005i			0.00982805i
$902$	1.67041	−	7.31855i	0.0556186	−	0.243681i
$903$		0			0
$904$	−3.58766	−	15.7186i	−0.119324	−	0.522791i
$905$	20.1111	−	4.59023i	0.668515	−	0.152584i
$906$		0			0
$907$	−12.4277	−	15.5838i	−0.412654	−	0.517452i	0.531454	−	0.847087i	$-0.321646\pi$
$907$	−12.4277	−	15.5838i	−0.412654	−	0.517452i	−0.944109	+	0.329635i	$0.893074\pi$
$908$	−5.96231	−	26.1226i	−0.197866	−	0.866908i
$909$		0			0
$910$	12.9801	+	2.59619i	0.430286	+	0.0860627i
$911$	−15.7428	−	3.59319i	−0.521582	−	0.119048i	−0.0463792	−	0.998924i	$-0.514768\pi$
$911$	−15.7428	−	3.59319i	−0.521582	−	0.119048i	−0.475203	+	0.879876i	$0.657625\pi$
$912$		0			0
$913$		−	2.38037i		−	0.0787787i
$914$	6.13536	+	1.40035i	0.202940	+	0.0463196i
$915$		0			0
$916$	17.3200	−	13.8123i	0.572270	−	0.456370i
$917$	11.8574	+	23.0119i	0.391566	+	0.759921i
$918$		0			0
$919$	6.14682	−	26.9310i	0.202765	−	0.888371i	−0.766479	−	0.642269i	$-0.777993\pi$
$919$	6.14682	−	26.9310i	0.202765	−	0.888371i	0.969244	−	0.246102i	$-0.0791497\pi$
$920$	10.2745	−	12.8838i	0.338739	−	0.424765i
$921$		0			0
$922$	0.462872	−	0.369128i	0.0152439	−	0.0121566i
$923$	16.1315	+	7.76851i	0.530974	+	0.255704i
$924$		0			0
$925$	−10.6472	+	5.12742i	−0.350078	+	0.168589i
$926$	−11.1750	+	23.2051i	−0.367233	+	0.762568i
$927$		0			0
$928$	3.67772	+	1.77110i	0.120727	+	0.0581391i
$929$	−9.30242	+	11.6649i	−0.305203	+	0.382712i	−0.910654	−	0.413171i	$-0.864421\pi$
$929$	−9.30242	+	11.6649i	−0.305203	+	0.382712i	0.605451	+	0.795883i	$0.292993\pi$
$930$		0			0
$931$	0.180000	+	3.33113i	0.00589926	+	0.109173i
$932$			22.4026i			0.733821i
$933$		0			0
$934$	11.0663	−	22.9795i	0.362101	−	0.751911i
$935$	−1.53519	+	0.350398i	−0.0502062	+	0.0114592i
$936$		0			0
$937$	−8.06826	−	16.7539i	−0.263579	−	0.547327i	0.726612	−	0.687048i	$-0.241094\pi$
$937$	−8.06826	−	16.7539i	−0.263579	−	0.547327i	−0.990191	+	0.139721i	$0.955379\pi$
$938$	0.615249	−	0.815725i	0.0200886	−	0.0266343i
$939$		0			0
$940$	11.4279	+	14.3301i	0.372737	+	0.467398i
$941$	−44.4338	+	21.3982i	−1.44850	+	0.697560i	−0.982334	−	0.187137i	$-0.940079\pi$
$941$	−44.4338	+	21.3982i	−1.44850	+	0.697560i	−0.466165	+	0.884698i	$0.654365\pi$
$942$		0			0
$943$	18.5503	+	4.23399i	0.604081	+	0.137878i
$944$	6.08571	−	7.63124i	0.198073	−	0.248376i
$945$		0			0
$946$	−1.67463	−	2.09992i	−0.0544468	−	0.0682741i
$947$	22.7340	+	47.2077i	0.738757	+	1.53404i	0.842054	+	0.539394i	$0.181347\pi$
$947$	22.7340	+	47.2077i	0.738757	+	1.53404i	−0.103297	+	0.994651i	$0.532939\pi$
$948$		0			0
$949$	−16.6281			−0.539772
$950$	−1.00399			−0.0325738
$951$		0			0
$952$	0.385878	−	0.511614i	0.0125064	−	0.0165815i
$953$	22.3456	−	5.10024i	0.723846	−	0.165213i	0.155303	−	0.987867i	$-0.450365\pi$
$953$	22.3456	−	5.10024i	0.723846	−	0.165213i	0.568543	+	0.822654i	$0.307507\pi$
$954$		0			0
$955$	−49.3939	+	39.3903i	−1.59835	+	1.27464i
$956$	4.53906	−	3.61978i	0.146804	−	0.117072i
$957$		0			0
$958$	−1.13826	+	0.259800i	−0.0367755	+	0.00839377i
$959$	50.3897	−	25.9644i	1.62717	−	0.838434i
$960$		0			0
$961$	13.0347			0.420475
$962$	10.5277			0.339427
$963$		0			0
$964$	7.16952	+	14.8877i	0.230915	+	0.479499i
$965$	24.6046	+	30.8532i	0.792050	+	0.993199i
$966$		0			0
$967$	−13.6726	+	17.1448i	−0.439680	+	0.551341i	−0.951459	−	0.307776i	$-0.900415\pi$
$967$	−13.6726	+	17.1448i	−0.439680	+	0.551341i	0.511779	+	0.859117i	$0.328987\pi$
$968$	−4.92576	−	1.12427i	−0.158320	−	0.0361355i
$969$		0			0
$970$	−40.6011	+	19.5525i	−1.30362	+	0.627792i
$971$	3.77252	+	4.73059i	0.121066	+	0.151812i	0.838671	−	0.544638i	$-0.183333\pi$
$971$	3.77252	+	4.73059i	0.121066	+	0.151812i	−0.717605	+	0.696450i	$0.754762\pi$
$972$		0			0
$973$	15.6595	+	7.02706i	0.502019	+	0.225277i
$974$	−6.36377	−	13.2145i	−0.203908	−	0.423420i
$975$		0			0
$976$	8.96382	−	2.04593i	0.286925	−	0.0654887i
$977$	3.51275	−	7.29431i	0.112383	−	0.233366i	−0.837190	−	0.546912i	$-0.815803\pi$
$977$	3.51275	−	7.29431i	0.112383	−	0.233366i	0.949573	+	0.313547i	$0.101517\pi$
$978$		0			0
$979$		−	16.7795i		−	0.536275i
$980$	−3.16475	+	18.3906i	−0.101094	+	0.587465i
$981$		0			0
$982$	10.4782	−	13.1393i	0.334374	−	0.419292i
$983$	7.14215	+	3.43948i	0.227799	+	0.109702i	0.544302	−	0.838889i	$-0.316794\pi$
$983$	7.14215	+	3.43948i	0.227799	+	0.109702i	−0.316503	+	0.948591i	$0.602509\pi$
$984$		0			0
$985$	9.62037	−	19.9769i	0.306531	−	0.636517i
$986$	0.890770	−	0.428972i	0.0283679	−	0.0136613i
$987$		0			0
$988$	0.805839	+	0.388072i	0.0256372	+	0.0123462i
$989$	5.32265	−	4.24467i	0.169250	−	0.134973i
$990$		0			0
$991$	−24.9261	+	31.2563i	−0.791803	+	0.992889i	0.208088	+	0.978110i	$0.433276\pi$
$991$	−24.9261	+	31.2563i	−0.791803	+	0.992889i	−0.999891	+	0.0147792i	$0.995295\pi$
$992$	−0.943165	+	4.13228i	−0.0299455	+	0.131200i
$993$		0			0
$994$	−10.3338	+	23.0283i	−0.327768	+	0.730414i
$995$	−41.6172	+	33.1886i	−1.31936	+	1.05215i
$996$		0			0
$997$	−35.9519	−	8.20578i	−1.13861	−	0.259880i	−0.388663	−	0.921380i	$-0.627063\pi$
$997$	−35.9519	−	8.20578i	−1.13861	−	0.259880i	−0.749945	+	0.661500i	$0.769920\pi$
$998$		−	7.98609i		−	0.252795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.v.a.251.1	✓	96
3.2	odd	2	inner	882.2.v.a.251.16	yes	96
49.41	odd	14	inner	882.2.v.a.629.16	yes	96
147.41	even	14	inner	882.2.v.a.629.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.v.a.251.1	✓	96	1.1	even	1	trivial
882.2.v.a.251.16	yes	96	3.2	odd	2	inner
882.2.v.a.629.1	yes	96	147.41	even	14	inner
882.2.v.a.629.16	yes	96	49.41	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-2.40184 - 1.15666i) q^{5} +(-0.0714045 - 2.64479i) q^{7} +(0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(-0.781831 - 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-2.40184 - 1.15666i) q^{5} +(-0.0714045 - 2.64479i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.15666 + 2.40184i) q^{10} +(-1.90670 - 1.52054i) q^{11} +(1.46732 + 1.17015i) q^{13} +(-1.59317 + 2.11230i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(-0.0538962 + 0.236135i) q^{17} -0.476570i q^{19} +(0.593205 - 2.59900i) q^{20} +(0.542676 + 2.37762i) q^{22} +(-6.02654 + 1.37552i) q^{23} +(1.31351 + 1.64709i) q^{25} +(-0.417622 - 1.82972i) q^{26} +(2.56259 - 0.658135i) q^{28} +(3.97962 + 0.908321i) q^{29} +4.23855i q^{31} +(0.974928 + 0.222521i) q^{32} +(0.189365 - 0.151014i) q^{34} +(-2.88763 + 6.43495i) q^{35} +(-1.24822 + 5.46883i) q^{37} +(-0.297136 + 0.372597i) q^{38} +(-2.08424 + 1.66212i) q^{40} +(-2.77328 - 1.33554i) q^{41} +(-0.992268 + 0.477851i) q^{43} +(1.05814 - 2.19725i) q^{44} +(5.56936 + 2.68206i) q^{46} +(-4.28679 + 5.37547i) q^{47} +(-6.98980 + 0.377699i) q^{49} -2.10671i q^{50} +(-0.814303 + 1.69092i) q^{52} +(1.18745 - 0.271028i) q^{53} +(2.82083 + 5.85752i) q^{55} +(-2.41385 - 1.08320i) q^{56} +(-2.54506 - 3.19140i) q^{58} +(-8.79410 + 4.23502i) q^{59} +(-8.96382 - 2.04593i) q^{61} +(2.64269 - 3.31383i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-2.17080 - 4.50771i) q^{65} -0.386179 q^{67} -0.242207 q^{68} +(6.26976 - 3.23063i) q^{70} +(9.30088 - 2.12287i) q^{71} +(-6.92698 + 5.52408i) q^{73} +(4.38566 - 3.49745i) q^{74} +(0.464621 - 0.106047i) q^{76} +(-3.88537 + 5.15139i) q^{77} -7.54903 q^{79} +2.66584 q^{80} +(1.33554 + 2.77328i) q^{82} +(0.608561 + 0.763112i) q^{83} +(0.402579 - 0.504818i) q^{85} +(1.07372 + 0.245070i) q^{86} +(-2.19725 + 1.05814i) q^{88} +(4.28981 + 5.37926i) q^{89} +(2.99003 - 3.96431i) q^{91} +(-2.68206 - 5.56936i) q^{92} +(6.70310 - 1.52994i) q^{94} +(-0.551231 + 1.14464i) q^{95} +16.9042i q^{97} +(5.70034 + 4.06277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{4}+O(q^{10}) \) 96 * q + 16 * q^4	\( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) \) 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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