LMFDB - Embedded newform 1764.2.w.c.1109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1109.3
Character	$\chi$	$=$	1764.1109
Dual form			1764.2.w.c.509.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61937 - 0.614514i) q^{3} +(0.0565510 - 0.0979493i) q^{5} +(2.24475 + 1.99026i) q^{9} +O(q^{10})$	\(q+(-1.61937 - 0.614514i) q^{3} +(0.0565510 - 0.0979493i) q^{5} +(2.24475 + 1.99026i) q^{9} +(-4.86969 + 2.81151i) q^{11} +(2.71286 - 1.56627i) q^{13} +(-0.151769 + 0.123865i) q^{15} +(-0.615632 + 1.06631i) q^{17} +(3.38980 - 1.95710i) q^{19} +(-4.06316 - 2.34587i) q^{23} +(2.49360 + 4.31905i) q^{25} +(-2.41204 - 4.60240i) q^{27} +(-0.117222 - 0.0676783i) q^{29} -6.82790i q^{31} +(9.61356 - 1.56040i) q^{33} +(-3.39182 - 5.87480i) q^{37} +(-5.35563 + 0.869287i) q^{39} +(-1.27192 - 2.20303i) q^{41} +(-2.88806 + 5.00226i) q^{43} +(0.321887 - 0.107320i) q^{45} +5.32646 q^{47} +(1.65220 - 1.34843i) q^{51} +(2.48935 + 1.43723i) q^{53} +0.635976i q^{55} +(-6.69202 + 1.08620i) q^{57} -11.4458 q^{59} +0.0386207i q^{61} -0.354297i q^{65} -10.4899 q^{67} +(5.13821 + 6.29570i) q^{69} -12.4663i q^{71} +(-11.3768 - 6.56842i) q^{73} +(-1.38396 - 8.52651i) q^{75} +11.2236 q^{79} +(1.07776 + 8.93524i) q^{81} +(-0.344701 + 0.597040i) q^{83} +(0.0696293 + 0.120601i) q^{85} +(0.148237 + 0.181631i) q^{87} +(5.37075 + 9.30241i) q^{89} +(-4.19584 + 11.0569i) q^{93} -0.442705i q^{95} +(-5.89327 - 3.40248i) q^{97} +(-16.5268 - 3.38079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{9}+O(q^{10}) $ 48 * q - 8 * q^9	$ 48 q - 8 q^{9} + 24 q^{11} + 24 q^{15} - 48 q^{23} - 24 q^{25} + 56 q^{39} + 72 q^{51} - 48 q^{53} + 16 q^{57} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 48 q^{93} - 40 q^{99}+O(q^{100}) $ 48 * q - 8 * q^9 + 24 * q^11 + 24 * q^15 - 48 * q^23 - 24 * q^25 + 56 * q^39 + 72 * q^51 - 48 * q^53 + 16 * q^57 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 48 * q^93 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.61937	−	0.614514i	−0.934946	−	0.354790i
$3$	−1.61937	−	0.614514i	−0.934946	−	0.354790i
$4$		0			0
$5$	0.0565510	−	0.0979493i	0.0252904	−	0.0438043i	−0.853103	−	0.521742i	$-0.825282\pi$
$5$	0.0565510	−	0.0979493i	0.0252904	−	0.0438043i	0.878394	+	0.477938i	$0.158616\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.24475	+	1.99026i	0.748248	+	0.663419i
$10$		0			0
$11$	−4.86969	+	2.81151i	−1.46827	+	0.847703i	−0.999368	−	0.0355493i	$-0.988682\pi$
$11$	−4.86969	+	2.81151i	−1.46827	+	0.847703i	−0.468897	+	0.883253i	$0.655349\pi$
$12$		0			0
$13$	2.71286	−	1.56627i	0.752412	−	0.434405i	−0.0741527	−	0.997247i	$-0.523625\pi$
$13$	2.71286	−	1.56627i	0.752412	−	0.434405i	0.826565	+	0.562842i	$0.190292\pi$
$14$		0			0
$15$	−0.151769	+	0.123865i	−0.0391865	+	0.0319818i
$16$		0			0
$17$	−0.615632	+	1.06631i	−0.149313	+	0.258617i	−0.930974	−	0.365086i	$-0.881039\pi$
$17$	−0.615632	+	1.06631i	−0.149313	+	0.258617i	0.781661	+	0.623704i	$0.214373\pi$
$18$		0			0
$19$	3.38980	−	1.95710i	0.777673	−	0.448990i	−0.0579318	−	0.998321i	$-0.518451\pi$
$19$	3.38980	−	1.95710i	0.777673	−	0.448990i	0.835605	+	0.549331i	$0.185117\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.06316	−	2.34587i	−0.847227	−	0.489147i	0.0124873	−	0.999922i	$-0.496025\pi$
$23$	−4.06316	−	2.34587i	−0.847227	−	0.489147i	−0.859714	+	0.510775i	$0.829358\pi$
$24$		0			0
$25$	2.49360	+	4.31905i	0.498721	+	0.863810i
$26$		0			0
$27$	−2.41204	−	4.60240i	−0.464198	−	0.885732i
$28$		0			0
$29$	−0.117222	−	0.0676783i	−0.0217676	−	0.0125675i	0.489077	−	0.872241i	$-0.337334\pi$
$29$	−0.117222	−	0.0676783i	−0.0217676	−	0.0125675i	−0.510844	+	0.859673i	$0.670667\pi$
$30$		0			0
$31$		−	6.82790i		−	1.22633i	−0.789956	−	0.613164i	$-0.789897\pi$
$31$		−	6.82790i		−	1.22633i	0.789956	−	0.613164i	$-0.210103\pi$
$32$		0			0
$33$	9.61356	−	1.56040i	1.67351	−	0.271631i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.39182	−	5.87480i	−0.557611	−	0.965811i	−0.997695	−	0.0678544i	$-0.978385\pi$
$37$	−3.39182	−	5.87480i	−0.557611	−	0.965811i	0.440084	−	0.897957i	$-0.354949\pi$
$38$		0			0
$39$	−5.35563	+	0.869287i	−0.857587	+	0.139197i
$40$		0			0
$41$	−1.27192	−	2.20303i	−0.198640	−	0.344055i	0.749448	−	0.662064i	$-0.230319\pi$
$41$	−1.27192	−	2.20303i	−0.198640	−	0.344055i	−0.948088	+	0.318009i	$0.896986\pi$
$42$		0			0
$43$	−2.88806	+	5.00226i	−0.440425	+	0.762838i	−0.997721	−	0.0674759i	$-0.978505\pi$
$43$	−2.88806	+	5.00226i	−0.440425	+	0.762838i	0.557296	+	0.830314i	$0.311839\pi$
$44$		0			0
$45$	0.321887	−	0.107320i	0.0479841	−	0.0159983i
$46$		0			0
$47$	5.32646			0.776944			0.388472	−	0.921461i	$-0.373003\pi$
$47$	5.32646			0.776944			0.388472	+	0.921461i	$0.373003\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.65220	−	1.34843i	0.231354	−	0.188818i
$52$		0			0
$53$	2.48935	+	1.43723i	0.341939	+	0.197419i	0.661129	−	0.750272i	$-0.270078\pi$
$53$	2.48935	+	1.43723i	0.341939	+	0.197419i	−0.319190	+	0.947691i	$0.603411\pi$
$54$		0			0
$55$			0.635976i			0.0857550i
$56$		0			0
$57$	−6.69202	+	1.08620i	−0.886380	+	0.143871i
$58$		0			0
$59$	−11.4458			−1.49012			−0.745058	−	0.666999i	$-0.767578\pi$
$59$	−11.4458			−1.49012			−0.745058	+	0.666999i	$0.767578\pi$
$60$		0			0
$61$			0.0386207i			0.00494488i	0.999997	+	0.00247244i	$0.000787002\pi$
$61$			0.0386207i			0.00494488i	−0.999997	+	0.00247244i	$0.999213\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.354297i		−	0.0439451i
$66$		0			0
$67$	−10.4899			−1.28155			−0.640774	−	0.767730i	$-0.721386\pi$
$67$	−10.4899			−1.28155			−0.640774	+	0.767730i	$0.721386\pi$
$68$		0			0
$69$	5.13821	+	6.29570i	0.618567	+	0.757913i
$70$		0			0
$71$		−	12.4663i		−	1.47948i	−0.672894	−	0.739739i	$-0.734949\pi$
$71$		−	12.4663i		−	1.47948i	0.672894	−	0.739739i	$-0.265051\pi$
$72$		0			0
$73$	−11.3768	−	6.56842i	−1.33156	−	0.768775i	−0.346019	−	0.938227i	$-0.612467\pi$
$73$	−11.3768	−	6.56842i	−1.33156	−	0.768775i	−0.985538	+	0.169452i	$0.945800\pi$
$74$		0			0
$75$	−1.38396	−	8.52651i	−0.159806	−	0.984557i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	11.2236			1.26275			0.631377	−	0.775476i	$-0.282490\pi$
$79$	11.2236			1.26275			0.631377	+	0.775476i	$0.282490\pi$
$80$		0			0
$81$	1.07776	+	8.93524i	0.119751	+	0.992804i
$82$		0			0
$83$	−0.344701	+	0.597040i	−0.0378359	+	0.0655337i	−0.884323	−	0.466875i	$-0.845380\pi$
$83$	−0.344701	+	0.597040i	−0.0378359	+	0.0655337i	0.846487	+	0.532409i	$0.178713\pi$
$84$		0			0
$85$	0.0696293	+	0.120601i	0.00755235	+	0.0130811i
$86$		0			0
$87$	0.148237	+	0.181631i	0.0158927	+	0.0194729i
$88$		0			0
$89$	5.37075	+	9.30241i	0.569298	+	0.986053i	0.996636	+	0.0819609i	$0.0261183\pi$
$89$	5.37075	+	9.30241i	0.569298	+	0.986053i	−0.427338	+	0.904092i	$0.640548\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.19584	+	11.0569i	−0.435089	+	1.14655i
$94$		0			0
$95$		−	0.442705i		−	0.0454205i
$96$		0			0
$97$	−5.89327	−	3.40248i	−0.598371	−	0.345470i	0.170029	−	0.985439i	$-0.445614\pi$
$97$	−5.89327	−	3.40248i	−0.598371	−	0.345470i	−0.768401	+	0.639969i	$0.778947\pi$
$98$		0			0
$99$	−16.5268	−	3.38079i	−1.66101	−	0.339782i
$100$		0			0
$101$	−8.14757	−	14.1120i	−0.810713	−	1.40420i	−0.912365	−	0.409377i	$-0.865746\pi$
$101$	−8.14757	−	14.1120i	−0.810713	−	1.40420i	0.101652	−	0.994820i	$-0.467587\pi$
$102$		0			0
$103$	−15.3680	−	8.87273i	−1.51426	−	0.874256i	−0.999860	−	0.0167032i	$-0.994683\pi$
$103$	−15.3680	−	8.87273i	−1.51426	−	0.874256i	−0.514396	−	0.857553i	$-0.671984\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.2674	+	6.50525i	−1.08926	+	0.628887i	−0.933380	−	0.358889i	$-0.883156\pi$
$107$	−11.2674	+	6.50525i	−1.08926	+	0.628887i	−0.155883	+	0.987775i	$0.549822\pi$
$108$		0			0
$109$	−0.685898	+	1.18801i	−0.0656971	+	0.113791i	−0.897003	−	0.442024i	$-0.854260\pi$
$109$	−0.685898	+	1.18801i	−0.0656971	+	0.113791i	0.831306	+	0.555815i	$0.187594\pi$
$110$		0			0
$111$	1.88247	+	11.5978i	0.178677	+	1.10082i
$112$		0			0
$113$	−7.75422	+	4.47690i	−0.729455	+	0.421151i	−0.818223	−	0.574901i	$-0.805041\pi$
$113$	−7.75422	+	4.47690i	−0.729455	+	0.421151i	0.0887675	+	0.996052i	$0.471707\pi$
$114$		0			0
$115$	−0.459552	+	0.265322i	−0.0428534	+	0.0247414i
$116$		0			0
$117$	9.20696	+	1.88341i	0.851184	+	0.174121i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.3092	−	17.8561i	0.937202	−	1.62328i
$122$		0			0
$123$	0.705921	+	4.34914i	0.0636507	+	0.392148i
$124$		0			0
$125$	1.12957			0.101032
$126$		0			0
$127$	−7.21996			−0.640668			−0.320334	−	0.947305i	$-0.603795\pi$
$127$	−7.21996			−0.640668			−0.320334	+	0.947305i	$0.603795\pi$
$128$		0			0
$129$	7.75081	−	6.32578i	0.682420	−	0.556954i
$130$		0			0
$131$	−4.16622	+	7.21611i	−0.364005	+	0.630474i	−0.988616	−	0.150461i	$-0.951924\pi$
$131$	−4.16622	+	7.21611i	−0.364005	+	0.630474i	0.624611	+	0.780936i	$0.285257\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.587205	−	0.0240126i	−0.0505386	−	0.00206667i
$136$		0			0
$137$	7.10942	−	4.10463i	0.607399	−	0.350682i	−0.164548	−	0.986369i	$-0.552616\pi$
$137$	7.10942	−	4.10463i	0.607399	−	0.350682i	0.771947	+	0.635687i	$0.219283\pi$
$138$		0			0
$139$	3.19880	−	1.84683i	0.271318	−	0.156646i	−0.358168	−	0.933657i	$-0.616599\pi$
$139$	3.19880	−	1.84683i	0.271318	−	0.156646i	0.629487	+	0.777011i	$0.283265\pi$
$140$		0			0
$141$	−8.62553	−	3.27318i	−0.726401	−	0.275652i
$142$		0			0
$143$	−8.80718	+	15.2545i	−0.736494	+	1.27564i
$144$		0			0
$145$	−0.0132581	+	0.00765456i	−0.00110102	+	0.000635677i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−20.4407	−	11.8014i	−1.67456	−	0.966810i	−0.965031	−	0.262137i	$-0.915573\pi$
$149$	−20.4407	−	11.8014i	−1.67456	−	0.966810i	−0.709533	−	0.704672i	$-0.751094\pi$
$150$		0			0
$151$	−2.19194	−	3.79656i	−0.178378	−	0.308959i	0.762947	−	0.646461i	$-0.223752\pi$
$151$	−2.19194	−	3.79656i	−0.178378	−	0.308959i	−0.941325	+	0.337501i	$0.890418\pi$
$152$		0			0
$153$	−3.50416	+	1.16832i	−0.283294	+	0.0944530i
$154$		0			0
$155$	−0.668788	−	0.386125i	−0.0537184	−	0.0310143i
$156$		0			0
$157$		−	14.1053i		−	1.12572i	−0.826551	−	0.562861i	$-0.809700\pi$
$157$		−	14.1053i		−	1.12572i	0.826551	−	0.562861i	$-0.190300\pi$
$158$		0			0
$159$	−3.14800	−	3.85715i	−0.249652	−	0.305892i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.80340	−	11.7838i	−0.532884	−	0.922982i	−0.999263	−	0.0383965i	$-0.987775\pi$
$163$	−6.80340	−	11.7838i	−0.532884	−	0.922982i	0.466379	−	0.884585i	$-0.345558\pi$
$164$		0			0
$165$	0.390816	−	1.02988i	0.0304250	−	0.0801763i
$166$		0			0
$167$	−8.49355	−	14.7113i	−0.657251	−	1.13839i	−0.981324	−	0.192360i	$-0.938386\pi$
$167$	−8.49355	−	14.7113i	−0.657251	−	1.13839i	0.324074	−	0.946032i	$-0.394947\pi$
$168$		0			0
$169$	−1.59359	+	2.76018i	−0.122584	+	0.212322i
$170$		0			0
$171$	11.5044	+	2.35337i	0.879761	+	0.179967i
$172$		0			0
$173$	−1.77136			−0.134674			−0.0673371	−	0.997730i	$-0.521450\pi$
$173$	−1.77136			−0.134674			−0.0673371	+	0.997730i	$0.521450\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	18.5350	+	7.03361i	1.39318	+	0.528678i
$178$		0			0
$179$	−7.13609	−	4.12002i	−0.533376	−	0.307945i	0.209014	−	0.977913i	$-0.432975\pi$
$179$	−7.13609	−	4.12002i	−0.533376	−	0.307945i	−0.742390	+	0.669968i	$0.766308\pi$
$180$		0			0
$181$			0.934986i			0.0694970i	0.999396	+	0.0347485i	$0.0110630\pi$
$181$			0.934986i			0.0694970i	−0.999396	+	0.0347485i	$0.988937\pi$
$182$		0			0
$183$	0.0237330	−	0.0625414i	0.00175439	−	0.00462319i
$184$		0			0
$185$	−0.767243			−0.0564088
$186$		0			0
$187$		−	6.92343i		−	0.506291i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			11.2825i			0.816377i	0.912898	+	0.408188i	$0.133839\pi$
$191$			11.2825i			0.816377i	−0.912898	+	0.408188i	$0.866161\pi$
$192$		0			0
$193$	20.9886			1.51079			0.755396	−	0.655268i	$-0.227444\pi$
$193$	20.9886			1.51079			0.755396	+	0.655268i	$0.227444\pi$
$194$		0			0
$195$	−0.217720	+	0.573739i	−0.0155913	+	0.0410863i
$196$		0			0
$197$		−	17.2865i		−	1.23161i	−0.787898	−	0.615805i	$-0.788831\pi$
$197$		−	17.2865i		−	1.23161i	0.787898	−	0.615805i	$-0.211169\pi$
$198$		0			0
$199$	−4.50187	−	2.59915i	−0.319129	−	0.184249i	0.331875	−	0.943323i	$-0.392319\pi$
$199$	−4.50187	−	2.59915i	−0.319129	−	0.184249i	−0.651004	+	0.759074i	$0.725652\pi$
$200$		0			0
$201$	16.9871	+	6.44620i	1.19818	+	0.454680i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.287713			−0.0200948
$206$		0			0
$207$	−4.45188	−	13.3526i	−0.309427	−	0.928069i
$208$		0			0
$209$	−11.0048	+	19.0609i	−0.761220	+	1.31847i
$210$		0			0
$211$	12.6664	+	21.9388i	0.871990	+	1.51033i	0.859935	+	0.510404i	$0.170504\pi$
$211$	12.6664	+	21.9388i	0.871990	+	1.51033i	0.0120556	+	0.999927i	$0.496162\pi$
$212$		0			0
$213$	−7.66072	+	20.1876i	−0.524904	+	1.38323i
$214$		0			0
$215$	0.326645	+	0.565766i	0.0222770	+	0.0385849i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	14.3870	+	17.6279i	0.972181	+	1.19119i
$220$		0			0
$221$			3.85698i			0.259449i
$222$		0			0
$223$	23.0004	+	13.2793i	1.54022	+	0.889247i	0.998824	+	0.0484802i	$0.0154378\pi$
$223$	23.0004	+	13.2793i	1.54022	+	0.889247i	0.541397	+	0.840767i	$0.317896\pi$
$224$		0			0
$225$	−2.99851	+	14.6581i	−0.199901	+	0.977205i
$226$		0			0
$227$	1.15231	+	1.99585i	0.0764813	+	0.132469i	0.901729	−	0.432301i	$-0.142298\pi$
$227$	1.15231	+	1.99585i	0.0764813	+	0.132469i	−0.825248	+	0.564770i	$0.808965\pi$
$228$		0			0
$229$	1.32361	+	0.764188i	0.0874668	+	0.0504990i	0.543095	−	0.839671i	$-0.317252\pi$
$229$	1.32361	+	0.764188i	0.0874668	+	0.0504990i	−0.455629	+	0.890170i	$0.650586\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.60738	−	0.928021i	0.105303	−	0.0607966i	−0.446424	−	0.894822i	$-0.647303\pi$
$233$	1.60738	−	0.928021i	0.105303	−	0.0607966i	0.551727	+	0.834025i	$0.313969\pi$
$234$		0			0
$235$	0.301217	−	0.521723i	0.0196492	−	0.0340335i
$236$		0			0
$237$	−18.1752	−	6.89706i	−1.18061	−	0.448013i
$238$		0			0
$239$	26.5014	−	15.3006i	1.71423	−	0.989712i	0.785578	−	0.618763i	$-0.212366\pi$
$239$	26.5014	−	15.3006i	1.71423	−	0.989712i	0.928653	−	0.370949i	$-0.120968\pi$
$240$		0			0
$241$	20.5380	−	11.8576i	1.32297	−	0.763817i	0.338769	−	0.940870i	$-0.389989\pi$
$241$	20.5380	−	11.8576i	1.32297	−	0.763817i	0.984201	+	0.177052i	$0.0566561\pi$
$242$		0			0
$243$	3.74553	−	15.1318i	0.240276	−	0.970705i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.13070	−	10.6187i	0.390087	−	0.675651i
$248$		0			0
$249$	0.925090	−	0.755008i	0.0586252	−	0.0478467i
$250$		0			0
$251$	14.5555			0.918736			0.459368	−	0.888246i	$-0.348076\pi$
$251$	14.5555			0.918736			0.459368	+	0.888246i	$0.348076\pi$
$252$		0			0
$253$	26.3817			1.65861
$254$		0			0
$255$	−0.0386446	−	0.238087i	−0.00242002	−	0.0149096i
$256$		0			0
$257$	−9.23554	+	15.9964i	−0.576097	+	0.997829i	0.419824	+	0.907605i	$0.362092\pi$
$257$	−9.23554	+	15.9964i	−0.576097	+	0.997829i	−0.995921	+	0.0902241i	$0.971242\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.128437	−	0.385223i	−0.00795005	−	0.0238447i
$262$		0			0
$263$	−20.3889	+	11.7716i	−1.25724	+	0.725865i	−0.972536	−	0.232751i	$-0.925227\pi$
$263$	−20.3889	+	11.7716i	−1.25724	+	0.725865i	−0.284699	+	0.958617i	$0.591894\pi$
$264$		0			0
$265$	0.281551	−	0.162554i	0.0172955	−	0.00998559i
$266$		0			0
$267$	−2.98079	−	18.3645i	−0.182421	−	1.12389i
$268$		0			0
$269$	−15.1399	+	26.2232i	−0.923099	+	1.59885i	−0.128509	+	0.991708i	$0.541019\pi$
$269$	−15.1399	+	26.2232i	−0.923099	+	1.59885i	−0.794590	+	0.607146i	$0.792314\pi$
$270$		0			0
$271$	−24.9128	+	14.3834i	−1.51334	+	0.873730i	−0.513467	+	0.858110i	$0.671639\pi$
$271$	−24.9128	+	14.3834i	−1.51334	+	0.873730i	−0.999878	+	0.0156202i	$0.995028\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−24.2861	−	14.0216i	−1.46451	−	0.845535i
$276$		0			0
$277$	2.50103	+	4.33191i	0.150272	+	0.260279i	0.931328	−	0.364183i	$-0.118652\pi$
$277$	2.50103	+	4.33191i	0.150272	+	0.260279i	−0.781055	+	0.624462i	$0.785318\pi$
$278$		0			0
$279$	13.5893	−	15.3269i	0.813569	−	0.917598i
$280$		0			0
$281$	11.4362	+	6.60270i	0.682227	+	0.393884i	0.800694	−	0.599074i	$-0.204465\pi$
$281$	11.4362	+	6.60270i	0.682227	+	0.393884i	−0.118467	+	0.992958i	$0.537798\pi$
$282$		0			0
$283$		−	11.3492i		−	0.674641i	−0.941390	−	0.337321i	$-0.890479\pi$
$283$		−	11.3492i		−	0.674641i	0.941390	−	0.337321i	$-0.109521\pi$
$284$		0			0
$285$	−0.272048	+	0.716904i	−0.0161147	+	0.0424657i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.74199	+	13.4095i	0.455411	+	0.788796i
$290$		0			0
$291$	7.45254	+	9.13139i	0.436876	+	0.535292i
$292$		0			0
$293$	−4.62606	−	8.01258i	−0.270258	−	0.468100i	0.698670	−	0.715444i	$-0.253776\pi$
$293$	−4.62606	−	8.01258i	−0.270258	−	0.468100i	−0.968928	+	0.247344i	$0.920442\pi$
$294$		0			0
$295$	−0.647272	+	1.12111i	−0.0376857	+	0.0652735i
$296$		0			0
$297$	24.6856	+	15.6307i	1.43240	+	0.906987i
$298$		0			0
$299$	−14.6970			−0.849952
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4.52194	+	27.8594i	0.259779	+	1.60048i
$304$		0			0
$305$	0.00378287	+	0.00218404i	0.000216607	+	0.000125058i
$306$		0			0
$307$		−	25.1926i		−	1.43782i	−0.695104	−	0.718909i	$-0.744642\pi$
$307$		−	25.1926i		−	1.43782i	0.695104	−	0.718909i	$-0.255358\pi$
$308$		0			0
$309$	19.4342	+	23.8121i	1.10557	+	1.35463i
$310$		0			0
$311$	23.1865			1.31478			0.657392	−	0.753548i	$-0.271659\pi$
$311$	23.1865			1.31478			0.657392	+	0.753548i	$0.271659\pi$
$312$		0			0
$313$		−	23.8472i		−	1.34793i	−0.738765	−	0.673963i	$-0.764591\pi$
$313$		−	23.8472i		−	1.34793i	0.738765	−	0.673963i	$-0.235409\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			10.3450i			0.581036i	0.956870	+	0.290518i	$0.0938275\pi$
$317$			10.3450i			0.581036i	−0.956870	+	0.290518i	$0.906172\pi$
$318$		0			0
$319$	0.761114			0.0426142
$320$		0			0
$321$	22.2438	−	3.61045i	1.24153	−	0.201515i
$322$		0			0
$323$			4.81942i			0.268159i
$324$		0			0
$325$	13.5296	+	7.81132i	0.750487	+	0.433294i
$326$		0			0
$327$	1.84077	−	1.50234i	0.101795	−	0.0830796i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−7.28956			−0.400671			−0.200335	−	0.979727i	$-0.564203\pi$
$331$	−7.28956			−0.400671			−0.200335	+	0.979727i	$0.564203\pi$
$332$		0			0
$333$	4.07859	−	19.9380i	0.223505	−	1.09260i
$334$		0			0
$335$	−0.593216	+	1.02748i	−0.0324109	+	0.0561373i
$336$		0			0
$337$	7.67533	+	13.2941i	0.418102	+	0.724173i	0.995749	−	0.0921135i	$-0.0293623\pi$
$337$	7.67533	+	13.2941i	0.418102	+	0.724173i	−0.577647	+	0.816287i	$0.696029\pi$
$338$		0			0
$339$	15.3081	−	2.48470i	0.831422	−	0.134950i
$340$		0			0
$341$	19.1967	+	33.2497i	1.03956	+	1.80057i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.907230	−	0.147255i	0.0488436	−	0.00792795i
$346$		0			0
$347$		−	18.3604i		−	0.985639i	−0.870132	−	0.492819i	$-0.835966\pi$
$347$		−	18.3604i		−	0.985639i	0.870132	−	0.492819i	$-0.164034\pi$
$348$		0			0
$349$	−14.6555	−	8.46135i	−0.784490	−	0.452925i	0.0535293	−	0.998566i	$-0.482953\pi$
$349$	−14.6555	−	8.46135i	−0.784490	−	0.452925i	−0.838019	+	0.545641i	$0.816286\pi$
$350$		0			0
$351$	−13.7521	−	8.70775i	−0.734034	−	0.464785i
$352$		0			0
$353$	11.1058	+	19.2358i	0.591101	+	1.02382i	0.994084	+	0.108610i	$0.0346400\pi$
$353$	11.1058	+	19.2358i	0.591101	+	1.02382i	−0.402983	+	0.915207i	$0.632027\pi$
$354$		0			0
$355$	−1.22107	−	0.704982i	−0.0648074	−	0.0374166i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.26853	+	2.46444i	−0.225285	+	0.130068i	−0.608395	−	0.793635i	$-0.708186\pi$
$359$	−4.26853	+	2.46444i	−0.225285	+	0.130068i	0.383110	+	0.923703i	$0.374853\pi$
$360$		0			0
$361$	−1.83951	+	3.18612i	−0.0968162	+	0.167691i
$362$		0			0
$363$	−27.6673	+	22.5805i	−1.45216	+	1.18517i
$364$		0			0
$365$	−1.28674	+	0.742902i	−0.0673512	+	0.0388853i
$366$		0			0
$367$	−6.85336	+	3.95679i	−0.357743	+	0.206543i	−0.668090	−	0.744080i	$-0.732888\pi$
$367$	−6.85336	+	3.95679i	−0.357743	+	0.206543i	0.310347	+	0.950623i	$0.399555\pi$
$368$		0			0
$369$	1.52946	−	7.47668i	0.0796203	−	0.389220i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.1651	−	27.9989i	0.837000	−	1.44973i	−0.0553923	−	0.998465i	$-0.517641\pi$
$373$	16.1651	−	27.9989i	0.837000	−	1.44973i	0.892392	−	0.451261i	$-0.149026\pi$
$374$		0			0
$375$	−1.82920	−	0.694139i	−0.0944596	−	0.0358452i
$376$		0			0
$377$	−0.424010			−0.0218376
$378$		0			0
$379$	9.46110			0.485984			0.242992	−	0.970028i	$-0.421871\pi$
$379$	9.46110			0.485984			0.242992	+	0.970028i	$0.421871\pi$
$380$		0			0
$381$	11.6918	+	4.43677i	0.598990	+	0.227303i
$382$		0			0
$383$	7.71048	−	13.3549i	0.393987	−	0.682406i	−0.598984	−	0.800761i	$-0.704429\pi$
$383$	7.71048	−	13.3549i	0.393987	−	0.682406i	0.992971	+	0.118355i	$0.0377621\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−16.4387	+	5.48083i	−0.835628	+	0.278606i
$388$		0			0
$389$	30.7483	−	17.7525i	1.55900	−	0.900089i	0.561647	−	0.827377i	$-0.310168\pi$
$389$	30.7483	−	17.7525i	1.55900	−	0.900089i	0.997353	−	0.0727122i	$-0.0231655\pi$
$390$		0			0
$391$	5.00282	−	2.88838i	0.253003	−	0.146072i
$392$		0			0
$393$	11.1811	−	9.12538i	0.564011	−	0.460314i
$394$		0			0
$395$	0.634707	−	1.09934i	0.0319356	−	0.0553140i
$396$		0			0
$397$	−14.5897	+	8.42339i	−0.732238	+	0.422758i	−0.819240	−	0.573450i	$-0.805605\pi$
$397$	−14.5897	+	8.42339i	−0.732238	+	0.422758i	0.0870024	+	0.996208i	$0.472271\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.48987	−	3.16958i	−0.274151	−	0.158281i	0.356622	−	0.934249i	$-0.383929\pi$
$401$	−5.48987	−	3.16958i	−0.274151	−	0.158281i	−0.630772	+	0.775968i	$0.717262\pi$
$402$		0			0
$403$	−10.6943	−	18.5231i	−0.532723	−	0.922704i
$404$		0			0
$405$	0.936148	+	0.399731i	0.0465176	+	0.0198628i
$406$		0			0
$407$	33.0342	+	19.0723i	1.63744	+	0.945378i
$408$		0			0
$409$			17.3680i			0.858792i	0.903116	+	0.429396i	$0.141274\pi$
$409$			17.3680i			0.858792i	−0.903116	+	0.429396i	$0.858726\pi$
$410$		0			0
$411$	−14.0352	+	2.27809i	−0.692304	+	0.112370i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.0389864	+	0.0675265i	0.00191377	+	0.00331474i
$416$		0			0
$417$	−6.31495	+	1.02500i	−0.309244	+	0.0501943i
$418$		0			0
$419$	−18.0242	−	31.2189i	−0.880542	−	1.52514i	−0.850740	−	0.525587i	$-0.823846\pi$
$419$	−18.0242	−	31.2189i	−0.880542	−	1.52514i	−0.0298018	−	0.999556i	$-0.509488\pi$
$420$		0			0
$421$	4.22463	−	7.31727i	0.205896	−	0.356622i	−0.744522	−	0.667598i	$-0.767323\pi$
$421$	4.22463	−	7.31727i	0.205896	−	0.356622i	0.950418	+	0.310976i	$0.100656\pi$
$422$		0			0
$423$	11.9565	+	10.6010i	0.581347	+	0.515439i
$424$		0			0
$425$	−6.14057			−0.297861
$426$		0			0
$427$		0			0
$428$		0			0
$429$	23.6362	−	19.2906i	1.14117	−	0.931358i
$430$		0			0
$431$	26.6040	+	15.3598i	1.28147	+	0.739856i	0.977117	−	0.212704i	$-0.0682270\pi$
$431$	26.6040	+	15.3598i	1.28147	+	0.739856i	0.304351	+	0.952560i	$0.401560\pi$
$432$		0			0
$433$			9.85040i			0.473380i	0.971585	+	0.236690i	$0.0760626\pi$
$433$			9.85040i			0.473380i	−0.971585	+	0.236690i	$0.923937\pi$
$434$		0			0
$435$	0.0261736	−	0.00424832i	0.00125493	−	0.000203691i
$436$		0			0
$437$	−18.3644			−0.878488
$438$		0			0
$439$			9.51745i			0.454243i	0.973866	+	0.227121i	$0.0729314\pi$
$439$			9.51745i			0.454243i	−0.973866	+	0.227121i	$0.927069\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			19.1399i			0.909364i	0.890654	+	0.454682i	$0.150247\pi$
$443$			19.1399i			0.909364i	−0.890654	+	0.454682i	$0.849753\pi$
$444$		0			0
$445$	1.21489			0.0575911
$446$		0			0
$447$	25.8489	+	31.6720i	1.22261	+	1.49803i
$448$		0			0
$449$		−	34.8874i		−	1.64644i	−0.567724	−	0.823219i	$-0.692176\pi$
$449$		−	34.8874i		−	1.64644i	0.567724	−	0.823219i	$-0.307824\pi$
$450$		0			0
$451$	12.3877	+	7.15203i	0.583313	+	0.336776i
$452$		0			0
$453$	1.21654	+	7.49503i	0.0571580	+	0.352147i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	32.4540			1.51813			0.759067	−	0.651013i	$-0.225656\pi$
$457$	32.4540			1.51813			0.759067	+	0.651013i	$0.225656\pi$
$458$		0			0
$459$	6.39249	+	0.261408i	0.298376	+	0.0122015i
$460$		0			0
$461$	−14.1696	+	24.5425i	−0.659946	+	1.14306i	0.320683	+	0.947186i	$0.396087\pi$
$461$	−14.1696	+	24.5425i	−0.659946	+	1.14306i	−0.980629	+	0.195873i	$0.937246\pi$
$462$		0			0
$463$	2.11604	+	3.66508i	0.0983405	+	0.170331i	0.910998	−	0.412411i	$-0.135313\pi$
$463$	2.11604	+	3.66508i	0.0983405	+	0.170331i	−0.812657	+	0.582742i	$0.801980\pi$
$464$		0			0
$465$	0.845739	+	1.03626i	0.0392202	+	0.0480554i
$466$		0			0
$467$	−5.61042	−	9.71752i	−0.259619	−	0.449673i	0.706521	−	0.707692i	$-0.250264\pi$
$467$	−5.61042	−	9.71752i	−0.259619	−	0.449673i	−0.966140	+	0.258019i	$0.916930\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−8.66788	+	22.8417i	−0.399395	+	1.05249i
$472$		0			0
$473$		−	32.4793i		−	1.49340i
$474$		0			0
$475$	16.9056	+	9.76047i	0.775684	+	0.447841i
$476$		0			0
$477$	2.72751	+	8.18066i	0.124884	+	0.374567i
$478$		0			0
$479$	−17.8043	−	30.8379i	−0.813498	−	1.40902i	−0.910401	−	0.413726i	$-0.864227\pi$
$479$	−17.8043	−	30.8379i	−0.813498	−	1.40902i	0.0969034	−	0.995294i	$-0.469106\pi$
$480$		0			0
$481$	−18.4030	−	10.6250i	−0.839107	−	0.484459i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.666542	+	0.384828i	−0.0302661	+	0.0174741i
$486$		0			0
$487$	12.3856	−	21.4525i	0.561244	−	0.972104i	−0.436144	−	0.899877i	$-0.643656\pi$
$487$	12.3856	−	21.4525i	0.561244	−	0.972104i	0.997388	−	0.0722269i	$-0.0230106\pi$
$488$		0			0
$489$	3.77592	+	23.2632i	0.170753	+	1.05200i
$490$		0			0
$491$	−14.4482	+	8.34166i	−0.652037	+	0.376454i	−0.789236	−	0.614090i	$-0.789523\pi$
$491$	−14.4482	+	8.34166i	−0.652037	+	0.376454i	0.137199	+	0.990543i	$0.456190\pi$
$492$		0			0
$493$	0.144332	−	0.0833299i	0.00650037	−	0.00375299i
$494$		0			0
$495$	−1.26576	+	1.42760i	−0.0568915	+	0.0641661i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−8.58644	+	14.8722i	−0.384382	+	0.665769i	−0.991683	−	0.128702i	$-0.958919\pi$
$499$	−8.58644	+	14.8722i	−0.384382	+	0.665769i	0.607301	+	0.794472i	$0.292252\pi$
$500$		0			0
$501$	4.71396	+	29.0424i	0.210604	+	1.29752i
$502$		0			0
$503$	38.7122			1.72609			0.863045	−	0.505127i	$-0.168554\pi$
$503$	38.7122			1.72609			0.863045	+	0.505127i	$0.168554\pi$
$504$		0			0
$505$	−1.84301			−0.0820131
$506$		0			0
$507$	4.27680	−	3.49049i	0.189939	−	0.155018i
$508$		0			0
$509$	−14.4933	+	25.1032i	−0.642406	+	1.11268i	0.342488	+	0.939522i	$0.388730\pi$
$509$	−14.4933	+	25.1032i	−0.642406	+	1.11268i	−0.984894	+	0.173158i	$0.944603\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−17.1837	−	10.8806i	−0.758679	−	0.480390i
$514$		0			0
$515$	−1.73816	+	1.00352i	−0.0765923	+	0.0442206i
$516$		0			0
$517$	−25.9382	+	14.9754i	−1.14076	+	0.658618i
$518$		0			0
$519$	2.86850	+	1.08853i	0.125913	+	0.0477811i
$520$		0			0
$521$	−3.43678	+	5.95267i	−0.150568	+	0.260791i	−0.931436	−	0.363904i	$-0.881444\pi$
$521$	−3.43678	+	5.95267i	−0.150568	+	0.260791i	0.780868	+	0.624696i	$0.214777\pi$
$522$		0			0
$523$	−16.8198	+	9.71091i	−0.735478	+	0.424628i	−0.820423	−	0.571757i	$-0.806262\pi$
$523$	−16.8198	+	9.71091i	−0.735478	+	0.424628i	0.0849449	+	0.996386i	$0.472929\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.28063	+	4.20348i	0.317149	+	0.183106i
$528$		0			0
$529$	−0.493834	−	0.855346i	−0.0214711	−	0.0371890i
$530$		0			0
$531$	−25.6929	−	22.7801i	−1.11498	−	0.988571i
$532$		0			0
$533$	−6.90107	−	3.98434i	−0.298919	−	0.172581i
$534$		0			0
$535$			1.47152i			0.0636192i
$536$		0			0
$537$	9.02418	+	11.0571i	0.389422	+	0.477148i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.62684	−	16.6742i	−0.413890	−	0.716879i	0.581421	−	0.813603i	$-0.302497\pi$
$541$	−9.62684	−	16.6742i	−0.413890	−	0.716879i	−0.995311	+	0.0967242i	$0.969164\pi$
$542$		0			0
$543$	0.574562	−	1.51409i	0.0246568	−	0.0649759i
$544$		0			0
$545$	0.0775765	+	0.134366i	0.00332301	+	0.00575563i
$546$		0			0
$547$	−9.03080	+	15.6418i	−0.386129	+	0.668795i	−0.991925	−	0.126825i	$-0.959521\pi$
$547$	−9.03080	+	15.6418i	−0.386129	+	0.668795i	0.605796	+	0.795620i	$0.292855\pi$
$548$		0			0
$549$	−0.0768651	+	0.0866937i	−0.00328052	+	0.00370000i
$550$		0			0
$551$	−0.529813			−0.0225708
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.24245	+	0.471482i	0.0527392	+	0.0200133i
$556$		0			0
$557$	−3.79413	−	2.19054i	−0.160763	−	0.0928163i	0.417460	−	0.908695i	$-0.362920\pi$
$557$	−3.79413	−	2.19054i	−0.160763	−	0.0928163i	−0.578223	+	0.815879i	$0.696254\pi$
$558$		0			0
$559$			18.0939i			0.765291i
$560$		0			0
$561$	−4.25455	+	11.2116i	−0.179627	+	0.473355i
$562$		0			0
$563$	43.8972			1.85005			0.925024	−	0.379909i	$-0.124045\pi$
$563$	43.8972			1.85005			0.925024	+	0.379909i	$0.124045\pi$
$564$		0			0
$565$			1.01269i			0.0426043i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			4.58113i			0.192051i	0.995379	+	0.0960254i	$0.0306130\pi$
$569$			4.58113i			0.192051i	−0.995379	+	0.0960254i	$0.969387\pi$
$570$		0			0
$571$	3.16869			0.132606			0.0663029	−	0.997800i	$-0.478880\pi$
$571$	3.16869			0.132606			0.0663029	+	0.997800i	$0.478880\pi$
$572$		0			0
$573$	6.93328	−	18.2707i	0.289642	−	0.763268i
$574$		0			0
$575$		−	23.3986i		−	0.975790i
$576$		0			0
$577$	−10.4992	−	6.06171i	−0.437087	−	0.252352i	0.265274	−	0.964173i	$-0.414538\pi$
$577$	−10.4992	−	6.06171i	−0.437087	−	0.252352i	−0.702361	+	0.711821i	$0.747871\pi$
$578$		0			0
$579$	−33.9884	−	12.8978i	−1.41251	−	0.536014i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−16.1632			−0.669409
$584$		0			0
$585$	0.705142	−	0.795306i	0.0291540	−	0.0328819i
$586$		0			0
$587$	−3.40737	+	5.90173i	−0.140637	+	0.243591i	−0.927737	−	0.373235i	$-0.878248\pi$
$587$	−3.40737	+	5.90173i	−0.140637	+	0.243591i	0.787100	+	0.616826i	$0.211582\pi$
$588$		0			0
$589$	−13.3629	−	23.1452i	−0.550609	−	0.953682i
$590$		0			0
$591$	−10.6228	+	27.9933i	−0.436963	+	1.15149i
$592$		0			0
$593$	−15.0992	−	26.1526i	−0.620050	−	1.07396i	−0.989476	−	0.144697i	$-0.953779\pi$
$593$	−15.0992	−	26.1526i	−0.620050	−	1.07396i	0.369426	−	0.929260i	$-0.379554\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.69299	+	6.97546i	0.232999	+	0.285487i
$598$		0			0
$599$			17.6120i			0.719607i	0.933028	+	0.359803i	$0.117156\pi$
$599$			17.6120i			0.719607i	−0.933028	+	0.359803i	$0.882844\pi$
$600$		0			0
$601$	−27.0004	−	15.5887i	−1.10137	−	0.635875i	−0.164788	−	0.986329i	$-0.552694\pi$
$601$	−27.0004	−	15.5887i	−1.10137	−	0.635875i	−0.936580	+	0.350454i	$0.886027\pi$
$602$		0			0
$603$	−23.5472	−	20.8776i	−0.958916	−	0.850203i
$604$		0			0
$605$	−1.16599	−	2.01956i	−0.0474044	−	0.0821069i
$606$		0			0
$607$	−0.765446	−	0.441931i	−0.0310685	−	0.0179374i	0.484385	−	0.874855i	$-0.339043\pi$
$607$	−0.765446	−	0.441931i	−0.0310685	−	0.0179374i	−0.515454	+	0.856917i	$0.672377\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.4499	−	8.34268i	0.584582	−	0.337509i
$612$		0			0
$613$	0.112197	−	0.194331i	0.00453159	−	0.00784895i	−0.863751	−	0.503919i	$-0.831891\pi$
$613$	0.112197	−	0.194331i	0.00453159	−	0.00784895i	0.868282	+	0.496070i	$0.165224\pi$
$614$		0			0
$615$	0.465915	+	0.176804i	0.0187875	+	0.00712942i
$616$		0			0
$617$	−41.3032	+	23.8464i	−1.66280	+	0.960020i	−0.691436	+	0.722438i	$0.743022\pi$
$617$	−41.3032	+	23.8464i	−1.66280	+	0.960020i	−0.971367	+	0.237583i	$0.923645\pi$
$618$		0			0
$619$	10.1722	−	5.87292i	0.408855	−	0.236053i	−0.281442	−	0.959578i	$-0.590813\pi$
$619$	10.1722	−	5.87292i	0.408855	−	0.236053i	0.690298	+	0.723525i	$0.257480\pi$
$620$		0			0
$621$	−0.996096	+	24.3586i	−0.0399719	+	0.977476i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.4041	+	21.4846i	−0.496166	+	0.859384i
$626$		0			0
$627$	29.5342	−	24.1042i	1.17948	−	0.962627i
$628$		0			0
$629$	8.35244			0.333034
$630$		0			0
$631$	−17.4415			−0.694335			−0.347168	−	0.937803i	$-0.612857\pi$
$631$	−17.4415			−0.694335			−0.347168	+	0.937803i	$0.612857\pi$
$632$		0			0
$633$	−7.02991	−	43.3109i	−0.279414	−	1.72145i
$634$		0			0
$635$	−0.408297	+	0.707190i	−0.0162028	+	0.0280640i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	24.8111	−	27.9837i	0.981513	−	1.10702i
$640$		0			0
$641$	−27.9439	+	16.1334i	−1.10372	+	0.637231i	−0.937195	−	0.348806i	$-0.886587\pi$
$641$	−27.9439	+	16.1334i	−1.10372	+	0.637231i	−0.166522	+	0.986038i	$0.553254\pi$
$642$		0			0
$643$	23.4858	−	13.5595i	0.926191	−	0.534736i	0.0405858	−	0.999176i	$-0.487078\pi$
$643$	23.4858	−	13.5595i	0.926191	−	0.534736i	0.885605	+	0.464440i	$0.153744\pi$
$644$		0			0
$645$	−0.181290	−	1.11692i	−0.00713827	−	0.0439785i
$646$		0			0
$647$	−20.2588	+	35.0893i	−0.796456	+	1.37950i	0.125454	+	0.992099i	$0.459961\pi$
$647$	−20.2588	+	35.0893i	−0.796456	+	1.37950i	−0.921910	+	0.387403i	$0.873372\pi$
$648$		0			0
$649$	55.7375	−	32.1800i	2.18789	−	1.26318i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.9550	−	10.3663i	−0.702633	−	0.405665i	0.105695	−	0.994399i	$-0.466293\pi$
$653$	−17.9550	−	10.3663i	−0.702633	−	0.405665i	−0.808327	+	0.588734i	$0.799627\pi$
$654$		0			0
$655$	0.471209	+	0.816157i	0.0184116	+	0.0318899i
$656$		0			0
$657$	−12.4653	−	37.3872i	−0.486316	−	1.45862i
$658$		0			0
$659$	15.2785	+	8.82104i	0.595165	+	0.343619i	0.767137	−	0.641483i	$-0.221681\pi$
$659$	15.2785	+	8.82104i	0.595165	+	0.343619i	−0.171972	+	0.985102i	$0.555014\pi$
$660$		0			0
$661$		−	4.63072i		−	0.180114i	−0.995937	−	0.0900571i	$-0.971295\pi$
$661$		−	4.63072i		−	0.180114i	0.995937	−	0.0900571i	$-0.0287049\pi$
$662$		0			0
$663$	2.37017	−	6.24590i	0.0920498	−	0.242571i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.317528	+	0.549975i	0.0122947	+	0.0212951i
$668$		0			0
$669$	−29.0860	−	35.6382i	−1.12453	−	1.37785i
$670$		0			0
$671$	−0.108583	−	0.188071i	−0.00419179	−	0.00726039i
$672$		0			0
$673$	7.90990	−	13.7004i	0.304904	−	0.528110i	−0.672336	−	0.740246i	$-0.734709\pi$
$673$	7.90990	−	13.7004i	0.304904	−	0.528110i	0.977240	+	0.212137i	$0.0680422\pi$
$674$		0			0
$675$	13.8633	−	21.8943i	0.533599	−	0.842711i
$676$		0			0
$677$	−12.2672			−0.471468			−0.235734	−	0.971818i	$-0.575749\pi$
$677$	−12.2672			−0.471468			−0.235734	+	0.971818i	$0.575749\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.639535	−	3.94014i	−0.0245070	−	0.150987i
$682$		0			0
$683$	−6.56676	−	3.79132i	−0.251270	−	0.145071i	0.369076	−	0.929399i	$-0.379674\pi$
$683$	−6.56676	−	3.79132i	−0.251270	−	0.145071i	−0.620346	+	0.784329i	$0.713008\pi$
$684$		0			0
$685$		−	0.928484i		−	0.0354756i
$686$		0			0
$687$	−1.67382	−	2.05089i	−0.0638602	−	0.0782461i
$688$		0			0
$689$	9.00435			0.343039
$690$		0			0
$691$			28.9241i			1.10032i	0.835058	+	0.550162i	$0.185434\pi$
$691$			28.9241i			1.10032i	−0.835058	+	0.550162i	$0.814566\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	0.417760i		−	0.0158465i
$696$		0			0
$697$	3.13213			0.118638
$698$		0			0
$699$	−3.17323	+	0.515056i	−0.120023	+	0.0194812i
$700$		0			0
$701$			14.8034i			0.559118i	0.960128	+	0.279559i	$0.0901883\pi$
$701$			14.8034i			0.559118i	−0.960128	+	0.279559i	$0.909812\pi$
$702$		0			0
$703$	−22.9952	−	13.2763i	−0.867279	−	0.500724i
$704$		0			0
$705$	−0.808389	+	0.659763i	−0.0304457	+	0.0248481i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.85894			−0.332704			−0.166352	−	0.986066i	$-0.553199\pi$
$709$	−8.85894			−0.332704			−0.166352	+	0.986066i	$0.553199\pi$
$710$		0			0
$711$	25.1941	+	22.3379i	0.944854	+	0.837735i
$712$		0			0
$713$	−16.0173	+	27.7429i	−0.599854	+	1.03898i
$714$		0			0
$715$	0.996111	+	1.72531i	0.0372524	+	0.0645231i
$716$		0			0
$717$	−52.3180	+	8.49189i	−1.95385	+	0.317135i
$718$		0			0
$719$	−3.59102	−	6.21983i	−0.133923	−	0.231961i	0.791263	−	0.611476i	$-0.209424\pi$
$719$	−3.59102	−	6.21983i	−0.133923	−	0.231961i	−0.925185	+	0.379516i	$0.876091\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−40.5454	+	6.58104i	−1.50790	+	0.244752i
$724$		0			0
$725$		−	0.675052i		−	0.0250708i
$726$		0			0
$727$	9.90439	+	5.71830i	0.367333	+	0.212080i	0.672293	−	0.740285i	$-0.265310\pi$
$727$	9.90439	+	5.71830i	0.367333	+	0.212080i	−0.304959	+	0.952365i	$0.598643\pi$
$728$		0			0
$729$	−15.3641	+	22.2023i	−0.569041	+	0.822309i
$730$		0			0
$731$	−3.55596	−	6.15910i	−0.131522	−	0.227803i
$732$		0			0
$733$	11.5803	+	6.68589i	0.427728	+	0.246949i	0.698378	−	0.715729i	$-0.253905\pi$
$733$	11.5803	+	6.68589i	0.427728	+	0.246949i	−0.270650	+	0.962678i	$0.587239\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	51.0826	−	29.4926i	1.88165	−	1.08637i
$738$		0			0
$739$	−8.75603	+	15.1659i	−0.322096	+	0.557886i	−0.980920	−	0.194410i	$-0.937721\pi$
$739$	−8.75603	+	15.1659i	−0.322096	+	0.557886i	0.658824	+	0.752297i	$0.271054\pi$
$740$		0			0
$741$	−16.4532	+	13.4282i	−0.604424	+	0.493298i
$742$		0			0
$743$	7.36210	−	4.25051i	0.270089	−	0.155936i	−0.358839	−	0.933399i	$-0.616827\pi$
$743$	7.36210	−	4.25051i	0.270089	−	0.155936i	0.628928	+	0.777463i	$0.283494\pi$
$744$		0			0
$745$	−2.31188	+	1.33476i	−0.0847008	+	0.0489020i
$746$		0			0
$747$	−1.96203	+	0.654159i	−0.0717869	+	0.0239344i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−11.3608	+	19.6774i	−0.414560	+	0.718038i	−0.995382	−	0.0959918i	$-0.969398\pi$
$751$	−11.3608	+	19.6774i	−0.414560	+	0.718038i	0.580822	+	0.814030i	$0.302731\pi$
$752$		0			0
$753$	−23.5708	−	8.94457i	−0.858969	−	0.325958i
$754$		0			0
$755$	−0.495827			−0.0180450
$756$		0			0
$757$	2.31506			0.0841425			0.0420712	−	0.999115i	$-0.486604\pi$
$757$	2.31506			0.0841425			0.0420712	+	0.999115i	$0.486604\pi$
$758$		0			0
$759$	−42.7219	−	16.2119i	−1.55071	−	0.588456i
$760$		0			0
$761$	13.5656	−	23.4963i	0.491752	−	0.851739i	−0.508203	−	0.861237i	$-0.669690\pi$
$761$	13.5656	−	23.4963i	0.491752	−	0.851739i	0.999955	+	0.00949790i	$0.00302332\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.0837278	+	0.409299i	−0.00302718	+	0.0147983i
$766$		0			0
$767$	−31.0509	+	17.9272i	−1.12118	+	0.647315i
$768$		0			0
$769$	19.1716	−	11.0687i	0.691345	−	0.399148i	−0.112771	−	0.993621i	$-0.535973\pi$
$769$	19.1716	−	11.0687i	0.691345	−	0.399148i	0.804116	+	0.594473i	$0.202639\pi$
$770$		0			0
$771$	24.7858	−	20.2288i	0.892640	−	0.728523i
$772$		0			0
$773$	24.2570	−	42.0143i	0.872462	−	1.51115i	0.0130206	−	0.999915i	$-0.495855\pi$
$773$	24.2570	−	42.0143i	0.872462	−	1.51115i	0.859442	−	0.511234i	$-0.170811\pi$
$774$		0			0
$775$	29.4901	−	17.0261i	1.05931	−	0.611595i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.62310	−	4.97855i	−0.308954	−	0.178375i
$780$		0			0
$781$	35.0492	+	60.7070i	1.25416	+	2.17227i
$782$		0			0
$783$	−0.0287374	+	0.702746i	−0.00102699	+	0.0251141i
$784$		0			0
$785$	−1.38160	−	0.797668i	−0.0493115	−	0.0284700i
$786$		0			0
$787$			4.33003i			0.154349i	0.997018	+	0.0771744i	$0.0245898\pi$
$787$			4.33003i			0.154349i	−0.997018	+	0.0771744i	$0.975410\pi$
$788$		0			0
$789$	40.2511	−	6.53327i	1.43298	−	0.232591i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.0604905	+	0.104773i	0.00214808	+	0.00372059i
$794$		0			0
$795$	−0.555828	+	0.0902180i	−0.0197132	+	0.00319970i
$796$		0			0
$797$	−0.401963	−	0.696221i	−0.0142383	−	0.0246614i	0.858818	−	0.512280i	$-0.171199\pi$
$797$	−0.401963	−	0.696221i	−0.0142383	−	0.0246614i	−0.873057	+	0.487619i	$0.837866\pi$
$798$		0			0
$799$	−3.27914	+	5.67963i	−0.116008	+	0.200931i
$800$		0			0
$801$	−6.45821	+	31.5707i	−0.228190	+	1.11550i
$802$		0			0
$803$	73.8688			2.60677
$804$		0			0
$805$		0			0
$806$		0			0
$807$	40.6317	−	33.1614i	1.43031	−	1.16734i
$808$		0			0
$809$	2.89142	+	1.66936i	0.101657	+	0.0586916i	0.549966	−	0.835187i	$-0.314640\pi$
$809$	2.89142	+	1.66936i	0.101657	+	0.0586916i	−0.448310	+	0.893878i	$0.647974\pi$
$810$		0			0
$811$			23.9391i			0.840616i	0.907382	+	0.420308i	$0.138078\pi$
$811$			23.9391i			0.840616i	−0.907382	+	0.420308i	$0.861922\pi$
$812$		0			0
$813$	49.1819	−	7.98286i	1.72489	−	0.279971i
$814$		0			0
$815$	−1.53896			−0.0539074
$816$		0			0
$817$			22.6089i			0.790985i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			20.2527i			0.706823i	0.935468	+	0.353411i	$0.114978\pi$
$821$			20.2527i			0.706823i	−0.935468	+	0.353411i	$0.885022\pi$
$822$		0			0
$823$	−27.3727			−0.954153			−0.477076	−	0.878862i	$-0.658303\pi$
$823$	−27.3727			−0.954153			−0.477076	+	0.878862i	$0.658303\pi$
$824$		0			0
$825$	30.7119	+	37.6304i	1.06925	+	1.31012i
$826$		0			0
$827$		−	0.732736i		−	0.0254797i	−0.999919	−	0.0127399i	$-0.995945\pi$
$827$		−	0.732736i		−	0.0254797i	0.999919	−	0.0127399i	$-0.00405533\pi$
$828$		0			0
$829$	24.2088	+	13.9770i	0.840806	+	0.485440i	0.857538	−	0.514420i	$-0.171993\pi$
$829$	24.2088	+	13.9770i	0.840806	+	0.485440i	−0.0167319	+	0.999860i	$0.505326\pi$
$830$		0			0
$831$	−1.38808	−	8.55190i	−0.0481520	−	0.296662i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.92128			−0.0664885
$836$		0			0
$837$	−31.4247	+	16.4692i	−1.08620	+	0.569258i
$838$		0			0
$839$	5.23496	−	9.06722i	0.180731	−	0.313035i	−0.761399	−	0.648284i	$-0.775487\pi$
$839$	5.23496	−	9.06722i	0.180731	−	0.313035i	0.942130	+	0.335249i	$0.108820\pi$
$840$		0			0
$841$	−14.4908	−	25.0989i	−0.499684	−	0.865478i
$842$		0			0
$843$	−14.4620	−	17.7199i	−0.498099	−	0.610307i
$844$		0			0
$845$	0.180239	+	0.312183i	0.00620040	+	0.0107394i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−6.97426	+	18.3786i	−0.239356	+	0.630753i
$850$		0			0
$851$			31.8270i			1.09101i
$852$		0			0
$853$	5.60649	+	3.23691i	0.191963	+	0.110830i	0.592901	−	0.805275i	$-0.297983\pi$
$853$	5.60649	+	3.23691i	0.191963	+	0.110830i	−0.400938	+	0.916105i	$0.631316\pi$
$854$		0			0
$855$	0.881095	−	0.993759i	0.0301328	−	0.0339858i
$856$		0			0
$857$	−15.3518	−	26.5901i	−0.524407	−	0.908299i	−0.999596	−	0.0284155i	$-0.990954\pi$
$857$	−15.3518	−	26.5901i	−0.524407	−	0.908299i	0.475190	−	0.879883i	$-0.342379\pi$
$858$		0			0
$859$	20.2979	+	11.7190i	0.692556	+	0.399848i	0.804569	−	0.593859i	$-0.202396\pi$
$859$	20.2979	+	11.7190i	0.692556	+	0.399848i	−0.112013	+	0.993707i	$0.535730\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.6023	−	18.2456i	1.07575	−	0.621086i	0.146006	−	0.989284i	$-0.453358\pi$
$863$	31.6023	−	18.2456i	1.07575	−	0.621086i	0.929748	+	0.368197i	$0.120025\pi$
$864$		0			0
$865$	−0.100172	+	0.173504i	−0.00340597	+	0.00589931i
$866$		0			0
$867$	−4.29684	−	26.4726i	−0.145928	−	0.899057i
$868$		0			0
$869$	−54.6554	+	31.5553i	−1.85406	+	1.07044i
$870$		0			0
$871$	−28.4577	+	16.4301i	−0.964252	+	0.556711i
$872$		0			0
$873$	−6.45708	−	19.3668i	−0.218539	−	0.655468i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.8083	+	37.7731i	−0.736415	+	1.27551i	0.217685	+	0.976019i	$0.430150\pi$
$877$	−21.8083	+	37.7731i	−0.736415	+	1.27551i	−0.954100	+	0.299489i	$0.903184\pi$
$878$		0			0
$879$	2.56749	+	15.8181i	0.0865992	+	0.533533i
$880$		0			0
$881$	18.3722			0.618974			0.309487	−	0.950904i	$-0.399843\pi$
$881$	18.3722			0.618974			0.309487	+	0.950904i	$0.399843\pi$
$882$		0			0
$883$	−38.9500			−1.31077			−0.655385	−	0.755295i	$-0.727494\pi$
$883$	−38.9500			−1.31077			−0.655385	+	0.755295i	$0.727494\pi$
$884$		0			0
$885$	1.73711	−	1.41774i	0.0583924	−	0.0476567i
$886$		0			0
$887$	19.7267	−	34.1676i	0.662357	−	1.14724i	−0.317637	−	0.948212i	$-0.602889\pi$
$887$	19.7267	−	34.1676i	0.662357	−	1.14724i	0.979995	−	0.199024i	$-0.0637772\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−30.3699	−	40.4816i	−1.01743	−	1.35619i
$892$		0			0
$893$	18.0556	−	10.4244i	0.604209	−	0.348840i
$894$		0			0
$895$	−0.807106	+	0.465983i	−0.0269786	+	0.0155761i
$896$		0			0
$897$	23.8000	+	9.03154i	0.794659	+	0.301554i
$898$		0			0
$899$	−0.462101	+	0.800383i	−0.0154119	+	0.0266943i
$900$		0			0
$901$	−3.06505	+	1.76961i	−0.102112	+	0.0589542i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0915812	+	0.0528744i	0.00304426	+	0.00175761i
$906$		0			0
$907$	−10.3062	−	17.8509i	−0.342213	−	0.592731i	0.642630	−	0.766177i	$-0.277843\pi$
$907$	−10.3062	−	17.8509i	−0.342213	−	0.592731i	−0.984843	+	0.173446i	$0.944510\pi$
$908$		0			0
$909$	9.79729	−	47.8936i	0.324955	−	1.58853i
$910$		0			0
$911$	4.40092	+	2.54087i	0.145809	+	0.0841829i	0.571130	−	0.820860i	$-0.306505\pi$
$911$	4.40092	+	2.54087i	0.145809	+	0.0841829i	−0.425321	+	0.905043i	$0.639839\pi$
$912$		0			0
$913$		−	3.87653i		−	0.128294i
$914$		0			0
$915$	−0.00478376	−	0.00586141i	−0.000158146	−	0.000193772i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	11.7798	+	20.4032i	0.388579	+	0.673038i	0.992259	−	0.124189i	$-0.0396328\pi$
$919$	11.7798	+	20.4032i	0.388579	+	0.673038i	−0.603680	+	0.797227i	$0.706300\pi$
$920$		0			0
$921$	−15.4812	+	40.7963i	−0.510124	+	1.34428i
$922$		0			0
$923$	−19.5256	−	33.8193i	−0.642693	−	1.11318i
$924$		0			0
$925$	16.9157	−	29.2988i	0.556185	−	0.963340i
$926$		0			0
$927$	−16.8383	−	50.5033i	−0.553042	−	1.65875i
$928$		0			0
$929$	−29.0420			−0.952836			−0.476418	−	0.879219i	$-0.658065\pi$
$929$	−29.0420			−0.952836			−0.476418	+	0.879219i	$0.658065\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−37.5476	−	14.2484i	−1.22925	−	0.466472i
$934$		0			0
$935$	−0.678145	−	0.391527i	−0.0221777	−	0.0128043i
$936$		0			0
$937$		−	48.5954i		−	1.58754i	−0.608217	−	0.793771i	$-0.708115\pi$
$937$		−	48.5954i		−	1.58754i	0.608217	−	0.793771i	$-0.291885\pi$
$938$		0			0
$939$	−14.6545	+	38.6176i	−0.478230	+	1.26024i
$940$		0			0
$941$	10.6218			0.346261			0.173130	−	0.984899i	$-0.444612\pi$
$941$	10.6218			0.346261			0.173130	+	0.984899i	$0.444612\pi$
$942$		0			0
$943$			11.9350i			0.388657i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			16.9282i			0.550091i	0.961431	+	0.275046i	$0.0886930\pi$
$947$			16.9282i			0.550091i	−0.961431	+	0.275046i	$0.911307\pi$
$948$		0			0
$949$	−41.1517			−1.33584
$950$		0			0
$951$	6.35717	−	16.7525i	0.206145	−	0.543237i
$952$		0			0
$953$			20.2937i			0.657378i	0.944438	+	0.328689i	$0.106607\pi$
$953$			20.2937i			0.657378i	−0.944438	+	0.328689i	$0.893393\pi$
$954$		0			0
$955$	1.10512	+	0.638040i	0.0357608	+	0.0206465i
$956$		0			0
$957$	−1.23253	−	0.467715i	−0.0398420	−	0.0151191i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.6203			−0.503880
$962$		0			0
$963$	−38.2396	−	7.82244i	−1.23225	−	0.252074i
$964$		0			0
$965$	1.18693	−	2.05582i	0.0382085	−	0.0661791i
$966$		0			0
$967$	−9.30930	−	16.1242i	−0.299367	−	0.518519i	0.676624	−	0.736328i	$-0.263442\pi$
$967$	−9.30930	−	16.1242i	−0.299367	−	0.518519i	−0.975991	+	0.217810i	$0.930109\pi$
$968$		0			0
$969$	2.96160	−	7.80444i	0.0951403	−	0.250715i
$970$		0			0
$971$	−0.819339	−	1.41914i	−0.0262938	−	0.0455423i	0.852579	−	0.522598i	$-0.175037\pi$
$971$	−0.819339	−	1.41914i	−0.0262938	−	0.0455423i	−0.878873	+	0.477056i	$0.841704\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−17.1093	−	20.9636i	−0.547937	−	0.671372i
$976$		0			0
$977$			13.0308i			0.416893i	0.978034	+	0.208447i	$0.0668408\pi$
$977$			13.0308i			0.416893i	−0.978034	+	0.208447i	$0.933159\pi$
$978$		0			0
$979$	−52.3077	−	30.1999i	−1.67176	−	0.965192i
$980$		0			0
$981$	−3.90411	+	1.30167i	−0.124649	+	0.0415590i
$982$		0			0
$983$	−18.6364	−	32.2792i	−0.594410	−	1.02955i	−0.993630	−	0.112693i	$-0.964052\pi$
$983$	−18.6364	−	32.2792i	−0.594410	−	1.02955i	0.399220	−	0.916855i	$-0.369281\pi$
$984$		0			0
$985$	−1.69320	−	0.977569i	−0.0539498	−	0.0311479i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	23.4693	−	13.5500i	0.746279	−	0.430864i
$990$		0			0
$991$	−12.2935	+	21.2929i	−0.390515	+	0.676392i	−0.992517	−	0.122103i	$-0.961036\pi$
$991$	−12.2935	+	21.2929i	−0.390515	+	0.676392i	0.602003	+	0.798494i	$0.294370\pi$
$992$		0			0
$993$	11.8045	+	4.47954i	0.374605	+	0.142154i
$994$		0			0
$995$	−0.509171	+	0.293970i	−0.0161418	+	0.00931947i
$996$		0			0
$997$	−47.2434	+	27.2760i	−1.49621	+	0.863840i	−0.999991	−	0.00435443i	$-0.998614\pi$
$997$	−47.2434	+	27.2760i	−1.49621	+	0.863840i	−0.496224	+	0.868194i	$0.665281\pi$
$998$		0			0
$999$	−18.8570	+	29.7807i	−0.596607	+	0.942221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.c.1109.3		48
3.2	odd	2		5292.2.w.c.521.12		48
7.2	even	3		1764.2.bm.c.1685.20		48
7.3	odd	6		1764.2.x.c.1469.10	yes	48
7.4	even	3		1764.2.x.c.1469.15	yes	48
7.5	odd	6		1764.2.bm.c.1685.5		48
7.6	odd	2	inner	1764.2.w.c.1109.22		48
9.4	even	3		5292.2.bm.c.2285.12		48
9.5	odd	6		1764.2.bm.c.1697.5		48
21.2	odd	6		5292.2.bm.c.4625.13		48
21.5	even	6		5292.2.bm.c.4625.12		48
21.11	odd	6		5292.2.x.c.4409.12		48
21.17	even	6		5292.2.x.c.4409.13		48
21.20	even	2		5292.2.w.c.521.13		48
63.4	even	3		5292.2.x.c.881.13		48
63.5	even	6	inner	1764.2.w.c.509.3		48
63.13	odd	6		5292.2.bm.c.2285.13		48
63.23	odd	6	inner	1764.2.w.c.509.22		48
63.31	odd	6		5292.2.x.c.881.12		48
63.32	odd	6		1764.2.x.c.293.10	✓	48
63.40	odd	6		5292.2.w.c.1097.12		48
63.41	even	6		1764.2.bm.c.1697.20		48
63.58	even	3		5292.2.w.c.1097.13		48
63.59	even	6		1764.2.x.c.293.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.w.c.509.3		48	63.5	even	6	inner
1764.2.w.c.509.22		48	63.23	odd	6	inner
1764.2.w.c.1109.3		48	1.1	even	1	trivial
1764.2.w.c.1109.22		48	7.6	odd	2	inner
1764.2.x.c.293.10	✓	48	63.32	odd	6
1764.2.x.c.293.15	yes	48	63.59	even	6
1764.2.x.c.1469.10	yes	48	7.3	odd	6
1764.2.x.c.1469.15	yes	48	7.4	even	3
1764.2.bm.c.1685.5		48	7.5	odd	6
1764.2.bm.c.1685.20		48	7.2	even	3
1764.2.bm.c.1697.5		48	9.5	odd	6
1764.2.bm.c.1697.20		48	63.41	even	6
5292.2.w.c.521.12		48	3.2	odd	2
5292.2.w.c.521.13		48	21.20	even	2
5292.2.w.c.1097.12		48	63.40	odd	6
5292.2.w.c.1097.13		48	63.58	even	3
5292.2.x.c.881.12		48	63.31	odd	6
5292.2.x.c.881.13		48	63.4	even	3
5292.2.x.c.4409.12		48	21.11	odd	6
5292.2.x.c.4409.13		48	21.17	even	6
5292.2.bm.c.2285.12		48	9.4	even	3
5292.2.bm.c.2285.13		48	63.13	odd	6
5292.2.bm.c.4625.12		48	21.5	even	6
5292.2.bm.c.4625.13		48	21.2	odd	6

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61937 - 0.614514i) q^{3} +(0.0565510 - 0.0979493i) q^{5} +(2.24475 + 1.99026i) q^{9} +O(q^{10})\)	\(q+(-1.61937 - 0.614514i) q^{3} +(0.0565510 - 0.0979493i) q^{5} +(2.24475 + 1.99026i) q^{9} +(-4.86969 + 2.81151i) q^{11} +(2.71286 - 1.56627i) q^{13} +(-0.151769 + 0.123865i) q^{15} +(-0.615632 + 1.06631i) q^{17} +(3.38980 - 1.95710i) q^{19} +(-4.06316 - 2.34587i) q^{23} +(2.49360 + 4.31905i) q^{25} +(-2.41204 - 4.60240i) q^{27} +(-0.117222 - 0.0676783i) q^{29} -6.82790i q^{31} +(9.61356 - 1.56040i) q^{33} +(-3.39182 - 5.87480i) q^{37} +(-5.35563 + 0.869287i) q^{39} +(-1.27192 - 2.20303i) q^{41} +(-2.88806 + 5.00226i) q^{43} +(0.321887 - 0.107320i) q^{45} +5.32646 q^{47} +(1.65220 - 1.34843i) q^{51} +(2.48935 + 1.43723i) q^{53} +0.635976i q^{55} +(-6.69202 + 1.08620i) q^{57} -11.4458 q^{59} +0.0386207i q^{61} -0.354297i q^{65} -10.4899 q^{67} +(5.13821 + 6.29570i) q^{69} -12.4663i q^{71} +(-11.3768 - 6.56842i) q^{73} +(-1.38396 - 8.52651i) q^{75} +11.2236 q^{79} +(1.07776 + 8.93524i) q^{81} +(-0.344701 + 0.597040i) q^{83} +(0.0696293 + 0.120601i) q^{85} +(0.148237 + 0.181631i) q^{87} +(5.37075 + 9.30241i) q^{89} +(-4.19584 + 11.0569i) q^{93} -0.442705i q^{95} +(-5.89327 - 3.40248i) q^{97} +(-16.5268 - 3.38079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{9}+O(q^{10}) \) 48 * q - 8 * q^9	\( 48 q - 8 q^{9} + 24 q^{11} + 24 q^{15} - 48 q^{23} - 24 q^{25} + 56 q^{39} + 72 q^{51} - 48 q^{53} + 16 q^{57} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 48 q^{93} - 40 q^{99}+O(q^{100}) \) 48 * q - 8 * q^9 + 24 * q^11 + 24 * q^15 - 48 * q^23 - 24 * q^25 + 56 * q^39 + 72 * q^51 - 48 * q^53 + 16 * q^57 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 48 * q^93 - 40 * q^99

Introduction

L-functions

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