LMFDB - Embedded newform 1764.2.x.c.1469.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

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, 3]))

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

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

chi := DirichletCharacter("1764.293");

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.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
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			1469.23
Character	$\chi$	$=$	1764.1469
Dual form			1764.2.x.c.293.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72468 - 0.159612i) q^{3} +(-1.31387 - 2.27569i) q^{5} +(2.94905 - 0.550559i) q^{9} +O(q^{10})$	\(q+(1.72468 - 0.159612i) q^{3} +(-1.31387 - 2.27569i) q^{5} +(2.94905 - 0.550559i) q^{9} +(5.18523 + 2.99370i) q^{11} +(-2.54231 + 1.46780i) q^{13} +(-2.62923 - 3.71513i) q^{15} +0.0334645 q^{17} +8.16799i q^{19} +(7.04605 - 4.06804i) q^{23} +(-0.952507 + 1.64979i) q^{25} +(4.99829 - 1.42024i) q^{27} +(-0.949006 - 0.547909i) q^{29} +(7.01724 - 4.05141i) q^{31} +(9.42070 + 4.33554i) q^{33} +0.211796 q^{37} +(-4.15039 + 2.93728i) q^{39} +(-2.23087 - 3.86399i) q^{41} +(3.78001 - 6.54717i) q^{43} +(-5.12757 - 5.98775i) q^{45} +(-3.53805 + 6.12809i) q^{47} +(0.0577156 - 0.00534133i) q^{51} +1.83833i q^{53} -15.7333i q^{55} +(1.30371 + 14.0872i) q^{57} +(2.36844 + 4.10225i) q^{59} +(-10.3773 - 5.99136i) q^{61} +(6.68053 + 3.85700i) q^{65} +(-3.81147 - 6.60166i) q^{67} +(11.5029 - 8.14070i) q^{69} -3.52461i q^{71} -2.59112i q^{73} +(-1.37944 + 2.99739i) q^{75} +(3.58952 - 6.21723i) q^{79} +(8.39377 - 3.24725i) q^{81} +(-0.932743 + 1.61556i) q^{83} +(-0.0439680 - 0.0761548i) q^{85} +(-1.72418 - 0.793495i) q^{87} +7.12250 q^{89} +(11.4559 - 8.10742i) q^{93} +(18.5878 - 10.7317i) q^{95} +(-13.2520 - 7.65104i) q^{97} +(16.9397 + 5.97378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{9}+O(q^{10}) $ 48 * q + 16 * q^9	$ 48 q + 16 q^{9} - 24 q^{11} + 24 q^{15} + 48 q^{23} - 24 q^{25} - 40 q^{39} - 24 q^{51} + 16 q^{57} - 72 q^{65} - 24 q^{79} + 96 q^{81} - 24 q^{85} - 96 q^{93} + 96 q^{95} - 40 q^{99}+O(q^{100}) $ 48 * q + 16 * q^9 - 24 * q^11 + 24 * q^15 + 48 * q^23 - 24 * q^25 - 40 * q^39 - 24 * q^51 + 16 * q^57 - 72 * q^65 - 24 * q^79 + 96 * q^81 - 24 * q^85 - 96 * q^93 + 96 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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			0
$2$		0			0
$3$	1.72468	−	0.159612i	0.995745	−	0.0921520i
$3$	1.72468	−	0.159612i	0.995745	−	0.0921520i
$4$		0			0
$5$	−1.31387	−	2.27569i	−0.587580	−	1.01772i	−0.994548	−	0.104277i	$-0.966747\pi$
$5$	−1.31387	−	2.27569i	−0.587580	−	1.01772i	0.406968	−	0.913442i	$-0.366586\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.94905	−	0.550559i	0.983016	−	0.183520i
$10$		0			0
$11$	5.18523	+	2.99370i	1.56341	+	0.902633i	0.996909	+	0.0785701i	$0.0250355\pi$
$11$	5.18523	+	2.99370i	1.56341	+	0.902633i	0.566498	+	0.824063i	$0.308298\pi$
$12$		0			0
$13$	−2.54231	+	1.46780i	−0.705110	+	0.407095i	−0.809248	−	0.587467i	$-0.800125\pi$
$13$	−2.54231	+	1.46780i	−0.705110	+	0.407095i	0.104138	+	0.994563i	$0.466792\pi$
$14$		0			0
$15$	−2.62923	−	3.71513i	−0.678865	−	0.959242i
$16$		0			0
$17$	0.0334645			0.00811633			0.00405817	−	0.999992i	$-0.498708\pi$
$17$	0.0334645			0.00811633			0.00405817	+	0.999992i	$0.498708\pi$
$18$		0			0
$19$			8.16799i			1.87387i	0.349509	+	0.936933i	$0.386348\pi$
$19$			8.16799i			1.87387i	−0.349509	+	0.936933i	$0.613652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.04605	−	4.06804i	1.46920	−	0.848244i	0.469799	−	0.882774i	$-0.344327\pi$
$23$	7.04605	−	4.06804i	1.46920	−	0.848244i	0.999404	+	0.0345292i	$0.0109932\pi$
$24$		0			0
$25$	−0.952507	+	1.64979i	−0.190501	+	0.329958i
$26$		0			0
$27$	4.99829	−	1.42024i	0.961922	−	0.273326i
$28$		0			0
$29$	−0.949006	−	0.547909i	−0.176226	−	0.101744i	0.409292	−	0.912403i	$-0.365776\pi$
$29$	−0.949006	−	0.547909i	−0.176226	−	0.101744i	−0.585518	+	0.810659i	$0.699109\pi$
$30$		0			0
$31$	7.01724	−	4.05141i	1.26033	−	0.727654i	0.287195	−	0.957872i	$-0.407277\pi$
$31$	7.01724	−	4.05141i	1.26033	−	0.727654i	0.973139	+	0.230218i	$0.0739439\pi$
$32$		0			0
$33$	9.42070	+	4.33554i	1.63993	+	0.754721i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.211796			0.0348191			0.0174095	−	0.999848i	$-0.494458\pi$
$37$	0.211796			0.0348191			0.0174095	+	0.999848i	$0.494458\pi$
$38$		0			0
$39$	−4.15039	+	2.93728i	−0.664595	+	0.470340i
$40$		0			0
$41$	−2.23087	−	3.86399i	−0.348404	−	0.603453i	0.637562	−	0.770399i	$-0.279943\pi$
$41$	−2.23087	−	3.86399i	−0.348404	−	0.603453i	−0.985966	+	0.166946i	$0.946610\pi$
$42$		0			0
$43$	3.78001	−	6.54717i	0.576446	−	0.998434i	−0.419437	−	0.907785i	$-0.637772\pi$
$43$	3.78001	−	6.54717i	0.576446	−	0.998434i	0.995883	−	0.0906496i	$-0.0288943\pi$
$44$		0			0
$45$	−5.12757	−	5.98775i	−0.764372	−	0.892602i
$46$		0			0
$47$	−3.53805	+	6.12809i	−0.516078	+	0.893873i	0.483748	+	0.875207i	$0.339275\pi$
$47$	−3.53805	+	6.12809i	−0.516078	+	0.893873i	−0.999826	+	0.0186658i	$0.994058\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.0577156	−	0.00534133i	0.00808180	−	0.000747936i
$52$		0			0
$53$			1.83833i			0.252514i	0.991998	+	0.126257i	$0.0402964\pi$
$53$			1.83833i			0.252514i	−0.991998	+	0.126257i	$0.959704\pi$
$54$		0			0
$55$		−	15.7333i		−	2.12148i
$56$		0			0
$57$	1.30371	+	14.0872i	0.172680	+	1.86589i
$58$		0			0
$59$	2.36844	+	4.10225i	0.308344	+	0.534068i	0.978000	−	0.208603i	$-0.0668918\pi$
$59$	2.36844	+	4.10225i	0.308344	+	0.534068i	−0.669656	+	0.742671i	$0.733558\pi$
$60$		0			0
$61$	−10.3773	−	5.99136i	−1.32868	−	0.767115i	−0.343586	−	0.939121i	$-0.611642\pi$
$61$	−10.3773	−	5.99136i	−1.32868	−	0.767115i	−0.985096	+	0.172006i	$0.944975\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.68053	+	3.85700i	0.828618	+	0.478403i
$66$		0			0
$67$	−3.81147	−	6.60166i	−0.465646	−	0.806522i	0.533585	−	0.845747i	$-0.320844\pi$
$67$	−3.81147	−	6.60166i	−0.465646	−	0.806522i	−0.999230	+	0.0392248i	$0.987511\pi$
$68$		0			0
$69$	11.5029	−	8.14070i	1.38478	−	0.980025i
$70$		0			0
$71$		−	3.52461i		−	0.418294i	−0.977884	−	0.209147i	$-0.932931\pi$
$71$		−	3.52461i		−	0.418294i	0.977884	−	0.209147i	$-0.0670687\pi$
$72$		0			0
$73$		−	2.59112i		−	0.303268i	−0.988437	−	0.151634i	$-0.951546\pi$
$73$		−	2.59112i		−	0.303268i	0.988437	−	0.151634i	$-0.0484535\pi$
$74$		0			0
$75$	−1.37944	+	2.99739i	−0.159285	+	0.346109i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.58952	−	6.21723i	0.403852	−	0.699493i	−0.590335	−	0.807159i	$-0.701004\pi$
$79$	3.58952	−	6.21723i	0.403852	−	0.699493i	0.994187	+	0.107666i	$0.0343376\pi$
$80$		0			0
$81$	8.39377	−	3.24725i	0.932641	−	0.360806i
$82$		0			0
$83$	−0.932743	+	1.61556i	−0.102382	+	0.177331i	−0.912666	−	0.408707i	$-0.865980\pi$
$83$	−0.932743	+	1.61556i	−0.102382	+	0.177331i	0.810284	+	0.586038i	$0.199313\pi$
$84$		0			0
$85$	−0.0439680	−	0.0761548i	−0.00476900	−	0.00826014i
$86$		0			0
$87$	−1.72418	−	0.793495i	−0.184852	−	0.0850716i
$88$		0			0
$89$	7.12250			0.754983			0.377492	−	0.926013i	$-0.376787\pi$
$89$	7.12250			0.754983			0.377492	+	0.926013i	$0.376787\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	11.4559	−	8.10742i	1.18792	−	0.840700i
$94$		0			0
$95$	18.5878	−	10.7317i	1.90707	−	1.10105i
$96$		0			0
$97$	−13.2520	−	7.65104i	−1.34554	−	0.776845i	−0.357922	−	0.933752i	$-0.616514\pi$
$97$	−13.2520	−	7.65104i	−1.34554	−	0.776845i	−0.987613	+	0.156907i	$0.949848\pi$
$98$		0			0
$99$	16.9397	+	5.97378i	1.70250	+	0.600387i
$100$		0			0
$101$	3.38758	−	5.86746i	0.337077	−	0.583834i	−0.646805	−	0.762655i	$-0.723895\pi$
$101$	3.38758	−	5.86746i	0.337077	−	0.583834i	0.983881	+	0.178822i	$0.0572286\pi$
$102$		0			0
$103$	4.22811	−	2.44110i	0.416608	−	0.240529i	−0.277017	−	0.960865i	$-0.589346\pi$
$103$	4.22811	−	2.44110i	0.416608	−	0.240529i	0.693625	+	0.720336i	$0.256012\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			14.8077i			1.43151i	0.698351	+	0.715756i	$0.253918\pi$
$107$			14.8077i			1.43151i	−0.698351	+	0.715756i	$0.746082\pi$
$108$		0			0
$109$	−11.6429			−1.11519			−0.557593	−	0.830114i	$-0.688275\pi$
$109$	−11.6429			−1.11519			−0.557593	+	0.830114i	$0.688275\pi$
$110$		0			0
$111$	0.365281	−	0.0338052i	0.0346709	−	0.00320865i
$112$		0			0
$113$	−1.24947	+	0.721383i	−0.117540	+	0.0678620i	−0.557618	−	0.830098i	$-0.688284\pi$
$113$	−1.24947	+	0.721383i	−0.117540	+	0.0678620i	0.440077	+	0.897960i	$0.354951\pi$
$114$		0			0
$115$	−18.5152	−	10.6897i	−1.72655	−	0.996824i
$116$		0			0
$117$	−6.68928	+	5.72831i	−0.618424	+	0.529583i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	12.4244	+	21.5197i	1.12949	+	1.95634i
$122$		0			0
$123$	−4.46428	−	6.30807i	−0.402531	−	0.568780i
$124$		0			0
$125$	−8.13282			−0.727421
$126$		0			0
$127$	8.25511			0.732523			0.366261	−	0.930512i	$-0.380638\pi$
$127$	8.25511			0.732523			0.366261	+	0.930512i	$0.380638\pi$
$128$		0			0
$129$	5.47431	−	11.8951i	0.481986	−	1.04731i
$130$		0			0
$131$	6.64453	+	11.5087i	0.580536	+	1.00552i	0.995416	+	0.0956411i	$0.0304901\pi$
$131$	6.64453	+	11.5087i	0.580536	+	1.00552i	−0.414880	+	0.909876i	$0.636177\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−9.79913	−	9.50854i	−0.843375	−	0.818365i
$136$		0			0
$137$	5.79362	+	3.34495i	0.494982	+	0.285778i	0.726639	−	0.687020i	$-0.241081\pi$
$137$	5.79362	+	3.34495i	0.494982	+	0.285778i	−0.231657	+	0.972798i	$0.574415\pi$
$138$		0			0
$139$	5.65156	−	3.26293i	0.479359	−	0.276758i	−0.240790	−	0.970577i	$-0.577407\pi$
$139$	5.65156	−	3.26293i	0.479359	−	0.276758i	0.720149	+	0.693819i	$0.244073\pi$
$140$		0			0
$141$	−5.12390	+	11.1337i	−0.431510	+	0.937627i
$142$		0			0
$143$	−17.5766			−1.46983
$144$		0			0
$145$			2.87952i			0.239131i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.68597	−	2.70544i	0.383889	−	0.221639i	−0.295620	−	0.955306i	$-0.595526\pi$
$149$	4.68597	−	2.70544i	0.383889	−	0.221639i	0.679509	+	0.733667i	$0.262193\pi$
$150$		0			0
$151$	−10.0358	+	17.3825i	−0.816699	+	1.41456i	0.0914023	+	0.995814i	$0.470865\pi$
$151$	−10.0358	+	17.3825i	−0.816699	+	1.41456i	−0.908101	+	0.418750i	$0.862468\pi$
$152$		0			0
$153$	0.0986884	−	0.0184242i	0.00797848	−	0.00148951i
$154$		0			0
$155$	−18.4395	−	10.6460i	−1.48110	−	0.855111i
$156$		0			0
$157$	−1.13796	+	0.657000i	−0.0908188	+	0.0524343i	−0.544722	−	0.838617i	$-0.683365\pi$
$157$	−1.13796	+	0.657000i	−0.0908188	+	0.0524343i	0.453903	+	0.891051i	$0.350031\pi$
$158$		0			0
$159$	0.293420	+	3.17053i	0.0232697	+	0.251440i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−16.6057			−1.30066			−0.650328	−	0.759654i	$-0.725368\pi$
$163$	−16.6057			−1.30066			−0.650328	+	0.759654i	$0.725368\pi$
$164$		0			0
$165$	−2.51122	−	27.1349i	−0.195498	−	2.11245i
$166$		0			0
$167$	6.18145	+	10.7066i	0.478335	+	0.828501i	0.999691	−	0.0248384i	$-0.00790711\pi$
$167$	6.18145	+	10.7066i	0.478335	+	0.828501i	−0.521356	+	0.853339i	$0.674574\pi$
$168$		0			0
$169$	−2.19111	+	3.79511i	−0.168547	+	0.291931i
$170$		0			0
$171$	4.49696	+	24.0878i	0.343891	+	1.84204i
$172$		0			0
$173$	−5.18456	+	8.97991i	−0.394174	+	0.682730i	−0.992995	−	0.118153i	$-0.962303\pi$
$173$	−5.18456	+	8.97991i	−0.394174	+	0.682730i	0.598821	+	0.800883i	$0.295636\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.73957	+	6.69705i	0.356248	+	0.503381i
$178$		0			0
$179$			22.6248i			1.69106i	0.533930	+	0.845528i	$0.320714\pi$
$179$			22.6248i			1.69106i	−0.533930	+	0.845528i	$0.679286\pi$
$180$		0			0
$181$		−	6.15765i		−	0.457695i	−0.973462	−	0.228847i	$-0.926504\pi$
$181$		−	6.15765i		−	0.457695i	0.973462	−	0.228847i	$-0.0734956\pi$
$182$		0			0
$183$	−18.8539	−	8.67684i	−1.39372	−	0.641410i
$184$		0			0
$185$	−0.278273	−	0.481982i	−0.0204590	−	0.0354360i
$186$		0			0
$187$	0.173521	+	0.100182i	0.0126891	+	0.00732607i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.9110	+	11.4956i	1.44071	+	0.831794i	0.997897	−	0.0648193i	$-0.0206471\pi$
$191$	19.9110	+	11.4956i	1.44071	+	0.831794i	0.442813	+	0.896614i	$0.353980\pi$
$192$		0			0
$193$	8.61512	+	14.9218i	0.620130	+	1.07410i	0.989461	+	0.144799i	$0.0462535\pi$
$193$	8.61512	+	14.9218i	0.620130	+	1.07410i	−0.369331	+	0.929298i	$0.620413\pi$
$194$		0			0
$195$	12.1374	+	5.58581i	0.869177	+	0.400008i
$196$		0			0
$197$			4.31094i			0.307141i	0.988138	+	0.153571i	$0.0490773\pi$
$197$			4.31094i			0.307141i	−0.988138	+	0.153571i	$0.950923\pi$
$198$		0			0
$199$			7.34313i			0.520541i	0.965536	+	0.260270i	$0.0838117\pi$
$199$			7.34313i			0.520541i	−0.965536	+	0.260270i	$0.916188\pi$
$200$		0			0
$201$	−7.62728	−	10.7774i	−0.537987	−	0.760180i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.86216	+	10.1536i	−0.409431	+	0.709155i
$206$		0			0
$207$	18.5394	−	15.8761i	1.28858	−	1.10347i
$208$		0			0
$209$	−24.4525	+	42.3529i	−1.69141	+	2.92961i
$210$		0			0
$211$	−6.79668	−	11.7722i	−0.467903	−	0.810431i	0.531425	−	0.847106i	$-0.321657\pi$
$211$	−6.79668	−	11.7722i	−0.467903	−	0.810431i	−0.999327	+	0.0366744i	$0.988324\pi$
$212$		0			0
$213$	−0.562569	−	6.07882i	−0.0385466	−	0.416514i
$214$		0			0
$215$	−19.8658			−1.35483
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.413574	−	4.46886i	−0.0279467	−	0.301978i
$220$		0			0
$221$	−0.0850771	+	0.0491193i	−0.00572291	+	0.00330412i
$222$		0			0
$223$	−22.6248	−	13.0624i	−1.51507	−	0.874725i	−0.999844	−	0.0176705i	$-0.994375\pi$
$223$	−22.6248	−	13.0624i	−1.51507	−	0.874725i	−0.515225	−	0.857055i	$-0.672292\pi$
$224$		0			0
$225$	−1.90068	+	5.38972i	−0.126712	+	0.359315i
$226$		0			0
$227$	1.58102	−	2.73840i	0.104936	−	0.181754i	−0.808776	−	0.588117i	$-0.799870\pi$
$227$	1.58102	−	2.73840i	0.104936	−	0.181754i	0.913712	+	0.406362i	$0.133203\pi$
$228$		0			0
$229$	11.7934	−	6.80892i	0.779330	−	0.449946i	−0.0568630	−	0.998382i	$-0.518110\pi$
$229$	11.7934	−	6.80892i	0.779330	−	0.449946i	0.836193	+	0.548436i	$0.184777\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	26.9929i		−	1.76836i	−0.467143	−	0.884182i	$-0.654717\pi$
$233$		−	26.9929i		−	1.76836i	0.467143	−	0.884182i	$-0.345283\pi$
$234$		0			0
$235$	18.5942			1.21295
$236$		0			0
$237$	5.19843	−	11.2957i	0.337674	−	0.733732i
$238$		0			0
$239$	−7.46107	+	4.30765i	−0.482617	+	0.278639i	−0.721506	−	0.692408i	$-0.756550\pi$
$239$	−7.46107	+	4.30765i	−0.482617	+	0.278639i	0.238890	+	0.971047i	$0.423217\pi$
$240$		0			0
$241$	20.1317	+	11.6230i	1.29680	+	0.748706i	0.979849	−	0.199737i	$-0.0640089\pi$
$241$	20.1317	+	11.6230i	1.29680	+	0.748706i	0.316947	+	0.948443i	$0.397342\pi$
$242$		0			0
$243$	13.9583	−	6.94022i	0.895424	−	0.445215i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.9890	−	20.7656i	−0.762842	−	1.32128i
$248$		0			0
$249$	−1.35082	+	2.93520i	−0.0856049	+	0.186011i
$250$		0			0
$251$	9.09095			0.573816			0.286908	−	0.957958i	$-0.407373\pi$
$251$	9.09095			0.573816			0.286908	+	0.957958i	$0.407373\pi$
$252$		0			0
$253$	48.7139			3.06261
$254$		0			0
$255$	−0.0879859	−	0.124325i	−0.00550989	−	0.00778553i
$256$		0			0
$257$	−7.36958	−	12.7645i	−0.459702	−	0.796226i	0.539243	−	0.842150i	$-0.318710\pi$
$257$	−7.36958	−	12.7645i	−0.459702	−	0.796226i	−0.998945	+	0.0459235i	$0.985377\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.10032	−	1.09333i	−0.191905	−	0.0676751i
$262$		0			0
$263$	−24.1622	−	13.9501i	−1.48991	−	0.860198i	−0.489974	−	0.871737i	$-0.662994\pi$
$263$	−24.1622	−	13.9501i	−1.48991	−	0.860198i	−0.999933	+	0.0115386i	$0.996327\pi$
$264$		0			0
$265$	4.18347	−	2.41533i	0.256989	−	0.148372i
$266$		0			0
$267$	12.2840	−	1.13684i	0.751771	−	0.0695732i
$268$		0			0
$269$	13.1498			0.801755			0.400878	−	0.916132i	$-0.368705\pi$
$269$	13.1498			0.801755			0.400878	+	0.916132i	$0.368705\pi$
$270$		0			0
$271$		−	17.8090i		−	1.08182i	−0.841080	−	0.540911i	$-0.818080\pi$
$271$		−	17.8090i		−	1.08182i	0.841080	−	0.540911i	$-0.181920\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.87794	+	5.70303i	−0.595662	+	0.343906i
$276$		0			0
$277$	−8.89435	+	15.4055i	−0.534410	+	0.925625i	0.464782	+	0.885425i	$0.346133\pi$
$277$	−8.89435	+	15.4055i	−0.534410	+	0.925625i	−0.999192	+	0.0401999i	$0.987201\pi$
$278$		0			0
$279$	18.4637	−	15.8112i	1.10539	−	0.946592i
$280$		0			0
$281$	−18.3680	−	10.6048i	−1.09574	−	0.632628i	−0.160644	−	0.987012i	$-0.551357\pi$
$281$	−18.3680	−	10.6048i	−1.09574	−	0.632628i	−0.935100	+	0.354384i	$0.884691\pi$
$282$		0			0
$283$	−16.2504	+	9.38216i	−0.965985	+	0.557711i	−0.898010	−	0.439976i	$-0.854987\pi$
$283$	−16.2504	+	9.38216i	−0.965985	+	0.557711i	−0.0679748	+	0.997687i	$0.521654\pi$
$284$		0			0
$285$	30.3451	−	21.4756i	1.79749	−	1.27210i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.9989			−0.999934
$290$		0			0
$291$	−24.0766	−	11.0804i	−1.41140	−	0.649546i
$292$		0			0
$293$	6.40500	+	11.0938i	0.374184	+	0.648106i	0.990205	−	0.139624i	$-0.0445894\pi$
$293$	6.40500	+	11.0938i	0.374184	+	0.648106i	−0.616020	+	0.787730i	$0.711256\pi$
$294$		0			0
$295$	6.22364	−	10.7797i	0.362354	−	0.627616i
$296$		0			0
$297$	30.1691	+	7.59908i	1.75059	+	0.440943i
$298$		0			0
$299$	−11.9422	+	20.6844i	−0.690633	+	1.19621i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4.90597	−	10.6602i	0.281841	−	0.612412i
$304$		0			0
$305$			31.4875i			1.80297i
$306$		0			0
$307$		−	3.97281i		−	0.226740i	−0.993553	−	0.113370i	$-0.963835\pi$
$307$		−	3.97281i		−	0.226740i	0.993553	−	0.113370i	$-0.0361646\pi$
$308$		0			0
$309$	6.90252	−	4.88498i	0.392670	−	0.277897i
$310$		0			0
$311$	−0.293203	−	0.507843i	−0.0166260	−	0.0287971i	0.857593	−	0.514329i	$-0.171959\pi$
$311$	−0.293203	−	0.507843i	−0.0166260	−	0.0287971i	−0.874219	+	0.485532i	$0.838626\pi$
$312$		0			0
$313$	−0.860061	−	0.496556i	−0.0486135	−	0.0280670i	0.475496	−	0.879718i	$-0.342269\pi$
$313$	−0.860061	−	0.496556i	−0.0486135	−	0.0280670i	−0.524110	+	0.851651i	$0.675602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.6022	−	11.8947i	−1.15714	−	0.668073i	−0.206520	−	0.978442i	$-0.566214\pi$
$317$	−20.6022	−	11.8947i	−1.15714	−	0.668073i	−0.950616	+	0.310369i	$0.899547\pi$
$318$		0			0
$319$	−3.28054	−	5.68207i	−0.183675	−	0.318135i
$320$		0			0
$321$	2.36348	+	25.5385i	0.131917	+	1.42542i
$322$		0			0
$323$			0.273338i			0.0152089i
$324$		0			0
$325$		−	5.59237i		−	0.310209i
$326$		0			0
$327$	−20.0803	+	1.85834i	−1.11044	+	0.102767i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.5486	+	23.4668i	−0.744697	+	1.28985i	0.205640	+	0.978628i	$0.434072\pi$
$331$	−13.5486	+	23.4668i	−0.744697	+	1.28985i	−0.950336	+	0.311224i	$0.899261\pi$
$332$		0			0
$333$	0.624597	−	0.116606i	0.0342277	−	0.00638999i
$334$		0			0
$335$	−10.0156	+	17.3475i	−0.547208	+	0.947793i
$336$		0			0
$337$	0.618503	+	1.07128i	0.0336920	+	0.0583562i	0.882380	−	0.470538i	$-0.155940\pi$
$337$	0.618503	+	1.07128i	0.0336920	+	0.0583562i	−0.848688	+	0.528894i	$0.822607\pi$
$338$		0			0
$339$	−2.03980	+	1.44359i	−0.110787	+	0.0784048i
$340$		0			0
$341$	48.5147			2.62722
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−33.6390	−	15.4812i	−1.81106	−	0.833477i
$346$		0			0
$347$	11.6468	−	6.72430i	0.625234	−	0.360979i	−0.153670	−	0.988122i	$-0.549109\pi$
$347$	11.6468	−	6.72430i	0.625234	−	0.360979i	0.778904	+	0.627143i	$0.215776\pi$
$348$		0			0
$349$	12.4728	+	7.20115i	0.667652	+	0.385469i	0.795186	−	0.606365i	$-0.207373\pi$
$349$	12.4728	+	7.20115i	0.667652	+	0.385469i	−0.127535	+	0.991834i	$0.540706\pi$
$350$		0			0
$351$	−10.6226	+	10.9472i	−0.566991	+	0.584319i
$352$		0			0
$353$	3.77665	−	6.54134i	0.201011	−	0.348161i	−0.747844	−	0.663875i	$-0.768911\pi$
$353$	3.77665	−	6.54134i	0.201011	−	0.348161i	0.948854	+	0.315714i	$0.102244\pi$
$354$		0			0
$355$	−8.02091	+	4.63087i	−0.425706	+	0.245781i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			24.0506i			1.26934i	0.772782	+	0.634672i	$0.218865\pi$
$359$			24.0506i			1.26934i	−0.772782	+	0.634672i	$0.781135\pi$
$360$		0			0
$361$	−47.7161			−2.51137
$362$		0			0
$363$	24.8630	+	35.1316i	1.30497	+	1.84393i
$364$		0			0
$365$	−5.89659	+	3.40440i	−0.308642	+	0.178194i
$366$		0			0
$367$	6.28058	+	3.62610i	0.327844	+	0.189281i	0.654883	−	0.755730i	$-0.272718\pi$
$367$	6.28058	+	3.62610i	0.327844	+	0.189281i	−0.327040	+	0.945011i	$0.606051\pi$
$368$		0			0
$369$	−8.70631	−	10.1669i	−0.453232	−	0.529265i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.15315	−	10.6576i	−0.318598	−	0.551828i	0.661598	−	0.749859i	$-0.269879\pi$
$373$	−6.15315	−	10.6576i	−0.318598	−	0.551828i	−0.980196	+	0.198031i	$0.936545\pi$
$374$		0			0
$375$	−14.0265	+	1.29809i	−0.724326	+	0.0670333i
$376$		0			0
$377$	3.21689			0.165678
$378$		0			0
$379$	−20.4289			−1.04936			−0.524680	−	0.851299i	$-0.675815\pi$
$379$	−20.4289			−1.04936			−0.524680	+	0.851299i	$0.675815\pi$
$380$		0			0
$381$	14.2374	−	1.31761i	0.729406	−	0.0675034i
$382$		0			0
$383$	−17.6460	−	30.5638i	−0.901668	−	1.56174i	−0.825328	−	0.564653i	$-0.809010\pi$
$383$	−17.6460	−	30.5638i	−0.901668	−	1.56174i	−0.0763399	−	0.997082i	$-0.524323\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.54283	−	21.3890i	0.383424	−	1.08727i
$388$		0			0
$389$	19.2835	+	11.1334i	0.977714	+	0.564484i	0.901579	−	0.432614i	$-0.142409\pi$
$389$	19.2835	+	11.1334i	0.977714	+	0.564484i	0.0761350	+	0.997098i	$0.475742\pi$
$390$		0			0
$391$	0.235792	−	0.136135i	0.0119245	−	0.00688463i
$392$		0			0
$393$	13.2966	+	18.7882i	0.670726	+	0.947741i
$394$		0			0
$395$	−18.8646			−0.949183
$396$		0			0
$397$		−	19.4634i		−	0.976840i	−0.872609	−	0.488420i	$-0.837573\pi$
$397$		−	19.4634i		−	0.976840i	0.872609	−	0.488420i	$-0.162427\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.45051	−	4.30155i	0.372061	−	0.214809i	−0.302298	−	0.953214i	$-0.597754\pi$
$401$	7.45051	−	4.30155i	0.372061	−	0.214809i	0.674358	+	0.738404i	$0.264420\pi$
$402$		0			0
$403$	−11.8933	+	20.5999i	−0.592449	+	1.02615i
$404$		0			0
$405$	−18.4181	−	14.8351i	−0.915200	−	0.737164i
$406$		0			0
$407$	1.09821	+	0.634053i	0.0544364	+	0.0314289i
$408$		0			0
$409$	−16.7571	+	9.67472i	−0.828585	+	0.478384i	−0.853368	−	0.521309i	$-0.825444\pi$
$409$	−16.7571	+	9.67472i	−0.828585	+	0.478384i	0.0247826	+	0.999693i	$0.492111\pi$
$410$		0			0
$411$	10.5260	+	4.84423i	0.519211	+	0.238948i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.90201			0.240630
$416$		0			0
$417$	9.22634	−	6.52957i	0.451816	−	0.319754i
$418$		0			0
$419$	−8.81222	−	15.2632i	−0.430505	−	0.745657i	0.566412	−	0.824122i	$-0.308331\pi$
$419$	−8.81222	−	15.2632i	−0.430505	−	0.745657i	−0.996917	+	0.0784657i	$0.974998\pi$
$420$		0			0
$421$	−5.77040	+	9.99463i	−0.281232	+	0.487109i	−0.971689	−	0.236266i	$-0.924076\pi$
$421$	−5.77040	+	9.99463i	−0.281232	+	0.487109i	0.690456	+	0.723374i	$0.257410\pi$
$422$		0			0
$423$	−7.06001	+	20.0199i	−0.343270	+	0.973402i
$424$		0			0
$425$	−0.0318752	+	0.0552094i	−0.00154617	+	0.00267805i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−30.3141	+	2.80544i	−1.46358	+	0.135448i
$430$		0			0
$431$		−	11.4413i		−	0.551110i	−0.961285	−	0.275555i	$-0.911138\pi$
$431$		−	11.4413i		−	0.551110i	0.961285	−	0.275555i	$-0.0888616\pi$
$432$		0			0
$433$			6.25525i			0.300608i	0.988640	+	0.150304i	$0.0480253\pi$
$433$			6.25525i			0.300608i	−0.988640	+	0.150304i	$0.951975\pi$
$434$		0			0
$435$	0.459606	+	4.96626i	0.0220364	+	0.238114i
$436$		0			0
$437$	33.2277	+	57.5521i	1.58950	+	2.75309i
$438$		0			0
$439$	−13.2543	−	7.65239i	−0.632595	−	0.365229i	0.149162	−	0.988813i	$-0.452343\pi$
$439$	−13.2543	−	7.65239i	−0.632595	−	0.365229i	−0.781756	+	0.623584i	$0.785676\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.4838	−	11.2490i	−0.925705	−	0.534456i	−0.0402540	−	0.999189i	$-0.512817\pi$
$443$	−19.4838	−	11.2490i	−0.925705	−	0.534456i	−0.885450	+	0.464734i	$0.846150\pi$
$444$		0			0
$445$	−9.35803	−	16.2086i	−0.443613	−	0.768361i
$446$		0			0
$447$	7.64997	−	5.41396i	0.361831	−	0.256072i
$448$		0			0
$449$		−	25.9709i		−	1.22564i	−0.790222	−	0.612821i	$-0.790035\pi$
$449$		−	25.9709i		−	1.22564i	0.790222	−	0.612821i	$-0.209965\pi$
$450$		0			0
$451$		−	26.7142i		−	1.25792i
$452$		0			0
$453$	−14.5340	+	31.5810i	−0.682869	+	1.48381i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.0222019	+	0.0384547i	−0.00103856	+	0.00179884i	−0.866544	−	0.499100i	$-0.833664\pi$
$457$	−0.0222019	+	0.0384547i	−0.00103856	+	0.00179884i	0.865506	+	0.500899i	$0.166997\pi$
$458$		0			0
$459$	0.167265	−	0.0475277i	0.00780727	−	0.00221840i
$460$		0			0
$461$	−1.46783	+	2.54236i	−0.0683636	+	0.118409i	−0.898181	−	0.439626i	$-0.855111\pi$
$461$	−1.46783	+	2.54236i	−0.0683636	+	0.118409i	0.829817	+	0.558035i	$0.188444\pi$
$462$		0			0
$463$	−19.2017	−	33.2583i	−0.892378	−	1.54564i	−0.837017	−	0.547177i	$-0.815702\pi$
$463$	−19.2017	−	33.2583i	−0.892378	−	1.54564i	−0.0553609	−	0.998466i	$-0.517631\pi$
$464$		0			0
$465$	−33.5015	−	15.4179i	−1.55359	−	0.714986i
$466$		0			0
$467$	17.2783			0.799542			0.399771	−	0.916615i	$-0.369090\pi$
$467$	17.2783			0.799542			0.399771	+	0.916615i	$0.369090\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.85775	+	1.31475i	−0.0856005	+	0.0605803i
$472$		0			0
$473$	39.2005	−	22.6324i	1.80244	−	1.04064i
$474$		0			0
$475$	−13.4755	−	7.78007i	−0.618297	−	0.356974i
$476$		0			0
$477$	1.01211	+	5.42133i	0.0463413	+	0.248226i
$478$		0			0
$479$	−18.4571	+	31.9686i	−0.843326	+	1.46068i	0.0437419	+	0.999043i	$0.486072\pi$
$479$	−18.4571	+	31.9686i	−0.843326	+	1.46068i	−0.887067	+	0.461640i	$0.847261\pi$
$480$		0			0
$481$	−0.538451	+	0.310875i	−0.0245513	+	0.0141747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			40.2099i			1.82584i
$486$		0			0
$487$	4.06398			0.184157			0.0920783	−	0.995752i	$-0.470649\pi$
$487$	4.06398			0.184157			0.0920783	+	0.995752i	$0.470649\pi$
$488$		0			0
$489$	−28.6395	+	2.65046i	−1.29512	+	0.119858i
$490$		0			0
$491$	4.30460	−	2.48526i	0.194264	−	0.112158i	−0.399713	−	0.916640i	$-0.630890\pi$
$491$	4.30460	−	2.48526i	0.194264	−	0.112158i	0.593977	+	0.804482i	$0.297557\pi$
$492$		0			0
$493$	−0.0317580	−	0.0183355i	−0.00143031	−	0.000825789i
$494$		0			0
$495$	−8.66211	−	46.3983i	−0.389333	−	2.08545i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.60335	−	7.97323i	−0.206074	−	0.356931i	0.744400	−	0.667734i	$-0.232735\pi$
$499$	−4.60335	−	7.97323i	−0.206074	−	0.356931i	−0.950474	+	0.310803i	$0.899402\pi$
$500$		0			0
$501$	12.3699	+	17.4788i	0.552648	+	0.780896i
$502$		0			0
$503$	−1.16946			−0.0521436			−0.0260718	−	0.999660i	$-0.508300\pi$
$503$	−1.16946			−0.0521436			−0.0260718	+	0.999660i	$0.508300\pi$
$504$		0			0
$505$	−17.8033			−0.792238
$506$		0			0
$507$	−3.17321	+	6.89508i	−0.140927	+	0.306221i
$508$		0			0
$509$	−4.86206	−	8.42133i	−0.215507	−	0.373269i	0.737922	−	0.674886i	$-0.235807\pi$
$509$	−4.86206	−	8.42133i	−0.215507	−	0.373269i	−0.953429	+	0.301617i	$0.902474\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	11.6005	+	40.8260i	0.512176	+	1.80251i
$514$		0			0
$515$	−11.1104	−	6.41458i	−0.489582	−	0.282660i
$516$		0			0
$517$	−36.6912	+	21.1837i	−1.61368	+	0.931658i
$518$		0			0
$519$	−7.50840	+	16.3150i	−0.329582	+	0.716149i
$520$		0			0
$521$	−12.4663			−0.546160			−0.273080	−	0.961991i	$-0.588042\pi$
$521$	−12.4663			−0.546160			−0.273080	+	0.961991i	$0.588042\pi$
$522$		0			0
$523$		−	18.0390i		−	0.788791i	−0.918941	−	0.394395i	$-0.870954\pi$
$523$		−	18.0390i		−	0.788791i	0.918941	−	0.394395i	$-0.129046\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.234828	−	0.135578i	0.0102293	−	0.00590588i
$528$		0			0
$529$	21.5979	−	37.4086i	0.939037	−	1.62646i
$530$		0			0
$531$	9.24317	+	10.7938i	0.401119	+	0.468410i
$532$		0			0
$533$	11.3431	+	6.54897i	0.491326	+	0.283667i
$534$		0			0
$535$	33.6976	−	19.4553i	1.45688	−	0.841128i
$536$		0			0
$537$	3.61119	+	39.0206i	0.155834	+	1.68386i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	3.75569			0.161470			0.0807349	−	0.996736i	$-0.474273\pi$
$541$	3.75569			0.161470			0.0807349	+	0.996736i	$0.474273\pi$
$542$		0			0
$543$	−0.982834	−	10.6200i	−0.0421775	−	0.455747i
$544$		0			0
$545$	15.2972	+	26.4956i	0.655262	+	1.13495i
$546$		0			0
$547$	5.05062	−	8.74793i	0.215949	−	0.374034i	−0.737617	−	0.675219i	$-0.764049\pi$
$547$	5.05062	−	8.74793i	0.215949	−	0.374034i	0.953566	+	0.301185i	$0.0973822\pi$
$548$		0			0
$549$	−33.9019	−	11.9555i	−1.44690	−	0.510247i
$550$		0			0
$551$	4.47531	−	7.75147i	0.190655	−	0.330224i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.556861	−	0.786850i	−0.0236375	−	0.0333999i
$556$		0			0
$557$			18.2232i			0.772140i	0.922469	+	0.386070i	$0.126168\pi$
$557$			18.2232i			0.772140i	−0.922469	+	0.386070i	$0.873832\pi$
$558$		0			0
$559$			22.1933i			0.938674i
$560$		0			0
$561$	0.315259	+	0.145087i	0.0133102	+	0.00612557i
$562$		0			0
$563$	−8.34691	−	14.4573i	−0.351780	−	0.609301i	0.634781	−	0.772692i	$-0.281090\pi$
$563$	−8.34691	−	14.4573i	−0.351780	−	0.609301i	−0.986561	+	0.163391i	$0.947757\pi$
$564$		0			0
$565$	3.28329	+	1.89561i	0.138129	+	0.0797487i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.8711	+	12.6273i	0.916886	+	0.529365i	0.882640	−	0.470049i	$-0.155764\pi$
$569$	21.8711	+	12.6273i	0.916886	+	0.529365i	0.0342459	+	0.999413i	$0.489097\pi$
$570$		0			0
$571$	2.88981	+	5.00529i	0.120935	+	0.209465i	0.920137	−	0.391598i	$-0.128078\pi$
$571$	2.88981	+	5.00529i	0.120935	+	0.209465i	−0.799202	+	0.601063i	$0.794744\pi$
$572$		0			0
$573$	36.1750	+	16.6483i	1.51123	+	0.695491i
$574$		0			0
$575$			15.4993i			0.646367i
$576$		0			0
$577$			33.0867i			1.37742i	0.725039	+	0.688708i	$0.241822\pi$
$577$			33.0867i			1.37742i	−0.725039	+	0.688708i	$0.758178\pi$
$578$		0			0
$579$	17.2400	+	24.3603i	0.716471	+	1.01238i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−5.50340	+	9.53218i	−0.227928	+	0.394782i
$584$		0			0
$585$	21.8247	+	7.69647i	0.902341	+	0.318210i
$586$		0			0
$587$	−14.1186	+	24.4541i	−0.582737	+	1.00933i	0.412417	+	0.910995i	$0.364685\pi$
$587$	−14.1186	+	24.4541i	−0.582737	+	1.00933i	−0.995153	+	0.0983341i	$0.968649\pi$
$588$		0			0
$589$	33.0919	+	57.3168i	1.36353	+	2.36170i
$590$		0			0
$591$	0.688077	+	7.43499i	0.0283037	+	0.305835i
$592$		0			0
$593$	−18.5954			−0.763621			−0.381810	−	0.924241i	$-0.624699\pi$
$593$	−18.5954			−0.763621			−0.381810	+	0.924241i	$0.624699\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.17205	+	12.6646i	0.0479688	+	0.518326i
$598$		0			0
$599$	7.77276	−	4.48760i	0.317586	−	0.183358i	−0.332730	−	0.943022i	$-0.607970\pi$
$599$	7.77276	−	4.48760i	0.317586	−	0.183358i	0.650316	+	0.759664i	$0.274636\pi$
$600$		0			0
$601$	−4.71245	−	2.72073i	−0.192225	−	0.110981i	0.400799	−	0.916166i	$-0.368733\pi$
$601$	−4.71245	−	2.72073i	−0.192225	−	0.110981i	−0.593024	+	0.805185i	$0.702066\pi$
$602$		0			0
$603$	−14.8748	−	17.3702i	−0.605750	−	0.707369i
$604$		0			0
$605$	32.6482	−	56.5483i	1.32734	−	2.29901i
$606$		0			0
$607$	−32.0240	+	18.4890i	−1.29981	+	0.750447i	−0.980372	−	0.197159i	$-0.936829\pi$
$607$	−32.0240	+	18.4890i	−1.29981	+	0.750447i	−0.319441	+	0.947606i	$0.603495\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	20.7727i		−	0.840372i
$612$		0			0
$613$	−11.8688			−0.479375			−0.239688	−	0.970850i	$-0.577045\pi$
$613$	−11.8688			−0.479375			−0.239688	+	0.970850i	$0.577045\pi$
$614$		0			0
$615$	−8.48972	+	18.4473i	−0.342339	+	0.743867i
$616$		0			0
$617$	16.2845	−	9.40188i	0.655591	−	0.378506i	−0.135004	−	0.990845i	$-0.543105\pi$
$617$	16.2845	−	9.40188i	0.655591	−	0.378506i	0.790595	+	0.612339i	$0.209771\pi$
$618$		0			0
$619$	−10.2892	−	5.94048i	−0.413558	−	0.238768i	0.278759	−	0.960361i	$-0.410077\pi$
$619$	−10.2892	−	5.94048i	−0.413558	−	0.238768i	−0.692318	+	0.721593i	$0.743410\pi$
$620$		0			0
$621$	29.4406	−	30.3403i	1.18141	−	1.21752i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.4480	+	26.7567i	0.617920	+	1.07027i
$626$		0			0
$627$	−35.4127	+	76.9482i	−1.41425	+	3.07302i
$628$		0			0
$629$	0.00708765			0.000282603
$630$		0			0
$631$	−28.3350			−1.12800			−0.563998	−	0.825776i	$-0.690738\pi$
$631$	−28.3350			−1.12800			−0.563998	+	0.825776i	$0.690738\pi$
$632$		0			0
$633$	−13.6011	−	19.2184i	−0.540595	−	0.763865i
$634$		0			0
$635$	−10.8461	−	18.7861i	−0.430416	−	0.745502i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.94050	−	10.3942i	−0.0767652	−	0.411190i
$640$		0			0
$641$	−24.5634	−	14.1817i	−0.970195	−	0.560142i	−0.0708994	−	0.997483i	$-0.522587\pi$
$641$	−24.5634	−	14.1817i	−0.970195	−	0.560142i	−0.899296	+	0.437341i	$0.855920\pi$
$642$		0			0
$643$	16.0912	−	9.29024i	0.634573	−	0.366371i	−0.147948	−	0.988995i	$-0.547267\pi$
$643$	16.0912	−	9.29024i	0.634573	−	0.366371i	0.782521	+	0.622624i	$0.213933\pi$
$644$		0			0
$645$	−34.2621	+	3.17081i	−1.34907	+	0.124851i
$646$		0			0
$647$	−42.8964			−1.68643			−0.843216	−	0.537574i	$-0.819341\pi$
$647$	−42.8964			−1.68643			−0.843216	+	0.537574i	$0.819341\pi$
$648$		0			0
$649$			28.3615i			1.11329i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.18721	+	1.84014i	−0.124725	+	0.0720101i	−0.561065	−	0.827772i	$-0.689608\pi$
$653$	−3.18721	+	1.84014i	−0.124725	+	0.0720101i	0.436339	+	0.899782i	$0.356275\pi$
$654$		0			0
$655$	17.4601	−	30.2418i	0.682223	−	1.18164i
$656$		0			0
$657$	−1.42657	−	7.64135i	−0.0556557	−	0.298117i
$658$		0			0
$659$	−13.7955	−	7.96483i	−0.537396	−	0.310266i	0.206627	−	0.978420i	$-0.433751\pi$
$659$	−13.7955	−	7.96483i	−0.537396	−	0.310266i	−0.744023	+	0.668154i	$0.767085\pi$
$660$		0			0
$661$	1.14378	−	0.660360i	0.0444878	−	0.0256850i	−0.477591	−	0.878582i	$-0.658490\pi$
$661$	1.14378	−	0.660360i	0.0444878	−	0.0256850i	0.522079	+	0.852897i	$0.325157\pi$
$662$		0			0
$663$	−0.138891	+	0.0982944i	−0.00539407	+	0.00381744i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.91565			−0.345215
$668$		0			0
$669$	−41.1055	−	18.9173i	−1.58923	−	0.731387i
$670$		0			0
$671$	−35.8726	−	62.1332i	−1.38485	−	2.39863i
$672$		0			0
$673$	21.7987	−	37.7565i	0.840280	−	1.45541i	−0.0493788	−	0.998780i	$-0.515724\pi$
$673$	21.7987	−	37.7565i	0.840280	−	1.45541i	0.889658	−	0.456627i	$-0.150943\pi$
$674$		0			0
$675$	−2.41781	+	9.59893i	−0.0930614	+	0.369463i
$676$		0			0
$677$	−14.4677	+	25.0588i	−0.556039	+	0.963088i	0.441782	+	0.897122i	$0.354346\pi$
$677$	−14.4677	+	25.0588i	−0.556039	+	0.963088i	−0.997822	+	0.0659663i	$0.978987\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.28967	−	4.97522i	0.0877403	−	0.190651i
$682$		0			0
$683$		−	2.20265i		−	0.0842820i	−0.999112	−	0.0421410i	$-0.986582\pi$
$683$		−	2.20265i		−	0.0842820i	0.999112	−	0.0421410i	$-0.0134179\pi$
$684$		0			0
$685$		−	17.5793i		−	0.671670i
$686$		0			0
$687$	19.2531	−	13.6256i	0.734550	−	0.519848i
$688$		0			0
$689$	−2.69831	−	4.67361i	−0.102797	−	0.178050i
$690$		0			0
$691$	25.8896	+	14.9474i	0.984888	+	0.568625i	0.903742	−	0.428077i	$-0.140809\pi$
$691$	25.8896	+	14.9474i	0.984888	+	0.568625i	0.0811456	+	0.996702i	$0.474142\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.8508	−	8.57413i	−0.563324	−	0.325235i
$696$		0			0
$697$	−0.0746551	−	0.129306i	−0.00282776	−	0.00489783i
$698$		0			0
$699$	−4.30839	−	46.5541i	−0.162958	−	1.76084i
$700$		0			0
$701$			45.4119i			1.71518i	0.514332	+	0.857591i	$0.328040\pi$
$701$			45.4119i			1.71518i	−0.514332	+	0.857591i	$0.671960\pi$
$702$		0			0
$703$			1.72995i			0.0652463i
$704$		0			0
$705$	32.0690	−	2.96785i	1.20779	−	0.111776i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.92591	−	13.7281i	0.297664	−	0.515569i	−0.677937	−	0.735120i	$-0.737126\pi$
$709$	7.92591	−	13.7281i	0.297664	−	0.515569i	0.975601	+	0.219551i	$0.0704592\pi$
$710$		0			0
$711$	7.16271	−	20.3112i	0.268623	−	0.761728i
$712$		0			0
$713$	32.9626	−	57.0928i	1.23446	−	2.13814i
$714$		0			0
$715$	23.0934	+	39.9989i	0.863644	+	1.49588i
$716$		0			0
$717$	−12.1804	+	8.62020i	−0.454886	+	0.321927i
$718$		0			0
$719$	6.60308			0.246253			0.123127	−	0.992391i	$-0.460708\pi$
$719$	6.60308			0.246253			0.123127	+	0.992391i	$0.460708\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	36.5759	+	16.8328i	1.36027	+	0.626018i
$724$		0			0
$725$	1.80787	−	1.04377i	0.0671426	−	0.0387648i
$726$		0			0
$727$	31.2086	+	18.0183i	1.15746	+	0.668261i	0.950694	−	0.310129i	$-0.100372\pi$
$727$	31.2086	+	18.0183i	1.15746	+	0.668261i	0.206767	+	0.978390i	$0.433706\pi$
$728$		0			0
$729$	22.9658	−	14.1976i	0.850586	−	0.525836i
$730$		0			0
$731$	0.126496	−	0.219098i	0.00467863	−	0.00810362i
$732$		0			0
$733$	−26.0312	+	15.0291i	−0.961486	+	0.555114i	−0.896630	−	0.442781i	$-0.853992\pi$
$733$	−26.0312	+	15.0291i	−0.961486	+	0.555114i	−0.0648557	+	0.997895i	$0.520659\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	45.6416i		−	1.68123i
$738$		0			0
$739$	9.67151			0.355772			0.177886	−	0.984051i	$-0.443074\pi$
$739$	9.67151			0.355772			0.177886	+	0.984051i	$0.443074\pi$
$740$		0			0
$741$	−23.9916	−	33.9004i	−0.881355	−	1.24536i
$742$		0			0
$743$	11.0205	−	6.36269i	0.404303	−	0.233424i	−0.284036	−	0.958814i	$-0.591674\pi$
$743$	11.0205	−	6.36269i	0.404303	−	0.233424i	0.688339	+	0.725389i	$0.258340\pi$
$744$		0			0
$745$	−12.3135	−	7.10920i	−0.451132	−	0.260461i
$746$		0			0
$747$	−1.86124	+	5.27789i	−0.0680994	+	0.193108i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.6870	−	18.5105i	−0.389975	−	0.675457i	0.602471	−	0.798141i	$-0.294183\pi$
$751$	−10.6870	−	18.5105i	−0.389975	−	0.675457i	−0.992446	+	0.122684i	$0.960850\pi$
$752$		0			0
$753$	15.6790	−	1.45102i	0.571374	−	0.0528783i
$754$		0			0
$755$	52.7428			1.91951
$756$		0			0
$757$	−7.21065			−0.262076			−0.131038	−	0.991377i	$-0.541831\pi$
$757$	−7.21065			−0.262076			−0.131038	+	0.991377i	$0.541831\pi$
$758$		0			0
$759$	84.0159	−	7.77531i	3.04958	−	0.282226i
$760$		0			0
$761$	−11.1620	−	19.3332i	−0.404623	−	0.700827i	0.589655	−	0.807655i	$-0.299264\pi$
$761$	−11.1620	−	19.3332i	−0.404623	−	0.700827i	−0.994277	+	0.106829i	$0.965930\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.171591	−	0.200377i	−0.00620390	−	0.00724465i
$766$		0			0
$767$	−12.0426	−	6.95280i	−0.434833	−	0.251051i
$768$		0			0
$769$	−13.3202	+	7.69042i	−0.480338	+	0.277324i	−0.720558	−	0.693395i	$-0.756114\pi$
$769$	−13.3202	+	7.69042i	−0.480338	+	0.277324i	0.240219	+	0.970719i	$0.422781\pi$
$770$		0			0
$771$	−14.7475	−	20.8384i	−0.531119	−	0.750476i
$772$		0			0
$773$	12.3505			0.444218			0.222109	−	0.975022i	$-0.428706\pi$
$773$	12.3505			0.444218			0.222109	+	0.975022i	$0.428706\pi$
$774$		0			0
$775$			15.4360i			0.554477i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31.5610	−	18.2218i	1.13079	−	0.652862i
$780$		0			0
$781$	10.5516	−	18.2759i	0.377566	−	0.653963i
$782$		0			0
$783$	−5.52157	−	1.39079i	−0.197325	−	0.0497028i
$784$		0			0
$785$	2.99025	+	1.72642i	0.106727	+	0.0616187i
$786$		0			0
$787$	12.5825	−	7.26452i	0.448518	−	0.258952i	−0.258686	−	0.965961i	$-0.583290\pi$
$787$	12.5825	−	7.26452i	0.448518	−	0.258952i	0.707204	+	0.707009i	$0.249956\pi$
$788$		0			0
$789$	−43.8987	−	20.2028i	−1.56284	−	0.719240i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	35.1766			1.24916
$794$		0			0
$795$	6.82964	−	4.83340i	0.242222	−	0.171423i
$796$		0			0
$797$	−22.0040	−	38.1120i	−0.779420	−	1.35000i	−0.932276	−	0.361747i	$-0.882181\pi$
$797$	−22.0040	−	38.1120i	−0.779420	−	1.35000i	0.152856	−	0.988248i	$-0.451153\pi$
$798$		0			0
$799$	−0.118399	+	0.205073i	−0.00418866	+	0.00725497i
$800$		0			0
$801$	21.0046	−	3.92136i	0.742161	−	0.138554i
$802$		0			0
$803$	7.75703	−	13.4356i	0.273740	−	0.474131i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	22.6792	−	2.09886i	0.798344	−	0.0738833i
$808$		0			0
$809$			47.8686i			1.68297i	0.540281	+	0.841484i	$0.318318\pi$
$809$			47.8686i			1.68297i	−0.540281	+	0.841484i	$0.681682\pi$
$810$		0			0
$811$		−	17.4775i		−	0.613720i	−0.951755	−	0.306860i	$-0.900722\pi$
$811$		−	17.4775i		−	0.613720i	0.951755	−	0.306860i	$-0.0992783\pi$
$812$		0			0
$813$	−2.84253	−	30.7149i	−0.0996919	−	1.07722i
$814$		0			0
$815$	21.8177	+	37.7893i	0.764240	+	1.32370i
$816$		0			0
$817$	53.4772	+	30.8751i	1.87093	+	1.08018i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.40574	−	3.69836i	−0.223562	−	0.129074i	0.384037	−	0.923318i	$-0.374534\pi$
$821$	−6.40574	−	3.69836i	−0.223562	−	0.129074i	−0.607598	+	0.794244i	$0.707867\pi$
$822$		0			0
$823$	21.4718	+	37.1903i	0.748460	+	1.29637i	0.948560	+	0.316596i	$0.102540\pi$
$823$	21.4718	+	37.1903i	0.748460	+	1.29637i	−0.200100	+	0.979775i	$0.564127\pi$
$824$		0			0
$825$	−16.1260	+	11.4126i	−0.561436	+	0.397334i
$826$		0			0
$827$			43.0042i			1.49540i	0.664035	+	0.747701i	$0.268843\pi$
$827$			43.0042i			1.49540i	−0.664035	+	0.747701i	$0.731157\pi$
$828$		0			0
$829$			11.6370i			0.404171i	0.979368	+	0.202085i	$0.0647718\pi$
$829$			11.6370i			0.404171i	−0.979368	+	0.202085i	$0.935228\pi$
$830$		0			0
$831$	−12.8810	+	27.9892i	−0.446838	+	0.970934i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	16.2432	−	28.1341i	0.562121	−	0.973621i
$836$		0			0
$837$	29.3202	−	30.2163i	1.01346	−	1.04443i
$838$		0			0
$839$	−0.936892	+	1.62274i	−0.0323451	+	0.0560234i	−0.881745	−	0.471727i	$-0.843631\pi$
$839$	−0.936892	+	1.62274i	−0.0323451	+	0.0560234i	0.849400	+	0.527750i	$0.176964\pi$
$840$		0			0
$841$	−13.8996	−	24.0748i	−0.479296	−	0.830166i
$842$		0			0
$843$	−33.3716	−	15.3581i	−1.14938	−	0.528961i
$844$		0			0
$845$	11.5153			0.396139
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−26.5292	+	18.7750i	−0.910480	+	0.644356i
$850$		0			0
$851$	1.49233	−	0.861595i	0.0511563	−	0.0295351i
$852$		0			0
$853$	34.9301	+	20.1669i	1.19598	+	0.690501i	0.959657	−	0.281173i	$-0.0907236\pi$
$853$	34.9301	+	20.1669i	1.19598	+	0.690501i	0.236325	+	0.971674i	$0.424057\pi$
$854$		0			0
$855$	48.9079	−	41.8819i	1.67262	−	1.43233i
$856$		0			0
$857$	16.1341	−	27.9450i	0.551129	−	0.954583i	−0.447065	−	0.894502i	$-0.647531\pi$
$857$	16.1341	−	27.9450i	0.551129	−	0.954583i	0.998193	−	0.0600814i	$-0.0191360\pi$
$858$		0			0
$859$	33.6905	−	19.4512i	1.14951	−	0.663668i	0.200740	−	0.979645i	$-0.435665\pi$
$859$	33.6905	−	19.4512i	1.14951	−	0.663668i	0.948767	+	0.315977i	$0.102332\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			38.2574i			1.30230i	0.758951	+	0.651148i	$0.225712\pi$
$863$			38.2574i			1.30230i	−0.758951	+	0.651148i	$0.774288\pi$
$864$		0			0
$865$	27.2473			0.926437
$866$		0			0
$867$	−29.3176	+	2.71322i	−0.995679	+	0.0921459i
$868$		0			0
$869$	37.2250	−	21.4919i	1.26277	−	0.729061i
$870$		0			0
$871$	19.3799	+	11.1890i	0.656663	+	0.379124i
$872$		0			0
$873$	−43.2931	−	15.2673i	−1.46525	−	0.516719i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.76152	−	8.24719i	−0.160785	−	0.278488i	0.774365	−	0.632739i	$-0.218069\pi$
$877$	−4.76152	−	8.24719i	−0.160785	−	0.278488i	−0.935150	+	0.354251i	$0.884736\pi$
$878$		0			0
$879$	12.8173	+	18.1109i	0.432316	+	0.610867i
$880$		0			0
$881$	16.5770			0.558493			0.279247	−	0.960219i	$-0.409915\pi$
$881$	16.5770			0.558493			0.279247	+	0.960219i	$0.409915\pi$
$882$		0			0
$883$	−34.9830			−1.17727			−0.588636	−	0.808398i	$-0.700335\pi$
$883$	−34.9830			−1.17727			−0.588636	+	0.808398i	$0.700335\pi$
$884$		0			0
$885$	9.01323	−	19.5848i	0.302976	−	0.658337i
$886$		0			0
$887$	17.3795	+	30.1022i	0.583547	+	1.01073i	0.995055	+	0.0993271i	$0.0316690\pi$
$887$	17.3795	+	30.1022i	0.583547	+	1.01073i	−0.411508	+	0.911406i	$0.634998\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	53.2449	+	8.29064i	1.78377	+	0.277747i
$892$		0			0
$893$	−50.0542	−	28.8988i	−1.67500	−	0.967061i
$894$		0			0
$895$	51.4870	−	29.7260i	1.72102	−	0.993632i
$896$		0			0
$897$	−17.2949	+	37.5801i	−0.577461	+	1.25476i
$898$		0			0
$899$	−8.87920			−0.296138
$900$		0			0
$901$			0.0615188i			0.00204949i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.0129	+	8.09035i	−0.465805	+	0.268932i
$906$		0			0
$907$	−15.9116	+	27.5597i	−0.528336	+	0.915105i	0.471118	+	0.882070i	$0.343851\pi$
$907$	−15.9116	+	27.5597i	−0.528336	+	0.915105i	−0.999454	+	0.0330347i	$0.989483\pi$
$908$		0			0
$909$	6.75975	−	19.1685i	0.224207	−	0.635778i
$910$		0			0
$911$	7.51591	+	4.33931i	0.249013	+	0.143768i	0.619312	−	0.785145i	$-0.287411\pi$
$911$	7.51591	+	4.33931i	0.249013	+	0.143768i	−0.370299	+	0.928913i	$0.620745\pi$
$912$		0			0
$913$	−9.67298	+	5.58470i	−0.320129	+	0.184827i
$914$		0			0
$915$	5.02577	+	54.3058i	0.166147	+	1.79530i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20.7844			0.685615			0.342808	−	0.939406i	$-0.388622\pi$
$919$	20.7844			0.685615			0.342808	+	0.939406i	$0.388622\pi$
$920$		0			0
$921$	−0.634108	−	6.85183i	−0.0208946	−	0.225775i
$922$		0			0
$923$	5.17343	+	8.96064i	0.170286	+	0.294943i
$924$		0			0
$925$	−0.201737	+	0.349419i	−0.00663308	+	0.0114888i
$926$		0			0
$927$	11.1249	−	9.52675i	0.365391	−	0.312900i
$928$		0			0
$929$	−20.5361	+	35.5695i	−0.673767	+	1.16700i	0.303060	+	0.952971i	$0.401992\pi$
$929$	−20.5361	+	35.5695i	−0.673767	+	1.16700i	−0.976828	+	0.214028i	$0.931342\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.586740	−	0.829069i	−0.0192090	−	0.0271425i
$934$		0			0
$935$		−	0.526507i		−	0.0172186i
$936$		0			0
$937$		−	8.38277i		−	0.273853i	−0.990581	−	0.136927i	$-0.956278\pi$
$937$		−	8.38277i		−	0.273853i	0.990581	−	0.136927i	$-0.0437225\pi$
$938$		0			0
$939$	−1.56259	−	0.719125i	−0.0509931	−	0.0234678i
$940$		0			0
$941$	4.99670	+	8.65453i	0.162888	+	0.282130i	0.935903	−	0.352257i	$-0.114586\pi$
$941$	4.99670	+	8.65453i	0.162888	+	0.282130i	−0.773015	+	0.634387i	$0.781253\pi$
$942$		0			0
$943$	−31.4377	−	18.1506i	−1.02375	−	0.591063i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.3659	+	11.7582i	0.661801	+	0.382091i	0.792963	−	0.609270i	$-0.208537\pi$
$947$	20.3659	+	11.7582i	0.661801	+	0.382091i	−0.131162	+	0.991361i	$0.541871\pi$
$948$		0			0
$949$	3.80326	+	6.58744i	0.123459	+	0.213837i
$950$		0			0
$951$	−37.4308	−	17.2262i	−1.21378	−	0.558598i
$952$		0			0
$953$		−	34.7300i		−	1.12501i	−0.826793	−	0.562507i	$-0.809837\pi$
$953$		−	34.7300i		−	1.12501i	0.826793	−	0.562507i	$-0.190163\pi$
$954$		0			0
$955$		−	60.4150i		−	1.95498i
$956$		0			0
$957$	−6.56482	−	9.27614i	−0.212210	−	0.299855i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	17.3278	−	30.0126i	0.558962	−	0.968150i
$962$		0			0
$963$	8.15250	+	43.6685i	0.262710	+	1.40720i
$964$		0			0
$965$	22.6383	−	39.2107i	0.728753	−	1.26224i
$966$		0			0
$967$	8.98645	+	15.5650i	0.288985	+	0.500536i	0.973568	−	0.228399i	$-0.0733489\pi$
$967$	8.98645	+	15.5650i	0.288985	+	0.500536i	−0.684583	+	0.728935i	$0.740016\pi$
$968$		0			0
$969$	0.0436279	+	0.471420i	0.00140153	+	0.0151442i
$970$		0			0
$971$	41.8002			1.34143			0.670717	−	0.741713i	$-0.265987\pi$
$971$	41.8002			1.34143			0.670717	+	0.741713i	$0.265987\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.892609	−	9.64506i	−0.0285864	−	0.308889i
$976$		0			0
$977$	−38.6499	+	22.3145i	−1.23652	+	0.713905i	−0.968381	−	0.249475i	$-0.919742\pi$
$977$	−38.6499	+	22.3145i	−1.23652	+	0.713905i	−0.268139	+	0.963380i	$0.586409\pi$
$978$		0			0
$979$	36.9318	+	21.3226i	1.18035	+	0.681473i
$980$		0			0
$981$	−34.3354	+	6.41010i	−1.09625	+	0.204659i
$982$		0			0
$983$	28.5601	−	49.4675i	0.910925	−	1.57777i	0.0981655	−	0.995170i	$-0.468703\pi$
$983$	28.5601	−	49.4675i	0.910925	−	1.57777i	0.812760	−	0.582599i	$-0.197964\pi$
$984$		0			0
$985$	9.81035	−	5.66401i	0.312584	−	0.180470i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	61.5089i		−	1.95587i
$990$		0			0
$991$	37.3583			1.18672			0.593362	−	0.804935i	$-0.297800\pi$
$991$	37.3583			1.18672			0.593362	+	0.804935i	$0.297800\pi$
$992$		0			0
$993$	−19.6214	+	42.6353i	−0.622665	+	1.35299i
$994$		0			0
$995$	16.7107	−	9.64792i	0.529764	−	0.305859i
$996$		0			0
$997$	−34.0530	−	19.6605i	−1.07847	−	0.622654i	−0.147986	−	0.988990i	$-0.547279\pi$
$997$	−34.0530	−	19.6605i	−1.07847	−	0.622654i	−0.930483	+	0.366335i	$0.880612\pi$
$998$		0			0
$999$	1.05862	−	0.300802i	0.0334932	−	0.00951695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.c.1469.23	yes	48
3.2	odd	2		5292.2.x.c.4409.20		48
7.2	even	3		1764.2.w.c.1109.9		48
7.3	odd	6		1764.2.bm.c.1685.18		48
7.4	even	3		1764.2.bm.c.1685.7		48
7.5	odd	6		1764.2.w.c.1109.16		48
7.6	odd	2	inner	1764.2.x.c.1469.2	yes	48
9.4	even	3		5292.2.x.c.881.5		48
9.5	odd	6	inner	1764.2.x.c.293.2	✓	48
21.2	odd	6		5292.2.w.c.521.20		48
21.5	even	6		5292.2.w.c.521.5		48
21.11	odd	6		5292.2.bm.c.4625.5		48
21.17	even	6		5292.2.bm.c.4625.20		48
21.20	even	2		5292.2.x.c.4409.5		48
63.4	even	3		5292.2.w.c.1097.5		48
63.5	even	6		1764.2.bm.c.1697.7		48
63.13	odd	6		5292.2.x.c.881.20		48
63.23	odd	6		1764.2.bm.c.1697.18		48
63.31	odd	6		5292.2.w.c.1097.20		48
63.32	odd	6		1764.2.w.c.509.16		48
63.40	odd	6		5292.2.bm.c.2285.5		48
63.41	even	6	inner	1764.2.x.c.293.23	yes	48
63.58	even	3		5292.2.bm.c.2285.20		48
63.59	even	6		1764.2.w.c.509.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.w.c.509.9		48	63.59	even	6
1764.2.w.c.509.16		48	63.32	odd	6
1764.2.w.c.1109.9		48	7.2	even	3
1764.2.w.c.1109.16		48	7.5	odd	6
1764.2.x.c.293.2	✓	48	9.5	odd	6	inner
1764.2.x.c.293.23	yes	48	63.41	even	6	inner
1764.2.x.c.1469.2	yes	48	7.6	odd	2	inner
1764.2.x.c.1469.23	yes	48	1.1	even	1	trivial
1764.2.bm.c.1685.7		48	7.4	even	3
1764.2.bm.c.1685.18		48	7.3	odd	6
1764.2.bm.c.1697.7		48	63.5	even	6
1764.2.bm.c.1697.18		48	63.23	odd	6
5292.2.w.c.521.5		48	21.5	even	6
5292.2.w.c.521.20		48	21.2	odd	6
5292.2.w.c.1097.5		48	63.4	even	3
5292.2.w.c.1097.20		48	63.31	odd	6
5292.2.x.c.881.5		48	9.4	even	3
5292.2.x.c.881.20		48	63.13	odd	6
5292.2.x.c.4409.5		48	21.20	even	2
5292.2.x.c.4409.20		48	3.2	odd	2
5292.2.bm.c.2285.5		48	63.40	odd	6
5292.2.bm.c.2285.20		48	63.58	even	3
5292.2.bm.c.4625.5		48	21.11	odd	6
5292.2.bm.c.4625.20		48	21.17	even	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72468 - 0.159612i) q^{3} +(-1.31387 - 2.27569i) q^{5} +(2.94905 - 0.550559i) q^{9} +O(q^{10})\)	\(q+(1.72468 - 0.159612i) q^{3} +(-1.31387 - 2.27569i) q^{5} +(2.94905 - 0.550559i) q^{9} +(5.18523 + 2.99370i) q^{11} +(-2.54231 + 1.46780i) q^{13} +(-2.62923 - 3.71513i) q^{15} +0.0334645 q^{17} +8.16799i q^{19} +(7.04605 - 4.06804i) q^{23} +(-0.952507 + 1.64979i) q^{25} +(4.99829 - 1.42024i) q^{27} +(-0.949006 - 0.547909i) q^{29} +(7.01724 - 4.05141i) q^{31} +(9.42070 + 4.33554i) q^{33} +0.211796 q^{37} +(-4.15039 + 2.93728i) q^{39} +(-2.23087 - 3.86399i) q^{41} +(3.78001 - 6.54717i) q^{43} +(-5.12757 - 5.98775i) q^{45} +(-3.53805 + 6.12809i) q^{47} +(0.0577156 - 0.00534133i) q^{51} +1.83833i q^{53} -15.7333i q^{55} +(1.30371 + 14.0872i) q^{57} +(2.36844 + 4.10225i) q^{59} +(-10.3773 - 5.99136i) q^{61} +(6.68053 + 3.85700i) q^{65} +(-3.81147 - 6.60166i) q^{67} +(11.5029 - 8.14070i) q^{69} -3.52461i q^{71} -2.59112i q^{73} +(-1.37944 + 2.99739i) q^{75} +(3.58952 - 6.21723i) q^{79} +(8.39377 - 3.24725i) q^{81} +(-0.932743 + 1.61556i) q^{83} +(-0.0439680 - 0.0761548i) q^{85} +(-1.72418 - 0.793495i) q^{87} +7.12250 q^{89} +(11.4559 - 8.10742i) q^{93} +(18.5878 - 10.7317i) q^{95} +(-13.2520 - 7.65104i) q^{97} +(16.9397 + 5.97378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{9}+O(q^{10}) \) 48 * q + 16 * q^9	\( 48 q + 16 q^{9} - 24 q^{11} + 24 q^{15} + 48 q^{23} - 24 q^{25} - 40 q^{39} - 24 q^{51} + 16 q^{57} - 72 q^{65} - 24 q^{79} + 96 q^{81} - 24 q^{85} - 96 q^{93} + 96 q^{95} - 40 q^{99}+O(q^{100}) \) 48 * q + 16 * q^9 - 24 * q^11 + 24 * q^15 + 48 * q^23 - 24 * q^25 - 40 * q^39 - 24 * q^51 + 16 * q^57 - 72 * q^65 - 24 * q^79 + 96 * q^81 - 24 * q^85 - 96 * q^93 + 96 * q^95 - 40 * q^99

Introduction

L-functions

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