LMFDB - Embedded newform 1176.2.u.c.521.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (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:	$9.39040727770$
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			521.8
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.c.1097.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02453 + 1.39655i) q^{3} +(2.00767 + 3.47739i) q^{5} +(-0.900685 - 2.86160i) q^{9} +(3.26634 + 1.88582i) q^{11} +4.48235i q^{13} +(-6.91326 - 0.758876i) q^{15} +(-2.05988 + 3.56782i) q^{17} +(5.69006 - 3.28516i) q^{19} +(4.33901 - 2.50513i) q^{23} +(-5.56150 + 9.63280i) q^{25} +(4.91914 + 1.67394i) q^{27} +1.23251i q^{29} +(-0.809487 - 0.467358i) q^{31} +(-5.98009 + 2.62952i) q^{33} +(-1.01181 - 1.75250i) q^{37} +(-6.25981 - 4.59229i) q^{39} +2.21527 q^{41} -3.14096 q^{43} +(8.14263 - 8.87719i) q^{45} +(-2.92829 - 5.07195i) q^{47} +(-2.87222 - 6.53206i) q^{51} +(-3.95157 - 2.28144i) q^{53} +15.1444i q^{55} +(-1.24175 + 11.3122i) q^{57} +(0.982768 - 1.70220i) q^{59} +(8.00812 - 4.62349i) q^{61} +(-15.5869 + 8.99909i) q^{65} +(-3.88026 + 6.72081i) q^{67} +(-0.946908 + 8.62621i) q^{69} -7.97495i q^{71} +(-12.8361 - 7.41091i) q^{73} +(-7.75474 - 17.6360i) q^{75} +(-1.85129 - 3.20653i) q^{79} +(-7.37753 + 5.15480i) q^{81} -9.15704 q^{83} -16.5423 q^{85} +(-1.72126 - 1.26275i) q^{87} +(6.53595 + 11.3206i) q^{89} +(1.48203 - 0.651666i) q^{93} +(22.8475 + 13.1910i) q^{95} -7.06073i q^{97} +(2.45453 - 11.0455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) $ 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.02453	+	1.39655i	−0.591511	+	0.806297i
$3$	−1.02453	+	1.39655i	−0.591511	+	0.806297i
$4$		0			0
$5$	2.00767	+	3.47739i	0.897859	+	1.55514i	0.830226	+	0.557426i	$0.188211\pi$
$5$	2.00767	+	3.47739i	0.897859	+	1.55514i	0.0676320	+	0.997710i	$0.478456\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.900685	−	2.86160i	−0.300228	−	0.953867i
$10$		0			0
$11$	3.26634	+	1.88582i	0.984838	+	0.568597i	0.903727	−	0.428109i	$-0.140820\pi$
$11$	3.26634	+	1.88582i	0.984838	+	0.568597i	0.0811107	+	0.996705i	$0.474153\pi$
$12$		0			0
$13$			4.48235i			1.24318i	0.783343	+	0.621590i	$0.213513\pi$
$13$			4.48235i			1.24318i	−0.783343	+	0.621590i	$0.786487\pi$
$14$		0			0
$15$	−6.91326	−	0.758876i	−1.78499	−	0.195941i
$16$		0			0
$17$	−2.05988	+	3.56782i	−0.499595	+	0.865325i	−1.00000		0.000467189i	$-0.999851\pi$
$17$	−2.05988	+	3.56782i	−0.499595	+	0.865325i	0.500405	+	0.865792i	$0.333185\pi$
$18$		0			0
$19$	5.69006	−	3.28516i	1.30539	−	0.753666i	0.324066	−	0.946035i	$-0.394950\pi$
$19$	5.69006	−	3.28516i	1.30539	−	0.753666i	0.981323	+	0.192368i	$0.0616168\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.33901	−	2.50513i	0.904747	−	0.522356i	0.0260094	−	0.999662i	$-0.491720\pi$
$23$	4.33901	−	2.50513i	0.904747	−	0.522356i	0.878737	+	0.477306i	$0.158387\pi$
$24$		0			0
$25$	−5.56150	+	9.63280i	−1.11230	+	1.92656i
$26$		0			0
$27$	4.91914	+	1.67394i	0.946689	+	0.322150i
$28$		0			0
$29$			1.23251i			0.228872i	0.993431	+	0.114436i	$0.0365061\pi$
$29$			1.23251i			0.228872i	−0.993431	+	0.114436i	$0.963494\pi$
$30$		0			0
$31$	−0.809487	−	0.467358i	−0.145388	−	0.0839399i	0.425541	−	0.904939i	$-0.360084\pi$
$31$	−0.809487	−	0.467358i	−0.145388	−	0.0839399i	−0.570929	+	0.820999i	$0.693417\pi$
$32$		0			0
$33$	−5.98009	+	2.62952i	−1.04100	+	0.457740i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.01181	−	1.75250i	−0.166340	−	0.288110i	0.770790	−	0.637089i	$-0.219862\pi$
$37$	−1.01181	−	1.75250i	−0.166340	−	0.288110i	−0.937130	+	0.348979i	$0.886528\pi$
$38$		0			0
$39$	−6.25981	−	4.59229i	−1.00237	−	0.735355i
$40$		0			0
$41$	2.21527			0.345967			0.172983	−	0.984925i	$-0.444659\pi$
$41$	2.21527			0.345967			0.172983	+	0.984925i	$0.444659\pi$
$42$		0			0
$43$	−3.14096			−0.478992			−0.239496	−	0.970897i	$-0.576982\pi$
$43$	−3.14096			−0.478992			−0.239496	+	0.970897i	$0.576982\pi$
$44$		0			0
$45$	8.14263	−	8.87719i	1.21383	−	1.32333i
$46$		0			0
$47$	−2.92829	−	5.07195i	−0.427136	−	0.739820i	0.569482	−	0.822004i	$-0.307144\pi$
$47$	−2.92829	−	5.07195i	−0.427136	−	0.739820i	−0.996617	+	0.0821836i	$0.973811\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.87222	−	6.53206i	−0.402192	−	0.914671i
$52$		0			0
$53$	−3.95157	−	2.28144i	−0.542790	−	0.313380i	0.203419	−	0.979092i	$-0.434795\pi$
$53$	−3.95157	−	2.28144i	−0.542790	−	0.313380i	−0.746209	+	0.665712i	$0.768128\pi$
$54$		0			0
$55$			15.1444i			2.04208i
$56$		0			0
$57$	−1.24175	+	11.3122i	−0.164474	+	1.49833i
$58$		0			0
$59$	0.982768	−	1.70220i	0.127946	−	0.221608i	−0.794935	−	0.606695i	$-0.792495\pi$
$59$	0.982768	−	1.70220i	0.127946	−	0.221608i	0.922880	+	0.385087i	$0.125828\pi$
$60$		0			0
$61$	8.00812	−	4.62349i	1.02533	−	0.591977i	0.109690	−	0.993966i	$-0.465014\pi$
$61$	8.00812	−	4.62349i	1.02533	−	0.591977i	0.915645	+	0.401989i	$0.131681\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−15.5869	+	8.99909i	−1.93331	+	1.11620i
$66$		0			0
$67$	−3.88026	+	6.72081i	−0.474050	+	0.821078i	−0.999559	−	0.0297101i	$-0.990542\pi$
$67$	−3.88026	+	6.72081i	−0.474050	+	0.821078i	0.525509	+	0.850788i	$0.323875\pi$
$68$		0			0
$69$	−0.946908	+	8.62621i	−0.113994	+	1.03847i
$70$		0			0
$71$		−	7.97495i		−	0.946452i	−0.880941	−	0.473226i	$-0.843089\pi$
$71$		−	7.97495i		−	0.946452i	0.880941	−	0.473226i	$-0.156911\pi$
$72$		0			0
$73$	−12.8361	−	7.41091i	−1.50235	−	0.867381i	−0.999996	−	0.00271822i	$-0.999135\pi$
$73$	−12.8361	−	7.41091i	−1.50235	−	0.867381i	−0.502352	−	0.864663i	$-0.667532\pi$
$74$		0			0
$75$	−7.75474	−	17.6360i	−0.895440	−	2.03643i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.85129	−	3.20653i	−0.208287	−	0.360763i	0.742888	−	0.669416i	$-0.233455\pi$
$79$	−1.85129	−	3.20653i	−0.208287	−	0.360763i	−0.951175	+	0.308652i	$0.900122\pi$
$80$		0			0
$81$	−7.37753	+	5.15480i	−0.819726	+	0.572756i
$82$		0			0
$83$	−9.15704			−1.00512			−0.502558	−	0.864543i	$-0.667608\pi$
$83$	−9.15704			−1.00512			−0.502558	+	0.864543i	$0.667608\pi$
$84$		0			0
$85$	−16.5423			−1.79426
$86$		0			0
$87$	−1.72126	−	1.26275i	−0.184539	−	0.135381i
$88$		0			0
$89$	6.53595	+	11.3206i	0.692809	+	1.19998i	0.970914	+	0.239430i	$0.0769604\pi$
$89$	6.53595	+	11.3206i	0.692809	+	1.19998i	−0.278105	+	0.960551i	$0.589706\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.48203	−	0.651666i	0.153679	−	0.0675746i
$94$		0			0
$95$	22.8475	+	13.1910i	2.34411	+	1.35337i
$96$		0			0
$97$		−	7.06073i		−	0.716908i	−0.933547	−	0.358454i	$-0.883304\pi$
$97$		−	7.06073i		−	0.716908i	0.933547	−	0.358454i	$-0.116696\pi$
$98$		0			0
$99$	2.45453	−	11.0455i	0.246689	−	1.11011i
$100$		0			0
$101$	−4.39465	+	7.61175i	−0.437284	+	0.757398i	−0.997479	−	0.0709630i	$-0.977393\pi$
$101$	−4.39465	+	7.61175i	−0.437284	+	0.757398i	0.560195	+	0.828361i	$0.310726\pi$
$102$		0			0
$103$	−14.7559	+	8.51934i	−1.45394	+	0.839435i	−0.998702	−	0.0509323i	$-0.983781\pi$
$103$	−14.7559	+	8.51934i	−1.45394	+	0.839435i	−0.455242	+	0.890368i	$0.650447\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.23983	−	1.87051i	0.313206	−	0.180829i	−0.335154	−	0.942163i	$-0.608788\pi$
$107$	3.23983	−	1.87051i	0.313206	−	0.180829i	0.648360	+	0.761334i	$0.275455\pi$
$108$		0			0
$109$	7.15850	−	12.3989i	0.685660	−	1.18760i	−0.287569	−	0.957760i	$-0.592847\pi$
$109$	7.15850	−	12.3989i	0.685660	−	1.18760i	0.973229	−	0.229838i	$-0.0738198\pi$
$110$		0			0
$111$	3.48408	+	0.382451i	0.330694	+	0.0363006i
$112$		0			0
$113$			3.14828i			0.296165i	0.988975	+	0.148083i	$0.0473102\pi$
$113$			3.14828i			0.296165i	−0.988975	+	0.148083i	$0.952690\pi$
$114$		0			0
$115$	17.4226	+	10.0590i	1.62467	+	0.938003i
$116$		0			0
$117$	12.8267	−	4.03718i	1.18583	−	0.373238i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.61264	+	2.79318i	0.146604	+	0.253926i
$122$		0			0
$123$	−2.26960	+	3.09372i	−0.204643	+	0.278952i
$124$		0			0
$125$	−24.5860			−2.19903
$126$		0			0
$127$	9.79366			0.869046			0.434523	−	0.900661i	$-0.356917\pi$
$127$	9.79366			0.869046			0.434523	+	0.900661i	$0.356917\pi$
$128$		0			0
$129$	3.21800	−	4.38650i	0.283329	−	0.386209i
$130$		0			0
$131$	5.66933	+	9.81956i	0.495331	+	0.857939i	0.999986	−	0.00538243i	$-0.00171329\pi$
$131$	5.66933	+	9.81956i	0.495331	+	0.857939i	−0.504654	+	0.863322i	$0.668380\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.05507	+	20.4665i	0.349005	+	1.76148i
$136$		0			0
$137$	14.4622	+	8.34973i	1.23558	+	0.713365i	0.968189	−	0.250221i	$-0.0805034\pi$
$137$	14.4622	+	8.34973i	1.23558	+	0.713365i	0.267396	+	0.963587i	$0.413837\pi$
$138$		0			0
$139$		−	1.74422i		−	0.147943i	−0.997260	−	0.0739713i	$-0.976433\pi$
$139$		−	1.74422i		−	0.147943i	0.997260	−	0.0739713i	$-0.0235673\pi$
$140$		0			0
$141$	10.0833	+	1.10686i	0.849170	+	0.0932144i
$142$		0			0
$143$	−8.45291	+	14.6409i	−0.706868	+	1.22433i
$144$		0			0
$145$	−4.28594	+	2.47449i	−0.355928	+	0.205495i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.03719	+	0.598824i	−0.0849703	+	0.0490576i	−0.541883	−	0.840454i	$-0.682288\pi$
$149$	−1.03719	+	0.598824i	−0.0849703	+	0.0490576i	0.456913	+	0.889511i	$0.348955\pi$
$150$		0			0
$151$	−0.369605	+	0.640174i	−0.0300780	+	0.0520966i	−0.880673	−	0.473725i	$-0.842909\pi$
$151$	−0.369605	+	0.640174i	−0.0300780	+	0.0520966i	0.850595	+	0.525822i	$0.176242\pi$
$152$		0			0
$153$	12.0650	+	2.68108i	0.975398	+	0.216753i
$154$		0			0
$155$		−	3.75320i		−	0.301465i
$156$		0			0
$157$	9.01105	+	5.20253i	0.719160	+	0.415207i	0.814444	−	0.580243i	$-0.197042\pi$
$157$	9.01105	+	5.20253i	0.719160	+	0.415207i	−0.0952831	+	0.995450i	$0.530376\pi$
$158$		0			0
$159$	7.23463	−	3.18115i	0.573743	−	0.252282i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−11.5225	−	19.9575i	−0.902509	−	1.56319i	−0.824226	−	0.566260i	$-0.808390\pi$
$163$	−11.5225	−	19.9575i	−0.902509	−	1.56319i	−0.0782826	−	0.996931i	$-0.524944\pi$
$164$		0			0
$165$	−21.1499	−	15.5159i	−1.64652	−	1.20791i
$166$		0			0
$167$	9.84130			0.761543			0.380771	−	0.924669i	$-0.375658\pi$
$167$	9.84130			0.761543			0.380771	+	0.924669i	$0.375658\pi$
$168$		0			0
$169$	−7.09145			−0.545496
$170$		0			0
$171$	−14.5258	−	13.3238i	−1.11081	−	1.01890i
$172$		0			0
$173$	7.98388	+	13.8285i	0.607003	+	1.05136i	0.991731	+	0.128331i	$0.0409619\pi$
$173$	7.98388	+	13.8285i	0.607003	+	1.05136i	−0.384728	+	0.923030i	$0.625705\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.37033	+	3.11644i	0.103001	+	0.234246i
$178$		0			0
$179$	−1.76158	−	1.01705i	−0.131667	−	0.0760179i	0.432720	−	0.901528i	$-0.357554\pi$
$179$	−1.76158	−	1.01705i	−0.131667	−	0.0760179i	−0.564387	+	0.825511i	$0.690887\pi$
$180$		0			0
$181$		−	7.58845i		−	0.564045i	−0.959408	−	0.282023i	$-0.908995\pi$
$181$		−	7.58845i		−	0.564045i	0.959408	−	0.282023i	$-0.0910053\pi$
$182$		0			0
$183$	−1.74762	+	15.9206i	−0.129188	+	1.17688i
$184$		0			0
$185$	4.06276	−	7.03690i	0.298700	−	0.517363i
$186$		0			0
$187$	−13.4566	+	7.76915i	−0.984041	+	0.568136i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.3333	−	11.1621i	1.39891	−	0.807660i	0.404629	−	0.914481i	$-0.367401\pi$
$191$	19.3333	−	11.1621i	1.39891	−	0.807660i	0.994278	+	0.106821i	$0.0340672\pi$
$192$		0			0
$193$	8.65531	−	14.9914i	0.623023	−	1.07911i	−0.365897	−	0.930655i	$-0.619238\pi$
$193$	8.65531	−	14.9914i	0.623023	−	1.07911i	0.988920	−	0.148452i	$-0.0474289\pi$
$194$		0			0
$195$	3.40155	−	30.9876i	0.243590	−	2.21907i
$196$		0			0
$197$		−	0.00885665i		−	0.000631010i	−1.00000		0.000315505i	$-0.999900\pi$
$197$		−	0.00885665i		−	0.000631010i	1.00000		0.000315505i	$-0.000100428\pi$
$198$		0			0
$199$	−16.7952	−	9.69670i	−1.19058	−	0.687381i	−0.232141	−	0.972682i	$-0.574573\pi$
$199$	−16.7952	−	9.69670i	−1.19058	−	0.687381i	−0.958438	+	0.285301i	$0.907906\pi$
$200$		0			0
$201$	−5.41049	−	12.3046i	−0.381627	−	0.867902i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	4.44753	+	7.70335i	0.310629	+	0.538025i
$206$		0			0
$207$	−11.0768	−	10.1602i	−0.769889	−	0.706182i
$208$		0			0
$209$	24.7809			1.71413
$210$		0			0
$211$	13.4174			0.923691			0.461845	−	0.886961i	$-0.347188\pi$
$211$	13.4174			0.923691			0.461845	+	0.886961i	$0.347188\pi$
$212$		0			0
$213$	11.1374	+	8.17056i	0.763121	+	0.559837i
$214$		0			0
$215$	−6.30602	−	10.9223i	−0.430067	−	0.744898i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	23.5006	−	10.3335i	1.58802	−	0.698272i
$220$		0			0
$221$	−15.9922	−	9.23312i	−1.07575	−	0.621087i
$222$		0			0
$223$		−	22.6164i		−	1.51451i	−0.653120	−	0.757255i	$-0.726540\pi$
$223$		−	22.6164i		−	1.51451i	0.653120	−	0.757255i	$-0.273460\pi$
$224$		0			0
$225$	32.5744	+	7.23868i	2.17163	+	0.482579i
$226$		0			0
$227$	−6.47910	+	11.2221i	−0.430033	+	0.744839i	−0.996876	−	0.0789871i	$-0.974831\pi$
$227$	−6.47910	+	11.2221i	−0.430033	+	0.744839i	0.566843	+	0.823826i	$0.308165\pi$
$228$		0			0
$229$	−0.531475	+	0.306847i	−0.0351209	+	0.0202770i	−0.517458	−	0.855709i	$-0.673121\pi$
$229$	−0.531475	+	0.306847i	−0.0351209	+	0.0202770i	0.482337	+	0.875986i	$0.339788\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.00441	−	4.04400i	0.458874	−	0.264931i	−0.252697	−	0.967546i	$-0.581317\pi$
$233$	7.00441	−	4.04400i	0.458874	−	0.264931i	0.711571	+	0.702614i	$0.247984\pi$
$234$		0			0
$235$	11.7581	−	20.3656i	0.767015	−	1.32851i
$236$		0			0
$237$	6.37478	+	0.699766i	0.414086	+	0.0454547i
$238$		0			0
$239$		−	24.8454i		−	1.60711i	−0.595229	−	0.803556i	$-0.702939\pi$
$239$		−	24.8454i		−	1.60711i	0.595229	−	0.803556i	$-0.297061\pi$
$240$		0			0
$241$	14.4774	+	8.35855i	0.932574	+	0.538422i	0.887625	−	0.460568i	$-0.152354\pi$
$241$	14.4774	+	8.35855i	0.932574	+	0.538422i	0.0449490	+	0.998989i	$0.485687\pi$
$242$		0			0
$243$	0.359563	−	15.5843i	0.0230660	−	0.999734i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	14.7252	+	25.5048i	0.936943	+	1.62283i
$248$		0			0
$249$	9.38165	−	12.7882i	0.594538	−	0.810422i
$250$		0			0
$251$	−4.42932			−0.279576			−0.139788	−	0.990181i	$-0.544642\pi$
$251$	−4.42932			−0.279576			−0.139788	+	0.990181i	$0.544642\pi$
$252$		0			0
$253$	18.8969			1.18804
$254$		0			0
$255$	16.9480	−	23.1021i	1.06133	−	1.44671i
$256$		0			0
$257$	1.76997	+	3.06567i	0.110408	+	0.191232i	0.915935	−	0.401327i	$-0.131451\pi$
$257$	1.76997	+	3.06567i	0.110408	+	0.191232i	−0.805527	+	0.592559i	$0.798118\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.52697	−	1.11011i	0.218314	−	0.0687139i
$262$		0			0
$263$	−12.5054	−	7.21999i	−0.771115	−	0.445204i	0.0621571	−	0.998066i	$-0.480202\pi$
$263$	−12.5054	−	7.21999i	−0.771115	−	0.445204i	−0.833272	+	0.552863i	$0.813535\pi$
$264$		0			0
$265$		−	18.3215i		−	1.12548i
$266$		0			0
$267$	−22.5060	−	2.47051i	−1.37734	−	0.151193i
$268$		0			0
$269$	1.67518	−	2.90149i	0.102137	−	0.176907i	−0.810428	−	0.585839i	$-0.800765\pi$
$269$	1.67518	−	2.90149i	0.102137	−	0.176907i	0.912565	+	0.408932i	$0.134099\pi$
$270$		0			0
$271$	−2.28534	+	1.31944i	−0.138824	+	0.0801502i	−0.567804	−	0.823164i	$-0.692207\pi$
$271$	−2.28534	+	1.31944i	−0.138824	+	0.0801502i	0.428979	+	0.903314i	$0.358873\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−36.3315	+	20.9760i	−2.19087	+	1.26490i
$276$		0			0
$277$	−5.95777	+	10.3192i	−0.357968	+	0.620018i	−0.987621	−	0.156858i	$-0.949864\pi$
$277$	−5.95777	+	10.3192i	−0.357968	+	0.620018i	0.629653	+	0.776876i	$0.283197\pi$
$278$		0			0
$279$	−0.608298	+	2.73737i	−0.0364179	+	0.163882i
$280$		0			0
$281$			23.9059i			1.42611i	0.701109	+	0.713054i	$0.252688\pi$
$281$			23.9059i			1.42611i	−0.701109	+	0.713054i	$0.747312\pi$
$282$		0			0
$283$	12.6715	+	7.31591i	0.753244	+	0.434886i	0.826865	−	0.562401i	$-0.190122\pi$
$283$	12.6715	+	7.31591i	0.753244	+	0.434886i	−0.0736209	+	0.997286i	$0.523455\pi$
$284$		0			0
$285$	−41.8298	+	18.3931i	−2.47779	+	1.08951i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.0137526	+	0.0238202i	0.000808977	+	0.00140119i
$290$		0			0
$291$	9.86064	+	7.23391i	0.578041	+	0.424060i
$292$		0			0
$293$	−23.0499			−1.34659			−0.673294	−	0.739375i	$-0.735121\pi$
$293$	−23.0499			−1.34659			−0.673294	+	0.739375i	$0.735121\pi$
$294$		0			0
$295$	7.89231			0.459508
$296$		0			0
$297$	12.9108	+	14.7443i	0.749161	+	0.855550i
$298$		0			0
$299$	11.2289	+	19.4490i	0.649382	+	1.12476i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.12773	−	13.9358i	−0.352029	−	0.800590i
$304$		0			0
$305$	32.1554	+	18.5649i	1.84121	+	1.06302i
$306$		0			0
$307$		−	6.05212i		−	0.345413i	−0.984973	−	0.172706i	$-0.944749\pi$
$307$		−	6.05212i		−	0.345413i	0.984973	−	0.172706i	$-0.0552512\pi$
$308$		0			0
$309$	3.22021	−	29.3356i	0.183191	−	1.66885i
$310$		0			0
$311$	−5.03492	+	8.72073i	−0.285504	+	0.494507i	−0.972731	−	0.231935i	$-0.925494\pi$
$311$	−5.03492	+	8.72073i	−0.285504	+	0.494507i	0.687227	+	0.726442i	$0.258828\pi$
$312$		0			0
$313$	16.0586	−	9.27145i	0.907687	−	0.524053i	0.0280007	−	0.999608i	$-0.491086\pi$
$313$	16.0586	−	9.27145i	0.907687	−	0.524053i	0.879686	+	0.475555i	$0.157753\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.5264	−	10.6962i	1.04055	−	0.600761i	0.120560	−	0.992706i	$-0.461531\pi$
$317$	18.5264	−	10.6962i	1.04055	−	0.600761i	0.919989	+	0.391945i	$0.128198\pi$
$318$		0			0
$319$	−2.32430	+	4.02581i	−0.130136	+	0.225402i
$320$		0			0
$321$	−0.707031	+	6.44096i	−0.0394626	+	0.359499i
$322$		0			0
$323$			27.0682i			1.50611i
$324$		0			0
$325$	−43.1776	−	24.9286i	−2.39506	−	1.38279i
$326$		0			0
$327$	9.98154	+	22.7002i	0.551981	+	1.25532i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	15.5927	+	27.0074i	0.857054	+	1.48446i	0.874726	+	0.484618i	$0.161041\pi$
$331$	15.5927	+	27.0074i	0.857054	+	1.48446i	−0.0176715	+	0.999844i	$0.505625\pi$
$332$		0			0
$333$	−4.10364	+	4.47384i	−0.224878	+	0.245165i
$334$		0			0
$335$	−31.1612			−1.70252
$336$		0			0
$337$	−1.80637			−0.0983995			−0.0491998	−	0.998789i	$-0.515667\pi$
$337$	−1.80637			−0.0983995			−0.0491998	+	0.998789i	$0.515667\pi$
$338$		0			0
$339$	−4.39672	−	3.22550i	−0.238797	−	0.175185i
$340$		0			0
$341$	−1.76271	−	3.05310i	−0.0954559	−	0.165334i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−31.8978	+	14.0258i	−1.71732	+	0.755125i
$346$		0			0
$347$	6.42998	+	3.71235i	0.345179	+	0.199289i	0.662560	−	0.749009i	$-0.269470\pi$
$347$	6.42998	+	3.71235i	0.345179	+	0.199289i	−0.317381	+	0.948298i	$0.602803\pi$
$348$		0			0
$349$		−	19.1105i		−	1.02296i	−0.859295	−	0.511480i	$-0.829097\pi$
$349$		−	19.1105i		−	1.02296i	0.859295	−	0.511480i	$-0.170903\pi$
$350$		0			0
$351$	−7.50319	+	22.0493i	−0.400491	+	1.17690i
$352$		0			0
$353$	−5.62455	+	9.74201i	−0.299365	+	0.518515i	−0.975991	−	0.217812i	$-0.930108\pi$
$353$	−5.62455	+	9.74201i	−0.299365	+	0.518515i	0.676626	+	0.736327i	$0.263441\pi$
$354$		0			0
$355$	27.7320	−	16.0111i	1.47186	−	0.849780i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.7712	+	11.9923i	−1.09626	+	0.632928i	−0.935237	−	0.354023i	$-0.884814\pi$
$359$	−20.7712	+	11.9923i	−1.09626	+	0.632928i	−0.161026	+	0.986950i	$0.551480\pi$
$360$		0			0
$361$	12.0845	−	20.9310i	0.636026	−	1.10163i
$362$		0			0
$363$	−5.55301	−	0.609560i	−0.291457	−	0.0319936i
$364$		0			0
$365$		−	59.5147i		−	3.11514i
$366$		0			0
$367$	24.1821	+	13.9615i	1.26229	+	0.728786i	0.973518	−	0.228611i	$-0.0734185\pi$
$367$	24.1821	+	13.9615i	1.26229	+	0.728786i	0.288776	+	0.957397i	$0.406752\pi$
$368$		0			0
$369$	−1.99526	−	6.33921i	−0.103869	−	0.330006i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.87475	+	11.9074i	0.355961	+	0.616543i	0.987282	−	0.158979i	$-0.0508203\pi$
$373$	6.87475	+	11.9074i	0.355961	+	0.616543i	−0.631321	+	0.775522i	$0.717487\pi$
$374$		0			0
$375$	25.1890	−	34.3354i	1.30075	−	1.77307i
$376$		0			0
$377$	−5.52456			−0.284529
$378$		0			0
$379$	37.2400			1.91289			0.956445	−	0.291913i	$-0.0942918\pi$
$379$	37.2400			1.91289			0.956445	+	0.291913i	$0.0942918\pi$
$380$		0			0
$381$	−10.0339	+	13.6773i	−0.514051	+	0.700709i
$382$		0			0
$383$	1.62622	+	2.81669i	0.0830959	+	0.143926i	0.904578	−	0.426308i	$-0.140186\pi$
$383$	1.62622	+	2.81669i	0.0830959	+	0.143926i	−0.821482	+	0.570234i	$0.806853\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.82901	+	8.98817i	0.143807	+	0.456895i
$388$		0			0
$389$	19.2223	+	11.0980i	0.974609	+	0.562691i	0.900638	−	0.434570i	$-0.143100\pi$
$389$	19.2223	+	11.0980i	0.974609	+	0.562691i	0.0739706	+	0.997260i	$0.476433\pi$
$390$		0			0
$391$			20.6411i			1.04387i
$392$		0			0
$393$	−19.5219	−	2.14294i	−0.984748	−	0.108097i
$394$		0			0
$395$	7.43358	−	12.8753i	0.374024	−	0.647829i
$396$		0			0
$397$	−2.36880	+	1.36763i	−0.118887	+	0.0686393i	−0.558264	−	0.829663i	$-0.688532\pi$
$397$	−2.36880	+	1.36763i	−0.118887	+	0.0686393i	0.439377	+	0.898303i	$0.355199\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.67543	−	2.12201i	0.183542	−	0.105968i	−0.405414	−	0.914133i	$-0.632873\pi$
$401$	3.67543	−	2.12201i	0.183542	−	0.105968i	0.588956	+	0.808165i	$0.299539\pi$
$402$		0			0
$403$	2.09486	−	3.62840i	0.104352	−	0.180744i
$404$		0			0
$405$	−32.7369	−	15.3054i	−1.62671	−	0.760532i
$406$		0			0
$407$		−	7.63235i		−	0.378322i
$408$		0			0
$409$	−15.8087	−	9.12717i	−0.781691	−	0.451310i	0.0553382	−	0.998468i	$-0.482376\pi$
$409$	−15.8087	−	9.12717i	−0.781691	−	0.451310i	−0.837029	+	0.547158i	$0.815710\pi$
$410$		0			0
$411$	−26.4777	+	11.6425i	−1.30605	+	0.574284i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.3843	−	31.8426i	−0.902452	−	1.56309i
$416$		0			0
$417$	2.43588	+	1.78700i	0.119286	+	0.0875098i
$418$		0			0
$419$	27.1802			1.32784			0.663919	−	0.747805i	$-0.268892\pi$
$419$	27.1802			1.32784			0.663919	+	0.747805i	$0.268892\pi$
$420$		0			0
$421$	−17.8910			−0.871954			−0.435977	−	0.899958i	$-0.643597\pi$
$421$	−17.8910			−0.871954			−0.435977	+	0.899958i	$0.643597\pi$
$422$		0			0
$423$	−11.8764	+	12.9478i	−0.577452	+	0.629546i
$424$		0			0
$425$	−22.9121	−	39.6849i	−1.11140	−	1.92500i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−11.7864	−	26.8049i	−0.569053	−	1.29415i
$430$		0			0
$431$	−5.64512	−	3.25921i	−0.271916	−	0.156991i	0.357842	−	0.933782i	$-0.383513\pi$
$431$	−5.64512	−	3.25921i	−0.271916	−	0.156991i	−0.629758	+	0.776791i	$0.716846\pi$
$432$		0			0
$433$			16.4285i			0.789506i	0.918787	+	0.394753i	$0.129170\pi$
$433$			16.4285i			0.789506i	−0.918787	+	0.394753i	$0.870830\pi$
$434$		0			0
$435$	0.935325	−	8.52069i	0.0448454	−	0.408536i
$436$		0			0
$437$	16.4595	−	28.5087i	0.787364	−	1.36375i
$438$		0			0
$439$	−15.8365	+	9.14319i	−0.755833	+	0.436381i	−0.827798	−	0.561027i	$-0.810407\pi$
$439$	−15.8365	+	9.14319i	−0.755833	+	0.436381i	0.0719643	+	0.997407i	$0.477073\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.588421	+	0.339725i	−0.0279567	+	0.0161408i	−0.513913	−	0.857842i	$-0.671805\pi$
$443$	−0.588421	+	0.339725i	−0.0279567	+	0.0161408i	0.485957	+	0.873983i	$0.338471\pi$
$444$		0			0
$445$	−26.2441	+	45.4561i	−1.24409	+	2.15483i
$446$		0			0
$447$	0.226348	−	2.06200i	0.0107059	−	0.0975294i
$448$		0			0
$449$			23.7906i			1.12275i	0.827562	+	0.561375i	$0.189727\pi$
$449$			23.7906i			1.12275i	−0.827562	+	0.561375i	$0.810273\pi$
$450$		0			0
$451$	7.23581	+	4.17760i	0.340721	+	0.196715i
$452$		0			0
$453$	−0.515363	−	1.17205i	−0.0242139	−	0.0550676i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.1594	+	21.0607i	0.568792	+	0.985177i	0.996686	+	0.0813481i	$0.0259226\pi$
$457$	12.1594	+	21.0607i	0.568792	+	0.985177i	−0.427893	+	0.903829i	$0.640744\pi$
$458$		0			0
$459$	−16.1052	+	14.1025i	−0.751726	+	0.658248i
$460$		0			0
$461$	−4.08266			−0.190148			−0.0950742	−	0.995470i	$-0.530309\pi$
$461$	−4.08266			−0.190148			−0.0950742	+	0.995470i	$0.530309\pi$
$462$		0			0
$463$	17.5152			0.814001			0.407001	−	0.913428i	$-0.366575\pi$
$463$	17.5152			0.814001			0.407001	+	0.913428i	$0.366575\pi$
$464$		0			0
$465$	5.24152	+	3.84526i	0.243070	+	0.178320i
$466$		0			0
$467$	−3.17097	−	5.49228i	−0.146735	−	0.254152i	0.783284	−	0.621664i	$-0.213543\pi$
$467$	−3.17097	−	5.49228i	−0.146735	−	0.254152i	−0.930019	+	0.367512i	$0.880210\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−16.4977	+	7.25422i	−0.760172	+	0.334257i
$472$		0			0
$473$	−10.2594	−	5.92329i	−0.471729	−	0.272353i
$474$		0			0
$475$			73.0816i			3.35321i
$476$		0			0
$477$	−2.96945	+	13.3627i	−0.135962	+	0.611835i
$478$		0			0
$479$	15.4881	−	26.8262i	0.707669	−	1.22572i	−0.258050	−	0.966131i	$-0.583080\pi$
$479$	15.4881	−	26.8262i	0.707669	−	1.22572i	0.965720	−	0.259588i	$-0.0835866\pi$
$480$		0			0
$481$	7.85533	−	4.53528i	0.358172	−	0.206791i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	24.5529	−	14.1756i	1.11489	−	0.643682i
$486$		0			0
$487$	−17.9715	+	31.1275i	−0.814366	+	1.41052i	0.0954161	+	0.995437i	$0.469582\pi$
$487$	−17.9715	+	31.1275i	−0.814366	+	1.41052i	−0.909782	+	0.415086i	$0.863751\pi$
$488$		0			0
$489$	39.6767	+	4.35535i	1.79424	+	0.196956i
$490$		0			0
$491$			23.7756i			1.07298i	0.843907	+	0.536490i	$0.180250\pi$
$491$			23.7756i			1.07298i	−0.843907	+	0.536490i	$0.819750\pi$
$492$		0			0
$493$	−4.39740	−	2.53884i	−0.198049	−	0.114344i
$494$		0			0
$495$	43.3374	−	13.6404i	1.94787	−	0.613089i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−8.64048	−	14.9657i	−0.386801	−	0.669959i	0.605216	−	0.796061i	$-0.293087\pi$
$499$	−8.64048	−	14.9657i	−0.386801	−	0.669959i	−0.992017	+	0.126102i	$0.959753\pi$
$500$		0			0
$501$	−10.0827	+	13.7438i	−0.450461	+	0.614029i
$502$		0			0
$503$	22.4974			1.00311			0.501554	−	0.865126i	$-0.332762\pi$
$503$	22.4974			1.00311			0.501554	+	0.865126i	$0.332762\pi$
$504$		0			0
$505$	−35.2920			−1.57048
$506$		0			0
$507$	7.26539	−	9.90354i	0.322667	−	0.439832i
$508$		0			0
$509$	1.68836	+	2.92432i	0.0748351	+	0.129618i	0.901015	−	0.433789i	$-0.142824\pi$
$509$	1.68836	+	2.92432i	0.0748351	+	0.129618i	−0.826179	+	0.563407i	$0.809490\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	33.4893	−	6.63531i	1.47859	−	0.292956i
$514$		0			0
$515$	−59.2501	−	34.2081i	−2.61087	−	1.50739i
$516$		0			0
$517$		−	22.0890i		−	0.971471i
$518$		0			0
$519$	−27.4918	−	3.01781i	−1.20676	−	0.132467i
$520$		0			0
$521$	−15.2787	+	26.4635i	−0.669371	+	1.15939i	0.308709	+	0.951157i	$0.400103\pi$
$521$	−15.2787	+	26.4635i	−0.669371	+	1.15939i	−0.978080	+	0.208229i	$0.933230\pi$
$522$		0			0
$523$	8.62638	−	4.98044i	0.377205	−	0.217780i	−0.299396	−	0.954129i	$-0.596785\pi$
$523$	8.62638	−	4.98044i	0.377205	−	0.217780i	0.676602	+	0.736349i	$0.263452\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.33490	−	1.92541i	0.145271	−	0.0838720i
$528$		0			0
$529$	1.05135	−	1.82099i	0.0457109	−	0.0791737i
$530$		0			0
$531$	−5.75620	−	1.27914i	−0.249798	−	0.0555100i
$532$		0			0
$533$			9.92960i			0.430099i
$534$		0			0
$535$	13.0090	+	7.51076i	0.562429	+	0.324718i
$536$		0			0
$537$	3.22515	−	1.41814i	0.139175	−	0.0611971i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−15.4359	−	26.7358i	−0.663642	−	1.14946i	−0.979652	−	0.200705i	$-0.935677\pi$
$541$	−15.4359	−	26.7358i	−0.663642	−	1.14946i	0.316010	−	0.948756i	$-0.397657\pi$
$542$		0			0
$543$	10.5976	+	7.77458i	0.454788	+	0.333639i
$544$		0			0
$545$	57.4877			2.46250
$546$		0			0
$547$	−38.9414			−1.66501			−0.832506	−	0.554016i	$-0.813095\pi$
$547$	−38.9414			−1.66501			−0.832506	+	0.554016i	$0.813095\pi$
$548$		0			0
$549$	−20.4434	−	18.7517i	−0.872502	−	0.800305i
$550$		0			0
$551$	4.04900	+	7.01308i	0.172493	+	0.298767i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	5.66495	+	12.8833i	0.240464	+	0.546867i
$556$		0			0
$557$	−39.3322	−	22.7084i	−1.66656	−	0.962188i	−0.969473	−	0.245200i	$-0.921146\pi$
$557$	−39.3322	−	22.7084i	−1.66656	−	0.962188i	−0.697086	−	0.716988i	$-0.745520\pi$
$558$		0			0
$559$		−	14.0789i		−	0.595473i
$560$		0			0
$561$	2.93664	−	26.7524i	0.123985	−	1.12949i
$562$		0			0
$563$	5.02435	−	8.70244i	0.211751	−	0.366764i	−0.740511	−	0.672044i	$-0.765417\pi$
$563$	5.02435	−	8.70244i	0.211751	−	0.366764i	0.952263	+	0.305280i	$0.0987500\pi$
$564$		0			0
$565$	−10.9478	+	6.32072i	−0.460578	+	0.265915i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.7959	+	12.0065i	−0.871808	+	0.503339i	−0.867949	−	0.496654i	$-0.834562\pi$
$569$	−20.7959	+	12.0065i	−0.871808	+	0.503339i	−0.00385959	+	0.999993i	$0.501229\pi$
$570$		0			0
$571$	7.86981	−	13.6309i	0.329341	−	0.570436i	−0.653040	−	0.757323i	$-0.726507\pi$
$571$	7.86981	−	13.6309i	0.329341	−	0.570436i	0.982381	+	0.186888i	$0.0598400\pi$
$572$		0			0
$573$	−4.21913	+	38.4357i	−0.176257	+	1.60567i
$574$		0			0
$575$			55.7291i			2.32406i
$576$		0			0
$577$	21.4412	+	12.3791i	0.892610	+	0.515348i	0.874795	−	0.484493i	$-0.160996\pi$
$577$	21.4412	+	12.3791i	0.892610	+	0.515348i	0.0178145	+	0.999841i	$0.494329\pi$
$578$		0			0
$579$	12.0686	+	27.4467i	0.501555	+	1.14065i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−8.60477	−	14.9039i	−0.356373	−	0.617256i
$584$		0			0
$585$	39.7907	+	36.4981i	1.64514	+	1.50901i
$586$		0			0
$587$	−23.8593			−0.984778			−0.492389	−	0.870375i	$-0.663876\pi$
$587$	−23.8593			−0.984778			−0.492389	+	0.870375i	$0.663876\pi$
$588$		0			0
$589$	−6.14137			−0.253051
$590$		0			0
$591$	0.0123687	+	0.00907388i	0.000508781	+	0.000373250i
$592$		0			0
$593$	−20.2197	−	35.0216i	−0.830324	−	1.43816i	−0.897781	−	0.440442i	$-0.854822\pi$
$593$	−20.2197	−	35.0216i	−0.830324	−	1.43816i	0.0674569	−	0.997722i	$-0.478511\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	30.7490	−	13.5207i	1.25847	−	0.553366i
$598$		0			0
$599$	−4.13793	−	2.38903i	−0.169071	−	0.0976132i	0.413077	−	0.910696i	$-0.364454\pi$
$599$	−4.13793	−	2.38903i	−0.169071	−	0.0976132i	−0.582148	+	0.813083i	$0.697787\pi$
$600$		0			0
$601$			4.52159i			0.184440i	0.995739	+	0.0922198i	$0.0293963\pi$
$601$			4.52159i			0.184440i	−0.995739	+	0.0922198i	$0.970604\pi$
$602$		0			0
$603$	22.7272	+	5.05043i	0.925523	+	0.205670i
$604$		0			0
$605$	−6.47532	+	11.2156i	−0.263259	+	0.455978i
$606$		0			0
$607$	−9.20269	+	5.31317i	−0.373526	+	0.215655i	−0.674998	−	0.737820i	$-0.735855\pi$
$607$	−9.20269	+	5.31317i	−0.373526	+	0.215655i	0.301472	+	0.953475i	$0.402522\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	22.7343	−	13.1256i	0.919730	−	0.531006i
$612$		0			0
$613$	11.6510	−	20.1801i	0.470578	−	0.815066i	−0.528855	−	0.848712i	$-0.677379\pi$
$613$	11.6510	−	20.1801i	0.470578	−	0.815066i	0.999434	+	0.0336463i	$0.0107120\pi$
$614$		0			0
$615$	−15.3147	−	1.68111i	−0.617549	−	0.0677890i
$616$		0			0
$617$		−	38.6616i		−	1.55646i	−0.627982	−	0.778228i	$-0.716119\pi$
$617$		−	38.6616i		−	1.55646i	0.627982	−	0.778228i	$-0.283881\pi$
$618$		0			0
$619$	−42.5873	−	24.5878i	−1.71173	−	0.988266i	−0.932235	−	0.361854i	$-0.882144\pi$
$619$	−42.5873	−	24.5878i	−1.71173	−	0.988266i	−0.779492	−	0.626412i	$-0.784523\pi$
$620$		0			0
$621$	25.5376	−	5.05982i	1.02479	−	0.203044i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−21.5530	−	37.3310i	−0.862122	−	1.49324i
$626$		0			0
$627$	−25.3887	+	34.6076i	−1.01393	+	1.38210i
$628$		0			0
$629$	8.33683			0.332411
$630$		0			0
$631$	−18.6538			−0.742597			−0.371298	−	0.928514i	$-0.621087\pi$
$631$	−18.6538			−0.742597			−0.371298	+	0.928514i	$0.621087\pi$
$632$		0			0
$633$	−13.7465	+	18.7380i	−0.546374	+	0.744769i
$634$		0			0
$635$	19.6625	+	34.0564i	0.780281	+	1.35149i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−22.8211	+	7.18292i	−0.902790	+	0.284152i
$640$		0			0
$641$	15.5921	+	9.00210i	0.615850	+	0.355561i	0.775252	−	0.631652i	$-0.217623\pi$
$641$	15.5921	+	9.00210i	0.615850	+	0.355561i	−0.159401	+	0.987214i	$0.550956\pi$
$642$		0			0
$643$			8.31261i			0.327817i	0.986476	+	0.163909i	$0.0524102\pi$
$643$			8.31261i			0.327817i	−0.986476	+	0.163909i	$0.947590\pi$
$644$		0			0
$645$	21.7143	+	2.38360i	0.854998	+	0.0938540i
$646$		0			0
$647$	−10.4982	+	18.1834i	−0.412726	+	0.714862i	−0.995187	−	0.0979967i	$-0.968757\pi$
$647$	−10.4982	+	18.1834i	−0.412726	+	0.714862i	0.582461	+	0.812859i	$0.302090\pi$
$648$		0			0
$649$	6.42011	−	3.70665i	0.252011	−	0.145499i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.74581	−	5.62674i	0.381383	−	0.220191i	−0.297037	−	0.954866i	$-0.595998\pi$
$653$	9.74581	−	5.62674i	0.381383	−	0.220191i	0.678420	+	0.734675i	$0.262665\pi$
$654$		0			0
$655$	−22.7643	+	39.4289i	−0.889475	+	1.54062i
$656$		0			0
$657$	−9.64581	+	43.4066i	−0.376319	+	1.69345i
$658$		0			0
$659$		−	30.5790i		−	1.19119i	−0.803286	−	0.595594i	$-0.796917\pi$
$659$		−	30.5790i		−	1.19119i	0.803286	−	0.595594i	$-0.203083\pi$
$660$		0			0
$661$	19.0053	+	10.9727i	0.739222	+	0.426790i	0.821786	−	0.569796i	$-0.192978\pi$
$661$	19.0053	+	10.9727i	0.739222	+	0.426790i	−0.0825645	+	0.996586i	$0.526311\pi$
$662$		0			0
$663$	29.2790	−	12.8743i	1.13710	−	0.499997i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.08761	+	5.34790i	0.119553	+	0.207071i
$668$		0			0
$669$	31.5849	+	23.1712i	1.22114	+	0.895849i
$670$		0			0
$671$	34.8763			1.34638
$672$		0			0
$673$	2.10181			0.0810190			0.0405095	−	0.999179i	$-0.487102\pi$
$673$	2.10181			0.0810190			0.0405095	+	0.999179i	$0.487102\pi$
$674$		0			0
$675$	−43.4825	+	38.0754i	−1.67364	+	1.46552i
$676$		0			0
$677$	−11.4653	−	19.8584i	−0.440646	−	0.763222i	0.557091	−	0.830451i	$-0.311917\pi$
$677$	−11.4653	−	19.8584i	−0.440646	−	0.763222i	−0.997738	+	0.0672293i	$0.978584\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−9.03421	−	20.5458i	−0.346192	−	0.787315i
$682$		0			0
$683$	41.7660	+	24.1136i	1.59813	+	0.922683i	0.991847	+	0.127436i	$0.0406749\pi$
$683$	41.7660	+	24.1136i	1.59813	+	0.922683i	0.606287	+	0.795246i	$0.292658\pi$
$684$		0			0
$685$			67.0541i			2.56200i
$686$		0			0
$687$	0.115985	−	1.05660i	0.00442509	−	0.0403119i
$688$		0			0
$689$	10.2262	−	17.7123i	0.389587	−	0.674785i
$690$		0			0
$691$	−16.7466	+	9.66867i	−0.637072	+	0.367813i	−0.783486	−	0.621410i	$-0.786560\pi$
$691$	−16.7466	+	9.66867i	−0.637072	+	0.367813i	0.146414	+	0.989223i	$0.453227\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.06533	−	3.50182i	0.230071	−	0.132832i
$696$		0			0
$697$	−4.56319	+	7.90368i	−0.172843	+	0.299373i
$698$		0			0
$699$	−1.52858	+	13.9252i	−0.0578163	+	0.526699i
$700$		0			0
$701$		−	22.3461i		−	0.844001i	−0.906596	−	0.422001i	$-0.861328\pi$
$701$		−	22.3461i		−	0.844001i	0.906596	−	0.422001i	$-0.138672\pi$
$702$		0			0
$703$	−11.5145	−	6.64789i	−0.434277	−	0.250730i
$704$		0			0
$705$	16.3951	+	37.2859i	0.617474	+	1.40427i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.0147	−	22.5421i	−0.488777	−	0.846587i	0.511139	−	0.859498i	$-0.329224\pi$
$709$	−13.0147	−	22.5421i	−0.488777	−	0.846587i	−0.999917	+	0.0129106i	$0.995890\pi$
$710$		0			0
$711$	−7.50839	+	8.18574i	−0.281587	+	0.306989i
$712$		0			0
$713$	−4.68317			−0.175386
$714$		0			0
$715$	−67.8827			−2.53867
$716$		0			0
$717$	34.6977	+	25.4548i	1.29581	+	0.950626i
$718$		0			0
$719$	−0.627787	−	1.08736i	−0.0234125	−	0.0405517i	0.854082	−	0.520139i	$-0.174120\pi$
$719$	−0.627787	−	1.08736i	−0.0234125	−	0.0405517i	−0.877494	+	0.479587i	$0.840786\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−26.5056	+	11.6548i	−0.985756	+	0.433448i
$724$		0			0
$725$	−11.8726	−	6.85463i	−0.440936	−	0.254575i
$726$		0			0
$727$		−	33.5608i		−	1.24470i	−0.782738	−	0.622351i	$-0.786178\pi$
$727$		−	33.5608i		−	1.24470i	0.782738	−	0.622351i	$-0.213822\pi$
$728$		0			0
$729$	21.3958	+	16.4687i	0.792438	+	0.609952i
$730$		0			0
$731$	6.47001	−	11.2064i	0.239302	−	0.414483i
$732$		0			0
$733$	0.0552513	−	0.0318993i	0.00204075	−	0.00117823i	−0.498979	−	0.866614i	$-0.666292\pi$
$733$	0.0552513	−	0.0318993i	0.00204075	−	0.00117823i	0.501020	+	0.865436i	$0.332958\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−25.3485	+	14.6350i	−0.933724	+	0.539086i
$738$		0			0
$739$	12.4280	−	21.5259i	0.457170	−	0.791842i	−0.541640	−	0.840611i	$-0.682196\pi$
$739$	12.4280	−	21.5259i	0.457170	−	0.791842i	0.998810	+	0.0487685i	$0.0155297\pi$
$740$		0			0
$741$	−50.7051	−	5.56595i	−1.86270	−	0.204470i
$742$		0			0
$743$			1.14074i			0.0418496i	0.999781	+	0.0209248i	$0.00666106\pi$
$743$			1.14074i			0.0418496i	−0.999781	+	0.0209248i	$0.993339\pi$
$744$		0			0
$745$	−4.16469	−	2.40449i	−0.152583	−	0.0880936i
$746$		0			0
$747$	8.24761	+	26.2038i	0.301764	+	0.958748i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.16929	−	15.8817i	−0.334592	−	0.579531i	0.648814	−	0.760947i	$-0.275265\pi$
$751$	−9.16929	−	15.8817i	−0.334592	−	0.579531i	−0.983406	+	0.181416i	$0.941932\pi$
$752$		0			0
$753$	4.53796	−	6.18575i	0.165373	−	0.225421i
$754$		0			0
$755$	−2.96818			−0.108023
$756$		0			0
$757$	−41.6253			−1.51290			−0.756449	−	0.654053i	$-0.773067\pi$
$757$	−41.6253			−1.51290			−0.756449	+	0.654053i	$0.773067\pi$
$758$		0			0
$759$	−19.3604	+	26.3904i	−0.702738	+	0.957911i
$760$		0			0
$761$	8.66684	+	15.0114i	0.314173	+	0.544163i	0.979261	−	0.202601i	$-0.0649395\pi$
$761$	8.66684	+	15.0114i	0.314173	+	0.544163i	−0.665088	+	0.746765i	$0.731606\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	14.8994	+	47.3375i	0.538689	+	1.71149i
$766$		0			0
$767$	7.62987	+	4.40511i	0.275499	+	0.159059i
$768$		0			0
$769$			15.7285i			0.567184i	0.958945	+	0.283592i	$0.0915261\pi$
$769$			15.7285i			0.567184i	−0.958945	+	0.283592i	$0.908474\pi$
$770$		0			0
$771$	−6.09474	−	0.669026i	−0.219497	−	0.0240944i
$772$		0			0
$773$	−7.12720	+	12.3447i	−0.256348	+	0.444007i	−0.965261	−	0.261289i	$-0.915852\pi$
$773$	−7.12720	+	12.3447i	−0.256348	+	0.444007i	0.708913	+	0.705296i	$0.249186\pi$
$774$		0			0
$775$	9.00392	−	5.19842i	0.323430	−	0.186733i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.6050	−	7.27750i	0.451621	−	0.260743i
$780$		0			0
$781$	15.0393	−	26.0489i	0.538149	−	0.932102i
$782$		0			0
$783$	−2.06316	+	6.06291i	−0.0737313	+	0.216671i
$784$		0			0
$785$			41.7799i			1.49119i
$786$		0			0
$787$	11.2126	+	6.47357i	0.399685	+	0.230758i	0.686348	−	0.727273i	$-0.259213\pi$
$787$	11.2126	+	6.47357i	0.399685	+	0.230758i	−0.286663	+	0.958031i	$0.592546\pi$
$788$		0			0
$789$	22.8952	−	10.0673i	0.815090	−	0.358405i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	20.7241	+	35.8952i	0.735934	+	1.27468i
$794$		0			0
$795$	25.5869	+	18.7709i	0.907473	+	0.665736i
$796$		0			0
$797$	−21.1678			−0.749803			−0.374901	−	0.927065i	$-0.622323\pi$
$797$	−21.1678			−0.749803			−0.374901	+	0.927065i	$0.622323\pi$
$798$		0			0
$799$	24.1278			0.853580
$800$		0			0
$801$	26.5082	−	28.8996i	0.936621	−	1.02112i
$802$		0			0
$803$	−27.9513	−	48.4131i	−0.986380	−	1.70846i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.33580	+	5.31213i	0.0822242	+	0.186996i
$808$		0			0
$809$	−36.0989	−	20.8417i	−1.26917	−	0.732756i	−0.294340	−	0.955701i	$-0.595100\pi$
$809$	−36.0989	−	20.8417i	−1.26917	−	0.732756i	−0.974831	+	0.222945i	$0.928433\pi$
$810$		0			0
$811$		−	31.7652i		−	1.11543i	−0.830033	−	0.557714i	$-0.811679\pi$
$811$		−	31.7652i		−	1.11543i	0.830033	−	0.557714i	$-0.188321\pi$
$812$		0			0
$813$	0.498732	−	4.54338i	0.0174913	−	0.159343i
$814$		0			0
$815$	46.2667	−	80.1362i	1.62065	−	2.80705i
$816$		0			0
$817$	−17.8722	+	10.3185i	−0.625270	+	0.361000i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.2908	+	7.09611i	−0.428953	+	0.247656i	−0.698900	−	0.715219i	$-0.746327\pi$
$821$	−12.2908	+	7.09611i	−0.428953	+	0.247656i	0.269948	+	0.962875i	$0.412994\pi$
$822$		0			0
$823$	−7.13017	+	12.3498i	−0.248542	+	0.430488i	−0.963122	−	0.269067i	$-0.913285\pi$
$823$	−7.13017	+	12.3498i	−0.248542	+	0.430488i	0.714579	+	0.699554i	$0.246618\pi$
$824$		0			0
$825$	7.92867	−	72.2291i	0.276041	−	2.51469i
$826$		0			0
$827$			43.8269i			1.52401i	0.647571	+	0.762006i	$0.275785\pi$
$827$			43.8269i			1.52401i	−0.647571	+	0.762006i	$0.724215\pi$
$828$		0			0
$829$	16.9331	+	9.77631i	0.588110	+	0.339545i	0.764350	−	0.644802i	$-0.223060\pi$
$829$	16.9331	+	9.77631i	0.588110	+	0.339545i	−0.176240	+	0.984347i	$0.556394\pi$
$830$		0			0
$831$	−8.30729	−	18.8926i	−0.288177	−	0.655376i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	19.7581	+	34.2221i	0.683758	+	1.18430i
$836$		0			0
$837$	−3.19965	−	3.65403i	−0.110596	−	0.126302i
$838$		0			0
$839$	−41.5510			−1.43450			−0.717251	−	0.696815i	$-0.754600\pi$
$839$	−41.5510			−1.43450			−0.717251	+	0.696815i	$0.754600\pi$
$840$		0			0
$841$	27.4809			0.947617
$842$		0			0
$843$	−33.3857	−	24.4923i	−1.14987	−	0.843559i
$844$		0			0
$845$	−14.2373	−	24.6597i	−0.489778	−	0.848321i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−23.1993	+	10.2010i	−0.796199	+	0.350098i
$850$		0			0
$851$	−8.78049	−	5.06942i	−0.300991	−	0.173777i
$852$		0			0
$853$			17.5344i			0.600367i	0.953882	+	0.300183i	$0.0970478\pi$
$853$			17.5344i			0.600367i	−0.953882	+	0.300183i	$0.902952\pi$
$854$		0			0
$855$	17.1690	−	77.2615i	0.587169	−	2.64229i
$856$		0			0
$857$	9.82141	−	17.0112i	0.335493	−	0.581091i	−0.648086	−	0.761567i	$-0.724430\pi$
$857$	9.82141	−	17.0112i	0.335493	−	0.581091i	0.983579	+	0.180476i	$0.0577638\pi$
$858$		0			0
$859$	−11.6418	+	6.72140i	−0.397213	+	0.229331i	−0.685281	−	0.728279i	$-0.740321\pi$
$859$	−11.6418	+	6.72140i	−0.397213	+	0.229331i	0.288068	+	0.957610i	$0.406987\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.5405	+	11.2817i	−0.665168	+	0.384035i	−0.794243	−	0.607600i	$-0.792132\pi$
$863$	−19.5405	+	11.2817i	−0.665168	+	0.384035i	0.129075	+	0.991635i	$0.458799\pi$
$864$		0			0
$865$	−32.0581	+	55.5262i	−1.09001	+	1.88795i
$866$		0			0
$867$	−0.0473560	−	0.00519832i	−0.00160829	−	0.000176544i
$868$		0			0
$869$		−	13.9648i		−	0.473725i
$870$		0			0
$871$	−30.1250	−	17.3927i	−1.02075	−	0.589329i
$872$		0			0
$873$	−20.2050	+	6.35949i	−0.683836	+	0.215236i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.78849	+	8.29391i	0.161696	+	0.280065i	0.935477	−	0.353388i	$-0.114970\pi$
$877$	4.78849	+	8.29391i	0.161696	+	0.280065i	−0.773781	+	0.633453i	$0.781637\pi$
$878$		0			0
$879$	23.6152	−	32.1902i	0.796522	−	1.08575i
$880$		0			0
$881$	4.74822			0.159971			0.0799857	−	0.996796i	$-0.474513\pi$
$881$	4.74822			0.159971			0.0799857	+	0.996796i	$0.474513\pi$
$882$		0			0
$883$	36.7930			1.23818			0.619092	−	0.785318i	$-0.287501\pi$
$883$	36.7930			1.23818			0.619092	+	0.785318i	$0.287501\pi$
$884$		0			0
$885$	−8.08589	+	11.0220i	−0.271804	+	0.370500i
$886$		0			0
$887$	−17.2408	−	29.8619i	−0.578889	−	1.00267i	−0.995607	−	0.0936294i	$-0.970153\pi$
$887$	−17.2408	−	29.8619i	−0.578889	−	1.00267i	0.416718	−	0.909036i	$-0.363180\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−33.8186	+	2.92463i	−1.13296	+	0.0979787i
$892$		0			0
$893$	−33.3243	−	19.2398i	−1.11516	−	0.643835i
$894$		0			0
$895$		−	8.16761i		−	0.273013i
$896$		0			0
$897$	−38.6657	−	4.24437i	−1.29101	−	0.141716i
$898$		0			0
$899$	0.576025	−	0.997705i	0.0192115	−	0.0332753i
$900$		0			0
$901$	16.2795	−	9.39900i	0.542350	−	0.313126i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	26.3880	−	15.2351i	0.877168	−	0.506433i
$906$		0			0
$907$	9.30335	−	16.1139i	0.308913	−	0.535053i	−0.669212	−	0.743072i	$-0.733368\pi$
$907$	9.30335	−	16.1139i	0.308913	−	0.535053i	0.978125	+	0.208019i	$0.0667015\pi$
$908$		0			0
$909$	25.7400	+	5.71994i	0.853742	+	0.189718i
$910$		0			0
$911$			27.0277i			0.895467i	0.894167	+	0.447733i	$0.147769\pi$
$911$			27.0277i			0.895467i	−0.894167	+	0.447733i	$0.852231\pi$
$912$		0			0
$913$	−29.9100	−	17.2685i	−0.989877	−	0.571506i
$914$		0			0
$915$	−58.8708	+	25.8862i	−1.94621	+	0.855771i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.84583	−	15.3214i	−0.291797	−	0.505407i	0.682438	−	0.730944i	$-0.260920\pi$
$919$	−8.84583	−	15.3214i	−0.291797	−	0.505407i	−0.974235	+	0.225537i	$0.927586\pi$
$920$		0			0
$921$	8.45207	+	6.20057i	0.278505	+	0.204316i
$922$		0			0
$923$	35.7465			1.17661
$924$		0			0
$925$	22.5087			0.740081
$926$		0			0
$927$	37.6694	+	34.5523i	1.23723	+	1.13485i
$928$		0			0
$929$	−11.3508	−	19.6601i	−0.372406	−	0.645026i	0.617529	−	0.786548i	$-0.288134\pi$
$929$	−11.3508	−	19.6601i	−0.372406	−	0.645026i	−0.989935	+	0.141522i	$0.954800\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.02050	−	15.9661i	−0.229841	−	0.522708i
$934$		0			0
$935$	−54.0327	−	31.1958i	−1.76706	−	1.02021i
$936$		0			0
$937$		−	29.4147i		−	0.960935i	−0.877012	−	0.480468i	$-0.840467\pi$
$937$		−	29.4147i		−	0.960935i	0.877012	−	0.480468i	$-0.159533\pi$
$938$		0			0
$939$	−3.50449	+	31.9255i	−0.114365	+	1.04185i
$940$		0			0
$941$	20.5512	−	35.5957i	0.669949	−	1.16039i	−0.307968	−	0.951397i	$-0.599649\pi$
$941$	20.5512	−	35.5957i	0.669949	−	1.16039i	0.977918	−	0.208990i	$-0.0670175\pi$
$942$		0			0
$943$	9.61207	−	5.54953i	0.313012	−	0.180718i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.831993	+	0.480351i	−0.0270361	+	0.0156093i	−0.513457	−	0.858115i	$-0.671635\pi$
$947$	−0.831993	+	0.480351i	−0.0270361	+	0.0156093i	0.486421	+	0.873725i	$0.338302\pi$
$948$		0			0
$949$	33.2183	−	57.5357i	1.07831	−	1.86769i
$950$		0			0
$951$	−4.04305	+	36.8316i	−0.131105	+	1.19435i
$952$		0			0
$953$			14.0678i			0.455702i	0.973696	+	0.227851i	$0.0731699\pi$
$953$			14.0678i			0.455702i	−0.973696	+	0.227851i	$0.926830\pi$
$954$		0			0
$955$	77.6298	+	44.8196i	2.51204	+	1.45033i
$956$		0			0
$957$	−3.24092	−	7.37055i	−0.104764	−	0.238256i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.0632	−	26.0901i	−0.485908	−	0.841618i
$962$		0			0
$963$	−8.27073	−	7.58635i	−0.266521	−	0.244467i
$964$		0			0
$965$	69.5081			2.23754
$966$		0			0
$967$	40.1695			1.29177			0.645883	−	0.763437i	$-0.276490\pi$
$967$	40.1695			1.29177			0.645883	+	0.763437i	$0.276490\pi$
$968$		0			0
$969$	−37.8019	−	27.7321i	−1.21437	−	0.890883i
$970$		0			0
$971$	−24.7784	−	42.9175i	−0.795177	−	1.37729i	−0.922727	−	0.385455i	$-0.874045\pi$
$971$	−24.7784	−	42.9175i	−0.795177	−	1.37729i	0.127550	−	0.991832i	$-0.459289\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	79.0505	−	34.7595i	2.53164	−	1.11319i
$976$		0			0
$977$	13.0979	+	7.56208i	0.419039	+	0.241932i	0.694666	−	0.719332i	$-0.255552\pi$
$977$	13.0979	+	7.56208i	0.419039	+	0.241932i	−0.275627	+	0.961265i	$0.588885\pi$
$978$		0			0
$979$			49.3025i			1.57572i
$980$		0			0
$981$	−41.9283	−	9.31729i	−1.33867	−	0.297478i
$982$		0			0
$983$	−14.2454	+	24.6737i	−0.454358	+	0.786970i	−0.998651	−	0.0519245i	$-0.983464\pi$
$983$	−14.2454	+	24.6737i	−0.454358	+	0.786970i	0.544293	+	0.838895i	$0.316798\pi$
$984$		0			0
$985$	0.0307980	−	0.0177812i	0.000981307	−	0.000566558i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.6287	+	7.86851i	−0.433366	+	0.250204i
$990$		0			0
$991$	−5.14988	+	8.91986i	−0.163591	+	0.283349i	−0.936154	−	0.351590i	$-0.885641\pi$
$991$	−5.14988	+	8.91986i	−0.163591	+	0.283349i	0.772563	+	0.634938i	$0.218975\pi$
$992$		0			0
$993$	−53.6923	−	5.89386i	−1.70387	−	0.187036i
$994$		0			0
$995$		−	77.8712i		−	2.46868i
$996$		0			0
$997$	17.7056	+	10.2223i	0.560742	+	0.323744i	0.753443	−	0.657513i	$-0.228392\pi$
$997$	17.7056	+	10.2223i	0.560742	+	0.323744i	−0.192701	+	0.981257i	$0.561725\pi$
$998$		0			0
$999$	−2.04363	−	10.3145i	−0.0646577	−	0.326337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.c.521.8		48
3.2	odd	2	inner	1176.2.u.c.521.15		48
7.2	even	3	inner	1176.2.u.c.1097.10		48
7.3	odd	6		1176.2.k.b.881.1	✓	24
7.4	even	3		1176.2.k.b.881.24	yes	24
7.5	odd	6	inner	1176.2.u.c.1097.15		48
7.6	odd	2	inner	1176.2.u.c.521.17		48
21.2	odd	6	inner	1176.2.u.c.1097.17		48
21.5	even	6	inner	1176.2.u.c.1097.8		48
21.11	odd	6		1176.2.k.b.881.2	yes	24
21.17	even	6		1176.2.k.b.881.23	yes	24
21.20	even	2	inner	1176.2.u.c.521.10		48
28.3	even	6		2352.2.k.j.881.24		24
28.11	odd	6		2352.2.k.j.881.1		24
84.11	even	6		2352.2.k.j.881.23		24
84.59	odd	6		2352.2.k.j.881.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.k.b.881.1	✓	24	7.3	odd	6
1176.2.k.b.881.2	yes	24	21.11	odd	6
1176.2.k.b.881.23	yes	24	21.17	even	6
1176.2.k.b.881.24	yes	24	7.4	even	3
1176.2.u.c.521.8		48	1.1	even	1	trivial
1176.2.u.c.521.10		48	21.20	even	2	inner
1176.2.u.c.521.15		48	3.2	odd	2	inner
1176.2.u.c.521.17		48	7.6	odd	2	inner
1176.2.u.c.1097.8		48	21.5	even	6	inner
1176.2.u.c.1097.10		48	7.2	even	3	inner
1176.2.u.c.1097.15		48	7.5	odd	6	inner
1176.2.u.c.1097.17		48	21.2	odd	6	inner
2352.2.k.j.881.1		24	28.11	odd	6
2352.2.k.j.881.2		24	84.59	odd	6
2352.2.k.j.881.23		24	84.11	even	6
2352.2.k.j.881.24		24	28.3	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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02453 + 1.39655i) q^{3} +(2.00767 + 3.47739i) q^{5} +(-0.900685 - 2.86160i) q^{9} +(3.26634 + 1.88582i) q^{11} +4.48235i q^{13} +(-6.91326 - 0.758876i) q^{15} +(-2.05988 + 3.56782i) q^{17} +(5.69006 - 3.28516i) q^{19} +(4.33901 - 2.50513i) q^{23} +(-5.56150 + 9.63280i) q^{25} +(4.91914 + 1.67394i) q^{27} +1.23251i q^{29} +(-0.809487 - 0.467358i) q^{31} +(-5.98009 + 2.62952i) q^{33} +(-1.01181 - 1.75250i) q^{37} +(-6.25981 - 4.59229i) q^{39} +2.21527 q^{41} -3.14096 q^{43} +(8.14263 - 8.87719i) q^{45} +(-2.92829 - 5.07195i) q^{47} +(-2.87222 - 6.53206i) q^{51} +(-3.95157 - 2.28144i) q^{53} +15.1444i q^{55} +(-1.24175 + 11.3122i) q^{57} +(0.982768 - 1.70220i) q^{59} +(8.00812 - 4.62349i) q^{61} +(-15.5869 + 8.99909i) q^{65} +(-3.88026 + 6.72081i) q^{67} +(-0.946908 + 8.62621i) q^{69} -7.97495i q^{71} +(-12.8361 - 7.41091i) q^{73} +(-7.75474 - 17.6360i) q^{75} +(-1.85129 - 3.20653i) q^{79} +(-7.37753 + 5.15480i) q^{81} -9.15704 q^{83} -16.5423 q^{85} +(-1.72126 - 1.26275i) q^{87} +(6.53595 + 11.3206i) q^{89} +(1.48203 - 0.651666i) q^{93} +(22.8475 + 13.1910i) q^{95} -7.06073i q^{97} +(2.45453 - 11.0455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) \) 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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