LMFDB - Embedded newform 85.2.l.a.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, degree $4$, 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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	85.76
Dual form			85.2.l.a.66.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.44607 + 1.44607i) q^{2} +(-1.22292 + 2.95240i) q^{3} -2.18224i q^{4} +(0.923880 + 0.382683i) q^{5} +(-2.50094 - 6.03781i) q^{6} +(1.08781 - 0.450584i) q^{7} +(0.263530 + 0.263530i) q^{8} +(-5.09981 - 5.09981i) q^{9} +(-1.88938 + 0.782608i) q^{10} +(1.88376 + 4.54781i) q^{11} +(6.44284 + 2.66871i) q^{12} -2.46296i q^{13} +(-0.921468 + 2.22462i) q^{14} +(-2.25967 + 2.25967i) q^{15} +3.60231 q^{16} +(-1.36268 + 3.89141i) q^{17} +14.7494 q^{18} +(-1.44372 + 1.44372i) q^{19} +(0.835107 - 2.01613i) q^{20} +3.76267i q^{21} +(-9.30051 - 3.85240i) q^{22} +(-0.0455480 - 0.109963i) q^{23} +(-1.10032 + 0.455769i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.56162 + 3.56162i) q^{26} +(12.4361 - 5.15122i) q^{27} +(-0.983282 - 2.37385i) q^{28} +(0.984309 + 0.407714i) q^{29} -6.53528i q^{30} +(1.06989 - 2.58295i) q^{31} +(-5.73626 + 5.73626i) q^{32} -15.7307 q^{33} +(-3.65672 - 7.59779i) q^{34} +1.17743 q^{35} +(-11.1290 + 11.1290i) q^{36} +(0.885823 - 2.13857i) q^{37} -4.17544i q^{38} +(7.27165 + 3.01202i) q^{39} +(0.142621 + 0.344319i) q^{40} +(-0.662952 + 0.274604i) q^{41} +(-5.44108 - 5.44108i) q^{42} +(7.13881 + 7.13881i) q^{43} +(9.92441 - 4.11082i) q^{44} +(-2.76000 - 6.66322i) q^{45} +(0.224879 + 0.0931480i) q^{46} -3.39482i q^{47} +(-4.40535 + 10.6355i) q^{48} +(-3.96945 + 3.96945i) q^{49} -2.04505 q^{50} +(-9.82256 - 8.78209i) q^{51} -5.37477 q^{52} +(9.84581 - 9.84581i) q^{53} +(-10.5345 + 25.4326i) q^{54} +4.92251i q^{55} +(0.405412 + 0.167927i) q^{56} +(-2.49688 - 6.02800i) q^{57} +(-2.01296 + 0.833797i) q^{58} +(1.07276 + 1.07276i) q^{59} +(4.93114 + 4.93114i) q^{60} +(7.46606 - 3.09254i) q^{61} +(2.18799 + 5.28228i) q^{62} +(-7.84549 - 3.24971i) q^{63} -9.38544i q^{64} +(0.942535 - 2.27548i) q^{65} +(22.7476 - 22.7476i) q^{66} +4.92534 q^{67} +(8.49199 + 2.97370i) q^{68} +0.380355 q^{69} +(-1.70265 + 1.70265i) q^{70} +(2.53962 - 6.13119i) q^{71} -2.68790i q^{72} +(3.38802 + 1.40336i) q^{73} +(1.81155 + 4.37348i) q^{74} +(-2.95240 + 1.22292i) q^{75} +(3.15054 + 3.15054i) q^{76} +(4.09834 + 4.09834i) q^{77} +(-14.8709 + 6.15973i) q^{78} +(3.13055 + 7.55781i) q^{79} +(3.32810 + 1.37854i) q^{80} +21.3794i q^{81} +(0.561579 - 1.35577i) q^{82} +(-4.30539 + 4.30539i) q^{83} +8.21104 q^{84} +(-2.74813 + 3.07372i) q^{85} -20.6464 q^{86} +(-2.40747 + 2.40747i) q^{87} +(-0.702056 + 1.69491i) q^{88} -8.46170i q^{89} +(13.6266 + 5.64433i) q^{90} +(-1.10977 - 2.67922i) q^{91} +(-0.239965 + 0.0993966i) q^{92} +(6.31751 + 6.31751i) q^{93} +(4.90915 + 4.90915i) q^{94} +(-1.88631 + 0.781336i) q^{95} +(-9.92072 - 23.9507i) q^{96} +(-4.14772 - 1.71804i) q^{97} -11.4802i q^{98} +(13.5861 - 32.7998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.44607	+	1.44607i	−1.02253	+	1.02253i	−0.0227858	+	0.999740i	$0.507254\pi$
$2$	−1.44607	+	1.44607i	−1.02253	+	1.02253i	−0.999740	+	0.0227858i	$0.992746\pi$
$3$	−1.22292	+	2.95240i	−0.706056	+	1.70457i	0.00357297	+	0.999994i	$0.498863\pi$
$3$	−1.22292	+	2.95240i	−0.706056	+	1.70457i	−0.709629	+	0.704576i	$0.751137\pi$
$4$		−	2.18224i		−	1.09112i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$6$	−2.50094	−	6.03781i	−1.02101	−	2.46493i
$7$	1.08781	−	0.450584i	0.411152	−	0.170305i	−0.167513	−	0.985870i	$-0.553574\pi$
$7$	1.08781	−	0.450584i	0.411152	−	0.170305i	0.578665	+	0.815565i	$0.303574\pi$
$8$	0.263530	+	0.263530i	0.0931719	+	0.0931719i
$9$	−5.09981	−	5.09981i	−1.69994	−	1.69994i
$10$	−1.88938	+	0.782608i	−0.597475	+	0.247482i
$11$	1.88376	+	4.54781i	0.567976	+	1.37122i	0.903258	+	0.429098i	$0.141169\pi$
$11$	1.88376	+	4.54781i	0.567976	+	1.37122i	−0.335281	+	0.942118i	$0.608831\pi$
$12$	6.44284	+	2.66871i	1.85989	+	0.770391i
$13$		−	2.46296i		−	0.683103i	−0.939863	−	0.341551i	$-0.889048\pi$
$13$		−	2.46296i		−	0.683103i	0.939863	−	0.341551i	$-0.110952\pi$
$14$	−0.921468	+	2.22462i	−0.246273	+	0.594555i
$15$	−2.25967	+	2.25967i	−0.583444	+	0.583444i
$16$	3.60231			0.900578
$17$	−1.36268	+	3.89141i	−0.330499	+	0.943806i
$17$	−1.36268	+	3.89141i	−0.330499	+	0.943806i
$18$	14.7494			3.47646
$19$	−1.44372	+	1.44372i	−0.331212	+	0.331212i	−0.853047	−	0.521834i	$-0.825248\pi$
$19$	−1.44372	+	1.44372i	−0.331212	+	0.331212i	0.521834	+	0.853047i	$0.325248\pi$
$20$	0.835107	−	2.01613i	0.186736	−	0.450819i
$21$			3.76267i			0.821082i
$22$	−9.30051	−	3.85240i	−1.98288	−	0.821334i
$23$	−0.0455480	−	0.109963i	−0.00949741	−	0.0229288i	0.919060	−	0.394118i	$-0.128950\pi$
$23$	−0.0455480	−	0.109963i	−0.00949741	−	0.0229288i	−0.928557	+	0.371190i	$0.878950\pi$
$24$	−1.10032	+	0.455769i	−0.224603	+	0.0930334i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	3.56162	+	3.56162i	0.698491	+	0.698491i
$27$	12.4361	−	5.15122i	2.39334	−	0.991353i
$28$	−0.983282	−	2.37385i	−0.185823	−	0.448616i
$29$	0.984309	+	0.407714i	0.182782	+	0.0757106i	0.472197	−	0.881493i	$-0.343461\pi$
$29$	0.984309	+	0.407714i	0.182782	+	0.0757106i	−0.289416	+	0.957204i	$0.593461\pi$
$30$		−	6.53528i		−	1.19317i
$31$	1.06989	−	2.58295i	0.192159	−	0.463912i	−0.798208	−	0.602382i	$-0.794218\pi$
$31$	1.06989	−	2.58295i	0.192159	−	0.463912i	0.990367	+	0.138470i	$0.0442184\pi$
$32$	−5.73626	+	5.73626i	−1.01404	+	1.01404i
$33$	−15.7307			−2.73836
$34$	−3.65672	−	7.59779i	−0.627123	−	1.30301i
$35$	1.17743			0.199022
$36$	−11.1290	+	11.1290i	−1.85483	+	1.85483i
$37$	0.885823	−	2.13857i	0.145628	−	0.351578i	−0.834187	−	0.551481i	$-0.814063\pi$
$37$	0.885823	−	2.13857i	0.145628	−	0.351578i	0.979816	+	0.199903i	$0.0640628\pi$
$38$		−	4.17544i		−	0.677346i
$39$	7.27165	+	3.01202i	1.16440	+	0.482309i
$40$	0.142621	+	0.344319i	0.0225504	+	0.0544415i
$41$	−0.662952	+	0.274604i	−0.103536	+	0.0428859i	−0.433850	−	0.900985i	$-0.642845\pi$
$41$	−0.662952	+	0.274604i	−0.103536	+	0.0428859i	0.330314	+	0.943871i	$0.392845\pi$
$42$	−5.44108	−	5.44108i	−0.839577	−	0.839577i
$43$	7.13881	+	7.13881i	1.08866	+	1.08866i	0.995667	+	0.0929914i	$0.0296429\pi$
$43$	7.13881	+	7.13881i	1.08866	+	1.08866i	0.0929914	+	0.995667i	$0.470357\pi$
$44$	9.92441	−	4.11082i	1.49616	−	0.619730i
$45$	−2.76000	−	6.66322i	−0.411436	−	0.993294i
$46$	0.224879	+	0.0931480i	0.0331566	+	0.0137339i
$47$		−	3.39482i		−	0.495186i	−0.968864	−	0.247593i	$-0.920360\pi$
$47$		−	3.39482i		−	0.495186i	0.968864	−	0.247593i	$-0.0796396\pi$
$48$	−4.40535	+	10.6355i	−0.635858	+	1.53510i
$49$	−3.96945	+	3.96945i	−0.567065	+	0.567065i
$50$	−2.04505			−0.289214
$51$	−9.82256	−	8.78209i	−1.37543	−	1.22974i
$52$	−5.37477			−0.745347
$53$	9.84581	−	9.84581i	1.35243	−	1.35243i	0.469487	−	0.882940i	$-0.344439\pi$
$53$	9.84581	−	9.84581i	1.35243	−	1.35243i	0.882940	−	0.469487i	$-0.155561\pi$
$54$	−10.5345	+	25.4326i	−1.43357	+	3.46093i
$55$			4.92251i			0.663752i
$56$	0.405412	+	0.167927i	0.0541754	+	0.0224402i
$57$	−2.49688	−	6.02800i	−0.330720	−	0.798429i
$58$	−2.01296	+	0.833797i	−0.264315	+	0.109483i
$59$	1.07276	+	1.07276i	0.139661	+	0.139661i	0.773481	−	0.633820i	$-0.218514\pi$
$59$	1.07276	+	1.07276i	0.139661	+	0.139661i	−0.633820	+	0.773481i	$0.718514\pi$
$60$	4.93114	+	4.93114i	0.636607	+	0.636607i
$61$	7.46606	−	3.09254i	0.955931	−	0.395959i	0.150474	−	0.988614i	$-0.451920\pi$
$61$	7.46606	−	3.09254i	0.955931	−	0.395959i	0.805457	+	0.592655i	$0.201920\pi$
$62$	2.18799	+	5.28228i	0.277875	+	0.670850i
$63$	−7.84549	−	3.24971i	−0.988439	−	0.409425i
$64$		−	9.38544i		−	1.17318i
$65$	0.942535	−	2.27548i	0.116907	−	0.282239i
$66$	22.7476	−	22.7476i	2.80004	−	2.80004i
$67$	4.92534			0.601726			0.300863	−	0.953667i	$-0.402725\pi$
$67$	4.92534			0.601726			0.300863	+	0.953667i	$0.402725\pi$
$68$	8.49199	+	2.97370i	1.02981	+	0.360614i
$69$	0.380355			0.0457894
$70$	−1.70265	+	1.70265i	−0.203506	+	0.203506i
$71$	2.53962	−	6.13119i	0.301398	−	0.727639i	−0.698530	−	0.715581i	$-0.746162\pi$
$71$	2.53962	−	6.13119i	0.301398	−	0.727639i	0.999927	−	0.0120574i	$-0.00383809\pi$
$72$		−	2.68790i		−	0.316773i
$73$	3.38802	+	1.40336i	0.396537	+	0.164251i	0.572036	−	0.820228i	$-0.306154\pi$
$73$	3.38802	+	1.40336i	0.396537	+	0.164251i	−0.175499	+	0.984480i	$0.556154\pi$
$74$	1.81155	+	4.37348i	0.210589	+	0.508407i
$75$	−2.95240	+	1.22292i	−0.340914	+	0.141211i
$76$	3.15054	+	3.15054i	0.361392	+	0.361392i
$77$	4.09834	+	4.09834i	0.467049	+	0.467049i
$78$	−14.8709	+	6.15973i	−1.68380	+	0.697452i
$79$	3.13055	+	7.55781i	0.352214	+	0.850320i	0.996346	+	0.0854058i	$0.0272187\pi$
$79$	3.13055	+	7.55781i	0.352214	+	0.850320i	−0.644132	+	0.764914i	$0.722781\pi$
$80$	3.32810	+	1.37854i	0.372093	+	0.154126i
$81$			21.3794i			2.37549i
$82$	0.561579	−	1.35577i	0.0620160	−	0.149720i
$83$	−4.30539	+	4.30539i	−0.472578	+	0.472578i	−0.902748	−	0.430170i	$-0.858454\pi$
$83$	−4.30539	+	4.30539i	−0.472578	+	0.472578i	0.430170	+	0.902748i	$0.358454\pi$
$84$	8.21104			0.895898
$85$	−2.74813	+	3.07372i	−0.298077	+	0.333392i
$86$	−20.6464			−2.22636
$87$	−2.40747	+	2.40747i	−0.258108	+	0.258108i
$88$	−0.702056	+	1.69491i	−0.0748394	+	0.180678i
$89$		−	8.46170i		−	0.896938i	−0.893798	−	0.448469i	$-0.851969\pi$
$89$		−	8.46170i		−	0.896938i	0.893798	−	0.448469i	$-0.148031\pi$
$90$	13.6266	+	5.64433i	1.43637	+	0.594965i
$91$	−1.10977	−	2.67922i	−0.116336	−	0.280859i
$92$	−0.239965	+	0.0993966i	−0.0250180	+	0.0103628i
$93$	6.31751	+	6.31751i	0.655096	+	0.655096i
$94$	4.90915	+	4.90915i	0.506341	+	0.506341i
$95$	−1.88631	+	0.781336i	−0.193532	+	0.0801634i
$96$	−9.92072	−	23.9507i	−1.01253	−	2.44446i
$97$	−4.14772	−	1.71804i	−0.421137	−	0.174441i	0.162043	−	0.986784i	$-0.448192\pi$
$97$	−4.14772	−	1.71804i	−0.421137	−	0.174441i	−0.583180	+	0.812343i	$0.698192\pi$
$98$		−	11.4802i		−	1.15968i
$99$	13.5861	−	32.7998i	1.36546	−	3.29650i
$100$	1.54308	−	1.54308i	0.154308	−	0.154308i
$101$	−17.7855			−1.76972			−0.884861	−	0.465854i	$-0.845747\pi$
$101$	−17.7855			−1.76972			−0.884861	+	0.465854i	$0.845747\pi$
$102$	26.9036	−	1.50459i	2.66386	−	0.148977i
$103$	−11.3352			−1.11689			−0.558445	−	0.829542i	$-0.688602\pi$
$103$	−11.3352			−1.11689			−0.558445	+	0.829542i	$0.688602\pi$
$104$	0.649065	−	0.649065i	0.0636460	−	0.0636460i
$105$	−1.43991	+	3.47625i	−0.140521	+	0.339248i
$106$			28.4755i			2.76578i
$107$	−11.9056	−	4.93146i	−1.15096	−	0.476742i	−0.276102	−	0.961128i	$-0.589043\pi$
$107$	−11.9056	−	4.93146i	−1.15096	−	0.476742i	−0.874854	+	0.484386i	$0.839043\pi$
$108$	−11.2412	−	27.1386i	−1.08168	−	2.61142i
$109$	10.4593	−	4.33237i	1.00182	−	0.414966i	0.179354	−	0.983785i	$-0.442599\pi$
$109$	10.4593	−	4.33237i	1.00182	−	0.414966i	0.822463	+	0.568819i	$0.192599\pi$
$110$	−7.11830	−	7.11830i	−0.678703	−	0.678703i
$111$	5.23061	+	5.23061i	0.496467	+	0.496467i
$112$	3.91862	−	1.62314i	0.370274	−	0.153373i
$113$	−2.23904	−	5.40551i	−0.210631	−	0.508508i	0.782890	−	0.622161i	$-0.213745\pi$
$113$	−2.23904	−	5.40551i	−0.210631	−	0.508508i	−0.993521	+	0.113653i	$0.963745\pi$
$114$	12.3276	+	5.10625i	1.15458	+	0.478244i
$115$		−	0.119023i		−	0.0110989i
$116$	0.889730	−	2.14800i	0.0826093	−	0.199437i
$117$	−12.5606	+	12.5606i	−1.16123	+	1.16123i
$118$	−3.10257			−0.285615
$119$	0.271076	+	4.84710i	0.0248495	+	0.444333i
$120$	−1.19098			−0.108721
$121$	−9.35583	+	9.35583i	−0.850530	+	0.850530i
$122$	−6.32441	+	15.2685i	−0.572585	+	1.38234i
$123$		−	2.29312i		−	0.206764i
$124$	−5.63662	−	2.33477i	−0.506184	−	0.209668i
$125$	0.382683	+	0.923880i	0.0342282	+	0.0826343i
$126$	16.0444	−	6.64582i	1.42935	−	0.592057i
$127$	−4.81114	−	4.81114i	−0.426920	−	0.426920i	0.460658	−	0.887578i	$-0.347613\pi$
$127$	−4.81114	−	4.81114i	−0.426920	−	0.426920i	−0.887578	+	0.460658i	$0.847613\pi$
$128$	2.09949	+	2.09949i	0.185570	+	0.185570i
$129$	−29.8069	+	12.3464i	−2.62435	+	1.08704i
$130$	1.92753	+	4.65348i	0.169056	+	0.408137i
$131$	1.75560	+	0.727194i	0.153388	+	0.0635352i	0.458056	−	0.888923i	$-0.348546\pi$
$131$	1.75560	+	0.727194i	0.153388	+	0.0635352i	−0.304669	+	0.952458i	$0.598546\pi$
$132$			34.3281i			2.98787i
$133$	−0.919971	+	2.22101i	−0.0797716	+	0.192586i
$134$	−7.12239	+	7.12239i	−0.615281	+	0.615281i
$135$	13.4608			1.15852
$136$	−1.38461	+	0.666397i	−0.118729	+	0.0571431i
$137$	19.3637			1.65435			0.827174	−	0.561946i	$-0.189947\pi$
$137$	19.3637			1.65435			0.827174	+	0.561946i	$0.189947\pi$
$138$	−0.550021	+	0.550021i	−0.0468209	+	0.0468209i
$139$	3.16744	−	7.64688i	0.268659	−	0.648600i	−0.730762	−	0.682632i	$-0.760835\pi$
$139$	3.16744	−	7.64688i	0.268659	−	0.648600i	0.999421	+	0.0340327i	$0.0108350\pi$
$140$		−	2.56944i		−	0.217157i
$141$	10.0229	+	4.15161i	0.844079	+	0.349629i
$142$	5.19366	+	12.5386i	0.435842	+	1.05222i
$143$	11.2011	−	4.63964i	0.936682	−	0.387986i
$144$	−18.3711	−	18.3711i	−1.53092	−	1.53092i
$145$	0.753357	+	0.753357i	0.0625629	+	0.0625629i
$146$	−6.92867	+	2.86995i	−0.573421	+	0.237519i
$147$	−6.86507	−	16.5738i	−0.566222	−	1.36698i
$148$	−4.66686	−	1.93308i	−0.383614	−	0.158898i
$149$			4.93485i			0.404279i	0.979357	+	0.202139i	$0.0647894\pi$
$149$			4.93485i			0.404279i	−0.979357	+	0.202139i	$0.935211\pi$
$150$	2.50094	−	6.03781i	0.204201	−	0.492985i
$151$	−0.503992	+	0.503992i	−0.0410142	+	0.0410142i	−0.727316	−	0.686302i	$-0.759233\pi$
$151$	−0.503992	+	0.503992i	−0.0410142	+	0.0410142i	0.686302	+	0.727316i	$0.259233\pi$
$152$	−0.760928			−0.0617194
$153$	26.7949	−	12.8960i	2.16624	−	1.04258i
$154$	−11.8530			−0.955140
$155$	1.97691	−	1.97691i	0.158789	−	0.158789i
$156$	6.57294	−	15.8685i	0.526256	−	1.27050i
$157$		−	5.88566i		−	0.469727i	−0.972028	−	0.234863i	$-0.924536\pi$
$157$		−	5.88566i		−	0.469727i	0.972028	−	0.234863i	$-0.0754642\pi$
$158$	−15.4561	−	6.40213i	−1.22962	−	0.509326i
$159$	17.0281	+	41.1095i	1.35042	+	3.26019i
$160$	−7.49478	+	3.10444i	−0.592514	+	0.245427i
$161$	−0.0990947	−	0.0990947i	−0.00780976	−	0.00780976i
$162$	−30.9161	−	30.9161i	−2.42900	−	2.42900i
$163$	5.44737	−	2.25638i	0.426671	−	0.176733i	−0.159006	−	0.987278i	$-0.550829\pi$
$163$	5.44737	−	2.25638i	0.426671	−	0.176733i	0.585677	+	0.810545i	$0.300829\pi$
$164$	0.599251	+	1.44672i	0.0467936	+	0.112970i
$165$	−14.5332	−	6.01986i	−1.13141	−	0.468646i
$166$		−	12.4518i		−	0.966446i
$167$	−4.12089	+	9.94871i	−0.318884	+	0.769854i	0.680430	+	0.732813i	$0.261793\pi$
$167$	−4.12089	+	9.94871i	−0.318884	+	0.769854i	−0.999314	+	0.0370408i	$0.988207\pi$
$168$	−0.991576	+	0.991576i	−0.0765018	+	0.0765018i
$169$	6.93382			0.533371
$170$	−0.470824	−	8.41881i	−0.0361106	−	0.645693i
$171$	14.7254			1.12608
$172$	15.5786	−	15.5786i	1.18786	−	1.18786i
$173$	3.71087	−	8.95884i	0.282132	−	0.681128i	−0.717753	−	0.696298i	$-0.754829\pi$
$173$	3.71087	−	8.95884i	0.282132	−	0.681128i	0.999885	+	0.0151704i	$0.00482908\pi$
$174$		−	6.96274i		−	0.527844i
$175$	1.08781	+	0.450584i	0.0822304	+	0.0340609i
$176$	6.78591	+	16.3826i	0.511507	+	1.23489i
$177$	−4.47912	+	1.85531i	−0.336671	+	0.139454i
$178$	12.2362	+	12.2362i	0.917143	+	0.917143i
$179$	−11.1126	−	11.1126i	−0.830594	−	0.830594i	0.157004	−	0.987598i	$-0.449817\pi$
$179$	−11.1126	−	11.1126i	−0.830594	−	0.830594i	−0.987598	+	0.157004i	$0.949817\pi$
$180$	−14.5407	+	6.02297i	−1.08380	+	0.448926i
$181$	−1.52658	−	3.68550i	−0.113470	−	0.273941i	0.856935	−	0.515425i	$-0.172366\pi$
$181$	−1.52658	−	3.68550i	−0.113470	−	0.273941i	−0.970405	+	0.241484i	$0.922366\pi$
$182$	5.47915	+	2.26954i	0.406142	+	0.168230i
$183$			25.8247i			1.90902i
$184$	0.0169752	−	0.0409817i	0.00125143	−	0.00302121i
$185$	1.63679	−	1.63679i	0.120339	−	0.120339i
$186$	−18.2711			−1.33970
$187$	−20.2644	+	1.13329i	−1.48188	+	0.0828745i
$188$	−7.40832			−0.540307
$189$	11.2071	−	11.2071i	0.815193	−	0.815193i
$190$	1.59787	−	3.85761i	0.115922	−	0.279860i
$191$		−	19.2007i		−	1.38931i	−0.719343	−	0.694655i	$-0.755557\pi$
$191$		−	19.2007i		−	1.38931i	0.719343	−	0.694655i	$-0.244443\pi$
$192$	27.7096	+	11.4777i	1.99977	+	0.828330i
$193$	−4.50016	−	10.8643i	−0.323929	−	0.782033i	−0.999018	−	0.0442973i	$-0.985895\pi$
$193$	−4.50016	−	10.8643i	−0.323929	−	0.782033i	0.675090	−	0.737736i	$-0.264105\pi$
$194$	8.48231	−	3.51349i	0.608994	−	0.252254i
$195$	5.56548	+	5.56548i	0.398552	+	0.398552i
$196$	8.66229	+	8.66229i	0.618735	+	0.618735i
$197$	17.6821	−	7.32418i	1.25980	−	0.521826i	0.349952	−	0.936768i	$-0.386198\pi$
$197$	17.6821	−	7.32418i	1.25980	−	0.521826i	0.909848	+	0.414942i	$0.136198\pi$
$198$	27.7843	+	67.0773i	1.97455	+	4.76697i
$199$	9.65379	+	3.99873i	0.684339	+	0.283463i	0.697640	−	0.716449i	$-0.254234\pi$
$199$	9.65379	+	3.99873i	0.684339	+	0.283463i	−0.0133003	+	0.999912i	$0.504234\pi$
$200$			0.372688i			0.0263530i
$201$	−6.02332	+	14.5416i	−0.424852	+	1.02568i
$202$	25.7191	−	25.7191i	1.80959	−	1.80959i
$203$	1.25445			0.0880449
$204$	−19.1646	+	21.4352i	−1.34179	+	1.50076i
$205$	−0.717574			−0.0501176
$206$	16.3915	−	16.3915i	1.14205	−	1.14205i
$207$	−0.328502	+	0.793074i	−0.0228325	+	0.0551224i
$208$		−	8.87236i		−	0.615187i
$209$	−9.28540	−	3.84614i	−0.642284	−	0.266043i
$210$	−2.94469	−	7.10912i	−0.203203	−	0.490576i
$211$	−20.1248	+	8.33599i	−1.38545	+	0.573873i	−0.945933	−	0.324361i	$-0.894851\pi$
$211$	−20.1248	+	8.33599i	−1.38545	+	0.573873i	−0.439518	+	0.898234i	$0.644851\pi$
$212$	−21.4859	−	21.4859i	−1.47566	−	1.47566i
$213$	14.9960	+	14.9960i	1.02751	+	1.02751i
$214$	24.3476	−	10.0851i	1.66436	−	0.689402i
$215$	3.86350	+	9.32730i	0.263488	+	0.636117i
$216$	4.63480	+	1.91980i	0.315358	+	0.130626i
$217$		−	3.29183i		−	0.223464i
$218$	−8.85993	+	21.3898i	−0.600070	+	1.44870i
$219$	−8.28658	+	8.28658i	−0.559955	+	0.559955i
$220$	10.7421			0.724232
$221$	9.58440	+	3.35623i	0.644717	+	0.225765i
$222$	−15.1277			−1.01530
$223$	−14.1552	+	14.1552i	−0.947905	+	0.947905i	−0.998709	−	0.0508034i	$-0.983822\pi$
$223$	−14.1552	+	14.1552i	−0.947905	+	0.947905i	0.0508034	+	0.998709i	$0.483822\pi$
$224$	−3.65527	+	8.82460i	−0.244228	+	0.589618i
$225$		−	7.21221i		−	0.480814i
$226$	11.0546	+	4.57895i	0.735338	+	0.304587i
$227$	5.27349	+	12.7313i	0.350014	+	0.845008i	0.996617	+	0.0821817i	$0.0261888\pi$
$227$	5.27349	+	12.7313i	0.350014	+	0.845008i	−0.646604	+	0.762826i	$0.723811\pi$
$228$	−13.1545	+	5.44879i	−0.871181	+	0.360855i
$229$	2.57403	+	2.57403i	0.170096	+	0.170096i	0.787022	−	0.616925i	$-0.211622\pi$
$229$	2.57403	+	2.57403i	0.170096	+	0.170096i	−0.616925	+	0.787022i	$0.711622\pi$
$230$	0.172115	+	0.172115i	0.0113489	+	0.0113489i
$231$	−17.1119	+	7.08798i	−1.12588	+	0.466355i
$232$	0.151950	+	0.366840i	0.00997601	+	0.0240842i
$233$	13.0828	+	5.41909i	0.857085	+	0.355016i	0.767567	−	0.640969i	$-0.221467\pi$
$233$	13.0828	+	5.41909i	0.857085	+	0.355016i	0.0895185	+	0.995985i	$0.471467\pi$
$234$		−	36.3271i		−	2.37478i
$235$	1.29914	−	3.13641i	0.0847467	−	0.204597i
$236$	2.34102	−	2.34102i	0.152387	−	0.152387i
$237$	−26.1421			−1.69811
$238$	−7.40125	−	6.61726i	−0.479752	−	0.428933i
$239$	−22.6621			−1.46589			−0.732944	−	0.680289i	$-0.761854\pi$
$239$	−22.6621			−1.46589			−0.732944	+	0.680289i	$0.761854\pi$
$240$	−8.14003	+	8.14003i	−0.525437	+	0.525437i
$241$	2.31331	−	5.58483i	0.149014	−	0.359751i	−0.831693	−	0.555236i	$-0.812628\pi$
$241$	2.31331	−	5.58483i	0.149014	−	0.359751i	0.980707	+	0.195485i	$0.0626281\pi$
$242$		−	27.0584i		−	1.73938i
$243$	−25.8121	−	10.6917i	−1.65585	−	0.685875i
$244$	−6.74866	−	16.2927i	−0.432039	−	1.04303i
$245$	−5.18634	+	2.14825i	−0.331343	+	0.137247i
$246$	3.31601	+	3.31601i	0.211421	+	0.211421i
$247$	3.55583	+	3.55583i	0.226252	+	0.226252i
$248$	0.962635	−	0.398737i	0.0611274	−	0.0253198i
$249$	−7.44607	−	17.9764i	−0.471875	−	1.13921i
$250$	−1.88938	−	0.782608i	−0.119495	−	0.0494965i
$251$		−	0.706952i		−	0.0446224i	−0.999751	−	0.0223112i	$-0.992898\pi$
$251$		−	0.706952i		−	0.0446224i	0.999751	−	0.0223112i	$-0.00710247\pi$
$252$	−7.09164	+	17.1207i	−0.446731	+	1.07850i
$253$	0.414287	−	0.414287i	0.0260460	−	0.0260460i
$254$	13.9145			0.873073
$255$	−5.71410	−	11.8725i	−0.357831	−	0.743486i
$256$	12.6989			0.793679
$257$	10.6578	−	10.6578i	0.664817	−	0.664817i	−0.291695	−	0.956511i	$-0.594219\pi$
$257$	10.6578	−	10.6578i	0.664817	−	0.664817i	0.956511	+	0.291695i	$0.0942192\pi$
$258$	25.2490	−	60.9566i	1.57194	−	3.79499i
$259$		−	2.72548i		−	0.169353i
$260$	−4.96564	−	2.05684i	−0.307956	−	0.127560i
$261$	−2.94052	−	7.09905i	−0.182014	−	0.439420i
$262$	−3.59030	+	1.48715i	−0.221809	+	0.0918764i
$263$	−10.2737	−	10.2737i	−0.633504	−	0.633504i	0.315441	−	0.948945i	$-0.397848\pi$
$263$	−10.2737	−	10.2737i	−0.633504	−	0.633504i	−0.948945	+	0.315441i	$0.897848\pi$
$264$	−4.14550	−	4.14550i	−0.255138	−	0.255138i
$265$	12.8642	−	5.32851i	0.790240	−	0.327328i
$266$	−1.88139	−	4.54207i	−0.115355	−	0.278492i
$267$	24.9823	+	10.3480i	1.52889	+	0.633289i
$268$		−	10.7483i		−	0.656555i
$269$	−10.8530	+	26.2015i	−0.661720	+	1.59753i	0.133387	+	0.991064i	$0.457415\pi$
$269$	−10.8530	+	26.2015i	−0.661720	+	1.59753i	−0.795107	+	0.606470i	$0.792585\pi$
$270$	−19.4652	+	19.4652i	−1.18462	+	1.18462i
$271$	−9.29673			−0.564736			−0.282368	−	0.959306i	$-0.591120\pi$
$271$	−9.29673			−0.564736			−0.282368	+	0.959306i	$0.591120\pi$
$272$	−4.90880	+	14.0181i	−0.297640	+	0.849971i
$273$	9.26731			0.560883
$274$	−28.0012	+	28.0012i	−1.69161	+	1.69161i
$275$	−1.88376	+	4.54781i	−0.113595	+	0.274243i
$276$		−	0.830026i		−	0.0499617i
$277$	−20.7007	−	8.57453i	−1.24379	−	0.515193i	−0.338891	−	0.940826i	$-0.610052\pi$
$277$	−20.7007	−	8.57453i	−1.24379	−	0.515193i	−0.904896	+	0.425632i	$0.860052\pi$
$278$	6.47758	+	15.6383i	0.388500	+	0.937921i
$279$	−18.6288	+	7.71631i	−1.11528	+	0.461963i
$280$	0.310289	+	0.310289i	0.0185433	+	0.0185433i
$281$	−22.0979	−	22.0979i	−1.31825	−	1.31825i	−0.915162	−	0.403085i	$-0.867938\pi$
$281$	−22.0979	−	22.0979i	−1.31825	−	1.31825i	−0.403085	−	0.915162i	$-0.632062\pi$
$282$	−20.4973	+	8.49027i	−1.22060	+	0.505588i
$283$	4.49480	+	10.8514i	0.267188	+	0.645050i	0.999349	−	0.0360824i	$-0.0114879\pi$
$283$	4.49480	+	10.8514i	0.267188	+	0.645050i	−0.732160	+	0.681132i	$0.761488\pi$
$284$	−13.3797	−	5.54206i	−0.793941	−	0.328861i
$285$		−	6.52466i		−	0.386488i
$286$	−9.48831	+	22.9068i	−0.561055	+	1.35451i
$287$	−0.597431	+	0.597431i	−0.0352652	+	0.0352652i
$288$	58.5076			3.44759
$289$	−13.2862	−	10.6055i	−0.781541	−	0.623854i
$290$	−2.17882			−0.127944
$291$	10.1447	−	10.1447i	0.594693	−	0.594693i
$292$	3.06247	−	7.39346i	0.179218	−	0.432670i
$293$			26.5905i			1.55344i	0.629848	+	0.776718i	$0.283117\pi$
$293$			26.5905i			1.55344i	−0.629848	+	0.776718i	$0.716883\pi$
$294$	33.8942	+	14.0394i	1.97675	+	0.818796i
$295$	0.580573	+	1.40163i	0.0338023	+	0.0816059i
$296$	0.797017	−	0.330135i	0.0463257	−	0.0191887i
$297$	46.8535	+	46.8535i	2.71872	+	2.71872i
$298$	−7.13614	−	7.13614i	−0.413386	−	0.413386i
$299$	−0.270834	+	0.112183i	−0.0156627	+	0.00648771i
$300$	2.66871	+	6.44284i	0.154078	+	0.371978i
$301$	10.9823	+	4.54901i	0.633008	+	0.262200i
$302$		−	1.45761i		−	0.0838763i
$303$	21.7503	−	52.5099i	1.24952	−	3.01662i
$304$	−5.20073	+	5.20073i	−0.298282	+	0.298282i
$305$	8.08120			0.462728
$306$	−20.0987	+	57.3958i	−1.14896	+	3.28110i
$307$	18.6981			1.06715			0.533577	−	0.845751i	$-0.320847\pi$
$307$	18.6981			1.06715			0.533577	+	0.845751i	$0.320847\pi$
$308$	8.94356	−	8.94356i	0.509606	−	0.509606i
$309$	13.8621	−	33.4660i	0.788586	−	1.90382i
$310$			5.71749i			0.324732i
$311$	7.35993	+	3.04858i	0.417343	+	0.172869i	0.581466	−	0.813571i	$-0.302479\pi$
$311$	7.35993	+	3.04858i	0.417343	+	0.172869i	−0.164123	+	0.986440i	$0.552479\pi$
$312$	1.12254	+	2.71006i	0.0635514	+	0.153427i
$313$	−7.37958	+	3.05672i	−0.417118	+	0.172776i	−0.581364	−	0.813643i	$-0.697481\pi$
$313$	−7.37958	+	3.05672i	−0.417118	+	0.172776i	0.164246	+	0.986419i	$0.447481\pi$
$314$	8.51107	+	8.51107i	0.480308	+	0.480308i
$315$	−6.00468	−	6.00468i	−0.338325	−	0.338325i
$316$	16.4929	−	6.83160i	0.927801	−	0.384308i
$317$	5.98211	+	14.4421i	0.335989	+	0.811149i	0.998092	+	0.0617365i	$0.0196638\pi$
$317$	5.98211	+	14.4421i	0.335989	+	0.811149i	−0.662104	+	0.749412i	$0.730336\pi$
$318$	−84.0710	−	34.8234i	−4.71447	−	1.95280i
$319$			5.24449i			0.293635i
$320$	3.59165	−	8.67101i	0.200779	−	0.484724i
$321$	29.1193	−	29.1193i	1.62528	−	1.62528i
$322$	0.286596			0.0159714
$323$	−3.65078	−	7.58545i	−0.203135	−	0.422066i
$324$	46.6550			2.59194
$325$	1.74158	−	1.74158i	0.0966053	−	0.0966053i
$326$	−4.61441	+	11.1402i	−0.255568	+	0.616996i
$327$			36.1781i			2.00065i
$328$	−0.247074	−	0.102341i	−0.0136424	−	0.00565086i
$329$	−1.52965	−	3.69291i	−0.0843325	−	0.203597i
$330$	29.7212	−	12.3109i	1.63610	−	0.677695i
$331$	−3.13284	−	3.13284i	−0.172197	−	0.172197i	0.615747	−	0.787944i	$-0.288854\pi$
$331$	−3.13284	−	3.13284i	−0.172197	−	0.172197i	−0.787944	+	0.615747i	$0.788854\pi$
$332$	9.39539	+	9.39539i	0.515639	+	0.515639i
$333$	−15.4238	+	6.38875i	−0.845219	+	0.350101i
$334$	−8.42743	−	20.3456i	−0.461129	−	1.11326i
$335$	4.55042	+	1.88485i	0.248616	+	0.102980i
$336$			13.5543i			0.739448i
$337$	2.30990	−	5.57660i	0.125828	−	0.303777i	−0.848394	−	0.529365i	$-0.822430\pi$
$337$	2.30990	−	5.57660i	0.125828	−	0.303777i	0.974223	+	0.225588i	$0.0724303\pi$
$338$	−10.0268	+	10.0268i	−0.545385	+	0.545385i
$339$	18.6974			1.01550
$340$	6.70759	+	5.99708i	0.363770	+	0.325237i
$341$	13.7622			0.745266
$342$	−21.2940	+	21.2940i	−1.15145	+	1.15145i
$343$	−5.68351	+	13.7212i	−0.306881	+	0.740875i
$344$			3.76258i			0.202865i
$345$	0.351403	+	0.145556i	0.0189189	+	0.00783646i
$346$	7.58893	+	18.3213i	0.407983	+	0.984959i
$347$	0.0860097	−	0.0356264i	0.00461724	−	0.00191253i	−0.380374	−	0.924833i	$-0.624205\pi$
$347$	0.0860097	−	0.0356264i	0.00461724	−	0.00191253i	0.384991	+	0.922920i	$0.374205\pi$
$348$	5.25368	+	5.25368i	0.281627	+	0.281627i
$349$	−6.74736	−	6.74736i	−0.361178	−	0.361178i	0.503069	−	0.864247i	$-0.332204\pi$
$349$	−6.74736	−	6.74736i	−0.361178	−	0.361178i	−0.864247	+	0.503069i	$0.832204\pi$
$350$	−2.22462	+	0.921468i	−0.118911	+	0.0492545i
$351$	−12.6873	−	30.6298i	−0.677196	−	1.63490i
$352$	−36.8932	−	15.2816i	−1.96641	−	0.814515i
$353$			17.2138i			0.916197i	0.888901	+	0.458099i	$0.151469\pi$
$353$			17.2138i			0.916197i	−0.888901	+	0.458099i	$0.848531\pi$
$354$	3.79421	−	9.16003i	0.201660	−	0.486850i
$355$	4.69261	−	4.69261i	0.249058	−	0.249058i
$356$	−18.4655			−0.978667
$357$	−14.6421	−	5.12732i	−0.774942	−	0.271366i
$358$	32.1392			1.69861
$359$	12.5475	−	12.5475i	0.662232	−	0.662232i	−0.293673	−	0.955906i	$-0.594878\pi$
$359$	12.5475	−	12.5475i	0.662232	−	0.662232i	0.955906	+	0.293673i	$0.0948778\pi$
$360$	1.02862	−	2.48330i	0.0542128	−	0.130881i
$361$			14.8313i			0.780597i
$362$	7.53704	+	3.12194i	0.396138	+	0.164086i
$363$	−16.1807	−	39.0637i	−0.849266	−	2.05031i
$364$	−5.84671	+	2.42179i	−0.306451	+	0.126936i
$365$	2.59308	+	2.59308i	0.135728	+	0.135728i
$366$	−37.3444	−	37.3444i	−1.95202	−	1.95202i
$367$	−33.5406	+	13.8930i	−1.75081	+	0.725208i	−0.753071	+	0.657939i	$0.771428\pi$
$367$	−33.5406	+	13.8930i	−1.75081	+	0.725208i	−0.997735	+	0.0672686i	$0.978572\pi$
$368$	−0.164078	−	0.396119i	−0.00855316	−	0.0206492i
$369$	4.78135	+	1.98050i	0.248907	+	0.103101i
$370$			4.73382i			0.246100i
$371$	6.27397	−	15.1467i	0.325728	−	0.786377i
$372$	13.7863	−	13.7863i	0.714788	−	0.714788i
$373$	−5.89146			−0.305048			−0.152524	−	0.988300i	$-0.548740\pi$
$373$	−5.89146			−0.305048			−0.152524	+	0.988300i	$0.548740\pi$
$374$	27.6649	−	30.9425i	1.43052	−	1.60000i
$375$	−3.19566			−0.165023
$376$	0.894638	−	0.894638i	0.0461374	−	0.0461374i
$377$	1.00418	−	2.42432i	0.0517181	−	0.124859i
$378$			32.4124i			1.66711i
$379$	27.0452	+	11.2025i	1.38922	+	0.575432i	0.946929	−	0.321442i	$-0.104167\pi$
$379$	27.0452	+	11.2025i	1.38922	+	0.575432i	0.442287	+	0.896874i	$0.354167\pi$
$380$	1.70506	+	4.11638i	0.0874678	+	0.211166i
$381$	20.0881	−	8.32075i	1.02914	−	0.426285i
$382$	27.7655	+	27.7655i	1.42061	+	1.42061i
$383$	−8.70178	−	8.70178i	−0.444640	−	0.444640i	0.448928	−	0.893568i	$-0.351806\pi$
$383$	−8.70178	−	8.70178i	−0.444640	−	0.444640i	−0.893568	+	0.448928i	$0.851806\pi$
$384$	−8.76605	+	3.63102i	−0.447340	+	0.185294i
$385$	2.21801	+	5.35474i	0.113040	+	0.272903i
$386$	22.2182	+	9.20306i	1.13087	+	0.468424i
$387$		−	72.8131i		−	3.70130i
$388$	−3.74918	+	9.05132i	−0.190336	+	0.459511i
$389$	−1.50316	+	1.50316i	−0.0762134	+	0.0762134i	−0.744186	−	0.667973i	$-0.767162\pi$
$389$	−1.50316	+	1.50316i	−0.0762134	+	0.0762134i	0.667973	+	0.744186i	$0.267162\pi$
$390$	−16.0962			−0.815061
$391$	0.489977	−	0.0274021i	0.0247792	−	0.00138578i
$392$	−2.09214			−0.105669
$393$	−4.29394	+	4.29394i	−0.216600	+	0.216600i
$394$	−14.9783	+	36.1609i	−0.754597	+	1.82176i
$395$			8.18051i			0.411606i
$396$	−71.5770	−	29.6481i	−3.59688	−	1.48988i
$397$	−9.64298	−	23.2802i	−0.483968	−	1.16840i	−0.957709	−	0.287737i	$-0.907097\pi$
$397$	−9.64298	−	23.2802i	−0.483968	−	1.16840i	0.473742	−	0.880664i	$-0.342903\pi$
$398$	−19.7425	+	8.17762i	−0.989603	+	0.409907i
$399$	−5.43224	−	5.43224i	−0.271952	−	0.271952i
$400$	2.54722	+	2.54722i	0.127361	+	0.127361i
$401$	30.3662	−	12.5781i	1.51641	−	0.628119i	0.539545	−	0.841957i	$-0.318596\pi$
$401$	30.3662	−	12.5781i	1.51641	−	0.628119i	0.976869	+	0.213838i	$0.0685964\pi$
$402$	−12.3180	−	29.7383i	−0.614366	−	1.48321i
$403$	−6.36172	−	2.63511i	−0.316900	−	0.131264i
$404$			38.8122i			1.93098i
$405$	−8.18154	+	19.7520i	−0.406544	+	0.981484i
$406$	−1.81402	+	1.81402i	−0.0900282	+	0.0900282i
$407$	11.3945			0.564803
$408$	−0.274195	−	4.90288i	−0.0135747	−	0.242729i
$409$	−16.5721			−0.819437			−0.409719	−	0.912212i	$-0.634373\pi$
$409$	−16.5721			−0.819437			−0.409719	+	0.912212i	$0.634373\pi$
$410$	1.03766	−	1.03766i	0.0512465	−	0.0512465i
$411$	−23.6803	+	57.1693i	−1.16806	+	2.81995i
$412$			24.7361i			1.21866i
$413$	1.65032	+	0.683586i	0.0812070	+	0.0336371i
$414$	−0.671804	−	1.62188i	−0.0330173	−	0.0797109i
$415$	−5.62526	+	2.33006i	−0.276133	+	0.114378i
$416$	14.1282	+	14.1282i	0.692691	+	0.692691i
$417$	18.7031	+	18.7031i	0.915895	+	0.915895i
$418$	18.9891	−	7.86555i	0.928789	−	0.384717i
$419$	2.03536	+	4.91380i	0.0994339	+	0.240055i	0.965767	−	0.259413i	$-0.0835290\pi$
$419$	2.03536	+	4.91380i	0.0994339	+	0.240055i	−0.866333	+	0.499468i	$0.833529\pi$
$420$	7.58601	+	3.14223i	0.370160	+	0.153325i
$421$			3.72116i			0.181358i	0.995880	+	0.0906791i	$0.0289037\pi$
$421$			3.72116i			0.181358i	−0.995880	+	0.0906791i	$0.971096\pi$
$422$	17.0475	−	41.1564i	0.829861	−	2.00346i
$423$	−17.3129	+	17.3129i	−0.841784	+	0.841784i
$424$	5.18933			0.252016
$425$	−3.71521	+	1.78808i	−0.180214	+	0.0867348i
$426$	−43.3705			−2.10131
$427$	6.72817	−	6.72817i	0.325599	−	0.325599i
$428$	−10.7616	+	25.9808i	−0.520182	+	1.25583i
$429$			38.7440i			1.87058i
$430$	−19.0748	−	7.90105i	−0.919870	−	0.381023i
$431$	0.249747	+	0.602943i	0.0120299	+	0.0290428i	0.929780	−	0.368115i	$-0.119997\pi$
$431$	0.249747	+	0.602943i	0.0120299	+	0.0290428i	−0.917750	+	0.397158i	$0.869997\pi$
$432$	44.7989	−	18.5563i	2.15539	−	0.892790i
$433$	3.75811	+	3.75811i	0.180603	+	0.180603i	0.791619	−	0.611016i	$-0.209239\pi$
$433$	3.75811	+	3.75811i	0.180603	+	0.180603i	−0.611016	+	0.791619i	$0.709239\pi$
$434$	4.76022	+	4.76022i	0.228498	+	0.228498i
$435$	−3.14551	+	1.30291i	−0.150816	+	0.0624699i
$436$	−9.45427	−	22.8246i	−0.452777	−	1.09310i
$437$	0.224514	+	0.0929967i	0.0107400	+	0.00444863i
$438$		−	23.9660i		−	1.14514i
$439$	−2.11850	+	5.11452i	−0.101111	+	0.244103i	−0.966337	−	0.257278i	$-0.917174\pi$
$439$	−2.11850	+	5.11452i	−0.101111	+	0.244103i	0.865227	+	0.501381i	$0.167174\pi$
$440$	−1.29723	+	1.29723i	−0.0618430	+	0.0618430i
$441$	40.4869			1.92795
$442$	−18.7131	+	9.00637i	−0.890090	+	0.428390i
$443$	14.9894			0.712169			0.356084	−	0.934454i	$-0.384112\pi$
$443$	14.9894			0.712169			0.356084	+	0.934454i	$0.384112\pi$
$444$	11.4144	−	11.4144i	0.541705	−	0.541705i
$445$	3.23815	−	7.81759i	0.153503	−	0.370589i
$446$		−	40.9390i		−	1.93852i
$447$	−14.5697	−	6.03495i	−0.689121	−	0.285443i
$448$	−4.22893	−	10.2095i	−0.199798	−	0.482355i
$449$	−19.1997	+	7.95276i	−0.906088	+	0.375314i	−0.786558	−	0.617517i	$-0.788139\pi$
$449$	−19.1997	+	7.95276i	−0.906088	+	0.375314i	−0.119530	+	0.992831i	$0.538139\pi$
$450$	10.4294	+	10.4294i	0.491645	+	0.491645i
$451$	−2.49769	−	2.49769i	−0.117612	−	0.117612i
$452$	−11.7961	+	4.88611i	−0.554843	+	0.229823i
$453$	−0.871641	−	2.10433i	−0.0409533	−	0.0988700i
$454$	−26.0362	−	10.7846i	−1.22194	−	0.506144i
$455$		−	2.89997i		−	0.135953i
$456$	0.930557	−	2.24656i	0.0435773	−	0.105205i
$457$	11.0623	−	11.0623i	0.517472	−	0.517472i	−0.399334	−	0.916806i	$-0.630758\pi$
$457$	11.0623	−	11.0623i	0.517472	−	0.517472i	0.916806	+	0.399334i	$0.130758\pi$
$458$	−7.44445			−0.347856
$459$	3.09902	+	55.4137i	0.144650	+	2.58649i
$460$	−0.259736			−0.0121102
$461$	5.22808	−	5.22808i	0.243496	−	0.243496i	−0.574799	−	0.818295i	$-0.694920\pi$
$461$	5.22808	−	5.22808i	0.243496	−	0.243496i	0.818295	+	0.574799i	$0.194920\pi$
$462$	14.4953	−	34.9947i	0.674382	−	1.62810i
$463$		−	17.2150i		−	0.800049i	−0.916504	−	0.400025i	$-0.869002\pi$
$463$		−	17.2150i		−	0.800049i	0.916504	−	0.400025i	$-0.130998\pi$
$464$	3.54579	+	1.46871i	0.164609	+	0.0681833i
$465$	3.41901	+	8.25423i	0.158553	+	0.382781i
$466$	−26.7551	+	11.0823i	−1.23941	+	0.513379i
$467$	−25.6956	−	25.6956i	−1.18905	−	1.18905i	−0.977330	−	0.211722i	$-0.932093\pi$
$467$	−25.6956	−	25.6956i	−1.18905	−	1.18905i	−0.211722	−	0.977330i	$-0.567907\pi$
$468$	27.4103	+	27.4103i	1.26704	+	1.26704i
$469$	5.35781	−	2.21928i	0.247401	−	0.102477i
$470$	2.65682	+	6.41412i	0.122550	+	0.295861i
$471$	17.3768	+	7.19771i	0.800681	+	0.331653i
$472$			0.565409i			0.0260250i
$473$	−19.0181	+	45.9138i	−0.874454	+	2.11112i
$474$	37.8033	−	37.8033i	1.73636	−	1.73636i
$475$	−2.04173			−0.0936810
$476$	10.5775	−	0.591552i	0.484821	−	0.0271137i
$477$	−100.423			−4.59807
$478$	32.7709	−	32.7709i	1.49891	−	1.49891i
$479$	11.6213	−	28.0562i	0.530989	−	1.28192i	−0.399880	−	0.916567i	$-0.630948\pi$
$479$	11.6213	−	28.0562i	0.530989	−	1.28192i	0.930869	−	0.365353i	$-0.119052\pi$
$480$		−	25.9241i		−	1.18327i
$481$	−5.26721	−	2.18175i	−0.240164	−	0.0994792i
$482$	4.73084	+	11.4213i	0.215484	+	0.520225i
$483$	0.413753	−	0.171382i	0.0188264	−	0.00779815i
$484$	20.4167	+	20.4167i	0.928030	+	0.928030i
$485$	−3.17453	−	3.17453i	−0.144148	−	0.144148i
$486$	52.7871	−	21.8651i	2.39447	−	0.991823i
$487$	9.67548	+	23.3587i	0.438438	+	1.05848i	0.976488	+	0.215570i	$0.0691609\pi$
$487$	9.67548	+	23.3587i	0.438438	+	1.05848i	−0.538051	+	0.842912i	$0.680839\pi$
$488$	2.78251	+	1.15255i	0.125958	+	0.0521736i
$489$			18.8422i			0.852074i
$490$	4.39329	−	10.6063i	0.198468	−	0.479145i
$491$	−20.3605	+	20.3605i	−0.918857	+	0.918857i	−0.996946	−	0.0780890i	$-0.975118\pi$
$491$	−20.3605	+	20.3605i	−0.918857	+	0.918857i	0.0780890	+	0.996946i	$0.475118\pi$
$492$	−5.00413			−0.225604
$493$	−2.92788	+	3.27477i	−0.131865	+	0.147488i
$494$	−10.2840			−0.462697
$495$	25.1039	−	25.1039i	1.12833	−	1.12833i
$496$	3.85409	−	9.30460i	0.173054	−	0.417789i
$497$		−	7.81386i		−	0.350500i
$498$	36.7627	+	15.2276i	1.64737	+	0.682365i
$499$	−5.72345	−	13.8176i	−0.256217	−	0.618562i	0.742465	−	0.669885i	$-0.233656\pi$
$499$	−5.72345	−	13.8176i	−0.256217	−	0.618562i	−0.998682	+	0.0513222i	$0.983656\pi$
$500$	2.01613	−	0.835107i	0.0901639	−	0.0373471i
$501$	−24.3330	−	24.3330i	−1.08712	−	1.08712i
$502$	1.02230	+	1.02230i	0.0456276	+	0.0456276i
$503$	−30.0985	+	12.4672i	−1.34203	+	0.555886i	−0.934062	−	0.357112i	$-0.883761\pi$
$503$	−30.0985	+	12.4672i	−1.34203	+	0.555886i	−0.407965	+	0.912998i	$0.633761\pi$
$504$	−1.21113	−	2.92392i	−0.0539479	−	0.130242i
$505$	−16.4317	−	6.80621i	−0.731199	−	0.302873i
$506$			1.19818i			0.0532655i
$507$	−8.47953	+	20.4714i	−0.376589	+	0.909167i
$508$	−10.4991	+	10.4991i	−0.465820	+	0.465820i
$509$	33.1868			1.47098			0.735490	−	0.677535i	$-0.236952\pi$
$509$	33.1868			1.47098			0.735490	+	0.677535i	$0.236952\pi$
$510$	25.4315	+	8.90551i	1.12613	+	0.394343i
$511$	4.31784			0.191010
$512$	−22.5624	+	22.5624i	−0.997127	+	0.997127i
$513$	−10.5174	+	25.3912i	−0.464355	+	1.12105i
$514$			30.8239i			1.35958i
$515$	−10.4724	−	4.33779i	−0.461467	−	0.191146i
$516$	26.9428	+	65.0457i	1.18609	+	2.86348i
$517$	15.4390	−	6.39505i	0.679007	−	0.281254i
$518$	3.94124	+	3.94124i	0.173168	+	0.173168i
$519$	21.9120	+	21.9120i	0.961829	+	0.961829i
$520$	0.848044	−	0.351271i	0.0371892	−	0.0154043i
$521$	10.9704	+	26.4849i	0.480622	+	1.16032i	0.959314	+	0.282341i	$0.0911109\pi$
$521$	10.9704	+	26.4849i	0.480622	+	1.16032i	−0.478692	+	0.877983i	$0.658889\pi$
$522$	14.5179	+	6.01352i	0.635432	+	0.263205i
$523$		−	42.6141i		−	1.86338i	−0.363248	−	0.931692i	$-0.618332\pi$
$523$		−	42.6141i		−	1.86338i	0.363248	−	0.931692i	$-0.381668\pi$
$524$	1.58691	−	3.83114i	0.0693245	−	0.167364i
$525$	−2.66061	+	2.66061i	−0.116118	+	0.116118i
$526$	29.7130			1.29555
$527$	8.59342	+	7.68314i	0.374335	+	0.334683i
$528$	−56.6667			−2.46610
$529$	16.2534	−	16.2534i	0.706671	−	0.706671i
$530$	−10.8971	+	26.3079i	−0.473339	+	1.14274i
$531$		−	10.9417i		−	0.474831i
$532$	4.84676	+	2.00760i	0.210134	+	0.0870403i
$533$	0.676339	+	1.63283i	0.0292955	+	0.0707255i
$534$	−51.0902	+	21.1622i	−2.21089	+	0.915780i
$535$	−9.11214	−	9.11214i	−0.393952	−	0.393952i
$536$	1.29797	+	1.29797i	0.0560640	+	0.0560640i
$537$	46.3987	−	19.2190i	2.00225	−	0.829360i
$538$	−22.1950	−	53.5834i	−0.956894	−	2.31015i
$539$	−25.5298	−	10.5748i	−1.09965	−	0.455489i
$540$		−	29.3747i		−	1.26408i
$541$	−8.45588	+	20.4143i	−0.363547	+	0.877679i	0.631229	+	0.775596i	$0.282551\pi$
$541$	−8.45588	+	20.4143i	−0.363547	+	0.877679i	−0.994776	+	0.102083i	$0.967449\pi$
$542$	13.4437	−	13.4437i	0.577457	−	0.577457i
$543$	12.7480			0.547068
$544$	−14.5055	−	30.1388i	−0.621916	−	1.29219i
$545$	11.3210			0.484940
$546$	−13.4012	+	13.4012i	−0.573518	+	0.573518i
$547$	−14.8041	+	35.7403i	−0.632979	+	1.52815i	0.202882	+	0.979203i	$0.434969\pi$
$547$	−14.8041	+	35.7403i	−0.632979	+	1.52815i	−0.835860	+	0.548942i	$0.815031\pi$
$548$		−	42.2561i		−	1.80509i
$549$	−53.8468	−	22.3041i	−2.29813	−	0.951915i
$550$	−3.85240	−	9.30051i	−0.164267	−	0.396575i
$551$	−2.00969	+	0.832442i	−0.0856158	+	0.0354632i
$552$	0.100235	+	0.100235i	0.00426629	+	0.00426629i
$553$	6.81085	+	6.81085i	0.289627	+	0.289627i
$554$	42.3341	−	17.5354i	1.79860	−	0.745006i
$555$	2.83079	+	6.83412i	0.120160	+	0.290092i
$556$	−16.6873	−	6.91211i	−0.707700	−	0.293139i
$557$			33.9638i			1.43909i	0.694445	+	0.719546i	$0.255650\pi$
$557$			33.9638i			1.43909i	−0.694445	+	0.719546i	$0.744350\pi$
$558$	15.7803	−	38.0969i	0.668031	−	1.61277i
$559$	17.5826	−	17.5826i	0.743666	−	0.743666i
$560$	4.24148			0.179235
$561$	21.4359	−	61.2145i	0.905023	−	2.58448i
$562$	63.9101			2.69589
$563$	1.60778	−	1.60778i	0.0677597	−	0.0677597i	−0.672415	−	0.740175i	$-0.734743\pi$
$563$	1.60778	−	1.60778i	0.0677597	−	0.0677597i	0.740175	+	0.672415i	$0.234743\pi$
$564$	9.05981	−	21.8723i	0.381487	−	0.920991i
$565$		−	5.85089i		−	0.246149i
$566$	−22.1917	−	9.19211i	−0.932787	−	0.386373i
$567$	9.63321	+	23.2566i	0.404557	+	0.976687i
$568$	2.28502	−	0.946486i	0.0958773	−	0.0397137i
$569$	−4.01656	−	4.01656i	−0.168383	−	0.168383i	0.617885	−	0.786268i	$-0.287990\pi$
$569$	−4.01656	−	4.01656i	−0.168383	−	0.168383i	−0.786268	+	0.617885i	$0.787990\pi$
$570$	9.43512	+	9.43512i	0.395194	+	0.395194i
$571$	11.9760	−	4.96060i	0.501178	−	0.207595i	−0.117749	−	0.993043i	$-0.537568\pi$
$571$	11.9760	−	4.96060i	0.501178	−	0.207595i	0.618927	+	0.785449i	$0.287568\pi$
$572$	−10.1248	−	24.4434i	−0.423339	−	1.02203i
$573$	56.6880	+	23.4810i	2.36818	+	0.980931i
$574$		−	1.72785i		−	0.0721193i
$575$	0.0455480	−	0.109963i	0.00189948	−	0.00458576i
$576$	−47.8639	+	47.8639i	−1.99433	+	1.99433i
$577$	−27.7816			−1.15656			−0.578281	−	0.815838i	$-0.696276\pi$
$577$	−27.7816			−1.15656			−0.578281	+	0.815838i	$0.696276\pi$
$578$	34.5491	−	3.87646i	1.43705	−	0.161239i
$579$	37.5793			1.56174
$580$	1.64401	−	1.64401i	0.0682636	−	0.0682636i
$581$	−2.74349	+	6.62337i	−0.113819	+	0.274784i
$582$			29.3399i			1.21618i
$583$	63.3241	+	26.2297i	2.62262	+	1.08632i
$584$	0.523016	+	1.26267i	0.0216426	+	0.0522498i
$585$	−16.4113	+	6.79776i	−0.678522	+	0.281053i
$586$	−38.4518	−	38.4518i	−1.58843	−	1.58843i
$587$	4.87317	+	4.87317i	0.201137	+	0.201137i	0.800487	−	0.599350i	$-0.204574\pi$
$587$	4.87317	+	4.87317i	0.201137	+	0.201137i	−0.599350	+	0.800487i	$0.704574\pi$
$588$	−36.1679	+	14.9812i	−1.49154	+	0.617815i
$589$	2.18444	+	5.27369i	0.0900081	+	0.217299i
$590$	−2.86640	−	1.18730i	−0.118008	−	0.0488805i
$591$			61.1617i			2.51585i
$592$	3.19101	−	7.70378i	0.131150	−	0.316623i
$593$	−9.84816	+	9.84816i	−0.404416	+	0.404416i	−0.879786	−	0.475370i	$-0.842314\pi$
$593$	−9.84816	+	9.84816i	−0.404416	+	0.404416i	0.475370	+	0.879786i	$0.342314\pi$
$594$	−135.507			−5.55992
$595$	−1.60447	+	4.58188i	−0.0657767	+	0.187839i
$596$	10.7690			0.441117
$597$	−23.6117	+	23.6117i	−0.966363	+	0.966363i
$598$	0.229420	−	0.553869i	0.00938168	−	0.0226494i
$599$		−	19.3270i		−	0.789681i	−0.918750	−	0.394841i	$-0.870800\pi$
$599$		−	19.3270i		−	0.789681i	0.918750	−	0.394841i	$-0.129200\pi$
$600$	−1.10032	−	0.455769i	−0.0449205	−	0.0186067i
$601$	−16.1400	−	38.9654i	−0.658365	−	1.58943i	−0.800329	−	0.599561i	$-0.795342\pi$
$601$	−16.1400	−	38.9654i	−0.658365	−	1.58943i	0.141964	−	0.989872i	$-0.454658\pi$
$602$	−22.4593	+	9.30295i	−0.915374	+	0.379160i
$603$	−25.1183	−	25.1183i	−1.02290	−	1.02290i
$604$	1.09983	+	1.09983i	0.0447514	+	0.0447514i
$605$	−12.2240	+	5.06334i	−0.496976	+	0.205854i
$606$	44.4805	+	107.386i	1.80690	+	4.36224i
$607$	17.4134	+	7.21286i	0.706787	+	0.292761i	0.706974	−	0.707239i	$-0.250060\pi$
$607$	17.4134	+	7.21286i	0.706787	+	0.292761i	−0.000187126		1.00000i	$0.500060\pi$
$608$		−	16.5631i		−	0.671723i
$609$	−1.53409	+	3.70363i	−0.0621646	+	0.150079i
$610$	−11.6860	+	11.6860i	−0.473152	+	0.473152i
$611$	−8.36132			−0.338263
$612$	−28.1422	−	58.4728i	−1.13758	−	2.36362i
$613$	16.1284			0.651420			0.325710	−	0.945470i	$-0.394397\pi$
$613$	16.1284			0.651420			0.325710	+	0.945470i	$0.394397\pi$
$614$	−27.0387	+	27.0387i	−1.09119	+	1.09119i
$615$	0.877539	−	2.11857i	0.0353858	−	0.0854288i
$616$			2.16007i			0.0870318i
$617$	34.8772	+	14.4466i	1.40410	+	0.581598i	0.950813	−	0.309766i	$-0.100251\pi$
$617$	34.8772	+	14.4466i	1.40410	+	0.581598i	0.453289	+	0.891364i	$0.350251\pi$
$618$	28.3487	+	68.4398i	1.14035	+	2.75305i
$619$	45.0105	−	18.6439i	1.80912	−	0.749363i	0.826714	−	0.562622i	$-0.190207\pi$
$619$	45.0105	−	18.6439i	1.80912	−	0.749363i	0.982409	−	0.186742i	$-0.0597928\pi$
$620$	−4.31408	−	4.31408i	−0.173258	−	0.173258i
$621$	−1.13288	−	1.13288i	−0.0454610	−	0.0454610i
$622$	−15.0514	+	6.23451i	−0.603508	+	0.249981i
$623$	−3.81271	−	9.20469i	−0.152753	−	0.368778i
$624$	26.1948	+	10.8502i	1.04863	+	0.434357i
$625$			1.00000i			0.0400000i
$626$	6.25115	−	15.0916i	0.249846	−	0.603183i
$627$	22.7107	−	22.7107i	0.906977	−	0.906977i
$628$	−12.8439			−0.512528
$629$	7.11495	+	6.36129i	0.283692	+	0.253641i
$630$	17.3664			0.691893
$631$	27.6845	−	27.6845i	1.10210	−	1.10210i	0.107944	−	0.994157i	$-0.465573\pi$
$631$	27.6845	−	27.6845i	1.10210	−	1.10210i	0.994157	−	0.107944i	$-0.0344268\pi$
$632$	−1.16672	+	2.81670i	−0.0464095	+	0.112042i
$633$		−	69.6109i		−	2.76678i
$634$	−29.5348	−	12.2337i	−1.17298	−	0.485863i
$635$	−2.60377	−	6.28606i	−0.103327	−	0.249455i
$636$	89.7107	−	37.1594i	3.55726	−	1.47347i
$637$	9.77661	+	9.77661i	0.387363	+	0.387363i
$638$	−7.58390	−	7.58390i	−0.300249	−	0.300249i
$639$	−44.2195	+	18.3163i	−1.74930	+	0.724582i
$640$	1.13623	+	2.74311i	0.0449136	+	0.108431i
$641$	−46.1341	−	19.1094i	−1.82219	−	0.754775i	−0.974540	−	0.224214i	$-0.928018\pi$
$641$	−46.1341	−	19.1094i	−1.82219	−	0.754775i	−0.847647	−	0.530560i	$-0.821982\pi$
$642$			84.2170i			3.32378i
$643$	−5.98451	+	14.4479i	−0.236006	+	0.569769i	−0.996863	−	0.0791509i	$-0.974779\pi$
$643$	−5.98451	+	14.4479i	−0.236006	+	0.569769i	0.760856	+	0.648920i	$0.224779\pi$
$644$	−0.216248	+	0.216248i	−0.00852138	+	0.00852138i
$645$	−32.2627			−1.27034
$646$	16.2484	+	5.68980i	0.639284	+	0.223862i
$647$	−24.8287			−0.976118			−0.488059	−	0.872811i	$-0.662295\pi$
$647$	−24.8287			−0.976118			−0.488059	+	0.872811i	$0.662295\pi$
$648$	−5.63411	+	5.63411i	−0.221329	+	0.221329i
$649$	−2.85788	+	6.89953i	−0.112182	+	0.270830i
$650$			5.03689i			0.197563i
$651$	9.71880	+	4.02566i	0.380910	+	0.157778i
$652$	−4.92395	−	11.8875i	−0.192837	−	0.465549i
$653$	15.5216	−	6.42926i	0.607408	−	0.251596i	−0.0577120	−	0.998333i	$-0.518381\pi$
$653$	15.5216	−	6.42926i	0.607408	−	0.251596i	0.665120	+	0.746737i	$0.268381\pi$
$654$	−52.3161	−	52.3161i	−2.04572	−	2.04572i
$655$	1.34368	+	1.34368i	0.0525019	+	0.0525019i
$656$	−2.38816	+	0.989208i	−0.0932420	+	0.0386221i
$657$	−10.1214	−	24.4351i	−0.394872	−	0.953304i
$658$	7.55219	+	3.12822i	0.294415	+	0.121951i
$659$			13.1974i			0.514097i	0.966399	+	0.257048i	$0.0827500\pi$
$659$			13.1974i			0.514097i	−0.966399	+	0.257048i	$0.917250\pi$
$660$	−13.1368	+	31.7150i	−0.511348	+	1.23450i
$661$	−27.0038	+	27.0038i	−1.05033	+	1.05033i	−0.0516626	+	0.998665i	$0.516452\pi$
$661$	−27.0038	+	27.0038i	−1.05033	+	1.05033i	−0.998665	+	0.0516626i	$0.983548\pi$
$662$	9.06062			0.352151
$663$	−21.6299	+	24.1926i	−0.840038	+	0.939562i
$664$	−2.26920			−0.0880620
$665$	−1.69988	+	1.69988i	−0.0659187	+	0.0659187i
$666$	13.0653	−	31.5425i	0.506271	−	1.22225i
$667$		−	0.126808i		−	0.00491001i
$668$	21.7105	+	8.99276i	0.840003	+	0.347941i
$669$	−24.4812	−	59.1027i	−0.946496	−	2.28504i
$670$	−9.30585	+	3.85461i	−0.359516	+	0.148917i
$671$	28.1286	+	28.1286i	1.08589	+	1.08589i
$672$	−21.5836	−	21.5836i	−0.832607	−	0.832607i
$673$	−22.5107	+	9.32426i	−0.867726	+	0.359424i	−0.771724	−	0.635958i	$-0.780605\pi$
$673$	−22.5107	+	9.32426i	−0.867726	+	0.359424i	−0.0960015	+	0.995381i	$0.530605\pi$
$674$	4.72387	+	11.4044i	0.181957	+	0.439283i
$675$	12.4361	+	5.15122i	0.478668	+	0.198271i
$676$		−	15.1312i		−	0.581971i
$677$	17.7055	−	42.7449i	0.680478	−	1.64282i	−0.0826551	−	0.996578i	$-0.526340\pi$
$677$	17.7055	−	42.7449i	0.680478	−	1.64282i	0.763133	−	0.646241i	$-0.223660\pi$
$678$	−27.0378	+	27.0378i	−1.03838	+	1.03838i
$679$	−5.28604			−0.202859
$680$	−1.53423	+	0.0858024i	−0.0588352	+	0.00329037i
$681$	−44.0371			−1.68750
$682$	−19.9011	+	19.9011i	−0.762054	+	0.762054i
$683$	6.31128	−	15.2368i	0.241495	−	0.583019i	−0.755937	−	0.654644i	$-0.772818\pi$
$683$	6.31128	−	15.2368i	0.241495	−	0.583019i	0.997432	+	0.0716249i	$0.0228185\pi$
$684$		−	32.1343i		−	1.22869i
$685$	17.8897	+	7.41015i	0.683530	+	0.283127i
$686$	−11.6231	−	28.0606i	−0.443771	−	1.07136i
$687$	−10.7474	+	4.45172i	−0.410039	+	0.169844i
$688$	25.7162	+	25.7162i	0.980422	+	0.980422i
$689$	−24.2499	−	24.2499i	−0.923846	−	0.923846i
$690$	−0.718637	+	0.297669i	−0.0273580	+	0.0113321i
$691$	−9.89442	−	23.8872i	−0.376401	−	0.908713i	−0.992634	−	0.121149i	$-0.961342\pi$
$691$	−9.89442	−	23.8872i	−0.376401	−	0.908713i	0.616233	−	0.787564i	$-0.288658\pi$
$692$	−19.5503	−	8.09801i	−0.743192	−	0.307840i
$693$		−	41.8015i		−	1.58791i
$694$	−0.0728579	+	0.175894i	−0.00276565	+	0.00667686i
$695$	5.85267	−	5.85267i	0.222004	−	0.222004i
$696$	−1.26888			−0.0480968
$697$	−0.165204	−	2.95402i	−0.00625756	−	0.111891i
$698$	19.5143			0.738628
$699$	−31.9987	+	31.9987i	−1.21030	+	1.21030i
$700$	0.983282	−	2.37385i	0.0371646	−	0.0897232i
$701$		−	8.67606i		−	0.327690i	−0.986486	−	0.163845i	$-0.947610\pi$
$701$		−	8.67606i		−	0.327690i	0.986486	−	0.163845i	$-0.0523897\pi$
$702$	62.6395	+	25.9461i	2.36417	+	0.979273i
$703$	1.80861	+	4.36637i	0.0682131	+	0.164681i
$704$	42.6832	−	17.6800i	1.60868	−	0.666338i
$705$	7.67118	+	7.67118i	0.288913	+	0.288913i
$706$	−24.8923	−	24.8923i	−0.936835	−	0.936835i
$707$	−19.3472	+	8.01386i	−0.727625	+	0.301392i
$708$	4.04873	+	9.77451i	0.152161	+	0.367349i
$709$	33.1887	+	13.7472i	1.24643	+	0.516287i	0.905718	−	0.423881i	$-0.139333\pi$
$709$	33.1887	+	13.7472i	1.24643	+	0.516287i	0.340710	+	0.940168i	$0.389333\pi$
$710$			13.5717i			0.509337i
$711$	22.5782	−	54.5085i	0.846748	−	2.04423i
$712$	2.22991	−	2.22991i	0.0835695	−	0.0835695i
$713$	−0.332760			−0.0124620
$714$	28.5880	−	13.7590i	1.06988	−	0.514919i
$715$	12.1240			0.453411
$716$	−24.2503	+	24.2503i	−0.906278	+	0.906278i
$717$	27.7140	−	66.9075i	1.03500	−	2.49871i
$718$			36.2892i			1.35430i
$719$	−9.01058	−	3.73231i	−0.336038	−	0.139192i	0.208283	−	0.978069i	$-0.433213\pi$
$719$	−9.01058	−	3.73231i	−0.336038	−	0.139192i	−0.544321	+	0.838877i	$0.683213\pi$
$720$	−9.94236	−	24.0030i	−0.370530	−	0.894538i
$721$	−12.3305	+	5.10745i	−0.459211	+	0.190212i
$722$	−21.4472	−	21.4472i	−0.798181	−	0.798181i
$723$	13.6597	+	13.6597i	0.508008	+	0.508008i
$724$	−8.04264	+	3.33137i	−0.298902	+	0.123809i
$725$	0.407714	+	0.984309i	0.0151421	+	0.0365563i
$726$	79.8872	+	33.0904i	2.96489	+	1.22810i
$727$		−	11.0694i		−	0.410542i	−0.978705	−	0.205271i	$-0.934192\pi$
$727$		−	11.0694i		−	0.410542i	0.978705	−	0.205271i	$-0.0658076\pi$
$728$	0.413598	−	0.998514i	0.0153290	−	0.0370074i
$729$	17.7800	−	17.7800i	0.658518	−	0.658518i
$730$	−7.49954			−0.277570
$731$	−37.5080	+	18.0521i	−1.38728	+	0.667682i
$732$	56.3557			2.08297
$733$	−29.8140	+	29.8140i	−1.10121	+	1.10121i	−0.106940	+	0.994266i	$0.534105\pi$
$733$	−29.8140	+	29.8140i	−1.10121	+	1.10121i	−0.994266	+	0.106940i	$0.965895\pi$
$734$	28.4119	−	68.5923i	1.04870	−	2.53179i
$735$		−	17.9393i		−	0.661701i
$736$	0.892048	+	0.369499i	0.0328813	+	0.0136199i
$737$	9.27818	+	22.3995i	0.341766	+	0.825097i
$738$	−9.77812	+	4.05023i	−0.359937	+	0.149091i
$739$	33.3484	+	33.3484i	1.22674	+	1.22674i	0.965190	+	0.261549i	$0.0842332\pi$
$739$	33.3484	+	33.3484i	1.22674	+	1.22674i	0.261549	+	0.965190i	$0.415767\pi$
$740$	−3.57186	−	3.57186i	−0.131304	−	0.131304i
$741$	−14.8467	+	6.14972i	−0.545409	+	0.225916i
$742$	12.8306	+	30.9758i	0.471026	+	1.13716i
$743$	29.3327	+	12.1500i	1.07611	+	0.445740i	0.849144	−	0.528162i	$-0.177118\pi$
$743$	29.3327	+	12.1500i	1.07611	+	0.445740i	0.226969	+	0.973902i	$0.427118\pi$
$744$			3.32971i			0.122073i
$745$	−1.88849	+	4.55921i	−0.0691888	+	0.167037i
$746$	8.51946	−	8.51946i	0.311920	−	0.311920i
$747$	43.9133			1.60670
$748$	2.47311	+	44.2217i	0.0904259	+	1.61691i
$749$	−15.1730			−0.554409
$750$	4.62114	−	4.62114i	0.168740	−	0.168740i
$751$	−8.49116	+	20.4995i	−0.309847	+	0.748036i	0.689863	+	0.723940i	$0.257671\pi$
$751$	−8.49116	+	20.4995i	−0.309847	+	0.748036i	−0.999710	+	0.0240961i	$0.992329\pi$
$752$		−	12.2292i		−	0.445954i
$753$	2.08721	+	0.864549i	0.0760620	+	0.0315059i
$754$	2.05361	+	4.95785i	0.0747881	+	0.180554i
$755$	−0.658497	+	0.272758i	−0.0239651	+	0.00992669i
$756$	−24.4565	−	24.4565i	−0.889473	−	0.889473i
$757$	9.23768	+	9.23768i	0.335749	+	0.335749i	0.854765	−	0.519016i	$-0.173701\pi$
$757$	9.23768	+	9.23768i	0.335749	+	0.335749i	−0.519016	+	0.854765i	$0.673701\pi$
$758$	−55.3088	+	22.9096i	−2.00890	+	0.832115i
$759$	0.716500	+	1.72978i	0.0260073	+	0.0627872i
$760$	−0.703005	−	0.291194i	−0.0255007	−	0.0105627i
$761$			18.9811i			0.688065i	0.938958	+	0.344033i	$0.111793\pi$
$761$			18.9811i			0.688065i	−0.938958	+	0.344033i	$0.888207\pi$
$762$	−17.0164	+	41.0812i	−0.616438	+	1.48821i
$763$	9.42556	−	9.42556i	0.341228	−	0.341228i
$764$	−41.9004			−1.51590
$765$	29.6903	−	1.66044i	1.07346	−	0.0600333i
$766$	25.1668			0.909313
$767$	2.64217	−	2.64217i	0.0954031	−	0.0954031i
$768$	−15.5297	+	37.4921i	−0.560381	+	1.35288i
$769$			22.0057i			0.793544i	0.917917	+	0.396772i	$0.129870\pi$
$769$			22.0057i			0.793544i	−0.917917	+	0.396772i	$0.870130\pi$
$770$	−10.9507	−	4.53594i	−0.394637	−	0.163464i
$771$	18.4325	+	44.4999i	0.663829	+	1.60262i
$772$	−23.7086	+	9.82043i	−0.853291	+	0.353445i
$773$	−9.36282	−	9.36282i	−0.336757	−	0.336757i	0.518388	−	0.855145i	$-0.326532\pi$
$773$	−9.36282	−	9.36282i	−0.336757	−	0.336757i	−0.855145	+	0.518388i	$0.826532\pi$
$774$	105.293	+	105.293i	3.78467	+	3.78467i
$775$	2.58295	−	1.06989i	0.0927824	−	0.0384317i
$776$	−0.640293	−	1.54580i	−0.0229852	−	0.0554912i
$777$	8.04672	+	3.33306i	0.288674	+	0.119573i
$778$		−	4.34736i		−	0.155860i
$779$	0.560667	−	1.35357i	0.0200880	−	0.0484966i
$780$	12.1452	−	12.1452i	0.434868	−	0.434868i
$781$	32.6676			1.16894
$782$	−0.668916	+	0.748167i	−0.0239204	+	0.0267544i
$783$	14.3412			0.512514
$784$	−14.2992	+	14.2992i	−0.510686	+	0.510686i
$785$	2.25234	−	5.43764i	0.0803896	−	0.194078i
$786$		−	12.4187i		−	0.442959i
$787$	−11.0739	−	4.58697i	−0.394743	−	0.163508i	0.176477	−	0.984305i	$-0.443530\pi$
$787$	−11.0739	−	4.58697i	−0.394743	−	0.163508i	−0.571220	+	0.820797i	$0.693530\pi$
$788$	−15.9831	−	38.5866i	−0.569375	−	1.37459i
$789$	42.8961	−	17.7681i	1.52714	−	0.632563i
$790$	−11.8296	−	11.8296i	−0.420878	−	0.420878i
$791$	−4.87128	−	4.87128i	−0.173203	−	0.173203i
$792$	12.2241	−	5.06338i	0.434364	−	0.179919i
$793$	−7.61681	−	18.3886i	−0.270481	−	0.652999i
$794$	47.6093	+	19.7204i	1.68959	+	0.699851i
$795$			44.4966i			1.57813i
$796$	8.72619	−	21.0669i	0.309292	−	0.746696i
$797$	−16.4888	+	16.4888i	−0.584062	+	0.584062i	−0.936017	−	0.351955i	$-0.885517\pi$
$797$	−16.4888	+	16.4888i	−0.584062	+	0.584062i	0.351955	+	0.936017i	$0.385517\pi$
$798$	15.7108			0.556157
$799$	13.2107	+	4.62606i	0.467360	+	0.163658i
$800$	−8.11229			−0.286813
$801$	−43.1530	+	43.1530i	−1.52474	+	1.52474i
$802$	−25.7228	+	62.1004i	−0.908305	+	2.19284i
$803$			18.0517i			0.637030i
$804$	31.7332	+	13.1443i	1.11914	+	0.463564i
$805$	−0.0536297	−	0.129474i	−0.00189020	−	0.00456334i
$806$	13.0100	−	5.38894i	0.458259	−	0.189817i
$807$	−64.0849	−	64.0849i	−2.25590	−	2.25590i
$808$	−4.68701	−	4.68701i	−0.164889	−	0.164889i
$809$	−28.4685	+	11.7920i	−1.00090	+	0.414586i	−0.822127	−	0.569304i	$-0.807213\pi$
$809$	−28.4685	+	11.7920i	−1.00090	+	0.414586i	−0.178772	+	0.983890i	$0.557213\pi$
$810$	−16.7317	−	40.3939i	−0.587891	−	1.41930i
$811$	35.6681	+	14.7742i	1.25248	+	0.518793i	0.907593	−	0.419852i	$-0.137918\pi$
$811$	35.6681	+	14.7742i	1.25248	+	0.518793i	0.344885	+	0.938645i	$0.387918\pi$
$812$		−	2.73750i		−	0.0960675i
$813$	11.3692	−	27.4477i	0.398735	−	0.962632i
$814$	−16.4772	+	16.4772i	−0.577526	+	0.577526i
$815$	5.89619			0.206535
$816$	−35.3839	−	31.6358i	−1.23868	−	1.10747i
$817$	−20.6129			−0.721154
$818$	23.9644	−	23.9644i	0.837896	−	0.837896i
$819$	−8.00391	+	19.3231i	−0.279679	+	0.675205i
$820$			1.56592i			0.0546842i
$821$	19.9465	+	8.26210i	0.696137	+	0.288349i	0.702554	−	0.711630i	$-0.252043\pi$
$821$	19.9465	+	8.26210i	0.696137	+	0.288349i	−0.00641740	+	0.999979i	$0.502043\pi$
$822$	−48.4274	−	116.914i	−1.68910	−	4.07785i
$823$	−23.4714	+	9.72219i	−0.818163	+	0.338894i	−0.752206	−	0.658928i	$-0.771010\pi$
$823$	−23.4714	+	9.72219i	−0.818163	+	0.338894i	−0.0659572	+	0.997822i	$0.521010\pi$
$824$	−2.98716	−	2.98716i	−0.104063	−	0.104063i
$825$	−11.1233	−	11.1233i	−0.387262	−	0.387262i
$826$	−3.37500	+	1.39797i	−0.117431	+	0.0486416i
$827$	5.69519	+	13.7494i	0.198041	+	0.478113i	0.991436	−	0.130594i	$-0.0416884\pi$
$827$	5.69519	+	13.7494i	0.198041	+	0.478113i	−0.793395	+	0.608707i	$0.791688\pi$
$828$	1.73068	+	0.716870i	0.0601452	+	0.0249129i
$829$		−	29.8580i		−	1.03701i	−0.855075	−	0.518505i	$-0.826489\pi$
$829$		−	29.8580i		−	1.03701i	0.855075	−	0.518505i	$-0.173511\pi$
$830$	4.76509	−	11.5040i	0.165399	−	0.399308i
$831$	50.6309	−	50.6309i	1.75637	−	1.75637i
$832$	−23.1160			−0.801402
$833$	−10.0377	−	20.8559i	−0.347785	−	0.722613i
$834$	−54.0920			−1.87305
$835$	−7.61441	+	7.61441i	−0.263508	+	0.263508i
$836$	−8.39319	+	20.2630i	−0.290285	+	0.700809i
$837$		−	37.6333i		−	1.30080i
$838$	−10.0490	−	4.16242i	−0.347136	−	0.143788i
$839$	−12.3297	−	29.7664i	−0.425667	−	1.02765i	−0.980646	−	0.195787i	$-0.937274\pi$
$839$	−12.3297	−	29.7664i	−0.425667	−	1.02765i	0.554979	−	0.831864i	$-0.312726\pi$
$840$	−1.29556	+	0.536637i	−0.0447010	+	0.0185157i
$841$	−19.7035	−	19.7035i	−0.679430	−	0.679430i
$842$	−5.38106	−	5.38106i	−0.185443	−	0.185443i
$843$	92.2658	−	38.2177i	3.17780	−	1.31629i
$844$	18.1911	+	43.9172i	0.626164	+	1.51169i
$845$	6.40601	+	2.65346i	0.220373	+	0.0912817i
$846$		−	50.0715i		−	1.72149i
$847$	−5.96174	+	14.3929i	−0.204848	+	0.494547i
$848$	35.4677	−	35.4677i	1.21797	−	1.21797i
$849$	−37.5345			−1.28818
$850$	2.78675	−	7.95814i	0.0955849	−	0.272962i
$851$	−0.275510			−0.00944435
$852$	32.7248	−	32.7248i	1.12113	−	1.12113i
$853$	−2.54304	+	6.13944i	−0.0870719	+	0.210210i	−0.961417	−	0.275094i	$-0.911291\pi$
$853$	−2.54304	+	6.13944i	−0.0870719	+	0.210210i	0.874345	+	0.485304i	$0.161291\pi$
$854$			19.4588i			0.665867i
$855$	13.6045	+	5.63516i	0.465264	+	0.192719i
$856$	−1.83789	−	4.43707i	−0.0628179	−	0.151656i
$857$	−31.9012	+	13.2139i	−1.08972	+	0.451378i	−0.853910	−	0.520420i	$-0.825775\pi$
$857$	−31.9012	+	13.2139i	−1.08972	+	0.451378i	−0.235813	+	0.971798i	$0.575775\pi$
$858$	−56.0266	−	56.0266i	−1.91272	−	1.91272i
$859$	−33.0671	−	33.0671i	−1.12823	−	1.12823i	−0.990464	−	0.137770i	$-0.956007\pi$
$859$	−33.0671	−	33.0671i	−1.12823	−	1.12823i	−0.137770	−	0.990464i	$-0.543993\pi$
$860$	20.3544	−	8.43107i	0.694079	−	0.287497i
$861$	−1.03324	−	2.49447i	−0.0352128	−	0.0850113i
$862$	−1.23305	−	0.510746i	−0.0419979	−	0.0173961i
$863$		−	40.3468i		−	1.37342i	−0.726930	−	0.686711i	$-0.759054\pi$
$863$		−	40.3468i		−	1.37342i	0.726930	−	0.686711i	$-0.240946\pi$
$864$	−41.7882	+	100.886i	−1.42166	+	3.43220i
$865$	6.85680	−	6.85680i	0.233138	−	0.233138i
$866$	−10.8690			−0.369343
$867$	47.5597	−	26.2564i	1.61521	−	0.891716i
$868$	−7.18356			−0.243826
$869$	−28.4743	+	28.4743i	−0.965923	+	0.965923i
$870$	2.66453	−	6.43274i	0.0903359	−	0.218090i
$871$		−	12.1309i		−	0.411041i
$872$	3.89804	+	1.61462i	0.132004	+	0.0546780i
$873$	12.3909	+	29.9143i	0.419368	+	1.01244i
$874$	−0.459143	+	0.190183i	−0.0155307	+	0.00643304i
$875$	0.832570	+	0.832570i	0.0281460	+	0.0281460i
$876$	18.0833	+	18.0833i	0.610978	+	0.610978i
$877$	14.3511	−	5.94444i	0.484604	−	0.200729i	−0.126986	−	0.991904i	$-0.540530\pi$
$877$	14.3511	−	5.94444i	0.484604	−	0.200729i	0.611590	+	0.791175i	$0.290530\pi$
$878$	−4.33245	−	10.4595i	−0.146213	−	0.352990i
$879$	−78.5060	−	32.5182i	−2.64794	−	1.09681i
$880$			17.7324i			0.597760i
$881$	−12.7047	+	30.6719i	−0.428033	+	1.03336i	0.551878	+	0.833925i	$0.313911\pi$
$881$	−12.7047	+	30.6719i	−0.428033	+	1.03336i	−0.979911	+	0.199437i	$0.936089\pi$
$882$	−58.5469	+	58.5469i	−1.97138	+	1.97138i
$883$	−34.1078			−1.14782			−0.573909	−	0.818919i	$-0.694574\pi$
$883$	−34.1078			−1.14782			−0.573909	+	0.818919i	$0.694574\pi$
$884$	7.32410	−	20.9155i	0.246336	−	0.703463i
$885$	−4.84816			−0.162969
$886$	−21.6758	+	21.6758i	−0.728211	+	0.728211i
$887$	12.3801	−	29.8882i	0.415683	−	1.00355i	−0.567901	−	0.823097i	$-0.692244\pi$
$887$	12.3801	−	29.8882i	0.415683	−	1.00355i	0.983584	−	0.180451i	$-0.0577556\pi$
$888$			2.75685i			0.0925137i
$889$	−7.40141	−	3.06576i	−0.248235	−	0.102822i
$890$	6.62219	+	15.9874i	0.221976	+	0.535898i
$891$	−97.2295	+	40.2738i	−3.25731	+	1.34922i
$892$	30.8901	+	30.8901i	1.03428	+	1.03428i
$893$	4.90118	+	4.90118i	0.164012	+	0.164012i
$894$	29.7957	−	12.3418i	0.996518	−	0.412771i
$895$	−6.01409	−	14.5193i	−0.201029	−	0.485327i
$896$	3.22983	+	1.33784i	0.107901	+	0.0446941i
$897$		−	0.936801i		−	0.0312789i
$898$	16.2638	−	39.2643i	0.542730	−	1.31027i
$899$	2.10621	−	2.10621i	0.0702461	−	0.0702461i
$900$	−15.7388			−0.524626
$901$	24.8974	+	51.7308i	0.829453	+	1.72340i
$902$	7.22367			0.240522
$903$	−26.8610	+	26.8610i	−0.893877	+	0.893877i
$904$	0.834462	−	2.01457i	0.0277538	−	0.0670036i
$905$		−	3.98916i		−	0.132604i
$906$	4.30346	+	1.78255i	0.142973	+	0.0592213i
$907$	10.6991	+	25.8300i	0.355259	+	0.857670i	0.995953	+	0.0898744i	$0.0286466\pi$
$907$	10.6991	+	25.8300i	0.355259	+	0.857670i	−0.640694	+	0.767796i	$0.721353\pi$
$908$	27.7828	−	11.5080i	0.922004	−	0.381907i
$909$	90.7026	+	90.7026i	3.00841	+	3.00841i
$910$	4.19356	+	4.19356i	0.139015	+	0.139015i
$911$	11.3723	−	4.71057i	0.376782	−	0.156068i	−0.186252	−	0.982502i	$-0.559634\pi$
$911$	11.3723	−	4.71057i	0.376782	−	0.156068i	0.563034	+	0.826434i	$0.309634\pi$
$912$	−8.99454	−	21.7147i	−0.297839	−	0.719047i
$913$	−27.6904	−	11.4698i	−0.916420	−	0.379593i
$914$			31.9937i			1.05826i
$915$	−9.88270	+	23.8589i	−0.326712	+	0.788752i
$916$	5.61714	−	5.61714i	0.185596	−	0.185596i
$917$	2.23742			0.0738860
$918$	−84.6135	−	75.6506i	−2.79266	−	2.49684i
$919$	20.0893			0.662683			0.331342	−	0.943511i	$-0.392499\pi$
$919$	20.0893			0.662683			0.331342	+	0.943511i	$0.392499\pi$
$920$	0.0313660	−	0.0313660i	0.00103411	−	0.00103411i
$921$	−22.8663	+	55.2042i	−0.753471	+	1.81904i
$922$			15.1203i			0.497962i
$923$	−15.1009	−	6.25500i	−0.497052	−	0.205886i
$924$	15.4677	+	37.3423i	0.508849	+	1.22847i
$925$	2.13857	−	0.885823i	0.0703156	−	0.0291257i
$926$	24.8941	+	24.8941i	0.818071	+	0.818071i
$927$	57.8073	+	57.8073i	1.89864	+	1.89864i
$928$	−7.98500	+	3.30750i	−0.262120	+	0.108574i
$929$	2.31962	+	5.60006i	0.0761043	+	0.183732i	0.957353	−	0.288921i	$-0.0932965\pi$
$929$	2.31962	+	5.60006i	0.0761043	+	0.183732i	−0.881249	+	0.472653i	$0.843296\pi$
$930$	−16.8803	−	6.99206i	−0.553528	−	0.229279i
$931$		−	11.4616i		−	0.375638i
$932$	11.8257	−	28.5499i	0.387365	−	0.935183i
$933$	−18.0013	+	18.0013i	−0.589335	+	0.589335i
$934$	74.3154			2.43167
$935$	−19.1555	−	6.70782i	−0.626453	−	0.219369i
$936$	−6.62021			−0.216388
$937$	24.1663	−	24.1663i	0.789479	−	0.789479i	−0.191929	−	0.981409i	$-0.561474\pi$
$937$	24.1663	−	24.1663i	0.789479	−	0.789479i	0.981409	+	0.191929i	$0.0614745\pi$
$938$	−4.53854	+	10.9570i	−0.148189	+	0.357759i
$939$		−	25.5256i		−	0.832997i
$940$	−6.84439	−	2.83504i	−0.223239	−	0.0924688i
$941$	13.7852	+	33.2804i	0.449385	+	1.08491i	0.972553	+	0.232681i	$0.0747499\pi$
$941$	13.7852	+	33.2804i	0.449385	+	1.08491i	−0.523168	+	0.852229i	$0.675250\pi$
$942$	−35.5365	+	14.7197i	−1.15784	+	0.479594i
$943$	0.0603923	+	0.0603923i	0.00196664	+	0.00196664i
$944$	3.86441	+	3.86441i	0.125776	+	0.125776i
$945$	14.6427	−	6.06521i	0.476328	−	0.197301i
$946$	−38.8930	−	93.8961i	−1.26452	−	3.05283i
$947$	−36.4150	−	15.0836i	−1.18333	−	0.490151i	−0.297752	−	0.954643i	$-0.596237\pi$
$947$	−36.4150	−	15.0836i	−1.18333	−	0.490151i	−0.885577	+	0.464492i	$0.846237\pi$
$948$			57.0483i			1.85284i
$949$	3.45643	−	8.34456i	0.112200	−	0.270876i
$950$	2.95248	−	2.95248i	0.0957913	−	0.0957913i
$951$	−49.9545			−1.61989
$952$	−1.20592	+	1.34879i	−0.0390841	+	0.0437147i
$953$	−6.36027			−0.206029			−0.103015	−	0.994680i	$-0.532849\pi$
$953$	−6.36027			−0.206029			−0.103015	+	0.994680i	$0.532849\pi$
$954$	145.219	−	145.219i	4.70165	−	4.70165i
$955$	7.34777	−	17.7391i	0.237768	−	0.574024i
$956$			49.4540i			1.59946i
$957$	−15.4838	−	6.41361i	−0.500521	−	0.207323i
$958$	23.7661	+	57.3764i	0.767847	+	1.85375i
$959$	21.0639	−	8.72495i	0.680189	−	0.281743i
$960$	21.2080	+	21.2080i	0.684485	+	0.684485i
$961$	16.3933	+	16.3933i	0.528817	+	0.528817i
$962$	10.7717	−	4.46179i	0.347294	−	0.143854i
$963$	35.5667	+	85.8657i	1.14612	+	2.76698i
$964$	−12.1874	−	5.04820i	−0.392531	−	0.162592i
$965$		−	11.7595i		−	0.378551i
$966$	−0.350485	+	0.846146i	−0.0112767	+	0.0272243i
$967$	24.2838	−	24.2838i	0.780913	−	0.780913i	−0.199072	−	0.979985i	$-0.563793\pi$
$967$	24.2838	−	24.2838i	0.780913	−	0.780913i	0.979985	+	0.199072i	$0.0637926\pi$
$968$	−4.93109			−0.158491
$969$	26.8599	−	1.50215i	0.862865	−	0.0482559i
$970$	9.18118			0.294790
$971$	5.64699	−	5.64699i	0.181221	−	0.181221i	−0.610667	−	0.791888i	$-0.709099\pi$
$971$	5.64699	−	5.64699i	0.181221	−	0.181221i	0.791888	+	0.610667i	$0.209099\pi$
$972$	−23.3319	+	56.3282i	−0.748371	+	1.80673i
$973$		−	9.74552i		−	0.312427i
$974$	−47.7697	−	19.7869i	−1.53064	−	0.634012i
$975$	3.01202	+	7.27165i	0.0964617	+	0.232879i
$976$	26.8951	−	11.1403i	0.860890	−	0.356592i
$977$	−10.6765	−	10.6765i	−0.341572	−	0.341572i	0.515386	−	0.856958i	$-0.327649\pi$
$977$	−10.6765	−	10.6765i	−0.341572	−	0.341572i	−0.856958	+	0.515386i	$0.827649\pi$
$978$	−27.2472	−	27.2472i	−0.871268	−	0.871268i
$979$	38.4822	−	15.9399i	1.22990	−	0.509440i
$980$	4.68800	+	11.3178i	0.149753	+	0.361535i
$981$	−75.4345	−	31.2460i	−2.40844	−	0.997608i
$982$		−	58.8855i		−	1.87911i
$983$	19.2464	−	46.4649i	0.613864	−	1.48200i	−0.244859	−	0.969559i	$-0.578742\pi$
$983$	19.2464	−	46.4649i	0.613864	−	1.48200i	0.858723	−	0.512440i	$-0.171258\pi$
$984$	0.604306	−	0.604306i	0.0192646	−	0.0192646i
$985$	19.1390			0.609819
$986$	−0.501620	−	8.96947i	−0.0159748	−	0.285646i
$987$	12.7736			0.406588
$988$	7.75967	−	7.75967i	0.246868	−	0.246868i
$989$	0.459844	−	1.11016i	0.0146222	−	0.0353010i
$990$			72.6039i			2.30750i
$991$	−12.0211	−	4.97931i	−0.381863	−	0.158173i	0.183490	−	0.983021i	$-0.441260\pi$
$991$	−12.0211	−	4.97931i	−0.381863	−	0.158173i	−0.565354	+	0.824849i	$0.691260\pi$
$992$	8.67929	+	20.9537i	0.275568	+	0.665280i
$993$	13.0806	−	5.41817i	0.415101	−	0.171941i
$994$	11.2994	+	11.2994i	0.358395	+	0.358395i
$995$	7.38869	+	7.38869i	0.234237	+	0.234237i
$996$	−39.2288	+	16.2491i	−1.24301	+	0.514872i
$997$	3.57765	+	8.63721i	0.113305	+	0.273543i	0.970352	−	0.241695i	$-0.0777034\pi$
$997$	3.57765	+	8.63721i	0.113305	+	0.273543i	−0.857047	+	0.515238i	$0.827703\pi$
$998$	28.2578	+	11.7048i	0.894485	+	0.370508i
$999$		−	31.1586i		−	0.985814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.76.1	yes	24
3.2	odd	2		765.2.be.b.586.6		24
5.2	odd	4		425.2.n.f.399.1		24
5.3	odd	4		425.2.n.c.399.6		24
5.4	even	2		425.2.m.b.76.6		24
17.6	odd	16		1445.2.d.j.866.3		24
17.7	odd	16		1445.2.a.q.1.11		12
17.10	odd	16		1445.2.a.p.1.11		12
17.11	odd	16		1445.2.d.j.866.4		24
17.15	even	8	inner	85.2.l.a.66.1	✓	24
51.32	odd	8		765.2.be.b.406.6		24
85.24	odd	16		7225.2.a.bq.1.2		12
85.32	odd	8		425.2.n.c.49.6		24
85.44	odd	16		7225.2.a.bs.1.2		12
85.49	even	8		425.2.m.b.151.6		24
85.83	odd	8		425.2.n.f.49.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.1	✓	24	17.15	even	8	inner
85.2.l.a.76.1	yes	24	1.1	even	1	trivial
425.2.m.b.76.6		24	5.4	even	2
425.2.m.b.151.6		24	85.49	even	8
425.2.n.c.49.6		24	85.32	odd	8
425.2.n.c.399.6		24	5.3	odd	4
425.2.n.f.49.1		24	85.83	odd	8
425.2.n.f.399.1		24	5.2	odd	4
765.2.be.b.406.6		24	51.32	odd	8
765.2.be.b.586.6		24	3.2	odd	2
1445.2.a.p.1.11		12	17.10	odd	16
1445.2.a.q.1.11		12	17.7	odd	16
1445.2.d.j.866.3		24	17.6	odd	16
1445.2.d.j.866.4		24	17.11	odd	16
7225.2.a.bq.1.2		12	85.24	odd	16
7225.2.a.bs.1.2		12	85.44	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44607 + 1.44607i) q^{2} +(-1.22292 + 2.95240i) q^{3} -2.18224i q^{4} +(0.923880 + 0.382683i) q^{5} +(-2.50094 - 6.03781i) q^{6} +(1.08781 - 0.450584i) q^{7} +(0.263530 + 0.263530i) q^{8} +(-5.09981 - 5.09981i) q^{9} +(-1.88938 + 0.782608i) q^{10} +(1.88376 + 4.54781i) q^{11} +(6.44284 + 2.66871i) q^{12} -2.46296i q^{13} +(-0.921468 + 2.22462i) q^{14} +(-2.25967 + 2.25967i) q^{15} +3.60231 q^{16} +(-1.36268 + 3.89141i) q^{17} +14.7494 q^{18} +(-1.44372 + 1.44372i) q^{19} +(0.835107 - 2.01613i) q^{20} +3.76267i q^{21} +(-9.30051 - 3.85240i) q^{22} +(-0.0455480 - 0.109963i) q^{23} +(-1.10032 + 0.455769i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.56162 + 3.56162i) q^{26} +(12.4361 - 5.15122i) q^{27} +(-0.983282 - 2.37385i) q^{28} +(0.984309 + 0.407714i) q^{29} -6.53528i q^{30} +(1.06989 - 2.58295i) q^{31} +(-5.73626 + 5.73626i) q^{32} -15.7307 q^{33} +(-3.65672 - 7.59779i) q^{34} +1.17743 q^{35} +(-11.1290 + 11.1290i) q^{36} +(0.885823 - 2.13857i) q^{37} -4.17544i q^{38} +(7.27165 + 3.01202i) q^{39} +(0.142621 + 0.344319i) q^{40} +(-0.662952 + 0.274604i) q^{41} +(-5.44108 - 5.44108i) q^{42} +(7.13881 + 7.13881i) q^{43} +(9.92441 - 4.11082i) q^{44} +(-2.76000 - 6.66322i) q^{45} +(0.224879 + 0.0931480i) q^{46} -3.39482i q^{47} +(-4.40535 + 10.6355i) q^{48} +(-3.96945 + 3.96945i) q^{49} -2.04505 q^{50} +(-9.82256 - 8.78209i) q^{51} -5.37477 q^{52} +(9.84581 - 9.84581i) q^{53} +(-10.5345 + 25.4326i) q^{54} +4.92251i q^{55} +(0.405412 + 0.167927i) q^{56} +(-2.49688 - 6.02800i) q^{57} +(-2.01296 + 0.833797i) q^{58} +(1.07276 + 1.07276i) q^{59} +(4.93114 + 4.93114i) q^{60} +(7.46606 - 3.09254i) q^{61} +(2.18799 + 5.28228i) q^{62} +(-7.84549 - 3.24971i) q^{63} -9.38544i q^{64} +(0.942535 - 2.27548i) q^{65} +(22.7476 - 22.7476i) q^{66} +4.92534 q^{67} +(8.49199 + 2.97370i) q^{68} +0.380355 q^{69} +(-1.70265 + 1.70265i) q^{70} +(2.53962 - 6.13119i) q^{71} -2.68790i q^{72} +(3.38802 + 1.40336i) q^{73} +(1.81155 + 4.37348i) q^{74} +(-2.95240 + 1.22292i) q^{75} +(3.15054 + 3.15054i) q^{76} +(4.09834 + 4.09834i) q^{77} +(-14.8709 + 6.15973i) q^{78} +(3.13055 + 7.55781i) q^{79} +(3.32810 + 1.37854i) q^{80} +21.3794i q^{81} +(0.561579 - 1.35577i) q^{82} +(-4.30539 + 4.30539i) q^{83} +8.21104 q^{84} +(-2.74813 + 3.07372i) q^{85} -20.6464 q^{86} +(-2.40747 + 2.40747i) q^{87} +(-0.702056 + 1.69491i) q^{88} -8.46170i q^{89} +(13.6266 + 5.64433i) q^{90} +(-1.10977 - 2.67922i) q^{91} +(-0.239965 + 0.0993966i) q^{92} +(6.31751 + 6.31751i) q^{93} +(4.90915 + 4.90915i) q^{94} +(-1.88631 + 0.781336i) q^{95} +(-9.92072 - 23.9507i) q^{96} +(-4.14772 - 1.71804i) q^{97} -11.4802i q^{98} +(13.5861 - 32.7998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more