LMFDB - Embedded newform 588.2.ba.a.103.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(103,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 29]))

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

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

chi := DirichletCharacter("588.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.ba (of order $42$, degree $12$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	588.103
Dual form			588.2.ba.a.451.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.677412 - 1.24142i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.08223 + 1.68190i) q^{4} +(-2.31910 - 0.173792i) q^{5} +(-0.139610 + 1.40731i) q^{6} +(2.40273 - 1.10766i) q^{7} +(2.82105 + 0.204152i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.677412 - 1.24142i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.08223 + 1.68190i) q^{4} +(-2.31910 - 0.173792i) q^{5} +(-0.139610 + 1.40731i) q^{6} +(2.40273 - 1.10766i) q^{7} +(2.82105 + 0.204152i) q^{8} +(0.365341 + 0.930874i) q^{9} +(1.35524 + 2.99670i) q^{10} +(2.24897 + 0.882657i) q^{11} +(1.84162 - 0.780012i) q^{12} +(3.82081 - 3.04699i) q^{13} +(-3.00270 - 2.23244i) q^{14} +(1.81823 + 1.44999i) q^{15} +(-1.65758 - 3.64039i) q^{16} +(-2.70055 - 2.91050i) q^{17} +(0.908115 - 1.08413i) q^{18} +(0.971336 - 1.68240i) q^{19} +(2.80209 - 3.71241i) q^{20} +(-2.60919 - 0.438313i) q^{21} +(-0.427738 - 3.38983i) q^{22} +(-6.20584 + 6.68831i) q^{23} +(-2.21586 - 1.75783i) q^{24} +(0.403865 + 0.0608728i) q^{25} +(-6.37085 - 2.67914i) q^{26} +(0.222521 - 0.974928i) q^{27} +(-0.737320 + 5.23988i) q^{28} +(-1.60608 - 7.03668i) q^{29} +(0.568349 - 3.23942i) q^{30} +(-0.265148 - 0.459249i) q^{31} +(-3.39637 + 4.52379i) q^{32} +(-1.36097 - 1.99618i) q^{33} +(-1.78375 + 5.32411i) q^{34} +(-5.76466 + 2.15119i) q^{35} +(-1.96102 - 0.392948i) q^{36} +(-3.47535 - 1.07200i) q^{37} +(-2.74656 - 0.0661511i) q^{38} +(-4.87333 + 0.365206i) q^{39} +(-6.50682 - 0.963725i) q^{40} +(-3.28894 - 6.82956i) q^{41} +(1.22337 + 3.53601i) q^{42} +(1.70532 - 3.54114i) q^{43} +(-3.91844 + 2.82732i) q^{44} +(-0.685483 - 2.22228i) q^{45} +(12.5069 + 3.17329i) q^{46} +(12.8750 - 1.94060i) q^{47} +(-0.681151 + 3.94158i) q^{48} +(4.54618 - 5.32280i) q^{49} +(-0.198015 - 0.542600i) q^{50} +(0.591755 + 3.92604i) q^{51} +(0.989762 + 9.72375i) q^{52} +(-6.79355 + 2.09553i) q^{53} +(-1.36103 + 0.384187i) q^{54} +(-5.06220 - 2.43783i) q^{55} +(7.00434 - 2.63424i) q^{56} +(-1.75029 + 0.842893i) q^{57} +(-7.64747 + 6.76054i) q^{58} +(-0.801147 - 10.6906i) q^{59} +(-4.40647 + 1.48886i) q^{60} +(2.07021 - 6.71145i) q^{61} +(-0.390505 + 0.640259i) q^{62} +(1.90890 + 1.83196i) q^{63} +(7.91664 + 1.15184i) q^{64} +(-9.39038 + 6.40225i) q^{65} +(-1.55615 + 3.04177i) q^{66} +(-0.163371 + 0.0943225i) q^{67} +(7.81777 - 1.39224i) q^{68} +(8.89517 - 2.03026i) q^{69} +(6.57558 + 5.69910i) q^{70} +(1.08118 + 0.246771i) q^{71} +(0.840606 + 2.70063i) q^{72} +(-0.660177 + 4.37999i) q^{73} +(1.02344 + 5.04054i) q^{74} +(-0.299398 - 0.277801i) q^{75} +(1.77843 + 3.45443i) q^{76} +(6.38135 - 0.370312i) q^{77} +(3.75463 + 5.80243i) q^{78} +(-6.88049 - 3.97245i) q^{79} +(3.21141 + 8.73050i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-6.25035 + 8.70938i) q^{82} +(-1.19435 + 1.49767i) q^{83} +(3.56093 - 3.91405i) q^{84} +(5.75701 + 7.21907i) q^{85} +(-5.55124 + 0.281797i) q^{86} +(-2.63690 + 6.71871i) q^{87} +(6.16427 + 2.94915i) q^{88} +(-13.3203 + 5.22782i) q^{89} +(-2.29442 + 2.35637i) q^{90} +(5.80533 - 11.5532i) q^{91} +(-4.53295 - 17.6759i) q^{92} +(-0.0396290 + 0.528812i) q^{93} +(-11.1308 - 14.6687i) q^{94} +(-2.54501 + 3.73285i) q^{95} +(5.35456 - 1.82448i) q^{96} +7.98622i q^{97} +(-9.68745 - 2.03797i) q^{98} +2.41598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−0.677412	−	1.24142i	−0.479003	−	0.877813i
$2$	−0.677412	−	1.24142i	−0.479003	−	0.877813i
$3$	−0.826239	−	0.563320i	−0.477029	−	0.325233i
$3$	−0.826239	−	0.563320i	−0.477029	−	0.325233i
$4$	−1.08223	+	1.68190i	−0.541113	+	0.840950i
$5$	−2.31910	−	0.173792i	−1.03713	−	0.0777224i	−0.454735	−	0.890627i	$-0.650266\pi$
$5$	−2.31910	−	0.173792i	−1.03713	−	0.0777224i	−0.582397	+	0.812904i	$0.697885\pi$
$6$	−0.139610	+	1.40731i	−0.0569956	+	0.574530i
$7$	2.40273	−	1.10766i	0.908145	−	0.418656i
$7$	2.40273	−	1.10766i	0.908145	−	0.418656i
$8$	2.82105	+	0.204152i	0.997392	+	0.0721785i
$9$	0.365341	+	0.930874i	0.121780	+	0.310291i
$10$	1.35524	+	2.99670i	0.428564	+	0.947638i
$11$	2.24897	+	0.882657i	0.678091	+	0.266131i	0.679292	−	0.733868i	$-0.262287\pi$
$11$	2.24897	+	0.882657i	0.678091	+	0.266131i	−0.00120077	+	0.999999i	$0.500382\pi$
$12$	1.84162	−	0.780012i	0.531631	−	0.225170i
$13$	3.82081	−	3.04699i	1.05970	−	0.845084i	0.0713772	−	0.997449i	$-0.477261\pi$
$13$	3.82081	−	3.04699i	1.05970	−	0.845084i	0.988324	+	0.152366i	$0.0486892\pi$
$14$	−3.00270	−	2.23244i	−0.802506	−	0.596645i
$15$	1.81823	+	1.44999i	0.469465	+	0.374386i
$16$	−1.65758	−	3.64039i	−0.414394	−	0.910098i
$17$	−2.70055	−	2.91050i	−0.654979	−	0.705899i	0.314999	−	0.949092i	$-0.397996\pi$
$17$	−2.70055	−	2.91050i	−0.654979	−	0.705899i	−0.969978	+	0.243193i	$0.921805\pi$
$18$	0.908115	−	1.08413i	0.214045	−	0.255531i
$19$	0.971336	−	1.68240i	0.222840	−	0.385970i	−0.732829	−	0.680412i	$-0.761801\pi$
$19$	0.971336	−	1.68240i	0.222840	−	0.385970i	0.955669	+	0.294443i	$0.0951340\pi$
$20$	2.80209	−	3.71241i	0.626566	−	0.830120i
$21$	−2.60919	−	0.438313i	−0.569372	−	0.0956478i
$22$	−0.427738	−	3.38983i	−0.0911941	−	0.722715i
$23$	−6.20584	+	6.68831i	−1.29401	+	1.39461i	−0.420881	+	0.907116i	$0.638279\pi$
$23$	−6.20584	+	6.68831i	−1.29401	+	1.39461i	−0.873127	+	0.487493i	$0.837912\pi$
$24$	−2.21586	−	1.75783i	−0.452310	−	0.358816i
$25$	0.403865	+	0.0608728i	0.0807730	+	0.0121746i
$26$	−6.37085	−	2.67914i	−1.24943	−	0.525423i
$27$	0.222521	−	0.974928i	0.0428242	−	0.187625i
$28$	−0.737320	+	5.23988i	−0.139340	+	0.990245i
$29$	−1.60608	−	7.03668i	−0.298241	−	1.30668i	−0.872745	−	0.488176i	$-0.837662\pi$
$29$	−1.60608	−	7.03668i	−0.298241	−	1.30668i	0.574504	−	0.818502i	$-0.305195\pi$
$30$	0.568349	−	3.23942i	0.103766	−	0.591434i
$31$	−0.265148	−	0.459249i	−0.0476219	−	0.0824836i	0.841232	−	0.540674i	$-0.181831\pi$
$31$	−0.265148	−	0.459249i	−0.0476219	−	0.0824836i	−0.888854	+	0.458191i	$0.848498\pi$
$32$	−3.39637	+	4.52379i	−0.600400	+	0.799700i
$33$	−1.36097	−	1.99618i	−0.236915	−	0.347490i
$34$	−1.78375	+	5.32411i	−0.305911	+	0.913077i
$35$	−5.76466	+	2.15119i	−0.974406	+	0.363618i
$36$	−1.96102	−	0.392948i	−0.326836	−	0.0654913i
$37$	−3.47535	−	1.07200i	−0.571343	−	0.176236i	−0.00439631	−	0.999990i	$-0.501399\pi$
$37$	−3.47535	−	1.07200i	−0.571343	−	0.176236i	−0.566947	+	0.823754i	$0.691876\pi$
$38$	−2.74656	−	0.0661511i	−0.445550	−	0.0107311i
$39$	−4.87333	+	0.365206i	−0.780358	+	0.0584797i
$40$	−6.50682	−	0.963725i	−1.02882	−	0.152378i
$41$	−3.28894	−	6.82956i	−0.513647	−	1.06660i	−0.983003	−	0.183590i	$-0.941228\pi$
$41$	−3.28894	−	6.82956i	−0.513647	−	1.06660i	0.469356	−	0.883009i	$-0.344486\pi$
$42$	1.22337	+	3.53601i	0.188770	+	0.545618i
$43$	1.70532	−	3.54114i	0.260060	−	0.540019i	−0.729528	−	0.683951i	$-0.760260\pi$
$43$	1.70532	−	3.54114i	0.260060	−	0.540019i	0.989588	+	0.143932i	$0.0459745\pi$
$44$	−3.91844	+	2.82732i	−0.590727	+	0.426234i
$45$	−0.685483	−	2.22228i	−0.102186	−	0.331278i
$46$	12.5069	+	3.17329i	1.84404	+	0.467876i
$47$	12.8750	−	1.94060i	1.87802	−	0.283066i	0.892297	−	0.451450i	$-0.149093\pi$
$47$	12.8750	−	1.94060i	1.87802	−	0.283066i	0.985721	+	0.168384i	$0.0538549\pi$
$48$	−0.681151	+	3.94158i	−0.0983156	+	0.568918i
$49$	4.54618	−	5.32280i	0.649455	−	0.760400i
$50$	−0.198015	−	0.542600i	−0.0280035	−	0.0767353i
$51$	0.591755	+	3.92604i	0.0828623	+	0.549755i
$52$	0.989762	+	9.72375i	0.137255	+	1.34844i
$53$	−6.79355	+	2.09553i	−0.933167	+	0.287844i	−0.723813	−	0.689996i	$-0.757612\pi$
$53$	−6.79355	+	2.09553i	−0.933167	+	0.287844i	−0.209354	+	0.977840i	$0.567136\pi$
$54$	−1.36103	+	0.384187i	−0.185213	+	0.0522812i
$55$	−5.06220	−	2.43783i	−0.682586	−	0.328716i
$56$	7.00434	−	2.63424i	0.935994	−	0.352015i
$57$	−1.75029	+	0.842893i	−0.231831	+	0.111644i
$58$	−7.64747	+	6.76054i	−1.00416	+	0.887702i
$59$	−0.801147	−	10.6906i	−0.104300	−	1.39179i	−0.766394	−	0.642371i	$-0.777951\pi$
$59$	−0.801147	−	10.6906i	−0.104300	−	1.39179i	0.662093	−	0.749421i	$-0.269668\pi$
$60$	−4.40647	+	1.48886i	−0.568873	+	0.192212i
$61$	2.07021	−	6.71145i	0.265063	−	0.859313i	−0.720999	−	0.692936i	$-0.756317\pi$
$61$	2.07021	−	6.71145i	0.265063	−	0.859313i	0.986062	−	0.166377i	$-0.0532068\pi$
$62$	−0.390505	+	0.640259i	−0.0495942	+	0.0813130i
$63$	1.90890	+	1.83196i	0.240499	+	0.230805i
$64$	7.91664	+	1.15184i	0.989581	+	0.143980i
$65$	−9.39038	+	6.40225i	−1.16473	+	0.794102i
$66$	−1.55615	+	3.04177i	−0.191549	+	0.374416i
$67$	−0.163371	+	0.0943225i	−0.0199590	+	0.0115233i	−0.509946	−	0.860206i	$-0.670335\pi$
$67$	−0.163371	+	0.0943225i	−0.0199590	+	0.0115233i	0.489987	+	0.871730i	$0.337001\pi$
$68$	7.81777	−	1.39224i	0.948043	−	0.168833i
$69$	8.89517	−	2.03026i	1.07085	−	0.244415i
$70$	6.57558	+	5.69910i	0.785932	+	0.681172i
$71$	1.08118	+	0.246771i	0.128312	+	0.0292864i	0.286195	−	0.958172i	$-0.407610\pi$
$71$	1.08118	+	0.246771i	0.128312	+	0.0292864i	−0.157883	+	0.987458i	$0.550467\pi$
$72$	0.840606	+	2.70063i	0.0990663	+	0.318272i
$73$	−0.660177	+	4.37999i	−0.0772679	+	0.512639i	0.916398	+	0.400268i	$0.131083\pi$
$73$	−0.660177	+	4.37999i	−0.0772679	+	0.512639i	−0.993666	+	0.112372i	$0.964155\pi$
$74$	1.02344	+	5.04054i	0.118973	+	0.585950i
$75$	−0.299398	−	0.277801i	−0.0345715	−	0.0320777i
$76$	1.77843	+	3.45443i	0.204000	+	0.396250i
$77$	6.38135	−	0.370312i	0.727223	−	0.0422010i
$78$	3.75463	+	5.80243i	0.425128	+	0.656996i
$79$	−6.88049	−	3.97245i	−0.774116	−	0.446936i	0.0602250	−	0.998185i	$-0.480818\pi$
$79$	−6.88049	−	3.97245i	−0.774116	−	0.446936i	−0.834341	+	0.551249i	$0.814152\pi$
$80$	3.21141	+	8.73050i	0.359047	+	0.976100i
$81$	−0.733052	+	0.680173i	−0.0814502	+	0.0755747i
$82$	−6.25035	+	8.70938i	−0.690236	+	0.961790i
$83$	−1.19435	+	1.49767i	−0.131097	+	0.164391i	−0.843047	−	0.537839i	$-0.819241\pi$
$83$	−1.19435	+	1.49767i	−0.131097	+	0.164391i	0.711950	+	0.702230i	$0.247812\pi$
$84$	3.56093	−	3.91405i	0.388530	−	0.427057i
$85$	5.75701	+	7.21907i	0.624436	+	0.783018i
$86$	−5.55124	+	0.281797i	−0.598605	+	0.0303870i
$87$	−2.63690	+	6.71871i	−0.282705	+	0.720321i
$88$	6.16427	+	2.94915i	0.657114	+	0.314381i
$89$	−13.3203	+	5.22782i	−1.41195	+	0.554148i	−0.944099	−	0.329661i	$-0.893066\pi$
$89$	−13.3203	+	5.22782i	−1.41195	+	0.554148i	−0.467847	+	0.883809i	$0.654970\pi$
$90$	−2.29442	+	2.35637i	−0.241853	+	0.248383i
$91$	5.80533	−	11.5532i	0.608564	−	1.21111i
$92$	−4.53295	−	17.6759i	−0.472592	−	1.84284i
$93$	−0.0396290	+	0.528812i	−0.00410934	+	0.0548353i
$94$	−11.1308	−	14.6687i	−1.14805	−	1.51296i
$95$	−2.54501	+	3.73285i	−0.261113	+	0.382982i
$96$	5.35456	−	1.82448i	0.546497	−	0.186210i
$97$			7.98622i			0.810878i	0.914122	+	0.405439i	$0.132881\pi$
$97$			7.98622i			0.810878i	−0.914122	+	0.405439i	$0.867119\pi$
$98$	−9.68745	−	2.03797i	−0.978580	−	0.205866i
$99$			2.41598i			0.242815i
$100$	−0.539455	+	0.613382i	−0.0539455	+	0.0613382i
$101$	3.73699	−	5.48115i	0.371844	−	0.545395i	−0.594018	−	0.804452i	$-0.702459\pi$
$101$	3.73699	−	5.48115i	0.371844	−	0.545395i	0.965862	+	0.259057i	$0.0834116\pi$
$102$	4.47298	−	3.39416i	0.442891	−	0.336072i
$103$	−0.470153	+	6.27375i	−0.0463255	+	0.618171i	0.924931	+	0.380135i	$0.124123\pi$
$103$	−0.470153	+	6.27375i	−0.0463255	+	0.618171i	−0.971256	+	0.238036i	$0.923496\pi$
$104$	11.4007	−	7.81569i	1.11793	−	0.766392i
$105$	5.97480	+	1.46995i	0.583081	+	0.143452i
$106$	7.20347	+	7.01408i	0.699662	+	0.681268i
$107$	10.6458	−	4.17818i	1.02917	−	0.403920i	0.210141	−	0.977671i	$-0.432608\pi$
$107$	10.6458	−	4.17818i	1.02917	−	0.403920i	0.819029	+	0.573752i	$0.194513\pi$
$108$	1.39891	+	1.42935i	0.134611	+	0.137539i
$109$	0.889958	−	2.26758i	0.0852425	−	0.217194i	−0.881896	−	0.471444i	$-0.843733\pi$
$109$	0.889958	−	2.26758i	0.0852425	−	0.217194i	0.967139	+	0.254249i	$0.0818283\pi$
$110$	0.402839	+	7.93570i	0.0384092	+	0.756639i
$111$	2.26759	+	2.84346i	0.215230	+	0.269889i
$112$	−8.01501	−	6.91083i	−0.757347	−	0.653012i
$113$	10.3918	−	13.0308i	0.977574	−	1.22584i	0.00341092	−	0.999994i	$-0.498914\pi$
$113$	10.3918	−	13.0308i	0.977574	−	1.22584i	0.974163	−	0.225845i	$-0.0725143\pi$
$114$	2.23205	+	1.60185i	0.209050	+	0.150027i
$115$	15.5543	−	14.4323i	1.45045	−	1.34582i
$116$	13.5731	+	4.91401i	1.26023	+	0.456254i
$117$	4.23226	+	2.44350i	0.391273	+	0.225901i
$118$	−12.7287	+	8.23647i	−1.17177	+	0.758229i
$119$	−9.71251	−	4.00184i	−0.890344	−	0.366848i
$120$	4.83330	+	4.46169i	0.441218	+	0.407294i
$121$	−3.78477	−	3.51175i	−0.344070	−	0.319250i
$122$	−9.73408	+	1.97643i	−0.881282	+	0.178937i
$123$	−1.12978	+	7.49558i	−0.101869	+	0.675853i
$124$	1.05936	+	0.0510592i	0.0951334	+	0.00458525i
$125$	10.4104	+	2.37612i	0.931139	+	0.212526i
$126$	0.981110	−	3.61074i	0.0874042	−	0.321670i
$127$	−18.6058	+	4.24666i	−1.65100	+	0.376830i	−0.943886	−	0.330270i	$-0.892860\pi$
$127$	−18.6058	+	4.24666i	−1.65100	+	0.376830i	−0.707113	+	0.707100i	$0.750003\pi$
$128$	−3.93291	−	10.6081i	−0.347624	−	0.937634i
$129$	−3.40380	+	1.96519i	−0.299688	+	0.173025i
$130$	14.3090	+	7.32040i	1.25498	+	0.642041i
$131$	4.50986	−	3.07477i	0.394028	−	0.268644i	−0.350057	−	0.936728i	$-0.613838\pi$
$131$	4.50986	−	3.07477i	0.394028	−	0.268644i	0.744086	+	0.668084i	$0.232885\pi$
$132$	4.83025	−	0.128703i	0.420419	−	0.0112022i
$133$	0.470325	−	5.11826i	0.0407824	−	0.443809i
$134$	0.227763	+	0.138917i	0.0196757	+	0.0120006i
$135$	−0.685483	+	2.22228i	−0.0589970	+	0.191264i
$136$	−7.02419	−	8.76198i	−0.602320	−	0.751334i
$137$	−0.612421	−	8.17219i	−0.0523227	−	0.698198i	−0.960263	−	0.279098i	$-0.909965\pi$
$137$	−0.612421	−	8.17219i	−0.0523227	−	0.698198i	0.907940	−	0.419100i	$-0.137654\pi$
$138$	−8.54610	−	9.66727i	−0.727492	−	0.822933i
$139$	17.8959	−	8.61821i	1.51791	−	0.730987i	0.525139	−	0.851016i	$-0.324013\pi$
$139$	17.8959	−	8.61821i	1.51791	−	0.730987i	0.992770	+	0.120029i	$0.0382989\pi$
$140$	2.62057	−	12.0237i	0.221479	−	1.01619i
$141$	−11.7310	−	5.64937i	−0.987932	−	0.475763i
$142$	−0.426056	−	1.50935i	−0.0357538	−	0.126662i
$143$	11.2823	−	3.48014i	0.943477	−	0.291024i
$144$	2.78316	−	2.87298i	0.231930	−	0.239415i
$145$	2.50173	+	16.5979i	0.207757	+	1.37838i
$146$	5.88460	−	2.14750i	0.487013	−	0.177729i
$147$	−6.75467	+	1.83695i	−0.557116	+	0.151509i
$148$	5.56411	−	4.68504i	0.457367	−	0.385108i
$149$	3.95381	−	0.595941i	0.323909	−	0.0488214i	0.0149247	−	0.999889i	$-0.495249\pi$
$149$	3.95381	−	0.595941i	0.323909	−	0.0488214i	0.308984	+	0.951067i	$0.400011\pi$
$150$	−0.142050	+	0.559863i	−0.0115984	+	0.0457126i
$151$	4.08757	+	13.2516i	0.332642	+	1.07840i	0.955234	+	0.295851i	$0.0956032\pi$
$151$	4.08757	+	13.2516i	0.332642	+	1.07840i	−0.622593	+	0.782546i	$0.713921\pi$
$152$	3.08365	−	4.54784i	0.250117	−	0.368879i
$153$	1.72268	−	3.57719i	0.139271	−	0.289199i
$154$	−4.78252	−	7.67106i	−0.385386	−	0.618151i
$155$	0.535090	+	1.11112i	0.0429794	+	0.0892477i
$156$	4.65980	−	8.59169i	0.373083	−	0.687886i
$157$	−20.2112	+	1.51462i	−1.61303	+	0.120880i	−0.850463	−	0.526035i	$-0.823678\pi$
$157$	−20.2112	+	1.51462i	−1.61303	+	0.120880i	−0.762563	+	0.646914i	$0.776059\pi$
$158$	−0.270537	+	11.2325i	−0.0215228	+	0.893613i
$159$	6.79355	+	2.09553i	0.538764	+	0.166187i
$160$	8.66273	−	9.90085i	0.684849	−	0.782731i
$161$	−7.50258	+	22.9441i	−0.591286	+	1.80825i
$162$	1.34096	+	0.449265i	0.105355	+	0.0352976i
$163$	5.44564	+	7.98729i	0.426535	+	0.625613i	0.978005	−	0.208583i	$-0.0668850\pi$
$163$	5.44564	+	7.98729i	0.426535	+	0.625613i	−0.551469	+	0.834195i	$0.685933\pi$
$164$	15.0460	+	1.85945i	1.17490	+	0.145199i
$165$	2.80931	+	4.86586i	0.218704	+	0.378807i
$166$	2.66830	+	0.468147i	0.207100	+	0.0363353i
$167$	1.88567	+	8.26166i	0.145918	+	0.639307i	0.993994	+	0.109433i	$0.0349035\pi$
$167$	1.88567	+	8.26166i	0.145918	+	0.639307i	−0.848077	+	0.529874i	$0.822239\pi$
$168$	−7.27118	−	1.76917i	−0.560984	−	0.136495i
$169$	2.42164	−	10.6099i	0.186280	−	0.816145i
$170$	5.06199	−	12.0371i	0.388237	−	0.923206i
$171$	1.92097	+	0.289540i	0.146900	+	0.0221417i
$172$	4.11030	+	6.70050i	0.313408	+	0.510908i
$173$	−5.48015	+	5.90620i	−0.416648	+	0.449040i	−0.906146	−	0.422964i	$-0.860990\pi$
$173$	−5.48015	+	5.90620i	−0.416648	+	0.449040i	0.489498	+	0.872004i	$0.337180\pi$
$174$	10.1270	−	1.27785i	0.767724	−	0.0968734i
$175$	1.03780	−	0.301084i	0.0784505	−	0.0227598i
$176$	−0.514630	−	9.65022i	−0.0387917	−	0.727412i
$177$	−5.36027	+	9.28426i	−0.402902	+	0.697848i
$178$	15.5132	+	12.9946i	1.16277	+	0.973987i
$179$	−4.50940	−	4.85998i	−0.337049	−	0.363252i	0.541671	−	0.840591i	$-0.317792\pi$
$179$	−4.50940	−	4.85998i	−0.337049	−	0.363252i	−0.878719	+	0.477339i	$0.841602\pi$
$180$	4.47950	+	1.25210i	0.333883	+	0.0933257i
$181$	12.6022	+	10.0499i	0.936712	+	0.747003i	0.967592	−	0.252520i	$-0.0812594\pi$
$181$	12.6022	+	10.0499i	0.936712	+	0.747003i	−0.0308794	+	0.999523i	$0.509831\pi$
$182$	−18.2750	+	0.619482i	−1.35463	+	0.0459191i
$183$	−5.49118	+	4.37907i	−0.405920	+	0.323710i
$184$	−18.8724	+	17.6011i	−1.39129	+	1.29757i
$185$	7.87337	+	3.09007i	0.578861	+	0.227186i
$186$	0.683321	−	0.309028i	0.0501035	−	0.0226590i
$187$	−3.50449	−	8.92929i	−0.256274	−	0.652974i
$188$	−10.6698	+	23.7547i	−0.778175	+	1.73249i
$189$	−0.545231	−	2.58896i	−0.0396597	−	0.188319i
$190$	6.35804	+	0.630742i	0.461261	+	0.0457588i
$191$	14.3126	+	1.07258i	1.03563	+	0.0776095i	0.581678	−	0.813419i	$-0.302396\pi$
$191$	14.3126	+	1.07258i	1.03563	+	0.0776095i	0.453948	+	0.891028i	$0.350015\pi$
$192$	−5.89218	−	5.41130i	−0.425232	−	0.390527i
$193$	19.9873	+	13.6271i	1.43872	+	0.980902i	0.996465	+	0.0840118i	$0.0267733\pi$
$193$	19.9873	+	13.6271i	1.43872	+	0.980902i	0.442254	+	0.896890i	$0.354179\pi$
$194$	9.91422	−	5.40996i	0.711799	−	0.388413i
$195$	11.3652			0.813880
$196$	4.03242	+	13.4067i	0.288030	+	0.957621i
$197$	3.60051			0.256525			0.128263	−	0.991740i	$-0.459060\pi$
$197$	3.60051			0.256525			0.128263	+	0.991740i	$0.459060\pi$
$198$	2.99924	−	1.63662i	0.213147	−	0.116309i
$199$	−5.30599	−	3.61756i	−0.376132	−	0.256442i	0.360467	−	0.932772i	$-0.382617\pi$
$199$	−5.30599	−	3.61756i	−0.376132	−	0.256442i	−0.736599	+	0.676330i	$0.763570\pi$
$200$	1.12690	+	0.254175i	0.0796836	+	0.0179729i
$201$	0.188117	+	0.0140975i	0.0132688	+	0.000994358i
$202$	−9.33587	−	0.926154i	−0.656870	−	0.0651640i
$203$	−11.6532	−	15.1282i	−0.817894	−	1.06179i
$204$	−7.24362	−	3.25358i	−0.507155	−	0.227797i
$205$	6.44046	+	16.4100i	0.449821	+	1.14613i
$206$	8.10682	−	3.66626i	0.564829	−	0.255441i
$207$	−8.49322	−	3.33334i	−0.590320	−	0.231683i
$208$	−17.4255	−	8.85861i	−1.20824	−	0.614234i
$209$	3.66949	−	2.92632i	0.253824	−	0.202418i
$210$	−2.22258	−	8.41297i	−0.153373	−	0.580550i
$211$	11.6617	+	9.29987i	0.802823	+	0.640230i	0.936450	−	0.350802i	$-0.114091\pi$
$211$	11.6617	+	9.29987i	0.802823	+	0.640230i	−0.133627	+	0.991032i	$0.542662\pi$
$212$	3.82768	−	13.6939i	0.262886	−	0.940502i
$213$	−0.754298	−	0.812940i	−0.0516836	−	0.0557017i
$214$	−12.3985	−	10.3855i	−0.847541	−	0.709941i
$215$	−4.57024	+	7.91589i	−0.311688	+	0.539859i
$216$	0.826776	−	2.70489i	0.0562550	−	0.184045i
$217$	−1.14577	−	0.809757i	−0.0777798	−	0.0549699i
$218$	−3.41787	+	0.431276i	−0.231487	+	0.0292097i
$219$	3.01280	−	3.24703i	0.203586	−	0.219414i
$220$	9.57862	−	5.87583i	0.645790	−	0.396149i
$221$	−19.1865	−	2.89190i	−1.29063	−	0.194531i
$222$	1.99383	−	4.74121i	0.133817	−	0.318209i
$223$	0.986173	−	4.32071i	0.0660391	−	0.289336i	−0.931115	−	0.364725i	$-0.881163\pi$
$223$	0.986173	−	4.32071i	0.0660391	−	0.289336i	0.997154	+	0.0753894i	$0.0240200\pi$
$224$	−3.14975	+	14.6314i	−0.210451	+	0.977604i
$225$	0.0908835	+	0.398187i	0.00605890	+	0.0265458i
$226$	−23.2162	−	4.07323i	−1.54432	−	0.270947i
$227$	1.67422	+	2.89984i	0.111122	+	0.192469i	0.916223	−	0.400669i	$-0.131222\pi$
$227$	1.67422	+	2.89984i	0.111122	+	0.192469i	−0.805101	+	0.593138i	$0.797889\pi$
$228$	0.476541	−	3.85601i	0.0315597	−	0.255370i
$229$	−15.8007	−	23.1754i	−1.04414	−	1.53147i	−0.832422	−	0.554143i	$-0.813046\pi$
$229$	−15.8007	−	23.1754i	−1.04414	−	1.53147i	−0.211719	−	0.977331i	$-0.567906\pi$
$230$	−28.4532	−	9.53278i	−1.87615	−	0.628573i
$231$	−5.48112	−	3.28878i	−0.360632	−	0.216386i
$232$	−3.09427	−	20.1787i	−0.203149	−	1.32480i
$233$	11.9577	+	3.68846i	0.783374	+	0.241639i	0.660542	−	0.750789i	$-0.270326\pi$
$233$	11.9577	+	3.68846i	0.783374	+	0.241639i	0.122831	+	0.992428i	$0.460803\pi$
$234$	0.166410	−	6.90925i	0.0108786	−	0.451672i
$235$	−30.1958	+	2.26286i	−1.96975	+	0.147613i
$236$	18.8475	+	10.2221i	1.22687	+	0.665405i
$237$	3.44717	+	7.15812i	0.223918	+	0.464970i
$238$	1.61142	+	14.7682i	0.104453	+	0.957278i
$239$	−8.15498	+	16.9340i	−0.527502	+	1.09537i	0.451641	+	0.892200i	$0.350839\pi$
$239$	−8.15498	+	16.9340i	−0.527502	+	1.09537i	−0.979144	+	0.203170i	$0.934876\pi$
$240$	2.26467	−	9.02253i	0.146184	−	0.582402i
$241$	−3.81052	−	12.3534i	−0.245457	−	0.795753i	−0.991529	−	0.129887i	$-0.958538\pi$
$241$	−3.81052	−	12.3534i	−0.245457	−	0.795753i	0.746071	−	0.665866i	$-0.231938\pi$
$242$	−1.79570	+	7.07738i	−0.115432	+	0.454951i
$243$	0.988831	−	0.149042i	0.0634335	−	0.00956107i
$244$	9.04755	+	10.7452i	0.579210	+	0.687890i
$245$	−11.4681	+	11.5540i	−0.732671	+	0.738159i
$246$	10.0705	−	3.67507i	0.642069	−	0.234314i
$247$	−1.41498	−	9.38779i	−0.0900331	−	0.597331i
$248$	−0.654238	−	1.34969i	−0.0415442	−	0.0857057i
$249$	1.83049	−	0.564631i	0.116002	−	0.0357820i
$250$	−4.10242	−	14.5333i	−0.259460	−	0.919167i
$251$	6.83427	+	3.29121i	0.431375	+	0.207739i	0.636955	−	0.770901i	$-0.280194\pi$
$251$	6.83427	+	3.29121i	0.431375	+	0.207739i	−0.205580	+	0.978640i	$0.565908\pi$
$252$	−5.14704	+	1.22799i	−0.324233	+	0.0773562i
$253$	−19.8603	+	9.56420i	−1.24860	+	0.601296i
$254$	17.8757	+	20.2208i	1.12162	+	1.26877i
$255$	−0.690023	−	9.20772i	−0.0432109	−	0.576610i
$256$	−10.5049	+	12.0685i	−0.656555	+	0.754278i
$257$	−0.227102	+	0.736245i	−0.0141662	+	0.0459257i	−0.962380	−	0.271707i	$-0.912412\pi$
$257$	−0.227102	+	0.736245i	−0.0141662	+	0.0459257i	0.948214	+	0.317633i	$0.102888\pi$
$258$	4.74539	+	2.89429i	0.295435	+	0.180191i
$259$	−9.53772	+	1.27377i	−0.592645	+	0.0791482i
$260$	−0.605443	−	22.7224i	−0.0375480	−	1.40918i
$261$	5.96349	−	4.06584i	0.369131	−	0.251669i
$262$	−6.87210	−	3.51572i	−0.424560	−	0.217202i
$263$	−24.9799	+	14.4221i	−1.54033	+	0.889308i	−0.541508	+	0.840695i	$0.682147\pi$
$263$	−24.9799	+	14.4221i	−1.54033	+	0.889308i	−0.998818	+	0.0486122i	$0.984520\pi$
$264$	−3.43184	−	5.90916i	−0.211215	−	0.363684i
$265$	16.1191	−	3.67908i	0.990190	−	0.226004i
$266$	−6.67249	+	2.88330i	−0.409117	+	0.176787i
$267$	13.9507	+	3.18415i	0.853767	+	0.194867i
$268$	0.0181636	−	0.376852i	0.00110952	−	0.0230199i
$269$	1.44326	−	9.57541i	0.0879972	−	0.583823i	−0.900763	−	0.434311i	$-0.856992\pi$
$269$	1.44326	−	9.57541i	0.0879972	−	0.583823i	0.988760	−	0.149512i	$-0.0477702\pi$
$270$	3.22313	−	0.654432i	0.196153	−	0.0398274i
$271$	−2.66258	−	2.47051i	−0.161740	−	0.150073i	0.595151	−	0.803614i	$-0.297092\pi$
$271$	−2.66258	−	2.47051i	−0.161740	−	0.150073i	−0.756891	+	0.653541i	$0.773283\pi$
$272$	−6.11898	+	14.6554i	−0.371018	+	0.888615i
$273$	−11.3048	+	6.27548i	−0.684195	+	0.379809i
$274$	−9.73023	+	6.29621i	−0.587824	+	0.380368i
$275$	0.854552	+	0.493376i	0.0515314	+	0.0297517i
$276$	−6.21187	+	17.1580i	−0.373911	+	1.03279i
$277$	18.4038	−	17.0763i	1.10578	−	1.02601i	0.106280	−	0.994336i	$-0.466106\pi$
$277$	18.4038	−	17.0763i	1.10578	−	1.02601i	0.999498	−	0.0316762i	$-0.0100845\pi$
$278$	−22.8217	−	16.3782i	−1.36875	−	0.982297i
$279$	0.330634	−	0.414601i	0.0197945	−	0.0248215i
$280$	−16.7016	+	4.89176i	−0.998110	+	0.292339i
$281$	13.8917	+	17.4197i	0.828711	+	1.03917i	0.998557	+	0.0537002i	$0.0171015\pi$
$281$	13.8917	+	17.4197i	0.828711	+	1.03917i	−0.169846	+	0.985471i	$0.554327\pi$
$282$	0.933532	+	18.3900i	0.0555911	+	1.09511i
$283$	9.36444	−	23.8602i	0.556658	−	1.41834i	−0.324665	−	0.945829i	$-0.605252\pi$
$283$	9.36444	−	23.8602i	0.556658	−	1.41834i	0.881324	−	0.472513i	$-0.156653\pi$
$284$	−1.58512	+	1.55137i	−0.0940596	+	0.0920567i
$285$	4.20558	−	1.65057i	0.249117	−	0.0977712i
$286$	−11.9631	−	11.6486i	−0.707393	−	0.688796i
$287$	−15.4673	−	12.7665i	−0.913003	−	0.753585i
$288$	−5.45191	−	1.50887i	−0.321257	−	0.0889111i
$289$	0.0923703	−	1.23260i	0.00543355	−	0.0725056i
$290$	18.9102	−	14.3493i	1.11044	−	0.842619i
$291$	4.49880	−	6.59852i	0.263724	−	0.386812i
$292$	−6.65225	−	5.85049i	−0.389293	−	0.342374i
$293$			16.5720i			0.968145i	0.875028	+	0.484073i	$0.160843\pi$
$293$			16.5720i			0.968145i	−0.875028	+	0.484073i	$0.839157\pi$
$294$	6.85611	+	7.14099i	0.399857	+	0.416471i
$295$			24.9317i			1.45158i
$296$	−9.58527	−	3.73367i	−0.557133	−	0.217015i
$297$	1.36097	−	1.99618i	0.0789716	−	0.115830i
$298$	−3.41817	−	4.50462i	−0.198009	−	0.260946i
$299$	−3.33211	+	44.4639i	−0.192701	+	2.57141i
$300$	0.791249	−	0.202915i	0.0456828	−	0.0117153i
$301$	0.175050	−	10.3973i	0.0100897	−	0.599291i
$302$	13.6817	−	14.0511i	0.787295	−	0.808553i
$303$	−6.17529	+	2.42362i	−0.354761	+	0.139233i
$304$	−7.73466	−	0.747329i	−0.443613	−	0.0428623i
$305$	−5.96741	+	15.2047i	−0.341693	+	0.870620i
$306$	−5.60775	+	0.284666i	−0.320574	+	0.0162733i
$307$	−6.06847	−	7.60962i	−0.346346	−	0.434304i	0.577897	−	0.816110i	$-0.303874\pi$
$307$	−6.06847	−	7.60962i	−0.346346	−	0.434304i	−0.924242	+	0.381806i	$0.875302\pi$
$308$	−6.28323	+	11.1336i	−0.358020	+	0.634393i
$309$	3.92259	−	4.91877i	0.223148	−	0.279819i
$310$	1.01689	−	1.41696i	0.0577556	−	0.0804778i
$311$	−8.22929	+	7.63566i	−0.466640	+	0.432979i	−0.878120	−	0.478440i	$-0.841202\pi$
$311$	−8.22929	+	7.63566i	−0.466640	+	0.432979i	0.411480	+	0.911419i	$0.365012\pi$
$312$	−13.8225	+	0.0353649i	−0.782543	+	0.00200214i
$313$	1.18942	+	0.686711i	0.0672299	+	0.0388152i	0.533238	−	0.845965i	$-0.320975\pi$
$313$	1.18942	+	0.686711i	0.0672299	+	0.0388152i	−0.466008	+	0.884780i	$0.654308\pi$
$314$	15.5716	+	24.0644i	0.878754	+	1.35803i
$315$	−4.10856	−	4.58025i	−0.231491	−	0.258068i
$316$	14.1275	−	7.27321i	0.794735	−	0.409150i
$317$	18.1708	+	16.8600i	1.02057	+	0.946954i	0.998605	−	0.0528048i	$-0.0168161\pi$
$317$	18.1708	+	16.8600i	1.02057	+	0.946954i	0.0219687	+	0.999759i	$0.493007\pi$
$318$	−2.00061	−	9.85317i	−0.112189	−	0.552538i
$319$	2.59895	−	17.2429i	0.145513	−	0.965418i
$320$	−18.1593	−	4.04709i	−1.01514	−	0.226239i
$321$	−11.1496	−	2.54483i	−0.622312	−	0.142039i
$322$	33.5655	−	6.22882i	1.87053	−	0.347118i
$323$	−7.51977	+	1.71634i	−0.418411	+	0.0954996i
$324$	−0.350655	−	1.96902i	−0.0194809	−	0.109390i
$325$	1.72857	−	0.997990i	0.0958838	−	0.0553585i
$326$	6.22660	−	12.1710i	0.344859	−	0.674089i
$327$	−2.01269	+	1.37223i	−0.111302	+	0.0758844i
$328$	−7.88401	−	19.9380i	−0.435322	−	1.10089i
$329$	28.7857	−	18.9239i	1.58701	−	1.04331i
$330$	4.13750	−	6.78371i	0.227762	−	0.373431i
$331$	−3.99362	+	12.9470i	−0.219509	+	0.711632i	0.777102	+	0.629375i	$0.216689\pi$
$331$	−3.99362	+	12.9470i	−0.219509	+	0.711632i	−0.996611	+	0.0822569i	$0.973787\pi$
$332$	−1.22637	−	3.62960i	−0.0673060	−	0.199200i
$333$	−0.271788	−	3.62675i	−0.0148939	−	0.198745i
$334$	8.97878	−	7.93745i	0.491297	−	0.434318i
$335$	0.395267	−	0.190351i	0.0215957	−	0.0104000i
$336$	2.72930	+	10.2250i	0.148896	+	0.557820i
$337$	−4.96416	−	2.39061i	−0.270415	−	0.130225i	0.293763	−	0.955878i	$-0.405092\pi$
$337$	−4.96416	−	2.39061i	−0.270415	−	0.130225i	−0.564178	+	0.825653i	$0.690807\pi$
$338$	−14.8117	+	4.18101i	−0.805651	+	0.227417i
$339$	−15.9266	+	4.91271i	−0.865015	+	0.266822i
$340$	−18.3721	+	1.87007i	−0.996369	+	0.101419i
$341$	−0.190950	−	1.26687i	−0.0103405	−	0.0686051i
$342$	−0.941851	−	2.58086i	−0.0509295	−	0.139557i
$343$	5.02739	−	17.8249i	0.271454	−	0.962452i
$344$	5.53374	−	9.64160i	0.298359	−	0.519840i
$345$	−20.9816	+	3.16247i	−1.12961	+	0.170262i
$346$	11.0444	+	2.80222i	0.593749	+	0.150648i
$347$	−2.28086	−	7.39437i	−0.122443	−	0.396950i	0.873512	−	0.486802i	$-0.161837\pi$
$347$	−2.28086	−	7.39437i	−0.122443	−	0.396950i	−0.995955	+	0.0898519i	$0.971361\pi$
$348$	−8.44648	−	11.7062i	−0.452779	−	0.627516i
$349$	−6.33880	+	13.1627i	−0.339308	+	0.704581i	−0.998893	−	0.0470496i	$-0.985018\pi$
$349$	−6.33880	+	13.1627i	−0.339308	+	0.704581i	0.659584	+	0.751631i	$0.270732\pi$
$350$	−1.07679	−	1.08439i	−0.0575569	−	0.0579629i
$351$	−2.12039	−	4.40303i	−0.113178	−	0.235016i
$352$	−11.6313	+	7.17604i	−0.619951	+	0.382484i
$353$	23.2196	−	1.74007i	1.23585	−	0.0926143i	0.559273	−	0.828984i	$-0.311080\pi$
$353$	23.2196	−	1.74007i	1.23585	−	0.0926143i	0.676580	+	0.736369i	$0.263461\pi$
$354$	15.1567	+	0.365051i	0.805571	+	0.0194023i
$355$	−2.46447	−	0.760187i	−0.130800	−	0.0403465i
$356$	5.62286	−	28.0611i	0.298011	−	1.48723i
$357$	5.77054	+	8.77773i	0.305409	+	0.464567i
$358$	−2.97853	+	8.89026i	−0.157420	+	0.469865i
$359$	4.28011	+	6.27777i	0.225895	+	0.331328i	0.922408	−	0.386217i	$-0.126218\pi$
$359$	4.28011	+	6.27777i	0.225895	+	0.331328i	−0.696513	+	0.717545i	$0.745266\pi$
$360$	−1.48010	−	6.40911i	−0.0780081	−	0.337790i
$361$	7.61301	+	13.1861i	0.400685	+	0.694007i
$362$	3.93923	−	22.4525i	0.207042	−	1.18008i
$363$	1.14888	+	5.03358i	0.0603007	+	0.264195i
$364$	13.1487	+	22.2672i	0.689180	+	1.16712i
$365$	2.29223	−	10.0429i	0.119981	−	0.525669i
$366$	9.15603	+	3.85040i	0.478594	+	0.201264i
$367$	−22.9847	−	3.46439i	−1.19979	−	0.180840i	−0.481416	−	0.876492i	$-0.659877\pi$
$367$	−22.9847	−	3.46439i	−1.19979	−	0.180840i	−0.718378	+	0.695653i	$0.755115\pi$
$368$	34.6347	+	11.5053i	1.80546	+	0.599756i
$369$	5.15587	−	5.55671i	0.268404	−	0.289271i
$370$	−1.49746	−	11.8674i	−0.0778490	−	0.616955i
$371$	−14.0019	+	12.5599i	−0.726943	+	0.652079i
$372$	−0.846522	−	0.638946i	−0.0438901	−	0.0331278i
$373$	−14.4972	+	25.1099i	−0.750636	+	1.30014i	0.196880	+	0.980428i	$0.436919\pi$
$373$	−14.4972	+	25.1099i	−0.750636	+	1.30014i	−0.947515	+	0.319711i	$0.896414\pi$
$374$	−8.71098	+	10.3993i	−0.450434	+	0.537737i
$375$	−7.26300	−	7.82766i	−0.375060	−	0.404218i
$376$	36.7173	−	2.84607i	1.89355	−	0.146775i
$377$	−27.5772	−	21.9921i	−1.42030	−	1.13265i
$378$	−2.84463	+	2.43065i	−0.146312	+	0.125019i
$379$	−10.5499	+	8.41323i	−0.541909	+	0.432158i	−0.855805	−	0.517299i	$-0.826937\pi$
$379$	−10.5499	+	8.41323i	−0.541909	+	0.432158i	0.313895	+	0.949458i	$0.398366\pi$
$380$	−3.52400	−	8.32024i	−0.180777	−	0.426819i
$381$	17.7651	+	6.97228i	0.910133	+	0.357201i
$382$	−8.36403	−	18.4945i	−0.427941	−	0.946262i
$383$	0.158923	+	0.404928i	0.00812057	+	0.0206909i	0.934877	−	0.354973i	$-0.115510\pi$
$383$	0.158923	+	0.404928i	0.00812057	+	0.0206909i	−0.926756	+	0.375664i	$0.877415\pi$
$384$	−2.72624	+	10.9803i	−0.139123	+	0.560338i
$385$	−14.8633	−	0.250241i	−0.757506	−	0.0127534i
$386$	3.37727	−	34.0437i	0.171898	−	1.73278i
$387$	3.91938	+	0.293717i	0.199233	+	0.0149305i
$388$	−13.4320	−	8.64289i	−0.681908	−	0.438776i
$389$	−3.53268	−	2.40854i	−0.179114	−	0.122118i	0.470444	−	0.882430i	$-0.344094\pi$
$389$	−3.53268	−	2.40854i	−0.179114	−	0.122118i	−0.649558	+	0.760312i	$0.725046\pi$
$390$	−7.69893	−	14.1090i	−0.389851	−	0.714434i
$391$	36.2255			1.83200
$392$	13.9117	−	14.0878i	0.702646	−	0.711540i
$393$	−5.45830			−0.275335
$394$	−2.43903	−	4.46972i	−0.122876	−	0.225181i
$395$	15.2662	+	10.4083i	0.768124	+	0.523698i
$396$	−4.06344	−	2.61464i	−0.204196	−	0.131390i
$397$	−5.19902	−	0.389613i	−0.260931	−	0.0195541i	−0.0563780	−	0.998409i	$-0.517955\pi$
$397$	−5.19902	−	0.389613i	−0.260931	−	0.0195541i	−0.204553	+	0.978855i	$0.565574\pi$
$398$	−0.896556	+	9.03752i	−0.0449403	+	0.453010i
$399$	−3.27182	+	3.96396i	−0.163796	+	0.198446i
$400$	−0.447836	−	1.57113i	−0.0223918	−	0.0785564i
$401$	5.43918	+	13.8588i	0.271620	+	0.692075i	0.999976	+	0.00687737i	$0.00218915\pi$
$401$	5.43918	+	13.8588i	0.271620	+	0.692075i	−0.728357	+	0.685198i	$0.759716\pi$
$402$	−0.109932	−	0.243082i	−0.00548292	−	0.0121238i
$403$	−2.41241	−	0.946800i	−0.120171	−	0.0471635i
$404$	5.17449	+	12.2171i	0.257441	+	0.607823i
$405$	1.81823	−	1.44999i	0.0903485	−	0.0720506i
$406$	−10.8864	+	24.7145i	−0.540283	+	1.22656i
$407$	−6.86975	−	5.47844i	−0.340521	−	0.271556i
$408$	0.867863	+	11.1964i	0.0429656	+	0.554302i
$409$	−2.76232	−	2.97707i	−0.136588	−	0.147207i	0.661053	−	0.750339i	$-0.270110\pi$
$409$	−2.76232	−	2.97707i	−0.136588	−	0.147207i	−0.797641	+	0.603132i	$0.793919\pi$
$410$	16.0088	−	19.1116i	0.790619	−	0.943857i
$411$	−4.09755	+	7.09717i	−0.202117	+	0.350078i
$412$	−10.0430	−	7.58037i	−0.494784	−	0.373458i
$413$	−13.7664	−	24.7991i	−0.677402	−	1.22028i
$414$	1.61535	+	12.8017i	0.0793900	+	0.629167i
$415$	3.03011	−	3.26568i	0.148742	−	0.160306i
$416$	0.807049	+	27.6332i	0.0395689	+	1.35483i
$417$	−19.6411	−	2.96042i	−0.961828	−	0.144972i
$418$	−6.11854	−	2.57304i	−0.299268	−	0.125851i
$419$	1.58827	−	6.95867i	0.0775921	−	0.339953i	−0.921200	−	0.389089i	$-0.872790\pi$
$419$	1.58827	−	6.95867i	0.0775921	−	0.339953i	0.998792	+	0.0491363i	$0.0156469\pi$
$420$	−8.93839	+	8.45820i	−0.436149	+	0.412718i
$421$	3.60818	+	15.8085i	0.175852	+	0.770458i	0.983517	+	0.180816i	$0.0578739\pi$
$421$	3.60818	+	15.8085i	0.175852	+	0.770458i	−0.807665	+	0.589642i	$0.799269\pi$
$422$	3.64525	−	20.7768i	0.177448	−	1.01140i
$423$	6.51024	+	11.2761i	0.316538	+	0.548261i
$424$	−19.5928	+	4.52469i	−0.951509	+	0.219738i
$425$	−0.913486	−	1.33984i	−0.0443106	−	0.0649917i
$426$	−0.498225	+	1.48709i	−0.0241391	+	0.0720499i
$427$	−2.45985	−	18.4188i	−0.119041	−	0.891351i
$428$	−4.49390	+	22.4269i	−0.217221	+	1.08405i
$429$	−11.2823	−	3.48014i	−0.544717	−	0.168023i
$430$	12.9228	+	0.311248i	0.623195	+	0.0150097i
$431$	29.5513	−	2.21457i	1.42344	−	0.106672i	0.659375	−	0.751814i	$-0.270821\pi$
$431$	29.5513	−	2.21457i	1.42344	−	0.106672i	0.764062	+	0.645143i	$0.223202\pi$
$432$	−3.91796	+	0.805955i	−0.188503	+	0.0387765i
$433$	−5.93281	−	12.3196i	−0.285113	−	0.592043i	0.708394	−	0.705817i	$-0.249420\pi$
$433$	−5.93281	−	12.3196i	−0.285113	−	0.592043i	−0.993507	+	0.113775i	$0.963706\pi$
$434$	−0.229087	+	1.97091i	−0.0109965	+	0.0946069i
$435$	7.28289	−	15.1231i	0.349188	−	0.725096i
$436$	2.85070	+	3.95085i	0.136524	+	0.189211i
$437$	5.22447	+	16.9373i	0.249920	+	0.810222i
$438$	−6.07182	−	1.54056i	−0.290123	−	0.0736109i
$439$	12.5894	−	1.89755i	0.600862	−	0.0905653i	0.158434	−	0.987370i	$-0.449355\pi$
$439$	12.5894	−	1.89755i	0.600862	−	0.0905653i	0.442428	+	0.896804i	$0.354117\pi$
$440$	−13.7830	−	7.91068i	−0.657080	−	0.377127i
$441$	6.61576	+	2.28729i	0.315036	+	0.108918i
$442$	9.40714	+	25.7775i	0.447452	+	1.22611i
$443$	−4.30047	−	28.5317i	−0.204321	−	1.35558i	−0.822150	−	0.569271i	$-0.807226\pi$
$443$	−4.30047	−	28.5317i	−0.204321	−	1.35558i	0.617829	−	0.786313i	$-0.288013\pi$
$444$	−7.23646	+	0.736585i	−0.343427	+	0.0349568i
$445$	31.7996	−	9.80888i	1.50745	−	0.464986i
$446$	−6.03184	+	1.70265i	−0.285616	+	0.0806228i
$447$	−3.60250	−	1.73487i	−0.170392	−	0.0820566i
$448$	20.2974	−	6.00137i	0.958961	−	0.283538i
$449$	3.30043	−	1.58940i	0.155757	−	0.0750085i	−0.354381	−	0.935101i	$-0.615309\pi$
$449$	3.30043	−	1.58940i	0.155757	−	0.0750085i	0.510138	+	0.860092i	$0.329594\pi$
$450$	0.432749	−	0.382561i	0.0204000	−	0.0180341i
$451$	−1.36859	−	18.2625i	−0.0644442	−	0.859949i
$452$	10.6704	+	31.5802i	0.501892	+	1.48541i
$453$	4.08757	−	13.2516i	0.192051	−	0.622613i
$454$	2.46577	−	4.04279i	0.115724	−	0.189738i
$455$	−15.4710	+	25.7842i	−0.725292	+	1.20878i
$456$	−5.10972	+	2.02052i	−0.239285	+	0.0946195i
$457$	17.3597	−	11.8357i	0.812054	−	0.553649i	−0.0845822	−	0.996417i	$-0.526956\pi$
$457$	17.3597	−	11.8357i	0.812054	−	0.553649i	0.896637	+	0.442767i	$0.146003\pi$
$458$	−18.0667	+	35.3146i	−0.844201	+	1.65014i
$459$	−3.43845	+	1.98519i	−0.160493	+	0.0926608i
$460$	7.44042	+	41.7799i	0.346911	+	1.94800i
$461$	−22.3270	+	5.09599i	−1.03987	+	0.237344i	−0.708171	−	0.706041i	$-0.750479\pi$
$461$	−22.3270	+	5.09599i	−1.03987	+	0.237344i	−0.331700	+	0.943385i	$0.607622\pi$
$462$	−0.369759	+	9.03221i	−0.0172027	+	0.420217i
$463$	31.5050	+	7.19082i	1.46416	+	0.334186i	0.879036	−	0.476756i	$-0.158187\pi$
$463$	31.5050	+	7.19082i	1.46416	+	0.334186i	0.585127	+	0.810942i	$0.301045\pi$
$464$	−22.9541	+	17.5106i	−1.06562	+	0.812908i
$465$	0.183807	−	1.21948i	0.00852386	−	0.0565521i
$466$	−3.52137	−	17.3431i	−0.163124	−	0.803402i
$467$	−1.86815	−	1.73339i	−0.0864476	−	0.0802116i	0.635766	−	0.771882i	$-0.280685\pi$
$467$	−1.86815	−	1.73339i	−0.0864476	−	0.0802116i	−0.722213	+	0.691671i	$0.756875\pi$
$468$	−8.68998	+	4.47383i	−0.401695	+	0.206803i
$469$	−0.288059	+	0.407591i	−0.0133013	+	0.0188208i
$470$	23.2641	+	35.9526i	1.07309	+	1.65837i
$471$	17.5525	+	10.1339i	0.808775	+	0.466946i
$472$	−0.0775794	−	30.3222i	−0.00357088	−	1.39569i
$473$	6.96085	−	6.45872i	0.320060	−	0.296972i
$474$	6.55104	−	9.12836i	0.300899	−	0.419280i
$475$	0.494701	−	0.620335i	0.0226984	−	0.0284629i
$476$	17.2418	−	12.0046i	0.790278	−	0.550229i
$477$	−4.43264	−	5.55836i	−0.202957	−	0.254500i
$478$	26.5464	−	1.34757i	1.21420	−	0.0616366i
$479$	15.9354	−	40.6028i	0.728108	−	1.85519i	0.285994	−	0.958231i	$-0.407676\pi$
$479$	15.9354	−	40.6028i	0.728108	−	1.85519i	0.442115	−	0.896959i	$-0.354228\pi$
$480$	−12.7348	+	3.30057i	−0.581263	+	0.150650i
$481$	−16.5450	+	6.49344i	−0.754388	+	0.296075i
$482$	−12.7544	+	13.0988i	−0.580948	+	0.596634i
$483$	19.1238	−	14.7310i	0.870163	−	0.670283i
$484$	10.0024	−	2.56510i	0.454654	−	0.116595i
$485$	1.38794	−	18.5208i	0.0630233	−	0.840988i
$486$	−0.854869	−	1.12659i	−0.0387777	−	0.0511030i
$487$	−19.8308	+	29.0864i	−0.898617	+	1.31803i	0.0490588	+	0.998796i	$0.484378\pi$
$487$	−19.8308	+	29.0864i	−0.898617	+	1.31803i	−0.947676	+	0.319234i	$0.896575\pi$
$488$	7.21031	−	18.5107i	0.326395	−	0.837939i
$489$		−	9.66704i		−	0.437159i
$490$	22.1120	+	6.40987i	0.998917	+	0.289568i
$491$		−	0.887108i		−	0.0400346i	−0.999800	−	0.0200173i	$-0.993628\pi$
$491$		−	0.887108i		−	0.0400346i	0.999800	−	0.0200173i	$-0.00637213\pi$
$492$	−11.3841	−	10.0121i	−0.513237	−	0.451379i
$493$	−16.1429	+	23.6774i	−0.727042	+	1.06637i
$494$	−10.6956	+	8.11598i	−0.481219	+	0.365155i
$495$	0.419880	−	5.60290i	0.0188722	−	0.251832i
$496$	−1.23234	+	1.72648i	−0.0553338	+	0.0775213i
$497$	2.87111	−	0.604650i	0.128787	−	0.0271222i
$498$	−1.94094	−	1.88991i	−0.0869754	−	0.0846888i
$499$	25.9863	−	10.1989i	1.16330	−	0.456563i	0.296413	−	0.955060i	$-0.404210\pi$
$499$	25.9863	−	10.1989i	1.16330	−	0.456563i	0.866892	+	0.498496i	$0.166114\pi$
$500$	−15.2628	+	14.9378i	−0.682575	+	0.668041i
$501$	3.09595	−	7.88834i	0.138317	−	0.352425i
$502$	−0.543857	−	10.7137i	−0.0242735	−	0.478175i
$503$	21.8301	+	27.3741i	0.973358	+	1.22055i	0.975375	+	0.220554i	$0.0707867\pi$
$503$	21.8301	+	27.3741i	0.973358	+	1.22055i	−0.00201663	+	0.999998i	$0.500642\pi$
$504$	5.01112	+	5.55776i	0.223213	+	0.247562i
$505$	−9.61903	+	12.0619i	−0.428041	+	0.536747i
$506$	25.3267	+	18.1759i	1.12591	+	0.808019i
$507$	−7.97761	+	7.40214i	−0.354298	+	0.328741i
$508$	12.9932	−	35.8890i	0.576482	−	1.59232i
$509$	−26.2446	−	15.1523i	−1.16327	−	0.671616i	−0.211186	−	0.977446i	$-0.567733\pi$
$509$	−26.2446	−	15.1523i	−1.16327	−	0.671616i	−0.952086	+	0.305830i	$0.901066\pi$
$510$	−10.9632	+	7.09402i	−0.485457	+	0.314129i
$511$	3.26531	+	11.2552i	0.144449	+	0.497899i
$512$	22.0981	+	4.86561i	0.976607	+	0.215031i
$513$	−1.42408	−	1.32135i	−0.0628746	−	0.0583391i
$514$	1.06783	−	0.216814i	0.0470999	−	0.00956326i
$515$	2.18066	−	14.4678i	0.0960915	−	0.637525i
$516$	0.378434	−	7.85163i	0.0166596	−	0.345649i
$517$	30.6685	+	6.99989i	1.34880	+	0.307855i
$518$	8.04224	+	10.9774i	0.353356	+	0.482319i
$519$	7.85500	−	1.79285i	0.344796	−	0.0786975i
$520$	−27.7978	+	16.1440i	−1.21901	+	0.707962i
$521$	17.5565	−	10.1363i	0.769166	−	0.444078i	−0.0634112	−	0.997987i	$-0.520198\pi$
$521$	17.5565	−	10.1363i	0.769166	−	0.444078i	0.832577	+	0.553909i	$0.186865\pi$
$522$	−9.08714	−	4.64892i	−0.397733	−	0.203478i
$523$	−6.14131	+	4.18708i	−0.268541	+	0.183088i	−0.690102	−	0.723712i	$-0.742435\pi$
$523$	−6.14131	+	4.18708i	−0.268541	+	0.183088i	0.421562	+	0.906800i	$0.361482\pi$
$524$	0.290772	+	10.9127i	0.0127024	+	0.476725i
$525$	−1.02708	−	0.335848i	−0.0448254	−	0.0146576i
$526$	34.8256	+	21.2407i	1.51847	+	0.926138i
$527$	−0.620600	+	2.01193i	−0.0270337	+	0.0876413i
$528$	−5.01095	+	8.26328i	−0.218074	+	0.359613i
$529$	−4.50219	−	60.0775i	−0.195747	−	2.61207i
$530$	−15.4866	−	17.5183i	−0.672693	−	0.760945i
$531$	9.65887	−	4.65147i	0.419159	−	0.201856i
$532$	8.09941	+	6.33015i	0.351154	+	0.274447i
$533$	−33.3761	−	16.0731i	−1.44568	−	0.696201i
$534$	−5.49750	−	19.4756i	−0.237900	−	0.842790i
$535$	−25.4148	+	7.83944i	−1.09878	+	0.338929i
$536$	−0.480135	+	0.232736i	−0.0207387	+	0.0100527i
$537$	0.988119	+	6.55574i	0.0426405	+	0.282901i
$538$	−12.8647	+	4.69481i	−0.554639	+	0.202408i
$539$	14.9225	−	7.95812i	0.642756	−	0.342780i
$540$	−2.99581	−	3.55792i	−0.128919	−	0.153109i
$541$	41.2060	−	6.21081i	1.77159	−	0.267024i	0.819550	−	0.573008i	$-0.194224\pi$
$541$	41.2060	−	6.21081i	1.77159	−	0.267024i	0.952037	+	0.305984i	$0.0989855\pi$
$542$	−1.26327	+	4.97892i	−0.0542620	+	0.213863i
$543$	−4.75110	−	15.4027i	−0.203889	−	0.660992i
$544$	22.3385	−	2.33156i	0.957757	−	0.0999647i
$545$	−2.45799	+	5.10406i	−0.105289	+	0.218634i
$546$	15.4485	+	9.78282i	0.661133	+	0.418666i
$547$	6.71746	+	13.9489i	0.287218	+	0.596414i	0.993796	−	0.111222i	$-0.0354763\pi$
$547$	6.71746	+	13.9489i	0.287218	+	0.596414i	−0.706578	+	0.707635i	$0.749762\pi$
$548$	14.4076	+	7.81412i	0.615462	+	0.333803i
$549$	7.00384	−	0.524865i	0.298917	−	0.0224007i
$550$	0.0336005	−	1.39507i	0.00143273	−	0.0594861i
$551$	−13.3986	−	4.13291i	−0.570798	−	0.176068i
$552$	25.5082	−	3.91151i	1.08570	−	0.166485i
$553$	−20.9321	−	1.92348i	−0.890122	−	0.0817948i
$554$	−33.6657	−	11.2791i	−1.43032	−	0.479204i
$555$	−4.76458	−	6.98836i	−0.202245	−	0.296639i
$556$	−4.87242	+	39.4259i	−0.206637	+	1.67203i
$557$	16.5902	+	28.7351i	0.702950	+	1.21755i	0.967426	+	0.253153i	$0.0814677\pi$
$557$	16.5902	+	28.7351i	0.702950	+	1.21755i	−0.264476	+	0.964392i	$0.585199\pi$
$558$	−0.738668	−	0.129598i	−0.0312703	−	0.00548631i
$559$	−4.27412	−	18.7261i	−0.180776	−	0.792031i
$560$	17.3866	+	17.4199i	0.734716	+	0.736123i
$561$	−2.13450	+	9.35188i	−0.0901188	+	0.394836i
$562$	12.2146	−	29.0457i	0.515243	−	1.22522i
$563$	20.0143	+	3.01667i	0.843501	+	0.127137i	0.556556	−	0.830810i	$-0.312122\pi$
$563$	20.0143	+	3.01667i	0.843501	+	0.127137i	0.286945	+	0.957947i	$0.407360\pi$
$564$	22.1973	−	13.6165i	0.934675	−	0.573360i
$565$	−26.3642	+	28.4138i	−1.10915	+	1.19538i
$566$	−35.9640	+	4.53803i	−1.51168	+	0.190748i
$567$	−1.00792	+	2.44624i	−0.0423288	+	0.102732i
$568$	2.99967	+	0.916878i	0.125863	+	0.0384713i
$569$	6.66502	−	11.5442i	0.279412	−	0.483956i	−0.691827	−	0.722064i	$-0.743194\pi$
$569$	6.66502	−	11.5442i	0.279412	−	0.483956i	0.971239	+	0.238108i	$0.0765271\pi$
$570$	−4.89795	−	4.10275i	−0.205152	−	0.171845i
$571$	15.9064	+	17.1430i	0.665661	+	0.717411i	0.972123	−	0.234471i	$-0.0753359\pi$
$571$	15.9064	+	17.1430i	0.665661	+	0.717411i	−0.306463	+	0.951883i	$0.599145\pi$
$572$	−6.35679	+	22.7421i	−0.265791	+	0.950894i
$573$	−11.2214	−	8.94881i	−0.468783	−	0.373842i
$574$	−5.37087	+	27.8495i	−0.224176	+	1.16242i
$575$	−2.91346	+	2.32341i	−0.121500	+	0.0968927i
$576$	1.82005	+	7.79021i	0.0758356	+	0.324592i
$577$	18.4190	+	7.22893i	0.766793	+	0.300944i	0.716311	−	0.697781i	$-0.245829\pi$
$577$	18.4190	+	7.22893i	0.766793	+	0.300944i	0.0504820	+	0.998725i	$0.483924\pi$
$578$	−1.59274	+	0.720306i	−0.0662491	+	0.0299608i
$579$	−8.83787	−	22.5185i	−0.367289	−	0.935837i
$580$	−30.6234	−	13.7550i	−1.27157	−	0.571145i
$581$	−1.21079	+	4.92143i	−0.0502322	+	0.204175i
$582$	−11.2390	−	1.11496i	−0.465874	−	0.0462164i
$583$	−17.1282	−	1.28358i	−0.709376	−	0.0531604i
$584$	−2.75658	+	12.2214i	−0.114068	+	0.505725i
$585$	−9.39038	−	6.40225i	−0.388244	−	0.264701i
$586$	20.5727	−	11.2261i	0.849851	−	0.463744i
$587$	−15.0204			−0.619960			−0.309980	−	0.950743i	$-0.600322\pi$
$587$	−15.0204			−0.619960			−0.309980	+	0.950743i	$0.600322\pi$
$588$	4.22052	−	13.3487i	0.174051	−	0.550490i
$589$	−1.03019			−0.0424482
$590$	30.9506	−	16.8890i	1.27422	−	0.695311i
$591$	−2.97488	−	2.02824i	−0.122370	−	0.0834305i
$592$	1.85815	+	14.4285i	0.0763693	+	0.593009i
$593$	41.4881	+	3.10910i	1.70371	+	0.127675i	0.890705	−	0.454581i	$-0.150211\pi$
$593$	41.4881	+	3.10910i	1.70371	+	0.127675i	0.813005	+	0.582257i	$0.197830\pi$
$594$	−3.40003	−	0.337295i	−0.139505	−	0.0138394i
$595$	21.8288	+	10.9686i	0.894893	+	0.449670i
$596$	−3.27660	+	7.29486i	−0.134215	+	0.298809i
$597$	2.34617	+	5.97794i	0.0960223	+	0.244661i
$598$	57.4554	−	25.9839i	2.34953	−	1.06256i
$599$	29.6493	+	11.6365i	1.21144	+	0.475454i	0.883135	−	0.469118i	$-0.155428\pi$
$599$	29.6493	+	11.6365i	1.21144	+	0.475454i	0.328303	+	0.944573i	$0.393523\pi$
$600$	−0.787903	−	0.844812i	−0.0321660	−	0.0344893i
$601$	−21.1658	+	16.8792i	−0.863372	+	0.688517i	−0.951519	−	0.307591i	$-0.900477\pi$
$601$	−21.1658	+	16.8792i	−0.863372	+	0.688517i	0.0881462	+	0.996108i	$0.471906\pi$
$602$	−13.0260	+	6.82596i	−0.530899	+	0.278205i
$603$	−0.147489	−	0.117618i	−0.00600620	−	0.00478978i
$604$	−26.7115	−	7.46630i	−1.08687	−	0.303800i
$605$	8.16694	+	8.80187i	0.332033	+	0.357847i
$606$	7.19194	+	6.02431i	0.292152	+	0.244721i
$607$	−10.2185	+	17.6990i	−0.414757	+	0.718379i	−0.995403	−	0.0957765i	$-0.969467\pi$
$607$	−10.2185	+	17.6990i	−0.414757	+	0.718379i	0.580646	+	0.814156i	$0.302800\pi$
$608$	4.31181	+	10.1082i	0.174867	+	0.409941i
$609$	1.10629	+	19.0640i	0.0448292	+	0.772512i
$610$	22.9178	−	2.89182i	0.927914	−	0.117087i
$611$	43.2801	−	46.6448i	1.75092	−	1.88705i
$612$	4.15215	+	6.76871i	0.167841	+	0.273609i
$613$	−30.7416	−	4.63356i	−1.24164	−	0.187148i	−0.504815	−	0.863228i	$-0.668439\pi$
$613$	−30.7416	−	4.63356i	−1.24164	−	0.187148i	−0.736828	+	0.676080i	$0.763677\pi$
$614$	−5.33584	+	12.6883i	−0.215337	+	0.512060i
$615$	3.92274	−	17.1866i	0.158180	−	0.693032i
$616$	18.0777	+	0.258095i	0.728372	+	0.0103989i
$617$	−8.13251	−	35.6309i	−0.327403	−	1.43444i	−0.824062	−	0.566499i	$-0.808297\pi$
$617$	−8.13251	−	35.6309i	−0.327403	−	1.43444i	0.496660	−	0.867945i	$-0.334560\pi$
$618$	−8.76345	−	1.53753i	−0.352518	−	0.0618484i
$619$	6.79013	+	11.7608i	0.272918	+	0.472708i	0.969608	−	0.244664i	$-0.0786778\pi$
$619$	6.79013	+	11.7608i	0.272918	+	0.472708i	−0.696690	+	0.717373i	$0.745344\pi$
$620$	−2.44789	−	0.302520i	−0.0983096	−	0.0121495i
$621$	5.13969	+	7.53854i	0.206249	+	0.302511i
$622$	15.0537	+	5.04348i	0.603597	+	0.202225i
$623$	−26.2143	+	27.3153i	−1.05026	+	1.09437i
$624$	9.40741	+	17.1355i	0.376598	+	0.685968i
$625$	−25.6813	−	7.92164i	−1.02725	−	0.316866i
$626$	0.0467672	−	1.94175i	0.00186919	−	0.0776079i
$627$	−4.68033	+	0.350743i	−0.186915	+	0.0140073i
$628$	19.3256	−	35.6323i	0.771175	−	1.42188i
$629$	6.26527	+	13.0100i	0.249813	+	0.518742i
$630$	−2.90281	+	8.20315i	−0.115651	+	0.326821i
$631$	1.28594	−	2.67027i	0.0511923	−	0.106302i	−0.873804	−	0.486279i	$-0.838354\pi$
$631$	1.28594	−	2.67027i	0.0511923	−	0.106302i	0.924996	+	0.379977i	$0.124068\pi$
$632$	−18.5992	−	12.6112i	−0.739838	−	0.501645i
$633$	−4.39652	−	14.2532i	−0.174746	−	0.566513i
$634$	8.62119	−	33.9787i	0.342391	−	1.34947i
$635$	43.8868	−	6.61487i	1.74159	−	0.262503i
$636$	−10.8766	+	9.15824i	−0.431287	+	0.363148i
$637$	1.15156	−	34.1896i	0.0456266	−	1.35464i
$638$	−23.1662	+	8.45419i	−0.917158	+	0.334704i
$639$	0.165285	+	1.09659i	0.00653857	+	0.0433806i
$640$	7.27721	+	25.2848i	0.287657	+	0.999469i
$641$	−2.77099	+	0.854736i	−0.109447	+	0.0337601i	−0.348995	−	0.937125i	$-0.613477\pi$
$641$	−2.77099	+	0.854736i	−0.109447	+	0.0337601i	0.239548	+	0.970885i	$0.423001\pi$
$642$	4.39371	+	15.5652i	0.173406	+	0.614311i
$643$	−30.8432	−	14.8533i	−1.21634	−	0.585757i	−0.288048	−	0.957616i	$-0.593006\pi$
$643$	−30.8432	−	14.8533i	−1.21634	−	0.585757i	−0.928289	+	0.371859i	$0.878720\pi$
$644$	−30.4703	−	37.4493i	−1.20070	−	1.47571i
$645$	8.23529	−	3.96591i	0.324264	−	0.156157i
$646$	7.22467	+	8.17249i	0.284251	+	0.321542i
$647$	−1.09712	−	14.6400i	−0.0431322	−	0.575559i	−0.976343	−	0.216229i	$-0.930624\pi$
$647$	−1.09712	−	14.6400i	−0.0431322	−	0.575559i	0.933211	−	0.359330i	$-0.116995\pi$
$648$	−2.20683	+	1.76915i	−0.0866926	+	0.0694987i
$649$	7.63434	−	24.7499i	0.299674	−	0.971520i
$650$	−2.40987	−	1.46982i	−0.0945230	−	0.0576512i
$651$	0.490526	+	1.31449i	0.0192252	+	0.0515188i
$652$	−19.3272	+	0.514979i	−0.756913	+	0.0201681i
$653$	8.44950	−	5.76077i	0.330654	−	0.225436i	−0.386600	−	0.922247i	$-0.626351\pi$
$653$	8.44950	−	5.76077i	0.330654	−	0.225436i	0.717255	+	0.696811i	$0.245398\pi$
$654$	3.06692	+	1.56902i	0.119926	+	0.0613535i
$655$	−10.9932	+	6.34692i	−0.429539	+	0.247995i
$656$	−19.4106	+	23.2936i	−0.757856	+	0.909461i
$657$	−4.31841	+	0.985649i	−0.168477	+	0.0384538i
$658$	−42.9922	−	22.9157i	−1.67601	−	0.893348i
$659$	−14.4709	−	3.30290i	−0.563707	−	0.128663i	−0.0688348	−	0.997628i	$-0.521928\pi$
$659$	−14.4709	−	3.30290i	−0.563707	−	0.128663i	−0.494873	+	0.868966i	$0.664785\pi$
$660$	−11.2242	−	0.540986i	−0.436901	−	0.0210578i
$661$	6.71962	−	44.5817i	0.261363	−	1.73403i	−0.344789	−	0.938680i	$-0.612050\pi$
$661$	6.71962	−	44.5817i	0.261363	−	1.73403i	0.606152	−	0.795349i	$-0.292712\pi$
$662$	18.7779	−	3.81271i	0.729826	−	0.148185i
$663$	14.2236	+	13.1976i	0.552398	+	0.512551i
$664$	−3.67508	+	3.98117i	−0.142621	+	0.154500i
$665$	−1.98025	+	11.7880i	−0.0767907	+	0.457120i
$666$	−4.31820	+	2.79421i	−0.167327	+	0.108273i
$667$	57.0305	+	32.9266i	2.20823	+	1.27492i
$668$	−15.9360	−	5.76947i	−0.616583	−	0.223228i
$669$	−3.24876	+	3.01441i	−0.125604	+	0.116544i
$670$	−0.504063	−	0.361745i	−0.0194736	−	0.0139754i
$671$	10.5797	−	13.2666i	0.408427	−	0.512151i
$672$	10.8446	−	10.3147i	0.418341	−	0.397900i
$673$	−1.17228	−	1.46999i	−0.0451880	−	0.0566639i	0.758724	−	0.651412i	$-0.225823\pi$
$673$	−1.17228	−	1.46999i	−0.0451880	−	0.0566639i	−0.803912	+	0.594748i	$0.797252\pi$
$674$	0.395038	+	7.78202i	0.0152163	+	0.299752i
$675$	0.149215	−	0.380194i	0.00574329	−	0.0146337i
$676$	15.2240	+	15.5552i	0.585539	+	0.598278i
$677$	−26.3642	+	10.3472i	−1.01326	+	0.397674i	−0.813122	−	0.582094i	$-0.802234\pi$
$677$	−26.3642	+	10.3472i	−1.01326	+	0.397674i	−0.200136	+	0.979768i	$0.564138\pi$
$678$	16.8876	+	16.4436i	0.648564	+	0.631513i
$679$	8.84600	+	19.1887i	0.339478	+	0.736394i
$680$	14.7670	+	21.5407i	0.566290	+	0.826046i
$681$	0.250230	−	3.33908i	0.00958882	−	0.127954i
$682$	−1.44336	+	1.09524i	−0.0552693	+	0.0419391i
$683$	−15.0911	+	22.1345i	−0.577444	+	0.846955i	−0.998185	−	0.0602260i	$-0.980818\pi$
$683$	−15.0911	+	22.1345i	−0.577444	+	0.846955i	0.420741	+	0.907181i	$0.361770\pi$
$684$	−2.56590	+	2.91754i	−0.0981098	+	0.111555i
$685$			19.0586i			0.728190i
$686$	−25.5337	+	5.83369i	−0.974880	+	0.222731i
$687$			28.0493i			1.07015i
$688$	−15.7178	−	0.338331i	−0.599237	−	0.0128987i
$689$	−19.5718	+	28.7065i	−0.745626	+	1.09363i
$690$	18.1391	+	23.9046i	0.690546	+	0.910033i
$691$	−0.406927	+	5.43007i	−0.0154802	+	0.206570i	0.984100	+	0.177613i	$0.0568375\pi$
$691$	−0.406927	+	5.43007i	−0.0154802	+	0.206570i	−0.999581	+	0.0289566i	$0.990782\pi$
$692$	−4.00288	−	15.6089i	−0.152167	−	0.593362i
$693$	2.67608	+	5.80494i	0.101656	+	0.220512i
$694$	−7.63440	+	7.84053i	−0.289798	+	0.297622i
$695$	−43.0001	+	16.8763i	−1.63109	+	0.640155i
$696$	−8.81046	+	18.4155i	−0.333960	+	0.698037i
$697$	−10.9955	+	28.0160i	−0.416483	+	1.06118i
$698$	20.6343	−	1.04746i	0.781020	−	0.0396469i
$699$	−7.80212	−	9.78355i	−0.295103	−	0.370048i
$700$	−0.616744	+	2.07132i	−0.0233107	+	0.0782886i
$701$	−11.4451	+	14.3517i	−0.432277	+	0.542058i	−0.949489	−	0.313799i	$-0.898398\pi$
$701$	−11.4451	+	14.3517i	−0.432277	+	0.542058i	0.517213	+	0.855857i	$0.326970\pi$
$702$	−4.02962	+	5.61495i	−0.152088	+	0.211923i
$703$	−5.17927	+	4.80566i	−0.195340	+	0.181249i
$704$	16.7876	+	9.57815i	0.632708	+	0.360990i
$705$	26.2236	+	15.1402i	0.987639	+	0.570214i
$706$	−17.8894	−	27.6464i	−0.673275	−	1.04049i
$707$	2.90771	−	17.3090i	0.109356	−	0.650973i
$708$	−9.81418	−	19.0631i	−0.368839	−	0.716435i
$709$	−20.8763	−	19.3704i	−0.784026	−	0.727470i	0.182732	−	0.983163i	$-0.441506\pi$
$709$	−20.8763	−	19.3704i	−0.784026	−	0.727470i	−0.966758	+	0.255693i	$0.917696\pi$
$710$	0.725751	+	3.57439i	0.0272370	+	0.134144i
$711$	1.18413	−	7.85617i	0.0444082	−	0.294629i
$712$	−38.6444	+	12.0286i	−1.44826	+	0.450791i
$713$	4.71706	+	1.07664i	0.176655	+	0.0403204i
$714$	6.98778	−	13.1098i	0.261511	−	0.490621i
$715$	−26.7697	+	6.11001i	−1.00113	+	0.228502i
$716$	13.0542	−	2.32477i	0.487858	−	0.0868808i
$717$	16.2772	−	9.39766i	0.607884	−	0.350962i
$718$	4.89392	−	9.56603i	0.182639	−	0.357001i
$719$	−12.9519	+	8.83049i	−0.483026	+	0.329322i	−0.780230	−	0.625492i	$-0.784898\pi$
$719$	−12.9519	+	8.83049i	−0.483026	+	0.329322i	0.297204	+	0.954814i	$0.403946\pi$
$720$	−6.95373	+	6.17903i	−0.259150	+	0.230279i
$721$	5.81953	+	15.5949i	0.216731	+	0.580784i
$722$	11.2123	−	18.3834i	0.417279	−	0.684158i
$723$	−3.81052	+	12.3534i	−0.141715	+	0.459428i
$724$	−30.5413	+	10.3193i	−1.13506	+	0.383515i
$725$	−0.220295	−	2.93963i	−0.00818155	−	0.109175i
$726$	5.47050	−	4.83605i	0.203029	−	0.179483i
$727$	−11.3696	+	5.47532i	−0.421676	+	0.203068i	−0.632674	−	0.774418i	$-0.718043\pi$
$727$	−11.3696	+	5.47532i	−0.421676	+	0.203068i	0.210998	+	0.977486i	$0.432329\pi$
$728$	18.7357	−	31.4071i	0.694392	−	1.16402i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−14.0202	+	3.95758i	−0.518911	+	0.146477i
$731$	−14.9118	+	4.59968i	−0.551533	+	0.170125i
$732$	−1.42246	−	13.9748i	−0.0525758	−	0.516522i
$733$	−0.408385	−	2.70946i	−0.0150840	−	0.100076i	0.980022	−	0.198889i	$-0.0637334\pi$
$733$	−0.408385	−	2.70946i	−0.0150840	−	0.100076i	−0.995106	+	0.0988133i	$0.968495\pi$
$734$	11.2694	+	30.8804i	0.415961	+	1.13982i
$735$	15.9840	−	3.08615i	0.589579	−	0.113834i
$736$	−9.17911	−	50.7899i	−0.338347	−	1.87214i
$737$	−0.450672	+	0.0679279i	−0.0166007	+	0.00250216i
$738$	−10.3908	−	2.63640i	−0.382492	−	0.0970472i
$739$	3.84234	+	12.4566i	0.141343	+	0.458222i	0.998372	−	0.0570465i	$-0.0181683\pi$
$739$	3.84234	+	12.4566i	0.141343	+	0.458222i	−0.857029	+	0.515269i	$0.827692\pi$
$740$	−13.7179	+	9.89807i	−0.504282	+	0.363860i
$741$	−4.11922	+	8.55364i	−0.151323	+	0.314226i
$742$	25.0772	+	8.87394i	0.920612	+	0.325773i
$743$	−9.87262	−	20.5007i	−0.362191	−	0.752098i	0.637643	−	0.770332i	$-0.279910\pi$
$743$	−9.87262	−	20.5007i	−0.362191	−	0.752098i	−0.999834	+	0.0182346i	$0.994195\pi$
$744$	−0.219753	+	1.48372i	−0.00805655	+	0.0543957i
$745$	−9.27285	+	0.694904i	−0.339731	+	0.0254593i
$746$	40.9923	+	0.987304i	1.50084	+	0.0361478i
$747$	−1.83049	−	0.564631i	−0.0669741	−	0.0206588i
$748$	18.8108	+	3.76931i	0.687792	+	0.137819i
$749$	20.9510	−	21.8309i	0.765533	−	0.797685i
$750$	−4.79733	+	14.3190i	−0.175174	+	0.522854i
$751$	20.5586	+	30.1539i	0.750193	+	1.10033i	0.991528	+	0.129890i	$0.0414623\pi$
$751$	20.5586	+	30.1539i	0.750193	+	1.10033i	−0.241335	+	0.970442i	$0.577585\pi$
$752$	−28.4059	−	43.6535i	−1.03586	−	1.59188i
$753$	−3.79273	−	6.56921i	−0.138215	−	0.239395i
$754$	−8.62018	+	49.1325i	−0.313929	+	1.78930i
$755$	−7.17645	−	31.4421i	−0.261178	−	1.14430i
$756$	4.94444	+	1.88482i	0.179827	+	0.0685501i
$757$	−9.31681	+	40.8196i	−0.338625	+	1.48361i	0.463306	+	0.886198i	$0.346663\pi$
$757$	−9.31681	+	40.8196i	−0.338625	+	1.48361i	−0.801931	+	0.597416i	$0.796194\pi$
$758$	17.5909	+	7.39753i	0.638931	+	0.268690i
$759$	21.7970	+	3.28537i	0.791182	+	0.119252i
$760$	−7.94167	+	10.0110i	−0.288075	+	0.363136i
$761$	13.5126	−	14.5632i	0.489833	−	0.527914i	−0.438964	−	0.898505i	$-0.644654\pi$
$761$	13.5126	−	14.5632i	0.489833	−	0.527914i	0.928796	+	0.370591i	$0.120845\pi$
$762$	−3.37878	−	26.7770i	−0.122400	−	0.970027i
$763$	−0.373375	−	6.43413i	−0.0135171	−	0.232931i
$764$	−17.2935	+	22.9117i	−0.625656	+	0.828915i
$765$	−4.61677	+	7.99648i	−0.166920	+	0.289113i
$766$	0.395028	−	0.471593i	0.0142730	−	0.0170393i
$767$	−35.6351	−	38.4055i	−1.28671	−	1.38674i
$768$	15.4779	−	4.05381i	0.558512	−	0.146279i
$769$	−2.65626	−	2.11830i	−0.0957872	−	0.0763877i	0.574425	−	0.818557i	$-0.305226\pi$
$769$	−2.65626	−	2.11830i	−0.0957872	−	0.0763877i	−0.670212	+	0.742169i	$0.733797\pi$
$770$	9.75796	+	18.6211i	0.351653	+	0.671058i
$771$	0.602382	−	0.480384i	0.0216943	−	0.0173006i
$772$	−44.5502	+	18.8691i	−1.60340	+	0.679112i
$773$	12.9657	+	5.08864i	0.466342	+	0.183026i	0.586865	−	0.809685i	$-0.300362\pi$
$773$	12.9657	+	5.08864i	0.466342	+	0.183026i	−0.120523	+	0.992711i	$0.538457\pi$
$774$	−2.29041	−	5.06455i	−0.0823272	−	0.182041i
$775$	−0.0791280	−	0.201615i	−0.00284236	−	0.00724222i
$776$	−1.63040	+	22.5295i	−0.0585279	+	0.808763i
$777$	8.59797	+	4.32035i	0.308450	+	0.154992i
$778$	−0.596919	+	6.01710i	−0.0214006	+	0.215723i
$779$	−14.6847	−	1.10047i	−0.526135	−	0.0394284i
$780$	−12.2997	+	19.1152i	−0.440401	+	0.684432i
$781$	2.21372	+	1.50929i	0.0792132	+	0.0540066i
$782$	−24.5396	−	44.9709i	−0.877534	−	1.60816i
$783$	−7.21764			−0.257937
$784$	−26.9127	−	7.72694i	−0.961169	−	0.275962i
$785$	47.1349			1.68232
$786$	3.69752	+	6.77602i	0.131886	+	0.241693i
$787$	11.1396	+	7.59488i	0.397085	+	0.270728i	0.745357	−	0.666665i	$-0.232279\pi$
$787$	11.1396	+	7.59488i	0.397085	+	0.270728i	−0.348272	+	0.937394i	$0.613231\pi$
$788$	−3.89656	+	6.05569i	−0.138809	+	0.215725i
$789$	28.7636	+	2.15554i	1.02401	+	0.0767391i
$790$	2.57953	−	26.0024i	0.0917757	−	0.925122i
$791$	10.5348	−	42.8201i	0.374575	−	1.52251i
$792$	−0.493227	+	6.81561i	−0.0175260	+	0.242182i
$793$	−12.5399	−	31.9510i	−0.445304	−	1.13462i
$794$	3.03821	+	6.71808i	0.107822	+	0.238416i
$795$	−15.3907	−	6.04042i	−0.545853	−	0.214232i
$796$	11.8267	−	5.00913i	0.419185	−	0.177544i
$797$	−12.6410	+	10.0808i	−0.447766	+	0.357081i	−0.821263	−	0.570550i	$-0.806730\pi$
$797$	−12.6410	+	10.0808i	−0.447766	+	0.357081i	0.373497	+	0.927631i	$0.378159\pi$
$798$	7.13729	+	1.37645i	0.252657	+	0.0487259i
$799$	−40.4178	−	32.2321i	−1.42988	−	1.14029i
$800$	−1.64705	+	1.62025i	−0.0582321	+	0.0572845i
$801$	−9.73289	−	10.4896i	−0.343895	−	0.370630i
$802$	13.5200	−	16.1404i	0.477407	−	0.569937i
$803$	−5.35075	+	9.26778i	−0.188824	+	0.327053i
$804$	−0.227296	+	0.301138i	−0.00801611	+	0.0106203i
$805$	21.3867	−	51.9058i	0.753784	−	1.82944i
$806$	0.458822	+	3.63617i	0.0161613	+	0.128079i
$807$	−6.58650	+	7.09856i	−0.231856	+	0.249881i
$808$	11.6612	−	14.6997i	0.410240	−	0.517134i
$809$	−7.09423	−	1.06928i	−0.249420	−	0.0375940i	0.0231422	−	0.999732i	$-0.492633\pi$
$809$	−7.09423	−	1.06928i	−0.249420	−	0.0375940i	−0.272562	+	0.962138i	$0.587871\pi$
$810$	−3.03173	−	1.27494i	−0.106524	−	0.0447967i
$811$	−7.51121	+	32.9088i	−0.263754	+	1.15558i	0.653388	+	0.757023i	$0.273347\pi$
$811$	−7.51121	+	32.9088i	−0.263754	+	1.15558i	−0.917142	+	0.398560i	$0.869510\pi$
$812$	38.0555	−	3.22737i	1.33549	−	0.113258i
$813$	0.808237	+	3.54112i	0.0283461	+	0.124192i
$814$	−2.14737	+	12.2394i	−0.0752654	+	0.428990i
$815$	−11.2409	−	19.4697i	−0.393750	−	0.681995i
$816$	13.3114	−	8.66193i	0.465993	−	0.303228i
$817$	−4.30119	−	6.30868i	−0.150479	−	0.220713i
$818$	−1.82455	+	5.44589i	−0.0637941	+	0.190411i
$819$	12.8755	+	1.18315i	0.449907	+	0.0413427i
$820$	−34.5701	−	6.92714i	−1.20724	−	0.241906i
$821$	−32.0514	−	9.88654i	−1.11860	−	0.345043i	−0.320309	−	0.947313i	$-0.603787\pi$
$821$	−32.0514	−	9.88654i	−1.11860	−	0.345043i	−0.798292	+	0.602271i	$0.794263\pi$
$822$	11.5863	+	0.279057i	0.404118	+	0.00973321i
$823$	−16.6520	+	1.24790i	−0.580452	+	0.0434989i	−0.361721	−	0.932286i	$-0.617811\pi$
$823$	−16.6520	+	1.24790i	−0.580452	+	0.0434989i	−0.218731	+	0.975785i	$0.570192\pi$
$824$	−2.60712	+	17.6026i	−0.0908234	+	0.613215i
$825$	−0.428135	−	0.889032i	−0.0149058	−	0.0309521i
$826$	−21.4604	+	33.8891i	−0.746704	+	1.17915i
$827$	17.8836	−	37.1357i	0.621873	−	1.29133i	−0.317442	−	0.948278i	$-0.602824\pi$
$827$	17.8836	−	37.1357i	0.621873	−	1.29133i	0.939315	−	0.343056i	$-0.111462\pi$
$828$	14.7979	−	10.6773i	0.514264	−	0.371063i
$829$	−3.31116	−	10.7345i	−0.115001	−	0.372825i	0.879713	−	0.475505i	$-0.157734\pi$
$829$	−3.31116	−	10.7345i	−0.115001	−	0.372825i	−0.994714	+	0.102680i	$0.967258\pi$
$830$	−6.10669	−	1.54941i	−0.211966	−	0.0537808i
$831$	−24.8253	+	3.74182i	−0.861182	+	0.129802i
$832$	33.7576	−	19.7210i	1.17034	−	0.683702i
$833$	−27.7692	+	1.14281i	−0.962145	+	0.0395962i
$834$	9.63001	+	26.3882i	0.333460	+	0.913748i
$835$	−2.93724	−	19.4873i	−0.101647	−	0.674387i
$836$	0.950565	+	9.33866i	0.0328760	+	0.322984i
$837$	−0.506736	+	0.156307i	−0.0175153	+	0.00540277i
$838$	−9.71451	+	2.74218i	−0.335582	+	0.0947271i
$839$	−17.9346	−	8.63686i	−0.619172	−	0.298177i	0.0978790	−	0.995198i	$-0.468794\pi$
$839$	−17.9346	−	8.63686i	−0.619172	−	0.298177i	−0.717051	+	0.697021i	$0.754508\pi$
$840$	16.5551	+	5.36657i	0.571206	+	0.185164i
$841$	−20.8072	+	10.0202i	−0.717491	+	0.345526i
$842$	17.1807	−	15.1881i	0.592085	−	0.523417i
$843$	−1.66503	−	22.2183i	−0.0573467	−	0.765239i
$844$	−28.2620	+	9.54921i	−0.972819	+	0.328697i
$845$	−7.45993	+	24.1845i	−0.256630	+	0.831973i
$846$	9.58816	−	15.7204i	0.329648	−	0.540480i
$847$	−12.9836	−	4.24555i	−0.446121	−	0.145879i
$848$	18.8894	+	21.2577i	0.648665	+	0.729992i
$849$	−21.1782	+	14.4390i	−0.726834	+	0.495547i
$850$	−1.04449	+	2.04164i	−0.0358257	+	0.0700276i
$851$	28.7373	−	16.5915i	0.985103	−	0.568750i
$852$	2.18360	−	0.388870i	0.0748090	−	0.0133225i
$853$	32.1680	−	7.34214i	1.10141	−	0.251390i	0.367086	−	0.930187i	$-0.380355\pi$
$853$	32.1680	−	7.34214i	1.10141	−	0.251390i	0.734326	+	0.678797i	$0.237498\pi$
$854$	−21.1991	+	15.5309i	−0.725419	+	0.531455i
$855$	−4.40461	−	1.00532i	−0.150634	−	0.0343813i
$856$	30.8854	−	9.61348i	1.05564	−	0.328582i
$857$	−1.03543	+	6.86965i	−0.0353697	+	0.234663i	−0.999530	−	0.0306579i	$-0.990240\pi$
$857$	−1.03543	+	6.86965i	−0.0353697	+	0.234663i	0.964160	+	0.265321i	$0.0854778\pi$
$858$	3.32250	+	16.3636i	0.113428	+	0.558643i
$859$	13.0976	+	12.1528i	0.446886	+	0.414649i	0.871248	−	0.490843i	$-0.163311\pi$
$859$	13.0976	+	12.1528i	0.446886	+	0.414649i	−0.424362	+	0.905493i	$0.639502\pi$
$860$	−8.36771	−	16.2535i	−0.285336	−	0.554239i
$861$	5.58800	+	19.2612i	0.190438	+	0.656421i
$862$	−22.7676	−	35.1853i	−0.775468	−	1.19842i
$863$	35.1815	+	20.3120i	1.19759	+	0.691429i	0.960017	−	0.279940i	$-0.0903147\pi$
$863$	35.1815	+	20.3120i	1.19759	+	0.691429i	0.237573	+	0.971370i	$0.423648\pi$
$864$	3.65460	+	4.31786i	0.124332	+	0.146896i
$865$	13.7355	−	12.7447i	0.467020	−	0.433331i
$866$	−11.2748	+	15.7105i	−0.383133	+	0.533866i
$867$	−0.770666	+	0.966384i	−0.0261732	+	0.0328201i
$868$	2.60191	−	1.05073i	0.0883146	−	0.0356640i
$869$	−11.9677	−	15.0071i	−0.405978	−	0.509080i
$870$	−23.7076	+	1.20346i	−0.803761	+	0.0408013i
$871$	−0.336811	+	0.858179i	−0.0114124	+	0.0290783i
$872$	2.97354	−	6.21526i	0.100697	−	0.210475i
$873$	−7.43416	+	2.91769i	−0.251608	+	0.0987489i
$874$	17.4871	−	17.9593i	0.591511	−	0.607482i
$875$	27.6454	−	5.82207i	0.934585	−	0.196822i
$876$	2.20065	+	8.58125i	0.0743529	+	0.289933i
$877$	4.10243	−	54.7432i	0.138529	−	1.84855i	−0.305082	−	0.952326i	$-0.598684\pi$
$877$	4.10243	−	54.7432i	0.138529	−	1.84855i	0.443611	−	0.896219i	$-0.353697\pi$
$878$	−10.8839	−	14.3433i	−0.367314	−	0.484063i
$879$	9.33533	−	13.6924i	0.314873	−	0.461834i
$880$	−0.483657	+	22.4693i	−0.0163041	+	0.757438i
$881$		−	51.9904i		−	1.75160i	−0.482674	−	0.875800i	$-0.660334\pi$
$881$		−	51.9904i		−	1.75160i	0.482674	−	0.875800i	$-0.339666\pi$
$882$	−1.64213	−	9.76235i	−0.0552932	−	0.328715i
$883$			2.91424i			0.0980719i	0.998797	+	0.0490360i	$0.0156149\pi$
$883$			2.91424i			0.0980719i	−0.998797	+	0.0490360i	$0.984385\pi$
$884$	25.6280	−	29.1401i	0.861965	−	0.980089i
$885$	14.0445	−	20.5995i	0.472102	−	0.692446i
$886$	−32.5066	+	24.6664i	−1.09208	+	0.828684i
$887$	−2.53845	+	33.8733i	−0.0852330	+	1.13735i	0.776543	+	0.630065i	$0.216972\pi$
$887$	−2.53845	+	33.8733i	−0.0852330	+	1.13735i	−0.861775	+	0.507290i	$0.830647\pi$
$888$	5.81647	+	8.48448i	0.195188	+	0.284720i
$889$	−40.0008	+	30.8125i	−1.34159	+	1.03342i
$890$	−33.7183	−	32.8319i	−1.13024	−	1.10053i
$891$	−2.24897	+	0.882657i	−0.0753435	+	0.0295701i
$892$	6.19974	+	6.33462i	0.207583	+	0.212099i
$893$	9.24112	−	23.5460i	0.309242	−	0.787936i
$894$	0.286679	+	5.64742i	0.00958800	+	0.188878i
$895$	9.61313	+	12.0545i	0.321331	+	0.402937i
$896$	−21.1999	−	21.1321i	−0.708239	−	0.705973i
$897$	27.8005	−	34.8608i	0.928233	−	1.16397i
$898$	−4.20886	−	3.02052i	−0.140451	−	0.100796i
$899$	−2.80574	+	2.60335i	−0.0935767	+	0.0868265i
$900$	−0.768067	−	0.278071i	−0.0256022	−	0.00926902i
$901$	24.4454	+	14.1135i	0.814393	+	0.470190i
$902$	−21.7443	+	14.0702i	−0.724005	+	0.468488i
$903$	−6.00165	+	8.49205i	−0.199722	+	0.282598i
$904$	31.9759	−	34.6392i	1.06350	−	1.15208i
$905$	−27.4791	−	25.4969i	−0.913436	−	0.847545i
$906$	−19.2197	+	3.90240i	−0.638531	+	0.129649i
$907$	3.60649	−	23.9275i	0.119752	−	0.794500i	−0.845651	−	0.533736i	$-0.820788\pi$
$907$	3.60649	−	23.9275i	0.119752	−	0.794500i	0.965403	−	0.260764i	$-0.0839744\pi$
$908$	−6.68912	−	0.322403i	−0.221986	−	0.0106993i
$909$	6.46754	+	1.47617i	0.214515	+	0.0489616i
$910$	42.4891	+	1.73941i	1.40850	+	0.0576609i
$911$	9.85867	−	2.25018i	0.326632	−	0.0745517i	−0.0560603	−	0.998427i	$-0.517854\pi$
$911$	9.85867	−	2.25018i	0.326632	−	0.0745517i	0.382693	+	0.923876i	$0.374997\pi$
$912$	5.96969	+	4.97456i	0.197676	+	0.164724i
$913$	−4.00800	+	2.31402i	−0.132645	+	0.0765828i
$914$	−26.4527	−	13.5330i	−0.874977	−	0.447633i
$915$	13.4956	−	9.20117i	0.446152	−	0.304181i
$916$	56.0786	−	1.49423i	1.85289	−	0.0493707i
$917$	7.43016	−	12.3832i	0.245366	−	0.408930i
$918$	4.79370	+	2.92376i	0.158216	+	0.0964983i
$919$	−11.0285	+	35.7537i	−0.363798	+	1.17940i	0.570012	+	0.821636i	$0.306938\pi$
$919$	−11.0285	+	35.7537i	−0.363798	+	1.17940i	−0.933810	+	0.357768i	$0.883538\pi$
$920$	46.8260	−	37.5389i	1.54381	−	1.23762i
$921$	0.727353	+	9.70585i	0.0239671	+	0.319819i
$922$	21.4508	+	24.2650i	0.706445	+	0.799124i
$923$	4.88287	−	2.35147i	0.160722	−	0.0773995i
$924$	11.4632	−	5.65951i	0.377112	−	0.186184i
$925$	−1.33831	−	0.644498i	−0.0440035	−	0.0211910i
$926$	−12.4151	−	43.9820i	−0.407986	−	1.44534i
$927$	−6.01184	+	1.85441i	−0.197455	+	0.0609067i
$928$	37.2873	+	16.6336i	1.22401	+	0.546026i
$929$	0.0250773	+	0.166377i	0.000822758	+	0.00545864i	0.989238	−	0.146312i	$-0.0467405\pi$
$929$	0.0250773	+	0.166377i	0.000822758	+	0.00545864i	−0.988416	+	0.151771i	$0.951502\pi$
$930$	−1.63840	+	0.597910i	−0.0537251	+	0.0196063i
$931$	−4.53922	−	12.8187i	−0.148767	−	0.420117i
$932$	−19.1445	+	16.1199i	−0.627100	+	0.528024i
$933$	11.1007	−	1.67316i	0.363420	−	0.0547768i
$934$	−0.886349	+	3.49337i	−0.0290022	+	0.114306i
$935$	6.57541	+	21.3170i	0.215039	+	0.697139i
$936$	11.4406	+	7.75725i	0.373947	+	0.253554i
$937$	−23.7962	+	49.4133i	−0.777388	+	1.61426i	0.0116601	+	0.999932i	$0.496288\pi$
$937$	−23.7962	+	49.4133i	−0.777388	+	1.61426i	−0.789048	+	0.614331i	$0.789426\pi$
$938$	0.701125	+	0.0814945i	0.0228925	+	0.00266089i
$939$	−0.595905	−	1.23741i	−0.0194466	−	0.0403814i
$940$	28.8727	−	53.2352i	0.941724	−	1.73634i
$941$	5.71325	−	0.428149i	0.186247	−	0.0139573i	0.0187198	−	0.999825i	$-0.494041\pi$
$941$	5.71325	−	0.428149i	0.186247	−	0.0139573i	0.167527	+	0.985868i	$0.446422\pi$
$942$	0.690152	−	28.6547i	0.0224864	−	0.933622i
$943$	66.0889	+	20.3857i	2.15215	+	0.663851i
$944$	−37.5899	+	20.6369i	−1.22345	+	0.671674i
$945$	0.814502	+	6.09882i	0.0264957	+	0.198395i
$946$	−12.7333	−	4.26609i	−0.413996	−	0.138702i
$947$	14.8244	+	21.7434i	0.481729	+	0.706566i	0.987766	−	0.155946i	$-0.0498424\pi$
$947$	14.8244	+	21.7434i	0.481729	+	0.706566i	−0.506037	+	0.862512i	$0.668890\pi$
$948$	−15.7698	−	1.94890i	−0.512181	−	0.0632974i
$949$	10.8234	+	18.7467i	0.351342	+	0.608542i
$950$	−1.10521	−	0.193907i	−0.0358578	−	0.00629116i
$951$	−5.51582	−	24.1664i	−0.178863	−	0.783649i
$952$	−26.5825	−	13.2722i	−0.861544	−	0.430155i
$953$	−0.530570	+	2.32458i	−0.0171868	+	0.0753005i	−0.982794	−	0.184705i	$-0.940867\pi$
$953$	−0.530570	+	2.32458i	−0.0171868	+	0.0753005i	0.965607	+	0.260005i	$0.0837243\pi$
$954$	−3.89751	+	9.26805i	−0.126186	+	0.300064i
$955$	−33.0060	−	4.97486i	−1.06805	−	0.160983i
$956$	−19.6558	−	32.0423i	−0.635713	−	1.03632i
$957$	−11.8606	+	12.7827i	−0.383400	+	0.413207i
$958$	−61.1998	+	7.72235i	−1.97728	+	0.249498i
$959$	−10.5235	−	18.9572i	−0.339821	−	0.612160i
$960$	12.7241	+	13.5734i	0.410669	+	0.438079i
$961$	15.3594	−	26.6032i	0.495464	−	0.858169i
$962$	19.2688	+	16.1405i	0.621253	+	0.520391i
$963$	7.77871	+	8.38345i	0.250665	+	0.270153i
$964$	24.9011	+	6.96026i	0.802009	+	0.224175i
$965$	−43.9843	−	35.0763i	−1.41590	−	1.12915i
$966$	−31.2420	−	13.7617i	−1.00519	−	0.442774i
$967$	−22.9383	+	18.2927i	−0.737647	+	0.588254i	−0.918577	−	0.395242i	$-0.870661\pi$
$967$	−22.9383	+	18.2927i	−0.737647	+	0.588254i	0.180930	+	0.983496i	$0.442089\pi$
$968$	−9.96009	−	10.6795i	−0.320130	−	0.343252i
$969$	7.17997	+	2.81793i	0.230654	+	0.0905250i
$970$	−23.9323	+	10.8232i	−0.768419	+	0.347513i
$971$	12.0780	+	30.7742i	0.387601	+	0.987590i	0.982909	+	0.184093i	$0.0589347\pi$
$971$	12.0780	+	30.7742i	0.387601	+	0.987590i	−0.595308	+	0.803497i	$0.702970\pi$
$972$	−0.819464	+	1.82441i	−0.0262843	+	0.0585180i
$973$	33.4529	−	40.5297i	1.07245	−	1.29932i
$974$	49.5419	+	4.91474i	1.58742	+	0.157478i
$975$	−1.99040	−	0.149160i	−0.0637438	−	0.00477694i
$976$	−27.8638	+	3.58838i	−0.891899	+	0.114861i
$977$	−16.8865	−	11.5130i	−0.540248	−	0.368335i	0.262240	−	0.965003i	$-0.415539\pi$
$977$	−16.8865	−	11.5130i	−0.540248	−	0.368335i	−0.802488	+	0.596668i	$0.796491\pi$
$978$	−12.0008	+	6.54857i	−0.383744	+	0.209400i
$979$	−34.5713			−1.10490
$980$	−7.02161	−	31.7923i	−0.224297	−	1.01557i
$981$	2.43596			0.0777744
$982$	−1.10127	+	0.600938i	−0.0351429	+	0.0191767i
$983$	−5.34136	−	3.64168i	−0.170363	−	0.116152i	0.475137	−	0.879912i	$-0.342399\pi$
$983$	−5.34136	−	3.64168i	−0.170363	−	0.116152i	−0.645500	+	0.763760i	$0.723351\pi$
$984$	−4.71739	+	20.9148i	−0.150385	+	0.666738i
$985$	−8.34993	−	0.625741i	−0.266051	−	0.0199378i
$986$	40.3289	+	4.00078i	1.28433	+	0.127411i
$987$	−34.4440	−	0.579903i	−1.09637	−	0.0184585i
$988$	17.3207	+	7.77985i	0.551043	+	0.247510i
$989$	13.1013	+	33.3815i	0.416596	+	1.06147i
$990$	−7.23996	+	3.27423i	−0.230101	+	0.104062i
$991$	8.33474	+	3.27114i	0.264762	+	0.103911i	0.494009	−	0.869457i	$-0.335531\pi$
$991$	8.33474	+	3.27114i	0.264762	+	0.103911i	−0.229247	+	0.973368i	$0.573626\pi$
$992$	2.97808	+	0.360311i	0.0945543	+	0.0114399i
$993$	10.5930	−	8.44763i	0.336158	−	0.268077i
$994$	−2.69554	−	3.15464i	−0.0854975	−	0.100059i
$995$	11.6764	+	9.31163i	0.370167	+	0.295199i
$996$	−1.03135	+	3.68976i	−0.0326795	+	0.116914i
$997$	30.8136	+	33.2092i	0.975877	+	1.05175i	0.998647	+	0.0520047i	$0.0165611\pi$
$997$	30.8136	+	33.2092i	0.975877	+	1.05175i	−0.0227696	+	0.999741i	$0.507248\pi$
$998$	−30.2644	−	25.3509i	−0.958004	−	0.802469i
$999$	−1.81846	+	3.14967i	−0.0575336	+	0.0996511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.ba.a.103.10	✓	336
4.3	odd	2		588.2.ba.b.103.14	yes	336
49.10	odd	42		588.2.ba.b.451.14	yes	336
196.59	even	42	inner	588.2.ba.a.451.10	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.ba.a.103.10	✓	336	1.1	even	1	trivial
588.2.ba.a.451.10	yes	336	196.59	even	42	inner
588.2.ba.b.103.14	yes	336	4.3	odd	2
588.2.ba.b.451.14	yes	336	49.10	odd	42

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.ba (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.677412 - 1.24142i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.08223 + 1.68190i) q^{4} +(-2.31910 - 0.173792i) q^{5} +(-0.139610 + 1.40731i) q^{6} +(2.40273 - 1.10766i) q^{7} +(2.82105 + 0.204152i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.677412 - 1.24142i) q^{2} +(-0.826239 - 0.563320i) q^{3} +(-1.08223 + 1.68190i) q^{4} +(-2.31910 - 0.173792i) q^{5} +(-0.139610 + 1.40731i) q^{6} +(2.40273 - 1.10766i) q^{7} +(2.82105 + 0.204152i) q^{8} +(0.365341 + 0.930874i) q^{9} +(1.35524 + 2.99670i) q^{10} +(2.24897 + 0.882657i) q^{11} +(1.84162 - 0.780012i) q^{12} +(3.82081 - 3.04699i) q^{13} +(-3.00270 - 2.23244i) q^{14} +(1.81823 + 1.44999i) q^{15} +(-1.65758 - 3.64039i) q^{16} +(-2.70055 - 2.91050i) q^{17} +(0.908115 - 1.08413i) q^{18} +(0.971336 - 1.68240i) q^{19} +(2.80209 - 3.71241i) q^{20} +(-2.60919 - 0.438313i) q^{21} +(-0.427738 - 3.38983i) q^{22} +(-6.20584 + 6.68831i) q^{23} +(-2.21586 - 1.75783i) q^{24} +(0.403865 + 0.0608728i) q^{25} +(-6.37085 - 2.67914i) q^{26} +(0.222521 - 0.974928i) q^{27} +(-0.737320 + 5.23988i) q^{28} +(-1.60608 - 7.03668i) q^{29} +(0.568349 - 3.23942i) q^{30} +(-0.265148 - 0.459249i) q^{31} +(-3.39637 + 4.52379i) q^{32} +(-1.36097 - 1.99618i) q^{33} +(-1.78375 + 5.32411i) q^{34} +(-5.76466 + 2.15119i) q^{35} +(-1.96102 - 0.392948i) q^{36} +(-3.47535 - 1.07200i) q^{37} +(-2.74656 - 0.0661511i) q^{38} +(-4.87333 + 0.365206i) q^{39} +(-6.50682 - 0.963725i) q^{40} +(-3.28894 - 6.82956i) q^{41} +(1.22337 + 3.53601i) q^{42} +(1.70532 - 3.54114i) q^{43} +(-3.91844 + 2.82732i) q^{44} +(-0.685483 - 2.22228i) q^{45} +(12.5069 + 3.17329i) q^{46} +(12.8750 - 1.94060i) q^{47} +(-0.681151 + 3.94158i) q^{48} +(4.54618 - 5.32280i) q^{49} +(-0.198015 - 0.542600i) q^{50} +(0.591755 + 3.92604i) q^{51} +(0.989762 + 9.72375i) q^{52} +(-6.79355 + 2.09553i) q^{53} +(-1.36103 + 0.384187i) q^{54} +(-5.06220 - 2.43783i) q^{55} +(7.00434 - 2.63424i) q^{56} +(-1.75029 + 0.842893i) q^{57} +(-7.64747 + 6.76054i) q^{58} +(-0.801147 - 10.6906i) q^{59} +(-4.40647 + 1.48886i) q^{60} +(2.07021 - 6.71145i) q^{61} +(-0.390505 + 0.640259i) q^{62} +(1.90890 + 1.83196i) q^{63} +(7.91664 + 1.15184i) q^{64} +(-9.39038 + 6.40225i) q^{65} +(-1.55615 + 3.04177i) q^{66} +(-0.163371 + 0.0943225i) q^{67} +(7.81777 - 1.39224i) q^{68} +(8.89517 - 2.03026i) q^{69} +(6.57558 + 5.69910i) q^{70} +(1.08118 + 0.246771i) q^{71} +(0.840606 + 2.70063i) q^{72} +(-0.660177 + 4.37999i) q^{73} +(1.02344 + 5.04054i) q^{74} +(-0.299398 - 0.277801i) q^{75} +(1.77843 + 3.45443i) q^{76} +(6.38135 - 0.370312i) q^{77} +(3.75463 + 5.80243i) q^{78} +(-6.88049 - 3.97245i) q^{79} +(3.21141 + 8.73050i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-6.25035 + 8.70938i) q^{82} +(-1.19435 + 1.49767i) q^{83} +(3.56093 - 3.91405i) q^{84} +(5.75701 + 7.21907i) q^{85} +(-5.55124 + 0.281797i) q^{86} +(-2.63690 + 6.71871i) q^{87} +(6.16427 + 2.94915i) q^{88} +(-13.3203 + 5.22782i) q^{89} +(-2.29442 + 2.35637i) q^{90} +(5.80533 - 11.5532i) q^{91} +(-4.53295 - 17.6759i) q^{92} +(-0.0396290 + 0.528812i) q^{93} +(-11.1308 - 14.6687i) q^{94} +(-2.54501 + 3.73285i) q^{95} +(5.35456 - 1.82448i) q^{96} +7.98622i q^{97} +(-9.68745 - 2.03797i) q^{98} +2.41598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Introduction

L-functions

Modular forms

Varieties

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