LMFDB - Embedded newform 722.2.i.b.501.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.9
Character	$\chi$	$=$	722.501
Dual form			722.2.i.b.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926494 - 0.376309i) q^{2} +(0.365417 + 0.0818918i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0129978 - 0.471537i) q^{5} +(-0.307740 - 0.213382i) q^{6} +(0.329212 + 1.30003i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.58625 - 1.22048i) q^{9} +O(q^{10})$	\(q+(-0.926494 - 0.376309i) q^{2} +(0.365417 + 0.0818918i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0129978 - 0.471537i) q^{5} +(-0.307740 - 0.213382i) q^{6} +(0.329212 + 1.30003i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.58625 - 1.22048i) q^{9} +(-0.165401 + 0.441767i) q^{10} +(-0.280557 + 3.38582i) q^{11} +(0.204821 + 0.313503i) q^{12} +(-1.83600 - 5.87002i) q^{13} +(0.184200 - 1.32836i) q^{14} +(0.0338654 - 0.173372i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(5.61431 - 5.46169i) q^{17} +(1.93687 + 2.10400i) q^{18} +(-2.65559 - 3.45656i) q^{19} +(0.319485 - 0.347053i) q^{20} +(0.0138379 + 0.502012i) q^{21} +(1.53405 - 3.03137i) q^{22} +(5.27771 - 1.18276i) q^{23} +(-0.0717919 - 0.367535i) q^{24} +(4.77023 - 0.263181i) q^{25} +(-0.507900 + 6.12944i) q^{26} +(-1.73166 - 1.34781i) q^{27} +(-0.670533 + 1.16140i) q^{28} +(-8.16186 - 2.30795i) q^{29} +(-0.0966176 + 0.147884i) q^{30} +(8.12114 + 6.32094i) q^{31} +(0.350638 - 0.936511i) q^{32} +(-0.379792 + 1.21426i) q^{33} +(-7.25691 + 2.94750i) q^{34} +(0.608733 - 0.172133i) q^{35} +(-1.00274 - 2.67820i) q^{36} +(0.380544 - 4.59249i) q^{37} +(1.15965 + 4.20181i) q^{38} +(-0.190199 - 2.29536i) q^{39} +(-0.426600 + 0.201317i) q^{40} +(-1.81336 - 1.57925i) q^{41} +(0.176091 - 0.470319i) q^{42} +(-2.16446 - 5.78102i) q^{43} +(-2.56202 + 2.23127i) q^{44} +(-0.541886 + 1.23538i) q^{45} +(-5.33486 - 0.890230i) q^{46} +(3.26829 + 2.26618i) q^{47} +(-0.0717919 + 0.367535i) q^{48} +(4.57462 - 2.47566i) q^{49} +(-4.51863 - 1.55125i) q^{50} +(2.49883 - 1.53603i) q^{51} +(2.77713 - 5.48776i) q^{52} +(7.26632 + 5.03836i) q^{53} +(1.09718 + 1.90038i) q^{54} +(1.60019 + 0.0882848i) q^{55} +(1.05829 - 0.823700i) q^{56} +(-0.687333 - 1.48056i) q^{57} +(6.69341 + 5.20969i) q^{58} +(-0.675864 - 0.588610i) q^{59} +(0.145166 - 0.100656i) q^{60} +(-5.90471 - 8.03365i) q^{61} +(-5.14556 - 8.91237i) q^{62} +(0.735236 - 3.76400i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-2.74407 + 0.942039i) q^{65} +(0.808813 - 0.982087i) q^{66} +(-3.70161 - 0.409695i) q^{67} +7.83266 q^{68} +2.02542 q^{69} +(-0.628763 - 0.0695914i) q^{70} +(-1.52523 + 2.07515i) q^{71} +(-0.0787989 + 2.85868i) q^{72} +(4.87763 - 4.74503i) q^{73} +(-2.08077 + 4.11171i) q^{74} +(1.76467 + 0.294472i) q^{75} +(0.506771 - 4.32934i) q^{76} +(-4.49403 + 0.749921i) q^{77} +(-0.687546 + 2.19821i) q^{78} +(-6.01990 - 16.0784i) q^{79} +(0.471000 - 0.0259858i) q^{80} +(4.93166 + 5.98818i) q^{81} +(1.08578 + 2.14555i) q^{82} +(-7.34974 + 3.97748i) q^{83} +(-0.340133 + 0.369483i) q^{84} +(-2.64836 - 2.57637i) q^{85} +(-0.170091 + 6.17058i) q^{86} +(-2.79348 - 1.51176i) q^{87} +(3.21335 - 1.10314i) q^{88} +(2.18929 + 2.12978i) q^{89} +(0.966937 - 0.940651i) q^{90} +(7.02676 - 4.31933i) q^{91} +(4.60771 + 2.83235i) q^{92} +(2.44997 + 2.97483i) q^{93} +(-2.17527 - 3.32949i) q^{94} +(-1.59538 + 1.29714i) q^{95} +(0.204821 - 0.313503i) q^{96} +(-8.72515 + 0.965699i) q^{97} +(-5.16997 + 0.572212i) q^{98} +(4.85792 - 8.41416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$3$	0.365417	+	0.0818918i	0.210974	+	0.0472803i	0.322886	−	0.946438i	$-0.395347\pi$
$3$	0.365417	+	0.0818918i	0.210974	+	0.0472803i	−0.111913	+	0.993718i	$0.535698\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	−0.0129978	−	0.471537i	−0.00581280	−	0.210878i	−0.996950	−	0.0780382i	$-0.975134\pi$
$5$	−0.0129978	−	0.471537i	−0.00581280	−	0.210878i	0.991138	−	0.132839i	$-0.0424095\pi$
$6$	−0.307740	−	0.213382i	−0.125634	−	0.0871129i
$7$	0.329212	+	1.30003i	0.124431	+	0.491365i	0.999966	+	0.00821167i	$0.00261388\pi$
$7$	0.329212	+	1.30003i	0.124431	+	0.491365i	−0.875536	+	0.483153i	$0.839491\pi$
$8$	−0.401695	−	0.915773i	−0.142021	−	0.323775i
$9$	−2.58625	−	1.22048i	−0.862083	−	0.406827i
$10$	−0.165401	+	0.441767i	−0.0523045	+	0.139699i
$11$	−0.280557	+	3.38582i	−0.0845912	+	1.02086i	0.813648	+	0.581358i	$0.197478\pi$
$11$	−0.280557	+	3.38582i	−0.0845912	+	1.02086i	−0.898239	+	0.439507i	$0.855153\pi$
$12$	0.204821	+	0.313503i	0.0591269	+	0.0905004i
$13$	−1.83600	−	5.87002i	−0.509214	−	1.62805i	−0.752857	−	0.658184i	$-0.771325\pi$
$13$	−1.83600	−	5.87002i	−0.509214	−	1.62805i	0.243642	−	0.969865i	$-0.421658\pi$
$14$	0.184200	−	1.32836i	0.0492296	−	0.355018i
$15$	0.0338654	−	0.173372i	0.00874401	−	0.0447644i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	5.61431	−	5.46169i	1.36167	−	1.32465i	0.462785	−	0.886471i	$-0.346850\pi$
$17$	5.61431	−	5.46169i	1.36167	−	1.32465i	0.898886	−	0.438183i	$-0.144378\pi$
$18$	1.93687	+	2.10400i	0.456524	+	0.495917i
$19$	−2.65559	−	3.45656i	−0.609234	−	0.792990i
$19$	−2.65559	−	3.45656i	−0.609234	−	0.792990i
$20$	0.319485	−	0.347053i	0.0714389	−	0.0776034i
$21$	0.0138379	+	0.502012i	0.00301967	+	0.109548i
$22$	1.53405	−	3.03137i	0.327061	−	0.646290i
$23$	5.27771	−	1.18276i	1.10048	−	0.246623i	0.369642	−	0.929174i	$-0.379480\pi$
$23$	5.27771	−	1.18276i	1.10048	−	0.246623i	0.730838	+	0.682551i	$0.239130\pi$
$24$	−0.0717919	−	0.367535i	−0.0146545	−	0.0750227i
$25$	4.77023	−	0.263181i	0.954046	−	0.0526362i
$26$	−0.507900	+	6.12944i	−0.0996073	+	1.20208i
$27$	−1.73166	−	1.34781i	−0.333259	−	0.259386i
$28$	−0.670533	+	1.16140i	−0.126719	+	0.219483i
$29$	−8.16186	−	2.30795i	−1.51562	−	0.428576i	−0.590117	−	0.807318i	$-0.700918\pi$
$29$	−8.16186	−	2.30795i	−1.51562	−	0.428576i	−0.925503	+	0.378741i	$0.876357\pi$
$30$	−0.0966176	+	0.147884i	−0.0176399	+	0.0269998i
$31$	8.12114	+	6.32094i	1.45860	+	1.13527i	0.963918	+	0.266201i	$0.0857683\pi$
$31$	8.12114	+	6.32094i	1.45860	+	1.13527i	0.494683	+	0.869074i	$0.335284\pi$
$32$	0.350638	−	0.936511i	0.0619845	−	0.165553i
$33$	−0.379792	+	1.21426i	−0.0661132	+	0.211376i
$34$	−7.25691	+	2.94750i	−1.24455	+	0.505492i
$35$	0.608733	−	0.172133i	0.102895	−	0.0290958i
$36$	−1.00274	−	2.67820i	−0.167123	−	0.446367i
$37$	0.380544	−	4.59249i	0.0625611	−	0.755000i	−0.891040	−	0.453926i	$-0.850023\pi$
$37$	0.380544	−	4.59249i	0.0625611	−	0.755000i	0.953601	−	0.301075i	$-0.0973453\pi$
$38$	1.15965	+	4.20181i	0.188120	+	0.681624i
$39$	−0.190199	−	2.29536i	−0.0304561	−	0.367551i
$40$	−0.426600	+	0.201317i	−0.0674513	+	0.0318311i
$41$	−1.81336	−	1.57925i	−0.283199	−	0.246638i	0.503471	−	0.864012i	$-0.332056\pi$
$41$	−1.81336	−	1.57925i	−0.283199	−	0.246638i	−0.786670	+	0.617374i	$0.788197\pi$
$42$	0.176091	−	0.470319i	0.0271715	−	0.0725718i
$43$	−2.16446	−	5.78102i	−0.330077	−	0.881597i	−0.991325	−	0.131430i	$-0.958043\pi$
$43$	−2.16446	−	5.78102i	−0.330077	−	0.881597i	0.661248	−	0.750167i	$-0.270027\pi$
$44$	−2.56202	+	2.23127i	−0.386239	+	0.336376i
$45$	−0.541886	+	1.23538i	−0.0807796	+	0.184159i
$46$	−5.33486	−	0.890230i	−0.786582	−	0.131257i
$47$	3.26829	+	2.26618i	0.476729	+	0.330557i	0.783676	−	0.621170i	$-0.213342\pi$
$47$	3.26829	+	2.26618i	0.476729	+	0.330557i	−0.306947	+	0.951727i	$0.599307\pi$
$48$	−0.0717919	+	0.367535i	−0.0103623	+	0.0530490i
$49$	4.57462	−	2.47566i	0.653517	−	0.353666i
$50$	−4.51863	−	1.55125i	−0.639030	−	0.219379i
$51$	2.49883	−	1.53603i	0.349906	−	0.215087i
$52$	2.77713	−	5.48776i	0.385119	−	0.761015i
$53$	7.26632	+	5.03836i	0.998106	+	0.692072i	0.951757	−	0.306854i	$-0.0992763\pi$
$53$	7.26632	+	5.03836i	0.998106	+	0.692072i	0.0463496	+	0.998925i	$0.485241\pi$
$54$	1.09718	+	1.90038i	0.149308	+	0.258609i
$55$	1.60019	+	0.0882848i	0.215769	+	0.0119043i
$56$	1.05829	−	0.823700i	0.141420	−	0.110071i
$57$	−0.687333	−	1.48056i	−0.0910395	−	0.196105i
$58$	6.69341	+	5.20969i	0.878888	+	0.684066i
$59$	−0.675864	−	0.588610i	−0.0879900	−	0.0766305i	0.611638	−	0.791137i	$-0.290511\pi$
$59$	−0.675864	−	0.588610i	−0.0879900	−	0.0766305i	−0.699628	+	0.714507i	$0.746651\pi$
$60$	0.145166	−	0.100656i	0.0187408	−	0.0129946i
$61$	−5.90471	−	8.03365i	−0.756021	−	1.02860i	−0.998294	−	0.0583954i	$-0.981402\pi$
$61$	−5.90471	−	8.03365i	−0.756021	−	1.02860i	0.242273	−	0.970208i	$-0.422107\pi$
$62$	−5.14556	−	8.91237i	−0.653487	−	1.13187i
$63$	0.735236	−	3.76400i	0.0926310	−	0.474219i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	−2.74407	+	0.942039i	−0.340359	+	0.116846i
$66$	0.808813	−	0.982087i	0.0995580	−	0.120887i
$67$	−3.70161	−	0.409695i	−0.452224	−	0.0500522i	−0.118988	−	0.992896i	$-0.537965\pi$
$67$	−3.70161	−	0.409695i	−0.452224	−	0.0500522i	−0.333236	+	0.942843i	$0.608141\pi$
$68$	7.83266			0.949849
$69$	2.02542			0.243832
$70$	−0.628763	−	0.0695914i	−0.0751515	−	0.00831777i
$71$	−1.52523	+	2.07515i	−0.181011	+	0.246275i	−0.886806	−	0.462141i	$-0.847081\pi$
$71$	−1.52523	+	2.07515i	−0.181011	+	0.246275i	0.705795	+	0.708416i	$0.250590\pi$
$72$	−0.0787989	+	2.85868i	−0.00928654	+	0.336898i
$73$	4.87763	−	4.74503i	0.570884	−	0.555364i	−0.354179	−	0.935177i	$-0.615240\pi$
$73$	4.87763	−	4.74503i	0.570884	−	0.555364i	0.925063	+	0.379813i	$0.124012\pi$
$74$	−2.08077	+	4.11171i	−0.241884	+	0.477977i
$75$	1.76467	+	0.294472i	0.203767	+	0.0340027i
$76$	0.506771	−	4.32934i	0.0581306	−	0.496609i
$77$	−4.49403	+	0.749921i	−0.512143	+	0.0854615i
$78$	−0.687546	+	2.19821i	−0.0778493	+	0.248898i
$79$	−6.01990	−	16.0784i	−0.677291	−	1.80896i	−0.581473	−	0.813565i	$-0.697524\pi$
$79$	−6.01990	−	16.0784i	−0.677291	−	1.80896i	−0.0958179	−	0.995399i	$-0.530547\pi$
$80$	0.471000	−	0.0259858i	0.0526594	−	0.00290530i
$81$	4.93166	+	5.98818i	0.547962	+	0.665353i
$82$	1.08578	+	2.14555i	0.119904	+	0.236937i
$83$	−7.34974	+	3.97748i	−0.806738	+	0.436585i	−0.826304	−	0.563224i	$-0.809561\pi$
$83$	−7.34974	+	3.97748i	−0.806738	+	0.436585i	0.0195663	+	0.999809i	$0.493771\pi$
$84$	−0.340133	+	0.369483i	−0.0371115	+	0.0403139i
$85$	−2.64836	−	2.57637i	−0.287255	−	0.279446i
$86$	−0.170091	+	6.17058i	−0.0183414	+	0.665391i
$87$	−2.79348	−	1.51176i	−0.299492	−	0.162077i
$88$	3.21335	−	1.10314i	0.342544	−	0.117595i
$89$	2.18929	+	2.12978i	0.232065	+	0.225756i	0.804132	−	0.594451i	$-0.202630\pi$
$89$	2.18929	+	2.12978i	0.232065	+	0.225756i	−0.572068	+	0.820207i	$0.693858\pi$
$90$	0.966937	−	0.940651i	0.101924	−	0.0991533i
$91$	7.02676	−	4.31933i	0.736605	−	0.452789i
$92$	4.60771	+	2.83235i	0.480387	+	0.295293i
$93$	2.44997	+	2.97483i	0.254050	+	0.308476i
$94$	−2.17527	−	3.32949i	−0.224362	−	0.343411i
$95$	−1.59538	+	1.29714i	−0.163683	+	0.133083i
$96$	0.204821	−	0.313503i	0.0209045	−	0.0319967i
$97$	−8.72515	+	0.965699i	−0.885905	+	0.0980519i	−0.541432	−	0.840744i	$-0.682118\pi$
$97$	−8.72515	+	0.965699i	−0.885905	+	0.0980519i	−0.344473	+	0.938796i	$0.611942\pi$
$98$	−5.16997	+	0.572212i	−0.522246	+	0.0578022i
$99$	4.85792	−	8.41416i	0.488239	−	0.845655i
$100$	3.60273	+	3.13762i	0.360273	+	0.313762i
$101$	−1.76075	−	0.830918i	−0.175201	−	0.0826794i	0.337169	−	0.941444i	$-0.390531\pi$
$101$	−1.76075	−	0.830918i	−0.175201	−	0.0826794i	−0.512370	+	0.858765i	$0.671232\pi$
$102$	−2.89317	+	0.482785i	−0.286467	+	0.0478029i
$103$	1.26944	−	5.01289i	0.125081	−	0.493935i	−0.874873	−	0.484353i	$-0.839055\pi$
$103$	1.26944	−	5.01289i	0.125081	−	0.493935i	0.999954	−	0.00958195i	$-0.00305008\pi$
$104$	−4.63809	+	4.03932i	−0.454802	+	0.396088i
$105$	0.236538	−	0.0130501i	0.0230837	−	0.00127356i
$106$	−4.83622	−	7.40239i	−0.469736	−	0.718984i
$107$	−5.47796	+	4.26367i	−0.529574	+	0.412184i	−0.843392	−	0.537299i	$-0.819445\pi$
$107$	−5.47796	+	4.26367i	−0.529574	+	0.412184i	0.313817	+	0.949483i	$0.398392\pi$
$108$	−0.301404	−	2.17357i	−0.0290026	−	0.209152i
$109$	3.14909	−	2.18353i	0.301628	−	0.209144i	−0.409316	−	0.912393i	$-0.634233\pi$
$109$	3.14909	−	2.18353i	0.301628	−	0.209144i	0.710944	+	0.703248i	$0.248268\pi$
$110$	−1.44934	−	0.683961i	−0.138189	−	0.0652131i
$111$	0.515144	−	1.64701i	0.0488954	−	0.156327i
$112$	−1.29046	+	0.364909i	−0.121937	+	0.0344806i
$113$	−3.27153	+	12.9190i	−0.307760	+	1.21532i	0.601427	+	0.798928i	$0.294599\pi$
$113$	−3.27153	+	12.9190i	−0.307760	+	1.21532i	−0.909187	+	0.416388i	$0.863296\pi$
$114$	0.0796621	+	1.63038i	0.00746104	+	0.152699i
$115$	−0.626315	−	2.47326i	−0.0584042	−	0.230633i
$116$	−4.24095	−	7.34554i	−0.393762	−	0.682016i
$117$	−2.41589	+	17.4221i	−0.223349	+	1.61068i
$118$	0.404684	+	0.799678i	0.0372542	+	0.0736163i
$119$	8.94865	+	5.50072i	0.820322	+	0.504250i
$120$	−0.172373	+	0.0386297i	−0.0157354	+	0.00352639i
$121$	−0.535112	−	0.0892943i	−0.0486465	−	0.00811767i
$122$	2.44754	+	9.66513i	0.221590	+	0.875040i
$123$	−0.533303	−	0.725585i	−0.0480863	−	0.0654238i
$124$	1.41352	+	10.1936i	0.126938	+	0.915411i
$125$	−0.380872	−	4.59644i	−0.0340662	−	0.411118i
$126$	−2.09762	+	3.21064i	−0.186871	+	0.286027i
$127$	−3.74821	+	6.49209i	−0.332600	+	0.576080i	−0.983021	−	0.183494i	$-0.941259\pi$
$127$	−3.74821	+	6.49209i	−0.332600	+	0.576080i	0.650421	+	0.759574i	$0.274592\pi$
$128$	0.904357	−	0.426776i	0.0799346	−	0.0377221i
$129$	−0.317512	−	2.28973i	−0.0279554	−	0.201600i
$130$	2.89686	+	0.159824i	0.254071	+	0.0140175i
$131$	−1.09423	+	7.89101i	−0.0956032	+	0.689441i	0.880801	+	0.473488i	$0.157005\pi$
$131$	−1.09423	+	7.89101i	−0.0956032	+	0.689441i	−0.976404	+	0.215953i	$0.930714\pi$
$132$	−1.11893	+	0.605534i	−0.0973902	+	0.0527050i
$133$	3.61938	−	4.59029i	0.313840	−	0.398029i
$134$	3.27535	+	1.77253i	0.282947	+	0.153123i
$135$	−0.613034	+	0.834063i	−0.0527615	+	0.0717847i
$136$	−7.25691	−	2.94750i	−0.622275	−	0.252746i
$137$	−14.1714	−	1.56849i	−1.21074	−	0.134005i	−0.518122	−	0.855307i	$-0.673369\pi$
$137$	−14.1714	−	1.56849i	−1.21074	−	0.134005i	−0.692621	+	0.721302i	$0.743544\pi$
$138$	−1.87654	−	0.762186i	−0.159742	−	0.0648816i
$139$	11.9418	−	14.5001i	1.01289	−	1.22988i	0.0398605	−	0.999205i	$-0.487309\pi$
$139$	11.9418	−	14.5001i	1.01289	−	1.22988i	0.973030	−	0.230679i	$-0.0740949\pi$
$140$	0.556357	+	0.301085i	0.0470208	+	0.0254464i
$141$	1.00871	+	1.09575i	0.0849484	+	0.0922786i
$142$	2.19401	−	1.34865i	0.184117	−	0.113177i
$143$	20.3899	−	4.56949i	1.70509	−	0.382120i
$144$	1.14875	−	2.61890i	0.0957295	−	0.218241i
$145$	−0.982199	+	3.87862i	−0.0815672	+	0.322102i
$146$	−6.30470	+	2.56075i	−0.521781	+	0.211929i
$147$	1.87438	−	0.530024i	0.154596	−	0.0437156i
$148$	3.47509	−	3.02646i	0.285651	−	0.248774i
$149$	3.46803	+	17.7544i	0.284112	+	1.45449i	0.801115	+	0.598510i	$0.204240\pi$
$149$	3.46803	+	17.7544i	0.284112	+	1.45449i	−0.517003	+	0.855983i	$0.672952\pi$
$150$	−1.52415	−	0.936890i	−0.124446	−	0.0764968i
$151$	−1.91118	−	0.656109i	−0.155530	−	0.0533934i	0.245835	−	0.969312i	$-0.420938\pi$
$151$	−1.91118	−	0.656109i	−0.155530	−	0.0533934i	−0.401365	+	0.915918i	$0.631464\pi$
$152$	−2.09869	+	3.82041i	−0.170226	+	0.309876i
$153$	−21.1859	+	7.27312i	−1.71278	+	0.587997i
$154$	4.44590	+	0.996349i	0.358261	+	0.0802881i
$155$	2.87500	−	3.91158i	0.230925	−	0.314185i
$156$	1.46421	−	1.77790i	0.117231	−	0.142346i
$157$	20.3935	+	4.57029i	1.62758	+	0.364749i	0.934458	−	0.356073i	$-0.115885\pi$
$157$	20.3935	+	4.57029i	1.62758	+	0.364749i	0.693120	+	0.720822i	$0.256235\pi$
$158$	−0.473065	+	17.1619i	−0.0376350	+	1.36533i
$159$	2.24264	+	2.43615i	0.177853	+	0.193199i
$160$	−0.446157	−	0.153166i	−0.0352718	−	0.0121088i
$161$	3.27512	+	6.47180i	0.258115	+	0.510050i
$162$	−2.31574	−	7.40384i	−0.181942	−	0.581701i
$163$	−9.79347	+	7.62256i	−0.767084	+	0.597045i	−0.920330	−	0.391143i	$-0.872080\pi$
$163$	−9.79347	+	7.62256i	−0.767084	+	0.597045i	0.153246	+	0.988188i	$0.451027\pi$
$164$	−0.198574	−	2.39643i	−0.0155060	−	0.187130i
$165$	0.577506	+	0.163303i	0.0449587	+	0.0127131i
$166$	8.30625	−	0.919335i	0.644690	−	0.0713543i
$167$	14.9116	+	4.21659i	1.15389	+	0.326290i	0.794717	−	0.606981i	$-0.207619\pi$
$167$	14.9116	+	4.21659i	1.15389	+	0.326290i	0.359175	+	0.933270i	$0.383058\pi$
$168$	0.454171	−	0.214328i	0.0350401	−	0.0165358i
$169$	−20.4031	+	14.1472i	−1.56947	+	1.08824i
$170$	1.48418	+	3.38359i	0.113831	+	0.259510i
$171$	2.64935	+	12.1806i	0.202601	+	0.931476i
$172$	2.47964	−	5.65300i	0.189071	−	0.431037i
$173$	−1.01632	−	5.20299i	−0.0772694	−	0.395576i	−0.999950	−	0.0100108i	$-0.996813\pi$
$173$	−1.01632	−	5.20299i	−0.0772694	−	0.395576i	0.922680	−	0.385565i	$-0.125994\pi$
$174$	2.01925	+	2.45184i	0.153079	+	0.185874i
$175$	1.91256	+	6.11480i	0.144576	+	0.462235i
$176$	−3.39227	−	0.187157i	−0.255702	−	0.0141075i
$177$	−0.198770	−	0.270436i	−0.0149404	−	0.0203272i
$178$	−1.22691	−	2.79708i	−0.0919610	−	0.209650i
$179$	2.28879	−	0.381932i	0.171073	−	0.0285470i	−0.0784382	−	0.996919i	$-0.524993\pi$
$179$	2.28879	−	0.381932i	0.171073	−	0.0285470i	0.249511	+	0.968372i	$0.419730\pi$
$180$	−1.24984	+	0.507640i	−0.0931574	+	0.0378373i
$181$	−14.0063	+	5.68887i	−1.04108	+	0.422850i	−0.831841	−	0.555014i	$-0.812713\pi$
$181$	−14.0063	+	5.68887i	−1.04108	+	0.422850i	−0.209239	+	0.977865i	$0.567099\pi$
$182$	−8.13566	+	1.35760i	−0.603055	+	0.100632i
$183$	−1.49979	−	3.41918i	−0.110868	−	0.252753i
$184$	−3.20318	−	4.35808i	−0.236141	−	0.321282i
$185$	−2.17047	−	0.119748i	−0.159576	−	0.00880408i
$186$	−1.15042	−	3.67811i	−0.0843532	−	0.269692i
$187$	16.9172	+	20.5414i	1.23711	+	1.50213i
$188$	0.762452	+	3.90333i	0.0556075	+	0.284679i
$189$	1.18211	−	2.69493i	0.0859856	−	0.196027i
$190$	1.96624	−	0.601433i	0.142646	−	0.0436325i
$191$	−7.84282	−	17.8798i	−0.567486	−	1.29374i	−0.931972	−	0.362530i	$-0.881913\pi$
$191$	−7.84282	−	17.8798i	−0.567486	−	1.29374i	0.364486	−	0.931209i	$-0.381245\pi$
$192$	−0.307740	+	0.213382i	−0.0222092	+	0.0153995i
$193$	−12.9500	+	6.11127i	−0.932165	+	0.439899i	−0.831815	−	0.555053i	$-0.812698\pi$
$193$	−12.9500	+	6.11127i	−0.932165	+	0.439899i	−0.100350	+	0.994952i	$0.531996\pi$
$194$	8.44720	+	2.38864i	0.606474	+	0.171494i
$195$	−1.07987	+	0.119520i	−0.0773313	+	0.00855903i
$196$	5.00528	+	1.41536i	0.357520	+	0.101097i
$197$	1.96339	+	23.6945i	0.139885	+	1.68817i	0.599758	+	0.800181i	$0.295263\pi$
$197$	1.96339	+	23.6945i	0.139885	+	1.68817i	−0.459873	+	0.887985i	$0.652105\pi$
$198$	−7.66716	+	5.96759i	−0.544882	+	0.424098i
$199$	0.756507	+	2.41869i	0.0536274	+	0.171456i	0.977361	−	0.211580i	$-0.0678609\pi$
$199$	0.756507	+	2.41869i	0.0536274	+	0.171456i	−0.923733	+	0.383036i	$0.874878\pi$
$200$	−2.15719	−	4.26273i	−0.152537	−	0.301421i
$201$	−1.31908	−	0.452841i	−0.0930409	−	0.0319410i
$202$	1.31864	+	1.43243i	0.0927793	+	0.100785i
$203$	0.313425	−	11.3705i	0.0219981	−	0.798050i
$204$	2.86218	+	0.641431i	0.200393	+	0.0449091i
$205$	−0.721107	+	0.875592i	−0.0503643	+	0.0611540i
$206$	−3.06252	+	4.16671i	−0.213376	+	0.290308i
$207$	−15.0930	−	3.38242i	−1.04904	−	0.235095i
$208$	5.81720	−	1.99705i	0.403350	−	0.138470i
$209$	12.4484	−	8.02160i	0.861071	−	0.554865i
$210$	−0.224062	−	0.0769204i	−0.0154617	−	0.00530801i
$211$	19.4666	+	11.9661i	1.34013	+	0.823778i	0.993457	−	0.114206i	$-0.0364325\pi$
$211$	19.4666	+	11.9661i	1.34013	+	0.823778i	0.346678	+	0.937984i	$0.387310\pi$
$212$	1.69514	+	8.67819i	0.116423	+	0.596021i
$213$	−0.727282	+	0.633390i	−0.0498325	+	0.0433992i
$214$	6.67976	−	1.88886i	0.456619	−	0.129119i
$215$	−2.69783	+	1.09576i	−0.183990	+	0.0747305i
$216$	−0.538686	+	2.12722i	−0.0366529	+	0.144739i
$217$	−5.54383	+	12.6387i	−0.376340	+	0.857968i
$218$	−3.73929	+	0.837995i	−0.253257	+	0.0567562i
$219$	2.17095	−	1.33448i	0.146699	−	0.0901756i
$220$	1.08543	+	1.17909i	0.0731794	+	0.0794940i
$221$	−42.3681	−	22.9284i	−2.84998	−	1.54233i
$222$	−1.09706	+	1.33209i	−0.0736301	+	0.0894040i
$223$	5.68120	+	2.30750i	0.380441	+	0.154522i	0.558513	−	0.829496i	$-0.311372\pi$
$223$	5.68120	+	2.30750i	0.380441	+	0.154522i	−0.178072	+	0.984017i	$0.556986\pi$
$224$	1.33293	+	0.147528i	0.0890599	+	0.00985715i
$225$	−12.6582	−	5.14132i	−0.843880	−	0.342755i
$226$	7.89259	−	10.7383i	0.525007	−	0.714298i
$227$	−7.73427	−	4.18558i	−0.513342	−	0.277807i	0.198556	−	0.980089i	$-0.436375\pi$
$227$	−7.73427	−	4.18558i	−0.513342	−	0.277807i	−0.711898	+	0.702283i	$0.752164\pi$
$228$	0.539720	−	1.54051i	0.0357438	−	0.102023i
$229$	16.1996	−	8.76680i	1.07050	−	0.579327i	0.157599	−	0.987503i	$-0.449625\pi$
$229$	16.1996	−	8.76680i	1.07050	−	0.579327i	0.912903	+	0.408177i	$0.133835\pi$
$230$	−0.350435	+	2.52715i	−0.0231070	+	0.166636i
$231$	−1.70361	−	0.0939907i	−0.112089	−	0.00618413i
$232$	1.16502	+	8.40151i	0.0764873	+	0.551586i
$233$	6.35153	−	2.99736i	0.416103	−	0.196364i	−0.207278	−	0.978282i	$-0.566460\pi$
$233$	6.35153	−	2.99736i	0.416103	−	0.196364i	0.623381	+	0.781918i	$0.285759\pi$
$234$	8.79441	−	15.2324i	0.574909	−	0.995771i
$235$	1.02611	−	1.57058i	0.0669359	−	0.102453i
$236$	−0.0740113	−	0.893183i	−0.00481772	−	0.0581413i
$237$	−0.883080	−	6.36831i	−0.0573622	−	0.413666i
$238$	−6.22090	−	8.46384i	−0.403241	−	0.548629i
$239$	7.25983	+	28.6684i	0.469599	+	1.85441i	0.517699	+	0.855563i	$0.326789\pi$
$239$	7.25983	+	28.6684i	0.469599	+	1.85441i	−0.0481004	+	0.998843i	$0.515317\pi$
$240$	0.174239	+	0.0290754i	0.0112471	+	0.00187681i
$241$	2.46219	−	0.551790i	0.158604	−	0.0355439i	−0.138656	−	0.990341i	$-0.544278\pi$
$241$	2.46219	−	0.551790i	0.158604	−	0.0355439i	0.297260	+	0.954797i	$0.403927\pi$
$242$	0.462175	+	0.284098i	0.0297098	+	0.0182625i
$243$	4.28422	+	8.46585i	0.274833	+	0.543084i
$244$	1.36944	−	9.87572i	0.0876697	−	0.632228i
$245$	−1.22683	−	2.12492i	−0.0783790	−	0.135756i
$246$	0.221058	+	0.872938i	0.0140941	+	0.0556565i
$247$	−15.4144	+	21.9346i	−0.980796	+	1.39567i
$248$	2.52632	−	9.97622i	0.160422	−	0.633491i
$249$	−3.01144	+	0.851554i	−0.190842	+	0.0539650i
$250$	−1.37681	+	4.40190i	−0.0870770	+	0.278401i
$251$	18.3371	+	8.65351i	1.15743	+	0.546205i	0.906668	−	0.421844i	$-0.138617\pi$
$251$	18.3371	+	8.65351i	1.15743	+	0.546205i	0.250762	+	0.968049i	$0.419319\pi$
$252$	3.15163	−	2.18529i	0.198534	−	0.137660i
$253$	2.52393	+	18.2012i	0.158678	+	1.14430i
$254$	5.91573	−	4.60439i	0.371186	−	0.288905i
$255$	−0.756772	−	1.15833i	−0.0473909	−	0.0725372i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	17.7997	−	15.5018i	1.11032	−	0.966976i	0.110678	−	0.993856i	$-0.464698\pi$
$257$	17.7997	−	15.5018i	1.11032	−	0.966976i	0.999639	+	0.0268808i	$0.00855746\pi$
$258$	−0.567474	+	2.24091i	−0.0353294	+	0.139513i
$259$	6.09565	−	1.01718i	0.378765	−	0.0632047i
$260$	−2.62378	−	1.23819i	−0.162720	−	0.0767893i
$261$	18.2918	+	15.9303i	1.13223	+	0.986063i
$262$	3.98326	−	6.89920i	0.246086	−	0.426234i
$263$	−1.77326	+	0.196265i	−0.109344	+	0.0121022i	−0.164514	−	0.986375i	$-0.552605\pi$
$263$	−1.77326	+	0.196265i	−0.109344	+	0.0121022i	0.0551697	+	0.998477i	$0.482430\pi$
$264$	1.26455	−	0.139960i	0.0778276	−	0.00861396i
$265$	2.28132	−	3.49183i	0.140141	−	0.214501i
$266$	−5.08071	+	2.89087i	−0.311518	+	0.177250i
$267$	0.625593	+	0.957542i	0.0382857	+	0.0586006i
$268$	−2.36757	−	2.87479i	−0.144623	−	0.175606i
$269$	−7.21642	−	4.43592i	−0.439993	−	0.270463i	0.285914	−	0.958255i	$-0.407703\pi$
$269$	−7.21642	−	4.43592i	−0.439993	−	0.270463i	−0.725907	+	0.687793i	$0.758580\pi$
$270$	0.881838	−	0.542064i	0.0536669	−	0.0329889i
$271$	1.47446	−	1.43438i	0.0895672	−	0.0871323i	−0.651151	−	0.758948i	$-0.725713\pi$
$271$	1.47446	−	1.43438i	0.0895672	−	0.0871323i	0.740718	+	0.671816i	$0.234485\pi$
$272$	5.61431	+	5.46169i	0.340418	+	0.331163i
$273$	2.92141	−	1.00292i	0.176812	−	0.0606997i
$274$	12.5395	+	6.78602i	0.757537	+	0.409958i
$275$	−0.447239	+	16.2250i	−0.0269695	+	0.978404i
$276$	1.45179	+	1.41232i	0.0873874	+	0.0850118i
$277$	−4.36175	+	4.73812i	−0.262072	+	0.284686i	−0.852859	−	0.522142i	$-0.825133\pi$
$277$	−4.36175	+	4.73812i	−0.262072	+	0.284686i	0.590787	+	0.806828i	$0.298817\pi$
$278$	−16.5205	+	8.94047i	−0.990836	+	0.536214i
$279$	−13.2887	−	26.2592i	−0.795574	−	1.57210i
$280$	−0.402160	−	0.488316i	−0.0240337	−	0.0291825i
$281$	−4.69344	+	0.258945i	−0.279987	+	0.0154473i	−0.194537	−	0.980895i	$-0.562321\pi$
$281$	−4.69344	+	0.258945i	−0.279987	+	0.0154473i	−0.0854501	+	0.996342i	$0.527233\pi$
$282$	−0.522221	−	1.39479i	−0.0310978	−	0.0830585i
$283$	−7.47106	+	23.8863i	−0.444109	+	1.41989i	0.415805	+	0.909454i	$0.363500\pi$
$283$	−7.47106	+	23.8863i	−0.444109	+	1.41989i	−0.859913	+	0.510440i	$0.829482\pi$
$284$	−2.54025	+	0.423893i	−0.150736	+	0.0251534i
$285$	−0.689204	+	0.343347i	−0.0408249	+	0.0203381i
$286$	−20.6107	−	3.43932i	−1.21874	−	0.203371i
$287$	1.45610	−	2.87733i	0.0859508	−	0.169843i
$288$	−2.04983	+	1.99410i	−0.120787	+	0.117504i
$289$	1.22205	−	44.3337i	0.0718852	−	2.60786i
$290$	2.36956	−	3.22391i	0.139145	−	0.189314i
$291$	−3.26740	−	0.361636i	−0.191538	−	0.0211995i
$292$	6.80490			0.398227
$293$	−0.932027			−0.0544496			−0.0272248	−	0.999629i	$-0.508667\pi$
$293$	−0.932027			−0.0544496			−0.0272248	+	0.999629i	$0.508667\pi$
$294$	−1.93605	−	0.214282i	−0.112913	−	0.0124972i
$295$	−0.268767	+	0.326345i	−0.0156482	+	0.0190006i
$296$	−4.35854	+	1.49629i	−0.253335	+	0.0869700i
$297$	5.04927	−	5.48497i	0.292989	−	0.318270i
$298$	3.46803	−	17.7544i	0.200897	−	1.02848i
$299$	−16.6327	−	28.8087i	−0.961895	−	1.66605i
$300$	1.05955	+	1.44157i	0.0611733	+	0.0832293i
$301$	6.80292	−	4.71704i	0.392114	−	0.271886i
$302$	1.52380	+	1.32708i	0.0876847	+	0.0763647i
$303$	−0.575362	−	0.447822i	−0.0330537	−	0.0257267i
$304$	3.38208	−	2.74983i	0.193976	−	0.157713i
$305$	−3.71142	+	2.88871i	−0.212515	+	0.165407i
$306$	22.3655	+	1.23394i	1.27855	+	0.0705397i
$307$	−10.0393	−	17.3886i	−0.572972	−	0.992417i	−0.996259	−	0.0864213i	$-0.972457\pi$
$307$	−10.0393	−	17.3886i	−0.572972	−	0.992417i	0.423286	−	0.905996i	$-0.360876\pi$
$308$	−3.74416	−	2.59614i	−0.213343	−	0.147929i
$309$	0.874388	−	1.72784i	0.0497422	−	0.0982932i
$310$	−4.13563	+	2.54216i	−0.234888	+	0.144385i
$311$	6.48712	+	2.22703i	0.367851	+	0.126283i	0.502426	−	0.864620i	$-0.332441\pi$
$311$	6.48712	+	2.22703i	0.367851	+	0.126283i	−0.134576	+	0.990903i	$0.542967\pi$
$312$	−2.02562	+	1.09621i	−0.114678	+	0.0620608i
$313$	1.88108	−	9.63007i	0.106325	−	0.544324i	−0.889798	−	0.456354i	$-0.849155\pi$
$313$	1.88108	−	9.63007i	0.106325	−	0.544324i	0.996123	−	0.0879697i	$-0.0280379\pi$
$314$	−17.1746	−	11.9086i	−0.969219	−	0.672042i
$315$	−1.78442	−	0.297767i	−0.100541	−	0.0167773i
$316$	6.89648	−	15.7224i	0.387957	−	0.884454i
$317$	9.24689	−	8.05313i	0.519357	−	0.452309i	−0.356907	−	0.934140i	$-0.616169\pi$
$317$	9.24689	−	8.05313i	0.519357	−	0.452309i	0.876264	+	0.481831i	$0.160028\pi$
$318$	−1.16104	−	3.10101i	−0.0651080	−	0.173896i
$319$	10.1042	−	26.9871i	0.565726	−	1.51099i
$320$	0.355724	+	0.309800i	0.0198856	+	0.0173184i
$321$	−2.35090	+	1.10942i	−0.131214	+	0.0619216i
$322$	−0.598974	−	7.22854i	−0.0333795	−	0.402831i
$323$	−33.7880	−	4.90223i	−1.88001	−	0.272767i
$324$	−0.640613	+	7.73105i	−0.0355896	+	0.429503i
$325$	−10.3030	−	27.5181i	−0.571508	−	1.52643i
$326$	11.9420	−	3.37688i	0.661408	−	0.187028i
$327$	1.32954	−	0.540014i	0.0735239	−	0.0298628i
$328$	−0.717822	+	2.29500i	−0.0396351	+	0.126720i
$329$	−1.87014	+	4.99493i	−0.103104	+	0.275379i
$330$	−0.473603	−	0.368620i	−0.0260710	−	0.0202919i
$331$	9.03465	−	13.8286i	0.496589	−	0.760086i	−0.497638	−	0.867385i	$-0.665799\pi$
$331$	9.03465	−	13.8286i	0.496589	−	0.760086i	0.994227	+	0.107299i	$0.0342201\pi$
$332$	−8.04164	−	2.27396i	−0.441343	−	0.124800i
$333$	−6.58922	+	11.4129i	−0.361087	+	0.625421i
$334$	−12.2287	−	9.51801i	−0.669127	−	0.520802i
$335$	−0.145073	+	1.75077i	−0.00792620	+	0.0956550i
$336$	−0.501441	+	0.0276652i	−0.0273558	+	0.00150926i
$337$	−4.99744	−	25.5841i	−0.272228	−	1.39366i	−0.827256	−	0.561825i	$-0.810100\pi$
$337$	−4.99744	−	25.5841i	−0.272228	−	1.39366i	0.555028	−	0.831832i	$-0.312707\pi$
$338$	24.2270	−	5.42941i	1.31778	−	0.295321i
$339$	−2.25343	+	4.45290i	−0.122390	+	0.241848i
$340$	−0.101808	−	3.69339i	−0.00552129	−	0.200302i
$341$	−23.6800	+	25.7234i	−1.28235	+	1.39300i
$342$	2.12908	−	12.2823i	0.115127	−	0.664148i
$343$	11.0824	+	12.0387i	0.598394	+	0.650029i
$344$	−4.42465	+	4.30436i	−0.238561	+	0.232076i
$345$	−0.0263261	−	0.955062i	−0.00141735	−	0.0514188i
$346$	−1.01632	+	5.20299i	−0.0546377	+	0.279715i
$347$	2.67726	−	19.3070i	0.143723	−	1.03645i	−0.772280	−	0.635282i	$-0.780884\pi$
$347$	2.67726	−	19.3070i	0.143723	−	1.03645i	0.916003	−	0.401171i	$-0.131397\pi$
$348$	−0.948175	−	3.03148i	−0.0508275	−	0.162505i
$349$	−9.74766	−	14.9199i	−0.521781	−	0.798645i	0.474901	−	0.880039i	$-0.342484\pi$
$349$	−9.74766	−	14.9199i	−0.521781	−	0.798645i	−0.996682	+	0.0813944i	$0.974063\pi$
$350$	0.529079	−	6.38504i	0.0282805	−	0.341295i
$351$	−4.73232	+	12.6395i	−0.252593	+	0.674645i
$352$	3.07249	+	1.44994i	0.163764	+	0.0772822i
$353$	−4.50687	−	10.2746i	−0.239876	−	0.546863i	0.754062	−	0.656804i	$-0.228092\pi$
$353$	−4.50687	−	10.2746i	−0.239876	−	0.546863i	−0.993938	+	0.109940i	$0.964934\pi$
$354$	0.0823914	+	0.325356i	0.00437905	+	0.0172925i
$355$	0.998334	+	0.692229i	0.0529861	+	0.0367397i
$356$	0.0841602	+	3.05318i	0.00446048	+	0.161818i
$357$	2.81952	+	2.74288i	0.149225	+	0.145168i
$358$	−2.26428	−	0.507437i	−0.119671	−	0.0268189i
$359$	−18.8553	−	7.65835i	−0.995144	−	0.404192i	−0.180135	−	0.983642i	$-0.557654\pi$
$359$	−18.8553	−	7.65835i	−0.995144	−	0.404192i	−0.815008	+	0.579449i	$0.803268\pi$
$360$	1.34900			0.0710984
$361$	−4.89568	+	18.3584i	−0.257667	+	0.966234i
$362$	15.1175			0.794559
$363$	−0.188226	−	0.0764509i	−0.00987932	−	0.00401263i
$364$	8.04852	+	1.80371i	0.421857	+	0.0945403i
$365$	−2.30086	−	2.23831i	−0.120432	−	0.117158i
$366$	0.102878	+	3.73223i	0.00537754	+	0.195087i
$367$	27.3785	+	18.9838i	1.42915	+	0.990947i	0.995975	+	0.0896356i	$0.0285702\pi$
$367$	27.3785	+	18.9838i	1.42915	+	0.990947i	0.433171	+	0.901312i	$0.357395\pi$
$368$	1.32774	+	5.24312i	0.0692131	+	0.273317i
$369$	2.76234	+	6.29751i	0.143802	+	0.327835i
$370$	1.96587	+	0.927716i	0.102201	+	0.0482296i
$371$	−4.15785	+	11.1051i	−0.215865	+	0.576549i
$372$	−0.318246	+	3.84066i	−0.0165003	+	0.199129i
$373$	2.01698	+	3.08722i	0.104435	+	0.159850i	0.885560	−	0.464525i	$-0.153775\pi$
$373$	2.01698	+	3.08722i	0.104435	+	0.159850i	−0.781125	+	0.624375i	$0.785354\pi$
$374$	−7.94374	−	25.3976i	−0.410761	−	1.31328i
$375$	0.237234	−	1.71081i	0.0122507	−	0.0883457i
$376$	0.762452	−	3.90333i	0.0393204	−	0.201299i
$377$	1.43744	+	52.1477i	0.0740319	+	2.68574i
$378$	−2.10934	+	2.05200i	−0.108493	+	0.105543i
$379$	−5.68014	−	6.17028i	−0.291769	−	0.316946i	0.572569	−	0.819856i	$-0.305947\pi$
$379$	−5.68014	−	6.17028i	−0.291769	−	0.316946i	−0.864339	+	0.502910i	$0.832263\pi$
$380$	−2.04803	−	0.182689i	−0.105062	−	0.00937175i
$381$	−1.90131	+	2.06537i	−0.0974069	+	0.105812i
$382$	0.537979	+	19.5169i	0.0275254	+	0.998570i
$383$	8.99517	−	17.7749i	0.459632	−	0.908257i	−0.538224	−	0.842802i	$-0.680904\pi$
$383$	8.99517	−	17.7749i	0.459632	−	0.908257i	0.997856	−	0.0654551i	$-0.0208499\pi$
$384$	0.365417	−	0.0818918i	0.0186476	−	0.00417902i
$385$	0.412028	+	2.10936i	0.0209989	+	0.107503i
$386$	14.2979	−	0.788835i	0.727742	−	0.0401507i
$387$	−1.45778	+	17.5928i	−0.0741033	+	0.894293i
$388$	−6.92741	−	5.39182i	−0.351686	−	0.273728i
$389$	1.11855	−	1.93739i	0.0567127	−	0.0982293i	−0.836275	−	0.548310i	$-0.815271\pi$
$389$	1.11855	−	1.93739i	0.0567127	−	0.0982293i	0.892988	+	0.450081i	$0.148605\pi$
$390$	1.04547	+	0.295631i	0.0529396	+	0.0149699i
$391$	23.1708	−	35.4656i	1.17180	−	1.79357i
$392$	−4.10475	−	3.19485i	−0.207321	−	0.161364i
$393$	−1.04606	+	2.79390i	−0.0527667	+	0.140934i
$394$	7.09741	−	22.6917i	0.357562	−	1.14319i
$395$	−7.50333	+	3.04759i	−0.377533	+	0.153341i
$396$	9.34924	−	2.64371i	0.469817	−	0.132852i
$397$	13.7826	+	36.8118i	0.691731	+	1.84753i	0.499848	+	0.866113i	$0.333389\pi$
$397$	13.7826	+	36.8118i	0.691731	+	1.84753i	0.191883	+	0.981418i	$0.438541\pi$
$398$	0.209276	−	2.52558i	0.0104900	−	0.126596i
$399$	1.69849	−	1.38097i	0.0850309	−	0.0691350i
$400$	0.394521	+	4.76117i	0.0197261	+	0.238058i
$401$	−15.7864	+	7.44977i	−0.788334	+	0.372024i	−0.778273	−	0.627926i	$-0.783904\pi$
$401$	−15.7864	+	7.44977i	−0.788334	+	0.372024i	−0.0100607	+	0.999949i	$0.503202\pi$
$402$	1.05171	+	0.915938i	0.0524547	+	0.0456828i
$403$	22.1936	−	59.2765i	1.10554	−	2.95277i
$404$	−0.682678	−	1.82335i	−0.0339645	−	0.0907152i
$405$	2.75955	−	2.40329i	0.137123	−	0.119420i
$406$	−4.56920	+	10.4167i	−0.226766	+	0.516973i
$407$	15.4426	+	2.57691i	0.765461	+	0.127733i
$408$	−2.41042	−	1.67135i	−0.119334	−	0.0827441i
$409$	−2.42710	+	12.4254i	−0.120012	+	0.614397i	0.872129	+	0.489276i	$0.162739\pi$
$409$	−2.42710	+	12.4254i	−0.120012	+	0.614397i	−0.992141	+	0.125121i	$0.960068\pi$
$410$	0.997595	−	0.539871i	0.0492677	−	0.0266624i
$411$	−5.05002	−	1.73367i	−0.249099	−	0.0855158i
$412$	4.40538	−	2.70798i	0.217038	−	0.133412i
$413$	0.542708	−	1.07242i	0.0267049	−	0.0527704i
$414$	12.7108	+	8.81344i	0.624699	+	0.433157i
$415$	1.97106	+	3.41397i	0.0967554	+	0.167585i
$416$	−6.14111	−	0.338814i	−0.301092	−	0.0166117i
$417$	5.55118	−	4.32065i	0.271842	−	0.211583i
$418$	−14.5519	+	2.74753i	−0.711758	+	0.134386i
$419$	2.32811	+	1.81204i	0.113736	+	0.0885241i	0.669484	−	0.742827i	$-0.266515\pi$
$419$	2.32811	+	1.81204i	0.113736	+	0.0885241i	−0.555748	+	0.831351i	$0.687568\pi$
$420$	0.178646	+	0.155583i	0.00871702	+	0.00759166i
$421$	16.0799	−	11.1496i	0.783686	−	0.543396i	−0.109017	−	0.994040i	$-0.534770\pi$
$421$	16.0799	−	11.1496i	0.783686	−	0.543396i	0.892704	+	0.450644i	$0.148806\pi$
$422$	−13.5327	−	18.4119i	−0.658763	−	0.896279i
$423$	−5.68678	−	9.84979i	−0.276501	−	0.478913i
$424$	1.69514	−	8.67819i	0.0823235	−	0.421450i
$425$	25.3441	−	27.5311i	1.22937	−	1.33545i
$426$	0.912173	−	0.313149i	0.0441949	−	0.0151721i
$427$	8.50008	−	10.3211i	0.411348	−	0.499472i
$428$	−6.89955	−	0.763642i	−0.333502	−	0.0369120i
$429$	7.82503			0.377796
$430$	2.91187			0.140423
$431$	21.0452	+	2.32928i	1.01371	+	0.112197i	0.601485	−	0.798884i	$-0.294576\pi$
$431$	21.0452	+	2.32928i	1.01371	+	0.112197i	0.412226	+	0.911082i	$0.364751\pi$
$432$	1.29958	−	1.76815i	0.0625262	−	0.0850699i
$433$	0.140622	−	5.10150i	0.00675785	−	0.245162i	−0.988697	−	0.149928i	$-0.952096\pi$
$433$	0.140622	−	5.10150i	0.00675785	−	0.245162i	0.995455	−	0.0952348i	$-0.0303602\pi$
$434$	9.89237	−	9.62344i	0.474849	−	0.461940i
$435$	−0.676539	+	1.33688i	−0.0324376	+	0.0640984i
$436$	3.77978	+	0.630733i	0.181019	+	0.0302067i
$437$	−18.1037	−	15.1018i	−0.866020	−	0.722418i
$438$	−2.51355	+	0.419437i	−0.120102	+	0.0200415i
$439$	−8.37250	+	26.7684i	−0.399598	+	1.27759i	0.509308	+	0.860584i	$0.329901\pi$
$439$	−8.37250	+	26.7684i	−0.399598	+	1.27759i	−0.908906	+	0.417001i	$0.863081\pi$
$440$	−0.561939	−	1.50087i	−0.0267894	−	0.0715513i
$441$	−14.8526	+	0.819441i	−0.707267	+	0.0390210i
$442$	30.6256	+	37.1866i	1.45671	+	1.76878i
$443$	9.48689	+	18.7466i	0.450736	+	0.890678i	0.998537	+	0.0540695i	$0.0172192\pi$
$443$	9.48689	+	18.7466i	0.450736	+	0.890678i	−0.547802	+	0.836608i	$0.684535\pi$
$444$	1.51770	−	0.821338i	0.0720269	−	0.0389790i
$445$	0.975813	−	1.06002i	0.0462580	−	0.0502495i
$446$	−4.39526	−	4.27577i	−0.208122	−	0.202464i
$447$	−0.186662	+	6.77175i	−0.00882880	+	0.320293i
$448$	−1.17943	−	0.638277i	−0.0557229	−	0.0301557i
$449$	24.0571	−	8.25882i	1.13533	−	0.389758i	0.307948	−	0.951403i	$-0.400358\pi$
$449$	24.0571	−	8.25882i	1.13533	−	0.389758i	0.827378	+	0.561646i	$0.189832\pi$
$450$	9.79303	+	9.52680i	0.461648	+	0.449098i
$451$	5.85583	−	5.69664i	0.275740	−	0.268244i
$452$	−11.3533	+	6.97887i	−0.534016	+	0.328259i
$453$	−0.644648	−	0.396264i	−0.0302882	−	0.0186181i
$454$	5.59069	+	6.78840i	0.262384	+	0.318595i
$455$	−2.12806	−	3.25723i	−0.0997649	−	0.152702i
$456$	−1.07976	+	1.22417i	−0.0505643	+	0.0573272i
$457$	−10.1006	+	15.4601i	−0.472486	+	0.723193i	−0.991290	−	0.131700i	$-0.957956\pi$
$457$	−10.1006	+	15.4601i	−0.472486	+	0.723193i	0.518804	+	0.854893i	$0.326378\pi$
$458$	−18.3079	+	2.02632i	−0.855472	+	0.0946836i
$459$	−17.0834	+	1.89079i	−0.797386	+	0.0882546i
$460$	1.27567	−	2.20952i	0.0594783	−	0.103019i
$461$	−6.90008	−	6.00928i	−0.321369	−	0.279880i	0.480985	−	0.876729i	$-0.340279\pi$
$461$	−6.90008	−	6.00928i	−0.321369	−	0.279880i	−0.802354	+	0.596848i	$0.796419\pi$
$462$	1.54301	+	0.728165i	0.0717875	+	0.0338773i
$463$	12.3632	−	2.06305i	0.574567	−	0.0958782i	0.129825	−	0.991537i	$-0.458559\pi$
$463$	12.3632	−	2.06305i	0.574567	−	0.0958782i	0.444742	+	0.895659i	$0.353295\pi$
$464$	2.08218	−	8.22236i	0.0966629	−	0.381713i
$465$	1.37090	−	1.19392i	0.0635739	−	0.0553666i
$466$	−7.01259	+	0.386895i	−0.324852	+	0.0179226i
$467$	−2.10906	−	3.22816i	−0.0975958	−	0.149382i	0.785030	−	0.619458i	$-0.212647\pi$
$467$	−2.10906	−	3.22816i	−0.0975958	−	0.149382i	−0.882626	+	0.470076i	$0.844226\pi$
$468$	−13.8801	+	10.8033i	−0.641606	+	0.499382i
$469$	−0.686002	−	4.94708i	−0.0316766	−	0.228435i
$470$	−1.54170	+	1.06899i	−0.0711135	+	0.0493090i
$471$	7.07786	+	3.34012i	0.326130	+	0.153905i
$472$	−0.267542	+	0.855380i	−0.0123146	+	0.0393721i
$473$	20.1808	−	5.70657i	0.927912	−	0.262389i
$474$	−1.57829	+	6.23251i	−0.0724931	+	0.286269i
$475$	−13.5775	−	15.7897i	−0.622977	−	0.724481i
$476$	2.57861	+	10.1827i	0.118190	+	0.466723i
$477$	−12.6433	−	21.8988i	−0.578897	−	1.00268i
$478$	4.06200	−	29.2930i	0.185792	−	1.33983i
$479$	7.01191	+	13.8559i	0.320382	+	0.633093i	0.994407	−	0.105616i	$-0.0336814\pi$
$479$	7.01191	+	13.8559i	0.320382	+	0.633093i	−0.674025	+	0.738709i	$0.735436\pi$
$480$	−0.150490	−	0.0925060i	−0.00686891	−	0.00422230i
$481$	−27.6566	+	6.19800i	−1.26103	+	0.282604i
$482$	−2.48885	−	0.415316i	−0.113364	−	0.0189171i
$483$	0.666794	+	2.63311i	0.0303402	+	0.119811i
$484$	−0.321294	−	0.437136i	−0.0146043	−	0.0198698i
$485$	0.568771	+	4.10168i	0.0258266	+	0.186248i
$486$	−0.783526	−	9.45575i	−0.0355414	−	0.428921i
$487$	−3.83287	+	5.86665i	−0.173684	+	0.265843i	−0.913389	−	0.407088i	$-0.866544\pi$
$487$	−3.83287	+	5.86665i	−0.173684	+	0.265843i	0.739705	+	0.672932i	$0.234965\pi$
$488$	−4.98511	+	8.63446i	−0.225665	+	0.390864i
$489$	−4.20292	+	1.98341i	−0.190063	+	0.0896928i
$490$	0.337018	+	2.43040i	0.0152249	+	0.109794i
$491$	−11.7624	−	0.648951i	−0.530831	−	0.0292868i	−0.212310	−	0.977202i	$-0.568099\pi$
$491$	−11.7624	−	0.648951i	−0.530831	−	0.0292868i	−0.318521	+	0.947916i	$0.603186\pi$
$492$	0.123686	−	0.891958i	0.00557619	−	0.0402126i
$493$	−58.4286	+	31.6200i	−2.63149	+	1.42409i
$494$	22.5356	−	14.5217i	1.01392	−	0.653362i
$495$	−4.03073	−	2.18132i	−0.181168	−	0.0980432i
$496$	−6.09477	+	8.29223i	−0.273663	+	0.372332i
$497$	−3.19988	−	1.29968i	−0.143534	−	0.0582985i
$498$	3.11053	+	0.344273i	0.139386	+	0.0154273i
$499$	−32.7756	−	13.3123i	−1.46724	−	0.595940i	−0.503787	−	0.863828i	$-0.668060\pi$
$499$	−32.7756	−	13.3123i	−1.46724	−	0.595940i	−0.963450	+	0.267888i	$0.913674\pi$
$500$	2.93208	−	3.56023i	0.131127	−	0.159218i
$501$	5.10363	+	2.76195i	0.228014	+	0.123395i
$502$	−13.7329	−	14.9179i	−0.612928	−	0.665817i
$503$	−2.53063	+	1.55557i	−0.112835	+	0.0693595i	−0.578941	−	0.815370i	$-0.696534\pi$
$503$	−2.53063	+	1.55557i	−0.112835	+	0.0693595i	0.466106	+	0.884729i	$0.345657\pi$
$504$	−3.74231	+	0.838671i	−0.166696	+	0.0373574i
$505$	−0.368923	+	0.841059i	−0.0164168	+	0.0374266i
$506$	4.51089	−	17.8131i	0.200534	−	0.791890i
$507$	−8.61417	+	3.49877i	−0.382569	+	0.155386i
$508$	−7.21356	+	2.03980i	−0.320050	+	0.0905015i
$509$	−13.0621	+	11.3758i	−0.578967	+	0.504223i	−0.895918	−	0.444219i	$-0.853481\pi$
$509$	−13.0621	+	11.3758i	−0.578967	+	0.504223i	0.316951	+	0.948442i	$0.397341\pi$
$510$	0.265256	+	1.35796i	0.0117457	+	0.0601316i
$511$	7.77446	+	4.77894i	0.343922	+	0.211408i
$512$	0.945817	+	0.324699i	0.0417996	+	0.0143498i
$513$	−0.0601957	+	9.56484i	−0.00265771	+	0.422298i
$514$	−22.3248	+	7.66412i	−0.984705	+	0.338050i
$515$	−2.38026	−	0.533429i	−0.104887	−	0.0235057i
$516$	1.36904	−	1.86264i	0.0602684	−	0.0819982i
$517$	−8.58983	+	10.4301i	−0.377780	+	0.458713i
$518$	−6.03036	−	1.35143i	−0.264959	−	0.0593786i
$519$	0.0547021	−	1.98449i	0.00240115	−	0.0871094i
$520$	1.96497	+	2.13453i	0.0861697	+	0.0936053i
$521$	−17.4641	−	5.99543i	−0.765115	−	0.262664i	−0.0856037	−	0.996329i	$-0.527282\pi$
$521$	−17.4641	−	5.99543i	−0.765115	−	0.262664i	−0.679511	+	0.733665i	$0.737808\pi$
$522$	−10.9525	−	21.6427i	−0.479378	−	0.947277i
$523$	−7.01276	−	22.4210i	−0.306646	−	0.980403i	−0.972220	−	0.234071i	$-0.924795\pi$
$523$	−7.01276	−	22.4210i	−0.306646	−	0.980403i	0.665573	−	0.746333i	$-0.268187\pi$
$524$	−6.28670	+	4.89313i	−0.274636	+	0.213758i
$525$	0.198130	+	2.39107i	0.00864710	+	0.104355i
$526$	1.71677	+	0.485457i	0.0748548	+	0.0211669i
$527$	80.1176	−	8.86742i	3.48998	−	0.386271i
$528$	−1.22427	−	0.346189i	−0.0532793	−	0.0150660i
$529$	5.65512	−	2.66872i	0.245875	−	0.116031i
$530$	−3.42764	+	2.37667i	−0.148887	+	0.103236i
$531$	1.02956	+	2.34717i	0.0446793	+	0.101859i
$532$	5.79510	−	0.766455i	0.251250	−	0.0332300i
$533$	−5.94093	+	13.5439i	−0.257330	+	0.586654i
$534$	−0.219277	−	1.12257i	−0.00948902	−	0.0485785i
$535$	2.08168	+	2.52764i	0.0899988	+	0.109280i
$536$	1.11173	+	3.55441i	0.0480196	+	0.153527i
$537$	0.867641	+	0.0478691i	0.0374415	+	0.00206570i
$538$	5.01669	+	6.82546i	0.216285	+	0.294266i
$539$	7.09871	+	16.1834i	0.305763	+	0.697069i
$540$	−1.02100	+	0.170375i	−0.0439369	+	0.00733177i
$541$	7.22136	−	2.93306i	0.310470	−	0.126102i	−0.215754	−	0.976448i	$-0.569221\pi$
$541$	7.22136	−	2.93306i	0.310470	−	0.126102i	0.526225	+	0.850346i	$0.323607\pi$
$542$	−1.90585	+	0.774090i	−0.0818633	+	0.0332500i
$543$	−5.58401	+	0.931806i	−0.239633	+	0.0399876i
$544$	−3.14634	−	7.17294i	−0.134898	−	0.307537i
$545$	−1.07055	−	1.45653i	−0.0458571	−	0.0623909i
$546$	−3.08408	−	0.170154i	−0.131987	−	0.00728190i
$547$	4.87237	+	15.5778i	0.208327	+	0.666060i	0.998580	+	0.0532780i	$0.0169670\pi$
$547$	4.87237	+	15.5778i	0.208327	+	0.666060i	−0.790252	+	0.612781i	$0.790051\pi$
$548$	−9.06410	−	11.0059i	−0.387199	−	0.470150i
$549$	5.46614	+	27.9836i	0.233289	+	1.19431i
$550$	6.51998	−	14.8641i	0.278013	−	0.633806i
$551$	13.6970	+	34.3410i	0.583510	+	1.46298i
$552$	−0.813604	−	1.85483i	−0.0346293	−	0.0789468i
$553$	18.9206	−	13.1193i	0.804586	−	0.557888i
$554$	5.82413	−	2.74847i	0.247444	−	0.116771i
$555$	−0.783321	−	0.221502i	−0.0332501	−	0.00940224i
$556$	18.6706	−	2.06646i	0.791808	−	0.0876373i
$557$	37.4474	+	10.5891i	1.58670	+	0.448675i	0.947338	−	0.320235i	$-0.103762\pi$
$557$	37.4474	+	10.5891i	1.58670	+	0.448675i	0.639357	+	0.768910i	$0.279200\pi$
$558$	2.43033	+	29.3297i	0.102884	+	1.24162i
$559$	−29.9607	+	23.3194i	−1.26720	+	0.986304i
$560$	0.188841	+	0.603759i	0.00797999	+	0.0255135i
$561$	4.49965	+	8.89154i	0.189975	+	0.375401i
$562$	4.44589	+	1.52628i	0.187539	+	0.0643821i
$563$	8.81588	+	9.57660i	0.371545	+	0.403606i	0.893279	−	0.449503i	$-0.148399\pi$
$563$	8.81588	+	9.57660i	0.371545	+	0.403606i	−0.521734	+	0.853108i	$0.674715\pi$
$564$	−0.0410379	+	1.48878i	−0.00172801	+	0.0626890i
$565$	6.13430	+	1.37473i	0.258072	+	0.0578353i
$566$	15.9105	−	19.3191i	0.668770	−	0.812042i
$567$	−6.16125	+	8.38268i	−0.258748	+	0.352039i
$568$	2.51304	+	0.563186i	0.105445	+	0.0236308i
$569$	20.3412	−	6.98315i	0.852748	−	0.292749i	0.136539	−	0.990635i	$-0.456402\pi$
$569$	20.3412	−	6.98315i	0.852748	−	0.292749i	0.716209	+	0.697886i	$0.245876\pi$
$570$	0.767748	−	0.0587550i	0.0321574	−	0.00246098i
$571$	−26.9945	−	9.26723i	−1.12969	−	0.387822i	−0.304404	−	0.952543i	$-0.598457\pi$
$571$	−26.9945	−	9.26723i	−1.12969	−	0.387822i	−0.825282	+	0.564721i	$0.808984\pi$
$572$	17.8014	+	10.9425i	0.744316	+	0.457529i
$573$	−1.40169	−	7.17585i	−0.0585563	−	0.299775i
$574$	−2.43183	+	2.11788i	−0.101503	+	0.0883988i
$575$	24.8646	−	7.03105i	1.03693	−	0.293215i
$576$	2.64955	−	1.07616i	0.110398	−	0.0448398i
$577$	−7.74772	+	30.5950i	−0.322542	+	1.27369i	0.569596	+	0.821925i	$0.307100\pi$
$577$	−7.74772	+	30.5950i	−0.322542	+	1.27369i	−0.892138	+	0.451764i	$0.850795\pi$
$578$	−17.8154	+	40.6150i	−0.741023	+	1.68936i
$579$	−5.23263	+	1.17266i	−0.217461	+	0.0487341i
$580$	−3.40857	+	2.09524i	−0.141533	+	0.0870001i
$581$	−7.59046	−	8.24544i	−0.314905	−	0.342078i
$582$	2.89114	+	1.56461i	0.119842	+	0.0648550i
$583$	−19.0976	+	23.1889i	−0.790942	+	0.960388i
$584$	−6.30470	−	2.56075i	−0.260890	−	0.105964i
$585$	8.24657	+	0.912730i	0.340954	+	0.0377368i
$586$	0.863517	+	0.350730i	0.0356716	+	0.0144885i
$587$	17.9364	−	24.4033i	0.740312	−	1.00723i	−0.258834	−	0.965922i	$-0.583338\pi$
$587$	17.9364	−	24.4033i	0.740312	−	1.00723i	0.999146	−	0.0413096i	$-0.0131530\pi$
$588$	1.71311	+	0.927087i	0.0706473	+	0.0382324i
$589$	0.282305	−	44.8571i	0.0116322	−	1.84830i
$590$	0.371818	−	0.201218i	0.0153075	−	0.00828400i
$591$	−1.22294	+	8.81917i	−0.0503048	+	0.362772i
$592$	4.60123	+	0.253857i	0.189109	+	0.0104335i
$593$	1.23099	+	8.87724i	0.0505506	+	0.364544i	0.998882	+	0.0472642i	$0.0150503\pi$
$593$	1.23099	+	8.87724i	0.0505506	+	0.364544i	−0.948332	+	0.317280i	$0.897230\pi$
$594$	−6.74217	+	3.18171i	−0.276635	+	0.130547i
$595$	2.47748	−	4.29112i	0.101567	−	0.175919i
$596$	−9.89424	+	15.1443i	−0.405284	+	0.620333i
$597$	0.0783697	+	0.945781i	0.00320746	+	0.0387082i
$598$	4.56913	+	32.9501i	0.186845	+	1.34743i
$599$	11.6359	+	15.8312i	0.475431	+	0.646847i	0.975723	−	0.219010i	$-0.0702827\pi$
$599$	11.6359	+	15.8312i	0.475431	+	0.646847i	−0.500292	+	0.865857i	$0.666774\pi$
$600$	−0.439192	−	1.73433i	−0.0179299	−	0.0708037i
$601$	−16.1974	−	2.70286i	−0.660705	−	0.110252i	−0.175264	−	0.984522i	$-0.556078\pi$
$601$	−16.1974	−	2.70286i	−0.660705	−	0.110252i	−0.485441	+	0.874269i	$0.661341\pi$
$602$	−8.07794	+	1.81031i	−0.329232	+	0.0737826i
$603$	9.07327	+	5.57732i	0.369492	+	0.227126i
$604$	−0.912398	−	1.80295i	−0.0371250	−	0.0733609i
$605$	−0.0351503	+	0.253485i	−0.00142906	+	0.0103057i
$606$	0.364550	+	0.631419i	0.0148088	+	0.0256496i
$607$	8.39070	+	33.1341i	0.340568	+	1.34487i	0.868544	+	0.495613i	$0.165056\pi$
$607$	8.39070	+	33.1341i	0.340568	+	1.34487i	−0.527976	+	0.849259i	$0.677049\pi$
$608$	−4.16826	+	1.27499i	−0.169045	+	0.0517076i
$609$	1.04568	−	4.12929i	0.0423731	−	0.167327i
$610$	4.52565	−	1.27973i	0.183238	−	0.0518149i
$611$	7.30195	−	23.3456i	0.295405	−	0.944463i
$612$	−20.2572	−	9.55960i	−0.818849	−	0.386424i
$613$	35.6048	−	24.6878i	1.43806	−	0.997131i	0.443144	−	0.896450i	$-0.353863\pi$
$613$	35.6048	−	24.6878i	1.43806	−	0.997131i	0.994919	−	0.100680i	$-0.0321020\pi$
$614$	2.75786	+	19.8883i	0.111298	+	0.802625i
$615$	−0.335209	+	0.260903i	−0.0135169	+	0.0105206i
$616$	2.49199	+	3.81428i	0.100405	+	0.153682i
$617$	−16.9099	+	0.932945i	−0.680767	+	0.0375590i	−0.392171	−	0.919892i	$-0.628276\pi$
$617$	−16.9099	+	0.932945i	−0.680767	+	0.0375590i	−0.288595	+	0.957451i	$0.593188\pi$
$618$	−1.46032	+	1.27179i	−0.0587425	+	0.0511589i
$619$	2.38208	−	9.40662i	0.0957439	−	0.378084i	−0.902917	−	0.429815i	$-0.858579\pi$
$619$	2.38208	−	9.40662i	0.0957439	−	0.378084i	0.998661	+	0.0517304i	$0.0164737\pi$
$620$	4.78828	−	0.799023i	0.192302	−	0.0320895i
$621$	−10.7334	−	5.06520i	−0.430715	−	0.203259i
$622$	−5.17222	−	4.50449i	−0.207387	−	0.180614i
$623$	−2.04803	+	3.54730i	−0.0820527	+	0.142119i
$624$	2.28924	−	0.253373i	0.0916431	−	0.0101431i
$625$	21.5800	−	2.38847i	0.863200	−	0.0955389i
$626$	−5.36669	+	8.21433i	−0.214496	+	0.328311i
$627$	5.20574	−	1.91181i	0.207897	−	0.0763502i
$628$	11.4309	+	17.4962i	0.456141	+	0.698175i
$629$	−22.9462	−	27.8621i	−0.914926	−	1.11093i
$630$	1.54120	+	0.947373i	0.0614029	+	0.0377442i
$631$	4.36793	−	2.68496i	0.173885	−	0.106887i	−0.433996	−	0.900915i	$-0.642897\pi$
$631$	4.36793	−	2.68496i	0.173885	−	0.106887i	0.607881	+	0.794028i	$0.292020\pi$
$632$	−12.3060	+	11.9715i	−0.489508	+	0.476200i
$633$	6.13349	+	5.96676i	0.243785	+	0.237157i
$634$	−11.5977	+	3.98148i	−0.460602	+	0.158125i
$635$	3.10998	+	1.68304i	0.123416	+	0.0667892i
$636$	−0.0912388	+	3.30998i	−0.00361786	+	0.131249i
$637$	−22.9312	−	22.3078i	−0.908566	−	0.883866i
$638$	−19.5170	+	21.2011i	−0.772685	+	0.839359i
$639$	6.47730	−	3.50534i	0.256238	−	0.138669i
$640$	−0.212996	−	0.420891i	−0.00841939	−	0.0166372i
$641$	−11.3366	−	13.7653i	−0.447769	−	0.543696i	0.498579	−	0.866844i	$-0.333855\pi$
$641$	−11.3366	−	13.7653i	−0.447769	−	0.543696i	−0.946348	+	0.323148i	$0.895259\pi$
$642$	2.59558	−	0.143202i	0.102439	−	0.00565173i
$643$	−3.50465	−	9.36051i	−0.138210	−	0.369142i	0.849038	−	0.528332i	$-0.177182\pi$
$643$	−3.50465	−	9.36051i	−0.138210	−	0.369142i	−0.987248	+	0.159189i	$0.949112\pi$
$644$	−2.16522	+	6.92260i	−0.0853217	+	0.272789i
$645$	−1.07557	+	0.179480i	−0.0423504	+	0.00706703i
$646$	29.4596	+	17.2566i	1.15907	+	0.678953i
$647$	−24.4876	−	4.08625i	−0.962706	−	0.160647i	−0.337688	−	0.941258i	$-0.609645\pi$
$647$	−24.4876	−	4.08625i	−0.962706	−	0.160647i	−0.625018	+	0.780611i	$0.714908\pi$
$648$	3.50279	−	6.92170i	0.137603	−	0.271910i
$649$	2.18255	−	2.12322i	0.0856726	−	0.0833435i
$650$	−0.809647	+	29.3725i	−0.0317570	+	1.15208i
$651$	−3.06081	+	4.16438i	−0.119963	+	0.163215i
$652$	−12.3350	−	1.36523i	−0.483075	−	0.0534667i
$653$	26.5110			1.03746			0.518728	−	0.854939i	$-0.326406\pi$
$653$	26.5110			1.03746			0.518728	+	0.854939i	$0.326406\pi$
$654$	−1.43503			−0.0561139
$655$	3.73512	+	0.413403i	0.145943	+	0.0161530i
$656$	1.52869	−	1.85618i	0.0596853	−	0.0724718i
$657$	−18.4060	+	6.31878i	−0.718086	+	0.246519i
$658$	3.61231	−	3.92402i	0.140823	−	0.152974i
$659$	−4.46614	+	22.8641i	−0.173976	+	0.890660i	0.787614	+	0.616169i	$0.211316\pi$
$659$	−4.46614	+	22.8641i	−0.173976	+	0.890660i	−0.961590	+	0.274491i	$0.911491\pi$
$660$	0.300075	+	0.519746i	0.0116804	+	0.0202311i
$661$	22.2148	+	30.2243i	0.864054	+	1.17559i	0.983167	+	0.182707i	$0.0584861\pi$
$661$	22.2148	+	30.2243i	0.864054	+	1.17559i	−0.119113	+	0.992881i	$0.538005\pi$
$662$	−13.5744	+	9.41225i	−0.527583	+	0.365818i
$663$	−13.6043	−	11.8480i	−0.528349	−	0.460140i
$664$	6.59482	+	5.13296i	0.255929	+	0.199197i
$665$	−2.21154	−	1.64701i	−0.0857596	−	0.0638683i
$666$	10.3996	−	8.09437i	0.402978	−	0.313650i
$667$	−45.8057	−	2.52717i	−1.77361	−	0.0978525i
$668$	7.74814	+	13.4202i	0.299784	+	0.519242i
$669$	1.88704	+	1.30844i	0.0729571	+	0.0505874i
$670$	0.793242	−	1.56749i	0.0306456	−	0.0605574i
$671$	28.8571	−	17.7384i	1.11402	−	0.684784i
$672$	0.474992	+	0.163065i	0.0183232	+	0.00629037i
$673$	−16.8380	+	9.11229i	−0.649059	+	0.351253i	−0.766888	−	0.641781i	$-0.778196\pi$
$673$	−16.8380	+	9.11229i	−0.649059	+	0.351253i	0.117829	+	0.993034i	$0.462406\pi$
$674$	−4.99744	+	25.5841i	−0.192494	+	0.985464i
$675$	−8.61516	−	5.97362i	−0.331598	−	0.229925i
$676$	−24.4893	−	4.08655i	−0.941898	−	0.157175i
$677$	−11.5065	+	26.2323i	−0.442233	+	1.00819i	0.543429	+	0.839455i	$0.317126\pi$
$677$	−11.5065	+	26.2323i	−0.442233	+	1.00819i	−0.985662	+	0.168734i	$0.946032\pi$
$678$	3.76346	−	3.27760i	0.144535	−	0.125875i
$679$	−4.12786	−	11.0250i	−0.158413	−	0.423102i
$680$	−1.29553	+	3.46021i	−0.0496814	+	0.132693i
$681$	−2.48347	−	2.16286i	−0.0951667	−	0.0828808i
$682$	31.6194	−	14.9215i	1.21077	−	0.571375i
$683$	0.743115	+	8.96806i	0.0284345	+	0.343153i	0.995921	+	0.0902304i	$0.0287603\pi$
$683$	0.743115	+	8.96806i	0.0284345	+	0.343153i	−0.967486	+	0.252923i	$0.918608\pi$
$684$	−6.59451	+	10.5782i	−0.252147	+	0.404469i
$685$	−0.555403	+	6.70272i	−0.0212209	+	0.256098i
$686$	−5.73751	−	15.3242i	−0.219059	−	0.585081i
$687$	6.63755	−	1.87692i	0.253238	−	0.0716089i
$688$	5.71918	−	2.32293i	0.218042	−	0.0885609i
$689$	16.2343	−	51.9038i	0.618476	−	1.97738i
$690$	−0.335008	+	0.894766i	−0.0127535	+	0.0340632i
$691$	−1.83608	−	1.42908i	−0.0698479	−	0.0543648i	0.578687	−	0.815550i	$-0.303565\pi$
$691$	−1.83608	−	1.42908i	−0.0698479	−	0.0543648i	−0.648535	+	0.761185i	$0.724618\pi$
$692$	2.89955	−	4.43809i	0.110224	−	0.168711i
$693$	12.5379	+	3.54539i	0.476277	+	0.134678i
$694$	−9.74586	+	16.8803i	−0.369948	+	0.640768i
$695$	−6.99256	−	5.44253i	−0.265243	−	0.206447i
$696$	−0.262297	+	3.16546i	−0.00994236	+	0.119986i
$697$	−18.8061	+	1.03756i	−0.712334	+	0.0393005i
$698$	3.41665	+	17.4913i	0.129322	+	0.662057i
$699$	2.56642	−	0.575147i	0.0970708	−	0.0217541i
$700$	−2.89294	+	5.71660i	−0.109343	+	0.216067i
$701$	0.284807	+	10.3323i	0.0107570	+	0.390244i	0.985770	+	0.168098i	$0.0537624\pi$
$701$	0.284807	+	10.3323i	0.0107570	+	0.390244i	−0.975013	+	0.222146i	$0.928694\pi$
$702$	9.14082	−	9.92958i	0.344998	−	0.374768i
$703$	−16.8848	+	10.8804i	−0.636822	+	0.410362i
$704$	−2.30101	−	2.49957i	−0.0867228	−	0.0942060i
$705$	0.503574	−	0.489885i	0.0189657	−	0.0184501i
$706$	0.309149	+	11.2154i	0.0116350	+	0.422096i
$707$	0.500557	−	2.56257i	0.0188254	−	0.0963755i
$708$	0.0460995	−	0.332445i	0.00173252	−	0.0124941i
$709$	4.11297	+	13.1499i	0.154466	+	0.493855i	0.999142	−	0.0414234i	$-0.0131893\pi$
$709$	4.11297	+	13.1499i	0.154466	+	0.493855i	−0.844676	+	0.535278i	$0.820207\pi$
$710$	−0.664458	−	1.01703i	−0.0249367	−	0.0381684i
$711$	−4.05445	+	48.9300i	−0.152054	+	1.83502i
$712$	1.07096	−	2.86042i	0.0401361	−	0.107199i
$713$	50.3372	+	23.7547i	1.88514	+	0.889621i
$714$	−1.58010	−	3.60227i	−0.0591339	−	0.134812i
$715$	−2.41971	−	9.55521i	−0.0904920	−	0.357345i
$716$	1.90689	+	1.32221i	0.0712638	+	0.0494132i
$717$	0.305155	+	11.0704i	0.0113962	+	0.413433i
$718$	14.5874	+	14.1908i	0.544397	+	0.529597i
$719$	4.80390	+	1.07658i	0.179155	+	0.0401496i	0.307335	−	0.951601i	$-0.400563\pi$
$719$	4.80390	+	1.07658i	0.179155	+	0.0401496i	−0.128180	+	0.991751i	$0.540914\pi$
$720$	−1.24984	−	0.507640i	−0.0465787	−	0.0189186i
$721$	6.93482			0.258266
$722$	11.4443	−	15.1667i	0.425912	−	0.564446i
$723$	0.944914			0.0351417
$724$	−14.0063	−	5.68887i	−0.520540	−	0.211425i
$725$	−39.5414	−	8.86143i	−1.46853	−	0.329105i
$726$	0.145621	+	0.141663i	0.00540451	+	0.00525759i
$727$	−0.302114	−	10.9601i	−0.0112048	−	0.406489i	−0.984343	−	0.176265i	$-0.943598\pi$
$727$	−0.302114	−	10.9601i	−0.0112048	−	0.406489i	0.973138	−	0.230223i	$-0.0739456\pi$
$728$	−6.77815	−	4.69986i	−0.251215	−	0.174189i
$729$	−4.84085	−	19.1161i	−0.179291	−	0.708003i
$730$	1.28943	+	2.93961i	0.0477241	+	0.108800i
$731$	−43.7260	−	20.6348i	−1.61727	−	0.763206i
$732$	1.30916	−	3.49661i	0.0483879	−	0.129238i
$733$	−0.375967	+	4.53725i	−0.0138867	+	0.167587i	0.986112	+	0.166081i	$0.0531112\pi$
$733$	−0.375967	+	4.53725i	−0.0138867	+	0.167587i	−0.999999	+	0.00150667i	$0.999520\pi$
$734$	−18.2222	−	27.8912i	−0.672594	−	1.02948i
$735$	−0.274289	−	0.876950i	−0.0101173	−	0.0323468i
$736$	0.742894	−	5.35736i	0.0273834	−	0.197475i
$737$	2.42567	−	12.4181i	0.0893507	−	0.457425i
$738$	−0.189483	−	6.87410i	−0.00697498	−	0.253039i
$739$	4.45993	−	4.33868i	0.164061	−	0.159601i	−0.610685	−	0.791874i	$-0.709106\pi$
$739$	4.45993	−	4.33868i	0.164061	−	0.159601i	0.774746	+	0.632273i	$0.217878\pi$
$740$	−1.47226	−	1.59930i	−0.0541213	−	0.0587914i
$741$	−7.42896	+	6.75296i	−0.272910	+	0.248076i
$742$	8.03119	−	8.72419i	0.294834	−	0.320275i
$743$	−1.30350	−	47.2887i	−0.0478209	−	1.73485i	−0.520711	−	0.853733i	$-0.674333\pi$
$743$	−1.30350	−	47.2887i	−0.0478209	−	1.73485i	0.472890	−	0.881121i	$-0.343211\pi$
$744$	1.74013	−	3.43859i	0.0637963	−	0.126065i
$745$	8.32676	−	1.86607i	0.305069	−	0.0683675i
$746$	−0.706971	−	3.61930i	−0.0258841	−	0.132512i
$747$	23.8627	−	1.31654i	0.873089	−	0.0481697i
$748$	−2.19751	+	26.5200i	−0.0803489	+	0.969667i
$749$	−7.34631	−	5.71786i	−0.268428	−	0.208926i
$750$	−0.863589	+	1.49578i	−0.0315338	+	0.0546182i
$751$	−21.9121	−	6.19616i	−0.799585	−	0.226101i	−0.152285	−	0.988337i	$-0.548663\pi$
$751$	−21.9121	−	6.19616i	−0.799585	−	0.226101i	−0.647300	+	0.762235i	$0.724102\pi$
$752$	−2.17527	+	3.32949i	−0.0793238	+	0.121414i
$753$	5.99205	+	4.66380i	0.218362	+	0.169958i
$754$	18.2919	−	48.8554i	0.666151	−	1.77921i
$755$	−0.284539	+	0.909721i	−0.0103554	+	0.0331081i
$756$	2.72648	−	1.10740i	0.0991611	−	0.0402758i
$757$	44.9290	−	12.7047i	1.63297	−	0.461761i	0.672492	−	0.740105i	$-0.265224\pi$
$757$	44.9290	−	12.7047i	1.63297	−	0.461761i	0.960482	+	0.278344i	$0.0897854\pi$
$758$	2.94068	+	7.85422i	0.106810	+	0.285278i
$759$	−0.568248	+	6.85773i	−0.0206261	+	0.248920i
$760$	1.82874	+	0.939953i	0.0663354	+	0.0340957i
$761$	−1.28249	−	15.4773i	−0.0464901	−	0.561052i	−0.979533	−	0.201286i	$-0.935488\pi$
$761$	−1.28249	−	15.4773i	−0.0464901	−	0.561052i	0.933042	−	0.359766i	$-0.117144\pi$
$762$	2.53877	−	1.19807i	0.0919699	−	0.0434016i
$763$	3.87537	+	3.37506i	0.140298	+	0.122185i
$764$	6.84595	−	18.2847i	0.247678	−	0.661518i
$765$	3.70492	+	9.89539i	0.133952	+	0.357769i
$766$	−15.0229	+	13.0834i	−0.542798	+	0.472723i
$767$	−2.21427	+	5.04802i	−0.0799525	+	0.182273i
$768$	−0.369373	−	0.0616375i	−0.0133286	−	0.00222415i
$769$	0.858372	+	0.595182i	0.0309537	+	0.0214628i	0.585184	−	0.810901i	$-0.301022\pi$
$769$	0.858372	+	0.595182i	0.0309537	+	0.0214628i	−0.554230	+	0.832363i	$0.686987\pi$
$770$	0.412028	−	2.10936i	0.0148485	−	0.0760159i
$771$	7.77379	−	4.20697i	0.279966	−	0.151510i
$772$	−13.5437	−	4.64957i	−0.487450	−	0.167342i
$773$	26.1301	−	16.0621i	0.939833	−	0.577713i	0.0331152	−	0.999452i	$-0.489457\pi$
$773$	26.1301	−	16.0621i	0.939833	−	0.577713i	0.906718	+	0.421739i	$0.138580\pi$
$774$	7.97097	−	15.7511i	0.286511	−	0.566160i
$775$	40.4033	+	28.0150i	1.45133	+	1.00633i
$776$	4.38921	+	7.60234i	0.157564	+	0.272908i
$777$	2.31075	+	0.127488i	0.0828978	+	0.00457360i
$778$	−1.76539	+	1.37406i	−0.0632922	+	0.0492623i
$779$	−0.643260	+	10.4618i	−0.0230472	+	0.374834i
$780$	−0.857375	−	0.667322i	−0.0306990	−	0.0238940i
$781$	−6.59817	−	5.74635i	−0.236101	−	0.205621i
$782$	−34.8137	+	24.1393i	−1.24494	+	0.863219i
$783$	11.0229	+	14.9972i	0.393927	+	0.535957i
$784$	2.60077	+	4.50467i	0.0928847	+	0.160881i
$785$	1.88999	−	9.67569i	0.0674566	−	0.345340i
$786$	2.02054	−	2.19489i	0.0720702	−	0.0782891i
$787$	18.9976	−	6.52189i	0.677192	−	0.232480i	0.0354160	−	0.999373i	$-0.488724\pi$
$787$	18.9976	−	6.52189i	0.677192	−	0.232480i	0.641776	+	0.766892i	$0.278198\pi$
$788$	−15.1148	+	18.3529i	−0.538443	+	0.653795i
$789$	−0.664052	−	0.0734973i	−0.0236409	−	0.00261657i
$790$	8.09862			0.288136
$791$	−17.8721			−0.635458
$792$	−9.65687	−	1.06882i	−0.343142	−	0.0379789i
$793$	−36.3166	+	49.4105i	−1.28964	+	1.75462i
$794$	1.08309	−	39.2924i	0.0384374	−	1.39444i
$795$	1.11959	−	1.08915i	0.0397076	−	0.0386282i
$796$	−1.14429	+	2.26118i	−0.0405584	+	0.0801455i
$797$	3.14819	+	0.525339i	0.111514	+	0.0186085i	0.220089	−	0.975480i	$-0.429365\pi$
$797$	3.14819	+	0.525339i	0.111514	+	0.0186085i	−0.108574	+	0.994088i	$0.534629\pi$
$798$	−2.09331	+	0.640303i	−0.0741025	+	0.0226665i
$799$	30.7264	−	5.12733i	1.08702	−	0.181392i
$800$	1.42615	−	4.55965i	0.0504220	−	0.161208i
$801$	−3.06271	−	8.18012i	−0.108215	−	0.289030i
$802$	17.4294	−	0.961607i	0.615454	−	0.0339555i
$803$	14.6974	+	17.8461i	0.518660	+	0.629774i
$804$	−0.629730	−	1.24438i	−0.0222089	−	0.0438859i
$805$	3.00913	−	1.62846i	0.106058	−	0.0573956i
$806$	−42.8685	+	46.5676i	−1.50998	+	1.64028i
$807$	−2.27374	−	2.21192i	−0.0800393	−	0.0778634i
$808$	−0.0536473	+	1.94622i	−0.00188730	+	0.0684679i
$809$	0.275787	+	0.149248i	0.00969616	+	0.00524730i	0.480788	−	0.876837i	$-0.340351\pi$
$809$	0.275787	+	0.149248i	0.00969616	+	0.00524730i	−0.471092	+	0.882084i	$0.656140\pi$
$810$	−3.46108	+	1.18819i	−0.121610	+	0.0417488i
$811$	15.9754	+	15.5411i	0.560972	+	0.545722i	0.922179	−	0.386763i	$-0.126407\pi$
$811$	15.9754	+	15.5411i	0.560972	+	0.545722i	−0.361207	+	0.932486i	$0.617635\pi$
$812$	8.15325	−	7.93160i	0.286123	−	0.278345i
$813$	0.656257	−	0.403400i	0.0230160	−	0.0141479i
$814$	−13.3377	−	8.19868i	−0.467488	−	0.287364i
$815$	3.72161	+	4.51891i	0.130362	+	0.158290i
$816$	1.60430	+	2.45556i	0.0561616	+	0.0859617i
$817$	−14.2345	+	22.8336i	−0.498003	+	0.798847i
$818$	6.92449	−	10.5987i	0.242109	−	0.370576i
$819$	−23.4446	+	2.59485i	−0.819221	+	0.0906713i
$820$	−1.12742	+	0.124783i	−0.0393714	+	0.00435762i
$821$	−2.99167	+	5.18172i	−0.104410	+	0.180843i	−0.913497	−	0.406846i	$-0.866629\pi$
$821$	−2.99167	+	5.18172i	−0.104410	+	0.180843i	0.809087	+	0.587689i	$0.199962\pi$
$822$	4.02641	+	3.50661i	0.140437	+	0.122307i
$823$	−12.6612	−	5.97496i	−0.441341	−	0.208274i	0.193206	−	0.981158i	$-0.438112\pi$
$823$	−12.6612	−	5.97496i	−0.441341	−	0.208274i	−0.634547	+	0.772884i	$0.718813\pi$
$824$	−5.10060	+	0.851139i	−0.177688	+	0.0296508i
$825$	−1.49212	+	5.89226i	−0.0519490	+	0.205142i
$826$	−0.906378	+	0.789365i	−0.0315369	+	0.0274655i
$827$	−45.0308	+	2.48442i	−1.56588	+	0.0863918i	−0.817125	−	0.576460i	$-0.804434\pi$
$827$	−45.0308	+	2.48442i	−1.56588	+	0.0863918i	−0.748751	+	0.662852i	$0.769346\pi$
$828$	−8.45986	−	12.9488i	−0.294000	−	0.450001i
$829$	32.1036	−	24.9872i	1.11500	−	0.867841i	0.122794	−	0.992432i	$-0.460814\pi$
$829$	32.1036	−	24.9872i	1.11500	−	0.867841i	0.992208	+	0.124591i	$0.0397618\pi$
$830$	−0.541464	−	3.90475i	−0.0187945	−	0.135536i
$831$	−1.98187	+	1.37420i	−0.0687503	+	0.0476704i
$832$	5.56220	+	2.62486i	0.192835	+	0.0910008i
$833$	12.1621	−	38.8843i	0.421390	−	1.34726i
$834$	−6.76904	+	1.91410i	−0.234393	+	0.0662799i
$835$	1.79446	−	7.08616i	0.0620999	−	0.245227i
$836$	14.5162	+	2.93046i	0.502053	+	0.101352i
$837$	−5.54368	−	21.8915i	−0.191618	−	0.756681i
$838$	−1.47509	−	2.55494i	−0.0509563	−	0.0882589i
$839$	1.29895	−	9.36738i	0.0448449	−	0.323398i	−0.954812	−	0.297210i	$-0.903944\pi$
$839$	1.29895	−	9.36738i	0.0448449	−	0.323398i	0.999657	−	0.0261880i	$-0.00833684\pi$
$840$	−0.106967	−	0.211373i	−0.00369071	−	0.00729305i
$841$	36.5837	+	22.4879i	1.26151	+	0.775445i
$842$	−19.0936	+	4.27898i	−0.658009	+	0.147463i
$843$	−1.73627	−	0.289732i	−0.0598003	−	0.00997890i
$844$	5.60941	+	22.1511i	0.193084	+	0.762471i
$845$	6.93611	+	9.43692i	0.238610	+	0.324640i
$846$	1.56220	+	11.2658i	0.0537095	+	0.387325i
$847$	−0.0600800	−	0.725058i	−0.00206437	−	0.0249133i
$848$	−4.83622	+	7.40239i	−0.166077	+	0.254199i
$849$	−4.68615	+	8.11664i	−0.160828	+	0.278562i
$850$	−33.8414	+	15.9701i	−1.16075	+	0.547771i
$851$	−3.42342	−	24.6879i	−0.117353	−	0.846291i
$852$	−0.962964	−	0.0531282i	−0.0329906	−	0.00182014i
$853$	−6.48279	+	46.7505i	−0.221966	+	1.60071i	0.472600	+	0.881277i	$0.343315\pi$
$853$	−6.48279	+	46.7505i	−0.221966	+	1.60071i	−0.694567	+	0.719428i	$0.744404\pi$
$854$	−11.7592	+	6.36376i	−0.402391	+	0.217763i
$855$	5.70918	−	1.40759i	0.195250	−	0.0481385i
$856$	6.10503	+	3.30387i	0.208665	+	0.112924i
$857$	−20.0331	+	27.2560i	−0.684317	+	0.931047i	−0.999840	−	0.0178707i	$-0.994311\pi$
$857$	−20.0331	+	27.2560i	−0.684317	+	0.931047i	0.315523	+	0.948918i	$0.397820\pi$
$858$	−7.24984	−	2.94463i	−0.247506	−	0.100528i
$859$	−34.3301	−	3.79965i	−1.17133	−	0.129642i	−0.496781	−	0.867876i	$-0.665485\pi$
$859$	−34.3301	−	3.79965i	−1.17133	−	0.129642i	−0.674545	+	0.738233i	$0.735660\pi$
$860$	−2.69783	−	1.09576i	−0.0919952	−	0.0373652i
$861$	0.767713	−	0.932182i	0.0261636	−	0.0317687i
$862$	−18.6217	−	10.0776i	−0.634258	−	0.343243i
$863$	−6.80557	−	7.39282i	−0.231664	−	0.251655i	0.609052	−	0.793130i	$-0.291550\pi$
$863$	−6.80557	−	7.39282i	−0.231664	−	0.251655i	−0.840716	+	0.541476i	$0.817866\pi$
$864$	−1.86942	+	1.14913i	−0.0635991	+	0.0390942i
$865$	−2.44019	+	0.546860i	−0.0829691	+	0.0185938i
$866$	−2.05003	+	4.67359i	−0.0696627	+	0.158815i
$867$	4.07712	−	16.1002i	0.138466	−	0.546791i
$868$	−12.7866	+	5.19347i	−0.434006	+	0.176278i
$869$	56.1276	−	15.8714i	1.90400	−	0.538400i
$870$	1.12989	−	0.984021i	0.0383068	−	0.0333615i
$871$	4.39125	+	22.4807i	0.148792	+	0.761731i
$872$	−3.26459	−	2.00674i	−0.110553	−	0.0679567i
$873$	23.7440	+	8.15133i	0.803613	+	0.275881i
$874$	11.0901	+	20.8044i	0.375127	+	0.703718i
$875$	5.85012	−	2.00835i	0.197770	−	0.0678946i
$876$	2.48662	+	0.557266i	0.0840153	+	0.0188283i
$877$	17.3120	−	23.5538i	0.584584	−	0.795355i	−0.408501	−	0.912758i	$-0.633948\pi$
$877$	17.3120	−	23.5538i	0.584584	−	0.795355i	0.993084	+	0.117403i	$0.0374570\pi$
$878$	17.8303	−	21.6501i	0.601742	−	0.730655i
$879$	−0.340578	−	0.0763254i	−0.0114874	−	0.00257439i
$880$	−0.0441592	+	1.60201i	−0.00148861	+	0.0540038i
$881$	−33.9847	−	36.9173i	−1.14497	−	1.24377i	−0.965611	−	0.259991i	$-0.916280\pi$
$881$	−33.9847	−	36.9173i	−1.14497	−	1.24377i	−0.179364	−	0.983783i	$-0.557404\pi$
$882$	14.0692	+	4.82996i	0.473735	+	0.162633i
$883$	11.5246	+	22.7732i	0.387832	+	0.766378i	0.999698	−	0.0245843i	$-0.00782621\pi$
$883$	11.5246	+	22.7732i	0.387832	+	0.766378i	−0.611865	+	0.790962i	$0.709581\pi$
$884$	−14.3807	−	45.9778i	−0.483677	−	1.54640i
$885$	−0.124937	+	0.0972423i	−0.00419971	+	0.00326876i
$886$	−1.73502	−	20.9386i	−0.0582892	−	0.703447i
$887$	25.6836	+	7.26264i	0.862372	+	0.243856i	0.674443	−	0.738327i	$-0.264384\pi$
$887$	25.6836	+	7.26264i	0.862372	+	0.243856i	0.187929	+	0.982183i	$0.439822\pi$
$888$	−1.71522	+	0.189840i	−0.0575589	+	0.00637062i
$889$	−9.67386	−	2.73551i	−0.324451	−	0.0917460i
$890$	−1.30298	+	0.614890i	−0.0436759	+	0.0206112i
$891$	−21.6585	+	15.0177i	−0.725588	+	0.503111i
$892$	2.46317	+	5.61546i	0.0824730	+	0.188019i
$893$	−0.846036	−	17.3151i	−0.0283115	−	0.579428i
$894$	2.72121	−	6.20374i	0.0910110	−	0.207484i
$895$	−0.209845	−	1.07429i	−0.00701433	−	0.0359095i
$896$	0.852547	+	1.03519i	0.0284816	+	0.0345833i
$897$	−3.71868	−	11.8893i	−0.124163	−	0.396971i
$898$	−25.3966	−	1.40117i	−0.847497	−	0.0467577i
$899$	−51.6952	−	70.3339i	−1.72413	−	2.34577i
$900$	−5.48815	−	12.5117i	−0.182938	−	0.417058i
$901$	68.3133	−	11.3995i	2.27585	−	0.379772i
$902$	−7.56909	+	3.07430i	−0.252023	+	0.102363i
$903$	2.87219	−	1.16658i	0.0955805	−	0.0388214i
$904$	13.1450	−	2.19352i	0.437197	−	0.0729553i
$905$	2.86456	+	6.53054i	0.0952213	+	0.217083i
$906$	0.448145	+	0.609723i	0.0148886	+	0.0202567i
$907$	−47.8348	−	2.63912i	−1.58833	−	0.0876305i	−0.760775	−	0.649016i	$-0.775181\pi$
$907$	−47.8348	−	2.63912i	−1.58833	−	0.0876305i	−0.827554	+	0.561386i	$0.810268\pi$
$908$	−2.62520	−	8.39324i	−0.0871204	−	0.278539i
$909$	3.53962	+	4.29792i	0.117402	+	0.142553i
$910$	0.745905	+	3.81862i	0.0247265	+	0.126586i
$911$	−2.55611	+	5.82735i	−0.0846878	+	0.193069i	−0.953015	−	0.302923i	$-0.902037\pi$
$911$	−2.55611	+	5.82735i	−0.0846878	+	0.193069i	0.868327	+	0.495992i	$0.165195\pi$
$912$	1.46106	−	0.727868i	0.0483804	−	0.0241021i
$913$	−11.4050	−	26.0008i	−0.377451	−	0.860501i
$914$	15.1759	−	10.5228i	0.501975	−	0.348062i
$915$	−1.59278	+	0.751649i	−0.0526555	+	0.0248487i
$916$	17.7247	+	5.01206i	0.585640	+	0.165603i
$917$	−10.6188	+	1.17529i	−0.350663	+	0.0388114i
$918$	16.5392	+	4.67684i	0.545875	+	0.154359i
$919$	−0.850656	−	10.2659i	−0.0280605	−	0.338640i	−0.996126	−	0.0879415i	$-0.971971\pi$
$919$	−0.850656	−	10.2659i	−0.0280605	−	0.338640i	0.968065	−	0.250699i	$-0.0806604\pi$
$920$	−2.01336	+	1.56706i	−0.0663785	+	0.0516645i
$921$	−2.24454	−	7.17621i	−0.0739602	−	0.236464i
$922$	4.13153	+	8.16413i	0.136065	+	0.268871i
$923$	14.9815	+	5.14315i	0.493121	+	0.169289i
$924$	−1.15558	−	1.25529i	−0.0380157	−	0.0412960i
$925$	0.606629	−	22.0074i	0.0199458	−	0.723598i
$926$	−12.2308	−	2.74098i	−0.401928	−	0.0900742i
$927$	−9.40121	+	11.4153i	−0.308776	+	0.374926i
$928$	−5.02328	+	6.83442i	−0.164897	+	0.224351i
$929$	−39.7628	−	8.91105i	−1.30457	−	0.292362i	−0.489645	−	0.871922i	$-0.662874\pi$
$929$	−39.7628	−	8.91105i	−1.30457	−	0.292362i	−0.814930	+	0.579560i	$0.803224\pi$
$930$	−1.71941	+	0.590275i	−0.0563818	+	0.0193559i
$931$	−20.7056	−	9.23813i	−0.678599	−	0.302767i
$932$	6.64272	+	2.28045i	0.217589	+	0.0746985i
$933$	2.18813	+	1.34504i	0.0716360	+	0.0440345i
$934$	0.739247	+	3.78453i	0.0241889	+	0.123834i
$935$	9.46613	−	8.24406i	0.309576	−	0.269610i
$936$	16.9252	−	4.78598i	0.553216	−	0.156435i
$937$	25.4114	−	10.3212i	0.830155	−	0.337180i	0.0786457	−	0.996903i	$-0.474940\pi$
$937$	25.4114	−	10.3212i	0.830155	−	0.337180i	0.751509	+	0.659723i	$0.229326\pi$
$938$	−1.22606	+	4.84159i	−0.0400322	+	0.158084i
$939$	1.47600	−	3.36494i	0.0481675	−	0.109811i
$940$	1.83065	−	0.410259i	0.0597093	−	0.0133812i
$941$	9.66958	−	5.94387i	0.315219	−	0.193765i	−0.357023	−	0.934095i	$-0.616208\pi$
$941$	9.66958	−	5.94387i	0.315219	−	0.193765i	0.672243	+	0.740331i	$0.265331\pi$
$942$	−5.30067	−	5.75807i	−0.172705	−	0.187608i
$943$	−11.4383	−	6.19008i	−0.372481	−	0.201577i
$944$	0.569764	−	0.691826i	0.0185442	−	0.0225170i
$945$	−1.28612	−	0.522378i	−0.0418376	−	0.0169930i
$946$	−20.8448	−	2.30710i	−0.677722	−	0.0750103i
$947$	42.4415	+	17.2382i	1.37916	+	0.560167i	0.940901	−	0.338681i	$-0.109981\pi$
$947$	42.4415	+	17.2382i	1.37916	+	0.560167i	0.438261	+	0.898848i	$0.355595\pi$
$948$	3.80762	−	5.18046i	0.123666	−	0.168254i
$949$	−36.8088	−	19.9199i	−1.19486	−	0.646627i
$950$	6.63764	+	19.7384i	0.215353	+	0.640398i
$951$	4.03846	−	2.18550i	0.130956	−	0.0708698i
$952$	1.44278	−	10.4046i	0.0467607	−	0.337213i
$953$	−9.06390	−	0.500069i	−0.293608	−	0.0161988i	−0.0923152	−	0.995730i	$-0.529427\pi$
$953$	−9.06390	−	0.500069i	−0.293608	−	0.0161988i	−0.201293	+	0.979531i	$0.564514\pi$
$954$	3.47321	+	25.0469i	0.112449	+	0.810925i
$955$	−8.32906	+	3.93058i	−0.269522	+	0.127190i
$956$	−14.7867	+	25.6113i	−0.478235	+	0.828328i
$957$	5.90227	−	9.03409i	0.190793	−	0.292031i
$958$	−1.28238	−	15.4761i	−0.0414319	−	0.500009i
$959$	−2.62631	−	18.9396i	−0.0848080	−	0.611591i
$960$	0.104617	+	0.142337i	0.00337651	+	0.00459391i
$961$	18.3886	+	72.6151i	0.593182	+	2.34242i
$962$	27.9561	+	4.66505i	0.901340	+	0.150407i
$963$	19.3711	−	4.34116i	0.624225	−	0.139892i
$964$	2.14962	+	1.32137i	0.0692345	+	0.0425583i
$965$	3.05001	+	6.02699i	0.0981834	+	0.194016i
$966$	0.373083	−	2.69048i	0.0120038	−	0.0865649i
$967$	−3.22110	−	5.57911i	−0.103584	−	0.179412i	0.809575	−	0.587016i	$-0.199698\pi$
$967$	−3.22110	−	5.57911i	−0.103584	−	0.179412i	−0.913159	+	0.407604i	$0.866364\pi$
$968$	0.133178	+	0.525910i	0.00428052	+	0.0169034i
$969$	−11.9452	−	4.55832i	−0.383737	−	0.146434i
$970$	1.01654	−	4.01421i	0.0326390	−	0.128889i
$971$	−16.0409	+	4.53594i	−0.514778	+	0.145565i	−0.519578	−	0.854423i	$-0.673911\pi$
$971$	−16.0409	+	4.53594i	−0.514778	+	0.145565i	0.00480007	+	0.999988i	$0.498472\pi$
$972$	−2.83235	+	9.05554i	−0.0908478	+	0.290457i
$973$	22.7820	+	10.7511i	0.730357	+	0.344664i
$974$	5.75881	−	3.99307i	0.184524	−	0.127946i
$975$	−1.51138	−	10.8993i	−0.0484030	−	0.349057i
$976$	7.86790	−	6.12383i	0.251845	−	0.196019i
$977$	7.80953	+	11.9534i	0.249849	+	0.382423i	0.939962	−	0.341279i	$-0.110860\pi$
$977$	7.80953	+	11.9534i	0.249849	+	0.382423i	−0.690113	+	0.723702i	$0.742439\pi$
$978$	4.64036	−	0.256016i	0.148382	−	0.00818648i
$979$	−7.82527	+	6.81504i	−0.250097	+	0.217810i
$980$	0.602336	−	2.37857i	0.0192409	−	0.0759806i
$981$	−10.8093	+	1.80375i	−0.345114	+	0.0575893i
$982$	10.6536	+	5.02756i	0.339970	+	0.160436i
$983$	45.3306	+	39.4785i	1.44582	+	1.25917i	0.909854	+	0.414929i	$0.136194\pi$
$983$	45.3306	+	39.4785i	1.44582	+	1.25917i	0.535968	+	0.844238i	$0.319947\pi$
$984$	−0.450246	+	0.779849i	−0.0143533	+	0.0248607i
$985$	11.1473	−	1.23379i	0.355184	−	0.0393117i
$986$	66.0326	−	7.30849i	2.10291	−	0.232750i
$987$	−1.09243	+	1.67208i	−0.0347723	+	0.0532229i
$988$	−26.3437	+	4.97391i	−0.838105	+	0.158241i
$989$	−18.2610	−	27.9505i	−0.580665	−	0.888774i
$990$	2.91360	+	3.53779i	0.0926002	+	0.112438i
$991$	−19.9249	−	12.2478i	−0.632935	−	0.389063i	0.169733	−	0.985490i	$-0.445709\pi$
$991$	−19.9249	−	12.2478i	−0.632935	−	0.389063i	−0.802668	+	0.596427i	$0.796587\pi$
$992$	8.76721	−	5.38918i	0.278359	−	0.171107i
$993$	4.43386	−	4.31332i	0.140704	−	0.136879i
$994$	2.47559	+	2.40829i	0.0785209	+	0.0763863i
$995$	1.13067	−	0.388159i	0.0358446	−	0.0123055i
$996$	−2.75233	−	1.48949i	−0.0872110	−	0.0471962i
$997$	−0.624697	+	22.6628i	−0.0197843	+	0.717739i	0.923089	+	0.384587i	$0.125656\pi$
$997$	−0.624697	+	22.6628i	−0.0197843	+	0.717739i	−0.942873	+	0.333152i	$0.891888\pi$
$998$	25.3569	+	24.6675i	0.802657	+	0.780837i
$999$	−6.84877	+	7.43975i	−0.216685	+	0.235383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.501.9	yes	612
361.49	even	57	inner	722.2.i.b.49.9	✓	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.49.9	✓	612	361.49	even	57	inner
722.2.i.b.501.9	yes	612	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926494 - 0.376309i) q^{2} +(0.365417 + 0.0818918i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0129978 - 0.471537i) q^{5} +(-0.307740 - 0.213382i) q^{6} +(0.329212 + 1.30003i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.58625 - 1.22048i) q^{9} +O(q^{10})\)	\(q+(-0.926494 - 0.376309i) q^{2} +(0.365417 + 0.0818918i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0129978 - 0.471537i) q^{5} +(-0.307740 - 0.213382i) q^{6} +(0.329212 + 1.30003i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.58625 - 1.22048i) q^{9} +(-0.165401 + 0.441767i) q^{10} +(-0.280557 + 3.38582i) q^{11} +(0.204821 + 0.313503i) q^{12} +(-1.83600 - 5.87002i) q^{13} +(0.184200 - 1.32836i) q^{14} +(0.0338654 - 0.173372i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(5.61431 - 5.46169i) q^{17} +(1.93687 + 2.10400i) q^{18} +(-2.65559 - 3.45656i) q^{19} +(0.319485 - 0.347053i) q^{20} +(0.0138379 + 0.502012i) q^{21} +(1.53405 - 3.03137i) q^{22} +(5.27771 - 1.18276i) q^{23} +(-0.0717919 - 0.367535i) q^{24} +(4.77023 - 0.263181i) q^{25} +(-0.507900 + 6.12944i) q^{26} +(-1.73166 - 1.34781i) q^{27} +(-0.670533 + 1.16140i) q^{28} +(-8.16186 - 2.30795i) q^{29} +(-0.0966176 + 0.147884i) q^{30} +(8.12114 + 6.32094i) q^{31} +(0.350638 - 0.936511i) q^{32} +(-0.379792 + 1.21426i) q^{33} +(-7.25691 + 2.94750i) q^{34} +(0.608733 - 0.172133i) q^{35} +(-1.00274 - 2.67820i) q^{36} +(0.380544 - 4.59249i) q^{37} +(1.15965 + 4.20181i) q^{38} +(-0.190199 - 2.29536i) q^{39} +(-0.426600 + 0.201317i) q^{40} +(-1.81336 - 1.57925i) q^{41} +(0.176091 - 0.470319i) q^{42} +(-2.16446 - 5.78102i) q^{43} +(-2.56202 + 2.23127i) q^{44} +(-0.541886 + 1.23538i) q^{45} +(-5.33486 - 0.890230i) q^{46} +(3.26829 + 2.26618i) q^{47} +(-0.0717919 + 0.367535i) q^{48} +(4.57462 - 2.47566i) q^{49} +(-4.51863 - 1.55125i) q^{50} +(2.49883 - 1.53603i) q^{51} +(2.77713 - 5.48776i) q^{52} +(7.26632 + 5.03836i) q^{53} +(1.09718 + 1.90038i) q^{54} +(1.60019 + 0.0882848i) q^{55} +(1.05829 - 0.823700i) q^{56} +(-0.687333 - 1.48056i) q^{57} +(6.69341 + 5.20969i) q^{58} +(-0.675864 - 0.588610i) q^{59} +(0.145166 - 0.100656i) q^{60} +(-5.90471 - 8.03365i) q^{61} +(-5.14556 - 8.91237i) q^{62} +(0.735236 - 3.76400i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-2.74407 + 0.942039i) q^{65} +(0.808813 - 0.982087i) q^{66} +(-3.70161 - 0.409695i) q^{67} +7.83266 q^{68} +2.02542 q^{69} +(-0.628763 - 0.0695914i) q^{70} +(-1.52523 + 2.07515i) q^{71} +(-0.0787989 + 2.85868i) q^{72} +(4.87763 - 4.74503i) q^{73} +(-2.08077 + 4.11171i) q^{74} +(1.76467 + 0.294472i) q^{75} +(0.506771 - 4.32934i) q^{76} +(-4.49403 + 0.749921i) q^{77} +(-0.687546 + 2.19821i) q^{78} +(-6.01990 - 16.0784i) q^{79} +(0.471000 - 0.0259858i) q^{80} +(4.93166 + 5.98818i) q^{81} +(1.08578 + 2.14555i) q^{82} +(-7.34974 + 3.97748i) q^{83} +(-0.340133 + 0.369483i) q^{84} +(-2.64836 - 2.57637i) q^{85} +(-0.170091 + 6.17058i) q^{86} +(-2.79348 - 1.51176i) q^{87} +(3.21335 - 1.10314i) q^{88} +(2.18929 + 2.12978i) q^{89} +(0.966937 - 0.940651i) q^{90} +(7.02676 - 4.31933i) q^{91} +(4.60771 + 2.83235i) q^{92} +(2.44997 + 2.97483i) q^{93} +(-2.17527 - 3.32949i) q^{94} +(-1.59538 + 1.29714i) q^{95} +(0.204821 - 0.313503i) q^{96} +(-8.72515 + 0.965699i) q^{97} +(-5.16997 + 0.572212i) q^{98} +(4.85792 - 8.41416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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