LMFDB - Embedded newform 76.2.i.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.2
Root			$-1.26253 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	76.9
Dual form			76.2.i.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86622 - 1.56594i) q^{3} +(-2.06765 - 0.752564i) q^{5} +(-1.48413 + 2.57059i) q^{7} +(0.509650 - 2.89037i) q^{9} +O(q^{10})$	\(q+(1.86622 - 1.56594i) q^{3} +(-2.06765 - 0.752564i) q^{5} +(-1.48413 + 2.57059i) q^{7} +(0.509650 - 2.89037i) q^{9} +(1.34956 + 2.33751i) q^{11} +(3.64418 + 3.05783i) q^{13} +(-5.03717 + 1.83338i) q^{15} +(-1.19836 - 6.79626i) q^{17} +(-4.33264 + 0.477728i) q^{19} +(1.25569 + 7.12136i) q^{21} +(-4.86497 + 1.77070i) q^{23} +(-0.121388 - 0.101857i) q^{25} +(0.0792304 + 0.137231i) q^{27} +(1.17057 - 6.63861i) q^{29} +(2.14339 - 3.71247i) q^{31} +(6.17900 + 2.24897i) q^{33} +(5.00321 - 4.19819i) q^{35} -5.02546 q^{37} +11.5892 q^{39} +(1.42844 - 1.19860i) q^{41} +(8.50895 + 3.09700i) q^{43} +(-3.22896 + 5.59273i) q^{45} +(0.108919 - 0.617710i) q^{47} +(-0.905299 - 1.56802i) q^{49} +(-12.8790 - 10.8067i) q^{51} +(-6.42007 + 2.33671i) q^{53} +(-1.03130 - 5.84880i) q^{55} +(-7.33756 + 7.67622i) q^{57} +(0.623372 + 3.53532i) q^{59} +(9.43969 - 3.43576i) q^{61} +(6.67357 + 5.59979i) q^{63} +(-5.23369 - 9.06501i) q^{65} +(-1.58002 + 8.96073i) q^{67} +(-6.30628 + 10.9228i) q^{69} +(-0.533286 - 0.194100i) q^{71} +(-0.598968 + 0.502594i) q^{73} -0.386038 q^{75} -8.01173 q^{77} +(2.42448 - 2.03438i) q^{79} +(8.63662 + 3.14347i) q^{81} +(3.64810 - 6.31870i) q^{83} +(-2.63682 + 14.9542i) q^{85} +(-8.21115 - 14.2221i) q^{87} +(7.84414 + 6.58201i) q^{89} +(-13.2689 + 4.82948i) q^{91} +(-1.81347 - 10.2847i) q^{93} +(9.31792 + 2.27281i) q^{95} +(-1.47083 - 8.34147i) q^{97} +(7.44408 - 2.70942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.86622	−	1.56594i	1.07746	−	0.904098i	0.0817546	−	0.996652i	$-0.473948\pi$
$3$	1.86622	−	1.56594i	1.07746	−	0.904098i	0.995708	+	0.0925543i	$0.0295032\pi$
$4$		0			0
$5$	−2.06765	−	0.752564i	−0.924682	−	0.336557i	−0.164583	−	0.986363i	$-0.552628\pi$
$5$	−2.06765	−	0.752564i	−0.924682	−	0.336557i	−0.760100	+	0.649806i	$0.774850\pi$
$6$		0			0
$7$	−1.48413	+	2.57059i	−0.560949	+	0.971593i	0.436465	+	0.899721i	$0.356230\pi$
$7$	−1.48413	+	2.57059i	−0.560949	+	0.971593i	−0.997414	+	0.0718714i	$0.977103\pi$
$8$		0			0
$9$	0.509650	−	2.89037i	0.169883	−	0.963456i
$10$		0			0
$11$	1.34956	+	2.33751i	0.406909	+	0.704787i	0.994542	−	0.104341i	$-0.0332733\pi$
$11$	1.34956	+	2.33751i	0.406909	+	0.704787i	−0.587633	+	0.809128i	$0.699940\pi$
$12$		0			0
$13$	3.64418	+	3.05783i	1.01071	+	0.848090i	0.988432	−	0.151662i	$-0.0484625\pi$
$13$	3.64418	+	3.05783i	1.01071	+	0.848090i	0.0222816	+	0.999752i	$0.492907\pi$
$14$		0			0
$15$	−5.03717	+	1.83338i	−1.30059	+	0.473376i
$16$		0			0
$17$	−1.19836	−	6.79626i	−0.290646	−	1.64834i	−0.684390	−	0.729116i	$-0.739931\pi$
$17$	−1.19836	−	6.79626i	−0.290646	−	1.64834i	0.393744	−	0.919220i	$-0.371180\pi$
$18$		0			0
$19$	−4.33264	+	0.477728i	−0.993976	+	0.109598i
$19$	−4.33264	+	0.477728i	−0.993976	+	0.109598i
$20$		0			0
$21$	1.25569	+	7.12136i	0.274014	+	1.55401i
$22$		0			0
$23$	−4.86497	+	1.77070i	−1.01442	+	0.369217i	−0.795127	−	0.606442i	$-0.792596\pi$
$23$	−4.86497	+	1.77070i	−1.01442	+	0.369217i	−0.219289	+	0.975660i	$0.570374\pi$
$24$		0			0
$25$	−0.121388	−	0.101857i	−0.0242776	−	0.0203713i
$26$		0			0
$27$	0.0792304	+	0.137231i	0.0152479	+	0.0264101i
$28$		0			0
$29$	1.17057	−	6.63861i	0.217369	−	1.23276i	−0.659380	−	0.751810i	$-0.729181\pi$
$29$	1.17057	−	6.63861i	0.217369	−	1.23276i	0.876749	−	0.480949i	$-0.159708\pi$
$30$		0			0
$31$	2.14339	−	3.71247i	0.384965	−	0.666779i	−0.606799	−	0.794855i	$-0.707547\pi$
$31$	2.14339	−	3.71247i	0.384965	−	0.666779i	0.991764	+	0.128076i	$0.0408802\pi$
$32$		0			0
$33$	6.17900	+	2.24897i	1.07563	+	0.391496i
$34$		0			0
$35$	5.00321	−	4.19819i	0.845696	−	0.709623i
$36$		0			0
$37$	−5.02546			−0.826181			−0.413091	−	0.910690i	$-0.635551\pi$
$37$	−5.02546			−0.826181			−0.413091	+	0.910690i	$0.635551\pi$
$38$		0			0
$39$	11.5892			1.85576
$40$		0			0
$41$	1.42844	−	1.19860i	0.223085	−	0.187190i	−0.524395	−	0.851475i	$-0.675708\pi$
$41$	1.42844	−	1.19860i	0.223085	−	0.187190i	0.747479	+	0.664285i	$0.231264\pi$
$42$		0			0
$43$	8.50895	+	3.09700i	1.29760	+	0.472289i	0.896215	−	0.443620i	$-0.146306\pi$
$43$	8.50895	+	3.09700i	1.29760	+	0.472289i	0.401387	+	0.915908i	$0.368528\pi$
$44$		0			0
$45$	−3.22896	+	5.59273i	−0.481346	+	0.833715i
$46$		0			0
$47$	0.108919	−	0.617710i	0.0158875	−	0.0901022i	−0.975833	−	0.218518i	$-0.929878\pi$
$47$	0.108919	−	0.617710i	0.0158875	−	0.0901022i	0.991720	+	0.128415i	$0.0409890\pi$
$48$		0			0
$49$	−0.905299	−	1.56802i	−0.129328	−	0.224003i
$50$		0			0
$51$	−12.8790	−	10.8067i	−1.80342	−	1.51325i
$52$		0			0
$53$	−6.42007	+	2.33671i	−0.881864	+	0.320972i	−0.742962	−	0.669334i	$-0.766580\pi$
$53$	−6.42007	+	2.33671i	−0.881864	+	0.320972i	−0.138902	+	0.990306i	$0.544357\pi$
$54$		0			0
$55$	−1.03130	−	5.84880i	−0.139061	−	0.788652i
$56$		0			0
$57$	−7.33756	+	7.67622i	−0.971884	+	1.01674i
$58$		0			0
$59$	0.623372	+	3.53532i	0.0811561	+	0.460259i	0.998120	+	0.0612890i	$0.0195211\pi$
$59$	0.623372	+	3.53532i	0.0811561	+	0.460259i	−0.916964	+	0.398970i	$0.869368\pi$
$60$		0			0
$61$	9.43969	−	3.43576i	1.20863	−	0.439905i	0.342400	−	0.939554i	$-0.388760\pi$
$61$	9.43969	−	3.43576i	1.20863	−	0.439905i	0.866228	+	0.499650i	$0.166538\pi$
$62$		0			0
$63$	6.67357	+	5.59979i	0.840791	+	0.705507i
$64$		0			0
$65$	−5.23369	−	9.06501i	−0.649159	−	1.12438i
$66$		0			0
$67$	−1.58002	+	8.96073i	−0.193030	+	1.09473i	0.722167	+	0.691719i	$0.243146\pi$
$67$	−1.58002	+	8.96073i	−0.193030	+	1.09473i	−0.915196	+	0.403008i	$0.867965\pi$
$68$		0			0
$69$	−6.30628	+	10.9228i	−0.759187	+	1.31495i
$70$		0			0
$71$	−0.533286	−	0.194100i	−0.0632894	−	0.0230355i	0.310181	−	0.950677i	$-0.399610\pi$
$71$	−0.533286	−	0.194100i	−0.0632894	−	0.0230355i	−0.373471	+	0.927642i	$0.621832\pi$
$72$		0			0
$73$	−0.598968	+	0.502594i	−0.0701039	+	0.0588242i	−0.677166	−	0.735830i	$-0.736792\pi$
$73$	−0.598968	+	0.502594i	−0.0701039	+	0.0588242i	0.607062	+	0.794654i	$0.292348\pi$
$74$		0			0
$75$	−0.386038			−0.0445759
$76$		0			0
$77$	−8.01173			−0.913021
$78$		0			0
$79$	2.42448	−	2.03438i	0.272775	−	0.228885i	−0.496130	−	0.868248i	$-0.665246\pi$
$79$	2.42448	−	2.03438i	0.272775	−	0.228885i	0.768905	+	0.639363i	$0.220802\pi$
$80$		0			0
$81$	8.63662	+	3.14347i	0.959625	+	0.349275i
$82$		0			0
$83$	3.64810	−	6.31870i	0.400431	−	0.693568i	−0.593346	−	0.804947i	$-0.702194\pi$
$83$	3.64810	−	6.31870i	0.400431	−	0.693568i	0.993778	+	0.111380i	$0.0355269\pi$
$84$		0			0
$85$	−2.63682	+	14.9542i	−0.286003	+	1.62201i
$86$		0			0
$87$	−8.21115	−	14.2221i	−0.880328	−	1.52477i
$88$		0			0
$89$	7.84414	+	6.58201i	0.831477	+	0.697692i	0.955630	−	0.294571i	$-0.0951768\pi$
$89$	7.84414	+	6.58201i	0.831477	+	0.697692i	−0.124152	+	0.992263i	$0.539621\pi$
$90$		0			0
$91$	−13.2689	+	4.82948i	−1.39096	+	0.506267i
$92$		0			0
$93$	−1.81347	−	10.2847i	−0.188048	−	1.06647i
$94$		0			0
$95$	9.31792	+	2.27281i	0.955998	+	0.233186i
$96$		0			0
$97$	−1.47083	−	8.34147i	−0.149340	−	0.846948i	−0.963780	−	0.266700i	$-0.914067\pi$
$97$	−1.47083	−	8.34147i	−0.149340	−	0.846948i	0.814440	−	0.580248i	$-0.197044\pi$
$98$		0			0
$99$	7.44408	−	2.70942i	0.748158	−	0.272307i
$100$		0			0
$101$	7.17480	+	6.02037i	0.713920	+	0.599050i	0.925696	−	0.378269i	$-0.123480\pi$
$101$	7.17480	+	6.02037i	0.713920	+	0.599050i	−0.211776	+	0.977318i	$0.567925\pi$
$102$		0			0
$103$	−6.00311	−	10.3977i	−0.591504	−	1.02452i	−0.994030	−	0.109107i	$-0.965201\pi$
$103$	−6.00311	−	10.3977i	−0.591504	−	1.02452i	0.402526	−	0.915409i	$-0.368132\pi$
$104$		0			0
$105$	2.76295	−	15.6695i	0.269637	−	1.52918i
$106$		0			0
$107$	−7.15153	+	12.3868i	−0.691364	+	1.19748i	0.280027	+	0.959992i	$0.409657\pi$
$107$	−7.15153	+	12.3868i	−0.691364	+	1.19748i	−0.971391	+	0.237486i	$0.923677\pi$
$108$		0			0
$109$	2.08076	+	0.757335i	0.199301	+	0.0725396i	0.439742	−	0.898124i	$-0.355070\pi$
$109$	2.08076	+	0.757335i	0.199301	+	0.0725396i	−0.240441	+	0.970664i	$0.577292\pi$
$110$		0			0
$111$	−9.37862	+	7.86960i	−0.890179	+	0.746949i
$112$		0			0
$113$	−7.64213			−0.718911			−0.359455	−	0.933162i	$-0.617038\pi$
$113$	−7.64213			−0.718911			−0.359455	+	0.933162i	$0.617038\pi$
$114$		0			0
$115$	11.3916			1.06228
$116$		0			0
$117$	10.6955	−	8.97460i	0.988800	−	0.829702i
$118$		0			0
$119$	19.2490	+	7.00605i	1.76455	+	0.642244i
$120$		0			0
$121$	1.85735	−	3.21703i	0.168850	−	0.292457i
$122$		0			0
$123$	0.788836	−	4.47371i	0.0711270	−	0.403381i
$124$		0			0
$125$	5.67521	+	9.82975i	0.507606	+	0.879200i
$126$		0			0
$127$	−3.55943	−	2.98672i	−0.315848	−	0.265028i	0.471056	−	0.882103i	$-0.343873\pi$
$127$	−3.55943	−	2.98672i	−0.315848	−	0.265028i	−0.786904	+	0.617075i	$0.788317\pi$
$128$		0			0
$129$	20.7293	−	7.54485i	1.82511	−	0.664287i
$130$		0			0
$131$	0.00139646	+	0.00791975i	0.000122010	+	0.000691951i	0.984869	−	0.173302i	$-0.0554437\pi$
$131$	0.00139646	+	0.00791975i	0.000122010	+	0.000691951i	−0.984747	+	0.173994i	$0.944333\pi$
$132$		0			0
$133$	5.20217	−	11.8465i	0.451085	−	1.02722i
$134$		0			0
$135$	−0.0605457	−	0.343372i	−0.00521095	−	0.0295528i
$136$		0			0
$137$	−14.6907	+	5.34697i	−1.25511	+	0.456822i	−0.882125	−	0.471015i	$-0.843888\pi$
$137$	−14.6907	+	5.34697i	−1.25511	+	0.456822i	−0.372984	+	0.927838i	$0.621665\pi$
$138$		0			0
$139$	−5.96207	−	5.00277i	−0.505697	−	0.424330i	0.353915	−	0.935278i	$-0.384850\pi$
$139$	−5.96207	−	5.00277i	−0.505697	−	0.424330i	−0.859612	+	0.510948i	$0.829295\pi$
$140$		0			0
$141$	−0.764032	−	1.32334i	−0.0643431	−	0.111446i
$142$		0			0
$143$	−2.22967	+	12.6451i	−0.186454	+	1.05743i
$144$		0			0
$145$	−7.41630	+	12.8454i	−0.615890	+	1.06675i
$146$		0			0
$147$	−4.14493	−	1.50863i	−0.341868	−	0.124430i
$148$		0			0
$149$	−0.400779	+	0.336294i	−0.0328331	+	0.0275502i	−0.659057	−	0.752093i	$-0.729044\pi$
$149$	−0.400779	+	0.336294i	−0.0328331	+	0.0275502i	0.626223	+	0.779644i	$0.284600\pi$
$150$		0			0
$151$	0.0730868			0.00594772			0.00297386	−	0.999996i	$-0.499053\pi$
$151$	0.0730868			0.00594772			0.00297386	+	0.999996i	$0.499053\pi$
$152$		0			0
$153$	−20.2544			−1.63747
$154$		0			0
$155$	−7.22566	+	6.06305i	−0.580379	+	0.486996i
$156$		0			0
$157$	−13.4211	−	4.88487i	−1.07112	−	0.389855i	−0.254523	−	0.967067i	$-0.581918\pi$
$157$	−13.4211	−	4.88487i	−1.07112	−	0.389855i	−0.816594	+	0.577212i	$0.804141\pi$
$158$		0			0
$159$	−8.32209	+	14.4143i	−0.659985	+	1.14313i
$160$		0			0
$161$	2.66850	−	15.1338i	0.210307	−	1.19271i
$162$		0			0
$163$	−0.158689	−	0.274858i	−0.0124295	−	0.0215286i	0.859744	−	0.510726i	$-0.170623\pi$
$163$	−0.158689	−	0.274858i	−0.0124295	−	0.0215286i	−0.872173	+	0.489197i	$0.837290\pi$
$164$		0			0
$165$	−11.0835	−	9.30018i	−0.862851	−	0.724018i
$166$		0			0
$167$	−0.822400	+	0.299329i	−0.0636392	+	0.0231628i	−0.373644	−	0.927572i	$-0.621892\pi$
$167$	−0.822400	+	0.299329i	−0.0636392	+	0.0231628i	0.310004	+	0.950735i	$0.399669\pi$
$168$		0			0
$169$	1.67230	+	9.48408i	0.128638	+	0.729545i
$170$		0			0
$171$	−0.827319	+	12.7664i	−0.0632667	+	0.976271i
$172$		0			0
$173$	3.78253	+	21.4518i	0.287581	+	1.63095i	0.695919	+	0.718121i	$0.254997\pi$
$173$	3.78253	+	21.4518i	0.287581	+	1.63095i	−0.408338	+	0.912831i	$0.633891\pi$
$174$		0			0
$175$	0.441988	−	0.160870i	0.0334111	−	0.0121607i
$176$		0			0
$177$	6.69946	+	5.62151i	0.503562	+	0.422539i
$178$		0			0
$179$	2.96398	+	5.13376i	0.221538	+	0.383715i	0.955275	−	0.295718i	$-0.0955590\pi$
$179$	2.96398	+	5.13376i	0.221538	+	0.383715i	−0.733737	+	0.679433i	$0.762226\pi$
$180$		0			0
$181$	2.09038	−	11.8552i	0.155377	−	0.881187i	−0.803063	−	0.595894i	$-0.796798\pi$
$181$	2.09038	−	11.8552i	0.155377	−	0.881187i	0.958440	−	0.285293i	$-0.0920910\pi$
$182$		0			0
$183$	12.2363	−	21.1939i	0.904534	−	1.56670i
$184$		0			0
$185$	10.3909	+	3.78198i	0.763955	+	0.278057i
$186$		0			0
$187$	14.2691	−	11.9732i	1.04346	−	0.875566i
$188$		0			0
$189$	−0.470353			−0.0342132
$190$		0			0
$191$	−8.38465			−0.606692			−0.303346	−	0.952880i	$-0.598104\pi$
$191$	−8.38465			−0.606692			−0.303346	+	0.952880i	$0.598104\pi$
$192$		0			0
$193$	0.715575	−	0.600439i	0.0515082	−	0.0432205i	−0.616670	−	0.787222i	$-0.711519\pi$
$193$	0.715575	−	0.600439i	0.0515082	−	0.0432205i	0.668178	+	0.744001i	$0.267074\pi$
$194$		0			0
$195$	−23.9625	−	8.72164i	−1.71599	−	0.624570i
$196$		0			0
$197$	11.1803	−	19.3648i	0.796562	−	1.37969i	−0.125280	−	0.992121i	$-0.539983\pi$
$197$	11.1803	−	19.3648i	0.796562	−	1.37969i	0.921843	−	0.387565i	$-0.126684\pi$
$198$		0			0
$199$	−2.50746	+	14.2205i	−0.177749	+	1.00806i	0.757174	+	0.653213i	$0.226580\pi$
$199$	−2.50746	+	14.2205i	−0.177749	+	1.00806i	−0.934923	+	0.354851i	$0.884532\pi$
$200$		0			0
$201$	11.0833	+	19.1969i	0.781758	+	1.35405i
$202$		0			0
$203$	15.3279	+	12.8616i	1.07581	+	0.902709i
$204$		0			0
$205$	−3.85554	+	1.40330i	−0.269283	+	0.0980109i
$206$		0			0
$207$	2.63855	+	14.9640i	0.183392	+	1.04007i
$208$		0			0
$209$	−6.96387	−	9.48288i	−0.481701	−	0.655945i
$210$		0			0
$211$	−3.15065	−	17.8682i	−0.216900	−	1.23010i	−0.877579	−	0.479432i	$-0.840843\pi$
$211$	−3.15065	−	17.8682i	−0.216900	−	1.23010i	0.660679	−	0.750668i	$-0.270268\pi$
$212$		0			0
$213$	−1.29918	+	0.472863i	−0.0890183	+	0.0324000i
$214$		0			0
$215$	−15.2629	−	12.8071i	−1.04092	−	0.873434i
$216$		0			0
$217$	6.36216	+	11.0196i	0.431892	+	0.748058i
$218$		0			0
$219$	−0.330772	+	1.87590i	−0.0223515	+	0.126762i
$220$		0			0
$221$	16.4148	−	28.4312i	1.10418	−	1.91249i
$222$		0			0
$223$	−3.08215	−	1.12181i	−0.206396	−	0.0751219i	0.236754	−	0.971570i	$-0.423917\pi$
$223$	−3.08215	−	1.12181i	−0.206396	−	0.0751219i	−0.443149	+	0.896448i	$0.646139\pi$
$224$		0			0
$225$	−0.356268	+	0.298945i	−0.0237512	+	0.0199296i
$226$		0			0
$227$	11.5190			0.764543			0.382272	−	0.924050i	$-0.375142\pi$
$227$	11.5190			0.764543			0.382272	+	0.924050i	$0.375142\pi$
$228$		0			0
$229$	15.3682			1.01556			0.507780	−	0.861487i	$-0.330466\pi$
$229$	15.3682			1.01556			0.507780	+	0.861487i	$0.330466\pi$
$230$		0			0
$231$	−14.9516	+	12.5459i	−0.983746	+	0.825461i
$232$		0			0
$233$	−12.8920	−	4.69229i	−0.844581	−	0.307402i	−0.116752	−	0.993161i	$-0.537248\pi$
$233$	−12.8920	−	4.69229i	−0.844581	−	0.307402i	−0.727829	+	0.685759i	$0.759471\pi$
$234$		0			0
$235$	−0.690073	+	1.19524i	−0.0450154	+	0.0779689i
$236$		0			0
$237$	1.33888	−	7.59318i	0.0869698	−	0.493230i
$238$		0			0
$239$	−8.39945	−	14.5483i	−0.543315	−	0.941050i	−0.998711	−	0.0507604i	$-0.983836\pi$
$239$	−8.39945	−	14.5483i	−0.543315	−	0.941050i	0.455396	−	0.890289i	$-0.349498\pi$
$240$		0			0
$241$	17.2571	+	14.4804i	1.11163	+	0.932765i	0.998151	−	0.0607762i	$-0.0193576\pi$
$241$	17.2571	+	14.4804i	1.11163	+	0.932765i	0.113474	+	0.993541i	$0.463802\pi$
$242$		0			0
$243$	20.5936	−	7.49547i	1.32108	−	0.480834i
$244$		0			0
$245$	0.691806	+	3.92342i	0.0441978	+	0.250658i
$246$		0			0
$247$	−17.2497	−	11.5076i	−1.09757	−	0.732208i
$248$		0			0
$249$	−3.08657	−	17.5048i	−0.195603	−	1.10932i
$250$		0			0
$251$	14.5743	−	5.30463i	0.919924	−	0.334825i	0.161716	−	0.986837i	$-0.448297\pi$
$251$	14.5743	−	5.30463i	0.919924	−	0.334825i	0.758208	+	0.652012i	$0.226075\pi$
$252$		0			0
$253$	−10.7046	−	8.98226i	−0.672995	−	0.564710i
$254$		0			0
$255$	18.4965	+	32.0369i	1.15830	+	2.00623i
$256$		0			0
$257$	−5.05935	+	28.6930i	−0.315594	+	1.78982i	0.253277	+	0.967394i	$0.418492\pi$
$257$	−5.05935	+	28.6930i	−0.315594	+	1.78982i	−0.568870	+	0.822427i	$0.692619\pi$
$258$		0			0
$259$	7.45846	−	12.9184i	0.463446	−	0.802712i
$260$		0			0
$261$	−18.5914	−	6.76673i	−1.15078	−	0.418850i
$262$		0			0
$263$	2.90918	−	2.44110i	0.179388	−	0.150524i	−0.548672	−	0.836038i	$-0.684867\pi$
$263$	2.90918	−	2.44110i	0.179388	−	0.150524i	0.728060	+	0.685513i	$0.240422\pi$
$264$		0			0
$265$	15.0330			0.923470
$266$		0			0
$267$	24.9459			1.52667
$268$		0			0
$269$	−6.09243	+	5.11215i	−0.371462	+	0.311693i	−0.809340	−	0.587341i	$-0.800175\pi$
$269$	−6.09243	+	5.11215i	−0.371462	+	0.311693i	0.437878	+	0.899035i	$0.355730\pi$
$270$		0			0
$271$	0.640257	+	0.233034i	0.0388928	+	0.0141558i	0.361393	−	0.932413i	$-0.382301\pi$
$271$	0.640257	+	0.233034i	0.0388928	+	0.0141558i	−0.322500	+	0.946569i	$0.604523\pi$
$272$		0			0
$273$	−17.2000	+	29.7912i	−1.04099	+	1.80305i
$274$		0			0
$275$	0.0742704	−	0.421208i	0.00447867	−	0.0253998i
$276$		0			0
$277$	6.97191	+	12.0757i	0.418901	+	0.725558i	0.995829	−	0.0912367i	$-0.0290820\pi$
$277$	6.97191	+	12.0757i	0.418901	+	0.725558i	−0.576928	+	0.816795i	$0.695749\pi$
$278$		0			0
$279$	−9.63801	−	8.08725i	−0.577013	−	0.484171i
$280$		0			0
$281$	−25.1212	+	9.14338i	−1.49861	+	0.545448i	−0.955700	−	0.294344i	$-0.904899\pi$
$281$	−25.1212	+	9.14338i	−1.49861	+	0.545448i	−0.542908	+	0.839792i	$0.682677\pi$
$282$		0			0
$283$	0.879102	+	4.98563i	0.0522572	+	0.296365i	0.999724	−	0.0234886i	$-0.00747733\pi$
$283$	0.879102	+	4.98563i	0.0522572	+	0.296365i	−0.947467	+	0.319854i	$0.896366\pi$
$284$		0			0
$285$	20.9484	−	10.3498i	1.24087	−	0.613067i
$286$		0			0
$287$	0.961127	+	5.45082i	0.0567335	+	0.321752i
$288$		0			0
$289$	−28.7784	+	10.4745i	−1.69284	+	0.616145i
$290$		0			0
$291$	−15.8072	−	13.2638i	−0.926632	−	0.777536i
$292$		0			0
$293$	−0.625879	−	1.08405i	−0.0365642	−	0.0633311i	0.847164	−	0.531331i	$-0.178308\pi$
$293$	−0.625879	−	1.08405i	−0.0365642	−	0.0633311i	−0.883728	+	0.468000i	$0.844975\pi$
$294$		0			0
$295$	1.37164	−	7.77893i	0.0798597	−	0.452907i
$296$		0			0
$297$	−0.213853	+	0.370404i	−0.0124090	+	0.0214930i
$298$		0			0
$299$	−23.1434	−	8.42349i	−1.33841	−	0.487143i
$300$		0			0
$301$	−20.5895	+	17.2767i	−1.18676	+	0.995811i
$302$		0			0
$303$	22.8173			1.31082
$304$		0			0
$305$	−22.1036			−1.26565
$306$		0			0
$307$	−18.5543	+	15.5689i	−1.05895	+	0.888564i	−0.994006	−	0.109325i	$-0.965131\pi$
$307$	−18.5543	+	15.5689i	−1.05895	+	0.888564i	−0.0649432	+	0.997889i	$0.520687\pi$
$308$		0			0
$309$	−27.4853	−	10.0038i	−1.56359	−	0.569099i
$310$		0			0
$311$	15.7119	−	27.2139i	0.890942	−	1.54316i	0.0521949	−	0.998637i	$-0.483378\pi$
$311$	15.7119	−	27.2139i	0.890942	−	1.54316i	0.838747	−	0.544521i	$-0.183288\pi$
$312$		0			0
$313$	3.65444	−	20.7254i	0.206561	−	1.17147i	−0.688402	−	0.725329i	$-0.741688\pi$
$313$	3.65444	−	20.7254i	0.206561	−	1.17147i	0.894964	−	0.446139i	$-0.147201\pi$
$314$		0			0
$315$	−9.58442	−	16.6007i	−0.540021	−	0.935344i
$316$		0			0
$317$	7.82632	+	6.56706i	0.439570	+	0.368843i	0.835548	−	0.549417i	$-0.185150\pi$
$317$	7.82632	+	6.56706i	0.439570	+	0.368843i	−0.395978	+	0.918260i	$0.629595\pi$
$318$		0			0
$319$	17.0976	−	6.22301i	0.957281	−	0.348422i
$320$		0			0
$321$	6.05073	+	34.3154i	0.337719	+	1.91530i
$322$		0			0
$323$	8.43885	+	28.8733i	0.469550	+	1.60655i
$324$		0			0
$325$	−0.130899	−	0.742368i	−0.00726100	−	0.0411792i
$326$		0			0
$327$	5.06910	−	1.84500i	0.280322	−	0.102029i
$328$		0			0
$329$	1.42623	+	1.19675i	0.0786306	+	0.0659789i
$330$		0			0
$331$	13.6834	+	23.7003i	0.752105	+	1.30268i	0.946801	+	0.321821i	$0.104295\pi$
$331$	13.6834	+	23.7003i	0.752105	+	1.30268i	−0.194695	+	0.980864i	$0.562372\pi$
$332$		0			0
$333$	−2.56123	+	14.5254i	−0.140354	+	0.795989i
$334$		0			0
$335$	10.0104	−	17.3386i	0.546929	−	0.947309i
$336$		0			0
$337$	−1.26806	−	0.461535i	−0.0690754	−	0.0251414i	0.307251	−	0.951628i	$-0.400591\pi$
$337$	−1.26806	−	0.461535i	−0.0690754	−	0.0251414i	−0.376327	+	0.926487i	$0.622813\pi$
$338$		0			0
$339$	−14.2619	+	11.9671i	−0.774599	+	0.649966i
$340$		0			0
$341$	11.5706			0.626583
$342$		0			0
$343$	−15.4035			−0.831712
$344$		0			0
$345$	21.2593	−	17.8387i	1.14456	−	0.960402i
$346$		0			0
$347$	−9.33198	−	3.39656i	−0.500967	−	0.182337i	0.0791620	−	0.996862i	$-0.474776\pi$
$347$	−9.33198	−	3.39656i	−0.500967	−	0.182337i	−0.580129	+	0.814525i	$0.696998\pi$
$348$		0			0
$349$	3.32804	−	5.76434i	0.178146	−	0.308558i	−0.763100	−	0.646281i	$-0.776323\pi$
$349$	3.32804	−	5.76434i	0.178146	−	0.308558i	0.941246	+	0.337723i	$0.109657\pi$
$350$		0			0
$351$	−0.130899	+	0.742368i	−0.00698690	+	0.0396247i
$352$		0			0
$353$	−10.8285	−	18.7556i	−0.576345	−	0.998259i	−0.995894	−	0.0905262i	$-0.971145\pi$
$353$	−10.8285	−	18.7556i	−0.576345	−	0.998259i	0.419549	−	0.907733i	$-0.362188\pi$
$354$		0			0
$355$	0.956578	+	0.802664i	0.0507699	+	0.0426010i
$356$		0			0
$357$	46.8939	−	17.0680i	2.48189	−	0.903333i
$358$		0			0
$359$	−1.67956	−	9.52525i	−0.0886437	−	0.502724i	−0.996511	−	0.0834652i	$-0.973401\pi$
$359$	−1.67956	−	9.52525i	−0.0886437	−	0.502724i	0.907867	−	0.419258i	$-0.137710\pi$
$360$		0			0
$361$	18.5436	−	4.13965i	0.975976	−	0.217876i
$362$		0			0
$363$	−1.57146	−	8.91219i	−0.0824802	−	0.467769i
$364$		0			0
$365$	1.61669	−	0.588428i	0.0846215	−	0.0307997i
$366$		0			0
$367$	19.8828	+	16.6837i	1.03788	+	0.870881i	0.991767	−	0.128056i	$-0.0408736\pi$
$367$	19.8828	+	16.6837i	1.03788	+	0.870881i	0.0461083	+	0.998936i	$0.485318\pi$
$368$		0			0
$369$	−2.73640	−	4.73958i	−0.142451	−	0.246733i
$370$		0			0
$371$	3.52149	−	19.9714i	0.182827	−	1.03686i
$372$		0			0
$373$	−9.13616	+	15.8243i	−0.473052	+	0.819351i	−0.999524	−	0.0308418i	$-0.990181\pi$
$373$	−9.13616	+	15.8243i	−0.473052	+	0.819351i	0.526472	+	0.850193i	$0.323515\pi$
$374$		0			0
$375$	25.9840	+	9.45741i	1.34181	+	0.488379i
$376$		0			0
$377$	24.5655	−	20.6129i	1.26519	−	1.06162i
$378$		0			0
$379$	−31.1455			−1.59983			−0.799917	−	0.600110i	$-0.795123\pi$
$379$	−31.1455			−1.59983			−0.799917	+	0.600110i	$0.795123\pi$
$380$		0			0
$381$	−11.3197			−0.579926
$382$		0			0
$383$	−22.1294	+	18.5687i	−1.13076	+	0.948819i	−0.999097	−	0.0424761i	$-0.986475\pi$
$383$	−22.1294	+	18.5687i	−1.13076	+	0.948819i	−0.131661	+	0.991295i	$0.542031\pi$
$384$		0			0
$385$	16.5655	+	6.02934i	0.844255	+	0.307284i
$386$		0			0
$387$	13.2881	−	23.0156i	0.675470	−	1.16995i
$388$		0			0
$389$	−1.07456	+	6.09416i	−0.0544826	+	0.308986i	−0.999855	−	0.0170051i	$-0.994587\pi$
$389$	−1.07456	+	6.09416i	−0.0544826	+	0.308986i	0.945373	+	0.325991i	$0.105698\pi$
$390$		0			0
$391$	17.8642	+	30.9417i	0.903431	+	1.56479i
$392$		0			0
$393$	0.0150080	+	0.0125932i	0.000757053	+	0.000635243i
$394$		0			0
$395$	−6.54397	+	2.38181i	−0.329263	+	0.119842i
$396$		0			0
$397$	−1.25366	−	7.10986i	−0.0629194	−	0.356834i	−0.999971	−	0.00764217i	$-0.997567\pi$
$397$	−1.25366	−	7.10986i	−0.0629194	−	0.356834i	0.937051	−	0.349191i	$-0.113544\pi$
$398$		0			0
$399$	−8.84252	−	30.2544i	−0.442680	−	1.51462i
$400$		0			0
$401$	−4.01252	−	22.7561i	−0.200376	−	1.13639i	−0.904552	−	0.426362i	$-0.859795\pi$
$401$	−4.01252	−	22.7561i	−0.200376	−	1.13639i	0.704177	−	0.710025i	$-0.251316\pi$
$402$		0			0
$403$	19.1630	−	6.97477i	0.954578	−	0.347438i
$404$		0			0
$405$	−15.4919	−	12.9992i	−0.769797	−	0.645937i
$406$		0			0
$407$	−6.78219	−	11.7471i	−0.336181	−	0.582282i
$408$		0			0
$409$	−1.47083	+	8.34147i	−0.0727276	+	0.412459i	0.926609	+	0.376027i	$0.122710\pi$
$409$	−1.47083	+	8.34147i	−0.0727276	+	0.412459i	−0.999336	+	0.0364315i	$0.988401\pi$
$410$		0			0
$411$	−19.0430	+	32.9834i	−0.939321	+	1.62695i
$412$		0			0
$413$	−10.0130	−	3.64444i	−0.492709	−	0.179331i
$414$		0			0
$415$	−12.2982	+	10.3194i	−0.603697	+	0.506562i
$416$		0			0
$417$	−18.9606			−0.928505
$418$		0			0
$419$	−34.4402			−1.68251			−0.841257	−	0.540635i	$-0.818184\pi$
$419$	−34.4402			−1.68251			−0.841257	+	0.540635i	$0.818184\pi$
$420$		0			0
$421$	8.18476	−	6.86783i	0.398901	−	0.334718i	−0.421168	−	0.906983i	$-0.638380\pi$
$421$	8.18476	−	6.86783i	0.398901	−	0.334718i	0.820069	+	0.572265i	$0.193935\pi$
$422$		0			0
$423$	−1.72990	−	0.629631i	−0.0841105	−	0.0306137i
$424$		0			0
$425$	−0.546777	+	0.947046i	−0.0265226	+	0.0459385i
$426$		0			0
$427$	−5.17779	+	29.3647i	−0.250571	+	1.42106i
$428$		0			0
$429$	15.6404	+	27.0900i	0.755126	+	1.30792i
$430$		0			0
$431$	−9.45533	−	7.93396i	−0.455447	−	0.382166i	0.386005	−	0.922497i	$-0.373855\pi$
$431$	−9.45533	−	7.93396i	−0.455447	−	0.382166i	−0.841453	+	0.540331i	$0.818299\pi$
$432$		0			0
$433$	33.6628	−	12.2522i	1.61773	−	0.588805i	0.634782	−	0.772691i	$-0.281090\pi$
$433$	33.6628	−	12.2522i	1.61773	−	0.588805i	0.982948	+	0.183886i	$0.0588676\pi$
$434$		0			0
$435$	6.27475	+	35.5859i	0.300851	+	1.70621i
$436$		0			0
$437$	20.2323	−	9.99596i	0.967840	−	0.478172i
$438$		0			0
$439$	−3.66200	−	20.7682i	−0.174778	−	0.991213i	−0.938400	−	0.345550i	$-0.887692\pi$
$439$	−3.66200	−	20.7682i	−0.174778	−	0.991213i	0.763623	−	0.645663i	$-0.223419\pi$
$440$		0			0
$441$	−4.99355	+	1.81750i	−0.237788	+	0.0865478i
$442$		0			0
$443$	7.17585	+	6.02125i	0.340935	+	0.286078i	0.797138	−	0.603797i	$-0.206346\pi$
$443$	7.17585	+	6.02125i	0.340935	+	0.286078i	−0.456203	+	0.889876i	$0.650791\pi$
$444$		0			0
$445$	−11.2656	−	19.5125i	−0.534039	−	0.924983i
$446$		0			0
$447$	−0.221325	+	1.25520i	−0.0104683	+	0.0593687i
$448$		0			0
$449$	−4.05742	+	7.02766i	−0.191481	+	0.331656i	−0.945741	−	0.324920i	$-0.894663\pi$
$449$	−4.05742	+	7.02766i	−0.191481	+	0.331656i	0.754260	+	0.656576i	$0.227996\pi$
$450$		0			0
$451$	4.72952	+	1.72141i	0.222704	+	0.0810578i
$452$		0			0
$453$	0.136396	−	0.114450i	0.00640844	−	0.00537732i
$454$		0			0
$455$	31.0699			1.45658
$456$		0			0
$457$	4.33380			0.202727			0.101363	−	0.994849i	$-0.467680\pi$
$457$	4.33380			0.202727			0.101363	+	0.994849i	$0.467680\pi$
$458$		0			0
$459$	0.837711	−	0.702923i	0.0391010	−	0.0328097i
$460$		0			0
$461$	24.1245	+	8.78061i	1.12359	+	0.408954i	0.835962	−	0.548788i	$-0.184911\pi$
$461$	24.1245	+	8.78061i	1.12359	+	0.408954i	0.287629	+	0.957742i	$0.407133\pi$
$462$		0			0
$463$	−0.875824	+	1.51697i	−0.0407030	+	0.0704996i	−0.885659	−	0.464336i	$-0.846293\pi$
$463$	−0.875824	+	1.51697i	−0.0407030	+	0.0704996i	0.844956	+	0.534835i	$0.179626\pi$
$464$		0			0
$465$	−3.99027	+	22.6300i	−0.185044	+	1.04944i
$466$		0			0
$467$	−8.64997	−	14.9822i	−0.400273	−	0.693293i	0.593486	−	0.804844i	$-0.297751\pi$
$467$	−8.64997	−	14.9822i	−0.400273	−	0.693293i	−0.993759	+	0.111551i	$0.964418\pi$
$468$		0			0
$469$	−20.6894	−	17.3605i	−0.955349	−	0.801633i
$470$		0			0
$471$	−32.6961	+	11.9004i	−1.50656	+	0.548341i
$472$		0			0
$473$	4.24408	+	24.0694i	0.195143	+	1.10671i
$474$		0			0
$475$	0.574590	+	0.383318i	0.0263640	+	0.0175878i
$476$		0			0
$477$	3.48197	+	19.7473i	0.159429	+	0.904165i
$478$		0			0
$479$	−8.04717	+	2.92893i	−0.367684	+	0.133826i	−0.519253	−	0.854621i	$-0.673790\pi$
$479$	−8.04717	+	2.92893i	−0.367684	+	0.133826i	0.151569	+	0.988447i	$0.451568\pi$
$480$		0			0
$481$	−18.3137	−	15.3670i	−0.835033	−	0.700676i
$482$		0			0
$483$	−18.7187	−	32.4218i	−0.851731	−	1.47524i
$484$		0			0
$485$	−3.23633	+	18.3541i	−0.146954	+	0.833419i
$486$		0			0
$487$	−2.01043	+	3.48216i	−0.0911011	+	0.157792i	−0.907975	−	0.419025i	$-0.862372\pi$
$487$	−2.01043	+	3.48216i	−0.0911011	+	0.157792i	0.816874	+	0.576817i	$0.195705\pi$
$488$		0			0
$489$	−0.726562	−	0.264447i	−0.0328563	−	0.0119587i
$490$		0			0
$491$	6.40117	−	5.37122i	0.288881	−	0.242400i	−0.486817	−	0.873504i	$-0.661842\pi$
$491$	6.40117	−	5.37122i	0.288881	−	0.242400i	0.775698	+	0.631104i	$0.217398\pi$
$492$		0			0
$493$	−46.5205			−2.09518
$494$		0			0
$495$	−17.4308			−0.783455
$496$		0			0
$497$	1.29042	−	1.08279i	0.0578833	−	0.0485698i
$498$		0			0
$499$	7.57293	+	2.75632i	0.339011	+	0.123390i	0.505915	−	0.862583i	$-0.331155\pi$
$499$	7.57293	+	2.75632i	0.339011	+	0.123390i	−0.166904	+	0.985973i	$0.553377\pi$
$500$		0			0
$501$	−1.06605	+	1.84645i	−0.0476274	+	0.0824931i
$502$		0			0
$503$	−1.17379	+	6.65690i	−0.0523367	+	0.296816i	−0.999730	−	0.0232569i	$-0.992596\pi$
$503$	−1.17379	+	6.65690i	−0.0523367	+	0.296816i	0.947393	+	0.320073i	$0.103708\pi$
$504$		0			0
$505$	−10.3043	−	17.8475i	−0.458535	−	0.794205i
$506$		0			0
$507$	17.9724	+	15.0807i	0.798183	+	0.669755i
$508$		0			0
$509$	−8.14794	+	2.96561i	−0.361151	+	0.131448i	−0.516221	−	0.856455i	$-0.672662\pi$
$509$	−8.14794	+	2.96561i	−0.361151	+	0.131448i	0.155070	+	0.987903i	$0.450440\pi$
$510$		0			0
$511$	−0.403016	−	2.28562i	−0.0178284	−	0.101110i
$512$		0			0
$513$	−0.408836	−	0.556722i	−0.0180505	−	0.0245799i
$514$		0			0
$515$	4.58742	+	26.0165i	0.202146	+	1.14643i
$516$		0			0
$517$	1.59090	−	0.579040i	0.0699676	−	0.0254661i
$518$		0			0
$519$	40.6514	+	34.1106i	1.78440	+	1.49729i
$520$		0			0
$521$	−18.9134	−	32.7589i	−0.828610	−	1.43519i	−0.899129	−	0.437684i	$-0.855799\pi$
$521$	−18.9134	−	32.7589i	−0.828610	−	1.43519i	0.0705193	−	0.997510i	$-0.477534\pi$
$522$		0			0
$523$	1.16685	−	6.61751i	0.0510226	−	0.289363i	−0.948611	−	0.316446i	$-0.897510\pi$
$523$	1.16685	−	6.61751i	0.0510226	−	0.289363i	0.999633	+	0.0270822i	$0.00862160\pi$
$524$		0			0
$525$	0.572932	−	0.992347i	0.0250048	−	0.0433096i
$526$		0			0
$527$	−27.7995	−	10.1182i	−1.21096	−	0.440755i
$528$		0			0
$529$	2.91353	−	2.44474i	0.126675	−	0.106293i
$530$		0			0
$531$	10.5361			0.457226
$532$		0			0
$533$	8.87062			0.384229
$534$		0			0
$535$	24.1087	−	20.2296i	1.04231	−	0.874603i
$536$		0			0
$537$	13.5706	+	4.93930i	0.585615	+	0.213146i
$538$		0			0
$539$	2.44352	−	4.23230i	0.105250	−	0.182298i
$540$		0			0
$541$	6.42812	−	36.4557i	0.276366	−	1.56735i	−0.458222	−	0.888838i	$-0.651513\pi$
$541$	6.42812	−	36.4557i	0.276366	−	1.56735i	0.734588	−	0.678514i	$-0.237376\pi$
$542$		0			0
$543$	−14.6634	−	25.3977i	−0.629267	−	1.08992i
$544$		0			0
$545$	−3.73235	−	3.13181i	−0.159876	−	0.134152i
$546$		0			0
$547$	32.4038	−	11.7940i	1.38549	−	0.504275i	0.461649	−	0.887063i	$-0.347258\pi$
$547$	32.4038	−	11.7940i	1.38549	−	0.504275i	0.923837	+	0.382787i	$0.125036\pi$
$548$		0			0
$549$	−5.11969	−	29.0352i	−0.218503	−	1.23919i
$550$		0			0
$551$	−1.90019	+	29.3219i	−0.0809508	+	1.24916i
$552$		0			0
$553$	1.63131	+	9.25162i	0.0693704	+	0.393419i
$554$		0			0
$555$	25.3141	−	9.21358i	1.07452	−	0.391095i
$556$		0			0
$557$	32.0493	+	26.8925i	1.35797	+	1.13947i	0.976603	+	0.215051i	$0.0689917\pi$
$557$	32.0493	+	26.8925i	1.35797	+	1.13947i	0.381369	+	0.924423i	$0.375453\pi$
$558$		0			0
$559$	21.5380	+	37.3050i	0.910962	+	1.57783i
$560$		0			0
$561$	7.87991	−	44.6892i	0.332690	−	1.88678i
$562$		0			0
$563$	7.86717	−	13.6263i	0.331562	−	0.574282i	−0.651257	−	0.758858i	$-0.725758\pi$
$563$	7.86717	−	13.6263i	0.331562	−	0.574282i	0.982818	+	0.184576i	$0.0590912\pi$
$564$		0			0
$565$	15.8013	+	5.75119i	0.664764	+	0.241954i
$566$		0			0
$567$	−20.8985	+	17.5359i	−0.877654	+	0.736439i
$568$		0			0
$569$	41.4620			1.73818			0.869089	−	0.494656i	$-0.164706\pi$
$569$	41.4620			1.73818			0.869089	+	0.494656i	$0.164706\pi$
$570$		0			0
$571$	12.3160			0.515408			0.257704	−	0.966224i	$-0.417034\pi$
$571$	12.3160			0.515408			0.257704	+	0.966224i	$0.417034\pi$
$572$		0			0
$573$	−15.6476	+	13.1299i	−0.653688	+	0.548509i
$574$		0			0
$575$	0.770907	+	0.280587i	0.0321490	+	0.0117013i
$576$		0			0
$577$	−5.49834	+	9.52341i	−0.228899	+	0.396465i	−0.957482	−	0.288493i	$-0.906846\pi$
$577$	−5.49834	+	9.52341i	−0.228899	+	0.396465i	0.728583	+	0.684957i	$0.240179\pi$
$578$		0			0
$579$	0.395167	−	2.24110i	0.0164226	−	0.0931370i
$580$		0			0
$581$	10.8285	+	18.7556i	0.449244	+	0.778113i
$582$		0			0
$583$	−14.1264	−	11.8535i	−0.585055	−	0.490920i
$584$		0			0
$585$	−28.8686	+	10.5073i	−1.19357	+	0.434423i
$586$		0			0
$587$	−7.13565	−	40.4683i	−0.294520	−	1.67030i	−0.669148	−	0.743129i	$-0.733341\pi$
$587$	−7.13565	−	40.4683i	−0.294520	−	1.67030i	0.374628	−	0.927175i	$-0.377770\pi$
$588$		0			0
$589$	−7.51300	+	17.1087i	−0.309568	+	0.704954i
$590$		0			0
$591$	−9.45936	−	53.6467i	−0.389106	−	2.20673i
$592$		0			0
$593$	24.1916	−	8.80504i	0.993432	−	0.361580i	0.206384	−	0.978471i	$-0.433831\pi$
$593$	24.1916	−	8.80504i	0.993432	−	0.361580i	0.787048	+	0.616892i	$0.211608\pi$
$594$		0			0
$595$	−34.5277	−	28.9722i	−1.41550	−	1.18774i
$596$		0			0
$597$	17.5890	+	30.4651i	0.719871	+	1.24685i
$598$		0			0
$599$	−4.76463	+	27.0215i	−0.194677	+	1.10407i	0.718200	+	0.695837i	$0.244966\pi$
$599$	−4.76463	+	27.0215i	−0.194677	+	1.10407i	−0.912877	+	0.408234i	$0.866145\pi$
$600$		0			0
$601$	−12.5425	+	21.7242i	−0.511618	+	0.886148i	0.488292	+	0.872681i	$0.337620\pi$
$601$	−12.5425	+	21.7242i	−0.511618	+	0.886148i	−0.999909	+	0.0134673i	$0.995713\pi$
$602$		0			0
$603$	25.0945	+	9.13366i	1.02193	+	0.371951i
$604$		0			0
$605$	−6.26138	+	5.25392i	−0.254561	+	0.213602i
$606$		0			0
$607$	7.83141			0.317867			0.158934	−	0.987289i	$-0.449194\pi$
$607$	7.83141			0.317867			0.158934	+	0.987289i	$0.449194\pi$
$608$		0			0
$609$	48.7458			1.97528
$610$		0			0
$611$	2.28577	−	1.91799i	0.0924725	−	0.0775936i
$612$		0			0
$613$	−8.42277	−	3.06564i	−0.340193	−	0.123820i	0.166274	−	0.986080i	$-0.446826\pi$
$613$	−8.42277	−	3.06564i	−0.340193	−	0.123820i	−0.506466	+	0.862260i	$0.669049\pi$
$614$		0			0
$615$	−4.99779	+	8.65643i	−0.201530	+	0.349061i
$616$		0			0
$617$	0.703095	−	3.98745i	0.0283055	−	0.160529i	−0.967379	−	0.253335i	$-0.918473\pi$
$617$	0.703095	−	3.98745i	0.0283055	−	0.160529i	0.995684	+	0.0928062i	$0.0295837\pi$
$618$		0			0
$619$	−13.0871	−	22.6676i	−0.526016	−	0.911087i	−0.999541	−	0.0303060i	$-0.990352\pi$
$619$	−13.0871	−	22.6676i	−0.526016	−	0.911087i	0.473525	−	0.880781i	$-0.342982\pi$
$620$		0			0
$621$	−0.628449	−	0.527331i	−0.0252188	−	0.0211611i
$622$		0			0
$623$	−28.5614	+	10.3955i	−1.14429	+	0.416487i
$624$		0			0
$625$	−4.19926	−	23.8152i	−0.167970	−	0.952608i
$626$		0			0
$627$	−27.8458	−	6.79210i	−1.11205	−	0.271251i
$628$		0			0
$629$	6.02234	+	34.1544i	0.240126	+	1.36182i
$630$		0			0
$631$	−41.3624	+	15.0547i	−1.64661	+	0.599317i	−0.988177	−	0.153321i	$-0.951003\pi$
$631$	−41.3624	+	15.0547i	−1.64661	+	0.599317i	−0.658435	+	0.752638i	$0.728781\pi$
$632$		0			0
$633$	−33.8605	−	28.4123i	−1.34583	−	1.12929i
$634$		0			0
$635$	5.11197	+	8.85419i	0.202862	+	0.351368i
$636$		0			0
$637$	1.49568	−	8.48242i	0.0592610	−	0.336086i
$638$		0			0
$639$	−0.832810	+	1.44247i	−0.0329455	+	0.0570632i
$640$		0			0
$641$	4.91616	+	1.78934i	0.194177	+	0.0706745i	0.437278	−	0.899326i	$-0.355943\pi$
$641$	4.91616	+	1.78934i	0.194177	+	0.0706745i	−0.243101	+	0.970001i	$0.578165\pi$
$642$		0			0
$643$	10.2920	−	8.63602i	0.405877	−	0.340571i	−0.416883	−	0.908960i	$-0.636878\pi$
$643$	10.2920	−	8.63602i	0.405877	−	0.340571i	0.822760	+	0.568389i	$0.192433\pi$
$644$		0			0
$645$	−48.5390			−1.91122
$646$		0			0
$647$	15.4880			0.608895			0.304448	−	0.952529i	$-0.401528\pi$
$647$	15.4880			0.608895			0.304448	+	0.952529i	$0.401528\pi$
$648$		0			0
$649$	−7.42257	+	6.22828i	−0.291361	+	0.244481i
$650$		0			0
$651$	29.1292	+	10.6022i	1.14167	+	0.415532i
$652$		0			0
$653$	−5.03649	+	8.72346i	−0.197093	+	0.341375i	−0.947585	−	0.319505i	$-0.896483\pi$
$653$	−5.03649	+	8.72346i	−0.197093	+	0.341375i	0.750492	+	0.660880i	$0.229817\pi$
$654$		0			0
$655$	0.00307271	−	0.0174262i	0.000120061	−	0.000680898i
$656$		0			0
$657$	1.14742	+	1.98738i	0.0447650	+	0.0775352i
$658$		0			0
$659$	18.8606	+	15.8259i	0.734704	+	0.616490i	0.931410	−	0.363973i	$-0.118580\pi$
$659$	18.8606	+	15.8259i	0.734704	+	0.616490i	−0.196706	+	0.980463i	$0.563024\pi$
$660$		0			0
$661$	−44.4545	+	16.1801i	−1.72908	+	0.629333i	−0.998564	−	0.0535638i	$-0.982942\pi$
$661$	−44.4545	+	16.1801i	−1.72908	+	0.629333i	−0.730515	+	0.682897i	$0.760720\pi$
$662$		0			0
$663$	−13.8881	−	78.7635i	−0.539370	−	3.05892i
$664$		0			0
$665$	−19.6715	+	20.5794i	−0.762828	+	0.798035i
$666$		0			0
$667$	6.06024	+	34.3694i	0.234654	+	1.33079i
$668$		0			0
$669$	−7.50865	+	2.73293i	−0.290301	+	0.105661i
$670$		0			0
$671$	20.7706	+	17.4286i	0.801841	+	0.672824i
$672$		0			0
$673$	7.44102	+	12.8882i	0.286830	+	0.496805i	0.973051	−	0.230588i	$-0.0740651\pi$
$673$	7.44102	+	12.8882i	0.286830	+	0.496805i	−0.686221	+	0.727393i	$0.740732\pi$
$674$		0			0
$675$	0.00436027	−	0.0247283i	0.000167827	−	0.000951794i
$676$		0			0
$677$	1.25311	−	2.17046i	0.0481611	−	0.0834175i	−0.840940	−	0.541129i	$-0.817997\pi$
$677$	1.25311	−	2.17046i	0.0481611	−	0.0834175i	0.889101	+	0.457711i	$0.151331\pi$
$678$		0			0
$679$	23.6254	+	8.59895i	0.906660	+	0.329997i
$680$		0			0
$681$	21.4970	−	18.0381i	0.823766	−	0.691222i
$682$		0			0
$683$	−29.5227			−1.12965			−0.564827	−	0.825209i	$-0.691057\pi$
$683$	−29.5227			−1.12965			−0.564827	+	0.825209i	$0.691057\pi$
$684$		0			0
$685$	34.3992			1.31432
$686$		0			0
$687$	28.6805	−	24.0658i	1.09423	−	0.918166i
$688$		0			0
$689$	−30.5412	−	11.1161i	−1.16353	−	0.423489i
$690$		0			0
$691$	−20.8238	+	36.0678i	−0.792173	+	1.37208i	0.132445	+	0.991190i	$0.457717\pi$
$691$	−20.8238	+	36.0678i	−0.792173	+	1.37208i	−0.924619	+	0.380894i	$0.875616\pi$
$692$		0			0
$693$	−4.08317	+	23.1568i	−0.155107	+	0.879655i
$694$		0			0
$695$	8.56259	+	14.8308i	0.324798	+	0.562566i
$696$		0			0
$697$	−9.85781	−	8.27169i	−0.373391	−	0.313313i
$698$		0			0
$699$	−31.4071	+	11.4313i	−1.18793	+	0.432370i
$700$		0			0
$701$	7.62364	+	43.2358i	0.287941	+	1.63299i	0.694588	+	0.719408i	$0.255587\pi$
$701$	7.62364	+	43.2358i	0.287941	+	1.63299i	−0.406647	+	0.913585i	$0.633302\pi$
$702$		0			0
$703$	21.7735	−	2.40081i	0.821204	−	0.0905481i
$704$		0			0
$705$	0.583853	+	3.31120i	0.0219892	+	0.124707i
$706$		0			0
$707$	−26.1243	+	9.50846i	−0.982505	+	0.357603i
$708$		0			0
$709$	15.4412	+	12.9567i	0.579907	+	0.486599i	0.884916	−	0.465750i	$-0.154215\pi$
$709$	15.4412	+	12.9567i	0.579907	+	0.486599i	−0.305010	+	0.952349i	$0.598660\pi$
$710$		0			0
$711$	−4.64446	−	8.04444i	−0.174181	−	0.301690i
$712$		0			0
$713$	−3.85387	+	21.8564i	−0.144328	+	0.818527i
$714$		0			0
$715$	14.1264	−	24.4676i	0.528297	−	0.915038i
$716$		0			0
$717$	−38.4570	−	13.9972i	−1.43620	−	0.522735i
$718$		0			0
$719$	17.5142	−	14.6962i	0.653170	−	0.548074i	−0.254861	−	0.966978i	$-0.582030\pi$
$719$	17.5142	−	14.6962i	0.653170	−	0.548074i	0.908031	+	0.418903i	$0.137585\pi$
$720$		0			0
$721$	35.6377			1.32722
$722$		0			0
$723$	54.8810			2.04105
$724$		0			0
$725$	−0.818278	+	0.686617i	−0.0303901	+	0.0255003i
$726$		0			0
$727$	−10.1790	−	3.70485i	−0.377518	−	0.137405i	0.146290	−	0.989242i	$-0.453267\pi$
$727$	−10.1790	−	3.70485i	−0.377518	−	0.137405i	−0.523808	+	0.851836i	$0.675489\pi$
$728$		0			0
$729$	12.9084	−	22.3580i	0.478088	−	0.828073i
$730$		0			0
$731$	10.8512	−	61.5404i	0.401347	−	2.27615i
$732$		0			0
$733$	−11.9702	−	20.7331i	−0.442131	−	0.765794i	0.555716	−	0.831372i	$-0.312444\pi$
$733$	−11.9702	−	20.7331i	−0.442131	−	0.765794i	−0.997847	+	0.0655783i	$0.979111\pi$
$734$		0			0
$735$	7.43492	+	6.23864i	0.274241	+	0.230116i
$736$		0			0
$737$	−23.0782	+	8.39976i	−0.850095	+	0.309409i
$738$		0			0
$739$	0.980265	+	5.55936i	0.0360596	+	0.204504i	0.997515	−	0.0704574i	$-0.0224459\pi$
$739$	0.980265	+	5.55936i	0.0360596	+	0.204504i	−0.961455	+	0.274962i	$0.911335\pi$
$740$		0			0
$741$	−50.2120	+	5.53650i	−1.84458	+	0.203389i
$742$		0			0
$743$	7.01282	+	39.7717i	0.257275	+	1.45908i	0.790164	+	0.612895i	$0.209995\pi$
$743$	7.01282	+	39.7717i	0.257275	+	1.45908i	−0.532889	+	0.846185i	$0.678894\pi$
$744$		0			0
$745$	1.08175	−	0.393726i	0.0396324	−	0.0144250i
$746$		0			0
$747$	−16.4041	−	13.7647i	−0.600195	−	0.503623i
$748$		0			0
$749$	−21.2276	−	36.7673i	−0.775641	−	1.34345i
$750$		0			0
$751$	4.21819	−	23.9225i	0.153924	−	0.872946i	−0.805839	−	0.592135i	$-0.798285\pi$
$751$	4.21819	−	23.9225i	0.153924	−	0.872946i	0.959763	−	0.280811i	$-0.0906036\pi$
$752$		0			0
$753$	18.8922	−	32.7222i	0.688469	−	1.19246i
$754$		0			0
$755$	−0.151118	−	0.0550025i	−0.00549975	−	0.00200174i
$756$		0			0
$757$	6.92712	−	5.81254i	0.251770	−	0.211260i	−0.508164	−	0.861260i	$-0.669676\pi$
$757$	6.92712	−	5.81254i	0.251770	−	0.211260i	0.759934	+	0.650000i	$0.225231\pi$
$758$		0			0
$759$	−34.0429			−1.23568
$760$		0			0
$761$	−42.8970			−1.55502			−0.777508	−	0.628874i	$-0.783516\pi$
$761$	−42.8970			−1.55502			−0.777508	+	0.628874i	$0.783516\pi$
$762$		0			0
$763$	−5.03493	+	4.22481i	−0.182277	+	0.152948i
$764$		0			0
$765$	41.8791	+	15.2428i	1.51414	+	0.551103i
$766$		0			0
$767$	−8.53872	+	14.7895i	−0.308315	+	0.534018i
$768$		0			0
$769$	0.909951	−	5.16059i	0.0328137	−	0.186095i	−0.963995	−	0.265919i	$-0.914325\pi$
$769$	0.909951	−	5.16059i	0.0328137	−	0.186095i	0.996809	+	0.0798236i	$0.0254357\pi$
$770$		0			0
$771$	35.4898	+	61.4701i	1.27813	+	2.21379i
$772$		0			0
$773$	27.4974	+	23.0731i	0.989014	+	0.829881i	0.985425	−	0.170113i	$-0.0544132\pi$
$773$	27.4974	+	23.0731i	0.989014	+	0.829881i	0.00358889	+	0.999994i	$0.498858\pi$
$774$		0			0
$775$	−0.638321	+	0.232330i	−0.0229292	+	0.00834554i
$776$		0			0
$777$	−6.31041	−	35.7881i	−0.226385	−	1.28389i
$778$		0			0
$779$	−5.61631	+	5.87552i	−0.201225	+	0.210512i
$780$		0			0
$781$	−0.265992	−	1.50851i	−0.00951794	−	0.0539789i
$782$		0			0
$783$	1.00377	−	0.365341i	0.0358717	−	0.0130562i
$784$		0			0
$785$	24.0739	+	20.2004i	0.859235	+	0.720984i
$786$		0			0
$787$	−22.6443	−	39.2211i	−0.807182	−	1.39808i	−0.914808	−	0.403890i	$-0.867658\pi$
$787$	−22.6443	−	39.2211i	−0.807182	−	1.39808i	0.107625	−	0.994192i	$-0.465675\pi$
$788$		0			0
$789$	1.60656	−	9.11124i	0.0571949	−	0.324369i
$790$		0			0
$791$	11.3419	−	19.6448i	0.403273	−	0.698489i
$792$		0			0
$793$	44.9059	+	16.3444i	1.59466	+	0.580407i
$794$		0			0
$795$	28.0549	−	23.5408i	0.995004	−	0.834907i
$796$		0			0
$797$	37.2723			1.32025			0.660127	−	0.751154i	$-0.270503\pi$
$797$	37.2723			1.32025			0.660127	+	0.751154i	$0.270503\pi$
$798$		0			0
$799$	−4.32864			−0.153136
$800$		0			0
$801$	23.0222	−	19.3179i	0.813449	−	0.682565i
$802$		0			0
$803$	−1.98317	−	0.721814i	−0.0699844	−	0.0254722i
$804$		0			0
$805$	−16.9067	+	29.2833i	−0.595883	+	1.03210i
$806$		0			0
$807$	−3.36446	+	19.0808i	−0.118435	+	0.671676i
$808$		0			0
$809$	−2.61611	−	4.53124i	−0.0919775	−	0.159310i	0.816366	−	0.577535i	$-0.195985\pi$
$809$	−2.61611	−	4.53124i	−0.0919775	−	0.159310i	−0.908343	+	0.418226i	$0.862652\pi$
$810$		0			0
$811$	−33.3145	−	27.9542i	−1.16983	−	0.981605i	−0.169838	−	0.985472i	$-0.554325\pi$
$811$	−33.3145	−	27.9542i	−1.16983	−	0.981605i	−0.999993	+	0.00386735i	$0.998769\pi$
$812$		0			0
$813$	1.55978	−	0.567713i	0.0547038	−	0.0199106i
$814$		0			0
$815$	0.121266	+	0.687735i	0.00424777	+	0.0240903i
$816$		0			0
$817$	−38.3457	−	9.35324i	−1.34155	−	0.327228i
$818$		0			0
$819$	7.19648	+	40.8133i	0.251466	+	1.42613i
$820$		0			0
$821$	36.2624	−	13.1984i	1.26557	−	0.460628i	0.379933	−	0.925014i	$-0.375947\pi$
$821$	36.2624	−	13.1984i	1.26557	−	0.460628i	0.885633	+	0.464386i	$0.153725\pi$
$822$		0			0
$823$	10.3336	+	8.67094i	0.360207	+	0.302250i	0.804873	−	0.593447i	$-0.202233\pi$
$823$	10.3336	+	8.67094i	0.360207	+	0.302250i	−0.444666	+	0.895696i	$0.646678\pi$
$824$		0			0
$825$	−0.520984	−	0.902370i	−0.0181383	−	0.0314165i
$826$		0			0
$827$	8.53781	−	48.4203i	0.296889	−	1.68374i	−0.362536	−	0.931970i	$-0.618089\pi$
$827$	8.53781	−	48.4203i	0.296889	−	1.68374i	0.659425	−	0.751771i	$-0.270800\pi$
$828$		0			0
$829$	−6.05265	+	10.4835i	−0.210217	+	0.364107i	−0.951782	−	0.306774i	$-0.900750\pi$
$829$	−6.05265	+	10.4835i	−0.210217	+	0.364107i	0.741565	+	0.670881i	$0.234084\pi$
$830$		0			0
$831$	31.9210	+	11.6183i	1.10733	+	0.403034i
$832$		0			0
$833$	−9.57183	+	8.03172i	−0.331644	+	0.278283i
$834$		0			0
$835$	1.92570			0.0666416
$836$		0			0
$837$	0.679287			0.0234796
$838$		0			0
$839$	43.5857	−	36.5727i	1.50474	−	1.26263i	0.631472	−	0.775399i	$-0.282451\pi$
$839$	43.5857	−	36.5727i	1.50474	−	1.26263i	0.873273	−	0.487232i	$-0.161993\pi$
$840$		0			0
$841$	−15.4498	−	5.62326i	−0.532751	−	0.193906i
$842$		0			0
$843$	−32.5637	+	56.4020i	−1.12155	+	1.94259i
$844$		0			0
$845$	3.67964	−	20.8683i	0.126584	−	0.717891i
$846$		0			0
$847$	5.51311	+	9.54899i	0.189433	+	0.328107i
$848$		0			0
$849$	9.44782	+	7.92766i	0.324248	+	0.272077i
$850$		0			0
$851$	24.4487	−	8.89861i	0.838092	−	0.305041i
$852$		0			0
$853$	−5.35913	−	30.3931i	−0.183493	−	1.04064i	−0.927876	−	0.372888i	$-0.878367\pi$
$853$	−5.35913	−	30.3931i	−0.183493	−	1.04064i	0.744383	−	0.667753i	$-0.232744\pi$
$854$		0			0
$855$	11.3181	−	25.7739i	0.387072	−	0.881447i
$856$		0			0
$857$	4.90830	+	27.8363i	0.167664	+	0.950871i	0.946275	+	0.323364i	$0.104814\pi$
$857$	4.90830	+	27.8363i	0.167664	+	0.950871i	−0.778611	+	0.627507i	$0.784075\pi$
$858$		0			0
$859$	33.2948	−	12.1183i	1.13600	−	0.413471i	0.295534	−	0.955332i	$-0.404502\pi$
$859$	33.2948	−	12.1183i	1.13600	−	0.413471i	0.840468	+	0.541861i	$0.182280\pi$
$860$		0			0
$861$	10.3294	+	8.66736i	0.352023	+	0.295383i
$862$		0			0
$863$	−4.50441	−	7.80186i	−0.153332	−	0.265578i	0.779119	−	0.626877i	$-0.215667\pi$
$863$	−4.50441	−	7.80186i	−0.153332	−	0.265578i	−0.932450	+	0.361298i	$0.882334\pi$
$864$		0			0
$865$	8.32290	−	47.2015i	0.282987	−	1.60490i
$866$		0			0
$867$	−37.3043	+	64.6130i	−1.26692	+	2.19437i
$868$		0			0
$869$	8.02737	+	2.92172i	0.272310	+	0.0991127i
$870$		0			0
$871$	−33.1583	+	27.8231i	−1.12352	+	0.942749i
$872$		0			0
$873$	−24.8595			−0.841367
$874$		0			0
$875$	−33.6911			−1.13897
$876$		0			0
$877$	−1.25149	+	1.05012i	−0.0422598	+	0.0354602i	−0.663673	−	0.748023i	$-0.731003\pi$
$877$	−1.25149	+	1.05012i	−0.0422598	+	0.0354602i	0.621413	+	0.783483i	$0.286559\pi$
$878$		0			0
$879$	−2.86559	−	1.04299i	−0.0966541	−	0.0351792i
$880$		0			0
$881$	13.3392	−	23.1041i	0.449408	−	0.778398i	−0.548939	−	0.835862i	$-0.684968\pi$
$881$	13.3392	−	23.1041i	0.449408	−	0.778398i	0.998348	+	0.0574642i	$0.0183015\pi$
$882$		0			0
$883$	−5.34421	+	30.3085i	−0.179847	+	1.01996i	0.752552	+	0.658532i	$0.228822\pi$
$883$	−5.34421	+	30.3085i	−0.179847	+	1.01996i	−0.932399	+	0.361430i	$0.882289\pi$
$884$		0			0
$885$	−9.62160	−	16.6651i	−0.323427	−	0.560191i
$886$		0			0
$887$	−23.1877	−	19.4568i	−0.778566	−	0.653294i	0.164321	−	0.986407i	$-0.447457\pi$
$887$	−23.1877	−	19.4568i	−0.778566	−	0.653294i	−0.942887	+	0.333113i	$0.891901\pi$
$888$		0			0
$889$	12.9603	−	4.71716i	0.434675	−	0.158209i
$890$		0			0
$891$	4.30777	+	24.4306i	0.144316	+	0.818454i
$892$		0			0
$893$	−0.176809	+	2.72835i	−0.00591669	+	0.0913007i
$894$		0			0
$895$	−2.26499	−	12.8454i	−0.0757103	−	0.429375i
$896$		0			0
$897$	−56.3813	+	20.5211i	−1.88252	+	0.685180i
$898$		0			0
$899$	−22.1366	−	18.5748i	−0.738298	−	0.619505i
$900$		0			0
$901$	23.5745	+	40.8322i	0.785381	+	1.36032i
$902$		0			0
$903$	−11.3703	+	64.4841i	−0.378380	+	2.14590i
$904$		0			0
$905$	−13.2440	+	22.9392i	−0.440244	+	0.762525i
$906$		0			0
$907$	−43.7836	−	15.9359i	−1.45381	−	0.529144i	−0.510159	−	0.860080i	$-0.670413\pi$
$907$	−43.7836	−	15.9359i	−1.45381	−	0.529144i	−0.943653	+	0.330936i	$0.892636\pi$
$908$		0			0
$909$	21.0577	−	17.6695i	0.698441	−	0.586061i
$910$		0			0
$911$	−58.0481			−1.92322			−0.961609	−	0.274422i	$-0.911513\pi$
$911$	−58.0481			−1.92322			−0.961609	+	0.274422i	$0.911513\pi$
$912$		0			0
$913$	19.6934			0.651757
$914$		0			0
$915$	−41.2502	+	34.6130i	−1.36369	+	1.14427i
$916$		0			0
$917$	−0.0224310	−	0.00816421i	−0.000740736	−	0.000269606i
$918$		0			0
$919$	10.9348	−	18.9396i	0.360705	−	0.624759i	−0.627372	−	0.778720i	$-0.715870\pi$
$919$	10.9348	−	18.9396i	0.360705	−	0.624759i	0.988077	+	0.153960i	$0.0492028\pi$
$920$		0			0
$921$	−10.2464	+	58.1100i	−0.337629	+	1.91479i
$922$		0			0
$923$	−1.34987	−	2.33804i	−0.0444314	−	0.0769574i
$924$		0			0
$925$	0.610031	+	0.511877i	0.0200577	+	0.0168304i
$926$		0			0
$927$	−33.1126	+	12.0520i	−1.08756	+	0.395840i
$928$		0			0
$929$	−6.03214	−	34.2100i	−0.197908	−	1.12239i	−0.908216	−	0.418502i	$-0.862555\pi$
$929$	−6.03214	−	34.2100i	−0.197908	−	1.12239i	0.710308	−	0.703891i	$-0.248556\pi$
$930$		0			0
$931$	4.67143	+	6.36120i	0.153100	+	0.208480i
$932$		0			0
$933$	−13.2935	−	75.3911i	−0.435209	−	2.46819i
$934$		0			0
$935$	−38.5141	+	14.0180i	−1.25955	+	0.458437i
$936$		0			0
$937$	26.4906	+	22.2282i	0.865409	+	0.726165i	0.963126	−	0.269050i	$-0.0867095\pi$
$937$	26.4906	+	22.2282i	0.865409	+	0.726165i	−0.0977170	+	0.995214i	$0.531154\pi$
$938$		0			0
$939$	−25.6348	−	44.4008i	−0.836560	−	1.44896i
$940$		0			0
$941$	4.06376	−	23.0467i	0.132475	−	0.751302i	−0.844110	−	0.536170i	$-0.819871\pi$
$941$	4.06376	−	23.0467i	0.132475	−	0.751302i	0.976585	−	0.215132i	$-0.0690182\pi$
$942$		0			0
$943$	−4.82694	+	8.36051i	−0.157187	+	0.272256i
$944$		0			0
$945$	0.972528	+	0.353971i	0.0316363	+	0.0115147i
$946$		0			0
$947$	−5.16816	+	4.33660i	−0.167943	+	0.140921i	−0.722885	−	0.690968i	$-0.757185\pi$
$947$	−5.16816	+	4.33660i	−0.167943	+	0.140921i	0.554943	+	0.831889i	$0.312740\pi$
$948$		0			0
$949$	−3.71960			−0.120743
$950$		0			0
$951$	24.8893			0.807090
$952$		0			0
$953$	12.9566	−	10.8719i	0.419707	−	0.352176i	−0.408345	−	0.912828i	$-0.633894\pi$
$953$	12.9566	−	10.8719i	0.419707	−	0.352176i	0.828051	+	0.560652i	$0.189449\pi$
$954$		0			0
$955$	17.3365	+	6.30999i	0.560997	+	0.204186i
$956$		0			0
$957$	22.1630	−	38.3874i	0.716427	−	1.24089i
$958$		0			0
$959$	8.05803	−	45.6994i	0.260207	−	1.47571i
$960$		0			0
$961$	6.31173	+	10.9322i	0.203604	+	0.352653i
$962$		0			0
$963$	32.1576	+	26.9835i	1.03627	+	0.869530i
$964$		0			0
$965$	−1.93143	+	0.702983i	−0.0621749	+	0.0226298i
$966$		0			0
$967$	9.00763	+	51.0848i	0.289666	+	1.64278i	0.688127	+	0.725591i	$0.258433\pi$
$967$	9.00763	+	51.0848i	0.289666	+	1.64278i	−0.398461	+	0.917185i	$0.630456\pi$
$968$		0			0
$969$	60.9627	+	40.6691i	1.95840	+	1.30648i
$970$		0			0
$971$	3.29208	+	18.6703i	0.105648	+	0.599159i	0.990960	+	0.134161i	$0.0428339\pi$
$971$	3.29208	+	18.6703i	0.105648	+	0.599159i	−0.885312	+	0.464998i	$0.846055\pi$
$972$		0			0
$973$	21.7086	−	7.90129i	0.695946	−	0.253304i
$974$		0			0
$975$	−1.40679	−	1.18044i	−0.0450535	−	0.0378043i
$976$		0			0
$977$	1.93320	+	3.34840i	0.0618485	+	0.107125i	0.895292	−	0.445480i	$-0.146967\pi$
$977$	1.93320	+	3.34840i	0.0618485	+	0.107125i	−0.833443	+	0.552605i	$0.813634\pi$
$978$		0			0
$979$	−4.79938	+	27.2186i	−0.153389	+	0.869911i
$980$		0			0
$981$	3.24944	−	5.62819i	0.103747	−	0.179694i
$982$		0			0
$983$	44.9954	+	16.3770i	1.43513	+	0.522345i	0.938397	−	0.345558i	$-0.112310\pi$
$983$	44.9954	+	16.3770i	1.43513	+	0.522345i	0.496734	+	0.867903i	$0.334533\pi$
$984$		0			0
$985$	−37.6902	+	31.6258i	−1.20091	+	1.00768i
$986$		0			0
$987$	4.53570			0.144373
$988$		0			0
$989$	−46.8797			−1.49069
$990$		0			0
$991$	30.2666	−	25.3967i	0.961449	−	0.806751i	−0.0197392	−	0.999805i	$-0.506284\pi$
$991$	30.2666	−	25.3967i	0.961449	−	0.806751i	0.981188	+	0.193054i	$0.0618392\pi$
$992$		0			0
$993$	62.6495	+	22.8025i	1.98812	+	0.723617i
$994$		0			0
$995$	15.8864	−	27.5160i	0.503632	−	0.872317i
$996$		0			0
$997$	1.96319	−	11.1338i	0.0621748	−	0.352611i	−0.937810	−	0.347148i	$-0.887150\pi$
$997$	1.96319	−	11.1338i	0.0621748	−	0.352611i	0.999985	−	0.00546247i	$-0.00173877\pi$
$998$		0			0
$999$	−0.398169	−	0.689650i	−0.0125975	−	0.0218196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.i.a.9.2	✓	12
3.2	odd	2		684.2.bo.c.541.2		12
4.3	odd	2		304.2.u.e.161.1		12
19.4	even	9		1444.2.e.g.429.2		12
19.6	even	9		1444.2.a.h.1.5		6
19.9	even	9		1444.2.e.g.653.2		12
19.10	odd	18		1444.2.e.h.653.5		12
19.13	odd	18		1444.2.a.g.1.2		6
19.15	odd	18		1444.2.e.h.429.5		12
19.17	even	9	inner	76.2.i.a.17.2	yes	12
57.17	odd	18		684.2.bo.c.397.2		12
76.51	even	18		5776.2.a.by.1.5		6
76.55	odd	18		304.2.u.e.17.1		12
76.63	odd	18		5776.2.a.bw.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.9.2	✓	12	1.1	even	1	trivial
76.2.i.a.17.2	yes	12	19.17	even	9	inner
304.2.u.e.17.1		12	76.55	odd	18
304.2.u.e.161.1		12	4.3	odd	2
684.2.bo.c.397.2		12	57.17	odd	18
684.2.bo.c.541.2		12	3.2	odd	2
1444.2.a.g.1.2		6	19.13	odd	18
1444.2.a.h.1.5		6	19.6	even	9
1444.2.e.g.429.2		12	19.4	even	9
1444.2.e.g.653.2		12	19.9	even	9
1444.2.e.h.429.5		12	19.15	odd	18
1444.2.e.h.653.5		12	19.10	odd	18
5776.2.a.bw.1.2		6	76.63	odd	18
5776.2.a.by.1.5		6	76.51	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86622 - 1.56594i) q^{3} +(-2.06765 - 0.752564i) q^{5} +(-1.48413 + 2.57059i) q^{7} +(0.509650 - 2.89037i) q^{9} +O(q^{10})\)	\(q+(1.86622 - 1.56594i) q^{3} +(-2.06765 - 0.752564i) q^{5} +(-1.48413 + 2.57059i) q^{7} +(0.509650 - 2.89037i) q^{9} +(1.34956 + 2.33751i) q^{11} +(3.64418 + 3.05783i) q^{13} +(-5.03717 + 1.83338i) q^{15} +(-1.19836 - 6.79626i) q^{17} +(-4.33264 + 0.477728i) q^{19} +(1.25569 + 7.12136i) q^{21} +(-4.86497 + 1.77070i) q^{23} +(-0.121388 - 0.101857i) q^{25} +(0.0792304 + 0.137231i) q^{27} +(1.17057 - 6.63861i) q^{29} +(2.14339 - 3.71247i) q^{31} +(6.17900 + 2.24897i) q^{33} +(5.00321 - 4.19819i) q^{35} -5.02546 q^{37} +11.5892 q^{39} +(1.42844 - 1.19860i) q^{41} +(8.50895 + 3.09700i) q^{43} +(-3.22896 + 5.59273i) q^{45} +(0.108919 - 0.617710i) q^{47} +(-0.905299 - 1.56802i) q^{49} +(-12.8790 - 10.8067i) q^{51} +(-6.42007 + 2.33671i) q^{53} +(-1.03130 - 5.84880i) q^{55} +(-7.33756 + 7.67622i) q^{57} +(0.623372 + 3.53532i) q^{59} +(9.43969 - 3.43576i) q^{61} +(6.67357 + 5.59979i) q^{63} +(-5.23369 - 9.06501i) q^{65} +(-1.58002 + 8.96073i) q^{67} +(-6.30628 + 10.9228i) q^{69} +(-0.533286 - 0.194100i) q^{71} +(-0.598968 + 0.502594i) q^{73} -0.386038 q^{75} -8.01173 q^{77} +(2.42448 - 2.03438i) q^{79} +(8.63662 + 3.14347i) q^{81} +(3.64810 - 6.31870i) q^{83} +(-2.63682 + 14.9542i) q^{85} +(-8.21115 - 14.2221i) q^{87} +(7.84414 + 6.58201i) q^{89} +(-13.2689 + 4.82948i) q^{91} +(-1.81347 - 10.2847i) q^{93} +(9.31792 + 2.27281i) q^{95} +(-1.47083 - 8.34147i) q^{97} +(7.44408 - 2.70942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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