LMFDB - Embedded newform 378.2.u.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.500000 + 2.22827i$ of defining polynomial
Character	$\chi$	$=$	378.43
Dual form			378.2.u.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.67071 - 0.456871i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.78124 - 0.648319i) q^{5} +(-0.986166 - 1.42389i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.58254 + 1.52660i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.67071 - 0.456871i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.78124 - 0.648319i) q^{5} +(-0.986166 - 1.42389i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.58254 + 1.52660i) q^{9} +(-0.947779 - 1.64160i) q^{10} +(4.90067 - 1.78370i) q^{11} +(0.159815 - 1.72466i) q^{12} +(4.25805 - 3.57293i) q^{13} +(0.766044 - 0.642788i) q^{14} +(2.67974 + 1.89695i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.07824 + 3.59961i) q^{17} +(0.997061 + 2.82946i) q^{18} +(1.35633 - 2.34922i) q^{19} +(0.329160 - 1.86676i) q^{20} +(-0.740046 + 1.56599i) q^{21} +(4.90067 + 1.78370i) q^{22} +(0.529358 + 3.00214i) q^{23} +(1.23102 - 1.21844i) q^{24} +(-1.07772 - 0.904313i) q^{25} +5.55849 q^{26} +(-3.61721 - 3.73039i) q^{27} +1.00000 q^{28} +(-3.78733 - 3.17795i) q^{29} +(0.833463 + 3.17565i) q^{30} +(-1.79730 - 10.1930i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-9.00252 + 0.741067i) q^{33} +(-0.721763 + 4.09332i) q^{34} +(-0.947779 + 1.64160i) q^{35} +(-1.05495 + 2.80839i) q^{36} +(5.29467 + 9.17063i) q^{37} +(2.54906 - 0.927781i) q^{38} +(-8.74633 + 4.02394i) q^{39} +(1.45208 - 1.21844i) q^{40} +(-0.771960 + 0.647752i) q^{41} +(-1.57351 + 0.723928i) q^{42} +(8.48794 - 3.08936i) q^{43} +(2.60759 + 4.51648i) q^{44} +(-3.61040 - 4.39355i) q^{45} +(-1.52423 + 2.64004i) q^{46} +(-1.04196 + 5.90923i) q^{47} +(1.72621 - 0.142098i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.244299 - 1.38549i) q^{50} +(-1.82757 - 6.96338i) q^{51} +(4.25805 + 3.57293i) q^{52} -1.27451 q^{53} +(-0.373098 - 5.18274i) q^{54} -9.88569 q^{55} +(0.766044 + 0.642788i) q^{56} +(-3.33932 + 3.30521i) q^{57} +(-0.858518 - 4.86890i) q^{58} +(-3.28812 - 1.19678i) q^{59} +(-1.40280 + 2.96843i) q^{60} +(-2.40588 + 13.6444i) q^{61} +(5.17513 - 8.96359i) q^{62} +(1.95186 - 2.27821i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-9.90102 + 3.60367i) q^{65} +(-7.37268 - 5.21902i) q^{66} +(6.83683 - 5.73678i) q^{67} +(-3.18404 + 2.67173i) q^{68} +(0.487187 - 5.25755i) q^{69} +(-1.78124 + 0.648319i) q^{70} +(-1.93862 - 3.35779i) q^{71} +(-2.61334 + 1.47324i) q^{72} +(5.00701 - 8.67239i) q^{73} +(-1.83882 + 10.4285i) q^{74} +(1.38740 + 2.00322i) q^{75} +(2.54906 + 0.927781i) q^{76} +(-0.905608 - 5.13596i) q^{77} +(-9.28662 - 2.53951i) q^{78} +(-7.44513 - 6.24720i) q^{79} +1.89556 q^{80} +(4.33900 + 7.88499i) q^{81} -1.00772 q^{82} +(2.87989 + 2.41651i) q^{83} +(-1.67071 - 0.456871i) q^{84} +(-1.36814 - 7.75913i) q^{85} +(8.48794 + 3.08936i) q^{86} +(4.87562 + 7.03975i) q^{87} +(-0.905608 + 5.13596i) q^{88} +(-6.98840 + 12.1043i) q^{89} +(0.0583890 - 5.68637i) q^{90} +(-2.77925 - 4.81379i) q^{91} +(-2.86461 + 1.04263i) q^{92} +(-1.65412 + 17.8507i) q^{93} +(-4.59657 + 3.85698i) q^{94} +(-3.93899 + 3.30521i) q^{95} +(1.41369 + 1.00073i) q^{96} +(-1.06598 + 0.387987i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(15.3792 + 2.87488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.67071	−	0.456871i	−0.964584	−	0.263775i
$3$	−1.67071	−	0.456871i	−0.964584	−	0.263775i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.78124	−	0.648319i	−0.796595	−	0.289937i	−0.0885205	−	0.996074i	$-0.528214\pi$
$5$	−1.78124	−	0.648319i	−0.796595	−	0.289937i	−0.708075	+	0.706137i	$0.750436\pi$
$6$	−0.986166	−	1.42389i	−0.402601	−	0.581303i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.58254	+	1.52660i	0.860846	+	0.508866i
$10$	−0.947779	−	1.64160i	−0.299714	−	0.519120i
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.527454	−	0.849584i	$-0.323147\pi$
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.950155	+	0.311778i	$0.100925\pi$
$12$	0.159815	−	1.72466i	0.0461345	−	0.497867i
$13$	4.25805	−	3.57293i	1.18097	−	0.990952i	0.180999	−	0.983483i	$-0.442067\pi$
$13$	4.25805	−	3.57293i	1.18097	−	0.990952i	0.999972	−	0.00746894i	$-0.00237746\pi$
$14$	0.766044	−	0.642788i	0.204734	−	0.171792i
$15$	2.67974	+	1.89695i	0.691905	+	0.489790i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.07824	+	3.59961i	0.504046	+	0.873033i	0.999989	+	0.00467830i	$0.00148915\pi$
$17$	2.07824	+	3.59961i	0.504046	+	0.873033i	−0.495943	+	0.868355i	$0.665178\pi$
$18$	0.997061	+	2.82946i	0.235010	+	0.666911i
$19$	1.35633	−	2.34922i	0.311162	−	0.538949i	−0.667452	−	0.744653i	$-0.732615\pi$
$19$	1.35633	−	2.34922i	0.311162	−	0.538949i	0.978614	+	0.205704i	$0.0659483\pi$
$20$	0.329160	−	1.86676i	0.0736024	−	0.417420i
$21$	−0.740046	+	1.56599i	−0.161491	+	0.341728i
$22$	4.90067	+	1.78370i	1.04483	+	0.380286i
$23$	0.529358	+	3.00214i	0.110379	+	0.625989i	0.988935	+	0.148350i	$0.0473963\pi$
$23$	0.529358	+	3.00214i	0.110379	+	0.625989i	−0.878556	+	0.477639i	$0.841493\pi$
$24$	1.23102	−	1.21844i	0.251280	−	0.248713i
$25$	−1.07772	−	0.904313i	−0.215544	−	0.180863i
$26$	5.55849			1.09011
$27$	−3.61721	−	3.73039i	−0.696133	−	0.717913i
$28$	1.00000			0.188982
$29$	−3.78733	−	3.17795i	−0.703290	−	0.590130i	0.219418	−	0.975631i	$-0.429584\pi$
$29$	−3.78733	−	3.17795i	−0.703290	−	0.590130i	−0.922708	+	0.385501i	$0.874029\pi$
$30$	0.833463	+	3.17565i	0.152169	+	0.579792i
$31$	−1.79730	−	10.1930i	−0.322805	−	1.83072i	−0.524669	−	0.851306i	$-0.675811\pi$
$31$	−1.79730	−	10.1930i	−0.322805	−	1.83072i	0.201864	−	0.979414i	$-0.435300\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−9.00252	+	0.741067i	−1.56714	+	0.129003i
$34$	−0.721763	+	4.09332i	−0.123781	+	0.701999i
$35$	−0.947779	+	1.64160i	−0.160204	+	0.277481i
$36$	−1.05495	+	2.80839i	−0.175825	+	0.468066i
$37$	5.29467	+	9.17063i	0.870438	+	1.50764i	0.861545	+	0.507682i	$0.169498\pi$
$37$	5.29467	+	9.17063i	0.870438	+	1.50764i	0.00889327	+	0.999960i	$0.497169\pi$
$38$	2.54906	−	0.927781i	0.413512	−	0.150506i
$39$	−8.74633	+	4.02394i	−1.40053	+	0.644347i
$40$	1.45208	−	1.21844i	0.229594	−	0.192652i
$41$	−0.771960	+	0.647752i	−0.120560	+	0.101162i	−0.701074	−	0.713088i	$-0.747296\pi$
$41$	−0.771960	+	0.647752i	−0.120560	+	0.101162i	0.580514	+	0.814250i	$0.302851\pi$
$42$	−1.57351	+	0.723928i	−0.242798	+	0.111704i
$43$	8.48794	−	3.08936i	1.29440	−	0.471122i	0.399230	−	0.916851i	$-0.369277\pi$
$43$	8.48794	−	3.08936i	1.29440	−	0.471122i	0.895168	+	0.445728i	$0.147055\pi$
$44$	2.60759	+	4.51648i	0.393109	+	0.680886i
$45$	−3.61040	−	4.39355i	−0.538207	−	0.654951i
$46$	−1.52423	+	2.64004i	−0.224735	+	0.389252i
$47$	−1.04196	+	5.90923i	−0.151985	+	0.861950i	0.809505	+	0.587112i	$0.199735\pi$
$47$	−1.04196	+	5.90923i	−0.151985	+	0.861950i	−0.961491	+	0.274838i	$0.911376\pi$
$48$	1.72621	−	0.142098i	0.249157	−	0.0205101i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	−0.244299	−	1.38549i	−0.0345491	−	0.195938i
$51$	−1.82757	−	6.96338i	−0.255911	−	0.975069i
$52$	4.25805	+	3.57293i	0.590485	+	0.495476i
$53$	−1.27451			−0.175068			−0.0875339	−	0.996162i	$-0.527899\pi$
$53$	−1.27451			−0.175068			−0.0875339	+	0.996162i	$0.527899\pi$
$54$	−0.373098	−	5.18274i	−0.0507723	−	0.705282i
$55$	−9.88569			−1.33299
$56$	0.766044	+	0.642788i	0.102367	+	0.0858961i
$57$	−3.33932	+	3.30521i	−0.442304	+	0.437785i
$58$	−0.858518	−	4.86890i	−0.112729	−	0.639318i
$59$	−3.28812	−	1.19678i	−0.428077	−	0.155807i	0.118991	−	0.992895i	$-0.462034\pi$
$59$	−3.28812	−	1.19678i	−0.428077	−	0.155807i	−0.547068	+	0.837088i	$0.684256\pi$
$60$	−1.40280	+	2.96843i	−0.181101	+	0.383223i
$61$	−2.40588	+	13.6444i	−0.308042	+	1.74699i	0.300789	+	0.953691i	$0.402750\pi$
$61$	−2.40588	+	13.6444i	−0.308042	+	1.74699i	−0.608831	+	0.793300i	$0.708361\pi$
$62$	5.17513	−	8.96359i	0.657242	−	1.13838i
$63$	1.95186	−	2.27821i	0.245911	−	0.287028i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−9.90102	+	3.60367i	−1.22807	+	0.446981i
$66$	−7.37268	−	5.21902i	−0.907514	−	0.642417i
$67$	6.83683	−	5.73678i	0.835251	−	0.700859i	−0.121239	−	0.992623i	$-0.538687\pi$
$67$	6.83683	−	5.73678i	0.835251	−	0.700859i	0.956490	+	0.291764i	$0.0942423\pi$
$68$	−3.18404	+	2.67173i	−0.386122	+	0.323995i
$69$	0.487187	−	5.25755i	0.0586504	−	0.632935i
$70$	−1.78124	+	0.648319i	−0.212899	+	0.0774889i
$71$	−1.93862	−	3.35779i	−0.230072	−	0.398496i	0.727757	−	0.685835i	$-0.240563\pi$
$71$	−1.93862	−	3.35779i	−0.230072	−	0.398496i	−0.957829	+	0.287339i	$0.907229\pi$
$72$	−2.61334	+	1.47324i	−0.307985	+	0.173624i
$73$	5.00701	−	8.67239i	0.586026	−	1.01503i	−0.408721	−	0.912659i	$-0.634025\pi$
$73$	5.00701	−	8.67239i	0.586026	−	1.01503i	0.994747	−	0.102367i	$-0.0326416\pi$
$74$	−1.83882	+	10.4285i	−0.213758	+	1.21228i
$75$	1.38740	+	2.00322i	0.160203	+	0.231312i
$76$	2.54906	+	0.927781i	0.292397	+	0.106424i
$77$	−0.905608	−	5.13596i	−0.103204	−	0.585297i
$78$	−9.28662	−	2.53951i	−1.05150	−	0.287543i
$79$	−7.44513	−	6.24720i	−0.837642	−	0.702865i	0.119390	−	0.992847i	$-0.461906\pi$
$79$	−7.44513	−	6.24720i	−0.837642	−	0.702865i	−0.957032	+	0.289982i	$0.906351\pi$
$80$	1.89556			0.211930
$81$	4.33900	+	7.88499i	0.482111	+	0.876110i
$82$	−1.00772			−0.111284
$83$	2.87989	+	2.41651i	0.316109	+	0.265247i	0.787011	−	0.616938i	$-0.211627\pi$
$83$	2.87989	+	2.41651i	0.316109	+	0.265247i	−0.470903	+	0.882185i	$0.656072\pi$
$84$	−1.67071	−	0.456871i	−0.182289	−	0.0498487i
$85$	−1.36814	−	7.75913i	−0.148396	−	0.841596i
$86$	8.48794	+	3.08936i	0.915278	+	0.333134i
$87$	4.87562	+	7.03975i	0.522721	+	0.754740i
$88$	−0.905608	+	5.13596i	−0.0965381	+	0.547495i
$89$	−6.98840	+	12.1043i	−0.740768	+	1.28305i	0.211377	+	0.977405i	$0.432205\pi$
$89$	−6.98840	+	12.1043i	−0.740768	+	1.28305i	−0.952146	+	0.305644i	$0.901128\pi$
$90$	0.0583890	−	5.68637i	0.00615474	−	0.599396i
$91$	−2.77925	−	4.81379i	−0.291344	−	0.504623i
$92$	−2.86461	+	1.04263i	−0.298656	+	0.108702i
$93$	−1.65412	+	17.8507i	−0.171524	+	1.85103i
$94$	−4.59657	+	3.85698i	−0.474100	+	0.397817i
$95$	−3.93899	+	3.30521i	−0.404132	+	0.339107i
$96$	1.41369	+	1.00073i	0.144285	+	0.102137i
$97$	−1.06598	+	0.387987i	−0.108234	+	0.0393941i	−0.395570	−	0.918436i	$-0.629453\pi$
$97$	−1.06598	+	0.387987i	−0.108234	+	0.0393941i	0.287335	+	0.957830i	$0.407231\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	15.3792	+	2.87488i	1.54566	+	0.288937i
$100$	0.703431	−	1.21838i	0.0703431	−	0.121838i
$101$	−0.646320	+	3.66546i	−0.0643112	+	0.364727i	0.935620	+	0.353008i	$0.114841\pi$
$101$	−0.646320	+	3.66546i	−0.0643112	+	0.364727i	−0.999931	+	0.0117185i	$0.996270\pi$
$102$	3.07598	−	6.50900i	0.304567	−	0.644487i
$103$	−0.291324	−	0.106033i	−0.0287050	−	0.0104478i	0.327628	−	0.944807i	$-0.393751\pi$
$103$	−0.291324	−	0.106033i	−0.0287050	−	0.0104478i	−0.356333	+	0.934359i	$0.615973\pi$
$104$	0.965222	+	5.47405i	0.0946478	+	0.536774i
$105$	2.33346	−	2.30963i	0.227723	−	0.225396i
$106$	−0.976334	−	0.819241i	−0.0948299	−	0.0795718i
$107$	11.8843			1.14890			0.574448	−	0.818541i	$-0.305217\pi$
$107$	11.8843			1.14890			0.574448	+	0.818541i	$0.305217\pi$
$108$	3.04559	−	4.21003i	0.293062	−	0.405111i
$109$	−13.2862			−1.27259			−0.636296	−	0.771445i	$-0.719534\pi$
$109$	−13.2862			−1.27259			−0.636296	+	0.771445i	$0.719534\pi$
$110$	−7.57288	−	6.35440i	−0.722045	−	0.605868i
$111$	−4.65605	−	17.7404i	−0.441933	−	1.68385i
$112$	0.173648	+	0.984808i	0.0164082	+	0.0930556i
$113$	−12.0671	−	4.39206i	−1.13517	−	0.413170i	−0.295006	−	0.955495i	$-0.595322\pi$
$113$	−12.0671	−	4.39206i	−1.13517	−	0.413170i	−0.840168	+	0.542325i	$0.817544\pi$
$114$	−4.68261	+	0.385462i	−0.438567	+	0.0361018i
$115$	1.00343	−	5.69073i	0.0935702	−	0.530663i
$116$	2.47201	−	4.28164i	0.229520	−	0.397540i
$117$	16.4510	−	2.72690i	1.52090	−	0.252102i
$118$	−1.74957	−	3.03035i	−0.161061	−	0.278966i
$119$	3.90580	−	1.42160i	0.358045	−	0.130318i
$120$	−2.98268	+	1.37225i	−0.272280	+	0.125268i
$121$	12.4085	−	10.4120i	1.12805	−	0.946544i
$122$	−10.6135	+	8.90577i	−0.960900	+	0.806291i
$123$	1.58566	−	0.729518i	0.142974	−	0.0657784i
$124$	9.72606	−	3.54000i	0.873426	−	0.317901i
$125$	6.07229	+	10.5175i	0.543122	+	0.940715i
$126$	2.95962	−	0.490582i	0.263664	−	0.0437045i
$127$	−2.61394	+	4.52747i	−0.231949	+	0.401748i	−0.958382	−	0.285490i	$-0.907844\pi$
$127$	−2.61394	+	4.52747i	−0.231949	+	0.401748i	0.726432	+	0.687238i	$0.241177\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−15.5923	+	1.28352i	−1.37283	+	0.113008i
$130$	−9.90102	−	3.60367i	−0.868376	−	0.316063i
$131$	−0.968590	−	5.49315i	−0.0846261	−	0.479939i	−0.997437	−	0.0715553i	$-0.977204\pi$
$131$	−0.968590	−	5.49315i	−0.0846261	−	0.479939i	0.912810	−	0.408383i	$-0.133907\pi$
$132$	−2.29308	−	8.73707i	−0.199587	−	0.760464i
$133$	−2.07801	−	1.74366i	−0.180186	−	0.151194i
$134$	8.92484			0.770989
$135$	4.02465	+	8.98983i	0.346386	+	0.773721i
$136$	−4.15647			−0.356414
$137$	13.3511	+	11.2029i	1.14066	+	0.957129i	0.999460	−	0.0328513i	$-0.0104588\pi$
$137$	13.3511	+	11.2029i	1.14066	+	0.957129i	0.141202	+	0.989981i	$0.454903\pi$
$138$	3.75270	−	3.71436i	0.319451	−	0.316187i
$139$	0.393760	+	2.23312i	0.0333983	+	0.189411i	0.996943	−	0.0781378i	$-0.0248974\pi$
$139$	0.393760	+	2.23312i	0.0333983	+	0.189411i	−0.963544	+	0.267549i	$0.913786\pi$
$140$	−1.78124	−	0.648319i	−0.150542	−	0.0547929i
$141$	4.44057	−	9.39657i	0.373963	−	0.791334i
$142$	0.673275	−	3.81833i	0.0565000	−	0.320427i
$143$	14.4943	−	25.1048i	1.21207	−	2.09937i
$144$	−2.94892	−	0.551252i	−0.245743	−	0.0459377i
$145$	4.68583	+	8.11609i	0.389137	+	0.674005i
$146$	9.41009	−	3.42499i	0.778785	−	0.283455i
$147$	1.41369	+	1.00073i	0.116600	+	0.0825392i
$148$	−8.11190	+	6.80669i	−0.666794	+	0.559507i
$149$	0.422702	−	0.354689i	0.0346291	−	0.0290573i	−0.625309	−	0.780377i	$-0.715027\pi$
$149$	0.422702	−	0.354689i	0.0346291	−	0.0290573i	0.659938	+	0.751320i	$0.270583\pi$
$150$	−0.224837	+	2.42636i	−0.0183579	+	0.198111i
$151$	−14.4242	+	5.24999i	−1.17383	+	0.427238i	−0.854018	−	0.520244i	$-0.825841\pi$
$151$	−14.4242	+	5.24999i	−1.17383	+	0.427238i	−0.319809	+	0.947482i	$0.603619\pi$
$152$	1.35633	+	2.34922i	0.110013	+	0.190547i
$153$	−0.128032	+	12.4688i	−0.0103508	+	1.00804i
$154$	2.60759	−	4.51648i	0.210126	−	0.363949i
$155$	−3.40689	+	19.3215i	−0.273648	+	1.55194i
$156$	−5.48160	−	7.91471i	−0.438879	−	0.633684i
$157$	10.8571	+	3.95167i	0.866493	+	0.315378i	0.736746	−	0.676170i	$-0.236361\pi$
$157$	10.8571	+	3.95167i	0.866493	+	0.315378i	0.129747	+	0.991547i	$0.458584\pi$
$158$	−1.68767	−	9.57127i	−0.134264	−	0.761449i
$159$	2.12934	+	0.582288i	0.168868	+	0.0461785i
$160$	1.45208	+	1.21844i	0.114797	+	0.0963262i
$161$	3.04845			0.240252
$162$	−1.74451	+	8.82931i	−0.137061	+	0.693696i
$163$	−7.32769			−0.573949			−0.286974	−	0.957938i	$-0.592649\pi$
$163$	−7.32769			−0.573949			−0.286974	+	0.957938i	$0.592649\pi$
$164$	−0.771960	−	0.647752i	−0.0602800	−	0.0505809i
$165$	16.5161	+	4.51648i	1.28578	+	0.351608i
$166$	0.652817	+	3.70231i	0.0506685	+	0.287355i
$167$	1.08894	+	0.396342i	0.0842647	+	0.0306698i	0.383809	−	0.923413i	$-0.374612\pi$
$167$	1.08894	+	0.396342i	0.0842647	+	0.0306698i	−0.299544	+	0.954083i	$0.596834\pi$
$168$	−0.986166	−	1.42389i	−0.0760844	−	0.109856i
$169$	3.10775	−	17.6249i	0.239058	−	1.35576i
$170$	3.93941	−	6.82327i	0.302139	−	0.523321i
$171$	7.08908	−	3.99640i	0.542116	−	0.305612i
$172$	4.51634	+	7.82252i	0.344367	+	0.596462i
$173$	−16.9085	+	6.15418i	−1.28553	+	0.467894i	−0.892257	−	0.451528i	$-0.850879\pi$
$173$	−16.9085	+	6.15418i	−1.28553	+	0.467894i	−0.393271	+	0.919422i	$0.628657\pi$
$174$	−0.790125	+	8.52675i	−0.0598992	+	0.646411i
$175$	−1.07772	+	0.904313i	−0.0814678	+	0.0683596i
$176$	−3.99506	+	3.35226i	−0.301139	+	0.252686i
$177$	4.94672	+	3.50172i	0.371818	+	0.263205i
$178$	−13.1339	+	4.78034i	−0.984426	+	0.358302i
$179$	1.47375	+	2.55260i	0.110153	+	0.190790i	0.915832	−	0.401562i	$-0.131533\pi$
$179$	1.47375	+	2.55260i	0.110153	+	0.190790i	−0.805679	+	0.592353i	$0.798199\pi$
$180$	3.69986	−	4.31848i	0.275771	−	0.321881i
$181$	−6.81730	+	11.8079i	−0.506726	+	0.877675i	0.493244	+	0.869891i	$0.335811\pi$
$181$	−6.81730	+	11.8079i	−0.506726	+	0.877675i	−0.999970	+	0.00778391i	$0.997522\pi$
$182$	0.965222	−	5.47405i	0.0715470	−	0.405763i
$183$	10.2533	−	21.6967i	0.757944	−	1.60387i
$184$	−2.86461	−	1.04263i	−0.211182	−	0.0768639i
$185$	−3.48559	−	19.7677i	−0.256265	−	1.45335i
$186$	−12.7413	+	12.6112i	−0.934241	+	0.924697i
$187$	16.6054	+	13.9336i	1.21430	+	1.01892i
$188$	−6.00039			−0.437624
$189$	−4.30184	+	2.91448i	−0.312912	+	0.211997i
$190$	−5.14199			−0.373039
$191$	−3.88381	−	3.25890i	−0.281022	−	0.235806i	0.491371	−	0.870950i	$-0.336496\pi$
$191$	−3.88381	−	3.25890i	−0.281022	−	0.235806i	−0.772393	+	0.635145i	$0.780940\pi$
$192$	0.439693	+	1.67531i	0.0317321	+	0.120905i
$193$	2.97118	+	16.8504i	0.213870	+	1.21292i	0.882856	+	0.469643i	$0.155617\pi$
$193$	2.97118	+	16.8504i	0.213870	+	1.21292i	−0.668986	+	0.743275i	$0.733272\pi$
$194$	−1.06598	−	0.387987i	−0.0765332	−	0.0278558i
$195$	18.1881	−	1.49721i	1.30248	−	0.107217i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	−0.276694	+	0.479248i	−0.0197136	+	0.0341450i	−0.875714	−	0.482830i	$-0.839609\pi$
$197$	−0.276694	+	0.479248i	−0.0197136	+	0.0341450i	0.856000	+	0.516975i	$0.172942\pi$
$198$	9.93318	+	12.0878i	0.705920	+	0.859044i
$199$	2.08088	+	3.60419i	0.147510	+	0.255495i	0.930307	−	0.366783i	$-0.119541\pi$
$199$	2.08088	+	3.60419i	0.147510	+	0.255495i	−0.782797	+	0.622278i	$0.786208\pi$
$200$	1.32202	−	0.481175i	0.0934807	−	0.0340242i
$201$	−14.0433	+	6.46094i	−0.990539	+	0.455720i
$202$	−2.85122	+	2.39246i	−0.200611	+	0.168333i
$203$	−3.78733	+	3.17795i	−0.265819	+	0.223048i
$204$	6.54024	−	3.00898i	0.457908	−	0.210671i
$205$	1.79500	−	0.653326i	0.125368	−	0.0456302i
$206$	−0.155010	−	0.268486i	−0.0108001	−	0.0187063i
$207$	−3.21597	+	8.56126i	−0.223525	+	0.595048i
$208$	−2.77925	+	4.81379i	−0.192706	+	0.333777i
$209$	2.45660	−	13.9321i	0.169926	−	0.963701i
$210$	3.27213	−	0.269355i	0.225799	−	0.0185872i
$211$	0.710096	+	0.258454i	0.0488850	+	0.0177927i	0.366347	−	0.930478i	$-0.380608\pi$
$211$	0.710096	+	0.258454i	0.0488850	+	0.0177927i	−0.317462	+	0.948271i	$0.602831\pi$
$212$	−0.221317	−	1.25515i	−0.0152001	−	0.0862041i
$213$	1.70479	+	6.49558i	0.116810	+	0.445070i
$214$	9.10388	+	7.63906i	0.622328	+	0.522195i
$215$	−17.1220			−1.16771
$216$	5.03922	−	1.26740i	0.342875	−	0.0862359i
$217$	−10.3503			−0.702622
$218$	−10.1779	−	8.54023i	−0.689331	−	0.578418i
$219$	−12.3274	+	12.2015i	−0.833009	+	0.824500i
$220$	−1.71663	−	9.73550i	−0.115735	−	0.656367i
$221$	21.7104	+	7.90193i	1.46040	+	0.531541i
$222$	7.83659	−	16.5828i	0.525958	−	1.11297i
$223$	−2.98689	+	16.9395i	−0.200017	+	1.13435i	0.705074	+	0.709134i	$0.250914\pi$
$223$	−2.98689	+	16.9395i	−0.200017	+	1.13435i	−0.905091	+	0.425219i	$0.860197\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−1.40273	−	3.98066i	−0.0935151	−	0.265378i
$226$	−6.42076	−	11.1211i	−0.427102	−	0.739763i
$227$	4.72912	−	1.72126i	0.313883	−	0.114244i	−0.180275	−	0.983616i	$-0.557699\pi$
$227$	4.72912	−	1.72126i	0.313883	−	0.114244i	0.494158	+	0.869372i	$0.335476\pi$
$228$	−3.83486	−	2.71464i	−0.253970	−	0.179782i
$229$	20.7207	−	17.3867i	1.36926	−	1.14894i	0.396260	−	0.918138i	$-0.370308\pi$
$229$	20.7207	−	17.3867i	1.36926	−	1.14894i	0.973000	−	0.230806i	$-0.0741364\pi$
$230$	4.42660	−	3.71436i	0.291881	−	0.244918i
$231$	−0.833463	+	8.99443i	−0.0548378	+	0.591790i
$232$	4.64585	−	1.69095i	0.305015	−	0.111016i
$233$	−11.5197	−	19.9528i	−0.754682	−	1.30715i	−0.945532	−	0.325529i	$-0.894458\pi$
$233$	−11.5197	−	19.9528i	−0.754682	−	1.30715i	0.190850	−	0.981619i	$-0.438876\pi$
$234$	14.3550	+	8.48558i	0.938417	+	0.554720i
$235$	5.68705	−	9.85025i	0.370982	−	0.642560i
$236$	0.607620	−	3.44599i	0.0395527	−	0.224315i
$237$	9.58447	+	13.8387i	0.622579	+	0.898922i
$238$	3.90580	+	1.42160i	0.253176	+	0.0921484i
$239$	−5.07323	−	28.7717i	−0.328160	−	1.86109i	−0.486467	−	0.873699i	$-0.661714\pi$
$239$	−5.07323	−	28.7717i	−0.328160	−	1.86109i	0.158306	−	0.987390i	$-0.449397\pi$
$240$	−3.16693	−	0.866025i	−0.204424	−	0.0559017i
$241$	6.13594	+	5.14866i	0.395251	+	0.331655i	0.818654	−	0.574286i	$-0.194720\pi$
$241$	6.13594	+	5.14866i	0.395251	+	0.331655i	−0.423404	+	0.905941i	$0.639165\pi$
$242$	16.1982			1.04126
$243$	−3.64679	−	15.1559i	−0.233941	−	0.972251i
$244$	−13.8549			−0.886971
$245$	1.45208	+	1.21844i	0.0927701	+	0.0778433i
$246$	1.68361	+	0.460399i	0.107343	+	0.0293540i
$247$	−2.61831	−	14.8492i	−0.166599	−	0.944830i
$248$	9.72606	+	3.54000i	0.617606	+	0.224790i
$249$	−3.70742	−	5.35303i	−0.234948	−	0.339234i
$250$	−2.10888	+	11.9601i	−0.133377	+	0.756421i
$251$	−7.78091	+	13.4769i	−0.491126	+	0.850656i	−0.999948	−	0.0102162i	$-0.996748\pi$
$251$	−7.78091	+	13.4769i	−0.491126	+	0.850656i	0.508821	+	0.860872i	$0.330081\pi$
$252$	2.58254	+	1.52660i	0.162685	+	0.0961666i
$253$	7.94913	+	13.7683i	0.499757	+	0.865605i
$254$	−4.91259	+	1.78804i	−0.308243	+	0.112191i
$255$	−1.25915	+	13.5883i	−0.0788511	+	0.850933i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−8.60939	+	7.22413i	−0.537039	+	0.450629i	−0.870524	−	0.492126i	$-0.836220\pi$
$257$	−8.60939	+	7.22413i	−0.537039	+	0.450629i	0.333485	+	0.942755i	$0.391775\pi$
$258$	−12.7694	−	9.03931i	−0.794990	−	0.562763i
$259$	9.95072	−	3.62177i	0.618308	−	0.225046i
$260$	−5.26822	−	9.12483i	−0.326721	−	0.565898i
$261$	−4.92948	−	13.9889i	−0.305127	−	0.865891i
$262$	2.78895	−	4.83059i	0.172302	−	0.298435i
$263$	−3.12500	+	17.7228i	−0.192696	+	1.09283i	0.722966	+	0.690883i	$0.242778\pi$
$263$	−3.12500	+	17.7228i	−0.192696	+	1.09283i	−0.915662	+	0.401949i	$0.868333\pi$
$264$	3.85948	−	8.16694i	0.237534	−	0.502641i
$265$	2.27022	+	0.826291i	0.139458	+	0.0507587i
$266$	−0.471047	−	2.67144i	−0.0288817	−	0.163796i
$267$	17.2057	−	17.0299i	1.05297	−	1.04221i
$268$	6.83683	+	5.73678i	0.417626	+	0.350429i
$269$	14.3946			0.877656			0.438828	−	0.898571i	$-0.355394\pi$
$269$	14.3946			0.877656			0.438828	+	0.898571i	$0.355394\pi$
$270$	−2.69549	+	9.47360i	−0.164042	+	0.576545i
$271$	0.498093			0.0302570			0.0151285	−	0.999886i	$-0.495184\pi$
$271$	0.498093			0.0302570			0.0151285	+	0.999886i	$0.495184\pi$
$272$	−3.18404	−	2.67173i	−0.193061	−	0.161997i
$273$	2.44403	+	9.31221i	0.147919	+	0.563600i
$274$	3.02645	+	17.1639i	0.182835	+	1.03691i
$275$	−6.89457	−	2.50942i	−0.415758	−	0.151324i
$276$	5.26228	−	0.433178i	0.316752	−	0.0260743i
$277$	−0.358695	+	2.03426i	−0.0215519	+	0.122227i	−0.993686	−	0.112200i	$-0.964210\pi$
$277$	−0.358695	+	2.03426i	−0.0215519	+	0.122227i	0.972134	+	0.234427i	$0.0753214\pi$
$278$	−1.13379	+	1.96378i	−0.0680000	+	0.117780i
$279$	10.9190	−	29.0676i	0.653705	−	1.74023i
$280$	−0.947779	−	1.64160i	−0.0566406	−	0.0981044i
$281$	3.98743	−	1.45130i	0.237870	−	0.0865776i	−0.220335	−	0.975424i	$-0.570715\pi$
$281$	3.98743	−	1.45130i	0.237870	−	0.0865776i	0.458205	+	0.888847i	$0.348493\pi$
$282$	9.44167	−	4.34385i	0.562243	−	0.258673i
$283$	−15.4012	+	12.9231i	−0.915503	+	0.768199i	−0.973158	−	0.230138i	$-0.926082\pi$
$283$	−15.4012	+	12.9231i	−0.915503	+	0.768199i	0.0576546	+	0.998337i	$0.481638\pi$
$284$	2.97014	−	2.49224i	0.176245	−	0.147887i
$285$	8.09096	−	3.72243i	0.479267	−	0.220497i
$286$	27.2403	−	9.91467i	1.61076	−	0.586267i
$287$	0.503861	+	0.872713i	0.0297420	+	0.0515146i
$288$	−1.90466	−	2.31781i	−0.112233	−	0.136578i
$289$	−0.138122	+	0.239235i	−0.00812485	+	0.0140727i
$290$	−1.62737	+	9.22928i	−0.0955625	+	0.541962i
$291$	1.95821	−	0.161195i	0.114792	−	0.00944944i
$292$	9.41009	+	3.42499i	0.550684	+	0.200433i
$293$	−4.25843	−	24.1508i	−0.248780	−	1.41090i	−0.811547	−	0.584287i	$-0.801374\pi$
$293$	−4.25843	−	24.1508i	−0.248780	−	1.41090i	0.562766	−	0.826616i	$-0.309737\pi$
$294$	0.439693	+	1.67531i	0.0256434	+	0.0977062i
$295$	5.08105	+	4.26350i	0.295830	+	0.248231i
$296$	−10.5893			−0.615492
$297$	−24.3807	−	11.8294i	−1.41471	−	0.686411i
$298$	0.551799			0.0319648
$299$	12.9805	+	10.8919i	0.750680	+	0.629895i
$300$	−1.73187	+	1.71418i	−0.0999895	+	0.0989681i
$301$	−1.56851	−	8.89545i	−0.0904073	−	0.512725i
$302$	−14.4242	−	5.24999i	−0.830021	−	0.302103i
$303$	2.75446	−	5.82863i	0.158239	−	0.334846i
$304$	−0.471047	+	2.67144i	−0.0270164	+	0.153218i
$305$	13.1314	−	22.7443i	0.751902	−	1.30233i
$306$	−8.11284	+	9.46932i	−0.463780	+	0.541325i
$307$	3.13404	+	5.42832i	0.178869	+	0.309811i	0.941494	−	0.337031i	$-0.109423\pi$
$307$	3.13404	+	5.42832i	0.178869	+	0.309811i	−0.762624	+	0.646842i	$0.776089\pi$
$308$	4.90067	−	1.78370i	0.279242	−	0.101636i
$309$	0.438274	+	0.310248i	0.0249325	+	0.0176494i
$310$	−15.0294	+	12.6112i	−0.853614	+	0.716267i
$311$	−2.68637	+	2.25413i	−0.152330	+	0.127820i	−0.715768	−	0.698339i	$-0.753923\pi$
$311$	−2.68637	+	2.25413i	−0.152330	+	0.127820i	0.563437	+	0.826159i	$0.309479\pi$
$312$	0.888328	−	9.58652i	0.0502917	−	0.542730i
$313$	−29.6417	+	10.7887i	−1.67545	+	0.609813i	−0.992675	−	0.120817i	$-0.961449\pi$
$313$	−29.6417	+	10.7887i	−1.67545	+	0.609813i	−0.682773	+	0.730630i	$0.739226\pi$
$314$	5.77695	+	10.0060i	0.326012	+	0.564670i
$315$	−4.95374	+	2.79262i	−0.279112	+	0.157346i
$316$	4.85946	−	8.41683i	0.273366	−	0.473484i
$317$	5.25323	−	29.7925i	0.295051	−	1.67332i	−0.371945	−	0.928255i	$-0.621309\pi$
$317$	5.25323	−	29.7925i	0.295051	−	1.67332i	0.666996	−	0.745061i	$-0.267580\pi$
$318$	1.25688	+	1.81477i	0.0704825	+	0.101767i
$319$	−24.2290	−	8.81863i	−1.35656	−	0.493748i
$320$	0.329160	+	1.86676i	0.0184006	+	0.104355i
$321$	−19.8552	−	5.42958i	−1.10821	−	0.303049i
$322$	2.33525	+	1.95951i	0.130138	+	0.109199i
$323$	11.2751			0.627361
$324$	−7.01174	+	5.64230i	−0.389541	+	0.313461i
$325$	−7.82002			−0.433777
$326$	−5.61333	−	4.71015i	−0.310894	−	0.260871i
$327$	22.1975	+	6.07010i	1.22752	+	0.335677i
$328$	−0.174989	−	0.992413i	−0.00966216	−	0.0547968i
$329$	5.63853	+	2.05226i	0.310862	+	0.113145i
$330$	9.74893	+	14.0762i	0.536661	+	0.774868i
$331$	−3.79018	+	21.4952i	−0.208327	+	1.18148i	0.683791	+	0.729678i	$0.260330\pi$
$331$	−3.79018	+	21.4952i	−0.208327	+	1.18148i	−0.892118	+	0.451803i	$0.850781\pi$
$332$	−1.87971	+	3.25576i	−0.103163	+	0.178683i
$333$	−0.326184	+	31.7663i	−0.0178748	+	1.74078i
$334$	0.579413	+	1.00357i	0.0317041	+	0.0549130i
$335$	−15.8973	+	5.78614i	−0.868562	+	0.316131i
$336$	0.159815	−	1.72466i	0.00871860	−	0.0940880i
$337$	−5.59205	+	4.69228i	−0.304618	+	0.255605i	−0.782263	−	0.622948i	$-0.785935\pi$
$337$	−5.59205	+	4.69228i	−0.304618	+	0.255605i	0.477645	+	0.878553i	$0.341490\pi$
$338$	13.7098	−	11.5039i	0.745713	−	0.625727i
$339$	18.1540	+	12.8509i	0.985988	+	0.697967i
$340$	7.40368	−	2.69472i	0.401521	−	0.146142i
$341$	−26.9893	−	46.7468i	−1.46155	−	2.53148i
$342$	7.99939	+	1.49535i	0.432557	+	0.0808595i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−1.56851	+	8.89545i	−0.0845682	+	0.479610i
$345$	−4.27637	+	9.04912i	−0.230232	+	0.487188i
$346$	−16.9085	−	6.15418i	−0.909006	−	0.330851i
$347$	−2.40536	−	13.6415i	−0.129126	−	0.732312i	−0.978771	−	0.204957i	$-0.934295\pi$
$347$	−2.40536	−	13.6415i	−0.129126	−	0.732312i	0.849645	−	0.527356i	$-0.176816\pi$
$348$	−6.08616	+	6.02399i	−0.326252	+	0.322919i
$349$	−1.42764	−	1.19793i	−0.0764197	−	0.0641237i	0.603778	−	0.797153i	$-0.293661\pi$
$349$	−1.42764	−	1.19793i	−0.0764197	−	0.0641237i	−0.680197	+	0.733029i	$0.738106\pi$
$350$	−1.40686			−0.0751999
$351$	−28.7307	−	2.96014i	−1.53353	−	0.158000i
$352$	−5.21519			−0.277970
$353$	8.01636	+	6.72652i	0.426668	+	0.358017i	0.830693	−	0.556731i	$-0.187945\pi$
$353$	8.01636	+	6.72652i	0.426668	+	0.358017i	−0.404025	+	0.914748i	$0.632389\pi$
$354$	1.53855	+	5.86216i	0.0817729	+	0.311570i
$355$	1.27623	+	7.23787i	0.0677354	+	0.384146i
$356$	−13.1339	−	4.78034i	−0.696095	−	0.253358i
$357$	−7.17495	+	0.590625i	−0.379739	+	0.0312592i
$358$	−0.511826	+	2.90271i	−0.0270509	+	0.153413i
$359$	−14.0935	+	24.4106i	−0.743825	+	1.28834i	0.206917	+	0.978359i	$0.433657\pi$
$359$	−14.0935	+	24.4106i	−0.743825	+	1.28834i	−0.950742	+	0.309984i	$0.899676\pi$
$360$	5.61012	−	0.929926i	0.295679	−	0.0490114i
$361$	5.82076	+	10.0819i	0.306356	+	0.530624i
$362$	−12.8123	+	4.66331i	−0.673401	+	0.245098i
$363$	−25.4880	+	11.7263i	−1.33777	+	0.615471i
$364$	4.25805	−	3.57293i	0.223183	−	0.187272i
$365$	−14.5412	+	12.2015i	−0.761119	+	0.638655i
$366$	21.8008	−	10.0300i	1.13955	−	0.524274i
$367$	−3.14417	+	1.14438i	−0.164124	+	0.0597363i	−0.422776	−	0.906234i	$-0.638944\pi$
$367$	−3.14417	+	1.14438i	−0.164124	+	0.0597363i	0.258651	+	0.965971i	$0.416722\pi$
$368$	−1.52423	−	2.64004i	−0.0794558	−	0.137621i
$369$	−2.98247	+	0.494371i	−0.155261	+	0.0257359i
$370$	10.0363	−	17.3835i	0.521765	−	0.903723i
$371$	−0.221317	+	1.25515i	−0.0114902	+	0.0651642i
$372$	−17.8667	+	1.47075i	−0.926348	+	0.0762548i
$373$	−14.8122	−	5.39119i	−0.766945	−	0.279145i	−0.0712272	−	0.997460i	$-0.522692\pi$
$373$	−14.8122	−	5.39119i	−0.766945	−	0.279145i	−0.695718	+	0.718315i	$0.744914\pi$
$374$	3.76413	+	21.3474i	0.194639	+	1.10385i
$375$	−5.33988	−	20.3460i	−0.275750	−	1.05066i
$376$	−4.59657	−	3.85698i	−0.237050	−	0.198908i
$377$	−27.4812			−1.41536
$378$	−5.16879	−	0.532543i	−0.265854	−	0.0273911i
$379$	−8.90527			−0.457433			−0.228716	−	0.973493i	$-0.573453\pi$
$379$	−8.90527			−0.457433			−0.228716	+	0.973493i	$0.573453\pi$
$380$	−3.93899	−	3.30521i	−0.202066	−	0.169553i
$381$	6.43560	−	6.36985i	0.329706	−	0.326337i
$382$	−0.880388	−	4.99293i	−0.0450445	−	0.255460i
$383$	5.35349	+	1.94851i	0.273551	+	0.0995643i	0.475153	−	0.879903i	$-0.342393\pi$
$383$	5.35349	+	1.94851i	0.273551	+	0.0995643i	−0.201602	+	0.979467i	$0.564615\pi$
$384$	−0.740046	+	1.56599i	−0.0377653	+	0.0799142i
$385$	−1.71663	+	9.73550i	−0.0874876	+	0.496167i
$386$	−8.55517	+	14.8180i	−0.435447	+	0.754216i
$387$	26.6366	+	4.97928i	1.35402	+	0.253111i
$388$	−0.567199	−	0.982417i	−0.0287951	−	0.0498747i
$389$	−6.78624	+	2.46999i	−0.344076	+	0.125233i	−0.508277	−	0.861193i	$-0.669717\pi$
$389$	−6.78624	+	2.46999i	−0.344076	+	0.125233i	0.164201	+	0.986427i	$0.447495\pi$
$390$	14.8953	+	10.5442i	0.754253	+	0.533925i
$391$	−9.70640	+	8.14464i	−0.490874	+	0.411892i
$392$	0.766044	−	0.642788i	0.0386911	−	0.0324657i
$393$	−0.891428	+	9.61998i	−0.0449666	+	0.485264i
$394$	−0.520014	+	0.189270i	−0.0261979	+	0.00953527i
$395$	9.21139	+	15.9546i	0.463475	+	0.802763i
$396$	−0.160644	+	15.6447i	−0.00807266	+	0.786178i
$397$	5.50881	−	9.54154i	0.276479	−	0.478876i	−0.694028	−	0.719948i	$-0.744166\pi$
$397$	5.50881	−	9.54154i	0.276479	−	0.478876i	0.970507	+	0.241072i	$0.0774989\pi$
$398$	−0.722683	+	4.09854i	−0.0362248	+	0.205441i
$399$	2.67513	+	3.86253i	0.133924	+	0.193368i
$400$	1.32202	+	0.481175i	0.0661008	+	0.0240587i
$401$	3.62789	+	20.5748i	0.181168	+	1.02746i	0.930780	+	0.365579i	$0.119129\pi$
$401$	3.62789	+	20.5748i	0.181168	+	1.02746i	−0.749612	+	0.661877i	$0.769760\pi$
$402$	−14.9108	−	4.07750i	−0.743684	−	0.203367i
$403$	−44.0719	−	36.9808i	−2.19538	−	1.84214i
$404$	−3.72201			−0.185177
$405$	−2.61682	−	16.8581i	−0.130031	−	0.837687i
$406$	−4.94401			−0.245367
$407$	42.3051	+	35.4982i	2.09698	+	1.75958i
$408$	6.94425	+	1.89897i	0.343792	+	0.0940131i
$409$	2.99994	+	17.0135i	0.148337	+	0.841263i	0.964627	+	0.263620i	$0.0849164\pi$
$409$	2.99994	+	17.0135i	0.148337	+	0.841263i	−0.816289	+	0.577643i	$0.803972\pi$
$410$	1.79500	+	0.653326i	0.0886486	+	0.0322655i
$411$	−17.1875	−	24.8165i	−0.847799	−	1.22411i
$412$	0.0538345	−	0.305310i	0.00265223	−	0.0150416i
$413$	−1.74957	+	3.03035i	−0.0860909	+	0.149114i
$414$	−7.96665	+	4.49112i	−0.391539	+	0.220726i
$415$	−3.56310	−	6.17148i	−0.174906	−	0.302946i
$416$	−5.22327	+	1.90112i	−0.256092	+	0.0932099i
$417$	0.362391	−	3.91080i	0.0177464	−	0.191513i
$418$	10.8372	−	9.09351i	0.530066	−	0.444778i
$419$	8.67727	−	7.28110i	0.423913	−	0.355705i	−0.405737	−	0.913990i	$-0.632985\pi$
$419$	8.67727	−	7.28110i	0.423913	−	0.355705i	0.829649	+	0.558285i	$0.188541\pi$
$420$	2.67974	+	1.89695i	0.130758	+	0.0925617i
$421$	11.0051	−	4.00554i	0.536358	−	0.195218i	−0.0596172	−	0.998221i	$-0.518988\pi$
$421$	11.0051	−	4.00554i	0.536358	−	0.195218i	0.595975	+	0.803003i	$0.296766\pi$
$422$	0.377834	+	0.654428i	0.0183927	+	0.0318571i
$423$	−11.7119	+	13.6702i	−0.569453	+	0.664666i
$424$	0.637257	−	1.10376i	0.0309479	−	0.0536034i
$425$	1.01542	−	5.75874i	0.0492552	−	0.279340i
$426$	−2.86933	+	6.07172i	−0.139020	+	0.294176i
$427$	13.0194	+	4.73866i	0.630051	+	0.229320i
$428$	2.06368	+	11.7037i	0.0997518	+	0.565721i
$429$	−35.6854	+	35.3209i	−1.72291	+	1.70531i
$430$	−13.1162	−	11.0058i	−0.632518	−	0.530746i
$431$	−30.2845			−1.45875			−0.729376	−	0.684113i	$-0.760190\pi$
$431$	−30.2845			−1.45875			−0.729376	+	0.684113i	$0.760190\pi$
$432$	4.67493	+	2.26826i	0.224923	+	0.109132i
$433$	−2.45937			−0.118190			−0.0590949	−	0.998252i	$-0.518821\pi$
$433$	−2.45937			−0.118190			−0.0590949	+	0.998252i	$0.518821\pi$
$434$	−7.92876	−	6.65302i	−0.380593	−	0.319355i
$435$	−4.12065	−	15.7004i	−0.197570	−	0.752779i
$436$	−2.30713	−	13.0844i	−0.110492	−	0.626629i
$437$	7.77068	+	2.82830i	0.371722	+	0.135296i
$438$	−17.2863	+	1.42297i	−0.825972	+	0.0679921i
$439$	0.684779	−	3.88358i	0.0326827	−	0.185353i	−0.964096	−	0.265554i	$-0.914445\pi$
$439$	0.684779	−	3.88358i	0.0326827	−	0.185353i	0.996779	+	0.0802011i	$0.0255562\pi$
$440$	4.94284	−	8.56126i	0.235641	−	0.408142i
$441$	−1.90466	−	2.31781i	−0.0906983	−	0.110372i
$442$	11.5519	+	20.0084i	0.549466	+	0.951702i
$443$	28.8433	−	10.4981i	1.37039	−	0.498781i	0.451138	−	0.892454i	$-0.351018\pi$
$443$	28.8433	−	10.4981i	1.37039	−	0.498781i	0.919250	+	0.393673i	$0.128796\pi$
$444$	16.6624	−	7.66591i	0.790763	−	0.363808i
$445$	20.2954	−	17.0299i	0.962096	−	0.807294i
$446$	−13.1766	+	11.0565i	−0.623930	+	0.523539i
$447$	−0.868260	+	0.399462i	−0.0410673	+	0.0188939i
$448$	−0.939693	+	0.342020i	−0.0443963	+	0.0161589i
$449$	0.113719	+	0.196967i	0.00536673	+	0.00929545i	0.868696	−	0.495345i	$-0.164958\pi$
$449$	0.113719	+	0.196967i	0.00536673	+	0.00929545i	−0.863330	+	0.504641i	$0.831625\pi$
$450$	1.48417	−	3.95102i	0.0699645	−	0.186253i
$451$	−2.62773	+	4.55136i	−0.123735	+	0.214315i
$452$	2.22991	−	12.6464i	0.104886	−	0.594838i
$453$	26.4972	−	2.18119i	1.24495	−	0.102481i
$454$	4.72912	+	1.72126i	0.221949	+	0.0807828i
$455$	1.82963	+	10.3764i	0.0857745	+	0.486452i
$456$	−1.19273	−	4.54454i	−0.0558548	−	0.212817i
$457$	5.57486	+	4.67786i	0.260781	+	0.218821i	0.763798	−	0.645455i	$-0.223332\pi$
$457$	5.57486	+	4.67786i	0.260781	+	0.218821i	−0.503017	+	0.864276i	$0.667777\pi$
$458$	27.0489			1.26391
$459$	5.91052	−	20.7732i	0.275879	−	0.969608i
$460$	5.77852			0.269425
$461$	−8.11642	−	6.81049i	−0.378019	−	0.317196i	0.433905	−	0.900959i	$-0.357135\pi$
$461$	−8.11642	−	6.81049i	−0.378019	−	0.317196i	−0.811924	+	0.583763i	$0.801580\pi$
$462$	−6.41998	+	6.35440i	−0.298685	+	0.295633i
$463$	2.36174	+	13.3941i	0.109759	+	0.622475i	0.989212	+	0.146490i	$0.0467975\pi$
$463$	2.36174	+	13.3941i	0.109759	+	0.622475i	−0.879453	+	0.475986i	$0.842091\pi$
$464$	4.64585	+	1.69095i	0.215678	+	0.0785004i
$465$	14.5193	−	30.7240i	0.673318	−	1.42479i
$466$	4.00076	−	22.6894i	0.185332	−	1.05107i
$467$	−13.4701	+	23.3310i	−0.623323	+	1.07963i	0.365539	+	0.930796i	$0.380885\pi$
$467$	−13.4701	+	23.3310i	−0.623323	+	1.07963i	−0.988863	+	0.148832i	$0.952449\pi$
$468$	5.54215	+	15.7276i	0.256186	+	0.727006i
$469$	−4.46242	−	7.72914i	−0.206055	−	0.356899i
$470$	10.6882	−	3.89017i	0.493008	−	0.179440i
$471$	−16.3337	−	11.5624i	−0.752617	−	0.532767i
$472$	2.68050	−	2.24921i	0.123380	−	0.103528i
$473$	36.0861	−	30.2798i	1.65924	−	1.39227i
$474$	−1.55323	+	16.7619i	−0.0713420	+	0.769898i
$475$	−3.58617	+	1.30526i	−0.164545	+	0.0598894i
$476$	2.07824	+	3.59961i	0.0952558	+	0.164988i
$477$	−3.29148	−	1.94567i	−0.150706	−	0.0890860i
$478$	14.6078	−	25.3014i	0.668145	−	1.15726i
$479$	5.36246	−	30.4120i	0.245017	−	1.38956i	−0.575436	−	0.817847i	$-0.695167\pi$
$479$	5.36246	−	30.4120i	0.245017	−	1.38956i	0.820453	−	0.571714i	$-0.193721\pi$
$480$	−1.86934	−	2.69907i	−0.0853231	−	0.123195i
$481$	55.3110	+	20.1315i	2.52196	+	0.917920i
$482$	1.39090	+	7.88821i	0.0633540	+	0.359298i
$483$	−5.09308	−	1.39275i	−0.231743	−	0.0633723i
$484$	12.4085	+	10.4120i	0.564024	+	0.473272i
$485$	2.15032			0.0976408
$486$	6.94842	−	13.9542i	0.315187	−	0.632975i
$487$	−2.33261			−0.105701			−0.0528504	−	0.998602i	$-0.516831\pi$
$487$	−2.33261			−0.105701			−0.0528504	+	0.998602i	$0.516831\pi$
$488$	−10.6135	−	8.90577i	−0.480450	−	0.403145i
$489$	12.2424	+	3.34781i	0.553622	+	0.151393i
$490$	0.329160	+	1.86676i	0.0148699	+	0.0843316i
$491$	−22.3025	−	8.11744i	−1.00650	−	0.366335i	−0.214410	−	0.976744i	$-0.568783\pi$
$491$	−22.3025	−	8.11744i	−1.00650	−	0.366335i	−0.792087	+	0.610409i	$0.791005\pi$
$492$	0.993782	+	1.43489i	0.0448032	+	0.0646899i
$493$	3.56841	−	20.2374i	0.160713	−	0.911448i
$494$	7.53912	−	13.0581i	0.339201	−	0.587514i
$495$	−25.5302	−	15.0915i	−1.14750	−	0.678311i
$496$	5.17513	+	8.96359i	0.232370	+	0.402477i
$497$	−3.64341	+	1.32609i	−0.163429	+	0.0594834i
$498$	0.600811	−	6.48374i	0.0269230	−	0.290543i
$499$	4.50898	−	3.78348i	0.201850	−	0.169372i	−0.536260	−	0.844053i	$-0.680163\pi$
$499$	4.50898	−	3.78348i	0.201850	−	0.169372i	0.738109	+	0.674681i	$0.235719\pi$
$500$	−9.30328	+	7.80638i	−0.416056	+	0.349112i
$501$	−1.63822	−	1.15968i	−0.0731905	−	0.0518105i
$502$	−14.6233	+	5.32245i	−0.652671	+	0.237553i
$503$	20.4763	+	35.4659i	0.912991	+	1.58135i	0.809816	+	0.586684i	$0.199567\pi$
$503$	20.4763	+	35.4659i	0.912991	+	1.58135i	0.103176	+	0.994663i	$0.467100\pi$
$504$	0.997061	+	2.82946i	0.0444126	+	0.126034i
$505$	3.52764	−	6.11005i	0.156978	−	0.271894i
$506$	−2.76070	+	15.6567i	−0.122728	+	0.696026i
$507$	−13.2445	+	28.0263i	−0.588207	+	1.24469i
$508$	−4.91259	−	1.78804i	−0.217961	−	0.0793313i
$509$	1.15295	+	6.53872i	0.0511037	+	0.289823i	0.999640	−	0.0268462i	$-0.00854644\pi$
$509$	1.15295	+	6.53872i	0.0511037	+	0.289823i	−0.948536	+	0.316670i	$0.897435\pi$
$510$	−9.69897	+	9.59989i	−0.429478	+	0.425090i
$511$	−7.67118	−	6.43688i	−0.339353	−	0.284751i
$512$	1.00000			0.0441942
$513$	−13.6696	+	3.43802i	−0.603529	+	0.151792i
$514$	−11.2388			−0.495720
$515$	0.450175	+	0.377742i	0.0198371	+	0.0166453i
$516$	−3.97160	−	15.1325i	−0.174840	−	0.666173i
$517$	5.43400	+	30.8178i	0.238987	+	1.35536i
$518$	9.95072	+	3.62177i	0.437209	+	0.159131i
$519$	31.0608	−	2.55686i	1.36342	−	0.112234i
$520$	1.82963	−	10.3764i	0.0802347	−	0.455034i
$521$	8.26758	−	14.3199i	0.362209	−	0.627365i	−0.626115	−	0.779731i	$-0.715356\pi$
$521$	8.26758	−	14.3199i	0.362209	−	0.627365i	0.988324	+	0.152366i	$0.0486892\pi$
$522$	5.21569	−	13.8847i	0.228285	−	0.607718i
$523$	10.7884	+	18.6861i	0.471744	+	0.817084i	0.999477	−	0.0323257i	$-0.0102914\pi$
$523$	10.7884	+	18.6861i	0.471744	+	0.817084i	−0.527734	+	0.849410i	$0.676958\pi$
$524$	5.24150	−	1.90775i	0.228976	−	0.0833405i
$525$	2.21371	−	1.01847i	0.0966141	−	0.0444495i
$526$	−13.7859	+	11.5677i	−0.601092	+	0.504376i
$527$	32.9557	−	27.6531i	1.43557	−	1.20459i
$528$	8.20614	−	3.77542i	0.357126	−	0.164304i
$529$	12.8803	−	4.68805i	0.560013	−	0.203828i
$530$	1.20796	+	2.09224i	0.0524703	+	0.0908812i
$531$	−6.66470	−	8.11036i	−0.289223	−	0.351960i
$532$	1.35633	−	2.34922i	0.0588042	−	0.101852i
$533$	−0.972676	+	5.51632i	−0.0421313	+	0.238938i
$534$	24.1269	−	1.98607i	1.04407	−	0.0859457i
$535$	−21.1688	−	7.70479i	−0.915205	−	0.333107i
$536$	1.54978	+	8.78925i	0.0669404	+	0.379638i
$537$	−1.29599	−	4.93797i	−0.0559261	−	0.213089i
$538$	11.0269	+	9.25269i	0.475405	+	0.398912i
$539$	−5.21519			−0.224634
$540$	−8.15438	+	5.52457i	−0.350909	+	0.237740i
$541$	−16.5181			−0.710168			−0.355084	−	0.934834i	$-0.615548\pi$
$541$	−16.5181			−0.710168			−0.355084	+	0.934834i	$0.615548\pi$
$542$	0.381561	+	0.320168i	0.0163895	+	0.0137524i
$543$	16.7844	−	16.6130i	0.720288	−	0.712930i
$544$	−0.721763	−	4.09332i	−0.0309454	−	0.175500i
$545$	23.6660	+	8.61372i	1.01374	+	0.368971i
$546$	−4.11354	+	8.70455i	−0.176043	+	0.372521i
$547$	3.76845	−	21.3720i	0.161127	−	0.913799i	−0.791841	−	0.610728i	$-0.790877\pi$
$547$	3.76845	−	21.3720i	0.161127	−	0.913799i	0.952968	−	0.303071i	$-0.0980120\pi$
$548$	−8.71432	+	15.0936i	−0.372257	+	0.644769i
$549$	−27.0428	+	31.5645i	−1.15416	+	1.34714i
$550$	−3.66852	−	6.35407i	−0.156426	−	0.270938i
$551$	−12.6026	+	4.58696i	−0.536888	+	0.195411i
$552$	4.30958	+	3.05069i	0.183428	+	0.129846i
$553$	−7.44513	+	6.24720i	−0.316599	+	0.265658i
$554$	−1.58237	+	1.32777i	−0.0672287	+	0.0564115i
$555$	−3.20791	+	34.6186i	−0.136168	+	1.46948i
$556$	−2.13082	+	0.775556i	−0.0903670	+	0.0328909i
$557$	10.5893	+	18.3412i	0.448683	+	0.777142i	0.998301	−	0.0582743i	$-0.0185598\pi$
$557$	10.5893	+	18.3412i	0.448683	+	0.777142i	−0.549617	+	0.835417i	$0.685226\pi$
$558$	27.0488	−	15.2485i	1.14507	−	0.645519i
$559$	25.1040	−	43.4814i	1.06179	−	1.83907i
$560$	0.329160	−	1.86676i	0.0139096	−	0.0788850i
$561$	−21.3769	−	30.8654i	−0.902533	−	1.30314i
$562$	3.98743	+	1.45130i	0.168199	+	0.0612196i
$563$	−3.43969	−	19.5075i	−0.144966	−	0.822141i	−0.967395	−	0.253273i	$-0.918493\pi$
$563$	−3.43969	−	19.5075i	−0.144966	−	0.822141i	0.822429	−	0.568868i	$-0.192618\pi$
$564$	10.0249	+	2.74141i	0.422125	+	0.115434i
$565$	18.6469	+	15.6466i	0.784482	+	0.658258i
$566$	−20.1048			−0.845067
$567$	8.51866	−	2.90387i	0.357750	−	0.121951i
$568$	3.87724			0.162685
$569$	15.3941	+	12.9172i	0.645355	+	0.541517i	0.905658	−	0.424010i	$-0.139378\pi$
$569$	15.3941	+	12.9172i	0.645355	+	0.541517i	−0.260302	+	0.965527i	$0.583822\pi$
$570$	8.59076	+	2.34922i	0.359828	+	0.0983982i
$571$	−5.81283	−	32.9662i	−0.243260	−	1.37959i	−0.824500	−	0.565862i	$-0.808544\pi$
$571$	−5.81283	−	32.9662i	−0.243260	−	1.37959i	0.581241	−	0.813732i	$-0.302567\pi$
$572$	27.2403	+	9.91467i	1.13898	+	0.414553i
$573$	4.99981	+	7.21907i	0.208870	+	0.301581i
$574$	−0.174989	+	0.992413i	−0.00730391	+	0.0414225i
$575$	2.14437	−	3.71417i	0.0894266	−	0.154891i
$576$	0.0308031	−	2.99984i	0.00128346	−	0.124993i
$577$	11.5217	+	19.9561i	0.479654	+	0.830784i	0.999728	−	0.0233368i	$-0.00742900\pi$
$577$	11.5217	+	19.9561i	0.479654	+	0.830784i	−0.520074	+	0.854121i	$0.674096\pi$
$578$	−0.259585	+	0.0944813i	−0.0107973	+	0.00392991i
$579$	2.73448	−	29.5096i	0.113641	−	1.22638i
$580$	−7.17911	+	6.02399i	−0.298096	+	0.250132i
$581$	2.87989	−	2.41651i	0.119478	−	0.100254i
$582$	1.60369	+	1.13523i	0.0664751	+	0.0470568i
$583$	−6.24597	+	2.27335i	−0.258682	+	0.0941525i
$584$	5.00701	+	8.67239i	0.207191	+	0.358866i
$585$	−31.0711	−	5.80824i	−1.28463	−	0.240141i
$586$	12.2617	−	21.2378i	0.506525	−	0.877327i
$587$	2.43414	−	13.8047i	0.100468	−	0.569780i	−0.892467	−	0.451113i	$-0.851027\pi$
$587$	2.43414	−	13.8047i	0.100468	−	0.569780i	0.992934	−	0.118666i	$-0.0378619\pi$
$588$	−0.740046	+	1.56599i	−0.0305190	+	0.0645804i
$589$	−26.3834	−	9.60278i	−1.08711	−	0.395676i
$590$	1.15178	+	6.53207i	0.0474180	+	0.268921i
$591$	0.681229	−	0.674270i	0.0280220	−	0.0277358i
$592$	−8.11190	−	6.80669i	−0.333397	−	0.279753i
$593$	13.5978			0.558396			0.279198	−	0.960234i	$-0.409931\pi$
$593$	13.5978			0.558396			0.279198	+	0.960234i	$0.409931\pi$
$594$	−11.0729	−	24.7334i	−0.454326	−	1.01482i
$595$	−7.87883			−0.323001
$596$	0.422702	+	0.354689i	0.0173146	+	0.0145286i
$597$	−1.82990	−	6.97225i	−0.0748927	−	0.285355i
$598$	2.94243	+	16.6874i	0.120325	+	0.682397i
$599$	17.7013	+	6.44274i	0.723255	+	0.263243i	0.677307	−	0.735701i	$-0.263147\pi$
$599$	17.7013	+	6.44274i	0.723255	+	0.263243i	0.0459478	+	0.998944i	$0.485369\pi$
$600$	−2.42854	+	0.199912i	−0.0991448	+	0.00816137i
$601$	4.95593	−	28.1065i	0.202157	−	1.14649i	−0.699695	−	0.714442i	$-0.746681\pi$
$601$	4.95593	−	28.1065i	0.202157	−	1.14649i	0.901852	−	0.432046i	$-0.142208\pi$
$602$	4.51634	−	7.82252i	0.184072	−	0.318822i
$603$	26.4141	−	4.37837i	1.07567	−	0.178301i
$604$	−7.67497	−	13.2934i	−0.312290	−	0.540902i
$605$	−28.8529	+	10.5016i	−1.17304	+	0.426950i
$606$	5.85661	−	2.69446i	0.237908	−	0.109455i
$607$	−22.2377	+	18.6597i	−0.902602	+	0.757373i	−0.970697	−	0.240306i	$-0.922752\pi$
$607$	−22.2377	+	18.6597i	−0.902602	+	0.757373i	0.0680956	+	0.997679i	$0.478308\pi$
$608$	−2.07801	+	1.74366i	−0.0842745	+	0.0707147i
$609$	7.77944	−	3.57911i	0.315239	−	0.145033i
$610$	24.6790	−	8.98241i	0.999222	−	0.363687i
$611$	16.6766	+	28.8847i	0.674662	+	1.16855i
$612$	−12.3016	+	2.03909i	−0.497261	+	0.0824253i
$613$	5.63203	−	9.75496i	0.227475	−	0.393999i	−0.729584	−	0.683891i	$-0.760286\pi$
$613$	5.63203	−	9.75496i	0.227475	−	0.393999i	0.957059	+	0.289892i	$0.0936195\pi$
$614$	−1.08844	+	6.17286i	−0.0439259	+	0.249116i
$615$	−3.29740	+	0.271435i	−0.132964	+	0.0109453i
$616$	4.90067	+	1.78370i	0.197454	+	0.0718673i
$617$	8.29844	+	47.0628i	0.334083	+	1.89468i	0.436107	+	0.899895i	$0.356357\pi$
$617$	8.29844	+	47.0628i	0.334083	+	1.89468i	−0.102024	+	0.994782i	$0.532532\pi$
$618$	0.136314	+	0.519381i	0.00548334	+	0.0208926i
$619$	24.3805	+	20.4577i	0.979937	+	0.822265i	0.984080	−	0.177727i	$-0.0568744\pi$
$619$	24.3805	+	20.4577i	0.979937	+	0.822265i	−0.00414314	+	0.999991i	$0.501319\pi$
$620$	−19.6195			−0.787939
$621$	9.28434	−	12.8341i	0.372568	−	0.515014i
$622$	−3.50681			−0.140610
$623$	10.7068	+	8.98411i	0.428961	+	0.359941i
$624$	6.84259	−	6.77269i	0.273923	−	0.271125i
$625$	−2.77602	−	15.7436i	−0.111041	−	0.629743i
$626$	−29.6417	−	10.7887i	−1.18472	−	0.431203i
$627$	−10.4694	+	22.1541i	−0.418108	+	0.884748i
$628$	−2.00632	+	11.3784i	−0.0800607	+	0.454047i
$629$	−22.0071	+	38.1175i	−0.877481	+	1.51984i
$630$	−5.58985	−	1.04493i	−0.222705	−	0.0416310i
$631$	18.3742	+	31.8251i	0.731467	+	1.26694i	0.956256	+	0.292531i	$0.0944974\pi$
$631$	18.3742	+	31.8251i	0.731467	+	1.26694i	−0.224789	+	0.974407i	$0.572169\pi$
$632$	9.13280	−	3.32407i	0.363283	−	0.132224i
$633$	−1.06828	−	0.756224i	−0.0424605	−	0.0300572i
$634$	23.1745	−	19.4457i	0.920376	−	0.772287i
$635$	7.59129	−	6.36985i	0.301251	−	0.252780i
$636$	−0.203686	+	2.19810i	−0.00807667	+	0.0871605i
$637$	−5.22327	+	1.90112i	−0.206954	+	0.0753250i
$638$	−12.8920	−	22.3295i	−0.510398	−	0.884035i
$639$	0.119431	−	11.6311i	0.00472461	−	0.460119i
$640$	−0.947779	+	1.64160i	−0.0374642	+	0.0648900i
$641$	−1.24036	+	7.03441i	−0.0489911	+	0.277842i	−0.999456	−	0.0329905i	$-0.989497\pi$
$641$	−1.24036	+	7.03441i	−0.0489911	+	0.277842i	0.950465	+	0.310833i	$0.100608\pi$
$642$	−11.7199	−	16.9219i	−0.462546	−	0.667856i
$643$	13.6591	+	4.97149i	0.538660	+	0.196056i	0.597001	−	0.802240i	$-0.296359\pi$
$643$	13.6591	+	4.97149i	0.538660	+	0.196056i	−0.0583407	+	0.998297i	$0.518581\pi$
$644$	0.529358	+	3.00214i	0.0208596	+	0.118301i
$645$	28.6058	+	7.82252i	1.12635	+	0.308012i
$646$	8.63719	+	7.24747i	0.339826	+	0.285148i
$647$	−41.2483			−1.62164			−0.810819	−	0.585297i	$-0.800978\pi$
$647$	−41.2483			−1.62164			−0.810819	+	0.585297i	$0.800978\pi$
$648$	−8.99810	−	0.184809i	−0.353479	−	0.00725997i
$649$	−18.2487			−0.716324
$650$	−5.99049	−	5.02661i	−0.234966	−	0.197160i
$651$	17.2923	+	4.72873i	0.677738	+	0.185334i
$652$	−1.27244	−	7.21636i	−0.0498326	−	0.282615i
$653$	4.36264	+	1.58787i	0.170723	+	0.0621382i	0.425968	−	0.904738i	$-0.359934\pi$
$653$	4.36264	+	1.58787i	0.170723	+	0.0621382i	−0.255244	+	0.966877i	$0.582156\pi$
$654$	13.1024	+	18.9182i	0.512346	+	0.739761i
$655$	−1.83602	+	10.4126i	−0.0717392	+	0.406853i
$656$	0.503861	−	0.872713i	0.0196725	−	0.0340737i
$657$	26.1700	−	14.7531i	1.02099	−	0.575573i
$658$	3.00020	+	5.19649i	0.116960	+	0.202580i
$659$	−8.54953	+	3.11177i	−0.333042	+	0.121218i	−0.503128	−	0.864212i	$-0.667818\pi$
$659$	−8.54953	+	3.11177i	−0.333042	+	0.121218i	0.170086	+	0.985429i	$0.445595\pi$
$660$	−1.57988	+	17.0495i	−0.0614966	+	0.663650i
$661$	11.3995	−	9.56531i	0.443389	−	0.372047i	−0.393587	−	0.919287i	$-0.628766\pi$
$661$	11.3995	−	9.56531i	0.443389	−	0.372047i	0.836976	+	0.547240i	$0.184322\pi$
$662$	−16.7203	+	14.0300i	−0.649852	+	0.545290i
$663$	−32.6616	−	23.1207i	−1.26847	−	0.897933i
$664$	−3.53270	+	1.28580i	−0.137096	+	0.0498987i
$665$	2.57099	+	4.45309i	0.0996988	+	0.172683i
$666$	−20.6689	+	24.1247i	−0.800902	+	0.934815i
$667$	7.53579	−	13.0524i	0.291787	−	0.505390i
$668$	−0.201228	+	1.14122i	−0.00778574	+	0.0441551i
$669$	12.7294	−	26.9363i	0.492147	−	1.04142i
$670$	−15.8973	−	5.78614i	−0.614166	−	0.223538i
$671$	12.5471	+	71.1583i	0.484376	+	2.74703i
$672$	1.23102	−	1.21844i	0.0474875	−	0.0470024i
$673$	−22.6443	−	19.0008i	−0.872872	−	0.732427i	0.0918288	−	0.995775i	$-0.470729\pi$
$673$	−22.6443	−	19.0008i	−0.872872	−	0.732427i	−0.964701	+	0.263348i	$0.915173\pi$
$674$	−7.29990			−0.281182
$675$	0.524898	+	7.29140i	0.0202033	+	0.280646i
$676$	17.8968			0.688339
$677$	−30.6658	−	25.7316i	−1.17858	−	0.988947i	−0.999987	−	0.00502400i	$-0.998401\pi$
$677$	−30.6658	−	25.7316i	−1.17858	−	0.988947i	−0.178594	−	0.983923i	$-0.557155\pi$
$678$	5.64632	+	21.5135i	0.216846	+	0.826222i
$679$	0.196986	+	1.11716i	0.00755963	+	0.0428728i
$680$	7.40368	+	2.69472i	0.283918	+	0.103338i
$681$	−8.68739	+	0.715126i	−0.332901	+	0.0274037i
$682$	9.37328	−	53.1585i	0.358921	−	2.03554i
$683$	14.1375	−	24.4869i	0.540958	−	0.936966i	−0.457892	−	0.889008i	$-0.651395\pi$
$683$	14.1375	−	24.4869i	0.540958	−	0.936966i	0.998849	−	0.0479581i	$-0.0152714\pi$
$684$	5.16669	+	6.28742i	0.197553	+	0.240405i
$685$	−16.5185	−	28.6109i	−0.631139	−	1.09317i
$686$	−0.939693	+	0.342020i	−0.0358776	+	0.0130584i
$687$	−42.5617	+	19.5814i	−1.62383	+	0.747078i
$688$	−6.91943	+	5.80609i	−0.263801	+	0.221355i
$689$	−5.42694	+	4.55375i	−0.206750	+	0.173484i
$690$	−9.09255	+	4.18323i	−0.346147	+	0.159253i
$691$	19.6082	−	7.13681i	0.745932	−	0.271497i	0.0590392	−	0.998256i	$-0.481196\pi$
$691$	19.6082	−	7.13681i	0.745932	−	0.271497i	0.686893	+	0.726759i	$0.258974\pi$
$692$	−8.99682	−	15.5829i	−0.342008	−	0.592375i
$693$	5.50177	−	14.6463i	0.208995	−	0.556367i
$694$	6.92596	−	11.9961i	0.262906	−	0.455366i
$695$	0.746395	−	4.23302i	0.0283124	−	0.160567i
$696$	−8.53441	+	0.702533i	−0.323496	+	0.0266294i
$697$	−3.93597	−	1.43258i	−0.149085	−	0.0542626i
$698$	−0.323619	−	1.83533i	−0.0122492	−	0.0694684i
$699$	10.1303	+	38.5983i	0.383162	+	1.45992i
$700$	−1.07772	−	0.904313i	−0.0407339	−	0.0341798i
$701$	19.6530			0.742285			0.371143	−	0.928576i	$-0.378966\pi$
$701$	19.6530			0.742285			0.371143	+	0.928576i	$0.378966\pi$
$702$	−20.1062	−	20.7353i	−0.758861	−	0.782604i
$703$	28.7252			1.08339
$704$	−3.99506	−	3.35226i	−0.150570	−	0.126343i
$705$	−14.0017	+	13.8587i	−0.527334	+	0.521947i
$706$	1.81716	+	10.3056i	0.0683897	+	0.387857i
$707$	3.49754	+	1.27300i	0.131539	+	0.0478761i
$708$	−2.58953	+	5.47964i	−0.0973204	+	0.205937i
$709$	3.79902	−	21.5453i	0.142675	−	0.809151i	−0.826529	−	0.562894i	$-0.809688\pi$
$709$	3.79902	−	21.5453i	0.142675	−	0.809151i	0.969204	−	0.246257i	$-0.0792008\pi$
$710$	−3.67476	+	6.36488i	−0.137911	+	0.238870i
$711$	−9.69036	−	27.4993i	−0.363417	−	1.03131i
$712$	−6.98840	−	12.1043i	−0.261901	−	0.453626i
$713$	29.6494	−	10.7915i	1.11038	−	0.404145i
$714$	−5.87598	−	4.15952i	−0.219903	−	0.155666i
$715$	−42.0938	+	35.3209i	−1.57422	+	1.32093i
$716$	−2.25791	+	1.89461i	−0.0843820	+	0.0708049i
$717$	−4.66908	+	50.3870i	−0.174370	+	1.88174i
$718$	−26.4871	+	9.64050i	−0.988488	+	0.359780i
$719$	−8.48735	−	14.7005i	−0.316525	−	0.548237i	0.663236	−	0.748411i	$-0.269183\pi$
$719$	−8.48735	−	14.7005i	−0.316525	−	0.548237i	−0.979760	+	0.200174i	$0.935849\pi$
$720$	4.89535	+	2.89375i	0.182439	+	0.107844i
$721$	−0.155010	+	0.268486i	−0.00577288	+	0.00999892i
$722$	−2.02153	+	11.4647i	−0.0752335	+	0.426671i
$723$	−7.89909	−	11.4053i	−0.293770	−	0.424166i
$724$	−12.8123	−	4.66331i	−0.476167	−	0.173310i
$725$	1.20782	+	6.84987i	0.0448572	+	0.254398i
$726$	−27.0624	−	7.40048i	−1.00438	−	0.274657i
$727$	−0.247457	−	0.207641i	−0.00917769	−	0.00770100i	0.638187	−	0.769881i	$-0.279685\pi$
$727$	−0.247457	−	0.207641i	−0.00917769	−	0.00770100i	−0.647365	+	0.762180i	$0.724129\pi$
$728$	5.55849			0.206011
$729$	−0.831566	+	26.9872i	−0.0307988	+	0.999526i
$730$	−18.9821			−0.702560
$731$	28.7604	+	24.1328i	1.06374	+	0.892585i
$732$	23.1475	+	6.32991i	0.855558	+	0.233960i
$733$	−1.89800	−	10.7641i	−0.0701043	−	0.397581i	−0.999588	−	0.0287171i	$-0.990858\pi$
$733$	−1.89800	−	10.7641i	−0.0701043	−	0.397581i	0.929483	−	0.368864i	$-0.120253\pi$
$734$	−3.14417	−	1.14438i	−0.116053	−	0.0422400i
$735$	−1.86934	−	2.69907i	−0.0689515	−	0.0995569i
$736$	0.529358	−	3.00214i	0.0195124	−	0.110660i
$737$	23.2724	−	40.3089i	0.857248	−	1.48480i
$738$	−2.60248	−	1.53839i	−0.0957987	−	0.0566288i
$739$	11.1476	+	19.3083i	0.410073	+	0.710267i	0.994897	−	0.100893i	$-0.0321700\pi$
$739$	11.1476	+	19.3083i	0.410073	+	0.710267i	−0.584825	+	0.811160i	$0.698837\pi$
$740$	18.8622	−	6.86526i	0.693387	−	0.252372i
$741$	−2.40972	+	26.0049i	−0.0885234	+	0.955313i
$742$	−0.976334	+	0.819241i	−0.0358423	+	0.0300753i
$743$	−18.6297	+	15.6321i	−0.683456	+	0.573487i	−0.917014	−	0.398855i	$-0.869408\pi$
$743$	−18.6297	+	15.6321i	−0.683456	+	0.573487i	0.233558	+	0.972343i	$0.424963\pi$
$744$	−14.6321	−	10.3579i	−0.536439	−	0.379738i
$745$	−0.982887	+	0.357742i	−0.0360102	+	0.0131066i
$746$	−7.88139	−	13.6510i	−0.288558	−	0.499798i
$747$	3.74838	+	10.6372i	0.137146	+	0.389193i
$748$	−10.8384	+	18.7726i	−0.396291	+	0.686395i
$749$	2.06368	−	11.7037i	0.0754053	−	0.427645i
$750$	8.98754	−	19.0183i	0.328179	−	0.694451i
$751$	26.1975	+	9.53510i	0.955960	+	0.347941i	0.772449	−	0.635077i	$-0.219032\pi$
$751$	26.1975	+	9.53510i	0.955960	+	0.347941i	0.183511	+	0.983018i	$0.441254\pi$
$752$	−1.04196	−	5.90923i	−0.0379963	−	0.215488i
$753$	19.1568	−	18.9612i	0.698114	−	0.690983i
$754$	−21.0518	−	17.6646i	−0.766663	−	0.643307i
$755$	29.0967			1.05894
$756$	−3.61721	−	3.73039i	−0.131557	−	0.135673i
$757$	53.7890			1.95499			0.977497	−	0.210949i	$-0.0676555\pi$
$757$	53.7890			1.95499			0.977497	+	0.210949i	$0.0676555\pi$
$758$	−6.82183	−	5.72420i	−0.247780	−	0.207912i
$759$	−6.99034	−	26.6345i	−0.253733	−	0.966772i
$760$	−0.892897	−	5.06387i	−0.0323888	−	0.183686i
$761$	37.6927	+	13.7190i	1.36636	+	0.497314i	0.918014	−	0.396547i	$-0.129792\pi$
$761$	37.6927	+	13.7190i	1.36636	+	0.497314i	0.448344	+	0.893861i	$0.352014\pi$
$762$	9.02441	−	0.742869i	0.326920	−	0.0269113i
$763$	−2.30713	+	13.0844i	−0.0835238	+	0.473687i
$764$	2.53497	−	4.39071i	0.0917122	−	0.158850i
$765$	8.31178	−	22.1269i	0.300513	−	0.799998i
$766$	2.84853	+	4.93380i	0.102922	+	0.178266i
$767$	−18.2770	+	6.65228i	−0.659944	+	0.240200i
$768$	−1.57351	+	0.723928i	−0.0567791	+	0.0261225i
$769$	20.0635	−	16.8353i	0.723509	−	0.607096i	−0.204845	−	0.978795i	$-0.565669\pi$
$769$	20.0635	−	16.8353i	0.723509	−	0.607096i	0.928354	+	0.371698i	$0.121224\pi$
$770$	−7.57288	+	6.35440i	−0.272908	+	0.228997i
$771$	17.6843	−	8.13605i	0.636884	−	0.293013i
$772$	−16.0785	+	5.85208i	−0.578676	+	0.210621i
$773$	−25.7229	−	44.5534i	−0.925189	−	1.60247i	−0.791258	−	0.611483i	$-0.790573\pi$
$773$	−25.7229	−	44.5534i	−0.925189	−	1.60247i	−0.133931	−	0.990991i	$-0.542760\pi$
$774$	17.2042	+	20.9360i	0.618393	+	0.752530i
$775$	−7.28069	+	12.6105i	−0.261530	+	0.452983i
$776$	0.196986	−	1.11716i	0.00707139	−	0.0401038i
$777$	−18.2794	+	1.50472i	−0.655771	+	0.0539816i
$778$	−6.78624	−	2.46999i	−0.243298	−	0.0885534i
$779$	0.474685	+	2.69207i	0.0170073	+	0.0964534i
$780$	4.63280	+	17.6518i	0.165881	+	0.632037i
$781$	−15.4898	−	12.9975i	−0.554269	−	0.465087i
$782$	−12.6708			−0.453107
$783$	1.84460	+	25.6235i	0.0659207	+	0.915710i
$784$	1.00000			0.0357143
$785$	−16.7772	−	14.0778i	−0.598805	−	0.502457i
$786$	−6.86647	+	6.79633i	−0.244919	+	0.242417i
$787$	6.48345	+	36.7695i	0.231110	+	1.31069i	0.850653	+	0.525727i	$0.176207\pi$
$787$	6.48345	+	36.7695i	0.231110	+	1.31069i	−0.619543	+	0.784962i	$0.712682\pi$
$788$	−0.520014	−	0.189270i	−0.0185247	−	0.00674245i
$789$	13.3180	−	28.1819i	0.474133	−	1.00330i
$790$	−3.19908	+	18.1429i	−0.113818	+	0.645495i
$791$	−6.42076	+	11.1211i	−0.228296	+	0.395420i
$792$	−10.1793	+	11.8813i	−0.361706	+	0.422184i
$793$	38.5062	+	66.6948i	1.36740	+	2.36840i
$794$	10.3532	−	3.76825i	0.367421	−	0.133730i
$795$	−3.41536	−	2.41769i	−0.121130	−	0.0857466i
$796$	−3.18810	+	2.67513i	−0.112999	+	0.0948175i
$797$	−29.7379	+	24.9531i	−1.05337	+	0.883883i	−0.993444	−	0.114320i	$-0.963531\pi$
$797$	−29.7379	+	24.9531i	−1.05337	+	0.883883i	−0.0599264	+	0.998203i	$0.519087\pi$
$798$	−0.433521	+	4.67841i	−0.0153465	+	0.165614i
$799$	−23.4364	+	8.53014i	−0.829119	+	0.301775i
$800$	0.703431	+	1.21838i	0.0248700	+	0.0430761i
$801$	−36.5261	+	20.5912i	−1.29059	+	0.727555i
$802$	−10.4461	+	18.0932i	−0.368864	+	0.638892i
$803$	9.06877	−	51.4315i	0.320030	−	1.81498i
$804$	−8.80138	−	12.7080i	−0.310401	−	0.448178i
$805$	−5.43003	−	1.97637i	−0.191383	−	0.0696579i
$806$	−9.99030	−	56.6578i	−0.351893	−	1.99569i
$807$	−24.0492	−	6.57649i	−0.846573	−	0.231503i
$808$	−2.85122	−	2.39246i	−0.100306	−	0.0841664i
$809$	4.41959			0.155385			0.0776923	−	0.996977i	$-0.475245\pi$
$809$	4.41959			0.155385			0.0776923	+	0.996977i	$0.475245\pi$
$810$	8.83159	−	14.5961i	0.310311	−	0.512856i
$811$	−9.88154			−0.346988			−0.173494	−	0.984835i	$-0.555506\pi$
$811$	−9.88154			−0.346988			−0.173494	+	0.984835i	$0.555506\pi$
$812$	−3.78733	−	3.17795i	−0.132909	−	0.111524i
$813$	−0.832168	−	0.227564i	−0.0291854	−	0.00798102i
$814$	9.58978	+	54.3864i	0.336122	+	1.90624i
$815$	13.0524	+	4.75068i	0.457205	+	0.166409i
$816$	4.09897	+	5.91838i	0.143493	+	0.207185i
$817$	4.25481	−	24.1302i	0.148857	−	0.844210i
$818$	−8.63798	+	14.9614i	−0.302020	+	0.523114i
$819$	0.171219	−	16.6746i	0.00598286	−	0.582657i
$820$	0.955098	+	1.65428i	0.0333535	+	0.0577699i
$821$	9.44976	−	3.43943i	0.329799	−	0.120037i	−0.171813	−	0.985130i	$-0.554963\pi$
$821$	9.44976	−	3.43943i	0.329799	−	0.120037i	0.501612	+	0.865093i	$0.332740\pi$
$822$	2.78535	−	30.0585i	0.0971502	−	1.04841i
$823$	−37.7149	+	31.6465i	−1.31466	+	1.10313i	−0.327249	+	0.944938i	$0.606121\pi$
$823$	−37.7149	+	31.6465i	−1.31466	+	1.10313i	−0.987409	+	0.158190i	$0.949434\pi$
$824$	0.237489	−	0.199277i	0.00827333	−	0.00694215i
$825$	10.3723	+	7.34243i	0.361118	+	0.255631i
$826$	−3.28812	+	1.19678i	−0.114408	+	0.0416413i
$827$	22.1800	+	38.4168i	0.771273	+	1.33588i	0.936866	+	0.349690i	$0.113713\pi$
$827$	22.1800	+	38.4168i	0.771273	+	1.33588i	−0.165593	+	0.986194i	$0.552954\pi$
$828$	−8.98964	−	1.68047i	−0.312412	−	0.0584002i
$829$	7.52947	−	13.0414i	0.261509	−	0.452947i	−0.705134	−	0.709074i	$-0.749113\pi$
$829$	7.52947	−	13.0414i	0.261509	−	0.452947i	0.966643	+	0.256127i	$0.0824465\pi$
$830$	1.23745	−	7.01794i	0.0429526	−	0.243596i
$831$	1.52867	−	3.23478i	0.0530290	−	0.112213i
$832$	−5.22327	−	1.90112i	−0.181084	−	0.0659093i
$833$	−0.721763	−	4.09332i	−0.0250076	−	0.141825i
$834$	2.79142	−	2.76291i	0.0966590	−	0.0956716i
$835$	−1.68271	−	1.41196i	−0.0582325	−	0.0488629i
$836$	14.1470			0.489284
$837$	−31.5227	+	43.5749i	−1.08958	+	1.50617i
$838$	11.3274			0.391298
$839$	−27.9790	−	23.4772i	−0.965943	−	0.810522i	0.0159670	−	0.999873i	$-0.494917\pi$
$839$	−27.9790	−	23.4772i	−0.965943	−	0.810522i	−0.981910	+	0.189350i	$0.939362\pi$
$840$	0.833463	+	3.17565i	0.0287572	+	0.109570i
$841$	−0.791273	−	4.48753i	−0.0272853	−	0.154743i
$842$	11.0051	+	4.00554i	0.379262	+	0.138040i
$843$	−7.32489	+	0.602968i	−0.252283	+	0.0207673i
$844$	−0.131221	+	0.744188i	−0.00451680	+	0.0256160i
$845$	−16.9622	+	29.3794i	−0.583518	+	1.01068i
$846$	−17.7589	+	2.94368i	−0.610562	+	0.101206i
$847$	−8.09909	−	14.0280i	−0.278288	−	0.482009i
$848$	1.19765	−	0.435909i	0.0411275	−	0.0149692i
$849$	31.6350	−	14.5544i	1.08571	−	0.499506i
$850$	4.47950	−	3.75875i	0.153646	−	0.128924i
$851$	−24.7287	+	20.7499i	−0.847690	+	0.711297i
$852$	−6.10087	+	2.80684i	−0.209012	+	0.0961607i
$853$	−15.3355	+	5.58167i	−0.525078	+	0.191113i	−0.590939	−	0.806716i	$-0.701243\pi$
$853$	−15.3355	+	5.58167i	−0.525078	+	0.191113i	0.0658612	+	0.997829i	$0.479021\pi$
$854$	6.92746	+	11.9987i	0.237053	+	0.410588i
$855$	−15.2183	+	2.52257i	−0.520455	+	0.0862699i
$856$	−5.94213	+	10.2921i	−0.203098	+	0.351776i
$857$	0.882674	−	5.00589i	0.0301516	−	0.170998i	−0.966014	−	0.258492i	$-0.916775\pi$
$857$	0.882674	−	5.00589i	0.0301516	−	0.170998i	0.996165	+	0.0874935i	$0.0278857\pi$
$858$	−50.0404	+	4.11921i	−1.70835	+	0.140628i
$859$	−18.8930	−	6.87651i	−0.644622	−	0.234623i	−0.00103913	−	0.999999i	$-0.500331\pi$
$859$	−18.8930	−	6.87651i	−0.644622	−	0.234623i	−0.643583	+	0.765376i	$0.722553\pi$
$860$	−2.97320	−	16.8618i	−0.101385	−	0.574984i
$861$	−0.443088	−	1.68825i	−0.0151004	−	0.0575354i
$862$	−23.1993	−	19.4665i	−0.790170	−	0.663031i
$863$	−42.5155			−1.44725			−0.723623	−	0.690196i	$-0.757524\pi$
$863$	−42.5155			−1.44725			−0.723623	+	0.690196i	$0.757524\pi$
$864$	2.12320	+	4.74258i	0.0722327	+	0.161346i
$865$	34.1080			1.15971
$866$	−1.88399	−	1.58085i	−0.0640204	−	0.0537195i
$867$	0.340062	−	0.336588i	0.0115491	−	0.0114311i
$868$	−1.79730	−	10.1930i	−0.0610045	−	0.345974i
$869$	−47.6293	−	17.3356i	−1.61571	−	0.588071i
$870$	6.93545	−	14.6759i	0.235134	−	0.497561i
$871$	8.61445	−	48.8550i	0.291890	−	1.65539i
$872$	6.64312	−	11.5062i	0.224965	−	0.389650i
$873$	−3.34525	−	0.625339i	−0.113219	−	0.0211645i
$874$	4.13469	+	7.16150i	0.139858	+	0.242241i
$875$	11.4122	−	4.15369i	0.385802	−	0.140420i
$876$	−14.1567	−	10.0214i	−0.478312	−	0.338591i
$877$	8.07205	−	6.77326i	0.272574	−	0.228717i	−0.496246	−	0.868182i	$-0.665289\pi$
$877$	8.07205	−	6.77326i	0.272574	−	0.228717i	0.768820	+	0.639465i	$0.220844\pi$
$878$	3.02089	−	2.53482i	0.101950	−	0.0855462i
$879$	−3.91919	+	42.2945i	−0.132191	+	1.42656i
$880$	9.28951	−	3.38110i	0.313149	−	0.113977i
$881$	−20.9308	−	36.2532i	−0.705176	−	1.22140i	−0.966628	−	0.256184i	$-0.917535\pi$
$881$	−20.9308	−	36.2532i	−0.705176	−	1.22140i	0.261452	−	0.965216i	$-0.415799\pi$
$882$	0.0308031	−	2.99984i	0.00103719	−	0.101010i
$883$	−10.2564	+	17.7647i	−0.345157	+	0.597829i	−0.985382	−	0.170358i	$-0.945508\pi$
$883$	−10.2564	+	17.7647i	−0.345157	+	0.597829i	0.640226	+	0.768187i	$0.278841\pi$
$884$	−4.01192	+	22.7527i	−0.134935	+	0.765256i
$885$	−6.54108	−	9.44446i	−0.219876	−	0.317472i
$886$	28.8433	+	10.4981i	0.969011	+	0.352691i
$887$	1.89360	+	10.7392i	0.0635810	+	0.360586i	0.999954	+	0.00957951i	$0.00304930\pi$
$887$	1.89360	+	10.7392i	0.0635810	+	0.360586i	−0.936373	+	0.351006i	$0.885840\pi$
$888$	17.6917	+	4.83796i	0.593694	+	0.162351i
$889$	4.00478	+	3.36041i	0.134316	+	0.112705i
$890$	26.4938			0.888075
$891$	35.3285	+	30.9023i	1.18355	+	1.03527i
$892$	−17.2008			−0.575926
$893$	12.4689	+	10.4626i	0.417255	+	0.350119i
$894$	−0.921895	−	0.252101i	−0.0308328	−	0.00843151i
$895$	−0.970196	−	5.50226i	−0.0324301	−	0.183920i
$896$	−0.939693	−	0.342020i	−0.0313929	−	0.0114261i
$897$	−16.7104	−	24.1276i	−0.557944	−	0.805597i
$898$	−0.0394942	+	0.223983i	−0.00131794	+	0.00747440i
$899$	−25.5859	+	44.3161i	−0.853338	+	1.47802i
$900$	3.67661	−	2.07265i	0.122554	−	0.0690884i
$901$	−2.64874	−	4.58775i	−0.0882423	−	0.152840i
$902$	−4.93852	+	1.79747i	−0.164435	+	0.0598493i
$903$	−1.44355	+	15.5783i	−0.0480384	+	0.518414i
$904$	9.83717	−	8.25436i	0.327179	−	0.274536i
$905$	19.7985	−	16.6130i	0.658126	−	0.552233i
$906$	21.7001	+	15.3612i	0.720938	+	0.510342i
$907$	23.6675	−	8.61426i	0.785866	−	0.286032i	0.0822496	−	0.996612i	$-0.473790\pi$
$907$	23.6675	−	8.61426i	0.785866	−	0.286032i	0.703617	+	0.710580i	$0.251567\pi$
$908$	2.51631	+	4.35839i	0.0835068	+	0.144638i
$909$	−7.26483	+	8.47952i	−0.240959	+	0.281248i
$910$	−5.26822	+	9.12483i	−0.174640	+	0.302485i
$911$	3.72895	−	21.1479i	0.123545	−	0.700661i	−0.858616	−	0.512620i	$-0.828675\pi$
$911$	3.72895	−	21.1479i	0.123545	−	0.700661i	0.982161	−	0.188041i	$-0.0602139\pi$
$912$	2.00749	−	4.24799i	0.0664745	−	0.140665i
$913$	18.4237	+	6.70568i	0.609736	+	0.221926i
$914$	1.26372	+	7.16690i	0.0418001	+	0.237060i
$915$	−32.3299	+	31.9997i	−1.06880	+	1.05788i
$916$	20.7207	+	17.3867i	0.684630	+	0.574472i
$917$	−5.57789			−0.184198
$918$	17.8805	−	12.1140i	0.590143	−	0.399820i
$919$	11.5230			0.380107			0.190054	−	0.981774i	$-0.439134\pi$
$919$	11.5230			0.380107			0.190054	+	0.981774i	$0.439134\pi$
$920$	4.42660	+	3.71436i	0.145941	+	0.122459i
$921$	−2.75603	−	10.5010i	−0.0908143	−	0.346020i
$922$	−1.83984	−	10.4343i	−0.0605920	−	0.343634i
$923$	−20.2519	−	7.37108i	−0.666598	−	0.242622i
$924$	−9.00252	+	0.741067i	−0.296161	+	0.0243793i
$925$	2.58696	−	14.6714i	0.0850588	−	0.482392i
$926$	−6.80035	+	11.7785i	−0.223473	+	0.387067i
$927$	−0.590485	−	0.718569i	−0.0193941	−	0.0236009i
$928$	2.47201	+	4.28164i	0.0811475	+	0.140552i
$929$	10.6611	−	3.88034i	0.349781	−	0.127310i	−0.161154	−	0.986929i	$-0.551522\pi$
$929$	10.6611	−	3.88034i	0.349781	−	0.127310i	0.510935	+	0.859619i	$0.329299\pi$
$930$	30.8715	−	14.2031i	1.01232	−	0.465738i
$931$	−2.07801	+	1.74366i	−0.0681041	+	0.0571461i
$932$	17.6492	−	14.8095i	0.578120	−	0.485100i
$933$	5.51800	−	2.53868i	0.180651	−	0.0831126i
$934$	−25.3156	+	9.21411i	−0.828351	+	0.301495i
$935$	−20.5448	−	35.5846i	−0.671886	−	1.16374i
$936$	−5.86394	+	15.6104i	−0.191669	+	0.510243i
$937$	−17.5880	+	30.4632i	−0.574574	+	0.995191i	0.421514	+	0.906822i	$0.361499\pi$
$937$	−17.5880	+	30.4632i	−0.574574	+	0.995191i	−0.996088	+	0.0883688i	$0.971835\pi$
$938$	1.54978	−	8.78925i	0.0506022	−	0.286979i
$939$	54.4517	−	4.48234i	1.77696	−	0.146276i
$940$	10.6882	+	3.89017i	0.348609	+	0.126883i
$941$	−7.27486	−	41.2578i	−0.237154	−	1.34496i	−0.838031	−	0.545623i	$-0.816293\pi$
$941$	−7.27486	−	41.2578i	−0.237154	−	1.34496i	0.600877	−	0.799342i	$-0.294818\pi$
$942$	−5.08017	−	19.3564i	−0.165521	−	0.630666i
$943$	−2.35328	−	1.97464i	−0.0766335	−	0.0643031i
$944$	3.49915			0.113888
$945$	9.55212	−	2.40244i	0.310731	−	0.0781513i
$946$	47.1071			1.53158
$947$	−33.3044	−	27.9457i	−1.08225	−	0.908115i	−0.0861432	−	0.996283i	$-0.527454\pi$
$947$	−33.3044	−	27.9457i	−1.08225	−	0.908115i	−0.996106	+	0.0881682i	$0.971899\pi$
$948$	−11.9642	+	11.8419i	−0.388578	+	0.384608i
$949$	−9.66574	−	54.8172i	−0.313763	−	1.77944i
$950$	−3.58617	−	1.30526i	−0.116351	−	0.0423482i
$951$	−22.3880	+	47.3746i	−0.725980	+	1.53623i
$952$	−0.721763	+	4.09332i	−0.0233925	+	0.132665i
$953$	26.5875	−	46.0509i	0.861254	−	1.49174i	−0.00946552	−	0.999955i	$-0.503013\pi$
$953$	26.5875	−	46.0509i	0.861254	−	1.49174i	0.870719	−	0.491780i	$-0.163654\pi$
$954$	−1.27077	−	3.60619i	−0.0411426	−	0.116755i
$955$	4.80519	+	8.32284i	0.155492	+	0.269321i
$956$	27.4537	−	9.99232i	0.887915	−	0.323175i
$957$	36.4506	+	25.8029i	1.17828	+	0.834089i
$958$	23.6564	−	19.8500i	0.764302	−	0.641326i
$959$	13.3511	−	11.2029i	0.431130	−	0.361761i
$960$	0.302938	−	3.26920i	0.00977727	−	0.105513i
$961$	−71.5368	+	26.0373i	−2.30764	+	0.839912i
$962$	29.4304	+	50.9749i	0.948873	+	1.64350i
$963$	30.6916	+	18.1425i	0.989022	+	0.584634i
$964$	−4.00495	+	6.93678i	−0.128991	+	0.223419i
$965$	5.63204	−	31.9409i	0.181302	−	1.02821i
$966$	−3.00628	−	4.34068i	−0.0967255	−	0.139659i
$967$	−7.80582	−	2.84109i	−0.251018	−	0.0913632i	0.213447	−	0.976955i	$-0.431531\pi$
$967$	−7.80582	−	2.84109i	−0.251018	−	0.0913632i	−0.464465	+	0.885592i	$0.653753\pi$
$968$	2.81278	+	15.9521i	0.0904063	+	0.512719i
$969$	−18.8373	−	5.15125i	−0.605142	−	0.165482i
$970$	1.64724	+	1.38220i	0.0528896	+	0.0443796i
$971$	7.96527			0.255618			0.127809	−	0.991799i	$-0.459206\pi$
$971$	7.96527			0.255618			0.127809	+	0.991799i	$0.459206\pi$
$972$	14.2924	−	6.22318i	0.458428	−	0.199608i
$973$	2.26757			0.0726951
$974$	−1.78689	−	1.49938i	−0.0572555	−	0.0480431i
$975$	13.0650	+	3.57274i	0.418414	+	0.114419i
$976$	−2.40588	−	13.6444i	−0.0770104	−	0.436748i
$977$	−26.9767	−	9.81870i	−0.863060	−	0.314128i	−0.127706	−	0.991812i	$-0.540762\pi$
$977$	−26.9767	−	9.81870i	−0.863060	−	0.314128i	−0.735353	+	0.677684i	$0.762984\pi$
$978$	7.22632	+	10.4339i	0.231072	+	0.333638i
$979$	−12.6575	+	71.7842i	−0.404535	+	2.29423i
$980$	−0.947779	+	1.64160i	−0.0302757	+	0.0524390i
$981$	−34.3122	−	20.2827i	−1.09551	−	0.647578i
$982$	−11.8669	−	20.5541i	−0.378688	−	0.655907i
$983$	38.4209	−	13.9841i	1.22544	−	0.446022i	0.353404	−	0.935471i	$-0.385024\pi$
$983$	38.4209	−	13.9841i	1.22544	−	0.446022i	0.872032	+	0.489448i	$0.162802\pi$
$984$	−0.161049	+	1.73798i	−0.00513405	+	0.0554048i
$985$	0.803564	−	0.674270i	0.0256037	−	0.0214840i
$986$	15.7419	−	13.2090i	0.501325	−	0.420662i
$987$	−8.48272	−	6.00480i	−0.270008	−	0.191135i
$988$	14.1689	−	5.15706i	0.450773	−	0.164068i
$989$	13.7678	+	23.8466i	0.437792	+	0.758278i
$990$	−9.85663	−	27.9712i	−0.313264	−	0.888983i
$991$	26.1038	−	45.2132i	0.829216	−	1.43624i	−0.0694380	−	0.997586i	$-0.522121\pi$
$991$	26.1038	−	45.2132i	0.829216	−	1.43624i	0.898654	−	0.438658i	$-0.144546\pi$
$992$	−1.79730	+	10.1930i	−0.0570645	+	0.323629i
$993$	16.1528	−	34.1806i	0.512594	−	1.08469i
$994$	−3.64341	−	1.32609i	−0.115562	−	0.0420611i
$995$	−1.36989	−	7.76901i	−0.0434283	−	0.246294i
$996$	4.62791	−	4.58064i	0.146641	−	0.145143i
$997$	1.59761	+	1.34056i	0.0505969	+	0.0424559i	0.667735	−	0.744399i	$-0.267264\pi$
$997$	1.59761	+	1.34056i	0.0505969	+	0.0424559i	−0.617139	+	0.786855i	$0.711708\pi$
$998$	5.88605			0.186320
$999$	15.0581	−	52.9233i	0.476416	−	1.67442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.43.1	✓	12
27.22	even	9	inner	378.2.u.b.211.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.43.1	✓	12	1.1	even	1	trivial
378.2.u.b.211.1	yes	12	27.22	even	9	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.67071 - 0.456871i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.78124 - 0.648319i) q^{5} +(-0.986166 - 1.42389i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.58254 + 1.52660i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.67071 - 0.456871i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.78124 - 0.648319i) q^{5} +(-0.986166 - 1.42389i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.58254 + 1.52660i) q^{9} +(-0.947779 - 1.64160i) q^{10} +(4.90067 - 1.78370i) q^{11} +(0.159815 - 1.72466i) q^{12} +(4.25805 - 3.57293i) q^{13} +(0.766044 - 0.642788i) q^{14} +(2.67974 + 1.89695i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.07824 + 3.59961i) q^{17} +(0.997061 + 2.82946i) q^{18} +(1.35633 - 2.34922i) q^{19} +(0.329160 - 1.86676i) q^{20} +(-0.740046 + 1.56599i) q^{21} +(4.90067 + 1.78370i) q^{22} +(0.529358 + 3.00214i) q^{23} +(1.23102 - 1.21844i) q^{24} +(-1.07772 - 0.904313i) q^{25} +5.55849 q^{26} +(-3.61721 - 3.73039i) q^{27} +1.00000 q^{28} +(-3.78733 - 3.17795i) q^{29} +(0.833463 + 3.17565i) q^{30} +(-1.79730 - 10.1930i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-9.00252 + 0.741067i) q^{33} +(-0.721763 + 4.09332i) q^{34} +(-0.947779 + 1.64160i) q^{35} +(-1.05495 + 2.80839i) q^{36} +(5.29467 + 9.17063i) q^{37} +(2.54906 - 0.927781i) q^{38} +(-8.74633 + 4.02394i) q^{39} +(1.45208 - 1.21844i) q^{40} +(-0.771960 + 0.647752i) q^{41} +(-1.57351 + 0.723928i) q^{42} +(8.48794 - 3.08936i) q^{43} +(2.60759 + 4.51648i) q^{44} +(-3.61040 - 4.39355i) q^{45} +(-1.52423 + 2.64004i) q^{46} +(-1.04196 + 5.90923i) q^{47} +(1.72621 - 0.142098i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.244299 - 1.38549i) q^{50} +(-1.82757 - 6.96338i) q^{51} +(4.25805 + 3.57293i) q^{52} -1.27451 q^{53} +(-0.373098 - 5.18274i) q^{54} -9.88569 q^{55} +(0.766044 + 0.642788i) q^{56} +(-3.33932 + 3.30521i) q^{57} +(-0.858518 - 4.86890i) q^{58} +(-3.28812 - 1.19678i) q^{59} +(-1.40280 + 2.96843i) q^{60} +(-2.40588 + 13.6444i) q^{61} +(5.17513 - 8.96359i) q^{62} +(1.95186 - 2.27821i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-9.90102 + 3.60367i) q^{65} +(-7.37268 - 5.21902i) q^{66} +(6.83683 - 5.73678i) q^{67} +(-3.18404 + 2.67173i) q^{68} +(0.487187 - 5.25755i) q^{69} +(-1.78124 + 0.648319i) q^{70} +(-1.93862 - 3.35779i) q^{71} +(-2.61334 + 1.47324i) q^{72} +(5.00701 - 8.67239i) q^{73} +(-1.83882 + 10.4285i) q^{74} +(1.38740 + 2.00322i) q^{75} +(2.54906 + 0.927781i) q^{76} +(-0.905608 - 5.13596i) q^{77} +(-9.28662 - 2.53951i) q^{78} +(-7.44513 - 6.24720i) q^{79} +1.89556 q^{80} +(4.33900 + 7.88499i) q^{81} -1.00772 q^{82} +(2.87989 + 2.41651i) q^{83} +(-1.67071 - 0.456871i) q^{84} +(-1.36814 - 7.75913i) q^{85} +(8.48794 + 3.08936i) q^{86} +(4.87562 + 7.03975i) q^{87} +(-0.905608 + 5.13596i) q^{88} +(-6.98840 + 12.1043i) q^{89} +(0.0583890 - 5.68637i) q^{90} +(-2.77925 - 4.81379i) q^{91} +(-2.86461 + 1.04263i) q^{92} +(-1.65412 + 17.8507i) q^{93} +(-4.59657 + 3.85698i) q^{94} +(-3.93899 + 3.30521i) q^{95} +(1.41369 + 1.00073i) q^{96} +(-1.06598 + 0.387987i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(15.3792 + 2.87488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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