LMFDB - Embedded newform 361.2.e.f.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	361.28
Dual form			361.2.e.f.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 2.49362i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.26604 + 0.460802i) q^{5} +(1.26604 + 1.06234i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +O(q^{10})$	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.26604 + 0.460802i) q^{5} +(1.26604 + 1.06234i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +(0.592396 - 3.35965i) q^{10} +(0.592396 + 1.02606i) q^{11} +(1.43969 - 2.49362i) q^{12} +(2.08125 + 1.74638i) q^{13} +(3.64543 + 1.32683i) q^{14} +(-0.826352 + 0.300767i) q^{15} +(5.08512 - 4.26692i) q^{16} +(0.673648 + 3.82045i) q^{17} +6.51754 q^{18} -5.94356 q^{20} +(-0.173648 - 0.984808i) q^{21} +(2.29813 - 1.92836i) q^{22} +(4.75877 - 1.73205i) q^{23} +(-3.74510 - 1.36310i) q^{24} +(-2.43969 - 2.04715i) q^{25} +(3.43969 - 5.95772i) q^{26} +(-1.81908 - 3.15074i) q^{27} +(1.17365 - 6.65609i) q^{28} +(-0.807934 + 4.58202i) q^{29} +(1.11334 + 1.92836i) q^{30} +(1.91875 - 3.32337i) q^{31} +(-3.52094 - 2.95442i) q^{32} +(-0.726682 - 0.264490i) q^{33} +(9.23055 - 3.35965i) q^{34} +(-1.58125 + 1.32683i) q^{35} +(-1.97178 - 11.1825i) q^{36} -4.10607 q^{37} -1.77332 q^{39} +(1.42855 + 8.10170i) q^{40} +(-7.64930 + 6.41852i) q^{41} +(-2.37939 + 0.866025i) q^{42} +(8.17752 + 2.97637i) q^{43} +(-4.00387 - 3.35965i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.0996702 - 0.565258i) q^{47} +(-0.752374 + 4.26692i) q^{48} +(2.32635 + 4.02936i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(-1.93969 - 1.62760i) q^{51} +(-11.2626 - 4.09927i) q^{52} +(-2.76604 + 1.00676i) q^{53} +(-7.05690 + 5.92145i) q^{54} +(0.277189 + 1.57202i) q^{55} -9.35504 q^{56} +11.7811 q^{58} +(-0.683448 - 3.87603i) q^{59} +(2.97178 - 2.49362i) q^{60} +(4.24510 - 1.54509i) q^{61} +(-9.13088 - 3.32337i) q^{62} +(-3.02094 - 2.53487i) q^{63} +(0.819078 - 1.41868i) q^{64} +(1.83022 + 3.17004i) q^{65} +(-0.340022 + 1.92836i) q^{66} +(-0.674992 + 3.82807i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(4.00387 + 3.35965i) q^{70} +(6.51754 + 2.37219i) q^{71} +(-14.7690 + 5.37549i) q^{72} +(4.69459 - 3.93923i) q^{73} +(1.80541 + 10.2390i) q^{74} +2.07873 q^{75} -1.81521 q^{77} +(0.779715 + 4.42198i) q^{78} +(7.51367 - 6.30472i) q^{79} +(8.40420 - 3.05888i) q^{80} +(-5.02481 - 1.82888i) q^{81} +(19.3687 + 16.2523i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(2.20574 + 3.82045i) q^{84} +(-0.907604 + 5.14728i) q^{85} +(3.82635 - 21.7003i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(-3.61721 + 6.26519i) q^{88} +(-1.85844 - 1.55942i) q^{89} +(8.25150 + 3.00330i) q^{90} +(-3.91147 + 1.42366i) q^{91} +(-17.1138 + 14.3602i) q^{92} +(0.434945 + 2.46669i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(1.27972 + 7.25762i) q^{97} +(9.02481 - 7.57272i) q^{98} +(-2.86571 + 1.04303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	$ 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} + 3 q^{12} + 15 q^{13} + 6 q^{14} - 6 q^{15} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} + 6 q^{28} + 6 q^{29} + 9 q^{31} - 18 q^{32} + 9 q^{33} + 18 q^{34} - 12 q^{35} + 3 q^{36} - 24 q^{39} + 9 q^{40} - 6 q^{41} - 3 q^{42} + 24 q^{43} - 15 q^{45} - 18 q^{46} + 15 q^{47} - 21 q^{48} + 15 q^{49} - 15 q^{50} - 6 q^{51} - 21 q^{52} - 12 q^{53} - 6 q^{54} - 9 q^{55} - 6 q^{56} + 36 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 3 q^{62} - 15 q^{63} - 12 q^{64} - 12 q^{65} + 18 q^{66} + 6 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} + 30 q^{75} - 18 q^{77} - 21 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 45 q^{82} + 3 q^{84} - 9 q^{85} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 3 q^{89} + 9 q^{90} - 3 q^{91} - 30 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 + 3 * q^12 + 15 * q^13 + 6 * q^14 - 6 * q^15 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 + 6 * q^28 + 6 * q^29 + 9 * q^31 - 18 * q^32 + 9 * q^33 + 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 + 9 * q^40 - 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 - 18 * q^46 + 15 * q^47 - 21 * q^48 + 15 * q^49 - 15 * q^50 - 6 * q^51 - 21 * q^52 - 12 * q^53 - 6 * q^54 - 9 * q^55 - 6 * q^56 + 36 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 - 12 * q^65 + 18 * q^66 + 6 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 + 30 * q^75 - 18 * q^77 - 21 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 + 3 * q^84 - 9 * q^85 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 3 * q^89 + 9 * q^90 - 3 * q^91 - 30 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 27 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	−0.594292	−	0.804249i	$-0.702568\pi$
$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	0.283383	−	0.959007i	$-0.408543\pi$
$3$	−0.500000	+	0.419550i	−0.288675	+	0.242227i	−0.775612	−	0.631210i	$-0.782559\pi$
$3$	−0.500000	+	0.419550i	−0.288675	+	0.242227i	0.486937	+	0.873437i	$0.338114\pi$
$4$	−4.14543	+	1.50881i	−2.07271	+	0.754407i
$5$	1.26604	+	0.460802i	0.566192	+	0.206077i	0.609226	−	0.792996i	$-0.291480\pi$
$5$	1.26604	+	0.460802i	0.566192	+	0.206077i	−0.0430339	+	0.999074i	$0.513702\pi$
$6$	1.26604	+	1.06234i	0.516860	+	0.433697i
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	−0.973699	−	0.227836i	$-0.926835\pi$
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	0.684162	+	0.729330i	$0.260168\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$	−0.446967	+	2.53487i	−0.148989	+	0.844958i
$10$	0.592396	−	3.35965i	0.187332	−	1.06241i
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	0.941406	−	0.337275i	$-0.109505\pi$
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	−0.762792	+	0.646644i	$0.776172\pi$
$12$	1.43969	−	2.49362i	0.415603	−	0.719846i
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	0.884038	−	0.467415i	$-0.154815\pi$
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	−0.306803	+	0.951773i	$0.599259\pi$
$14$	3.64543	+	1.32683i	0.974282	+	0.354610i
$15$	−0.826352	+	0.300767i	−0.213363	+	0.0776578i
$16$	5.08512	−	4.26692i	1.27128	−	1.06673i
$17$	0.673648	+	3.82045i	0.163384	+	0.926595i	0.950715	+	0.310065i	$0.100351\pi$
$17$	0.673648	+	3.82045i	0.163384	+	0.926595i	−0.787332	+	0.616530i	$0.788538\pi$
$18$	6.51754			1.53620
$19$		0			0
$19$		0			0
$20$	−5.94356			−1.32902
$21$	−0.173648	−	0.984808i	−0.0378931	−	0.214903i
$22$	2.29813	−	1.92836i	0.489964	−	0.411128i
$23$	4.75877	−	1.73205i	0.992272	−	0.361158i	0.205673	−	0.978621i	$-0.434062\pi$
$23$	4.75877	−	1.73205i	0.992272	−	0.361158i	0.786600	+	0.617463i	$0.211840\pi$
$24$	−3.74510	−	1.36310i	−0.764465	−	0.278243i
$25$	−2.43969	−	2.04715i	−0.487939	−	0.409429i
$26$	3.43969	−	5.95772i	0.674579	−	1.16841i
$27$	−1.81908	−	3.15074i	−0.350082	−	0.606359i
$28$	1.17365	−	6.65609i	0.221799	−	1.25788i
$29$	−0.807934	+	4.58202i	−0.150029	+	0.850859i	0.813161	+	0.582039i	$0.197745\pi$
$29$	−0.807934	+	4.58202i	−0.150029	+	0.850859i	−0.963190	+	0.268820i	$0.913366\pi$
$30$	1.11334	+	1.92836i	0.203267	+	0.352069i
$31$	1.91875	−	3.32337i	0.344617	−	0.596895i	−0.640667	−	0.767819i	$-0.721342\pi$
$31$	1.91875	−	3.32337i	0.344617	−	0.596895i	0.985284	+	0.170924i	$0.0546753\pi$
$32$	−3.52094	−	2.95442i	−0.622421	−	0.522273i
$33$	−0.726682	−	0.264490i	−0.126499	−	0.0460419i
$34$	9.23055	−	3.35965i	1.58303	−	0.576175i
$35$	−1.58125	+	1.32683i	−0.267280	+	0.224275i
$36$	−1.97178	−	11.1825i	−0.328630	−	1.86375i
$37$	−4.10607			−0.675033			−0.337517	−	0.941320i	$-0.609587\pi$
$37$	−4.10607			−0.675033			−0.337517	+	0.941320i	$0.609587\pi$
$38$		0			0
$39$	−1.77332			−0.283958
$40$	1.42855	+	8.10170i	0.225873	+	1.28099i
$41$	−7.64930	+	6.41852i	−1.19462	+	1.00241i	−0.194853	+	0.980833i	$0.562423\pi$
$41$	−7.64930	+	6.41852i	−1.19462	+	1.00241i	−0.999767	+	0.0215727i	$0.993133\pi$
$42$	−2.37939	+	0.866025i	−0.367147	+	0.133631i
$43$	8.17752	+	2.97637i	1.24706	+	0.453893i	0.879407	−	0.476070i	$-0.157939\pi$
$43$	8.17752	+	2.97637i	1.24706	+	0.453893i	0.367653	+	0.929963i	$0.380162\pi$
$44$	−4.00387	−	3.35965i	−0.603606	−	0.506486i
$45$	−1.73396	+	3.00330i	−0.258483	+	0.447705i
$46$	−6.41147	−	11.1050i	−0.945320	−	1.63734i
$47$	0.0996702	−	0.565258i	0.0145384	−	0.0824513i	−0.976675	−	0.214722i	$-0.931116\pi$
$47$	0.0996702	−	0.565258i	0.0145384	−	0.0824513i	0.991214	+	0.132270i	$0.0422267\pi$
$48$	−0.752374	+	4.26692i	−0.108596	+	0.615877i
$49$	2.32635	+	4.02936i	0.332336	+	0.575623i
$50$	−4.03209	+	6.98378i	−0.570223	+	0.987656i
$51$	−1.93969	−	1.62760i	−0.271611	−	0.227909i
$52$	−11.2626	−	4.09927i	−1.56185	−	0.568466i
$53$	−2.76604	+	1.00676i	−0.379945	+	0.138289i	−0.524931	−	0.851145i	$-0.675909\pi$
$53$	−2.76604	+	1.00676i	−0.379945	+	0.138289i	0.144985	+	0.989434i	$0.453687\pi$
$54$	−7.05690	+	5.92145i	−0.960323	+	0.805807i
$55$	0.277189	+	1.57202i	0.0373761	+	0.211971i
$56$	−9.35504			−1.25012
$57$		0			0
$58$	11.7811			1.54693
$59$	−0.683448	−	3.87603i	−0.0889774	−	0.504616i	−0.996427	−	0.0844555i	$-0.973085\pi$
$59$	−0.683448	−	3.87603i	−0.0889774	−	0.504616i	0.907450	−	0.420160i	$-0.138026\pi$
$60$	2.97178	−	2.49362i	0.383655	−	0.321925i
$61$	4.24510	−	1.54509i	0.543529	−	0.197829i	−0.0556399	−	0.998451i	$-0.517720\pi$
$61$	4.24510	−	1.54509i	0.543529	−	0.197829i	0.599169	+	0.800622i	$0.295498\pi$
$62$	−9.13088	−	3.32337i	−1.15962	−	0.422068i
$63$	−3.02094	−	2.53487i	−0.380603	−	0.319364i
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	1.83022	+	3.17004i	0.227011	+	0.393195i
$66$	−0.340022	+	1.92836i	−0.0418539	+	0.237365i
$67$	−0.674992	+	3.82807i	−0.0824634	+	0.467673i	0.915412	+	0.402519i	$0.131865\pi$
$67$	−0.674992	+	3.82807i	−0.0824634	+	0.467673i	−0.997875	+	0.0651547i	$0.979246\pi$
$68$	−8.55690	−	14.8210i	−1.03768	−	1.79731i
$69$	−1.65270	+	2.86257i	−0.198962	+	0.344613i
$70$	4.00387	+	3.35965i	0.478554	+	0.401555i
$71$	6.51754	+	2.37219i	0.773490	+	0.281527i	0.698455	−	0.715654i	$-0.253871\pi$
$71$	6.51754	+	2.37219i	0.773490	+	0.281527i	0.0750345	+	0.997181i	$0.476093\pi$
$72$	−14.7690	+	5.37549i	−1.74055	+	0.633508i
$73$	4.69459	−	3.93923i	0.549461	−	0.461052i	−0.325298	−	0.945612i	$-0.605465\pi$
$73$	4.69459	−	3.93923i	0.549461	−	0.461052i	0.874758	+	0.484560i	$0.161020\pi$
$74$	1.80541	+	10.2390i	0.209874	+	1.19026i
$75$	2.07873			0.240031
$76$		0			0
$77$	−1.81521			−0.206862
$78$	0.779715	+	4.42198i	0.0882853	+	0.500691i
$79$	7.51367	−	6.30472i	0.845354	−	0.709336i	−0.113407	−	0.993549i	$-0.536177\pi$
$79$	7.51367	−	6.30472i	0.845354	−	0.709336i	0.958761	+	0.284212i	$0.0917321\pi$
$80$	8.40420	−	3.05888i	0.939618	−	0.341993i
$81$	−5.02481	−	1.82888i	−0.558313	−	0.203209i
$82$	19.3687	+	16.2523i	2.13892	+	1.79476i
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	0.300112	+	0.953904i	$0.402976\pi$
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	−0.976161	+	0.217047i	$0.930357\pi$
$84$	2.20574	+	3.82045i	0.240666	+	0.416845i
$85$	−0.907604	+	5.14728i	−0.0984434	+	0.558301i
$86$	3.82635	−	21.7003i	0.412606	−	2.34001i
$87$	−1.51842	−	2.62998i	−0.162792	−	0.281963i
$88$	−3.61721	+	6.26519i	−0.385596	+	0.667872i
$89$	−1.85844	−	1.55942i	−0.196994	−	0.165298i	0.538955	−	0.842335i	$-0.318819\pi$
$89$	−1.85844	−	1.55942i	−0.196994	−	0.165298i	−0.735949	+	0.677037i	$0.763264\pi$
$90$	8.25150	+	3.00330i	0.869784	+	0.316576i
$91$	−3.91147	+	1.42366i	−0.410034	+	0.149240i
$92$	−17.1138	+	14.3602i	−1.78424	+	1.49715i
$93$	0.434945	+	2.46669i	0.0451017	+	0.255784i
$94$	−1.45336			−0.149903
$95$		0			0
$96$	3.00000			0.306186
$97$	1.27972	+	7.25762i	0.129935	+	0.736900i	0.978253	+	0.207413i	$0.0665044\pi$
$97$	1.27972	+	7.25762i	0.129935	+	0.736900i	−0.848318	+	0.529487i	$0.822384\pi$
$98$	9.02481	−	7.57272i	0.911644	−	0.764960i
$99$	−2.86571	+	1.04303i	−0.288015	+	0.104829i
$100$	13.2023	+	4.80526i	1.32023	+	0.480526i
$101$	1.66250	+	1.39501i	0.165425	+	0.138808i	0.721742	−	0.692162i	$-0.243342\pi$
$101$	1.66250	+	1.39501i	0.165425	+	0.138808i	−0.556317	+	0.830970i	$0.687786\pi$
$102$	−3.20574	+	5.55250i	−0.317415	+	0.549779i
$103$	6.23783	+	10.8042i	0.614631	+	1.06457i	0.990449	+	0.137879i	$0.0440285\pi$
$103$	6.23783	+	10.8042i	0.614631	+	1.06457i	−0.375818	+	0.926694i	$0.622638\pi$
$104$	−2.88073	+	16.3374i	−0.282479	+	1.60202i
$105$	0.233956	−	1.32683i	0.0228317	−	0.129485i
$106$	3.72668	+	6.45480i	0.361967	+	0.626946i
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	−0.658191	−	0.752851i	$-0.728678\pi$
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	0.981083	+	0.193585i	$0.0620116\pi$
$108$	12.2947	+	10.3165i	1.18306	+	0.992706i
$109$	−8.88326	−	3.23324i	−0.850862	−	0.309688i	−0.120470	−	0.992717i	$-0.538440\pi$
$109$	−8.88326	−	3.23324i	−0.850862	−	0.309688i	−0.730392	+	0.683029i	$0.760662\pi$
$110$	3.79813	−	1.38241i	0.362138	−	0.131807i
$111$	2.05303	−	1.72270i	0.194865	−	0.163511i
$112$	1.76604	+	10.0157i	0.166876	+	0.946398i
$113$	1.31046			0.123278			0.0616388	−	0.998099i	$-0.480367\pi$
$113$	1.31046			0.123278			0.0616388	+	0.998099i	$0.480367\pi$
$114$		0			0
$115$	6.82295			0.636243
$116$	−3.56418	−	20.2135i	−0.330926	−	1.87677i
$117$	−5.35710	+	4.49514i	−0.495264	+	0.415576i
$118$	−9.36484	+	3.40852i	−0.862103	+	0.313780i
$119$	−5.58512	−	2.03282i	−0.511987	−	0.186348i
$120$	−4.11334	−	3.45150i	−0.375495	−	0.315078i
$121$	4.79813	−	8.31061i	0.436194	−	0.755510i
$122$	−5.71941	−	9.90630i	−0.517811	−	0.896875i
$123$	1.13176	−	6.41852i	0.102047	−	0.578739i
$124$	−2.93969	+	16.6718i	−0.263992	+	1.49717i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$	−4.99273	+	8.64766i	−0.444787	+	0.770394i
$127$	−11.1099	−	9.32234i	−0.985848	−	0.827224i	−0.000886250	−	1.00000i	$-0.500282\pi$
$127$	−11.1099	−	9.32234i	−0.985848	−	0.827224i	−0.984961	+	0.172775i	$0.944727\pi$
$128$	−12.5360	−	4.56272i	−1.10803	−	0.403291i
$129$	−5.33750	+	1.94269i	−0.469940	+	0.171044i
$130$	7.10014	−	5.95772i	0.622723	−	0.522527i
$131$	−3.43969	−	19.5075i	−0.300527	−	1.70438i	−0.643845	−	0.765156i	$-0.722662\pi$
$131$	−3.43969	−	19.5075i	−0.300527	−	1.70438i	0.343318	−	0.939219i	$-0.388449\pi$
$132$	3.41147			0.296931
$133$		0			0
$134$	9.84255			0.850267
$135$	−0.851167	−	4.82721i	−0.0732568	−	0.415460i
$136$	−18.1459	+	15.2262i	−1.55600	+	1.30564i
$137$	−9.58899	+	3.49011i	−0.819243	+	0.298180i	−0.717436	−	0.696624i	$-0.754685\pi$
$137$	−9.58899	+	3.49011i	−0.819243	+	0.298180i	−0.101807	+	0.994804i	$0.532462\pi$
$138$	7.86484	+	2.86257i	0.669499	+	0.243678i
$139$	−1.27197	−	1.06731i	−0.107887	−	0.0905283i	0.587248	−	0.809407i	$-0.300211\pi$
$139$	−1.27197	−	1.06731i	−0.107887	−	0.0905283i	−0.695136	+	0.718879i	$0.744656\pi$
$140$	4.55303	−	7.88609i	0.384802	−	0.666496i
$141$	0.187319	+	0.324446i	0.0157751	+	0.0273232i
$142$	3.04963	−	17.2953i	0.255919	−	1.45139i
$143$	−0.558963	+	3.17004i	−0.0467429	+	0.265092i
$144$	8.54323	+	14.7973i	0.711936	+	1.23311i
$145$	−3.13429	+	5.42874i	−0.260288	+	0.450832i
$146$	−11.8871	−	9.97448i	−0.983786	−	0.825494i
$147$	−2.85369	−	1.03866i	−0.235369	−	0.0856672i
$148$	17.0214	−	6.19529i	1.39915	−	0.509249i
$149$	8.58512	−	7.20377i	0.703321	−	0.590156i	−0.219396	−	0.975636i	$-0.570409\pi$
$149$	8.58512	−	7.20377i	0.703321	−	0.590156i	0.922716	+	0.385480i	$0.125964\pi$
$150$	−0.914000	−	5.18355i	−0.0746278	−	0.423235i
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$		0			0
$153$	−9.98545			−0.807276
$154$	0.798133	+	4.52644i	0.0643154	+	0.364751i
$155$	3.96064	−	3.32337i	0.318126	−	0.266939i
$156$	7.35117	−	2.67561i	0.588564	−	0.214220i
$157$	−10.3302	−	3.75989i	−0.824441	−	0.300072i	−0.104866	−	0.994486i	$-0.533441\pi$
$157$	−10.3302	−	3.75989i	−0.824441	−	0.300072i	−0.719576	+	0.694414i	$0.755664\pi$
$158$	−19.0253	−	15.9641i	−1.51357	−	1.27004i
$159$	0.960637	−	1.66387i	0.0761835	−	0.131954i
$160$	−3.09627	−	5.36289i	−0.244781	−	0.423974i
$161$	−1.34730	+	7.64090i	−0.106182	+	0.602187i
$162$	−2.35117	+	13.3341i	−0.184725	+	1.04763i
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	0.962973	−	0.269596i	$-0.0868902\pi$
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	−0.714964	+	0.699161i	$0.753557\pi$
$164$	22.0253	−	38.1489i	1.71989	−	2.97893i
$165$	−0.798133	−	0.669713i	−0.0621346	−	0.0521371i
$166$	29.3097	+	10.6679i	2.27488	+	0.827988i
$167$	12.9474	−	4.71248i	1.00190	−	0.364663i	0.211585	−	0.977360i	$-0.432138\pi$
$167$	12.9474	−	4.71248i	1.00190	−	0.364663i	0.790318	+	0.612697i	$0.209915\pi$
$168$	4.67752	−	3.92490i	0.360878	−	0.302813i
$169$	−0.975652	−	5.53320i	−0.0750501	−	0.425631i
$170$	13.2344			1.01503
$171$		0			0
$172$	−38.3901			−2.92722
$173$	4.38413	+	24.8637i	0.333319	+	1.89035i	0.443231	+	0.896407i	$0.353832\pi$
$173$	4.38413	+	24.8637i	0.333319	+	1.89035i	−0.109912	+	0.993941i	$0.535057\pi$
$174$	−5.89053	+	4.94274i	−0.446560	+	0.374708i
$175$	4.58512	−	1.66885i	0.346603	−	0.126153i
$176$	7.39053	+	2.68993i	0.557082	+	0.202761i
$177$	1.96791	+	1.65127i	0.147917	+	0.124117i
$178$	−3.07145	+	5.31991i	−0.230215	+	0.398744i
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	0.736264	−	0.676695i	$-0.236588\pi$
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	−0.954167	+	0.299276i	$0.903255\pi$
$180$	2.65657	−	15.0662i	0.198009	−	1.12297i
$181$	2.35504	−	13.3561i	0.175049	−	0.992750i	−0.763039	−	0.646352i	$-0.776294\pi$
$181$	2.35504	−	13.3561i	0.175049	−	0.992750i	0.938088	−	0.346397i	$-0.112595\pi$
$182$	5.26991	+	9.12776i	0.390632	+	0.676595i
$183$	−1.47431	+	2.55358i	−0.108984	+	0.188766i
$184$	23.6878	+	19.8764i	1.74629	+	1.46531i
$185$	−5.19846	−	1.89209i	−0.382199	−	0.139109i
$186$	5.95976	−	2.16918i	0.436991	−	0.159052i
$187$	−3.52094	+	2.95442i	−0.257477	+	0.216049i
$188$	0.439693	+	2.49362i	0.0320679	+	0.181866i
$189$	5.57398			0.405447
$190$		0			0
$191$	−10.2841			−0.744128			−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841			−0.744128			−0.372064	+	0.928207i	$0.621350\pi$
$192$	0.185670	+	1.05299i	0.0133996	+	0.0759927i
$193$	10.5719	−	8.87089i	0.760983	−	0.638541i	−0.177399	−	0.984139i	$-0.556768\pi$
$193$	10.5719	−	8.87089i	0.760983	−	0.638541i	0.938383	+	0.345598i	$0.112324\pi$
$194$	17.5351	−	6.38225i	1.25895	−	0.458219i
$195$	−2.24510	−	0.817150i	−0.160775	−	0.0585173i
$196$	−15.7233	−	13.1934i	−1.12309	−	0.942385i
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	−0.689211	−	0.724560i	$-0.742043\pi$
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	0.972093	+	0.234594i	$0.0753762\pi$
$198$	3.86097	+	6.68739i	0.274387	+	0.475252i
$199$	4.69459	−	26.6244i	0.332791	−	1.88735i	−0.115248	−	0.993337i	$-0.536766\pi$
$199$	4.69459	−	26.6244i	0.332791	−	1.88735i	0.448039	−	0.894014i	$-0.352123\pi$
$200$	3.37686	−	19.1511i	0.238780	−	1.35419i
$201$	−1.26857	−	2.19723i	−0.0894781	−	0.154981i
$202$	2.74763	−	4.75903i	0.193322	−	0.334844i
$203$	−5.46064	−	4.58202i	−0.383262	−	0.321595i
$204$	10.4966	+	3.82045i	0.734909	+	0.267485i
$205$	−12.6420	+	4.60132i	−0.882957	+	0.321370i
$206$	24.1989	−	20.3053i	1.68602	−	1.41474i
$207$	2.26352	+	12.8370i	0.157325	+	0.892237i
$208$	18.0351			1.25051
$209$		0			0
$210$	−3.41147			−0.235414
$211$	−1.40167	−	7.94929i	−0.0964952	−	0.547252i	−0.994279	−	0.106815i	$-0.965935\pi$
$211$	−1.40167	−	7.94929i	−0.0964952	−	0.547252i	0.897784	−	0.440437i	$-0.145176\pi$
$212$	9.94743	−	8.34689i	0.683193	−	0.573267i
$213$	−4.25402	+	1.54834i	−0.291481	+	0.106090i
$214$	−15.8944	−	5.78509i	−1.08652	−	0.395461i
$215$	8.98158	+	7.53644i	0.612539	+	0.513981i
$216$	11.1074	−	19.2386i	0.755764	−	1.30902i
$217$	2.93969	+	5.09170i	0.199559	+	0.345647i
$218$	−4.15657	+	23.5731i	−0.281519	+	1.59657i
$219$	−0.694593	+	3.93923i	−0.0469362	+	0.266189i
$220$	−3.52094	−	6.09845i	−0.237382	−	0.411158i
$221$	−5.26991	+	9.12776i	−0.354493	+	0.614000i
$222$	−5.19846	−	4.36203i	−0.348898	−	0.292760i
$223$	14.5424	+	5.29298i	0.973828	+	0.354444i	0.779438	−	0.626480i	$-0.215505\pi$
$223$	14.5424	+	5.29298i	0.973828	+	0.354444i	0.194390	+	0.980924i	$0.437727\pi$
$224$	6.61721	−	2.40847i	0.442131	−	0.160923i
$225$	6.27972	−	5.26931i	0.418648	−	0.351287i
$226$	−0.576199	−	3.26779i	−0.0383282	−	0.217370i
$227$	9.87258			0.655266			0.327633	−	0.944805i	$-0.393749\pi$
$227$	9.87258			0.655266			0.327633	+	0.944805i	$0.393749\pi$
$228$		0			0
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$	−3.00000	−	17.0138i	−0.197814	−	1.12186i
$231$	0.907604	−	0.761570i	0.0597159	−	0.0501076i
$232$	−26.6964	+	9.71670i	−1.75270	+	0.637932i
$233$	−3.32160	−	1.20897i	−0.217606	−	0.0792019i	0.230917	−	0.972973i	$-0.425827\pi$
$233$	−3.32160	−	1.20897i	−0.217606	−	0.0792019i	−0.448523	+	0.893772i	$0.648050\pi$
$234$	13.5646	+	11.3821i	0.886749	+	0.744070i
$235$	0.386659	−	0.669713i	0.0252229	−	0.0436873i
$236$	8.68139	+	15.0366i	0.565110	+	0.978800i
$237$	−1.11169	+	6.30472i	−0.0722122	+	0.409535i
$238$	−2.61334	+	14.8210i	−0.169398	+	0.960702i
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	0.604825	−	0.796358i	$-0.293243\pi$
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	−0.992079	+	0.125615i	$0.959910\pi$
$240$	−2.91875	+	5.05542i	−0.188404	+	0.326326i
$241$	9.88326	+	8.29304i	0.636636	+	0.534201i	0.902983	−	0.429676i	$-0.141372\pi$
$241$	9.88326	+	8.29304i	0.636636	+	0.534201i	−0.266347	+	0.963877i	$0.585817\pi$
$242$	−22.8332	−	8.31061i	−1.46777	−	0.534226i
$243$	13.5360	−	4.92669i	0.868332	−	0.316047i
$244$	−15.2665	+	12.8101i	−0.977338	+	0.820084i
$245$	1.08853	+	6.17334i	0.0695434	+	0.394400i
$246$	−16.5030			−1.05219
$247$		0			0
$248$	23.4320			1.48793
$249$	−1.39615	−	7.91799i	−0.0884777	−	0.501782i
$250$	−21.3897	+	17.9480i	−1.35280	+	1.13513i
$251$	−13.4966	+	4.91236i	−0.851898	+	0.310065i	−0.730814	−	0.682577i	$-0.760859\pi$
$251$	−13.4966	+	4.91236i	−0.851898	+	0.310065i	−0.121084	+	0.992642i	$0.538637\pi$
$252$	16.3478	+	5.95010i	1.02981	+	0.374821i
$253$	4.59627	+	3.85673i	0.288965	+	0.242470i
$254$	−18.3614	+	31.8029i	−1.15210	+	1.99549i
$255$	−1.70574	−	2.95442i	−0.106817	−	0.185013i
$256$	−5.29679	+	30.0396i	−0.331049	+	1.87747i
$257$	0.864370	−	4.90209i	0.0539180	−	0.305784i	−0.945908	−	0.324435i	$-0.894826\pi$
$257$	0.864370	−	4.90209i	0.0539180	−	0.305784i	0.999826	+	0.0186508i	$0.00593707\pi$
$258$	7.19119	+	12.4555i	0.447704	+	0.775446i
$259$	3.14543	−	5.44804i	0.195447	−	0.338525i
$260$	−12.3701	−	10.3797i	−0.767158	−	0.643722i
$261$	−11.2537	−	4.09602i	−0.696588	−	0.253537i
$262$	−47.1318	+	17.1546i	−2.91181	+	1.05981i
$263$	−18.4179	+	15.4544i	−1.13569	+	0.952961i	−0.999289	−	0.0376922i	$-0.987999\pi$
$263$	−18.4179	+	15.4544i	−1.13569	+	0.952961i	−0.136405	+	0.990653i	$0.543555\pi$
$264$	−0.819955	−	4.65020i	−0.0504648	−	0.286200i
$265$	−3.96585			−0.243620
$266$		0			0
$267$	1.58347			0.0969070
$268$	−2.97771	−	16.8874i	−0.181893	−	1.03156i
$269$	−10.0437	+	8.42767i	−0.612375	+	0.513844i	−0.895396	−	0.445270i	$-0.853108\pi$
$269$	−10.0437	+	8.42767i	−0.612375	+	0.513844i	0.283021	+	0.959114i	$0.408663\pi$
$270$	−11.6630	+	4.24497i	−0.709786	+	0.258341i
$271$	24.9675	+	9.08743i	1.51667	+	0.552022i	0.960313	−	0.278923i	$-0.0899775\pi$
$271$	24.9675	+	9.08743i	1.51667	+	0.552022i	0.556354	+	0.830945i	$0.312200\pi$
$272$	19.7271	+	16.5530i	1.19613	+	1.00368i
$273$	1.35844	−	2.35289i	0.0822166	−	0.142403i
$274$	12.9192	+	22.3767i	0.780478	+	1.35183i
$275$	0.655230	−	3.71599i	0.0395118	−	0.224083i
$276$	2.53209	−	14.3602i	0.152414	−	0.864382i
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	0.999989	−	0.00459317i	$-0.00146206\pi$
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	−0.503973	+	0.863720i	$0.668129\pi$
$278$	−2.10220	+	3.64111i	−0.126081	+	0.218379i
$279$	7.56670	+	6.34922i	0.453007	+	0.380118i
$280$	−11.8439	−	4.31082i	−0.707808	−	0.257621i
$281$	18.2208	−	6.63181i	1.08696	−	0.395621i	0.264465	−	0.964395i	$-0.414805\pi$
$281$	18.2208	−	6.63181i	1.08696	−	0.395621i	0.822494	+	0.568774i	$0.192582\pi$
$282$	0.726682	−	0.609758i	0.0432733	−	0.0363106i
$283$	−1.96404	−	11.1386i	−0.116750	−	0.662123i	−0.985869	−	0.167519i	$-0.946424\pi$
$283$	−1.96404	−	11.1386i	−0.116750	−	0.662123i	0.869119	−	0.494604i	$-0.164687\pi$
$284$	−30.5972			−1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	−2.65657	−	15.0662i	−0.156813	−	0.889328i
$288$	9.06283	−	7.60462i	0.534033	−	0.448107i
$289$	1.83275	−	0.667066i	0.107809	−	0.0392392i
$290$	14.9153	+	5.42874i	0.875859	+	0.318787i
$291$	−3.68479	−	3.09191i	−0.216006	−	0.181251i
$292$	−13.5175	+	23.4131i	−0.791054	+	1.37015i
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	0.803445	−	0.595379i	$-0.202998\pi$
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	−0.917336	+	0.398115i	$0.869665\pi$
$294$	−1.33527	+	7.57272i	−0.0778748	+	0.441650i
$295$	0.920807	−	5.22216i	0.0536115	−	0.304046i
$296$	−12.5360	−	21.7129i	−0.728638	−	1.26204i
$297$	2.15523	−	3.73297i	0.125059	−	0.216609i
$298$	−21.7383	−	18.2406i	−1.25927	−	1.05665i
$299$	12.9290	+	4.70578i	0.747704	+	0.272142i
$300$	−8.61721	+	3.13641i	−0.497515	+	0.181081i
$301$	−10.2135	+	8.57013i	−0.588695	+	0.493974i
$302$	4.85504	+	27.5343i	0.279376	+	1.58442i
$303$	−1.41653			−0.0813773
$304$		0			0
$305$	6.08647			0.348510
$306$	4.39053	+	24.8999i	0.250990	+	1.42343i
$307$	17.7533	−	14.8968i	1.01323	−	0.850205i	0.0244724	−	0.999701i	$-0.492209\pi$
$307$	17.7533	−	14.8968i	1.01323	−	0.850205i	0.988762	+	0.149496i	$0.0477650\pi$
$308$	7.52481	−	2.73881i	0.428766	−	0.156058i
$309$	−7.65183	−	2.78504i	−0.435297	−	0.158435i
$310$	−10.0287	−	8.41507i	−0.569591	−	0.477944i
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	−0.812780	−	0.582570i	$-0.802047\pi$
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	0.910911	+	0.412603i	$0.135380\pi$
$312$	−5.41400	−	9.37732i	−0.306507	−	0.530886i
$313$	−3.97477	+	22.5421i	−0.224668	+	1.27415i	0.638652	+	0.769496i	$0.279492\pi$
$313$	−3.97477	+	22.5421i	−0.224668	+	1.27415i	−0.863320	+	0.504657i	$0.831619\pi$
$314$	−4.83363	+	27.4129i	−0.272777	+	1.54700i
$315$	−2.65657	−	4.60132i	−0.149681	−	0.259255i
$316$	−21.6348	+	37.4725i	−1.21705	+	2.10799i
$317$	20.0096	+	16.7900i	1.12385	+	0.943021i	0.998792	−	0.0491289i	$-0.0156445\pi$
$317$	20.0096	+	16.7900i	1.12385	+	0.943021i	0.125056	+	0.992150i	$0.460089\pi$
$318$	−4.57145	−	1.66387i	−0.256354	−	0.0933053i
$319$	−5.18004	+	1.88538i	−0.290027	+	0.105561i
$320$	1.69072	−	1.41868i	0.0945143	−	0.0793069i
$321$	0.757122	+	4.29385i	0.0422584	+	0.239659i
$322$	19.6459			1.09482
$323$		0			0
$324$	23.5895			1.31053
$325$	−1.50253	−	8.52125i	−0.0833452	−	0.472674i
$326$	12.2836	−	10.3072i	0.680325	−	0.570860i
$327$	5.79813	−	2.11035i	0.320638	−	0.116703i
$328$	−57.2948	−	20.8536i	−3.16358	−	1.15145i
$329$	0.673648	+	0.565258i	0.0371394	+	0.0311637i
$330$	−1.31908	+	2.28471i	−0.0726128	+	0.125769i
$331$	−9.52229	−	16.4931i	−0.523392	−	0.906542i	−0.999629	−	0.0272251i	$-0.991333\pi$
$331$	−9.52229	−	16.4931i	−0.523392	−	0.906542i	0.476237	−	0.879317i	$-0.342000\pi$
$332$	9.43629	−	53.5159i	0.517884	−	2.93706i
$333$	1.83527	−	10.4084i	0.100572	−	0.570375i
$334$	−17.4440	−	30.2139i	−0.954495	−	1.65323i
$335$	−2.61856	+	4.53547i	−0.143067	+	0.247799i
$336$	−5.08512	−	4.26692i	−0.277416	−	0.232780i
$337$	−1.59879	−	0.581913i	−0.0870918	−	0.0316988i	0.298107	−	0.954533i	$-0.403645\pi$
$337$	−1.59879	−	0.581913i	−0.0870918	−	0.0316988i	−0.385199	+	0.922834i	$0.625867\pi$
$338$	−13.3687	+	4.86581i	−0.727162	+	0.264665i
$339$	−0.655230	+	0.549803i	−0.0355872	+	0.0298612i
$340$	−4.00387	−	22.7071i	−0.217140	−	1.23146i
$341$	4.54664			0.246214
$342$		0			0
$343$	−17.8530			−0.963970
$344$	9.22715	+	52.3298i	0.497495	+	2.82143i
$345$	−3.41147	+	2.86257i	−0.183668	+	0.154115i
$346$	60.0729	−	21.8647i	3.22954	−	1.17546i
$347$	4.60607	+	1.67647i	0.247267	+	0.0899977i	0.462680	−	0.886525i	$-0.346888\pi$
$347$	4.60607	+	1.67647i	0.247267	+	0.0899977i	−0.215414	+	0.976523i	$0.569110\pi$
$348$	10.2626	+	8.61138i	0.550135	+	0.461618i
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	−0.193566	−	0.981087i	$-0.562006\pi$
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	0.946430	−	0.322910i	$-0.104661\pi$
$350$	−6.17752	−	10.6998i	−0.330202	−	0.571927i
$351$	1.71641	−	9.73427i	0.0916154	−	0.519577i
$352$	0.945622	−	5.36289i	0.0504018	−	0.285843i
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	0.955237	−	0.295841i	$-0.0955997\pi$
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	−0.733824	+	0.679340i	$0.762266\pi$
$354$	3.25237	−	5.63328i	0.172862	−	0.299405i
$355$	7.15839	+	6.00660i	0.379928	+	0.318797i
$356$	10.0569	+	3.66041i	0.533015	+	0.194002i
$357$	3.64543	−	1.32683i	0.192937	−	0.0702232i
$358$	−11.3097	+	9.49000i	−0.597739	+	0.501562i
$359$	4.32888	+	24.5503i	0.228469	+	1.29571i	0.855940	+	0.517075i	$0.172979\pi$
$359$	4.32888	+	24.5503i	0.228469	+	1.29571i	−0.627471	+	0.778640i	$0.715910\pi$
$360$	−21.1753			−1.11604
$361$		0			0
$362$	−34.3405			−1.80490
$363$	1.08765	+	6.16836i	0.0570867	+	0.323755i
$364$	14.0667	−	11.8034i	0.737296	−	0.618664i
$365$	7.75877	−	2.82396i	0.406113	−	0.147813i
$366$	7.01589	+	2.55358i	0.366727	+	0.133478i
$367$	−1.98087	−	1.66214i	−0.103400	−	0.0867632i	0.589622	−	0.807679i	$-0.299277\pi$
$367$	−1.98087	−	1.66214i	−0.103400	−	0.0867632i	−0.693022	+	0.720916i	$0.743721\pi$
$368$	16.8084	−	29.1130i	0.876198	−	1.51762i
$369$	−12.8512	−	22.2589i	−0.669005	−	1.15875i
$370$	−2.43242	+	13.7949i	−0.126455	+	0.717164i
$371$	0.783119	−	4.44129i	0.0406575	−	0.230580i
$372$	−5.52481	−	9.56926i	−0.286448	−	0.496143i
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	−0.386622	−	0.922238i	$-0.626358\pi$
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	0.991993	−	0.126295i	$-0.0403086\pi$
$374$	8.91534	+	7.48086i	0.461001	+	0.386826i
$375$	6.76352	+	2.46172i	0.349267	+	0.127123i
$376$	3.29339	−	1.19869i	0.169843	−	0.0618179i
$377$	−9.68345	+	8.12538i	−0.498723	+	0.418478i
$378$	−2.45084	−	13.8994i	−0.126057	−	0.714907i
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$		0			0
$381$	9.46616			0.484966
$382$	4.52182	+	25.6445i	0.231357	+	1.31209i
$383$	−21.0514	+	17.6643i	−1.07568	+	0.902601i	−0.995555	−	0.0941836i	$-0.969976\pi$
$383$	−21.0514	+	17.6643i	−1.07568	+	0.902601i	−0.0801235	+	0.996785i	$0.525531\pi$
$384$	8.18227	−	2.97810i	0.417550	−	0.151976i
$385$	−2.29813	−	0.836452i	−0.117124	−	0.0426295i
$386$	−26.7690	−	22.4619i	−1.36251	−	1.14328i
$387$	−11.1998	+	19.3986i	−0.569318	+	0.986088i
$388$	−16.2554	−	28.1551i	−0.825241	−	1.42936i
$389$	−0.580375	+	3.29147i	−0.0294262	+	0.166884i	−0.995979	−	0.0895817i	$-0.971447\pi$
$389$	−0.580375	+	3.29147i	−0.0294262	+	0.166884i	0.966553	+	0.256466i	$0.0825581\pi$
$390$	−1.05051	+	5.95772i	−0.0531945	+	0.301681i
$391$	9.82295	+	17.0138i	0.496768	+	0.860427i
$392$	−14.2049	+	24.6035i	−0.717454	+	1.24267i
$393$	9.90420	+	8.31061i	0.499601	+	0.419215i
$394$	−18.8944	−	6.87700i	−0.951886	−	0.346458i
$395$	12.4179	−	4.51974i	0.624811	−	0.227413i
$396$	10.3059	−	8.64766i	0.517890	−	0.434561i
$397$	−2.27884	−	12.9239i	−0.114372	−	0.648633i	−0.987059	−	0.160355i	$-0.948736\pi$
$397$	−2.27884	−	12.9239i	−0.114372	−	0.648633i	0.872688	−	0.488279i	$-0.162375\pi$
$398$	−68.4552			−3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	2.97178	+	16.8538i	0.148404	+	0.841639i	0.964571	+	0.263823i	$0.0849836\pi$
$401$	2.97178	+	16.8538i	0.148404	+	0.841639i	−0.816167	+	0.577816i	$0.803905\pi$
$402$	−4.92127	+	4.12944i	−0.245451	+	0.205958i
$403$	9.79726	−	3.56591i	0.488036	−	0.177631i
$404$	−8.99660	−	3.27449i	−0.447597	−	0.162912i
$405$	−5.51889	−	4.63089i	−0.274236	−	0.230111i
$406$	−9.02481	+	15.6314i	−0.447894	+	0.775775i
$407$	−2.43242	−	4.21307i	−0.120571	−	0.208834i
$408$	2.68479	−	15.2262i	0.132917	−	0.753810i
$409$	−1.52775	+	8.66431i	−0.0755425	+	0.428423i	0.923457	+	0.383702i	$0.125351\pi$
$409$	−1.52775	+	8.66431i	−0.0755425	+	0.428423i	−0.999000	+	0.0447208i	$0.985760\pi$
$410$	17.0326	+	29.5013i	0.841178	+	1.45696i
$411$	3.33022	−	5.76811i	0.164268	−	0.284520i
$412$	−42.1600	−	35.3765i	−2.07708	−	1.74287i
$413$	5.66637	+	2.06239i	0.278824	+	0.101484i
$414$	31.0155	−	11.2887i	1.52433	−	0.554810i
$415$	−12.7135	+	10.6679i	−0.624080	+	0.523665i
$416$	−2.16843	−	12.2978i	−0.106316	−	0.602949i
$417$	1.08378			0.0530728
$418$		0			0
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$	1.03209	+	5.85327i	0.0503608	+	0.285610i
$421$	−3.69459	+	3.10013i	−0.180063	+	0.151091i	−0.728365	−	0.685190i	$-0.759719\pi$
$421$	−3.69459	+	3.10013i	−0.180063	+	0.151091i	0.548301	+	0.836281i	$0.315275\pi$
$422$	−19.2062	+	6.99049i	−0.934943	+	0.340292i
$423$	1.38831	+	0.505303i	0.0675018	+	0.0245687i
$424$	−13.7686	−	11.5532i	−0.668661	−	0.561073i
$425$	6.17752	−	10.6998i	0.299654	−	0.519015i
$426$	5.73143	+	9.92713i	0.277689	+	0.480971i
$427$	−1.20187	+	6.81612i	−0.0581624	+	0.329855i
$428$	−5.11721	+	29.0211i	−0.247350	+	1.40279i
$429$	−1.05051	−	1.81953i	−0.0507190	−	0.0878478i
$430$	14.8439	−	25.7104i	0.715836	−	1.23986i
$431$	0.998656	+	0.837972i	0.0481036	+	0.0403637i	0.666522	−	0.745485i	$-0.267782\pi$
$431$	0.998656	+	0.837972i	0.0481036	+	0.0403637i	−0.618419	+	0.785849i	$0.712226\pi$
$432$	−22.6942	−	8.26001i	−1.09187	−	0.397410i
$433$	−18.6284	+	6.78017i	−0.895222	+	0.325834i	−0.748336	−	0.663319i	$-0.769147\pi$
$433$	−18.6284	+	6.78017i	−0.895222	+	0.325834i	−0.146885	+	0.989154i	$0.546925\pi$
$434$	11.4042	−	9.56926i	0.547419	−	0.459339i
$435$	−0.710485	−	4.02936i	−0.0340651	−	0.193193i
$436$	41.7033			1.99722
$437$		0			0
$438$	10.1284			0.483952
$439$	−6.00253	−	34.0420i	−0.286485	−	1.62474i	−0.699933	−	0.714209i	$-0.746787\pi$
$439$	−6.00253	−	34.0420i	−0.286485	−	1.62474i	0.413448	−	0.910528i	$-0.364324\pi$
$440$	−7.46657	+	6.26519i	−0.355955	+	0.298681i
$441$	−11.2537	+	4.09602i	−0.535891	+	0.195048i
$442$	25.0783	+	9.12776i	1.19285	+	0.434163i
$443$	13.0305	+	10.9339i	0.619098	+	0.519485i	0.897520	−	0.440974i	$-0.145367\pi$
$443$	13.0305	+	10.9339i	0.619098	+	0.519485i	−0.278422	+	0.960459i	$0.589811\pi$
$444$	−5.91147	+	10.2390i	−0.280546	+	0.485920i
$445$	−1.63429	−	2.83067i	−0.0774726	−	0.134186i
$446$	6.80453	−	38.5904i	0.322204	−	1.82731i
$447$	−1.27022	+	7.20377i	−0.0600793	+	0.340727i
$448$	1.25490	+	2.17355i	0.0592885	+	0.102691i
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.0344512	+	0.999406i	$0.510968\pi$
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.848286	+	0.529539i	$0.822365\pi$
$450$	−15.9008	−	13.3424i	−0.749571	−	0.628965i
$451$	−11.1172	−	4.04633i	−0.523489	−	0.190534i
$452$	−5.43242	+	1.97724i	−0.255519	+	0.0930015i
$453$	5.52094	−	4.63262i	0.259397	−	0.217660i
$454$	−4.34090	−	24.6185i	−0.203729	−	1.15540i
$455$	−5.60813			−0.262913
$456$		0			0
$457$	9.11112			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$458$	−8.84611	−	50.1688i	−0.413352	−	2.34423i
$459$	10.8118	−	9.07218i	0.504652	−	0.423453i
$460$	−28.2841	+	10.2946i	−1.31875	+	0.479986i
$461$	22.9739	+	8.36181i	1.07000	+	0.389449i	0.816177	−	0.577802i	$-0.196089\pi$
$461$	22.9739	+	8.36181i	1.07000	+	0.389449i	0.253824	+	0.967250i	$0.418312\pi$
$462$	−2.29813	−	1.92836i	−0.106919	−	0.0897156i
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	−0.863098	−	0.505037i	$-0.831479\pi$
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	0.868924	+	0.494946i	$0.164812\pi$
$464$	15.4427	+	26.7475i	0.716909	+	1.24172i
$465$	−0.586000	+	3.32337i	−0.0271751	+	0.154118i
$466$	−1.55422	+	8.81439i	−0.0719976	+	0.408319i
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	0.631761	−	0.775163i	$-0.282332\pi$
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	−0.987192	+	0.159539i	$0.948999\pi$
$468$	15.4251	−	26.7171i	0.713028	−	1.23500i
$469$	−4.56212	−	3.82807i	−0.210659	−	0.176764i
$470$	−1.84002	−	0.669713i	−0.0848739	−	0.0308916i
$471$	6.74257	−	2.45410i	0.310681	−	0.113079i
$472$	18.4099	−	15.4477i	0.847383	−	0.711039i
$473$	1.79039	+	10.1538i	0.0823223	+	0.466873i
$474$	16.2104			0.744567
$475$		0			0
$476$	26.2199			1.20179
$477$	−1.31567	−	7.46156i	−0.0602406	−	0.341641i
$478$	−23.2251	+	19.4882i	−1.06229	+	0.891368i
$479$	0.675870	−	0.245996i	0.0308813	−	0.0112399i	−0.326533	−	0.945186i	$-0.605881\pi$
$479$	0.675870	−	0.245996i	0.0308813	−	0.0112399i	0.357415	+	0.933946i	$0.383658\pi$
$480$	3.79813	+	1.38241i	0.173360	+	0.0630980i
$481$	−8.54576	−	7.17074i	−0.389653	−	0.326958i
$482$	16.3341	−	28.2915i	0.743998	−	1.28864i
$483$	−2.53209	−	4.38571i	−0.115214	−	0.199557i
$484$	−7.35117	+	41.6905i	−0.334144	+	1.89502i
$485$	−1.72416	+	9.77817i	−0.0782899	+	0.444004i
$486$	−18.2369	−	31.5873i	−0.827245	−	1.43283i
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	−0.967865	−	0.251471i	$-0.919086\pi$
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	0.701713	+	0.712460i	$0.252419\pi$
$488$	21.1309	+	17.7309i	0.956550	+	0.802641i
$489$	−3.88413	−	1.41371i	−0.175647	−	0.0639301i
$490$	14.9153	−	5.42874i	0.673807	−	0.245246i
$491$	0.0680482	−	0.0570992i	0.00307097	−	0.00257685i	−0.641251	−	0.767331i	$-0.721584\pi$
$491$	0.0680482	−	0.0570992i	0.00307097	−	0.00257685i	0.644322	+	0.764754i	$0.277140\pi$
$492$	4.99273	+	28.3152i	0.225089	+	1.27655i
$493$	−18.0496			−0.812914
$494$		0			0
$495$	−4.10876			−0.184675
$496$	−4.42350	−	25.0869i	−0.198621	−	1.12643i
$497$	−8.14022	+	6.83045i	−0.365139	+	0.306388i
$498$	−19.1306	+	6.96296i	−0.857262	+	0.312018i
$499$	−13.8045	−	5.02444i	−0.617976	−	0.224925i	0.0140137	−	0.999902i	$-0.495539\pi$
$499$	−13.8045	−	5.02444i	−0.617976	−	0.224925i	−0.631989	+	0.774977i	$0.717761\pi$
$500$	37.2656	+	31.2696i	1.66657	+	1.39842i
$501$	−4.49660	+	7.78833i	−0.200893	+	0.347957i
$502$	18.1839	+	31.4955i	0.811588	+	1.40571i
$503$	−0.851577	+	4.82953i	−0.0379700	+	0.215338i	−0.997889	−	0.0649381i	$-0.979315\pi$
$503$	−0.851577	+	4.82953i	−0.0379700	+	0.215338i	0.959919	+	0.280276i	$0.0904261\pi$
$504$	4.18139	−	23.7138i	0.186254	−	1.05630i
$505$	1.46198	+	2.53223i	0.0650573	+	0.112683i
$506$	7.59627	−	13.1571i	0.337695	−	0.584905i
$507$	2.80928	+	2.35726i	0.124764	+	0.104690i
$508$	60.1211	+	21.8823i	2.66744	+	0.970870i
$509$	−6.02704	+	2.19366i	−0.267144	+	0.0972324i	−0.472119	−	0.881535i	$-0.656511\pi$
$509$	−6.02704	+	2.19366i	−0.267144	+	0.0972324i	0.204975	+	0.978767i	$0.434289\pi$
$510$	−6.61721	+	5.55250i	−0.293015	+	0.245869i
$511$	1.63041	+	9.24654i	0.0721253	+	0.409043i
$512$	50.5553			2.23425
$513$		0			0
$514$	−12.6040			−0.555939
$515$	2.91875	+	16.5530i	0.128615	+	0.729414i
$516$	19.1951	−	16.1066i	0.845015	−	0.709052i
$517$	0.639033	−	0.232589i	0.0281046	−	0.0102293i
$518$	−14.9684	−	5.44804i	−0.657673	−	0.239373i
$519$	−12.6236	−	10.5925i	−0.554115	−	0.464958i
$520$	−11.1755	+	19.3565i	−0.490076	+	0.848837i
$521$	17.9067	+	31.0154i	0.784508	+	1.35881i	0.929293	+	0.369344i	$0.120418\pi$
$521$	17.9067	+	31.0154i	0.784508	+	1.35881i	−0.144785	+	0.989463i	$0.546249\pi$
$522$	−5.26574	+	29.8635i	−0.230475	+	1.30709i
$523$	6.73277	−	38.1835i	0.294404	−	1.66965i	−0.375213	−	0.926939i	$-0.622430\pi$
$523$	6.73277	−	38.1835i	0.294404	−	1.66965i	0.669616	−	0.742707i	$-0.266459\pi$
$524$	43.6921	+	75.6770i	1.90870	+	3.30596i
$525$	−1.59240	+	2.75811i	−0.0694979	+	0.120374i
$526$	46.6357	+	39.1320i	2.03341	+	1.70624i
$527$	13.9893	+	5.09170i	0.609384	+	0.221798i
$528$	−4.82383	+	1.75573i	−0.209930	+	0.0764083i
$529$	2.02687	−	1.70075i	0.0881250	−	0.0739456i
$530$	1.74376	+	9.88933i	0.0757439	+	0.429565i
$531$	10.1307			0.439636
$532$		0			0
$533$	−27.1293			−1.17510
$534$	−0.696242	−	3.94858i	−0.0301293	−	0.170872i
$535$	6.89440	−	5.78509i	0.298071	−	0.250111i
$536$	−22.3037	+	8.11787i	−0.963371	+	0.350638i
$537$	3.57620	+	1.30163i	0.154324	+	0.0561695i
$538$	25.4315	+	21.3396i	1.09643	+	0.920015i
$539$	−2.75624	+	4.77396i	−0.118720	+	0.205629i
$540$	10.8118	+	18.7266i	0.465266	+	0.805864i
$541$	1.64796	−	9.34602i	0.0708512	−	0.401817i	−0.928671	−	0.370905i	$-0.879048\pi$
$541$	1.64796	−	9.34602i	0.0708512	−	0.401817i	0.999522	−	0.0309122i	$-0.00984123\pi$
$542$	11.6826	−	66.2552i	0.501809	−	2.84590i
$543$	4.42602	+	7.66610i	0.189939	+	0.328984i
$544$	8.91534	−	15.4418i	0.382242	−	0.662063i
$545$	−9.75671	−	8.18685i	−0.417932	−	0.350686i
$546$	−6.46451	−	2.35289i	−0.276655	−	0.100694i
$547$	−13.3550	+	4.86084i	−0.571020	+	0.207834i	−0.611361	−	0.791352i	$-0.709378\pi$
$547$	−13.3550	+	4.86084i	−0.571020	+	0.207834i	0.0403411	+	0.999186i	$0.487156\pi$
$548$	34.4846	−	28.9360i	1.47311	−	1.23608i
$549$	2.01919	+	11.4514i	0.0861769	+	0.488734i
$550$	−9.55438			−0.407400
$551$		0			0
$552$	−20.1830			−0.859047
$553$	2.60947	+	14.7990i	0.110966	+	0.629319i
$554$	32.0257	−	26.8728i	1.36064	−	1.14172i
$555$	3.39306	−	1.23497i	0.144027	−	0.0524216i
$556$	6.88326	+	2.50530i	0.291915	+	0.106248i
$557$	17.2665	+	14.4883i	0.731606	+	0.613890i	0.930569	−	0.366117i	$-0.119313\pi$
$557$	17.2665	+	14.4883i	0.731606	+	0.613890i	−0.198963	+	0.980007i	$0.563757\pi$
$558$	12.5055	−	21.6602i	0.529401	−	0.916949i
$559$	11.8216	+	20.4756i	0.500001	+	0.866026i
$560$	−2.37939	+	13.4942i	−0.100547	+	0.570233i
$561$	0.520945	−	2.95442i	0.0219943	−	0.124736i
$562$	−24.5488	−	42.5197i	−1.03553	−	1.79358i
$563$	21.4859	−	37.2147i	0.905524	−	1.56841i	0.0853106	−	0.996354i	$-0.472812\pi$
$563$	21.4859	−	37.2147i	0.905524	−	1.56841i	0.820213	−	0.572058i	$-0.193855\pi$
$564$	−1.26604	−	1.06234i	−0.0533101	−	0.0447325i
$565$	1.65910	+	0.603863i	0.0697989	+	0.0254047i
$566$	−26.9119	+	9.79515i	−1.13119	+	0.411721i
$567$	6.27584	−	5.26606i	0.263561	−	0.221154i
$568$	7.35410	+	41.7072i	0.308571	+	1.74999i
$569$	7.42696			0.311354			0.155677	−	0.987808i	$-0.450244\pi$
$569$	7.42696			0.311354			0.155677	+	0.987808i	$0.450244\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	−2.46585	−	13.9845i	−0.103102	−	0.584723i
$573$	5.14203	−	4.31467i	0.214811	−	0.180248i
$574$	−36.4013	+	13.2490i	−1.51936	+	0.553002i
$575$	−15.1557	−	5.51622i	−0.632036	−	0.230042i
$576$	3.23009	+	2.71036i	0.134587	+	0.112932i
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	−0.897723	−	0.440560i	$-0.854780\pi$
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	0.830398	+	0.557171i	$0.188113\pi$
$578$	−2.46926	−	4.27688i	−0.102707	−	0.177895i
$579$	−1.56418	+	8.87089i	−0.0650050	+	0.368662i
$580$	4.80200	−	27.2335i	0.199392	−	1.13081i
$581$	−9.43629	−	16.3441i	−0.391483	−	0.678069i
$582$	−6.08987	+	10.5480i	−0.252433	+	0.437227i
$583$	−2.67159	−	2.24173i	−0.110646	−	0.0928429i
$584$	35.1634	+	12.7984i	1.45507	+	0.529603i
$585$	−8.85369	+	3.22248i	−0.366055	+	0.133233i
$586$	−7.56283	+	6.34597i	−0.312418	+	0.262150i
$587$	−7.08630	−	40.1884i	−0.292483	−	1.65875i	−0.677260	−	0.735744i	$-0.736833\pi$
$587$	−7.08630	−	40.1884i	−0.292483	−	1.65875i	0.384776	−	0.923010i	$-0.374279\pi$
$588$	13.3969			0.552480
$589$		0			0
$590$	−13.4270			−0.552779
$591$	0.900025	+	5.10430i	0.0370221	+	0.209963i
$592$	−20.8799	+	17.5203i	−0.858157	+	0.720079i
$593$	10.3969	−	3.78417i	0.426951	−	0.155397i	−0.119602	−	0.992822i	$-0.538162\pi$
$593$	10.3969	−	3.78417i	0.426951	−	0.155397i	0.546553	+	0.837425i	$0.315940\pi$
$594$	−10.2562	−	3.73297i	−0.420819	−	0.153166i
$595$	−6.13429	−	5.14728i	−0.251481	−	0.211018i
$596$	−24.7199	+	42.8161i	−1.01257	+	1.75381i
$597$	8.82295	+	15.2818i	0.361099	+	0.625442i
$598$	6.04963	−	34.3092i	0.247388	−	1.40301i
$599$	−7.73736	+	43.8807i	−0.316140	+	1.79292i	0.249615	+	0.968345i	$0.419696\pi$
$599$	−7.73736	+	43.8807i	−0.316140	+	1.79292i	−0.565755	+	0.824573i	$0.691415\pi$
$600$	6.34642	+	10.9923i	0.259091	+	0.448760i
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	−0.810533	−	0.585693i	$-0.800823\pi$
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	0.912491	+	0.409096i	$0.134156\pi$
$602$	25.8614	+	21.7003i	1.05403	+	0.884439i
$603$	−9.40198	−	3.42204i	−0.382878	−	0.139356i
$604$	45.7734	−	16.6601i	1.86249	−	0.677892i
$605$	9.90420	−	8.31061i	0.402663	−	0.337874i
$606$	0.622836	+	3.53228i	0.0253010	+	0.143489i
$607$	−31.1881			−1.26589			−0.632943	−	0.774199i	$-0.718153\pi$
$607$	−31.1881			−1.26589			−0.632943	+	0.774199i	$0.718153\pi$
$608$		0			0
$609$	4.65270			0.188537
$610$	−2.67617	−	15.1773i	−0.108355	−	0.614513i
$611$	1.19459	−	1.00238i	0.0483280	−	0.0405520i
$612$	41.3940	−	15.0662i	1.67325	−	0.609014i
$613$	−15.3824	−	5.59873i	−0.621288	−	0.226130i	0.0121468	−	0.999926i	$-0.496133\pi$
$613$	−15.3824	−	5.59873i	−0.621288	−	0.226130i	−0.633435	+	0.773796i	$0.718356\pi$
$614$	−44.9530	−	37.7200i	−1.81415	−	1.52226i
$615$	4.39053	−	7.60462i	0.177043	−	0.306648i
$616$	−5.54189	−	9.59883i	−0.223289	−	0.386748i
$617$	2.78850	−	15.8143i	0.112261	−	0.636661i	−0.875810	−	0.482657i	$-0.839672\pi$
$617$	2.78850	−	15.8143i	0.112261	−	0.636661i	0.988070	−	0.154005i	$-0.0492171\pi$
$618$	−3.58037	+	20.3053i	−0.144024	+	0.816799i
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	0.520558	−	0.853826i	$-0.325724\pi$
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	−0.999714	+	0.0239031i	$0.992391\pi$
$620$	−11.4042	+	19.7527i	−0.458004	+	0.793286i
$621$	−14.1138	−	11.8429i	−0.566368	−	0.475239i
$622$	−8.23530	−	2.99740i	−0.330205	−	0.120185i
$623$	3.49273	−	1.27125i	0.139933	−	0.0509315i
$624$	−9.01754	+	7.56662i	−0.360991	+	0.302907i
$625$	0.185259	+	1.05066i	0.00741037	+	0.0420263i
$626$	57.9590			2.31651
$627$		0			0
$628$	48.4962			1.93521
$629$	−2.76604	−	15.6870i	−0.110289	−	0.625482i
$630$	−10.3059	+	8.64766i	−0.410596	+	0.344531i
$631$	−20.1780	+	7.34419i	−0.803273	+	0.292367i	−0.710842	−	0.703352i	$-0.751686\pi$
$631$	−20.1780	+	7.34419i	−0.803273	+	0.292367i	−0.0924309	+	0.995719i	$0.529464\pi$
$632$	56.2789	+	20.4838i	2.23865	+	0.814803i
$633$	4.03596	+	3.38657i	0.160415	+	0.134604i
$634$	33.0699	−	57.2787i	1.31337	−	2.27483i
$635$	−9.76991	−	16.9220i	−0.387707	−	0.671529i
$636$	−1.47178	+	8.34689i	−0.0583599	+	0.330976i
$637$	−2.19506	+	12.4488i	−0.0869714	+	0.493239i
$638$	6.97906	+	12.0881i	0.276303	+	0.478572i
$639$	−8.92633	+	15.4609i	−0.353120	+	0.611622i
$640$	−13.7686	−	11.5532i	−0.544251	−	0.456680i
$641$	−11.9846	−	4.36203i	−0.473362	−	0.172290i	0.0943126	−	0.995543i	$-0.469935\pi$
$641$	−11.9846	−	4.36203i	−0.473362	−	0.172290i	−0.567675	+	0.823253i	$0.692157\pi$
$642$	10.3743	−	3.77595i	0.409442	−	0.149025i
$643$	21.9151	−	18.3889i	0.864247	−	0.725189i	−0.0986316	−	0.995124i	$-0.531447\pi$
$643$	21.9151	−	18.3889i	0.864247	−	0.725189i	0.962879	+	0.269935i	$0.0870021\pi$
$644$	−5.94356	−	33.7076i	−0.234209	−	1.32827i
$645$	−7.65270			−0.301325
$646$		0			0
$647$	16.7128			0.657046			0.328523	−	0.944496i	$-0.393449\pi$
$647$	16.7128			0.657046			0.328523	+	0.944496i	$0.393449\pi$
$648$	−5.66978	−	32.1549i	−0.222730	−	1.26316i
$649$	3.57217	−	2.99740i	0.140220	−	0.117658i
$650$	−20.5881	+	7.49346i	−0.807532	+	0.293918i
$651$	−3.60607	−	1.31250i	−0.141333	−	0.0514410i
$652$	−21.4008	−	17.9574i	−0.838120	−	0.703266i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−7.81180	−	13.5304i	−0.305466	−	0.529082i
$655$	4.63429	−	26.2823i	0.181077	−	1.02694i
$656$	−11.5103	+	65.2780i	−0.449400	+	2.54868i
$657$	7.88713	+	13.6609i	0.307706	+	0.532963i
$658$	1.11334	−	1.92836i	0.0434025	−	0.0751754i
$659$	−33.6300	−	28.2189i	−1.31004	−	1.09925i	−0.988316	−	0.152419i	$-0.951294\pi$
$659$	−33.6300	−	28.2189i	−1.31004	−	1.09925i	−0.321723	−	0.946834i	$-0.604262\pi$
$660$	4.31908	+	1.57202i	0.168120	+	0.0611906i
$661$	10.1074	−	3.67880i	0.393133	−	0.143089i	−0.137887	−	0.990448i	$-0.544031\pi$
$661$	10.1074	−	3.67880i	0.393133	−	0.143089i	0.531020	+	0.847359i	$0.321809\pi$
$662$	−36.9406	+	30.9969i	−1.43574	+	1.20473i
$663$	−1.19459	−	6.77487i	−0.0463941	−	0.263114i
$664$	−75.2158			−2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	4.09152	+	23.2042i	0.158424	+	0.898469i
$668$	−46.5624	+	39.0705i	−1.80155	+	1.51168i
$669$	−9.49185	+	3.45475i	−0.366976	+	0.133568i
$670$	12.4611	+	4.53547i	0.481414	+	0.175221i
$671$	4.10014	+	3.44042i	0.158284	+	0.132816i
$672$	−2.29813	+	3.98048i	−0.0886524	+	0.153550i
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	0.817643	−	0.575726i	$-0.195280\pi$
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	−0.907415	+	0.420237i	$0.861947\pi$
$674$	−0.748093	+	4.24265i	−0.0288155	+	0.163421i
$675$	−2.01202	+	11.4107i	−0.0774428	+	0.439200i
$676$	12.3931	+	21.4654i	0.476656	+	0.825592i
$677$	−1.63429	+	2.83067i	−0.0628107	+	0.108791i	−0.895721	−	0.444617i	$-0.853340\pi$
$677$	−1.63429	+	2.83067i	−0.0628107	+	0.108791i	0.832910	+	0.553408i	$0.186673\pi$
$678$	1.65910	+	1.39215i	0.0637174	+	0.0534652i
$679$	−10.6099	−	3.86170i	−0.407172	−	0.148198i
$680$	−29.9898	+	10.9154i	−1.15006	+	0.418586i
$681$	−4.93629	+	4.14204i	−0.189159	+	0.158723i
$682$	−1.99912	−	11.3376i	−0.0765504	−	0.434139i
$683$	6.21894			0.237961			0.118981	−	0.992897i	$-0.462037\pi$
$683$	6.21894			0.237961			0.118981	+	0.992897i	$0.462037\pi$
$684$		0			0
$685$	−13.7483			−0.525297
$686$	7.84982	+	44.5186i	0.299708	+	1.69973i
$687$	−10.0594	+	8.44086i	−0.383791	+	0.322039i
$688$	54.2836	−	19.7576i	2.06954	−	0.753253i
$689$	−7.51501	−	2.73524i	−0.286299	−	0.104204i
$690$	8.63816	+	7.24827i	0.328849	+	0.275937i
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	−0.996193	−	0.0871792i	$-0.972215\pi$
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	0.573596	+	0.819139i	$0.305548\pi$
$692$	−55.6887	−	96.4557i	−2.11697	−	3.66670i
$693$	0.811337	−	4.60132i	0.0308201	−	0.174790i
$694$	2.15523	−	12.2229i	0.0818114	−	0.463976i
$695$	−1.11856	−	1.93739i	−0.0424292	−	0.0734896i
$696$	9.27156	−	16.0588i	0.351438	−	0.608708i
$697$	−29.6746	−	24.8999i	−1.12400	−	0.943152i
$698$	−66.9304	−	24.3607i	−2.53335	−	0.922065i
$699$	2.16802	−	0.789096i	0.0820022	−	0.0298463i
$700$	−16.4893	+	13.8362i	−0.623238	+	0.522959i
$701$	−4.82264	−	27.3506i	−0.182149	−	1.03302i	−0.929564	−	0.368660i	$-0.879817\pi$
$701$	−4.82264	−	27.3506i	−0.182149	−	1.03302i	0.747416	−	0.664357i	$-0.231294\pi$
$702$	−25.0283			−0.944631
$703$		0			0
$704$	1.94087			0.0731495
$705$	0.0876485	+	0.497079i	0.00330103	+	0.0187211i
$706$	16.1382	−	13.5415i	0.607368	−	0.509642i
$707$	−3.12449	+	1.13722i	−0.117508	+	0.0427695i
$708$	−10.6493	−	3.87603i	−0.400225	−	0.145670i
$709$	−4.67886	−	3.92603i	−0.175718	−	0.147445i	0.550687	−	0.834712i	$-0.314366\pi$
$709$	−4.67886	−	3.92603i	−0.175718	−	0.147445i	−0.726405	+	0.687267i	$0.758810\pi$
$710$	11.8307	−	20.4914i	0.443998	−	0.769027i
$711$	12.6233	+	21.8642i	0.473411	+	0.819972i
$712$	2.57233	−	14.5884i	0.0964021	−	0.546724i
$713$	3.37464	−	19.1385i	0.126381	−	0.716743i
$714$	−4.91147	−	8.50692i	−0.183807	−	0.318364i
$715$	−2.16843	+	3.75584i	−0.0810948	+	0.140460i
$716$	19.7041	+	16.5337i	0.736378	+	0.617895i
$717$	7.34389	+	2.67296i	0.274263	+	0.0998235i
$718$	59.3157	−	21.5892i	2.21364	−	0.805700i
$719$	29.6642	−	24.8912i	1.10629	−	0.928284i	0.108455	−	0.994101i	$-0.465410\pi$
$719$	29.6642	−	24.8912i	1.10629	−	0.928284i	0.997832	+	0.0658171i	$0.0209654\pi$
$720$	3.99747	+	22.6708i	0.148977	+	0.844891i
$721$	−19.1138			−0.711835
$722$		0			0
$723$	−8.42097			−0.313179
$724$	10.3892	+	58.9200i	0.386111	+	2.18974i
$725$	11.3512	−	9.52476i	0.421572	−	0.353741i
$726$	14.9033	−	5.42437i	0.553114	−	0.201317i
$727$	10.4098	+	3.78887i	0.386079	+	0.140521i	0.527765	−	0.849390i	$-0.323030\pi$
$727$	10.4098	+	3.78887i	0.386079	+	0.140521i	−0.141686	+	0.989912i	$0.545252\pi$
$728$	−19.4702	−	16.3374i	−0.721613	−	0.605505i
$729$	3.31996	−	5.75033i	0.122961	−	0.212975i
$730$	−10.4534	−	18.1058i	−0.386896	−	0.670124i
$731$	−5.86231	+	33.2468i	−0.216825	+	1.22968i
$732$	2.25877	−	12.8101i	0.0834866	−	0.473476i
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	0.974266	−	0.225400i	$-0.0723689\pi$
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	−0.682335	+	0.731039i	$0.739036\pi$
$734$	−3.27379	+	5.67036i	−0.120838	+	0.209297i
$735$	−3.13429	−	2.62998i	−0.115610	−	0.0970082i
$736$	−21.8726	−	7.96097i	−0.806234	−	0.293445i
$737$	−4.32770	+	1.57515i	−0.159413	+	0.0580215i
$738$	−49.8546	+	41.8330i	−1.83517	+	1.53989i
$739$	0.269037	+	1.52579i	0.00989670	+	0.0561270i	0.989356	−	0.145514i	$-0.0464836\pi$
$739$	0.269037	+	1.52579i	0.00989670	+	0.0561270i	−0.979459	+	0.201641i	$0.935373\pi$
$740$	24.4047			0.897133
$741$		0			0
$742$	−11.4192			−0.419213
$743$	6.62701	+	37.5836i	0.243121	+	1.37881i	0.824815	+	0.565402i	$0.191279\pi$
$743$	6.62701	+	37.5836i	0.243121	+	1.37881i	−0.581694	+	0.813408i	$0.697610\pi$
$744$	−11.7160	+	9.83089i	−0.429530	+	0.360418i
$745$	14.1887	−	5.16425i	0.519832	−	0.189204i
$746$	−55.6379	−	20.2505i	−2.03705	−	0.741425i
$747$	−24.2888	−	20.3807i	−0.888681	−	0.745692i
$748$	10.1382	−	17.5598i	0.370688	−	0.642050i
$749$	5.11721	+	8.86327i	0.186979	+	0.323857i
$750$	3.16473	−	17.9480i	0.115559	−	0.655370i
$751$	−4.40167	+	24.9631i	−0.160619	+	0.910918i	0.792848	+	0.609420i	$0.208598\pi$
$751$	−4.40167	+	24.9631i	−0.160619	+	0.910918i	−0.953467	+	0.301498i	$0.902513\pi$
$752$	−1.90508	−	3.29969i	−0.0694710	−	0.120327i
$753$	4.68732	−	8.11867i	0.170815	−	0.295861i
$754$	24.5194	+	20.5742i	0.892942	+	0.749267i
$755$	−13.9795	−	5.08813i	−0.508767	−	0.185176i
$756$	−23.1065	+	8.41009i	−0.840377	+	0.305872i
$757$	32.4577	−	27.2352i	1.17970	−	0.989882i	0.179714	−	0.983719i	$-0.442483\pi$
$757$	32.4577	−	27.2352i	1.17970	−	0.989882i	0.999981	−	0.00616293i	$-0.00196173\pi$
$758$	−11.1853	−	63.4348i	−0.406267	−	2.30405i
$759$	−3.91622			−0.142150
$760$		0			0
$761$	−2.85710			−0.103570			−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710			−0.103570			−0.0517848	+	0.998658i	$0.516491\pi$
$762$	−4.16220	−	23.6050i	−0.150781	−	0.855119i
$763$	11.0949	−	9.30975i	0.401663	−	0.337035i
$764$	42.6318	−	15.5167i	1.54236	−	0.561375i
$765$	−12.6420	−	4.60132i	−0.457073	−	0.166361i
$766$	53.3041	+	44.7275i	1.92596	+	1.61607i
$767$	5.34658	−	9.26055i	0.193054	−	0.334379i
$768$	−9.95471	−	17.2421i	−0.359210	−	0.622169i
$769$	3.32026	−	18.8301i	0.119732	−	0.679032i	−0.864567	−	0.502518i	$-0.832407\pi$
$769$	3.32026	−	18.8301i	0.119732	−	0.679032i	0.984298	−	0.176514i	$-0.0564819\pi$
$770$	−1.07532	+	6.09845i	−0.0387519	+	0.219773i
$771$	1.62449	+	2.81369i	0.0585044	+	0.101333i
$772$	−30.4406	+	52.7247i	−1.09558	+	1.89760i
$773$	1.92649	+	1.61652i	0.0692910	+	0.0581420i	0.676775	−	0.736190i	$-0.263377\pi$
$773$	1.92649	+	1.61652i	0.0692910	+	0.0581420i	−0.607484	+	0.794332i	$0.707821\pi$
$774$	53.2973	+	19.3986i	1.91573	+	0.697270i
$775$	−11.4846	+	4.18004i	−0.412538	+	0.150152i
$776$	−34.4714	+	28.9249i	−1.23745	+	1.03834i
$777$	0.713011	+	4.04369i	0.0255791	+	0.145066i
$778$	8.46286			0.303408
$779$		0			0
$780$	10.5398			0.377386
$781$	1.42696	+	8.09267i	0.0510605	+	0.289578i
$782$	38.1070	−	31.9756i	1.36270	−	1.14344i
$783$	15.9064	−	5.78946i	0.568449	−	0.206899i
$784$	29.0228	+	10.5634i	1.03653	+	0.377265i
$785$	−11.3460	−	9.52038i	−0.404954	−	0.339797i
$786$	16.3687	−	28.3514i	0.583852	−	1.01126i
$787$	−1.36303	−	2.36083i	−0.0485866	−	0.0841545i	0.840709	−	0.541487i	$-0.182138\pi$
$787$	−1.36303	−	2.36083i	−0.0485866	−	0.0841545i	−0.889296	+	0.457332i	$0.848805\pi$
$788$	−6.08306	+	34.4988i	−0.216700	+	1.22897i
$789$	2.72503	−	15.4544i	0.0970137	−	0.550192i
$790$	−16.7306	−	28.9782i	−0.595246	−	1.03100i
$791$	−1.00387	+	1.73875i	−0.0356935	+	0.0618230i
$792$	−14.2647	−	11.9695i	−0.506874	−	0.425318i
$793$	11.5334	+	4.19783i	0.409564	+	0.149069i
$794$	−31.2254	+	11.3651i	−1.10815	+	0.403333i
$795$	1.98293	−	1.66387i	0.0703271	−	0.0590115i
$796$	20.7101	+	117.453i	0.734049	+	4.16300i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	2.54189	+	14.4158i	0.0898693	+	0.509674i
$801$	4.78359	−	4.01390i	0.169020	−	0.141824i
$802$	40.7203	−	14.8210i	1.43789	−	0.523347i
$803$	6.82295	+	2.48335i	0.240777	+	0.0876355i
$804$	8.57398	+	7.19442i	0.302381	+	0.253728i
$805$	−5.22668	+	9.05288i	−0.184216	+	0.319072i
$806$	−13.1998	−	22.8627i	−0.464943	−	0.805306i
$807$	1.48602	−	8.42767i	0.0523105	−	0.296668i
$808$	−2.30113	+	13.0503i	−0.0809533	+	0.459109i
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.717633	−	0.696422i	$-0.754774\pi$
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.244302	−	0.969699i	$-0.578559\pi$
$810$	−9.12108	+	15.7982i	−0.320482	+	0.555091i
$811$	−1.76991	−	1.48513i	−0.0621501	−	0.0521501i	0.611183	−	0.791489i	$-0.290694\pi$
$811$	−1.76991	−	1.48513i	−0.0621501	−	0.0521501i	−0.673334	+	0.739339i	$0.735138\pi$
$812$	29.5501	+	10.7554i	1.03701	+	0.377439i
$813$	−16.2964	+	5.93140i	−0.571539	+	0.208023i
$814$	−9.43629	+	7.91799i	−0.330742	+	0.277525i
$815$	1.48158	+	8.40247i	0.0518975	+	0.294326i
$816$	−16.8084			−0.588412
$817$		0			0
$818$	22.2772			0.778906
$819$	−1.86050	−	10.5514i	−0.0650111	−	0.368696i
$820$	45.4641	−	38.1489i	1.58768	−	1.33222i
$821$	−1.04411	+	0.380025i	−0.0364397	+	0.0132630i	−0.360176	−	0.932884i	$-0.617283\pi$
$821$	−1.04411	+	0.380025i	−0.0364397	+	0.0132630i	0.323736	+	0.946147i	$0.395061\pi$
$822$	−15.8478	−	5.76811i	−0.552754	−	0.201186i
$823$	15.8170	+	13.2721i	0.551347	+	0.462635i	0.875397	−	0.483405i	$-0.160600\pi$
$823$	15.8170	+	13.2721i	0.551347	+	0.462635i	−0.324050	+	0.946040i	$0.605045\pi$
$824$	−38.0886	+	65.9714i	−1.32688	+	2.29822i
$825$	1.23143	+	2.13290i	0.0428729	+	0.0742580i
$826$	2.65136	−	15.0366i	0.0922526	−	0.523190i
$827$	6.30437	−	35.7538i	0.219224	−	1.24328i	−0.654199	−	0.756322i	$-0.726994\pi$
$827$	6.30437	−	35.7538i	0.219224	−	1.24328i	0.873424	−	0.486961i	$-0.161895\pi$
$828$	−28.7520	−	49.7999i	−0.999200	−	1.73066i
$829$	3.57486	−	6.19183i	0.124160	−	0.215051i	−0.797244	−	0.603657i	$-0.793710\pi$
$829$	3.57486	−	6.19183i	0.124160	−	0.215051i	0.921404	+	0.388606i	$0.127043\pi$
$830$	32.1917	+	27.0120i	1.11739	+	0.937600i
$831$	−10.1267	−	3.68582i	−0.351292	−	0.127860i
$832$	4.18227	−	1.52222i	0.144994	−	0.0527735i
$833$	−13.8268	+	11.6021i	−0.479071	+	0.401988i
$834$	−0.476529	−	2.70253i	−0.0165009	−	0.0935810i
$835$	18.5635			0.642418
$836$		0			0
$837$	−13.9614			−0.482577
$838$	−3.00758	−	17.0568i	−0.103895	−	0.589218i
$839$	−26.5103	+	22.2448i	−0.915236	+	0.767974i	−0.973108	−	0.230350i	$-0.926013\pi$
$839$	−26.5103	+	22.2448i	−0.915236	+	0.767974i	0.0578718	+	0.998324i	$0.481569\pi$
$840$	7.73055	−	2.81369i	0.266729	−	0.0970816i
$841$	6.90895	+	2.51465i	0.238240	+	0.0867121i
$842$	9.35504	+	7.84981i	0.322396	+	0.270522i
$843$	−6.32800	+	10.9604i	−0.217948	+	0.377497i
$844$	17.8045	+	30.8384i	0.612857	+	1.06150i
$845$	1.31449	−	7.45486i	0.0452199	−	0.256455i
$846$	0.649605	−	3.68409i	0.0223339	−	0.126662i
$847$	7.35117	+	12.7326i	0.252589	+	0.437497i
$848$	−9.76991	+	16.9220i	−0.335500	+	0.581103i
$849$	5.65523	+	4.74530i	0.194087	+	0.162858i
$850$	−29.3974	−	10.6998i	−1.00832	−	0.366999i
$851$	−19.5398	+	7.11192i	−0.669817	+	0.243793i
$852$	15.2986	−	12.8370i	0.524121	−	0.439790i
$853$	5.77395	+	32.7457i	0.197696	+	1.12119i	0.908526	+	0.417827i	$0.137208\pi$
$853$	5.77395	+	32.7457i	0.197696	+	1.12119i	−0.710830	+	0.703364i	$0.751681\pi$
$854$	17.5253			0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	−0.674830	−	3.82715i	−0.0230518	−	0.130733i	0.971110	−	0.238632i	$-0.0766989\pi$
$857$	−0.674830	−	3.82715i	−0.0230518	−	0.130733i	−0.994162	+	0.107899i	$0.965588\pi$
$858$	−4.07532	+	3.41960i	−0.139129	+	0.116743i
$859$	−1.55778	+	0.566986i	−0.0531508	+	0.0193453i	−0.368459	−	0.929644i	$-0.620114\pi$
$859$	−1.55778	+	0.566986i	−0.0531508	+	0.0193453i	0.315308	+	0.948989i	$0.397892\pi$
$860$	−48.6036	−	17.6903i	−1.65737	−	0.603233i
$861$	7.64930	+	6.41852i	0.260687	+	0.218743i
$862$	1.65048	−	2.85872i	0.0562156	−	0.0973684i
$863$	26.3594	+	45.6558i	0.897284	+	1.55414i	0.830953	+	0.556343i	$0.187796\pi$
$863$	26.3594	+	45.6558i	0.897284	+	1.55414i	0.0663308	+	0.997798i	$0.478871\pi$
$864$	−2.90373	+	16.4679i	−0.0987870	+	0.560249i
$865$	−5.90673	+	33.4987i	−0.200835	+	1.13899i
$866$	25.0979	+	43.4709i	0.852862	+	1.47720i
$867$	−0.636507	+	1.10246i	−0.0216169	+	0.0374416i
$868$	−19.8687	−	16.6718i	−0.674388	−	0.565879i
$869$	10.9201	+	3.97459i	0.370439	+	0.134829i
$870$	−9.73530	+	3.54336i	−0.330058	+	0.120131i
$871$	−8.09009	+	6.78839i	−0.274122	+	0.230016i
$872$	−10.0235	−	56.8459i	−0.339438	−	1.92505i
$873$	−18.9691			−0.642008
$874$		0			0
$875$	16.8949			0.571151
$876$	−3.06418	−	17.3778i	−0.103529	−	0.587142i
$877$	−16.2324	+	13.6206i	−0.548128	+	0.459934i	−0.874307	−	0.485374i	$-0.838683\pi$
$877$	−16.2324	+	13.6206i	−0.548128	+	0.459934i	0.326179	+	0.945308i	$0.394239\pi$
$878$	−82.2486	+	29.9360i	−2.77576	+	1.01029i
$879$	2.39141	+	0.870401i	0.0806602	+	0.0293579i
$880$	8.11721	+	6.81115i	0.273631	+	0.229604i
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	0.458106	+	0.888898i	$0.348528\pi$
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	−0.998861	+	0.0477179i	$0.984805\pi$
$882$	15.1621	+	26.2615i	0.510534	+	0.884271i
$883$	−8.21301	+	46.5783i	−0.276390	+	1.56748i	0.458122	+	0.888889i	$0.348522\pi$
$883$	−8.21301	+	46.5783i	−0.276390	+	1.56748i	−0.734512	+	0.678595i	$0.762589\pi$
$884$	8.07398	−	45.7898i	0.271557	−	1.54008i
$885$	1.73055	+	2.99740i	0.0581719	+	0.100757i
$886$	21.5355	−	37.3007i	0.723501	−	1.25314i
$887$	8.09177	+	6.78980i	0.271695	+	0.227979i	0.768447	−	0.639913i	$-0.221030\pi$
$887$	8.09177	+	6.78980i	0.271695	+	0.227979i	−0.496752	+	0.867892i	$0.665474\pi$
$888$	15.3776	+	5.59700i	0.516039	+	0.187823i
$889$	20.8799	−	7.59964i	0.700288	−	0.254884i
$890$	−6.34002	+	5.31991i	−0.212518	+	0.178324i
$891$	−1.10014	−	6.23919i	−0.0368560	−	0.209021i
$892$	−68.2704			−2.28586
$893$		0			0
$894$	18.5220			0.619468
$895$	−1.36412	−	7.73632i	−0.0455976	−	0.258597i
$896$	15.6570	−	13.1378i	0.523065	−	0.438904i
$897$	−8.43882	+	3.07148i	−0.281764	+	0.102554i
$898$	89.0121	+	32.3978i	2.97037	+	1.08113i
$899$	13.6775	+	11.4768i	0.456171	+	0.382773i
$900$	−18.0817	+	31.3185i	−0.602724	+	1.04395i
$901$	−5.70961	−	9.88933i	−0.190215	−	0.329461i
$902$	−5.20187	+	29.5013i	−0.173203	+	0.982284i
$903$	1.51114	−	8.57013i	0.0502877	−	0.285196i
$904$	4.00088	+	6.92972i	0.133067	+	0.230479i
$905$	9.13610	−	15.8242i	0.303694	−	0.526014i
$906$	−13.9795	−	11.7302i	−0.464439	−	0.389710i
$907$	−40.3320	−	14.6797i	−1.33920	−	0.487430i	−0.429642	−	0.902999i	$-0.641360\pi$
$907$	−40.3320	−	14.6797i	−1.33920	−	0.487430i	−0.909561	+	0.415569i	$0.863582\pi$
$908$	−40.9261	+	14.8959i	−1.35818	+	0.494337i
$909$	−4.27925	+	3.59072i	−0.141934	+	0.119097i
$910$	2.46585	+	13.9845i	0.0817422	+	0.463583i
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$		0			0
$913$	−14.5945			−0.483008
$914$	−4.00609	−	22.7197i	−0.132510	−	0.751500i
$915$	−3.04323	+	2.55358i	−0.100606	+	0.0844186i
$916$	−83.4013	+	30.3556i	−2.75566	+	1.00298i
$917$	28.5180	+	10.3797i	0.941748	+	0.342768i
$918$	−27.3764	−	22.9716i	−0.903557	−	0.758175i
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	−0.589285	−	0.807925i	$-0.700590\pi$
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	0.994326	+	0.106373i	$0.0339237\pi$
$920$	20.8307	+	36.0798i	0.686767	+	1.18952i
$921$	−2.62671	+	14.8968i	−0.0865529	+	0.490866i
$922$	10.7497	−	60.9648i	0.354024	−	2.00777i
$923$	9.42190	+	16.3192i	0.310126	+	0.537154i
$924$	−2.61334	+	4.52644i	−0.0859726	+	0.148909i
$925$	10.0175	+	8.40571i	0.329375	+	0.276378i
$926$	−0.596571	−	0.217134i	−0.0196046	−	0.00713547i
$927$	−30.1755	+	10.9830i	−0.991092	+	0.360728i
$928$	16.3819	−	13.7461i	0.537763	−	0.451236i
$929$	−3.86840	−	21.9388i	−0.126918	−	0.719789i	−0.980150	−	0.198257i	$-0.936472\pi$
$929$	−3.86840	−	21.9388i	−0.126918	−	0.719789i	0.853232	−	0.521532i	$-0.174639\pi$
$930$	8.54488			0.280198
$931$		0			0
$932$	15.5936			0.510785
$933$	0.392284	+	2.22475i	0.0128428	+	0.0728352i
$934$	−29.7973	+	25.0029i	−0.974996	+	0.818119i
$935$	−5.81908	+	2.11797i	−0.190304	+	0.0692651i
$936$	−40.1257	−	14.6046i	−1.31155	−	0.477365i
$937$	−7.31702	−	6.13971i	−0.239037	−	0.200576i	0.515398	−	0.856951i	$-0.327644\pi$
$937$	−7.31702	−	6.13971i	−0.239037	−	0.200576i	−0.754434	+	0.656376i	$0.772089\pi$
$938$	−7.53983	+	13.0594i	−0.246184	+	0.426403i
$939$	−7.47013	−	12.9386i	−0.243779	−	0.422237i
$940$	−0.592396	+	3.35965i	−0.0193218	+	0.109580i
$941$	−9.67664	+	54.8790i	−0.315449	+	1.78900i	0.254238	+	0.967142i	$0.418175\pi$
$941$	−9.67664	+	54.8790i	−0.315449	+	1.78900i	−0.569688	+	0.821861i	$0.692936\pi$
$942$	−9.08424	−	15.7344i	−0.295981	−	0.512654i
$943$	−25.2841	+	43.7933i	−0.823362	+	1.42610i
$944$	−20.0141	−	16.7939i	−0.651405	−	0.546593i
$945$	7.05690	+	2.56850i	0.229561	+	0.0835534i
$946$	24.5326	−	8.92912i	0.797622	−	0.290311i
$947$	−20.7160	+	17.3828i	−0.673180	+	0.564865i	−0.914005	−	0.405704i	$-0.867026\pi$
$947$	−20.7160	+	17.3828i	−0.673180	+	0.564865i	0.240825	+	0.970569i	$0.422582\pi$
$948$	−4.90420	−	27.8131i	−0.159281	−	0.903328i
$949$	16.6500			0.540482
$950$		0			0
$951$	−17.0490			−0.552852
$952$	−6.30200	−	35.7404i	−0.204249	−	1.15835i
$953$	17.7194	−	14.8683i	0.573988	−	0.481633i	−0.308979	−	0.951069i	$-0.599987\pi$
$953$	17.7194	−	14.8683i	0.573988	−	0.481633i	0.882967	+	0.469436i	$0.155543\pi$
$954$	−18.0278	+	6.56159i	−0.583672	+	0.212439i
$955$	−13.0201	−	4.73892i	−0.421319	−	0.153348i
$956$	40.4634	+	33.9528i	1.30868	+	1.09811i
$957$	1.79901	−	3.11598i	0.0581538	−	0.100725i
$958$	−0.910597	−	1.57720i	−0.0294200	−	0.0509570i
$959$	2.71482	−	15.3965i	0.0876662	−	0.497180i
$960$	−0.250152	+	1.41868i	−0.00807363	+	0.0457878i
$961$	8.13681	+	14.0934i	0.262478	+	0.454625i
$962$	−14.1236	+	24.4628i	−0.455363	+	0.788713i
$963$	13.1716	+	11.0523i	0.424449	+	0.356155i
$964$	−53.4830	−	19.4662i	−1.72257	−	0.626965i
$965$	17.4722	−	6.35938i	0.562452	−	0.204716i
$966$	−9.82295	+	8.24243i	−0.316048	+	0.265196i
$967$	6.77837	+	38.4421i	0.217978	+	1.23621i	0.875664	+	0.482921i	$0.160424\pi$
$967$	6.77837	+	38.4421i	0.217978	+	1.23621i	−0.657686	+	0.753292i	$0.728465\pi$
$968$	58.5954			1.88333
$969$		0			0
$970$	25.1411			0.807234
$971$	−7.15476	−	40.5767i	−0.229607	−	1.30217i	−0.853679	−	0.520800i	$-0.825634\pi$
$971$	−7.15476	−	40.5767i	−0.229607	−	1.30217i	0.624071	−	0.781367i	$-0.285477\pi$
$972$	−48.6789	+	40.8465i	−1.56138	+	1.31015i
$973$	2.39053	−	0.870082i	0.0766369	−	0.0278935i
$974$	27.9504	+	10.1731i	0.895589	+	0.325968i
$975$	4.32635	+	3.63024i	0.138554	+	0.116261i
$976$	14.9941	−	25.9705i	0.479948	−	0.831295i
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	0.628110	−	0.778125i	$-0.283829\pi$
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	−0.987931	+	0.154897i	$0.950495\pi$
$978$	−1.81743	+	10.3072i	−0.0581150	+	0.329586i
$979$	0.499123	−	2.83067i	0.0159520	−	0.0904685i
$980$	−13.8268	−	23.9488i	−0.441682	−	0.765015i
$981$	12.1664	−	21.0728i	0.388442	−	0.672802i
$982$	−0.172304	−	0.144580i	−0.00549844	−	0.00461374i
$983$	41.8597	+	15.2357i	1.33512	+	0.485943i	0.908271	−	0.418382i	$-0.137403\pi$
$983$	41.8597	+	15.2357i	1.33512	+	0.485943i	0.426845	+	0.904325i	$0.359625\pi$
$984$	37.3965	−	13.6112i	1.19216	−	0.433910i
$985$	8.19569	−	6.87700i	0.261136	−	0.219119i
$986$	7.93629	+	45.0089i	0.252743	+	1.43338i
$987$	−0.573978			−0.0182699
$988$		0			0
$989$	44.0702			1.40135
$990$	1.80659	+	10.2457i	0.0574172	+	0.325629i
$991$	−34.7245	+	29.1373i	−1.10306	+	0.925576i	−0.997627	−	0.0688503i	$-0.978067\pi$
$991$	−34.7245	+	29.1373i	−1.10306	+	0.925576i	−0.105432	+	0.994427i	$0.533622\pi$
$992$	−16.5744	+	6.03260i	−0.526239	+	0.191535i
$993$	11.6808	+	4.25147i	0.370680	+	0.134916i
$994$	20.6117	+	17.2953i	0.653765	+	0.548574i
$995$	18.2121	−	31.5443i	0.577363	−	1.00002i
$996$	17.7344	+	30.7169i	0.561937	+	0.973303i
$997$	−1.82177	+	10.3317i	−0.0576959	+	0.327210i	−0.999971	−	0.00763028i	$-0.997571\pi$
$997$	−1.82177	+	10.3317i	−0.0576959	+	0.327210i	0.942275	+	0.334840i	$0.108682\pi$
$998$	−6.45929	+	36.6325i	−0.204465	+	1.15958i
$999$	7.46926	+	12.9371i	0.236317	+	0.409313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.f.28.1		6
19.2	odd	18		361.2.e.b.245.1		6
19.3	odd	18		361.2.e.a.62.1		6
19.4	even	9		361.2.c.i.68.3		6
19.5	even	9		19.2.e.a.16.1	yes	6
19.6	even	9		361.2.a.g.1.1		3
19.7	even	3		361.2.e.g.99.1		6
19.8	odd	6		361.2.e.h.234.1		6
19.9	even	9		361.2.c.i.292.3		6
19.10	odd	18		361.2.c.h.292.1		6
19.11	even	3		19.2.e.a.6.1	✓	6
19.12	odd	6		361.2.e.a.99.1		6
19.13	odd	18		361.2.a.h.1.3		3
19.14	odd	18		361.2.e.h.54.1		6
19.15	odd	18		361.2.c.h.68.1		6
19.16	even	9		361.2.e.g.62.1		6
19.17	even	9	inner	361.2.e.f.245.1		6
19.18	odd	2		361.2.e.b.28.1		6
57.5	odd	18		171.2.u.c.73.1		6
57.11	odd	6		171.2.u.c.82.1		6
57.32	even	18		3249.2.a.s.1.1		3
57.44	odd	18		3249.2.a.z.1.3		3
76.11	odd	6		304.2.u.b.177.1		6
76.43	odd	18		304.2.u.b.225.1		6
76.51	even	18		5776.2.a.bi.1.2		3
76.63	odd	18		5776.2.a.br.1.2		3
95.24	even	18		475.2.l.a.301.1		6
95.43	odd	36		475.2.u.a.149.1		12
95.44	even	18		9025.2.a.bd.1.3		3
95.49	even	6		475.2.l.a.101.1		6
95.62	odd	36		475.2.u.a.149.2		12
95.68	odd	12		475.2.u.a.424.2		12
95.87	odd	12		475.2.u.a.424.1		12
95.89	odd	18		9025.2.a.x.1.1		3
133.5	odd	18		931.2.v.a.263.1		6
133.11	even	3		931.2.v.b.177.1		6
133.24	odd	18		931.2.x.b.814.1		6
133.30	even	3		931.2.x.a.557.1		6
133.62	odd	18		931.2.w.a.491.1		6
133.68	odd	6		931.2.x.b.557.1		6
133.81	even	9		931.2.x.a.814.1		6
133.87	odd	6		931.2.v.a.177.1		6
133.100	even	9		931.2.v.b.263.1		6
133.125	odd	6		931.2.w.a.785.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	19.11	even	3
19.2.e.a.16.1	yes	6	19.5	even	9
171.2.u.c.73.1		6	57.5	odd	18
171.2.u.c.82.1		6	57.11	odd	6
304.2.u.b.177.1		6	76.11	odd	6
304.2.u.b.225.1		6	76.43	odd	18
361.2.a.g.1.1		3	19.6	even	9
361.2.a.h.1.3		3	19.13	odd	18
361.2.c.h.68.1		6	19.15	odd	18
361.2.c.h.292.1		6	19.10	odd	18
361.2.c.i.68.3		6	19.4	even	9
361.2.c.i.292.3		6	19.9	even	9
361.2.e.a.62.1		6	19.3	odd	18
361.2.e.a.99.1		6	19.12	odd	6
361.2.e.b.28.1		6	19.18	odd	2
361.2.e.b.245.1		6	19.2	odd	18
361.2.e.f.28.1		6	1.1	even	1	trivial
361.2.e.f.245.1		6	19.17	even	9	inner
361.2.e.g.62.1		6	19.16	even	9
361.2.e.g.99.1		6	19.7	even	3
361.2.e.h.54.1		6	19.14	odd	18
361.2.e.h.234.1		6	19.8	odd	6
475.2.l.a.101.1		6	95.49	even	6
475.2.l.a.301.1		6	95.24	even	18
475.2.u.a.149.1		12	95.43	odd	36
475.2.u.a.149.2		12	95.62	odd	36
475.2.u.a.424.1		12	95.87	odd	12
475.2.u.a.424.2		12	95.68	odd	12
931.2.v.a.177.1		6	133.87	odd	6
931.2.v.a.263.1		6	133.5	odd	18
931.2.v.b.177.1		6	133.11	even	3
931.2.v.b.263.1		6	133.100	even	9
931.2.w.a.491.1		6	133.62	odd	18
931.2.w.a.785.1		6	133.125	odd	6
931.2.x.a.557.1		6	133.30	even	3
931.2.x.a.814.1		6	133.81	even	9
931.2.x.b.557.1		6	133.68	odd	6
931.2.x.b.814.1		6	133.24	odd	18
3249.2.a.s.1.1		3	57.32	even	18
3249.2.a.z.1.3		3	57.44	odd	18
5776.2.a.bi.1.2		3	76.51	even	18
5776.2.a.br.1.2		3	76.63	odd	18
9025.2.a.x.1.1		3	95.89	odd	18
9025.2.a.bd.1.3		3	95.44	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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.26604 + 0.460802i) q^{5} +(1.26604 + 1.06234i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +O(q^{10})\)	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.26604 + 0.460802i) q^{5} +(1.26604 + 1.06234i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +(0.592396 - 3.35965i) q^{10} +(0.592396 + 1.02606i) q^{11} +(1.43969 - 2.49362i) q^{12} +(2.08125 + 1.74638i) q^{13} +(3.64543 + 1.32683i) q^{14} +(-0.826352 + 0.300767i) q^{15} +(5.08512 - 4.26692i) q^{16} +(0.673648 + 3.82045i) q^{17} +6.51754 q^{18} -5.94356 q^{20} +(-0.173648 - 0.984808i) q^{21} +(2.29813 - 1.92836i) q^{22} +(4.75877 - 1.73205i) q^{23} +(-3.74510 - 1.36310i) q^{24} +(-2.43969 - 2.04715i) q^{25} +(3.43969 - 5.95772i) q^{26} +(-1.81908 - 3.15074i) q^{27} +(1.17365 - 6.65609i) q^{28} +(-0.807934 + 4.58202i) q^{29} +(1.11334 + 1.92836i) q^{30} +(1.91875 - 3.32337i) q^{31} +(-3.52094 - 2.95442i) q^{32} +(-0.726682 - 0.264490i) q^{33} +(9.23055 - 3.35965i) q^{34} +(-1.58125 + 1.32683i) q^{35} +(-1.97178 - 11.1825i) q^{36} -4.10607 q^{37} -1.77332 q^{39} +(1.42855 + 8.10170i) q^{40} +(-7.64930 + 6.41852i) q^{41} +(-2.37939 + 0.866025i) q^{42} +(8.17752 + 2.97637i) q^{43} +(-4.00387 - 3.35965i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.0996702 - 0.565258i) q^{47} +(-0.752374 + 4.26692i) q^{48} +(2.32635 + 4.02936i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(-1.93969 - 1.62760i) q^{51} +(-11.2626 - 4.09927i) q^{52} +(-2.76604 + 1.00676i) q^{53} +(-7.05690 + 5.92145i) q^{54} +(0.277189 + 1.57202i) q^{55} -9.35504 q^{56} +11.7811 q^{58} +(-0.683448 - 3.87603i) q^{59} +(2.97178 - 2.49362i) q^{60} +(4.24510 - 1.54509i) q^{61} +(-9.13088 - 3.32337i) q^{62} +(-3.02094 - 2.53487i) q^{63} +(0.819078 - 1.41868i) q^{64} +(1.83022 + 3.17004i) q^{65} +(-0.340022 + 1.92836i) q^{66} +(-0.674992 + 3.82807i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(4.00387 + 3.35965i) q^{70} +(6.51754 + 2.37219i) q^{71} +(-14.7690 + 5.37549i) q^{72} +(4.69459 - 3.93923i) q^{73} +(1.80541 + 10.2390i) q^{74} +2.07873 q^{75} -1.81521 q^{77} +(0.779715 + 4.42198i) q^{78} +(7.51367 - 6.30472i) q^{79} +(8.40420 - 3.05888i) q^{80} +(-5.02481 - 1.82888i) q^{81} +(19.3687 + 16.2523i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(2.20574 + 3.82045i) q^{84} +(-0.907604 + 5.14728i) q^{85} +(3.82635 - 21.7003i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(-3.61721 + 6.26519i) q^{88} +(-1.85844 - 1.55942i) q^{89} +(8.25150 + 3.00330i) q^{90} +(-3.91147 + 1.42366i) q^{91} +(-17.1138 + 14.3602i) q^{92} +(0.434945 + 2.46669i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(1.27972 + 7.25762i) q^{97} +(9.02481 - 7.57272i) q^{98} +(-2.86571 + 1.04303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} + 3 q^{12} + 15 q^{13} + 6 q^{14} - 6 q^{15} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} + 6 q^{28} + 6 q^{29} + 9 q^{31} - 18 q^{32} + 9 q^{33} + 18 q^{34} - 12 q^{35} + 3 q^{36} - 24 q^{39} + 9 q^{40} - 6 q^{41} - 3 q^{42} + 24 q^{43} - 15 q^{45} - 18 q^{46} + 15 q^{47} - 21 q^{48} + 15 q^{49} - 15 q^{50} - 6 q^{51} - 21 q^{52} - 12 q^{53} - 6 q^{54} - 9 q^{55} - 6 q^{56} + 36 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 3 q^{62} - 15 q^{63} - 12 q^{64} - 12 q^{65} + 18 q^{66} + 6 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} + 30 q^{75} - 18 q^{77} - 21 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 45 q^{82} + 3 q^{84} - 9 q^{85} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 3 q^{89} + 9 q^{90} - 3 q^{91} - 30 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 + 3 * q^12 + 15 * q^13 + 6 * q^14 - 6 * q^15 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 + 6 * q^28 + 6 * q^29 + 9 * q^31 - 18 * q^32 + 9 * q^33 + 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 + 9 * q^40 - 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 - 18 * q^46 + 15 * q^47 - 21 * q^48 + 15 * q^49 - 15 * q^50 - 6 * q^51 - 21 * q^52 - 12 * q^53 - 6 * q^54 - 9 * q^55 - 6 * q^56 + 36 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 - 12 * q^65 + 18 * q^66 + 6 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 + 30 * q^75 - 18 * q^77 - 21 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 + 3 * q^84 - 9 * q^85 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 3 * q^89 + 9 * q^90 - 3 * q^91 - 30 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 27 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more