LMFDB - Embedded newform 225.2.q.a.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.942959 + 1.04726i) q^{2} +(1.04996 - 1.37753i) q^{3} +(0.00147092 + 0.0139948i) q^{4} +(-2.16654 - 0.553283i) q^{5} +(0.452565 + 2.39853i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 - 1.66830i) q^{8} +(-0.795170 - 2.89270i) q^{9} +O(q^{10})$	\(q+(-0.942959 + 1.04726i) q^{2} +(1.04996 - 1.37753i) q^{3} +(0.00147092 + 0.0139948i) q^{4} +(-2.16654 - 0.553283i) q^{5} +(0.452565 + 2.39853i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 - 1.66830i) q^{8} +(-0.795170 - 2.89270i) q^{9} +(2.62239 - 1.74721i) q^{10} +(-2.10260 + 2.33518i) q^{11} +(0.0208227 + 0.0126678i) q^{12} +(0.989570 + 1.09903i) q^{13} +(6.85500 + 1.45708i) q^{14} +(-3.03694 + 2.40354i) q^{15} +(3.88487 - 0.825754i) q^{16} +(-2.39081 - 1.73703i) q^{17} +(3.77922 + 1.89494i) q^{18} +(-1.51211 - 1.09861i) q^{19} +(0.00455631 - 0.0311342i) q^{20} +(-8.54345 - 1.09669i) q^{21} +(-0.462874 - 4.40395i) q^{22} +(6.51302 + 1.38439i) q^{23} +(-4.70908 + 1.41146i) q^{24} +(4.38776 + 2.39741i) q^{25} -2.08409 q^{26} +(-4.81967 - 1.94185i) q^{27} +(0.0566152 - 0.0411334i) q^{28} +(-3.73405 - 1.66251i) q^{29} +(0.346571 - 5.44691i) q^{30} +(5.95196 - 2.64998i) q^{31} +(0.0398007 - 0.0689368i) q^{32} +(1.00913 + 5.34824i) q^{33} +(4.07356 - 0.865861i) q^{34} +(3.00427 + 10.7065i) q^{35} +(0.0393133 - 0.0153832i) q^{36} +(1.50355 - 4.62746i) q^{37} +(2.57639 - 0.547629i) q^{38} +(2.55295 - 0.209225i) q^{39} +(4.05181 + 4.88490i) q^{40} +(-1.63494 - 1.81578i) q^{41} +(9.20464 - 7.91309i) q^{42} +(-1.92193 - 3.32888i) q^{43} +(-0.0357732 - 0.0259908i) q^{44} +(0.122284 + 6.70709i) q^{45} +(-7.59132 + 5.51542i) q^{46} +(1.53134 + 0.681798i) q^{47} +(2.94145 - 6.21852i) q^{48} +(-8.86554 + 15.3556i) q^{49} +(-6.64819 + 2.33447i) q^{50} +(-4.90306 + 1.46960i) q^{51} +(-0.0139252 + 0.0154655i) q^{52} +(0.228304 - 0.165873i) q^{53} +(6.57837 - 3.21638i) q^{54} +(5.84738 - 3.89591i) q^{55} +(-1.47541 + 14.0376i) q^{56} +(-3.10103 + 0.929477i) q^{57} +(5.26214 - 2.34285i) q^{58} +(-2.02413 - 2.24803i) q^{59} +(-0.0381043 - 0.0389661i) q^{60} +(-5.19072 + 5.76488i) q^{61} +(-2.83723 + 8.73208i) q^{62} +(-10.4810 + 10.6174i) q^{63} +(2.48928 + 7.66123i) q^{64} +(-1.53587 - 2.92860i) q^{65} +(-6.55257 - 3.98635i) q^{66} +(-10.4257 + 4.64182i) q^{67} +(0.0207927 - 0.0360141i) q^{68} +(8.74544 - 7.51832i) q^{69} +(-14.0454 - 6.94956i) q^{70} +(13.0547 - 9.48483i) q^{71} +(-3.00001 + 7.96887i) q^{72} +(-2.03962 - 6.27730i) q^{73} +(3.42837 + 5.93811i) q^{74} +(7.90947 - 3.52707i) q^{75} +(0.0131507 - 0.0227777i) q^{76} +(15.2852 + 3.24898i) q^{77} +(-2.18821 + 2.87090i) q^{78} +(7.40257 + 3.29584i) q^{79} +(-8.87358 - 0.360405i) q^{80} +(-7.73541 + 4.60037i) q^{81} +3.44328 q^{82} +(1.00657 - 9.57689i) q^{83} +(0.00278130 - 0.121177i) q^{84} +(4.21871 + 5.08612i) q^{85} +(5.29851 + 1.12623i) q^{86} +(-6.21075 + 3.39820i) q^{87} +(8.72383 - 1.85431i) q^{88} +(0.845142 + 2.60108i) q^{89} +(-7.13939 - 6.19644i) q^{90} +(2.27269 - 6.99461i) q^{91} +(-0.00979414 + 0.0931851i) q^{92} +(2.59889 - 10.9814i) q^{93} +(-2.15801 + 0.960809i) q^{94} +(2.66820 + 3.21681i) q^{95} +(-0.0531733 - 0.127208i) q^{96} +(-8.97780 - 3.99717i) q^{97} +(-7.72146 - 23.7642i) q^{98} +(8.42689 + 4.22533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.942959	+	1.04726i	−0.666772	+	0.740526i	−0.977723	−	0.209900i	$-0.932686\pi$
$2$	−0.942959	+	1.04726i	−0.666772	+	0.740526i	0.310950	+	0.950426i	$0.399353\pi$
$3$	1.04996	−	1.37753i	0.606194	−	0.795317i
$3$	1.04996	−	1.37753i	0.606194	−	0.795317i
$4$	0.00147092	+	0.0139948i	0.000735459	+	0.00699742i
$5$	−2.16654	−	0.553283i	−0.968904	−	0.247436i
$5$	−2.16654	−	0.553283i	−0.968904	−	0.247436i
$6$	0.452565	+	2.39853i	0.184759	+	0.979198i
$7$	−2.48652	−	4.30678i	−0.939815	−	1.62781i	−0.765813	−	0.643063i	$-0.777663\pi$
$7$	−2.48652	−	4.30678i	−0.939815	−	1.62781i	−0.174002	−	0.984745i	$-0.555670\pi$
$8$	−2.29622	−	1.66830i	−0.811838	−	0.589835i
$9$	−0.795170	−	2.89270i	−0.265057	−	0.964233i
$10$	2.62239	−	1.74721i	0.829271	−	0.552515i
$11$	−2.10260	+	2.33518i	−0.633959	+	0.704082i	−0.971449	−	0.237246i	$-0.923755\pi$
$11$	−2.10260	+	2.33518i	−0.633959	+	0.704082i	0.337491	+	0.941329i	$0.390422\pi$
$12$	0.0208227	+	0.0126678i	0.00601100	+	0.00365688i
$13$	0.989570	+	1.09903i	0.274457	+	0.304816i	0.864577	−	0.502500i	$-0.167586\pi$
$13$	0.989570	+	1.09903i	0.274457	+	0.304816i	−0.590120	+	0.807316i	$0.700920\pi$
$14$	6.85500	+	1.45708i	1.83208	+	0.389420i
$15$	−3.03694	+	2.40354i	−0.784134	+	0.620592i
$16$	3.88487	−	0.825754i	0.971217	−	0.206439i
$17$	−2.39081	−	1.73703i	−0.579857	−	0.421291i	0.258816	−	0.965927i	$-0.416668\pi$
$17$	−2.39081	−	1.73703i	−0.579857	−	0.421291i	−0.838672	+	0.544636i	$0.816668\pi$
$18$	3.77922	+	1.89494i	0.890772	+	0.446643i
$19$	−1.51211	−	1.09861i	−0.346902	−	0.252039i	0.400666	−	0.916224i	$-0.368779\pi$
$19$	−1.51211	−	1.09861i	−0.346902	−	0.252039i	−0.747568	+	0.664185i	$0.768779\pi$
$20$	0.00455631	−	0.0311342i	0.00101882	−	0.00696181i
$21$	−8.54345	−	1.09669i	−1.86433	−	0.239317i
$22$	−0.462874	−	4.40395i	−0.0986850	−	0.938925i
$23$	6.51302	+	1.38439i	1.35806	+	0.288664i	0.828681	−	0.559722i	$-0.189092\pi$
$23$	6.51302	+	1.38439i	1.35806	+	0.288664i	0.529378	+	0.848386i	$0.322425\pi$
$24$	−4.70908	+	1.41146i	−0.961237	+	0.288114i
$25$	4.38776	+	2.39741i	0.877551	+	0.479483i
$26$	−2.08409			−0.408725
$27$	−4.81967	−	1.94185i	−0.927546	−	0.373709i
$28$	0.0566152	−	0.0411334i	0.0106993	−	0.00777347i
$29$	−3.73405	−	1.66251i	−0.693396	−	0.308720i	0.0296100	−	0.999562i	$-0.490573\pi$
$29$	−3.73405	−	1.66251i	−0.693396	−	0.308720i	−0.723006	+	0.690842i	$0.757240\pi$
$30$	0.346571	−	5.44691i	0.0632749	−	0.994465i
$31$	5.95196	−	2.64998i	1.06900	−	0.475951i	0.204650	−	0.978835i	$-0.434394\pi$
$31$	5.95196	−	2.64998i	1.06900	−	0.475951i	0.864354	+	0.502884i	$0.167728\pi$
$32$	0.0398007	−	0.0689368i	0.00703584	−	0.0121864i
$33$	1.00913	+	5.34824i	0.175666	+	0.931008i
$34$	4.07356	−	0.865861i	0.698609	−	0.148494i
$35$	3.00427	+	10.7065i	0.507814	+	1.80973i
$36$	0.0393133	−	0.0153832i	0.00655221	−	0.00256387i
$37$	1.50355	−	4.62746i	0.247182	−	0.760749i	−0.748088	−	0.663600i	$-0.769028\pi$
$37$	1.50355	−	4.62746i	0.247182	−	0.760749i	0.995270	−	0.0971489i	$-0.0309723\pi$
$38$	2.57639	−	0.547629i	0.417946	−	0.0888372i
$39$	2.55295	−	0.209225i	0.408799	−	0.0335028i
$40$	4.05181	+	4.88490i	0.640647	+	0.772371i
$41$	−1.63494	−	1.81578i	−0.255335	−	0.283578i	0.601826	−	0.798627i	$-0.294440\pi$
$41$	−1.63494	−	1.81578i	−0.255335	−	0.283578i	−0.857160	+	0.515050i	$0.827774\pi$
$42$	9.20464	−	7.91309i	1.42031	−	1.22102i
$43$	−1.92193	−	3.32888i	−0.293091	−	0.507649i	0.681448	−	0.731867i	$-0.261351\pi$
$43$	−1.92193	−	3.32888i	−0.293091	−	0.507649i	−0.974539	+	0.224218i	$0.928017\pi$
$44$	−0.0357732	−	0.0259908i	−0.00539301	−	0.00391825i
$45$	0.122284	+	6.70709i	0.0182290	+	0.999834i
$46$	−7.59132	+	5.51542i	−1.11928	+	0.813204i
$47$	1.53134	+	0.681798i	0.223369	+	0.0994504i	0.515370	−	0.856968i	$-0.327654\pi$
$47$	1.53134	+	0.681798i	0.223369	+	0.0994504i	−0.292001	+	0.956418i	$0.594321\pi$
$48$	2.94145	−	6.21852i	0.424562	−	0.897567i
$49$	−8.86554	+	15.3556i	−1.26651	+	2.19365i
$50$	−6.64819	+	2.33447i	−0.940196	+	0.330143i
$51$	−4.90306	+	1.46960i	−0.686565	+	0.205786i
$52$	−0.0139252	+	0.0154655i	−0.00193107	+	0.00214467i
$53$	0.228304	−	0.165873i	0.0313600	−	0.0227844i	−0.571995	−	0.820257i	$-0.693830\pi$
$53$	0.228304	−	0.165873i	0.0313600	−	0.0227844i	0.603355	+	0.797473i	$0.293830\pi$
$54$	6.57837	−	3.21638i	0.895203	−	0.437693i
$55$	5.84738	−	3.89591i	0.788460	−	0.525324i
$56$	−1.47541	+	14.0376i	−0.197160	+	1.87585i
$57$	−3.10103	+	0.929477i	−0.410741	+	0.123112i
$58$	5.26214	−	2.34285i	0.690952	−	0.307632i
$59$	−2.02413	−	2.24803i	−0.263520	−	0.292668i	0.596835	−	0.802364i	$-0.296425\pi$
$59$	−2.02413	−	2.24803i	−0.263520	−	0.292668i	−0.860355	+	0.509696i	$0.829758\pi$
$60$	−0.0381043	−	0.0389661i	−0.00491924	−	0.00503050i
$61$	−5.19072	+	5.76488i	−0.664603	+	0.738117i	−0.977329	−	0.211727i	$-0.932091\pi$
$61$	−5.19072	+	5.76488i	−0.664603	+	0.738117i	0.312725	+	0.949844i	$0.398758\pi$
$62$	−2.83723	+	8.73208i	−0.360328	+	1.10898i
$63$	−10.4810	+	10.6174i	−1.32048	+	1.33766i
$64$	2.48928	+	7.66123i	0.311161	+	0.957654i
$65$	−1.53587	−	2.92860i	−0.190501	−	0.363248i
$66$	−6.55257	−	3.98635i	−0.806565	−	0.490685i
$67$	−10.4257	+	4.64182i	−1.27370	+	0.567088i	−0.928462	−	0.371427i	$-0.878869\pi$
$67$	−10.4257	+	4.64182i	−1.27370	+	0.567088i	−0.345239	+	0.938515i	$0.612202\pi$
$68$	0.0207927	−	0.0360141i	0.00252149	−	0.00436735i
$69$	8.74544	−	7.51832i	1.05283	−	0.905100i
$70$	−14.0454	−	6.94956i	−1.67875	−	0.830632i
$71$	13.0547	−	9.48483i	1.54931	−	1.12564i	0.605175	−	0.796092i	$-0.293103\pi$
$71$	13.0547	−	9.48483i	1.54931	−	1.12564i	0.944138	−	0.329550i	$-0.106897\pi$
$72$	−3.00001	+	7.96887i	−0.353555	+	0.939141i
$73$	−2.03962	−	6.27730i	−0.238719	−	0.734703i	−0.996606	−	0.0823167i	$-0.973768\pi$
$73$	−2.03962	−	6.27730i	−0.238719	−	0.734703i	0.757887	−	0.652386i	$-0.226232\pi$
$74$	3.42837	+	5.93811i	0.398540	+	0.690291i
$75$	7.90947	−	3.52707i	0.913307	−	0.407271i
$76$	0.0131507	−	0.0227777i	0.00150849	−	0.00261278i
$77$	15.2852	+	3.24898i	1.74191	+	0.370255i
$78$	−2.18821	+	2.87090i	−0.247767	+	0.325065i
$79$	7.40257	+	3.29584i	0.832854	+	0.370811i	0.778449	−	0.627708i	$-0.216007\pi$
$79$	7.40257	+	3.29584i	0.832854	+	0.370811i	0.0544056	+	0.998519i	$0.482674\pi$
$80$	−8.87358	−	0.360405i	−0.992097	−	0.0402944i
$81$	−7.73541	+	4.60037i	−0.859490	+	0.511153i
$82$	3.44328			0.380247
$83$	1.00657	−	9.57689i	0.110486	−	1.05120i	−0.789043	−	0.614338i	$-0.789423\pi$
$83$	1.00657	−	9.57689i	0.110486	−	1.05120i	0.899528	−	0.436862i	$-0.143910\pi$
$84$	0.00278130	−	0.121177i	0.000303465	−	0.0132215i
$85$	4.21871	+	5.08612i	0.457583	+	0.551667i
$86$	5.29851	+	1.12623i	0.571353	+	0.121445i
$87$	−6.21075	+	3.39820i	−0.665863	+	0.364325i
$88$	8.72383	−	1.85431i	0.929964	−	0.197670i
$89$	0.845142	+	2.60108i	0.0895849	+	0.275714i	0.985805	−	0.167896i	$-0.0536974\pi$
$89$	0.845142	+	2.60108i	0.0895849	+	0.275714i	−0.896220	+	0.443610i	$0.853697\pi$
$90$	−7.13939	−	6.19644i	−0.752557	−	0.653163i
$91$	2.27269	−	6.99461i	0.238242	−	0.733234i
$92$	−0.00979414	+	0.0931851i	−0.00102111	+	0.00971521i
$93$	2.59889	−	10.9814i	0.269492	−	1.13871i
$94$	−2.15801	+	0.960809i	−0.222582	+	0.0990999i
$95$	2.66820	+	3.21681i	0.273751	+	0.330038i
$96$	−0.0531733	−	0.127208i	−0.00542698	−	0.0129831i
$97$	−8.97780	−	3.99717i	−0.911557	−	0.405851i	−0.103279	−	0.994652i	$-0.532934\pi$
$97$	−8.97780	−	3.99717i	−0.911557	−	0.405851i	−0.808278	+	0.588801i	$0.799600\pi$
$98$	−7.72146	−	23.7642i	−0.779985	−	2.40055i
$99$	8.42689	+	4.22533i	0.846934	+	0.424662i
$100$	−0.0270974	+	0.0649324i	−0.00270974	+	0.00649324i
$101$	−3.76987	−	6.52961i	−0.375116	−	0.649720i	0.615228	−	0.788349i	$-0.289064\pi$
$101$	−3.76987	−	6.52961i	−0.375116	−	0.649720i	−0.990344	+	0.138629i	$0.955731\pi$
$102$	3.08432	−	6.52056i	0.305393	−	0.645631i
$103$	−0.0323012	−	0.307325i	−0.00318273	−	0.0302817i	0.992815	−	0.119657i	$-0.0381795\pi$
$103$	−0.0323012	−	0.307325i	−0.00318273	−	0.0302817i	−0.995998	+	0.0893755i	$0.971513\pi$
$104$	−0.438760	−	4.17452i	−0.0430239	−	0.409346i
$105$	17.9029	+	7.10296i	1.74715	+	0.693178i
$106$	−0.0415693	+	0.395506i	−0.00403757	+	0.0384149i
$107$	10.6092			1.02563			0.512814	−	0.858500i	$-0.328603\pi$
$107$	10.6092			1.02563			0.512814	+	0.858500i	$0.328603\pi$
$108$	0.0200865	−	0.0703069i	0.00193283	−	0.00676528i
$109$	2.72546	−	8.38810i	0.261052	−	0.803434i	−0.731525	−	0.681814i	$-0.761191\pi$
$109$	2.72546	−	8.38810i	0.261052	−	0.803434i	0.992577	−	0.121620i	$-0.0388088\pi$
$110$	−1.43380	+	9.79742i	−0.136707	+	0.934147i
$111$	−4.79578	−	6.92983i	−0.455196	−	0.657750i
$112$	−13.2161	−	14.6780i	−1.24881	−	1.38694i
$113$	−5.87451	−	6.52430i	−0.552627	−	0.613755i	0.400510	−	0.916292i	$-0.368833\pi$
$113$	−5.87451	−	6.52430i	−0.552627	−	0.613755i	−0.953138	+	0.302537i	$0.902166\pi$
$114$	1.95073	−	4.12404i	0.182703	−	0.386252i
$115$	−13.3447	−	6.60286i	−1.24440	−	0.615720i
$116$	0.0177741	−	0.0547029i	0.00165028	−	0.00507904i
$117$	2.39228	−	3.73644i	0.221167	−	0.345434i
$118$	4.26294			0.392436
$119$	−1.53619	+	14.6158i	−0.140822	+	1.33983i
$120$	10.9833	−	0.452531i	1.00264	−	0.0413102i
$121$	0.117700	+	1.11984i	0.0107000	+	0.101804i
$122$	−1.14270	−	10.8721i	−0.103455	−	0.984312i
$123$	−4.21792	+	0.345676i	−0.380317	+	0.0311686i
$124$	0.0458410	+	0.0793989i	0.00411664	+	0.00713023i
$125$	−8.17978	−	7.62175i	−0.731622	−	0.681710i
$126$	−1.23601	−	20.9881i	−0.110113	−	1.86977i
$127$	2.46680	+	7.59204i	0.218894	+	0.673685i	0.998854	+	0.0478565i	$0.0152390\pi$
$127$	2.46680	+	7.59204i	0.218894	+	0.673685i	−0.779961	+	0.625829i	$0.784761\pi$
$128$	−10.2252	−	4.55254i	−0.903785	−	0.402391i
$129$	−6.60357	−	0.847676i	−0.581412	−	0.0746337i
$130$	4.51527	+	1.15309i	0.396015	+	0.101133i
$131$	10.0119	−	4.45757i	0.874740	−	0.389459i	0.0802777	−	0.996773i	$-0.474419\pi$
$131$	10.0119	−	4.45757i	0.874740	−	0.389459i	0.794463	+	0.607313i	$0.207753\pi$
$132$	−0.0733634	+	0.0219894i	−0.00638547	+	0.00191393i
$133$	−0.971588	+	9.24404i	−0.0842474	+	0.801560i
$134$	4.96980	−	15.2955i	0.429325	−	1.32133i
$135$	9.36760	+	6.87372i	0.806235	+	0.591596i
$136$	2.59195	+	7.97720i	0.222258	+	0.684039i
$137$	6.73097	−	1.43071i	0.575066	−	0.122234i	0.0888069	−	0.996049i	$-0.471695\pi$
$137$	6.73097	−	1.43071i	0.575066	−	0.122234i	0.486259	+	0.873815i	$0.338361\pi$
$138$	−0.372934	+	16.2482i	−0.0317463	+	1.38314i
$139$	−7.39649	−	1.57217i	−0.627362	−	0.133350i	−0.116750	−	0.993161i	$-0.537248\pi$
$139$	−7.39649	−	1.57217i	−0.627362	−	0.133350i	−0.510612	+	0.859811i	$0.670581\pi$
$140$	−0.145417	+	0.0577927i	−0.0122900	+	0.00488437i
$141$	2.54704	−	1.39361i	0.214500	−	0.117363i
$142$	−2.37699	+	22.6155i	−0.199472	+	1.89785i
$143$	−4.64710			−0.388610
$144$	−5.47779	−	10.5811i	−0.456482	−	0.881761i
$145$	7.17012	+	5.66787i	0.595446	+	0.470691i
$146$	8.49726	+	3.78322i	0.703238	+	0.313102i
$147$	11.8443	+	28.3353i	0.976900	+	2.33705i
$148$	0.0669721	+	0.0142354i	0.00550508	+	0.00117014i
$149$	7.49125	−	12.9752i	0.613707	−	1.06297i	−0.376903	−	0.926253i	$-0.623011\pi$
$149$	7.49125	−	12.9752i	0.613707	−	1.06297i	0.990610	−	0.136719i	$-0.0436558\pi$
$150$	−3.76454	+	11.6092i	−0.307373	+	0.947885i
$151$	2.80456	+	4.85765i	0.228232	+	0.395310i	0.957284	−	0.289149i	$-0.0933722\pi$
$151$	2.80456	+	4.85765i	0.228232	+	0.395310i	−0.729052	+	0.684458i	$0.760039\pi$
$152$	1.63932	+	5.04532i	0.132967	+	0.409230i
$153$	−3.12359	+	8.29712i	−0.252527	+	0.670783i
$154$	−17.8159	+	12.9440i	−1.43564	+	1.04306i
$155$	−14.3613	+	2.44817i	−1.15353	+	0.196641i
$156$	0.00668326	+	0.0354204i	0.000535089	+	0.00283590i
$157$	7.68556	−	13.3118i	0.613374	−	1.06240i	−0.377293	−	0.926094i	$-0.623145\pi$
$157$	7.68556	−	13.3118i	0.613374	−	1.06240i	0.990667	−	0.136302i	$-0.0435216\pi$
$158$	−10.4319	+	4.64459i	−0.829919	+	0.369504i
$159$	0.0112158	−	0.488656i	0.000889469	−	0.0387529i
$160$	−0.124371	+	0.127333i	−0.00983241	+	0.0100666i
$161$	−10.2325	−	31.4924i	−0.806434	−	2.48195i
$162$	2.47638	−	12.4390i	0.194562	−	0.977297i
$163$	−6.69457	+	20.6038i	−0.524359	+	1.61381i	0.241221	+	0.970470i	$0.422452\pi$
$163$	−6.69457	+	20.6038i	−0.524359	+	1.61381i	−0.765580	+	0.643341i	$0.777548\pi$
$164$	0.0230068	−	0.0255516i	0.00179653	−	0.00199525i
$165$	0.772781	−	12.1455i	0.0601609	−	0.945524i
$166$	9.08036	+	10.0848i	0.704772	+	0.782729i
$167$	−15.0769	+	6.71267i	−1.16669	+	0.519442i	−0.896360	−	0.443327i	$-0.853798\pi$
$167$	−15.0769	+	6.71267i	−1.16669	+	0.519442i	−0.270325	+	0.962769i	$0.587131\pi$
$168$	17.7881	+	16.7713i	1.37238	+	1.29394i
$169$	1.13025	−	10.7537i	0.0869427	−	0.827204i
$170$	−9.30457	−	0.377909i	−0.713628	−	0.0289843i
$171$	−1.97557	+	5.24766i	−0.151076	+	0.401299i
$172$	0.0437602	−	0.0317936i	0.00333668	−	0.00242424i
$173$	8.08314	−	8.97723i	0.614550	−	0.682527i	−0.352879	−	0.935669i	$-0.614797\pi$
$173$	8.08314	−	8.97723i	0.614550	−	0.682527i	0.967429	+	0.253142i	$0.0814641\pi$
$174$	2.29768	−	9.70865i	0.174187	−	0.736011i
$175$	−0.585110	−	24.8583i	−0.0442302	−	1.87911i
$176$	−6.24005	+	10.8081i	−0.470362	+	0.814690i
$177$	−5.22198	+	0.427963i	−0.392508	+	0.0321677i
$178$	−3.52095	−	1.56763i	−0.263906	−	0.117499i
$179$	−10.7597	+	7.81740i	−0.804220	+	0.584300i	−0.912149	−	0.409859i	$-0.865578\pi$
$179$	−10.7597	+	7.81740i	−0.804220	+	0.584300i	0.107929	+	0.994159i	$0.465578\pi$
$180$	−0.0936848	+	0.0115769i	−0.00698286	+	0.000862893i
$181$	−16.9365	−	12.3051i	−1.25888	−	0.914629i	−0.260176	−	0.965561i	$-0.583781\pi$
$181$	−16.9365	−	12.3051i	−1.25888	−	0.914629i	−0.998702	+	0.0509324i	$0.983781\pi$
$182$	5.18214	+	8.97573i	0.384126	+	0.665325i
$183$	2.49124	+	13.2033i	0.184158	+	0.976012i
$184$	−12.6458	−	14.0446i	−0.932259	−	1.03538i
$185$	−5.81779	+	9.19366i	−0.427732	+	0.675931i
$186$	9.04972	+	13.0767i	0.663558	+	0.958830i
$187$	9.08319	−	1.93069i	0.664228	−	0.141186i
$188$	−0.00728918	+	0.0224338i	−0.000531618	+	0.00163615i
$189$	3.62110	+	25.5857i	0.263396	+	1.86108i
$190$	−5.88484	−	0.239016i	−0.426931	−	0.0173400i
$191$	4.74448	−	1.00847i	0.343299	−	0.0729704i	−0.0330360	−	0.999454i	$-0.510518\pi$
$191$	4.74448	−	1.00847i	0.343299	−	0.0729704i	0.376335	+	0.926484i	$0.377184\pi$
$192$	13.1672	+	4.61492i	0.950262	+	0.333053i
$193$	1.77174	−	3.06874i	0.127533	−	0.220893i	−0.795187	−	0.606364i	$-0.792628\pi$
$193$	1.77174	−	3.06874i	0.127533	−	0.220893i	0.922720	+	0.385471i	$0.125961\pi$
$194$	12.6518	−	5.63293i	0.908345	−	0.404421i
$195$	−5.64682	−	0.959211i	−0.404377	−	0.0686905i
$196$	−0.227939	−	0.101485i	−0.0162814	−	0.00724894i
$197$	−17.3425	+	12.6000i	−1.23560	+	0.897715i	−0.997297	−	0.0734759i	$-0.976591\pi$
$197$	−17.3425	+	12.6000i	−1.23560	+	0.897715i	−0.238302	+	0.971191i	$0.576591\pi$
$198$	−12.3712	+	4.84084i	−0.879186	+	0.344024i
$199$	18.9405			1.34265			0.671327	−	0.741162i	$-0.265725\pi$
$199$	18.9405			1.34265			0.671327	+	0.741162i	$0.265725\pi$
$200$	−6.07566	−	12.8251i	−0.429614	−	0.906873i
$201$	−4.55232	+	19.2354i	−0.321096	+	1.35676i
$202$	10.3930	+	2.20911i	0.731252	+	0.155432i
$203$	2.12474	+	20.2156i	0.149128	+	1.41886i
$204$	−0.0277789	−	0.0664559i	−0.00194491	−	0.00465284i
$205$	2.53751	+	4.83855i	0.177228	+	0.337939i
$206$	0.352309	+	0.255967i	0.0245465	+	0.0178341i
$207$	−1.17435	−	19.9410i	−0.0816229	−	1.38600i
$208$	4.75188	+	3.45244i	0.329483	+	0.239384i
$209$	5.74482	−	1.22110i	0.397378	−	0.0844652i
$210$	−24.3204	+	12.0512i	−1.67826	+	0.831614i
$211$	22.2117	+	4.72124i	1.52911	+	0.325023i	0.894239	−	0.447591i	$-0.147718\pi$
$211$	22.2117	+	4.72124i	1.52911	+	0.325023i	0.634876	+	0.772614i	$0.281051\pi$
$212$	0.00265718	+	0.00295110i	0.000182496	+	0.000202682i
$213$	0.641333	−	27.9420i	0.0439434	−	1.91455i
$214$	−10.0040	+	11.1106i	−0.683861	+	0.759504i
$215$	2.32212	+	8.27551i	0.158367	+	0.564385i
$216$	7.82746	+	12.4996i	0.532591	+	0.850490i
$217$	−26.2125	−	19.0445i	−1.77942	−	1.29283i
$218$	6.21454	+	10.7639i	0.420902	+	0.729023i
$219$	−10.7887	−	3.78128i	−0.729032	−	0.255515i
$220$	0.0631237	+	0.0761026i	0.00425580	+	0.00513084i
$221$	−0.456833	−	4.34648i	−0.0307299	−	0.292376i
$222$	11.7796	+	1.51210i	0.790593	+	0.101485i
$223$	14.4275	−	16.0233i	0.966135	−	1.07300i	−0.0311608	−	0.999514i	$-0.509920\pi$
$223$	14.4275	−	16.0233i	0.966135	−	1.07300i	0.997296	−	0.0734876i	$-0.0234129\pi$
$224$	−0.395861			−0.0264496
$225$	3.44598	−	14.5988i	0.229732	−	0.973254i
$226$	12.3721			0.822978
$227$	−1.45263	+	1.61331i	−0.0964143	+	0.107079i	−0.789421	−	0.613852i	$-0.789619\pi$
$227$	−1.45263	+	1.61331i	−0.0964143	+	0.107079i	0.693007	+	0.720931i	$0.256286\pi$
$228$	−0.0175692	−	0.0420312i	−0.00116355	−	0.00278358i
$229$	2.01777	+	19.1978i	0.133338	+	1.26863i	0.832645	+	0.553807i	$0.186825\pi$
$229$	2.01777	+	19.1978i	0.133338	+	1.26863i	−0.699307	+	0.714821i	$0.746508\pi$
$230$	19.4985	−	7.74920i	1.28569	−	0.510967i
$231$	20.5244	−	17.6446i	1.35041	−	1.16093i
$232$	5.80065	+	10.0470i	0.380832	+	0.659620i
$233$	21.4951	+	15.6171i	1.40819	+	1.02311i	0.993583	+	0.113108i	$0.0360805\pi$
$233$	21.4951	+	15.6171i	1.40819	+	1.02311i	0.414606	+	0.910001i	$0.363920\pi$
$234$	1.65721	+	6.02866i	0.108335	+	0.394106i
$235$	−2.94048	−	2.32440i	−0.191816	−	0.151627i
$236$	0.0284835	−	0.0316341i	0.00185412	−	0.00205920i
$237$	12.3125	−	6.73676i	0.799783	−	0.437599i
$238$	−13.8580	−	15.3909i	−0.898283	−	0.997644i
$239$	7.22328	+	1.53536i	0.467235	+	0.0993139i	0.435512	−	0.900183i	$-0.356567\pi$
$239$	7.22328	+	1.53536i	0.467235	+	0.0993139i	0.0317229	+	0.999497i	$0.489901\pi$
$240$	−9.81337	+	11.8452i	−0.633450	+	0.764605i
$241$	13.7901	−	2.93118i	0.888300	−	0.188814i	0.258908	−	0.965902i	$-0.416637\pi$
$241$	13.7901	−	2.93118i	0.888300	−	0.188814i	0.629392	+	0.777088i	$0.283304\pi$
$242$	−1.28376	−	0.932703i	−0.0825229	−	0.0599564i
$243$	−1.78472	+	15.4860i	−0.114490	+	0.993424i
$244$	−0.0883137	−	0.0641637i	−0.00565371	−	0.00410766i
$245$	27.7035	−	28.3632i	1.76991	−	1.81206i
$246$	3.61531	−	4.74322i	0.230504	−	0.302417i
$247$	−0.288932	−	2.74901i	−0.0183843	−	0.174915i
$248$	−18.0880	−	3.84473i	−1.14859	−	0.244140i
$249$	−12.1356	−	11.4419i	−0.769061	−	0.725103i
$250$	15.6952	−	1.37937i	0.992650	−	0.0872393i
$251$	23.6990			1.49587			0.747934	−	0.663773i	$-0.231046\pi$
$251$	23.6990			1.49587			0.747934	+	0.663773i	$0.231046\pi$
$252$	−0.164005	−	0.131063i	−0.0103314	−	0.00825618i
$253$	−16.9271	+	12.2982i	−1.06420	+	0.773184i
$254$	−10.2770	−	4.57559i	−0.644833	−	0.287098i
$255$	11.4358	−	0.471172i	0.716135	−	0.0295059i
$256$	−0.308513	+	0.137359i	−0.0192821	+	0.00858493i
$257$	−3.54893	+	6.14694i	−0.221376	+	0.383435i	−0.955226	−	0.295877i	$-0.904388\pi$
$257$	−3.54893	+	6.14694i	−0.221376	+	0.383435i	0.733850	+	0.679312i	$0.237722\pi$
$258$	7.11464	−	6.11635i	0.442938	−	0.380787i
$259$	−23.6680	+	5.03079i	−1.47066	+	0.312598i
$260$	0.0387261	−	0.0258019i	0.00240169	−	0.00160017i
$261$	−1.83993	+	12.1235i	−0.113889	+	0.750424i
$262$	−4.77253	+	14.6883i	−0.294848	+	0.907449i
$263$	−14.4622	+	3.07404i	−0.891777	+	0.189553i	−0.630942	−	0.775830i	$-0.717331\pi$
$263$	−14.4622	+	3.07404i	−0.891777	+	0.189553i	−0.260836	+	0.965383i	$0.583998\pi$
$264$	6.60531	−	13.9643i	0.406529	−	0.859442i
$265$	−0.586404	+	0.233053i	−0.0360225	+	0.0143163i
$266$	−8.76476	−	9.73426i	−0.537402	−	0.596846i
$267$	4.47043	+	1.56682i	0.273586	+	0.0958879i
$268$	−0.0802969	−	0.139078i	−0.00490491	−	0.00849556i
$269$	5.30527	+	3.85450i	0.323468	+	0.235013i	0.737654	−	0.675179i	$-0.235934\pi$
$269$	5.30527	+	3.85450i	0.323468	+	0.235013i	−0.414186	+	0.910192i	$0.635934\pi$
$270$	−16.0318	+	3.32869i	−0.975667	+	0.202578i
$271$	−4.15808	+	3.02102i	−0.252585	+	0.183514i	−0.706872	−	0.707342i	$-0.749894\pi$
$271$	−4.15808	+	3.02102i	−0.252585	+	0.183514i	0.454286	+	0.890856i	$0.349894\pi$
$272$	−10.7223	−	4.77389i	−0.650137	−	0.289460i
$273$	−7.24905	−	10.4747i	−0.438732	−	0.633961i
$274$	−4.84870	+	8.39819i	−0.292920	+	0.507353i
$275$	−14.8241	+	5.20538i	−0.893927	+	0.313896i
$276$	0.118082	+	0.111332i	0.00710768	+	0.00670141i
$277$	−3.81783	+	4.24013i	−0.229391	+	0.254765i	−0.846842	−	0.531845i	$-0.821499\pi$
$277$	−3.81783	+	4.24013i	−0.229391	+	0.254765i	0.617451	+	0.786610i	$0.288166\pi$
$278$	8.62106	−	6.26357i	0.517057	−	0.375664i
$279$	−12.3984	−	15.1100i	−0.742274	−	0.904614i
$280$	10.9633	−	29.5966i	0.655182	−	1.76874i
$281$	−0.542467	+	5.16123i	−0.0323609	+	0.307893i	0.966354	+	0.257215i	$0.0828049\pi$
$281$	−0.542467	+	5.16123i	−0.0323609	+	0.307893i	−0.998715	+	0.0506781i	$0.983862\pi$
$282$	−0.942284	+	3.98154i	−0.0561122	+	0.237097i
$283$	5.54358	−	2.46816i	0.329532	−	0.146717i	−0.235301	−	0.971923i	$-0.575607\pi$
$283$	5.54358	−	2.46816i	0.329532	−	0.146717i	0.564832	+	0.825206i	$0.308941\pi$
$284$	0.151941	+	0.168748i	0.00901605	+	0.0100133i
$285$	7.23275	−	0.298001i	0.428431	−	0.0176521i
$286$	4.38202	−	4.86673i	0.259114	−	0.287776i
$287$	−3.75487	+	11.5563i	−0.221643	+	0.682147i
$288$	−0.231062	−	0.0603149i	−0.0136155	−	0.00355409i
$289$	−2.55457	−	7.86216i	−0.150269	−	0.462480i
$290$	−12.6969	+	2.16443i	−0.745586	+	0.127100i
$291$	−14.9325	+	8.17030i	−0.875361	+	0.478952i
$292$	0.0848498	−	0.0377776i	0.00496546	−	0.00221077i
$293$	−2.94596	+	5.10256i	−0.172105	+	0.298094i	−0.939156	−	0.343492i	$-0.888390\pi$
$293$	−2.94596	+	5.10256i	−0.172105	+	0.298094i	0.767051	+	0.641587i	$0.221723\pi$
$294$	−40.8431	−	14.3149i	−2.38202	−	0.834864i
$295$	3.14156	+	5.99035i	0.182909	+	0.348772i
$296$	−11.1725	+	8.11730i	−0.649388	+	0.471808i
$297$	14.6684	−	7.17185i	0.851147	−	0.416153i
$298$	6.52452	+	20.0804i	0.377955	+	1.16323i
$299$	4.92361	+	8.52794i	0.284740	+	0.493184i
$300$	0.0609950	+	0.105504i	0.00352155	+	0.00609127i
$301$	−9.55782	+	16.5546i	−0.550904	+	0.954193i
$302$	−7.73181	−	1.64345i	−0.444916	−	0.0945698i
$303$	−12.9529	−	1.66272i	−0.744127	−	0.0955207i
$304$	−6.78153	−	3.01933i	−0.388948	−	0.173171i
$305$	14.4355	−	9.61788i	0.826574	−	0.550718i
$306$	−5.74384	−	11.0951i	−0.328354	−	0.634262i
$307$	−31.9044			−1.82088			−0.910439	−	0.413643i	$-0.864256\pi$
$307$	−31.9044			−1.82088			−0.910439	+	0.413643i	$0.864256\pi$
$308$	−0.0229856	+	0.218694i	−0.00130973	+	0.0124612i
$309$	−0.457264	−	0.278183i	−0.0260129	−	0.0158253i
$310$	10.9783	−	17.3486i	0.623523	−	0.985333i
$311$	15.7006	+	3.33726i	0.890299	+	0.189239i	0.630283	−	0.776366i	$-0.282939\pi$
$311$	15.7006	+	3.33726i	0.890299	+	0.189239i	0.260016	+	0.965604i	$0.416272\pi$
$312$	−6.21120	−	3.77867i	−0.351640	−	0.213925i
$313$	4.35879	−	0.926489i	0.246373	−	0.0523682i	−0.0830697	−	0.996544i	$-0.526472\pi$
$313$	4.35879	−	0.926489i	0.246373	−	0.0523682i	0.329443	+	0.944175i	$0.393139\pi$
$314$	6.69375	+	20.6012i	0.377750	+	1.16260i
$315$	28.5819	−	17.2039i	1.61041	−	0.969333i
$316$	−0.0352362	+	0.108446i	−0.00198219	+	0.00610055i
$317$	−1.52500	+	14.5094i	−0.0856528	+	0.814932i	0.864392	+	0.502818i	$0.167704\pi$
$317$	−1.52500	+	14.5094i	−0.0856528	+	0.814932i	−0.950045	+	0.312113i	$0.898963\pi$
$318$	0.501174	+	0.472528i	0.0281045	+	0.0264980i
$319$	11.7335	−	5.22408i	0.656949	−	0.292492i
$320$	−1.15430	−	17.9756i	−0.0645272	−	1.00487i
$321$	11.1392	−	14.6145i	0.621730	−	0.815699i
$322$	42.6296	+	18.9799i	2.37566	+	1.05771i
$323$	1.70685	+	5.25315i	0.0949718	+	0.292293i
$324$	−0.0757597	−	0.101489i	−0.00420887	−	0.00563828i
$325$	1.70716	+	7.19468i	0.0946965	+	0.399089i
$326$	−15.2648	−	26.4395i	−0.845440	−	1.46435i
$327$	−8.69322	−	12.5616i	−0.480736	−	0.694656i
$328$	0.724907	+	6.89703i	0.0400263	+	0.380825i
$329$	−0.871361	−	8.29045i	−0.0480397	−	0.457067i
$330$	11.9908	+	12.2620i	0.660071	+	0.675000i
$331$	−2.46597	+	23.4622i	−0.135542	+	1.28960i	0.689400	+	0.724381i	$0.257874\pi$
$331$	−2.46597	+	23.4622i	−0.135542	+	1.28960i	−0.824943	+	0.565217i	$0.808793\pi$
$332$	0.135508			0.00743696
$333$	−14.5814	−	0.669707i	−0.799056	−	0.0366997i
$334$	7.18697	−	22.1192i	0.393253	−	1.21031i
$335$	25.1559	−	4.28831i	1.37441	−	0.234295i
$336$	−34.0958	+	2.79429i	−1.86008	+	0.152441i
$337$	−5.57566	−	6.19239i	−0.303725	−	0.337321i	0.571890	−	0.820330i	$-0.306210\pi$
$337$	−5.57566	−	6.19239i	−0.303725	−	0.337321i	−0.875615	+	0.483009i	$0.839544\pi$
$338$	10.1961	+	11.3239i	0.554595	+	0.615940i
$339$	−15.1554	+	1.24205i	−0.823129	+	0.0674589i
$340$	−0.0649741	+	0.0665215i	−0.00352372	+	0.00360763i
$341$	−6.32643	+	19.4707i	−0.342595	+	1.05440i
$342$	−3.63280	−	7.01727i	−0.196439	−	0.379450i
$343$	53.3661			2.88150
$344$	−1.14040	+	10.8502i	−0.0614865	+	0.585005i
$345$	−23.1071	+	11.4500i	−1.24404	+	0.616448i
$346$	1.77945	+	16.9303i	0.0956638	+	0.910180i
$347$	−1.57690	−	15.0032i	−0.0846522	−	0.805412i	−0.951667	−	0.307130i	$-0.900631\pi$
$347$	−1.57690	−	15.0032i	−0.0846522	−	0.805412i	0.867015	−	0.498282i	$-0.166035\pi$
$348$	−0.0566928	−	0.0819201i	−0.00303905	−	0.00439138i
$349$	−3.03867	−	5.26314i	−0.162656	−	0.281729i	0.773164	−	0.634206i	$-0.218673\pi$
$349$	−3.03867	−	5.26314i	−0.162656	−	0.281729i	−0.935821	+	0.352477i	$0.885340\pi$
$350$	26.5849	+	22.8276i	1.42102	+	1.22019i
$351$	−2.63526	−	7.21855i	−0.140660	−	0.385298i
$352$	0.0772947	+	0.237888i	0.00411982	+	0.0126795i
$353$	−21.2867	−	9.47745i	−1.13298	−	0.504434i	−0.247394	−	0.968915i	$-0.579574\pi$
$353$	−21.2867	−	9.47745i	−1.13298	−	0.504434i	−0.885583	+	0.464481i	$0.846241\pi$
$354$	4.47592	−	5.87233i	0.237892	−	0.312111i
$355$	−33.5314	+	13.3263i	−1.77966	+	0.707284i
$356$	−0.0351586	+	0.0156536i	−0.00186340	+	0.000829640i
$357$	18.5208	+	17.4622i	0.980224	+	0.924196i
$358$	1.95911	−	18.6397i	0.103542	−	0.985140i
$359$	1.23779	−	3.80952i	0.0653279	−	0.201059i	−0.913065	−	0.407815i	$-0.866291\pi$
$359$	1.23779	−	3.80952i	0.0653279	−	0.201059i	0.978392	+	0.206756i	$0.0662908\pi$
$360$	10.9087	−	15.6050i	0.574938	−	0.822455i
$361$	−4.79179	−	14.7476i	−0.252200	−	0.776191i
$362$	28.8570	−	6.13375i	1.51669	−	0.322383i
$363$	1.66620	+	1.01365i	0.0874526	+	0.0532031i
$364$	0.101231	+	0.0215174i	0.00530597	+	0.00112782i
$365$	0.945785	+	14.7285i	0.0495047	+	0.770924i
$366$	−16.1764	−	9.84114i	−0.845554	−	0.514405i
$367$	2.40040	−	22.8383i	0.125300	−	1.19215i	−0.733447	−	0.679747i	$-0.762090\pi$
$367$	2.40040	−	22.8383i	0.125300	−	1.19215i	0.858746	−	0.512401i	$-0.171244\pi$
$368$	26.4454			1.37856
$369$	−3.95246	+	6.17325i	−0.205757	+	0.321366i
$370$	−4.14223	−	14.7620i	−0.215344	−	0.767439i
$371$	−1.28206	−	0.570810i	−0.0665612	−	0.0296350i
$372$	0.157505	+	0.0202184i	0.00816627	+	0.00104827i
$373$	−19.9847	−	4.24788i	−1.03477	−	0.219947i	−0.340939	−	0.940085i	$-0.610745\pi$
$373$	−19.9847	−	4.24788i	−1.03477	−	0.219947i	−0.693830	+	0.720138i	$0.744078\pi$
$374$	−6.54313	+	11.3330i	−0.338337	+	0.586017i
$375$	−19.0876	+	3.26535i	−0.985681	+	0.168622i
$376$	−2.37886	−	4.12031i	−0.122680	−	0.212489i
$377$	−1.86796	−	5.74900i	−0.0962050	−	0.296088i
$378$	−30.2094	−	20.3340i	−1.55381	−	1.04587i
$379$	2.11954	−	1.53993i	0.108873	−	0.0791011i	−0.532016	−	0.846734i	$-0.678566\pi$
$379$	2.11954	−	1.53993i	0.108873	−	0.0791011i	0.640890	+	0.767633i	$0.278566\pi$
$380$	−0.0410941	+	0.0420727i	−0.00210808	+	0.00215828i
$381$	13.0483	+	4.57325i	0.668485	+	0.234294i
$382$	−3.41772	+	5.91966i	−0.174866	+	0.302876i
$383$	−10.0917	+	4.49311i	−0.515661	+	0.229587i	−0.648032	−	0.761613i	$-0.724408\pi$
$383$	−10.0917	+	4.49311i	−0.515661	+	0.229587i	0.132371	+	0.991200i	$0.457741\pi$
$384$	−17.0073	+	9.30548i	−0.867898	+	0.474868i
$385$	−31.3184	−	15.4961i	−1.59613	−	0.789754i
$386$	1.54310	+	4.74917i	0.0785417	+	0.241727i
$387$	−8.10118	+	8.20659i	−0.411806	+	0.417164i
$388$	0.0427342	−	0.131522i	0.00216950	−	0.00667704i
$389$	−8.38557	+	9.31312i	−0.425165	+	0.472194i	−0.917226	−	0.398367i	$-0.869577\pi$
$389$	−8.38557	+	9.31312i	−0.425165	+	0.472194i	0.492061	+	0.870561i	$0.336244\pi$
$390$	6.32927	−	5.00921i	0.320495	−	0.253651i
$391$	−13.1667	−	14.6231i	−0.665868	−	0.739521i
$392$	45.9751	−	20.4694i	2.32209	−	1.03386i
$393$	4.37162	−	18.4719i	0.220519	−	0.931784i
$394$	3.15769	−	30.0434i	0.159082	−	1.51356i
$395$	−14.2144	−	11.2363i	−0.715204	−	0.565358i
$396$	−0.0467376	+	0.124148i	−0.00234865	+	0.00623868i
$397$	25.5180	−	18.5399i	1.28071	−	0.930493i	0.281140	−	0.959667i	$-0.409288\pi$
$397$	25.5180	−	18.5399i	1.28071	−	0.930493i	0.999574	+	0.0291737i	$0.00928761\pi$
$398$	−17.8601	+	19.8356i	−0.895244	+	0.994269i
$399$	11.7138	+	11.0443i	0.586424	+	0.552905i
$400$	19.0255	+	5.69043i	0.951276	+	0.284521i
$401$	4.83754	−	8.37886i	0.241575	−	0.418420i	−0.719588	−	0.694401i	$-0.755669\pi$
$401$	4.83754	−	8.37886i	0.241575	−	0.418420i	0.961163	+	0.275981i	$0.0890026\pi$
$402$	−15.8519	−	22.9057i	−0.790619	−	1.14243i
$403$	8.80229	+	3.91903i	0.438473	+	0.195221i
$404$	0.0858357	−	0.0623633i	0.00427049	−	0.00310269i
$405$	19.3044	−	5.68701i	0.959241	−	0.282590i
$406$	−23.1745	−	16.8373i	−1.15013	−	0.835621i
$407$	7.64456	+	13.2408i	0.378927	+	0.656320i
$408$	13.7103	+	4.80525i	0.678759	+	0.237895i
$409$	7.22914	+	8.02878i	0.357458	+	0.396998i	0.894873	−	0.446320i	$-0.147266\pi$
$409$	7.22914	+	8.02878i	0.357458	+	0.396998i	−0.537415	+	0.843318i	$0.680599\pi$
$410$	−7.46000	−	1.90511i	−0.368423	−	0.0940866i
$411$	5.09640	−	10.7743i	0.251387	−	0.531457i
$412$	0.00425346		0.000904101i	0.000209553		4.45418e-5i
$413$	−4.64870	+	14.3072i	−0.228748	+	0.704013i
$414$	21.9908	+	17.5737i	1.08079	+	0.863701i
$415$	−7.47951	+	20.1918i	−0.367154	+	0.991175i
$416$	0.115149	−	0.0244757i	0.00564565	−	0.00120002i
$417$	−9.93173	+	8.53816i	−0.486359	+	0.418116i
$418$	−4.13832	+	7.16778i	−0.202412	+	0.350588i
$419$	−35.1358	+	15.6435i	−1.71650	+	0.764234i	−0.718889	+	0.695125i	$0.755349\pi$
$419$	−35.1358	+	15.6435i	−1.71650	+	0.764234i	−0.997609	+	0.0691098i	$0.977984\pi$
$420$	−0.0730712	+	0.260996i	−0.00356551	+	0.0127353i
$421$	−5.69593	−	2.53599i	−0.277603	−	0.123597i	0.263213	−	0.964738i	$-0.415218\pi$
$421$	−5.69593	−	2.53599i	−0.277603	−	0.123597i	−0.540816	+	0.841141i	$0.681884\pi$
$422$	−25.8891	+	18.8095i	−1.26026	+	0.915632i
$423$	0.754557	−	4.97186i	0.0366878	−	0.241740i
$424$	−0.800965			−0.0388983
$425$	−6.32592	−	13.3534i	−0.306852	−	0.647735i
$426$	28.6578	+	27.0198i	1.38848	+	1.30911i
$427$	37.7348	+	8.02079i	1.82612	+	0.388153i
$428$	0.0156052	+	0.148474i	0.000754308	+	0.00717676i
$429$	−4.87927	+	6.40151i	−0.235573	+	0.309068i
$430$	−10.8563	−	5.37160i	−0.523536	−	0.259041i
$431$	−5.18988	−	3.77067i	−0.249988	−	0.181627i	0.455734	−	0.890116i	$-0.349377\pi$
$431$	−5.18988	−	3.77067i	−0.249988	−	0.181627i	−0.705721	+	0.708489i	$0.749377\pi$
$432$	−20.3273	−	3.56395i	−0.977996	−	0.171471i
$433$	−12.6872	−	9.21781i	−0.609709	−	0.442980i	0.239603	−	0.970871i	$-0.422983\pi$
$433$	−12.6872	−	9.21781i	−0.609709	−	0.442980i	−0.849312	+	0.527891i	$0.822983\pi$
$434$	44.6619	−	9.49319i	2.14384	−	0.455688i
$435$	15.3360	−	3.92602i	0.735304	−	0.188238i
$436$	0.121399	+	0.0258042i	0.00581396	+	0.00123580i
$437$	−8.32750	−	9.24863i	−0.398359	−	0.442422i
$438$	14.1333	−	7.73298i	0.675314	−	0.369496i
$439$	10.4247	−	11.5778i	0.497545	−	0.552579i	−0.441103	−	0.897456i	$-0.645413\pi$
$439$	10.4247	−	11.5778i	0.497545	−	0.552579i	0.938648	+	0.344877i	$0.112079\pi$
$440$	−19.9265	−	0.809322i	−0.949957	−	0.0385829i
$441$	51.4687	+	13.4351i	2.45089	+	0.639764i
$442$	4.98267	+	3.62012i	0.237002	+	0.172192i
$443$	−0.149149	−	0.258333i	−0.00708627	−	0.0122738i	0.862461	−	0.506124i	$-0.168922\pi$
$443$	−0.149149	−	0.258333i	−0.00708627	−	0.0122738i	−0.869547	+	0.493851i	$0.835589\pi$
$444$	0.0899277	−	0.0773095i	0.00426778	−	0.00366895i
$445$	−0.391898	−	6.10294i	−0.0185777	−	0.289307i
$446$	3.17611	+	30.2187i	0.150393	+	1.43090i
$447$	−10.0082	−	23.9429i	−0.473373	−	1.13246i
$448$	26.8055	−	29.7706i	1.26644	−	1.40653i
$449$	−0.00271457			−0.000128108			−6.40542e−5	−	1.00000i	$-0.500020\pi$
$449$	−0.00271457			−0.000128108			−6.40542e−5		1.00000i	$0.500020\pi$
$450$	12.0394	+	17.3749i	0.567540	+	0.819062i
$451$	7.67781			0.361534
$452$	0.0826657	−	0.0918096i	0.00388827	−	0.00431836i
$453$	9.63622	+	1.23697i	0.452749	+	0.0581177i
$454$	−0.319786	−	3.04256i	−0.0150083	−	0.142795i
$455$	−8.79386	+	13.8966i	−0.412262	+	0.651484i
$456$	8.67130	+	3.03917i	0.406071	+	0.142322i
$457$	1.96454	+	3.40268i	0.0918972	+	0.159171i	0.908309	−	0.418299i	$-0.137374\pi$
$457$	1.96454	+	3.40268i	0.0918972	+	0.159171i	−0.816412	+	0.577470i	$0.804040\pi$
$458$	−22.0078	−	15.9896i	−1.02836	−	0.747146i
$459$	8.14988	+	13.0145i	0.380404	+	0.607464i
$460$	0.0727771	−	0.196470i	0.00339325	−	0.00916045i
$461$	5.18666	−	5.76037i	0.241567	−	0.268287i	−0.610154	−	0.792283i	$-0.708892\pi$
$461$	5.18666	−	5.76037i	0.241567	−	0.268287i	0.851721	+	0.523995i	$0.175559\pi$
$462$	−0.875230	+	38.1326i	−0.0407194	+	1.77409i
$463$	17.2617	+	19.1710i	0.802218	+	0.890953i	0.995932	−	0.0901048i	$-0.0287202\pi$
$463$	17.2617	+	19.1710i	0.802218	+	0.890953i	−0.193714	+	0.981058i	$0.562054\pi$
$464$	−15.8791	−	3.37521i	−0.737170	−	0.156690i
$465$	−11.7064	+	22.3536i	−0.542871	+	1.03662i
$466$	−36.6241	+	7.78470i	−1.69658	+	0.360619i
$467$	15.4805	+	11.2472i	0.716350	+	0.520459i	0.885216	−	0.465180i	$-0.154011\pi$
$467$	15.4805	+	11.2472i	0.716350	+	0.520459i	−0.168866	+	0.985639i	$0.554011\pi$
$468$	0.0558098	+	0.0279836i	0.00257981	+	0.00129354i
$469$	45.9149	+	33.3591i	2.12015	+	1.54038i
$470$	5.20701	−	0.887636i	0.240182	−	0.0409436i
$471$	−10.2678	−	24.5639i	−0.473117	−	1.13185i
$472$	0.897469	+	8.53884i	0.0413093	+	0.393032i
$473$	11.8146	+	2.51127i	0.543235	+	0.115468i
$474$	−4.55504	+	19.2469i	−0.209220	+	0.884039i
$475$	−4.00094	−	8.44560i	−0.183576	−	0.387511i
$476$	−0.206806			−0.00947893
$477$	−0.661361	−	0.528519i	−0.0302816	−	0.0241992i
$478$	−8.41917	+	6.11689i	−0.385084	+	0.279780i
$479$	−9.97990	−	4.44334i	−0.455993	−	0.203021i	0.165869	−	0.986148i	$-0.446957\pi$
$479$	−9.97990	−	4.44334i	−0.455993	−	0.203021i	−0.621862	+	0.783127i	$0.713624\pi$
$480$	0.0448202	+	0.305020i	0.00204575	+	0.0139222i
$481$	6.57358	−	2.92674i	0.299729	−	0.133448i
$482$	−9.93380	+	17.2059i	−0.452472	+	0.783705i
$483$	−54.1254	−	18.9702i	−2.46279	−	0.863174i
$484$	−0.0154989	+	0.00329439i	−0.000704496	+	0.000149745i
$485$	17.2392	+	13.6273i	0.782790	+	0.618783i
$486$	−14.5349	−	16.4717i	−0.659318	−	0.747171i
$487$	−8.95137	+	27.5495i	−0.405625	+	1.24839i	0.514746	+	0.857343i	$0.327886\pi$
$487$	−8.95137	+	27.5495i	−0.405625	+	1.24839i	−0.920372	+	0.391044i	$0.872114\pi$
$488$	21.5366	−	4.57775i	0.974917	−	0.207225i
$489$	21.3532	+	30.8551i	0.965627	+	1.39531i
$490$	3.58049	+	55.7582i	0.161750	+	2.51890i
$491$	−16.3812	−	18.1931i	−0.739272	−	0.821045i	0.249828	−	0.968290i	$-0.419626\pi$
$491$	−16.3812	−	18.1931i	−0.739272	−	0.821045i	−0.989100	+	0.147245i	$0.952959\pi$
$492$	−0.0110419	−	0.0585206i	−0.000497807	−	0.00263831i
$493$	6.03959	+	10.4609i	0.272010	+	0.471134i
$494$	3.15138	+	2.28961i	0.141787	+	0.103015i
$495$	−15.9194	−	13.8168i	−0.715522	−	0.621018i
$496$	20.9343	−	15.2097i	0.939980	−	0.682935i
$497$	−73.3099	−	32.6397i	−3.28840	−	1.46409i
$498$	23.4261	−	1.91986i	1.04975	−	0.0860312i
$499$	12.7554	−	22.0929i	0.571008	−	0.989016i	−0.425454	−	0.904980i	$-0.639886\pi$
$499$	12.7554	−	22.0929i	0.571008	−	0.989016i	0.996463	−	0.0840358i	$-0.0267810\pi$
$500$	0.0946335	−	0.125686i	0.00423214	−	0.00562084i
$501$	−6.58324	+	27.8169i	−0.294117	+	1.24277i
$502$	−22.3472	+	24.8191i	−0.997403	+	1.10773i
$503$	−8.07131	+	5.86415i	−0.359882	+	0.261470i	−0.753003	−	0.658017i	$-0.771395\pi$
$503$	−8.07131	+	5.86415i	−0.359882	+	0.261470i	0.393121	+	0.919487i	$0.371395\pi$
$504$	41.7797	−	6.89436i	1.86102	−	0.307099i
$505$	4.55484	+	16.2324i	0.202688	+	0.722334i
$506$	3.08206	−	29.3238i	0.137014	−	1.30360i
$507$	−13.6267	−	12.8479i	−0.605185	−	0.570593i
$508$	−0.102621	+	0.0456898i	−0.00455307	+	0.00202716i
$509$	16.6010	+	18.4372i	0.735825	+	0.817216i	0.988641	−	0.150298i	$-0.0480234\pi$
$509$	16.6010	+	18.4372i	0.735825	+	0.817216i	−0.252816	+	0.967514i	$0.581357\pi$
$510$	−10.2900	+	12.4205i	−0.455649	+	0.549990i
$511$	−21.9634	+	24.3928i	−0.971603	+	1.07907i
$512$	7.06462	−	21.7427i	0.312215	−	0.960899i
$513$	5.15454	+	8.23124i	0.227578	+	0.363418i
$514$	−3.09095	−	9.51297i	−0.136336	−	0.419599i
$515$	−0.100056	+	0.683703i	−0.00440900	+	0.0301276i
$516$	0.00214978	−	0.0936629i	9.46388e−5	−	0.00412328i
$517$	−4.81192	+	2.14241i	−0.211628	+	0.0942229i
$518$	17.0494	−	29.5304i	0.749108	−	1.29749i
$519$	−3.87943	−	20.5605i	−0.170288	−	0.902505i
$520$	−1.35910	+	9.28701i	−0.0596006	+	0.407262i
$521$	1.27373	−	0.925421i	0.0558033	−	0.0405434i	−0.559534	−	0.828807i	$-0.689020\pi$
$521$	1.27373	−	0.925421i	0.0558033	−	0.0405434i	0.615337	+	0.788264i	$0.289020\pi$
$522$	−10.9615	−	13.3588i	−0.479770	−	0.584699i
$523$	−1.55314	−	4.78007i	−0.0679141	−	0.209018i	0.911340	−	0.411655i	$-0.135049\pi$
$523$	−1.55314	−	4.78007i	−0.0679141	−	0.209018i	−0.979254	+	0.202637i	$0.935049\pi$
$524$	0.0771096	+	0.133558i	0.00336855	+	0.00583450i
$525$	−34.8574	−	25.2942i	−1.52130	−	1.10393i
$526$	10.4179	−	18.0444i	0.454244	−	0.786773i
$527$	−18.8331	−	4.00310i	−0.820382	−	0.174378i
$528$	8.33665	+	19.9439i	0.362806	+	0.867947i
$529$	19.4914	+	8.67812i	0.847451	+	0.377309i
$530$	0.308888	−	0.833878i	0.0134172	−	0.0362213i
$531$	−4.89333	+	7.64277i	−0.212353	+	0.331668i
$532$	−0.130798			−0.00567082
$533$	0.377712	−	3.59369i	0.0163605	−	0.155660i
$534$	−5.85630	+	3.20426i	−0.253427	+	0.138662i
$535$	−22.9852	−	5.86988i	−0.993736	−	0.253777i
$536$	31.6837	+	6.73458i	1.36853	+	0.290889i
$537$	−0.528587	+	23.0298i	−0.0228102	+	0.993808i
$538$	−9.03932	+	1.92137i	−0.389713	+	0.0828360i
$539$	−17.2173	−	52.9893i	−0.741600	−	2.28241i
$540$	−0.0824177	+	0.141209i	−0.00354669	+	0.00607666i
$541$	−5.34859	+	16.4613i	−0.229954	+	0.707725i	0.767797	+	0.640693i	$0.221353\pi$
$541$	−5.34859	+	16.4613i	−0.229954	+	0.707725i	−0.997751	+	0.0670319i	$0.978647\pi$
$542$	0.757097	−	7.20330i	0.0325201	−	0.309408i
$543$	−34.7332	+	10.4107i	−1.49054	+	0.446764i
$544$	−0.214901	+	0.0956801i	−0.00921380	+	0.00410225i
$545$	−10.5458	+	16.6652i	−0.451732	+	0.713857i
$546$	17.8054	+	2.28561i	0.761999	+	0.0978149i
$547$	12.6377	+	5.62664i	0.540347	+	0.240578i	0.658716	−	0.752392i	$-0.271100\pi$
$547$	12.6377	+	5.62664i	0.540347	+	0.240578i	−0.118369	+	0.992970i	$0.537767\pi$
$548$	0.0299233	+	0.0920944i	0.00127826	+	0.00393408i
$549$	20.8036	+	10.4311i	0.887874	+	0.445190i
$550$	8.52712	−	20.4332i	0.363597	−	0.871273i
$551$	3.81985	+	6.61617i	0.162731	+	0.281858i
$552$	−32.6243	+	2.67370i	−1.38858	+	0.113800i
$553$	−4.21220	−	40.0764i	−0.179121	−	1.70422i
$554$	−0.840469	−	7.99653i	−0.0357081	−	0.339740i
$555$	6.55609	+	17.6671i	0.278290	+	0.749928i
$556$	0.0111227	−	0.105825i	0.000471707	−	0.00448799i
$557$	18.9380			0.802431			0.401215	−	0.915984i	$-0.368588\pi$
$557$	18.9380			0.802431			0.401215	+	0.915984i	$0.368588\pi$
$558$	27.5154	+	1.26375i	1.16482	+	0.0534987i
$559$	1.75665	−	5.40641i	0.0742984	−	0.228667i
$560$	20.5121	+	39.1127i	0.866796	+	1.65281i
$561$	6.87740	−	14.5395i	0.290364	−	0.613858i
$562$	−4.89364	−	5.43493i	−0.206426	−	0.229259i
$563$	−8.37358	−	9.29981i	−0.352904	−	0.391940i	0.540388	−	0.841416i	$-0.318277\pi$
$563$	−8.37358	−	9.29981i	−0.352904	−	0.391940i	−0.893292	+	0.449476i	$0.851611\pi$
$564$	0.0232498	+	0.0335956i	0.000978994	+	0.00141463i
$565$	9.11755	+	17.3854i	0.383578	+	0.731409i
$566$	−2.64256	+	8.13296i	−0.111075	+	0.341854i
$567$	39.0470	+	21.8758i	1.63982	+	0.918695i
$568$	−45.8002			−1.92173
$569$	−0.312160	+	2.97000i	−0.0130864	+	0.124509i	−0.999115	−	0.0420690i	$-0.986605\pi$
$569$	−0.312160	+	2.97000i	−0.0130864	+	0.124509i	0.986028	+	0.166578i	$0.0532717\pi$
$570$	−6.50810	+	7.85558i	−0.272594	+	0.329034i
$571$	1.27998	+	12.1782i	0.0535653	+	0.509640i	0.988105	+	0.153781i	$0.0491450\pi$
$571$	1.27998	+	12.1782i	0.0535653	+	0.509640i	−0.934540	+	0.355859i	$0.884188\pi$
$572$	−0.00683550	−	0.0650355i	−0.000285807	−	0.00271927i
$573$	3.59232	−	7.59451i	0.150071	−	0.317265i
$574$	−8.56178	−	14.8294i	−0.357362	−	0.618969i
$575$	25.2586	+	21.6888i	1.05336	+	0.904484i
$576$	20.1822	−	13.2927i	0.840926	−	0.553864i
$577$	9.05957	+	27.8825i	0.377155	+	1.16076i	0.942013	+	0.335575i	$0.108931\pi$
$577$	9.05957	+	27.8825i	0.377155	+	1.16076i	−0.564859	+	0.825188i	$0.691069\pi$
$578$	10.6426	+	4.73839i	0.442674	+	0.197091i
$579$	−2.36703	−	5.66268i	−0.0983703	−	0.235333i
$580$	−0.0687743	+	0.108682i	−0.00285570	+	0.00451276i
$581$	−43.7484	+	19.4780i	−1.81499	+	0.808085i
$582$	5.52433	−	23.3425i	0.228991	−	0.967579i
$583$	−0.0926910	+	0.881896i	−0.00383887	+	0.0365244i
$584$	−5.78903	+	17.8168i	−0.239552	+	0.737265i
$585$	−7.25028	+	6.77153i	−0.299762	+	0.279968i
$586$	−2.56579	−	7.89669i	−0.105992	−	0.326209i
$587$	32.2023	−	6.84480i	1.32913	−	0.282515i	0.512008	−	0.858980i	$-0.328902\pi$
$587$	32.2023	−	6.84480i	1.32913	−	0.282515i	0.817122	+	0.576465i	$0.195568\pi$
$588$	−0.379126	+	0.207438i	−0.0156349	+	0.00855459i
$589$	−11.9113	−	2.53183i	−0.490798	−	0.104322i
$590$	−9.23582	−	2.35861i	−0.380233	−	0.0971026i
$591$	−0.851973	+	37.1193i	−0.0350455	+	1.52688i
$592$	2.01996	−	19.2186i	0.0830198	−	0.789880i
$593$	4.25001			0.174527			0.0872635	−	0.996185i	$-0.472188\pi$
$593$	4.25001			0.174527			0.0872635	+	0.996185i	$0.472188\pi$
$594$	−6.32090	+	22.1244i	−0.259350	+	0.907776i
$595$	11.4149	−	30.8158i	0.467965	−	1.26332i
$596$	0.192605	+	0.0857534i	0.00788942	+	0.00351260i
$597$	19.8867	−	26.0910i	0.813909	−	1.06783i
$598$	−13.5737	−	2.88519i	−0.555072	−	0.117984i
$599$	5.93409	−	10.2782i	0.242460	−	0.419954i	−0.718954	−	0.695058i	$-0.755379\pi$
$599$	5.93409	−	10.2782i	0.242460	−	0.419954i	0.961415	+	0.275104i	$0.0887122\pi$
$600$	−24.0462	−	5.09646i	−0.981680	−	0.208062i
$601$	−1.60271	−	2.77598i	−0.0653759	−	0.113234i	0.831485	−	0.555548i	$-0.187491\pi$
$601$	−1.60271	−	2.77598i	−0.0653759	−	0.113234i	−0.896861	+	0.442313i	$0.854158\pi$
$602$	−8.32440	−	25.6199i	−0.339277	−	1.04419i
$603$	21.7176	+	26.4673i	0.884408	+	1.07783i
$604$	−0.0638567	+	0.0463946i	−0.00259829	+	0.00188777i
$605$	0.364588	−	2.49130i	0.0148226	−	0.101286i
$606$	13.9554	−	11.9972i	0.566899	−	0.487354i
$607$	20.6184	−	35.7121i	0.836876	−	1.44951i	−0.0556185	−	0.998452i	$-0.517713\pi$
$607$	20.6184	−	35.7121i	0.836876	−	1.44951i	0.892494	−	0.451059i	$-0.148954\pi$
$608$	−0.135918	+	0.0605146i	−0.00551220	+	0.00245419i
$609$	30.0784	+	18.2986i	1.21884	+	0.741498i
$610$	−3.53963	+	24.1870i	−0.143315	+	0.979303i
$611$	0.766055	+	2.35768i	0.0309913	+	0.0953813i
$612$	−0.120712	−	0.0315098i	−0.00487947	−	0.00127371i
$613$	1.02258	−	3.14717i	0.0413015	−	0.127113i	−0.928280	−	0.371883i	$-0.878712\pi$
$613$	1.02258	−	3.14717i	0.0413015	−	0.127113i	0.969581	+	0.244770i	$0.0787123\pi$
$614$	30.0845	−	33.4122i	1.21411	−	1.34841i
$615$	9.32952	+	1.58478i	0.376203	+	0.0639045i
$616$	−29.6781	−	32.9608i	−1.19576	−	1.32803i
$617$	−24.4957	+	10.9062i	−0.986158	+	0.439066i	−0.835482	−	0.549517i	$-0.814812\pi$
$617$	−24.4957	+	10.9062i	−0.986158	+	0.439066i	−0.150676	+	0.988583i	$0.548145\pi$
$618$	0.722512	−	0.216560i	0.0290637	−	0.00871132i
$619$	3.28028	−	31.2098i	0.131845	−	1.25443i	−0.705879	−	0.708333i	$-0.749448\pi$
$619$	3.28028	−	31.2098i	0.131845	−	1.25443i	0.837724	−	0.546093i	$-0.183886\pi$
$620$	−0.0553861	−	0.197384i	−0.00222436	−	0.00792711i
$621$	−28.7024	−	19.3196i	−1.15179	−	0.775268i
$622$	−18.3000	+	13.2957i	−0.733763	+	0.533110i
$623$	9.10081	−	10.1075i	0.364616	−	0.404947i
$624$	9.74511	−	2.92092i	0.390117	−	0.116930i
$625$	13.5048	+	21.0385i	0.540192	+	0.841542i
$626$	−3.13988	+	5.43843i	−0.125495	+	0.217363i
$627$	4.34973	−	9.19576i	0.173712	−	0.367243i
$628$	0.197601	+	0.0879777i	0.00788515	+	0.00351069i
$629$	−11.6327	+	8.45166i	−0.463827	+	0.336990i
$630$	−8.93448	+	46.1553i	−0.355958	+	1.83887i
$631$	0.499112	+	0.362626i	0.0198693	+	0.0144359i	0.597676	−	0.801738i	$-0.296091\pi$
$631$	0.499112	+	0.362626i	0.0198693	+	0.0144359i	−0.577806	+	0.816174i	$0.696091\pi$
$632$	−11.4995	−	19.9177i	−0.457426	−	0.792285i
$633$	29.8250	−	25.6401i	1.18544	−	1.01910i
$634$	−13.7572	−	15.2789i	−0.546367	−	0.606802i
$635$	−1.14387	−	17.8133i	−0.0453932	−	0.706898i
$636$	0.00685516		0.000561809i	0.000271825		2.22772e-5i
$637$	−25.6493	+	5.45193i	−1.01626	+	0.216013i
$638$	−5.59320	+	17.2141i	−0.221437	+	0.681513i
$639$	−37.8175	−	30.2214i	−1.49604	−	1.19554i
$640$	19.6343	+	15.5206i	0.776116	+	0.613507i
$641$	−8.34297	+	1.77335i	−0.329527	+	0.0700432i	−0.369705	−	0.929149i	$-0.620541\pi$
$641$	−8.34297	+	1.77335i	−0.329527	+	0.0700432i	0.0401771	+	0.999193i	$0.487208\pi$
$642$	4.80134	+	25.4465i	0.189494	+	1.00429i
$643$	−9.71503	+	16.8269i	−0.383124	+	0.663589i	−0.991507	−	0.130054i	$-0.958485\pi$
$643$	−9.71503	+	16.8269i	−0.383124	+	0.663589i	0.608383	+	0.793643i	$0.291818\pi$
$644$	0.425680	−	0.189525i	0.0167742	−	0.00746834i
$645$	13.8379	+	5.49016i	0.544866	+	0.216175i
$646$	−7.11091	−	3.16598i	−0.279775	−	0.124564i
$647$	23.3550	−	16.9684i	0.918180	−	0.667097i	−0.0248902	−	0.999690i	$-0.507924\pi$
$647$	23.3550	−	16.9684i	0.918180	−	0.667097i	0.943070	+	0.332593i	$0.107924\pi$
$648$	25.4371	+	2.34153i	0.999262	+	0.0919839i
$649$	9.50548			0.373123
$650$	−9.14450	−	4.99644i	−0.358677	−	0.195976i
$651$	−53.7565	+	16.1125i	−2.10688	+	0.631500i
$652$	−0.298194	−	0.0633830i	−0.0116782	−	0.00248227i
$653$	−1.37680	−	13.0994i	−0.0538783	−	0.512618i	−0.987866	−	0.155311i	$-0.950362\pi$
$653$	−1.37680	−	13.0994i	−0.0538783	−	0.512618i	0.933987	−	0.357306i	$-0.116305\pi$
$654$	21.3526	+	2.74095i	0.834952	+	0.107180i
$655$	−24.1574	+	4.11809i	−0.943906	+	0.160907i
$656$	−7.85092	−	5.70403i	−0.306527	−	0.222705i
$657$	−16.5365	+	10.8915i	−0.645150	+	0.424919i
$658$	9.50393	+	6.90501i	0.370502	+	0.269185i
$659$	−1.69666	+	0.360637i	−0.0660926	+	0.0140484i	−0.240839	−	0.970565i	$-0.577423\pi$
$659$	−1.69666	+	0.360637i	−0.0660926	+	0.0140484i	0.174747	+	0.984613i	$0.444089\pi$
$660$	0.171111	−	0.00705004i	0.00666048	−	0.000274423i
$661$	−5.83439	−	1.24014i	−0.226931	−	0.0482357i	0.0930425	−	0.995662i	$-0.470341\pi$
$661$	−5.83439	−	1.24014i	−0.226931	−	0.0482357i	−0.319974	+	0.947426i	$0.603674\pi$
$662$	−22.2457	−	24.7064i	−0.864604	−	0.960240i
$663$	−6.46705	−	3.93432i	−0.251160	−	0.152797i
$664$	−18.2885	+	20.3114i	−0.709731	+	0.788236i
$665$	7.21955	−	19.4900i	0.279962	−	0.755789i
$666$	14.4510	−	14.6390i	0.559966	−	0.567252i
$667$	−22.0184	−	15.9973i	−0.852556	−	0.619418i
$668$	−0.116120	−	0.201125i	−0.00449280	−	0.00778176i
$669$	−6.92434	−	36.6981i	−0.267710	−	1.41883i
$670$	−19.2300	+	30.3885i	−0.742918	+	1.17401i
$671$	−2.54799	−	24.2425i	−0.0983640	−	0.935871i
$672$	−0.415638	+	0.545309i	−0.0160336	+	0.0210358i
$673$	−24.9866	+	27.7504i	−0.963163	+	1.06970i	0.0343633	+	0.999409i	$0.489060\pi$
$673$	−24.9866	+	27.7504i	−0.963163	+	1.06970i	−0.997526	+	0.0702917i	$0.977607\pi$
$674$	11.7427			0.452311
$675$	−16.4921	−	20.0751i	−0.634782	−	0.772691i
$676$	0.152158			0.00585224
$677$	12.4093	−	13.7819i	0.476927	−	0.529681i	−0.455888	−	0.890037i	$-0.650678\pi$
$677$	12.4093	−	13.7819i	0.476927	−	0.529681i	0.932815	+	0.360356i	$0.117345\pi$
$678$	12.9902	−	17.0429i	0.498885	−	0.654528i
$679$	5.10853	+	48.6044i	0.196047	+	1.86527i
$680$	−1.20190	−	18.7170i	−0.0460909	−	0.717763i
$681$	0.697176	+	3.69494i	0.0267158	+	0.141591i
$682$	−14.4254	−	24.9855i	−0.552377	−	0.956745i
$683$	23.3543	+	16.9679i	0.893628	+	0.649259i	0.936821	−	0.349808i	$-0.113753\pi$
$683$	23.3543	+	16.9679i	0.893628	+	0.649259i	−0.0431936	+	0.999067i	$0.513753\pi$
$684$	−0.0763462	−	0.0199289i	−0.00291917	−	0.000762001i
$685$	−15.3745	−	0.624441i	−0.587429	−	0.0238587i
$686$	−50.3220	+	55.8883i	−1.92130	+	2.13382i
$687$	28.5641	+	17.3774i	1.08979	+	0.662989i
$688$	−10.2153	−	11.3452i	−0.389454	−	0.432532i
$689$	0.408222	+	0.0867703i	0.0155520	+	0.00330569i
$690$	9.79784	−	34.9960i	0.372997	−	1.33228i
$691$	32.8123	−	6.97447i	1.24824	−	0.265321i	0.464030	−	0.885819i	$-0.346403\pi$
$691$	32.8123	−	6.97447i	1.24824	−	0.265321i	0.784208	+	0.620498i	$0.213070\pi$
$692$	0.137525	+	0.0999175i	0.00522790	+	0.00379829i
$693$	−2.75605	−	46.7991i	−0.104694	−	1.77775i
$694$	17.1992	+	12.4959i	0.652872	+	0.474339i
$695$	15.1549	+	7.49852i	0.574858	+	0.284435i
$696$	19.9305	+	2.55841i	0.755464	+	0.0969761i
$697$	0.754767	+	7.18113i	0.0285888	+	0.272005i
$698$	8.37723	+	1.78063i	0.317083	+	0.0673980i
$699$	44.0819	−	13.2128i	1.66733	−	0.499753i
$700$	0.347027	−	0.0447530i	0.0131164	−	0.00169151i
$701$	−29.9242			−1.13022			−0.565110	−	0.825015i	$-0.691166\pi$
$701$	−29.9242			−1.13022			−0.565110	+	0.825015i	$0.691166\pi$
$702$	10.0446	+	4.04699i	0.379111	+	0.152744i
$703$	−7.35732	+	5.34540i	−0.277486	+	0.201606i
$704$	−23.1243	−	10.2956i	−0.871530	−	0.388030i
$705$	−6.28932	+	1.61007i	−0.236869	+	0.0606386i
$706$	29.9978	−	13.3559i	1.12898	−	0.502656i
$707$	−18.7477	+	32.4720i	−0.705080	+	1.22123i
$708$	−0.0136704	−	0.0724513i	−0.000513764	−	0.00272289i
$709$	21.0159	−	4.46707i	0.789270	−	0.167764i	0.204395	−	0.978888i	$-0.434477\pi$
$709$	21.0159	−	4.46707i	0.789270	−	0.167764i	0.584874	+	0.811124i	$0.301144\pi$
$710$	17.6626	−	47.6822i	0.662866	−	1.78948i
$711$	3.64756	−	24.0342i	0.136794	−	0.901351i
$712$	2.39876	−	7.38262i	0.0898973	−	0.276675i
$713$	42.4338	−	9.01959i	1.58916	−	0.337786i
$714$	−35.7518	+	2.93001i	−1.33798	+	0.109653i
$715$	10.0681	+	2.57116i	0.376526	+	0.0961559i
$716$	−0.125230	−	0.139082i	−0.00468006	−	0.00519774i
$717$	9.69915	−	8.33821i	0.362221	−	0.311396i
$718$	2.82238	+	4.88851i	0.105330	+	0.182437i
$719$	1.84892	+	1.34332i	0.0689531	+	0.0500973i	0.621728	−	0.783233i	$-0.286431\pi$
$719$	1.84892	+	1.34332i	0.0689531	+	0.0500973i	−0.552775	+	0.833331i	$0.686431\pi$
$720$	6.01346	+	25.9552i	0.224109	+	0.967292i
$721$	−1.24326	+	0.903284i	−0.0463016	+	0.0336401i
$722$	19.9631	+	8.88814i	0.742949	+	0.330782i
$723$	10.4413	−	22.0739i	0.388316	−	0.820938i
$724$	0.147295	−	0.255123i	0.00547419	−	0.00948158i
$725$	−12.3984	−	16.2467i	−0.460465	−	0.603389i
$726$	−2.63272	+	0.789109i	−0.0977092	+	0.0292866i
$727$	31.1394	−	34.5838i	1.15490	−	1.28264i	0.201985	−	0.979389i	$-0.435261\pi$
$727$	31.1394	−	34.5838i	1.15490	−	1.28264i	0.952910	−	0.303253i	$-0.0980727\pi$
$728$	−16.8877	+	12.2697i	−0.625901	+	0.454744i
$729$	19.4585	+	18.7181i	0.720684	+	0.693264i
$730$	−16.3164	−	12.8979i	−0.603898	−	0.477372i
$731$	−1.18738	+	11.2972i	−0.0439168	+	0.417840i
$732$	−0.181113	+	0.0542854i	−0.00669413	+	0.00200645i
$733$	−31.6045	+	14.0712i	−1.16734	+	0.519732i	−0.896566	−	0.442911i	$-0.853946\pi$
$733$	−31.6045	+	14.0712i	−1.16734	+	0.519732i	−0.270772	+	0.962643i	$0.587279\pi$
$734$	21.6542	+	24.0494i	0.799270	+	0.887679i
$735$	−9.98364	−	67.9426i	−0.368252	−	2.50610i
$736$	0.354658	−	0.393888i	0.0130729	−	0.0145189i
$737$	11.0816	−	34.1057i	0.408197	−	1.25630i
$738$	−2.73800	−	9.96038i	−0.100787	−	0.366647i
$739$	2.02765	+	6.24048i	0.0745885	+	0.229560i	0.981399	−	0.191978i	$-0.0614904\pi$
$739$	2.02765	+	6.24048i	0.0745885	+	0.229560i	−0.906811	+	0.421538i	$0.861490\pi$
$740$	−0.137221	−	0.0678960i	−0.00504436	−	0.00249591i
$741$	−4.09020	−	2.48833i	−0.150257	−	0.0914112i
$742$	1.80672	−	0.804402i	0.0663267	−	0.0295305i
$743$	−3.23803	+	5.60843i	−0.118792	+	0.205753i	−0.919289	−	0.393583i	$-0.871235\pi$
$743$	−3.23803	+	5.60843i	−0.118792	+	0.205753i	0.800497	+	0.599336i	$0.204569\pi$
$744$	−24.2879	+	20.8799i	−0.890438	+	0.765496i
$745$	−23.4090	+	23.9665i	−0.857641	+	0.878065i
$746$	23.2934	−	16.9236i	0.852832	−	0.619619i
$747$	−28.5035	+	4.70355i	−1.04289	+	0.172094i
$748$	0.0403803	+	0.124278i	0.00147645	+	0.00454405i
$749$	−26.3799	−	45.6914i	−0.963901	−	1.66953i
$750$	14.5792	−	23.0688i	0.532356	−	0.842355i
$751$	24.7422	−	42.8547i	0.902855	−	1.56379i	0.0790844	−	0.996868i	$-0.474800\pi$
$751$	24.7422	−	42.8547i	0.902855	−	1.56379i	0.823771	−	0.566923i	$-0.191866\pi$
$752$	6.51206	+	1.38418i	0.237470	+	0.0504759i
$753$	24.8830	−	32.6461i	0.906787	−	1.18969i
$754$	7.78212	+	3.46482i	0.283408	+	0.126181i
$755$	−3.38854	−	12.0760i	−0.123321	−	0.439490i
$756$	−0.352741	+	0.0883112i	−0.0128291	+	0.00321185i
$757$	6.28412			0.228400			0.114200	−	0.993458i	$-0.463569\pi$
$757$	6.28412			0.228400			0.114200	+	0.993458i	$0.463569\pi$
$758$	−0.385922	+	3.67180i	−0.0140173	+	0.133366i
$759$	−0.831567	+	36.2302i	−0.0301840	+	1.31507i
$760$	−0.760166	−	11.8379i	−0.0275741	−	0.429405i
$761$	7.67240	+	1.63082i	0.278124	+	0.0591172i	0.344862	−	0.938653i	$-0.387926\pi$
$761$	7.67240	+	1.63082i	0.278124	+	0.0591172i	−0.0667376	+	0.997771i	$0.521259\pi$
$762$	−17.0934	+	9.35261i	−0.619228	+	0.338809i
$763$	−42.9026	+	9.11922i	−1.55318	+	0.330138i
$764$	0.0210921	+	0.0649149i	0.000763087	+	0.00234854i
$765$	11.3580	−	16.2478i	0.410650	−	0.587440i
$766$	4.81058	−	14.8054i	0.173813	−	0.534943i
$767$	0.467625	−	4.44916i	0.0168850	−	0.160650i
$768$	−0.134711	+	0.569207i	−0.00486095	+	0.0205395i
$769$	−14.8963	+	6.63227i	−0.537175	+	0.239166i	−0.657348	−	0.753587i	$-0.728322\pi$
$769$	−14.8963	+	6.63227i	−0.537175	+	0.239166i	0.120173	+	0.992753i	$0.461655\pi$
$770$	45.7604	−	18.1864i	1.64909	−	0.655393i
$771$	4.74134	+	11.3428i	0.170755	+	0.408501i
$772$	0.0455527	+	0.0202814i	0.00163948	+	0.000729942i
$773$	5.02215	+	15.4566i	0.180634	+	0.555934i	0.999846	−	0.0175566i	$-0.00558874\pi$
$773$	5.02215	+	15.4566i	0.180634	+	0.555934i	−0.819212	+	0.573491i	$0.805589\pi$
$774$	−0.955363	−	16.2225i	−0.0343398	−	0.583107i
$775$	32.4689	+	2.64183i	1.16632	+	0.0948974i
$776$	13.9465	+	24.1561i	0.500652	+	0.867154i
$777$	−17.9204	+	37.8855i	−0.642891	+	1.35913i
$778$	−1.84603	−	17.5638i	−0.0661833	−	0.629692i
$779$	0.477366	+	4.54183i	0.0171034	+	0.162728i
$780$	0.00511799	−	0.0804374i	0.000183254	−	0.00288012i
$781$	−5.30019	+	50.4280i	−0.189656	+	1.80445i
$782$	27.7298			0.991617
$783$	14.7686	+	15.2637i	0.527786	+	0.545480i
$784$	−21.7615	+	66.9751i	−0.777198	+	2.39197i
$785$	−24.0162	+	24.5882i	−0.857176	+	0.877589i
$786$	15.2226	+	21.9965i	0.542974	+	0.784588i
$787$	−1.83213	−	2.03479i	−0.0653085	−	0.0725325i	0.709605	−	0.704600i	$-0.248873\pi$
$787$	−1.83213	−	2.03479i	−0.0653085	−	0.0725325i	−0.774914	+	0.632067i	$0.782207\pi$
$788$	−0.201845	−	0.224171i	−0.00719043	−	0.00798578i
$789$	−10.9502	+	23.1497i	−0.389836	+	0.824151i
$790$	25.1709	−	4.29087i	0.895541	−	0.152662i
$791$	−13.4916	+	41.5230i	−0.479707	+	1.47639i
$792$	−12.3009	−	23.7609i	−0.437093	−	0.844308i
$793$	−11.4723			−0.407395
$794$	−4.64629	+	44.2065i	−0.164891	+	1.56883i
$795$	−0.294664	+	1.05248i	−0.0104507	+	0.0373278i
$796$	0.0278599	+	0.265069i	0.000987466	+	0.00939512i
$797$	0.988024	+	9.40042i	0.0349976	+	0.332980i	0.997986	+	0.0634366i	$0.0202061\pi$
$797$	0.988024	+	9.40042i	0.0349976	+	0.332980i	−0.962988	+	0.269543i	$0.913127\pi$
$798$	−22.6119	+	1.85314i	−0.800451	+	0.0656004i
$799$	−2.47685	−	4.29003i	−0.0876246	−	0.151770i
$800$	0.339906	−	0.207059i	0.0120175	−	0.00732065i
$801$	6.85211	−	4.51304i	0.242107	−	0.159461i
$802$	4.21326	+	12.9671i	0.148775	+	0.457884i
$803$	18.9471	+	8.43580i	0.668629	+	0.297693i
$804$	−0.275893	−	0.0354153i	−0.00972999	−	0.00124900i
$805$	4.74488	+	73.8909i	0.167235	+	2.60431i
$806$	−12.4044	+	5.52281i	−0.436928	+	0.194533i
$807$	10.8800	−	3.26109i	0.382994	−	0.114796i
$808$	−2.23691	+	21.2827i	−0.0786941	+	0.748724i
$809$	9.23232	−	28.4142i	0.324591	−	0.998989i	−0.647034	−	0.762462i	$-0.723991\pi$
$809$	9.23232	−	28.4142i	0.324591	−	0.998989i	0.971625	−	0.236528i	$-0.0760094\pi$
$810$	−12.2474	+	25.5793i	−0.430330	+	0.898766i
$811$	0.848346	+	2.61094i	0.0297894	+	0.0916825i	0.964846	−	0.262817i	$-0.0846514\pi$
$811$	0.848346	+	2.61094i	0.0297894	+	0.0916825i	−0.935056	+	0.354499i	$0.884651\pi$
$812$	−0.279789	+	0.0594709i	−0.00981866	+	0.00208702i
$813$	−0.204272	+	8.89983i	−0.00716412	+	0.312131i
$814$	−21.0750	−	4.47964i	−0.738680	−	0.157011i
$815$	25.9037	−	40.9348i	0.907368	−	1.43388i
$816$	−17.8342	+	9.75793i	−0.624322	+	0.341596i
$817$	−0.750979	+	7.14509i	−0.0262734	+	0.249975i
$818$	−15.2250			−0.532330
$819$	−22.0405	−	1.01229i	−0.770156	−	0.0353724i
$820$	−0.0639823	+	0.0426292i	−0.00223436	+	0.00148868i
$821$	−26.3281	−	11.7220i	−0.918857	−	0.409102i	−0.107870	−	0.994165i	$-0.534403\pi$
$821$	−26.3281	−	11.7220i	−0.918857	−	0.409102i	−0.810988	+	0.585063i	$0.801070\pi$
$822$	6.47781	+	15.4970i	0.225940	+	0.540519i
$823$	−27.0969	−	5.75963i	−0.944540	−	0.200768i	−0.290198	−	0.956967i	$-0.593721\pi$
$823$	−27.0969	−	5.75963i	−0.944540	−	0.200768i	−0.654342	+	0.756199i	$0.727054\pi$
$824$	−0.438542	+	0.759576i	−0.0152773	+	0.0264611i
$825$	−8.39414	+	25.8860i	−0.292247	+	0.901237i
$826$	−10.5999	−	18.3595i	−0.368817	−	0.638810i
$827$	−5.96739	−	18.3657i	−0.207506	−	0.638639i	−0.999601	−	0.0282408i	$-0.991009\pi$
$827$	−5.96739	−	18.3657i	−0.207506	−	0.638639i	0.792095	−	0.610398i	$-0.208991\pi$
$828$	0.277344	−	0.0457665i	0.00963838	−	0.00159049i
$829$	−0.588767	+	0.427764i	−0.0204487	+	0.0148569i	−0.597963	−	0.801524i	$-0.704023\pi$
$829$	−0.588767	+	0.427764i	−0.0204487	+	0.0148569i	0.577514	+	0.816381i	$0.304023\pi$
$830$	−14.0932	−	26.8730i	−0.489182	−	0.932775i
$831$	1.83233	+	9.71113i	0.0635629	+	0.336875i
$832$	−5.95659	+	10.3171i	−0.206508	+	0.357682i
$833$	47.8688	−	21.3126i	1.65856	−	0.738437i
$834$	0.423522	−	18.4523i	0.0146654	−	0.638949i
$835$	36.3786	−	6.20145i	1.25893	−	0.214610i
$836$	0.0255393	+	0.0786018i	0.000883294	+	0.00271850i
$837$	−33.8323	+	1.21425i	−1.16942	+	0.0419707i
$838$	16.7488	−	51.5476i	0.578579	−	1.78068i
$839$	−1.13752	+	1.26335i	−0.0392717	+	0.0436156i	−0.762461	−	0.647035i	$-0.776009\pi$
$839$	−1.13752	+	1.26335i	−0.0392717	+	0.0436156i	0.723189	+	0.690650i	$0.242676\pi$
$840$	−29.2592	−	46.1775i	−1.00954	−	1.59328i
$841$	−8.22557	−	9.13542i	−0.283640	−	0.315015i
$842$	8.02688	−	3.57380i	0.276624	−	0.123161i
$843$	6.54018	+	6.16635i	0.225256	+	0.212380i
$844$	−0.0334015	+	0.317794i	−0.00114973	+	0.0109389i
$845$	−8.39855	+	22.6728i	−0.288919	+	0.779969i
$846$	4.49532	+	5.47847i	0.154552	+	0.188354i
$847$	4.53025	−	3.29142i	0.155661	−	0.113094i
$848$	0.749962	−	0.832917i	0.0257538	−	0.0286025i
$849$	2.42057	−	10.2279i	0.0830739	−	0.351021i
$850$	19.9496	+	5.96681i	0.684265	+	0.204660i
$851$	16.1988	−	28.0572i	0.555289	−	0.961789i
$852$	0.391987	−	0.0321250i	0.0134293	−	0.00110058i
$853$	27.9591	+	12.4482i	0.957303	+	0.426219i	0.825089	−	0.565003i	$-0.191125\pi$
$853$	27.9591	+	12.4482i	0.957303	+	0.426219i	0.132214	+	0.991221i	$0.457792\pi$
$854$	−43.9823	+	31.9550i	−1.50504	+	1.09348i
$855$	7.18359	−	10.2762i	0.245673	−	0.351439i
$856$	−24.3611	−	17.6994i	−0.832644	−	0.604951i
$857$	11.3582	+	19.6730i	0.387989	+	0.672017i	0.992179	−	0.124824i	$-0.0398365\pi$
$857$	11.3582	+	19.6730i	0.387989	+	0.672017i	−0.604190	+	0.796840i	$0.706503\pi$
$858$	−2.10311	−	11.1462i	−0.0717991	−	0.380526i
$859$	−19.2543	−	21.3841i	−0.656949	−	0.729616i	0.318966	−	0.947766i	$-0.396664\pi$
$859$	−19.2543	−	21.3841i	−0.656949	−	0.729616i	−0.975915	+	0.218150i	$0.929998\pi$
$860$	−0.112399	+	0.0446703i	−0.00383277	+	0.00152324i
$861$	11.9767	+	17.3061i	0.408164	+	0.589790i
$862$	8.84273	−	1.87958i	0.301184	−	0.0640187i
$863$	4.01032	−	12.3425i	0.136513	−	0.420143i	−0.859309	−	0.511456i	$-0.829106\pi$
$863$	4.01032	−	12.3425i	0.136513	−	0.420143i	0.995822	+	0.0913127i	$0.0291063\pi$
$864$	−0.325691	+	0.254966i	−0.0110802	+	0.00867412i
$865$	−22.4794	+	14.9772i	−0.764321	+	0.509241i
$866$	21.6170	−	4.59483i	0.734575	−	0.156139i
$867$	−13.5126	−	4.73596i	−0.458910	−	0.160842i
$868$	0.227969	−	0.394853i	0.00773776	−	0.0134022i
$869$	−23.2610	+	10.3565i	−0.789076	+	0.351319i
$870$	−10.3496	+	19.7629i	−0.350886	+	0.670024i
$871$	−15.4184	−	6.86473i	−0.522434	−	0.232603i
$872$	−20.2522	+	14.7141i	−0.685825	+	0.498281i
$873$	−4.42374	+	29.1485i	−0.149721	+	0.986527i
$874$	17.5382			0.593239
$875$	−12.4860	+	54.1801i	−0.422104	+	1.83162i
$876$	0.0370492	−	0.156548i	0.00125178	−	0.00528927i
$877$	1.99186	+	0.423383i	0.0672604	+	0.0142966i	0.241419	−	0.970421i	$-0.422387\pi$
$877$	1.99186	+	0.423383i	0.0672604	+	0.0142966i	−0.174159	+	0.984718i	$0.555721\pi$
$878$	2.29493	+	21.8348i	0.0774502	+	0.736889i
$879$	3.93578	+	9.41562i	0.132750	+	0.317581i
$880$	19.4992	−	19.9636i	0.657319	−	0.672973i
$881$	41.9767	+	30.4979i	1.41423	+	1.02750i	0.992690	+	0.120689i	$0.0385104\pi$
$881$	41.9767	+	30.4979i	1.41423	+	1.02750i	0.421540	+	0.906810i	$0.361490\pi$
$882$	−62.6028	+	41.2324i	−2.10795	+	1.38837i
$883$	−3.04267	−	2.21063i	−0.102394	−	0.0743937i	0.535410	−	0.844592i	$-0.320157\pi$
$883$	−3.04267	−	2.21063i	−0.102394	−	0.0743937i	−0.637804	+	0.770199i	$0.720157\pi$
$884$	0.0601563	−	0.0127866i	0.00202328	−	0.000430061i
$885$	11.5504	+	1.96203i	0.388262	+	0.0659530i
$886$	0.411183	+	0.0873997i	0.0138140	+	0.00293625i
$887$	34.2865	+	38.0790i	1.15123	+	1.27857i	0.954534	+	0.298101i	$0.0963533\pi$
$887$	34.2865	+	38.0790i	1.15123	+	1.27857i	0.196692	+	0.980465i	$0.436980\pi$
$888$	−0.548865	+	23.9133i	−0.0184187	+	0.802477i
$889$	26.5635	−	29.5017i	0.890910	−	0.989456i
$890$	6.76092	+	5.34440i	0.226626	+	0.179145i
$891$	5.52180	−	27.7363i	0.184987	−	0.929201i
$892$	0.245466	+	0.178341i	0.00821880	+	0.00597131i
$893$	−1.56653	−	2.71331i	−0.0524219	−	0.0907973i
$894$	34.5118	+	12.0959i	1.15425	+	0.404547i
$895$	27.6366	−	10.9835i	0.923788	−	0.367138i
$896$	5.81830	+	55.3575i	0.194376	+	1.84936i
$897$	16.9171	+	2.17158i	0.564845	+	0.0725070i
$898$	0.00255972	−	0.00284286i	8.54191e−5	−	9.48675e-5i
$899$	−26.6305			−0.888178
$900$	0.209377	+	0.0267524i	0.00697923	+	0.000891746i
$901$	−0.833958			−0.0277832
$902$	−7.23986	+	8.04067i	−0.241061	+	0.267725i
$903$	12.7692	+	30.5479i	0.424931	+	1.01657i
$904$	2.60467	+	24.7817i	0.0866299	+	0.824228i
$905$	29.8853	+	36.0300i	0.993421	+	1.19768i
$906$	−10.3820	+	8.92524i	−0.344918	+	0.296521i
$907$	16.7448	+	29.0028i	0.556002	+	0.963023i	0.997825	+	0.0659210i	$0.0209985\pi$
$907$	16.7448	+	29.0028i	0.556002	+	0.963023i	−0.441823	+	0.897102i	$0.645668\pi$
$908$	−0.0247147	−	0.0179563i	−0.000820185	−	0.000595900i
$909$	−15.8905	+	16.0972i	−0.527055	+	0.533912i
$910$	−6.26117	−	22.3134i	−0.207556	−	0.739683i
$911$	22.7597	−	25.2772i	0.754063	−	0.837472i	−0.236910	−	0.971531i	$-0.576135\pi$
$911$	22.7597	−	25.2772i	0.754063	−	0.837472i	0.990973	+	0.134060i	$0.0428015\pi$
$912$	−11.2796	+	6.17158i	−0.373503	+	0.204361i
$913$	20.2473	+	22.4869i	0.670088	+	0.744209i
$914$	−5.41597	−	1.15120i	−0.179144	−	0.0380783i
$915$	1.90777	−	29.9837i	0.0630691	−	0.991230i
$916$	−0.265703	+	0.0564768i	−0.00877906	+	0.00186605i
$917$	−44.0924	−	32.0350i	−1.45606	−	1.05789i
$918$	−21.3146	−	3.73706i	−0.703486	−	0.123341i
$919$	−28.2156	−	20.4998i	−0.930745	−	0.676226i	0.0154297	−	0.999881i	$-0.495088\pi$
$919$	−28.2156	−	20.4998i	−0.930745	−	0.676226i	−0.946175	+	0.323655i	$0.895088\pi$
$920$	19.6269	+	37.4247i	0.647081	+	1.23386i
$921$	−33.4983	+	43.9492i	−1.10381	+	1.44817i
$922$	1.14181	+	10.8636i	0.0376035	+	0.357773i
$923$	23.3427	+	4.96164i	0.768334	+	0.163314i
$924$	0.277123	+	0.261283i	0.00911667	+	0.00859557i
$925$	17.6911	−	16.6995i	0.581681	−	0.549077i
$926$	−36.3541			−1.19467
$927$	−0.863315	+	0.337813i	−0.0283550	+	0.0110953i
$928$	−0.263226	+	0.191245i	−0.00864081	+	0.00627792i
$929$	−37.3574	−	16.6326i	−1.22566	−	0.545697i	−0.311186	−	0.950349i	$-0.600726\pi$
$929$	−37.3574	−	16.6326i	−1.22566	−	0.545697i	−0.914471	+	0.404652i	$0.867393\pi$
$930$	−12.3714	−	33.3382i	−0.405675	−	1.09320i
$931$	30.2755	−	13.4795i	0.992240	−	0.441774i
$932$	−0.186941	+	0.323792i	−0.00612346	+	0.0106061i
$933$	21.0822	−	18.1240i	0.690199	−	0.593354i
$934$	−26.3762	+	5.60643i	−0.863056	+	0.183448i
$935$	−20.7473	−	0.842660i	−0.678508	−	0.0275579i
$936$	−11.7267	+	4.58865i	−0.383301	+	0.149985i
$937$	9.99024	−	30.7468i	0.326367	−	1.00445i	−0.644453	−	0.764644i	$-0.722915\pi$
$937$	9.99024	−	30.7468i	0.326367	−	1.00445i	0.970820	−	0.239810i	$-0.0770852\pi$
$938$	−78.2316	+	16.6286i	−2.55435	+	0.542945i
$939$	3.30029	−	6.97713i	0.107701	−	0.227690i
$940$	0.0282045	−	0.0445706i	0.000919929	−	0.00145373i
$941$	4.51267	+	5.01183i	0.147109	+	0.163381i	0.812196	−	0.583385i	$-0.198272\pi$
$941$	4.51267	+	5.01183i	0.147109	+	0.163381i	−0.665087	+	0.746766i	$0.731605\pi$
$942$	35.4070	+	12.4096i	1.15362	+	0.404328i
$943$	−8.13465	−	14.0896i	−0.264901	−	0.458822i
$944$	−9.71980	−	7.06185i	−0.316353	−	0.229844i
$945$	6.31087	−	57.4358i	0.205293	−	1.86839i
$946$	−13.7706	+	10.0049i	−0.447721	+	0.325288i
$947$	48.1289	+	21.4284i	1.56398	+	0.696329i	0.992267	−	0.124124i	$-0.0396121\pi$
$947$	48.1289	+	21.4284i	1.56398	+	0.696329i	0.571714	+	0.820453i	$0.306279\pi$
$948$	0.112391	+	0.162402i	0.00365028	+	0.00527459i
$949$	4.88059	−	8.45343i	0.158431	−	0.274410i
$950$	12.6175	+	3.77382i	0.409365	+	0.122439i
$951$	18.3860	+	17.3351i	0.596207	+	0.562128i
$952$	27.9111	−	30.9984i	0.904603	−	1.00466i
$953$	35.1915	−	25.5681i	1.13996	−	0.828232i	0.152849	−	0.988249i	$-0.451155\pi$
$953$	35.1915	−	25.5681i	1.13996	−	0.828232i	0.987114	+	0.160017i	$0.0511551\pi$
$954$	1.17713	−	0.194247i	0.0381111	−	0.00628897i
$955$	−10.8371	−	0.440152i	−0.350679	−	0.0142430i
$956$	−0.0108622	+	0.103347i	−0.000351309	+	0.00334248i
$957$	5.12335	−	21.6483i	0.165615	−	0.699789i
$958$	14.0640	−	6.26168i	0.454386	−	0.202306i
$959$	−22.8984	−	25.4313i	−0.739429	−	0.821219i
$960$	−25.9739	−	17.2836i	−0.838303	−	0.557825i
$961$	7.66036	−	8.50769i	0.247108	−	0.274442i
$962$	−3.13354	+	9.64405i	−0.101029	+	0.310937i
$963$	−8.43610	−	30.6892i	−0.271850	−	0.988945i
$964$	0.0613056	+	0.188679i	0.00197452	+	0.00607695i
$965$	−5.53642	+	5.66827i	−0.178224	+	0.182468i
$966$	70.9048	−	38.7954i	2.28132	−	1.24822i
$967$	−10.1922	+	4.53786i	−0.327759	+	0.145928i	−0.564018	−	0.825762i	$-0.690745\pi$
$967$	−10.1922	+	4.53786i	−0.327759	+	0.145928i	0.236259	+	0.971690i	$0.424079\pi$
$968$	1.59797	−	2.76777i	0.0513608	−	0.0889595i
$969$	9.02849	+	3.16436i	0.290037	+	0.101654i
$970$	−30.5271	+	5.20394i	−0.980167	+	0.167089i
$971$	−36.1891	+	26.2929i	−1.16136	+	0.843781i	−0.989950	−	0.141418i	$-0.954834\pi$
$971$	−36.1891	+	26.2929i	−1.16136	+	0.843781i	−0.171415	+	0.985199i	$0.554834\pi$
$972$	−0.219349	−	0.00219831i	−0.00703562	−	7.05108e-5i
$973$	11.6205	+	35.7643i	0.372537	+	1.14655i
$974$	−20.4108	−	35.3525i	−0.654003	−	1.13277i
$975$	11.7033	+	5.20245i	0.374807	+	0.166612i
$976$	−15.4049	+	26.6820i	−0.493098	+	0.854071i
$977$	23.8820	+	5.07627i	0.764052	+	0.162404i	0.573425	−	0.819258i	$-0.305615\pi$
$977$	23.8820	+	5.07627i	0.764052	+	0.162404i	0.190627	+	0.981663i	$0.438948\pi$
$978$	−52.4485	−	6.73262i	−1.67712	−	0.215285i
$979$	−7.85098	−	3.49548i	−0.250918	−	0.111716i
$980$	0.437689	+	0.345986i	0.0139815	+	0.0110521i
$981$	−26.4314	−	1.21396i	−0.843891	−	0.0387589i
$982$	34.4998			1.10093
$983$	−2.88753	+	27.4731i	−0.0920980	+	0.876254i	0.846766	+	0.531966i	$0.178546\pi$
$983$	−2.88753	+	27.4731i	−0.0920980	+	0.876254i	−0.938864	+	0.344289i	$0.888120\pi$
$984$	10.2620	+	6.24302i	0.327140	+	0.199020i
$985$	44.5444	−	17.7031i	1.41930	−	0.564069i
$986$	−16.6504	−	3.53914i	−0.530256	−	0.112709i
$987$	−12.3352	−	7.50431i	−0.392635	−	0.238865i
$988$	0.0380469	−	0.00808713i	0.00121043	−	0.000257286i
$989$	−7.90911	−	24.3417i	−0.251495	−	0.774023i
$990$	29.4811	−	3.64307i	0.936970	−	0.115784i
$991$	−10.4706	+	32.2253i	−0.332610	+	1.02367i	0.635277	+	0.772284i	$0.280886\pi$
$991$	−10.4706	+	32.2253i	−0.332610	+	1.02367i	−0.967887	+	0.251385i	$0.919114\pi$
$992$	0.0542107	−	0.515780i	0.00172119	−	0.0163760i
$993$	29.7306	+	28.0313i	0.943473	+	0.889545i
$994$	103.310	−	45.9968i	3.27681	−	1.45893i
$995$	−41.0352	−	10.4794i	−1.30090	−	0.332220i
$996$	0.142278	−	0.186666i	0.00450824	−	0.00591473i
$997$	13.3910	+	5.96206i	0.424097	+	0.188820i	0.607677	−	0.794185i	$-0.292102\pi$
$997$	13.3910	+	5.96206i	0.424097	+	0.188820i	−0.183579	+	0.983005i	$0.558768\pi$
$998$	11.1093	+	34.1909i	0.351659	+	1.08229i
$999$	−16.2324	+	19.3831i	−0.513571	+	0.613256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.9	✓	224
3.2	odd	2		675.2.r.a.631.20		224
9.2	odd	6		675.2.r.a.181.9		224
9.7	even	3	inner	225.2.q.a.106.20	yes	224
25.21	even	5	inner	225.2.q.a.121.20	yes	224
75.71	odd	10		675.2.r.a.496.9		224
225.146	odd	30		675.2.r.a.46.20		224
225.196	even	15	inner	225.2.q.a.196.9	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.9	✓	224	1.1	even	1	trivial
225.2.q.a.106.20	yes	224	9.7	even	3	inner
225.2.q.a.121.20	yes	224	25.21	even	5	inner
225.2.q.a.196.9	yes	224	225.196	even	15	inner
675.2.r.a.46.20		224	225.146	odd	30
675.2.r.a.181.9		224	9.2	odd	6
675.2.r.a.496.9		224	75.71	odd	10
675.2.r.a.631.20		224	3.2	odd	2

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.942959 + 1.04726i) q^{2} +(1.04996 - 1.37753i) q^{3} +(0.00147092 + 0.0139948i) q^{4} +(-2.16654 - 0.553283i) q^{5} +(0.452565 + 2.39853i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 - 1.66830i) q^{8} +(-0.795170 - 2.89270i) q^{9} +O(q^{10})\)	\(q+(-0.942959 + 1.04726i) q^{2} +(1.04996 - 1.37753i) q^{3} +(0.00147092 + 0.0139948i) q^{4} +(-2.16654 - 0.553283i) q^{5} +(0.452565 + 2.39853i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 - 1.66830i) q^{8} +(-0.795170 - 2.89270i) q^{9} +(2.62239 - 1.74721i) q^{10} +(-2.10260 + 2.33518i) q^{11} +(0.0208227 + 0.0126678i) q^{12} +(0.989570 + 1.09903i) q^{13} +(6.85500 + 1.45708i) q^{14} +(-3.03694 + 2.40354i) q^{15} +(3.88487 - 0.825754i) q^{16} +(-2.39081 - 1.73703i) q^{17} +(3.77922 + 1.89494i) q^{18} +(-1.51211 - 1.09861i) q^{19} +(0.00455631 - 0.0311342i) q^{20} +(-8.54345 - 1.09669i) q^{21} +(-0.462874 - 4.40395i) q^{22} +(6.51302 + 1.38439i) q^{23} +(-4.70908 + 1.41146i) q^{24} +(4.38776 + 2.39741i) q^{25} -2.08409 q^{26} +(-4.81967 - 1.94185i) q^{27} +(0.0566152 - 0.0411334i) q^{28} +(-3.73405 - 1.66251i) q^{29} +(0.346571 - 5.44691i) q^{30} +(5.95196 - 2.64998i) q^{31} +(0.0398007 - 0.0689368i) q^{32} +(1.00913 + 5.34824i) q^{33} +(4.07356 - 0.865861i) q^{34} +(3.00427 + 10.7065i) q^{35} +(0.0393133 - 0.0153832i) q^{36} +(1.50355 - 4.62746i) q^{37} +(2.57639 - 0.547629i) q^{38} +(2.55295 - 0.209225i) q^{39} +(4.05181 + 4.88490i) q^{40} +(-1.63494 - 1.81578i) q^{41} +(9.20464 - 7.91309i) q^{42} +(-1.92193 - 3.32888i) q^{43} +(-0.0357732 - 0.0259908i) q^{44} +(0.122284 + 6.70709i) q^{45} +(-7.59132 + 5.51542i) q^{46} +(1.53134 + 0.681798i) q^{47} +(2.94145 - 6.21852i) q^{48} +(-8.86554 + 15.3556i) q^{49} +(-6.64819 + 2.33447i) q^{50} +(-4.90306 + 1.46960i) q^{51} +(-0.0139252 + 0.0154655i) q^{52} +(0.228304 - 0.165873i) q^{53} +(6.57837 - 3.21638i) q^{54} +(5.84738 - 3.89591i) q^{55} +(-1.47541 + 14.0376i) q^{56} +(-3.10103 + 0.929477i) q^{57} +(5.26214 - 2.34285i) q^{58} +(-2.02413 - 2.24803i) q^{59} +(-0.0381043 - 0.0389661i) q^{60} +(-5.19072 + 5.76488i) q^{61} +(-2.83723 + 8.73208i) q^{62} +(-10.4810 + 10.6174i) q^{63} +(2.48928 + 7.66123i) q^{64} +(-1.53587 - 2.92860i) q^{65} +(-6.55257 - 3.98635i) q^{66} +(-10.4257 + 4.64182i) q^{67} +(0.0207927 - 0.0360141i) q^{68} +(8.74544 - 7.51832i) q^{69} +(-14.0454 - 6.94956i) q^{70} +(13.0547 - 9.48483i) q^{71} +(-3.00001 + 7.96887i) q^{72} +(-2.03962 - 6.27730i) q^{73} +(3.42837 + 5.93811i) q^{74} +(7.90947 - 3.52707i) q^{75} +(0.0131507 - 0.0227777i) q^{76} +(15.2852 + 3.24898i) q^{77} +(-2.18821 + 2.87090i) q^{78} +(7.40257 + 3.29584i) q^{79} +(-8.87358 - 0.360405i) q^{80} +(-7.73541 + 4.60037i) q^{81} +3.44328 q^{82} +(1.00657 - 9.57689i) q^{83} +(0.00278130 - 0.121177i) q^{84} +(4.21871 + 5.08612i) q^{85} +(5.29851 + 1.12623i) q^{86} +(-6.21075 + 3.39820i) q^{87} +(8.72383 - 1.85431i) q^{88} +(0.845142 + 2.60108i) q^{89} +(-7.13939 - 6.19644i) q^{90} +(2.27269 - 6.99461i) q^{91} +(-0.00979414 + 0.0931851i) q^{92} +(2.59889 - 10.9814i) q^{93} +(-2.15801 + 0.960809i) q^{94} +(2.66820 + 3.21681i) q^{95} +(-0.0531733 - 0.127208i) q^{96} +(-8.97780 - 3.99717i) q^{97} +(-7.72146 - 23.7642i) q^{98} +(8.42689 + 4.22533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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