LMFDB - Embedded newform 507.2.p.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24255 - 0.471239i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.175147 - 0.155167i) q^{4} +(-1.73849 - 0.211091i) q^{5} +(-0.318029 - 1.29030i) q^{6} +(-0.0913225 - 0.174001i) q^{7} +(1.37966 + 2.62872i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-1.24255 - 0.471239i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.175147 - 0.155167i) q^{4} +(-1.73849 - 0.211091i) q^{5} +(-0.318029 - 1.29030i) q^{6} +(-0.0913225 - 0.174001i) q^{7} +(1.37966 + 2.62872i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(2.06070 + 1.08154i) q^{10} +(-1.16700 + 0.442585i) q^{11} +(0.0282049 - 0.232288i) q^{12} +(2.96074 - 2.05767i) q^{13} +(0.0314774 + 0.259240i) q^{14} +(-0.813852 - 1.55067i) q^{15} +(-0.419137 - 3.45191i) q^{16} +(1.65435 - 0.868270i) q^{17} +(0.881231 - 0.994705i) q^{18} -5.47529i q^{19} +(0.271738 + 0.306728i) q^{20} +(0.0913225 - 0.174001i) q^{21} +1.65862 q^{22} -2.82934 q^{23} +(-1.37966 + 2.62872i) q^{24} +(-1.87691 - 0.462617i) q^{25} +(-4.64853 + 1.16155i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-0.0110042 + 0.0446459i) q^{28} +(1.98455 - 5.23282i) q^{29} +(0.280522 + 2.31030i) q^{30} +(-1.62722 - 6.60189i) q^{31} +(0.315081 - 1.27833i) q^{32} +(-1.02717 - 0.709006i) q^{33} +(-2.46478 + 0.299279i) q^{34} +(0.122034 + 0.321776i) q^{35} +(0.207191 - 0.108742i) q^{36} +(-0.996164 - 4.04160i) q^{37} +(-2.58017 + 6.80334i) q^{38} +(3.37532 + 1.26775i) q^{39} +(-1.84363 - 4.86125i) q^{40} +(-1.57961 + 1.09032i) q^{41} +(-0.195469 + 0.173170i) q^{42} +(11.8683 + 2.92527i) q^{43} +(0.273071 + 0.103562i) q^{44} +(0.813852 - 1.55067i) q^{45} +(3.51561 + 1.33329i) q^{46} +(-1.26581 - 1.42881i) q^{47} +(2.60277 - 2.30585i) q^{48} +(3.95452 - 5.72911i) q^{49} +(2.11416 + 1.45930i) q^{50} +(1.65435 + 0.868270i) q^{51} +(-0.837847 - 0.0990135i) q^{52} +(0.884847 - 0.464403i) q^{53} +(1.31922 + 0.160183i) q^{54} +(2.12225 - 0.523087i) q^{55} +(0.331405 - 0.480123i) q^{56} +(4.50608 - 3.11032i) q^{57} +(-4.93181 + 5.56687i) q^{58} +(-14.7242 - 1.78784i) q^{59} +(-0.0980680 + 0.397877i) q^{60} +(5.21304 + 2.73602i) q^{61} +(-1.08916 + 8.97002i) q^{62} +(0.195077 - 0.0236866i) q^{63} +(-4.94452 + 7.16338i) q^{64} +(-5.58159 + 2.95226i) q^{65} +(0.942206 + 1.36502i) q^{66} +(-8.58642 - 9.69206i) q^{67} +(-0.424481 - 0.104625i) q^{68} +(-1.60725 - 2.32850i) q^{69} -0.457331i q^{70} +(10.3628 - 7.15292i) q^{71} +(-2.94713 + 0.357847i) q^{72} +(1.75148 - 0.664248i) q^{73} +(-0.666769 + 5.49133i) q^{74} +(-0.685480 - 1.80746i) q^{75} +(-0.849583 + 0.958981i) q^{76} +(0.183583 + 0.162641i) q^{77} +(-3.59661 - 3.16583i) q^{78} +(4.10805 - 3.63942i) q^{79} +6.08959i q^{80} +(-0.748511 - 0.663123i) q^{81} +(2.47655 - 0.610414i) q^{82} +(0.312266 + 0.215542i) q^{83} +(-0.0429940 + 0.0163055i) q^{84} +(-3.05936 + 1.16026i) q^{85} +(-13.3685 - 9.22761i) q^{86} +(5.43388 - 1.33933i) q^{87} +(-2.77350 - 2.45711i) q^{88} +11.0934i q^{89} +(-1.74199 + 1.54327i) q^{90} +(-0.628418 - 0.327259i) q^{91} +(0.495551 + 0.439020i) q^{92} +(4.50889 - 5.08948i) q^{93} +(0.899532 + 2.37187i) q^{94} +(-1.15579 + 9.51875i) q^{95} +(1.23103 - 0.466870i) q^{96} +(-5.72423 + 0.695048i) q^{97} +(-7.61348 + 5.25520i) q^{98} -1.24811i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−1.24255	−	0.471239i	−0.878618	−	0.333216i	−0.126281	−	0.991994i	$-0.540304\pi$
$2$	−1.24255	−	0.471239i	−0.878618	−	0.333216i	−0.752337	+	0.658779i	$0.771073\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	−0.175147	−	0.155167i	−0.0875735	−	0.0775834i
$5$	−1.73849	−	0.211091i	−0.777478	−	0.0944029i	−0.277829	−	0.960631i	$-0.589615\pi$
$5$	−1.73849	−	0.211091i	−0.777478	−	0.0944029i	−0.499649	+	0.866228i	$0.666538\pi$
$6$	−0.318029	−	1.29030i	−0.129835	−	0.526761i
$7$	−0.0913225	−	0.174001i	−0.0345167	−	0.0657660i	0.867587	−	0.497286i	$-0.165670\pi$
$7$	−0.0913225	−	0.174001i	−0.0345167	−	0.0657660i	−0.902104	+	0.431520i	$0.857978\pi$
$8$	1.37966	+	2.62872i	0.487784	+	0.929395i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	2.06070	+	1.08154i	0.651650	+	0.342012i
$11$	−1.16700	+	0.442585i	−0.351864	+	0.133444i	−0.524203	−	0.851593i	$-0.675637\pi$
$11$	−1.16700	+	0.442585i	−0.351864	+	0.133444i	0.172339	+	0.985038i	$0.444867\pi$
$12$	0.0282049	−	0.232288i	0.00814205	−	0.0670558i
$13$	2.96074	−	2.05767i	0.821162	−	0.570695i
$13$	2.96074	−	2.05767i	0.821162	−	0.570695i
$14$	0.0314774	+	0.259240i	0.00841269	+	0.0692847i
$15$	−0.813852	−	1.55067i	−0.210136	−	0.400380i
$16$	−0.419137	−	3.45191i	−0.104784	−	0.862976i
$17$	1.65435	−	0.868270i	0.401239	−	0.210586i	−0.252018	−	0.967722i	$-0.581094\pi$
$17$	1.65435	−	0.868270i	0.401239	−	0.210586i	0.653257	+	0.757136i	$0.273402\pi$
$18$	0.881231	−	0.994705i	0.207708	−	0.234454i
$19$		−	5.47529i		−	1.25612i	−0.778166	−	0.628059i	$-0.783850\pi$
$19$		−	5.47529i		−	1.25612i	0.778166	−	0.628059i	$-0.216150\pi$
$20$	0.271738	+	0.306728i	0.0607624	+	0.0685866i
$21$	0.0913225	−	0.174001i	0.0199282	−	0.0379700i
$22$	1.65862			0.353620
$23$	−2.82934			−0.589958			−0.294979	−	0.955504i	$-0.595313\pi$
$23$	−2.82934			−0.589958			−0.294979	+	0.955504i	$0.595313\pi$
$24$	−1.37966	+	2.62872i	−0.281622	+	0.536586i
$25$	−1.87691	−	0.462617i	−0.375382	−	0.0925233i
$26$	−4.64853	+	1.16155i	−0.911653	+	0.227799i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	−0.0110042	+	0.0446459i	−0.00207960	+	0.00843728i
$29$	1.98455	−	5.23282i	0.368521	−	0.971710i	−0.614614	−	0.788828i	$-0.710688\pi$
$29$	1.98455	−	5.23282i	0.368521	−	0.971710i	0.983135	−	0.182882i	$-0.0585427\pi$
$30$	0.280522	+	2.31030i	0.0512160	+	0.421802i
$31$	−1.62722	−	6.60189i	−0.292257	−	1.18574i	−0.915048	−	0.403346i	$-0.867847\pi$
$31$	−1.62722	−	6.60189i	−0.292257	−	1.18574i	0.622790	−	0.782389i	$-0.285999\pi$
$32$	0.315081	−	1.27833i	0.0556990	−	0.225980i
$33$	−1.02717	−	0.709006i	−0.178808	−	0.123422i
$34$	−2.46478	+	0.299279i	−0.422707	+	0.0513259i
$35$	0.122034	+	0.321776i	0.0206274	+	0.0543901i
$36$	0.207191	−	0.108742i	0.0345319	−	0.0181237i
$37$	−0.996164	−	4.04160i	−0.163768	−	0.664434i	−0.994222	−	0.107346i	$-0.965765\pi$
$37$	−0.996164	−	4.04160i	−0.163768	−	0.664434i	0.830453	−	0.557088i	$-0.188081\pi$
$38$	−2.58017	+	6.80334i	−0.418558	+	1.10365i
$39$	3.37532	+	1.26775i	0.540484	+	0.203003i
$40$	−1.84363	−	4.86125i	−0.291504	−	0.768632i
$41$	−1.57961	+	1.09032i	−0.246693	+	0.170280i	−0.684995	−	0.728548i	$-0.740196\pi$
$41$	−1.57961	+	1.09032i	−0.246693	+	0.170280i	0.438302	+	0.898828i	$0.355580\pi$
$42$	−0.195469	+	0.173170i	−0.0301615	+	0.0267208i
$43$	11.8683	+	2.92527i	1.80990	+	0.446100i	0.991671	−	0.128795i	$-0.0411109\pi$
$43$	11.8683	+	2.92527i	1.80990	+	0.446100i	0.818227	+	0.574895i	$0.194957\pi$
$44$	0.273071	+	0.103562i	0.0411670	+	0.0156126i
$45$	0.813852	−	1.55067i	0.121322	−	0.231160i
$46$	3.51561	+	1.33329i	0.518348	+	0.196583i
$47$	−1.26581	−	1.42881i	−0.184638	−	0.208413i	0.648903	−	0.760871i	$-0.275228\pi$
$47$	−1.26581	−	1.42881i	−0.184638	−	0.208413i	−0.833540	+	0.552458i	$0.813690\pi$
$48$	2.60277	−	2.30585i	0.375677	−	0.332821i
$49$	3.95452	−	5.72911i	0.564931	−	0.818444i
$50$	2.11416	+	1.45930i	0.298987	+	0.206376i
$51$	1.65435	+	0.868270i	0.231655	+	0.121582i
$52$	−0.837847	−	0.0990135i	−0.116189	−	0.0137307i
$53$	0.884847	−	0.464403i	0.121543	−	0.0637907i	−0.402856	−	0.915263i	$-0.631982\pi$
$53$	0.884847	−	0.464403i	0.121543	−	0.0637907i	0.524399	+	0.851473i	$0.324290\pi$
$54$	1.31922	+	0.160183i	0.179523	+	0.0217981i
$55$	2.12225	−	0.523087i	0.286164	−	0.0705331i
$56$	0.331405	−	0.480123i	0.0442859	−	0.0641592i
$57$	4.50608	−	3.11032i	0.596844	−	0.411972i
$58$	−4.93181	+	5.56687i	−0.647579	+	0.730965i
$59$	−14.7242	−	1.78784i	−1.91693	−	0.232757i	−0.927076	−	0.374873i	$-0.877686\pi$
$59$	−14.7242	−	1.78784i	−1.91693	−	0.232757i	−0.989850	+	0.142116i	$0.954609\pi$
$60$	−0.0980680	+	0.397877i	−0.0126605	+	0.0513657i
$61$	5.21304	+	2.73602i	0.667462	+	0.350311i	0.764182	−	0.645001i	$-0.223143\pi$
$61$	5.21304	+	2.73602i	0.667462	+	0.350311i	−0.0967202	+	0.995312i	$0.530835\pi$
$62$	−1.08916	+	8.97002i	−0.138323	+	1.13919i
$63$	0.195077	−	0.0236866i	0.0245774	−	0.00298423i
$64$	−4.94452	+	7.16338i	−0.618065	+	0.895422i
$65$	−5.58159	+	2.95226i	−0.692310	+	0.366183i
$66$	0.942206	+	1.36502i	0.115978	+	0.168022i
$67$	−8.58642	−	9.69206i	−1.04900	−	1.18407i	−0.982495	−	0.186288i	$-0.940354\pi$
$67$	−8.58642	−	9.69206i	−1.04900	−	1.18407i	−0.0665030	−	0.997786i	$-0.521184\pi$
$68$	−0.424481	−	0.104625i	−0.0514759	−	0.0126877i
$69$	−1.60725	−	2.32850i	−0.193490	−	0.280319i
$70$		−	0.457331i		−	0.0546615i
$71$	10.3628	−	7.15292i	1.22984	−	0.848896i	0.237372	−	0.971419i	$-0.423714\pi$
$71$	10.3628	−	7.15292i	1.22984	−	0.848896i	0.992466	+	0.122523i	$0.0390984\pi$
$72$	−2.94713	+	0.357847i	−0.347323	+	0.0421727i
$73$	1.75148	−	0.664248i	0.204995	−	0.0777444i	−0.249970	−	0.968254i	$-0.580421\pi$
$73$	1.75148	−	0.664248i	0.204995	−	0.0777444i	0.454965	+	0.890509i	$0.349652\pi$
$74$	−0.666769	+	5.49133i	−0.0775103	+	0.638354i
$75$	−0.685480	−	1.80746i	−0.0791524	−	0.208708i
$76$	−0.849583	+	0.958981i	−0.0974539	+	0.110003i
$77$	0.183583	+	0.162641i	0.0209213	+	0.0185346i
$78$	−3.59661	−	3.16583i	−0.407236	−	0.358460i
$79$	4.10805	−	3.63942i	0.462192	−	0.409466i	−0.399631	−	0.916676i	$-0.630862\pi$
$79$	4.10805	−	3.63942i	0.462192	−	0.409466i	0.861823	+	0.507210i	$0.169323\pi$
$80$			6.08959i			0.680837i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	2.47655	−	0.610414i	0.273489	−	0.0674090i
$83$	0.312266	+	0.215542i	0.0342757	+	0.0236588i	0.585079	−	0.810976i	$-0.301063\pi$
$83$	0.312266	+	0.215542i	0.0342757	+	0.0236588i	−0.550804	+	0.834635i	$0.685679\pi$
$84$	−0.0429940	+	0.0163055i	−0.00469103	+	0.00177907i
$85$	−3.05936	+	1.16026i	−0.331834	+	0.125848i
$86$	−13.3685	−	9.22761i	−1.44156	−	0.995039i
$87$	5.43388	−	1.33933i	0.582573	−	0.143591i
$88$	−2.77350	−	2.45711i	−0.295656	−	0.261928i
$89$			11.0934i			1.17590i	0.808897	+	0.587951i	$0.200065\pi$
$89$			11.0934i			1.17590i	−0.808897	+	0.587951i	$0.799935\pi$
$90$	−1.74199	+	1.54327i	−0.183622	+	0.162675i
$91$	−0.628418	−	0.327259i	−0.0658761	−	0.0343060i
$92$	0.495551	+	0.439020i	0.0516647	+	0.0457710i
$93$	4.50889	−	5.08948i	0.467550	−	0.527754i
$94$	0.899532	+	2.37187i	0.0927796	+	0.244640i
$95$	−1.15579	+	9.51875i	−0.118581	+	0.976604i
$96$	1.23103	−	0.466870i	0.125642	−	0.0476497i
$97$	−5.72423	+	0.695048i	−0.581208	+	0.0705714i	−0.405860	−	0.913935i	$-0.633028\pi$
$97$	−5.72423	+	0.695048i	−0.581208	+	0.0705714i	−0.175348	+	0.984507i	$0.556105\pi$
$98$	−7.61348	+	5.25520i	−0.769077	+	0.530856i
$99$		−	1.24811i		−	0.125439i
$100$	0.256953	+	0.372260i	0.0256953	+	0.0372260i
$101$	−1.07501	−	0.264967i	−0.106968	−	0.0263652i	0.185468	−	0.982650i	$-0.440620\pi$
$101$	−1.07501	−	0.264967i	−0.106968	−	0.0263652i	−0.292436	+	0.956285i	$0.594466\pi$
$102$	−1.64646	−	1.85847i	−0.163024	−	0.184016i
$103$	6.04590	+	8.75900i	0.595720	+	0.863049i	0.998637	−	0.0521869i	$-0.0166192\pi$
$103$	6.04590	+	8.75900i	0.595720	+	0.863049i	−0.402917	+	0.915236i	$0.632004\pi$
$104$	9.49387	+	4.94408i	0.930951	+	0.484807i
$105$	−0.195494	+	0.283221i	−0.0190782	+	0.0276396i
$106$	−1.31831	+	0.160072i	−0.128046	+	0.0155476i
$107$	0.195479	−	1.60991i	0.0188977	−	0.155636i	−0.980205	−	0.197984i	$-0.936561\pi$
$107$	0.195479	−	1.60991i	0.0188977	−	0.155636i	0.999103	+	0.0423476i	$0.0134837\pi$
$108$	0.207191	+	0.108742i	0.0199370	+	0.0104637i
$109$	−3.93521	+	15.9658i	−0.376925	+	1.52924i	0.409936	+	0.912114i	$0.365551\pi$
$109$	−3.93521	+	15.9658i	−0.376925	+	1.52924i	−0.786861	+	0.617130i	$0.788295\pi$
$110$	−2.88351	−	0.350121i	−0.274932	−	0.0333827i
$111$	2.76028	−	3.11572i	0.261994	−	0.295731i
$112$	−0.562357	+	0.388167i	−0.0531377	+	0.0366783i
$113$	3.16665	−	4.58768i	0.297893	−	0.431573i	−0.645244	−	0.763977i	$-0.723244\pi$
$113$	3.16665	−	4.58768i	0.297893	−	0.431573i	0.943137	+	0.332404i	$0.107860\pi$
$114$	−7.06474	+	1.74130i	−0.661674	+	0.163088i
$115$	4.91879	+	0.597249i	0.458679	+	0.0556938i
$116$	−1.15955	+	0.608578i	−0.107661	+	0.0565050i
$117$	0.874063	+	3.49800i	0.0808071	+	0.323390i
$118$	17.4531	+	9.16009i	1.60669	+	0.843255i
$119$	−0.302159	−	0.208565i	−0.0276989	−	0.0191191i
$120$	2.95343	−	4.27879i	0.269610	−	0.390598i
$121$	−7.06761	+	6.26136i	−0.642510	+	0.569214i
$122$	−5.18817	−	5.85624i	−0.469715	−	0.530199i
$123$	−1.79464	−	0.680616i	−0.161817	−	0.0613691i
$124$	−0.739392	+	1.40879i	−0.0663993	+	0.126513i
$125$	11.3526	+	4.30549i	1.01541	+	0.385094i
$126$	−0.253555	−	0.0624958i	−0.0225885	−	0.00556757i
$127$	4.76817	−	4.22423i	0.423107	−	0.374840i	−0.424533	−	0.905413i	$-0.639562\pi$
$127$	4.76817	−	4.22423i	0.423107	−	0.374840i	0.847639	+	0.530573i	$0.178023\pi$
$128$	7.35243	−	5.07501i	0.649869	−	0.448572i
$129$	4.33451	+	11.4292i	0.381632	+	1.00628i
$130$	8.32664	−	1.03809i	0.730295	−	0.0910461i
$131$	4.80313	−	12.6648i	0.419652	−	1.10653i	−0.543933	−	0.839128i	$-0.683066\pi$
$131$	4.80313	−	12.6648i	0.419652	−	1.10653i	0.963585	−	0.267402i	$-0.0861651\pi$
$132$	0.0698921	+	0.283563i	0.00608332	+	0.0246810i
$133$	−0.952703	+	0.500017i	−0.0826099	+	0.0433570i
$134$	6.10182	+	16.0892i	0.527117	+	1.38989i
$135$	1.73849	−	0.211091i	0.149626	−	0.0181678i
$136$	4.56489	+	3.15091i	0.391436	+	0.270189i
$137$	−1.64631	+	6.67934i	−0.140654	+	0.570655i	0.857744	+	0.514076i	$0.171865\pi$
$137$	−1.64631	+	6.67934i	−0.140654	+	0.570655i	−0.998398	+	0.0565784i	$0.981981\pi$
$138$	0.899813	+	3.65069i	0.0765972	+	0.310767i
$139$	1.53775	+	12.6645i	0.130431	+	1.07419i	0.900080	+	0.435725i	$0.143508\pi$
$139$	1.53775	+	12.6645i	0.130431	+	1.07419i	−0.769649	+	0.638467i	$0.779569\pi$
$140$	0.0285551	−	0.0752937i	0.00241335	−	0.00636348i
$141$	0.456822	−	1.85340i	0.0384713	−	0.156084i
$142$	−16.2471	+	4.00454i	−1.36342	+	0.336054i
$143$	−2.54449	+	3.71168i	−0.212781	+	0.310386i
$144$	3.37622	+	0.832162i	0.281351	+	0.0693469i
$145$	−4.55472	+	8.67830i	−0.378249	+	0.720694i
$146$	−2.48933			−0.206018
$147$	6.96138			0.574165
$148$	−0.452646	+	0.862446i	−0.0372073	+	0.0708926i
$149$	1.01518	+	1.14590i	0.0831669	+	0.0938760i	0.788621	−	0.614880i	$-0.210795\pi$
$149$	1.01518	+	1.14590i	0.0831669	+	0.0938760i	−0.705454	+	0.708756i	$0.749257\pi$
$150$			2.56889i			0.209749i
$151$	−7.80288	+	8.80763i	−0.634989	+	0.716755i	−0.974635	−	0.223798i	$-0.928154\pi$
$151$	−7.80288	+	8.80763i	−0.634989	+	0.716755i	0.339646	+	0.940553i	$0.389693\pi$
$152$	14.3930	−	7.55404i	1.16743	−	0.612714i
$153$	0.225206	+	1.85474i	0.0182068	+	0.149947i
$154$	−0.151470	−	0.288601i	−0.0122058	−	0.0232562i
$155$	1.43531	+	11.8208i	0.115287	+	0.949473i
$156$	−0.394465	−	0.745781i	−0.0315825	−	0.0597103i
$157$	1.45160	−	11.9550i	0.115851	−	0.954116i	−0.812641	−	0.582764i	$-0.801971\pi$
$157$	1.45160	−	11.9550i	0.115851	−	0.954116i	0.928492	−	0.371352i	$-0.121106\pi$
$158$	−6.81951	+	2.58630i	−0.542531	+	0.205755i
$159$	0.884847	+	0.464403i	0.0701729	+	0.0368296i
$160$	−0.817612	+	2.15586i	−0.0646379	+	0.170436i
$161$	0.258382	+	0.492307i	0.0203634	+	0.0387992i
$162$	0.617576	+	1.17669i	0.0485214	+	0.0924497i
$163$	3.14590	+	12.7634i	0.246406	+	0.999709i	0.955593	+	0.294689i	$0.0952160\pi$
$163$	3.14590	+	12.7634i	0.246406	+	0.999709i	−0.709187	+	0.705020i	$0.750938\pi$
$164$	0.445845	+	0.0541354i	0.0348147	+	0.00422727i
$165$	1.63607	+	1.44943i	0.127368	+	0.112838i
$166$	−0.286436	−	0.414974i	−0.0222318	−	0.0322083i
$167$	−15.5374	−	5.89257i	−1.20232	−	0.455980i	−0.329563	−	0.944133i	$-0.606902\pi$
$167$	−15.5374	−	5.89257i	−1.20232	−	0.455980i	−0.872758	+	0.488153i	$0.837671\pi$
$168$	0.583394			0.0450098
$169$	4.53198	−	12.1845i	0.348614	−	0.937267i
$170$	4.34818			0.333490
$171$	5.11949	+	1.94156i	0.391497	+	0.148475i
$172$	−1.62479	−	2.35392i	−0.123889	−	0.179485i
$173$	7.96228	+	7.05396i	0.605361	+	0.536303i	0.909167	−	0.416431i	$-0.136719\pi$
$173$	7.96228	+	7.05396i	0.605361	+	0.536303i	−0.303807	+	0.952734i	$0.598258\pi$
$174$	−7.38303	−	0.896462i	−0.559706	−	0.0679606i
$175$	0.0909086	+	0.368831i	0.00687204	+	0.0278810i
$176$	2.01689	+	3.84287i	0.152029	+	0.289667i
$177$	−6.89293	−	13.1334i	−0.518104	−	0.987165i
$178$	5.22765	−	13.7842i	0.391829	−	1.03317i
$179$	−16.9742	−	8.90873i	−1.26871	−	0.665870i	−0.310129	−	0.950694i	$-0.600372\pi$
$179$	−16.9742	−	8.90873i	−1.26871	−	0.665870i	−0.958580	+	0.284825i	$0.908065\pi$
$180$	−0.383156	+	0.145312i	−0.0285587	+	0.0108309i
$181$	−0.235210	+	1.93713i	−0.0174830	+	0.143986i	−0.998836	−	0.0482264i	$-0.984643\pi$
$181$	−0.235210	+	1.93713i	−0.0174830	+	0.143986i	0.981353	+	0.192212i	$0.0615662\pi$
$182$	0.626627	+	0.702772i	0.0464486	+	0.0520929i
$183$	0.709649	+	5.84449i	0.0524588	+	0.432037i
$184$	−3.90353	−	7.43756i	−0.287772	−	0.548304i
$185$	0.878679	+	7.23657i	0.0646017	+	0.532043i
$186$	−8.00089	+	4.19919i	−0.586654	+	0.307900i
$187$	−1.54634	+	1.74546i	−0.113080	+	0.127641i
$188$			0.446664i			0.0325763i
$189$	0.130310	+	0.147089i	0.00947865	+	0.0106992i
$190$	5.92173	−	11.2829i	0.429607	−	0.818549i
$191$	−0.289973			−0.0209817			−0.0104908	−	0.999945i	$-0.503339\pi$
$191$	−0.289973			−0.0209817			−0.0104908	+	0.999945i	$0.503339\pi$
$192$	−8.70415			−0.628168
$193$	8.86701	−	16.8947i	0.638261	−	1.21611i	−0.324534	−	0.945874i	$-0.605207\pi$
$193$	8.86701	−	16.8947i	0.638261	−	1.21611i	0.962795	−	0.270232i	$-0.0871003\pi$
$194$	7.44020	+	1.83384i	0.534175	+	0.131662i
$195$	−5.60036	−	2.91648i	−0.401050	−	0.208853i
$196$	−1.58159	+	0.389827i	−0.112971	+	0.0278448i
$197$	2.22020	−	9.00771i	0.158183	−	0.641773i	−0.837293	−	0.546755i	$-0.815863\pi$
$197$	2.22020	−	9.00771i	0.158183	−	0.641773i	0.995476	−	0.0950181i	$-0.0302909\pi$
$198$	−0.588156	+	1.55084i	−0.0417984	+	0.110213i
$199$	1.34273	+	11.0584i	0.0951834	+	0.783906i	0.959646	+	0.281209i	$0.0907356\pi$
$199$	1.34273	+	11.0584i	0.0951834	+	0.783906i	−0.864463	+	0.502696i	$0.832341\pi$
$200$	−1.37341	−	5.57213i	−0.0971146	−	0.394009i
$201$	3.09877	−	12.5722i	0.218570	−	0.886775i
$202$	1.21090	+	0.835822i	0.0851984	+	0.0588082i
$203$	−1.09175	+	0.132562i	−0.0766256	+	0.00930404i
$204$	−0.155028	−	0.408775i	−0.0108541	−	0.0286200i
$205$	2.97629	−	1.56208i	0.207873	−	0.109100i
$206$	−3.38478	−	13.7326i	−0.235829	−	0.956794i
$207$	1.00330	−	2.64548i	0.0697340	−	0.183874i
$208$	−8.34384	−	9.35775i	−0.578541	−	0.648843i
$209$	2.42328	+	6.38967i	0.167622	+	0.441982i
$210$	0.376376	−	0.259794i	0.0259724	−	0.0179275i
$211$	−10.3257	+	9.14776i	−0.710849	+	0.629758i	−0.939020	−	0.343864i	$-0.888264\pi$
$211$	−10.3257	+	9.14776i	−0.710849	+	0.629758i	0.228170	+	0.973621i	$0.426726\pi$
$212$	−0.227038	−	0.0559599i	−0.0155931	−	0.00384334i
$213$	11.7735	+	4.46509i	0.806706	+	0.305943i
$214$	−1.00155	+	1.90829i	−0.0684643	+	0.130448i
$215$	−20.0155	−	7.59086i	−1.36504	−	0.517692i
$216$	−1.96867	−	2.22216i	−0.133951	−	0.151199i
$217$	−1.00013	+	0.886039i	−0.0678933	+	0.0601482i
$218$	12.4134	−	17.9839i	0.840742	−	1.21802i
$219$	1.54162	+	1.06410i	0.104173	+	0.0719054i
$220$	−0.452871	−	0.237685i	−0.0305326	−	0.0160247i
$221$	3.11149	−	5.97483i	0.209301	−	0.401911i
$222$	−4.89805	+	2.57069i	−0.328735	+	0.172534i
$223$	−25.4399	−	3.08896i	−1.70358	−	0.206852i	−0.789886	−	0.613254i	$-0.789860\pi$
$223$	−25.4399	−	3.08896i	−1.70358	−	0.206852i	−0.913695	+	0.406402i	$0.866783\pi$
$224$	−0.251205	+	0.0619164i	−0.0167843	+	0.00413697i
$225$	1.09812	−	1.59090i	0.0732077	−	0.106060i
$226$	−6.09663	+	4.20820i	−0.405542	+	0.279925i
$227$	15.7713	−	17.8021i	1.04678	−	1.18157i	0.0637749	−	0.997964i	$-0.479686\pi$
$227$	15.7713	−	17.8021i	1.04678	−	1.18157i	0.983001	−	0.183601i	$-0.0587755\pi$
$228$	−1.27184	−	0.154430i	−0.0842299	−	0.0102274i
$229$	1.16466	−	4.72522i	0.0769631	−	0.312252i	−0.919826	−	0.392327i	$-0.871670\pi$
$229$	1.16466	−	4.72522i	0.0769631	−	0.312252i	0.996789	+	0.0800757i	$0.0255162\pi$
$230$	−5.83041	−	3.06004i	−0.384446	−	0.201773i
$231$	−0.0295634	+	0.243477i	−0.00194513	+	0.0160196i
$232$	16.4936	−	2.00269i	1.08286	−	0.131483i
$233$	5.59071	−	8.09954i	0.366260	−	0.530619i	−0.595917	−	0.803046i	$-0.703211\pi$
$233$	5.59071	−	8.09954i	0.366260	−	0.530619i	0.962176	+	0.272428i	$0.0878265\pi$
$234$	0.562323	−	4.75835i	0.0367602	−	0.311063i
$235$	1.89900	+	2.75118i	0.123877	+	0.179467i
$236$	2.30149	+	2.59784i	0.149814	+	0.169105i
$237$	5.32882	+	1.31344i	0.346144	+	0.0853168i
$238$	0.277165	+	0.401542i	0.0179659	+	0.0260281i
$239$		−	4.09134i		−	0.264647i	−0.991207	−	0.132323i	$-0.957756\pi$
$239$		−	4.09134i		−	0.264647i	0.991207	−	0.132323i	$-0.0422437\pi$
$240$	−5.01163	+	3.45928i	−0.323500	+	0.223296i
$241$	−7.55173	+	0.916946i	−0.486450	+	0.0590657i	−0.360088	−	0.932919i	$-0.617253\pi$
$241$	−7.55173	+	0.916946i	−0.486450	+	0.0590657i	−0.126362	+	0.991984i	$0.540330\pi$
$242$	11.7325	−	4.44954i	0.754192	−	0.286027i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−0.488511	−	1.28810i	−0.0312737	−	0.0824619i
$245$	−8.08427	+	9.12525i	−0.516485	+	0.582991i
$246$	1.90920	+	1.69140i	0.121726	+	0.107840i
$247$	−11.2663	−	16.2109i	−0.716861	−	1.03148i
$248$	15.1095	−	13.3859i	0.959457	−	0.850005i
$249$			0.379432i			0.0240455i
$250$	−12.0773	−	10.6996i	−0.763838	−	0.676702i
$251$	1.27680	−	0.314702i	0.0805906	−	0.0198638i	−0.198814	−	0.980037i	$-0.563709\pi$
$251$	1.27680	−	0.314702i	0.0805906	−	0.0198638i	0.279405	+	0.960173i	$0.409863\pi$
$252$	−0.0378425	−	0.0261208i	−0.00238385	−	0.00164545i
$253$	3.30184	−	1.25222i	0.207585	−	0.0787266i
$254$	−7.91533	+	3.00189i	−0.496652	+	0.188355i
$255$	−2.69279	−	1.85870i	−0.168629	−	0.116396i
$256$	5.37512	−	1.32485i	0.335945	−	0.0828031i
$257$	−14.7795	−	13.0935i	−0.921922	−	0.816751i	0.0614959	−	0.998107i	$-0.480413\pi$
$257$	−14.7795	−	13.0935i	−0.921922	−	0.816751i	−0.983417	+	0.181356i	$0.941951\pi$
$258$		−	16.2439i		−	1.01130i
$259$	−0.612268	+	0.542422i	−0.0380445	+	0.0337045i
$260$	1.43569	+	0.348997i	0.0890378	+	0.0216439i
$261$	4.18904	+	3.71117i	0.259295	+	0.229716i
$262$	−11.9363	+	13.4733i	−0.737427	+	0.832383i
$263$	−6.30506	−	16.6251i	−0.388787	−	1.02515i	−0.976394	−	0.215999i	$-0.930699\pi$
$263$	−6.30506	−	16.6251i	−0.388787	−	1.02515i	0.587607	−	0.809147i	$-0.300070\pi$
$264$	0.446631	−	3.67834i	0.0274883	−	0.226386i
$265$	−1.63633	+	0.620579i	−0.100519	+	0.0381218i
$266$	1.41941	−	0.172348i	0.0870298	−	0.0105673i
$267$	−9.12971	+	6.30179i	−0.558729	+	0.385663i
$268$			3.02986i			0.185078i
$269$	12.8021	+	18.5470i	0.780556	+	1.13083i	0.988281	+	0.152643i	$0.0487786\pi$
$269$	12.8021	+	18.5470i	0.780556	+	1.13083i	−0.207725	+	0.978187i	$0.566606\pi$
$270$	−2.25965	−	0.556953i	−0.137518	−	0.0338951i
$271$	−4.44911	−	5.02201i	−0.270264	−	0.305065i	0.597672	−	0.801741i	$-0.296092\pi$
$271$	−4.44911	−	5.02201i	−0.270264	−	0.305065i	−0.867936	+	0.496675i	$0.834554\pi$
$272$	−3.69059	−	5.34674i	−0.223775	−	0.324194i
$273$	−0.0876535	−	0.703082i	−0.00530503	−	0.0425525i
$274$	5.19319	−	7.52364i	0.313732	−	0.454520i
$275$	2.39510	−	0.290818i	0.144430	−	0.0175370i
$276$	−0.0798012	+	0.657222i	−0.00480347	+	0.0395601i
$277$	7.74854	+	4.06675i	0.465565	+	0.244347i	0.681159	−	0.732136i	$-0.261476\pi$
$277$	7.74854	+	4.06675i	0.465565	+	0.244347i	−0.215594	+	0.976483i	$0.569169\pi$
$278$	4.05728	−	16.4610i	0.243339	−	0.987266i
$279$	6.74990	+	0.819586i	0.404106	+	0.0490673i
$280$	−0.677496	+	0.764735i	−0.0404881	+	0.0457016i
$281$	6.48217	−	4.47432i	0.386694	−	0.266916i	−0.358818	−	0.933407i	$-0.616820\pi$
$281$	6.48217	−	4.47432i	0.386694	−	0.266916i	0.745512	+	0.666492i	$0.232205\pi$
$282$	−1.44102	+	2.08768i	−0.0858114	+	0.124319i
$283$	−18.2040	+	4.48689i	−1.08212	+	0.266718i	−0.739773	−	0.672856i	$-0.765067\pi$
$283$	−18.2040	+	4.48689i	−1.08212	+	0.266718i	−0.342345	+	0.939574i	$0.611221\pi$
$284$	−2.92491	−	0.355148i	−0.173562	−	0.0210742i
$285$	−8.49034	+	4.45608i	−0.502925	+	0.263955i
$286$	4.91076	−	3.41290i	0.290379	−	0.201809i
$287$	0.333970	+	0.175281i	0.0197136	+	0.0103465i
$288$	1.08353	+	0.747910i	0.0638479	+	0.0440710i
$289$	−7.67412	+	11.1179i	−0.451419	+	0.653993i
$290$	9.74904	−	8.63690i	0.572483	−	0.507176i
$291$	−3.82375	−	4.31612i	−0.224152	−	0.253015i
$292$	−0.409836	−	0.155430i	−0.0239838	−	0.00909586i
$293$	3.76401	−	7.17172i	0.219896	−	0.418976i	−0.750370	−	0.661018i	$-0.770125\pi$
$293$	3.76401	−	7.17172i	0.219896	−	0.418976i	0.970266	+	0.242042i	$0.0778170\pi$
$294$	−8.64989	−	3.28047i	−0.504472	−	0.191321i
$295$	25.2205	+	6.21630i	1.46839	+	0.361927i
$296$	9.24988	−	8.19468i	0.537638	−	0.476306i
$297$	1.02717	−	0.709006i	0.0596026	−	0.0411407i
$298$	−0.721424	−	1.90224i	−0.0417910	−	0.110194i
$299$	−8.37694	+	5.82185i	−0.484451	+	0.336686i
$300$	−0.160398	+	0.422936i	−0.00926060	+	0.0244182i
$301$	−0.574844	−	2.33223i	−0.0331334	−	0.134428i
$302$	13.8460	−	7.26694i	0.796748	−	0.418165i
$303$	−0.392613	−	1.03524i	−0.0225550	−	0.0594727i
$304$	−18.9002	+	2.29490i	−1.08400	+	0.131621i
$305$	−8.48529	−	5.85697i	−0.485866	−	0.335369i
$306$	0.594193	−	2.41074i	0.0339678	−	0.137813i
$307$	5.04777	+	20.4796i	0.288091	+	1.16883i	0.919407	+	0.393307i	$0.128669\pi$
$307$	5.04777	+	20.4796i	0.288091	+	1.16883i	−0.631316	+	0.775526i	$0.717485\pi$
$308$	−0.00691766	−	0.0569721i	−0.000394171	−	0.00324629i
$309$	−3.77405	+	9.95135i	−0.214698	+	0.566113i
$310$	3.78699	−	15.3644i	0.215086	−	0.872639i
$311$	−10.7083	+	2.63937i	−0.607214	+	0.149665i	−0.530922	−	0.847421i	$-0.678154\pi$
$311$	−10.7083	+	2.63937i	−0.607214	+	0.149665i	−0.0762923	+	0.997085i	$0.524308\pi$
$312$	1.32423	+	10.6219i	0.0749699	+	0.601345i
$313$	−20.3341	−	5.01191i	−1.14935	−	0.283290i	−0.381781	−	0.924253i	$-0.624689\pi$
$313$	−20.3341	−	5.01191i	−1.14935	−	0.283290i	−0.767572	+	0.640963i	$0.778535\pi$
$314$	−7.43737	+	14.1707i	−0.419715	+	0.799701i
$315$	−0.344140			−0.0193901
$316$	−1.28423			−0.0722436
$317$	8.84976	−	16.8618i	0.497052	−	0.947054i	−0.499675	−	0.866213i	$-0.666547\pi$
$317$	8.84976	−	16.8618i	0.497052	−	0.947054i	0.996727	−	0.0808407i	$-0.0257605\pi$
$318$	−0.880625	−	0.994020i	−0.0493830	−	0.0557419i
$319$			6.98503i			0.391087i
$320$	10.1081	−	11.4097i	0.565062	−	0.637824i
$321$	1.43598	−	0.753659i	0.0801485	−	0.0420652i
$322$	−0.0890603	−	0.733477i	−0.00496313	−	0.0408751i
$323$	−4.75403	−	9.05805i	−0.264521	−	0.504003i
$324$	0.0282049	+	0.232288i	0.00156694	+	0.0129049i
$325$	−6.50896	+	2.49238i	−0.361052	+	0.138252i
$326$	2.10567	−	17.3417i	0.116622	−	0.960469i
$327$	−15.3750	+	5.83098i	−0.850241	+	0.322454i
$328$	−5.04548	−	2.64807i	−0.278590	−	0.146215i
$329$	−0.133016	+	0.350735i	−0.00733341	+	0.0193366i
$330$	−1.34987	−	2.57197i	−0.0743081	−	0.141582i
$331$	1.46412	+	2.78965i	0.0804753	+	0.153333i	0.922368	−	0.386311i	$-0.126251\pi$
$331$	1.46412	+	2.78965i	0.0804753	+	0.153333i	−0.841893	+	0.539644i	$0.818559\pi$
$332$	−0.0212476	−	0.0862049i	−0.00116611	−	0.00473111i
$333$	4.13220	+	0.501740i	0.226443	+	0.0274952i
$334$	16.5293	+	14.6437i	0.904442	+	0.801265i
$335$	12.8815	+	18.6621i	0.703793	+	1.01962i
$336$	−0.638910	−	0.242307i	−0.0348554	−	0.0132189i
$337$	27.3808			1.49152			0.745762	−	0.666212i	$-0.232085\pi$
$337$	27.3808			1.49152			0.745762	+	0.666212i	$0.232085\pi$
$338$	−11.3730	+	13.0042i	−0.618610	+	0.707336i
$339$	5.57445			0.302763
$340$	0.715873	+	0.271495i	0.0388236	+	0.0147239i
$341$	4.82087	+	6.98423i	0.261064	+	0.378217i
$342$	−5.44630	−	4.82500i	−0.294502	−	0.260906i
$343$	−2.72354	−	0.330698i	−0.147057	−	0.0178560i
$344$	8.68449	+	35.2344i	0.468236	+	1.89971i
$345$	2.30266	+	4.38736i	0.123971	+	0.236208i
$346$	−6.56946	−	12.5171i	−0.353176	−	0.672921i
$347$	−6.97249	+	18.3849i	−0.374303	+	0.986955i	0.607037	+	0.794674i	$0.292358\pi$
$347$	−6.97249	+	18.3849i	−0.374303	+	0.986955i	−0.981340	+	0.192282i	$0.938411\pi$
$348$	−1.15955	−	0.608578i	−0.0621583	−	0.0326232i
$349$	21.3417	−	8.09385i	1.14240	−	0.433254i	0.290454	−	0.956889i	$-0.406194\pi$
$349$	21.3417	−	8.09385i	1.14240	−	0.433254i	0.851942	+	0.523635i	$0.175425\pi$
$350$	0.0608484	−	0.501132i	0.00325248	−	0.0267866i
$351$	−2.38227	+	2.70643i	−0.127156	+	0.144459i
$352$	0.198072	+	1.63127i	0.0105573	+	0.0869468i
$353$	6.76357	+	12.8869i	0.359988	+	0.685901i	0.996338	−	0.0855001i	$-0.0272488\pi$
$353$	6.76357	+	12.8869i	0.359988	+	0.685901i	−0.636350	+	0.771401i	$0.719556\pi$
$354$	2.37588	+	19.5671i	0.126277	+	1.03998i
$355$	−19.5256	+	10.2478i	−1.03631	+	0.543898i
$356$	1.72133	−	1.94298i	0.0912304	−	0.102978i
$357$		−	0.367150i		−	0.0194317i
$358$	16.8932	+	19.0685i	0.892832	+	1.00780i
$359$	1.04261	−	1.98652i	0.0550268	−	0.104845i	−0.856389	−	0.516330i	$-0.827298\pi$
$359$	1.04261	−	1.98652i	0.0550268	−	0.104845i	0.911416	+	0.411486i	$0.134990\pi$
$360$	5.19911			0.274017
$361$	−10.9788			−0.577832
$362$	1.20511	−	2.29615i	0.0633393	−	0.120683i
$363$	−9.16785	−	2.25967i	−0.481188	−	0.118602i
$364$	0.0592859	+	0.154828i	0.00310743	+	0.00811520i
$365$	−3.18515	+	0.785069i	−0.166718	+	0.0410924i
$366$	1.87237	−	7.59650i	0.0978703	−	0.397076i
$367$	11.0289	−	29.0809i	0.575706	−	1.51801i	−0.258191	−	0.966094i	$-0.583127\pi$
$367$	11.0289	−	29.0809i	0.575706	−	1.51801i	0.833898	−	0.551919i	$-0.186104\pi$
$368$	1.18588	+	9.76661i	0.0618184	+	0.509120i
$369$	−0.459334	−	1.86359i	−0.0239120	−	0.0970147i
$370$	2.31835	−	9.40590i	0.120525	−	0.488989i
$371$	−0.161613	−	0.111553i	−0.00839052	−	0.00579156i
$372$	−1.57944	+	0.191778i	−0.0818900	+	0.00994324i
$373$	0.406586	+	1.07208i	0.0210522	+	0.0555101i	0.945130	−	0.326694i	$-0.105935\pi$
$373$	0.406586	+	1.07208i	0.0210522	+	0.0555101i	−0.924078	+	0.382204i	$0.875165\pi$
$374$	2.74395	−	1.44013i	0.141886	−	0.0744675i
$375$	2.90569	+	11.7888i	0.150049	+	0.608772i
$376$	2.00955	−	5.29875i	0.103635	−	0.273262i
$377$	−4.89170	−	19.5766i	−0.251935	−	1.00824i
$378$	−0.0926028	−	0.244174i	−0.00476298	−	0.0125589i
$379$	0.724664	−	0.500199i	0.0372235	−	0.0256935i	−0.549308	−	0.835620i	$-0.685109\pi$
$379$	0.724664	−	0.500199i	0.0372235	−	0.0256935i	0.586531	+	0.809927i	$0.300493\pi$
$380$	1.67943	−	1.48784i	0.0861528	−	0.0763247i
$381$	6.18510	+	1.52449i	0.316872	+	0.0781021i
$382$	0.360307	+	0.136646i	0.0184349	+	0.00699144i
$383$	7.07368	−	13.4778i	0.361448	−	0.688682i	−0.635034	−	0.772484i	$-0.719014\pi$
$383$	7.07368	−	13.4778i	0.361448	−	0.688682i	0.996482	+	0.0838019i	$0.0267063\pi$
$384$	8.35331	+	3.16799i	0.426278	+	0.161666i
$385$	−0.284826	−	0.321503i	−0.0145161	−	0.0163853i
$386$	−18.9792	+	16.8141i	−0.966014	+	0.855814i
$387$	−6.94373	+	10.0597i	−0.352970	+	0.511365i
$388$	1.11043	+	0.766475i	0.0563736	+	0.0389119i
$389$	26.3081	+	13.8076i	1.33387	+	0.700071i	0.972621	−	0.232397i	$-0.0746567\pi$
$389$	26.3081	+	13.8076i	1.33387	+	0.700071i	0.361253	+	0.932468i	$0.382349\pi$
$390$	5.58440	+	6.26299i	0.282777	+	0.317139i
$391$	−4.68072	+	2.45663i	−0.236714	+	0.124237i
$392$	20.5161	+	2.49111i	1.03622	+	0.125820i
$393$	13.1514	−	3.24154i	0.663402	−	0.163514i
$394$	−7.00350	+	10.1463i	−0.352831	+	0.511164i
$395$	−7.91007	+	5.45993i	−0.397999	+	0.274719i
$396$	−0.193665	+	0.218602i	−0.00973202	+	0.0109852i
$397$	11.3657	+	1.38004i	0.570428	+	0.0692624i	0.400668	−	0.916223i	$-0.368778\pi$
$397$	11.3657	+	1.38004i	0.570428	+	0.0692624i	0.169759	+	0.985486i	$0.445701\pi$
$398$	3.54271	−	14.3733i	0.177580	−	0.720471i
$399$	−0.952703	−	0.500017i	−0.0476948	−	0.0250322i
$400$	−0.810226	+	6.67282i	−0.0405113	+	0.333641i
$401$	16.3625	−	1.98677i	0.817104	−	0.0992143i	0.298696	−	0.954348i	$-0.403448\pi$
$401$	16.3625	−	1.98677i	0.817104	−	0.0992143i	0.518407	+	0.855134i	$0.326525\pi$
$402$	−9.77490	+	14.1614i	−0.487528	+	0.706306i
$403$	−18.4023	−	16.1982i	−0.916684	−	0.806890i
$404$	0.147171	+	0.213214i	0.00732204	+	0.0106078i
$405$	1.16130	+	1.31084i	0.0577055	+	0.0651361i
$406$	1.41902	+	0.349758i	0.0704249	+	0.0173582i
$407$	2.95127	+	4.27566i	0.146289	+	0.211937i
$408$			5.54675i			0.274605i
$409$	20.3755	−	14.0642i	1.00750	−	0.695429i	0.0545391	−	0.998512i	$-0.482631\pi$
$409$	20.3755	−	14.0642i	1.00750	−	0.695429i	0.952964	+	0.303082i	$0.0980157\pi$
$410$	−4.43431	+	0.538423i	−0.218995	+	0.0265908i
$411$	−6.43220	+	2.43941i	−0.317277	+	0.120327i
$412$	0.300184	−	2.47224i	0.0147890	−	0.121798i
$413$	1.03356	+	2.72529i	0.0508584	+	0.134103i
$414$	−2.49330	+	2.81436i	−0.122539	+	0.138318i
$415$	−0.497374	−	0.440635i	−0.0244151	−	0.0216299i
$416$	−1.69752	−	4.43315i	−0.0832277	−	0.217353i
$417$	−9.54916	+	8.45982i	−0.467625	+	0.414279i
$418$		−	9.08145i		−	0.444188i
$419$	−22.5970	−	20.0192i	−1.10393	−	0.978000i	−0.104071	−	0.994570i	$-0.533187\pi$
$419$	−22.5970	−	20.0192i	−1.10393	−	0.978000i	−0.999863	+	0.0165703i	$0.994725\pi$
$420$	0.0781867	−	0.0192713i	0.00381512	−	0.000940342i
$421$	18.1153	+	12.5041i	0.882883	+	0.609410i	0.920871	−	0.389868i	$-0.127479\pi$
$421$	18.1153	+	12.5041i	0.882883	+	0.609410i	−0.0379875	+	0.999278i	$0.512095\pi$
$422$	17.1410	−	6.50072i	0.834410	−	0.316450i
$423$	1.78482	−	0.676894i	0.0867810	−	0.0329117i
$424$	2.44158	+	1.68530i	0.118573	+	0.0818454i
$425$	−3.50674	+	0.864335i	−0.170102	+	0.0419264i
$426$	−12.5251	−	11.0962i	−0.606841	−	0.537614i
$427$		−	1.15693i		−	0.0559879i
$428$	−0.284043	+	0.251640i	−0.0137297	+	0.0121635i
$429$	−4.50009	+	0.0144002i	−0.217266	+	0.000695248i
$430$	21.2932	+	18.8641i	1.02685	+	0.909708i
$431$	−21.9804	+	24.8107i	−1.05876	+	1.19509i	−0.0785932	+	0.996907i	$0.525043\pi$
$431$	−21.9804	+	24.8107i	−1.05876	+	1.19509i	−0.980165	+	0.198184i	$0.936496\pi$
$432$	1.23305	+	3.25129i	0.0593253	+	0.156428i
$433$	−0.271023	+	2.23207i	−0.0130245	+	0.107267i	−0.997771	−	0.0667273i	$-0.978744\pi$
$433$	−0.271023	+	2.23207i	−0.0130245	+	0.107267i	0.984747	+	0.173994i	$0.0556673\pi$
$434$	1.66025	−	0.629651i	0.0796947	−	0.0302242i
$435$	−9.72948	+	1.18137i	−0.466493	+	0.0566425i
$436$	3.16660	−	2.18575i	0.151653	−	0.104678i
$437$			15.4915i			0.741057i
$438$	−1.41410	−	2.04868i	−0.0675682	−	0.0978895i
$439$	13.7362	+	3.38566i	0.655591	+	0.161589i	0.553060	−	0.833141i	$-0.313460\pi$
$439$	13.7362	+	3.38566i	0.655591	+	0.161589i	0.102531	+	0.994730i	$0.467306\pi$
$440$	4.30304	+	4.85712i	0.205139	+	0.231554i
$441$	3.95452	+	5.72911i	0.188310	+	0.272815i
$442$	−6.68176	+	5.95780i	−0.317819	+	0.283384i
$443$	−20.6415	+	29.9044i	−0.980707	+	1.42080i	−0.0748594	+	0.997194i	$0.523851\pi$
$443$	−20.6415	+	29.9044i	−0.980707	+	1.42080i	−0.905847	+	0.423605i	$0.860765\pi$
$444$	−0.966911	+	0.117404i	−0.0458876	+	0.00557176i
$445$	2.34173	−	19.2859i	0.111008	−	0.914237i
$446$	30.1548	+	15.8265i	1.42787	+	0.749404i
$447$	−0.366371	+	1.48642i	−0.0173287	+	0.0703055i
$448$	1.69798	+	0.206172i	0.0802219	+	0.00974070i
$449$	3.27719	−	3.69919i	0.154660	−	0.174575i	−0.666074	−	0.745886i	$-0.732026\pi$
$449$	3.27719	−	3.69919i	0.154660	−	0.174575i	0.820734	+	0.571311i	$0.193565\pi$
$450$	−2.11416	+	1.45930i	−0.0996624	+	0.0687920i
$451$	1.36084	−	1.97152i	0.0640795	−	0.0928351i
$452$	−1.26649	+	0.312161i	−0.0595705	+	0.0146828i
$453$	−11.6811	−	1.41834i	−0.548825	−	0.0666394i
$454$	−27.9857	+	14.6880i	−1.31343	+	0.689343i
$455$	1.02342	+	0.701591i	0.0479786	+	0.0328911i
$456$	14.3930	+	7.55404i	0.674015	+	0.353751i
$457$	−9.26092	−	6.39235i	−0.433208	−	0.299022i	0.331433	−	0.943479i	$-0.392468\pi$
$457$	−9.26092	−	6.39235i	−0.433208	−	0.299022i	−0.764640	+	0.644457i	$0.777083\pi$
$458$	−3.67386	+	5.32251i	−0.171668	+	0.248705i
$459$	−1.39849	+	1.23895i	−0.0652758	+	0.0578293i
$460$	−0.768838	−	0.867839i	−0.0358473	−	0.0404632i
$461$	37.3872	+	14.1791i	1.74130	+	0.660387i	0.999942	−	0.0107280i	$-0.00341490\pi$
$461$	37.3872	+	14.1791i	1.74130	+	0.660387i	0.741354	+	0.671115i	$0.234184\pi$
$462$	0.151470	−	0.288601i	0.00704701	−	0.0134270i
$463$	24.7831	+	9.39897i	1.15177	+	0.436807i	0.855247	−	0.518220i	$-0.173405\pi$
$463$	24.7831	+	9.39897i	1.15177	+	0.436807i	0.296519	+	0.955027i	$0.404174\pi$
$464$	−18.8950	−	4.65720i	−0.877178	−	0.216205i
$465$	−8.91301	+	7.89624i	−0.413331	+	0.366179i
$466$	−10.7636	+	7.42956i	−0.498613	+	0.344168i
$467$	−5.14973	−	13.5787i	−0.238301	−	0.628348i	0.761503	−	0.648162i	$-0.224462\pi$
$467$	−5.14973	−	13.5787i	−0.238301	−	0.628348i	−0.999804	+	0.0198137i	$0.993693\pi$
$468$	0.389684	−	0.748290i	0.0180132	−	0.0345897i
$469$	−0.902291	+	2.37915i	−0.0416639	+	0.109859i
$470$	−1.06315	−	4.31336i	−0.0490394	−	0.198961i
$471$	10.6634	−	5.59659i	0.491344	−	0.257877i
$472$	−15.6147	−	41.1725i	−0.718723	−	1.89512i
$473$	−15.1450	+	1.83893i	−0.696367	+	0.0845543i
$474$	−6.00240	−	4.14316i	−0.275700	−	0.190302i
$475$	−2.53296	+	10.2766i	−0.116220	+	0.471524i
$476$	0.0205599	+	0.0834146i	0.000942360	+	0.00382330i
$477$	0.120454	+	0.992026i	0.00551520	+	0.0454217i
$478$	−1.92800	+	5.08371i	−0.0881845	+	0.232524i
$479$	−7.37229	+	29.9106i	−0.336849	+	1.36665i	0.521355	+	0.853340i	$0.325427\pi$
$479$	−7.37229	+	29.9106i	−0.336849	+	1.36665i	−0.858204	+	0.513309i	$0.828419\pi$
$480$	−2.23870	+	0.551790i	−0.102182	+	0.0251856i
$481$	−11.2657	−	9.91634i	−0.513670	−	0.452146i
$482$	9.81553	+	2.41931i	0.447085	+	0.110197i
$483$	−0.258382	+	0.492307i	−0.0117568	+	0.0224007i
$484$	2.20943			0.100428
$485$	10.0983			0.458538
$486$	−0.617576	+	1.17669i	−0.0280138	+	0.0533759i
$487$	−7.23113	−	8.16226i	−0.327674	−	0.369867i	0.561468	−	0.827498i	$-0.310237\pi$
$487$	−7.23113	−	8.16226i	−0.327674	−	0.369867i	−0.889142	+	0.457631i	$0.848698\pi$
$488$			17.4784i			0.791211i
$489$	−8.71702	+	9.83948i	−0.394197	+	0.444957i
$490$	14.3453	−	7.52900i	0.648055	−	0.340125i
$491$	−1.11361	−	9.17139i	−0.0502565	−	0.413899i	−0.996026	−	0.0890612i	$-0.971613\pi$
$491$	−1.11361	−	9.17139i	−0.0502565	−	0.413899i	0.945770	−	0.324838i	$-0.105310\pi$
$492$	0.208716	+	0.397676i	0.00940966	+	0.0179286i
$493$	−1.26037	−	10.3800i	−0.0567640	−	0.467494i
$494$	6.35984	+	25.4521i	0.286143	+	1.14514i
$495$	−0.263465	+	2.16983i	−0.0118419	+	0.0975264i
$496$	−22.1071	+	8.38411i	−0.992637	+	0.376458i
$497$	−2.19097	−	1.14991i	−0.0982784	−	0.0515805i
$498$	0.178803	−	0.471465i	0.00801235	−	0.0211268i
$499$	4.62599	+	8.81409i	0.207088	+	0.394573i	0.966742	−	0.255755i	$-0.0823239\pi$
$499$	4.62599	+	8.81409i	0.207088	+	0.394573i	−0.759654	+	0.650328i	$0.774632\pi$
$500$	−1.32031	−	2.51564i	−0.0590462	−	0.112503i
$501$	−3.97677	−	16.1344i	−0.177669	−	0.720832i
$502$	−1.73479	−	0.210641i	−0.0774273	−	0.00940138i
$503$	−16.2333	−	14.3814i	−0.723806	−	0.641236i	0.218559	−	0.975824i	$-0.429864\pi$
$503$	−16.2333	−	14.3814i	−0.723806	−	0.641236i	−0.942365	+	0.334588i	$0.891403\pi$
$504$	0.331405	+	0.480123i	0.0147620	+	0.0213864i
$505$	1.81297	+	0.687568i	0.0806760	+	0.0305964i
$506$	−4.69281			−0.208621
$507$	12.6021	−	3.19182i	0.559678	−	0.141754i
$508$	−1.49059			−0.0661343
$509$	−8.53805	−	3.23806i	−0.378442	−	0.143524i	0.158046	−	0.987432i	$-0.449480\pi$
$509$	−8.53805	−	3.23806i	−0.378442	−	0.143524i	−0.536489	+	0.843907i	$0.680250\pi$
$510$	2.47005	+	3.57848i	0.109376	+	0.158458i
$511$	−0.275529	−	0.244097i	−0.0121887	−	0.0107982i
$512$	−25.0407	−	3.04049i	−1.10665	−	0.134372i
$513$	1.31032	+	5.31619i	0.0578522	+	0.234715i
$514$	12.1942	+	23.2341i	0.537863	+	1.02481i
$515$	−8.66181	−	16.5037i	−0.381685	−	0.727239i
$516$	1.01425	−	2.67436i	0.0446499	−	0.117732i
$517$	2.10957	+	1.10719i	0.0927789	+	0.0486941i
$518$	1.01639	−	0.385464i	0.0446574	−	0.0169363i
$519$	−1.28221	+	10.5599i	−0.0562827	+	0.463530i
$520$	−15.4614	−	10.5993i	−0.678026	−	0.464811i
$521$	−1.58609	−	13.0626i	−0.0694879	−	0.572284i	−0.985319	−	0.170721i	$-0.945390\pi$
$521$	−1.58609	−	13.0626i	−0.0694879	−	0.572284i	0.915831	−	0.401563i	$-0.131533\pi$
$522$	−3.45627	−	6.58536i	−0.151277	−	0.288234i
$523$	2.20084	+	18.1255i	0.0962360	+	0.792575i	0.958298	+	0.285772i	$0.0922499\pi$
$523$	2.20084	+	18.1255i	0.0962360	+	0.792575i	−0.862062	+	0.506803i	$0.830827\pi$
$524$	−2.80641	+	1.47292i	−0.122599	+	0.0643448i
$525$	−0.251900	+	0.284336i	−0.0109938	+	0.0124094i
$526$			23.6287i			1.03026i
$527$	−8.42422	−	9.50898i	−0.366965	−	0.414218i
$528$	−2.01689	+	3.84287i	−0.0877741	+	0.167240i
$529$	−14.9948			−0.651949
$530$	2.32567			0.101021
$531$	6.89293	−	13.1334i	0.299128	−	0.569940i
$532$	0.244449	+	0.0602513i	0.0105982	+	0.00261223i
$533$	−2.43328	+	6.47847i	−0.105397	+	0.280614i
$534$	14.3138	−	3.52804i	0.619419	−	0.152673i
$535$	−0.679678	+	2.75756i	−0.0293850	+	0.119220i
$536$	13.6314	−	35.9431i	0.588788	−	1.55251i
$537$	−2.31068	−	19.0302i	−0.0997134	−	0.821214i
$538$	−7.16720	−	29.0785i	−0.309000	−	1.25366i
$539$	−2.07931	+	8.43608i	−0.0895621	+	0.363368i
$540$	−0.337246	−	0.232784i	−0.0145128	−	0.0100174i
$541$	0.963408	−	0.116979i	0.0414202	−	0.00502932i	−0.0998004	−	0.995007i	$-0.531820\pi$
$541$	0.963408	−	0.116979i	0.0414202	−	0.00502932i	0.141221	+	0.989978i	$0.454897\pi$
$542$	3.16170	+	8.33671i	0.135807	+	0.358093i
$543$	−1.72784	+	0.906841i	−0.0741488	+	0.0389163i
$544$	−0.588685	−	2.38839i	−0.0252397	−	0.102401i
$545$	10.2116	−	26.9257i	0.437416	−	1.15337i
$546$	−0.222405	+	0.914923i	−0.00951806	+	0.0391551i
$547$	5.67072	+	14.9525i	0.242462	+	0.639321i	0.999908	−	0.0135776i	$-0.00432203\pi$
$547$	5.67072	+	14.9525i	0.242462	+	0.639321i	−0.757445	+	0.652899i	$0.773553\pi$
$548$	1.32476	−	0.914415i	0.0565909	−	0.0390619i
$549$	−4.40679	+	3.90408i	−0.188077	+	0.166622i
$550$	−3.11309	−	0.767307i	−0.132743	−	0.0327181i
$551$	−28.6512	−	10.8660i	−1.22058	−	0.462906i
$552$	3.90353	−	7.43756i	0.166145	−	0.316563i
$553$	−1.00842	−	0.382442i	−0.0428823	−	0.0162631i
$554$	−7.71158	−	8.70457i	−0.327633	−	0.369822i
$555$	−5.45643	+	4.83398i	−0.231613	+	0.205191i
$556$	1.69578	−	2.45676i	0.0719172	−	0.104190i
$557$	2.18521	+	1.50834i	0.0925902	+	0.0639104i	0.613460	−	0.789726i	$-0.289777\pi$
$557$	2.18521	+	1.50834i	0.0925902	+	0.0639104i	−0.520870	+	0.853636i	$0.674392\pi$
$558$	−8.00089	−	4.19919i	−0.338705	−	0.177766i
$559$	41.1582	−	15.7601i	1.74081	−	0.666580i
$560$	1.05959	−	0.556117i	0.0447759	−	0.0235002i
$561$	−2.31491	−	0.281081i	−0.0977356	−	0.0118673i
$562$	−10.1629	+	2.50494i	−0.428697	+	0.105664i
$563$	2.90115	−	4.20304i	0.122269	−	0.177137i	−0.757070	−	0.653334i	$-0.773370\pi$
$563$	2.90115	−	4.20304i	0.122269	−	0.177137i	0.879339	+	0.476197i	$0.157985\pi$
$564$	−0.367597	+	0.253734i	−0.0154786	+	0.0106841i
$565$	−6.47362	+	7.30721i	−0.272347	+	0.307417i
$566$	24.7339	+	3.00324i	1.03964	+	0.126236i
$567$	−0.0470278	+	0.190799i	−0.00197498	+	0.00801282i
$568$	33.1002	+	17.3723i	1.38885	+	0.728927i
$569$	−5.14720	+	42.3910i	−0.215782	+	1.77712i	0.334748	+	0.942308i	$0.391349\pi$
$569$	−5.14720	+	42.3910i	−0.215782	+	1.77712i	−0.550530	+	0.834816i	$0.685574\pi$
$570$	12.6496	−	1.53594i	0.529833	−	0.0643333i
$571$	7.92756	−	11.4851i	0.331758	−	0.480634i	−0.621236	−	0.783623i	$-0.713369\pi$
$571$	7.92756	−	11.4851i	0.331758	−	0.480634i	0.952994	+	0.302989i	$0.0979846\pi$
$572$	1.02159	−	0.255270i	0.0427148	−	0.0106734i
$573$	−0.164723	−	0.238643i	−0.00688142	−	0.00996945i
$574$	−0.332377	−	0.375176i	−0.0138731	−	0.0156595i
$575$	5.31042	+	1.30890i	0.221460	+	0.0545849i
$576$	−4.94452	−	7.16338i	−0.206022	−	0.298474i
$577$			18.7204i			0.779339i	0.920955	+	0.389669i	$0.127411\pi$
$577$			18.7204i			0.779339i	−0.920955	+	0.389669i	$0.872589\pi$
$578$	14.7747	−	10.1982i	0.614546	−	0.424190i
$579$	18.9411	−	2.29986i	0.787165	−	0.0955791i
$580$	2.14433	−	0.813238i	0.0890385	−	0.0337679i
$581$	0.00898745	−	0.0740183i	0.000372862	−	0.00307080i
$582$	2.71729	+	7.16491i	0.112635	+	0.296995i
$583$	−0.827079	+	0.933579i	−0.0342541	+	0.0386649i
$584$	4.16257	+	3.68772i	0.172249	+	0.152599i
$585$	−0.781155	−	6.26576i	−0.0322968	−	0.259057i
$586$	−8.05658	+	7.13750i	−0.332814	+	0.294848i
$587$			28.5110i			1.17677i	0.808579	+	0.588387i	$0.200237\pi$
$587$			28.5110i			1.17677i	−0.808579	+	0.588387i	$0.799763\pi$
$588$	−1.21927	−	1.08018i	−0.0502817	−	0.0445457i
$589$	−36.1473	+	8.90950i	−1.48942	+	0.367110i
$590$	−28.4085	−	19.6090i	−1.16956	−	0.807288i
$591$	8.67442	−	3.28977i	0.356818	−	0.135323i
$592$	−13.5337	+	5.13265i	−0.556231	+	0.210951i
$593$	−35.9945	−	24.8452i	−1.47812	−	1.02027i	−0.988978	−	0.148065i	$-0.952696\pi$
$593$	−35.9945	−	24.8452i	−1.47812	−	1.02027i	−0.489139	−	0.872206i	$-0.662689\pi$
$594$	−1.61043	+	0.396935i	−0.0660766	+	0.0162864i
$595$	0.481275	+	0.426372i	0.0197303	+	0.0174796i
$596$		−	0.358224i		−	0.0146734i
$597$	−8.33809	+	7.38690i	−0.341255	+	0.302326i
$598$	13.1523	−	3.28643i	0.537837	−	0.134392i
$599$	24.2746	+	21.5054i	0.991831	+	0.878686i	0.992614	−	0.121314i	$-0.0387107\pi$
$599$	24.2746	+	21.5054i	0.991831	+	0.878686i	−0.000782884		1.00000i	$0.500249\pi$
$600$	3.80559	−	4.29563i	0.155363	−	0.175368i
$601$	−0.219536	−	0.578869i	−0.00895506	−	0.0236126i	0.930464	−	0.366383i	$-0.119404\pi$
$601$	−0.219536	−	0.578869i	−0.00895506	−	0.0236126i	−0.939419	+	0.342770i	$0.888635\pi$
$602$	−0.384764	+	3.16881i	−0.0156818	+	0.129151i
$603$	12.1070	−	4.59159i	0.493036	−	0.186984i
$604$	2.73330	−	0.331883i	0.111217	−	0.0135041i
$605$	13.6087	−	9.39341i	0.553273	−	0.381897i
$606$			1.47135i			0.0597695i
$607$	−16.3891	−	23.7437i	−0.665212	−	0.963727i	−0.999772	−	0.0213520i	$-0.993203\pi$
$607$	−16.3891	−	23.7437i	−0.665212	−	0.963727i	0.334560	−	0.942375i	$-0.391412\pi$
$608$	−6.99925	−	1.72516i	−0.283857	−	0.0699645i
$609$	−0.729280	−	0.823187i	−0.0295519	−	0.0333572i
$610$	7.78340	+	11.2762i	0.315141	+	0.456560i
$611$	−6.68776	−	1.62570i	−0.270558	−	0.0657689i
$612$	0.248350	−	0.359796i	0.0100389	−	0.0145439i
$613$	39.1091	−	4.74870i	1.57960	−	0.191798i	0.716777	−	0.697303i	$-0.245617\pi$
$613$	39.1091	−	4.74870i	1.57960	−	0.191798i	0.862824	+	0.505504i	$0.168694\pi$
$614$	3.37865	−	27.8257i	0.136351	−	1.12295i
$615$	2.97629	+	1.56208i	0.120016	+	0.0629891i
$616$	−0.174255	+	0.706979i	−0.00702092	+	0.0284850i
$617$	−8.27945	−	1.00531i	−0.333318	−	0.0404721i	−0.0478331	−	0.998855i	$-0.515232\pi$
$617$	−8.27945	−	1.00531i	−0.333318	−	0.0404721i	−0.285485	+	0.958383i	$0.592155\pi$
$618$	9.37892	−	10.5866i	0.377276	−	0.425856i
$619$	−13.8888	+	9.58676i	−0.558239	+	0.385324i	−0.813515	−	0.581544i	$-0.802449\pi$
$619$	−13.8888	+	9.58676i	−0.558239	+	0.385324i	0.255277	+	0.966868i	$0.417833\pi$
$620$	1.58281	−	2.29310i	0.0635672	−	0.0920930i
$621$	2.74712	−	0.677105i	0.110238	−	0.0271713i
$622$	14.5495	+	1.76663i	0.583380	+	0.0708352i
$623$	1.93026	−	1.01308i	0.0773343	−	0.0405882i
$624$	2.96144	−	12.1827i	0.118552	−	0.487697i
$625$	−10.2693	−	5.38976i	−0.410773	−	0.215590i
$626$	22.9044	+	15.8098i	0.915445	+	0.631886i
$627$	−3.88201	+	5.62406i	−0.155033	+	0.224604i
$628$	−2.10927	+	1.86865i	−0.0841690	+	0.0745672i
$629$	−5.15720	−	5.82128i	−0.205631	−	0.232110i
$630$	0.427612	+	0.162172i	0.0170365	+	0.00646108i
$631$	−5.43857	+	10.3623i	−0.216506	+	0.412518i	−0.969351	−	0.245680i	$-0.920989\pi$
$631$	−5.43857	+	10.3623i	−0.216506	+	0.412518i	0.752845	+	0.658198i	$0.228681\pi$
$632$	15.2347	+	5.77778i	0.606005	+	0.229828i
$633$	−13.3941	−	3.30135i	−0.532368	−	0.131217i
$634$	−18.9422	+	16.7814i	−0.752293	+	0.666473i
$635$	−9.18113	+	6.33728i	−0.364342	+	0.251487i
$636$	−0.0829184	−	0.218638i	−0.00328793	−	0.00866955i
$637$	−0.0803178	−	25.0995i	−0.00318231	−	0.994478i
$638$	3.29162	−	8.67928i	0.130316	−	0.343616i
$639$	3.01340	+	12.2258i	0.119208	+	0.483647i
$640$	−13.8534	+	7.27084i	−0.547605	+	0.287405i
$641$	−5.81011	−	15.3200i	−0.229486	−	0.605104i	0.769971	−	0.638079i	$-0.220271\pi$
$641$	−5.81011	−	15.3200i	−0.229486	−	0.605104i	−0.999456	+	0.0329755i	$0.989502\pi$
$642$	−2.13943	+	0.259774i	−0.0844367	+	0.0102525i
$643$	−1.66069	−	1.14629i	−0.0654913	−	0.0452054i	0.534869	−	0.844935i	$-0.320361\pi$
$643$	−1.66069	−	1.14629i	−0.0654913	−	0.0452054i	−0.600361	+	0.799729i	$0.704976\pi$
$644$	0.0311347	−	0.126318i	0.00122688	−	0.00497764i
$645$	−5.12292	−	20.7845i	−0.201715	−	0.818389i
$646$	1.63864	+	13.4954i	0.0644713	+	0.530969i
$647$	4.85198	−	12.7936i	0.190751	−	0.502969i	−0.805186	−	0.593022i	$-0.797935\pi$
$647$	4.85198	−	12.7936i	0.190751	−	0.502969i	0.995937	+	0.0900534i	$0.0287038\pi$
$648$	0.710476	−	2.88251i	0.0279101	−	0.113236i
$649$	17.9744	−	4.43029i	0.705557	−	0.173904i
$650$	9.26223	−	0.0296389i	0.363295	−	0.00116253i
$651$	−1.29733	−	0.319764i	−0.0508466	−	0.0125326i
$652$	1.42946	−	2.72362i	0.0559822	−	0.106665i
$653$	−3.99079			−0.156172			−0.0780859	−	0.996947i	$-0.524881\pi$
$653$	−3.99079			−0.156172			−0.0780859	+	0.996947i	$0.524881\pi$
$654$	21.8521			0.854484
$655$	−11.0236	+	21.0038i	−0.430729	+	0.820686i
$656$	4.42576	+	4.99565i	0.172797	+	0.195048i
$657$			1.87321i			0.0730808i
$658$	0.330559	−	0.373124i	0.0128865	−	0.0145459i
$659$	−40.9088	+	21.4706i	−1.59358	+	0.836377i	−0.594094	+	0.804396i	$0.702489\pi$
$659$	−40.9088	+	21.4706i	−1.59358	+	0.836377i	−0.999488	+	0.0319807i	$0.989818\pi$
$660$	−0.0616491	−	0.507726i	−0.00239969	−	0.0197632i
$661$	16.1528	+	30.7766i	0.628271	+	1.19707i	0.966660	+	0.256064i	$0.0824256\pi$
$661$	16.1528	+	30.7766i	0.628271	+	1.19707i	−0.338389	+	0.941006i	$0.609882\pi$
$662$	−0.504659	−	4.15624i	−0.0196141	−	0.161537i
$663$	6.68472	−	0.833387i	0.259613	−	0.0323661i
$664$	−0.135779	+	1.11824i	−0.00526923	+	0.0433960i
$665$	1.76182	−	0.668169i	0.0683204	−	0.0259105i
$666$	−4.89805	−	2.57069i	−0.189795	−	0.0996123i
$667$	−5.61496	+	14.8054i	−0.217412	+	0.573269i
$668$	1.80700	+	3.44296i	0.0699151	+	0.133212i
$669$	−11.9093	−	22.6913i	−0.460441	−	0.877298i
$670$	−7.21168	−	29.2589i	−0.278612	−	1.13037i
$671$	−7.29454	−	0.885718i	−0.281603	−	0.0341928i
$672$	−0.193657	−	0.171565i	−0.00747047	−	0.00661826i
$673$	−6.27890	−	9.09656i	−0.242034	−	0.350646i	0.683075	−	0.730348i	$-0.260642\pi$
$673$	−6.27890	−	9.09656i	−0.242034	−	0.350646i	−0.925109	+	0.379702i	$0.876027\pi$
$674$	−34.0221	−	12.9029i	−1.31048	−	0.497000i
$675$	1.93308			0.0744044
$676$	−2.68439	+	1.43086i	−0.103246	+	0.0550331i
$677$	30.1284			1.15793			0.578965	−	0.815353i	$-0.303457\pi$
$677$	30.1284			1.15793			0.578965	+	0.815353i	$0.303457\pi$
$678$	−6.92656	−	2.62690i	−0.266013	−	0.100885i
$679$	0.643690	+	0.932546i	0.0247025	+	0.0357878i
$680$	−7.27089	−	6.44145i	−0.278826	−	0.247018i
$681$	23.6099	+	2.86676i	0.904734	+	0.109855i
$682$	−2.69895	−	10.9501i	−0.103348	−	0.419299i
$683$	−0.601273	−	1.14563i	−0.0230071	−	0.0438363i	0.873681	−	0.486499i	$-0.161726\pi$
$683$	−0.601273	−	1.14563i	−0.0230071	−	0.0438363i	−0.896688	+	0.442663i	$0.854034\pi$
$684$	−0.595397	−	1.13443i	−0.0227656	−	0.0433761i
$685$	4.27205	−	11.2645i	0.163227	−	0.430393i
$686$	3.22831	+	1.69435i	0.123257	+	0.0646905i
$687$	4.55039	−	1.72573i	0.173608	−	0.0658409i
$688$	5.12332	−	42.1943i	0.195325	−	1.60864i
$689$	1.66421	−	3.19570i	0.0634015	−	0.121747i
$690$	−0.793691	−	6.53664i	−0.0302153	−	0.248845i
$691$	−1.05762	−	2.01514i	−0.0402339	−	0.0766594i	0.864509	−	0.502617i	$-0.167629\pi$
$691$	−1.05762	−	2.01514i	−0.0402339	−	0.0766594i	−0.904743	+	0.425958i	$0.859937\pi$
$692$	−0.300029	−	2.47096i	−0.0114054	−	0.0939319i
$693$	−0.217171	+	0.113980i	−0.00824965	+	0.00432975i
$694$	17.3274	−	19.5586i	0.657738	−	0.742433i
$695$		−	22.3418i		−	0.847473i
$696$	11.0176	+	12.4363i	0.417623	+	0.471399i
$697$	−1.66653	+	3.17530i	−0.0631242	+	0.120273i
$698$	−30.3324			−1.14810
$699$	9.84168			0.372247
$700$	0.0413079	−	0.0787056i	0.00156129	−	0.00297479i
$701$	7.71651	+	1.90195i	0.291448	+	0.0718356i	0.382329	−	0.924026i	$-0.375122\pi$
$701$	7.71651	+	1.90195i	0.291448	+	0.0718356i	−0.0908807	+	0.995862i	$0.528968\pi$
$702$	4.23548	−	2.24027i	0.159858	−	0.0845534i
$703$	−22.1289	+	5.45429i	−0.834608	+	0.205712i
$704$	2.59986	−	10.5480i	0.0979858	−	0.397544i
$705$	−1.18542	+	3.12569i	−0.0446454	+	0.117720i
$706$	−2.33129	−	19.1999i	−0.0877394	−	0.722599i
$707$	0.0520684	+	0.211250i	0.00195823	+	0.00794487i
$708$	−0.830588	+	3.36983i	−0.0312154	+	0.126646i
$709$	8.00612	+	5.52623i	0.300676	+	0.207542i	0.708844	−	0.705365i	$-0.249217\pi$
$709$	8.00612	+	5.52623i	0.300676	+	0.207542i	−0.408168	+	0.912907i	$0.633832\pi$
$710$	29.0907	−	3.53226i	1.09176	−	0.132563i
$711$	1.94618	+	5.13165i	0.0729874	+	0.192452i
$712$	−29.1616	+	15.3052i	−1.09288	+	0.573586i
$713$	4.60396	+	18.6790i	0.172420	+	0.699534i
$714$	−0.173015	+	0.456204i	−0.00647494	+	0.0170730i
$715$	5.20709	−	5.91561i	0.194734	−	0.221231i
$716$	1.59064	+	4.19417i	0.0594449	+	0.156743i
$717$	3.36711	−	2.32415i	0.125747	−	0.0867968i
$718$	−2.23162	+	1.97705i	−0.0832835	+	0.0737827i
$719$	11.6463	+	2.87056i	0.434335	+	0.107054i	0.450420	−	0.892817i	$-0.351274\pi$
$719$	11.6463	+	2.87056i	0.434335	+	0.107054i	−0.0160854	+	0.999871i	$0.505120\pi$
$720$	−5.69387	−	2.15940i	−0.212198	−	0.0804760i
$721$	0.971943	−	1.85188i	0.0361971	−	0.0689677i
$722$	13.6418	+	5.17363i	0.507693	+	0.192543i
$723$	−5.04450	−	5.69407i	−0.187607	−	0.211765i
$724$	0.341775	−	0.302786i	0.0127020	−	0.0112530i
$725$	−6.14561	+	8.90345i	−0.228242	+	0.330666i
$726$	10.3267	+	7.12801i	0.383260	+	0.264545i
$727$	30.0293	+	15.7606i	1.11372	+	0.584527i	0.918178	−	0.396168i	$-0.129660\pi$
$727$	30.0293	+	15.7606i	1.11372	+	0.584527i	0.195545	+	0.980695i	$0.437352\pi$
$728$	−0.00673098	−	2.10344i	−0.000249467	−	0.0779588i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	4.32768	+	0.525475i	0.160175	+	0.0194487i
$731$	22.1743	−	5.46546i	0.820144	−	0.202147i
$732$	0.782577	−	1.13376i	0.0289249	−	0.0419049i
$733$	−10.5814	+	7.30384i	−0.390835	+	0.269774i	−0.747235	−	0.664560i	$-0.768619\pi$
$733$	−10.5814	+	7.30384i	−0.390835	+	0.269774i	0.356401	+	0.934333i	$0.384004\pi$
$734$	−27.4081	+	30.9374i	−1.01165	+	1.14192i
$735$	−12.1023	−	1.46949i	−0.446401	−	0.0542029i
$736$	−0.891472	+	3.61684i	−0.0328601	+	0.133319i
$737$	14.3099	+	7.51042i	0.527113	+	0.276650i
$738$	−0.307449	+	2.53207i	−0.0113173	+	0.0932067i
$739$	29.1073	−	3.53427i	1.07073	−	0.130010i	0.433859	−	0.900981i	$-0.357152\pi$
$739$	29.1073	−	3.53427i	1.07073	−	0.130010i	0.636871	+	0.770971i	$0.280229\pi$
$740$	0.968977	−	1.40381i	0.0356203	−	0.0516049i
$741$	6.94131	−	18.4809i	0.254995	−	0.678912i
$742$	0.148244	+	0.214769i	0.00544223	+	0.00788443i
$743$	24.2820	+	27.4087i	0.890818	+	1.00553i	0.999934	+	0.0114971i	$0.00365972\pi$
$743$	24.2820	+	27.4087i	0.890818	+	1.00553i	−0.109115	+	0.994029i	$0.534802\pi$
$744$	19.5996	+	4.83086i	0.718555	+	0.177108i
$745$	−1.52300	−	2.20644i	−0.0557982	−	0.0808377i
$746$		−	1.52371i		−	0.0557871i
$747$	−0.312266	+	0.215542i	−0.0114252	+	0.00788626i
$748$	0.541676	−	0.0657713i	0.0198056	−	0.00240484i
$749$	−0.297977	+	0.113008i	−0.0108879	+	0.00412922i
$750$	1.94488	−	16.0175i	0.0710170	−	0.584877i
$751$	−12.2539	−	32.3110i	−0.447153	−	1.17904i	−0.949330	−	0.314280i	$-0.898237\pi$
$751$	−12.2539	−	32.3110i	−0.447153	−	1.17904i	0.502178	−	0.864764i	$-0.332532\pi$
$752$	−4.40156	+	4.96833i	−0.160508	+	0.181177i
$753$	0.984297	+	0.872011i	0.0358698	+	0.0317778i
$754$	−3.14704	+	26.6301i	−0.114608	+	0.969811i
$755$	15.4245	−	13.6649i	0.561354	−	0.497316i
$756$		−	0.0459821i		−	0.00167235i
$757$	29.4628	+	26.1017i	1.07084	+	0.948684i	0.998813	−	0.0487182i	$-0.0155136\pi$
$757$	29.4628	+	26.1017i	1.07084	+	0.948684i	0.0720305	+	0.997402i	$0.477052\pi$
$758$	−1.13615	+	0.280035i	−0.0412667	+	0.0101713i
$759$	2.90622	+	2.00602i	0.105489	+	0.0728138i
$760$	−26.6168	+	10.0944i	−0.965492	+	0.366163i
$761$	−48.2912	+	18.3144i	−1.75055	+	0.663898i	−0.750559	+	0.660803i	$0.770216\pi$
$761$	−48.2912	+	18.3144i	−1.75055	+	0.663898i	−0.999995	+	0.00309444i	$0.999015\pi$
$762$	−6.96693	−	4.80892i	−0.252385	−	0.174209i
$763$	3.13743	−	0.773306i	0.113582	−	0.0279956i
$764$	0.0507879	+	0.0449941i	0.00183744	+	0.00162783i
$765$		−	3.27199i		−	0.118299i
$766$	−15.1407	+	13.4135i	−0.547055	+	0.484648i
$767$	−47.2733	+	25.0042i	−1.70694	+	0.902850i
$768$	4.14375	+	3.67104i	0.149525	+	0.132467i
$769$	27.2966	−	30.8115i	0.984341	−	1.11109i	−0.00946394	−	0.999955i	$-0.503013\pi$
$769$	27.2966	−	30.8115i	0.984341	−	1.11109i	0.993805	−	0.111136i	$-0.0354490\pi$
$770$	0.202408	+	0.533706i	0.00729427	+	0.0192334i
$771$	2.38003	−	19.6013i	0.0857145	−	0.705923i
$772$	−4.17452	+	1.58319i	−0.150244	+	0.0569802i
$773$	28.7877	−	3.49545i	1.03542	−	0.125723i	0.414863	−	0.909884i	$-0.363830\pi$
$773$	28.7877	−	3.49545i	1.03542	−	0.125723i	0.620557	+	0.784161i	$0.286906\pi$
$774$	13.3685	−	9.22761i	0.480521	−	0.331680i
$775$			13.1439i			0.472144i
$776$	−9.72459	−	14.0885i	−0.349092	−	0.505748i
$777$	−0.794212	−	0.195756i	−0.0284922	−	0.00702270i
$778$	−26.1826	−	29.5540i	−0.938691	−	1.05956i
$779$	5.96984	+	8.64880i	0.213892	+	0.309875i
$780$	0.528347	+	1.37980i	0.0189179	+	0.0494049i
$781$	−8.92762	+	12.9339i	−0.319455	+	0.462811i
$782$	6.97371	−	0.846761i	0.249379	−	0.0302801i
$783$	−0.674584	+	5.55570i	−0.0241077	+	0.198544i
$784$	−21.4338	−	11.2493i	−0.765494	−	0.401762i
$785$	−5.04721	+	20.4773i	−0.180143	+	0.730867i
$786$	−17.8689	−	2.16968i	−0.637362	−	0.0773898i
$787$	11.3880	−	12.8544i	0.405939	−	0.458210i	−0.509617	−	0.860402i	$-0.670213\pi$
$787$	11.3880	−	12.8544i	0.405939	−	0.458210i	0.915556	+	0.402191i	$0.131751\pi$
$788$	−1.78656	+	1.23317i	−0.0636436	+	0.0439300i
$789$	10.1005	−	14.6331i	0.359587	−	0.520951i
$790$	12.4016	−	3.05672i	0.441230	−	0.108753i
$791$	−1.08745	−	0.132040i	−0.0386651	−	0.00469480i
$792$	3.28093	−	1.72196i	0.116583	−	0.0611874i
$793$	21.0643	−	2.62609i	0.748015	−	0.0932553i
$794$	−13.4721	−	7.07073i	−0.478109	−	0.250931i
$795$	−1.44027	−	0.994146i	−0.0510811	−	0.0352587i
$796$	1.48071	−	2.14519i	0.0524825	−	0.0760341i
$797$	−16.3802	+	14.5116i	−0.580216	+	0.514027i	−0.901398	−	0.432991i	$-0.857458\pi$
$797$	−16.3802	+	14.5116i	−0.580216	+	0.514027i	0.321182	+	0.947017i	$0.395920\pi$
$798$	0.948158	+	1.07025i	0.0335644	+	0.0378864i
$799$	−3.33469	−	1.26468i	−0.117973	−	0.0447412i
$800$	−1.18276	+	2.25356i	−0.0418168	+	0.0796753i
$801$	−10.3725	−	3.93378i	−0.366496	−	0.138993i
$802$	−21.2675	−	5.24197i	−0.750982	−	0.185100i
$803$	−1.74999	+	1.55036i	−0.0617558	+	0.0547109i
$804$	−2.49353	+	1.72116i	−0.0879400	+	0.0607006i
$805$	−0.345275	−	0.910414i	−0.0121693	−	0.0320879i
$806$	15.2326	+	28.7990i	0.536547	+	1.01440i
$807$	−7.99148	+	21.0718i	−0.281313	+	0.741762i
$808$	−0.786627	−	3.19147i	−0.0276735	−	0.112276i
$809$	−10.4548	+	5.48712i	−0.367572	+	0.192917i	−0.638389	−	0.769714i	$-0.720399\pi$
$809$	−10.4548	+	5.48712i	−0.367572	+	0.192917i	0.270816	+	0.962631i	$0.412706\pi$
$810$	−0.825262	−	2.17604i	−0.0289968	−	0.0764582i
$811$	3.98210	−	0.483514i	0.139830	−	0.0169785i	−0.0503222	−	0.998733i	$-0.516025\pi$
$811$	3.98210	−	0.483514i	0.139830	−	0.0169785i	0.190153	+	0.981755i	$0.439102\pi$
$812$	0.211786	+	0.146185i	0.00743222	+	0.00513009i
$813$	1.60565	−	6.51438i	0.0563126	−	0.228469i
$814$	−1.65226	−	6.70349i	−0.0579117	−	0.234957i
$815$	−2.77488	−	22.8532i	−0.0971999	−	0.800513i
$816$	2.30379	−	6.07459i	0.0806487	−	0.212653i
$817$	16.0167	−	64.9824i	0.560354	−	2.27345i
$818$	−31.9452	+	7.87379i	−1.11694	+	0.275301i
$819$	0.528832	−	0.471534i	0.0184789	−	0.0164767i
$820$	−0.763672	−	0.188228i	−0.0266686	−	0.00657321i
$821$	−10.5220	+	20.0479i	−0.367219	+	0.699678i	−0.997025	−	0.0770747i	$-0.975442\pi$
$821$	−10.5220	+	20.0479i	−0.367219	+	0.699678i	0.629806	+	0.776752i	$0.283134\pi$
$822$	9.14190			0.318860
$823$	−14.8076			−0.516159			−0.258080	−	0.966124i	$-0.583090\pi$
$823$	−14.8076			−0.516159			−0.258080	+	0.966124i	$0.583090\pi$
$824$	−14.6837	+	27.9774i	−0.511531	+	0.974641i
$825$	1.59991	+	1.80593i	0.0557018	+	0.0628743i
$826$		−	3.87337i		−	0.134772i
$827$	24.5975	−	27.7649i	0.855339	−	0.965479i	−0.144371	−	0.989524i	$-0.546116\pi$
$827$	24.5975	−	27.7649i	0.855339	−	0.965479i	0.999711	+	0.0240449i	$0.00765448\pi$
$828$	−0.586215	+	0.307669i	−0.0203724	+	0.0106923i
$829$	6.04107	+	49.7527i	0.209815	+	1.72798i	0.593773	+	0.804633i	$0.297638\pi$
$829$	6.04107	+	49.7527i	0.209815	+	1.72798i	−0.383958	+	0.923351i	$0.625439\pi$
$830$	0.410370	+	0.781894i	0.0142441	+	0.0271399i
$831$	1.05481	+	8.68710i	0.0365908	+	0.301352i
$832$	0.100425	+	31.3831i	0.00348162	+	1.08801i
$833$	1.56774	−	12.9115i	0.0543191	−	0.447358i
$834$	15.8519	−	6.01185i	0.548908	−	0.208173i
$835$	25.7678	+	13.5240i	0.891732	+	0.468017i
$836$	0.567033	−	1.49514i	0.0196113	−	0.0517106i
$837$	3.15987	+	6.02063i	0.109221	+	0.208104i
$838$	18.6441	+	35.5234i	0.644051	+	1.22714i
$839$	−12.7738	−	51.8254i	−0.441001	−	1.78921i	−0.597870	−	0.801593i	$-0.703986\pi$
$839$	−12.7738	−	51.8254i	−0.441001	−	1.78921i	0.156869	−	0.987619i	$-0.449860\pi$
$840$	−1.01423	−	0.123149i	−0.0349941	−	0.00424905i
$841$	−1.73718	−	1.53900i	−0.0599027	−	0.0530691i
$842$	−16.6168	−	24.0736i	−0.572652	−	0.829630i
$843$	7.36459	+	2.79302i	0.253650	+	0.0961967i
$844$	3.22794			0.111110
$845$	−10.4508	+	20.2259i	−0.359520	+	0.695794i
$846$	−2.53672			−0.0872141
$847$	1.73491	+	0.657965i	0.0596122	+	0.0226079i
$848$	−1.97395	−	2.85976i	−0.0677857	−	0.0982045i
$849$	−14.0337	−	12.4328i	−0.481636	−	0.426692i
$850$	4.76463	+	0.578530i	0.163425	+	0.0198434i
$851$	2.81849	+	11.4351i	0.0966165	+	0.391989i
$852$	−1.36926	−	2.60890i	−0.0469100	−	0.0893795i
$853$	−23.7112	−	45.1779i	−0.811856	−	1.54686i	−0.837015	−	0.547180i	$-0.815701\pi$
$853$	−23.7112	−	45.1779i	−0.811856	−	1.54686i	0.0251589	−	0.999683i	$-0.491991\pi$
$854$	−0.545191	+	1.43755i	−0.0186561	+	0.0491920i
$855$	−8.49034	−	4.45608i	−0.290364	−	0.152395i
$856$	4.50171	−	1.70728i	0.153865	−	0.0583535i
$857$	5.50549	−	45.3418i	0.188064	−	1.54885i	−0.527047	−	0.849836i	$-0.676701\pi$
$857$	5.50549	−	45.3418i	0.188064	−	1.54885i	0.715111	−	0.699011i	$-0.246376\pi$
$858$	5.59839	+	2.10272i	0.191126	+	0.0717858i
$859$	−0.0606853	−	0.499789i	−0.00207056	−	0.0170526i	0.991637	−	0.129059i	$-0.0411955\pi$
$859$	−0.0606853	−	0.499789i	−0.00207056	−	0.0170526i	−0.993708	+	0.112006i	$0.964272\pi$
$860$	2.32780	+	4.43525i	0.0793773	+	0.151241i
$861$	0.0454632	+	0.374423i	0.00154938	+	0.0127603i
$862$	39.0036	−	20.4707i	1.32847	−	0.697234i
$863$	16.4046	−	18.5170i	0.558420	−	0.630326i	−0.399716	−	0.916639i	$-0.630891\pi$
$863$	16.4046	−	18.5170i	0.558420	−	0.630326i	0.958136	+	0.286313i	$0.0924298\pi$
$864$			1.31659i			0.0447914i
$865$	−12.3533	−	13.9440i	−0.420026	−	0.474111i
$866$	1.38860	−	2.64576i	0.0471865	−	0.0899065i
$867$	−13.5092			−0.458798
$868$	0.312654			0.0106122
$869$	−3.18335	+	6.06536i	−0.107988	+	0.205753i
$870$	12.6461	+	3.11699i	0.428743	+	0.105676i
$871$	−45.3653	−	11.0277i	−1.53714	−	0.373658i
$872$	−47.3989	+	11.6828i	−1.60513	+	0.395629i
$873$	1.37996	−	5.59872i	0.0467046	−	0.189488i
$874$	7.30017	−	19.2490i	0.246932	−	0.651106i
$875$	−0.287594	−	2.36855i	−0.00972246	−	0.0800717i
$876$	−0.104897	−	0.425583i	−0.00354413	−	0.0143791i
$877$	−8.87686	+	36.0149i	−0.299750	+	1.21614i	0.607080	+	0.794640i	$0.292341\pi$
$877$	−8.87686	+	36.0149i	−0.299750	+	1.21614i	−0.906831	+	0.421495i	$0.861506\pi$
$878$	−15.4725	−	10.6799i	−0.522170	−	0.360428i
$879$	8.04041	−	0.976283i	0.271196	−	0.0329292i
$880$	−2.69516	−	7.10655i	−0.0908538	−	0.239562i
$881$	41.8986	−	21.9901i	1.41160	−	0.740865i	0.425181	−	0.905108i	$-0.360210\pi$
$881$	41.8986	−	21.9901i	1.41160	−	0.740865i	0.986420	+	0.164243i	$0.0525181\pi$
$882$	−2.21392	−	8.98224i	−0.0745467	−	0.302448i
$883$	12.8895	−	33.9868i	0.433766	−	1.14375i	−0.522857	−	0.852420i	$-0.675134\pi$
$883$	12.8895	−	33.9868i	0.433766	−	1.14375i	0.956623	−	0.291327i	$-0.0940968\pi$
$884$	−1.47206	+	0.563675i	−0.0495109	+	0.0189584i
$885$	9.21097	+	24.2873i	0.309623	+	0.816410i
$886$	39.7402	−	27.4307i	1.33510	−	0.921553i
$887$	21.1699	−	18.7549i	0.710815	−	0.629727i	−0.228195	−	0.973615i	$-0.573283\pi$
$887$	21.1699	−	18.7549i	0.710815	−	0.629727i	0.939011	+	0.343888i	$0.111744\pi$
$888$	11.9986	+	2.95739i	0.402647	+	0.0992436i
$889$	−1.17046	−	0.443897i	−0.0392560	−	0.0148878i
$890$	−11.9980	+	22.8602i	−0.402173	+	0.766276i
$891$	1.16700	+	0.442585i	0.0390960	+	0.0148272i
$892$	3.97642	+	4.48845i	0.133140	+	0.150284i
$893$	−7.82314	+	6.93070i	−0.261791	+	0.231927i
$894$	1.15570	−	1.67431i	0.0386523	−	0.0559975i
$895$	27.6289	+	19.0709i	0.923533	+	0.637469i
$896$	−1.55450	−	0.815863i	−0.0519321	−	0.0272561i
$897$	−9.54994	−	3.58690i	−0.318863	−	0.119763i
$898$	−5.81529	+	3.05210i	−0.194059	+	0.101850i
$899$	−37.7758	−	4.58682i	−1.25989	−	0.152979i
$900$	−0.439186	+	0.108250i	−0.0146395	+	0.00360832i
$901$	1.06062	−	1.53657i	0.0353343	−	0.0511906i
$902$	−2.61997	+	1.80844i	−0.0872355	+	0.0602143i
$903$	1.59284	−	1.79795i	0.0530065	−	0.0598319i
$904$	16.4287	+	1.99480i	0.546409	+	0.0663461i
$905$	0.817823	−	3.31804i	0.0271853	−	0.110295i
$906$	13.8460	+	7.26694i	0.460002	+	0.241428i
$907$	−0.605480	+	4.98658i	−0.0201046	+	0.165577i	−0.999303	−	0.0373285i	$-0.988115\pi$
$907$	−0.605480	+	4.98658i	−0.0201046	+	0.165577i	0.979198	+	0.202905i	$0.0650383\pi$
$908$	−5.52458	+	0.670806i	−0.183340	+	0.0222615i
$909$	0.628952	−	0.911195i	0.0208610	−	0.0302224i
$910$	−0.941037	−	1.35404i	−0.0311951	−	0.0448860i
$911$	−21.1910	−	30.7005i	−0.702090	−	1.01715i	−0.998079	−	0.0619619i	$-0.980264\pi$
$911$	−21.1910	−	30.7005i	−0.702090	−	1.01715i	0.295988	−	0.955192i	$-0.404351\pi$
$912$	−12.6252	−	14.2509i	−0.418062	−	0.471894i
$913$	−0.459810	−	0.113333i	−0.0152175	−	0.00375078i
$914$	8.49487	+	12.3069i	0.280985	+	0.407078i
$915$		−	10.3104i		−	0.340851i
$916$	−0.937185	+	0.646892i	−0.0309655	+	0.0213739i
$917$	−2.64232	+	0.320836i	−0.0872571	+	0.0105949i
$918$	2.32154	−	0.880443i	0.0766222	−	0.0290590i
$919$	−3.08361	+	25.3958i	−0.101719	+	0.837731i	0.849153	+	0.528147i	$0.177113\pi$
$919$	−3.08361	+	25.3958i	−0.101719	+	0.837731i	−0.950872	+	0.309584i	$0.899810\pi$
$920$	5.21626	+	13.7541i	0.171975	+	0.453461i
$921$	−13.9869	+	15.7880i	−0.460885	+	0.520231i
$922$	−39.7739	−	35.2366i	−1.30988	−	1.16046i
$923$	15.9632	−	42.5012i	0.525435	−	1.39894i
$924$	0.0429574	−	0.0380570i	0.00141320	−	0.00125198i
$925$			8.04656i			0.264569i
$926$	−26.3651	−	23.3575i	−0.866412	−	0.767574i
$927$	−10.3337	+	2.54703i	−0.339403	+	0.0836554i
$928$	−6.06400	−	4.18568i	−0.199061	−	0.137402i
$929$	−14.4262	+	5.47112i	−0.473307	+	0.179502i	−0.579712	−	0.814821i	$-0.696835\pi$
$929$	−14.4262	+	5.47112i	−0.473307	+	0.179502i	0.106406	+	0.994323i	$0.466066\pi$
$930$	14.7959	−	5.61135i	0.485177	−	0.184003i
$931$	−31.3685	−	21.6521i	−1.02806	−	0.709620i
$932$	−2.23598	+	0.551119i	−0.0732419	+	0.0180525i
$933$	−8.25519	−	7.31346i	−0.270263	−	0.239432i
$934$			19.2990i			0.631484i
$935$	3.05676	−	2.70805i	0.0999668	−	0.0885628i
$936$	−7.98937	+	7.12373i	−0.261141	+	0.232846i
$937$	−17.3616	−	15.3811i	−0.567180	−	0.502477i	0.330096	−	0.943947i	$-0.392919\pi$
$937$	−17.3616	−	15.3811i	−0.567180	−	0.502477i	−0.897276	+	0.441470i	$0.854457\pi$
$938$	2.24229	−	2.53102i	0.0732134	−	0.0826408i
$939$	−7.42637	−	19.5817i	−0.242351	−	0.639026i
$940$	0.0942868	−	0.776522i	0.00307530	−	0.0253274i
$941$	14.6233	−	5.54588i	0.476706	−	0.180791i	−0.104537	−	0.994521i	$-0.533336\pi$
$941$	14.6233	−	5.54588i	0.476706	−	0.180791i	0.581243	+	0.813730i	$0.302567\pi$
$942$	−15.8872	+	1.92905i	−0.517633	+	0.0628520i
$943$	4.46924	−	3.08490i	0.145539	−	0.100458i
$944$			51.5759i			1.67865i
$945$	−0.195494	−	0.283221i	−0.00635941	−	0.00921319i
$946$	19.6850	+	4.85193i	0.640016	+	0.157750i
$947$	34.7313	+	39.2036i	1.12862	+	1.27395i	0.957417	+	0.288709i	$0.0932260\pi$
$947$	34.7313	+	39.2036i	1.12862	+	1.27395i	0.171200	+	0.985236i	$0.445236\pi$
$948$	−0.729526	−	1.05690i	−0.0236939	−	0.0343265i
$949$	3.81887	−	5.57064i	0.123966	−	0.180830i
$950$	7.99008	−	11.5756i	0.259233	−	0.375563i
$951$	18.9042	−	2.29539i	0.613012	−	0.0744331i
$952$	0.131384	−	1.08204i	0.00425817	−	0.0350692i
$953$	32.3647	+	16.9863i	1.04840	+	0.550240i	0.898733	−	0.438497i	$-0.144489\pi$
$953$	32.3647	+	16.9863i	1.04840	+	0.550240i	0.149663	+	0.988737i	$0.452181\pi$
$954$	0.317811	−	1.28941i	0.0102895	−	0.0417461i
$955$	0.504116	+	0.0612107i	0.0163128	+	0.00198073i
$956$	−0.634840	+	0.716586i	−0.0205322	+	0.0231761i
$957$	−5.74857	+	3.96795i	−0.185825	+	0.128266i
$958$	23.2555	−	33.6914i	0.751351	−	1.08852i
$959$	1.31255	−	0.323516i	0.0423846	−	0.0104469i
$960$	15.1321	+	1.83737i	0.488387	+	0.0593009i
$961$	−13.4880	+	7.07906i	−0.435097	+	0.228357i
$962$	9.32523	+	17.6304i	0.300657	+	0.568427i
$963$	1.43598	+	0.753659i	0.0462737	+	0.0242863i
$964$	1.46494	+	1.01118i	0.0471826	+	0.0325678i
$965$	−18.9816	+	27.4995i	−0.611038	+	0.885241i
$966$	0.553048	−	0.489958i	0.0177940	−	0.0157641i
$967$	20.9387	+	23.6349i	0.673343	+	0.760047i	0.981536	−	0.191276i	$-0.0612627\pi$
$967$	20.9387	+	23.6349i	0.673343	+	0.760047i	−0.308193	+	0.951324i	$0.599724\pi$
$968$	−26.2103	−	9.94025i	−0.842431	−	0.319492i
$969$	4.75403	−	9.05805i	0.152721	−	0.290986i
$970$	−12.5476	−	4.75869i	−0.402880	−	0.152792i
$971$	−28.9977	−	7.14729i	−0.930580	−	0.229367i	−0.255243	−	0.966877i	$-0.582156\pi$
$971$	−28.9977	−	7.14729i	−0.930580	−	0.229367i	−0.675337	+	0.737509i	$0.736002\pi$
$972$	−0.175147	+	0.155167i	−0.00561785	+	0.00497698i
$973$	2.06320	−	1.42413i	0.0661433	−	0.0456554i
$974$	5.13870	+	13.5496i	0.164655	+	0.434158i
$975$	−5.74869	−	3.94094i	−0.184106	−	0.126211i
$976$	7.25949	−	19.1417i	0.232371	−	0.612711i
$977$	8.14015	+	33.0259i	0.260426	+	1.05659i	0.944849	+	0.327506i	$0.106208\pi$
$977$	8.14015	+	33.0259i	0.260426	+	1.05659i	−0.684423	+	0.729085i	$0.739946\pi$
$978$	15.4681	−	8.11829i	0.494616	−	0.259594i
$979$	−4.90978	−	12.9460i	−0.156917	−	0.413757i
$980$	2.83187	−	0.343851i	0.0904608	−	0.0109839i
$981$	−13.5328	−	9.34103i	−0.432070	−	0.298236i
$982$	−2.93819	+	11.9207i	−0.0937616	+	0.380406i
$983$	8.96126	+	36.3573i	0.285820	+	1.15962i	0.921723	+	0.387848i	$0.126782\pi$
$983$	8.96126	+	36.3573i	0.285820	+	1.15962i	−0.635903	+	0.771769i	$0.719372\pi$
$984$	−0.686839	−	5.65662i	−0.0218956	−	0.180327i
$985$	−5.76126	+	15.1912i	−0.183569	+	0.484031i
$986$	−3.32540	+	13.4917i	−0.105902	+	0.429663i
$987$	−0.364211	+	0.0897698i	−0.0115930	+	0.00285741i
$988$	−0.542128	+	4.58746i	−0.0172474	+	0.145946i
$989$	−33.5795	−	8.27659i	−1.06776	−	0.263180i
$990$	1.34987	−	2.57197i	0.0429018	−	0.0817426i
$991$	−8.94477			−0.284140			−0.142070	−	0.989857i	$-0.545376\pi$
$991$	−8.94477			−0.284140			−0.142070	+	0.989857i	$0.545376\pi$
$992$	−8.95213			−0.284231
$993$	−1.46412	+	2.78965i	−0.0464624	+	0.0885268i
$994$	2.18052	+	2.46129i	0.0691618	+	0.0780675i
$995$		−	19.5083i		−	0.618455i
$996$	0.0588752	−	0.0664564i	0.00186553	−	0.00210575i
$997$	26.0197	−	13.6562i	0.824051	−	0.432496i	0.000680915	−	1.00000i	$-0.499783\pi$
$997$	26.0197	−	13.6562i	0.824051	−	0.432496i	0.823370	+	0.567504i	$0.192091\pi$
$998$	−1.59450	−	13.1319i	−0.0504732	−	0.415684i
$999$	1.93443	+	3.68576i	0.0612028	+	0.116612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.25.4	✓	168
169.142	even	26	inner	507.2.p.a.142.4	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.4	✓	168	1.1	even	1	trivial
507.2.p.a.142.4	yes	168	169.142	even	26	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24255 - 0.471239i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.175147 - 0.155167i) q^{4} +(-1.73849 - 0.211091i) q^{5} +(-0.318029 - 1.29030i) q^{6} +(-0.0913225 - 0.174001i) q^{7} +(1.37966 + 2.62872i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-1.24255 - 0.471239i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.175147 - 0.155167i) q^{4} +(-1.73849 - 0.211091i) q^{5} +(-0.318029 - 1.29030i) q^{6} +(-0.0913225 - 0.174001i) q^{7} +(1.37966 + 2.62872i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(2.06070 + 1.08154i) q^{10} +(-1.16700 + 0.442585i) q^{11} +(0.0282049 - 0.232288i) q^{12} +(2.96074 - 2.05767i) q^{13} +(0.0314774 + 0.259240i) q^{14} +(-0.813852 - 1.55067i) q^{15} +(-0.419137 - 3.45191i) q^{16} +(1.65435 - 0.868270i) q^{17} +(0.881231 - 0.994705i) q^{18} -5.47529i q^{19} +(0.271738 + 0.306728i) q^{20} +(0.0913225 - 0.174001i) q^{21} +1.65862 q^{22} -2.82934 q^{23} +(-1.37966 + 2.62872i) q^{24} +(-1.87691 - 0.462617i) q^{25} +(-4.64853 + 1.16155i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-0.0110042 + 0.0446459i) q^{28} +(1.98455 - 5.23282i) q^{29} +(0.280522 + 2.31030i) q^{30} +(-1.62722 - 6.60189i) q^{31} +(0.315081 - 1.27833i) q^{32} +(-1.02717 - 0.709006i) q^{33} +(-2.46478 + 0.299279i) q^{34} +(0.122034 + 0.321776i) q^{35} +(0.207191 - 0.108742i) q^{36} +(-0.996164 - 4.04160i) q^{37} +(-2.58017 + 6.80334i) q^{38} +(3.37532 + 1.26775i) q^{39} +(-1.84363 - 4.86125i) q^{40} +(-1.57961 + 1.09032i) q^{41} +(-0.195469 + 0.173170i) q^{42} +(11.8683 + 2.92527i) q^{43} +(0.273071 + 0.103562i) q^{44} +(0.813852 - 1.55067i) q^{45} +(3.51561 + 1.33329i) q^{46} +(-1.26581 - 1.42881i) q^{47} +(2.60277 - 2.30585i) q^{48} +(3.95452 - 5.72911i) q^{49} +(2.11416 + 1.45930i) q^{50} +(1.65435 + 0.868270i) q^{51} +(-0.837847 - 0.0990135i) q^{52} +(0.884847 - 0.464403i) q^{53} +(1.31922 + 0.160183i) q^{54} +(2.12225 - 0.523087i) q^{55} +(0.331405 - 0.480123i) q^{56} +(4.50608 - 3.11032i) q^{57} +(-4.93181 + 5.56687i) q^{58} +(-14.7242 - 1.78784i) q^{59} +(-0.0980680 + 0.397877i) q^{60} +(5.21304 + 2.73602i) q^{61} +(-1.08916 + 8.97002i) q^{62} +(0.195077 - 0.0236866i) q^{63} +(-4.94452 + 7.16338i) q^{64} +(-5.58159 + 2.95226i) q^{65} +(0.942206 + 1.36502i) q^{66} +(-8.58642 - 9.69206i) q^{67} +(-0.424481 - 0.104625i) q^{68} +(-1.60725 - 2.32850i) q^{69} -0.457331i q^{70} +(10.3628 - 7.15292i) q^{71} +(-2.94713 + 0.357847i) q^{72} +(1.75148 - 0.664248i) q^{73} +(-0.666769 + 5.49133i) q^{74} +(-0.685480 - 1.80746i) q^{75} +(-0.849583 + 0.958981i) q^{76} +(0.183583 + 0.162641i) q^{77} +(-3.59661 - 3.16583i) q^{78} +(4.10805 - 3.63942i) q^{79} +6.08959i q^{80} +(-0.748511 - 0.663123i) q^{81} +(2.47655 - 0.610414i) q^{82} +(0.312266 + 0.215542i) q^{83} +(-0.0429940 + 0.0163055i) q^{84} +(-3.05936 + 1.16026i) q^{85} +(-13.3685 - 9.22761i) q^{86} +(5.43388 - 1.33933i) q^{87} +(-2.77350 - 2.45711i) q^{88} +11.0934i q^{89} +(-1.74199 + 1.54327i) q^{90} +(-0.628418 - 0.327259i) q^{91} +(0.495551 + 0.439020i) q^{92} +(4.50889 - 5.08948i) q^{93} +(0.899532 + 2.37187i) q^{94} +(-1.15579 + 9.51875i) q^{95} +(1.23103 - 0.466870i) q^{96} +(-5.72423 + 0.695048i) q^{97} +(-7.61348 + 5.25520i) q^{98} -1.24811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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