LMFDB - Embedded newform 348.2.t.a.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19538 - 0.755688i) q^{2} +(-1.14525 - 1.29939i) q^{3} +(0.857871 + 1.80667i) q^{4} +(0.278916 + 0.222428i) q^{5} +(0.387077 + 2.41871i) q^{6} +(0.870753 + 0.198744i) q^{7} +(0.339796 - 2.80794i) q^{8} +(-0.376812 + 2.97624i) q^{9} +O(q^{10})$	\(q+(-1.19538 - 0.755688i) q^{2} +(-1.14525 - 1.29939i) q^{3} +(0.857871 + 1.80667i) q^{4} +(0.278916 + 0.222428i) q^{5} +(0.387077 + 2.41871i) q^{6} +(0.870753 + 0.198744i) q^{7} +(0.339796 - 2.80794i) q^{8} +(-0.376812 + 2.97624i) q^{9} +(-0.165325 - 0.476660i) q^{10} +(1.36285 + 2.82998i) q^{11} +(1.36509 - 3.18379i) q^{12} +(0.155453 - 0.0748622i) q^{13} +(-0.890693 - 0.895592i) q^{14} +(-0.0304081 - 0.617156i) q^{15} +(-2.52811 + 3.09978i) q^{16} +7.72654 q^{17} +(2.69954 - 3.27299i) q^{18} +(1.08626 + 4.75922i) q^{19} +(-0.162580 + 0.694724i) q^{20} +(-0.738983 - 1.35906i) q^{21} +(0.509461 - 4.41279i) q^{22} +(-3.91185 - 4.90530i) q^{23} +(-4.03775 + 2.77427i) q^{24} +(-1.08428 - 4.75056i) q^{25} +(-0.242398 - 0.0279851i) q^{26} +(4.29883 - 2.91891i) q^{27} +(0.387930 + 1.74366i) q^{28} +(5.37471 - 0.335328i) q^{29} +(-0.430028 + 0.760715i) q^{30} +(3.10093 - 3.88845i) q^{31} +(5.36453 - 1.79495i) q^{32} +(2.11644 - 5.01189i) q^{33} +(-9.23616 - 5.83885i) q^{34} +(0.198661 + 0.249113i) q^{35} +(-5.70034 + 1.87246i) q^{36} +(0.771683 - 1.60242i) q^{37} +(2.29799 - 6.50995i) q^{38} +(-0.275307 - 0.116258i) q^{39} +(0.719340 - 0.707600i) q^{40} -3.46856 q^{41} +(-0.143655 + 2.18303i) q^{42} +(1.90773 + 2.39222i) q^{43} +(-3.94369 + 4.88997i) q^{44} +(-0.767099 + 0.746309i) q^{45} +(0.969270 + 8.81984i) q^{46} +(1.04352 + 2.16689i) q^{47} +(6.92313 - 0.265022i) q^{48} +(-5.58807 - 2.69107i) q^{49} +(-2.29381 + 6.49811i) q^{50} +(-8.84881 - 10.0398i) q^{51} +(0.268610 + 0.216630i) q^{52} +(7.22698 + 5.76332i) q^{53} +(-7.34453 + 0.240637i) q^{54} +(-0.249347 + 1.09246i) q^{55} +(0.853939 - 2.37749i) q^{56} +(4.94002 - 6.86196i) q^{57} +(-6.67823 - 3.66076i) q^{58} +8.58277 q^{59} +(1.08891 - 0.584378i) q^{60} +(10.4219 + 2.37874i) q^{61} +(-6.64525 + 2.30484i) q^{62} +(-0.919619 + 2.51668i) q^{63} +(-7.76908 - 1.90825i) q^{64} +(0.0600098 + 0.0136968i) q^{65} +(-6.31737 + 4.39175i) q^{66} +(-3.59225 + 7.45939i) q^{67} +(6.62838 + 13.9593i) q^{68} +(-1.89384 + 10.7008i) q^{69} +(-0.0492238 - 0.447910i) q^{70} +(-6.75848 + 3.25471i) q^{71} +(8.22907 + 2.06938i) q^{72} +(-5.35475 + 4.27027i) q^{73} +(-2.13338 + 1.33235i) q^{74} +(-4.93104 + 6.84948i) q^{75} +(-7.66646 + 6.04531i) q^{76} +(0.624261 + 2.73507i) q^{77} +(0.241242 + 0.347018i) q^{78} +(10.3730 + 4.99537i) q^{79} +(-1.39461 + 0.302255i) q^{80} +(-8.71603 - 2.24296i) q^{81} +(4.14625 + 2.62115i) q^{82} +(0.276222 + 1.21021i) q^{83} +(1.82141 - 2.50099i) q^{84} +(2.15506 + 1.71860i) q^{85} +(-0.472695 - 4.30127i) q^{86} +(-6.59111 - 6.59980i) q^{87} +(8.40950 - 2.86518i) q^{88} +(-0.438903 + 0.550367i) q^{89} +(1.48095 - 0.312435i) q^{90} +(0.150239 - 0.0342912i) q^{91} +(5.50640 - 11.2755i) q^{92} +(-8.60394 + 0.423927i) q^{93} +(0.390090 - 3.37884i) q^{94} +(-0.755609 + 1.56904i) q^{95} +(-8.47605 - 4.91493i) q^{96} +(-4.48476 + 1.02362i) q^{97} +(4.64626 + 7.43970i) q^{98} +(-8.93623 + 2.98979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.19538	−	0.755688i	−0.845262	−	0.534352i
$2$	−1.19538	−	0.755688i	−0.845262	−	0.534352i
$3$	−1.14525	−	1.29939i	−0.661210	−	0.750201i
$3$	−1.14525	−	1.29939i	−0.661210	−	0.750201i
$4$	0.857871	+	1.80667i	0.428936	+	0.903335i
$5$	0.278916	+	0.222428i	0.124735	+	0.0994730i	0.683870	−	0.729603i	$-0.260295\pi$
$5$	0.278916	+	0.222428i	0.124735	+	0.0994730i	−0.559135	+	0.829076i	$0.688867\pi$
$6$	0.387077	+	2.41871i	0.158024	+	0.987435i
$7$	0.870753	+	0.198744i	0.329114	+	0.0751180i	0.383885	−	0.923381i	$-0.374586\pi$
$7$	0.870753	+	0.198744i	0.329114	+	0.0751180i	−0.0547715	+	0.998499i	$0.517443\pi$
$8$	0.339796	−	2.80794i	0.120136	−	0.992757i
$9$	−0.376812	+	2.97624i	−0.125604	+	0.992080i
$10$	−0.165325	−	0.476660i	−0.0522803	−	0.150733i
$11$	1.36285	+	2.82998i	0.410913	+	0.853270i	0.999010	+	0.0444798i	$0.0141630\pi$
$11$	1.36285	+	2.82998i	0.410913	+	0.853270i	−0.588097	+	0.808790i	$0.700123\pi$
$12$	1.36509	−	3.18379i	0.394067	−	0.919082i
$13$	0.155453	−	0.0748622i	0.0431149	−	0.0207630i	−0.412202	−	0.911092i	$-0.635240\pi$
$13$	0.155453	−	0.0748622i	0.0431149	−	0.0207630i	0.455317	+	0.890329i	$0.349526\pi$
$14$	−0.890693	−	0.895592i	−0.238048	−	0.239357i
$15$	−0.0304081	−	0.617156i	−0.00785133	−	0.159349i
$16$	−2.52811	+	3.09978i	−0.632028	+	0.774945i
$17$	7.72654			1.87396			0.936981	−	0.349381i	$-0.113608\pi$
$17$	7.72654			1.87396			0.936981	+	0.349381i	$0.113608\pi$
$18$	2.69954	−	3.27299i	0.636288	−	0.771451i
$19$	1.08626	+	4.75922i	0.249205	+	1.09184i	0.932350	+	0.361556i	$0.117755\pi$
$19$	1.08626	+	4.75922i	0.249205	+	1.09184i	−0.683145	+	0.730283i	$0.739388\pi$
$20$	−0.162580	+	0.694724i	−0.0363541	+	0.155345i
$21$	−0.738983	−	1.35906i	−0.161259	−	0.296570i
$22$	0.509461	−	4.41279i	0.108617	−	0.940809i
$23$	−3.91185	−	4.90530i	−0.815676	−	1.02283i	−0.999207	−	0.0398117i	$-0.987324\pi$
$23$	−3.91185	−	4.90530i	−0.815676	−	1.02283i	0.183531	−	0.983014i	$-0.441247\pi$
$24$	−4.03775	+	2.77427i	−0.824203	+	0.566295i
$25$	−1.08428	−	4.75056i	−0.216857	−	0.950112i
$26$	−0.242398	−	0.0279851i	−0.0475381	−	0.00548833i
$27$	4.29883	−	2.91891i	0.827310	−	0.561745i
$28$	0.387930	+	1.74366i	0.0733118	+	0.329521i
$29$	5.37471	−	0.335328i	0.998059	−	0.0622689i
$29$	5.37471	−	0.335328i	0.998059	−	0.0622689i
$30$	−0.430028	+	0.760715i	−0.0785120	+	0.138887i
$31$	3.10093	−	3.88845i	0.556944	−	0.698386i	−0.421045	−	0.907040i	$-0.638337\pi$
$31$	3.10093	−	3.88845i	0.556944	−	0.698386i	0.977990	+	0.208654i	$0.0669082\pi$
$32$	5.36453	−	1.79495i	0.948323	−	0.317306i
$33$	2.11644	−	5.01189i	0.368425	−	0.872458i
$34$	−9.23616	−	5.83885i	−1.58399	−	1.00136i
$35$	0.198661	+	0.249113i	0.0335798	+	0.0421078i
$36$	−5.70034	+	1.87246i	−0.950057	+	0.312076i
$37$	0.771683	−	1.60242i	0.126864	−	0.263436i	−0.827857	−	0.560940i	$-0.810440\pi$
$37$	0.771683	−	1.60242i	0.126864	−	0.263436i	0.954721	+	0.297504i	$0.0961542\pi$
$38$	2.29799	−	6.50995i	0.372783	−	1.05605i
$39$	−0.275307	−	0.116258i	−0.0440844	−	0.0186161i
$40$	0.719340	−	0.707600i	0.113738	−	0.111881i
$41$	−3.46856			−0.541698			−0.270849	−	0.962622i	$-0.587304\pi$
$41$	−3.46856			−0.541698			−0.270849	+	0.962622i	$0.587304\pi$
$42$	−0.143655	+	2.18303i	−0.0221665	+	0.336849i
$43$	1.90773	+	2.39222i	0.290927	+	0.364811i	0.905719	−	0.423878i	$-0.139332\pi$
$43$	1.90773	+	2.39222i	0.290927	+	0.364811i	−0.614792	+	0.788689i	$0.710760\pi$
$44$	−3.94369	+	4.88997i	−0.594534	+	0.737190i
$45$	−0.767099	+	0.746309i	−0.114352	+	0.111253i
$46$	0.969270	+	8.81984i	0.142911	+	1.30041i
$47$	1.04352	+	2.16689i	0.152213	+	0.316074i	0.963107	−	0.269120i	$-0.0867328\pi$
$47$	1.04352	+	2.16689i	0.152213	+	0.316074i	−0.810894	+	0.585194i	$0.801019\pi$
$48$	6.92313	−	0.265022i	0.999268	−	0.0382526i
$49$	−5.58807	−	2.69107i	−0.798296	−	0.384439i
$50$	−2.29381	+	6.49811i	−0.324394	+	0.918972i
$51$	−8.84881	−	10.0398i	−1.23908	−	1.40585i
$52$	0.268610	+	0.216630i	0.0372495	+	0.0300412i
$53$	7.22698	+	5.76332i	0.992702	+	0.791653i	0.978078	−	0.208240i	$-0.0667735\pi$
$53$	7.22698	+	5.76332i	0.992702	+	0.791653i	0.0146239	+	0.999893i	$0.495345\pi$
$54$	−7.34453	+	0.240637i	−0.999464	+	0.0327465i
$55$	−0.249347	+	1.09246i	−0.0336220	+	0.147308i
$56$	0.853939	−	2.37749i	0.114112	−	0.317706i
$57$	4.94002	−	6.86196i	0.654322	−	0.908889i
$58$	−6.67823	−	3.66076i	−0.876895	−	0.480682i
$59$	8.58277			1.11738			0.558691	−	0.829376i	$-0.311304\pi$
$59$	8.58277			1.11738			0.558691	+	0.829376i	$0.311304\pi$
$60$	1.08891	−	0.584378i	0.140578	−	0.0754428i
$61$	10.4219	+	2.37874i	1.33439	+	0.304567i	0.829448	−	0.558585i	$-0.188655\pi$
$61$	10.4219	+	2.37874i	1.33439	+	0.304567i	0.504946	+	0.863151i	$0.331513\pi$
$62$	−6.64525	+	2.30484i	−0.843948	+	0.292715i
$63$	−0.919619	+	2.51668i	−0.115861	+	0.317072i
$64$	−7.76908	−	1.90825i	−0.971135	−	0.238532i
$65$	0.0600098	+	0.0136968i	0.00744330	+	0.00169888i
$66$	−6.31737	+	4.39175i	−0.777615	+	0.540587i
$67$	−3.59225	+	7.45939i	−0.438864	+	0.911310i	0.557822	+	0.829961i	$0.311637\pi$
$67$	−3.59225	+	7.45939i	−0.438864	+	0.911310i	−0.996686	+	0.0813491i	$0.974077\pi$
$68$	6.62838	+	13.9593i	0.803809	+	1.69282i
$69$	−1.89384	+	10.7008i	−0.227992	+	1.28822i
$70$	−0.0492238	−	0.447910i	−0.00588337	−	0.0535355i
$71$	−6.75848	+	3.25471i	−0.802084	+	0.386263i	−0.789572	−	0.613658i	$-0.789697\pi$
$71$	−6.75848	+	3.25471i	−0.802084	+	0.386263i	−0.0125125	+	0.999922i	$0.503983\pi$
$72$	8.22907	+	2.06938i	0.969806	+	0.243879i
$73$	−5.35475	+	4.27027i	−0.626726	+	0.499798i	−0.884581	−	0.466386i	$-0.845556\pi$
$73$	−5.35475	+	4.27027i	−0.626726	+	0.499798i	0.257855	+	0.966184i	$0.416984\pi$
$74$	−2.13338	+	1.33235i	−0.248001	+	0.154882i
$75$	−4.93104	+	6.84948i	−0.569388	+	0.790910i
$76$	−7.66646	+	6.04531i	−0.879404	+	0.693444i
$77$	0.624261	+	2.73507i	0.0711412	+	0.311690i
$78$	0.241242	+	0.347018i	0.0273153	+	0.0392921i
$79$	10.3730	+	4.99537i	1.16705	+	0.562023i	0.914113	−	0.405459i	$-0.132888\pi$
$79$	10.3730	+	4.99537i	1.16705	+	0.562023i	0.252940	+	0.967482i	$0.418602\pi$
$80$	−1.39461	+	0.302255i	−0.155922	+	0.0337932i
$81$	−8.71603	−	2.24296i	−0.968447	−	0.249218i
$82$	4.14625	+	2.62115i	0.457876	+	0.289457i
$83$	0.276222	+	1.21021i	0.0303193	+	0.132837i	0.987822	−	0.155585i	$-0.0497263\pi$
$83$	0.276222	+	1.21021i	0.0303193	+	0.132837i	−0.957503	+	0.288423i	$0.906869\pi$
$84$	1.82141	−	2.50099i	0.198732	−	0.272881i
$85$	2.15506	+	1.71860i	0.233749	+	0.186408i
$86$	−0.472695	−	4.30127i	−0.0509720	−	0.463818i
$87$	−6.59111	−	6.59980i	−0.706641	−	0.707573i
$88$	8.40950	−	2.86518i	0.896456	−	0.305429i
$89$	−0.438903	+	0.550367i	−0.0465236	+	0.0583388i	−0.804549	−	0.593886i	$-0.797593\pi$
$89$	−0.438903	+	0.550367i	−0.0465236	+	0.0583388i	0.758025	+	0.652225i	$0.226164\pi$
$90$	1.48095	−	0.312435i	0.156106	−	0.0329336i
$91$	0.150239	−	0.0342912i	0.0157494	−	0.00359469i
$92$	5.50640	−	11.2755i	0.574082	−	1.17556i
$93$	−8.60394	+	0.423927i	−0.892187	+	0.0439592i
$94$	0.390090	−	3.37884i	0.0402347	−	0.348500i
$95$	−0.755609	+	1.56904i	−0.0775238	+	0.160980i
$96$	−8.47605	−	4.91493i	−0.865084	−	0.501628i
$97$	−4.48476	+	1.02362i	−0.455359	+	0.103933i	−0.444047	−	0.896003i	$-0.646458\pi$
$97$	−4.48476	+	1.02362i	−0.455359	+	0.103933i	−0.0113115	+	0.999936i	$0.503601\pi$
$98$	4.64626	+	7.43970i	0.469343	+	0.751523i
$99$	−8.93623	+	2.98979i	−0.898125	+	0.300485i
$100$	7.65252	−	6.03432i	0.765252	−	0.603432i
$101$	−8.32814	−	10.4432i	−0.828681	−	1.03913i	−0.998559	−	0.0536684i	$-0.982909\pi$
$101$	−8.32814	−	10.4432i	−0.828681	−	1.03913i	0.169877	−	0.985465i	$-0.445663\pi$
$102$	2.99077	+	18.6883i	0.296130	+	1.85042i
$103$	−2.10909	−	4.37956i	−0.207814	−	0.431531i	0.770844	−	0.637024i	$-0.219835\pi$
$103$	−2.10909	−	4.37956i	−0.207814	−	0.431531i	−0.978659	+	0.205493i	$0.934120\pi$
$104$	−0.157386	−	0.461941i	−0.0154330	−	0.0452970i
$105$	0.0961779	−	0.543433i	0.00938600	−	0.0530337i
$106$	−4.28372	−	12.3507i	−0.416071	−	1.19961i
$107$	−2.99540	−	1.44251i	−0.289576	−	0.139452i	0.283457	−	0.958985i	$-0.408519\pi$
$107$	−2.99540	−	1.44251i	−0.289576	−	0.139452i	−0.573032	+	0.819533i	$0.694233\pi$
$108$	8.96136	+	5.26252i	0.862307	+	0.506386i
$109$	−0.402659	+	1.76417i	−0.0385678	+	0.168976i	−0.990544	−	0.137196i	$-0.956191\pi$
$109$	−0.402659	+	1.76417i	−0.0385678	+	0.168976i	0.951976	+	0.306172i	$0.0990483\pi$
$110$	1.12363	−	1.11748i	0.107133	−	0.106547i
$111$	−2.96593	+	0.832451i	−0.281513	+	0.0790127i
$112$	−2.81742	+	2.19670i	−0.266222	+	0.207568i
$113$	−0.329377	+	1.44309i	−0.0309852	+	0.135755i	−0.988055	−	0.154103i	$-0.950751\pi$
$113$	−0.329377	+	1.44309i	−0.0309852	+	0.135755i	0.957070	+	0.289858i	$0.0936082\pi$
$114$	−11.0907	+	4.46954i	−1.03874	+	0.418610i
$115$		−	2.23827i		−	0.208720i
$116$	5.21664	+	9.42267i	0.484353	+	0.874873i
$117$	0.164231	+	0.490874i	0.0151832	+	0.0453813i
$118$	−10.2597	−	6.48590i	−0.944480	−	0.597075i
$119$	6.72791	+	1.53560i	0.616746	+	0.140768i
$120$	−1.74327	−	0.124323i	−0.159138	−	0.0113491i
$121$	0.706965	−	0.886506i	0.0642696	−	0.0805915i
$122$	−10.6606	−	10.7192i	−0.965166	−	0.970474i
$123$	3.97236	+	4.50700i	0.358176	+	0.406382i
$124$	9.68534	+	2.26658i	0.869770	+	0.203545i
$125$	1.52817	−	3.17328i	0.136684	−	0.283826i
$126$	3.00112	−	2.31345i	0.267361	−	0.206098i
$127$	11.7992	−	5.68217i	1.04701	−	0.504211i	0.170377	−	0.985379i	$-0.445502\pi$
$127$	11.7992	−	5.68217i	1.04701	−	0.504211i	0.876629	+	0.481168i	$0.159787\pi$
$128$	7.84496	+	8.15209i	0.693403	+	0.720550i
$129$	0.923593	−	5.21857i	0.0813178	−	0.459470i
$130$	−0.0613840	−	0.0617216i	−0.00538374	−	0.00541335i
$131$	−10.3295	+	8.23748i	−0.902490	+	0.719712i	−0.960404	−	0.278610i	$-0.910126\pi$
$131$	−10.3295	+	8.23748i	−0.902490	+	0.719712i	0.0579141	+	0.998322i	$0.481555\pi$
$132$	10.8705	−	0.475851i	0.946152	−	0.0414175i
$133$			4.35999i			0.378059i
$134$	9.93108	−	6.20219i	0.857915	−	0.535788i
$135$	1.84826	+	0.142050i	0.159073	+	0.0122257i
$136$	2.62545	−	21.6957i	0.225130	−	1.86039i
$137$	−12.3853	−	5.96444i	−1.05815	−	0.509577i	−0.177878	−	0.984052i	$-0.556923\pi$
$137$	−12.3853	−	5.96444i	−1.05815	−	0.509577i	−0.880269	+	0.474476i	$0.842638\pi$
$138$	10.3503	−	11.3604i	0.881078	−	0.967058i
$139$	−11.8116	+	9.41946i	−1.00185	+	0.798948i	−0.979631	−	0.200805i	$-0.935644\pi$
$139$	−11.8116	+	9.41946i	−1.00185	+	0.798948i	−0.0222176	+	0.999753i	$0.507073\pi$
$140$	−0.279639	+	0.572621i	−0.0236338	+	0.0483953i
$141$	1.62054	−	3.83757i	0.136474	−	0.323181i
$142$	10.5385	+	1.21668i	0.884372	+	0.102102i
$143$	0.423716	+	0.337903i	0.0354330	+	0.0282568i
$144$	−8.27307	−	8.69231i	−0.689423	−	0.724359i
$145$	1.57368	+	1.10196i	0.130687	+	0.0915128i
$146$	9.62796	−	1.05808i	0.796816	−	0.0875673i
$147$	2.90299	+	10.3430i	0.239434	+	0.853077i
$148$	3.55704	+	0.0195098i	0.292387	+	0.00160369i
$149$	−12.5066	+	2.85456i	−1.02458	+	0.233855i	−0.701616	−	0.712555i	$-0.747538\pi$
$149$	−12.5066	+	2.85456i	−1.02458	+	0.233855i	−0.322968	+	0.946410i	$0.604681\pi$
$150$	11.0705	−	4.46141i	0.903906	−	0.364272i
$151$	8.31634	−	6.63206i	0.676774	−	0.539709i	−0.223679	−	0.974663i	$-0.571807\pi$
$151$	8.31634	−	6.63206i	0.676774	−	0.539709i	0.900453	+	0.434954i	$0.143235\pi$
$152$	13.7327	−	1.43299i	1.11387	−	0.116231i
$153$	−2.91145	+	22.9961i	−0.235377	+	1.85912i
$154$	1.32063	−	3.74119i	0.106419	−	0.301474i
$155$	1.72980	−	0.394816i	0.138941	−	0.0317124i
$156$	−0.0261389	−	0.597123i	−0.00209278	−	0.0478081i
$157$		−	1.32386i		−	0.105656i	−0.998604	−	0.0528278i	$-0.983177\pi$
$157$		−	1.32386i		−	0.105656i	0.998604	−	0.0528278i	$-0.0168234\pi$
$158$	−8.62474	−	13.8101i	−0.686148	−	1.09867i
$159$	−0.787901	−	15.9911i	−0.0624846	−	1.26817i
$160$	1.89550	+	0.692581i	0.149853	+	0.0547533i
$161$	−2.43135	−	5.04876i	−0.191617	−	0.397898i
$162$	8.72399	+	9.26779i	0.685421	+	0.728147i
$163$	18.1285	−	8.73023i	1.41993	−	0.683804i	0.442838	−	0.896602i	$-0.353972\pi$
$163$	18.1285	−	8.73023i	1.41993	−	0.683804i	0.977096	+	0.212798i	$0.0682575\pi$
$164$	−2.97558	−	6.26654i	−0.232353	−	0.489335i
$165$	1.70509	−	0.927142i	0.132741	−	0.0721779i
$166$	0.584348	−	1.65539i	0.0453542	−	0.128484i
$167$	1.96649	−	8.61577i	0.152172	−	0.666709i	−0.840080	−	0.542463i	$-0.817492\pi$
$167$	1.96649	−	8.61577i	0.152172	−	0.666709i	0.992252	−	0.124246i	$-0.0396510\pi$
$168$	−4.06725	+	1.61322i	−0.313795	+	0.124463i
$169$	−8.08681	+	10.1405i	−0.622062	+	0.780041i
$170$	−1.27739	−	3.68293i	−0.0979712	−	0.282468i
$171$	−14.5739	+	1.43964i	−1.11449	+	0.110092i
$172$	−2.68537	+	5.49886i	−0.204757	+	0.419284i
$173$		−	10.4171i		−	0.791999i	−0.918251	−	0.396000i	$-0.870398\pi$
$173$		−	10.4171i		−	0.791999i	0.918251	−	0.396000i	$-0.129602\pi$
$174$	2.89149	+	12.8701i	0.219204	+	0.975679i
$175$		−	4.35206i		−	0.328985i
$176$	−12.2177	−	2.92998i	−0.920946	−	0.220856i
$177$	−9.82941	−	11.1523i	−0.738824	−	0.838261i
$178$	0.940562	−	0.326225i	0.0704981	−	0.0244516i
$179$	8.75728	−	10.9813i	0.654550	−	0.820779i	−0.338188	−	0.941079i	$-0.609814\pi$
$179$	8.75728	−	10.9813i	0.654550	−	0.820779i	0.992738	+	0.120299i	$0.0383854\pi$
$180$	−2.00641	−	0.745658i	−0.149549	−	0.0555781i
$181$	−4.86465	+	21.3134i	−0.361587	+	1.58421i	0.387582	+	0.921835i	$0.373311\pi$
$181$	−4.86465	+	21.3134i	−0.361587	+	1.58421i	−0.749168	+	0.662380i	$0.769547\pi$
$182$	−0.205507	−	0.0725431i	−0.0152332	−	0.00537725i
$183$	−8.84481	−	16.2664i	−0.653827	−	1.20245i
$184$	−15.1030	+	9.31743i	−1.11341	+	0.686890i
$185$	0.571658	−	0.275296i	0.0420291	−	0.0202402i
$186$	10.6053	+	5.99514i	0.777621	+	0.439585i
$187$	10.5301	+	21.8659i	0.770036	+	1.59900i
$188$	−3.01965	+	3.74421i	−0.220231	+	0.273075i
$189$	4.32333	−	1.68729i	0.314476	−	0.122732i
$190$	2.08894	−	1.30459i	0.151548	−	0.0946452i
$191$		−	17.3581i		−	1.25599i	−0.778218	−	0.627995i	$-0.783876\pi$
$191$		−	17.3581i		−	1.25599i	0.778218	−	0.627995i	$-0.216124\pi$
$192$	6.41796	+	12.2805i	0.463177	+	0.886266i
$193$	19.0298	−	4.34344i	1.36980	−	0.312647i	0.526537	−	0.850152i	$-0.323490\pi$
$193$	19.0298	−	4.34344i	1.36980	−	0.312647i	0.843261	+	0.537505i	$0.180633\pi$
$194$	6.13454	+	2.16547i	0.440434	+	0.155472i
$195$	−0.0509286	−	0.0936622i	−0.00364708	−	0.00670729i
$196$	0.0680359	−	12.4044i	0.00485971	−	0.886028i
$197$	−8.17888	+	6.52244i	−0.582721	+	0.464705i	−0.869938	−	0.493161i	$-0.835841\pi$
$197$	−8.17888	+	6.52244i	−0.582721	+	0.464705i	0.287217	+	0.957866i	$0.407270\pi$
$198$	12.9415	+	3.17907i	0.919716	+	0.225926i
$199$	5.88144	−	1.34240i	0.416924	−	0.0951602i	−0.00891250	−	0.999960i	$-0.502837\pi$
$199$	5.88144	−	1.34240i	0.416924	−	0.0951602i	0.425837	+	0.904800i	$0.359980\pi$
$200$	−13.7077	+	1.43039i	−0.969283	+	0.101144i
$201$	13.8067	−	3.87513i	0.973846	−	0.273331i
$202$	2.06353	+	18.7770i	0.145190	+	1.32115i
$203$	4.74669	+	0.776202i	0.333152	+	0.0544787i
$204$	10.5474	−	24.5997i	0.738466	−	1.72232i
$205$	−0.967437	−	0.771505i	−0.0675687	−	0.0538843i
$206$	−0.788421	+	6.82905i	−0.0549319	+	0.475803i
$207$	16.0734	−	9.79422i	1.11718	−	0.680746i
$208$	−0.160946	+	0.671130i	−0.0111596	+	0.0465345i
$209$	−11.9881	+	9.56017i	−0.829232	+	0.661290i
$210$	−0.525635	+	0.576930i	−0.0362723	+	0.0398119i
$211$	−14.2481	−	6.86154i	−0.980883	−	0.472368i	−0.126474	−	0.991970i	$-0.540366\pi$
$211$	−14.2481	−	6.86154i	−0.980883	−	0.472368i	−0.854409	+	0.519602i	$0.826080\pi$
$212$	−4.21261	+	18.0010i	−0.289323	+	1.23631i
$213$	11.9693	+	5.05442i	0.820121	+	0.346323i
$214$	2.49055	+	3.98793i	0.170251	+	0.272609i
$215$			1.09156i			0.0744440i
$216$	−6.73541	−	13.0627i	−0.458287	−	0.888804i
$217$	3.47295	−	2.76959i	0.235759	−	0.188012i
$218$	1.81449	−	1.80457i	0.122893	−	0.122221i
$219$	11.6813	+	2.06737i	0.789346	+	0.139700i
$220$	−2.18763	+	0.486703i	−0.147490	+	0.0328135i
$221$	1.20111	−	0.578426i	0.0807956	−	0.0389091i
$222$	4.17449	+	1.24622i	0.280173	+	0.0836409i
$223$	−7.94505	+	16.4981i	−0.532040	+	1.10479i	0.445741	+	0.895162i	$0.352940\pi$
$223$	−7.94505	+	16.4981i	−0.532040	+	1.10479i	−0.977781	+	0.209630i	$0.932774\pi$
$224$	5.02791	−	0.496795i	0.335941	−	0.0331935i
$225$	14.5474	−	1.43703i	0.969826	−	0.0958018i
$226$	1.48426	−	1.47614i	0.0987315	−	0.0981915i
$227$	−3.07569	+	3.85680i	−0.204141	+	0.255985i	−0.873354	−	0.487086i	$-0.838060\pi$
$227$	−3.07569	+	3.85680i	−0.204141	+	0.255985i	0.669213	+	0.743071i	$0.266631\pi$
$228$	16.6352	+	3.03832i	1.10169	+	0.201218i
$229$	−25.3698	−	5.79048i	−1.67648	−	0.382646i	−0.724614	−	0.689155i	$-0.757982\pi$
$229$	−25.3698	−	5.79048i	−1.67648	−	0.382646i	−0.951868	+	0.306510i	$0.900839\pi$
$230$	−1.69144	+	2.67559i	−0.111530	+	0.176423i
$231$	2.83898	−	3.94349i	0.186791	−	0.259462i
$232$	0.884723	−	15.2058i	0.0580849	−	0.998312i
$233$			5.87543i			0.384912i	0.981306	+	0.192456i	$0.0616453\pi$
$233$			5.87543i			0.384912i	−0.981306	+	0.192456i	$0.938355\pi$
$234$	0.174629	−	0.710890i	0.0114158	−	0.0464723i
$235$	−0.190923	+	0.836490i	−0.0124545	+	0.0545666i
$236$	7.36291	+	15.5062i	0.479285	+	1.00937i
$237$	−5.38874	−	19.1995i	−0.350036	−	1.24714i
$238$	−6.88198	−	6.91983i	−0.446092	−	0.448546i
$239$	−0.590773	+	2.58834i	−0.0382139	+	0.167426i	−0.990434	−	0.137986i	$-0.955937\pi$
$239$	−0.590773	+	2.58834i	−0.0382139	+	0.167426i	0.952220	+	0.305412i	$0.0987942\pi$
$240$	1.98992	+	1.46598i	0.128449	+	0.0946287i
$241$	−11.9532	−	5.75636i	−0.769974	−	0.370800i	0.00729103	−	0.999973i	$-0.497679\pi$
$241$	−11.9532	−	5.75636i	−0.769974	−	0.370800i	−0.777265	+	0.629174i	$0.783393\pi$
$242$	−1.51501	+	0.525468i	−0.0973888	+	0.0337783i
$243$	7.06754	+	13.8942i	0.453383	+	0.891316i
$244$	4.64309	+	20.8697i	0.297243	+	1.33604i
$245$	−0.960033	−	1.99353i	−0.0613343	−	0.127362i
$246$	−1.34260	−	8.38944i	−0.0856011	−	0.534891i
$247$	0.525148	+	0.658514i	0.0334143	+	0.0419003i
$248$	−9.86485	−	10.0285i	−0.626419	−	0.636812i
$249$	1.25618	−	1.74491i	0.0796074	−	0.110579i
$250$	−4.22475	+	2.63845i	−0.267197	+	0.166870i
$251$	−4.53606	+	1.03533i	−0.286314	+	0.0653492i	−0.363266	−	0.931686i	$-0.618338\pi$
$251$	−4.53606	+	1.03533i	−0.286314	+	0.0653492i	0.0769520	+	0.997035i	$0.475481\pi$
$252$	−5.33573	+	0.497541i	−0.336119	+	0.0313421i
$253$	8.55064	−	17.7556i	0.537574	−	1.11628i
$254$	−18.3984	−	2.12412i	−1.15442	−	0.133279i
$255$	−0.234949	−	4.76848i	−0.0147131	−	0.298614i
$256$	−3.21728	−	15.6732i	−0.201080	−	0.979575i
$257$	−11.7636	+	2.68497i	−0.733795	+	0.167484i	−0.573060	−	0.819514i	$-0.694244\pi$
$257$	−11.7636	+	2.68497i	−0.733795	+	0.167484i	−0.160735	+	0.986998i	$0.551387\pi$
$258$	−5.04766	+	5.54023i	−0.314253	+	0.344920i
$259$	0.990416	−	1.24194i	0.0615414	−	0.0771705i
$260$	0.0267350	+	0.120168i	0.00165803	+	0.00745251i
$261$	−1.02724	+	16.1228i	−0.0635843	+	0.997976i
$262$	18.5726	−	2.04107i	1.14742	−	0.126098i
$263$	−22.7103	−	18.1109i	−1.40038	−	1.11677i	−0.977585	−	0.210540i	$-0.932478\pi$
$263$	−22.7103	−	18.1109i	−1.40038	−	1.11677i	−0.422794	−	0.906226i	$-0.638951\pi$
$264$	−13.3539	−	7.64586i	−0.821878	−	0.470570i
$265$	0.733796	+	3.21497i	0.0450767	+	0.197494i
$266$	3.29479	−	5.21185i	0.202017	−	0.319559i
$267$	1.21779	−	0.0600023i	0.0745277	−	0.00367208i
$268$	−16.5583	−	0.0908196i	−1.01146	−	0.00554769i
$269$	19.2427	+	9.26678i	1.17325	+	0.565005i	0.915936	−	0.401324i	$-0.131450\pi$
$269$	19.2427	+	9.26678i	1.17325	+	0.565005i	0.257309	+	0.966329i	$0.417164\pi$
$270$	−2.10203	−	1.56651i	−0.127926	−	0.0953350i
$271$	−4.21954	−	18.4870i	−0.256319	−	1.12301i	−0.925153	−	0.379595i	$-0.876063\pi$
$271$	−4.21954	−	18.4870i	−0.256319	−	1.12301i	0.668834	−	0.743412i	$-0.266794\pi$
$272$	−19.5336	+	23.9506i	−1.18440	+	1.45222i
$273$	−0.216619	−	0.155947i	−0.0131104	−	0.00943835i
$274$	10.2979	+	16.4892i	0.622118	+	0.996149i
$275$	11.9663	−	9.54278i	0.721593	−	0.575451i
$276$	−20.9575	+	5.75834i	−1.26149	+	0.346612i
$277$	−5.08293	+	2.44781i	−0.305404	+	0.147075i	−0.580308	−	0.814397i	$-0.697068\pi$
$277$	−5.08293	+	2.44781i	−0.305404	+	0.147075i	0.274905	+	0.961471i	$0.411354\pi$
$278$	21.2376	−	2.33394i	1.27374	−	0.139980i
$279$	10.4045	+	10.6943i	0.622901	+	0.640253i
$280$	0.766999	−	0.473181i	0.0458369	−	0.0282780i
$281$	−8.48242	+	17.6139i	−0.506019	+	1.05076i	0.478921	+	0.877858i	$0.341028\pi$
$281$	−8.48242	+	17.6139i	−0.506019	+	1.05076i	−0.984939	+	0.172900i	$0.944686\pi$
$282$	−4.83716	+	3.36273i	−0.288049	+	0.200248i
$283$	−24.5396	−	5.60101i	−1.45873	−	0.332946i	−0.581709	−	0.813397i	$-0.697616\pi$
$283$	−24.5396	−	5.60101i	−1.45873	−	0.332946i	−0.877021	+	0.480452i	$0.840473\pi$
$284$	−11.6781	−	9.41822i	−0.692968	−	0.558869i
$285$	2.90415	−	0.815110i	0.172027	−	0.0482830i
$286$	−0.251154	−	0.724120i	−0.0148510	−	0.0428181i
$287$	−3.02026	−	0.689354i	−0.178280	−	0.0406913i
$288$	3.32080	+	16.6425i	0.195680	+	0.980668i
$289$	42.6994			2.51173
$290$	−1.04841	−	2.50647i	−0.0615648	−	0.147185i
$291$	6.46624	+	4.65514i	0.379058	+	0.272889i
$292$	−12.3087	−	6.01093i	−0.720310	−	0.351763i
$293$	4.13166	−	18.1020i	0.241374	−	1.05753i	−0.698393	−	0.715715i	$-0.746101\pi$
$293$	4.13166	−	18.1020i	0.241374	−	1.05753i	0.939767	−	0.341815i	$-0.111042\pi$
$294$	4.34592	−	14.5576i	0.253459	−	0.849016i
$295$	2.39387	+	1.90905i	0.139377	+	0.111149i
$296$	−4.23728	−	2.71134i	−0.246287	−	0.157593i
$297$	14.1191	+	8.18757i	0.819273	+	0.475091i
$298$	17.1074	+	6.03884i	0.991003	+	0.349820i
$299$	−0.975329	−	0.469694i	−0.0564047	−	0.0271631i
$300$	−16.6049	−	3.03279i	−0.958687	−	0.175098i
$301$	1.18573	+	2.46218i	0.0683441	+	0.141918i
$302$	−14.9530	+	1.64328i	−0.860446	+	0.0945601i
$303$	−4.03191	+	22.7815i	−0.231627	+	1.30876i
$304$	−17.4987	−	8.66467i	−1.00362	−	0.496953i
$305$	2.37775	+	2.98160i	0.136150	+	0.170726i
$306$	20.8581	−	25.2889i	1.19238	−	1.44567i
$307$	−31.3915			−1.79160			−0.895802	−	0.444452i	$-0.853398\pi$
$307$	−31.3915			−1.79160			−0.895802	+	0.444452i	$0.853398\pi$
$308$	−4.40583	+	3.47417i	−0.251045	+	0.197959i
$309$	−3.27532	+	7.75620i	−0.186326	+	0.441235i
$310$	−2.36613	−	0.835235i	−0.134387	−	0.0474381i
$311$	−12.5907	+	26.1449i	−0.713955	+	1.48254i	0.155137	+	0.987893i	$0.450418\pi$
$311$	−12.5907	+	26.1449i	−0.713955	+	1.48254i	−0.869092	+	0.494650i	$0.835296\pi$
$312$	−0.419993	+	0.733543i	−0.0237774	+	0.0415287i
$313$	−11.2298	−	14.0817i	−0.634747	−	0.795947i	0.355588	−	0.934643i	$-0.384280\pi$
$313$	−11.2298	−	14.0817i	−0.634747	−	0.795947i	−0.990335	+	0.138696i	$0.955709\pi$
$314$	−1.00043	+	1.58252i	−0.0564573	+	0.0893067i
$315$	−0.816278	+	0.497394i	−0.0459920	+	0.0280250i
$316$	−0.126293	+	23.0260i	−0.00710456	+	1.29531i
$317$	7.35806	−	9.22672i	0.413270	−	0.518224i	−0.531011	−	0.847365i	$-0.678188\pi$
$317$	7.35806	−	9.22672i	0.413270	−	0.518224i	0.944281	+	0.329141i	$0.106759\pi$
$318$	−11.1424	+	19.7108i	−0.624836	+	1.10533i
$319$	8.27387	+	14.7533i	0.463248	+	0.826027i
$320$	−1.74247	−	2.26031i	−0.0974072	−	0.126355i
$321$	1.55610	+	5.54421i	0.0868530	+	0.309447i
$322$	−0.908892	+	7.87253i	−0.0506506	+	0.438719i
$323$	8.39303	+	36.7723i	0.467001	+	2.04606i
$324$	−3.42493	−	17.6712i	−0.190274	−	0.981731i
$325$	−0.524193	−	0.657317i	−0.0290770	−	0.0364614i
$326$	−28.2678	−	3.26355i	−1.56561	−	0.180751i
$327$	2.75348	−	1.49720i	0.152268	−	0.0827952i
$328$	−1.17860	+	9.73951i	−0.0650774	+	0.537774i
$329$	0.477992	+	2.09422i	0.0263525	+	0.115458i
$330$	−2.73887	−	0.180232i	−0.150770	−	0.00992146i
$331$	−2.21931			−0.121985			−0.0609923	−	0.998138i	$-0.519426\pi$
$331$	−2.21931			−0.121985			−0.0609923	+	0.998138i	$0.519426\pi$
$332$	−1.94948	+	1.53724i	−0.106992	+	0.0843671i
$333$	4.47840	+	2.90053i	0.245415	+	0.158948i
$334$	−8.86155	+	8.81308i	−0.484882	+	0.482230i
$335$	−2.66112	+	1.28153i	−0.145392	+	0.0700173i
$336$	6.08101	+	1.14516i	0.331746	+	0.0624736i
$337$	−4.63472	−	9.62409i	−0.252469	−	0.524258i	0.735759	−	0.677243i	$-0.236825\pi$
$337$	−4.63472	−	9.62409i	−0.252469	−	0.524258i	−0.988228	+	0.152986i	$0.951111\pi$
$338$	17.3299	−	6.01070i	0.942622	−	0.326939i
$339$	2.25236	−	1.22471i	0.122331	−	0.0665173i
$340$	−1.25618	+	5.36782i	−0.0681261	+	0.291111i
$341$	15.2303	+	3.47622i	0.824767	+	0.188248i
$342$	18.5093	+	9.29239i	1.00087	+	0.502475i
$343$	−9.21902	−	7.35192i	−0.497780	−	0.396967i
$344$	7.36546	−	4.54394i	0.397119	−	0.244993i
$345$	−2.90838	+	2.56338i	−0.156582	+	0.138008i
$346$	−7.87210	+	12.4524i	−0.423206	+	0.669447i
$347$	33.3327			1.78939			0.894696	−	0.446676i	$-0.147392\pi$
$347$	33.3327			1.78939			0.894696	+	0.446676i	$0.147392\pi$
$348$	6.26934	−	17.5697i	0.336072	−	0.941836i
$349$	2.61849			0.140165			0.0700823	−	0.997541i	$-0.477674\pi$
$349$	2.61849			0.140165			0.0700823	+	0.997541i	$0.477674\pi$
$350$	−3.28880	+	5.20237i	−0.175794	+	0.278078i
$351$	0.449750	−	0.775573i	0.0240059	−	0.0413970i
$352$	12.3907	+	12.7352i	0.660426	+	0.678791i
$353$	8.62159	+	6.87549i	0.458881	+	0.365945i	0.825478	−	0.564435i	$-0.190906\pi$
$353$	8.62159	+	6.87549i	0.458881	+	0.365945i	−0.366597	+	0.930380i	$0.619477\pi$
$354$	3.32220	+	20.7593i	0.176573	+	1.10334i
$355$	−2.60899	−	0.595485i	−0.138471	−	0.0316051i
$356$	−1.37085	−	0.320809i	−0.0726551	−	0.0170028i
$357$	−5.70979	−	10.5008i	−0.302194	−	0.555761i
$358$	−18.7667	+	6.50904i	−0.991851	+	0.344013i
$359$	8.91873	+	18.5199i	0.470712	+	0.977444i	0.992255	+	0.124219i	$0.0396425\pi$
$359$	8.91873	+	18.5199i	0.470712	+	0.977444i	−0.521543	+	0.853225i	$0.674643\pi$
$360$	1.83493	+	2.40756i	0.0967095	+	0.126890i
$361$	−4.35177	+	2.09570i	−0.229041	+	0.110300i
$362$	21.9214	−	21.8015i	1.15216	−	1.14586i
$363$	−1.96156	+	0.0966489i	−0.102955	+	0.00507275i
$364$	0.190839	+	0.242016i	0.0100027	+	0.0126851i
$365$	−2.44336			−0.127891
$366$	−1.71939	+	26.1284i	−0.0898740	+	1.36576i
$367$	4.37713	+	19.1775i	0.228484	+	1.00106i	0.950876	+	0.309571i	$0.100186\pi$
$367$	4.37713	+	19.1775i	0.228484	+	1.00106i	−0.722392	+	0.691484i	$0.756957\pi$
$368$	25.0949	+	0.275291i	1.30816	+	0.0143505i
$369$	1.30699	−	10.3233i	0.0680393	−	0.537408i
$370$	−0.891387	−	0.102912i	−0.0463410	−	0.00535011i
$371$	5.14749	+	6.45474i	0.267244	+	0.335114i
$372$	−8.14697	−	15.1808i	−0.422401	−	0.787088i
$373$	−2.83282	−	12.4114i	−0.146678	−	0.642638i	−0.993795	−	0.111231i	$-0.964521\pi$
$373$	−2.83282	−	12.4114i	−0.146678	−	0.642638i	0.847117	−	0.531407i	$-0.178336\pi$
$374$	3.93637	−	34.0956i	0.203545	−	1.76304i
$375$	−5.87345	+	1.64851i	−0.303303	+	0.0851285i
$376$	6.43909	−	2.19384i	0.332071	−	0.113139i
$377$	0.810412	−	0.454491i	0.0417383	−	0.0234075i
$378$	−6.44309	−	1.25014i	−0.331397	−	0.0643004i
$379$	−8.03920	+	10.0808i	−0.412946	+	0.517818i	−0.944190	−	0.329401i	$-0.893153\pi$
$379$	−8.03920	+	10.0808i	−0.412946	+	0.517818i	0.531244	+	0.847219i	$0.321725\pi$
$380$	−3.48295	−	0.0191034i	−0.178672	−	0.000979981i
$381$	−20.8963	−	8.82416i	−1.07055	−	0.452075i
$382$	−13.1173	+	20.7496i	−0.671141	+	1.06164i
$383$	−9.90997	−	12.4267i	−0.506376	−	0.634975i	0.461278	−	0.887255i	$-0.347391\pi$
$383$	−9.90997	−	12.4267i	−0.506376	−	0.634975i	−0.967654	+	0.252280i	$0.918820\pi$
$384$	1.60829	−	19.5298i	0.0820725	−	0.996626i
$385$	−0.434240	+	0.901708i	−0.0221309	+	0.0459553i
$386$	−26.0302	−	9.18856i	−1.32490	−	0.467686i
$387$	−7.83869	+	4.77646i	−0.398463	+	0.242801i
$388$	−5.69669	−	7.22436i	−0.289206	−	0.366761i
$389$	17.5475			0.889695			0.444847	−	0.895606i	$-0.353258\pi$
$389$	17.5475			0.889695			0.444847	+	0.895606i	$0.353258\pi$
$390$	−0.00990030	+	0.150448i	−0.000501321	+	0.00761824i
$391$	−30.2250	−	37.9010i	−1.52855	−	1.91674i
$392$	−9.45518	+	14.7766i	−0.477559	+	0.746329i
$393$	22.5335	+	3.98802i	1.13666	+	0.201169i
$394$	14.7058	−	1.61612i	0.740868	−	0.0814188i
$395$	1.78209	+	3.70054i	0.0896664	+	0.186194i
$396$	−13.0677	−	13.5800i	−0.656676	−	0.682419i
$397$	−32.6145	−	15.7063i	−1.63688	−	0.788278i	−0.999848	−	0.0174377i	$-0.994449\pi$
$397$	−32.6145	−	15.7063i	−1.63688	−	0.788278i	−0.637028	−	0.770840i	$-0.719837\pi$
$398$	−8.04500	−	2.83985i	−0.403259	−	0.142349i
$399$	5.66531	−	4.99327i	0.283620	−	0.249976i
$400$	17.4669	+	8.64892i	0.873345	+	0.432446i
$401$	−4.37132	−	3.48601i	−0.218293	−	0.174083i	0.508238	−	0.861217i	$-0.330297\pi$
$401$	−4.37132	−	3.48601i	−0.218293	−	0.174083i	−0.726531	+	0.687134i	$0.758869\pi$
$402$	−19.4326	−	5.80127i	−0.969210	−	0.289341i
$403$	0.190951	−	0.836613i	0.00951197	−	0.0416747i
$404$	11.7229	−	24.0051i	0.583235	−	1.19430i
$405$	−1.93214	−	2.56429i	−0.0960089	−	0.127421i
$406$	−5.08754	−	4.51488i	−0.252490	−	0.224069i
$407$	5.58649			0.276912
$408$	−31.1979	+	21.4355i	−1.54452	+	1.06121i
$409$	28.2499	+	6.44787i	1.39687	+	0.318826i	0.853686	−	0.520787i	$-0.174362\pi$
$409$	28.2499	+	6.44787i	1.39687	+	0.318826i	0.543184	+	0.839614i	$0.317219\pi$
$410$	0.573439	+	1.65332i	0.0283201	+	0.0816518i
$411$	6.43412	+	22.9241i	0.317372	+	1.13076i
$412$	6.10310	−	7.56752i	0.300678	−	0.372825i
$413$	7.47347	+	1.70577i	0.367746	+	0.0839355i
$414$	−26.6152	−	0.438635i	−1.30807	−	0.0215577i
$415$	−0.192141	+	0.398986i	−0.00943185	+	0.0195854i
$416$	0.699557	−	0.680631i	0.0342986	−	0.0333707i
$417$	25.7668	+	4.56025i	1.26180	+	0.223316i
$418$	21.5548	−	2.36880i	1.05428	−	0.115862i
$419$	−21.8100	+	10.5032i	−1.06549	+	0.513113i	−0.882651	−	0.470030i	$-0.844243\pi$
$419$	−21.8100	+	10.5032i	−1.06549	+	0.513113i	−0.182840	+	0.983143i	$0.558529\pi$
$420$	1.06431	−	0.292434i	0.0519332	−	0.0142693i
$421$	24.9736	−	19.9158i	1.21714	−	0.970637i	0.217155	−	0.976137i	$-0.430322\pi$
$421$	24.9736	−	19.9158i	1.21714	−	0.970637i	0.999985	+	0.00549998i	$0.00175071\pi$
$422$	11.8468	+	18.9693i	0.576692	+	0.923412i
$423$	−6.84240	+	2.28926i	−0.332689	+	0.111308i
$424$	18.6388	−	18.3346i	0.905179	−	0.890406i
$425$	−8.37777	−	36.7054i	−0.406382	−	1.78047i
$426$	−10.4883	−	15.0870i	−0.508158	−	0.730967i
$427$	8.60218	+	4.14259i	0.416288	+	0.200474i
$428$	0.0364696	−	6.64918i	0.00176282	−	0.321400i
$429$	−0.0461945	−	0.937554i	−0.00223029	−	0.0452655i
$430$	0.824882	−	1.30483i	0.0397793	−	0.0629247i
$431$	−8.30007	−	36.3650i	−0.399800	−	1.75164i	−0.628180	−	0.778068i	$-0.716200\pi$
$431$	−8.30007	−	36.3650i	−0.399800	−	1.75164i	0.228380	−	0.973572i	$-0.426657\pi$
$432$	−1.81995	+	20.7048i	−0.0875622	+	0.996159i
$433$	−6.38285	−	5.09015i	−0.306740	−	0.244617i	0.458006	−	0.888949i	$-0.348564\pi$
$433$	−6.38285	−	5.09015i	−0.306740	−	0.244617i	−0.764746	+	0.644332i	$0.777135\pi$
$434$	−6.24444	+	0.686243i	−0.299743	+	0.0329407i
$435$	−0.370385	−	3.30684i	−0.0177586	−	0.158551i
$436$	−3.53269	+	0.785954i	−0.169185	+	0.0376404i
$437$	19.0961	−	23.9458i	0.913490	−	1.14548i
$438$	−12.4013	−	11.2987i	−0.592555	−	0.539872i
$439$	21.9961	−	5.02047i	1.04982	−	0.239614i	0.337393	−	0.941364i	$-0.390455\pi$
$439$	21.9961	−	5.02047i	1.04982	−	0.239614i	0.712423	+	0.701750i	$0.247598\pi$
$440$	2.98284	+	1.07137i	0.142201	+	0.0510754i
$441$	10.1149	−	15.6174i	0.481663	−	0.743687i
$442$	−1.87290	−	0.216228i	−0.0890846	−	0.0102849i
$443$	−3.57302	+	7.41946i	−0.169759	+	0.352509i	−0.968440	−	0.249246i	$-0.919817\pi$
$443$	−3.57302	+	7.41946i	−0.169759	+	0.352509i	0.798681	+	0.601755i	$0.205532\pi$
$444$	−4.04835	−	4.64432i	−0.192126	−	0.220410i
$445$	−0.244834	+	0.0558819i	−0.0116063	+	0.00264905i
$446$	21.9647	−	13.7175i	1.04006	−	0.649542i
$447$	18.0324	+	12.9818i	0.852903	+	0.614018i
$448$	−6.38569	−	3.20567i	−0.301696	−	0.151454i
$449$	20.2360	+	25.3752i	0.954997	+	1.19753i	0.980233	+	0.197847i	$0.0633949\pi$
$449$	20.2360	+	25.3752i	0.954997	+	1.19753i	−0.0252359	+	0.999682i	$0.508034\pi$
$450$	−18.4756	−	9.27549i	−0.870949	−	0.437251i
$451$	−4.72711	−	9.81594i	−0.222591	−	0.462215i
$452$	−2.88976	+	0.642914i	−0.135923	+	0.0302401i
$453$	−18.1419	−	3.21078i	−0.852380	−	0.150856i
$454$	6.59116	−	2.28608i	0.309339	−	0.107291i
$455$	0.0495315	+	0.0238531i	0.00232207	+	0.00111825i
$456$	−17.5894	−	16.2030i	−0.823698	−	0.758774i
$457$	−8.51714	+	37.3160i	−0.398415	+	1.74557i	0.235224	+	0.971941i	$0.424418\pi$
$457$	−8.51714	+	37.3160i	−0.398415	+	1.74557i	−0.633639	+	0.773629i	$0.718439\pi$
$458$	25.9507	+	26.0935i	1.21260	+	1.21927i
$459$	33.2151	−	22.5531i	1.55035	−	1.05269i
$460$	4.04382	−	1.92015i	0.188544	−	0.0895274i
$461$	−7.10420	+	31.1255i	−0.330876	+	1.44966i	0.486563	+	0.873645i	$0.338250\pi$
$461$	−7.10420	+	31.1255i	−0.330876	+	1.44966i	−0.817439	+	0.576016i	$0.804607\pi$
$462$	−6.37370	+	2.56859i	−0.296532	+	0.119502i
$463$		−	31.9221i		−	1.48354i	−0.670652	−	0.741772i	$-0.733985\pi$
$463$		−	31.9221i		−	1.48354i	0.670652	−	0.741772i	$-0.266015\pi$
$464$	−12.5484	+	17.5082i	−0.582547	+	0.812797i
$465$	−2.49407	−	1.79552i	−0.115660	−	0.0832652i
$466$	4.43999	−	7.02338i	0.205679	−	0.325352i
$467$	−15.0744	−	3.44064i	−0.697562	−	0.159214i	−0.140987	−	0.990011i	$-0.545028\pi$
$467$	−15.0744	−	3.44064i	−0.697562	−	0.159214i	−0.556575	+	0.830798i	$0.687885\pi$
$468$	−0.745959	+	0.717819i	−0.0344819	+	0.0331812i
$469$	−4.61047	+	5.78135i	−0.212892	+	0.266958i
$470$	0.860351	−	0.855645i	0.0396850	−	0.0394680i
$471$	−1.72021	+	1.51615i	−0.0792630	+	0.0698605i
$472$	2.91639	−	24.0999i	0.134238	−	1.10929i
$473$	−4.16999	+	8.65907i	−0.191736	+	0.398145i
$474$	−8.06722	+	27.0229i	−0.370540	+	1.24120i
$475$	21.4311	−	10.3207i	0.983328	−	0.473546i
$476$	2.99735	+	13.4725i	0.137383	+	0.617509i
$477$	−19.8762	+	19.3375i	−0.910071	+	0.885405i
$478$	2.66218	−	2.64762i	0.121765	−	0.121099i
$479$	21.8287	−	17.4078i	0.997378	−	0.795382i	0.0184999	−	0.999829i	$-0.494111\pi$
$479$	21.8287	−	17.4078i	0.997378	−	0.795382i	0.978878	+	0.204447i	$0.0655395\pi$
$480$	−1.27089	−	3.25617i	−0.0580080	−	0.148623i
$481$		−	0.306870i		−	0.0139921i
$482$	9.93862	+	15.9139i	0.452692	+	0.724860i
$483$	−3.77578	+	8.94135i	−0.171804	+	0.406845i
$484$	2.20811	+	0.516744i	0.100369	+	0.0234884i
$485$	−1.47855	−	0.712035i	−0.0671377	−	0.0323318i
$486$	2.05131	−	21.9498i	0.0930493	−	0.995662i
$487$	15.3118	−	12.2107i	0.693843	−	0.553321i	−0.211826	−	0.977307i	$-0.567941\pi$
$487$	15.3118	−	12.2107i	0.693843	−	0.553321i	0.905669	+	0.423986i	$0.139370\pi$
$488$	10.2207	−	28.4559i	0.462669	−	1.28814i
$489$	−32.1056	−	13.5577i	−1.45186	−	0.613098i
$490$	−0.358881	+	3.10851i	−0.0162126	+	0.140428i
$491$	−23.7110	−	18.9089i	−1.07006	−	0.853348i	−0.0804017	−	0.996763i	$-0.525620\pi$
$491$	−23.7110	−	18.9089i	−1.07006	−	0.853348i	−0.989663	+	0.143415i	$0.954192\pi$
$492$	−4.73488	+	11.0432i	−0.213465	+	0.497865i
$493$	41.5280	−	2.59093i	1.87032	−	0.116690i
$494$	−0.130120	−	1.18402i	−0.00585438	−	0.0532717i
$495$	−3.15747	−	1.15377i	−0.141918	−	0.0518581i
$496$	4.21382	+	19.4427i	0.189206	+	0.873001i
$497$	−6.53182	+	1.49085i	−0.292992	+	0.0668735i
$498$	−2.82022	+	1.13654i	−0.126377	+	0.0509298i
$499$	−3.76050	+	2.99890i	−0.168343	+	0.134249i	−0.704038	−	0.710163i	$-0.748621\pi$
$499$	−3.76050	+	2.99890i	−0.168343	+	0.134249i	0.535694	+	0.844412i	$0.320050\pi$
$500$	7.04403	+	0.0386353i	0.315019	+	0.00172782i
$501$	−13.4473	+	7.31197i	−0.600783	+	0.326675i
$502$	6.20471	+	2.19024i	0.276930	+	0.0977551i
$503$	5.54671	−	1.26600i	0.247316	−	0.0564482i	−0.0970660	−	0.995278i	$-0.530946\pi$
$503$	5.54671	−	1.26600i	0.247316	−	0.0564482i	0.344381	+	0.938830i	$0.388089\pi$
$504$	6.75421	+	3.43739i	0.300857	+	0.153114i
$505$		−	4.76518i		−	0.212048i
$506$	−23.6390	+	14.7631i	−1.05088	+	0.656299i
$507$	22.4379	−	1.10554i	0.996501	−	0.0490989i
$508$	20.3880	+	16.4426i	0.904570	+	0.729522i
$509$	10.3240	+	21.4380i	0.457603	+	0.950222i	0.994317	+	0.106458i	$0.0339510\pi$
$509$	10.3240	+	21.4380i	0.457603	+	0.950222i	−0.536714	+	0.843764i	$0.680335\pi$
$510$	−3.32263	+	5.87770i	−0.147128	+	0.260269i
$511$	−5.51135	+	2.65413i	−0.243808	+	0.117412i
$512$	−7.99817	+	21.1667i	−0.353473	+	0.935445i
$513$	18.5614	+	17.2884i	0.819505	+	0.763300i
$514$	16.0910	+	5.68007i	0.709744	+	0.250537i
$515$	0.385880	−	1.69065i	0.0170039	−	0.0744990i
$516$	10.2206	−	2.80824i	0.449935	−	0.123626i
$517$	−4.71010	+	5.90627i	−0.207150	+	0.259758i
$518$	−2.12244	+	0.736148i	−0.0932549	+	0.0323445i
$519$	−13.5359	+	11.9302i	−0.594159	+	0.523677i
$520$	0.0588510	−	0.163850i	0.00258079	−	0.00718530i
$521$		−	19.7996i		−	0.867436i	−0.901049	−	0.433718i	$-0.857201\pi$
$521$		−	19.7996i		−	0.867436i	0.901049	−	0.433718i	$-0.142799\pi$
$522$	13.4117	−	18.4966i	0.587016	−	0.809575i
$523$			5.45272i			0.238431i	0.992868	+	0.119215i	$0.0380379\pi$
$523$			5.45272i			0.238431i	−0.992868	+	0.119215i	$0.961962\pi$
$524$	−23.7438	−	11.5953i	−1.03725	−	0.506541i
$525$	−5.65501	+	4.98419i	−0.246805	+	0.217528i
$526$	13.4613	+	38.8113i	0.586942	+	1.69226i
$527$	23.9595	−	30.0442i	1.04369	−	1.30875i
$528$	10.1852	+	19.2311i	0.443252	+	0.836927i
$529$	−3.64144	+	15.9542i	−0.158324	+	0.693661i
$530$	1.55235	−	4.39763i	0.0674297	−	0.191021i
$531$	−3.23409	+	25.5444i	−0.140347	+	1.10853i
$532$	−7.87706	+	3.74031i	−0.341514	+	0.162163i
$533$	−0.539197	+	0.259664i	−0.0233552	+	0.0112473i
$534$	−1.50107	−	0.848546i	−0.0649576	−	0.0367202i
$535$	−0.514610	−	1.06860i	−0.0222485	−	0.0461996i
$536$	19.7249	+	12.6215i	0.851986	+	0.545166i
$537$	−24.2982	+	1.19720i	−1.04854	+	0.0516631i
$538$	−15.9995	−	25.6188i	−0.689788	−	1.10450i
$539$		−	19.4816i		−	0.839133i
$540$	1.32893	+	3.46106i	0.0571882	+	0.148940i
$541$	−12.8265	+	2.92756i	−0.551453	+	0.125866i	−0.489163	−	0.872192i	$-0.662698\pi$
$541$	−12.8265	+	2.92756i	−0.551453	+	0.125866i	−0.0622904	+	0.998058i	$0.519840\pi$
$542$	−8.92647	+	25.2877i	−0.383425	+	1.08620i
$543$	33.2656	−	18.0881i	1.42756	−	0.776235i
$544$	41.4492	−	13.8688i	1.77712	−	0.594619i
$545$	−0.504709	+	0.402492i	−0.0216193	+	0.0172408i
$546$	0.141095	+	0.350113i	0.00603830	+	0.0149834i
$547$	−17.7069	+	4.04149i	−0.757093	+	0.172801i	−0.583608	−	0.812035i	$-0.698360\pi$
$547$	−17.7069	+	4.04149i	−0.757093	+	0.172801i	−0.173484	+	0.984837i	$0.555503\pi$
$548$	0.150793	−	27.4929i	0.00644158	−	1.17444i
$549$	−11.0068	+	30.1219i	−0.469759	+	1.28557i
$550$	−21.5156	+	2.36449i	−0.917429	+	0.100822i
$551$	7.43424	+	25.2152i	0.316709	+	1.07420i
$552$	29.4037	+	8.95389i	1.25150	+	0.381103i
$553$	8.03952	+	6.41130i	0.341875	+	0.272636i
$554$	7.92582	+	0.915044i	0.336736	+	0.0388765i
$555$	−1.01241	−	0.427522i	−0.0429743	−	0.0181473i
$556$	−27.1507	−	13.2590i	−1.15145	−	0.562308i
$557$	30.5460	−	24.3596i	1.29428	−	1.03215i	0.297273	−	0.954793i	$-0.403923\pi$
$557$	30.5460	−	24.3596i	1.29428	−	1.03215i	0.997003	−	0.0773581i	$-0.0246485\pi$
$558$	−4.35575	−	20.6464i	−0.184393	−	0.874030i
$559$	0.475650	+	0.229061i	0.0201178	+	0.00968824i
$560$	−1.27443	−	0.0139805i	−0.0538546	−	0.000590784i
$561$	16.3527	−	38.7246i	0.690413	−	1.63495i
$562$	23.4503	−	14.6453i	0.989193	−	0.617774i
$563$			3.93096i			0.165670i	0.996563	+	0.0828351i	$0.0263975\pi$
$563$			3.93096i			0.165670i	−0.996563	+	0.0828351i	$0.973603\pi$
$564$	8.32343	−	0.364355i	0.350480	−	0.0153421i
$565$	−0.412854	+	0.329240i	−0.0173689	+	0.0138512i
$566$	25.1016	+	25.2396i	1.05510	+	1.06090i
$567$	−7.14373	−	3.68532i	−0.300008	−	0.154769i
$568$	6.84254	+	20.0834i	0.287107	+	0.842679i
$569$	−29.8870	+	14.3928i	−1.25293	+	0.603378i	−0.938295	−	0.345836i	$-0.887595\pi$
$569$	−29.8870	+	14.3928i	−1.25293	+	0.603378i	−0.314632	+	0.949214i	$0.601881\pi$
$570$	−4.08753	−	1.22026i	−0.171208	−	0.0511111i
$571$	18.4838	−	38.3821i	0.773524	−	1.60624i	−0.0215803	−	0.999767i	$-0.506870\pi$
$571$	18.4838	−	38.3821i	0.773524	−	1.60624i	0.795104	−	0.606472i	$-0.207416\pi$
$572$	−0.246984	+	1.05539i	−0.0103269	+	0.0441282i
$573$	−22.5549	+	19.8794i	−0.942245	+	0.830472i
$574$	3.08942	+	3.10641i	0.128950	+	0.129659i
$575$	−19.0614	+	23.9022i	−0.794914	+	0.996791i
$576$	8.60690	−	22.4036i	0.358621	−	0.933483i
$577$	−24.5320	−	5.59926i	−1.02128	−	0.233100i	−0.321083	−	0.947051i	$-0.604047\pi$
$577$	−24.5320	−	5.59926i	−1.02128	−	0.233100i	−0.700196	+	0.713950i	$0.746904\pi$
$578$	−51.0421	−	32.2675i	−2.12307	−	1.34215i
$579$	−27.4377	−	19.7528i	−1.14027	−	0.820899i
$580$	−0.640862	+	3.78846i	−0.0266103	+	0.157307i
$581$			1.10869i			0.0459961i
$582$	−4.21179	−	10.4511i	−0.174584	−	0.433213i
$583$	−6.46082	+	28.3067i	−0.267580	+	1.17234i
$584$	10.1712	+	16.4869i	0.420885	+	0.682231i
$585$	−0.0633775	+	0.173443i	−0.00262034	+	0.00717097i
$586$	−18.6184	+	18.5165i	−0.769118	+	0.764911i
$587$	−0.762307	+	3.33989i	−0.0314638	+	0.137852i	−0.988220	−	0.153038i	$-0.951094\pi$
$587$	−0.762307	+	3.33989i	−0.0314638	+	0.137852i	0.956756	+	0.290890i	$0.0939514\pi$
$588$	−16.1960	+	14.1177i	−0.667913	+	0.582205i
$589$	21.8744	+	10.5341i	0.901318	+	0.434052i
$590$	−1.41895	−	4.09107i	−0.0584170	−	0.168427i
$591$	17.8420	+	3.15771i	0.733923	+	0.129891i
$592$	3.01624	+	6.44314i	0.123967	+	0.264812i
$593$	1.75088	+	3.63574i	0.0719001	+	0.149302i	0.933821	−	0.357741i	$-0.116453\pi$
$593$	1.75088	+	3.63574i	0.0719001	+	0.149302i	−0.861921	+	0.507043i	$0.830739\pi$
$594$	−10.6905	−	20.4569i	−0.438635	−	0.839357i
$595$	1.53496	+	1.92478i	0.0629273	+	0.0789083i
$596$	−15.8863	−	20.1465i	−0.650730	−	0.825235i
$597$	−8.48001	−	6.10488i	−0.347064	−	0.249856i
$598$	0.810948	+	1.29851i	0.0331621	+	0.0530999i
$599$	−3.14564	+	0.717972i	−0.128527	+	0.0293355i	−0.286301	−	0.958140i	$-0.592426\pi$
$599$	−3.14564	+	0.717972i	−0.128527	+	0.0293355i	0.157773	+	0.987475i	$0.449568\pi$
$600$	17.5574	+	16.1735i	0.716778	+	0.660281i
$601$	5.12898	−	10.6504i	0.209215	−	0.434440i	−0.769784	−	0.638305i	$-0.779636\pi$
$601$	5.12898	−	10.6504i	0.209215	−	0.434440i	0.978999	+	0.203865i	$0.0653503\pi$
$602$	0.443249	−	3.83929i	0.0180655	−	0.156478i
$603$	−20.8473	−	13.5022i	−0.848970	−	0.549852i
$604$	19.1163	+	9.33543i	0.777831	+	0.379853i
$605$	0.394368	−	0.0900119i	0.0160333	−	0.00365951i
$606$	22.0354	−	24.1857i	0.895126	−	0.982477i
$607$	1.54725	−	1.94019i	0.0628011	−	0.0787501i	−0.749439	−	0.662074i	$-0.769677\pi$
$607$	1.54725	−	1.94019i	0.0628011	−	0.0787501i	0.812240	+	0.583324i	$0.198248\pi$
$608$	14.3698	+	23.5812i	0.582774	+	0.956342i
$609$	−4.42756	−	7.05673i	−0.179414	−	0.285953i
$610$	−0.589155	−	5.36099i	−0.0238542	−	0.217060i
$611$	0.324436	+	0.258729i	0.0131253	+	0.0104671i
$612$	−44.0439	+	14.4676i	−1.78037	+	0.584819i
$613$	2.37966	+	10.4260i	0.0961136	+	0.421101i	0.999977	−	0.00671898i	$-0.00213873\pi$
$613$	2.37966	+	10.4260i	0.0961136	+	0.421101i	−0.903864	+	0.427820i	$0.859282\pi$
$614$	37.5247	+	23.7221i	1.51438	+	0.957348i
$615$	0.105472	+	2.14064i	0.00425305	+	0.0863190i
$616$	7.89203	−	0.823525i	0.317979	−	0.0331807i
$617$	1.67571	+	0.806982i	0.0674617	+	0.0324879i	0.467310	−	0.884093i	$-0.345223\pi$
$617$	1.67571	+	0.806982i	0.0674617	+	0.0324879i	−0.399849	+	0.916581i	$0.630937\pi$
$618$	9.77652	−	6.79650i	0.393269	−	0.273395i
$619$	7.36211	+	32.2555i	0.295908	+	1.29646i	0.876159	+	0.482022i	$0.160097\pi$
$619$	7.36211	+	32.2555i	0.295908	+	1.29646i	−0.580251	+	0.814438i	$0.697046\pi$
$620$	2.19725	+	2.78648i	0.0882436	+	0.111908i
$621$	−31.1345	−	9.66872i	−1.24938	−	0.387992i
$622$	34.8081	−	21.7385i	1.39568	−	0.871634i
$623$	−0.491558	+	0.392004i	−0.0196939	+	0.0157053i
$624$	1.05638	−	0.559479i	0.0422891	−	0.0223971i
$625$	−20.8188	+	10.0258i	−0.832754	+	0.401033i
$626$	2.78250	+	25.3193i	0.111211	+	1.01196i
$627$	26.1517	+	4.62837i	1.04440	+	0.184839i
$628$	2.39178	−	1.13570i	0.0954424	−	0.0453195i
$629$	5.96244	−	12.3811i	0.237738	−	0.493668i
$630$	1.35164	+	0.0222758i	0.0538505	+	0.000887490i
$631$	−13.5775	−	3.09897i	−0.540511	−	0.123368i	−0.0564552	−	0.998405i	$-0.517980\pi$
$631$	−13.5775	−	3.09897i	−0.540511	−	0.123368i	−0.484056	+	0.875037i	$0.660837\pi$
$632$	17.5514	−	27.4294i	0.698158	−	1.09108i
$633$	7.40187	+	26.3720i	0.294198	+	1.04819i
$634$	−15.7682	+	5.46904i	−0.626236	+	0.217203i
$635$	4.55485	+	1.03961i	0.180754	+	0.0412559i
$636$	28.2147	−	15.1418i	1.11878	−	0.600410i
$637$	−1.07014			−0.0424005
$638$	1.25847	−	23.8883i	0.0498234	−	0.945747i
$639$	−7.14014	−	21.3413i	−0.282459	−	0.844248i
$640$	0.374832	+	4.01869i	0.0148165	+	0.158853i
$641$	−6.75832	+	29.6101i	−0.266938	+	1.16953i	0.646617	+	0.762815i	$0.276183\pi$
$641$	−6.75832	+	29.6101i	−0.266938	+	1.16953i	−0.913555	+	0.406716i	$0.866674\pi$
$642$	2.32956	−	7.80336i	0.0919404	−	0.307974i
$643$	−16.6565	−	13.2831i	−0.656867	−	0.523834i	0.237375	−	0.971418i	$-0.423713\pi$
$643$	−16.6565	−	13.2831i	−0.656867	−	0.523834i	−0.894242	+	0.447584i	$0.852284\pi$
$644$	7.03565	−	8.72384i	0.277243	−	0.343767i
$645$	1.41836	−	1.25011i	0.0558480	−	0.0492231i
$646$	17.7555	−	50.2994i	0.698581	−	1.97900i
$647$	−11.6140	−	5.59300i	−0.456593	−	0.219883i	0.191427	−	0.981507i	$-0.438688\pi$
$647$	−11.6140	−	5.59300i	−0.456593	−	0.219883i	−0.648020	+	0.761623i	$0.724403\pi$
$648$	−9.25978	+	23.7119i	−0.363759	+	0.931493i
$649$	11.6970	+	24.2890i	0.459147	+	0.953429i
$650$	0.129883	+	1.18187i	0.00509445	+	0.0463568i
$651$	−7.57615	−	1.34084i	−0.296933	−	0.0525517i
$652$	31.3246	+	25.2628i	1.22676	+	0.989368i
$653$	−27.7486	−	34.7956i	−1.08589	−	1.36166i	−0.927303	−	0.374313i	$-0.877879\pi$
$653$	−27.7486	−	34.7956i	−1.08589	−	1.36166i	−0.158584	−	0.987346i	$-0.550693\pi$
$654$	−4.42287	−	0.291049i	−0.172948	−	0.0113809i
$655$	−4.71331			−0.184164
$656$	8.76891	−	10.7518i	0.342368	−	0.419786i
$657$	−10.6916	−	17.5461i	−0.417120	−	0.684539i
$658$	1.01119	−	2.86460i	0.0394205	−	0.111674i
$659$	−6.98132	+	14.4969i	−0.271954	+	0.564718i	−0.991558	−	0.129667i	$-0.958609\pi$
$659$	−6.98132	+	14.4969i	−0.271954	+	0.564718i	0.719604	+	0.694385i	$0.244323\pi$
$660$	3.13779	+	2.28518i	0.122138	+	0.0889503i
$661$	−12.8265	−	16.0839i	−0.498893	−	0.625592i	0.467086	−	0.884212i	$-0.345304\pi$
$661$	−12.8265	−	16.0839i	−0.498893	−	0.625592i	−0.965979	+	0.258620i	$0.916732\pi$
$662$	2.65293	+	1.67711i	0.103109	+	0.0651827i
$663$	−2.12717	−	0.898269i	−0.0826125	−	0.0348859i
$664$	3.49205	−	0.364391i	0.135518	−	0.0141411i
$665$	−0.969785	+	1.21607i	−0.0376066	+	0.0471572i
$666$	−3.16150	−	6.85151i	−0.122506	−	0.265490i
$667$	−22.6699	−	25.0528i	−0.877784	−	0.970049i
$668$	17.2529	−	3.83842i	0.667533	−	0.148513i
$669$	30.5364	−	8.57069i	1.18061	−	0.331362i
$670$	4.14948	+	0.479062i	0.160309	+	0.0185078i
$671$	7.47171	+	32.7357i	0.288442	+	1.26375i
$672$	−6.40374	−	5.96425i	−0.247030	−	0.230076i
$673$	−9.58448	−	12.0186i	−0.369455	−	0.463281i	0.562001	−	0.827137i	$-0.310032\pi$
$673$	−9.58448	−	12.0186i	−0.369455	−	0.463281i	−0.931456	+	0.363855i	$0.881460\pi$
$674$	−1.73256	+	15.0069i	−0.0667356	+	0.578042i
$675$	−18.5276	−	17.2569i	−0.713129	−	0.664220i
$676$	−25.2580	−	5.91092i	−0.971463	−	0.227343i
$677$	−8.94991	−	39.2121i	−0.343973	−	1.50704i	−0.790605	−	0.612327i	$-0.790234\pi$
$677$	−8.94991	−	39.2121i	−0.343973	−	1.50704i	0.446632	−	0.894718i	$-0.352623\pi$
$678$	−3.61793	−	0.238079i	−0.138946	−	0.00914336i
$679$	−4.10856			−0.157672
$680$	5.55801	−	5.46730i	0.213140	−	0.209662i
$681$	8.53391	−	0.420477i	0.327020	−	0.0161127i
$682$	−15.5791	−	15.6648i	−0.596554	−	0.599835i
$683$	20.3496	−	9.79984i	0.778655	−	0.374980i	−0.00195580	−	0.999998i	$-0.500623\pi$
$683$	20.3496	−	9.79984i	0.778655	−	0.374980i	0.780611	+	0.625018i	$0.214908\pi$
$684$	−15.1035	−	25.0952i	−0.577496	−	0.959538i
$685$	−2.12780	−	4.41842i	−0.0812990	−	0.168819i
$686$	5.46448	+	15.7551i	0.208635	+	0.601531i
$687$	21.5306	+	39.5967i	0.821444	+	1.51071i
$688$	−12.2383	−	0.134254i	−0.466582	−	0.00511839i
$689$	1.55491	+	0.354898i	0.0592373	+	0.0135205i
$690$	5.41374	−	0.866385i	0.206098	−	0.0329827i
$691$	2.35289	+	1.87637i	0.0895083	+	0.0713805i	0.667222	−	0.744859i	$-0.267483\pi$
$691$	2.35289	+	1.87637i	0.0895083	+	0.0713805i	−0.577713	+	0.816240i	$0.696055\pi$
$692$	18.8203	−	8.93655i	0.715441	−	0.339717i
$693$	−8.37545	+	0.827347i	−0.318157	+	0.0314283i
$694$	−39.8452	−	25.1891i	−1.51250	−	0.956165i
$695$	−5.38961			−0.204439
$696$	−20.7715	+	16.2649i	−0.787341	+	0.616518i
$697$	−26.8000			−1.01512
$698$	−3.13009	−	1.97876i	−0.118476	−	0.0748972i
$699$	7.63445	−	6.72883i	0.288762	−	0.254508i
$700$	7.86274	−	3.73351i	0.297183	−	0.141113i
$701$	4.27806	+	3.41164i	0.161580	+	0.128856i	0.700942	−	0.713218i	$-0.252763\pi$
$701$	4.27806	+	3.41164i	0.161580	+	0.128856i	−0.539362	+	0.842074i	$0.681335\pi$
$702$	−1.12371	+	0.587235i	−0.0424118	+	0.0221638i
$703$	8.46450	+	1.93197i	0.319245	+	0.0728655i
$704$	−5.18773	−	24.5870i	−0.195520	−	0.926656i
$705$	1.30558	−	0.709905i	0.0491709	−	0.0267366i
$706$	−5.11036	−	14.7341i	−0.192331	−	0.554524i
$707$	−5.17624	−	10.7486i	−0.194673	−	0.404242i
$708$	11.7162	−	27.3258i	0.440323	−	1.02697i
$709$	−15.3969	+	7.41474i	−0.578241	+	0.278466i	−0.700058	−	0.714086i	$-0.746842\pi$
$709$	−15.3969	+	7.41474i	−0.578241	+	0.278466i	0.121816	+	0.992553i	$0.461128\pi$
$710$	2.66874	+	2.68341i	0.100156	+	0.100707i
$711$	−18.7761	+	28.9902i	−0.704159	+	1.08722i
$712$	1.39626	+	1.41943i	0.0523271	+	0.0531953i
$713$	−31.2044			−1.16861
$714$	−1.10996	+	16.8673i	−0.0415391	+	0.631242i
$715$	0.0430223	+	0.188493i	0.00160894	+	0.00704924i
$716$	27.3522	+	6.40099i	1.02220	+	0.239216i
$717$	4.03984	−	2.19666i	0.150871	−	0.0820356i
$718$	3.33401	−	28.8781i	0.124424	−	1.07772i
$719$	15.1461	+	18.9926i	0.564853	+	0.708304i	0.979447	−	0.201703i	$-0.0646476\pi$
$719$	15.1461	+	18.9926i	0.564853	+	0.708304i	−0.414593	+	0.910007i	$0.636076\pi$
$720$	−0.374079	−	4.26459i	−0.0139411	−	0.158932i
$721$	−0.966082	−	4.23268i	−0.0359788	−	0.157633i
$722$	6.78572	+	0.783419i	0.252538	+	0.0291558i
$723$	6.20965	+	22.1243i	0.230940	+	0.822812i
$724$	−42.6796	+	9.49536i	−1.58617	+	0.352892i
$725$	−7.42072	−	25.1693i	−0.275599	−	0.934765i
$726$	2.41785	+	1.36680i	0.0897350	+	0.0507267i
$727$	−13.3216	+	16.7048i	−0.494071	+	0.619546i	−0.964881	−	0.262689i	$-0.915391\pi$
$727$	−13.3216	+	16.7048i	−0.494071	+	0.619546i	0.470809	+	0.882235i	$0.343962\pi$
$728$	−0.0452369	−	0.433516i	−0.00167659	−	0.0160672i
$729$	9.95990	−	25.0958i	0.368885	−	0.929475i
$730$	2.92074	+	1.84642i	0.108102	+	0.0683389i
$731$	14.7402	+	18.4836i	0.545185	+	0.683641i
$732$	21.8003	−	29.9341i	0.805761	−	1.10640i
$733$	−13.9662	+	29.0011i	−0.515853	+	1.07118i	0.466565	+	0.884487i	$0.345491\pi$
$733$	−13.9662	+	29.0011i	−0.515853	+	1.07118i	−0.982418	+	0.186693i	$0.940223\pi$
$734$	9.25984	−	26.2321i	0.341787	−	0.968245i
$735$	−1.49089	+	3.53054i	−0.0549923	+	0.130226i
$736$	−29.7900	−	19.2930i	−1.09807	−	0.711150i
$737$	−26.0056			−0.957928
$738$	−9.36352	+	11.3526i	−0.344676	+	0.417893i
$739$	0.0690815	+	0.0866254i	0.00254120	+	0.00318657i	0.783100	−	0.621895i	$-0.213637\pi$
$739$	0.0690815	+	0.0866254i	0.00254120	+	0.00318657i	−0.780559	+	0.625082i	$0.785066\pi$
$740$	0.987778	+	0.796629i	0.0363114	+	0.0292847i
$741$	0.254240	−	1.43653i	0.00933975	−	0.0527723i
$742$	−1.27543	−	11.6058i	−0.0468227	−	0.426061i
$743$	7.76412	+	16.1224i	0.284838	+	0.591472i	0.993468	−	0.114108i	$-0.0364009\pi$
$743$	7.76412	+	16.1224i	0.284838	+	0.591472i	−0.708630	+	0.705580i	$0.750687\pi$
$744$	−1.73322	+	24.3034i	−0.0635429	+	0.891006i
$745$	−4.12324	−	1.98565i	−0.151064	−	0.0727486i
$746$	−5.99284	+	16.9771i	−0.219414	+	0.621575i
$747$	−3.70595	+	0.366083i	−0.135594	+	0.0133943i
$748$	−30.4711	+	37.7825i	−1.11413	+	1.38147i
$749$	−2.32156	−	1.85138i	−0.0848280	−	0.0676480i
$750$	8.26676	+	2.46790i	0.301859	+	0.0901149i
$751$	−3.25070	+	14.2422i	−0.118620	+	0.519706i	0.880350	+	0.474324i	$0.157308\pi$
$751$	−3.25070	+	14.2422i	−0.118620	+	0.519706i	−0.998970	+	0.0453819i	$0.985550\pi$
$752$	−9.35503	−	2.24347i	−0.341143	−	0.0818108i
$753$	6.54021	+	4.70839i	0.238338	+	0.171583i
$754$	−1.31220	−	0.0691289i	−0.0477876	−	0.00251753i
$755$	3.79472			0.138104
$756$	6.75723	+	6.36337i	0.245758	+	0.231433i
$757$	15.7589	+	3.59686i	0.572766	+	0.130730i	0.499087	−	0.866552i	$-0.333669\pi$
$757$	15.7589	+	3.59686i	0.572766	+	0.130730i	0.0736790	+	0.997282i	$0.476526\pi$
$758$	17.2279	−	5.97532i	0.625745	−	0.217033i
$759$	−32.8640	+	9.22398i	−1.19289	+	0.334809i
$760$	4.14901	+	2.65486i	0.150501	+	0.0963018i
$761$	40.4839	+	9.24018i	1.46754	+	0.334956i	0.880285	−	0.474446i	$-0.157351\pi$
$761$	40.4839	+	9.24018i	1.46754	+	0.334956i	0.587255	+	0.809402i	$0.300209\pi$
$762$	18.3107	+	26.3393i	0.663328	+	0.954173i
$763$	−0.701233	+	1.45613i	−0.0253863	+	0.0527153i
$764$	31.3604	−	14.8910i	1.13458	−	0.538739i
$765$	−5.92702	+	5.76638i	−0.214292	+	0.208484i
$766$	2.45547	+	22.3435i	0.0887199	+	0.807303i
$767$	1.33422	−	0.642525i	0.0481758	−	0.0232002i
$768$	−16.6810	+	22.1302i	−0.601922	+	0.798555i
$769$	34.2833	−	27.3401i	1.23629	−	0.985908i	0.236390	−	0.971658i	$-0.424036\pi$
$769$	34.2833	−	27.3401i	1.23629	−	0.985908i	0.999898	−	0.0142494i	$-0.00453587\pi$
$770$	1.20049	−	0.749735i	0.0432627	−	0.0270186i
$771$	16.9611	+	12.2105i	0.610839	+	0.439752i
$772$	24.1723	+	30.6545i	0.869981	+	1.10328i
$773$	5.48880	+	24.0480i	0.197418	+	0.864946i	0.972466	+	0.233044i	$0.0748685\pi$
$773$	5.48880	+	24.0480i	0.197418	+	0.864946i	−0.775048	+	0.631902i	$0.782274\pi$
$774$	12.9797	+	0.213914i	0.466547	+	0.00768897i
$775$	−21.8346	−	10.5150i	−0.784322	−	0.377710i
$776$	1.35036	+	12.9408i	0.0484749	+	0.464547i
$777$	−2.74803	+	0.135399i	−0.0985852	+	0.00485742i
$778$	−20.9760	−	13.2604i	−0.752025	−	0.475410i
$779$	−3.76776	−	16.5076i	−0.134994	−	0.591447i
$780$	0.125527	−	0.172361i	0.00449457	−	0.00617153i
$781$	−18.4215	−	14.6907i	−0.659174	−	0.525674i
$782$	7.48910	+	68.1468i	0.267810	+	2.43693i
$783$	22.1262	−	17.1298i	0.790726	−	0.612171i
$784$	22.4690	−	10.5185i	0.802465	−	0.375659i
$785$	0.294464	−	0.369246i	0.0105099	−	0.0131790i
$786$	−23.9224	−	21.7955i	−0.853284	−	0.777419i
$787$	−15.2065	+	3.47079i	−0.542054	+	0.123720i	−0.484777	−	0.874638i	$-0.661099\pi$
$787$	−15.2065	+	3.47079i	−0.542054	+	0.123720i	−0.0572775	+	0.998358i	$0.518242\pi$
$788$	−18.8003	−	9.18112i	−0.669734	−	0.327064i
$789$	2.47593	+	50.2510i	0.0881455	+	1.78898i
$790$	0.666182	−	5.77025i	0.0237017	−	0.205296i
$791$	−0.573612	+	1.19112i	−0.0203953	+	0.0423512i
$792$	5.35866	+	26.1083i	0.190412	+	0.927719i
$793$	1.79820	−	0.410427i	0.0638559	−	0.0145747i
$794$	27.1177	+	43.4215i	0.962371	+	1.54097i
$795$	3.33711	−	4.63542i	0.118355	−	0.164401i
$796$	7.47079	+	9.47421i	0.264795	+	0.335805i
$797$	1.44952	+	1.81764i	0.0513445	+	0.0643840i	0.806841	−	0.590769i	$-0.201176\pi$
$797$	1.44952	+	1.81764i	0.0513445	+	0.0643840i	−0.755496	+	0.655153i	$0.772604\pi$
$798$	−10.5456	+	1.68765i	−0.373309	+	0.0597423i
$799$	8.06280	+	16.7426i	0.285241	+	0.592310i
$800$	−14.3437	−	23.5383i	−0.507127	−	0.832204i
$801$	−1.47264	−	1.51367i	−0.0520332	−	0.0534828i
$802$	2.59105	+	7.47046i	0.0914933	+	0.263791i
$803$	−19.3825	−	9.33410i	−0.683992	−	0.329393i
$804$	18.8454	+	21.6197i	0.664627	+	0.762468i
$805$	0.444842	−	1.94898i	0.0156786	−	0.0686926i
$806$	−0.860478	+	0.855772i	−0.0303091	+	0.0301433i
$807$	−9.99650	−	35.6164i	−0.351893	−	1.25376i
$808$	−32.1537	+	19.8364i	−1.13116	+	0.697842i
$809$	−6.80229	+	29.8028i	−0.239156	+	1.04781i	0.702619	+	0.711566i	$0.252014\pi$
$809$	−6.80229	+	29.8028i	−0.239156	+	1.04781i	−0.941775	+	0.336244i	$0.890843\pi$
$810$	0.371843	+	4.52540i	0.0130652	+	0.159006i
$811$			45.2459i			1.58880i	0.607395	+	0.794400i	$0.292214\pi$
$811$			45.2459i			1.58880i	−0.607395	+	0.794400i	$0.707786\pi$
$812$	2.66971	+	9.24159i	0.0936884	+	0.324316i
$813$	−19.1894	+	26.6551i	−0.673001	+	0.934834i
$814$	−6.67798	−	4.22164i	−0.234063	−	0.147968i
$815$	6.99818	+	1.59729i	0.245136	+	0.0559506i
$816$	53.4919	−	2.04770i	1.87259	−	0.0716840i
$817$	−9.31281	+	11.6779i	−0.325814	+	0.408558i
$818$	−28.8969	−	29.0558i	−1.01036	−	1.01591i
$819$	0.0454469	+	0.460070i	0.00158804	+	0.0160762i
$820$	0.563919	−	2.40969i	0.0196929	−	0.0841501i
$821$	1.59869	−	3.31972i	0.0557948	−	0.115859i	−0.871207	−	0.490915i	$-0.836662\pi$
$821$	1.59869	−	3.31972i	0.0557948	−	0.115859i	0.927002	+	0.375056i	$0.122377\pi$
$822$	9.63221	−	32.2652i	0.335962	−	1.12538i
$823$	−24.0115	+	11.5633i	−0.836989	+	0.403073i	−0.802732	−	0.596340i	$-0.796621\pi$
$823$	−24.0115	+	11.5633i	−0.836989	+	0.403073i	−0.0342572	+	0.999413i	$0.510907\pi$
$824$	−13.0142	+	4.43403i	−0.453371	+	0.154467i
$825$	−26.1041	−	4.61995i	−0.908829	−	0.160846i
$826$	−7.64462	−	7.68666i	−0.265990	−	0.267453i
$827$	−1.29782	+	1.03498i	−0.0451296	+	0.0359896i	−0.645795	−	0.763511i	$-0.723474\pi$
$827$	−1.29782	+	1.03498i	−0.0451296	+	0.0359896i	0.600665	+	0.799501i	$0.294902\pi$
$828$	31.4838	+	20.6371i	1.09414	+	0.717189i
$829$		−	49.7144i		−	1.72665i	−0.504648	−	0.863325i	$-0.668378\pi$
$829$		−	49.7144i		−	1.72665i	0.504648	−	0.863325i	$-0.331622\pi$
$830$	0.531191	−	0.331741i	0.0184379	−	0.0115149i
$831$	9.00187	+	3.80134i	0.312271	+	0.131867i
$832$	−1.35058	+	0.284966i	−0.0468230	+	0.00987943i
$833$	−43.1765	−	20.7927i	−1.49598	−	0.720424i
$834$	−27.3550	−	24.9229i	−0.947225	−	0.863008i
$835$	2.46488	−	1.96568i	0.0853007	−	0.0680250i
$836$	−27.5563	−	13.4571i	−0.953054	−	0.465423i
$837$	1.98035	−	25.7671i	0.0684510	−	0.890642i
$838$	34.0084	+	3.92631i	1.17480	+	0.135632i
$839$	−18.8579	−	15.0387i	−0.651046	−	0.519192i	0.241354	−	0.970437i	$-0.422409\pi$
$839$	−18.8579	−	15.0387i	−0.651046	−	0.519192i	−0.892400	+	0.451245i	$0.850980\pi$
$840$	−1.49325	−	0.454718i	−0.0515220	−	0.0156893i
$841$	28.7751	−	3.60459i	0.992245	−	0.124296i
$842$	−44.9031	+	4.93470i	−1.54746	+	0.170061i
$843$	32.6018	−	9.15038i	1.12286	−	0.315156i
$844$	0.173474	−	31.6280i	0.00597122	−	1.08868i
$845$	−4.51108	+	1.02963i	−0.155186	+	0.0354202i
$846$	9.90924	+	2.43419i	0.340687	+	0.0836891i
$847$	0.791779	−	0.631423i	0.0272059	−	0.0216959i
$848$	−36.1357	+	7.83171i	−1.24090	+	0.268942i
$849$	20.8261	+	38.3010i	0.714750	+	1.31449i
$850$	−17.7232	+	50.2079i	−0.607901	+	1.72212i
$851$	−10.8790	+	2.48307i	−0.372929	+	0.0851185i
$852$	1.13642	+	25.9606i	0.0389329	+	0.889394i
$853$			33.4487i			1.14526i	0.819814	+	0.572630i	$0.194077\pi$
$853$			33.4487i			1.14526i	−0.819814	+	0.572630i	$0.805923\pi$
$854$	−7.15237	−	11.4525i	−0.244749	−	0.391898i
$855$	−4.38511	−	2.84011i	−0.149968	−	0.0971296i
$856$	−5.06830	+	7.92074i	−0.173231	+	0.270725i
$857$	−13.5523	−	28.1416i	−0.462937	−	0.961299i	−0.993519	−	0.113665i	$-0.963741\pi$
$857$	−13.5523	−	28.1416i	−0.462937	−	0.961299i	0.530582	−	0.847634i	$-0.321973\pi$
$858$	−0.653278	+	1.15564i	−0.0223026	+	0.0394530i
$859$	24.9579	−	12.0191i	0.851551	−	0.410085i	0.0433980	−	0.999058i	$-0.486182\pi$
$859$	24.9579	−	12.0191i	0.851551	−	0.410085i	0.808153	+	0.588972i	$0.200467\pi$
$860$	−1.97210	+	0.936421i	−0.0672479	+	0.0319317i
$861$	2.56321	+	4.71396i	0.0873539	+	0.160651i
$862$	−17.5588	+	49.7423i	−0.598056	+	1.69423i
$863$	0.472987	−	2.07229i	0.0161007	−	0.0705416i	−0.966239	−	0.257646i	$-0.917053\pi$
$863$	0.472987	−	2.07229i	0.0161007	−	0.0705416i	0.982340	+	0.187104i	$0.0599103\pi$
$864$	17.8219	−	23.3748i	0.606313	−	0.795226i
$865$	2.31706	−	2.90551i	0.0787825	−	0.0987901i
$866$	3.78337	+	10.9081i	0.128564	+	0.370673i
$867$	−48.9015	−	55.4831i	−1.66078	−	1.88430i
$868$	7.98307	+	3.89853i	0.270963	+	0.132325i
$869$			36.1633i			1.22675i
$870$	−2.05619	+	4.23283i	−0.0697113	+	0.143506i
$871$			1.42851i			0.0484031i
$872$	4.81685	+	1.73010i	0.163119	+	0.0585886i
$873$	−1.35662	−	13.7334i	−0.0459148	−	0.464807i
$874$	−40.9226	+	14.1936i	−1.38423	+	0.480106i
$875$	1.96133	−	2.45942i	0.0663049	−	0.0831437i
$876$	6.28596	+	22.8777i	0.212383	+	0.772966i
$877$	−3.37772	+	14.7988i	−0.114058	+	0.499719i	0.885338	+	0.464948i	$0.153927\pi$
$877$	−3.37772	+	14.7988i	−0.114058	+	0.499719i	−0.999395	+	0.0347703i	$0.988930\pi$
$878$	−30.0876	−	10.6208i	−1.01541	−	0.358435i
$879$	−28.2533	+	15.3627i	−0.952959	+	0.518169i
$880$	−2.75601	−	3.53479i	−0.0929052	−	0.119158i
$881$	37.1922	−	17.9108i	1.25304	−	0.603431i	0.314712	−	0.949187i	$-0.398092\pi$
$881$	37.1922	−	17.9108i	1.25304	−	0.603431i	0.938324	+	0.345757i	$0.112378\pi$
$882$	−23.8931	+	11.0250i	−0.804522	+	0.371232i
$883$	2.64302	+	5.48829i	0.0889447	+	0.184696i	0.940696	−	0.339251i	$-0.110174\pi$
$883$	2.64302	+	5.48829i	0.0889447	+	0.184696i	−0.851751	+	0.523946i	$0.824459\pi$
$884$	2.07542	+	1.67380i	0.0698041	+	0.0562960i
$885$	−0.260986	−	5.29691i	−0.00877293	−	0.178054i
$886$	9.87792	−	6.16899i	0.331855	−	0.207251i
$887$		−	6.04075i		−	0.202828i	−0.994844	−	0.101414i	$-0.967663\pi$
$887$		−	6.04075i		−	0.202828i	0.994844	−	0.101414i	$-0.0323367\pi$
$888$	1.32966	+	8.61102i	0.0446206	+	0.288967i
$889$	11.4034	−	2.60276i	0.382459	−	0.0872938i
$890$	0.334900	+	0.118218i	0.0112259	+	0.00396269i
$891$	−5.53106	−	27.7230i	−0.185297	−	0.928754i
$892$	−36.6224	−	0.200867i	−1.22621	−	0.00672553i
$893$	−9.17917	+	7.32014i	−0.307169	+	0.244959i
$894$	−11.7454	−	29.1451i	−0.392825	−	0.974756i
$895$	4.88509	−	1.11499i	0.163291	−	0.0372700i
$896$	5.21085	+	8.65759i	0.174082	+	0.289230i
$897$	0.506680	+	1.80525i	0.0169176	+	0.0602754i
$898$	−5.01405	−	45.6251i	−0.167321	−	1.52253i
$899$	15.3627	−	21.9391i	0.512376	−	0.731711i
$900$	15.0760	+	25.0496i	0.502534	+	0.834985i
$901$	55.8395	+	44.5305i	1.86028	+	1.48353i
$902$	−1.76709	+	15.3060i	−0.0588378	+	0.509634i
$903$	1.84138	−	4.36053i	0.0612773	−	0.145109i
$904$	3.94021	+	1.41523i	0.131049	+	0.0470698i
$905$	−6.09754	+	4.86263i	−0.202689	+	0.161639i
$906$	19.2601	+	17.5477i	0.639874	+	0.582984i
$907$	53.5617	+	25.7940i	1.77849	+	0.856475i	0.959014	+	0.283358i	$0.0914485\pi$
$907$	53.5617	+	25.7940i	1.77849	+	0.856475i	0.819474	+	0.573117i	$0.194266\pi$
$908$	−9.60651	−	2.24813i	−0.318803	−	0.0746068i
$909$	34.2195	−	20.8515i	1.13499	−	0.691599i
$910$	−0.0411835	−	0.0659440i	−0.00136522	−	0.00218602i
$911$		−	34.8820i		−	1.15569i	−0.816146	−	0.577845i	$-0.803894\pi$
$911$		−	34.8820i		−	1.15569i	0.816146	−	0.577845i	$-0.196106\pi$
$912$	8.78162	+	32.6608i	0.290788	+	1.08151i
$913$	−3.04841	+	2.43102i	−0.100888	+	0.0804552i
$914$	38.3805	−	38.1706i	1.26951	−	1.26257i
$915$	1.15114	−	6.50429i	0.0380556	−	0.215025i
$916$	−11.3025	−	50.8023i	−0.373445	−	1.67855i
$917$	−10.6316	+	5.11989i	−0.351085	+	0.169074i
$918$	−56.7478	+	1.85929i	−1.87296	+	0.0613657i
$919$	4.78802	−	9.94243i	0.157942	−	0.327970i	−0.806949	−	0.590622i	$-0.798883\pi$
$919$	4.78802	−	9.94243i	0.157942	−	0.327970i	0.964891	+	0.262651i	$0.0845969\pi$
$920$	−6.28494	−	0.760556i	−0.207208	−	0.0250748i
$921$	35.9510	+	40.7896i	1.18463	+	1.34406i
$922$	32.0134	−	31.8383i	1.05431	−	1.04854i
$923$	−0.806971	+	1.01191i	−0.0265618	+	0.0333074i
$924$	9.56006	+	1.74609i	0.314503	+	0.0574420i
$925$	−8.44911	−	1.92845i	−0.277805	−	0.0634072i
$926$	−24.1231	+	38.1590i	−0.792735	+	1.25398i
$927$	13.8294	−	4.62688i	0.454216	−	0.151967i
$928$	28.2309	−	11.4462i	0.926725	−	0.375741i
$929$			8.26131i			0.271045i	0.990774	+	0.135522i	$0.0432713\pi$
$929$			8.26131i			0.271045i	−0.990774	+	0.135522i	$0.956729\pi$
$930$	1.62451	+	4.03107i	0.0532699	+	0.132184i
$931$	6.73730	−	29.5180i	0.220806	−	0.967415i
$932$	−10.6150	+	5.04036i	−0.347705	+	0.165103i
$933$	48.3919	−	13.5822i	1.58428	−	0.444662i
$934$	15.4196	+	15.5044i	0.504546	+	0.507321i
$935$	−1.92659	+	8.44095i	−0.0630063	+	0.276049i
$936$	1.43415	−	0.294355i	0.0468767	−	0.00962130i
$937$	−8.24964	−	3.97282i	−0.269504	−	0.129786i	0.294251	−	0.955728i	$-0.404930\pi$
$937$	−8.24964	−	3.97282i	−0.269504	−	0.129786i	−0.563755	+	0.825942i	$0.690644\pi$
$938$	9.88016	−	3.42684i	0.322599	−	0.111890i
$939$	−5.43670	+	30.7190i	−0.177420	+	1.00248i
$940$	−1.67505	+	0.372665i	−0.0546341	+	0.0121550i
$941$	16.9116	+	35.1172i	0.551301	+	1.14479i	0.971431	+	0.237324i	$0.0762703\pi$
$941$	16.9116	+	35.1172i	0.551301	+	1.14479i	−0.420130	+	0.907464i	$0.638015\pi$
$942$	3.20204	−	0.512437i	0.104328	−	0.0166961i
$943$	13.5685	+	17.0143i	0.441850	+	0.554062i
$944$	−21.6982	+	26.6047i	−0.706217	+	0.865910i
$945$	1.58115	+	0.491020i	0.0514348	+	0.0159729i
$946$	11.5283	−	7.19968i	0.374817	−	0.234082i
$947$	3.78741	−	0.864451i	0.123074	−	0.0280909i	−0.160540	−	0.987029i	$-0.551324\pi$
$947$	3.78741	−	0.864451i	0.123074	−	0.0280909i	0.283614	+	0.958938i	$0.408466\pi$
$948$	30.0643	−	26.2064i	0.976442	−	0.851143i
$949$	−0.512730	+	1.06469i	−0.0166439	+	0.0345614i
$950$	−33.4176	−	3.85810i	−1.08421	−	0.125173i
$951$	−20.4159	+	1.00592i	−0.662030	+	0.0326191i
$952$	6.59799	−	18.3698i	0.213842	−	0.595368i
$953$	11.4839	−	2.62113i	0.372001	−	0.0849067i	−0.0324334	−	0.999474i	$-0.510326\pi$
$953$	11.4839	−	2.62113i	0.372001	−	0.0849067i	0.404434	+	0.914567i	$0.367469\pi$
$954$	38.3728	−	8.09549i	1.24237	−	0.262101i
$955$	3.86094	−	4.84146i	0.124937	−	0.156666i
$956$	−5.18309	+	1.15313i	−0.167633	+	0.0372950i
$957$	9.69462	−	27.6472i	0.313383	−	0.893706i
$958$	−39.2484	+	4.31327i	−1.26806	+	0.139355i
$959$	−9.59913	−	7.65505i	−0.309972	−	0.247195i
$960$	−0.941448	+	4.85276i	−0.0303851	+	0.156622i
$961$	1.39391	+	6.10713i	0.0449649	+	0.197004i
$962$	−0.231898	+	0.366827i	−0.00747670	+	0.0118270i
$963$	5.42195	−	8.37147i	0.174720	−	0.269767i
$964$	0.145533	−	26.5337i	0.00468729	−	0.854594i
$965$	6.27384	+	3.02132i	0.201962	+	0.0972597i
$966$	11.2704	−	7.83500i	0.362618	−	0.252087i
$967$	1.39463	+	6.11026i	0.0448482	+	0.196493i	0.992389	−	0.123142i	$-0.0392970\pi$
$967$	1.39463	+	6.11026i	0.0448482	+	0.196493i	−0.947541	+	0.319634i	$0.896440\pi$
$968$	−2.24903	−	2.28635i	−0.0722867	−	0.0734860i
$969$	38.1693	−	53.0192i	1.22617	−	1.70322i
$970$	1.22936	+	1.96848i	0.0394724	+	0.0632040i
$971$	−2.25304	+	1.79674i	−0.0723035	+	0.0576601i	−0.658975	−	0.752165i	$-0.729010\pi$
$971$	−2.25304	+	1.79674i	−0.0723035	+	0.0576601i	0.586671	+	0.809825i	$0.300438\pi$
$972$	−19.0393	+	24.6882i	−0.610685	+	0.791874i
$973$	−12.1571	+	5.85453i	−0.389737	+	0.187688i
$974$	−27.5309	+	3.02555i	−0.882147	+	0.0969450i
$975$	−0.253778	+	1.43392i	−0.00812739	+	0.0459222i
$976$	−33.7214	+	26.2920i	−1.07940	+	0.841587i
$977$	−5.24002	+	10.8810i	−0.167643	+	0.348114i	−0.967818	−	0.251653i	$-0.919026\pi$
$977$	−5.24002	+	10.8810i	−0.167643	+	0.348114i	0.800175	+	0.599767i	$0.204740\pi$
$978$	28.1330	+	40.4684i	0.899596	+	1.29404i
$979$	−2.15568	−	0.492021i	−0.0688959	−	0.0157250i
$980$	2.77806	−	3.44465i	0.0887420	−	0.110035i
$981$	−5.09886	−	1.86317i	−0.162794	−	0.0594864i
$982$	14.0545	+	40.5215i	0.448496	+	1.29309i
$983$	25.4194	+	5.80180i	0.810752	+	0.185049i	0.607749	−	0.794129i	$-0.292073\pi$
$983$	25.4194	+	5.80180i	0.810752	+	0.185049i	0.203003	+	0.979178i	$0.434930\pi$
$984$	14.0052	−	9.62270i	0.446469	−	0.306760i
$985$	−3.73200			−0.118911
$986$	−51.5997	−	28.2850i	−1.64327	−	0.900779i
$987$	2.17378	−	3.01950i	0.0691922	−	0.0961117i
$988$	−0.739209	+	1.51369i	−0.0235174	+	0.0481569i
$989$	4.27181	−	18.7160i	0.135836	−	0.595134i
$990$	2.90249	+	3.76526i	0.0922473	+	0.119668i
$991$	−1.31368	−	1.04762i	−0.0417303	−	0.0332788i	0.602403	−	0.798192i	$-0.294210\pi$
$991$	−1.31368	−	1.04762i	−0.0417303	−	0.0332788i	−0.644133	+	0.764914i	$0.722782\pi$
$992$	9.65546	−	26.4257i	0.306561	−	0.839017i
$993$	2.54167	+	2.88375i	0.0806573	+	0.0915129i
$994$	8.93463	+	3.15389i	0.283389	+	0.100035i
$995$	1.93902	+	0.933781i	0.0614710	+	0.0296029i
$996$	4.23011	+	0.772605i	0.134036	+	0.0244809i
$997$	−14.1933	−	29.4727i	−0.449506	−	0.933410i	−0.995423	−	0.0955699i	$-0.969533\pi$
$997$	−14.1933	−	29.4727i	−0.449506	−	0.933410i	0.545916	−	0.837840i	$-0.316182\pi$
$998$	6.76147	−	0.743062i	0.214031	−	0.0235212i
$999$	−1.35998	−	9.14100i	−0.0430278	−	0.289208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.11	✓	336
3.2	odd	2	inner	348.2.t.a.35.46	yes	336
4.3	odd	2	inner	348.2.t.a.35.43	yes	336
12.11	even	2	inner	348.2.t.a.35.14	yes	336
29.5	even	14	inner	348.2.t.a.179.14	yes	336
87.5	odd	14	inner	348.2.t.a.179.43	yes	336
116.63	odd	14	inner	348.2.t.a.179.46	yes	336
348.179	even	14	inner	348.2.t.a.179.11	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.11	✓	336	1.1	even	1	trivial
348.2.t.a.35.14	yes	336	12.11	even	2	inner
348.2.t.a.35.43	yes	336	4.3	odd	2	inner
348.2.t.a.35.46	yes	336	3.2	odd	2	inner
348.2.t.a.179.11	yes	336	348.179	even	14	inner
348.2.t.a.179.14	yes	336	29.5	even	14	inner
348.2.t.a.179.43	yes	336	87.5	odd	14	inner
348.2.t.a.179.46	yes	336	116.63	odd	14	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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19538 - 0.755688i) q^{2} +(-1.14525 - 1.29939i) q^{3} +(0.857871 + 1.80667i) q^{4} +(0.278916 + 0.222428i) q^{5} +(0.387077 + 2.41871i) q^{6} +(0.870753 + 0.198744i) q^{7} +(0.339796 - 2.80794i) q^{8} +(-0.376812 + 2.97624i) q^{9} +O(q^{10})\)	\(q+(-1.19538 - 0.755688i) q^{2} +(-1.14525 - 1.29939i) q^{3} +(0.857871 + 1.80667i) q^{4} +(0.278916 + 0.222428i) q^{5} +(0.387077 + 2.41871i) q^{6} +(0.870753 + 0.198744i) q^{7} +(0.339796 - 2.80794i) q^{8} +(-0.376812 + 2.97624i) q^{9} +(-0.165325 - 0.476660i) q^{10} +(1.36285 + 2.82998i) q^{11} +(1.36509 - 3.18379i) q^{12} +(0.155453 - 0.0748622i) q^{13} +(-0.890693 - 0.895592i) q^{14} +(-0.0304081 - 0.617156i) q^{15} +(-2.52811 + 3.09978i) q^{16} +7.72654 q^{17} +(2.69954 - 3.27299i) q^{18} +(1.08626 + 4.75922i) q^{19} +(-0.162580 + 0.694724i) q^{20} +(-0.738983 - 1.35906i) q^{21} +(0.509461 - 4.41279i) q^{22} +(-3.91185 - 4.90530i) q^{23} +(-4.03775 + 2.77427i) q^{24} +(-1.08428 - 4.75056i) q^{25} +(-0.242398 - 0.0279851i) q^{26} +(4.29883 - 2.91891i) q^{27} +(0.387930 + 1.74366i) q^{28} +(5.37471 - 0.335328i) q^{29} +(-0.430028 + 0.760715i) q^{30} +(3.10093 - 3.88845i) q^{31} +(5.36453 - 1.79495i) q^{32} +(2.11644 - 5.01189i) q^{33} +(-9.23616 - 5.83885i) q^{34} +(0.198661 + 0.249113i) q^{35} +(-5.70034 + 1.87246i) q^{36} +(0.771683 - 1.60242i) q^{37} +(2.29799 - 6.50995i) q^{38} +(-0.275307 - 0.116258i) q^{39} +(0.719340 - 0.707600i) q^{40} -3.46856 q^{41} +(-0.143655 + 2.18303i) q^{42} +(1.90773 + 2.39222i) q^{43} +(-3.94369 + 4.88997i) q^{44} +(-0.767099 + 0.746309i) q^{45} +(0.969270 + 8.81984i) q^{46} +(1.04352 + 2.16689i) q^{47} +(6.92313 - 0.265022i) q^{48} +(-5.58807 - 2.69107i) q^{49} +(-2.29381 + 6.49811i) q^{50} +(-8.84881 - 10.0398i) q^{51} +(0.268610 + 0.216630i) q^{52} +(7.22698 + 5.76332i) q^{53} +(-7.34453 + 0.240637i) q^{54} +(-0.249347 + 1.09246i) q^{55} +(0.853939 - 2.37749i) q^{56} +(4.94002 - 6.86196i) q^{57} +(-6.67823 - 3.66076i) q^{58} +8.58277 q^{59} +(1.08891 - 0.584378i) q^{60} +(10.4219 + 2.37874i) q^{61} +(-6.64525 + 2.30484i) q^{62} +(-0.919619 + 2.51668i) q^{63} +(-7.76908 - 1.90825i) q^{64} +(0.0600098 + 0.0136968i) q^{65} +(-6.31737 + 4.39175i) q^{66} +(-3.59225 + 7.45939i) q^{67} +(6.62838 + 13.9593i) q^{68} +(-1.89384 + 10.7008i) q^{69} +(-0.0492238 - 0.447910i) q^{70} +(-6.75848 + 3.25471i) q^{71} +(8.22907 + 2.06938i) q^{72} +(-5.35475 + 4.27027i) q^{73} +(-2.13338 + 1.33235i) q^{74} +(-4.93104 + 6.84948i) q^{75} +(-7.66646 + 6.04531i) q^{76} +(0.624261 + 2.73507i) q^{77} +(0.241242 + 0.347018i) q^{78} +(10.3730 + 4.99537i) q^{79} +(-1.39461 + 0.302255i) q^{80} +(-8.71603 - 2.24296i) q^{81} +(4.14625 + 2.62115i) q^{82} +(0.276222 + 1.21021i) q^{83} +(1.82141 - 2.50099i) q^{84} +(2.15506 + 1.71860i) q^{85} +(-0.472695 - 4.30127i) q^{86} +(-6.59111 - 6.59980i) q^{87} +(8.40950 - 2.86518i) q^{88} +(-0.438903 + 0.550367i) q^{89} +(1.48095 - 0.312435i) q^{90} +(0.150239 - 0.0342912i) q^{91} +(5.50640 - 11.2755i) q^{92} +(-8.60394 + 0.423927i) q^{93} +(0.390090 - 3.37884i) q^{94} +(-0.755609 + 1.56904i) q^{95} +(-8.47605 - 4.91493i) q^{96} +(-4.48476 + 1.02362i) q^{97} +(4.64626 + 7.43970i) q^{98} +(-8.93623 + 2.98979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

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Database

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