LMFDB - Embedded newform 975.2.w.g.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 + 0.564882i$ of defining polynomial
Character	$\chi$	$=$	975.49
Dual form			975.2.w.g.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21545 - 2.10523i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.95466 + 3.38556i) q^{4} +(-2.10523 - 1.21545i) q^{6} +(0.650571 - 1.12682i) q^{7} +4.64136 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.21545 - 2.10523i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.95466 + 3.38556i) q^{4} +(-2.10523 - 1.21545i) q^{6} +(0.650571 - 1.12682i) q^{7} +4.64136 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.75159 + 1.58863i) q^{11} +3.90931i q^{12} +(1.19386 - 3.40216i) q^{13} -3.16296 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.564094 - 0.325680i) q^{17} -2.43091 q^{18} +(-2.17511 - 1.25580i) q^{19} -1.30114i q^{21} +(6.68886 + 3.86182i) q^{22} +(-1.54113 + 0.889774i) q^{23} +(4.01954 - 2.32068i) q^{24} +(-8.61341 + 1.62182i) q^{26} -1.00000i q^{27} +(2.54329 + 4.40510i) q^{28} +(-4.18965 - 7.25669i) q^{29} -8.50318i q^{31} +(0.430908 - 0.746354i) q^{32} +(-1.58863 + 2.75159i) q^{33} +1.58340i q^{34} +(1.95466 + 3.38556i) q^{36} +(-0.698857 - 1.21046i) q^{37} +6.10547i q^{38} +(-0.667168 - 3.54329i) q^{39} +(-10.0658 + 5.81147i) q^{41} +(-2.73920 + 1.58148i) q^{42} +(2.83522 + 1.63692i) q^{43} -12.4209i q^{44} +(3.74635 + 2.16296i) q^{46} -12.2105 q^{47} +(-3.00000 - 1.73205i) q^{48} +(2.65351 + 4.59602i) q^{49} -0.651360 q^{51} +(9.18465 + 10.6919i) q^{52} -6.35452i q^{53} +(-2.10523 + 1.21545i) q^{54} +(3.01954 - 5.22999i) q^{56} -2.51160 q^{57} +(-10.1847 + 17.6403i) q^{58} +(5.18377 + 2.99285i) q^{59} +(-6.49373 + 11.2475i) q^{61} +(-17.9011 + 10.3352i) q^{62} +(-0.650571 - 1.12682i) q^{63} -9.02320 q^{64} +7.72363 q^{66} +(-6.57727 - 11.3922i) q^{67} +(2.20522 - 1.27318i) q^{68} +(-0.889774 + 1.54113i) q^{69} +(-0.949658 - 0.548286i) q^{71} +(2.32068 - 4.01954i) q^{72} +12.2293 q^{73} +(-1.69886 + 2.94251i) q^{74} +(8.50318 - 4.90931i) q^{76} +4.13407i q^{77} +(-6.64852 + 5.71124i) q^{78} +1.33022 q^{79} +(-0.500000 - 0.866025i) q^{81} +(24.4690 + 14.1272i) q^{82} -14.2668 q^{83} +(4.40510 + 2.54329i) q^{84} -7.95839i q^{86} +(-7.25669 - 4.18965i) q^{87} +(-12.7711 + 7.37341i) q^{88} +(8.31719 - 4.80193i) q^{89} +(-3.05694 - 3.55862i) q^{91} -6.95681i q^{92} +(-4.25159 - 7.36397i) q^{93} +(14.8412 + 25.7058i) q^{94} -0.861816i q^{96} +(3.97341 - 6.88214i) q^{97} +(6.45045 - 11.1725i) q^{98} +3.17726i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^9	$ 8 q - 2 q^{2} - 4 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 6 q^{13} + 4 q^{14} - 6 q^{17} - 4 q^{18} - 12 q^{19} + 24 q^{22} + 12 q^{24} - 4 q^{26} + 4 q^{28} + 6 q^{29} - 12 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 30 q^{41} - 18 q^{42} - 30 q^{43} + 36 q^{46} - 76 q^{47} - 24 q^{48} + 8 q^{49} + 4 q^{51} + 20 q^{52} - 6 q^{54} + 4 q^{56} - 28 q^{58} + 30 q^{59} - 18 q^{62} - 6 q^{63} - 32 q^{64} - 14 q^{67} + 36 q^{68} - 4 q^{69} + 18 q^{71} + 44 q^{73} - 12 q^{74} - 26 q^{78} - 56 q^{79} - 4 q^{81} + 48 q^{82} - 40 q^{83} - 12 q^{84} - 6 q^{87} - 48 q^{88} + 18 q^{89} - 16 q^{91} + 16 q^{94} + 10 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 6 * q^13 + 4 * q^14 - 6 * q^17 - 4 * q^18 - 12 * q^19 + 24 * q^22 + 12 * q^24 - 4 * q^26 + 4 * q^28 + 6 * q^29 - 12 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 30 * q^41 - 18 * q^42 - 30 * q^43 + 36 * q^46 - 76 * q^47 - 24 * q^48 + 8 * q^49 + 4 * q^51 + 20 * q^52 - 6 * q^54 + 4 * q^56 - 28 * q^58 + 30 * q^59 - 18 * q^62 - 6 * q^63 - 32 * q^64 - 14 * q^67 + 36 * q^68 - 4 * q^69 + 18 * q^71 + 44 * q^73 - 12 * q^74 - 26 * q^78 - 56 * q^79 - 4 * q^81 + 48 * q^82 - 40 * q^83 - 12 * q^84 - 6 * q^87 - 48 * q^88 + 18 * q^89 - 16 * q^91 + 16 * q^94 + 10 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.21545	−	2.10523i	−0.859456	−	1.48862i	−0.872449	−	0.488705i	$-0.837469\pi$
$2$	−1.21545	−	2.10523i	−0.859456	−	1.48862i	0.0129932	−	0.999916i	$-0.495864\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.95466	+	3.38556i	−0.977328	+	1.69278i
$5$		0			0
$5$		0			0
$6$	−2.10523	−	1.21545i	−0.859456	−	0.496207i
$7$	0.650571	−	1.12682i	0.245893	−	0.425899i	−0.716489	−	0.697598i	$-0.754252\pi$
$7$	0.650571	−	1.12682i	0.245893	−	0.425899i	0.962382	+	0.271699i	$0.0875855\pi$
$8$	4.64136			1.64097
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.75159	+	1.58863i	−0.829636	+	0.478990i	−0.853728	−	0.520719i	$-0.825664\pi$
$11$	−2.75159	+	1.58863i	−0.829636	+	0.478990i	0.0240923	+	0.999710i	$0.492330\pi$
$12$			3.90931i			1.12852i
$13$	1.19386	−	3.40216i	0.331117	−	0.943590i
$13$	1.19386	−	3.40216i	0.331117	−	0.943590i
$14$	−3.16296			−0.845336
$15$		0			0
$16$	−1.73205	−	3.00000i	−0.433013	−	0.750000i
$17$	−0.564094	−	0.325680i	−0.136813	−	0.0789890i	0.430031	−	0.902814i	$-0.358503\pi$
$17$	−0.564094	−	0.325680i	−0.136813	−	0.0789890i	−0.566844	+	0.823825i	$0.691836\pi$
$18$	−2.43091			−0.572970
$19$	−2.17511	−	1.25580i	−0.499004	−	0.288100i	0.229298	−	0.973356i	$-0.426357\pi$
$19$	−2.17511	−	1.25580i	−0.499004	−	0.288100i	−0.728302	+	0.685256i	$0.759690\pi$
$20$		0			0
$21$		−	1.30114i		−	0.283933i
$22$	6.68886	+	3.86182i	1.42607	+	0.823342i
$23$	−1.54113	+	0.889774i	−0.321349	+	0.185531i	−0.651994	−	0.758225i	$-0.726067\pi$
$23$	−1.54113	+	0.889774i	−0.321349	+	0.185531i	0.330645	+	0.943755i	$0.392734\pi$
$24$	4.01954	−	2.32068i	0.820485	−	0.473707i
$25$		0			0
$26$	−8.61341	+	1.62182i	−1.68923	+	0.318066i
$27$		−	1.00000i		−	0.192450i
$28$	2.54329	+	4.40510i	0.480636	+	0.832486i
$29$	−4.18965	−	7.25669i	−0.777998	−	1.34753i	−0.933094	−	0.359633i	$-0.882902\pi$
$29$	−4.18965	−	7.25669i	−0.777998	−	1.34753i	0.155095	−	0.987899i	$-0.450431\pi$
$30$		0			0
$31$		−	8.50318i		−	1.52722i	−0.645680	−	0.763608i	$-0.723426\pi$
$31$		−	8.50318i		−	1.52722i	0.645680	−	0.763608i	$-0.276574\pi$
$32$	0.430908	−	0.746354i	0.0761745	−	0.131938i
$33$	−1.58863	+	2.75159i	−0.276545	+	0.478990i
$34$			1.58340i			0.271550i
$35$		0			0
$36$	1.95466	+	3.38556i	0.325776	+	0.564261i
$37$	−0.698857	−	1.21046i	−0.114891	−	0.198998i	0.802845	−	0.596188i	$-0.203319\pi$
$37$	−0.698857	−	1.21046i	−0.114891	−	0.198998i	−0.917736	+	0.397190i	$0.869985\pi$
$38$			6.10547i			0.990437i
$39$	−0.667168	−	3.54329i	−0.106832	−	0.567380i
$40$		0			0
$41$	−10.0658	+	5.81147i	−1.57201	+	0.907600i	−0.576086	+	0.817389i	$0.695421\pi$
$41$	−10.0658	+	5.81147i	−1.57201	+	0.907600i	−0.995923	+	0.0902108i	$0.971246\pi$
$42$	−2.73920	+	1.58148i	−0.422668	+	0.244028i
$43$	2.83522	+	1.63692i	0.432367	+	0.249627i	0.700355	−	0.713795i	$-0.253025\pi$
$43$	2.83522	+	1.63692i	0.432367	+	0.249627i	−0.267987	+	0.963422i	$0.586359\pi$
$44$		−	12.4209i		−	1.87252i
$45$		0			0
$46$	3.74635	+	2.16296i	0.552370	+	0.318911i
$47$	−12.2105			−1.78108			−0.890539	−	0.454907i	$-0.849673\pi$
$47$	−12.2105			−1.78108			−0.890539	+	0.454907i	$0.849673\pi$
$48$	−3.00000	−	1.73205i	−0.433013	−	0.250000i
$49$	2.65351	+	4.59602i	0.379073	+	0.656574i
$50$		0			0
$51$	−0.651360			−0.0912086
$52$	9.18465	+	10.6919i	1.27368	+	1.48271i
$53$		−	6.35452i		−	0.872861i	−0.899738	−	0.436431i	$-0.856242\pi$
$53$		−	6.35452i		−	0.872861i	0.899738	−	0.436431i	$-0.143758\pi$
$54$	−2.10523	+	1.21545i	−0.286485	+	0.165402i
$55$		0			0
$56$	3.01954	−	5.22999i	0.403503	−	0.698887i
$57$	−2.51160			−0.332669
$58$	−10.1847	+	17.6403i	−1.33731	+	2.31629i
$59$	5.18377	+	2.99285i	0.674869	+	0.389636i	0.797919	−	0.602765i	$-0.205934\pi$
$59$	5.18377	+	2.99285i	0.674869	+	0.389636i	−0.123050	+	0.992400i	$0.539268\pi$
$60$		0			0
$61$	−6.49373	+	11.2475i	−0.831437	+	1.44009i	0.0654609	+	0.997855i	$0.479148\pi$
$61$	−6.49373	+	11.2475i	−0.831437	+	1.44009i	−0.896898	+	0.442237i	$0.854185\pi$
$62$	−17.9011	+	10.3352i	−2.27345	+	1.31257i
$63$	−0.650571	−	1.12682i	−0.0819643	−	0.141966i
$64$	−9.02320			−1.12790
$65$		0			0
$66$	7.72363			0.950713
$67$	−6.57727	−	11.3922i	−0.803541	−	1.39177i	−0.917271	−	0.398263i	$-0.869613\pi$
$67$	−6.57727	−	11.3922i	−0.803541	−	1.39177i	0.113730	−	0.993512i	$-0.463720\pi$
$68$	2.20522	−	1.27318i	0.267422	−	0.154396i
$69$	−0.889774	+	1.54113i	−0.107116	+	0.185531i
$70$		0			0
$71$	−0.949658	−	0.548286i	−0.112704	−	0.0650695i	0.442589	−	0.896725i	$-0.354060\pi$
$71$	−0.949658	−	0.548286i	−0.112704	−	0.0650695i	−0.555292	+	0.831655i	$0.687394\pi$
$72$	2.32068	−	4.01954i	0.273495	−	0.473707i
$73$	12.2293			1.43134			0.715668	−	0.698440i	$-0.246122\pi$
$73$	12.2293			1.43134			0.715668	+	0.698440i	$0.246122\pi$
$74$	−1.69886	+	2.94251i	−0.197488	+	0.342059i
$75$		0			0
$76$	8.50318	−	4.90931i	0.975382	−	0.563137i
$77$			4.13407i			0.471121i
$78$	−6.64852	+	5.71124i	−0.752796	+	0.646671i
$79$	1.33022			0.149662			0.0748310	−	0.997196i	$-0.476158\pi$
$79$	1.33022			0.149662			0.0748310	+	0.997196i	$0.476158\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	24.4690	+	14.1272i	2.70214	+	1.56008i
$83$	−14.2668			−1.56599			−0.782995	−	0.622028i	$-0.786309\pi$
$83$	−14.2668			−1.56599			−0.782995	+	0.622028i	$0.786309\pi$
$84$	4.40510	+	2.54329i	0.480636	+	0.277495i
$85$		0			0
$86$		−	7.95839i		−	0.858175i
$87$	−7.25669	−	4.18965i	−0.777998	−	0.449178i
$88$	−12.7711	+	7.37341i	−1.36141	+	0.786009i
$89$	8.31719	−	4.80193i	0.881620	−	0.509004i	0.0104280	−	0.999946i	$-0.496681\pi$
$89$	8.31719	−	4.80193i	0.881620	−	0.509004i	0.871192	+	0.490942i	$0.163347\pi$
$90$		0			0
$91$	−3.05694	−	3.55862i	−0.320455	−	0.373044i
$92$		−	6.95681i		−	0.725298i
$93$	−4.25159	−	7.36397i	−0.440869	−	0.763608i
$94$	14.8412	+	25.7058i	1.53076	+	2.65135i
$95$		0			0
$96$		−	0.861816i		−	0.0879587i
$97$	3.97341	−	6.88214i	0.403438	−	0.698776i	−0.590700	−	0.806891i	$-0.701148\pi$
$97$	3.97341	−	6.88214i	0.403438	−	0.698776i	0.994138	+	0.108116i	$0.0344816\pi$
$98$	6.45045	−	11.1725i	0.651594	−	1.12859i
$99$			3.17726i			0.319327i
$100$		0			0
$101$	−1.06273	−	1.84070i	−0.105745	−	0.183157i	0.808297	−	0.588775i	$-0.200390\pi$
$101$	−1.06273	−	1.84070i	−0.105745	−	0.183157i	−0.914043	+	0.405618i	$0.867056\pi$
$102$	0.791698	+	1.37126i	0.0783898	+	0.135775i
$103$			0.985697i			0.0971236i	0.998820	+	0.0485618i	$0.0154638\pi$
$103$			0.985697i			0.0971236i	−0.998820	+	0.0485618i	$0.984536\pi$
$104$	5.54113	−	15.7907i	0.543353	−	1.54840i
$105$		0			0
$106$	−13.3777	+	7.72363i	−1.29936	+	0.750185i
$107$	10.6832	−	6.16796i	1.03279	−	0.596279i	0.115004	−	0.993365i	$-0.463312\pi$
$107$	10.6832	−	6.16796i	1.03279	−	0.596279i	0.917781	+	0.397086i	$0.129979\pi$
$108$	3.38556	+	1.95466i	0.325776	+	0.188087i
$109$			0.870235i			0.0833534i	0.999131	+	0.0416767i	$0.0132700\pi$
$109$			0.870235i			0.0833534i	−0.999131	+	0.0416767i	$0.986730\pi$
$110$		0			0
$111$	−1.21046	−	0.698857i	−0.114891	−	0.0663326i
$112$	−4.50729			−0.425899
$113$	13.0782	+	7.55068i	1.23029	+	0.710308i	0.967090	−	0.254434i	$-0.0818890\pi$
$113$	13.0782	+	7.55068i	1.23029	+	0.710308i	0.263199	+	0.964742i	$0.415222\pi$
$114$	3.05273	+	5.28749i	0.285915	+	0.495219i
$115$		0			0
$116$	32.7573			3.04144
$117$	−2.34943	−	2.73499i	−0.217205	−	0.252850i
$118$		−	14.5507i		−	1.33950i
$119$	−0.733967	+	0.423756i	−0.0672827	+	0.0388457i
$120$		0			0
$121$	−0.452503	+	0.783758i	−0.0411366	+	0.0712507i
$122$	31.5713			2.85833
$123$	−5.81147	+	10.0658i	−0.524003	+	0.907600i
$124$	28.7881	+	16.6208i	2.58524	+	1.49259i
$125$		0			0
$126$	−1.58148	+	2.73920i	−0.140889	+	0.244028i
$127$	−2.50828	+	1.44815i	−0.222573	+	0.128503i	−0.607141	−	0.794594i	$-0.707684\pi$
$127$	−2.50828	+	1.44815i	−0.222573	+	0.128503i	0.384568	+	0.923097i	$0.374350\pi$
$128$	10.1055	+	17.5032i	0.893205	+	1.54708i
$129$	3.27383			0.288245
$130$		0			0
$131$	15.7570			1.37670			0.688349	−	0.725380i	$-0.258336\pi$
$131$	15.7570			1.37670			0.688349	+	0.725380i	$0.258336\pi$
$132$	−6.21046	−	10.7568i	−0.540551	−	0.936261i
$133$	−2.83013	+	1.63397i	−0.245403	+	0.141684i
$134$	−15.9887	+	27.6933i	−1.38122	+	2.39234i
$135$		0			0
$136$	−2.61817	−	1.51160i	−0.224506	−	0.129619i
$137$	0.368870	−	0.638901i	0.0315147	−	0.0545850i	−0.849838	−	0.527044i	$-0.823300\pi$
$137$	0.368870	−	0.638901i	0.0315147	−	0.0545850i	0.881353	+	0.472459i	$0.156634\pi$
$138$	4.32592			0.368247
$139$	−9.87341	+	17.1013i	−0.837452	+	1.45051i	0.0545661	+	0.998510i	$0.482622\pi$
$139$	−9.87341	+	17.1013i	−0.837452	+	1.45051i	−0.892018	+	0.451999i	$0.850711\pi$
$140$		0			0
$141$	−10.5746	+	6.10523i	−0.890539	+	0.514153i
$142$			2.66566i			0.223697i
$143$	2.11977	+	11.2580i	0.177264	+	0.941437i
$144$	−3.46410			−0.288675
$145$		0			0
$146$	−14.8642	−	25.7456i	−1.23017	−	2.13072i
$147$	4.59602	+	2.65351i	0.379073	+	0.218858i
$148$	5.46410			0.449146
$149$	2.74140	+	1.58275i	0.224584	+	0.129664i	0.608071	−	0.793883i	$-0.291944\pi$
$149$	2.74140	+	1.58275i	0.224584	+	0.129664i	−0.383487	+	0.923546i	$0.625277\pi$
$150$		0			0
$151$			0.168843i			0.0137402i	0.999976	+	0.00687011i	$0.00218684\pi$
$151$			0.168843i			0.0137402i	−0.999976	+	0.00687011i	$0.997813\pi$
$152$	−10.0955	−	5.82862i	−0.818851	−	0.472764i
$153$	−0.564094	+	0.325680i	−0.0456043	+	0.0263297i
$154$	8.70316	−	5.02477i	0.701321	−	0.404908i
$155$		0			0
$156$	13.3001	+	4.66717i	1.06486	+	0.373673i
$157$		−	13.5512i		−	1.08150i	−0.841183	−	0.540750i	$-0.818141\pi$
$157$		−	13.5512i		−	1.08150i	0.841183	−	0.540750i	$-0.181859\pi$
$158$	−1.61683	−	2.80043i	−0.128628	−	0.222790i
$159$	−3.17726	−	5.50318i	−0.251973	−	0.436431i
$160$		0			0
$161$			2.31545i			0.182483i
$162$	−1.21545	+	2.10523i	−0.0954951	+	0.165402i
$163$	7.60307	−	13.1689i	0.595519	−	1.03147i	−0.397955	−	0.917405i	$-0.630280\pi$
$163$	7.60307	−	13.1689i	0.595519	−	1.03147i	0.993473	−	0.114064i	$-0.0363868\pi$
$164$		−	45.4377i		−	3.54809i
$165$		0			0
$166$	17.3407	+	30.0350i	1.34590	+	2.33117i
$167$	−3.73793	−	6.47429i	−0.289250	−	0.500996i	0.684381	−	0.729125i	$-0.260073\pi$
$167$	−3.73793	−	6.47429i	−0.289250	−	0.500996i	−0.973631	+	0.228129i	$0.926739\pi$
$168$		−	6.03908i		−	0.465925i
$169$	−10.1494	−	8.12340i	−0.780723	−	0.624877i
$170$		0			0
$171$	−2.17511	+	1.25580i	−0.166335	+	0.0960334i
$172$	−11.0838	+	6.39922i	−0.845130	+	0.487936i
$173$	−8.04886	−	4.64701i	−0.611943	−	0.353306i	0.161782	−	0.986826i	$-0.448276\pi$
$173$	−8.04886	−	4.64701i	−0.611943	−	0.353306i	−0.773726	+	0.633521i	$0.781609\pi$
$174$			20.3693i			1.54419i
$175$		0			0
$176$	9.53179	+	5.50318i	0.718485	+	0.414818i
$177$	5.98570			0.449913
$178$	−20.2183	−	11.6731i	−1.51543	−	0.874932i
$179$	−5.42376	−	9.39422i	−0.405391	−	0.702157i	0.588976	−	0.808150i	$-0.299531\pi$
$179$	−5.42376	−	9.39422i	−0.405391	−	0.702157i	−0.994367	+	0.105993i	$0.966198\pi$
$180$		0			0
$181$	−0.759361			−0.0564428			−0.0282214	−	0.999602i	$-0.508984\pi$
$181$	−0.759361			−0.0564428			−0.0282214	+	0.999602i	$0.508984\pi$
$182$	−3.77613	+	10.7609i	−0.279905	+	0.797651i
$183$			12.9875i			0.960061i
$184$	−7.15296	+	4.12976i	−0.527323	+	0.304450i
$185$		0			0
$186$	−10.3352	+	17.9011i	−0.757815	+	1.31257i
$187$	2.06954			0.151340
$188$	23.8672	−	41.3393i	1.74070	−	3.01498i
$189$	−1.12682	−	0.650571i	−0.0819643	−	0.0473221i
$190$		0			0
$191$	−3.34149	+	5.78763i	−0.241782	+	0.418778i	−0.961222	−	0.275776i	$-0.911065\pi$
$191$	−3.34149	+	5.78763i	−0.241782	+	0.418778i	0.719440	+	0.694554i	$0.244398\pi$
$192$	−7.81432	+	4.51160i	−0.563950	+	0.325597i
$193$	−7.91441	−	13.7082i	−0.569692	−	0.986735i	−0.996596	−	0.0824381i	$-0.973729\pi$
$193$	−7.91441	−	13.7082i	−0.569692	−	0.986735i	0.426905	−	0.904297i	$-0.359604\pi$
$194$	−19.3180			−1.38695
$195$		0			0
$196$	−20.7468			−1.48192
$197$	−3.41725	−	5.91886i	−0.243469	−	0.421701i	0.718231	−	0.695805i	$-0.244952\pi$
$197$	−3.41725	−	5.91886i	−0.243469	−	0.421701i	−0.961700	+	0.274104i	$0.911619\pi$
$198$	6.68886	−	3.86182i	0.475357	−	0.274447i
$199$	8.62135	−	14.9326i	0.611151	−	1.05854i	−0.379896	−	0.925029i	$-0.624040\pi$
$199$	8.62135	−	14.9326i	0.611151	−	1.05854i	0.991047	−	0.133515i	$-0.0426265\pi$
$200$		0			0
$201$	−11.3922	−	6.57727i	−0.803541	−	0.463925i
$202$	−2.58340	+	4.47457i	−0.181767	+	0.314830i
$203$	−10.9027			−0.765217
$204$	1.27318	−	2.20522i	0.0891408	−	0.154396i
$205$		0			0
$206$	2.07512	−	1.19807i	0.144580	−	0.0834734i
$207$			1.77955i			0.123687i
$208$	−12.2743	+	2.31114i	−0.851070	+	0.160249i
$209$	7.98001			0.551989
$210$		0			0
$211$	11.9066	+	20.6229i	0.819685	+	1.41974i	0.905915	+	0.423460i	$0.139185\pi$
$211$	11.9066	+	20.6229i	0.819685	+	1.41974i	−0.0862299	+	0.996275i	$0.527482\pi$
$212$	21.5137	+	12.4209i	1.47756	+	0.853072i
$213$	−1.09657			−0.0751358
$214$	−25.9699	−	14.9937i	−1.77527	−	1.02495i
$215$		0			0
$216$		−	4.64136i		−	0.315805i
$217$	−9.58158	−	5.53193i	−0.650440	−	0.375532i
$218$	1.83204	−	1.05773i	0.124082	−	0.0716386i
$219$	10.5909	−	6.11467i	0.715668	−	0.413191i
$220$		0			0
$221$	−1.78146	+	1.53032i	−0.119834	+	0.102941i
$222$			3.39771i			0.228040i
$223$	−5.39771	−	9.34911i	−0.361458	−	0.626063i	0.626743	−	0.779226i	$-0.284387\pi$
$223$	−5.39771	−	9.34911i	−0.361458	−	0.626063i	−0.988201	+	0.153163i	$0.951054\pi$
$224$	−0.560673	−	0.971114i	−0.0374615	−	0.0648853i
$225$		0			0
$226$		−	36.7100i		−	2.44191i
$227$	−5.27661	+	9.13935i	−0.350221	+	0.606600i	−0.986288	−	0.165034i	$-0.947227\pi$
$227$	−5.27661	+	9.13935i	−0.350221	+	0.606600i	0.636067	+	0.771634i	$0.280560\pi$
$228$	4.90931	−	8.50318i	0.325127	−	0.563137i
$229$		−	15.3248i		−	1.01269i	−0.862330	−	0.506346i	$-0.830996\pi$
$229$		−	15.3248i		−	1.01269i	0.862330	−	0.506346i	$-0.169004\pi$
$230$		0			0
$231$	2.06704	+	3.58021i	0.136001	+	0.235561i
$232$	−19.4457	−	33.6809i	−1.27667	−	2.21126i
$233$			9.96092i			0.652562i	0.945273	+	0.326281i	$0.105796\pi$
$233$			9.96092i			0.652562i	−0.945273	+	0.326281i	$0.894204\pi$
$234$	−2.90216	+	8.27034i	−0.189720	+	0.540649i
$235$		0			0
$236$	−20.2650	+	11.7000i	−1.31914	+	0.761604i
$237$	1.15201	−	0.665112i	0.0748310	−	0.0432037i
$238$	1.78421	+	1.03011i	0.115653	+	0.0667722i
$239$			2.47998i			0.160417i	0.996778	+	0.0802083i	$0.0255586\pi$
$239$			2.47998i			0.160417i	−0.996778	+	0.0802083i	$0.974441\pi$
$240$		0			0
$241$	24.6599	+	14.2374i	1.58848	+	0.917111i	0.993558	+	0.113329i	$0.0361514\pi$
$241$	24.6599	+	14.2374i	1.58848	+	0.917111i	0.594924	+	0.803782i	$0.297182\pi$
$242$	2.19999			0.141420
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−25.3860	−	43.9699i	−1.62517	−	2.81489i
$245$		0			0
$246$	28.2543			1.80143
$247$	−6.86920	+	5.90082i	−0.437077	+	0.375460i
$248$		−	39.4663i		−	2.50612i
$249$	−12.3555	+	7.13342i	−0.782995	+	0.452062i
$250$		0			0
$251$	13.4795	−	23.3472i	0.850820	−	1.47366i	−0.0296488	−	0.999560i	$-0.509439\pi$
$251$	13.4795	−	23.3472i	0.850820	−	1.47366i	0.880469	−	0.474104i	$-0.157228\pi$
$252$	5.08658			0.320424
$253$	2.82705	−	4.89659i	0.177735	−	0.307846i
$254$	6.09739	+	3.52033i	0.382584	+	0.220885i
$255$		0			0
$256$	15.5423	−	26.9200i	0.971391	−	1.68250i
$257$	−7.44114	+	4.29614i	−0.464166	+	0.267986i	−0.713794	−	0.700356i	$-0.753025\pi$
$257$	−7.44114	+	4.29614i	−0.464166	+	0.267986i	0.249629	+	0.968342i	$0.419691\pi$
$258$	−3.97919	−	6.89217i	−0.247734	−	0.429087i
$259$	−1.81863			−0.113004
$260$		0			0
$261$	−8.37930			−0.518666
$262$	−19.1519	−	33.1721i	−1.18321	−	2.04938i
$263$	−12.6739	+	7.31726i	−0.781504	+	0.451202i	−0.836963	−	0.547259i	$-0.815671\pi$
$263$	−12.6739	+	7.31726i	−0.781504	+	0.451202i	0.0554590	+	0.998461i	$0.482338\pi$
$264$	−7.37341	+	12.7711i	−0.453802	+	0.786009i
$265$		0			0
$266$	6.87978	+	3.97204i	0.421826	+	0.243541i
$267$	4.80193	−	8.31719i	0.293873	−	0.509004i
$268$	51.4252			3.14129
$269$	3.68759	−	6.38710i	0.224837	−	0.389428i	−0.731434	−	0.681912i	$-0.761149\pi$
$269$	3.68759	−	6.38710i	0.224837	−	0.389428i	0.956270	+	0.292484i	$0.0944819\pi$
$270$		0			0
$271$	−10.2106	+	5.89511i	−0.620251	+	0.358102i	−0.776967	−	0.629542i	$-0.783243\pi$
$271$	−10.2106	+	5.89511i	−0.620251	+	0.358102i	0.156716	+	0.987644i	$0.449909\pi$
$272$			2.25638i			0.136813i
$273$	−4.42670	−	1.55338i	−0.267916	−	0.0940149i
$274$	−1.79338			−0.108342
$275$		0			0
$276$	−3.47841	−	6.02477i	−0.209375	−	0.362649i
$277$	16.6718	+	9.62548i	1.00171	+	0.578339i	0.908755	−	0.417331i	$-0.137034\pi$
$277$	16.6718	+	9.62548i	1.00171	+	0.578339i	0.0929583	+	0.995670i	$0.470368\pi$
$278$	48.0027			2.87901
$279$	−7.36397	−	4.25159i	−0.440869	−	0.254536i
$280$		0			0
$281$		−	25.4911i		−	1.52067i	−0.649529	−	0.760336i	$-0.725034\pi$
$281$		−	25.4911i		−	1.52067i	0.649529	−	0.760336i	$-0.274966\pi$
$282$	25.7058	+	14.8412i	1.53076	+	0.883783i
$283$	4.47967	−	2.58634i	0.266289	−	0.153742i	−0.360911	−	0.932600i	$-0.617534\pi$
$283$	4.47967	−	2.58634i	0.266289	−	0.153742i	0.627200	+	0.778858i	$0.284201\pi$
$284$	3.71251	−	2.14342i	0.220297	−	0.127189i
$285$		0			0
$286$	21.1241	−	18.1461i	1.24909	−	1.07300i
$287$			15.1231i			0.892689i
$288$	−0.430908	−	0.746354i	−0.0253915	−	0.0439793i
$289$	−8.28787	−	14.3550i	−0.487521	−	0.844412i
$290$		0			0
$291$		−	7.94681i		−	0.465850i
$292$	−23.9042	+	41.4032i	−1.39889	+	2.42294i
$293$	12.9961	−	22.5099i	0.759242	−	1.31505i	−0.183996	−	0.982927i	$-0.558903\pi$
$293$	12.9961	−	22.5099i	0.759242	−	1.31505i	0.943238	−	0.332118i	$-0.107763\pi$
$294$		−	12.9009i		−	0.752395i
$295$		0			0
$296$	−3.24365	−	5.61817i	−0.188533	−	0.326549i
$297$	1.58863	+	2.75159i	0.0921817	+	0.159663i
$298$		−	7.69502i		−	0.445761i
$299$	1.18726	+	6.30545i	0.0686609	+	0.364654i
$300$		0			0
$301$	3.68903	−	2.12986i	0.212632	−	0.122763i
$302$	0.355452	−	0.205220i	0.0204540	−	0.0118091i
$303$	−1.84070	−	1.06273i	−0.105745	−	0.0610522i
$304$			8.70043i			0.499004i
$305$		0			0
$306$	1.37126	+	0.791698i	0.0783898	+	0.0452584i
$307$	−20.7454			−1.18400			−0.592001	−	0.805937i	$-0.701662\pi$
$307$	−20.7454			−1.18400			−0.592001	+	0.805937i	$0.701662\pi$
$308$	−13.9962	−	8.08069i	−0.797506	−	0.460440i
$309$	0.492848	+	0.853638i	0.0280372	+	0.0485618i
$310$		0			0
$311$	1.72617			0.0978819			0.0489410	−	0.998802i	$-0.484415\pi$
$311$	1.72617			0.0978819			0.0489410	+	0.998802i	$0.484415\pi$
$312$	−3.09657	−	16.4457i	−0.175309	−	0.931054i
$313$			6.29703i			0.355929i	0.984037	+	0.177965i	$0.0569513\pi$
$313$			6.29703i			0.355929i	−0.984037	+	0.177965i	$0.943049\pi$
$314$	−28.5283	+	16.4708i	−1.60994	+	0.929501i
$315$		0			0
$316$	−2.60013	+	4.50356i	−0.146269	+	0.253345i
$317$	10.5750			0.593950			0.296975	−	0.954885i	$-0.404022\pi$
$317$	10.5750			0.593950			0.296975	+	0.954885i	$0.404022\pi$
$318$	−7.72363	+	13.3777i	−0.433120	+	0.750185i
$319$	23.0564	+	13.3116i	1.29091	+	0.745307i
$320$		0			0
$321$	6.16796	−	10.6832i	0.344262	−	0.596279i
$322$	4.87454	−	2.81432i	0.271648	−	0.156836i
$323$	0.817977	+	1.41678i	0.0455135	+	0.0788316i
$324$	3.90931			0.217184
$325$		0			0
$326$	−36.9647			−2.04729
$327$	0.435118	+	0.753646i	0.0240621	+	0.0416767i
$328$	−46.7189	+	26.9732i	−2.57962	+	1.48934i
$329$	−7.94377	+	13.7590i	−0.437954	+	0.758559i
$330$		0			0
$331$	−4.99907	−	2.88621i	−0.274774	−	0.158641i	0.356281	−	0.934379i	$-0.384044\pi$
$331$	−4.99907	−	2.88621i	−0.274774	−	0.158641i	−0.631055	+	0.775738i	$0.717378\pi$
$332$	27.8868	−	48.3013i	1.53049	−	2.65088i
$333$	−1.39771			−0.0765943
$334$	−9.08658	+	15.7384i	−0.497195	+	0.861167i
$335$		0			0
$336$	−3.90343	+	2.25365i	−0.212950	+	0.122946i
$337$		−	2.08610i		−	0.113637i	−0.998385	−	0.0568186i	$-0.981904\pi$
$337$		−	2.08610i		−	0.113637i	0.998385	−	0.0568186i	$-0.0180957\pi$
$338$	−4.76548	+	31.2404i	−0.259208	+	1.69926i
$339$	15.1014			0.820193
$340$		0			0
$341$	13.5084	+	23.3973i	0.731522	+	1.26703i
$342$	5.28749	+	3.05273i	0.285915	+	0.165073i
$343$	16.0132			0.864632
$344$	13.1593	+	7.59753i	0.709502	+	0.409631i
$345$		0			0
$346$			22.5929i			1.21460i
$347$	−6.65390	−	3.84163i	−0.357200	−	0.206229i	0.310652	−	0.950524i	$-0.399453\pi$
$347$	−6.65390	−	3.84163i	−0.357200	−	0.206229i	−0.667852	+	0.744294i	$0.732786\pi$
$348$	28.3687	−	16.3786i	1.52072	−	0.877988i
$349$	14.5469	−	8.39867i	0.778679	−	0.449570i	−0.0572831	−	0.998358i	$-0.518244\pi$
$349$	14.5469	−	8.39867i	0.778679	−	0.449570i	0.835962	+	0.548788i	$0.184910\pi$
$350$		0			0
$351$	−3.40216	−	1.19386i	−0.181594	−	0.0637235i
$352$			2.73821i			0.145947i
$353$	0.0813396	+	0.140884i	0.00432927	+	0.00749851i	0.868182	−	0.496246i	$-0.165289\pi$
$353$	0.0813396	+	0.140884i	0.00432927	+	0.00749851i	−0.863853	+	0.503745i	$0.831955\pi$
$354$	−7.27534	−	12.6013i	−0.386680	−	0.669749i
$355$		0			0
$356$			37.5445i			1.98985i
$357$	−0.423756	+	0.733967i	−0.0224276	+	0.0388457i
$358$	−13.1847	+	22.8365i	−0.696830	+	1.20695i
$359$			19.3374i			1.02059i	0.860000	+	0.510295i	$0.170464\pi$
$359$			19.3374i			1.02059i	−0.860000	+	0.510295i	$0.829536\pi$
$360$		0			0
$361$	−6.34594	−	10.9915i	−0.333997	−	0.578499i
$362$	0.922968	+	1.59863i	0.0485101	+	0.0840220i
$363$			0.905006i			0.0475005i
$364$	18.0232	−	3.39360i	0.944672	−	0.177873i
$365$		0			0
$366$	27.3416	−	15.7857i	1.42917	−	0.825130i
$367$	1.96451	−	1.13421i	0.102547	−	0.0592054i	−0.447850	−	0.894109i	$-0.647810\pi$
$367$	1.96451	−	1.13421i	0.102547	−	0.0592054i	0.550396	+	0.834904i	$0.314477\pi$
$368$	5.33864	+	3.08227i	0.278296	+	0.160674i
$369$			11.6229i			0.605067i
$370$		0			0
$371$	−7.16042	−	4.13407i	−0.371751	−	0.214630i
$372$	33.2416			1.72350
$373$	10.3305	+	5.96434i	0.534895	+	0.308822i	0.743007	−	0.669283i	$-0.233399\pi$
$373$	10.3305	+	5.96434i	0.534895	+	0.308822i	−0.208112	+	0.978105i	$0.566732\pi$
$374$	−2.51543	−	4.35686i	−0.130070	−	0.225288i
$375$		0			0
$376$	−56.6732			−2.92270
$377$	−29.6903	+	5.59040i	−1.52913	+	0.287920i
$378$			3.16296i			0.162685i
$379$	9.97692	−	5.76018i	0.512480	−	0.295880i	−0.221372	−	0.975189i	$-0.571054\pi$
$379$	9.97692	−	5.76018i	0.512480	−	0.295880i	0.733853	+	0.679309i	$0.237720\pi$
$380$		0			0
$381$	−1.44815	+	2.50828i	−0.0741911	+	0.128503i
$382$	16.2457			0.831202
$383$	6.90524	−	11.9602i	0.352841	−	0.611139i	−0.633905	−	0.773411i	$-0.718549\pi$
$383$	6.90524	−	11.9602i	0.352841	−	0.611139i	0.986746	+	0.162272i	$0.0518822\pi$
$384$	17.5032	+	10.1055i	0.893205	+	0.515692i
$385$		0			0
$386$	−19.2392	+	33.3233i	−0.979249	+	1.69611i
$387$	2.83522	−	1.63692i	0.144122	−	0.0832091i
$388$	15.5333	+	26.9044i	0.788583	+	1.36587i
$389$	13.9037			0.704946			0.352473	−	0.935822i	$-0.385341\pi$
$389$	13.9037			0.704946			0.352473	+	0.935822i	$0.385341\pi$
$390$		0			0
$391$	1.15913			0.0586195
$392$	12.3159	+	21.3318i	0.622048	+	1.07742i
$393$	13.6460	−	7.87851i	0.688349	−	0.397418i
$394$	−8.30703	+	14.3882i	−0.418502	+	0.724867i
$395$		0			0
$396$	−10.7568	−	6.21046i	−0.540551	−	0.312087i
$397$	12.4866	−	21.6274i	0.626684	−	1.08545i	−0.361529	−	0.932361i	$-0.617745\pi$
$397$	12.4866	−	21.6274i	0.626684	−	1.08545i	0.988213	−	0.153087i	$-0.0489215\pi$
$398$	−41.9154			−2.10103
$399$	−1.63397	+	2.83013i	−0.0818010	+	0.141684i
$400$		0			0
$401$	−7.91663	+	4.57067i	−0.395338	+	0.228248i	−0.684470	−	0.729041i	$-0.739966\pi$
$401$	−7.91663	+	4.57067i	−0.395338	+	0.228248i	0.289133	+	0.957289i	$0.406633\pi$
$402$			31.9775i			1.59489i
$403$	−28.9292	−	10.1516i	−1.44107	−	0.505687i
$404$	8.30908			0.413392
$405$		0			0
$406$	13.2517	+	22.9526i	0.657670	+	1.13912i
$407$	3.84594	+	2.22045i	0.190636	+	0.110064i
$408$	−3.02320			−0.149671
$409$	21.1456	+	12.2084i	1.04558	+	0.603667i	0.921409	−	0.388594i	$-0.127039\pi$
$409$	21.1456	+	12.2084i	1.04558	+	0.603667i	0.124172	+	0.992261i	$0.460373\pi$
$410$		0			0
$411$		−	0.737739i		−	0.0363900i
$412$	−3.33714	−	1.92670i	−0.164409	−	0.0949216i
$413$	6.74482	−	3.89412i	0.331891	−	0.191617i
$414$	3.74635	−	2.16296i	0.184123	−	0.106304i
$415$		0			0
$416$	−2.02477	−	2.35706i	−0.0992727	−	0.115564i
$417$			19.7468i			0.967006i
$418$	−9.69933	−	16.7997i	−0.474410	−	0.821702i
$419$	3.48713	+	6.03989i	0.170358	+	0.295068i	0.938545	−	0.345157i	$-0.112174\pi$
$419$	3.48713	+	6.03989i	0.170358	+	0.295068i	−0.768187	+	0.640225i	$0.778841\pi$
$420$		0			0
$421$			0.673176i			0.0328086i	0.999865	+	0.0164043i	$0.00522189\pi$
$421$			0.673176i			0.0328086i	−0.999865	+	0.0164043i	$0.994778\pi$
$422$	28.9439	−	50.1322i	1.40897	−	2.44040i
$423$	−6.10523	+	10.5746i	−0.296846	+	0.514153i
$424$		−	29.4937i		−	1.43234i
$425$		0			0
$426$	1.33283	+	2.30853i	0.0645759	+	0.111849i
$427$	8.44928	+	14.6346i	0.408889	+	0.708217i
$428$			48.2249i			2.33104i
$429$	7.46475	+	8.68979i	0.360402	+	0.419547i
$430$		0			0
$431$	24.2754	−	14.0154i	1.16931	−	0.675099i	0.215790	−	0.976440i	$-0.430767\pi$
$431$	24.2754	−	14.0154i	1.16931	−	0.675099i	0.953517	+	0.301340i	$0.0974341\pi$
$432$	−3.00000	+	1.73205i	−0.144338	+	0.0833333i
$433$	2.30911	+	1.33317i	0.110969	+	0.0640679i	0.554457	−	0.832212i	$-0.312926\pi$
$433$	2.30911	+	1.33317i	0.110969	+	0.0640679i	−0.443488	+	0.896280i	$0.646259\pi$
$434$			26.8952i			1.29101i
$435$		0			0
$436$	−2.94624	−	1.70101i	−0.141099	−	0.0814636i
$437$	4.46951			0.213806
$438$	−25.7456	−	14.8642i	−1.23017	−	0.710239i
$439$	−11.0370	−	19.1166i	−0.526765	−	0.912384i	−0.999514	−	0.0311863i	$-0.990071\pi$
$439$	−11.0370	−	19.1166i	−0.526765	−	0.912384i	0.472749	−	0.881197i	$-0.343262\pi$
$440$		0			0
$441$	5.30703			0.252716
$442$	5.38697	+	1.89035i	0.256232	+	0.0899148i
$443$			14.6927i			0.698070i	0.937110	+	0.349035i	$0.113491\pi$
$443$			14.6927i			0.698070i	−0.937110	+	0.349035i	$0.886509\pi$
$444$	4.73205	−	2.73205i	0.224573	−	0.129657i
$445$		0			0
$446$	−13.1213	+	22.7268i	−0.621314	+	1.07615i
$447$	3.16549			0.149723
$448$	−5.87024	+	10.1675i	−0.277343	+	0.480371i
$449$	4.88200	+	2.81863i	0.230396	+	0.133019i	0.610755	−	0.791820i	$-0.290866\pi$
$449$	4.88200	+	2.81863i	0.230396	+	0.133019i	−0.380359	+	0.924839i	$0.624199\pi$
$450$		0			0
$451$	18.4646	−	31.9816i	0.869463	−	1.50595i
$452$	−51.1266	+	29.5180i	−2.40479	+	1.38841i
$453$	0.0844213	+	0.146222i	0.00396646	+	0.00687011i
$454$	25.6539			1.20400
$455$		0			0
$456$	−11.6572			−0.545900
$457$	2.53662	+	4.39355i	0.118658	+	0.205521i	0.919236	−	0.393707i	$-0.128808\pi$
$457$	2.53662	+	4.39355i	0.118658	+	0.205521i	−0.800578	+	0.599228i	$0.795474\pi$
$458$	−32.2622	+	18.6266i	−1.50751	+	0.870364i
$459$	−0.325680	+	0.564094i	−0.0152014	+	0.0263297i
$460$		0			0
$461$	28.6562	+	16.5446i	1.33465	+	0.770561i	0.986009	−	0.166695i	$-0.0533094\pi$
$461$	28.6562	+	16.5446i	1.33465	+	0.770561i	0.348642	+	0.937256i	$0.386643\pi$
$462$	5.02477	−	8.70316i	0.233774	−	0.404908i
$463$	−24.4976			−1.13850			−0.569251	−	0.822164i	$-0.692767\pi$
$463$	−24.4976			−1.13850			−0.569251	+	0.822164i	$0.692767\pi$
$464$	−14.5134	+	25.1379i	−0.673766	+	1.16700i
$465$		0			0
$466$	20.9700	−	12.1070i	0.971417	−	0.560848i
$467$			30.5932i			1.41569i	0.706370	+	0.707843i	$0.250332\pi$
$467$			30.5932i			1.41569i	−0.706370	+	0.707843i	$0.749668\pi$
$468$	13.8518	−	2.60817i	0.640301	−	0.120563i
$469$	−17.1159			−0.790341
$470$		0			0
$471$	−6.77558	−	11.7356i	−0.312202	−	0.540750i
$472$	24.0597	+	13.8909i	1.10744	+	0.639380i
$473$	−10.4018			−0.478276
$474$	−2.80043	−	1.61683i	−0.128628	−	0.0742633i
$475$		0			0
$476$		−	3.31319i		−	0.151860i
$477$	−5.50318	−	3.17726i	−0.251973	−	0.145477i
$478$	5.22093	−	3.01430i	0.238800	−	0.137871i
$479$	−12.0534	+	6.95901i	−0.550732	+	0.317965i	−0.749417	−	0.662098i	$-0.769666\pi$
$479$	−12.0534	+	6.95901i	−0.550732	+	0.317965i	0.198685	+	0.980063i	$0.436333\pi$
$480$		0			0
$481$	−4.95250	+	0.932511i	−0.225815	+	0.0425188i
$482$		−	69.2195i		−	3.15286i
$483$	1.15772	+	2.00524i	0.0526782	+	0.0912414i
$484$	−1.76897	−	3.06395i	−0.0804079	−	0.139271i
$485$		0			0
$486$			2.43091i			0.110268i
$487$	−15.2758	+	26.4585i	−0.692213	+	1.19895i	0.278898	+	0.960321i	$0.410031\pi$
$487$	−15.2758	+	26.4585i	−0.692213	+	1.19895i	−0.971111	+	0.238628i	$0.923302\pi$
$488$	−30.1398	+	52.2036i	−1.36436	+	2.36315i
$489$		−	15.2061i		−	0.687646i
$490$		0			0
$491$	−7.34214	−	12.7170i	−0.331346	−	0.573908i	0.651430	−	0.758709i	$-0.274169\pi$
$491$	−7.34214	−	12.7170i	−0.331346	−	0.573908i	−0.982776	+	0.184801i	$0.940836\pi$
$492$	−22.7189	−	39.3502i	−1.02425	−	1.77405i
$493$			5.45794i			0.245813i
$494$	20.7718	+	7.28906i	0.934566	+	0.327951i
$495$		0			0
$496$	−25.5095	+	14.7279i	−1.14541	+	0.661304i
$497$	−1.23564	+	0.713398i	−0.0554261	+	0.0320003i
$498$	30.0350	+	17.3407i	1.34590	+	0.777055i
$499$		−	16.1489i		−	0.722922i	−0.932387	−	0.361461i	$-0.882278\pi$
$499$		−	16.1489i		−	0.722922i	0.932387	−	0.361461i	$-0.117722\pi$
$500$		0			0
$501$	−6.47429	−	3.73793i	−0.289250	−	0.166999i
$502$	−65.5350			−2.92497
$503$	1.73951	+	1.00431i	0.0775610	+	0.0447799i	0.538279	−	0.842767i	$-0.319075\pi$
$503$	1.73951	+	1.00431i	0.0775610	+	0.0447799i	−0.460718	+	0.887547i	$0.652408\pi$
$504$	−3.01954	−	5.22999i	−0.134501	−	0.232962i
$505$		0			0
$506$	−13.7446			−0.611021
$507$	−12.8513	−	1.96037i	−0.570748	−	0.0870631i
$508$		−	11.3226i		−	0.502358i
$509$	33.2529	−	19.1986i	1.47391	−	0.850962i	0.474341	−	0.880341i	$-0.342686\pi$
$509$	33.2529	−	19.1986i	1.47391	−	0.850962i	0.999568	+	0.0293796i	$0.00935315\pi$
$510$		0			0
$511$	7.95606	−	13.7803i	0.351956	−	0.609605i
$512$	−35.1417			−1.55306
$513$	−1.25580	+	2.17511i	−0.0554449	+	0.0960334i
$514$	18.0887	+	10.4435i	0.797860	+	0.460644i
$515$		0			0
$516$	−6.39922	+	11.0838i	−0.281710	+	0.487936i
$517$	33.5982	−	19.3979i	1.47765	−	0.853119i
$518$	2.21046	+	3.82862i	0.0971219	+	0.168220i
$519$	−9.29402			−0.407962
$520$		0			0
$521$	31.2138			1.36750			0.683751	−	0.729716i	$-0.260348\pi$
$521$	31.2138			1.36750			0.683751	+	0.729716i	$0.260348\pi$
$522$	10.1847	+	17.6403i	0.445770	+	0.772096i
$523$	28.7591	−	16.6041i	1.25755	−	0.726045i	0.284949	−	0.958543i	$-0.408023\pi$
$523$	28.7591	−	16.6041i	1.25755	−	0.726045i	0.972597	+	0.232498i	$0.0746898\pi$
$524$	−30.7996	+	53.3464i	−1.34549	+	2.33045i
$525$		0			0
$526$	30.8090	+	17.7876i	1.34334	+	0.775576i
$527$	−2.76931	+	4.79659i	−0.120633	+	0.208943i
$528$	11.0064			0.478990
$529$	−9.91660	+	17.1761i	−0.431157	+	0.746785i
$530$		0			0
$531$	5.18377	−	2.99285i	0.224956	−	0.129879i
$532$		−	12.7754i		−	0.553885i
$533$	7.75446	+	41.1834i	0.335883	+	1.78385i
$534$	−23.3461			−1.01028
$535$		0			0
$536$	−30.5275	−	52.8752i	−1.31859	−	2.28386i
$537$	−9.39422	−	5.42376i	−0.405391	−	0.234052i
$538$	−17.9284			−0.772948
$539$	−14.6028	−	8.43091i	−0.628985	−	0.363145i
$540$		0			0
$541$			39.1911i			1.68496i	0.538731	+	0.842478i	$0.318904\pi$
$541$			39.1911i			1.68496i	−0.538731	+	0.842478i	$0.681096\pi$
$542$	24.8211	+	14.3305i	1.06616	+	0.615546i
$543$	−0.657626	+	0.379680i	−0.0282214	+	0.0162936i
$544$	−0.486145	+	0.280676i	−0.0208433	+	0.0120339i
$545$		0			0
$546$	2.11023	+	11.2073i	0.0903093	+	0.479627i
$547$		−	8.26842i		−	0.353532i	−0.984253	−	0.176766i	$-0.943436\pi$
$547$		−	8.26842i		−	0.353532i	0.984253	−	0.176766i	$-0.0565636\pi$
$548$	1.44203	+	2.49766i	0.0616004	+	0.106695i
$549$	6.49373	+	11.2475i	0.277146	+	0.480031i
$550$		0			0
$551$			21.0454i			0.896566i
$552$	−4.12976	+	7.15296i	−0.175774	+	0.304450i
$553$	0.865406	−	1.49893i	0.0368008	−	0.0637409i
$554$		−	46.7973i		−	1.98823i
$555$		0			0
$556$	−38.5983	−	66.8542i	−1.63693	−	2.83525i
$557$	22.5316	+	39.0259i	0.954695	+	1.65358i	0.735064	+	0.677997i	$0.237152\pi$
$557$	22.5316	+	39.0259i	0.954695	+	1.65358i	0.219631	+	0.975583i	$0.429515\pi$
$558$			20.6704i			0.875050i
$559$	8.95391	−	7.69164i	0.378710	−	0.325322i
$560$		0			0
$561$	1.79227	−	1.03477i	0.0756699	−	0.0436880i
$562$	−53.6646	+	30.9833i	−2.26371	+	1.30695i
$563$	−39.7313	−	22.9389i	−1.67447	−	0.966758i	−0.965083	−	0.261943i	$-0.915637\pi$
$563$	−39.7313	−	22.9389i	−1.67447	−	0.966758i	−0.709391	−	0.704816i	$-0.751030\pi$
$564$		−	47.7345i		−	2.00998i
$565$		0			0
$566$	−10.8897	−	6.28715i	−0.457727	−	0.264269i
$567$	−1.30114			−0.0546429
$568$	−4.40771	−	2.54479i	−0.184943	−	0.106777i
$569$	−3.06034	−	5.30066i	−0.128296	−	0.222215i	0.794720	−	0.606976i	$-0.207617\pi$
$569$	−3.06034	−	5.30066i	−0.128296	−	0.222215i	−0.923017	+	0.384760i	$0.874284\pi$
$570$		0			0
$571$	−19.2267			−0.804611			−0.402306	−	0.915505i	$-0.631791\pi$
$571$	−19.2267			−0.804611			−0.402306	+	0.915505i	$0.631791\pi$
$572$	−42.2579	−	14.8288i	−1.76689	−	0.620024i
$573$			6.68298i			0.279185i
$574$	31.8376	−	18.3815i	1.32888	−	0.767227i
$575$		0			0
$576$	−4.51160	+	7.81432i	−0.187983	+	0.325597i
$577$	−9.40689			−0.391614			−0.195807	−	0.980642i	$-0.562733\pi$
$577$	−9.40689			−0.391614			−0.195807	+	0.980642i	$0.562733\pi$
$578$	−20.1470	+	34.8957i	−0.838006	+	1.45147i
$579$	−13.7082	−	7.91441i	−0.569692	−	0.328912i
$580$		0			0
$581$	−9.28160	+	16.0762i	−0.385066	+	0.666954i
$582$	−16.7299	+	9.65899i	−0.693475	+	0.400378i
$583$	10.0950	+	17.4850i	0.418092	+	0.724157i
$584$	56.7608			2.34878
$585$		0			0
$586$	−63.1848			−2.61014
$587$	18.6143	+	32.2409i	0.768294	+	1.33072i	0.938487	+	0.345314i	$0.112227\pi$
$587$	18.6143	+	32.2409i	0.768294	+	1.33072i	−0.170193	+	0.985411i	$0.554439\pi$
$588$	−17.9673	+	10.3734i	−0.740958	+	0.427792i
$589$	−10.6783	+	18.4953i	−0.439991	+	0.762087i
$590$		0			0
$591$	−5.91886	−	3.41725i	−0.243469	−	0.140567i
$592$	−2.42091	+	4.19314i	−0.0994989	+	0.172337i
$593$	18.1214			0.744157			0.372078	−	0.928201i	$-0.378645\pi$
$593$	18.1214			0.744157			0.372078	+	0.928201i	$0.378645\pi$
$594$	3.86182	−	6.68886i	0.158452	−	0.274447i
$595$		0			0
$596$	−10.7170	+	6.18745i	−0.438985	+	0.253448i
$597$		−	17.2427i		−	0.705696i
$598$	11.8314	−	10.1634i	0.483820	−	0.415614i
$599$	7.18204			0.293450			0.146725	−	0.989177i	$-0.453127\pi$
$599$	7.18204			0.293450			0.146725	+	0.989177i	$0.453127\pi$
$600$		0			0
$601$	16.5370	+	28.6428i	0.674556	+	1.16837i	0.976598	+	0.215071i	$0.0689983\pi$
$601$	16.5370	+	28.6428i	0.674556	+	1.16837i	−0.302042	+	0.953295i	$0.597668\pi$
$602$	−8.96769	−	5.17750i	−0.365496	−	0.211019i
$603$	−13.1545			−0.535694
$604$	−0.571628	−	0.330029i	−0.0232592	−	0.0134287i
$605$		0			0
$606$			5.16679i			0.209887i
$607$	18.7185	+	10.8071i	0.759760	+	0.438648i	0.829210	−	0.558938i	$-0.188791\pi$
$607$	18.7185	+	10.8071i	0.759760	+	0.438648i	−0.0694496	+	0.997585i	$0.522124\pi$
$608$	−1.87454	+	1.08227i	−0.0760227	+	0.0438917i
$609$	−9.44199	+	5.45133i	−0.382609	+	0.220899i
$610$		0			0
$611$	−14.5776	+	41.5419i	−0.589745	+	1.68061i
$612$		−	2.54637i		−	0.102931i
$613$	−13.6769	−	23.6890i	−0.552403	−	0.956790i	−0.998101	−	0.0616062i	$-0.980378\pi$
$613$	−13.6769	−	23.6890i	−0.552403	−	0.956790i	0.445698	−	0.895184i	$-0.352956\pi$
$614$	25.2151	+	43.6738i	1.01760	+	1.76253i
$615$		0			0
$616$			19.1877i			0.773096i
$617$	−8.16518	+	14.1425i	−0.328718	+	0.569356i	−0.982258	−	0.187536i	$-0.939950\pi$
$617$	−8.16518	+	14.1425i	−0.328718	+	0.569356i	0.653540	+	0.756892i	$0.273283\pi$
$618$	1.19807	−	2.07512i	0.0481934	−	0.0834734i
$619$			35.8801i			1.44214i	0.692860	+	0.721072i	$0.256350\pi$
$619$			35.8801i			1.44214i	−0.692860	+	0.721072i	$0.743650\pi$
$620$		0			0
$621$	0.889774	+	1.54113i	0.0357054	+	0.0618436i
$622$	−2.09808	−	3.63397i	−0.0841252	−	0.145709i
$623$		−	12.4960i		−	0.500642i
$624$	−9.47429	+	8.13866i	−0.379275	+	0.325807i
$625$		0			0
$626$	13.2567	−	7.65375i	0.529844	−	0.305905i
$627$	6.91089	−	3.99000i	0.275994	−	0.159345i
$628$	45.8783	+	26.4878i	1.83074	+	1.05698i
$629$			0.910415i			0.0363006i
$630$		0			0
$631$	−6.10348	−	3.52385i	−0.242976	−	0.140282i	0.373568	−	0.927603i	$-0.378134\pi$
$631$	−6.10348	−	3.52385i	−0.242976	−	0.140282i	−0.616544	+	0.787321i	$0.711468\pi$
$632$	6.17406			0.245591
$633$	20.6229	+	11.9066i	0.819685	+	0.473245i
$634$	−12.8534	−	22.2627i	−0.510474	−	0.884166i
$635$		0			0
$636$	24.8418			0.985042
$637$	18.8043	−	3.54068i	0.745054	−	0.140287i
$638$		−	64.7186i		−	2.56223i
$639$	−0.949658	+	0.548286i	−0.0375679	+	0.0216898i
$640$		0			0
$641$	20.4752	−	35.4641i	0.808723	−	1.40075i	−0.105026	−	0.994469i	$-0.533493\pi$
$641$	20.4752	−	35.4641i	0.808723	−	1.40075i	0.913749	−	0.406279i	$-0.133174\pi$
$642$	−29.9875			−1.18351
$643$	−17.6094	+	30.5004i	−0.694448	+	1.20282i	0.275918	+	0.961181i	$0.411018\pi$
$643$	−17.6094	+	30.5004i	−0.694448	+	1.20282i	−0.970366	+	0.241638i	$0.922315\pi$
$644$	−7.83909	−	4.52590i	−0.308904	−	0.178346i
$645$		0			0
$646$	1.98843	−	3.44406i	0.0782336	−	0.135505i
$647$	24.6573	−	14.2359i	0.969377	−	0.559670i	0.0703308	−	0.997524i	$-0.477595\pi$
$647$	24.6573	−	14.2359i	0.969377	−	0.559670i	0.899046	+	0.437854i	$0.144261\pi$
$648$	−2.32068	−	4.01954i	−0.0911650	−	0.157902i
$649$	−19.0181			−0.746527
$650$		0			0
$651$	−11.0639			−0.433627
$652$	29.7228	+	51.4814i	1.16403	+	2.01617i
$653$	27.0775	−	15.6332i	1.05962	−	0.611774i	0.134295	−	0.990941i	$-0.457123\pi$
$653$	27.0775	−	15.6332i	1.05962	−	0.611774i	0.925328	+	0.379168i	$0.123790\pi$
$654$	1.05773	−	1.83204i	0.0413605	−	0.0716386i
$655$		0			0
$656$	34.8688	+	20.1315i	1.36140	+	0.786004i
$657$	6.11467	−	10.5909i	0.238556	−	0.413191i
$658$	38.6212			1.50561
$659$	−1.61118	+	2.79065i	−0.0627627	+	0.108708i	−0.895699	−	0.444660i	$-0.853324\pi$
$659$	−1.61118	+	2.79065i	−0.0627627	+	0.108708i	0.832937	+	0.553368i	$0.186658\pi$
$660$		0			0
$661$	25.9416	−	14.9774i	1.00901	−	0.582552i	0.0981086	−	0.995176i	$-0.468721\pi$
$661$	25.9416	−	14.9774i	1.00901	−	0.582552i	0.910902	+	0.412623i	$0.135387\pi$
$662$			14.0322i			0.545378i
$663$	−0.777632	+	2.21603i	−0.0302007	+	0.0860635i
$664$	−66.2176			−2.56974
$665$		0			0
$666$	1.69886	+	2.94251i	0.0658294	+	0.114020i
$667$	12.9136	+	7.45568i	0.500017	+	0.288685i
$668$	29.2255			1.13077
$669$	−9.34911	−	5.39771i	−0.361458	−	0.208688i
$670$		0			0
$671$		−	41.2646i		−	1.59300i
$672$	−0.971114	−	0.560673i	−0.0374615	−	0.0216284i
$673$	25.7792	−	14.8836i	0.993716	−	0.573722i	0.0873333	−	0.996179i	$-0.472165\pi$
$673$	25.7792	−	14.8836i	0.993716	−	0.573722i	0.906383	+	0.422457i	$0.138832\pi$
$674$	−4.39172	+	2.53556i	−0.169163	+	0.0976661i
$675$		0			0
$676$	47.3409	−	18.4830i	1.82080	−	0.710884i
$677$		−	24.8749i		−	0.956019i	−0.878355	−	0.478010i	$-0.841358\pi$
$677$		−	24.8749i		−	0.956019i	0.878355	−	0.478010i	$-0.158642\pi$
$678$	−18.3550	−	31.7918i	−0.704919	−	1.22096i
$679$	−5.16997	−	8.95465i	−0.198405	−	0.343648i
$680$		0			0
$681$			10.5532i			0.404400i
$682$	32.8377	−	56.8766i	1.25742	−	2.17792i
$683$	4.56567	−	7.90797i	0.174701	−	0.302590i	−0.765357	−	0.643606i	$-0.777438\pi$
$683$	4.56567	−	7.90797i	0.174701	−	0.302590i	0.940058	+	0.341016i	$0.110771\pi$
$684$		−	9.81863i		−	0.375425i
$685$		0			0
$686$	−19.4633	−	33.7114i	−0.743113	−	1.28711i
$687$	−7.66241	−	13.2717i	−0.292339	−	0.506346i
$688$		−	11.3409i		−	0.432367i
$689$	−21.6191	−	7.58641i	−0.823623	−	0.289019i
$690$		0			0
$691$	−28.5679	+	16.4937i	−1.08677	+	0.627449i	−0.932715	−	0.360613i	$-0.882567\pi$
$691$	−28.5679	+	16.4937i	−1.08677	+	0.627449i	−0.154057	+	0.988062i	$0.549234\pi$
$692$	31.4655	−	18.1666i	1.19614	−	0.690591i
$693$	3.58021	+	2.06704i	0.136001	+	0.0785202i
$694$			18.6773i			0.708980i
$695$		0			0
$696$	−33.6809	−	19.4457i	−1.27667	−	0.737087i
$697$	7.57072			0.286762
$698$	−35.3622	−	20.4164i	−1.33848	−	0.772772i
$699$	4.98046	+	8.62641i	0.188378	+	0.326281i
$700$		0			0
$701$	−24.6223			−0.929971			−0.464985	−	0.885318i	$-0.653940\pi$
$701$	−24.6223			−0.929971			−0.464985	+	0.885318i	$0.653940\pi$
$702$	1.62182	+	8.61341i	0.0612118	+	0.325092i
$703$			3.51050i			0.132401i
$704$	24.8281	−	14.3345i	0.935746	−	0.540253i
$705$		0			0
$706$	0.197729	−	0.342477i	0.00744163	−	0.0128893i
$707$	−2.76552			−0.104008
$708$	−11.7000	+	20.2650i	−0.439712	+	0.761604i
$709$	−43.1727	−	24.9258i	−1.62138	−	0.936107i	−0.986550	−	0.163458i	$-0.947735\pi$
$709$	−43.1727	−	24.9258i	−1.62138	−	0.936107i	−0.634834	−	0.772648i	$-0.718932\pi$
$710$		0			0
$711$	0.665112	−	1.15201i	0.0249437	−	0.0432037i
$712$	38.6031	−	22.2875i	1.44671	−	0.835260i
$713$	7.56591	+	13.1045i	0.283345	+	0.490769i
$714$	2.06022			0.0771019
$715$		0			0
$716$	42.4063			1.58480
$717$	1.23999	+	2.14773i	0.0463083	+	0.0802083i
$718$	40.7096	−	23.5037i	1.51927	−	0.877151i
$719$	6.33625	−	10.9747i	0.236302	−	0.409288i	−0.723348	−	0.690484i	$-0.757398\pi$
$719$	6.33625	−	10.9747i	0.236302	−	0.409288i	0.959650	+	0.281196i	$0.0907311\pi$
$720$		0			0
$721$	1.11071	+	0.641266i	0.0413648	+	0.0238820i
$722$	−15.4264	+	26.7193i	−0.574111	+	0.994389i
$723$	28.4748			1.05899
$724$	1.48429	−	2.57086i	0.0551632	−	0.0955454i
$725$		0			0
$726$	1.90524	−	1.09999i	0.0707102	−	0.0408246i
$727$		−	26.0757i		−	0.967093i	−0.875319	−	0.483547i	$-0.839348\pi$
$727$		−	26.0757i		−	0.967093i	0.875319	−	0.483547i	$-0.160652\pi$
$728$	−14.1884	−	16.5168i	−0.525856	−	0.612155i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−1.06622	−	1.84675i	−0.0394356	−	0.0683045i
$732$	−43.9699	−	25.3860i	−1.62517	−	0.938295i
$733$	−3.39408			−0.125363			−0.0626815	−	0.998034i	$-0.519965\pi$
$733$	−3.39408			−0.125363			−0.0626815	+	0.998034i	$0.519965\pi$
$734$	−4.77555	−	2.75716i	−0.176269	−	0.101769i
$735$		0			0
$736$			1.53364i			0.0565308i
$737$	36.1959	+	20.8977i	1.33329	+	0.769777i
$738$	24.4690	−	14.1272i	0.900715	−	0.520028i
$739$	5.88277	−	3.39642i	0.216401	−	0.124939i	−0.387882	−	0.921709i	$-0.626793\pi$
$739$	5.88277	−	3.39642i	0.216401	−	0.124939i	0.604283	+	0.796770i	$0.293460\pi$
$740$		0			0
$741$	−2.99849	+	8.54486i	−0.110152	+	0.313903i
$742$			20.0991i			0.737861i
$743$	−6.86681	−	11.8937i	−0.251919	−	0.436336i	0.712135	−	0.702042i	$-0.247728\pi$
$743$	−6.86681	−	11.8937i	−0.251919	−	0.436336i	−0.964054	+	0.265706i	$0.914395\pi$
$744$	−19.7332	−	34.1789i	−0.723453	−	1.25306i
$745$		0			0
$746$		−	28.9975i		−	1.06167i
$747$	−7.13342	+	12.3555i	−0.260998	+	0.452062i
$748$	−4.04524	+	7.00656i	−0.147909	+	0.256185i
$749$		−	16.0508i		−	0.586483i
$750$		0			0
$751$	−20.3873	−	35.3119i	−0.743944	−	1.28855i	−0.950686	−	0.310154i	$-0.899619\pi$
$751$	−20.3873	−	35.3119i	−0.743944	−	1.28855i	0.206742	−	0.978396i	$-0.433714\pi$
$752$	21.1491	+	36.6314i	0.771229	+	1.33581i
$753$		−	26.9591i		−	0.982443i
$754$	47.8562	+	55.7099i	1.74282	+	2.02883i
$755$		0			0
$756$	4.40510	−	2.54329i	0.160212	−	0.0924985i
$757$	11.7726	−	6.79693i	0.427884	−	0.247039i	−0.270561	−	0.962703i	$-0.587209\pi$
$757$	11.7726	−	6.79693i	0.427884	−	0.247039i	0.698445	+	0.715664i	$0.253876\pi$
$758$	−24.2530	−	14.0025i	−0.880908	−	0.508592i
$759$		−	5.65409i		−	0.205230i
$760$		0			0
$761$	8.49411	+	4.90408i	0.307911	+	0.177773i	0.645991	−	0.763345i	$-0.276444\pi$
$761$	8.49411	+	4.90408i	0.307911	+	0.177773i	−0.338080	+	0.941117i	$0.609777\pi$
$762$	7.04065			0.255056
$763$	0.980601	+	0.566150i	0.0355001	+	0.0204960i
$764$	−13.0629	−	22.6256i	−0.472600	−	0.818567i
$765$		0			0
$766$	−33.5720			−1.21301
$767$	16.3708	−	14.0630i	0.591117	−	0.507784i
$768$		−	31.0845i		−	1.12167i
$769$	−37.4841	+	21.6415i	−1.35171	+	0.780411i	−0.988489	−	0.151292i	$-0.951657\pi$
$769$	−37.4841	+	21.6415i	−1.35171	+	0.780411i	−0.363222	+	0.931703i	$0.618323\pi$
$770$		0			0
$771$	−4.29614	+	7.44114i	−0.154722	+	0.267986i
$772$	61.8798			2.22710
$773$	12.1104	−	20.9759i	0.435582	−	0.754449i	−0.561761	−	0.827299i	$-0.689876\pi$
$773$	12.1104	−	20.9759i	0.435582	−	0.754449i	0.997343	+	0.0728499i	$0.0232094\pi$
$774$	−6.89217	−	3.97919i	−0.247734	−	0.143029i
$775$		0			0
$776$	18.4420	−	31.9425i	0.662030	−	1.14667i
$777$	−1.57498	+	0.909313i	−0.0565020	+	0.0326214i
$778$	−16.8993	−	29.2705i	−0.605870	−	1.04940i
$779$	29.1922			1.04592
$780$		0			0
$781$	3.48409			0.124671
$782$	−1.40886	−	2.44022i	−0.0503809	−	0.0872623i
$783$	−7.25669	+	4.18965i	−0.259333	+	0.149726i
$784$	9.19204	−	15.9211i	0.328287	−	0.568610i
$785$		0			0
$786$	−33.1721	−	19.1519i	−1.18321	−	0.683127i
$787$	5.23875	−	9.07378i	0.186741	−	0.323445i	−0.757421	−	0.652927i	$-0.773541\pi$
$787$	5.23875	−	9.07378i	0.186741	−	0.323445i	0.944162	+	0.329482i	$0.106874\pi$
$788$	26.7182			0.951797
$789$	−7.31726	+	12.6739i	−0.260501	+	0.451202i
$790$		0			0
$791$	17.0166	−	9.82451i	0.605039	−	0.349319i
$792$			14.7468i			0.524006i
$793$	30.5131	+	35.5206i	1.08355	+	1.26137i
$794$	−60.7075			−2.15443
$795$		0			0
$796$	33.7035	+	58.3762i	1.19459	+	2.06909i
$797$	−40.0222	−	23.1068i	−1.41766	−	0.818486i	−0.421566	−	0.906798i	$-0.638519\pi$
$797$	−40.0222	−	23.1068i	−1.41766	−	0.818486i	−0.996093	+	0.0883119i	$0.971853\pi$
$798$	7.94408			0.281218
$799$	6.88785	+	3.97670i	0.243674	+	0.140686i
$800$		0			0
$801$		−	9.60386i		−	0.339336i
$802$	19.2446	+	11.1109i	0.679550	+	0.392339i
$803$	−33.6501	+	19.4279i	−1.18749	+	0.685596i
$804$	44.5355	−	25.7126i	1.57065	−	0.906814i
$805$		0			0
$806$	13.7907	+	73.2413i	0.485756	+	2.57982i
$807$		−	7.37519i		−	0.259619i
$808$	−4.93251	−	8.54336i	−0.173525	−	0.300554i
$809$	3.60640	+	6.24646i	0.126794	+	0.219614i	0.922433	−	0.386158i	$-0.126198\pi$
$809$	3.60640	+	6.24646i	0.126794	+	0.219614i	−0.795639	+	0.605772i	$0.792865\pi$
$810$		0			0
$811$		−	44.8652i		−	1.57543i	−0.616040	−	0.787714i	$-0.711264\pi$
$811$		−	44.8652i		−	1.57543i	0.616040	−	0.787714i	$-0.288736\pi$
$812$	21.3110	−	36.9117i	0.747868	−	1.29535i
$813$	−5.89511	+	10.2106i	−0.206750	+	0.358102i
$814$		−	10.7954i		−	0.378380i
$815$		0			0
$816$	1.12819	+	1.95408i	0.0394945	+	0.0684065i
$817$	−4.11128	−	7.12094i	−0.143835	−	0.249130i
$818$		−	59.3550i		−	2.07530i
$819$	−4.61032	+	0.868081i	−0.161098	+	0.0303332i
$820$		0			0
$821$	39.5195	−	22.8166i	1.37924	−	0.796304i	0.387171	−	0.922008i	$-0.373452\pi$
$821$	39.5195	−	22.8166i	1.37924	−	0.796304i	0.992068	+	0.125704i	$0.0401191\pi$
$822$	−1.55311	+	0.896688i	−0.0541709	+	0.0312756i
$823$	−12.0641	−	6.96523i	−0.420529	−	0.242793i	0.274775	−	0.961509i	$-0.411397\pi$
$823$	−12.0641	−	6.96523i	−0.420529	−	0.242793i	−0.695304	+	0.718716i	$0.744730\pi$
$824$			4.57498i			0.159377i
$825$		0			0
$826$	−16.3960	−	9.46626i	−0.570491	−	0.329373i
$827$	−17.8737			−0.621530			−0.310765	−	0.950487i	$-0.600585\pi$
$827$	−17.8737			−0.621530			−0.310765	+	0.950487i	$0.600585\pi$
$828$	−6.02477	−	3.47841i	−0.209375	−	0.120883i
$829$	17.7236	+	30.6981i	0.615565	+	1.06619i	0.990285	+	0.139051i	$0.0444053\pi$
$829$	17.7236	+	30.6981i	0.615565	+	1.06619i	−0.374721	+	0.927138i	$0.622261\pi$
$830$		0			0
$831$	19.2510			0.667809
$832$	−10.7724	+	30.6984i	−0.373467	+	1.06427i
$833$		−	3.45678i		−	0.119770i
$834$	41.5716	−	24.0014i	1.43951	−	0.831099i
$835$		0			0
$836$	−15.5982	+	27.0168i	−0.539474	+	0.934397i
$837$	−8.50318			−0.293913
$838$	8.47690	−	14.6824i	0.292830	−	0.507196i
$839$	6.08860	+	3.51526i	0.210202	+	0.121360i	0.601405	−	0.798944i	$-0.294608\pi$
$839$	6.08860	+	3.51526i	0.210202	+	0.121360i	−0.391203	+	0.920304i	$0.627941\pi$
$840$		0			0
$841$	−20.6063	+	35.6912i	−0.710563	+	1.23073i
$842$	1.41719	−	0.818215i	0.0488396	−	0.0281975i
$843$	−12.7456	−	22.0760i	−0.438980	−	0.760336i
$844$	−93.0933			−3.20440
$845$		0			0
$846$	29.6825			1.02051
$847$	0.588771	+	1.01978i	0.0202304	+	0.0350401i
$848$	−19.0636	+	11.0064i	−0.654646	+	0.377960i
$849$	2.58634	−	4.47967i	0.0887629	−	0.153742i
$850$		0			0
$851$	2.15406	+	1.24365i	0.0738404	+	0.0426318i
$852$	2.14342	−	3.71251i	0.0734324	−	0.127189i
$853$	−25.7138			−0.880425			−0.440212	−	0.897894i	$-0.645097\pi$
$853$	−25.7138			−0.880425			−0.440212	+	0.897894i	$0.645097\pi$
$854$	20.5394	−	35.5753i	0.702844	−	1.21736i
$855$		0			0
$856$	49.5847	−	28.6277i	1.69477	−	0.978476i
$857$			20.7578i			0.709072i	0.935042	+	0.354536i	$0.115361\pi$
$857$			20.7578i			0.709072i	−0.935042	+	0.354536i	$0.884639\pi$
$858$	9.22093	−	26.2770i	0.314797	−	0.897083i
$859$	9.79466			0.334190			0.167095	−	0.985941i	$-0.446561\pi$
$859$	9.79466			0.334190			0.167095	+	0.985941i	$0.446561\pi$
$860$		0			0
$861$	7.56156	+	13.0970i	0.257697	+	0.446345i
$862$	−59.0113	−	34.0702i	−2.00993	−	1.16044i
$863$	−23.1995			−0.789720			−0.394860	−	0.918741i	$-0.629207\pi$
$863$	−23.1995			−0.789720			−0.394860	+	0.918741i	$0.629207\pi$
$864$	−0.746354	−	0.430908i	−0.0253915	−	0.0146598i
$865$		0			0
$866$		−	6.48161i		−	0.220254i
$867$	−14.3550	−	8.28787i	−0.487521	−	0.281471i
$868$	37.4574	−	21.6260i	1.27139	−	0.734035i
$869$	−3.66023	+	2.11324i	−0.124165	+	0.0716866i
$870$		0			0
$871$	−46.6103	+	8.77629i	−1.57933	+	0.297373i
$872$			4.03908i			0.136780i
$873$	−3.97341	−	6.88214i	−0.134479	−	0.232925i
$874$	−5.43248	−	9.40934i	−0.183757	−	0.318276i
$875$		0			0
$876$			47.8083i			1.61529i
$877$	−28.7182	+	49.7414i	−0.969745	+	1.67965i	−0.273460	+	0.961883i	$0.588168\pi$
$877$	−28.7182	+	49.7414i	−0.969745	+	1.67965i	−0.696285	+	0.717765i	$0.745165\pi$
$878$	−26.8298	+	46.4706i	−0.905462	+	1.56831i
$879$		−	25.9923i		−	0.876697i
$880$		0			0
$881$	10.4314	+	18.0677i	0.351442	+	0.608716i	0.986502	−	0.163747i	$-0.0523580\pi$
$881$	10.4314	+	18.0677i	0.351442	+	0.608716i	−0.635060	+	0.772463i	$0.719025\pi$
$882$	−6.45045	−	11.1725i	−0.217198	−	0.376198i
$883$			39.9752i			1.34527i	0.739973	+	0.672637i	$0.234838\pi$
$883$			39.9752i			1.34527i	−0.739973	+	0.672637i	$0.765162\pi$
$884$	−1.69886	−	9.02252i	−0.0571387	−	0.303460i
$885$		0			0
$886$	30.9314	−	17.8583i	1.03916	−	0.599961i
$887$	−8.41420	+	4.85794i	−0.282521	+	0.163114i	−0.634564	−	0.772870i	$-0.718820\pi$
$887$	−8.41420	+	4.85794i	−0.282521	+	0.163114i	0.352043	+	0.935984i	$0.385487\pi$
$888$	−5.61817	−	3.24365i	−0.188533	−	0.108850i
$889$			3.76851i			0.126392i
$890$		0			0
$891$	2.75159	+	1.58863i	0.0921817	+	0.0532211i
$892$	42.2027			1.41305
$893$	26.5591	+	15.3339i	0.888765	+	0.513129i
$894$	−3.84751	−	6.66409i	−0.128680	−	0.222880i
$895$		0			0
$896$	26.2973			0.878531
$897$	4.18092	+	4.86705i	0.139597	+	0.162506i
$898$		−	13.7036i		−	0.457296i
$899$	−61.7049	+	35.6253i	−2.05797	+	1.18817i
$900$		0			0
$901$	−2.06954	+	3.58455i	−0.0689464	+	0.119419i
$902$	−89.7714			−2.98906
$903$	2.12986	−	3.68903i	0.0708774	−	0.122763i
$904$	60.7005	+	35.0454i	2.01887	+	1.16559i
$905$		0			0
$906$	0.205220	−	0.355452i	0.00681799	−	0.0118091i
$907$	8.57040	−	4.94812i	0.284576	−	0.164300i	−0.350917	−	0.936406i	$-0.614130\pi$
$907$	8.57040	−	4.94812i	0.284576	−	0.164300i	0.635493	+	0.772107i	$0.280797\pi$
$908$	−20.6279	−	35.7286i	−0.684561	−	1.18569i
$909$	−2.12546			−0.0704970
$910$		0			0
$911$	−48.9981			−1.62338			−0.811690	−	0.584088i	$-0.801452\pi$
$911$	−48.9981			−1.62338			−0.811690	+	0.584088i	$0.801452\pi$
$912$	4.35022	+	7.53480i	0.144050	+	0.249502i
$913$	39.2565	−	22.6648i	1.29920	−	0.750094i
$914$	6.16628	−	10.6803i	0.203962	−	0.353273i
$915$		0			0
$916$	51.8831	+	29.9547i	1.71427	+	0.989733i
$917$	10.2511	−	17.7554i	0.338520	−	0.586334i
$918$	1.58340			0.0522598
$919$	2.80648	−	4.86096i	0.0925771	−	0.160348i	−0.816018	−	0.578027i	$-0.803823\pi$
$919$	2.80648	−	4.86096i	0.0925771	−	0.160348i	0.908595	+	0.417679i	$0.137156\pi$
$920$		0			0
$921$	−17.9660	+	10.3727i	−0.592001	+	0.341792i
$922$		−	80.4370i		−	2.64905i
$923$	−2.99911	+	2.57632i	−0.0987170	+	0.0848005i
$924$	−16.1614			−0.531670
$925$		0			0
$926$	29.7757	+	51.5731i	0.978492	+	1.69480i
$927$	0.853638	+	0.492848i	0.0280372	+	0.0161873i
$928$	−7.22141			−0.237054
$929$	0.661356	+	0.381834i	0.0216984	+	0.0125276i	0.510810	−	0.859694i	$-0.329346\pi$
$929$	0.661356	+	0.381834i	0.0216984	+	0.0125276i	−0.489112	+	0.872221i	$0.662679\pi$
$930$		0			0
$931$		−	13.3291i		−	0.436844i
$932$	−33.7233	−	19.4702i	−1.10464	−	0.637767i
$933$	1.49490	−	0.863083i	0.0489410	−	0.0282561i
$934$	64.4057	−	37.1847i	2.10742	−	1.21672i
$935$		0			0
$936$	−10.9046	−	12.6941i	−0.356426	−	0.414920i
$937$			23.8968i			0.780674i	0.920672	+	0.390337i	$0.127641\pi$
$937$			23.8968i			0.780674i	−0.920672	+	0.390337i	$0.872359\pi$
$938$	20.8036	+	36.0329i	0.679263	+	1.17652i
$939$	3.14852	+	5.45339i	0.102748	+	0.177965i
$940$		0			0
$941$			5.76615i			0.187971i	0.995574	+	0.0939856i	$0.0299608\pi$
$941$			5.76615i			0.187971i	−0.995574	+	0.0939856i	$0.970039\pi$
$942$	−16.4708	+	28.5283i	−0.536648	+	0.929501i
$943$	10.3418	−	17.9125i	0.336775	−	0.583312i
$944$		−	20.7351i		−	0.674869i
$945$		0			0
$946$	12.6429	+	21.8982i	0.411057	+	0.711972i
$947$	−16.3554	−	28.3284i	−0.531479	−	0.920549i	−0.999325	−	0.0367391i	$-0.988303\pi$
$947$	−16.3554	−	28.3284i	−0.531479	−	0.920549i	0.467845	−	0.883810i	$-0.345030\pi$
$948$			5.20026i			0.168897i
$949$	14.6001	−	41.6062i	0.473940	−	1.35059i
$950$		0			0
$951$	9.15820	−	5.28749i	0.296975	−	0.171459i
$952$	−3.40661	+	1.96681i	−0.110409	+	0.0637446i
$953$	37.5863	+	21.7005i	1.21754	+	0.702947i	0.964391	−	0.264481i	$-0.0852006\pi$
$953$	37.5863	+	21.7005i	1.21754	+	0.702947i	0.253148	+	0.967427i	$0.418534\pi$
$954$			15.4473i			0.500124i
$955$		0			0
$956$	−8.39614	−	4.84751i	−0.271550	−	0.156780i
$957$	26.6232			0.860607
$958$	29.3006	+	16.9167i	0.946659	+	0.546554i
$959$	−0.479952	−	0.831302i	−0.0154985	−	0.0268441i
$960$		0			0
$961$	−41.3041			−1.33239
$962$	7.98269	+	9.29272i	0.257372	+	0.299609i
$963$		−	12.3359i		−	0.397519i
$964$	−96.4032	+	55.6584i	−3.10494	+	1.79264i
$965$		0			0
$966$	2.81432	−	4.87454i	0.0905492	−	0.156836i
$967$	−43.6204			−1.40274			−0.701369	−	0.712798i	$-0.747427\pi$
$967$	−43.6204			−1.40274			−0.701369	+	0.712798i	$0.747427\pi$
$968$	−2.10023	+	3.63770i	−0.0675039	+	0.116920i
$969$	1.41678	+	0.817977i	0.0455135	+	0.0262772i
$970$		0			0
$971$	−18.5097	+	32.0598i	−0.594005	+	1.02885i	0.399682	+	0.916654i	$0.369121\pi$
$971$	−18.5097	+	32.0598i	−0.594005	+	1.02885i	−0.993686	+	0.112193i	$0.964213\pi$
$972$	3.38556	−	1.95466i	0.108592	−	0.0626956i
$973$	12.8467	+	22.2512i	0.411847	+	0.713340i
$974$	74.2682			2.37971
$975$		0			0
$976$	44.9899			1.44009
$977$	−12.5389	−	21.7180i	−0.401155	−	0.694821i	0.592710	−	0.805416i	$-0.298058\pi$
$977$	−12.5389	−	21.7180i	−0.401155	−	0.694821i	−0.993866	+	0.110594i	$0.964725\pi$
$978$	−32.0124	+	18.4824i	−1.02364	+	0.591001i
$979$	−15.2570	+	26.4259i	−0.487616	+	0.844575i
$980$		0			0
$981$	0.753646	+	0.435118i	0.0240621	+	0.0138922i
$982$	−17.8481	+	30.9137i	−0.569554	+	0.986497i
$983$	−21.0019			−0.669857			−0.334928	−	0.942244i	$-0.608712\pi$
$983$	−21.0019			−0.669857			−0.334928	+	0.942244i	$0.608712\pi$
$984$	−26.9732	+	46.7189i	−0.859873	+	1.48934i
$985$		0			0
$986$	11.4902	−	6.63387i	0.365923	−	0.211266i
$987$			15.8875i			0.505706i
$988$	−6.55068	−	34.7902i	−0.208405	−	1.10682i
$989$	−5.82594			−0.185254
$990$		0			0
$991$	−1.51944	−	2.63175i	−0.0482666	−	0.0836003i	0.840883	−	0.541217i	$-0.182036\pi$
$991$	−1.51944	−	2.63175i	−0.0482666	−	0.0836003i	−0.889149	+	0.457617i	$0.848703\pi$
$992$	−6.34638	−	3.66409i	−0.201498	−	0.116335i
$993$	−5.77243			−0.183182
$994$	3.00373	+	1.73420i	0.0952725	+	0.0550056i
$995$		0			0
$996$		−	55.7736i		−	1.76725i
$997$	8.93516	+	5.15872i	0.282979	+	0.163378i	0.634771	−	0.772700i	$-0.281094\pi$
$997$	8.93516	+	5.15872i	0.282979	+	0.163378i	−0.351792	+	0.936078i	$0.614428\pi$
$998$	−33.9970	+	19.6282i	−1.07616	+	0.621319i
$999$	−1.21046	+	0.698857i	−0.0382971	+	0.0221109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.g.49.1		8
5.2	odd	4		195.2.bb.c.166.4	yes	8
5.3	odd	4		975.2.bc.i.751.1		8
5.4	even	2		975.2.w.j.49.4		8
13.4	even	6		975.2.w.j.199.4		8
15.2	even	4		585.2.bu.b.361.1		8
65.2	even	12		2535.2.a.bl.1.4		4
65.4	even	6	inner	975.2.w.g.199.1		8
65.17	odd	12		195.2.bb.c.121.4	✓	8
65.37	even	12		2535.2.a.bi.1.1		4
65.43	odd	12		975.2.bc.i.901.1		8
195.2	odd	12		7605.2.a.cg.1.1		4
195.17	even	12		585.2.bu.b.316.1		8
195.167	odd	12		7605.2.a.ck.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.4	✓	8	65.17	odd	12
195.2.bb.c.166.4	yes	8	5.2	odd	4
585.2.bu.b.316.1		8	195.17	even	12
585.2.bu.b.361.1		8	15.2	even	4
975.2.w.g.49.1		8	1.1	even	1	trivial
975.2.w.g.199.1		8	65.4	even	6	inner
975.2.w.j.49.4		8	5.4	even	2
975.2.w.j.199.4		8	13.4	even	6
975.2.bc.i.751.1		8	5.3	odd	4
975.2.bc.i.901.1		8	65.43	odd	12
2535.2.a.bi.1.1		4	65.37	even	12
2535.2.a.bl.1.4		4	65.2	even	12
7605.2.a.cg.1.1		4	195.2	odd	12
7605.2.a.ck.1.4		4	195.167	odd	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21545 - 2.10523i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.95466 + 3.38556i) q^{4} +(-2.10523 - 1.21545i) q^{6} +(0.650571 - 1.12682i) q^{7} +4.64136 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.21545 - 2.10523i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.95466 + 3.38556i) q^{4} +(-2.10523 - 1.21545i) q^{6} +(0.650571 - 1.12682i) q^{7} +4.64136 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.75159 + 1.58863i) q^{11} +3.90931i q^{12} +(1.19386 - 3.40216i) q^{13} -3.16296 q^{14} +(-1.73205 - 3.00000i) q^{16} +(-0.564094 - 0.325680i) q^{17} -2.43091 q^{18} +(-2.17511 - 1.25580i) q^{19} -1.30114i q^{21} +(6.68886 + 3.86182i) q^{22} +(-1.54113 + 0.889774i) q^{23} +(4.01954 - 2.32068i) q^{24} +(-8.61341 + 1.62182i) q^{26} -1.00000i q^{27} +(2.54329 + 4.40510i) q^{28} +(-4.18965 - 7.25669i) q^{29} -8.50318i q^{31} +(0.430908 - 0.746354i) q^{32} +(-1.58863 + 2.75159i) q^{33} +1.58340i q^{34} +(1.95466 + 3.38556i) q^{36} +(-0.698857 - 1.21046i) q^{37} +6.10547i q^{38} +(-0.667168 - 3.54329i) q^{39} +(-10.0658 + 5.81147i) q^{41} +(-2.73920 + 1.58148i) q^{42} +(2.83522 + 1.63692i) q^{43} -12.4209i q^{44} +(3.74635 + 2.16296i) q^{46} -12.2105 q^{47} +(-3.00000 - 1.73205i) q^{48} +(2.65351 + 4.59602i) q^{49} -0.651360 q^{51} +(9.18465 + 10.6919i) q^{52} -6.35452i q^{53} +(-2.10523 + 1.21545i) q^{54} +(3.01954 - 5.22999i) q^{56} -2.51160 q^{57} +(-10.1847 + 17.6403i) q^{58} +(5.18377 + 2.99285i) q^{59} +(-6.49373 + 11.2475i) q^{61} +(-17.9011 + 10.3352i) q^{62} +(-0.650571 - 1.12682i) q^{63} -9.02320 q^{64} +7.72363 q^{66} +(-6.57727 - 11.3922i) q^{67} +(2.20522 - 1.27318i) q^{68} +(-0.889774 + 1.54113i) q^{69} +(-0.949658 - 0.548286i) q^{71} +(2.32068 - 4.01954i) q^{72} +12.2293 q^{73} +(-1.69886 + 2.94251i) q^{74} +(8.50318 - 4.90931i) q^{76} +4.13407i q^{77} +(-6.64852 + 5.71124i) q^{78} +1.33022 q^{79} +(-0.500000 - 0.866025i) q^{81} +(24.4690 + 14.1272i) q^{82} -14.2668 q^{83} +(4.40510 + 2.54329i) q^{84} -7.95839i q^{86} +(-7.25669 - 4.18965i) q^{87} +(-12.7711 + 7.37341i) q^{88} +(8.31719 - 4.80193i) q^{89} +(-3.05694 - 3.55862i) q^{91} -6.95681i q^{92} +(-4.25159 - 7.36397i) q^{93} +(14.8412 + 25.7058i) q^{94} -0.861816i q^{96} +(3.97341 - 6.88214i) q^{97} +(6.45045 - 11.1725i) q^{98} +3.17726i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 6 q^{13} + 4 q^{14} - 6 q^{17} - 4 q^{18} - 12 q^{19} + 24 q^{22} + 12 q^{24} - 4 q^{26} + 4 q^{28} + 6 q^{29} - 12 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 30 q^{41} - 18 q^{42} - 30 q^{43} + 36 q^{46} - 76 q^{47} - 24 q^{48} + 8 q^{49} + 4 q^{51} + 20 q^{52} - 6 q^{54} + 4 q^{56} - 28 q^{58} + 30 q^{59} - 18 q^{62} - 6 q^{63} - 32 q^{64} - 14 q^{67} + 36 q^{68} - 4 q^{69} + 18 q^{71} + 44 q^{73} - 12 q^{74} - 26 q^{78} - 56 q^{79} - 4 q^{81} + 48 q^{82} - 40 q^{83} - 12 q^{84} - 6 q^{87} - 48 q^{88} + 18 q^{89} - 16 q^{91} + 16 q^{94} + 10 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 6 * q^13 + 4 * q^14 - 6 * q^17 - 4 * q^18 - 12 * q^19 + 24 * q^22 + 12 * q^24 - 4 * q^26 + 4 * q^28 + 6 * q^29 - 12 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 30 * q^41 - 18 * q^42 - 30 * q^43 + 36 * q^46 - 76 * q^47 - 24 * q^48 + 8 * q^49 + 4 * q^51 + 20 * q^52 - 6 * q^54 + 4 * q^56 - 28 * q^58 + 30 * q^59 - 18 * q^62 - 6 * q^63 - 32 * q^64 - 14 * q^67 + 36 * q^68 - 4 * q^69 + 18 * q^71 + 44 * q^73 - 12 * q^74 - 26 * q^78 - 56 * q^79 - 4 * q^81 + 48 * q^82 - 40 * q^83 - 12 * q^84 - 6 * q^87 - 48 * q^88 + 18 * q^89 - 16 * q^91 + 16 * q^94 + 10 * q^97 + 16 * q^98

Introduction

L-functions

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