LMFDB - Embedded newform 550.2.h.f.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(201,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("550.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$550 = 2 \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	550.h (of order $5$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.f.201.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.00000 + 3.07768i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.61803 + 1.90211i) q^{6} +(-0.809017 - 2.48990i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +(-2.54508 + 2.12663i) q^{11} -3.23607 q^{12} +(-1.30902 - 0.951057i) q^{13} +(0.809017 - 2.48990i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-4.23607 + 3.07768i) q^{17} +(-2.30902 - 7.10642i) q^{18} +(-1.26393 + 3.88998i) q^{19} +8.47214 q^{21} +(-3.30902 + 0.224514i) q^{22} -0.145898 q^{23} +(-2.61803 - 1.90211i) q^{24} +(-0.500000 - 1.53884i) q^{26} +(11.7082 - 8.50651i) q^{27} +(2.11803 - 1.53884i) q^{28} +(-0.381966 - 1.17557i) q^{29} +(5.85410 + 4.25325i) q^{31} -1.00000 q^{32} +(-4.00000 - 9.95959i) q^{33} -5.23607 q^{34} +(2.30902 - 7.10642i) q^{36} +(0.263932 + 0.812299i) q^{37} +(-3.30902 + 2.40414i) q^{38} +(4.23607 - 3.07768i) q^{39} +(-0.572949 + 1.76336i) q^{41} +(6.85410 + 4.97980i) q^{42} +9.23607 q^{43} +(-2.80902 - 1.76336i) q^{44} +(-0.118034 - 0.0857567i) q^{46} +(-3.50000 + 10.7719i) q^{47} +(-1.00000 - 3.07768i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(-5.23607 - 16.1150i) q^{51} +(0.500000 - 1.53884i) q^{52} +(0.736068 + 0.534785i) q^{53} +14.4721 q^{54} +2.61803 q^{56} +(-10.7082 - 7.77997i) q^{57} +(0.381966 - 1.17557i) q^{58} +(0.736068 + 2.26538i) q^{59} +(-7.23607 + 5.25731i) q^{61} +(2.23607 + 6.88191i) q^{62} +(-6.04508 + 18.6049i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.61803 - 10.4086i) q^{66} -0.763932 q^{67} +(-4.23607 - 3.07768i) q^{68} +(0.145898 - 0.449028i) q^{69} +(-10.7082 + 7.77997i) q^{71} +(6.04508 - 4.39201i) q^{72} +(0.527864 + 1.62460i) q^{73} +(-0.263932 + 0.812299i) q^{74} -4.09017 q^{76} +(7.35410 + 4.61653i) q^{77} +5.23607 q^{78} +(1.23607 + 0.898056i) q^{79} +(7.54508 + 23.2214i) q^{81} +(-1.50000 + 1.08981i) q^{82} +(12.7082 - 9.23305i) q^{83} +(2.61803 + 8.05748i) q^{84} +(7.47214 + 5.42882i) q^{86} +4.00000 q^{87} +(-1.23607 - 3.07768i) q^{88} -12.0344 q^{89} +(-1.30902 + 4.02874i) q^{91} +(-0.0450850 - 0.138757i) q^{92} +(-18.9443 + 13.7638i) q^{93} +(-9.16312 + 6.65740i) q^{94} +(1.00000 - 3.07768i) q^{96} +(-9.70820 - 7.05342i) q^{97} +0.145898 q^{98} +(24.7254 - 1.67760i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + q^{2} - 4 q^{3} - q^{4} - 6 q^{6} - q^{7} + q^{8} - 13 q^{9} + q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - q^{16} - 8 q^{17} - 7 q^{18} - 14 q^{19} + 16 q^{21} - 11 q^{22} - 14 q^{23} - 6 q^{24}+ \cdots + 43 q^{99}+O(q^{100})$ 4 * q + q^2 - 4 * q^3 - q^4 - 6 * q^6 - q^7 + q^8 - 13 * q^9 + q^11 - 4 * q^12 - 3 * q^13 + q^14 - q^16 - 8 * q^17 - 7 * q^18 - 14 * q^19 + 16 * q^21 - 11 * q^22 - 14 * q^23 - 6 * q^24 - 2 * q^26 + 20 * q^27 + 4 * q^28 - 6 * q^29 + 10 * q^31 - 4 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 + 10 * q^37 - 11 * q^38 + 8 * q^39 - 9 * q^41 + 14 * q^42 + 28 * q^43 - 9 * q^44 + 4 * q^46 - 14 * q^47 - 4 * q^48 - 4 * q^49 - 12 * q^51 + 2 * q^52 - 6 * q^53 + 40 * q^54 + 6 * q^56 - 16 * q^57 + 6 * q^58 - 6 * q^59 - 20 * q^61 - 13 * q^63 - q^64 + 6 * q^66 - 12 * q^67 - 8 * q^68 + 14 * q^69 - 16 * q^71 + 13 * q^72 + 20 * q^73 - 10 * q^74 + 6 * q^76 + 16 * q^77 + 12 * q^78 - 4 * q^79 + 19 * q^81 - 6 * q^82 + 24 * q^83 + 6 * q^84 + 12 * q^86 + 16 * q^87 + 4 * q^88 + 10 * q^89 - 3 * q^91 + 11 * q^92 - 40 * q^93 - 21 * q^94 + 4 * q^96 - 12 * q^97 + 14 * q^98 + 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$ .

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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

)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.00000	+	3.07768i	−0.577350	+	1.77690i	0.0506828	+	0.998715i	$0.483860\pi$
$3$	−1.00000	+	3.07768i	−0.577350	+	1.77690i	−0.628033	+	0.778187i	$0.716140\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−2.61803	+	1.90211i	−1.06881	+	0.776534i
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	−0.979385	−	0.202002i	$-0.935255\pi$
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	0.673605	−	0.739091i	$-0.264745\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$		0			0
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	−3.23607			−0.934172
$13$	−1.30902	−	0.951057i	−0.363056	−	0.263776i	0.391270	−	0.920276i	$-0.372036\pi$
$13$	−1.30902	−	0.951057i	−0.363056	−	0.263776i	−0.754326	+	0.656500i	$0.772036\pi$
$14$	0.809017	−	2.48990i	0.216219	−	0.665453i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.23607	+	3.07768i	−1.02740	+	0.746448i	−0.967786	−	0.251774i	$-0.918986\pi$
$17$	−4.23607	+	3.07768i	−1.02740	+	0.746448i	−0.0596113	+	0.998222i	$0.518986\pi$
$18$	−2.30902	−	7.10642i	−0.544241	−	1.67500i
$19$	−1.26393	+	3.88998i	−0.289966	+	0.892423i	0.694900	+	0.719106i	$0.255449\pi$
$19$	−1.26393	+	3.88998i	−0.289966	+	0.892423i	−0.984866	+	0.173317i	$0.944551\pi$
$20$		0			0
$21$	8.47214			1.84877
$22$	−3.30902	+	0.224514i	−0.705485	+	0.0478665i
$23$	−0.145898			−0.0304218			−0.0152109	−	0.999884i	$-0.504842\pi$
$23$	−0.145898			−0.0304218			−0.0152109	+	0.999884i	$0.504842\pi$
$24$	−2.61803	−	1.90211i	−0.534404	−	0.388267i
$25$		0			0
$26$	−0.500000	−	1.53884i	−0.0980581	−	0.301792i
$27$	11.7082	−	8.50651i	2.25324	−	1.63708i
$28$	2.11803	−	1.53884i	0.400271	−	0.290814i
$29$	−0.381966	−	1.17557i	−0.0709293	−	0.218298i	0.909308	−	0.416124i	$-0.136612\pi$
$29$	−0.381966	−	1.17557i	−0.0709293	−	0.218298i	−0.980237	+	0.197826i	$0.936612\pi$
$30$		0			0
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.972483	−	0.232972i	$-0.0748451\pi$
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.0789443	+	0.996879i	$0.474845\pi$
$32$	−1.00000			−0.176777
$33$	−4.00000	−	9.95959i	−0.696311	−	1.73374i
$34$	−5.23607			−0.897978
$35$		0			0
$36$	2.30902	−	7.10642i	0.384836	−	1.18440i
$37$	0.263932	+	0.812299i	0.0433902	+	0.133541i	0.970405	−	0.241484i	$-0.0776341\pi$
$37$	0.263932	+	0.812299i	0.0433902	+	0.133541i	−0.927015	+	0.375025i	$0.877634\pi$
$38$	−3.30902	+	2.40414i	−0.536793	+	0.390003i
$39$	4.23607	−	3.07768i	0.678314	−	0.492824i
$40$		0			0
$41$	−0.572949	+	1.76336i	−0.0894796	+	0.275390i	−0.985776	−	0.168066i	$-0.946248\pi$
$41$	−0.572949	+	1.76336i	−0.0894796	+	0.275390i	0.896296	+	0.443456i	$0.146248\pi$
$42$	6.85410	+	4.97980i	1.05761	+	0.768399i
$43$	9.23607			1.40849			0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607			1.40849			0.704244	+	0.709958i	$0.251286\pi$
$44$	−2.80902	−	1.76336i	−0.423475	−	0.265836i
$45$		0			0
$46$	−0.118034	−	0.0857567i	−0.0174032	−	0.0126441i
$47$	−3.50000	+	10.7719i	−0.510527	+	1.57124i	0.280748	+	0.959782i	$0.409418\pi$
$47$	−3.50000	+	10.7719i	−0.510527	+	1.57124i	−0.791275	+	0.611460i	$0.790582\pi$
$48$	−1.00000	−	3.07768i	−0.144338	−	0.444225i
$49$	0.118034	−	0.0857567i	0.0168620	−	0.0122510i
$50$		0			0
$51$	−5.23607	−	16.1150i	−0.733196	−	2.25655i
$52$	0.500000	−	1.53884i	0.0693375	−	0.213399i
$53$	0.736068	+	0.534785i	0.101107	+	0.0734583i	0.637190	−	0.770707i	$-0.280097\pi$
$53$	0.736068	+	0.534785i	0.101107	+	0.0734583i	−0.536083	+	0.844165i	$0.680097\pi$
$54$	14.4721			1.96941
$55$		0			0
$56$	2.61803			0.349850
$57$	−10.7082	−	7.77997i	−1.41834	−	1.03048i
$58$	0.381966	−	1.17557i	0.0501546	−	0.154360i
$59$	0.736068	+	2.26538i	0.0958279	+	0.294928i	0.987469	−	0.157816i	$-0.0504452\pi$
$59$	0.736068	+	2.26538i	0.0958279	+	0.294928i	−0.891641	+	0.452744i	$0.850445\pi$
$60$		0			0
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	−0.945129	−	0.326696i	$-0.894065\pi$
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	0.0186458	+	0.999826i	$0.494065\pi$
$62$	2.23607	+	6.88191i	0.283981	+	0.874003i
$63$	−6.04508	+	18.6049i	−0.761609	+	2.34399i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	2.61803	−	10.4086i	0.322258	−	1.28121i
$67$	−0.763932			−0.0933292			−0.0466646	−	0.998911i	$-0.514859\pi$
$67$	−0.763932			−0.0933292			−0.0466646	+	0.998911i	$0.514859\pi$
$68$	−4.23607	−	3.07768i	−0.513699	−	0.373224i
$69$	0.145898	−	0.449028i	0.0175641	−	0.0540566i
$70$		0			0
$71$	−10.7082	+	7.77997i	−1.27083	+	0.923312i	−0.999235	−	0.0390997i	$-0.987551\pi$
$71$	−10.7082	+	7.77997i	−1.27083	+	0.923312i	−0.271595	+	0.962412i	$0.587551\pi$
$72$	6.04508	−	4.39201i	0.712420	−	0.517603i
$73$	0.527864	+	1.62460i	0.0617818	+	0.190145i	0.977184	−	0.212397i	$-0.0681269\pi$
$73$	0.527864	+	1.62460i	0.0617818	+	0.190145i	−0.915402	+	0.402542i	$0.868127\pi$
$74$	−0.263932	+	0.812299i	−0.0306815	+	0.0944279i
$75$		0			0
$76$	−4.09017			−0.469175
$77$	7.35410	+	4.61653i	0.838078	+	0.526102i
$78$	5.23607			0.592868
$79$	1.23607	+	0.898056i	0.139069	+	0.101039i	0.655144	−	0.755504i	$-0.272608\pi$
$79$	1.23607	+	0.898056i	0.139069	+	0.101039i	−0.516076	+	0.856543i	$0.672608\pi$
$80$		0			0
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$	−1.50000	+	1.08981i	−0.165647	+	0.120350i
$83$	12.7082	−	9.23305i	1.39491	−	1.01346i	0.399600	−	0.916690i	$-0.369149\pi$
$83$	12.7082	−	9.23305i	1.39491	−	1.01346i	0.995307	−	0.0967693i	$-0.0308509\pi$
$84$	2.61803	+	8.05748i	0.285651	+	0.879143i
$85$		0			0
$86$	7.47214	+	5.42882i	0.805741	+	0.585405i
$87$	4.00000			0.428845
$88$	−1.23607	−	3.07768i	−0.131765	−	0.328082i
$89$	−12.0344			−1.27565			−0.637824	−	0.770182i	$-0.720165\pi$
$89$	−12.0344			−1.27565			−0.637824	+	0.770182i	$0.720165\pi$
$90$		0			0
$91$	−1.30902	+	4.02874i	−0.137222	+	0.422327i
$92$	−0.0450850	−	0.138757i	−0.00470043	−	0.0144664i
$93$	−18.9443	+	13.7638i	−1.96443	+	1.42724i
$94$	−9.16312	+	6.65740i	−0.945104	+	0.686658i
$95$		0			0
$96$	1.00000	−	3.07768i	0.102062	−	0.314115i
$97$	−9.70820	−	7.05342i	−0.985719	−	0.716167i	−0.0267394	−	0.999642i	$-0.508512\pi$
$97$	−9.70820	−	7.05342i	−0.985719	−	0.716167i	−0.958979	+	0.283476i	$0.908512\pi$
$98$	0.145898			0.0147379
$99$	24.7254	−	1.67760i	2.48500	−	0.168605i
$100$		0			0
$101$	−3.00000	−	2.17963i	−0.298511	−	0.216881i	0.428440	−	0.903570i	$-0.359063\pi$
$101$	−3.00000	−	2.17963i	−0.298511	−	0.216881i	−0.726951	+	0.686689i	$0.759063\pi$
$102$	5.23607	−	16.1150i	0.518448	−	1.59562i
$103$	3.50000	+	10.7719i	0.344865	+	1.06139i	0.961656	+	0.274259i	$0.0884325\pi$
$103$	3.50000	+	10.7719i	0.344865	+	1.06139i	−0.616791	+	0.787127i	$0.711567\pi$
$104$	1.30902	−	0.951057i	0.128360	−	0.0932588i
$105$		0			0
$106$	0.281153	+	0.865300i	0.0273080	+	0.0840453i
$107$	2.32624	−	7.15942i	0.224886	−	0.692128i	−0.773417	−	0.633897i	$-0.781454\pi$
$107$	2.32624	−	7.15942i	0.224886	−	0.692128i	0.998303	−	0.0582304i	$-0.0185458\pi$
$108$	11.7082	+	8.50651i	1.12662	+	0.818539i
$109$	7.52786			0.721039			0.360519	−	0.932752i	$-0.382599\pi$
$109$	7.52786			0.721039			0.360519	+	0.932752i	$0.382599\pi$
$110$		0			0
$111$	−2.76393			−0.262341
$112$	2.11803	+	1.53884i	0.200135	+	0.145407i
$113$	−1.94427	+	5.98385i	−0.182902	+	0.562914i	−0.999906	−	0.0137181i	$-0.995633\pi$
$113$	−1.94427	+	5.98385i	−0.182902	+	0.562914i	0.817004	+	0.576632i	$0.195633\pi$
$114$	−4.09017	−	12.5882i	−0.383080	−	1.17900i
$115$		0			0
$116$	1.00000	−	0.726543i	0.0928477	−	0.0674578i
$117$	3.73607	+	11.4984i	0.345400	+	1.06303i
$118$	−0.736068	+	2.26538i	−0.0677605	+	0.208546i
$119$	11.0902	+	8.05748i	1.01663	+	0.738628i
$120$		0			0
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	−8.94427			−0.809776
$123$	−4.85410	−	3.52671i	−0.437680	−	0.317993i
$124$	−2.23607	+	6.88191i	−0.200805	+	0.618014i
$125$		0			0
$126$	−15.8262	+	11.4984i	−1.40991	+	1.02436i
$127$	−1.92705	+	1.40008i	−0.170998	+	0.124237i	−0.669993	−	0.742368i	$-0.733703\pi$
$127$	−1.92705	+	1.40008i	−0.170998	+	0.124237i	0.498995	+	0.866605i	$0.333703\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−9.23607	+	28.4257i	−0.813190	+	2.50274i
$130$		0			0
$131$	11.4164			0.997456			0.498728	−	0.866758i	$-0.333801\pi$
$131$	11.4164			0.997456			0.498728	+	0.866758i	$0.333801\pi$
$132$	8.23607	−	6.88191i	0.716858	−	0.598993i
$133$	10.7082			0.928519
$134$	−0.618034	−	0.449028i	−0.0533900	−	0.0387901i
$135$		0			0
$136$	−1.61803	−	4.97980i	−0.138745	−	0.427014i
$137$	−4.23607	+	3.07768i	−0.361912	+	0.262944i	−0.753849	−	0.657048i	$-0.771805\pi$
$137$	−4.23607	+	3.07768i	−0.361912	+	0.262944i	0.391937	+	0.919992i	$0.371805\pi$
$138$	0.381966	−	0.277515i	0.0325151	−	0.0236236i
$139$	−2.51722	−	7.74721i	−0.213508	−	0.657110i	−0.999256	−	0.0385633i	$-0.987722\pi$
$139$	−2.51722	−	7.74721i	−0.213508	−	0.657110i	0.785748	−	0.618546i	$-0.212278\pi$
$140$		0			0
$141$	−29.6525	−	21.5438i	−2.49719	−	1.81431i
$142$	−13.2361			−1.11075
$143$	5.35410	−	0.363271i	0.447732	−	0.0303783i
$144$	7.47214			0.622678
$145$		0			0
$146$	−0.527864	+	1.62460i	−0.0436863	+	0.134453i
$147$	0.145898	+	0.449028i	0.0120335	+	0.0370352i
$148$	−0.690983	+	0.502029i	−0.0567985	+	0.0412665i
$149$	3.23607	−	2.35114i	0.265109	−	0.192613i	−0.447287	−	0.894390i	$-0.647610\pi$
$149$	3.23607	−	2.35114i	0.265109	−	0.192613i	0.712396	+	0.701777i	$0.247610\pi$
$150$		0			0
$151$	3.90983	−	12.0332i	0.318177	−	0.979250i	−0.656249	−	0.754544i	$-0.727858\pi$
$151$	3.90983	−	12.0332i	0.318177	−	0.979250i	0.974427	−	0.224705i	$-0.0721420\pi$
$152$	−3.30902	−	2.40414i	−0.268397	−	0.195002i
$153$	39.1246			3.16304
$154$	3.23607	+	8.05748i	0.260770	+	0.649290i
$155$		0			0
$156$	4.23607	+	3.07768i	0.339157	+	0.246412i
$157$	−2.66312	+	8.19624i	−0.212540	+	0.654131i	0.786779	+	0.617235i	$0.211747\pi$
$157$	−2.66312	+	8.19624i	−0.212540	+	0.654131i	−0.999319	+	0.0368962i	$0.988253\pi$
$158$	0.472136	+	1.45309i	0.0375611	+	0.115601i
$159$	−2.38197	+	1.73060i	−0.188902	+	0.137245i
$160$		0			0
$161$	0.118034	+	0.363271i	0.00930238	+	0.0286298i
$162$	−7.54508	+	23.2214i	−0.592798	+	1.82444i
$163$	−5.85410	−	4.25325i	−0.458529	−	0.333141i	0.334425	−	0.942422i	$-0.391458\pi$
$163$	−5.85410	−	4.25325i	−0.458529	−	0.333141i	−0.792954	+	0.609282i	$0.791458\pi$
$164$	−1.85410			−0.144781
$165$		0			0
$166$	15.7082			1.21919
$167$	6.39919	+	4.64928i	0.495184	+	0.359772i	0.807174	−	0.590313i	$-0.200996\pi$
$167$	6.39919	+	4.64928i	0.495184	+	0.359772i	−0.311990	+	0.950085i	$0.600996\pi$
$168$	−2.61803	+	8.05748i	−0.201986	+	0.621648i
$169$	−3.20820	−	9.87384i	−0.246785	−	0.759526i
$170$		0			0
$171$	24.7254	−	17.9641i	1.89080	−	1.37375i
$172$	2.85410	+	8.78402i	0.217623	+	0.669775i
$173$	3.89919	−	12.0005i	0.296450	−	0.912378i	−0.686281	−	0.727337i	$-0.740758\pi$
$173$	3.89919	−	12.0005i	0.296450	−	0.912378i	0.982731	−	0.185042i	$-0.0592421\pi$
$174$	3.23607	+	2.35114i	0.245326	+	0.178240i
$175$		0			0
$176$	0.809017	−	3.21644i	0.0609820	−	0.242448i
$177$	−7.70820			−0.579384
$178$	−9.73607	−	7.07367i	−0.729749	−	0.530194i
$179$	−0.899187	+	2.76741i	−0.0672084	+	0.206846i	−0.979021	−	0.203761i	$-0.934683\pi$
$179$	−0.899187	+	2.76741i	−0.0672084	+	0.206846i	0.911812	+	0.410607i	$0.134683\pi$
$180$		0			0
$181$	16.5623	−	12.0332i	1.23107	−	0.894422i	0.234097	−	0.972213i	$-0.424787\pi$
$181$	16.5623	−	12.0332i	1.23107	−	0.894422i	0.996970	+	0.0777911i	$0.0247867\pi$
$182$	−3.42705	+	2.48990i	−0.254030	+	0.184564i
$183$	−8.94427	−	27.5276i	−0.661180	−	2.03490i
$184$	0.0450850	−	0.138757i	0.00332371	−	0.0102293i
$185$		0			0
$186$	−23.4164			−1.71697
$187$	4.23607	−	16.8415i	0.309772	−	1.23157i
$188$	−11.3262			−0.826051
$189$	−30.6525	−	22.2703i	−2.22964	−	1.61993i
$190$		0			0
$191$	7.85410	+	24.1724i	0.568303	+	1.74906i	0.657928	+	0.753081i	$0.271433\pi$
$191$	7.85410	+	24.1724i	0.568303	+	1.74906i	−0.0896251	+	0.995976i	$0.528567\pi$
$192$	2.61803	−	1.90211i	0.188940	−	0.137273i
$193$	−4.38197	+	3.18368i	−0.315421	+	0.229167i	−0.734219	−	0.678913i	$-0.762451\pi$
$193$	−4.38197	+	3.18368i	−0.315421	+	0.229167i	0.418798	+	0.908079i	$0.362451\pi$
$194$	−3.70820	−	11.4127i	−0.266234	−	0.819383i
$195$		0			0
$196$	0.118034	+	0.0857567i	0.00843100	+	0.00612548i
$197$	4.90983			0.349811			0.174905	−	0.984585i	$-0.444038\pi$
$197$	4.90983			0.349811			0.174905	+	0.984585i	$0.444038\pi$
$198$	20.9894	+	13.1760i	1.49165	+	0.936380i
$199$	1.70820			0.121091			0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820			0.121091			0.0605457	+	0.998165i	$0.480716\pi$
$200$		0			0
$201$	0.763932	−	2.35114i	0.0538836	−	0.165837i
$202$	−1.14590	−	3.52671i	−0.0806251	−	0.248139i
$203$	−2.61803	+	1.90211i	−0.183750	+	0.133502i
$204$	13.7082	−	9.95959i	0.959766	−	0.697311i
$205$		0			0
$206$	−3.50000	+	10.7719i	−0.243857	+	0.750513i
$207$	0.881966	+	0.640786i	0.0613009	+	0.0445377i
$208$	1.61803			0.112190
$209$	−5.05573	−	12.5882i	−0.349712	−	0.870747i
$210$		0			0
$211$	−16.9443	−	12.3107i	−1.16649	−	0.847506i	−0.175907	−	0.984407i	$-0.556286\pi$
$211$	−16.9443	−	12.3107i	−1.16649	−	0.847506i	−0.990585	+	0.136901i	$0.956286\pi$
$212$	−0.281153	+	0.865300i	−0.0193097	+	0.0594290i
$213$	−13.2361	−	40.7364i	−0.906920	−	2.79121i
$214$	6.09017	−	4.42477i	0.416315	−	0.302471i
$215$		0			0
$216$	4.47214	+	13.7638i	0.304290	+	0.936509i
$217$	5.85410	−	18.0171i	0.397402	−	1.22308i
$218$	6.09017	+	4.42477i	0.412478	+	0.299683i
$219$	−5.52786			−0.373538
$220$		0			0
$221$	8.47214			0.569898
$222$	−2.23607	−	1.62460i	−0.150075	−	0.109036i
$223$	−2.98936	+	9.20029i	−0.200182	+	0.616097i	0.799695	+	0.600407i	$0.204995\pi$
$223$	−2.98936	+	9.20029i	−0.200182	+	0.616097i	−0.999877	+	0.0156905i	$0.995005\pi$
$224$	0.809017	+	2.48990i	0.0540547	+	0.166363i
$225$		0			0
$226$	−5.09017	+	3.69822i	−0.338593	+	0.246002i
$227$	5.09017	+	15.6659i	0.337846	+	1.03978i	0.965303	+	0.261133i	$0.0840960\pi$
$227$	5.09017	+	15.6659i	0.337846	+	1.03978i	−0.627456	+	0.778652i	$0.715904\pi$
$228$	4.09017	−	12.5882i	0.270878	−	0.833677i
$229$	22.7984	+	16.5640i	1.50656	+	1.09458i	0.967675	+	0.252199i	$0.0811537\pi$
$229$	22.7984	+	16.5640i	1.50656	+	1.09458i	0.538884	+	0.842380i	$0.318846\pi$
$230$		0			0
$231$	−21.5623	+	18.0171i	−1.41870	+	1.18544i
$232$	1.23607			0.0811518
$233$	12.3262	+	8.95554i	0.807519	+	0.586697i	0.913110	−	0.407713i	$-0.133674\pi$
$233$	12.3262	+	8.95554i	0.807519	+	0.586697i	−0.105591	+	0.994410i	$0.533674\pi$
$234$	−3.73607	+	11.4984i	−0.244234	+	0.751676i
$235$		0			0
$236$	−1.92705	+	1.40008i	−0.125440	+	0.0911377i
$237$	−4.00000	+	2.90617i	−0.259828	+	0.188776i
$238$	4.23607	+	13.0373i	0.274584	+	0.845081i
$239$	2.94427	−	9.06154i	0.190449	−	0.586142i	−0.809550	−	0.587050i	$-0.800289\pi$
$239$	2.94427	−	9.06154i	0.190449	−	0.586142i	1.00000		0.000908170i	$0.000289080\pi$
$240$		0			0
$241$	−1.85410			−0.119433			−0.0597166	−	0.998215i	$-0.519020\pi$
$241$	−1.85410			−0.119433			−0.0597166	+	0.998215i	$0.519020\pi$
$242$	7.94427	−	7.60845i	0.510677	−	0.489090i
$243$	−35.5967			−2.28353
$244$	−7.23607	−	5.25731i	−0.463242	−	0.336565i
$245$		0			0
$246$	−1.85410	−	5.70634i	−0.118213	−	0.363823i
$247$	5.35410	−	3.88998i	0.340673	−	0.247514i
$248$	−5.85410	+	4.25325i	−0.371736	+	0.270082i
$249$	15.7082	+	48.3449i	0.995467	+	3.06373i
$250$		0			0
$251$	8.11803	+	5.89810i	0.512406	+	0.372285i	0.813735	−	0.581235i	$-0.197430\pi$
$251$	8.11803	+	5.89810i	0.512406	+	0.372285i	−0.301330	+	0.953520i	$0.597430\pi$
$252$	−19.5623			−1.23231
$253$	0.371323	−	0.310271i	0.0233449	−	0.0195066i
$254$	−2.38197			−0.149458
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.70820	+	11.4127i	0.231311	+	0.711903i	0.997589	+	0.0693940i	$0.0221066\pi$
$257$	3.70820	+	11.4127i	0.231311	+	0.711903i	−0.766278	+	0.642509i	$0.777893\pi$
$258$	−24.1803	+	17.5680i	−1.50540	+	1.09374i
$259$	1.80902	−	1.31433i	0.112407	−	0.0816684i
$260$		0			0
$261$	−2.85410	+	8.78402i	−0.176664	+	0.543717i
$262$	9.23607	+	6.71040i	0.570606	+	0.414570i
$263$	−25.7984			−1.59080			−0.795398	−	0.606088i	$-0.792738\pi$
$263$	−25.7984			−1.59080			−0.795398	+	0.606088i	$0.792738\pi$
$264$	10.7082	−	0.726543i	0.659044	−	0.0447156i
$265$		0			0
$266$	8.66312	+	6.29412i	0.531170	+	0.385918i
$267$	12.0344	−	37.0382i	0.736496	−	2.26670i
$268$	−0.236068	−	0.726543i	−0.0144201	−	0.0443806i
$269$	−14.2361	+	10.3431i	−0.867988	+	0.630630i	−0.930046	−	0.367442i	$-0.880234\pi$
$269$	−14.2361	+	10.3431i	−0.867988	+	0.630630i	0.0620580	+	0.998073i	$0.480234\pi$
$270$		0			0
$271$	4.14590	+	12.7598i	0.251845	+	0.775100i	0.994435	+	0.105353i	$0.0335974\pi$
$271$	4.14590	+	12.7598i	0.251845	+	0.775100i	−0.742589	+	0.669747i	$0.766403\pi$
$272$	1.61803	−	4.97980i	0.0981077	−	0.301945i
$273$	−11.0902	−	8.05748i	−0.671208	−	0.487661i
$274$	−5.23607			−0.316322
$275$		0			0
$276$	0.472136			0.0284192
$277$	−0.500000	−	0.363271i	−0.0300421	−	0.0218269i	0.572663	−	0.819791i	$-0.305910\pi$
$277$	−0.500000	−	0.363271i	−0.0300421	−	0.0218269i	−0.602705	+	0.797964i	$0.705910\pi$
$278$	2.51722	−	7.74721i	0.150973	−	0.464647i
$279$	−16.7082	−	51.4226i	−1.00029	−	3.07859i
$280$		0			0
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	−0.930242	−	0.366947i	$-0.880403\pi$
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	0.0615273	+	0.998105i	$0.480403\pi$
$282$	−11.3262	−	34.8586i	−0.674468	−	2.07580i
$283$	−7.67376	+	23.6174i	−0.456158	+	1.40391i	0.413613	+	0.910453i	$0.364267\pi$
$283$	−7.67376	+	23.6174i	−0.456158	+	1.40391i	−0.869771	+	0.493456i	$0.835733\pi$
$284$	−10.7082	−	7.77997i	−0.635415	−	0.461656i
$285$		0			0
$286$	4.54508	+	2.85317i	0.268757	+	0.168711i
$287$	4.85410			0.286529
$288$	6.04508	+	4.39201i	0.356210	+	0.258802i
$289$	3.21885	−	9.90659i	0.189344	−	0.582741i
$290$		0			0
$291$	31.4164	−	22.8254i	1.84166	−	1.33805i
$292$	−1.38197	+	1.00406i	−0.0808734	+	0.0587580i
$293$	7.33688	+	22.5806i	0.428625	+	1.31917i	0.899480	+	0.436962i	$0.143946\pi$
$293$	7.33688	+	22.5806i	0.428625	+	1.31917i	−0.470855	+	0.882211i	$0.656054\pi$
$294$	−0.145898	+	0.449028i	−0.00850895	+	0.0261878i
$295$		0			0
$296$	−0.854102			−0.0496437
$297$	−11.7082	+	46.5488i	−0.679379	+	2.70103i
$298$	4.00000			0.231714
$299$	0.190983	+	0.138757i	0.0110448	+	0.00802454i
$300$		0			0
$301$	−7.47214	−	22.9969i	−0.430687	−	1.32552i
$302$	10.2361	−	7.43694i	0.589020	−	0.427948i
$303$	9.70820	−	7.05342i	0.557722	−	0.405209i
$304$	−1.26393	−	3.88998i	−0.0724915	−	0.223106i
$305$		0			0
$306$	31.6525	+	22.9969i	1.80945	+	1.31464i
$307$	26.9443			1.53779			0.768895	−	0.639375i	$-0.220807\pi$
$307$	26.9443			1.53779			0.768895	+	0.639375i	$0.220807\pi$
$308$	−2.11803	+	8.42075i	−0.120686	+	0.479817i
$309$	−36.6525			−2.08509
$310$		0			0
$311$	−0.763932	+	2.35114i	−0.0433186	+	0.133321i	−0.970377	−	0.241597i	$-0.922329\pi$
$311$	−0.763932	+	2.35114i	−0.0433186	+	0.133321i	0.927058	+	0.374917i	$0.122329\pi$
$312$	1.61803	+	4.97980i	0.0916031	+	0.281925i
$313$	22.1803	−	16.1150i	1.25371	−	0.910871i	0.255276	−	0.966868i	$-0.417834\pi$
$313$	22.1803	−	16.1150i	1.25371	−	0.910871i	0.998431	+	0.0559968i	$0.0178337\pi$
$314$	−6.97214	+	5.06555i	−0.393460	+	0.285866i
$315$		0			0
$316$	−0.472136	+	1.45309i	−0.0265597	+	0.0817424i
$317$	5.01722	+	3.64522i	0.281795	+	0.204736i	0.719700	−	0.694285i	$-0.244279\pi$
$317$	5.01722	+	3.64522i	0.281795	+	0.204736i	−0.437905	+	0.899021i	$0.644279\pi$
$318$	−2.94427			−0.165107
$319$	3.47214	+	2.17963i	0.194402	+	0.122036i
$320$		0			0
$321$	19.7082	+	14.3188i	1.10000	+	0.799200i
$322$	−0.118034	+	0.363271i	−0.00657778	+	0.0202443i
$323$	−6.61803	−	20.3682i	−0.368237	−	1.13332i
$324$	−19.7533	+	14.3516i	−1.09740	+	0.797311i
$325$		0			0
$326$	−2.23607	−	6.88191i	−0.123844	−	0.381154i
$327$	−7.52786	+	23.1684i	−0.416292	+	1.28121i
$328$	−1.50000	−	1.08981i	−0.0828236	−	0.0601749i
$329$	29.6525			1.63479
$330$		0			0
$331$	−14.3820			−0.790504			−0.395252	−	0.918573i	$-0.629343\pi$
$331$	−14.3820			−0.790504			−0.395252	+	0.918573i	$0.629343\pi$
$332$	12.7082	+	9.23305i	0.697453	+	0.506729i
$333$	1.97214	−	6.06961i	0.108072	−	0.332613i
$334$	2.44427	+	7.52270i	0.133745	+	0.411624i
$335$		0			0
$336$	−6.85410	+	4.97980i	−0.373922	+	0.271670i
$337$	−10.9443	−	33.6830i	−0.596172	−	1.83483i	−0.548801	−	0.835953i	$-0.684916\pi$
$337$	−10.9443	−	33.6830i	−0.596172	−	1.83483i	−0.0473712	−	0.998877i	$-0.515084\pi$
$338$	3.20820	−	9.87384i	0.174503	−	0.537066i
$339$	−16.4721	−	11.9677i	−0.894644	−	0.649997i
$340$		0			0
$341$	−23.9443	+	1.62460i	−1.29666	+	0.0879769i
$342$	30.5623			1.65262
$343$	−15.1353	−	10.9964i	−0.817227	−	0.593750i
$344$	−2.85410	+	8.78402i	−0.153883	+	0.473603i
$345$		0			0
$346$	10.2082	−	7.41669i	0.548796	−	0.398724i
$347$	−21.9443	+	15.9434i	−1.17803	+	0.855889i	−0.991948	−	0.126645i	$-0.959579\pi$
$347$	−21.9443	+	15.9434i	−1.17803	+	0.855889i	−0.186082	+	0.982534i	$0.559579\pi$
$348$	1.23607	+	3.80423i	0.0662602	+	0.203928i
$349$	9.56231	−	29.4298i	0.511858	−	1.57534i	−0.277068	−	0.960850i	$-0.589363\pi$
$349$	9.56231	−	29.4298i	0.511858	−	1.57534i	0.788926	−	0.614488i	$-0.210637\pi$
$350$		0			0
$351$	−23.4164			−1.24988
$352$	2.54508	−	2.12663i	0.135653	−	0.113350i
$353$	−11.7082			−0.623165			−0.311582	−	0.950219i	$-0.600859\pi$
$353$	−11.7082			−0.623165			−0.311582	+	0.950219i	$0.600859\pi$
$354$	−6.23607	−	4.53077i	−0.331443	−	0.240808i
$355$		0			0
$356$	−3.71885	−	11.4454i	−0.197098	−	0.606607i
$357$	−35.8885	+	26.0746i	−1.89942	+	1.38001i
$358$	−2.35410	+	1.71036i	−0.124418	+	0.0903951i
$359$	−9.41641	−	28.9807i	−0.496979	−	1.52954i	−0.813850	−	0.581075i	$-0.802632\pi$
$359$	−9.41641	−	28.9807i	−0.496979	−	1.52954i	0.316871	−	0.948469i	$-0.397368\pi$
$360$		0			0
$361$	1.83688	+	1.33457i	0.0966779	+	0.0702406i
$362$	20.4721			1.07599
$363$	31.3607	+	16.8415i	1.64601	+	0.883950i
$364$	−4.23607			−0.222030
$365$		0			0
$366$	8.94427	−	27.5276i	0.467525	−	1.43889i
$367$	−3.23607	−	9.95959i	−0.168921	−	0.519887i	0.830382	−	0.557194i	$-0.188122\pi$
$367$	−3.23607	−	9.95959i	−0.168921	−	0.519887i	−0.999304	+	0.0373073i	$0.988122\pi$
$368$	0.118034	−	0.0857567i	0.00615295	−	0.00447038i
$369$	11.2082	−	8.14324i	0.583476	−	0.423920i
$370$		0			0
$371$	0.736068	−	2.26538i	0.0382147	−	0.117613i
$372$	−18.9443	−	13.7638i	−0.982215	−	0.713621i
$373$	−6.96556			−0.360663			−0.180331	−	0.983606i	$-0.557717\pi$
$373$	−6.96556			−0.360663			−0.180331	+	0.983606i	$0.557717\pi$
$374$	13.3262	−	11.1352i	0.689083	−	0.575786i
$375$		0			0
$376$	−9.16312	−	6.65740i	−0.472552	−	0.343329i
$377$	−0.618034	+	1.90211i	−0.0318304	+	0.0979638i
$378$	−11.7082	−	36.0341i	−0.602205	−	1.85340i
$379$	8.35410	−	6.06961i	0.429121	−	0.311775i	−0.352176	−	0.935934i	$-0.614558\pi$
$379$	8.35410	−	6.06961i	0.429121	−	0.311775i	0.781297	+	0.624159i	$0.214558\pi$
$380$		0			0
$381$	−2.38197	−	7.33094i	−0.122032	−	0.375575i
$382$	−7.85410	+	24.1724i	−0.401851	+	1.23677i
$383$	−12.8262	−	9.31881i	−0.655390	−	0.476169i	0.209713	−	0.977763i	$-0.432747\pi$
$383$	−12.8262	−	9.31881i	−0.655390	−	0.476169i	−0.865103	+	0.501594i	$0.832747\pi$
$384$	3.23607			0.165140
$385$		0			0
$386$	−5.41641			−0.275688
$387$	−55.8328	−	40.5649i	−2.83814	−	2.06203i
$388$	3.70820	−	11.4127i	0.188256	−	0.579391i
$389$	3.76393	+	11.5842i	0.190839	+	0.587342i	1.00000		0.000245108i	$-7.80203e-5\pi$
$389$	3.76393	+	11.5842i	0.190839	+	0.587342i	−0.809161	+	0.587587i	$0.800078\pi$
$390$		0			0
$391$	0.618034	−	0.449028i	0.0312553	−	0.0227083i
$392$	0.0450850	+	0.138757i	0.00227713	+	0.00700830i
$393$	−11.4164	+	35.1361i	−0.575882	+	1.77238i
$394$	3.97214	+	2.88593i	0.200113	+	0.145391i
$395$		0			0
$396$	9.23607	+	22.9969i	0.464130	+	1.15564i
$397$	−6.79837			−0.341201			−0.170600	−	0.985340i	$-0.554571\pi$
$397$	−6.79837			−0.341201			−0.170600	+	0.985340i	$0.554571\pi$
$398$	1.38197	+	1.00406i	0.0692717	+	0.0503288i
$399$	−10.7082	+	32.9565i	−0.536081	+	1.64989i
$400$		0			0
$401$	8.69098	−	6.31437i	0.434007	−	0.315325i	−0.349242	−	0.937033i	$-0.613561\pi$
$401$	8.69098	−	6.31437i	0.434007	−	0.315325i	0.783249	+	0.621708i	$0.213561\pi$
$402$	2.00000	−	1.45309i	0.0997509	−	0.0724733i
$403$	−3.61803	−	11.1352i	−0.180227	−	0.554682i
$404$	1.14590	−	3.52671i	0.0570106	−	0.175460i
$405$		0			0
$406$	−3.23607			−0.160603
$407$	−2.39919	−	1.50609i	−0.118923	−	0.0746539i
$408$	16.9443			0.838866
$409$	18.8713	+	13.7108i	0.933127	+	0.677956i	0.946756	−	0.321951i	$-0.104339\pi$
$409$	18.8713	+	13.7108i	0.933127	+	0.677956i	−0.0136296	+	0.999907i	$0.504339\pi$
$410$		0			0
$411$	−5.23607	−	16.1150i	−0.258276	−	0.794892i
$412$	−9.16312	+	6.65740i	−0.451434	+	0.327986i
$413$	5.04508	−	3.66547i	0.248252	−	0.180366i
$414$	0.336881	+	1.03681i	0.0165568	+	0.0509566i
$415$		0			0
$416$	1.30902	+	0.951057i	0.0641798	+	0.0466294i
$417$	26.3607			1.29089
$418$	3.30902	−	13.1558i	0.161849	−	0.643471i
$419$	−1.61803			−0.0790461			−0.0395231	−	0.999219i	$-0.512584\pi$
$419$	−1.61803			−0.0790461			−0.0395231	+	0.999219i	$0.512584\pi$
$420$		0			0
$421$	−5.76393	+	17.7396i	−0.280917	+	0.864573i	0.706676	+	0.707537i	$0.250194\pi$
$421$	−5.76393	+	17.7396i	−0.280917	+	0.864573i	−0.987593	+	0.157036i	$0.949806\pi$
$422$	−6.47214	−	19.9192i	−0.315059	−	0.969651i
$423$	68.4681	−	49.7450i	3.32903	−	2.41868i
$424$	−0.736068	+	0.534785i	−0.0357466	+	0.0259714i
$425$		0			0
$426$	13.2361	−	40.7364i	0.641290	−	1.97369i
$427$	18.9443	+	13.7638i	0.916778	+	0.666078i
$428$	7.52786			0.363873
$429$	−4.23607	+	16.8415i	−0.204519	+	0.813115i
$430$		0			0
$431$	21.1803	+	15.3884i	1.02022	+	0.741234i	0.966328	−	0.257313i	$-0.0828370\pi$
$431$	21.1803	+	15.3884i	1.02022	+	0.741234i	0.0538929	+	0.998547i	$0.482837\pi$
$432$	−4.47214	+	13.7638i	−0.215166	+	0.662212i
$433$	−2.94427	−	9.06154i	−0.141493	−	0.435470i	0.855051	−	0.518545i	$-0.173526\pi$
$433$	−2.94427	−	9.06154i	−0.141493	−	0.435470i	−0.996543	+	0.0830748i	$0.973526\pi$
$434$	15.3262	−	11.1352i	0.735683	−	0.534505i
$435$		0			0
$436$	2.32624	+	7.15942i	0.111407	+	0.342874i
$437$	0.184405	−	0.567541i	0.00882130	−	0.0271492i
$438$	−4.47214	−	3.24920i	−0.213687	−	0.155253i
$439$	−13.1246			−0.626404			−0.313202	−	0.949687i	$-0.601402\pi$
$439$	−13.1246			−0.626404			−0.313202	+	0.949687i	$0.601402\pi$
$440$		0			0
$441$	−1.09017			−0.0519129
$442$	6.85410	+	4.97980i	0.326016	+	0.236865i
$443$	−0.416408	+	1.28157i	−0.0197841	+	0.0608893i	−0.960461	−	0.278414i	$-0.910191\pi$
$443$	−0.416408	+	1.28157i	−0.0197841	+	0.0608893i	0.940677	+	0.339303i	$0.110191\pi$
$444$	−0.854102	−	2.62866i	−0.0405339	−	0.124750i
$445$		0			0
$446$	−7.82624	+	5.68609i	−0.370583	+	0.269244i
$447$	4.00000	+	12.3107i	0.189194	+	0.582278i
$448$	−0.809017	+	2.48990i	−0.0382225	+	0.117637i
$449$	−2.54508	−	1.84911i	−0.120110	−	0.0872650i	0.526109	−	0.850417i	$-0.323651\pi$
$449$	−2.54508	−	1.84911i	−0.120110	−	0.0872650i	−0.646219	+	0.763152i	$0.723651\pi$
$450$		0			0
$451$	−2.29180	−	5.70634i	−0.107916	−	0.268701i
$452$	−6.29180			−0.295941
$453$	33.1246	+	24.0664i	1.55633	+	1.13074i
$454$	−5.09017	+	15.6659i	−0.238894	+	0.735239i
$455$		0			0
$456$	10.7082	−	7.77997i	0.501458	−	0.364330i
$457$	26.3262	−	19.1271i	1.23149	−	0.894729i	0.234489	−	0.972119i	$-0.424658\pi$
$457$	26.3262	−	19.1271i	1.23149	−	0.894729i	0.997001	+	0.0773894i	$0.0246585\pi$
$458$	8.70820	+	26.8011i	0.406908	+	1.25233i
$459$	−23.4164	+	72.0683i	−1.09298	+	3.36386i
$460$		0			0
$461$	28.5410			1.32929			0.664644	−	0.747160i	$-0.268583\pi$
$461$	28.5410			1.32929			0.664644	+	0.747160i	$0.268583\pi$
$462$	−28.0344	+	1.90211i	−1.30428	+	0.0884943i
$463$	−15.5066			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$463$	−15.5066			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$464$	1.00000	+	0.726543i	0.0464238	+	0.0337289i
$465$		0			0
$466$	4.70820	+	14.4904i	0.218103	+	0.671253i
$467$	13.9443	−	10.1311i	0.645264	−	0.468812i	−0.216391	−	0.976307i	$-0.569428\pi$
$467$	13.9443	−	10.1311i	0.645264	−	0.468812i	0.861655	+	0.507495i	$0.169428\pi$
$468$	−9.78115	+	7.10642i	−0.452134	+	0.328495i
$469$	0.618034	+	1.90211i	0.0285382	+	0.0878314i
$470$		0			0
$471$	−22.5623	−	16.3925i	−1.03962	−	0.755325i
$472$	−2.38197			−0.109639
$473$	−23.5066	+	19.6417i	−1.08083	+	0.903125i
$474$	−4.94427			−0.227098
$475$		0			0
$476$	−4.23607	+	13.0373i	−0.194160	+	0.597563i
$477$	−2.10081	−	6.46564i	−0.0961896	−	0.296041i
$478$	7.70820	−	5.60034i	0.352565	−	0.256153i
$479$	23.9443	−	17.3965i	1.09404	−	0.794868i	0.113965	−	0.993485i	$-0.463645\pi$
$479$	23.9443	−	17.3965i	1.09404	−	0.794868i	0.980077	+	0.198617i	$0.0636450\pi$
$480$		0			0
$481$	0.427051	−	1.31433i	0.0194718	−	0.0599282i
$482$	−1.50000	−	1.08981i	−0.0683231	−	0.0496397i
$483$	−1.23607			−0.0562430
$484$	10.8992	−	1.48584i	0.495418	−	0.0675382i
$485$		0			0
$486$	−28.7984	−	20.9232i	−1.30632	−	0.949098i
$487$	−11.4164	+	35.1361i	−0.517327	+	1.59217i	0.261681	+	0.965154i	$0.415723\pi$
$487$	−11.4164	+	35.1361i	−0.517327	+	1.59217i	−0.779008	+	0.627014i	$0.784277\pi$
$488$	−2.76393	−	8.50651i	−0.125117	−	0.385072i
$489$	18.9443	−	13.7638i	0.856690	−	0.622421i
$490$		0			0
$491$	11.2639	+	34.6668i	0.508334	+	1.56449i	0.795092	+	0.606489i	$0.207422\pi$
$491$	11.2639	+	34.6668i	0.508334	+	1.56449i	−0.286758	+	0.958003i	$0.592578\pi$
$492$	1.85410	−	5.70634i	0.0835894	−	0.257262i
$493$	5.23607	+	3.80423i	0.235821	+	0.171334i
$494$	6.61803			0.297759
$495$		0			0
$496$	−7.23607			−0.324909
$497$	28.0344	+	20.3682i	1.25752	+	0.913639i
$498$	−15.7082	+	48.3449i	−0.703901	+	2.16639i
$499$	−3.95492	−	12.1720i	−0.177046	−	0.544893i	0.822675	−	0.568512i	$-0.192481\pi$
$499$	−3.95492	−	12.1720i	−0.177046	−	0.544893i	−0.999721	+	0.0236199i	$0.992481\pi$
$500$		0			0
$501$	−20.7082	+	15.0454i	−0.925174	+	0.672178i
$502$	3.10081	+	9.54332i	0.138396	+	0.425939i
$503$	−2.31966	+	7.13918i	−0.103429	+	0.318320i	−0.989358	−	0.145499i	$-0.953521\pi$
$503$	−2.31966	+	7.13918i	−0.103429	+	0.318320i	0.885930	+	0.463819i	$0.153521\pi$
$504$	−15.8262	−	11.4984i	−0.704957	−	0.512181i
$505$		0			0
$506$	0.482779	−	0.0327561i	0.0214621	−	0.00145619i
$507$	33.5967			1.49208
$508$	−1.92705	−	1.40008i	−0.0854991	−	0.0621187i
$509$	−9.61803	+	29.6013i	−0.426312	+	1.31205i	0.475421	+	0.879759i	$0.342296\pi$
$509$	−9.61803	+	29.6013i	−0.426312	+	1.31205i	−0.901733	+	0.432294i	$0.857704\pi$
$510$		0			0
$511$	3.61803	−	2.62866i	0.160052	−	0.116285i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	18.2918	+	56.2964i	0.807603	+	2.48554i
$514$	−3.70820	+	11.4127i	−0.163562	+	0.503392i
$515$		0			0
$516$	−29.8885			−1.31577
$517$	−14.0000	−	34.8586i	−0.615719	−	1.53308i
$518$	2.23607			0.0982472
$519$	33.0344	+	24.0009i	1.45005	+	1.05352i
$520$		0			0
$521$	−2.66312	−	8.19624i	−0.116673	−	0.359084i	0.875619	−	0.483002i	$-0.160454\pi$
$521$	−2.66312	−	8.19624i	−0.116673	−	0.359084i	−0.992292	+	0.123919i	$0.960454\pi$
$522$	−7.47214	+	5.42882i	−0.327047	+	0.237613i
$523$	−5.94427	+	4.31877i	−0.259925	+	0.188846i	−0.710114	−	0.704087i	$-0.751357\pi$
$523$	−5.94427	+	4.31877i	−0.259925	+	0.188846i	0.450189	+	0.892933i	$0.351357\pi$
$524$	3.52786	+	10.8576i	0.154115	+	0.474319i
$525$		0			0
$526$	−20.8713	−	15.1639i	−0.910033	−	0.661178i
$527$	−37.8885			−1.65045
$528$	9.09017	+	5.70634i	0.395599	+	0.248337i
$529$	−22.9787			−0.999075
$530$		0			0
$531$	5.50000	−	16.9273i	0.238680	−	0.734580i
$532$	3.30902	+	10.1841i	0.143464	+	0.441537i
$533$	2.42705	−	1.76336i	0.105127	−	0.0763794i
$534$	31.5066	−	22.8909i	1.36342	−	0.990585i
$535$		0			0
$536$	0.236068	−	0.726543i	0.0101966	−	0.0313819i
$537$	−7.61803	−	5.53483i	−0.328742	−	0.238845i
$538$	−17.5967			−0.758650
$539$	−0.118034	+	0.469272i	−0.00508408	+	0.0202130i
$540$		0			0
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	0.718158	−	0.695880i	$-0.244986\pi$
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	−0.439899	+	0.898047i	$0.644986\pi$
$542$	−4.14590	+	12.7598i	−0.178082	+	0.548079i
$543$	20.4721	+	63.0068i	0.878543	+	2.70388i
$544$	4.23607	−	3.07768i	0.181620	−	0.131955i
$545$		0			0
$546$	−4.23607	−	13.0373i	−0.181287	−	0.557944i
$547$	4.81966	−	14.8334i	0.206074	−	0.634230i	−0.793594	−	0.608448i	$-0.791792\pi$
$547$	4.81966	−	14.8334i	0.206074	−	0.634230i	0.999668	−	0.0257820i	$-0.00820757\pi$
$548$	−4.23607	−	3.07768i	−0.180956	−	0.131472i
$549$	66.8328			2.85236
$550$		0			0
$551$	5.05573			0.215381
$552$	0.381966	+	0.277515i	0.0162576	+	0.0118118i
$553$	1.23607	−	3.80423i	0.0525630	−	0.161772i
$554$	−0.190983	−	0.587785i	−0.00811409	−	0.0249726i
$555$		0			0
$556$	6.59017	−	4.78804i	0.279485	−	0.203058i
$557$	−10.2639	−	31.5891i	−0.434897	−	1.33847i	−0.893192	−	0.449675i	$-0.851540\pi$
$557$	−10.2639	−	31.5891i	−0.434897	−	1.33847i	0.458296	−	0.888800i	$-0.348460\pi$
$558$	16.7082	−	51.4226i	0.707315	−	2.17689i
$559$	−12.0902	−	8.78402i	−0.511360	−	0.371525i
$560$		0			0
$561$	47.5967	+	29.8788i	2.00954	+	1.26148i
$562$	−18.0000			−0.759284
$563$	19.3262	+	14.0413i	0.814504	+	0.591772i	0.915133	−	0.403152i	$-0.132086\pi$
$563$	19.3262	+	14.0413i	0.814504	+	0.591772i	−0.100629	+	0.994924i	$0.532086\pi$
$564$	11.3262	−	34.8586i	0.476921	−	1.46781i
$565$		0			0
$566$	−20.0902	+	14.5964i	−0.844453	+	0.613531i
$567$	51.7148	−	37.5730i	2.17182	−	1.57792i
$568$	−4.09017	−	12.5882i	−0.171620	−	0.528191i
$569$	2.57295	−	7.91872i	0.107864	−	0.331970i	−0.882528	−	0.470259i	$-0.844160\pi$
$569$	2.57295	−	7.91872i	0.107864	−	0.331970i	0.990392	+	0.138289i	$0.0441604\pi$
$570$		0			0
$571$	−29.0902			−1.21739			−0.608693	−	0.793406i	$-0.708306\pi$
$571$	−29.0902			−1.21739			−0.608693	+	0.793406i	$0.708306\pi$
$572$	2.00000	+	4.97980i	0.0836242	+	0.208216i
$573$	−82.2492			−3.43601
$574$	3.92705	+	2.85317i	0.163912	+	0.119089i
$575$		0			0
$576$	2.30902	+	7.10642i	0.0962090	+	0.296101i
$577$	12.0902	−	8.78402i	0.503320	−	0.365684i	−0.306963	−	0.951721i	$-0.599313\pi$
$577$	12.0902	−	8.78402i	0.503320	−	0.365684i	0.810284	+	0.586038i	$0.199313\pi$
$578$	8.42705	−	6.12261i	0.350519	−	0.254667i
$579$	−5.41641	−	16.6700i	−0.225098	−	0.692781i
$580$		0			0
$581$	−33.2705	−	24.1724i	−1.38029	−	1.00284i
$582$	38.8328			1.60967
$583$	−3.01064	+	0.204270i	−0.124688	+	0.00845998i
$584$	−1.70820			−0.0706860
$585$		0			0
$586$	−7.33688	+	22.5806i	−0.303084	+	0.932796i
$587$	6.41641	+	19.7477i	0.264833	+	0.815074i	0.991732	+	0.128328i	$0.0409612\pi$
$587$	6.41641	+	19.7477i	0.264833	+	0.815074i	−0.726898	+	0.686745i	$0.759039\pi$
$588$	−0.381966	+	0.277515i	−0.0157520	+	0.0114445i
$589$	−23.9443	+	17.3965i	−0.986607	+	0.716812i
$590$		0			0
$591$	−4.90983	+	15.1109i	−0.201963	+	0.621579i
$592$	−0.690983	−	0.502029i	−0.0283992	−	0.0206332i
$593$	19.7082			0.809319			0.404659	−	0.914467i	$-0.367390\pi$
$593$	19.7082			0.809319			0.404659	+	0.914467i	$0.367390\pi$
$594$	−36.8328	+	30.7768i	−1.51127	+	1.26279i
$595$		0			0
$596$	3.23607	+	2.35114i	0.132555	+	0.0963065i
$597$	−1.70820	+	5.25731i	−0.0699121	+	0.215167i
$598$	0.0729490	+	0.224514i	0.00298311	+	0.00918106i
$599$	−13.3262	+	9.68208i	−0.544495	+	0.395599i	−0.825752	−	0.564034i	$-0.809249\pi$
$599$	−13.3262	+	9.68208i	−0.544495	+	0.395599i	0.281257	+	0.959633i	$0.409249\pi$
$600$		0			0
$601$	6.97214	+	21.4580i	0.284399	+	0.875291i	0.986578	+	0.163290i	$0.0522108\pi$
$601$	6.97214	+	21.4580i	0.284399	+	0.875291i	−0.702179	+	0.712001i	$0.747789\pi$
$602$	7.47214	−	22.9969i	0.304542	−	0.937282i
$603$	4.61803	+	3.35520i	0.188061	+	0.136634i
$604$	12.6525			0.514822
$605$		0			0
$606$	12.0000			0.487467
$607$	26.1803	+	19.0211i	1.06263	+	0.772044i	0.974573	−	0.224072i	$-0.0719350\pi$
$607$	26.1803	+	19.0211i	1.06263	+	0.772044i	0.0880546	+	0.996116i	$0.471935\pi$
$608$	1.26393	−	3.88998i	0.0512592	−	0.157760i
$609$	−3.23607	−	9.95959i	−0.131132	−	0.403583i
$610$		0			0
$611$	14.8262	−	10.7719i	0.599805	−	0.435784i
$612$	12.0902	+	37.2097i	0.488716	+	1.50411i
$613$	−3.56231	+	10.9637i	−0.143880	+	0.442818i	−0.996865	−	0.0791176i	$-0.974790\pi$
$613$	−3.56231	+	10.9637i	−0.143880	+	0.442818i	0.852985	+	0.521935i	$0.174790\pi$
$614$	21.7984	+	15.8374i	0.879711	+	0.639147i
$615$		0			0
$616$	−6.66312	+	5.56758i	−0.268465	+	0.224324i
$617$	−32.9443			−1.32629			−0.663143	−	0.748493i	$-0.730778\pi$
$617$	−32.9443			−1.32629			−0.663143	+	0.748493i	$0.730778\pi$
$618$	−29.6525	−	21.5438i	−1.19280	−	0.866618i
$619$	7.02786	−	21.6295i	0.282474	−	0.869365i	−0.704671	−	0.709534i	$-0.748905\pi$
$619$	7.02786	−	21.6295i	0.282474	−	0.869365i	0.987145	−	0.159830i	$-0.0510947\pi$
$620$		0			0
$621$	−1.70820	+	1.24108i	−0.0685479	+	0.0498029i
$622$	−2.00000	+	1.45309i	−0.0801927	+	0.0582634i
$623$	9.73607	+	29.9645i	0.390067	+	1.20050i
$624$	−1.61803	+	4.97980i	−0.0647732	+	0.199351i
$625$		0			0
$626$	27.4164			1.09578
$627$	43.7984	−	2.97168i	1.74914	−	0.118678i
$628$	−8.61803			−0.343897
$629$	−3.61803	−	2.62866i	−0.144260	−	0.104811i
$630$		0			0
$631$	2.29180	+	7.05342i	0.0912350	+	0.280792i	0.986254	−	0.165235i	$-0.0528383\pi$
$631$	2.29180	+	7.05342i	0.0912350	+	0.280792i	−0.895019	+	0.446028i	$0.852838\pi$
$632$	−1.23607	+	0.898056i	−0.0491681	+	0.0357227i
$633$	54.8328	−	39.8384i	2.17941	−	1.58343i
$634$	1.91641	+	5.89810i	0.0761103	+	0.234243i
$635$		0			0
$636$	−2.38197	−	1.73060i	−0.0944511	−	0.0686227i
$637$	−0.236068			−0.00935335
$638$	1.52786	+	3.80423i	0.0604887	+	0.150611i
$639$	98.9017			3.91249
$640$		0			0
$641$	11.7918	−	36.2914i	0.465748	−	1.43342i	−0.392291	−	0.919841i	$-0.628318\pi$
$641$	11.7918	−	36.2914i	0.465748	−	1.43342i	0.858039	−	0.513584i	$-0.171682\pi$
$642$	7.52786	+	23.1684i	0.297101	+	0.914383i
$643$	−10.8541	+	7.88597i	−0.428044	+	0.310992i	−0.780866	−	0.624698i	$-0.785222\pi$
$643$	−10.8541	+	7.88597i	−0.428044	+	0.310992i	0.352822	+	0.935690i	$0.385222\pi$
$644$	−0.309017	+	0.224514i	−0.0121770	+	0.00884709i
$645$		0			0
$646$	6.61803	−	20.3682i	0.260383	−	0.801377i
$647$	−5.70820	−	4.14725i	−0.224413	−	0.163045i	0.469898	−	0.882721i	$-0.344291\pi$
$647$	−5.70820	−	4.14725i	−0.224413	−	0.163045i	−0.694311	+	0.719675i	$0.744291\pi$
$648$	−24.4164			−0.959167
$649$	−6.69098	−	4.20025i	−0.262644	−	0.164874i
$650$		0			0
$651$	49.5967	+	36.0341i	1.94385	+	1.41229i
$652$	2.23607	−	6.88191i	0.0875712	−	0.269516i
$653$	−7.97214	−	24.5357i	−0.311974	−	0.960157i	−0.976982	−	0.213321i	$-0.931572\pi$
$653$	−7.97214	−	24.5357i	−0.311974	−	0.960157i	0.665008	−	0.746836i	$-0.268428\pi$
$654$	−19.7082	+	14.3188i	−0.770652	+	0.559911i
$655$		0			0
$656$	−0.572949	−	1.76336i	−0.0223699	−	0.0688475i
$657$	3.94427	−	12.1392i	0.153881	−	0.473596i
$658$	23.9894	+	17.4293i	0.935202	+	0.679464i
$659$	−13.3820			−0.521287			−0.260644	−	0.965435i	$-0.583935\pi$
$659$	−13.3820			−0.521287			−0.260644	+	0.965435i	$0.583935\pi$
$660$		0			0
$661$	2.18034			0.0848054			0.0424027	−	0.999101i	$-0.486499\pi$
$661$	2.18034			0.0848054			0.0424027	+	0.999101i	$0.486499\pi$
$662$	−11.6353	−	8.45351i	−0.452217	−	0.328555i
$663$	−8.47214	+	26.0746i	−0.329030	+	1.01265i
$664$	4.85410	+	14.9394i	0.188376	+	0.579761i
$665$		0			0
$666$	5.16312	−	3.75123i	0.200067	−	0.145357i
$667$	0.0557281	+	0.171513i	0.00215780	+	0.00664103i
$668$	−2.44427	+	7.52270i	−0.0945717	+	0.291062i
$669$	−25.3262	−	18.4006i	−0.979169	−	0.711408i
$670$		0			0
$671$	7.23607	−	28.7687i	0.279345	−	1.11060i
$672$	−8.47214			−0.326820
$673$	−3.23607	−	2.35114i	−0.124741	−	0.0906298i	0.523665	−	0.851924i	$-0.324564\pi$
$673$	−3.23607	−	2.35114i	−0.124741	−	0.0906298i	−0.648407	+	0.761294i	$0.724564\pi$
$674$	10.9443	−	33.6830i	0.421558	−	1.29742i
$675$		0			0
$676$	8.39919	−	6.10237i	0.323046	−	0.234706i
$677$	−8.09017	+	5.87785i	−0.310930	+	0.225904i	−0.732296	−	0.680987i	$-0.761551\pi$
$677$	−8.09017	+	5.87785i	−0.310930	+	0.225904i	0.421365	+	0.906891i	$0.361551\pi$
$678$	−6.29180	−	19.3642i	−0.241635	−	0.743676i
$679$	−9.70820	+	29.8788i	−0.372567	+	1.14664i
$680$		0			0
$681$	−53.3050			−2.04265
$682$	−20.3262	−	12.7598i	−0.778332	−	0.488597i
$683$	47.0132			1.79891			0.899454	−	0.437015i	$-0.143964\pi$
$683$	47.0132			1.79891			0.899454	+	0.437015i	$0.143964\pi$
$684$	24.7254	+	17.9641i	0.945400	+	0.686873i
$685$		0			0
$686$	−5.78115	−	17.7926i	−0.220725	−	0.679323i
$687$	−73.7771	+	53.6022i	−2.81477	+	2.04505i
$688$	−7.47214	+	5.42882i	−0.284873	+	0.206972i
$689$	−0.454915	−	1.40008i	−0.0173309	−	0.0533390i
$690$		0			0
$691$	−11.1180	−	8.07772i	−0.422950	−	0.307291i	0.355874	−	0.934534i	$-0.384183\pi$
$691$	−11.1180	−	8.07772i	−0.422950	−	0.307291i	−0.778824	+	0.627243i	$0.784183\pi$
$692$	12.6180			0.479666
$693$	−24.1803	−	60.2066i	−0.918535	−	2.28706i
$694$	−27.1246			−1.02964
$695$		0			0
$696$	−1.23607	+	3.80423i	−0.0468530	+	0.144199i
$697$	−3.00000	−	9.23305i	−0.113633	−	0.349727i
$698$	25.0344	−	18.1886i	0.947568	−	0.688448i
$699$	−39.8885	+	28.9807i	−1.50872	+	1.09615i
$700$		0			0
$701$	1.79837	−	5.53483i	0.0679236	−	0.209047i	−0.911334	−	0.411669i	$-0.864946\pi$
$701$	1.79837	−	5.53483i	0.0679236	−	0.209047i	0.979257	+	0.202621i	$0.0649461\pi$
$702$	−18.9443	−	13.7638i	−0.715005	−	0.519482i
$703$	−3.49342			−0.131757
$704$	3.30902	−	0.224514i	0.124713	−	0.00846169i
$705$		0			0
$706$	−9.47214	−	6.88191i	−0.356489	−	0.259004i
$707$	−3.00000	+	9.23305i	−0.112827	+	0.347245i
$708$	−2.38197	−	7.33094i	−0.0895198	−	0.275514i
$709$	−8.79837	+	6.39239i	−0.330430	+	0.240071i	−0.740613	−	0.671932i	$-0.765465\pi$
$709$	−8.79837	+	6.39239i	−0.330430	+	0.240071i	0.410183	+	0.912003i	$0.365465\pi$
$710$		0			0
$711$	−3.52786	−	10.8576i	−0.132305	−	0.407194i
$712$	3.71885	−	11.4454i	0.139370	−	0.428936i
$713$	−0.854102	−	0.620541i	−0.0319864	−	0.0232395i
$714$	−44.3607			−1.66016
$715$		0			0
$716$	−2.90983			−0.108745
$717$	24.9443	+	18.1231i	0.931561	+	0.676819i
$718$	9.41641	−	28.9807i	0.351417	−	1.08155i
$719$	7.36068	+	22.6538i	0.274507	+	0.844846i	0.989349	+	0.145560i	$0.0464984\pi$
$719$	7.36068	+	22.6538i	0.274507	+	0.844846i	−0.714842	+	0.699286i	$0.753502\pi$
$720$		0			0
$721$	23.9894	−	17.4293i	0.893410	−	0.649101i
$722$	0.701626	+	2.15938i	0.0261118	+	0.0803639i
$723$	1.85410	−	5.70634i	0.0689548	−	0.212221i
$724$	16.5623	+	12.0332i	0.615533	+	0.447211i
$725$		0			0
$726$	15.4721	+	32.0584i	0.574225	+	1.18980i
$727$	8.79837			0.326314			0.163157	−	0.986600i	$-0.447832\pi$
$727$	8.79837			0.326314			0.163157	+	0.986600i	$0.447832\pi$
$728$	−3.42705	−	2.48990i	−0.127015	−	0.0922818i
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$		0			0
$731$	−39.1246	+	28.4257i	−1.44708	+	1.05136i
$732$	23.4164	−	17.0130i	0.865495	−	0.628819i
$733$	−11.2016	−	34.4751i	−0.413742	−	1.27337i	−0.913372	−	0.407127i	$-0.866531\pi$
$733$	−11.2016	−	34.4751i	−0.413742	−	1.27337i	0.499630	−	0.866239i	$-0.333469\pi$
$734$	3.23607	−	9.95959i	0.119445	−	0.367615i
$735$		0			0
$736$	0.145898			0.00537787
$737$	1.94427	−	1.62460i	0.0716182	−	0.0598429i
$738$	13.8541			0.509977
$739$	25.7705	+	18.7234i	0.947984	+	0.688750i	0.950329	−	0.311247i	$-0.100747\pi$
$739$	25.7705	+	18.7234i	0.947984	+	0.688750i	−0.00234556	+	0.999997i	$0.500747\pi$
$740$		0			0
$741$	6.61803	+	20.3682i	0.243120	+	0.748245i
$742$	1.92705	−	1.40008i	0.0707443	−	0.0513987i
$743$	−14.3541	+	10.4289i	−0.526601	+	0.382598i	−0.819085	−	0.573672i	$-0.805518\pi$
$743$	−14.3541	+	10.4289i	−0.526601	+	0.382598i	0.292484	+	0.956270i	$0.405518\pi$
$744$	−7.23607	−	22.2703i	−0.265287	−	0.816470i
$745$		0			0
$746$	−5.63525	−	4.09425i	−0.206321	−	0.149901i
$747$	−117.374			−4.29448
$748$	17.3262	−	1.17557i	0.633510	−	0.0429831i
$749$	−19.7082			−0.720122
$750$		0			0
$751$	−3.38197	+	10.4086i	−0.123410	+	0.379816i	−0.993608	−	0.112886i	$-0.963991\pi$
$751$	−3.38197	+	10.4086i	−0.123410	+	0.379816i	0.870198	+	0.492702i	$0.163991\pi$
$752$	−3.50000	−	10.7719i	−0.127632	−	0.392810i
$753$	−26.2705	+	19.0866i	−0.957351	+	0.695556i
$754$	−1.61803	+	1.17557i	−0.0589253	+	0.0428118i
$755$		0			0
$756$	11.7082	−	36.0341i	0.425823	−	1.31055i
$757$	17.9615	+	13.0498i	0.652822	+	0.474303i	0.864231	−	0.503095i	$-0.167805\pi$
$757$	17.9615	+	13.0498i	0.652822	+	0.474303i	−0.211410	+	0.977398i	$0.567805\pi$
$758$	10.3262			0.375066
$759$	0.583592	+	1.45309i	0.0211831	+	0.0527436i
$760$		0			0
$761$	−5.32624	−	3.86974i	−0.193076	−	0.140278i	0.487048	−	0.873375i	$-0.338074\pi$
$761$	−5.32624	−	3.86974i	−0.193076	−	0.140278i	−0.680123	+	0.733098i	$0.738074\pi$
$762$	2.38197	−	7.33094i	0.0862895	−	0.265572i
$763$	−6.09017	−	18.7436i	−0.220479	−	0.678564i
$764$	−20.5623	+	14.9394i	−0.743918	+	0.540488i
$765$		0			0
$766$	−4.89919	−	15.0781i	−0.177015	−	0.544796i
$767$	1.19098	−	3.66547i	0.0430039	−	0.132352i
$768$	2.61803	+	1.90211i	0.0944702	+	0.0686366i
$769$	−32.0902			−1.15720			−0.578601	−	0.815611i	$-0.696401\pi$
$769$	−32.0902			−1.15720			−0.578601	+	0.815611i	$0.696401\pi$
$770$		0			0
$771$	−38.8328			−1.39853
$772$	−4.38197	−	3.18368i	−0.157710	−	0.114583i
$773$	11.6074	−	35.7239i	0.417489	−	1.28490i	−0.492517	−	0.870303i	$-0.663923\pi$
$773$	11.6074	−	35.7239i	0.417489	−	1.28490i	0.910006	−	0.414596i	$-0.136077\pi$
$774$	−21.3262	−	65.6354i	−0.766556	−	2.35922i
$775$		0			0
$776$	9.70820	−	7.05342i	0.348504	−	0.253203i
$777$	2.23607	+	6.88191i	0.0802185	+	0.246887i
$778$	−3.76393	+	11.5842i	−0.134944	+	0.415313i
$779$	−6.13525	−	4.45752i	−0.219818	−	0.159707i
$780$		0			0
$781$	10.7082	−	42.5730i	0.383170	−	1.52338i
$782$	0.763932			0.0273182
$783$	−14.4721	−	10.5146i	−0.517192	−	0.375762i
$784$	−0.0450850	+	0.138757i	−0.00161018	+	0.00495562i
$785$		0			0
$786$	−29.8885	+	21.7153i	−1.06609	+	0.774559i
$787$	−29.1246	+	21.1603i	−1.03818	+	0.754282i	−0.969929	−	0.243386i	$-0.921742\pi$
$787$	−29.1246	+	21.1603i	−1.03818	+	0.754282i	−0.0682508	+	0.997668i	$0.521742\pi$
$788$	1.51722	+	4.66953i	0.0540488	+	0.166345i
$789$	25.7984	−	79.3992i	0.918446	−	2.82669i
$790$		0			0
$791$	16.4721			0.585682
$792$	−6.04508	+	24.0337i	−0.214803	+	0.854000i
$793$	14.4721			0.513921
$794$	−5.50000	−	3.99598i	−0.195188	−	0.141812i
$795$		0			0
$796$	0.527864	+	1.62460i	0.0187096	+	0.0575824i
$797$	29.9615	−	21.7683i	1.06129	−	0.771073i	0.0869638	−	0.996211i	$-0.472284\pi$
$797$	29.9615	−	21.7683i	1.06129	−	0.771073i	0.974327	+	0.225139i	$0.0722835\pi$
$798$	−28.0344	+	20.3682i	−0.992408	+	0.721027i
$799$	−18.3262	−	56.4024i	−0.648336	−	1.99537i
$800$		0			0
$801$	72.7492	+	52.8554i	2.57047	+	1.86755i
$802$	10.7426			0.379336
$803$	−4.79837	−	3.01217i	−0.169331	−	0.106297i
$804$	2.47214			0.0871855
$805$		0			0
$806$	3.61803	−	11.1352i	0.127440	−	0.392219i
$807$	−17.5967	−	54.1572i	−0.619435	−	1.90642i
$808$	3.00000	−	2.17963i	0.105540	−	0.0766790i
$809$	7.30902	−	5.31031i	0.256971	−	0.186701i	−0.451839	−	0.892099i	$-0.649232\pi$
$809$	7.30902	−	5.31031i	0.256971	−	0.186701i	0.708811	+	0.705399i	$0.249232\pi$
$810$		0			0
$811$	−14.4058	+	44.3364i	−0.505855	+	1.55686i	0.293474	+	0.955967i	$0.405189\pi$
$811$	−14.4058	+	44.3364i	−0.505855	+	1.55686i	−0.799329	+	0.600894i	$0.794811\pi$
$812$	−2.61803	−	1.90211i	−0.0918750	−	0.0667511i
$813$	−43.4164			−1.52268
$814$	−1.05573	−	2.62866i	−0.0370033	−	0.0921343i
$815$		0			0
$816$	13.7082	+	9.95959i	0.479883	+	0.348655i
$817$	−11.6738	+	35.9281i	−0.408413	+	1.25697i
$818$	7.20820	+	22.1846i	0.252029	+	0.775665i
$819$	25.6074	−	18.6049i	0.894795	−	0.650106i
$820$		0			0
$821$	−7.52786	−	23.1684i	−0.262724	−	0.808582i	−0.992209	−	0.124585i	$-0.960240\pi$
$821$	−7.52786	−	23.1684i	−0.262724	−	0.808582i	0.729485	−	0.683997i	$-0.239760\pi$
$822$	5.23607	−	16.1150i	0.182629	−	0.562074i
$823$	−13.7812	−	10.0126i	−0.480381	−	0.349017i	0.321092	−	0.947048i	$-0.395950\pi$
$823$	−13.7812	−	10.0126i	−0.480381	−	0.349017i	−0.801473	+	0.598031i	$0.795950\pi$
$824$	−11.3262			−0.394568
$825$		0			0
$826$	6.23607			0.216981
$827$	17.7984	+	12.9313i	0.618910	+	0.449665i	0.852541	−	0.522661i	$-0.175061\pi$
$827$	17.7984	+	12.9313i	0.618910	+	0.449665i	−0.233631	+	0.972325i	$0.575061\pi$
$828$	−0.336881	+	1.03681i	−0.0117074	+	0.0360318i
$829$	−4.00000	−	12.3107i	−0.138926	−	0.427569i	0.857254	−	0.514893i	$-0.172168\pi$
$829$	−4.00000	−	12.3107i	−0.138926	−	0.427569i	−0.996180	+	0.0873239i	$0.972168\pi$
$830$		0			0
$831$	1.61803	−	1.17557i	0.0561290	−	0.0407801i
$832$	0.500000	+	1.53884i	0.0173344	+	0.0533497i
$833$	−0.236068	+	0.726543i	−0.00817927	+	0.0251732i
$834$	21.3262	+	15.4944i	0.738467	+	0.536528i
$835$		0			0
$836$	10.4098	−	8.69827i	0.360032	−	0.300836i
$837$	104.721			3.61970
$838$	−1.30902	−	0.951057i	−0.0452192	−	0.0328537i
$839$	−16.2361	+	49.9695i	−0.560531	+	1.72514i	0.120338	+	0.992733i	$0.461602\pi$
$839$	−16.2361	+	49.9695i	−0.560531	+	1.72514i	−0.680869	+	0.732405i	$0.738398\pi$
$840$		0			0
$841$	22.2254	−	16.1477i	0.766394	−	0.556818i
$842$	−15.0902	+	10.9637i	−0.520042	+	0.377832i
$843$	−18.0000	−	55.3983i	−0.619953	−	1.90802i
$844$	6.47214	−	19.9192i	0.222780	−	0.685647i
$845$		0			0
$846$	84.6312			2.90968
$847$	−28.5344	+	3.88998i	−0.980455	+	0.133661i
$848$	−0.909830			−0.0312437
$849$	−65.0132	−	47.2348i	−2.23125	−	1.62109i
$850$		0			0
$851$	−0.0385072	−	0.118513i	−0.00132001	−	0.00406257i
$852$	34.6525	−	25.1765i	1.18717	−	0.862533i
$853$	12.9164	−	9.38432i	0.442249	−	0.321313i	−0.344279	−	0.938867i	$-0.611877\pi$
$853$	12.9164	−	9.38432i	0.442249	−	0.321313i	0.786528	+	0.617555i	$0.211877\pi$
$854$	7.23607	+	22.2703i	0.247613	+	0.762075i
$855$		0			0
$856$	6.09017	+	4.42477i	0.208158	+	0.151235i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$	−13.3262	+	11.1352i	−0.454950	+	0.380148i
$859$	−30.9098			−1.05463			−0.527315	−	0.849670i	$-0.676801\pi$
$859$	−30.9098			−1.05463			−0.527315	+	0.849670i	$0.676801\pi$
$860$		0			0
$861$	−4.85410	+	14.9394i	−0.165427	+	0.509133i
$862$	8.09017	+	24.8990i	0.275552	+	0.848063i
$863$	−5.01722	+	3.64522i	−0.170788	+	0.124085i	−0.669896	−	0.742455i	$-0.733661\pi$
$863$	−5.01722	+	3.64522i	−0.170788	+	0.124085i	0.499108	+	0.866540i	$0.333661\pi$
$864$	−11.7082	+	8.50651i	−0.398321	+	0.289397i
$865$		0			0
$866$	2.94427	−	9.06154i	0.100050	−	0.307924i
$867$	27.2705	+	19.8132i	0.926155	+	0.672891i
$868$	18.9443			0.643010
$869$	−5.05573	+	0.343027i	−0.171504	+	0.0116364i
$870$		0			0
$871$	1.00000	+	0.726543i	0.0338837	+	0.0246180i
$872$	−2.32624	+	7.15942i	−0.0787764	+	0.242449i
$873$	27.7082	+	85.2771i	0.937781	+	2.88619i
$874$	0.482779	−	0.350760i	0.0163302	−	0.0118646i
$875$		0			0
$876$	−1.70820	−	5.25731i	−0.0577149	−	0.177628i
$877$	−0.736068	+	2.26538i	−0.0248552	+	0.0764966i	−0.962715	−	0.270519i	$-0.912805\pi$
$877$	−0.736068	+	2.26538i	−0.0248552	+	0.0764966i	0.937859	+	0.347015i	$0.112805\pi$
$878$	−10.6180	−	7.71445i	−0.358341	−	0.260350i
$879$	−76.8328			−2.59151
$880$		0			0
$881$	−27.4508			−0.924843			−0.462421	−	0.886660i	$-0.653019\pi$
$881$	−27.4508			−0.924843			−0.462421	+	0.886660i	$0.653019\pi$
$882$	−0.881966	−	0.640786i	−0.0296973	−	0.0215764i
$883$	−9.47214	+	29.1522i	−0.318763	+	0.981051i	0.655415	+	0.755269i	$0.272494\pi$
$883$	−9.47214	+	29.1522i	−0.318763	+	0.981051i	−0.974178	+	0.225782i	$0.927506\pi$
$884$	2.61803	+	8.05748i	0.0880540	+	0.271002i
$885$		0			0
$886$	−1.09017	+	0.792055i	−0.0366250	+	0.0266096i
$887$	−14.6074	−	44.9569i	−0.490468	−	1.50951i	−0.823902	−	0.566732i	$-0.808207\pi$
$887$	−14.6074	−	44.9569i	−0.490468	−	1.50951i	0.333434	−	0.942774i	$-0.391793\pi$
$888$	0.854102	−	2.62866i	0.0286618	−	0.0882119i
$889$	5.04508	+	3.66547i	0.169207	+	0.122936i
$890$		0			0
$891$	−68.5861	−	43.0548i	−2.29772	−	1.44239i
$892$	−9.67376			−0.323902
$893$	−37.4787	−	27.2299i	−1.25418	−	0.911213i
$894$	−4.00000	+	12.3107i	−0.133780	+	0.411733i
$895$		0			0
$896$	−2.11803	+	1.53884i	−0.0707585	+	0.0514091i
$897$	−0.618034	+	0.449028i	−0.0206356	+	0.0149926i
$898$	−0.972136	−	2.99193i	−0.0324406	−	0.0998419i
$899$	2.76393	−	8.50651i	0.0921823	−	0.283708i
$900$		0			0
$901$	−4.76393			−0.158710
$902$	1.50000	−	5.96361i	0.0499445	−	0.198566i
$903$	78.2492			2.60397
$904$	−5.09017	−	3.69822i	−0.169297	−	0.123001i
$905$		0			0
$906$	12.6525	+	38.9403i	0.420350	+	1.29371i
$907$	−10.2361	+	7.43694i	−0.339883	+	0.246939i	−0.744612	−	0.667497i	$-0.767366\pi$
$907$	−10.2361	+	7.43694i	−0.339883	+	0.246939i	0.404729	+	0.914436i	$0.367366\pi$
$908$	−13.3262	+	9.68208i	−0.442247	+	0.321311i
$909$	8.56231	+	26.3521i	0.283994	+	0.874043i
$910$		0			0
$911$	16.9443	+	12.3107i	0.561389	+	0.407873i	0.831967	−	0.554825i	$-0.187215\pi$
$911$	16.9443	+	12.3107i	0.561389	+	0.407873i	−0.270578	+	0.962698i	$0.587215\pi$
$912$	13.2361			0.438290
$913$	−12.7082	+	50.5245i	−0.420580	+	1.67212i
$914$	32.5410			1.07636
$915$		0			0
$916$	−8.70820	+	26.8011i	−0.287727	+	0.885533i
$917$	−9.23607	−	28.4257i	−0.305002	−	0.938699i
$918$	−61.3050	+	44.5407i	−2.02336	+	1.47006i
$919$	9.70820	−	7.05342i	0.320244	−	0.232671i	−0.416036	−	0.909348i	$-0.636581\pi$
$919$	9.70820	−	7.05342i	0.320244	−	0.232671i	0.736280	+	0.676677i	$0.236581\pi$
$920$		0			0
$921$	−26.9443	+	82.9259i	−0.887844	+	2.73250i
$922$	23.0902	+	16.7760i	0.760434	+	0.552488i
$923$	21.4164			0.704930
$924$	−23.7984	−	14.9394i	−0.782909	−	0.491470i
$925$		0			0
$926$	−12.5451	−	9.11454i	−0.412257	−	0.299522i
$927$	26.1525	−	80.4890i	0.858960	−	2.64361i
$928$	0.381966	+	1.17557i	0.0125386	+	0.0385900i
$929$	−43.0967	+	31.3116i	−1.41396	+	1.02730i	−0.421226	+	0.906956i	$0.638400\pi$
$929$	−43.0967	+	31.3116i	−1.41396	+	1.02730i	−0.992732	+	0.120345i	$0.961600\pi$
$930$		0			0
$931$	0.184405	+	0.567541i	0.00604364	+	0.0186004i
$932$	−4.70820	+	14.4904i	−0.154222	+	0.474648i
$933$	−6.47214	−	4.70228i	−0.211888	−	0.153946i
$934$	17.2361			0.563981
$935$		0			0
$936$	−12.0902			−0.395180
$937$	−38.9787	−	28.3197i	−1.27338	−	0.925164i	−0.274047	−	0.961716i	$-0.588362\pi$
$937$	−38.9787	−	28.3197i	−1.27338	−	0.925164i	−0.999332	+	0.0365522i	$0.988362\pi$
$938$	−0.618034	+	1.90211i	−0.0201795	+	0.0621062i
$939$	27.4164	+	84.3790i	0.894701	+	2.75361i
$940$		0			0
$941$	−45.3607	+	32.9565i	−1.47872	+	1.07435i	−0.500748	+	0.865593i	$0.666942\pi$
$941$	−45.3607	+	32.9565i	−1.47872	+	1.07435i	−0.977968	+	0.208757i	$0.933058\pi$
$942$	−8.61803	−	26.5236i	−0.280791	−	0.864185i
$943$	0.0835921	−	0.257270i	0.00272213	−	0.00837787i
$944$	−1.92705	−	1.40008i	−0.0627202	−	0.0455689i
$945$		0			0
$946$	−30.5623	+	2.07363i	−0.993666	+	0.0674194i
$947$	−49.9574			−1.62340			−0.811699	−	0.584076i	$-0.801457\pi$
$947$	−49.9574			−1.62340			−0.811699	+	0.584076i	$0.801457\pi$
$948$	−4.00000	−	2.90617i	−0.129914	−	0.0943880i
$949$	0.854102	−	2.62866i	0.0277253	−	0.0853298i
$950$		0			0
$951$	−16.2361	+	11.7962i	−0.526491	+	0.382518i
$952$	−11.0902	+	8.05748i	−0.359434	+	0.261144i
$953$	−4.85410	−	14.9394i	−0.157240	−	0.483934i	0.841141	−	0.540816i	$-0.181884\pi$
$953$	−4.85410	−	14.9394i	−0.157240	−	0.483934i	−0.998381	+	0.0568813i	$0.981884\pi$
$954$	2.10081	−	6.46564i	0.0680163	−	0.209333i
$955$		0			0
$956$	9.52786			0.308153
$957$	−10.1803	+	8.50651i	−0.329084	+	0.274976i
$958$	29.5967			0.956228
$959$	11.0902	+	8.05748i	0.358120	+	0.260190i
$960$		0			0
$961$	6.60081	+	20.3152i	0.212929	+	0.655329i
$962$	1.11803	−	0.812299i	0.0360469	−	0.0261896i
$963$	−45.5066	+	33.0625i	−1.46643	+	1.06542i
$964$	−0.572949	−	1.76336i	−0.0184534	−	0.0567939i
$965$		0			0
$966$	−1.00000	−	0.726543i	−0.0321745	−	0.0233761i
$967$	−3.90983			−0.125732			−0.0628658	−	0.998022i	$-0.520024\pi$
$967$	−3.90983			−0.125732			−0.0628658	+	0.998022i	$0.520024\pi$
$968$	9.69098	+	5.20431i	0.311480	+	0.167273i
$969$	69.3050			2.22640
$970$		0			0
$971$	12.1565	−	37.4140i	0.390122	−	1.20067i	−0.542574	−	0.840008i	$-0.682550\pi$
$971$	12.1565	−	37.4140i	0.390122	−	1.20067i	0.932696	−	0.360664i	$-0.117450\pi$
$972$	−11.0000	−	33.8545i	−0.352825	−	1.08588i
$973$	−17.2533	+	12.5352i	−0.553115	+	0.401862i
$974$	−29.8885	+	21.7153i	−0.957691	+	0.695803i
$975$		0			0
$976$	2.76393	−	8.50651i	0.0884713	−	0.272287i
$977$	−3.38197	−	2.45714i	−0.108199	−	0.0786109i	0.532370	−	0.846512i	$-0.321301\pi$
$977$	−3.38197	−	2.45714i	−0.108199	−	0.0786109i	−0.640569	+	0.767901i	$0.721301\pi$
$978$	23.4164			0.748774
$979$	30.6287	−	25.5928i	0.978897	−	0.817948i
$980$		0			0
$981$	−45.5066	−	33.0625i	−1.45291	−	1.05560i
$982$	−11.2639	+	34.6668i	−0.359447	+	1.10626i
$983$	−3.10081	−	9.54332i	−0.0989006	−	0.304385i	0.889350	−	0.457227i	$-0.151157\pi$
$983$	−3.10081	−	9.54332i	−0.0989006	−	0.304385i	−0.988251	+	0.152842i	$0.951157\pi$
$984$	4.85410	−	3.52671i	0.154743	−	0.112427i
$985$		0			0
$986$	2.00000	+	6.15537i	0.0636930	+	0.196027i
$987$	−29.6525	+	91.2609i	−0.943849	+	2.90487i
$988$	5.35410	+	3.88998i	0.170337	+	0.123757i
$989$	−1.34752			−0.0428488
$990$		0			0
$991$	54.7214			1.73828			0.869141	−	0.494565i	$-0.164673\pi$
$991$	54.7214			1.73828			0.869141	+	0.494565i	$0.164673\pi$
$992$	−5.85410	−	4.25325i	−0.185868	−	0.135041i
$993$	14.3820	−	44.2631i	0.456398	−	1.40465i
$994$	10.7082	+	32.9565i	0.339644	+	1.04532i
$995$		0			0
$996$	−41.1246	+	29.8788i	−1.30308	+	0.946745i
$997$	16.2148	+	49.9040i	0.513527	+	1.58047i	0.785946	+	0.618296i	$0.212177\pi$
$997$	16.2148	+	49.9040i	0.513527	+	1.58047i	−0.272418	+	0.962179i	$0.587823\pi$
$998$	3.95492	−	12.1720i	0.125191	−	0.385297i
$999$	10.0000	+	7.26543i	0.316386	+	0.229868i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.f.301.1		4
5.2	odd	4		550.2.ba.a.499.1		8
5.3	odd	4		550.2.ba.a.499.2		8
5.4	even	2		110.2.g.a.81.1	✓	4
11.3	even	5	inner	550.2.h.f.201.1		4
11.5	even	5		6050.2.a.bu.1.1		2
11.6	odd	10		6050.2.a.cm.1.1		2
15.14	odd	2		990.2.n.f.631.1		4
20.19	odd	2		880.2.bo.a.81.1		4
55.3	odd	20		550.2.ba.a.399.1		8
55.14	even	10		110.2.g.a.91.1	yes	4
55.39	odd	10		1210.2.a.p.1.2		2
55.47	odd	20		550.2.ba.a.399.2		8
55.49	even	10		1210.2.a.t.1.2		2
165.14	odd	10		990.2.n.f.91.1		4
220.39	even	10		9680.2.a.bi.1.1		2
220.159	odd	10		9680.2.a.bh.1.1		2
220.179	odd	10		880.2.bo.a.641.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.81.1	✓	4	5.4	even	2
110.2.g.a.91.1	yes	4	55.14	even	10
550.2.h.f.201.1		4	11.3	even	5	inner
550.2.h.f.301.1		4	1.1	even	1	trivial
550.2.ba.a.399.1		8	55.3	odd	20
550.2.ba.a.399.2		8	55.47	odd	20
550.2.ba.a.499.1		8	5.2	odd	4
550.2.ba.a.499.2		8	5.3	odd	4
880.2.bo.a.81.1		4	20.19	odd	2
880.2.bo.a.641.1		4	220.179	odd	10
990.2.n.f.91.1		4	165.14	odd	10
990.2.n.f.631.1		4	15.14	odd	2
1210.2.a.p.1.2		2	55.39	odd	10
1210.2.a.t.1.2		2	55.49	even	10
6050.2.a.bu.1.1		2	11.5	even	5
6050.2.a.cm.1.1		2	11.6	odd	10
9680.2.a.bh.1.1		2	220.159	odd	10
9680.2.a.bi.1.1		2	220.39	even	10

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	550.2.h.f.301.1

Level	$550$
Weight	$2$
Character	550.301
Analytic conductor	$4.392$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$