LMFDB - Embedded newform 550.2.h.k.201.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	550.201
Dual form			550.2.h.k.301.2

$q$-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} +(0.924349 + 2.84485i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.41998 - 1.75822i) q^{6} +(-1.56024 + 4.80193i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.81172 + 3.49592i) q^{9} +(3.28679 - 0.443888i) q^{11} +2.99126 q^{12} +(1.46673 - 1.06564i) q^{13} +(-1.56024 - 4.80193i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.35140 - 3.16148i) q^{17} +(1.83791 - 5.65652i) q^{18} +(0.910862 + 2.80335i) q^{19} -15.1030 q^{21} +(-2.39815 + 2.29104i) q^{22} +3.12048 q^{23} +(-2.41998 + 1.75822i) q^{24} +(-0.560242 + 1.72425i) q^{26} +(-7.13315 - 5.18254i) q^{27} +(4.08477 + 2.96776i) q^{28} +(0.711544 - 2.18991i) q^{29} +(0.137154 - 0.0996482i) q^{31} +1.00000 q^{32} +(4.30093 + 8.94012i) q^{33} +5.37863 q^{34} +(1.83791 + 5.65652i) q^{36} +(1.84870 - 5.68971i) q^{37} +(-2.38467 - 1.73256i) q^{38} +(4.38737 + 3.18761i) q^{39} +(2.94887 + 9.07570i) q^{41} +(12.2186 - 8.87732i) q^{42} -7.13922 q^{43} +(0.593510 - 3.26309i) q^{44} +(-2.52452 + 1.83417i) q^{46} +(1.03572 + 3.18761i) q^{47} +(0.924349 - 2.84485i) q^{48} +(-14.9611 - 10.8698i) q^{49} +(4.97173 - 15.3014i) q^{51} +(-0.560242 - 1.72425i) q^{52} +(2.27971 - 1.65631i) q^{53} +8.81706 q^{54} -5.04905 q^{56} +(-7.13315 + 5.18254i) q^{57} +(0.711544 + 2.18991i) q^{58} +(1.95158 - 6.00633i) q^{59} +(-3.14256 - 2.28320i) q^{61} +(-0.0523881 + 0.161234i) q^{62} +(-9.27971 - 28.5600i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.73440 - 4.70468i) q^{66} +6.12507 q^{67} +(-4.35140 + 3.16148i) q^{68} +(2.88442 + 8.87732i) q^{69} +(4.46673 + 3.24527i) q^{71} +(-4.81172 - 3.49592i) q^{72} +(-2.74852 + 8.45908i) q^{73} +(1.84870 + 5.68971i) q^{74} +2.94761 q^{76} +(-2.99666 + 16.4755i) q^{77} -5.42309 q^{78} +(-2.83995 + 2.06335i) q^{79} +(2.63630 - 8.11370i) q^{81} +(-7.72025 - 5.60909i) q^{82} +(-1.35577 - 0.985026i) q^{83} +(-4.66708 + 14.3638i) q^{84} +(5.77575 - 4.19633i) q^{86} +6.88768 q^{87} +(1.43784 + 2.98875i) q^{88} +17.2589 q^{89} +(2.82869 + 8.70580i) q^{91} +(0.964282 - 2.96776i) q^{92} +(0.410263 + 0.298073i) q^{93} +(-2.71154 - 1.97005i) q^{94} +(0.924349 + 2.84485i) q^{96} +(-7.16312 + 5.20431i) q^{97} +18.4929 q^{98} +(-14.2633 + 13.6262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} - 24 q^{9} + 5 q^{11} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 18 q^{17} + 11 q^{18} + 17 q^{19} - 40 q^{21} - 5 q^{22} + 4 q^{23} - q^{24}+ \cdots - 72 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 - 24 * q^9 + 5 * q^11 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 18 * q^17 + 11 * q^18 + 17 * q^19 - 40 * q^21 - 5 * q^22 + 4 * q^23 - q^24 + 6 * q^26 + 19 * q^27 + 8 * q^28 + 2 * q^29 - 2 * q^31 + 8 * q^32 + 23 * q^33 + 2 * q^34 + 11 * q^36 + 8 * q^37 - 18 * q^38 + 24 * q^39 + 6 * q^41 + 20 * q^42 + 16 * q^43 + 10 * q^44 - 6 * q^46 + 12 * q^47 + 4 * q^48 - 6 * q^49 - 17 * q^51 + 6 * q^52 - 8 * q^53 - 6 * q^54 - 12 * q^56 + 19 * q^57 + 2 * q^58 - 12 * q^59 - 2 * q^61 - 22 * q^62 - 48 * q^63 - 2 * q^64 - 27 * q^66 - 34 * q^67 - 18 * q^68 + 20 * q^69 + 20 * q^71 - 24 * q^72 - 26 * q^73 + 8 * q^74 + 2 * q^76 + 26 * q^77 - 36 * q^78 + 14 * q^79 + 35 * q^81 - 9 * q^82 - 9 * q^83 + 26 * q^86 - 56 * q^87 - 5 * q^88 + 2 * q^89 - 52 * q^91 + 4 * q^92 + 32 * q^93 - 18 * q^94 + 4 * q^96 - 26 * q^97 + 64 * q^98 - 72 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.924349	+	2.84485i	0.533673	+	1.64248i	0.746499	+	0.665387i	$0.231733\pi$
$3$	0.924349	+	2.84485i	0.533673	+	1.64248i	−0.212826	+	0.977090i	$0.568267\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−2.41998	−	1.75822i	−0.987951	−	0.717789i
$7$	−1.56024	+	4.80193i	−0.589716	+	1.81496i	−0.0102715	+	0.999947i	$0.503270\pi$
$7$	−1.56024	+	4.80193i	−0.589716	+	1.81496i	−0.579444	+	0.815012i	$0.696730\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−4.81172	+	3.49592i	−1.60391	+	1.16531i
$10$		0			0
$11$	3.28679	−	0.443888i	0.991003	−	0.133837i
$11$	3.28679	−	0.443888i	0.991003	−	0.133837i
$12$	2.99126			0.863501
$13$	1.46673	−	1.06564i	0.406798	−	0.295556i	−0.365506	−	0.930809i	$-0.619104\pi$
$13$	1.46673	−	1.06564i	0.406798	−	0.295556i	0.772304	+	0.635253i	$0.219104\pi$
$14$	−1.56024	−	4.80193i	−0.416992	−	1.28337i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.35140	−	3.16148i	−1.05537	−	0.766771i	−0.0821434	−	0.996621i	$-0.526177\pi$
$17$	−4.35140	−	3.16148i	−1.05537	−	0.766771i	−0.973226	+	0.229850i	$0.926177\pi$
$18$	1.83791	−	5.65652i	0.433200	−	1.33325i
$19$	0.910862	+	2.80335i	0.208966	+	0.643132i	0.999527	+	0.0307483i	$0.00978904\pi$
$19$	0.910862	+	2.80335i	0.208966	+	0.643132i	−0.790561	+	0.612383i	$0.790211\pi$
$20$		0			0
$21$	−15.1030			−3.29574
$22$	−2.39815	+	2.29104i	−0.511288	+	0.488451i
$23$	3.12048			0.650666			0.325333	−	0.945600i	$-0.394524\pi$
$23$	3.12048			0.650666			0.325333	+	0.945600i	$0.394524\pi$
$24$	−2.41998	+	1.75822i	−0.493976	+	0.358894i
$25$		0			0
$26$	−0.560242	+	1.72425i	−0.109872	+	0.338153i
$27$	−7.13315	−	5.18254i	−1.37278	−	0.997380i
$28$	4.08477	+	2.96776i	0.771948	+	0.560853i
$29$	0.711544	−	2.18991i	0.132130	−	0.406656i	−0.863002	−	0.505200i	$-0.831419\pi$
$29$	0.711544	−	2.18991i	0.132130	−	0.406656i	0.995133	+	0.0985446i	$0.0314187\pi$
$30$		0			0
$31$	0.137154	−	0.0996482i	0.0246336	−	0.0178973i	−0.575400	−	0.817872i	$-0.695154\pi$
$31$	0.137154	−	0.0996482i	0.0246336	−	0.0178973i	0.600034	+	0.799975i	$0.295154\pi$
$32$	1.00000			0.176777
$33$	4.30093	+	8.94012i	0.748697	+	1.55627i
$34$	5.37863			0.922427
$35$		0			0
$36$	1.83791	+	5.65652i	0.306319	+	0.942753i
$37$	1.84870	−	5.68971i	0.303924	−	0.935382i	−0.676152	−	0.736762i	$-0.736354\pi$
$37$	1.84870	−	5.68971i	0.303924	−	0.935382i	0.980077	−	0.198620i	$-0.0636461\pi$
$38$	−2.38467	−	1.73256i	−0.386844	−	0.281059i
$39$	4.38737	+	3.18761i	0.702541	+	0.510426i
$40$		0			0
$41$	2.94887	+	9.07570i	0.460537	+	1.41739i	0.864510	+	0.502615i	$0.167629\pi$
$41$	2.94887	+	9.07570i	0.460537	+	1.41739i	−0.403974	+	0.914771i	$0.632371\pi$
$42$	12.2186	−	8.87732i	1.88537	−	1.36980i
$43$	−7.13922			−1.08872			−0.544360	−	0.838852i	$-0.683228\pi$
$43$	−7.13922			−1.08872			−0.544360	+	0.838852i	$0.683228\pi$
$44$	0.593510	−	3.26309i	0.0894750	−	0.491929i
$45$		0			0
$46$	−2.52452	+	1.83417i	−0.372221	+	0.270434i
$47$	1.03572	+	3.18761i	0.151075	+	0.464961i	0.997742	−	0.0671620i	$-0.0213944\pi$
$47$	1.03572	+	3.18761i	0.151075	+	0.464961i	−0.846667	+	0.532123i	$0.821394\pi$
$48$	0.924349	−	2.84485i	0.133418	−	0.410619i
$49$	−14.9611	−	10.8698i	−2.13729	−	1.55284i
$50$		0			0
$51$	4.97173	−	15.3014i	0.696181	−	2.14262i
$52$	−0.560242	−	1.72425i	−0.0776915	−	0.239110i
$53$	2.27971	−	1.65631i	0.313143	−	0.227511i	−0.420101	−	0.907477i	$-0.638005\pi$
$53$	2.27971	−	1.65631i	0.313143	−	0.227511i	0.733244	+	0.679966i	$0.238005\pi$
$54$	8.81706			1.19985
$55$		0			0
$56$	−5.04905			−0.674707
$57$	−7.13315	+	5.18254i	−0.944809	+	0.686444i
$58$	0.711544	+	2.18991i	0.0934303	+	0.287549i
$59$	1.95158	−	6.00633i	0.254073	−	0.781958i	−0.739937	−	0.672676i	$-0.765145\pi$
$59$	1.95158	−	6.00633i	0.254073	−	0.781958i	0.994011	−	0.109282i	$-0.0348551\pi$
$60$		0			0
$61$	−3.14256	−	2.28320i	−0.402363	−	0.292334i	0.368140	−	0.929771i	$-0.379995\pi$
$61$	−3.14256	−	2.28320i	−0.402363	−	0.292334i	−0.770503	+	0.637436i	$0.779995\pi$
$62$	−0.0523881	+	0.161234i	−0.00665330	+	0.0204768i
$63$	−9.27971	−	28.5600i	−1.16913	−	3.59822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	−8.73440	−	4.70468i	−1.07513	−	0.579106i
$67$	6.12507			0.748296			0.374148	−	0.927369i	$-0.377935\pi$
$67$	6.12507			0.748296			0.374148	+	0.927369i	$0.377935\pi$
$68$	−4.35140	+	3.16148i	−0.527685	+	0.383385i
$69$	2.88442	+	8.87732i	0.347243	+	1.06870i
$70$		0			0
$71$	4.46673	+	3.24527i	0.530104	+	0.385143i	0.820396	−	0.571795i	$-0.193753\pi$
$71$	4.46673	+	3.24527i	0.530104	+	0.385143i	−0.290293	+	0.956938i	$0.593753\pi$
$72$	−4.81172	−	3.49592i	−0.567067	−	0.411998i
$73$	−2.74852	+	8.45908i	−0.321690	+	0.990061i	0.651222	+	0.758887i	$0.274257\pi$
$73$	−2.74852	+	8.45908i	−0.321690	+	0.990061i	−0.972912	+	0.231174i	$0.925743\pi$
$74$	1.84870	+	5.68971i	0.214907	+	0.661415i
$75$		0			0
$76$	2.94761			0.338114
$77$	−2.99666	+	16.4755i	−0.341501	+	1.87756i
$78$	−5.42309			−0.614044
$79$	−2.83995	+	2.06335i	−0.319520	+	0.232145i	−0.735971	−	0.677014i	$-0.763274\pi$
$79$	−2.83995	+	2.06335i	−0.319520	+	0.232145i	0.416451	+	0.909158i	$0.363274\pi$
$80$		0			0
$81$	2.63630	−	8.11370i	0.292922	−	0.901522i
$82$	−7.72025	−	5.60909i	−0.852559	−	0.619420i
$83$	−1.35577	−	0.985026i	−0.148815	−	0.108121i	0.510886	−	0.859648i	$-0.329317\pi$
$83$	−1.35577	−	0.985026i	−0.148815	−	0.108121i	−0.659702	+	0.751528i	$0.729317\pi$
$84$	−4.66708	+	14.3638i	−0.509220	+	1.56722i
$85$		0			0
$86$	5.77575	−	4.19633i	0.622815	−	0.452502i
$87$	6.88768			0.738437
$88$	1.43784	+	2.98875i	0.153274	+	0.318602i
$89$	17.2589			1.82944			0.914719	−	0.404090i	$-0.132412\pi$
$89$	17.2589			1.82944			0.914719	+	0.404090i	$0.132412\pi$
$90$		0			0
$91$	2.82869	+	8.70580i	0.296527	+	0.912616i
$92$	0.964282	−	2.96776i	0.100533	−	0.309410i
$93$	0.410263	+	0.298073i	0.0425422	+	0.0309087i
$94$	−2.71154	−	1.97005i	−0.279674	−	0.203195i
$95$		0			0
$96$	0.924349	+	2.84485i	0.0943410	+	0.290352i
$97$	−7.16312	+	5.20431i	−0.727305	+	0.528418i	−0.888710	−	0.458471i	$-0.848397\pi$
$97$	−7.16312	+	5.20431i	−0.727305	+	0.528418i	0.161405	+	0.986888i	$0.448397\pi$
$98$	18.4929			1.86806
$99$	−14.2633	+	13.6262i	−1.43351	+	1.36948i
$100$		0			0
$101$	8.11967	−	5.89928i	0.807937	−	0.587001i	−0.105295	−	0.994441i	$-0.533579\pi$
$101$	8.11967	−	5.89928i	0.807937	−	0.587001i	0.913232	+	0.407441i	$0.133579\pi$
$102$	4.97173	+	15.3014i	0.492274	+	1.51506i
$103$	−1.27179	+	3.91415i	−0.125313	+	0.385673i	−0.993958	−	0.109762i	$-0.964991\pi$
$103$	−1.27179	+	3.91415i	−0.125313	+	0.385673i	0.868645	+	0.495435i	$0.164991\pi$
$104$	1.46673	+	1.06564i	0.143825	+	0.104495i
$105$		0			0
$106$	−0.870773	+	2.67996i	−0.0845769	+	0.260301i
$107$	0.995784	+	3.06471i	0.0962661	+	0.296277i	0.987582	−	0.157107i	$-0.0502168\pi$
$107$	0.995784	+	3.06471i	0.0962661	+	0.296277i	−0.891315	+	0.453384i	$0.850217\pi$
$108$	−7.13315	+	5.18254i	−0.686388	+	0.498690i
$109$	−6.55942			−0.628279			−0.314139	−	0.949377i	$-0.601716\pi$
$109$	−6.55942			−0.628279			−0.314139	+	0.949377i	$0.601716\pi$
$110$		0			0
$111$	17.8952			1.69854
$112$	4.08477	−	2.96776i	0.385974	−	0.280427i
$113$	1.67876	+	5.16668i	0.157924	+	0.486041i	0.998445	−	0.0557379i	$-0.0177511\pi$
$113$	1.67876	+	5.16668i	0.157924	+	0.486041i	−0.840521	+	0.541779i	$0.817751\pi$
$114$	2.72462	−	8.38552i	0.255184	−	0.785376i
$115$		0			0
$116$	−1.86285	−	1.35344i	−0.172961	−	0.125663i
$117$	−3.33210	+	10.2551i	−0.308053	+	0.948089i
$118$	1.95158	+	6.00633i	0.179657	+	0.552928i
$119$	21.9704	−	15.9625i	2.01403	−	1.46328i
$120$		0			0
$121$	10.6059	−	2.91793i	0.964175	−	0.265267i
$122$	3.88442			0.351678
$123$	−23.0932	+	16.7782i	−2.08225	+	1.51284i
$124$	−0.0523881	−	0.161234i	−0.00470459	−	0.0144793i
$125$		0			0
$126$	24.2946	+	17.6511i	2.16434	+	1.57248i
$127$	13.6995	+	9.95324i	1.21563	+	0.883207i	0.995730	−	0.0923150i	$-0.0294267\pi$
$127$	13.6995	+	9.95324i	1.21563	+	0.883207i	0.219901	+	0.975522i	$0.429427\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−6.59913	−	20.3100i	−0.581021	−	1.78820i
$130$		0			0
$131$	−7.78267			−0.679975			−0.339987	−	0.940430i	$-0.610423\pi$
$131$	−7.78267			−0.679975			−0.339987	+	0.940430i	$0.610423\pi$
$132$	9.83162	−	1.32778i	0.855733	−	0.115569i
$133$	−14.8826			−1.29049
$134$	−4.95529	+	3.60023i	−0.428071	+	0.311012i
$135$		0			0
$136$	1.66209	−	5.11538i	0.142523	−	0.438640i
$137$	6.97381	+	5.06677i	0.595812	+	0.432883i	0.844390	−	0.535729i	$-0.179963\pi$
$137$	6.97381	+	5.06677i	0.595812	+	0.432883i	−0.248578	+	0.968612i	$0.579963\pi$
$138$	−7.55150	−	5.48648i	−0.642826	−	0.467041i
$139$	−4.94069	+	15.2059i	−0.419064	+	1.28975i	0.489501	+	0.872003i	$0.337179\pi$
$139$	−4.94069	+	15.2059i	−0.419064	+	1.28975i	−0.908565	+	0.417744i	$0.862821\pi$
$140$		0			0
$141$	−8.11092	+	5.89293i	−0.683063	+	0.496274i
$142$	−5.52118			−0.463327
$143$	4.34781	−	4.15361i	0.363582	−	0.347342i
$144$	5.94761			0.495634
$145$		0			0
$146$	−2.74852	−	8.45908i	−0.227469	−	0.700079i
$147$	17.0939	−	52.6096i	1.40988	−	4.33916i
$148$	−4.83995	−	3.51643i	−0.397842	−	0.289049i
$149$	−3.22324	−	2.34182i	−0.264058	−	0.191850i	0.447876	−	0.894096i	$-0.352181\pi$
$149$	−3.22324	−	2.34182i	−0.264058	−	0.191850i	−0.711934	+	0.702246i	$0.752181\pi$
$150$		0			0
$151$	2.79965	+	8.61644i	0.227832	+	0.701196i	0.997992	+	0.0633442i	$0.0201766\pi$
$151$	2.79965	+	8.61644i	0.227832	+	0.701196i	−0.770159	+	0.637851i	$0.779823\pi$
$152$	−2.38467	+	1.73256i	−0.193422	+	0.140529i
$153$	31.9900			2.58624
$154$	−7.25970	−	15.0903i	−0.585003	−	1.21601i
$155$		0			0
$156$	4.38737	−	3.18761i	0.351271	−	0.255213i
$157$	−6.93346	−	21.3390i	−0.553351	−	1.70304i	−0.700260	−	0.713888i	$-0.746932\pi$
$157$	−6.93346	−	21.3390i	−0.553351	−	1.70304i	0.146909	−	0.989150i	$-0.453068\pi$
$158$	1.08477	−	3.33857i	0.0862993	−	0.265602i
$159$	6.81920	+	4.95444i	0.540798	+	0.392913i
$160$		0			0
$161$	−4.86871	+	14.9843i	−0.383708	+	1.18093i
$162$	2.63630	+	8.11370i	0.207127	+	0.637473i
$163$	15.9544	−	11.5915i	1.24964	−	0.907920i	0.251443	−	0.967872i	$-0.419095\pi$
$163$	15.9544	−	11.5915i	1.24964	−	0.907920i	0.998201	+	0.0599520i	$0.0190948\pi$
$164$	9.54275			0.745164
$165$		0			0
$166$	1.67583			0.130069
$167$	−3.31543	+	2.40880i	−0.256556	+	0.186399i	−0.708627	−	0.705583i	$-0.750685\pi$
$167$	−3.31543	+	2.40880i	−0.256556	+	0.186399i	0.452072	+	0.891982i	$0.350685\pi$
$168$	−4.66708	−	14.3638i	−0.360073	−	1.10819i
$169$	−3.00151	+	9.23771i	−0.230886	+	0.710593i
$170$		0			0
$171$	−14.1831	−	10.3046i	−1.08461	−	0.788013i
$172$	−2.20614	+	6.78980i	−0.168217	+	0.517717i
$173$	3.98792	+	12.2735i	0.303196	+	0.933140i	0.980344	+	0.197294i	$0.0632154\pi$
$173$	3.98792	+	12.2735i	0.303196	+	0.933140i	−0.677149	+	0.735846i	$0.736785\pi$
$174$	−5.57225	+	4.04848i	−0.422431	+	0.306914i
$175$		0			0
$176$	−2.91998	−	1.57281i	−0.220102	−	0.118555i
$177$	18.8911			1.41994
$178$	−13.9627	+	10.1445i	−1.04655	+	0.760364i
$179$	4.17787	+	12.8582i	0.312268	+	0.961063i	0.976864	+	0.213860i	$0.0686038\pi$
$179$	4.17787	+	12.8582i	0.312268	+	0.961063i	−0.664596	+	0.747203i	$0.731396\pi$
$180$		0			0
$181$	18.1957	+	13.2199i	1.35247	+	0.982630i	0.998884	+	0.0472302i	$0.0150394\pi$
$181$	18.1957	+	13.2199i	1.35247	+	0.982630i	0.353591	+	0.935400i	$0.384961\pi$
$182$	−7.40560	−	5.38048i	−0.548940	−	0.398828i
$183$	3.59056	−	11.0506i	0.265421	−	0.816883i
$184$	0.964282	+	2.96776i	0.0710878	+	0.218786i
$185$		0			0
$186$	−0.507112			−0.0371833
$187$	−15.7055	−	8.45956i	−1.14850	−	0.618625i
$188$	3.35165			0.244444
$189$	36.0156	−	26.1669i	2.61975	−	1.90336i
$190$		0			0
$191$	5.13715	−	15.8105i	0.371711	−	1.14401i	−0.573959	−	0.818884i	$-0.694593\pi$
$191$	5.13715	−	15.8105i	0.371711	−	1.14401i	0.945671	−	0.325126i	$-0.105407\pi$
$192$	−2.41998	−	1.75822i	−0.174647	−	0.126888i
$193$	−6.42705	−	4.66953i	−0.462629	−	0.336120i	0.331933	−	0.943303i	$-0.392299\pi$
$193$	−6.42705	−	4.66953i	−0.462629	−	0.336120i	−0.794562	+	0.607183i	$0.792299\pi$
$194$	2.73607	−	8.42075i	0.196438	−	0.604575i
$195$		0			0
$196$	−14.9611	+	10.8698i	−1.06865	+	0.776418i
$197$	21.2833			1.51637			0.758187	−	0.652037i	$-0.226085\pi$
$197$	21.2833			1.51637			0.758187	+	0.652037i	$0.226085\pi$
$198$	3.52997	−	19.4076i	0.250864	−	1.37924i
$199$	−7.26273			−0.514841			−0.257421	−	0.966299i	$-0.582873\pi$
$199$	−7.26273			−0.514841			−0.257421	+	0.966299i	$0.582873\pi$
$200$		0			0
$201$	5.66170	+	17.4249i	0.399346	+	1.22906i
$202$	−3.10144	+	9.54524i	−0.218216	+	0.671601i
$203$	9.40560	+	6.83357i	0.660144	+	0.479622i
$204$	−13.0162	−	9.45679i	−0.911313	−	0.662108i
$205$		0			0
$206$	−1.27179	−	3.91415i	−0.0886095	−	0.272712i
$207$	−15.0149	+	10.9090i	−1.04361	+	0.758225i
$208$	−1.81298			−0.125708
$209$	4.23818	+	8.80968i	0.293161	+	0.609378i
$210$		0			0
$211$	−7.11636	+	5.17034i	−0.489911	+	0.355941i	−0.805150	−	0.593071i	$-0.797915\pi$
$211$	−7.11636	+	5.17034i	−0.489911	+	0.355941i	0.315239	+	0.949012i	$0.397915\pi$
$212$	−0.870773	−	2.67996i	−0.0598049	−	0.184061i
$213$	−5.10350	+	15.7070i	−0.349686	+	1.07622i
$214$	−2.60700	−	1.89409i	−0.178211	−	0.129478i
$215$		0			0
$216$	2.72462	−	8.38552i	0.185387	−	0.570563i
$217$	0.264510	+	0.814079i	0.0179561	+	0.0552633i
$218$	5.30669	−	3.85553i	0.359414	−	0.261130i
$219$	−26.6054			−1.79783
$220$		0			0
$221$	−9.75134			−0.655946
$222$	−14.4775	+	10.5185i	−0.971669	+	0.705959i
$223$	−6.13047	−	18.8677i	−0.410527	−	1.26347i	−0.916191	−	0.400742i	$-0.868753\pi$
$223$	−6.13047	−	18.8677i	−0.410527	−	1.26347i	0.505664	−	0.862730i	$-0.331247\pi$
$224$	−1.56024	+	4.80193i	−0.104248	+	0.320842i
$225$		0			0
$226$	−4.39504	−	3.19319i	−0.292354	−	0.212408i
$227$	1.83599	−	5.65060i	0.121859	−	0.375043i	−0.871457	−	0.490472i	$-0.836824\pi$
$227$	1.83599	−	5.65060i	0.121859	−	0.375043i	0.993316	+	0.115429i	$0.0368243\pi$
$228$	2.72462	+	8.38552i	0.180442	+	0.555345i
$229$	−8.15671	+	5.92619i	−0.539010	+	0.391614i	−0.823717	−	0.567001i	$-0.808104\pi$
$229$	−8.15671	+	5.92619i	−0.539010	+	0.391614i	0.284707	+	0.958615i	$0.408104\pi$
$230$		0			0
$231$	−49.6403	+	6.70404i	−3.26609	+	0.441094i
$232$	2.30260			0.151173
$233$	0.503963	−	0.366151i	0.0330157	−	0.0239873i	−0.571155	−	0.820842i	$-0.693504\pi$
$233$	0.503963	−	0.366151i	0.0330157	−	0.0239873i	0.604171	+	0.796855i	$0.293504\pi$
$234$	−3.33210	−	10.2551i	−0.217826	−	0.670400i
$235$		0			0
$236$	−5.10929	−	3.71212i	−0.332586	−	0.241638i
$237$	−8.49503	−	6.17200i	−0.551811	−	0.400914i
$238$	−8.39196	+	25.8278i	−0.543970	+	1.67417i
$239$	−3.24097	−	9.97467i	−0.209641	−	0.645208i	−0.999491	−	0.0319078i	$-0.989842\pi$
$239$	−3.24097	−	9.97467i	−0.209641	−	0.645208i	0.789850	−	0.613300i	$-0.210158\pi$
$240$		0			0
$241$	−13.4865			−0.868743			−0.434372	−	0.900734i	$-0.643030\pi$
$241$	−13.4865			−0.868743			−0.434372	+	0.900734i	$0.643030\pi$
$242$	−6.86526	+	8.59466i	−0.441315	+	0.552486i
$243$	−0.932028			−0.0597897
$244$	−3.14256	+	2.28320i	−0.201182	+	0.146167i
$245$		0			0
$246$	8.82083	−	27.1477i	0.562396	−	1.73088i
$247$	4.32336	+	3.14110i	0.275089	+	0.199864i
$248$	0.137154	+	0.0996482i	0.00870928	+	0.00632766i
$249$	1.54905	−	4.76748i	0.0981669	−	0.302127i
$250$		0			0
$251$	10.6402	−	7.73058i	0.671605	−	0.487950i	−0.198957	−	0.980008i	$-0.563755\pi$
$251$	10.6402	−	7.73058i	0.671605	−	0.487950i	0.870562	+	0.492059i	$0.163755\pi$
$252$	−30.0298			−1.89170
$253$	10.2564	−	1.38515i	0.644812	−	0.0870834i
$254$	−16.9335			−1.06250
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.09930	+	3.38330i	−0.0685724	+	0.211044i	−0.979471	−	0.201587i	$-0.935390\pi$
$257$	−1.09930	+	3.38330i	−0.0685724	+	0.211044i	0.910898	+	0.412631i	$0.135390\pi$
$258$	17.2767	+	12.5523i	1.07560	+	0.781471i
$259$	24.4372	+	17.7546i	1.51845	+	1.10322i
$260$		0			0
$261$	4.23199	+	13.0247i	0.261953	+	0.806210i
$262$	6.29631	−	4.57454i	0.388987	−	0.282616i
$263$	−12.4264			−0.766242			−0.383121	−	0.923698i	$-0.625151\pi$
$263$	−12.4264			−0.766242			−0.383121	+	0.923698i	$0.625151\pi$
$264$	−7.17349	+	6.85308i	−0.441498	+	0.421778i
$265$		0			0
$266$	12.0403	−	8.74779i	0.738238	−	0.536362i
$267$	15.9532	+	49.0990i	0.976322	+	3.00481i
$268$	1.89275	−	5.82529i	0.115618	−	0.355836i
$269$	6.35033	+	4.61378i	0.387186	+	0.281307i	0.764302	−	0.644859i	$-0.223084\pi$
$269$	6.35033	+	4.61378i	0.387186	+	0.281307i	−0.377115	+	0.926166i	$0.623084\pi$
$270$		0			0
$271$	7.97125	−	24.5330i	0.484219	−	1.49027i	−0.348891	−	0.937163i	$-0.613442\pi$
$271$	7.97125	−	24.5330i	0.484219	−	1.49027i	0.833109	−	0.553108i	$-0.186558\pi$
$272$	1.66209	+	5.11538i	0.100779	+	0.310165i
$273$	−22.1520	+	16.0944i	−1.34070	+	0.974077i
$274$	−8.62010			−0.520759
$275$		0			0
$276$	9.33416			0.561851
$277$	25.4230	−	18.4709i	1.52752	−	1.10981i	0.569924	−	0.821698i	$-0.306973\pi$
$277$	25.4230	−	18.4709i	1.52752	−	1.10981i	0.957597	−	0.288111i	$-0.0930273\pi$
$278$	−4.94069	−	15.2059i	−0.296323	−	0.911989i
$279$	−0.311584	+	0.958958i	−0.0186541	+	0.0574113i
$280$		0			0
$281$	−7.41994	−	5.39090i	−0.442636	−	0.321594i	0.344045	−	0.938953i	$-0.388203\pi$
$281$	−7.41994	−	5.39090i	−0.442636	−	0.321594i	−0.786682	+	0.617359i	$0.788203\pi$
$282$	3.09810	−	9.53496i	0.184489	−	0.567799i
$283$	−0.112007	−	0.344721i	−0.00665810	−	0.0204915i	0.947672	−	0.319245i	$-0.103429\pi$
$283$	−0.112007	−	0.344721i	−0.00665810	−	0.0204915i	−0.954330	+	0.298753i	$0.903429\pi$
$284$	4.46673	−	3.24527i	0.265052	−	0.192571i
$285$		0			0
$286$	−1.07602	+	5.91591i	−0.0636265	+	0.349815i
$287$	−48.1818			−2.84408
$288$	−4.81172	+	3.49592i	−0.283533	+	0.205999i
$289$	3.68645	+	11.3457i	0.216850	+	0.667397i
$290$		0			0
$291$	−21.4267	−	15.5674i	−1.25606	−	0.912579i
$292$	7.19573	+	5.22800i	0.421098	+	0.305946i
$293$	9.41434	−	28.9744i	0.549992	−	1.69270i	−0.158824	−	0.987307i	$-0.550770\pi$
$293$	9.41434	−	28.9744i	0.549992	−	1.69270i	0.708816	−	0.705394i	$-0.249230\pi$
$294$	17.0939	+	52.6096i	0.996935	+	3.06825i
$295$		0			0
$296$	5.98251			0.347726
$297$	−25.7456	−	13.8676i	−1.49391	−	0.804678i
$298$	3.98415			0.230795
$299$	4.57691	−	3.32532i	0.264690	−	0.192308i
$300$		0			0
$301$	11.1389	−	34.2820i	0.642036	−	1.97598i
$302$	−7.32958	−	5.32525i	−0.421770	−	0.306434i
$303$	24.2880	+	17.6463i	1.39531	+	1.01375i
$304$	0.910862	−	2.80335i	0.0522415	−	0.160783i
$305$		0			0
$306$	−25.8804	+	18.8032i	−1.47949	+	1.07491i
$307$	−13.0087			−0.742448			−0.371224	−	0.928543i	$-0.621062\pi$
$307$	−13.0087			−0.742448			−0.371224	+	0.928543i	$0.621062\pi$
$308$	14.7431	+	7.94120i	0.840066	+	0.452492i
$309$	−12.3108			−0.700335
$310$		0			0
$311$	1.89981	+	5.84701i	0.107728	+	0.331554i	0.990361	−	0.138509i	$-0.0442311\pi$
$311$	1.89981	+	5.84701i	0.107728	+	0.331554i	−0.882633	+	0.470063i	$0.844231\pi$
$312$	−1.67583	+	5.15766i	−0.0948750	+	0.291995i
$313$	−17.4443	−	12.6740i	−0.986009	−	0.716377i	−0.0269652	−	0.999636i	$-0.508584\pi$
$313$	−17.4443	−	12.6740i	−0.986009	−	0.716377i	−0.959043	+	0.283259i	$0.908584\pi$
$314$	18.1520	+	13.1882i	1.02438	+	0.744255i
$315$		0			0
$316$	1.08477	+	3.33857i	0.0610228	+	0.187809i
$317$	−6.44050	+	4.67930i	−0.361734	+	0.262815i	−0.753775	−	0.657132i	$-0.771769\pi$
$317$	−6.44050	+	4.67930i	−0.361734	+	0.262815i	0.392041	+	0.919948i	$0.371769\pi$
$318$	−8.42900			−0.472675
$319$	1.36662	−	7.51360i	0.0765159	−	0.420681i
$320$		0			0
$321$	−7.79819	+	5.66572i	−0.435253	+	0.316230i
$322$	−4.86871	−	14.9843i	−0.271323	−	0.835045i
$323$	4.89919	−	15.0781i	0.272598	−	0.838971i
$324$	−6.90193	−	5.01454i	−0.383440	−	0.278586i
$325$		0			0
$326$	−6.09404	+	18.7555i	−0.337517	+	1.03877i
$327$	−6.06320	−	18.6606i	−0.335296	−	1.03193i
$328$	−7.72025	+	5.60909i	−0.426279	+	0.309710i
$329$	−16.9227			−0.932976
$330$		0			0
$331$	−22.9563			−1.26179			−0.630896	−	0.775868i	$-0.717312\pi$
$331$	−22.9563			−1.26179			−0.630896	+	0.775868i	$0.717312\pi$
$332$	−1.35577	+	0.985026i	−0.0744077	+	0.0540603i
$333$	10.9953	+	33.8402i	0.602541	+	1.85443i
$334$	1.26638	−	3.89752i	0.0692933	−	0.213263i
$335$		0			0
$336$	12.2186	+	8.87732i	0.666578	+	0.484297i
$337$	3.78163	−	11.6387i	0.205999	−	0.633999i	−0.793672	−	0.608346i	$-0.791833\pi$
$337$	3.78163	−	11.6387i	0.205999	−	0.633999i	0.999671	−	0.0256533i	$-0.00816659\pi$
$338$	−3.00151	−	9.23771i	−0.163261	−	0.502465i
$339$	−13.1467	+	9.55164i	−0.714031	+	0.518774i
$340$		0			0
$341$	0.406563	−	0.388403i	0.0220166	−	0.0210332i
$342$	17.5313			0.947981
$343$	46.9458	−	34.1081i	2.53483	−	1.84166i
$344$	−2.20614	−	6.78980i	−0.118947	−	0.366081i
$345$		0			0
$346$	−10.4405	−	7.58547i	−0.561285	−	0.407797i
$347$	−23.5629	−	17.1194i	−1.26492	−	0.919019i	−0.265933	−	0.963992i	$-0.585680\pi$
$347$	−23.5629	−	17.1194i	−1.26492	−	0.919019i	−0.998988	+	0.0449727i	$0.985680\pi$
$348$	2.12841	−	6.55057i	0.114095	−	0.351148i
$349$	−0.486742	−	1.49804i	−0.0260547	−	0.0801882i	0.937184	−	0.348836i	$-0.113423\pi$
$349$	−0.486742	−	1.49804i	−0.0260547	−	0.0801882i	−0.963238	+	0.268648i	$0.913423\pi$
$350$		0			0
$351$	−15.9852			−0.853225
$352$	3.28679	−	0.443888i	0.175186	−	0.0236593i
$353$	−34.7890			−1.85163			−0.925817	−	0.377972i	$-0.876622\pi$
$353$	−34.7890			−1.85163			−0.925817	+	0.377972i	$0.876622\pi$
$354$	−15.2832	+	11.1039i	−0.812293	+	0.590165i
$355$		0			0
$356$	5.33329	−	16.4142i	0.282664	−	0.869949i
$357$	65.7192	+	47.7478i	3.47823	+	2.52708i
$358$	−10.9378	−	7.94677i	−0.578081	−	0.420000i
$359$	8.88597	−	27.3482i	0.468984	−	1.44338i	−0.384919	−	0.922951i	$-0.625770\pi$
$359$	8.88597	−	27.3482i	0.468984	−	1.44338i	0.853902	−	0.520433i	$-0.174230\pi$
$360$		0			0
$361$	8.34225	−	6.06100i	0.439066	−	0.319000i
$362$	−22.4911			−1.18211
$363$	18.1047	+	27.4751i	0.950248	+	1.44207i
$364$	9.15382			0.479791
$365$		0			0
$366$	3.59056	+	11.0506i	0.187681	+	0.577624i
$367$	−10.2676	+	31.6005i	−0.535966	+	1.64953i	0.205587	+	0.978639i	$0.434090\pi$
$367$	−10.2676	+	31.6005i	−0.535966	+	1.64953i	−0.741553	+	0.670894i	$0.765910\pi$
$368$	−2.52452	−	1.83417i	−0.131600	−	0.0956129i
$369$	−45.9170	−	33.3607i	−2.39035	−	1.73669i
$370$		0			0
$371$	4.39657	+	13.5313i	0.228259	+	0.702508i
$372$	0.410263	−	0.298073i	0.0212711	−	0.0154544i
$373$	14.9618			0.774691			0.387345	−	0.921935i	$-0.373392\pi$
$373$	14.9618			0.774691			0.387345	+	0.921935i	$0.373392\pi$
$374$	17.6784	−	2.38751i	0.914128	−	0.123455i
$375$		0			0
$376$	−2.71154	+	1.97005i	−0.139837	+	0.101598i
$377$	−1.29001	−	3.97026i	−0.0664392	−	0.204479i
$378$	−13.7567	+	42.3389i	−0.707571	+	2.17768i
$379$	6.56354	+	4.76869i	0.337147	+	0.244951i	0.743457	−	0.668784i	$-0.233185\pi$
$379$	6.56354	+	4.76869i	0.337147	+	0.244951i	−0.406310	+	0.913735i	$0.633185\pi$
$380$		0			0
$381$	−15.6524	+	48.1732i	−0.801898	+	2.46799i
$382$	5.13715	+	15.8105i	0.262840	+	0.808937i
$383$	12.5648	−	9.12888i	0.642033	−	0.466464i	−0.218515	−	0.975834i	$-0.570121\pi$
$383$	12.5648	−	9.12888i	0.642033	−	0.466464i	0.860548	+	0.509369i	$0.170121\pi$
$384$	2.99126			0.152647
$385$		0			0
$386$	7.94427			0.404353
$387$	34.3519	−	24.9581i	1.74621	−	1.26869i
$388$	2.73607	+	8.42075i	0.138903	+	0.427499i
$389$	11.2743	−	34.6988i	0.571630	−	1.75930i	−0.0757474	−	0.997127i	$-0.524134\pi$
$389$	11.2743	−	34.6988i	0.571630	−	1.75930i	0.647378	−	0.762170i	$-0.275866\pi$
$390$		0			0
$391$	−13.5785	−	9.86534i	−0.686693	−	0.498912i
$392$	5.71462	−	17.5878i	0.288632	−	0.888317i
$393$	−7.19390	−	22.1405i	−0.362884	−	1.11684i
$394$	−17.2186	+	12.5100i	−0.867460	+	0.630246i
$395$		0			0
$396$	8.55169	+	17.7759i	0.429739	+	0.893274i
$397$	30.3772			1.52459			0.762293	−	0.647232i	$-0.224074\pi$
$397$	30.3772			1.52459			0.762293	+	0.647232i	$0.224074\pi$
$398$	5.87567	−	4.26893i	0.294521	−	0.213982i
$399$	−13.7567	−	42.3389i	−0.688699	−	2.11960i
$400$		0			0
$401$	−1.90727	−	1.38571i	−0.0952445	−	0.0691992i	0.539144	−	0.842214i	$-0.318748\pi$
$401$	−1.90727	−	1.38571i	−0.0952445	−	0.0691992i	−0.634388	+	0.773015i	$0.718748\pi$
$402$	−14.8225	−	10.7692i	−0.739280	−	0.537119i
$403$	0.0949787	−	0.292314i	0.00473122	−	0.0145612i
$404$	−3.10144	−	9.54524i	−0.154302	−	0.474893i
$405$		0			0
$406$	−11.6260			−0.576987
$407$	3.55068	−	19.5215i	0.176001	−	0.967643i
$408$	16.0888			0.796517
$409$	16.3223	−	11.8588i	0.807085	−	0.586381i	−0.105899	−	0.994377i	$-0.533772\pi$
$409$	16.3223	−	11.8588i	0.807085	−	0.586381i	0.912984	+	0.407996i	$0.133772\pi$
$410$		0			0
$411$	−7.96798	+	24.5229i	−0.393031	+	1.20963i
$412$	3.32958	+	2.41908i	0.164037	+	0.119180i
$413$	25.7971	+	18.7427i	1.26939	+	0.922266i
$414$	5.73518	−	17.6511i	0.281869	−	0.867502i
$415$		0			0
$416$	1.46673	−	1.06564i	0.0719124	−	0.0522474i
$417$	−47.8255			−2.34202
$418$	−8.60696	−	4.63604i	−0.420980	−	0.226756i
$419$	7.54275			0.368488			0.184244	−	0.982881i	$-0.441016\pi$
$419$	7.54275			0.368488			0.184244	+	0.982881i	$0.441016\pi$
$420$		0			0
$421$	0.516598	+	1.58992i	0.0251774	+	0.0774882i	0.962856	−	0.270016i	$-0.0870291\pi$
$421$	0.516598	+	1.58992i	0.0251774	+	0.0774882i	−0.937678	+	0.347505i	$0.887029\pi$
$422$	2.71821	−	8.36579i	0.132320	−	0.407240i
$423$	−16.1272	−	11.7171i	−0.784132	−	0.569705i
$424$	2.27971	+	1.65631i	0.110713	+	0.0804374i
$425$		0			0
$426$	−5.10350	−	15.7070i	−0.247265	−	0.761005i
$427$	15.8669	−	11.5280i	0.767854	−	0.557879i
$428$	3.22243			0.155762
$429$	15.8353	+	8.52949i	0.764535	+	0.411808i
$430$		0			0
$431$	17.1367	−	12.4505i	0.825446	−	0.599721i	−0.0928215	−	0.995683i	$-0.529589\pi$
$431$	17.1367	−	12.4505i	0.825446	−	0.599721i	0.918267	+	0.395961i	$0.129589\pi$
$432$	2.72462	+	8.38552i	0.131088	+	0.403449i
$433$	−6.97355	+	21.4624i	−0.335128	+	1.03142i	0.631532	+	0.775350i	$0.282427\pi$
$433$	−6.97355	+	21.4624i	−0.335128	+	1.03142i	−0.966659	+	0.256066i	$0.917573\pi$
$434$	−0.692497	−	0.503128i	−0.0332409	−	0.0241509i
$435$		0			0
$436$	−2.02697	+	6.23838i	−0.0970744	+	0.298764i
$437$	2.84233	+	8.74779i	0.135967	+	0.418464i
$438$	21.5243	−	15.6383i	1.02847	−	0.747226i
$439$	7.11544			0.339601			0.169801	−	0.985478i	$-0.445688\pi$
$439$	7.11544			0.339601			0.169801	+	0.985478i	$0.445688\pi$
$440$		0			0
$441$	109.989			5.23755
$442$	7.88900	−	5.73170i	0.375242	−	0.272629i
$443$	−7.20620	−	22.1784i	−0.342377	−	1.05373i	−0.962973	−	0.269597i	$-0.913109\pi$
$443$	−7.20620	−	22.1784i	−0.342377	−	1.05373i	0.620596	−	0.784130i	$-0.286891\pi$
$444$	5.52993	−	17.0194i	0.262439	−	0.807704i
$445$		0			0
$446$	16.0498	+	11.6609i	0.759980	+	0.552157i
$447$	3.68274	−	11.3343i	0.174188	−	0.536095i
$448$	−1.56024	−	4.80193i	−0.0737145	−	0.226870i
$449$	−17.2062	+	12.5011i	−0.812013	+	0.589962i	−0.914413	−	0.404781i	$-0.867348\pi$
$449$	−17.2062	+	12.5011i	−0.812013	+	0.589962i	0.102401	+	0.994743i	$0.467348\pi$
$450$		0			0
$451$	13.7209	+	28.5209i	0.646092	+	1.34300i
$452$	5.43257			0.255527
$453$	−21.9246	+	15.9292i	−1.03011	+	0.748418i
$454$	1.83599	+	5.65060i	0.0861673	+	0.265196i
$455$		0			0
$456$	−7.13315	−	5.18254i	−0.334040	−	0.242695i
$457$	3.44287	+	2.50139i	0.161051	+	0.117010i	0.665392	−	0.746494i	$-0.268265\pi$
$457$	3.44287	+	2.50139i	0.161051	+	0.117010i	−0.504341	+	0.863505i	$0.668265\pi$
$458$	3.11558	−	9.58878i	0.145582	−	0.448054i
$459$	14.6547	+	45.1026i	0.684024	+	2.10521i
$460$		0			0
$461$	−5.57201			−0.259515			−0.129757	−	0.991546i	$-0.541420\pi$
$461$	−5.57201			−0.259515			−0.129757	+	0.991546i	$0.541420\pi$
$462$	36.2193	−	34.6015i	1.68508	−	1.60981i
$463$	−22.6292			−1.05167			−0.525835	−	0.850587i	$-0.676247\pi$
$463$	−22.6292			−1.05167			−0.525835	+	0.850587i	$0.676247\pi$
$464$	−1.86285	+	1.35344i	−0.0864805	+	0.0628317i
$465$		0			0
$466$	−0.192497	+	0.592444i	−0.00891724	+	0.0274445i
$467$	17.1903	+	12.4895i	0.795471	+	0.577944i	0.909582	−	0.415524i	$-0.136402\pi$
$467$	17.1903	+	12.4895i	0.795471	+	0.577944i	−0.114111	+	0.993468i	$0.536402\pi$
$468$	8.72355	+	6.33803i	0.403246	+	0.292976i
$469$	−9.55659	+	29.4122i	−0.441282	+	1.35813i
$470$		0			0
$471$	54.2974	−	39.4494i	2.50189	−	1.81773i
$472$	6.31543			0.290691
$473$	−23.4651	+	3.16902i	−1.07893	+	0.145711i
$474$	10.5004			0.482301
$475$		0			0
$476$	−8.39196	−	25.8278i	−0.384645	−	1.18381i
$477$	−5.17902	+	15.9394i	−0.237131	+	0.729814i
$478$	8.48496	+	6.16469i	0.388093	+	0.281966i
$479$	14.8803	+	10.8111i	0.679896	+	0.493974i	0.873323	−	0.487141i	$-0.161960\pi$
$479$	14.8803	+	10.8111i	0.679896	+	0.493974i	−0.193427	+	0.981115i	$0.561960\pi$
$480$		0			0
$481$	−3.35165	−	10.3153i	−0.152822	−	0.470338i
$482$	10.9108	−	7.92718i	0.496974	−	0.361073i
$483$	−47.1286			−2.14443
$484$	0.502293	−	10.9885i	0.0228315	−	0.499478i
$485$		0			0
$486$	0.754027	−	0.547833i	0.0342034	−	0.0248502i
$487$	−5.64345	−	17.3687i	−0.255729	−	0.787053i	−0.993685	−	0.112204i	$-0.964209\pi$
$487$	−5.64345	−	17.3687i	−0.255729	−	0.787053i	0.737956	−	0.674849i	$-0.235791\pi$
$488$	1.20035	−	3.69430i	0.0543373	−	0.167233i
$489$	47.7237	+	34.6733i	2.15814	+	1.56798i
$490$		0			0
$491$	0.0905551	−	0.278700i	0.00408670	−	0.0125776i	−0.948992	−	0.315299i	$-0.897895\pi$
$491$	0.0905551	−	0.278700i	0.00408670	−	0.0125776i	0.953079	+	0.302721i	$0.0978952\pi$
$492$	8.82083	+	27.1477i	0.397674	+	1.22391i
$493$	−10.0196	+	7.27963i	−0.451258	+	0.327858i
$494$	−5.34396			−0.240436
$495$		0			0
$496$	−0.169532			−0.00761219
$497$	−22.5527	+	16.3855i	−1.01163	+	0.734991i
$498$	1.54905	+	4.76748i	0.0694145	+	0.213636i
$499$	−1.84291	+	5.67189i	−0.0824999	+	0.253909i	−0.983795	−	0.179297i	$-0.942618\pi$
$499$	−1.84291	+	5.67189i	−0.0824999	+	0.253909i	0.901295	+	0.433206i	$0.142618\pi$
$500$		0			0
$501$	−9.91730	−	7.20534i	−0.443072	−	0.321911i
$502$	−4.06420	+	12.5083i	−0.181394	+	0.558274i
$503$	−0.974585	−	2.99947i	−0.0434546	−	0.133740i	0.926975	−	0.375122i	$-0.122399\pi$
$503$	−0.974585	−	2.99947i	−0.0434546	−	0.133740i	−0.970430	+	0.241382i	$0.922399\pi$
$504$	24.2946	−	17.6511i	1.08217	−	0.786241i
$505$		0			0
$506$	−7.48340	+	7.14914i	−0.332678	+	0.317818i
$507$	−29.0544			−1.29035
$508$	13.6995	−	9.95324i	0.607815	−	0.441604i
$509$	6.85900	+	21.1098i	0.304020	+	0.935677i	0.980041	+	0.198795i	$0.0637027\pi$
$509$	6.85900	+	21.1098i	0.304020	+	0.935677i	−0.676021	+	0.736882i	$0.736297\pi$
$510$		0			0
$511$	−36.3316	−	26.3964i	−1.60721	−	1.16771i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	8.03113	−	24.7173i	0.354583	−	1.09129i
$514$	−1.09930	−	3.38330i	−0.0484880	−	0.149231i
$515$		0			0
$516$	−21.3552			−0.940112
$517$	4.81913	+	10.0173i	0.211945	+	0.440558i
$518$	−30.2060			−1.32718
$519$	−31.2302	+	22.6901i	−1.37085	+	0.995984i
$520$		0			0
$521$	−1.99803	+	6.14931i	−0.0875354	+	0.269406i	−0.985237	−	0.171199i	$-0.945236\pi$
$521$	−1.99803	+	6.14931i	−0.0875354	+	0.269406i	0.897701	+	0.440605i	$0.145236\pi$
$522$	−11.0795	−	8.04972i	−0.484936	−	0.352327i
$523$	−2.40756	−	1.74920i	−0.105275	−	0.0764870i	0.533902	−	0.845546i	$-0.320725\pi$
$523$	−2.40756	−	1.74920i	−0.105275	−	0.0764870i	−0.639177	+	0.769059i	$0.720725\pi$
$524$	−2.40498	+	7.40176i	−0.105062	+	0.323347i
$525$		0			0
$526$	10.0531	−	7.30403i	0.438337	−	0.318471i
$527$	−0.911847			−0.0397207
$528$	1.77534	−	9.76073i	0.0772618	−	0.424781i
$529$	−13.2626			−0.576634
$530$		0			0
$531$	11.6072	+	35.7233i	0.503710	+	1.55026i
$532$	−4.59899	+	14.1542i	−0.199391	+	0.613664i
$533$	13.9967	+	10.1692i	0.606263	+	0.440476i
$534$	−41.7661	−	30.3448i	−1.80740	−	1.31315i
$535$		0			0
$536$	1.89275	+	5.82529i	0.0817544	+	0.251614i
$537$	−32.7178	+	23.7708i	−1.41188	+	1.02579i
$538$	−7.84944			−0.338413
$539$	−53.9988	−	29.0858i	−2.32589	−	1.25282i
$540$		0			0
$541$	−2.29794	+	1.66955i	−0.0987962	+	0.0717797i	−0.636087	−	0.771618i	$-0.719448\pi$
$541$	−2.29794	+	1.66955i	−0.0987962	+	0.0717797i	0.537290	+	0.843397i	$0.319448\pi$
$542$	7.97125	+	24.5330i	0.342394	+	1.05378i
$543$	−20.7896	+	63.9839i	−0.892168	+	2.74581i
$544$	−4.35140	−	3.16148i	−0.186565	−	0.135547i
$545$		0			0
$546$	8.46133	−	26.0413i	0.362111	−	1.11446i
$547$	8.25516	+	25.4068i	0.352965	+	1.08632i	0.957180	+	0.289494i	$0.0934870\pi$
$547$	8.25516	+	25.4068i	0.352965	+	1.08632i	−0.604215	+	0.796822i	$0.706513\pi$
$548$	6.97381	−	5.06677i	0.297906	−	0.216442i
$549$	23.1030			0.986012
$550$		0			0
$551$	6.78718			0.289144
$552$	−7.55150	+	5.48648i	−0.321413	+	0.233520i
$553$	−5.47703	−	16.8566i	−0.232907	−	0.716815i
$554$	−9.71073	+	29.8865i	−0.412569	+	1.26976i
$555$		0			0
$556$	12.9349	+	9.39776i	0.548562	+	0.398554i
$557$	5.76393	−	17.7396i	0.244226	−	0.751649i	−0.751537	−	0.659691i	$-0.770687\pi$
$557$	5.76393	−	17.7396i	0.244226	−	0.751649i	0.995763	−	0.0919585i	$-0.0293127\pi$
$558$	−0.311584	−	0.958958i	−0.0131904	−	0.0405959i
$559$	−10.4713	+	7.60786i	−0.442890	+	0.321778i
$560$		0			0
$561$	9.54889	−	52.4993i	0.403154	−	2.21652i
$562$	9.17155			0.386878
$563$	10.7790	−	7.83141i	0.454281	−	0.330055i	−0.337003	−	0.941504i	$-0.609413\pi$
$563$	10.7790	−	7.83141i	0.454281	−	0.330055i	0.791284	+	0.611449i	$0.209413\pi$
$564$	3.09810	+	9.53496i	0.130453	+	0.401494i
$565$		0			0
$566$	0.293237	+	0.213049i	0.0123257	+	0.00895512i
$567$	34.8482	+	25.3187i	1.46349	+	1.06328i
$568$	−1.70614	+	5.25096i	−0.0715880	+	0.220325i
$569$	2.42330	+	7.45816i	0.101590	+	0.312662i	0.988915	−	0.148483i	$-0.0474389\pi$
$569$	2.42330	+	7.45816i	0.101590	+	0.312662i	−0.887325	+	0.461145i	$0.847439\pi$
$570$		0			0
$571$	36.4787			1.52658			0.763292	−	0.646053i	$-0.223582\pi$
$571$	36.4787			1.52658			0.763292	+	0.646053i	$0.223582\pi$
$572$	−2.60677	−	5.41855i	−0.108994	−	0.226561i
$573$	49.7272			2.07738
$574$	38.9799	−	28.3206i	1.62699	−	1.18208i
$575$		0			0
$576$	1.83791	−	5.65652i	0.0765797	−	0.235688i
$577$	−16.2570	−	11.8114i	−0.676788	−	0.491715i	0.195503	−	0.980703i	$-0.437366\pi$
$577$	−16.2570	−	11.8114i	−0.676788	−	0.491715i	−0.872290	+	0.488988i	$0.837366\pi$
$578$	−9.65126	−	7.01205i	−0.401440	−	0.291663i
$579$	7.34328	−	22.6003i	0.305176	−	0.939236i
$580$		0			0
$581$	6.84536	−	4.97344i	0.283993	−	0.206333i
$582$	26.4849			1.09783
$583$	6.75771	−	6.45587i	0.279876	−	0.267375i
$584$	−8.89441			−0.368053
$585$		0			0
$586$	9.41434	+	28.9744i	0.388903	+	1.19692i
$587$	−4.38156	+	13.4850i	−0.180846	+	0.556587i	−0.999852	−	0.0171977i	$-0.994526\pi$
$587$	−4.38156	+	13.4850i	−0.180846	+	0.556587i	0.819006	+	0.573785i	$0.194526\pi$
$588$	−44.7524	−	32.5145i	−1.84556	−	1.34088i
$589$	0.404277	+	0.293724i	0.0166579	+	0.0121027i
$590$		0			0
$591$	19.6732	+	60.5480i	0.809248	+	2.49061i
$592$	−4.83995	+	3.51643i	−0.198921	+	0.144524i
$593$	−5.31185			−0.218132			−0.109066	−	0.994035i	$-0.534786\pi$
$593$	−5.31185			−0.218132			−0.109066	+	0.994035i	$0.534786\pi$
$594$	28.9798	−	3.91379i	1.18906	−	0.160585i
$595$		0			0
$596$	−3.22324	+	2.34182i	−0.132029	+	0.0959248i
$597$	−6.71330	−	20.6614i	−0.274757	−	0.845615i
$598$	−1.74822	+	5.38048i	−0.0714902	+	0.220024i
$599$	36.1271	+	26.2479i	1.47611	+	1.07246i	0.978783	+	0.204900i	$0.0656868\pi$
$599$	36.1271	+	26.2479i	1.47611	+	1.07246i	0.497332	+	0.867560i	$0.334313\pi$
$600$		0			0
$601$	−5.04697	+	15.5330i	−0.205870	+	0.633603i	0.793806	+	0.608171i	$0.208096\pi$
$601$	−5.04697	+	15.5330i	−0.205870	+	0.633603i	−0.999677	+	0.0254327i	$0.991904\pi$
$602$	11.1389	+	34.2820i	0.453988	+	1.39723i
$603$	−29.4721	+	21.4127i	−1.20020	+	0.871994i
$604$	9.05986			0.368640
$605$		0			0
$606$	−30.0216			−1.21954
$607$	15.0814	−	10.9573i	0.612136	−	0.444743i	−0.238030	−	0.971258i	$-0.576502\pi$
$607$	15.0814	−	10.9573i	0.612136	−	0.444743i	0.850166	+	0.526515i	$0.176502\pi$
$608$	0.910862	+	2.80335i	0.0369403	+	0.113691i
$609$	−10.7464	+	33.0742i	−0.435468	+	1.34023i
$610$		0			0
$611$	4.91598	+	3.57167i	0.198879	+	0.144494i
$612$	9.88545	−	30.4243i	0.399596	−	1.22983i
$613$	−3.12639	−	9.62205i	−0.126274	−	0.388631i	0.867857	−	0.496814i	$-0.165497\pi$
$613$	−3.12639	−	9.62205i	−0.126274	−	0.388631i	−0.994131	+	0.108183i	$0.965497\pi$
$614$	10.5243	−	7.64635i	0.424726	−	0.308581i
$615$		0			0
$616$	−16.5951	+	2.24121i	−0.668637	+	0.0903011i
$617$	−13.3311			−0.536691			−0.268346	−	0.963323i	$-0.586477\pi$
$617$	−13.3311			−0.536691			−0.268346	+	0.963323i	$0.586477\pi$
$618$	9.95962	−	7.23609i	0.400635	−	0.291078i
$619$	7.71248	+	23.7366i	0.309991	+	0.954053i	0.977768	+	0.209692i	$0.0672461\pi$
$619$	7.71248	+	23.7366i	0.309991	+	0.954053i	−0.667777	+	0.744362i	$0.732754\pi$
$620$		0			0
$621$	−22.2589	−	16.1720i	−0.893218	−	0.648961i
$622$	−4.97377	−	3.61365i	−0.199430	−	0.144894i
$623$	−26.9280	+	82.8760i	−1.07885	+	3.32036i
$624$	−1.67583	−	5.15766i	−0.0670867	−	0.206472i
$625$		0			0
$626$	21.5623			0.861803
$627$	−21.1447	+	20.2002i	−0.844437	+	0.806719i
$628$	−22.4372			−0.895340
$629$	−26.0323	+	18.9136i	−1.03798	+	0.754134i
$630$		0			0
$631$	6.26429	−	19.2795i	0.249377	−	0.767505i	−0.745508	−	0.666496i	$-0.767793\pi$
$631$	6.26429	−	19.2795i	0.249377	−	0.767505i	0.994886	−	0.101008i	$-0.0322068\pi$
$632$	−2.83995	−	2.06335i	−0.112967	−	0.0820755i
$633$	−21.2869	−	15.4658i	−0.846077	−	0.614711i
$634$	2.46005	−	7.57126i	0.0977011	−	0.300693i
$635$		0			0
$636$	6.81920	−	4.95444i	0.270399	−	0.196456i
$637$	−33.5272			−1.32840
$638$	3.31077	+	6.88191i	0.131075	+	0.272457i
$639$	−32.8379			−1.29905
$640$		0			0
$641$	−10.4170	−	32.0602i	−0.411446	−	1.26630i	−0.915391	−	0.402565i	$-0.868119\pi$
$641$	−10.4170	−	32.0602i	−0.411446	−	1.26630i	0.503945	−	0.863736i	$-0.331881\pi$
$642$	2.97865	−	9.16733i	0.117558	−	0.361806i
$643$	36.3871	+	26.4368i	1.43497	+	1.04256i	0.989065	+	0.147483i	$0.0471173\pi$
$643$	36.3871	+	26.4368i	1.43497	+	1.04256i	0.445903	+	0.895081i	$0.352883\pi$
$644$	12.7464	+	9.26083i	0.502280	+	0.364928i
$645$		0			0
$646$	4.89919	+	15.0781i	0.192756	+	0.593242i
$647$	15.9920	−	11.6189i	0.628710	−	0.456785i	−0.227243	−	0.973838i	$-0.572971\pi$
$647$	15.9920	−	11.6189i	0.628710	−	0.456785i	0.855953	+	0.517053i	$0.172971\pi$
$648$	8.53125			0.335139
$649$	3.74827	−	20.6078i	0.147132	−	0.808927i
$650$		0			0
$651$	−2.07144	+	1.50499i	−0.0811859	+	0.0589850i
$652$	−6.09404	−	18.7555i	−0.238661	−	0.734523i
$653$	9.46495	−	29.1301i	0.370392	−	1.13995i	−0.576143	−	0.817349i	$-0.695443\pi$
$653$	9.46495	−	29.1301i	0.370392	−	1.13995i	0.946535	−	0.322601i	$-0.104557\pi$
$654$	15.8737	+	11.5329i	0.620709	+	0.450971i
$655$		0			0
$656$	2.94887	−	9.07570i	0.115134	−	0.354346i
$657$	−16.3471	−	50.3113i	−0.637763	−	1.96283i
$658$	13.6907	−	9.94689i	0.533720	−	0.387770i
$659$	14.0711			0.548133			0.274067	−	0.961711i	$-0.411631\pi$
$659$	14.0711			0.548133			0.274067	+	0.961711i	$0.411631\pi$
$660$		0			0
$661$	−30.9905			−1.20539			−0.602696	−	0.797971i	$-0.705907\pi$
$661$	−30.9905			−1.20539			−0.602696	+	0.797971i	$0.705907\pi$
$662$	18.5720	−	13.4934i	0.721822	−	0.524434i
$663$	−9.01364	−	27.7411i	−0.350061	−	1.07738i
$664$	0.517859	−	1.59381i	0.0200968	−	0.0618516i
$665$		0			0
$666$	−28.7862	−	20.9144i	−1.11544	−	0.810416i
$667$	2.22036	−	6.83357i	0.0859727	−	0.264597i
$668$	1.26638	+	3.89752i	0.0489978	+	0.150800i
$669$	48.0090	−	34.8806i	1.85614	−	1.34856i
$670$		0			0
$671$	−11.3424	−	6.10945i	−0.437869	−	0.235853i
$672$	−15.1030			−0.582611
$673$	34.1765	−	24.8307i	1.31741	−	0.957152i	0.317446	−	0.948276i	$-0.397175\pi$
$673$	34.1765	−	24.8307i	1.31741	−	0.957152i	0.999961	−	0.00887590i	$-0.00282532\pi$
$674$	3.78163	+	11.6387i	0.145663	+	0.448305i
$675$		0			0
$676$	7.85807	+	5.70922i	0.302233	+	0.219585i
$677$	18.7311	+	13.6089i	0.719895	+	0.523034i	0.886350	−	0.463015i	$-0.153232\pi$
$677$	18.7311	+	13.6089i	0.719895	+	0.523034i	−0.166456	+	0.986049i	$0.553232\pi$
$678$	5.02159	−	15.4549i	0.192853	−	0.593541i
$679$	−13.8145	−	42.5168i	−0.530153	−	1.63164i
$680$		0			0
$681$	17.7722			0.681033
$682$	−0.100619	+	0.553197i	−0.00385289	+	0.0211830i
$683$	−7.03233			−0.269085			−0.134542	−	0.990908i	$-0.542956\pi$
$683$	−7.03233			−0.269085			−0.134542	+	0.990908i	$0.542956\pi$
$684$	−14.1831	+	10.3046i	−0.542304	+	0.394007i
$685$		0			0
$686$	−17.9317	+	55.1880i	−0.684635	+	2.10709i
$687$	−24.3988	−	17.7268i	−0.930872	−	0.676318i
$688$	5.77575	+	4.19633i	0.220198	+	0.159983i
$689$	1.57869	−	4.85872i	0.0601434	−	0.185102i
$690$		0			0
$691$	−9.92334	+	7.20973i	−0.377502	+	0.274271i	−0.760315	−	0.649555i	$-0.774955\pi$
$691$	−9.92334	+	7.20973i	−0.377502	+	0.274271i	0.382813	+	0.923826i	$0.374955\pi$
$692$	12.9052			0.490581
$693$	−43.1779	−	89.7515i	−1.64019	−	3.40938i
$694$	29.1253			1.10558
$695$		0			0
$696$	2.12841	+	6.55057i	0.0806772	+	0.248299i
$697$	15.8609	−	48.8148i	0.600774	−	1.84899i
$698$	1.27431	+	0.925839i	0.0482333	+	0.0350435i
$699$	1.50748	+	1.09525i	0.0570182	+	0.0414262i
$700$		0			0
$701$	−6.23273	−	19.1824i	−0.235407	−	0.724508i	−0.997067	−	0.0765314i	$-0.975615\pi$
$701$	−6.23273	−	19.1824i	−0.235407	−	0.724508i	0.761660	−	0.647977i	$-0.224385\pi$
$702$	12.9323	−	9.39584i	0.488097	−	0.354623i
$703$	17.6341			0.665084
$704$	−2.39815	+	2.29104i	−0.0903839	+	0.0863467i
$705$		0			0
$706$	28.1449	−	20.4485i	1.05925	−	0.769589i
$707$	15.6593	+	48.1944i	0.588929	+	1.81254i
$708$	5.83766	−	17.9665i	0.219393	−	0.675221i
$709$	−18.1795	−	13.2082i	−0.682746	−	0.496044i	0.191521	−	0.981488i	$-0.438658\pi$
$709$	−18.1795	−	13.2082i	−0.682746	−	0.496044i	−0.874268	+	0.485444i	$0.838658\pi$
$710$		0			0
$711$	6.45177	−	19.8565i	0.241960	−	0.744677i
$712$	5.33329	+	16.4142i	0.199873	+	0.615147i
$713$	0.427987	−	0.310950i	0.0160282	−	0.0116452i
$714$	−81.2334			−3.04008
$715$		0			0
$716$	13.5199			0.505261
$717$	25.3807	−	18.4402i	0.947859	−	0.688660i
$718$	8.88597	+	27.3482i	0.331622	+	1.02063i
$719$	8.80373	−	27.0951i	0.328324	−	1.01048i	−0.641594	−	0.767044i	$-0.721727\pi$
$719$	8.80373	−	27.0951i	0.328324	−	1.01048i	0.969918	−	0.243432i	$-0.0782734\pi$
$720$		0			0
$721$	−16.8112	−	12.2141i	−0.626082	−	0.454875i
$722$	−3.18645	+	9.80690i	−0.118588	+	0.364975i
$723$	−12.4663	−	38.3672i	−0.463625	−	1.42689i
$724$	18.1957	−	13.2199i	0.676237	−	0.491315i
$725$		0			0
$726$	−30.7965	−	11.5862i	−1.14296	−	0.430004i
$727$	16.1547			0.599144			0.299572	−	0.954074i	$-0.403156\pi$
$727$	16.1547			0.599144			0.299572	+	0.954074i	$0.403156\pi$
$728$	−7.40560	+	5.38048i	−0.274470	+	0.199414i
$729$	−8.77042	−	26.9926i	−0.324831	−	0.999726i
$730$		0			0
$731$	31.0656	+	22.5705i	1.14900	+	0.834799i
$732$	−9.40020	−	6.82964i	−0.347441	−	0.252431i
$733$	−10.7200	+	32.9927i	−0.395951	+	1.21861i	0.532267	+	0.846577i	$0.321340\pi$
$733$	−10.7200	+	32.9927i	−0.395951	+	1.21861i	−0.928218	+	0.372036i	$0.878660\pi$
$734$	−10.2676	−	31.6005i	−0.378985	−	1.16640i
$735$		0			0
$736$	3.12048			0.115023
$737$	20.1318	−	2.71885i	0.741564	−	0.100150i
$738$	56.7566			2.08924
$739$	9.86328	−	7.16609i	0.362827	−	0.263609i	−0.391404	−	0.920219i	$-0.628010\pi$
$739$	9.86328	−	7.16609i	0.362827	−	0.263609i	0.754230	+	0.656610i	$0.228010\pi$
$740$		0			0
$741$	−4.93969	+	15.2028i	−0.181464	+	0.558488i
$742$	−11.5104	−	8.36278i	−0.422559	−	0.307007i
$743$	8.00132	+	5.81330i	0.293540	+	0.213269i	0.724802	−	0.688958i	$-0.241931\pi$
$743$	8.00132	+	5.81330i	0.293540	+	0.213269i	−0.431262	+	0.902227i	$0.641931\pi$
$744$	−0.156706	+	0.482293i	−0.00574513	+	0.0176817i
$745$		0			0
$746$	−12.1043	+	8.79430i	−0.443171	+	0.321982i
$747$	9.96716			0.364679
$748$	−12.8988	+	12.3226i	−0.471626	+	0.450560i
$749$	−16.2702			−0.594499
$750$		0			0
$751$	−4.49402	−	13.8312i	−0.163989	−	0.504706i	0.834971	−	0.550293i	$-0.185484\pi$
$751$	−4.49402	−	13.8312i	−0.163989	−	0.504706i	−0.998960	+	0.0455871i	$0.985484\pi$
$752$	1.03572	−	3.18761i	0.0377687	−	0.116240i
$753$	31.8276	+	23.1241i	1.15986	+	0.842690i
$754$	3.37730	+	2.45375i	0.122994	+	0.0893605i
$755$		0			0
$756$	−13.7567	−	42.3389i	−0.500328	−	1.53985i
$757$	−25.4983	+	18.5256i	−0.926751	+	0.673324i	−0.945195	−	0.326506i	$-0.894129\pi$
$757$	−25.4983	+	18.5256i	−0.926751	+	0.673324i	0.0184440	+	0.999830i	$0.494129\pi$
$758$	−8.11299			−0.294677
$759$	13.4210	+	27.8975i	0.487151	+	1.01261i
$760$		0			0
$761$	−41.9810	+	30.5010i	−1.52181	+	1.10566i	−0.561228	+	0.827661i	$0.689671\pi$
$761$	−41.9810	+	30.5010i	−1.52181	+	1.10566i	−0.960582	+	0.277998i	$0.910329\pi$
$762$	−15.6524	−	48.1732i	−0.567028	−	1.74513i
$763$	10.2343	−	31.4979i	0.370506	−	1.14030i
$764$	−13.4492	−	9.77145i	−0.486577	−	0.353519i
$765$		0			0
$766$	−4.79934	+	14.7708i	−0.173407	+	0.533692i
$767$	−3.53817	−	10.8894i	−0.127756	−	0.393192i
$768$	−2.41998	+	1.75822i	−0.0873234	+	0.0634442i
$769$	−12.8352			−0.462850			−0.231425	−	0.972853i	$-0.574339\pi$
$769$	−12.8352			−0.462850			−0.231425	+	0.972853i	$0.574339\pi$
$770$		0			0
$771$	−10.6411			−0.383230
$772$	−6.42705	+	4.66953i	−0.231315	+	0.168060i
$773$	−3.60929	−	11.1083i	−0.129817	−	0.399536i	0.864931	−	0.501891i	$-0.167362\pi$
$773$	−3.60929	−	11.1083i	−0.129817	−	0.399536i	−0.994748	+	0.102355i	$0.967362\pi$
$774$	−13.1213	+	40.3831i	−0.471634	+	1.45154i
$775$		0			0
$776$	−7.16312	−	5.20431i	−0.257141	−	0.186824i
$777$	−27.9209	+	85.9316i	−1.00166	+	3.08278i
$778$	11.2743	+	34.6988i	0.404204	+	1.24401i
$779$	−22.7563	+	16.5334i	−0.815329	+	0.592371i
$780$		0			0
$781$	16.1217	+	8.68378i	0.576881	+	0.310730i
$782$	16.7839			0.600192
$783$	−16.4248	+	11.9333i	−0.586975	+	0.426463i
$784$	5.71462	+	17.5878i	0.204093	+	0.628135i
$785$		0			0
$786$	18.8339	+	13.6836i	0.671782	+	0.488078i
$787$	−10.4833	−	7.61658i	−0.373690	−	0.271502i	0.385049	−	0.922896i	$-0.374184\pi$
$787$	−10.4833	−	7.61658i	−0.373690	−	0.271502i	−0.758740	+	0.651394i	$0.774184\pi$
$788$	6.57691	−	20.2417i	0.234293	−	0.721079i
$789$	−11.4863	−	35.3511i	−0.408923	−	1.25853i
$790$		0			0
$791$	−27.4293			−0.975274
$792$	−17.3669	−	9.35447i	−0.617106	−	0.332397i
$793$	−7.04237			−0.250082
$794$	−24.5756	+	17.8552i	−0.872157	+	0.633659i
$795$		0			0
$796$	−2.24431	+	6.90727i	−0.0795473	+	0.244822i
$797$	−33.0257	−	23.9946i	−1.16983	−	0.849931i	−0.178842	−	0.983878i	$-0.557235\pi$
$797$	−33.0257	−	23.9946i	−1.16983	−	0.849931i	−0.990989	+	0.133946i	$0.957235\pi$
$798$	36.0156	+	26.1669i	1.27494	+	0.926298i
$799$	5.57074	−	17.1450i	0.197079	−	0.606545i
$800$		0			0
$801$	−83.0449	+	60.3357i	−2.93425	+	2.13186i
$802$	2.35751			0.0832467
$803$	−5.27892	+	29.0232i	−0.186289	+	1.02421i
$804$	18.3217			0.646155
$805$		0			0
$806$	0.0949787	+	0.292314i	0.00334548	+	0.0102963i
$807$	−7.25562	+	22.3305i	−0.255410	+	0.786071i
$808$	8.11967	+	5.89928i	0.285649	+	0.207536i
$809$	1.71042	+	1.24269i	0.0601351	+	0.0436907i	0.617447	−	0.786613i	$-0.288167\pi$
$809$	1.71042	+	1.24269i	0.0601351	+	0.0436907i	−0.557312	+	0.830303i	$0.688167\pi$
$810$		0			0
$811$	−1.79386	−	5.52093i	−0.0629910	−	0.193866i	0.914608	−	0.404341i	$-0.132499\pi$
$811$	−1.79386	−	5.52093i	−0.0629910	−	0.193866i	−0.977599	+	0.210475i	$0.932499\pi$
$812$	9.40560	−	6.83357i	0.330072	−	0.239811i
$813$	77.1609			2.70615
$814$	8.60187	+	17.8802i	0.301495	+	0.626702i
$815$		0			0
$816$	−13.0162	+	9.45679i	−0.455656	+	0.331054i
$817$	−6.50284	−	20.0137i	−0.227506	−	0.700191i
$818$	−6.23455	+	19.1880i	−0.217986	+	0.670892i
$819$	−44.0456	−	32.0010i	−1.53908	−	1.11821i
$820$		0			0
$821$	−16.0997	+	49.5496i	−0.561882	+	1.72929i	0.115157	+	0.993347i	$0.463263\pi$
$821$	−16.0997	+	49.5496i	−0.561882	+	1.72929i	−0.677039	+	0.735947i	$0.736737\pi$
$822$	−7.96798	−	24.5229i	−0.277915	−	0.855335i
$823$	−12.4971	+	9.07967i	−0.435621	+	0.316497i	−0.783893	−	0.620896i	$-0.786769\pi$
$823$	−12.4971	+	9.07967i	−0.435621	+	0.316497i	0.348271	+	0.937394i	$0.386769\pi$
$824$	−4.11558			−0.143373
$825$		0			0
$826$	−31.8869			−1.10949
$827$	5.68513	−	4.13049i	0.197691	−	0.143631i	−0.484536	−	0.874771i	$-0.661011\pi$
$827$	5.68513	−	4.13049i	0.197691	−	0.143631i	0.682227	+	0.731140i	$0.261011\pi$
$828$	5.73518	+	17.6511i	0.199311	+	0.613417i
$829$	3.58438	−	11.0316i	0.124491	−	0.383143i	−0.869317	−	0.494254i	$-0.835441\pi$
$829$	3.58438	−	11.0316i	0.124491	−	0.383143i	0.993808	+	0.111112i	$0.0354411\pi$
$830$		0			0
$831$	76.0467	+	55.2512i	2.63803	+	1.91664i
$832$	−0.560242	+	1.72425i	−0.0194229	+	0.0597775i
$833$	30.7368	+	94.5981i	1.06497	+	3.27763i
$834$	38.6916	−	28.1111i	1.33978	−	0.973408i
$835$		0			0
$836$	9.68817	−	1.30841i	0.335072	−	0.0452523i
$837$	−1.49477			−0.0516668
$838$	−6.10222	+	4.43352i	−0.210798	+	0.153153i
$839$	7.26350	+	22.3548i	0.250764	+	0.771772i	0.994635	+	0.103449i	$0.0329877\pi$
$839$	7.26350	+	22.3548i	0.250764	+	0.771772i	−0.743871	+	0.668323i	$0.767012\pi$
$840$		0			0
$841$	19.1721	+	13.9293i	0.661107	+	0.480322i
$842$	−1.35247	−	0.982627i	−0.0466092	−	0.0338636i
$843$	8.47771	−	26.0917i	0.291988	−	0.898646i
$844$	2.71821	+	8.36579i	0.0935646	+	0.287962i
$845$		0			0
$846$	19.9343			0.685356
$847$	−2.53610	+	55.4816i	−0.0871415	+	1.90637i
$848$	−2.81788			−0.0967664
$849$	0.877147	−	0.637285i	0.0301036	−	0.0218715i
$850$		0			0
$851$	5.76883	−	17.7546i	0.197753	−	0.608621i
$852$	13.3611	+	9.70743i	0.457745	+	0.332571i
$853$	9.24726	+	6.71853i	0.316620	+	0.230038i	0.734732	−	0.678358i	$-0.237308\pi$
$853$	9.24726	+	6.71853i	0.316620	+	0.230038i	−0.418112	+	0.908396i	$0.637308\pi$
$854$	−6.06063	+	18.6527i	−0.207390	+	0.638282i
$855$		0			0
$856$	−2.60700	+	1.89409i	−0.0891053	+	0.0647388i
$857$	24.1717			0.825691			0.412845	−	0.910801i	$-0.364535\pi$
$857$	24.1717			0.825691			0.412845	+	0.910801i	$0.364535\pi$
$858$	−17.8245	+	2.40725i	−0.608519	+	0.0821820i
$859$	11.9935			0.409214			0.204607	−	0.978844i	$-0.434408\pi$
$859$	11.9935			0.409214			0.204607	+	0.978844i	$0.434408\pi$
$860$		0			0
$861$	−44.5368	−	137.070i	−1.51781	−	4.67134i
$862$	−6.54564	+	20.1454i	−0.222945	+	0.686155i
$863$	−26.3458	−	19.1413i	−0.896821	−	0.651579i	0.0408264	−	0.999166i	$-0.487001\pi$
$863$	−26.3458	−	19.1413i	−0.896821	−	0.651579i	−0.937648	+	0.347588i	$0.887001\pi$
$864$	−7.13315	−	5.18254i	−0.242675	−	0.176314i
$865$		0			0
$866$	−6.97355	−	21.4624i	−0.236971	−	0.729322i
$867$	−28.8694	+	20.9748i	−0.980456	+	0.712343i
$868$	0.855973			0.0290536
$869$	−8.41842	+	8.04240i	−0.285576	+	0.272820i
$870$		0			0
$871$	8.98383	−	6.52714i	0.304406	−	0.221164i
$872$	−2.02697	−	6.23838i	−0.0686420	−	0.211258i
$873$	16.2731	−	50.0834i	0.550760	−	1.69506i
$874$	−7.44132	−	5.40643i	−0.251706	−	0.182875i
$875$		0			0
$876$	−8.22153	+	25.3033i	−0.277780	+	0.854919i
$877$	−3.68041	−	11.3271i	−0.124279	−	0.382491i	0.869490	−	0.493950i	$-0.164447\pi$
$877$	−3.68041	−	11.3271i	−0.124279	−	0.382491i	−0.993769	+	0.111460i	$0.964447\pi$
$878$	−5.75651	+	4.18235i	−0.194273	+	0.141147i
$879$	91.1300			3.07374
$880$		0			0
$881$	27.1618			0.915103			0.457551	−	0.889183i	$-0.348727\pi$
$881$	27.1618			0.915103			0.457551	+	0.889183i	$0.348727\pi$
$882$	−88.9826	+	64.6496i	−2.99620	+	2.17687i
$883$	9.52629	+	29.3189i	0.320585	+	0.986660i	0.973394	+	0.229137i	$0.0735904\pi$
$883$	9.52629	+	29.3189i	0.320585	+	0.986660i	−0.652809	+	0.757523i	$0.726410\pi$
$884$	−3.01333	+	9.27408i	−0.101349	+	0.311921i
$885$		0			0
$886$	18.8661	+	13.7070i	0.633818	+	0.460496i
$887$	2.13766	−	6.57904i	0.0717756	−	0.220903i	−0.908733	−	0.417377i	$-0.862949\pi$
$887$	2.13766	−	6.57904i	0.0717756	−	0.220903i	0.980509	+	0.196475i	$0.0629494\pi$
$888$	5.52993	+	17.0194i	0.185572	+	0.571133i
$889$	−69.1692	+	50.2544i	−2.31986	+	1.68548i
$890$		0			0
$891$	5.06338	−	27.8382i	0.169630	−	0.932616i
$892$	−19.8386			−0.664246
$893$	−7.99258	+	5.80695i	−0.267461	+	0.194322i
$894$	3.68274	+	11.3343i	0.123169	+	0.379076i
$895$		0			0
$896$	4.08477	+	2.96776i	0.136462	+	0.0991458i
$897$	13.6907	+	9.94689i	0.457120	+	0.332117i
$898$	6.57220	−	20.2272i	0.219317	−	0.674989i
$899$	−0.120629	−	0.371258i	−0.00402321	−	0.0123822i
$900$		0			0
$901$	−15.1563			−0.504930
$902$	−27.8646	−	15.0089i	−0.927790	−	0.499743i
$903$	107.824			3.58814
$904$	−4.39504	+	3.19319i	−0.146177	+	0.106204i
$905$		0			0
$906$	8.37447	−	25.7740i	0.278223	−	0.856283i
$907$	22.2689	+	16.1793i	0.739426	+	0.537224i	0.892531	−	0.450985i	$-0.148927\pi$
$907$	22.2689	+	16.1793i	0.739426	+	0.537224i	−0.153105	+	0.988210i	$0.548927\pi$
$908$	−4.80669	−	3.49226i	−0.159515	−	0.115895i
$909$	−18.4461	+	56.7714i	−0.611820	+	1.88299i
$910$		0			0
$911$	−36.0148	+	26.1663i	−1.19322	+	0.866928i	−0.993601	−	0.112945i	$-0.963972\pi$
$911$	−36.0148	+	26.1663i	−1.19322	+	0.866928i	−0.199623	+	0.979873i	$0.563972\pi$
$912$	8.81706			0.291962
$913$	−4.89337	−	2.63576i	−0.161947	−	0.0872309i
$914$	−4.25562			−0.140763
$915$		0			0
$916$	3.11558	+	9.58878i	0.102942	+	0.316822i
$917$	12.1428	−	37.3718i	0.400992	−	1.23413i
$918$	−38.3666	−	27.8749i	−1.26629	−	0.920010i
$919$	−33.7701	−	24.5354i	−1.11397	−	0.809348i	−0.130688	−	0.991424i	$-0.541718\pi$
$919$	−33.7701	−	24.5354i	−1.11397	−	0.809348i	−0.983285	+	0.182076i	$0.941718\pi$
$920$		0			0
$921$	−12.0246	−	37.0080i	−0.396225	−	1.21945i
$922$	4.50785	−	3.27515i	0.148458	−	0.107861i
$923$	10.0098			0.329477
$924$	−8.96378	+	49.2824i	−0.294887	+	1.62127i
$925$		0			0
$926$	18.3074	−	13.3011i	0.601619	−	0.437102i
$927$	−7.56409	−	23.2799i	−0.248437	−	0.764611i
$928$	0.711544	−	2.18991i	0.0233576	−	0.0718872i
$929$	−38.2654	−	27.8015i	−1.25545	−	0.912136i	−0.256923	−	0.966432i	$-0.582709\pi$
$929$	−38.2654	−	27.8015i	−1.25545	−	0.912136i	−0.998525	+	0.0542960i	$0.982709\pi$
$930$		0			0
$931$	16.8445	−	51.8420i	0.552055	−	1.69905i
$932$	−0.192497	−	0.592444i	−0.00630544	−	0.0194062i
$933$	−14.8778	+	10.8094i	−0.487078	+	0.353883i
$934$	−21.2484			−0.695268
$935$		0			0
$936$	−10.7829			−0.352450
$937$	−9.98269	+	7.25285i	−0.326120	+	0.236940i	−0.738783	−	0.673944i	$-0.764599\pi$
$937$	−9.98269	+	7.25285i	−0.326120	+	0.236940i	0.412662	+	0.910884i	$0.364599\pi$
$938$	−9.55659	−	29.4122i	−0.312034	−	0.960341i
$939$	19.9311	−	61.3416i	0.650427	−	2.00181i
$940$		0			0
$941$	−28.9491	−	21.0327i	−0.943714	−	0.685648i	0.00559818	−	0.999984i	$-0.498218\pi$
$941$	−28.9491	−	21.0327i	−0.943714	−	0.685648i	−0.949312	+	0.314336i	$0.898218\pi$
$942$	−20.7398	+	63.8304i	−0.675738	+	2.07971i
$943$	9.20191	+	28.3206i	0.299655	+	0.922244i
$944$	−5.10929	+	3.71212i	−0.166293	+	0.120819i
$945$		0			0
$946$	17.1210	−	16.3562i	0.556650	−	0.531786i
$947$	−16.7403			−0.543987			−0.271993	−	0.962299i	$-0.587683\pi$
$947$	−16.7403			−0.543987			−0.271993	+	0.962299i	$0.587683\pi$
$948$	−8.49503	+	6.17200i	−0.275906	+	0.200457i
$949$	4.98302	+	15.3361i	0.161756	+	0.497832i
$950$		0			0
$951$	−19.2652	−	13.9970i	−0.624716	−	0.453883i
$952$	21.9704	+	15.9625i	0.712066	+	0.517346i
$953$	−7.74615	+	23.8402i	−0.250922	+	0.772259i	0.743683	+	0.668532i	$0.233077\pi$
$953$	−7.74615	+	23.8402i	−0.250922	+	0.772259i	−0.994606	+	0.103727i	$0.966923\pi$
$954$	−5.17902	−	15.9394i	−0.167677	−	0.516056i
$955$		0			0
$956$	−10.4880			−0.339206
$957$	22.6383	−	3.05736i	0.731793	−	0.0988304i
$958$	−18.3930			−0.594251
$959$	−35.2111	+	25.5823i	−1.13703	+	0.826097i
$960$		0			0
$961$	−9.57065	+	29.4554i	−0.308730	+	0.950175i
$962$	8.77474	+	6.37522i	0.282909	+	0.205545i
$963$	−15.5054	−	11.2653i	−0.499655	−	0.363020i
$964$	−4.16756	+	12.8264i	−0.134228	+	0.413112i
$965$		0			0
$966$	38.1279	−	27.7015i	1.22674	−	0.891282i
$967$	43.9526			1.41342			0.706710	−	0.707503i	$-0.250179\pi$
$967$	43.9526			1.41342			0.706710	+	0.707503i	$0.250179\pi$
$968$	6.05253	+	9.18514i	0.194536	+	0.295222i
$969$	47.4237			1.52347
$970$		0			0
$971$	7.97024	+	24.5299i	0.255777	+	0.787201i	0.993676	+	0.112289i	$0.0358183\pi$
$971$	7.97024	+	24.5299i	0.255777	+	0.787201i	−0.737898	+	0.674912i	$0.764182\pi$
$972$	−0.288013	+	0.886412i	−0.00923801	+	0.0284317i
$973$	−65.3090	−	47.4497i	−2.09371	−	1.52117i
$974$	14.7747	+	10.7345i	0.473413	+	0.343955i
$975$		0			0
$976$	1.20035	+	3.69430i	0.0384223	+	0.118252i
$977$	19.9845	−	14.5196i	0.639359	−	0.464522i	−0.220271	−	0.975439i	$-0.570694\pi$
$977$	19.9845	−	14.5196i	0.639359	−	0.464522i	0.859630	+	0.510917i	$0.170694\pi$
$978$	−58.9897			−1.88628
$979$	56.7263	−	7.66102i	1.81298	−	0.244847i
$980$		0			0
$981$	31.5621	−	22.9312i	1.00770	−	0.732137i
$982$	0.0905551	+	0.278700i	0.00288973	+	0.00889368i
$983$	1.59867	−	4.92021i	0.0509898	−	0.156930i	−0.922319	−	0.386429i	$-0.873709\pi$
$983$	1.59867	−	4.92021i	0.0509898	−	0.156930i	0.973309	+	0.229498i	$0.0737085\pi$
$984$	−23.0932	−	16.7782i	−0.736186	−	0.534870i
$985$		0			0
$986$	3.82713	−	11.7787i	0.121881	−	0.375110i
$987$	−15.6424	−	48.1425i	−0.497904	−	1.53239i
$988$	4.32336	−	3.14110i	0.137544	−	0.0999318i
$989$	−22.2778			−0.708393
$990$		0			0
$991$	−54.0929			−1.71832			−0.859159	−	0.511709i	$-0.829013\pi$
$991$	−54.0929			−1.71832			−0.859159	+	0.511709i	$0.829013\pi$
$992$	0.137154	−	0.0996482i	0.00435464	−	0.00316383i
$993$	−21.2196	−	65.3073i	−0.673384	−	2.07246i
$994$	8.61438	−	26.5123i	0.273232	−	0.840920i
$995$		0			0
$996$	−4.05546	−	2.94646i	−0.128502	−	0.0933623i
$997$	−9.01050	+	27.7315i	−0.285365	+	0.878264i	0.700924	+	0.713236i	$0.252771\pi$
$997$	−9.01050	+	27.7315i	−0.285365	+	0.878264i	−0.986289	+	0.165028i	$0.947229\pi$
$998$	−1.84291	−	5.67189i	−0.0583362	−	0.179541i
$999$	−42.6742	+	31.0046i	−1.35015	+	0.980942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.k.201.2	✓	8
5.2	odd	4		550.2.ba.g.399.2		16
5.3	odd	4		550.2.ba.g.399.3		16
5.4	even	2		550.2.h.m.201.1	yes	8
11.2	odd	10		6050.2.a.cz.1.4		4
11.4	even	5	inner	550.2.h.k.301.2	yes	8
11.9	even	5		6050.2.a.dg.1.4		4
55.4	even	10		550.2.h.m.301.1	yes	8
55.9	even	10		6050.2.a.df.1.1		4
55.24	odd	10		6050.2.a.dn.1.1		4
55.37	odd	20		550.2.ba.g.499.3		16
55.48	odd	20		550.2.ba.g.499.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.k.201.2	✓	8	1.1	even	1	trivial
550.2.h.k.301.2	yes	8	11.4	even	5	inner
550.2.h.m.201.1	yes	8	5.4	even	2
550.2.h.m.301.1	yes	8	55.4	even	10
550.2.ba.g.399.2		16	5.2	odd	4
550.2.ba.g.399.3		16	5.3	odd	4
550.2.ba.g.499.2		16	55.48	odd	20
550.2.ba.g.499.3		16	55.37	odd	20
6050.2.a.cz.1.4		4	11.2	odd	10
6050.2.a.df.1.1		4	55.9	even	10
6050.2.a.dg.1.4		4	11.9	even	5
6050.2.a.dn.1.1		4	55.24	odd	10

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.924349 + 2.84485i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.41998 - 1.75822i) q^{6} +(-1.56024 + 4.80193i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.81172 + 3.49592i) q^{9} +(3.28679 - 0.443888i) q^{11} +2.99126 q^{12} +(1.46673 - 1.06564i) q^{13} +(-1.56024 - 4.80193i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.35140 - 3.16148i) q^{17} +(1.83791 - 5.65652i) q^{18} +(0.910862 + 2.80335i) q^{19} -15.1030 q^{21} +(-2.39815 + 2.29104i) q^{22} +3.12048 q^{23} +(-2.41998 + 1.75822i) q^{24} +(-0.560242 + 1.72425i) q^{26} +(-7.13315 - 5.18254i) q^{27} +(4.08477 + 2.96776i) q^{28} +(0.711544 - 2.18991i) q^{29} +(0.137154 - 0.0996482i) q^{31} +1.00000 q^{32} +(4.30093 + 8.94012i) q^{33} +5.37863 q^{34} +(1.83791 + 5.65652i) q^{36} +(1.84870 - 5.68971i) q^{37} +(-2.38467 - 1.73256i) q^{38} +(4.38737 + 3.18761i) q^{39} +(2.94887 + 9.07570i) q^{41} +(12.2186 - 8.87732i) q^{42} -7.13922 q^{43} +(0.593510 - 3.26309i) q^{44} +(-2.52452 + 1.83417i) q^{46} +(1.03572 + 3.18761i) q^{47} +(0.924349 - 2.84485i) q^{48} +(-14.9611 - 10.8698i) q^{49} +(4.97173 - 15.3014i) q^{51} +(-0.560242 - 1.72425i) q^{52} +(2.27971 - 1.65631i) q^{53} +8.81706 q^{54} -5.04905 q^{56} +(-7.13315 + 5.18254i) q^{57} +(0.711544 + 2.18991i) q^{58} +(1.95158 - 6.00633i) q^{59} +(-3.14256 - 2.28320i) q^{61} +(-0.0523881 + 0.161234i) q^{62} +(-9.27971 - 28.5600i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.73440 - 4.70468i) q^{66} +6.12507 q^{67} +(-4.35140 + 3.16148i) q^{68} +(2.88442 + 8.87732i) q^{69} +(4.46673 + 3.24527i) q^{71} +(-4.81172 - 3.49592i) q^{72} +(-2.74852 + 8.45908i) q^{73} +(1.84870 + 5.68971i) q^{74} +2.94761 q^{76} +(-2.99666 + 16.4755i) q^{77} -5.42309 q^{78} +(-2.83995 + 2.06335i) q^{79} +(2.63630 - 8.11370i) q^{81} +(-7.72025 - 5.60909i) q^{82} +(-1.35577 - 0.985026i) q^{83} +(-4.66708 + 14.3638i) q^{84} +(5.77575 - 4.19633i) q^{86} +6.88768 q^{87} +(1.43784 + 2.98875i) q^{88} +17.2589 q^{89} +(2.82869 + 8.70580i) q^{91} +(0.964282 - 2.96776i) q^{92} +(0.410263 + 0.298073i) q^{93} +(-2.71154 - 1.97005i) q^{94} +(0.924349 + 2.84485i) q^{96} +(-7.16312 + 5.20431i) q^{97} +18.4929 q^{98} +(-14.2633 + 13.6262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} - 24 q^{9} + 5 q^{11} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 18 q^{17} + 11 q^{18} + 17 q^{19} - 40 q^{21} - 5 q^{22} + 4 q^{23} - q^{24}+ \cdots - 72 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 - 24 * q^9 + 5 * q^11 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 18 * q^17 + 11 * q^18 + 17 * q^19 - 40 * q^21 - 5 * q^22 + 4 * q^23 - q^24 + 6 * q^26 + 19 * q^27 + 8 * q^28 + 2 * q^29 - 2 * q^31 + 8 * q^32 + 23 * q^33 + 2 * q^34 + 11 * q^36 + 8 * q^37 - 18 * q^38 + 24 * q^39 + 6 * q^41 + 20 * q^42 + 16 * q^43 + 10 * q^44 - 6 * q^46 + 12 * q^47 + 4 * q^48 - 6 * q^49 - 17 * q^51 + 6 * q^52 - 8 * q^53 - 6 * q^54 - 12 * q^56 + 19 * q^57 + 2 * q^58 - 12 * q^59 - 2 * q^61 - 22 * q^62 - 48 * q^63 - 2 * q^64 - 27 * q^66 - 34 * q^67 - 18 * q^68 + 20 * q^69 + 20 * q^71 - 24 * q^72 - 26 * q^73 + 8 * q^74 + 2 * q^76 + 26 * q^77 - 36 * q^78 + 14 * q^79 + 35 * q^81 - 9 * q^82 - 9 * q^83 + 26 * q^86 - 56 * q^87 - 5 * q^88 + 2 * q^89 - 52 * q^91 + 4 * q^92 + 32 * q^93 - 18 * q^94 + 4 * q^96 - 26 * q^97 + 64 * q^98 - 72 * q^99

Introduction

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