LMFDB - Embedded newform 550.2.h.m.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:	$8$
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			301.1
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.m.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} +(-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 $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

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
$3$	−0.924349	+	2.84485i	−0.533673	+	1.64248i	0.212826	+	0.977090i	$0.431733\pi$
$3$	−0.924349	+	2.84485i	−0.533673	+	1.64248i	−0.746499	+	0.665387i	$0.768267\pi$
$4$	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	0.579444	+	0.815012i	$0.303270\pi$
$7$	1.56024	+	4.80193i	0.589716	+	1.81496i	0.0102715	+	0.999947i	$0.496730\pi$
$8$	−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	$-0.380896\pi$
$13$	−1.46673	−	1.06564i	−0.406798	−	0.295556i	−0.772304	+	0.635253i	$0.780896\pi$
$14$	−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	$-0.473823\pi$
$17$	4.35140	−	3.16148i	1.05537	−	0.766771i	0.973226	+	0.229850i	$0.0738235\pi$
$18$	−1.83791	−	5.65652i	−0.433200	−	1.33325i
$19$	0.910862	−	2.80335i	0.208966	−	0.643132i	−0.790561	−	0.612383i	$-0.790211\pi$
$19$	0.910862	−	2.80335i	0.208966	−	0.643132i	0.999527	−	0.0307483i	$-0.00978904\pi$
$20$		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	$-0.605476\pi$
$23$	−3.12048			−0.650666			−0.325333	+	0.945600i	$0.605476\pi$
$24$	−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	0.995133	−	0.0985446i	$-0.0314187\pi$
$29$	0.711544	+	2.18991i	0.132130	+	0.406656i	−0.863002	+	0.505200i	$0.831419\pi$
$30$		0			0
$31$	0.137154	+	0.0996482i	0.0246336	+	0.0178973i	0.600034	−	0.799975i	$-0.295154\pi$
$31$	0.137154	+	0.0996482i	0.0246336	+	0.0178973i	−0.575400	+	0.817872i	$0.695154\pi$
$32$	−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	−0.980077	−	0.198620i	$-0.936354\pi$
$37$	−1.84870	−	5.68971i	−0.303924	−	0.935382i	0.676152	−	0.736762i	$-0.263646\pi$
$38$	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	−0.403974	−	0.914771i	$-0.632371\pi$
$41$	2.94887	−	9.07570i	0.460537	−	1.41739i	0.864510	−	0.502615i	$-0.167629\pi$
$42$	−12.2186	−	8.87732i	−1.88537	−	1.36980i
$43$	7.13922			1.08872			0.544360	−	0.838852i	$-0.316772\pi$
$43$	7.13922			1.08872			0.544360	+	0.838852i	$0.316772\pi$
$44$	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	$-0.978606\pi$
$47$	−1.03572	+	3.18761i	−0.151075	+	0.464961i	0.846667	+	0.532123i	$0.178606\pi$
$48$	−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	$-0.361995\pi$
$53$	−2.27971	−	1.65631i	−0.313143	−	0.227511i	−0.733244	+	0.679966i	$0.761995\pi$
$54$	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	0.994011	+	0.109282i	$0.0348551\pi$
$59$	1.95158	+	6.00633i	0.254073	+	0.781958i	−0.739937	+	0.672676i	$0.765145\pi$
$60$		0			0
$61$	−3.14256	+	2.28320i	−0.402363	+	0.292334i	−0.770503	−	0.637436i	$-0.779995\pi$
$61$	−3.14256	+	2.28320i	−0.402363	+	0.292334i	0.368140	+	0.929771i	$0.379995\pi$
$62$	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	$-0.622065\pi$
$67$	−6.12507			−0.748296			−0.374148	+	0.927369i	$0.622065\pi$
$68$	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	−0.290293	−	0.956938i	$-0.593753\pi$
$71$	4.46673	−	3.24527i	0.530104	−	0.385143i	0.820396	+	0.571795i	$0.193753\pi$
$72$	4.81172	−	3.49592i	0.567067	−	0.411998i
$73$	2.74852	+	8.45908i	0.321690	+	0.990061i	0.972912	+	0.231174i	$0.0742566\pi$
$73$	2.74852	+	8.45908i	0.321690	+	0.990061i	−0.651222	+	0.758887i	$0.725743\pi$
$74$	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	0.416451	−	0.909158i	$-0.363274\pi$
$79$	−2.83995	−	2.06335i	−0.319520	−	0.232145i	−0.735971	+	0.677014i	$0.763274\pi$
$80$		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	$-0.670683\pi$
$83$	1.35577	−	0.985026i	0.148815	−	0.108121i	0.659702	+	0.751528i	$0.270683\pi$
$84$	−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	$-0.151603\pi$
$97$	7.16312	+	5.20431i	0.727305	+	0.528418i	−0.161405	+	0.986888i	$0.551603\pi$
$98$	−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	0.913232	−	0.407441i	$-0.133579\pi$
$101$	8.11967	+	5.89928i	0.807937	+	0.587001i	−0.105295	+	0.994441i	$0.533579\pi$
$102$	−4.97173	+	15.3014i	−0.492274	+	1.51506i
$103$	1.27179	+	3.91415i	0.125313	+	0.385673i	0.993958	−	0.109762i	$-0.0350088\pi$
$103$	1.27179	+	3.91415i	0.125313	+	0.385673i	−0.868645	+	0.495435i	$0.835009\pi$
$104$	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	$-0.949783\pi$
$107$	−0.995784	+	3.06471i	−0.0962661	+	0.296277i	0.891315	+	0.453384i	$0.149783\pi$
$108$	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	$-0.982249\pi$
$113$	−1.67876	+	5.16668i	−0.157924	+	0.486041i	0.840521	+	0.541779i	$0.182249\pi$
$114$	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	$-0.970573\pi$
$127$	−13.6995	+	9.95324i	−1.21563	+	0.883207i	−0.219901	+	0.975522i	$0.570573\pi$
$128$	−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	$-0.820037\pi$
$137$	−6.97381	+	5.06677i	−0.595812	+	0.432883i	0.248578	+	0.968612i	$0.420037\pi$
$138$	7.55150	−	5.48648i	0.642826	−	0.467041i
$139$	−4.94069	−	15.2059i	−0.419064	−	1.28975i	−0.908565	−	0.417744i	$-0.862821\pi$
$139$	−4.94069	−	15.2059i	−0.419064	−	1.28975i	0.489501	−	0.872003i	$-0.337179\pi$
$140$		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	−0.711934	−	0.702246i	$-0.752181\pi$
$149$	−3.22324	+	2.34182i	−0.264058	+	0.191850i	0.447876	+	0.894096i	$0.352181\pi$
$150$		0			0
$151$	2.79965	−	8.61644i	0.227832	−	0.701196i	−0.770159	−	0.637851i	$-0.779823\pi$
$151$	2.79965	−	8.61644i	0.227832	−	0.701196i	0.997992	−	0.0633442i	$-0.0201766\pi$
$152$	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	−0.146909	−	0.989150i	$-0.546932\pi$
$157$	6.93346	−	21.3390i	0.553351	−	1.70304i	0.700260	−	0.713888i	$-0.253068\pi$
$158$	−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	$-0.580905\pi$
$163$	−15.9544	−	11.5915i	−1.24964	−	0.907920i	−0.998201	+	0.0599520i	$0.980905\pi$
$164$	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	$-0.249315\pi$
$167$	3.31543	+	2.40880i	0.256556	+	0.186399i	−0.452072	+	0.891982i	$0.649315\pi$
$168$	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	0.677149	+	0.735846i	$0.263215\pi$
$173$	−3.98792	+	12.2735i	−0.303196	+	0.933140i	−0.980344	+	0.197294i	$0.936785\pi$
$174$	−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	−0.664596	−	0.747203i	$-0.731396\pi$
$179$	4.17787	−	12.8582i	0.312268	−	0.961063i	0.976864	−	0.213860i	$-0.0686038\pi$
$180$		0			0
$181$	18.1957	−	13.2199i	1.35247	−	0.982630i	0.353591	−	0.935400i	$-0.384961\pi$
$181$	18.1957	−	13.2199i	1.35247	−	0.982630i	0.998884	−	0.0472302i	$-0.0150394\pi$
$182$	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	0.945671	+	0.325126i	$0.105407\pi$
$191$	5.13715	+	15.8105i	0.371711	+	1.14401i	−0.573959	+	0.818884i	$0.694593\pi$
$192$	2.41998	−	1.75822i	0.174647	−	0.126888i
$193$	6.42705	−	4.66953i	0.462629	−	0.336120i	−0.331933	−	0.943303i	$-0.607701\pi$
$193$	6.42705	−	4.66953i	0.462629	−	0.336120i	0.794562	+	0.607183i	$0.207701\pi$
$194$	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	$-0.773915\pi$
$197$	−21.2833			−1.51637			−0.758187	+	0.652037i	$0.773915\pi$
$198$	−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	0.315239	−	0.949012i	$-0.397915\pi$
$211$	−7.11636	−	5.17034i	−0.489911	−	0.355941i	−0.805150	+	0.593071i	$0.797915\pi$
$212$	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	−0.505664	−	0.862730i	$-0.668753\pi$
$223$	6.13047	−	18.8677i	0.410527	−	1.26347i	0.916191	−	0.400742i	$-0.131247\pi$
$224$	−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	$-0.163176\pi$
$227$	−1.83599	−	5.65060i	−0.121859	−	0.375043i	−0.993316	+	0.115429i	$0.963176\pi$
$228$	−2.72462	+	8.38552i	−0.180442	+	0.555345i
$229$	−8.15671	−	5.92619i	−0.539010	−	0.391614i	0.284707	−	0.958615i	$-0.408104\pi$
$229$	−8.15671	−	5.92619i	−0.539010	−	0.391614i	−0.823717	+	0.567001i	$0.808104\pi$
$230$		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	$-0.306496\pi$
$233$	−0.503963	−	0.366151i	−0.0330157	−	0.0239873i	−0.604171	+	0.796855i	$0.706496\pi$
$234$	−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	0.789850	+	0.613300i	$0.210158\pi$
$239$	−3.24097	+	9.97467i	−0.209641	+	0.645208i	−0.999491	+	0.0319078i	$0.989842\pi$
$240$		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	0.870562	−	0.492059i	$-0.163755\pi$
$251$	10.6402	+	7.73058i	0.671605	+	0.487950i	−0.198957	+	0.980008i	$0.563755\pi$
$252$	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	$-0.0646099\pi$
$257$	1.09930	+	3.38330i	0.0685724	+	0.211044i	−0.910898	+	0.412631i	$0.864610\pi$
$258$	−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	$-0.374849\pi$
$263$	12.4264			0.766242			0.383121	+	0.923698i	$0.374849\pi$
$264$	−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	−0.377115	−	0.926166i	$-0.623084\pi$
$269$	6.35033	−	4.61378i	0.387186	−	0.281307i	0.764302	+	0.644859i	$0.223084\pi$
$270$		0			0
$271$	7.97125	+	24.5330i	0.484219	+	1.49027i	0.833109	+	0.553108i	$0.186558\pi$
$271$	7.97125	+	24.5330i	0.484219	+	1.49027i	−0.348891	+	0.937163i	$0.613442\pi$
$272$	−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	−0.957597	−	0.288111i	$-0.906973\pi$
$277$	−25.4230	−	18.4709i	−1.52752	−	1.10981i	−0.569924	−	0.821698i	$-0.693027\pi$
$278$	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	−0.786682	−	0.617359i	$-0.788203\pi$
$281$	−7.41994	+	5.39090i	−0.442636	+	0.321594i	0.344045	+	0.938953i	$0.388203\pi$
$282$	−3.09810	−	9.53496i	−0.184489	−	0.567799i
$283$	0.112007	−	0.344721i	0.00665810	−	0.0204915i	−0.947672	−	0.319245i	$-0.896571\pi$
$283$	0.112007	−	0.344721i	0.00665810	−	0.0204915i	0.954330	+	0.298753i	$0.0965708\pi$
$284$	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	−0.708816	−	0.705394i	$-0.750770\pi$
$293$	−9.41434	−	28.9744i	−0.549992	−	1.69270i	0.158824	−	0.987307i	$-0.449230\pi$
$294$	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	$-0.378938\pi$
$307$	13.0087			0.742448			0.371224	+	0.928543i	$0.378938\pi$
$308$	−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	−0.882633	−	0.470063i	$-0.844231\pi$
$311$	1.89981	−	5.84701i	0.107728	−	0.331554i	0.990361	+	0.138509i	$0.0442311\pi$
$312$	1.67583	+	5.15766i	0.0948750	+	0.291995i
$313$	17.4443	−	12.6740i	0.986009	−	0.716377i	0.0269652	−	0.999636i	$-0.491416\pi$
$313$	17.4443	−	12.6740i	0.986009	−	0.716377i	0.959043	+	0.283259i	$0.0914157\pi$
$314$	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	$-0.228231\pi$
$317$	6.44050	+	4.67930i	0.361734	+	0.262815i	−0.392041	+	0.919948i	$0.628231\pi$
$318$	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	−0.999671	−	0.0256533i	$-0.991833\pi$
$337$	−3.78163	−	11.6387i	−0.205999	−	0.633999i	0.793672	−	0.608346i	$-0.208167\pi$
$338$	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	$-0.414320\pi$
$347$	23.5629	−	17.1194i	1.26492	−	0.919019i	0.998988	+	0.0449727i	$0.0143201\pi$
$348$	−2.12841	−	6.55057i	−0.114095	−	0.351148i
$349$	−0.486742	+	1.49804i	−0.0260547	+	0.0801882i	−0.963238	−	0.268648i	$-0.913423\pi$
$349$	−0.486742	+	1.49804i	−0.0260547	+	0.0801882i	0.937184	+	0.348836i	$0.113423\pi$
$350$		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	$-0.123378\pi$
$353$	34.7890			1.85163			0.925817	+	0.377972i	$0.123378\pi$
$354$	−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	0.853902	+	0.520433i	$0.174230\pi$
$359$	8.88597	+	27.3482i	0.468984	+	1.44338i	−0.384919	+	0.922951i	$0.625770\pi$
$360$		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	0.741553	+	0.670894i	$0.234090\pi$
$367$	10.2676	+	31.6005i	0.535966	+	1.64953i	−0.205587	+	0.978639i	$0.565910\pi$
$368$	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	$-0.626608\pi$
$373$	−14.9618			−0.774691			−0.387345	+	0.921935i	$0.626608\pi$
$374$	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	−0.406310	−	0.913735i	$-0.633185\pi$
$379$	6.56354	−	4.76869i	0.337147	−	0.244951i	0.743457	+	0.668784i	$0.233185\pi$
$380$		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	$-0.429879\pi$
$383$	−12.5648	−	9.12888i	−0.642033	−	0.466464i	−0.860548	+	0.509369i	$0.829879\pi$
$384$	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	0.647378	+	0.762170i	$0.275866\pi$
$389$	11.2743	+	34.6988i	0.571630	+	1.75930i	−0.0757474	+	0.997127i	$0.524134\pi$
$390$		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	$-0.775926\pi$
$397$	−30.3772			−1.52459			−0.762293	+	0.647232i	$0.775926\pi$
$398$	−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	−0.634388	−	0.773015i	$-0.718748\pi$
$401$	−1.90727	+	1.38571i	−0.0952445	+	0.0691992i	0.539144	+	0.842214i	$0.318748\pi$
$402$	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	0.912984	−	0.407996i	$-0.133772\pi$
$409$	16.3223	+	11.8588i	0.807085	+	0.586381i	−0.105899	+	0.994377i	$0.533772\pi$
$410$		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	−0.937678	−	0.347505i	$-0.887029\pi$
$421$	0.516598	−	1.58992i	0.0251774	−	0.0774882i	0.962856	+	0.270016i	$0.0870291\pi$
$422$	−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	0.918267	−	0.395961i	$-0.129589\pi$
$431$	17.1367	+	12.4505i	0.825446	+	0.599721i	−0.0928215	+	0.995683i	$0.529589\pi$
$432$	−2.72462	+	8.38552i	−0.131088	+	0.403449i
$433$	6.97355	+	21.4624i	0.335128	+	1.03142i	0.966659	+	0.256066i	$0.0824266\pi$
$433$	6.97355	+	21.4624i	0.335128	+	1.03142i	−0.631532	+	0.775350i	$0.717573\pi$
$434$	−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	−0.620596	−	0.784130i	$-0.713109\pi$
$443$	7.20620	−	22.1784i	0.342377	−	1.05373i	0.962973	−	0.269597i	$-0.0868906\pi$
$444$	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	0.102401	−	0.994743i	$-0.467348\pi$
$449$	−17.2062	−	12.5011i	−0.812013	−	0.589962i	−0.914413	+	0.404781i	$0.867348\pi$
$450$		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	$-0.731735\pi$
$457$	−3.44287	+	2.50139i	−0.161051	+	0.117010i	0.504341	+	0.863505i	$0.331735\pi$
$458$	−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	$-0.323753\pi$
$463$	22.6292			1.05167			0.525835	+	0.850587i	$0.323753\pi$
$464$	−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	$-0.863598\pi$
$467$	−17.1903	+	12.4895i	−0.795471	+	0.577944i	0.114111	+	0.993468i	$0.463598\pi$
$468$	−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	−0.193427	−	0.981115i	$-0.561960\pi$
$479$	14.8803	−	10.8111i	0.679896	−	0.493974i	0.873323	+	0.487141i	$0.161960\pi$
$480$		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	−0.737956	−	0.674849i	$-0.764209\pi$
$487$	5.64345	−	17.3687i	0.255729	−	0.787053i	0.993685	−	0.112204i	$-0.0357911\pi$
$488$	−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	0.953079	−	0.302721i	$-0.0978952\pi$
$491$	0.0905551	+	0.278700i	0.00408670	+	0.0125776i	−0.948992	+	0.315299i	$0.897895\pi$
$492$	−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	0.901295	−	0.433206i	$-0.142618\pi$
$499$	−1.84291	−	5.67189i	−0.0824999	−	0.253909i	−0.983795	+	0.179297i	$0.942618\pi$
$500$		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	$-0.877601\pi$
$503$	0.974585	−	2.99947i	0.0434546	−	0.133740i	0.970430	+	0.241382i	$0.0776008\pi$
$504$	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	−0.676021	−	0.736882i	$-0.736297\pi$
$509$	6.85900	−	21.1098i	0.304020	−	0.935677i	0.980041	−	0.198795i	$-0.0637027\pi$
$510$		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	0.897701	−	0.440605i	$-0.145236\pi$
$521$	−1.99803	−	6.14931i	−0.0875354	−	0.269406i	−0.985237	+	0.171199i	$0.945236\pi$
$522$	11.0795	−	8.04972i	0.484936	−	0.352327i
$523$	2.40756	−	1.74920i	0.105275	−	0.0764870i	−0.533902	−	0.845546i	$-0.679275\pi$
$523$	2.40756	−	1.74920i	0.105275	−	0.0764870i	0.639177	+	0.769059i	$0.279275\pi$
$524$	−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	0.537290	−	0.843397i	$-0.319448\pi$
$541$	−2.29794	−	1.66955i	−0.0987962	−	0.0717797i	−0.636087	+	0.771618i	$0.719448\pi$
$542$	−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	0.604215	+	0.796822i	$0.293487\pi$
$547$	−8.25516	+	25.4068i	−0.352965	+	1.08632i	−0.957180	+	0.289494i	$0.906513\pi$
$548$	−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	−0.995763	−	0.0919585i	$-0.970687\pi$
$557$	−5.76393	−	17.7396i	−0.244226	−	0.751649i	0.751537	−	0.659691i	$-0.229313\pi$
$558$	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	$-0.390587\pi$
$563$	−10.7790	−	7.83141i	−0.454281	−	0.330055i	−0.791284	+	0.611449i	$0.790587\pi$
$564$	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	−0.887325	−	0.461145i	$-0.847439\pi$
$569$	2.42330	−	7.45816i	0.101590	−	0.312662i	0.988915	+	0.148483i	$0.0474389\pi$
$570$		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	$-0.562634\pi$
$577$	16.2570	−	11.8114i	0.676788	−	0.491715i	0.872290	+	0.488988i	$0.162634\pi$
$578$	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	$-0.00547446\pi$
$587$	4.38156	+	13.4850i	0.180846	+	0.556587i	−0.819006	+	0.573785i	$0.805474\pi$
$588$	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	$-0.465214\pi$
$593$	5.31185			0.218132			0.109066	+	0.994035i	$0.465214\pi$
$594$	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	0.497332	−	0.867560i	$-0.334313\pi$
$599$	36.1271	−	26.2479i	1.47611	−	1.07246i	0.978783	−	0.204900i	$-0.0656868\pi$
$600$		0			0
$601$	−5.04697	−	15.5330i	−0.205870	−	0.633603i	−0.999677	−	0.0254327i	$-0.991904\pi$
$601$	−5.04697	−	15.5330i	−0.205870	−	0.633603i	0.793806	−	0.608171i	$-0.208096\pi$
$602$	−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	$-0.423498\pi$
$607$	−15.0814	−	10.9573i	−0.612136	−	0.444743i	−0.850166	+	0.526515i	$0.823498\pi$
$608$	−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	$-0.834503\pi$
$613$	3.12639	−	9.62205i	0.126274	−	0.388631i	0.994131	+	0.108183i	$0.0345032\pi$
$614$	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	$-0.413523\pi$
$617$	13.3311			0.536691			0.268346	+	0.963323i	$0.413523\pi$
$618$	−9.95962	−	7.23609i	−0.400635	−	0.291078i
$619$	7.71248	−	23.7366i	0.309991	−	0.954053i	−0.667777	−	0.744362i	$-0.732754\pi$
$619$	7.71248	−	23.7366i	0.309991	−	0.954053i	0.977768	−	0.209692i	$-0.0672461\pi$
$620$		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	0.994886	+	0.101008i	$0.0322068\pi$
$631$	6.26429	+	19.2795i	0.249377	+	0.767505i	−0.745508	+	0.666496i	$0.767793\pi$
$632$	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	0.503945	+	0.863736i	$0.331881\pi$
$641$	−10.4170	+	32.0602i	−0.411446	+	1.26630i	−0.915391	+	0.402565i	$0.868119\pi$
$642$	−2.97865	−	9.16733i	−0.117558	−	0.361806i
$643$	−36.3871	+	26.4368i	−1.43497	+	1.04256i	−0.445903	+	0.895081i	$0.647117\pi$
$643$	−36.3871	+	26.4368i	−1.43497	+	1.04256i	−0.989065	+	0.147483i	$0.952883\pi$
$644$	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	$-0.427029\pi$
$647$	−15.9920	−	11.6189i	−0.628710	−	0.456785i	−0.855953	+	0.517053i	$0.827029\pi$
$648$	−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	−0.946535	−	0.322601i	$-0.895443\pi$
$653$	−9.46495	−	29.1301i	−0.370392	−	1.13995i	0.576143	−	0.817349i	$-0.304557\pi$
$654$	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	−0.999961	−	0.00887590i	$-0.997175\pi$
$673$	−34.1765	−	24.8307i	−1.31741	−	0.957152i	−0.317446	−	0.948276i	$-0.602825\pi$
$674$	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	$-0.846768\pi$
$677$	−18.7311	+	13.6089i	−0.719895	+	0.523034i	0.166456	+	0.986049i	$0.446768\pi$
$678$	−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	$-0.457044\pi$
$683$	7.03233			0.269085			0.134542	+	0.990908i	$0.457044\pi$
$684$	−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	0.382813	−	0.923826i	$-0.374955\pi$
$691$	−9.92334	−	7.20973i	−0.377502	−	0.274271i	−0.760315	+	0.649555i	$0.774955\pi$
$692$	−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	0.761660	+	0.647977i	$0.224385\pi$
$701$	−6.23273	+	19.1824i	−0.235407	+	0.724508i	−0.997067	+	0.0765314i	$0.975615\pi$
$702$	−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	−0.874268	−	0.485444i	$-0.838658\pi$
$709$	−18.1795	+	13.2082i	−0.682746	+	0.496044i	0.191521	+	0.981488i	$0.438658\pi$
$710$		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	0.969918	+	0.243432i	$0.0782734\pi$
$719$	8.80373	+	27.0951i	0.328324	+	1.01048i	−0.641594	+	0.767044i	$0.721727\pi$
$720$		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	$-0.596844\pi$
$727$	−16.1547			−0.599144			−0.299572	+	0.954074i	$0.596844\pi$
$728$	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	0.928218	+	0.372036i	$0.121340\pi$
$733$	10.7200	+	32.9927i	0.395951	+	1.21861i	−0.532267	+	0.846577i	$0.678660\pi$
$734$	−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	0.754230	−	0.656610i	$-0.228010\pi$
$739$	9.86328	+	7.16609i	0.362827	+	0.263609i	−0.391404	+	0.920219i	$0.628010\pi$
$740$		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	$-0.758069\pi$
$743$	−8.00132	+	5.81330i	−0.293540	+	0.213269i	0.431262	+	0.902227i	$0.358069\pi$
$744$	−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	−0.998960	−	0.0455871i	$-0.985484\pi$
$751$	−4.49402	+	13.8312i	−0.163989	+	0.504706i	0.834971	+	0.550293i	$0.185484\pi$
$752$	−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	$-0.105871\pi$
$757$	25.4983	+	18.5256i	0.926751	+	0.673324i	−0.0184440	+	0.999830i	$0.505871\pi$
$758$	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	−0.960582	−	0.277998i	$-0.910329\pi$
$761$	−41.9810	−	30.5010i	−1.52181	−	1.10566i	−0.561228	−	0.827661i	$-0.689671\pi$
$762$	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	$-0.832638\pi$
$773$	3.60929	−	11.1083i	0.129817	−	0.399536i	0.994748	+	0.102355i	$0.0326378\pi$
$774$	−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	$-0.625816\pi$
$787$	10.4833	−	7.61658i	0.373690	−	0.271502i	0.758740	+	0.651394i	$0.225816\pi$
$788$	−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	$-0.442765\pi$
$797$	33.0257	−	23.9946i	1.16983	−	0.849931i	0.990989	+	0.133946i	$0.0427650\pi$
$798$	−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	−0.557312	−	0.830303i	$-0.688167\pi$
$809$	1.71042	−	1.24269i	0.0601351	−	0.0436907i	0.617447	+	0.786613i	$0.288167\pi$
$810$		0			0
$811$	−1.79386	+	5.52093i	−0.0629910	+	0.193866i	−0.977599	−	0.210475i	$-0.932499\pi$
$811$	−1.79386	+	5.52093i	−0.0629910	+	0.193866i	0.914608	+	0.404341i	$0.132499\pi$
$812$	−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	−0.677039	−	0.735947i	$-0.736737\pi$
$821$	−16.0997	−	49.5496i	−0.561882	−	1.72929i	0.115157	−	0.993347i	$-0.463263\pi$
$822$	7.96798	−	24.5229i	0.277915	−	0.855335i
$823$	12.4971	+	9.07967i	0.435621	+	0.316497i	0.783893	−	0.620896i	$-0.213231\pi$
$823$	12.4971	+	9.07967i	0.435621	+	0.316497i	−0.348271	+	0.937394i	$0.613231\pi$
$824$	−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	$-0.338989\pi$
$827$	−5.68513	−	4.13049i	−0.197691	−	0.143631i	−0.682227	+	0.731140i	$0.738989\pi$
$828$	−5.73518	+	17.6511i	−0.199311	+	0.613417i
$829$	3.58438	+	11.0316i	0.124491	+	0.383143i	0.993808	−	0.111112i	$-0.0354411\pi$
$829$	3.58438	+	11.0316i	0.124491	+	0.383143i	−0.869317	+	0.494254i	$0.835441\pi$
$830$		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	−0.743871	−	0.668323i	$-0.767012\pi$
$839$	7.26350	−	22.3548i	0.250764	−	0.771772i	0.994635	−	0.103449i	$-0.0329877\pi$
$840$		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	$-0.762692\pi$
$853$	−9.24726	+	6.71853i	−0.316620	+	0.230038i	0.418112	+	0.908396i	$0.362692\pi$
$854$	−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	$-0.635465\pi$
$857$	−24.1717			−0.825691			−0.412845	+	0.910801i	$0.635465\pi$
$858$	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	$-0.512999\pi$
$863$	26.3458	−	19.1413i	0.896821	−	0.651579i	0.937648	+	0.347588i	$0.112999\pi$
$864$	−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	$-0.835553\pi$
$877$	3.68041	−	11.3271i	0.124279	−	0.382491i	0.993769	+	0.111460i	$0.0355525\pi$
$878$	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	0.652809	+	0.757523i	$0.273590\pi$
$883$	−9.52629	+	29.3189i	−0.320585	+	0.986660i	−0.973394	+	0.229137i	$0.926410\pi$
$884$	−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	$-0.137051\pi$
$887$	−2.13766	−	6.57904i	−0.0717756	−	0.220903i	−0.980509	+	0.196475i	$0.937051\pi$
$888$	−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	$-0.851073\pi$
$907$	−22.2689	+	16.1793i	−0.739426	+	0.537224i	0.153105	+	0.988210i	$0.451073\pi$
$908$	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	−0.199623	−	0.979873i	$-0.563972\pi$
$911$	−36.0148	−	26.1663i	−1.19322	−	0.866928i	−0.993601	+	0.112945i	$0.963972\pi$
$912$	−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	−0.983285	−	0.182076i	$-0.941718\pi$
$919$	−33.7701	+	24.5354i	−1.11397	+	0.809348i	−0.130688	+	0.991424i	$0.541718\pi$
$920$		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	−0.998525	−	0.0542960i	$-0.982709\pi$
$929$	−38.2654	+	27.8015i	−1.25545	+	0.912136i	−0.256923	+	0.966432i	$0.582709\pi$
$930$		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	$-0.235401\pi$
$937$	9.98269	+	7.25285i	0.326120	+	0.236940i	−0.412662	+	0.910884i	$0.635401\pi$
$938$	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	−0.949312	−	0.314336i	$-0.898218\pi$
$941$	−28.9491	+	21.0327i	−0.943714	+	0.685648i	0.00559818	+	0.999984i	$0.498218\pi$
$942$	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	$-0.412317\pi$
$947$	16.7403			0.543987			0.271993	+	0.962299i	$0.412317\pi$
$948$	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	0.994606	+	0.103727i	$0.0330770\pi$
$953$	7.74615	+	23.8402i	0.250922	+	0.772259i	−0.743683	+	0.668532i	$0.766923\pi$
$954$	−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	$-0.749821\pi$
$967$	−43.9526			−1.41342			−0.706710	+	0.707503i	$0.749821\pi$
$968$	−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	−0.737898	−	0.674912i	$-0.764182\pi$
$971$	7.97024	−	24.5299i	0.255777	−	0.787201i	0.993676	−	0.112289i	$-0.0358183\pi$
$972$	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	$-0.429306\pi$
$977$	−19.9845	−	14.5196i	−0.639359	−	0.464522i	−0.859630	+	0.510917i	$0.829306\pi$
$978$	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	$-0.126291\pi$
$983$	−1.59867	−	4.92021i	−0.0509898	−	0.156930i	−0.973309	+	0.229498i	$0.926291\pi$
$984$	−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	0.986289	+	0.165028i	$0.0527714\pi$
$997$	9.01050	+	27.7315i	0.285365	+	0.878264i	−0.700924	+	0.713236i	$0.747229\pi$
$998$	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.m.301.1	yes	8
5.2	odd	4		550.2.ba.g.499.2		16
5.3	odd	4		550.2.ba.g.499.3		16
5.4	even	2		550.2.h.k.301.2	yes	8
11.3	even	5	inner	550.2.h.m.201.1	yes	8
11.5	even	5		6050.2.a.df.1.1		4
11.6	odd	10		6050.2.a.dn.1.1		4
55.3	odd	20		550.2.ba.g.399.2		16
55.14	even	10		550.2.h.k.201.2	✓	8
55.39	odd	10		6050.2.a.cz.1.4		4
55.47	odd	20		550.2.ba.g.399.3		16
55.49	even	10		6050.2.a.dg.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.k.201.2	✓	8	55.14	even	10
550.2.h.k.301.2	yes	8	5.4	even	2
550.2.h.m.201.1	yes	8	11.3	even	5	inner
550.2.h.m.301.1	yes	8	1.1	even	1	trivial
550.2.ba.g.399.2		16	55.3	odd	20
550.2.ba.g.399.3		16	55.47	odd	20
550.2.ba.g.499.2		16	5.2	odd	4
550.2.ba.g.499.3		16	5.3	odd	4
6050.2.a.cz.1.4		4	55.39	odd	10
6050.2.a.df.1.1		4	11.5	even	5
6050.2.a.dg.1.4		4	55.49	even	10
6050.2.a.dn.1.1		4	11.6	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

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