LMFDB - Embedded newform 950.2.f.c.493.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.3
Root			$-1.18980i$ of defining polynomial
Character	$\chi$	$=$	950.493
Dual form			950.2.f.c.607.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.776589 - 0.776589i) q^{3} +1.00000i q^{4} -1.09826 q^{6} +(-0.710512 + 0.710512i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.79382i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.776589 - 0.776589i) q^{3} +1.00000i q^{4} -1.09826 q^{6} +(-0.710512 + 0.710512i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.79382i q^{9} -0.677239 q^{11} +(0.776589 + 0.776589i) q^{12} +(1.71192 - 1.71192i) q^{13} +1.00482 q^{14} -1.00000 q^{16} +(0.103091 - 0.103091i) q^{17} +(1.26842 - 1.26842i) q^{18} +(1.96258 - 3.89208i) q^{19} +1.10355i q^{21} +(0.478880 + 0.478880i) q^{22} +(3.40607 + 3.40607i) q^{23} -1.09826i q^{24} -2.42102 q^{26} +(3.72283 + 3.72283i) q^{27} +(-0.710512 - 0.710512i) q^{28} +9.60108 q^{29} -4.78418i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.525936 + 0.525936i) q^{33} -0.145793 q^{34} -1.79382 q^{36} +(5.51106 + 5.51106i) q^{37} +(-4.13987 + 1.36437i) q^{38} -2.65892i q^{39} -5.92046i q^{41} +(0.780330 - 0.780330i) q^{42} +(1.28466 + 1.28466i) q^{43} -0.677239i q^{44} -4.81691i q^{46} +(3.99034 - 3.99034i) q^{47} +(-0.776589 + 0.776589i) q^{48} +5.99034i q^{49} -0.160119i q^{51} +(1.71192 + 1.71192i) q^{52} +(1.10968 - 1.10968i) q^{53} -5.26487i q^{54} +1.00482i q^{56} +(-1.49843 - 4.54666i) q^{57} +(-6.78899 - 6.78899i) q^{58} +7.60578 q^{59} -6.27453 q^{61} +(-3.38292 + 3.38292i) q^{62} +(-1.27453 - 1.27453i) q^{63} -1.00000i q^{64} +0.743786 q^{66} +(-1.59538 - 1.59538i) q^{67} +(0.103091 + 0.103091i) q^{68} +5.29023 q^{69} +5.83605i q^{71} +(1.26842 + 1.26842i) q^{72} +(1.31793 + 1.31793i) q^{73} -7.79382i q^{74} +(3.89208 + 1.96258i) q^{76} +(0.481186 - 0.481186i) q^{77} +(-1.88014 + 1.88014i) q^{78} -16.4322 q^{79} +0.400765 q^{81} +(-4.18640 + 4.18640i) q^{82} +(2.09826 + 2.09826i) q^{83} -1.10355 q^{84} -1.81678i q^{86} +(7.45610 - 7.45610i) q^{87} +(-0.478880 + 0.478880i) q^{88} +9.17944 q^{89} +2.43268i q^{91} +(-3.40607 + 3.40607i) q^{92} +(-3.71534 - 3.71534i) q^{93} -5.64320 q^{94} +1.09826 q^{96} +(0.694155 + 0.694155i) q^{97} +(4.23581 - 4.23581i) q^{98} -1.21484i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) $ 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.776589	−	0.776589i	0.448364	−	0.448364i	−0.446446	−	0.894810i	$-0.647311\pi$
$3$	0.776589	−	0.776589i	0.448364	−	0.448364i	0.894810	+	0.446446i	$0.147311\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−1.09826			−0.448364
$7$	−0.710512	+	0.710512i	−0.268548	+	0.268548i	−0.828515	−	0.559967i	$-0.810814\pi$
$7$	−0.710512	+	0.710512i	−0.268548	+	0.268548i	0.559967	+	0.828515i	$0.310814\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.79382i			0.597939i
$10$		0			0
$11$	−0.677239			−0.204195			−0.102098	−	0.994774i	$-0.532555\pi$
$11$	−0.677239			−0.204195			−0.102098	+	0.994774i	$0.532555\pi$
$12$	0.776589	+	0.776589i	0.224182	+	0.224182i
$13$	1.71192	−	1.71192i	0.474802	−	0.474802i	−0.428663	−	0.903465i	$-0.641015\pi$
$13$	1.71192	−	1.71192i	0.474802	−	0.474802i	0.903465	+	0.428663i	$0.141015\pi$
$14$	1.00482			0.268548
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.103091	−	0.103091i	0.0250033	−	0.0250033i	−0.694495	−	0.719498i	$-0.744372\pi$
$17$	0.103091	−	0.103091i	0.0250033	−	0.0250033i	0.719498	+	0.694495i	$0.244372\pi$
$18$	1.26842	−	1.26842i	0.298970	−	0.298970i
$19$	1.96258	−	3.89208i	0.450246	−	0.892905i
$19$	1.96258	−	3.89208i	0.450246	−	0.892905i
$20$		0			0
$21$			1.10355i			0.240815i
$22$	0.478880	+	0.478880i	0.102098	+	0.102098i
$23$	3.40607	+	3.40607i	0.710214	+	0.710214i	0.966580	−	0.256366i	$-0.0825252\pi$
$23$	3.40607	+	3.40607i	0.710214	+	0.710214i	−0.256366	+	0.966580i	$0.582525\pi$
$24$		−	1.09826i		−	0.224182i
$25$		0			0
$26$	−2.42102			−0.474802
$27$	3.72283	+	3.72283i	0.716459	+	0.716459i
$28$	−0.710512	−	0.710512i	−0.134274	−	0.134274i
$29$	9.60108			1.78288			0.891438	−	0.453143i	$-0.149697\pi$
$29$	9.60108			1.78288			0.891438	+	0.453143i	$0.149697\pi$
$30$		0			0
$31$		−	4.78418i		−	0.859263i	−0.903004	−	0.429632i	$-0.858643\pi$
$31$		−	4.78418i		−	0.859263i	0.903004	−	0.429632i	$-0.141357\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.525936	+	0.525936i	−0.0915538	+	0.0915538i
$34$	−0.145793			−0.0250033
$35$		0			0
$36$	−1.79382			−0.298970
$37$	5.51106	+	5.51106i	0.906013	+	0.906013i	0.995948	−	0.0899347i	$-0.0286659\pi$
$37$	5.51106	+	5.51106i	0.906013	+	0.906013i	−0.0899347	+	0.995948i	$0.528666\pi$
$38$	−4.13987	+	1.36437i	−0.671575	+	0.221329i
$39$		−	2.65892i		−	0.425768i
$40$		0			0
$41$		−	5.92046i		−	0.924620i	−0.886718	−	0.462310i	$-0.847021\pi$
$41$		−	5.92046i		−	0.924620i	0.886718	−	0.462310i	$-0.152979\pi$
$42$	0.780330	−	0.780330i	0.120407	−	0.120407i
$43$	1.28466	+	1.28466i	0.195909	+	0.195909i	0.798244	−	0.602335i	$-0.205763\pi$
$43$	1.28466	+	1.28466i	0.195909	+	0.195909i	−0.602335	+	0.798244i	$0.705763\pi$
$44$		−	0.677239i		−	0.102098i
$45$		0			0
$46$		−	4.81691i		−	0.710214i
$47$	3.99034	−	3.99034i	0.582052	−	0.582052i	−0.353415	−	0.935467i	$-0.614980\pi$
$47$	3.99034	−	3.99034i	0.582052	−	0.582052i	0.935467	+	0.353415i	$0.114980\pi$
$48$	−0.776589	+	0.776589i	−0.112091	+	0.112091i
$49$			5.99034i			0.855763i
$50$		0			0
$51$		−	0.160119i		−	0.0224211i
$52$	1.71192	+	1.71192i	0.237401	+	0.237401i
$53$	1.10968	−	1.10968i	0.152426	−	0.152426i	−0.626775	−	0.779201i	$-0.715625\pi$
$53$	1.10968	−	1.10968i	0.152426	−	0.152426i	0.779201	+	0.626775i	$0.215625\pi$
$54$		−	5.26487i		−	0.716459i
$55$		0			0
$56$			1.00482i			0.134274i
$57$	−1.49843	−	4.54666i	−0.198472	−	0.602220i
$58$	−6.78899	−	6.78899i	−0.891438	−	0.891438i
$59$	7.60578			0.990188			0.495094	−	0.868840i	$-0.335134\pi$
$59$	7.60578			0.990188			0.495094	+	0.868840i	$0.335134\pi$
$60$		0			0
$61$	−6.27453			−0.803371			−0.401686	−	0.915778i	$-0.631576\pi$
$61$	−6.27453			−0.803371			−0.401686	+	0.915778i	$0.631576\pi$
$62$	−3.38292	+	3.38292i	−0.429632	+	0.429632i
$63$	−1.27453	−	1.27453i	−0.160576	−	0.160576i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.743786			0.0915538
$67$	−1.59538	−	1.59538i	−0.194907	−	0.194907i	0.602905	−	0.797813i	$-0.294010\pi$
$67$	−1.59538	−	1.59538i	−0.194907	−	0.194907i	−0.797813	+	0.602905i	$0.794010\pi$
$68$	0.103091	+	0.103091i	0.0125016	+	0.0125016i
$69$	5.29023			0.636869
$70$		0			0
$71$			5.83605i			0.692612i	0.938122	+	0.346306i	$0.112564\pi$
$71$			5.83605i			0.692612i	−0.938122	+	0.346306i	$0.887436\pi$
$72$	1.26842	+	1.26842i	0.149485	+	0.149485i
$73$	1.31793	+	1.31793i	0.154252	+	0.154252i	0.780014	−	0.625762i	$-0.215212\pi$
$73$	1.31793	+	1.31793i	0.154252	+	0.154252i	−0.625762	+	0.780014i	$0.715212\pi$
$74$		−	7.79382i		−	0.906013i
$75$		0			0
$76$	3.89208	+	1.96258i	0.446452	+	0.225123i
$77$	0.481186	−	0.481186i	0.0548363	−	0.0548363i
$78$	−1.88014	+	1.88014i	−0.212884	+	0.212884i
$79$	−16.4322			−1.84877			−0.924386	−	0.381459i	$-0.875422\pi$
$79$	−16.4322			−1.84877			−0.924386	+	0.381459i	$0.875422\pi$
$80$		0			0
$81$	0.400765			0.0445294
$82$	−4.18640	+	4.18640i	−0.462310	+	0.462310i
$83$	2.09826	+	2.09826i	0.230314	+	0.230314i	0.812824	−	0.582510i	$-0.197929\pi$
$83$	2.09826	+	2.09826i	0.230314	+	0.230314i	−0.582510	+	0.812824i	$0.697929\pi$
$84$	−1.10355			−0.120407
$85$		0			0
$86$		−	1.81678i		−	0.195909i
$87$	7.45610	−	7.45610i	0.799378	−	0.799378i
$88$	−0.478880	+	0.478880i	−0.0510488	+	0.0510488i
$89$	9.17944			0.973018			0.486509	−	0.873675i	$-0.338270\pi$
$89$	9.17944			0.973018			0.486509	+	0.873675i	$0.338270\pi$
$90$		0			0
$91$			2.43268i			0.255015i
$92$	−3.40607	+	3.40607i	−0.355107	+	0.355107i
$93$	−3.71534	−	3.71534i	−0.385263	−	0.385263i
$94$	−5.64320			−0.582052
$95$		0			0
$96$	1.09826			0.112091
$97$	0.694155	+	0.694155i	0.0704808	+	0.0704808i	0.741468	−	0.670988i	$-0.234130\pi$
$97$	0.694155	+	0.694155i	0.0704808	+	0.0704808i	−0.670988	+	0.741468i	$0.734130\pi$
$98$	4.23581	−	4.23581i	0.427882	−	0.427882i
$99$		−	1.21484i		−	0.122096i
$100$		0			0
$101$	13.0404			1.29757			0.648783	−	0.760974i	$-0.275278\pi$
$101$	13.0404			1.29757			0.648783	+	0.760974i	$0.275278\pi$
$102$	−0.113221	+	0.113221i	−0.0112106	+	0.0112106i
$103$	8.25635	−	8.25635i	0.813522	−	0.813522i	−0.171638	−	0.985160i	$-0.554906\pi$
$103$	8.25635	−	8.25635i	0.813522	−	0.813522i	0.985160	+	0.171638i	$0.0549059\pi$
$104$		−	2.42102i		−	0.237401i
$105$		0			0
$106$	−1.56932			−0.152426
$107$	−12.3000	−	12.3000i	−1.18909	−	1.18909i	−0.977320	−	0.211768i	$-0.932078\pi$
$107$	−12.3000	−	12.3000i	−1.18909	−	1.18909i	−0.211768	−	0.977320i	$-0.567922\pi$
$108$	−3.72283	+	3.72283i	−0.358229	+	0.358229i
$109$	−11.3191			−1.08418			−0.542088	−	0.840322i	$-0.682366\pi$
$109$	−11.3191			−1.08418			−0.542088	+	0.840322i	$0.682366\pi$
$110$		0			0
$111$	8.55966			0.812447
$112$	0.710512	−	0.710512i	0.0671371	−	0.0671371i
$113$	1.72140	−	1.72140i	0.161936	−	0.161936i	−0.621488	−	0.783424i	$-0.713472\pi$
$113$	1.72140	−	1.72140i	0.161936	−	0.161936i	0.783424	+	0.621488i	$0.213472\pi$
$114$	−2.15543	+	4.27453i	−0.201874	+	0.400346i
$115$		0			0
$116$			9.60108i			0.891438i
$117$	3.07088	+	3.07088i	0.283903	+	0.283903i
$118$	−5.37810	−	5.37810i	−0.495094	−	0.495094i
$119$			0.146495i			0.0134292i
$120$		0			0
$121$	−10.5413			−0.958304
$122$	4.43676	+	4.43676i	0.401686	+	0.401686i
$123$	−4.59777	−	4.59777i	−0.414567	−	0.414567i
$124$	4.78418			0.429632
$125$		0			0
$126$			1.80246i			0.160576i
$127$	−10.8695	−	10.8695i	−0.964512	−	0.964512i	0.0348792	−	0.999392i	$-0.488895\pi$
$127$	−10.8695	−	10.8695i	−0.964512	−	0.964512i	−0.999392	+	0.0348792i	$0.988895\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	1.99531			0.175677
$130$		0			0
$131$	1.58764			0.138712			0.0693562	−	0.997592i	$-0.477906\pi$
$131$	1.58764			0.138712			0.0693562	+	0.997592i	$0.477906\pi$
$132$	−0.525936	−	0.525936i	−0.0457769	−	0.0457769i
$133$	1.37094	+	4.15981i	0.118875	+	0.360701i
$134$			2.25621i			0.194907i
$135$		0			0
$136$		−	0.145793i		−	0.0125016i
$137$	8.08378	−	8.08378i	0.690644	−	0.690644i	−0.271730	−	0.962374i	$-0.587596\pi$
$137$	8.08378	−	8.08378i	0.690644	−	0.690644i	0.962374	+	0.271730i	$0.0875957\pi$
$138$	−3.74076	−	3.74076i	−0.318434	−	0.318434i
$139$			8.37279i			0.710171i	0.934834	+	0.355086i	$0.115548\pi$
$139$			8.37279i			0.710171i	−0.934834	+	0.355086i	$0.884452\pi$
$140$		0			0
$141$		−	6.19772i		−	0.521942i
$142$	4.12671	−	4.12671i	0.346306	−	0.346306i
$143$	−1.15938	+	1.15938i	−0.0969522	+	0.0969522i
$144$		−	1.79382i		−	0.149485i
$145$		0			0
$146$		−	1.86384i		−	0.154252i
$147$	4.65204	+	4.65204i	0.383694	+	0.383694i
$148$	−5.51106	+	5.51106i	−0.453006	+	0.453006i
$149$			7.96043i			0.652144i	0.945345	+	0.326072i	$0.105725\pi$
$149$			7.96043i			0.652144i	−0.945345	+	0.326072i	$0.894275\pi$
$150$		0			0
$151$		−	12.8928i		−	1.04920i	−0.851349	−	0.524600i	$-0.824215\pi$
$151$		−	12.8928i		−	1.04920i	0.851349	−	0.524600i	$-0.175785\pi$
$152$	−1.36437	−	4.13987i	−0.110665	−	0.335788i
$153$	0.184927	+	0.184927i	0.0149504	+	0.0149504i
$154$	−0.680500			−0.0548363
$155$		0			0
$156$	2.65892			0.212884
$157$	−10.9624	+	10.9624i	−0.874893	+	0.874893i	−0.993001	−	0.118108i	$-0.962317\pi$
$157$	−10.9624	+	10.9624i	−0.874893	+	0.874893i	0.118108	+	0.993001i	$0.462317\pi$
$158$	11.6194	+	11.6194i	0.924386	+	0.924386i
$159$		−	1.72353i		−	0.136685i
$160$		0			0
$161$	−4.84011			−0.381454
$162$	−0.283383	−	0.283383i	−0.0222647	−	0.0222647i
$163$	13.1767	+	13.1767i	1.03208	+	1.03208i	0.999468	+	0.0326140i	$0.0103832\pi$
$163$	13.1767	+	13.1767i	1.03208	+	1.03208i	0.0326140	+	0.999468i	$0.489617\pi$
$164$	5.92046			0.462310
$165$		0			0
$166$		−	2.96739i		−	0.230314i
$167$	1.91900	+	1.91900i	0.148496	+	0.148496i	0.777446	−	0.628950i	$-0.216515\pi$
$167$	1.91900	+	1.91900i	0.148496	+	0.148496i	−0.628950	+	0.777446i	$0.716515\pi$
$168$	0.780330	+	0.780330i	0.0602037	+	0.0602037i
$169$			7.13864i			0.549126i
$170$		0			0
$171$	6.98168	+	3.52050i	0.533903	+	0.269220i
$172$	−1.28466	+	1.28466i	−0.0979544	+	0.0979544i
$173$	−10.4199	+	10.4199i	−0.792209	+	0.792209i	−0.981853	−	0.189644i	$-0.939267\pi$
$173$	−10.4199	+	10.4199i	−0.792209	+	0.792209i	0.189644	+	0.981853i	$0.439267\pi$
$174$	−10.5445			−0.799378
$175$		0			0
$176$	0.677239			0.0510488
$177$	5.90656	−	5.90656i	0.443965	−	0.443965i
$178$	−6.49084	−	6.49084i	−0.486509	−	0.486509i
$179$	−19.2866			−1.44155			−0.720773	−	0.693171i	$-0.756213\pi$
$179$	−19.2866			−1.44155			−0.720773	+	0.693171i	$0.756213\pi$
$180$		0			0
$181$		−	1.13628i		−	0.0844593i	−0.999108	−	0.0422296i	$-0.986554\pi$
$181$		−	1.13628i		−	0.0844593i	0.999108	−	0.0422296i	$-0.0134461\pi$
$182$	1.72017	−	1.72017i	0.127507	−	0.127507i
$183$	−4.87273	+	4.87273i	−0.360203	+	0.360203i
$184$	4.81691			0.355107
$185$		0			0
$186$			5.25428i			0.385263i
$187$	−0.0698173	+	0.0698173i	−0.00510555	+	0.00510555i
$188$	3.99034	+	3.99034i	0.291026	+	0.291026i
$189$	−5.29023			−0.384808
$190$		0			0
$191$	3.28513			0.237704			0.118852	−	0.992912i	$-0.462079\pi$
$191$	3.28513			0.237704			0.118852	+	0.992912i	$0.462079\pi$
$192$	−0.776589	−	0.776589i	−0.0560455	−	0.0560455i
$193$	16.5005	−	16.5005i	1.18773	−	1.18773i	0.210035	−	0.977694i	$-0.432642\pi$
$193$	16.5005	−	16.5005i	1.18773	−	1.18773i	0.977694	−	0.210035i	$-0.0673577\pi$
$194$		−	0.981684i		−	0.0704808i
$195$		0			0
$196$	−5.99034			−0.427882
$197$	−13.7277	+	13.7277i	−0.978061	+	0.978061i	−0.999764	−	0.0217032i	$-0.993091\pi$
$197$	−13.7277	+	13.7277i	−0.978061	+	0.978061i	0.0217032	+	0.999764i	$0.493091\pi$
$198$	−0.859023	+	0.859023i	−0.0610481	+	0.0610481i
$199$		−	0.479717i		−	0.0340062i	−0.999855	−	0.0170031i	$-0.994587\pi$
$199$		−	0.479717i		−	0.0340062i	0.999855	−	0.0170031i	$-0.00541252\pi$
$200$		0			0
$201$	−2.47792			−0.174779
$202$	−9.22094	−	9.22094i	−0.648783	−	0.648783i
$203$	−6.82169	+	6.82169i	−0.478789	+	0.478789i
$204$	0.160119			0.0112106
$205$		0			0
$206$	−11.6762			−0.813522
$207$	−6.10986	+	6.10986i	−0.424665	+	0.424665i
$208$	−1.71192	+	1.71192i	−0.118701	+	0.118701i
$209$	−1.32913	+	2.63587i	−0.0919380	+	0.182327i
$210$		0			0
$211$			14.1892i			0.976824i	0.872613	+	0.488412i	$0.162424\pi$
$211$			14.1892i			0.976824i	−0.872613	+	0.488412i	$0.837576\pi$
$212$	1.10968	+	1.10968i	0.0762129	+	0.0762129i
$213$	4.53221	+	4.53221i	0.310542	+	0.310542i
$214$			17.3949i			1.18909i
$215$		0			0
$216$	5.26487			0.358229
$217$	3.39922	+	3.39922i	0.230754	+	0.230754i
$218$	8.00383	+	8.00383i	0.542088	+	0.542088i
$219$	2.04699			0.138323
$220$		0			0
$221$		−	0.352968i		−	0.0237432i
$222$	−6.05260	−	6.05260i	−0.406224	−	0.406224i
$223$	−8.36064	+	8.36064i	−0.559870	+	0.559870i	−0.929270	−	0.369400i	$-0.879563\pi$
$223$	−8.36064	+	8.36064i	−0.559870	+	0.559870i	0.369400	+	0.929270i	$0.379563\pi$
$224$	−1.00482			−0.0671371
$225$		0			0
$226$	−2.43442			−0.161936
$227$	5.42863	+	5.42863i	0.360311	+	0.360311i	0.863927	−	0.503617i	$-0.167998\pi$
$227$	5.42863	+	5.42863i	0.360311	+	0.360311i	−0.503617	+	0.863927i	$0.667998\pi$
$228$	4.54666	−	1.49843i	0.301110	−	0.0992362i
$229$		−	20.6628i		−	1.36544i	−0.730681	−	0.682720i	$-0.760797\pi$
$229$		−	20.6628i		−	1.36544i	0.730681	−	0.682720i	$-0.239203\pi$
$230$		0			0
$231$		−	0.747368i		−	0.0491732i
$232$	6.78899	−	6.78899i	0.445719	−	0.445719i
$233$	18.3255	+	18.3255i	1.20054	+	1.20054i	0.974001	+	0.226543i	$0.0727423\pi$
$233$	18.3255	+	18.3255i	1.20054	+	1.20054i	0.226543	+	0.974001i	$0.427258\pi$
$234$		−	4.34288i		−	0.283903i
$235$		0			0
$236$			7.60578i			0.495094i
$237$	−12.7611	+	12.7611i	−0.828923	+	0.828923i
$238$	0.103588	−	0.103588i	0.00671459	−	0.00671459i
$239$			13.6676i			0.884082i	0.896995	+	0.442041i	$0.145746\pi$
$239$			13.6676i			0.884082i	−0.896995	+	0.442041i	$0.854254\pi$
$240$		0			0
$241$			11.1747i			0.719828i	0.932985	+	0.359914i	$0.117194\pi$
$241$			11.1747i			0.719828i	−0.932985	+	0.359914i	$0.882806\pi$
$242$	7.45386	+	7.45386i	0.479152	+	0.479152i
$243$	−10.8573	+	10.8573i	−0.696493	+	0.696493i
$244$		−	6.27453i		−	0.401686i
$245$		0			0
$246$			6.50222i			0.414567i
$247$	−3.30316	−	10.0227i	−0.210175	−	0.637731i
$248$	−3.38292	−	3.38292i	−0.214816	−	0.214816i
$249$	3.25898			0.206529
$250$		0			0
$251$	26.5183			1.67382			0.836910	−	0.547341i	$-0.184360\pi$
$251$	26.5183			1.67382			0.836910	+	0.547341i	$0.184360\pi$
$252$	1.27453	−	1.27453i	0.0802878	−	0.0802878i
$253$	−2.30672	−	2.30672i	−0.145022	−	0.145022i
$254$			15.3718i			0.964512i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.0616	−	12.0616i	−0.752383	−	0.752383i	0.222541	−	0.974923i	$-0.428565\pi$
$257$	−12.0616	−	12.0616i	−0.752383	−	0.752383i	−0.974923	+	0.222541i	$0.928565\pi$
$258$	−1.41089	−	1.41089i	−0.0878385	−	0.0878385i
$259$	−7.83135			−0.486617
$260$		0			0
$261$			17.2226i			1.06605i
$262$	−1.12263	−	1.12263i	−0.0693562	−	0.0693562i
$263$	−22.3035	−	22.3035i	−1.37529	−	1.37529i	−0.852401	−	0.522889i	$-0.824854\pi$
$263$	−22.3035	−	22.3035i	−1.37529	−	1.37529i	−0.522889	−	0.852401i	$-0.675146\pi$
$264$			0.743786i			0.0457769i
$265$		0			0
$266$	1.97203	−	3.91083i	0.120913	−	0.239788i
$267$	7.12865	−	7.12865i	0.436267	−	0.436267i
$268$	1.59538	−	1.59538i	0.0974536	−	0.0974536i
$269$	−21.7950			−1.32886			−0.664431	−	0.747349i	$-0.731326\pi$
$269$	−21.7950			−1.32886			−0.664431	+	0.747349i	$0.731326\pi$
$270$		0			0
$271$	−19.0693			−1.15838			−0.579189	−	0.815194i	$-0.696631\pi$
$271$	−19.0693			−1.15838			−0.579189	+	0.815194i	$0.696631\pi$
$272$	−0.103091	+	0.103091i	−0.00625082	+	0.00625082i
$273$	1.88920	+	1.88920i	0.114339	+	0.114339i
$274$	−11.4322			−0.690644
$275$		0			0
$276$			5.29023i			0.318434i
$277$	−21.6983	+	21.6983i	−1.30372	+	1.30372i	−0.377863	+	0.925861i	$0.623341\pi$
$277$	−21.6983	+	21.6983i	−1.30372	+	1.30372i	−0.925861	+	0.377863i	$0.876659\pi$
$278$	5.92046	−	5.92046i	0.355086	−	0.355086i
$279$	8.58194			0.513787
$280$		0			0
$281$			29.0478i			1.73284i	0.499312	+	0.866422i	$0.333586\pi$
$281$			29.0478i			1.73284i	−0.499312	+	0.866422i	$0.666414\pi$
$282$	−4.38245	+	4.38245i	−0.260971	+	0.260971i
$283$	−21.0008	−	21.0008i	−1.24837	−	1.24837i	−0.956440	−	0.291928i	$-0.905703\pi$
$283$	−21.0008	−	21.0008i	−1.24837	−	1.24837i	−0.291928	−	0.956440i	$-0.594297\pi$
$284$	−5.83605			−0.346306
$285$		0			0
$286$	1.63961			0.0969522
$287$	4.20656	+	4.20656i	0.248305	+	0.248305i
$288$	−1.26842	+	1.26842i	−0.0747424	+	0.0747424i
$289$			16.9787i			0.998750i
$290$		0			0
$291$	1.07815			0.0632021
$292$	−1.31793	+	1.31793i	−0.0771262	+	0.0771262i
$293$	10.0963	−	10.0963i	0.589830	−	0.589830i	−0.347755	−	0.937585i	$-0.613056\pi$
$293$	10.0963	−	10.0963i	0.589830	−	0.589830i	0.937585	+	0.347755i	$0.113056\pi$
$294$		−	6.57898i		−	0.383694i
$295$		0			0
$296$	7.79382			0.453006
$297$	−2.52124	−	2.52124i	−0.146297	−	0.146297i
$298$	5.62887	−	5.62887i	0.326072	−	0.326072i
$299$	11.6618			0.674422
$300$		0			0
$301$	−1.82553			−0.105222
$302$	−9.11658	+	9.11658i	−0.524600	+	0.524600i
$303$	10.1270	−	10.1270i	0.581782	−	0.581782i
$304$	−1.96258	+	3.89208i	−0.112561	+	0.223226i
$305$		0			0
$306$		−	0.261526i		−	0.0149504i
$307$	−9.38453	−	9.38453i	−0.535604	−	0.535604i	0.386631	−	0.922235i	$-0.373639\pi$
$307$	−9.38453	−	9.38453i	−0.535604	−	0.535604i	−0.922235	+	0.386631i	$0.873639\pi$
$308$	0.481186	+	0.481186i	0.0274181	+	0.0274181i
$309$		−	12.8236i		−	0.729508i
$310$		0			0
$311$	−6.41317			−0.363657			−0.181829	−	0.983330i	$-0.558202\pi$
$311$	−6.41317			−0.363657			−0.181829	+	0.983330i	$0.558202\pi$
$312$	−1.88014	−	1.88014i	−0.106442	−	0.106442i
$313$	0.560748	+	0.560748i	0.0316953	+	0.0316953i	0.722777	−	0.691082i	$-0.242865\pi$
$313$	0.560748	+	0.560748i	0.0316953	+	0.0316953i	−0.691082	+	0.722777i	$0.742865\pi$
$314$	15.5031			0.874893
$315$		0			0
$316$		−	16.4322i		−	0.924386i
$317$	21.1988	+	21.1988i	1.19065	+	1.19065i	0.976886	+	0.213759i	$0.0685708\pi$
$317$	21.1988	+	21.1988i	1.19065	+	1.19065i	0.213759	+	0.976886i	$0.431429\pi$
$318$	−1.21872	+	1.21872i	−0.0683423	+	0.0683423i
$319$	−6.50222			−0.364055
$320$		0			0
$321$	−19.1041			−1.06629
$322$	3.42247	+	3.42247i	0.190727	+	0.190727i
$323$	−0.198915	−	0.603563i	−0.0110679	−	0.0335832i
$324$			0.400765i			0.0222647i
$325$		0			0
$326$		−	18.6347i		−	1.03208i
$327$	−8.79032	+	8.79032i	−0.486106	+	0.486106i
$328$	−4.18640	−	4.18640i	−0.231155	−	0.231155i
$329$			5.67038i			0.312618i
$330$		0			0
$331$		−	23.2874i		−	1.27999i	−0.768378	−	0.639997i	$-0.778936\pi$
$331$		−	23.2874i		−	1.27999i	0.768378	−	0.639997i	$-0.221064\pi$
$332$	−2.09826	+	2.09826i	−0.115157	+	0.115157i
$333$	−9.88584	+	9.88584i	−0.541741	+	0.541741i
$334$		−	2.71387i		−	0.148496i
$335$		0			0
$336$		−	1.10355i		−	0.0602037i
$337$	0.775215	+	0.775215i	0.0422286	+	0.0422286i	0.727906	−	0.685677i	$-0.240494\pi$
$337$	0.775215	+	0.775215i	0.0422286	+	0.0422286i	−0.685677	+	0.727906i	$0.740494\pi$
$338$	5.04778	−	5.04778i	0.274563	−	0.274563i
$339$		−	2.67364i		−	0.145212i
$340$		0			0
$341$			3.24003i			0.175457i
$342$	−2.44742	−	7.42617i	−0.132342	−	0.401561i
$343$	−9.22980	−	9.22980i	−0.498362	−	0.498362i
$344$	1.81678			0.0979544
$345$		0			0
$346$	14.7359			0.792209
$347$	20.5297	−	20.5297i	1.10209	−	1.10209i	0.107937	−	0.994158i	$-0.465576\pi$
$347$	20.5297	−	20.5297i	1.10209	−	1.10209i	0.994158	−	0.107937i	$-0.0344244\pi$
$348$	7.45610	+	7.45610i	0.399689	+	0.399689i
$349$		−	25.8842i		−	1.38555i	−0.721153	−	0.692775i	$-0.756388\pi$
$349$		−	25.8842i		−	1.38555i	0.721153	−	0.692775i	$-0.243612\pi$
$350$		0			0
$351$	12.7464			0.680352
$352$	−0.478880	−	0.478880i	−0.0255244	−	0.0255244i
$353$	12.1417	+	12.1417i	0.646236	+	0.646236i	0.952081	−	0.305845i	$-0.0989391\pi$
$353$	12.1417	+	12.1417i	0.646236	+	0.646236i	−0.305845	+	0.952081i	$0.598939\pi$
$354$	−8.35314			−0.443965
$355$		0			0
$356$			9.17944i			0.486509i
$357$	0.113766	+	0.113766i	0.00602116	+	0.00602116i
$358$	13.6377	+	13.6377i	0.720773	+	0.720773i
$359$		−	12.6290i		−	0.666533i	−0.942833	−	0.333267i	$-0.891849\pi$
$359$		−	12.6290i		−	0.666533i	0.942833	−	0.333267i	$-0.108151\pi$
$360$		0			0
$361$	−11.2966	−	15.2770i	−0.594557	−	0.804053i
$362$	−0.803473	+	0.803473i	−0.0422296	+	0.0422296i
$363$	−8.18630	+	8.18630i	−0.429669	+	0.429669i
$364$	−2.43268			−0.127507
$365$		0			0
$366$	6.89109			0.360203
$367$	18.3728	−	18.3728i	0.959052	−	0.959052i	−0.0401420	−	0.999194i	$-0.512781\pi$
$367$	18.3728	−	18.3728i	0.959052	−	0.959052i	0.999194	+	0.0401420i	$0.0127810\pi$
$368$	−3.40607	−	3.40607i	−0.177554	−	0.177554i
$369$	10.6202			0.552867
$370$		0			0
$371$			1.57688i			0.0818674i
$372$	3.71534	−	3.71534i	0.192631	−	0.192631i
$373$	11.0965	−	11.0965i	0.574553	−	0.574553i	−0.358845	−	0.933397i	$-0.616829\pi$
$373$	11.0965	−	11.0965i	0.574553	−	0.574553i	0.933397	+	0.358845i	$0.116829\pi$
$374$	0.0987365			0.00510555
$375$		0			0
$376$		−	5.64320i		−	0.291026i
$377$	16.4363	−	16.4363i	0.846513	−	0.846513i
$378$	3.74076	+	3.74076i	0.192404	+	0.192404i
$379$	9.79393			0.503080			0.251540	−	0.967847i	$-0.419063\pi$
$379$	9.79393			0.503080			0.251540	+	0.967847i	$0.419063\pi$
$380$		0			0
$381$	−16.8823			−0.864905
$382$	−2.32294	−	2.32294i	−0.118852	−	0.118852i
$383$	−6.09618	+	6.09618i	−0.311500	+	0.311500i	−0.845491	−	0.533990i	$-0.820692\pi$
$383$	−6.09618	+	6.09618i	−0.311500	+	0.311500i	0.533990	+	0.845491i	$0.320692\pi$
$384$			1.09826i			0.0560455i
$385$		0			0
$386$	−23.3352			−1.18773
$387$	−2.30445	+	2.30445i	−0.117142	+	0.117142i
$388$	−0.694155	+	0.694155i	−0.0352404	+	0.0352404i
$389$			10.1349i			0.513860i	0.966430	+	0.256930i	$0.0827109\pi$
$389$			10.1349i			0.513860i	−0.966430	+	0.256930i	$0.917289\pi$
$390$		0			0
$391$	0.702271			0.0355153
$392$	4.23581	+	4.23581i	0.213941	+	0.213941i
$393$	1.23294	−	1.23294i	0.0621936	−	0.0621936i
$394$	19.4140			0.978061
$395$		0			0
$396$	1.21484			0.0610481
$397$	−16.8911	+	16.8911i	−0.847739	+	0.847739i	−0.989851	−	0.142111i	$-0.954611\pi$
$397$	−16.8911	+	16.8911i	−0.847739	+	0.847739i	0.142111	+	0.989851i	$0.454611\pi$
$398$	−0.339211	+	0.339211i	−0.0170031	+	0.0170031i
$399$	4.29512	+	2.16581i	0.215025	+	0.108426i
$400$		0			0
$401$			12.8498i			0.641689i	0.947132	+	0.320844i	$0.103967\pi$
$401$			12.8498i			0.641689i	−0.947132	+	0.320844i	$0.896033\pi$
$402$	1.75215	+	1.75215i	0.0873894	+	0.0873894i
$403$	−8.19014	−	8.19014i	−0.407980	−	0.407980i
$404$			13.0404i			0.648783i
$405$		0			0
$406$	9.64732			0.478789
$407$	−3.73230	−	3.73230i	−0.185003	−	0.185003i
$408$	−0.113221	−	0.113221i	−0.00560528	−	0.00560528i
$409$	−7.57304			−0.374463			−0.187231	−	0.982316i	$-0.559951\pi$
$409$	−7.57304			−0.374463			−0.187231	+	0.982316i	$0.559951\pi$
$410$		0			0
$411$		−	12.5556i		−	0.619320i
$412$	8.25635	+	8.25635i	0.406761	+	0.406761i
$413$	−5.40400	+	5.40400i	−0.265913	+	0.265913i
$414$	8.64065			0.424665
$415$		0			0
$416$	2.42102			0.118701
$417$	6.50222	+	6.50222i	0.318415	+	0.318415i
$418$	2.80368	−	0.924001i	0.137132	−	0.0451944i
$419$		−	21.5431i		−	1.05245i	−0.850345	−	0.526226i	$-0.823607\pi$
$419$		−	21.5431i		−	1.05245i	0.850345	−	0.526226i	$-0.176393\pi$
$420$		0			0
$421$		−	30.3252i		−	1.47796i	−0.673727	−	0.738981i	$-0.735308\pi$
$421$		−	30.3252i		−	1.47796i	0.673727	−	0.738981i	$-0.264692\pi$
$422$	10.0333	−	10.0333i	0.488412	−	0.488412i
$423$	7.15795	+	7.15795i	0.348031	+	0.348031i
$424$		−	1.56932i		−	0.0762129i
$425$		0			0
$426$		−	6.40952i		−	0.310542i
$427$	4.45813	−	4.45813i	0.215744	−	0.215744i
$428$	12.3000	−	12.3000i	0.594544	−	0.594544i
$429$			1.80072i			0.0869398i
$430$		0			0
$431$		−	17.2913i		−	0.832891i	−0.909161	−	0.416446i	$-0.863276\pi$
$431$		−	17.2913i		−	0.832891i	0.909161	−	0.416446i	$-0.136724\pi$
$432$	−3.72283	−	3.72283i	−0.179115	−	0.179115i
$433$	−18.8288	+	18.8288i	−0.904857	+	0.904857i	−0.995851	−	0.0909947i	$-0.970995\pi$
$433$	−18.8288	+	18.8288i	−0.904857	+	0.904857i	0.0909947	+	0.995851i	$0.470995\pi$
$434$		−	4.80722i		−	0.230754i
$435$		0			0
$436$		−	11.3191i		−	0.542088i
$437$	19.9414	−	6.57202i	0.953924	−	0.314382i
$438$	−1.44744	−	1.44744i	−0.0691613	−	0.0691613i
$439$	25.9130			1.23676			0.618379	−	0.785880i	$-0.287790\pi$
$439$	25.9130			1.23676			0.618379	+	0.785880i	$0.287790\pi$
$440$		0			0
$441$	−10.7456			−0.511695
$442$	−0.249586	+	0.249586i	−0.0118716	+	0.0118716i
$443$	−10.8926	−	10.8926i	−0.517521	−	0.517521i	0.399300	−	0.916821i	$-0.369253\pi$
$443$	−10.8926	−	10.8926i	−0.517521	−	0.517521i	−0.916821	+	0.399300i	$0.869253\pi$
$444$			8.55966i			0.406224i
$445$		0			0
$446$	11.8237			0.559870
$447$	6.18198	+	6.18198i	0.292398	+	0.292398i
$448$	0.710512	+	0.710512i	0.0335686	+	0.0335686i
$449$	−14.7142			−0.694406			−0.347203	−	0.937790i	$-0.612869\pi$
$449$	−14.7142			−0.694406			−0.347203	+	0.937790i	$0.612869\pi$
$450$		0			0
$451$			4.00956i			0.188803i
$452$	1.72140	+	1.72140i	0.0809678	+	0.0809678i
$453$	−10.0124	−	10.0124i	−0.470424	−	0.470424i
$454$		−	7.67724i		−	0.360311i
$455$		0			0
$456$	−4.27453	−	2.15543i	−0.200173	−	0.100937i
$457$	0.241730	−	0.241730i	0.0113077	−	0.0113077i	−0.701430	−	0.712738i	$-0.747455\pi$
$457$	0.241730	−	0.241730i	0.0113077	−	0.0113077i	0.712738	+	0.701430i	$0.247455\pi$
$458$	−14.6108	+	14.6108i	−0.682720	+	0.682720i
$459$	0.767581			0.0358276
$460$		0			0
$461$	−1.86311			−0.0867739			−0.0433869	−	0.999058i	$-0.513815\pi$
$461$	−1.86311			−0.0867739			−0.0433869	+	0.999058i	$0.513815\pi$
$462$	−0.528469	+	0.528469i	−0.0245866	+	0.0245866i
$463$	3.90354	+	3.90354i	0.181413	+	0.181413i	0.791971	−	0.610558i	$-0.209055\pi$
$463$	3.90354	+	3.90354i	0.181413	+	0.181413i	−0.610558	+	0.791971i	$0.709055\pi$
$464$	−9.60108			−0.445719
$465$		0			0
$466$		−	25.9162i		−	1.20054i
$467$	−2.44081	+	2.44081i	−0.112947	+	0.112947i	−0.761322	−	0.648374i	$-0.775449\pi$
$467$	−2.44081	+	2.44081i	−0.112947	+	0.112947i	0.648374	+	0.761322i	$0.275449\pi$
$468$	−3.07088	+	3.07088i	−0.141951	+	0.141951i
$469$	2.26708			0.104684
$470$		0			0
$471$			17.0265i			0.784541i
$472$	5.37810	−	5.37810i	0.247547	−	0.247547i
$473$	−0.870021	−	0.870021i	−0.0400036	−	0.0400036i
$474$	18.0469			0.828923
$475$		0			0
$476$	−0.146495			−0.00671459
$477$	1.99056	+	1.99056i	0.0911414	+	0.0911414i
$478$	9.66444	−	9.66444i	0.442041	−	0.442041i
$479$		−	32.4545i		−	1.48288i	−0.671017	−	0.741442i	$-0.734142\pi$
$479$		−	32.4545i		−	1.48288i	0.671017	−	0.741442i	$-0.265858\pi$
$480$		0			0
$481$	18.8690			0.860354
$482$	7.90174	−	7.90174i	0.359914	−	0.359914i
$483$	−3.75877	+	3.75877i	−0.171030	+	0.171030i
$484$		−	10.5413i		−	0.479152i
$485$		0			0
$486$	15.3545			0.696493
$487$	8.01517	+	8.01517i	0.363202	+	0.363202i	0.864990	−	0.501788i	$-0.167324\pi$
$487$	8.01517	+	8.01517i	0.363202	+	0.363202i	−0.501788	+	0.864990i	$0.667324\pi$
$488$	−4.43676	+	4.43676i	−0.200843	+	0.200843i
$489$	20.4658			0.925497
$490$		0			0
$491$	6.52483			0.294462			0.147231	−	0.989102i	$-0.452964\pi$
$491$	6.52483			0.294462			0.147231	+	0.989102i	$0.452964\pi$
$492$	4.59777	−	4.59777i	0.207283	−	0.207283i
$493$	0.989786	−	0.989786i	0.0445777	−	0.0445777i
$494$	−4.75145	+	9.42282i	−0.213778	+	0.423953i
$495$		0			0
$496$			4.78418i			0.214816i
$497$	−4.14658	−	4.14658i	−0.186000	−	0.186000i
$498$	−2.30445	−	2.30445i	−0.103265	−	0.103265i
$499$			4.18867i			0.187511i	0.995595	+	0.0937553i	$0.0298871\pi$
$499$			4.18867i			0.187511i	−0.995595	+	0.0937553i	$0.970113\pi$
$500$		0			0
$501$	2.98054			0.133161
$502$	−18.7513	−	18.7513i	−0.836910	−	0.836910i
$503$	−16.9041	−	16.9041i	−0.753717	−	0.753717i	0.221454	−	0.975171i	$-0.428920\pi$
$503$	−16.9041	−	16.9041i	−0.753717	−	0.753717i	−0.975171	+	0.221454i	$0.928920\pi$
$504$	−1.80246			−0.0802878
$505$		0			0
$506$			3.26219i			0.145022i
$507$	5.54379	+	5.54379i	0.246208	+	0.246208i
$508$	10.8695	−	10.8695i	0.482256	−	0.482256i
$509$	18.9406			0.839529			0.419764	−	0.907633i	$-0.362113\pi$
$509$	18.9406			0.839529			0.419764	+	0.907633i	$0.362113\pi$
$510$		0			0
$511$	−1.87282			−0.0828485
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	21.7959	−	7.18322i	0.962312	−	0.317147i
$514$			17.0577i			0.752383i
$515$		0			0
$516$			1.99531i			0.0878385i
$517$	−2.70241	+	2.70241i	−0.118852	+	0.118852i
$518$	5.53760	+	5.53760i	0.243308	+	0.243308i
$519$			16.1839i			0.710396i
$520$		0			0
$521$			3.71657i			0.162826i	0.996680	+	0.0814129i	$0.0259433\pi$
$521$			3.71657i			0.162826i	−0.996680	+	0.0814129i	$0.974057\pi$
$522$	12.1782	−	12.1782i	0.533026	−	0.533026i
$523$	14.4957	−	14.4957i	0.633852	−	0.633852i	−0.315180	−	0.949032i	$-0.602065\pi$
$523$	14.4957	−	14.4957i	0.633852	−	0.633852i	0.949032	+	0.315180i	$0.102065\pi$
$524$			1.58764i			0.0693562i
$525$		0			0
$526$			31.5418i			1.37529i
$527$	−0.493206	−	0.493206i	−0.0214844	−	0.0214844i
$528$	0.525936	−	0.525936i	0.0228884	−	0.0228884i
$529$			0.202583i			0.00880794i
$530$		0			0
$531$			13.6434i			0.592072i
$532$	−4.15981	+	1.37094i	−0.180350	+	0.0594377i
$533$	−10.1354	−	10.1354i	−0.439012	−	0.439012i
$534$	−10.0814			−0.436267
$535$		0			0
$536$	−2.25621			−0.0974536
$537$	−14.9777	+	14.9777i	−0.646338	+	0.646338i
$538$	15.4114	+	15.4114i	0.664431	+	0.664431i
$539$		−	4.05689i		−	0.174743i
$540$		0			0
$541$	−10.7281			−0.461236			−0.230618	−	0.973044i	$-0.574075\pi$
$541$	−10.7281			−0.461236			−0.230618	+	0.973044i	$0.574075\pi$
$542$	13.4840	+	13.4840i	0.579189	+	0.579189i
$543$	−0.882425	−	0.882425i	−0.0378685	−	0.0378685i
$544$	0.145793			0.00625082
$545$		0			0
$546$		−	2.67173i		−	0.114339i
$547$	9.22441	+	9.22441i	0.394407	+	0.394407i	0.876255	−	0.481848i	$-0.160034\pi$
$547$	9.22441	+	9.22441i	0.394407	+	0.394407i	−0.481848	+	0.876255i	$0.660034\pi$
$548$	8.08378	+	8.08378i	0.345322	+	0.345322i
$549$		−	11.2554i		−	0.480367i
$550$		0			0
$551$	18.8429	−	37.3682i	0.802733	−	1.59194i
$552$	3.74076	−	3.74076i	0.159217	−	0.159217i
$553$	11.6753	−	11.6753i	0.496485	−	0.496485i
$554$	30.6860			1.30372
$555$		0			0
$556$	−8.37279			−0.355086
$557$	6.06835	−	6.06835i	0.257124	−	0.257124i	−0.566759	−	0.823883i	$-0.691803\pi$
$557$	6.06835	−	6.06835i	0.257124	−	0.257124i	0.823883	+	0.566759i	$0.191803\pi$
$558$	−6.06835	−	6.06835i	−0.256894	−	0.256894i
$559$	4.39848			0.186036
$560$		0			0
$561$			0.108439i			0.00457829i
$562$	20.5399	−	20.5399i	0.866422	−	0.866422i
$563$	17.2321	−	17.2321i	0.726246	−	0.726246i	−0.243624	−	0.969870i	$-0.578336\pi$
$563$	17.2321	−	17.2321i	0.726246	−	0.726246i	0.969870	+	0.243624i	$0.0783362\pi$
$564$	6.19772			0.260971
$565$		0			0
$566$			29.6996i			1.24837i
$567$	−0.284748	+	0.284748i	−0.0119583	+	0.0119583i
$568$	4.12671	+	4.12671i	0.173153	+	0.173153i
$569$	22.7416			0.953378			0.476689	−	0.879072i	$-0.341837\pi$
$569$	22.7416			0.953378			0.476689	+	0.879072i	$0.341837\pi$
$570$		0			0
$571$	10.4971			0.439289			0.219645	−	0.975580i	$-0.429510\pi$
$571$	10.4971			0.439289			0.219645	+	0.975580i	$0.429510\pi$
$572$	−1.15938	−	1.15938i	−0.0484761	−	0.0484761i
$573$	2.55120	−	2.55120i	0.106578	−	0.106578i
$574$		−	5.94897i		−	0.248305i
$575$		0			0
$576$	1.79382			0.0747424
$577$	−17.6724	+	17.6724i	−0.735712	+	0.735712i	−0.971745	−	0.236033i	$-0.924153\pi$
$577$	−17.6724	+	17.6724i	−0.735712	+	0.735712i	0.236033	+	0.971745i	$0.424153\pi$
$578$	12.0058	−	12.0058i	0.499375	−	0.499375i
$579$		−	25.6282i		−	1.06507i
$580$		0			0
$581$	−2.98168			−0.123701
$582$	−0.762365	−	0.762365i	−0.0316011	−	0.0316011i
$583$	−0.751516	+	0.751516i	−0.0311246	+	0.0311246i
$584$	1.86384			0.0771262
$585$		0			0
$586$	−14.2783			−0.589830
$587$	8.93393	−	8.93393i	0.368743	−	0.368743i	−0.498276	−	0.867019i	$-0.666033\pi$
$587$	8.93393	−	8.93393i	0.368743	−	0.368743i	0.867019	+	0.498276i	$0.166033\pi$
$588$	−4.65204	+	4.65204i	−0.191847	+	0.191847i
$589$	−18.6204	−	9.38931i	−0.767240	−	0.386880i
$590$		0			0
$591$			21.3216i			0.877055i
$592$	−5.51106	−	5.51106i	−0.226503	−	0.226503i
$593$	16.6060	+	16.6060i	0.681925	+	0.681925i	0.960434	−	0.278509i	$-0.0898402\pi$
$593$	16.6060	+	16.6060i	0.681925	+	0.681925i	−0.278509	+	0.960434i	$0.589840\pi$
$594$			3.56558i			0.146297i
$595$		0			0
$596$	−7.96043			−0.326072
$597$	−0.372543	−	0.372543i	−0.0152472	−	0.0152472i
$598$	−8.24617	−	8.24617i	−0.337211	−	0.337211i
$599$	−45.7813			−1.87057			−0.935287	−	0.353891i	$-0.884858\pi$
$599$	−45.7813			−1.87057			−0.935287	+	0.353891i	$0.884858\pi$
$600$		0			0
$601$		−	38.5699i		−	1.57330i	−0.617399	−	0.786650i	$-0.711814\pi$
$601$		−	38.5699i		−	1.57330i	0.617399	−	0.786650i	$-0.288186\pi$
$602$	1.29085	+	1.29085i	0.0526110	+	0.0526110i
$603$	2.86183	−	2.86183i	0.116543	−	0.116543i
$604$	12.8928			0.524600
$605$		0			0
$606$	−14.3218			−0.581782
$607$	−18.1593	−	18.1593i	−0.737064	−	0.737064i	0.234945	−	0.972009i	$-0.424509\pi$
$607$	−18.1593	−	18.1593i	−0.737064	−	0.737064i	−0.972009	+	0.234945i	$0.924509\pi$
$608$	4.13987	−	1.36437i	0.167894	−	0.0553323i
$609$			10.5953i			0.429343i
$610$		0			0
$611$		−	13.6623i		−	0.552718i
$612$	−0.184927	+	0.184927i	−0.00747522	+	0.00747522i
$613$	−24.6575	−	24.6575i	−0.995905	−	0.995905i	0.00408651	−	0.999992i	$-0.498699\pi$
$613$	−24.6575	−	24.6575i	−0.995905	−	0.995905i	−0.999992	+	0.00408651i	$0.998699\pi$
$614$			13.2717i			0.535604i
$615$		0			0
$616$		−	0.680500i		−	0.0274181i
$617$	3.04724	−	3.04724i	0.122677	−	0.122677i	−0.643103	−	0.765780i	$-0.722353\pi$
$617$	3.04724	−	3.04724i	0.122677	−	0.122677i	0.765780	+	0.643103i	$0.222353\pi$
$618$	−9.06765	+	9.06765i	−0.364754	+	0.364754i
$619$			7.73607i			0.310939i	0.987841	+	0.155470i	$0.0496891\pi$
$619$			7.73607i			0.310939i	−0.987841	+	0.155470i	$0.950311\pi$
$620$		0			0
$621$			25.3604i			1.01768i
$622$	4.53480	+	4.53480i	0.181829	+	0.181829i
$623$	−6.52210	+	6.52210i	−0.261303	+	0.261303i
$624$			2.65892i			0.106442i
$625$		0			0
$626$		−	0.793017i		−	0.0316953i
$627$	1.01480	+	3.07918i	0.0405271	+	0.122970i
$628$	−10.9624	−	10.9624i	−0.437446	−	0.437446i
$629$	1.13628			0.0453066
$630$		0			0
$631$	−18.1803			−0.723748			−0.361874	−	0.932227i	$-0.617863\pi$
$631$	−18.1803			−0.723748			−0.361874	+	0.932227i	$0.617863\pi$
$632$	−11.6194	+	11.6194i	−0.462193	+	0.462193i
$633$	11.0192	+	11.0192i	0.437973	+	0.437973i
$634$		−	29.9797i		−	1.19065i
$635$		0			0
$636$	1.72353			0.0683423
$637$	10.2550	+	10.2550i	0.406318	+	0.406318i
$638$	4.59777	+	4.59777i	0.182027	+	0.182027i
$639$	−10.4688			−0.414140
$640$		0			0
$641$		−	2.10696i		−	0.0832200i	−0.999134	−	0.0416100i	$-0.986751\pi$
$641$		−	2.10696i		−	0.0832200i	0.999134	−	0.0416100i	$-0.0132487\pi$
$642$	13.5087	+	13.5087i	0.533144	+	0.533144i
$643$	2.44995	+	2.44995i	0.0966164	+	0.0966164i	0.753763	−	0.657146i	$-0.228237\pi$
$643$	2.44995	+	2.44995i	0.0966164	+	0.0966164i	−0.657146	+	0.753763i	$0.728237\pi$
$644$		−	4.84011i		−	0.190727i
$645$		0			0
$646$	−0.286130	+	0.567438i	−0.0112576	+	0.0223255i
$647$	−25.7229	+	25.7229i	−1.01127	+	1.01127i	−0.0113365	+	0.999936i	$0.503609\pi$
$647$	−25.7229	+	25.7229i	−1.01127	+	1.01127i	−0.999936	+	0.0113365i	$0.996391\pi$
$648$	0.283383	−	0.283383i	0.0111324	−	0.0111324i
$649$	−5.15092			−0.202191
$650$		0			0
$651$	5.27959			0.206923
$652$	−13.1767	+	13.1767i	−0.516041	+	0.516041i
$653$	−18.0538	−	18.0538i	−0.706499	−	0.706499i	0.259298	−	0.965797i	$-0.416509\pi$
$653$	−18.0538	−	18.0538i	−0.706499	−	0.706499i	−0.965797	+	0.259298i	$0.916509\pi$
$654$	12.4314			0.486106
$655$		0			0
$656$			5.92046i			0.231155i
$657$	−2.36413	+	2.36413i	−0.0922336	+	0.0922336i
$658$	4.00956	−	4.00956i	0.156309	−	0.156309i
$659$	13.7845			0.536970			0.268485	−	0.963284i	$-0.413477\pi$
$659$	13.7845			0.536970			0.268485	+	0.963284i	$0.413477\pi$
$660$		0			0
$661$			20.0442i			0.779629i	0.920893	+	0.389814i	$0.127461\pi$
$661$			20.0442i			0.779629i	−0.920893	+	0.389814i	$0.872539\pi$
$662$	−16.4667	+	16.4667i	−0.639997	+	0.639997i
$663$	−0.274111	−	0.274111i	−0.0106456	−	0.0106456i
$664$	2.96739			0.115157
$665$		0			0
$666$	13.9807			0.541741
$667$	32.7019	+	32.7019i	1.26622	+	1.26622i
$668$	−1.91900	+	1.91900i	−0.0742482	+	0.0742482i
$669$			12.9856i			0.502051i
$670$		0			0
$671$	4.24935			0.164044
$672$	−0.780330	+	0.780330i	−0.0301019	+	0.0301019i
$673$	−21.7390	+	21.7390i	−0.837977	+	0.837977i	−0.988592	−	0.150615i	$-0.951874\pi$
$673$	−21.7390	+	21.7390i	−0.837977	+	0.837977i	0.150615	+	0.988592i	$0.451874\pi$
$674$		−	1.09632i		−	0.0422286i
$675$		0			0
$676$	−7.13864			−0.274563
$677$	−9.79531	−	9.79531i	−0.376464	−	0.376464i	0.493361	−	0.869825i	$-0.335768\pi$
$677$	−9.79531	−	9.79531i	−0.376464	−	0.376464i	−0.869825	+	0.493361i	$0.835768\pi$
$678$	−1.89055	+	1.89055i	−0.0726061	+	0.0726061i
$679$	−0.986412			−0.0378550
$680$		0			0
$681$	8.43163			0.323101
$682$	2.29105	−	2.29105i	0.0877287	−	0.0877287i
$683$	−30.2432	+	30.2432i	−1.15723	+	1.15723i	−0.172155	+	0.985070i	$0.555073\pi$
$683$	−30.2432	+	30.2432i	−1.15723	+	1.15723i	−0.985070	+	0.172155i	$0.944927\pi$
$684$	−3.52050	+	6.98168i	−0.134610	+	0.266951i
$685$		0			0
$686$			13.0529i			0.498362i
$687$	−16.0465	−	16.0465i	−0.612214	−	0.612214i
$688$	−1.28466	−	1.28466i	−0.0489772	−	0.0489772i
$689$		−	3.79936i		−	0.144744i
$690$		0			0
$691$	−49.7253			−1.89164			−0.945819	−	0.324693i	$-0.894739\pi$
$691$	−49.7253			−1.89164			−0.945819	+	0.324693i	$0.894739\pi$
$692$	−10.4199	−	10.4199i	−0.396104	−	0.396104i
$693$	0.863161	+	0.863161i	0.0327888	+	0.0327888i
$694$	−29.0334			−1.10209
$695$		0			0
$696$		−	10.5445i		−	0.399689i
$697$	−0.610347	−	0.610347i	−0.0231185	−	0.0231185i
$698$	−18.3029	+	18.3029i	−0.692775	+	0.692775i
$699$	28.4628			1.07656
$700$		0			0
$701$	14.9990			0.566505			0.283252	−	0.959045i	$-0.408587\pi$
$701$	14.9990			0.566505			0.283252	+	0.959045i	$0.408587\pi$
$702$	−9.01306	−	9.01306i	−0.340176	−	0.340176i
$703$	32.2654	−	10.6336i	1.21691	−	0.401055i
$704$			0.677239i			0.0255244i
$705$		0			0
$706$		−	17.1709i		−	0.646236i
$707$	−9.26535	+	9.26535i	−0.348459	+	0.348459i
$708$	5.90656	+	5.90656i	0.221982	+	0.221982i
$709$			15.1955i			0.570680i	0.958426	+	0.285340i	$0.0921065\pi$
$709$			15.1955i			0.570680i	−0.958426	+	0.285340i	$0.907893\pi$
$710$		0			0
$711$		−	29.4765i		−	1.10545i
$712$	6.49084	−	6.49084i	0.243255	−	0.243255i
$713$	16.2952	−	16.2952i	0.610261	−	0.610261i
$714$		−	0.160890i		−	0.00602116i
$715$		0			0
$716$		−	19.2866i		−	0.720773i
$717$	10.6141	+	10.6141i	0.396391	+	0.396391i
$718$	−8.93006	+	8.93006i	−0.333267	+	0.333267i
$719$		−	27.5549i		−	1.02763i	−0.857902	−	0.513813i	$-0.828233\pi$
$719$		−	27.5549i		−	1.02763i	0.857902	−	0.513813i	$-0.171767\pi$
$720$		0			0
$721$			11.7325i			0.436940i
$722$	−2.81458	+	18.7904i	−0.104748	+	0.699305i
$723$	8.67819	+	8.67819i	0.322745	+	0.322745i
$724$	1.13628			0.0422296
$725$		0			0
$726$	11.5772			0.429669
$727$	27.0506	−	27.0506i	1.00325	−	1.00325i	0.00325631	−	0.999995i	$-0.498963\pi$
$727$	27.0506	−	27.0506i	1.00325	−	1.00325i	0.999995	−	0.00325631i	$-0.00103652\pi$
$728$	1.72017	+	1.72017i	0.0637537	+	0.0637537i
$729$			18.0656i			0.669095i
$730$		0			0
$731$	0.264874			0.00979672
$732$	−4.87273	−	4.87273i	−0.180101	−	0.180101i
$733$	5.01340	+	5.01340i	0.185174	+	0.185174i	0.793606	−	0.608432i	$-0.208201\pi$
$733$	5.01340	+	5.01340i	0.185174	+	0.185174i	−0.608432	+	0.793606i	$0.708201\pi$
$734$	−25.9831			−0.959052
$735$		0			0
$736$			4.81691i			0.177554i
$737$	1.08046	+	1.08046i	0.0397991	+	0.0397991i
$738$	−7.50963	−	7.50963i	−0.276433	−	0.276433i
$739$			26.0327i			0.957627i	0.877917	+	0.478814i	$0.158933\pi$
$739$			26.0327i			0.957627i	−0.877917	+	0.478814i	$0.841067\pi$
$740$		0			0
$741$	−10.3487	−	5.21834i	−0.380171	−	0.191700i
$742$	1.11502	−	1.11502i	0.0409337	−	0.0409337i
$743$	−8.93826	+	8.93826i	−0.327913	+	0.327913i	−0.851792	−	0.523879i	$-0.824484\pi$
$743$	−8.93826	+	8.93826i	−0.327913	+	0.327913i	0.523879	+	0.851792i	$0.324484\pi$
$744$	−5.25428			−0.192631
$745$		0			0
$746$	−15.6928			−0.574553
$747$	−3.76390	+	3.76390i	−0.137714	+	0.137714i
$748$	−0.0698173	−	0.0698173i	−0.00255277	−	0.00255277i
$749$	17.4786			0.638655
$750$		0			0
$751$		−	25.6961i		−	0.937664i	−0.883287	−	0.468832i	$-0.844675\pi$
$751$		−	25.6961i		−	0.937664i	0.883287	−	0.468832i	$-0.155325\pi$
$752$	−3.99034	+	3.99034i	−0.145513	+	0.145513i
$753$	20.5938	−	20.5938i	0.750481	−	0.750481i
$754$	−23.2445			−0.846513
$755$		0			0
$756$		−	5.29023i		−	0.192404i
$757$	−13.9825	+	13.9825i	−0.508202	+	0.508202i	−0.913974	−	0.405772i	$-0.867003\pi$
$757$	−13.9825	+	13.9825i	−0.508202	+	0.508202i	0.405772	+	0.913974i	$0.367003\pi$
$758$	−6.92535	−	6.92535i	−0.251540	−	0.251540i
$759$	−3.58275			−0.130046
$760$		0			0
$761$	−24.7475			−0.897097			−0.448549	−	0.893758i	$-0.648059\pi$
$761$	−24.7475			−0.897097			−0.448549	+	0.893758i	$0.648059\pi$
$762$	11.9376	+	11.9376i	0.432453	+	0.432453i
$763$	8.04238	−	8.04238i	0.291154	−	0.291154i
$764$			3.28513i			0.118852i
$765$		0			0
$766$	8.62130			0.311500
$767$	13.0205	−	13.0205i	0.470143	−	0.470143i
$768$	0.776589	−	0.776589i	0.0280228	−	0.0280228i
$769$			38.2772i			1.38031i	0.723660	+	0.690156i	$0.242458\pi$
$769$			38.2772i			1.38031i	−0.723660	+	0.690156i	$0.757542\pi$
$770$		0			0
$771$	−18.7338			−0.674683
$772$	16.5005	+	16.5005i	0.593864	+	0.593864i
$773$	−36.0262	+	36.0262i	−1.29577	+	1.29577i	−0.364615	+	0.931158i	$0.618799\pi$
$773$	−36.0262	+	36.0262i	−1.29577	+	1.29577i	−0.931158	+	0.364615i	$0.881201\pi$
$774$	3.25898			0.117142
$775$		0			0
$776$	0.981684			0.0352404
$777$	−6.08175	+	6.08175i	−0.218181	+	0.218181i
$778$	7.16645	−	7.16645i	0.256930	−	0.256930i
$779$	−23.0429	−	11.6194i	−0.825598	−	0.416306i
$780$		0			0
$781$		−	3.95240i		−	0.141428i
$782$	−0.496580	−	0.496580i	−0.0177577	−	0.0177577i
$783$	35.7432	+	35.7432i	1.27736	+	1.27736i
$784$		−	5.99034i		−	0.213941i
$785$		0			0
$786$	−1.74364			−0.0621936
$787$	−17.8998	−	17.8998i	−0.638058	−	0.638058i	0.312018	−	0.950076i	$-0.398995\pi$
$787$	−17.8998	−	17.8998i	−0.638058	−	0.638058i	−0.950076	+	0.312018i	$0.898995\pi$
$788$	−13.7277	−	13.7277i	−0.489031	−	0.489031i
$789$	−34.6412			−1.23326
$790$		0			0
$791$			2.44615i			0.0869751i
$792$	−0.859023	−	0.859023i	−0.0305241	−	0.0305241i
$793$	−10.7415	+	10.7415i	−0.381442	+	0.381442i
$794$	23.8876			0.847739
$795$		0			0
$796$	0.479717			0.0170031
$797$	−24.1376	−	24.1376i	−0.854997	−	0.854997i	0.135746	−	0.990744i	$-0.456657\pi$
$797$	−24.1376	−	24.1376i	−0.854997	−	0.854997i	−0.990744	+	0.135746i	$0.956657\pi$
$798$	−1.50565	−	4.56856i	−0.0532994	−	0.161725i
$799$		−	0.822738i		−	0.0291064i
$800$		0			0
$801$			16.4662i			0.581806i
$802$	9.08619	−	9.08619i	0.320844	−	0.320844i
$803$	−0.892555	−	0.892555i	−0.0314976	−	0.0314976i
$804$		−	2.47792i		−	0.0873894i
$805$		0			0
$806$			11.5826i			0.407980i
$807$	−16.9257	+	16.9257i	−0.595814	+	0.595814i
$808$	9.22094	−	9.22094i	0.324391	−	0.324391i
$809$			10.6607i			0.374811i	0.982283	+	0.187406i	$0.0600078\pi$
$809$			10.6607i			0.374811i	−0.982283	+	0.187406i	$0.939992\pi$
$810$		0			0
$811$			24.7697i			0.869780i	0.900484	+	0.434890i	$0.143213\pi$
$811$			24.7697i			0.869780i	−0.900484	+	0.434890i	$0.856787\pi$
$812$	−6.82169	−	6.82169i	−0.239394	−	0.239394i
$813$	−14.8090	+	14.8090i	−0.519375	+	0.519375i
$814$			5.27827i			0.185003i
$815$		0			0
$816$			0.160119i			0.00560528i
$817$	7.52124	−	2.47876i	0.263135	−	0.0867207i
$818$	5.35495	+	5.35495i	0.187231	+	0.187231i
$819$	−4.36379			−0.152483
$820$		0			0
$821$	−28.3901			−0.990822			−0.495411	−	0.868659i	$-0.664982\pi$
$821$	−28.3901			−0.990822			−0.495411	+	0.868659i	$0.664982\pi$
$822$	−8.87812	+	8.87812i	−0.309660	+	0.309660i
$823$	−9.42912	−	9.42912i	−0.328679	−	0.328679i	0.523405	−	0.852084i	$-0.324661\pi$
$823$	−9.42912	−	9.42912i	−0.328679	−	0.328679i	−0.852084	+	0.523405i	$0.824661\pi$
$824$		−	11.6762i		−	0.406761i
$825$		0			0
$826$	7.64241			0.265913
$827$	−17.9270	−	17.9270i	−0.623383	−	0.623383i	0.323012	−	0.946395i	$-0.395305\pi$
$827$	−17.9270	−	17.9270i	−0.623383	−	0.623383i	−0.946395	+	0.323012i	$0.895305\pi$
$828$	−6.10986	−	6.10986i	−0.212332	−	0.212332i
$829$	−29.4884			−1.02417			−0.512087	−	0.858934i	$-0.671127\pi$
$829$	−29.4884			−1.02417			−0.512087	+	0.858934i	$0.671127\pi$
$830$		0			0
$831$			33.7013i			1.16909i
$832$	−1.71192	−	1.71192i	−0.0593503	−	0.0593503i
$833$	0.617551	+	0.617551i	0.0213969	+	0.0213969i
$834$		−	9.19553i		−	0.318415i
$835$		0			0
$836$	−2.63587	−	1.32913i	−0.0911634	−	0.0459690i
$837$	17.8107	−	17.8107i	0.615627	−	0.615627i
$838$	−15.2333	+	15.2333i	−0.526226	+	0.526226i
$839$	22.4611			0.775445			0.387722	−	0.921776i	$-0.373262\pi$
$839$	22.4611			0.775445			0.387722	+	0.921776i	$0.373262\pi$
$840$		0			0
$841$	63.1808			2.17865
$842$	−21.4432	+	21.4432i	−0.738981	+	0.738981i
$843$	22.5582	+	22.5582i	0.776945	+	0.776945i
$844$	−14.1892			−0.488412
$845$		0			0
$846$		−	10.1229i		−	0.348031i
$847$	7.48976	−	7.48976i	0.257351	−	0.257351i
$848$	−1.10968	+	1.10968i	−0.0381064	+	0.0381064i
$849$	−32.6180			−1.11945
$850$		0			0
$851$			37.5421i			1.28693i
$852$	−4.53221	+	4.53221i	−0.155271	+	0.155271i
$853$	5.14650	+	5.14650i	0.176213	+	0.176213i	0.789703	−	0.613490i	$-0.210235\pi$
$853$	5.14650	+	5.14650i	0.176213	+	0.176213i	−0.613490	+	0.789703i	$0.710235\pi$
$854$	−6.30475			−0.215744
$855$		0			0
$856$	−17.3949			−0.594544
$857$	6.01712	+	6.01712i	0.205541	+	0.205541i	0.802369	−	0.596828i	$-0.203573\pi$
$857$	6.01712	+	6.01712i	0.205541	+	0.205541i	−0.596828	+	0.802369i	$0.703573\pi$
$858$	1.27330	−	1.27330i	0.0434699	−	0.0434699i
$859$			38.8313i			1.32491i	0.749104	+	0.662453i	$0.230484\pi$
$859$			38.8313i			1.32491i	−0.749104	+	0.662453i	$0.769516\pi$
$860$		0			0
$861$	6.53354			0.222662
$862$	−12.2268	+	12.2268i	−0.416446	+	0.416446i
$863$	30.6181	−	30.6181i	1.04225	−	1.04225i	0.0431846	−	0.999067i	$-0.486250\pi$
$863$	30.6181	−	30.6181i	1.04225	−	1.04225i	0.999067	−	0.0431846i	$-0.0137504\pi$
$864$			5.26487i			0.179115i
$865$		0			0
$866$	26.6280			0.904857
$867$	13.1855	+	13.1855i	0.447804	+	0.447804i
$868$	−3.39922	+	3.39922i	−0.115377	+	0.115377i
$869$	11.1285			0.377510
$870$		0			0
$871$	−5.46235			−0.185085
$872$	−8.00383	+	8.00383i	−0.271044	+	0.271044i
$873$	−1.24519	+	1.24519i	−0.0421432	+	0.0421432i
$874$	−18.7478	−	9.45354i	−0.634153	−	0.319771i
$875$		0			0
$876$			2.04699i			0.0691613i
$877$	−36.4948	−	36.4948i	−1.23234	−	1.23234i	−0.963062	−	0.269280i	$-0.913214\pi$
$877$	−36.4948	−	36.4948i	−1.23234	−	1.23234i	−0.269280	−	0.963062i	$-0.586786\pi$
$878$	−18.3232	−	18.3232i	−0.618379	−	0.618379i
$879$		−	15.6813i		−	0.528917i
$880$		0			0
$881$	53.9726			1.81838			0.909192	−	0.416377i	$-0.136700\pi$
$881$	53.9726			1.81838			0.909192	+	0.416377i	$0.136700\pi$
$882$	7.59828	+	7.59828i	0.255847	+	0.255847i
$883$	36.4911	+	36.4911i	1.22802	+	1.22802i	0.964710	+	0.263314i	$0.0848155\pi$
$883$	36.4911	+	36.4911i	1.22802	+	1.22802i	0.263314	+	0.964710i	$0.415184\pi$
$884$	0.352968			0.0118716
$885$		0			0
$886$			15.4044i			0.517521i
$887$	16.7204	+	16.7204i	0.561415	+	0.561415i	0.929709	−	0.368295i	$-0.120058\pi$
$887$	16.7204	+	16.7204i	0.561415	+	0.561415i	−0.368295	+	0.929709i	$0.620058\pi$
$888$	6.05260	−	6.05260i	0.203112	−	0.203112i
$889$	15.4458			0.518037
$890$		0			0
$891$	−0.271413			−0.00909269
$892$	−8.36064	−	8.36064i	−0.279935	−	0.279935i
$893$	−7.69939	−	23.3621i	−0.257650	−	0.781783i
$894$		−	8.74265i		−	0.292398i
$895$		0			0
$896$		−	1.00482i		−	0.0335686i
$897$	9.05647	−	9.05647i	0.302387	−	0.302387i
$898$	10.4045	+	10.4045i	0.347203	+	0.347203i
$899$		−	45.9333i		−	1.53196i
$900$		0			0
$901$		−	0.228796i		−	0.00762229i
$902$	2.83519	−	2.83519i	0.0944015	−	0.0944015i
$903$	−1.41769	+	1.41769i	−0.0471778	+	0.0471778i
$904$		−	2.43442i		−	0.0809678i
$905$		0			0
$906$			14.1597i			0.470424i
$907$	−32.5056	−	32.5056i	−1.07933	−	1.07933i	−0.996569	−	0.0827610i	$-0.973626\pi$
$907$	−32.5056	−	32.5056i	−1.07933	−	1.07933i	−0.0827610	−	0.996569i	$-0.526374\pi$
$908$	−5.42863	+	5.42863i	−0.180155	+	0.180155i
$909$			23.3921i			0.775866i
$910$		0			0
$911$			20.5743i			0.681656i	0.940126	+	0.340828i	$0.110707\pi$
$911$			20.5743i			0.681656i	−0.940126	+	0.340828i	$0.889293\pi$
$912$	1.49843	+	4.54666i	0.0496181	+	0.150555i
$913$	−1.42102	−	1.42102i	−0.0470291	−	0.0470291i
$914$	−0.341858			−0.0113077
$915$		0			0
$916$	20.6628			0.682720
$917$	−1.12803	+	1.12803i	−0.0372510	+	0.0372510i
$918$	−0.542762	−	0.542762i	−0.0179138	−	0.0179138i
$919$			51.2867i			1.69179i	0.533347	+	0.845897i	$0.320934\pi$
$919$			51.2867i			1.69179i	−0.533347	+	0.845897i	$0.679066\pi$
$920$		0			0
$921$	−14.5759			−0.480291
$922$	1.31742	+	1.31742i	0.0433869	+	0.0433869i
$923$	9.99087	+	9.99087i	0.328853	+	0.328853i
$924$	0.747368			0.0245866
$925$		0			0
$926$		−	5.52043i		−	0.181413i
$927$	14.8104	+	14.8104i	0.486437	+	0.486437i
$928$	6.78899	+	6.78899i	0.222860	+	0.222860i
$929$		−	6.29105i		−	0.206403i	−0.994660	−	0.103201i	$-0.967091\pi$
$929$		−	6.29105i		−	0.206403i	0.994660	−	0.103201i	$-0.0329086\pi$
$930$		0			0
$931$	23.3149	+	11.7565i	0.764115	+	0.385304i
$932$	−18.3255	+	18.3255i	−0.600272	+	0.600272i
$933$	−4.98040	+	4.98040i	−0.163051	+	0.163051i
$934$	3.45183			0.112947
$935$		0			0
$936$	4.34288			0.141951
$937$	26.3632	−	26.3632i	0.861249	−	0.861249i	−0.130234	−	0.991483i	$-0.541573\pi$
$937$	26.3632	−	26.3632i	0.861249	−	0.861249i	0.991483	+	0.130234i	$0.0415729\pi$
$938$	−1.60307	−	1.60307i	−0.0523420	−	0.0523420i
$939$	0.870942			0.0284221
$940$		0			0
$941$			21.6381i			0.705381i	0.935740	+	0.352690i	$0.114733\pi$
$941$			21.6381i			0.705381i	−0.935740	+	0.352690i	$0.885267\pi$
$942$	12.0396	−	12.0396i	0.392270	−	0.392270i
$943$	20.1655	−	20.1655i	0.656678	−	0.656678i
$944$	−7.60578			−0.247547
$945$		0			0
$946$			1.23040i			0.0400036i
$947$	8.43934	−	8.43934i	0.274242	−	0.274242i	−0.556563	−	0.830805i	$-0.687880\pi$
$947$	8.43934	−	8.43934i	0.274242	−	0.274242i	0.830805	+	0.556563i	$0.187880\pi$
$948$	−12.7611	−	12.7611i	−0.414461	−	0.414461i
$949$	4.51240			0.146479
$950$		0			0
$951$	32.9256			1.06769
$952$	0.103588	+	0.103588i	0.00335729	+	0.00335729i
$953$	0.120821	−	0.120821i	0.00391378	−	0.00391378i	−0.705147	−	0.709061i	$-0.749119\pi$
$953$	0.120821	−	0.120821i	0.00391378	−	0.00391378i	0.709061	+	0.705147i	$0.249119\pi$
$954$		−	2.81507i		−	0.0911414i
$955$		0			0
$956$	−13.6676			−0.442041
$957$	−5.04956	+	5.04956i	−0.163229	+	0.163229i
$958$	−22.9488	+	22.9488i	−0.741442	+	0.741442i
$959$			11.4873i			0.370943i
$960$		0			0
$961$	8.11166			0.261667
$962$	−13.3424	−	13.3424i	−0.430177	−	0.430177i
$963$	22.0640	−	22.0640i	0.711002	−	0.711002i
$964$	−11.1747			−0.359914
$965$		0			0
$966$	5.31571			0.171030
$967$	15.2763	−	15.2763i	0.491252	−	0.491252i	−0.417448	−	0.908701i	$-0.637076\pi$
$967$	15.2763	−	15.2763i	0.491252	−	0.491252i	0.908701	+	0.417448i	$0.137076\pi$
$968$	−7.45386	+	7.45386i	−0.239576	+	0.239576i
$969$	−0.623196	−	0.314246i	−0.0200199	−	0.0100950i
$970$		0			0
$971$			13.5969i			0.436344i	0.975910	+	0.218172i	$0.0700094\pi$
$971$			13.5969i			0.436344i	−0.975910	+	0.218172i	$0.929991\pi$
$972$	−10.8573	−	10.8573i	−0.348247	−	0.348247i
$973$	−5.94897	−	5.94897i	−0.190715	−	0.190715i
$974$		−	11.3352i		−	0.363202i
$975$		0			0
$976$	6.27453			0.200843
$977$	−37.7325	−	37.7325i	−1.20717	−	1.20717i	−0.971940	−	0.235229i	$-0.924416\pi$
$977$	−37.7325	−	37.7325i	−1.20717	−	1.20717i	−0.235229	−	0.971940i	$-0.575584\pi$
$978$	−14.4715	−	14.4715i	−0.462749	−	0.462749i
$979$	−6.21667			−0.198686
$980$		0			0
$981$		−	20.3045i		−	0.648271i
$982$	−4.61375	−	4.61375i	−0.147231	−	0.147231i
$983$	−40.6367	+	40.6367i	−1.29611	+	1.29611i	−0.365166	+	0.930943i	$0.618988\pi$
$983$	−40.6367	+	40.6367i	−1.29611	+	1.29611i	−0.930943	+	0.365166i	$0.881012\pi$
$984$	−6.50222			−0.207283
$985$		0			0
$986$	−1.39977			−0.0445777
$987$	4.40356	+	4.40356i	0.140167	+	0.140167i
$988$	10.0227	−	3.30316i	0.318865	−	0.105088i
$989$			8.75127i			0.278274i
$990$		0			0
$991$		−	32.4964i		−	1.03228i	−0.856504	−	0.516141i	$-0.827368\pi$
$991$		−	32.4964i		−	1.03228i	0.856504	−	0.516141i	$-0.172632\pi$
$992$	3.38292	−	3.38292i	0.107408	−	0.107408i
$993$	−18.0848	−	18.0848i	−0.573903	−	0.573903i
$994$			5.86416i			0.186000i
$995$		0			0
$996$			3.25898i			0.103265i
$997$	15.2681	−	15.2681i	0.483547	−	0.483547i	−0.422715	−	0.906262i	$-0.638923\pi$
$997$	15.2681	−	15.2681i	0.483547	−	0.483547i	0.906262	+	0.422715i	$0.138923\pi$
$998$	2.96184	−	2.96184i	0.0937553	−	0.0937553i
$999$			41.0335i			1.29824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.c.493.3		16
5.2	odd	4	inner	950.2.f.c.607.6		16
5.3	odd	4		190.2.f.b.37.3	✓	16
5.4	even	2		190.2.f.b.113.6	yes	16
15.8	even	4		1710.2.p.b.37.5		16
15.14	odd	2		1710.2.p.b.1063.1		16
19.18	odd	2	inner	950.2.f.c.493.6		16
95.18	even	4		190.2.f.b.37.6	yes	16
95.37	even	4	inner	950.2.f.c.607.3		16
95.94	odd	2		190.2.f.b.113.3	yes	16
285.113	odd	4		1710.2.p.b.37.1		16
285.284	even	2		1710.2.p.b.1063.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.3	✓	16	5.3	odd	4
190.2.f.b.37.6	yes	16	95.18	even	4
190.2.f.b.113.3	yes	16	95.94	odd	2
190.2.f.b.113.6	yes	16	5.4	even	2
950.2.f.c.493.3		16	1.1	even	1	trivial
950.2.f.c.493.6		16	19.18	odd	2	inner
950.2.f.c.607.3		16	95.37	even	4	inner
950.2.f.c.607.6		16	5.2	odd	4	inner
1710.2.p.b.37.1		16	285.113	odd	4
1710.2.p.b.37.5		16	15.8	even	4
1710.2.p.b.1063.1		16	15.14	odd	2
1710.2.p.b.1063.5		16	285.284	even	2

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.776589 - 0.776589i) q^{3} +1.00000i q^{4} -1.09826 q^{6} +(-0.710512 + 0.710512i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.79382i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.776589 - 0.776589i) q^{3} +1.00000i q^{4} -1.09826 q^{6} +(-0.710512 + 0.710512i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.79382i q^{9} -0.677239 q^{11} +(0.776589 + 0.776589i) q^{12} +(1.71192 - 1.71192i) q^{13} +1.00482 q^{14} -1.00000 q^{16} +(0.103091 - 0.103091i) q^{17} +(1.26842 - 1.26842i) q^{18} +(1.96258 - 3.89208i) q^{19} +1.10355i q^{21} +(0.478880 + 0.478880i) q^{22} +(3.40607 + 3.40607i) q^{23} -1.09826i q^{24} -2.42102 q^{26} +(3.72283 + 3.72283i) q^{27} +(-0.710512 - 0.710512i) q^{28} +9.60108 q^{29} -4.78418i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.525936 + 0.525936i) q^{33} -0.145793 q^{34} -1.79382 q^{36} +(5.51106 + 5.51106i) q^{37} +(-4.13987 + 1.36437i) q^{38} -2.65892i q^{39} -5.92046i q^{41} +(0.780330 - 0.780330i) q^{42} +(1.28466 + 1.28466i) q^{43} -0.677239i q^{44} -4.81691i q^{46} +(3.99034 - 3.99034i) q^{47} +(-0.776589 + 0.776589i) q^{48} +5.99034i q^{49} -0.160119i q^{51} +(1.71192 + 1.71192i) q^{52} +(1.10968 - 1.10968i) q^{53} -5.26487i q^{54} +1.00482i q^{56} +(-1.49843 - 4.54666i) q^{57} +(-6.78899 - 6.78899i) q^{58} +7.60578 q^{59} -6.27453 q^{61} +(-3.38292 + 3.38292i) q^{62} +(-1.27453 - 1.27453i) q^{63} -1.00000i q^{64} +0.743786 q^{66} +(-1.59538 - 1.59538i) q^{67} +(0.103091 + 0.103091i) q^{68} +5.29023 q^{69} +5.83605i q^{71} +(1.26842 + 1.26842i) q^{72} +(1.31793 + 1.31793i) q^{73} -7.79382i q^{74} +(3.89208 + 1.96258i) q^{76} +(0.481186 - 0.481186i) q^{77} +(-1.88014 + 1.88014i) q^{78} -16.4322 q^{79} +0.400765 q^{81} +(-4.18640 + 4.18640i) q^{82} +(2.09826 + 2.09826i) q^{83} -1.10355 q^{84} -1.81678i q^{86} +(7.45610 - 7.45610i) q^{87} +(-0.478880 + 0.478880i) q^{88} +9.17944 q^{89} +2.43268i q^{91} +(-3.40607 + 3.40607i) q^{92} +(-3.71534 - 3.71534i) q^{93} -5.64320 q^{94} +1.09826 q^{96} +(0.694155 + 0.694155i) q^{97} +(4.23581 - 4.23581i) q^{98} -1.21484i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) \) 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

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