LMFDB - Embedded newform 1148.2.n.d.953.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			953.1
Character	$\chi$	$=$	1148.953
Dual form			1148.2.n.d.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.33413 q^{3} +(-0.141417 - 0.435238i) q^{5} +(-0.809017 + 0.587785i) q^{7} +8.11640 q^{9} +O(q^{10})$	\(q-3.33413 q^{3} +(-0.141417 - 0.435238i) q^{5} +(-0.809017 + 0.587785i) q^{7} +8.11640 q^{9} +(-0.348117 + 1.07139i) q^{11} +(-5.36975 - 3.90135i) q^{13} +(0.471503 + 1.45114i) q^{15} +(0.0378111 - 0.116371i) q^{17} +(-1.20665 + 0.876684i) q^{19} +(2.69737 - 1.95975i) q^{21} +(-1.81662 - 1.31985i) q^{23} +(3.87565 - 2.81583i) q^{25} -17.0587 q^{27} +(-1.94001 - 5.97073i) q^{29} +(-0.240026 + 0.738725i) q^{31} +(1.16067 - 3.57216i) q^{33} +(0.370235 + 0.268992i) q^{35} +(2.08062 + 6.40349i) q^{37} +(17.9034 + 13.0076i) q^{39} +(3.79816 + 5.15500i) q^{41} +(-0.429030 - 0.311709i) q^{43} +(-1.14780 - 3.53256i) q^{45} +(0.0152358 + 0.0110694i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.126067 + 0.387994i) q^{51} +(1.48065 + 4.55697i) q^{53} +0.515541 q^{55} +(4.02313 - 2.92298i) q^{57} +(9.77967 + 7.10535i) q^{59} +(-6.92927 + 5.03441i) q^{61} +(-6.56631 + 4.77070i) q^{63} +(-0.938640 + 2.88884i) q^{65} +(2.98211 + 9.17800i) q^{67} +(6.05683 + 4.40054i) q^{69} +(-3.32855 + 10.2442i) q^{71} +7.92510 q^{73} +(-12.9219 + 9.38832i) q^{75} +(-0.348117 - 1.07139i) q^{77} +6.89152 q^{79} +32.5268 q^{81} +4.78081 q^{83} -0.0559960 q^{85} +(6.46824 + 19.9072i) q^{87} +(12.8243 - 9.31740i) q^{89} +6.63738 q^{91} +(0.800278 - 2.46300i) q^{93} +(0.552207 + 0.401202i) q^{95} +(2.06485 + 6.35495i) q^{97} +(-2.82546 + 8.69586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	−3.33413			−1.92496			−0.962480	−	0.271354i	$-0.912528\pi$
$3$	−3.33413			−1.92496			−0.962480	+	0.271354i	$0.912528\pi$
$4$		0			0
$5$	−0.141417	−	0.435238i	−0.0632437	−	0.194644i	0.914442	−	0.404717i	$-0.132630\pi$
$5$	−0.141417	−	0.435238i	−0.0632437	−	0.194644i	−0.977686	+	0.210073i	$0.932630\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$		0			0
$9$	8.11640			2.70547
$10$		0			0
$11$	−0.348117	+	1.07139i	−0.104961	+	0.323037i	−0.989721	−	0.143009i	$-0.954322\pi$
$11$	−0.348117	+	1.07139i	−0.104961	+	0.323037i	0.884760	+	0.466047i	$0.154322\pi$
$12$		0			0
$13$	−5.36975	−	3.90135i	−1.48930	−	1.08204i	−0.974408	−	0.224786i	$-0.927832\pi$
$13$	−5.36975	−	3.90135i	−1.48930	−	1.08204i	−0.514893	−	0.857254i	$-0.672168\pi$
$14$		0			0
$15$	0.471503	+	1.45114i	0.121742	+	0.374682i
$16$		0			0
$17$	0.0378111	−	0.116371i	0.00917053	−	0.0282240i	−0.946367	−	0.323095i	$-0.895277\pi$
$17$	0.0378111	−	0.116371i	0.00917053	−	0.0282240i	0.955537	+	0.294871i	$0.0952767\pi$
$18$		0			0
$19$	−1.20665	+	0.876684i	−0.276825	+	0.201125i	−0.717531	−	0.696526i	$-0.754728\pi$
$19$	−1.20665	+	0.876684i	−0.276825	+	0.201125i	0.440706	+	0.897651i	$0.354728\pi$
$20$		0			0
$21$	2.69737	−	1.95975i	0.588613	−	0.427653i
$22$		0			0
$23$	−1.81662	−	1.31985i	−0.378790	−	0.275207i	0.382056	−	0.924139i	$-0.375216\pi$
$23$	−1.81662	−	1.31985i	−0.378790	−	0.275207i	−0.760847	+	0.648932i	$0.775216\pi$
$24$		0			0
$25$	3.87565	−	2.81583i	0.775130	−	0.563165i
$26$		0			0
$27$	−17.0587			−3.28295
$28$		0			0
$29$	−1.94001	−	5.97073i	−0.360251	−	1.10874i	−0.952902	−	0.303278i	$-0.901919\pi$
$29$	−1.94001	−	5.97073i	−0.360251	−	1.10874i	0.592651	−	0.805459i	$-0.298081\pi$
$30$		0			0
$31$	−0.240026	+	0.738725i	−0.0431100	+	0.132679i	−0.970295	−	0.241925i	$-0.922221\pi$
$31$	−0.240026	+	0.738725i	−0.0431100	+	0.132679i	0.927185	+	0.374604i	$0.122221\pi$
$32$		0			0
$33$	1.16067	−	3.57216i	0.202046	−	0.621834i
$34$		0			0
$35$	0.370235	+	0.268992i	0.0625812	+	0.0454679i
$36$		0			0
$37$	2.08062	+	6.40349i	0.342052	+	1.05273i	0.963143	+	0.268989i	$0.0866895\pi$
$37$	2.08062	+	6.40349i	0.342052	+	1.05273i	−0.621092	+	0.783738i	$0.713311\pi$
$38$		0			0
$39$	17.9034	+	13.0076i	2.86684	+	2.08288i
$40$		0			0
$41$	3.79816	+	5.15500i	0.593172	+	0.805076i
$41$	3.79816	+	5.15500i	0.593172	+	0.805076i
$42$		0			0
$43$	−0.429030	−	0.311709i	−0.0654265	−	0.0475351i	0.554591	−	0.832123i	$-0.312875\pi$
$43$	−0.429030	−	0.311709i	−0.0654265	−	0.0475351i	−0.620018	+	0.784588i	$0.712875\pi$
$44$		0			0
$45$	−1.14780	−	3.53256i	−0.171104	−	0.526604i
$46$		0			0
$47$	0.0152358	+	0.0110694i	0.00222236	+	0.00161464i	0.588896	−	0.808209i	$-0.299563\pi$
$47$	0.0152358	+	0.0110694i	0.00222236	+	0.00161464i	−0.586674	+	0.809824i	$0.699563\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	−0.126067	+	0.387994i	−0.0176529	+	0.0543300i
$52$		0			0
$53$	1.48065	+	4.55697i	0.203383	+	0.625948i	0.999776	+	0.0211685i	$0.00673864\pi$
$53$	1.48065	+	4.55697i	0.203383	+	0.625948i	−0.796393	+	0.604779i	$0.793261\pi$
$54$		0			0
$55$	0.515541			0.0695155
$56$		0			0
$57$	4.02313	−	2.92298i	0.532877	−	0.387158i
$58$		0			0
$59$	9.77967	+	7.10535i	1.27321	+	0.925038i	0.999325	−	0.0367264i	$-0.0116930\pi$
$59$	9.77967	+	7.10535i	1.27321	+	0.925038i	0.273880	+	0.961764i	$0.411693\pi$
$60$		0			0
$61$	−6.92927	+	5.03441i	−0.887203	+	0.644590i	−0.935147	−	0.354260i	$-0.884733\pi$
$61$	−6.92927	+	5.03441i	−0.887203	+	0.644590i	0.0479445	+	0.998850i	$0.484733\pi$
$62$		0			0
$63$	−6.56631	+	4.77070i	−0.827277	+	0.601052i
$64$		0			0
$65$	−0.938640	+	2.88884i	−0.116424	+	0.358316i
$66$		0			0
$67$	2.98211	+	9.17800i	0.364323	+	1.12127i	0.950404	+	0.311018i	$0.100670\pi$
$67$	2.98211	+	9.17800i	0.364323	+	1.12127i	−0.586081	+	0.810252i	$0.699330\pi$
$68$		0			0
$69$	6.05683	+	4.40054i	0.729156	+	0.529763i
$70$		0			0
$71$	−3.32855	+	10.2442i	−0.395026	+	1.21577i	0.533915	+	0.845538i	$0.320720\pi$
$71$	−3.32855	+	10.2442i	−0.395026	+	1.21577i	−0.928941	+	0.370227i	$0.879280\pi$
$72$		0			0
$73$	7.92510			0.927563			0.463781	−	0.885950i	$-0.346492\pi$
$73$	7.92510			0.927563			0.463781	+	0.885950i	$0.346492\pi$
$74$		0			0
$75$	−12.9219	+	9.38832i	−1.49209	+	1.08407i
$76$		0			0
$77$	−0.348117	−	1.07139i	−0.0396716	−	0.122097i
$78$		0			0
$79$	6.89152			0.775357			0.387678	−	0.921795i	$-0.373277\pi$
$79$	6.89152			0.775357			0.387678	+	0.921795i	$0.373277\pi$
$80$		0			0
$81$	32.5268			3.61409
$82$		0			0
$83$	4.78081			0.524762			0.262381	−	0.964964i	$-0.415492\pi$
$83$	4.78081			0.524762			0.262381	+	0.964964i	$0.415492\pi$
$84$		0			0
$85$	−0.0559960			−0.00607362
$86$		0			0
$87$	6.46824	+	19.9072i	0.693468	+	2.13427i
$88$		0			0
$89$	12.8243	−	9.31740i	1.35937	−	0.987642i	0.360888	−	0.932609i	$-0.382474\pi$
$89$	12.8243	−	9.31740i	1.35937	−	0.987642i	0.998485	−	0.0550332i	$-0.0175265\pi$
$90$		0			0
$91$	6.63738			0.695786
$92$		0			0
$93$	0.800278	−	2.46300i	0.0829849	−	0.255401i
$94$		0			0
$95$	0.552207	+	0.401202i	0.0566553	+	0.0411625i
$96$		0			0
$97$	2.06485	+	6.35495i	0.209654	+	0.645248i	0.999490	+	0.0319302i	$0.0101654\pi$
$97$	2.06485	+	6.35495i	0.209654	+	0.645248i	−0.789836	+	0.613318i	$0.789835\pi$
$98$		0			0
$99$	−2.82546	+	8.69586i	−0.283969	+	0.873967i
$100$		0			0
$101$	−3.28900	+	2.38960i	−0.327267	+	0.237774i	−0.739270	−	0.673409i	$-0.764829\pi$
$101$	−3.28900	+	2.38960i	−0.327267	+	0.237774i	0.412003	+	0.911183i	$0.364829\pi$
$102$		0			0
$103$	−15.0028	+	10.9002i	−1.47827	+	1.07402i	−0.500157	+	0.865935i	$0.666725\pi$
$103$	−15.0028	+	10.9002i	−1.47827	+	1.07402i	−0.978110	+	0.208089i	$0.933275\pi$
$104$		0			0
$105$	−1.23441	−	0.896852i	−0.120466	−	0.0875238i
$106$		0			0
$107$	0.899997	−	0.653886i	0.0870060	−	0.0632136i	−0.543432	−	0.839453i	$-0.682875\pi$
$107$	0.899997	−	0.653886i	0.0870060	−	0.0632136i	0.630438	+	0.776240i	$0.282875\pi$
$108$		0			0
$109$	1.46745			0.140557			0.0702783	−	0.997527i	$-0.477611\pi$
$109$	1.46745			0.140557			0.0702783	+	0.997527i	$0.477611\pi$
$110$		0			0
$111$	−6.93705	−	21.3500i	−0.658435	−	2.02646i
$112$		0			0
$113$	0.371943	−	1.14472i	0.0349895	−	0.107687i	−0.932036	−	0.362365i	$-0.881970\pi$
$113$	0.371943	−	1.14472i	0.0349895	−	0.107687i	0.967026	+	0.254678i	$0.0819695\pi$
$114$		0			0
$115$	−0.317547	+	0.977309i	−0.0296114	+	0.0911345i
$116$		0			0
$117$	−43.5831	−	31.6649i	−4.02926	−	2.92743i
$118$		0			0
$119$	0.0378111	+	0.116371i	0.00346614	+	0.0106677i
$120$		0			0
$121$	7.87249	+	5.71970i	0.715681	+	0.519972i
$122$		0			0
$123$	−12.6635	−	17.1874i	−1.14183	−	1.54974i
$124$		0			0
$125$	−3.62481	−	2.63358i	−0.324213	−	0.235555i
$126$		0			0
$127$	−2.76033	−	8.49544i	−0.244940	−	0.753848i	−0.995646	−	0.0932119i	$-0.970287\pi$
$127$	−2.76033	−	8.49544i	−0.244940	−	0.753848i	0.750706	−	0.660636i	$-0.229713\pi$
$128$		0			0
$129$	1.43044	+	1.03928i	0.125943	+	0.0915032i
$130$		0			0
$131$	−0.435171	+	1.33932i	−0.0380210	+	0.117017i	−0.968266	−	0.249923i	$-0.919595\pi$
$131$	−0.435171	+	1.33932i	−0.0380210	+	0.117017i	0.930245	+	0.366940i	$0.119595\pi$
$132$		0			0
$133$	0.460900	−	1.41850i	0.0399651	−	0.123000i
$134$		0			0
$135$	2.41240	+	7.42460i	0.207626	+	0.639008i
$136$		0			0
$137$	−19.1771			−1.63841			−0.819203	−	0.573504i	$-0.805584\pi$
$137$	−19.1771			−1.63841			−0.819203	+	0.573504i	$0.805584\pi$
$138$		0			0
$139$	9.62790	−	6.99508i	0.816628	−	0.593315i	−0.0991168	−	0.995076i	$-0.531602\pi$
$139$	9.62790	−	6.99508i	0.816628	−	0.593315i	0.915745	+	0.401761i	$0.131602\pi$
$140$		0			0
$141$	−0.0507980	−	0.0369069i	−0.00427796	−	0.00310812i
$142$		0			0
$143$	6.04919	−	4.39499i	0.505858	−	0.367528i
$144$		0			0
$145$	−2.32434	+	1.68873i	−0.193026	+	0.140241i
$146$		0			0
$147$	−1.03030	+	3.17094i	−0.0849779	+	0.261535i
$148$		0			0
$149$	5.05824	+	15.5677i	0.414387	+	1.27535i	0.912798	+	0.408411i	$0.133917\pi$
$149$	5.05824	+	15.5677i	0.414387	+	1.27535i	−0.498411	+	0.866941i	$0.666083\pi$
$150$		0			0
$151$	2.71076	+	1.96948i	0.220598	+	0.160274i	0.692596	−	0.721326i	$-0.256467\pi$
$151$	2.71076	+	1.96948i	0.220598	+	0.160274i	−0.471998	+	0.881600i	$0.656467\pi$
$152$		0			0
$153$	0.306890	−	0.944510i	0.0248106	−	0.0763591i
$154$		0			0
$155$	0.355465			0.0285516
$156$		0			0
$157$	19.6546	−	14.2799i	1.56861	−	1.13966i	0.640132	−	0.768265i	$-0.278880\pi$
$157$	19.6546	−	14.2799i	1.56861	−	1.13966i	0.928475	−	0.371394i	$-0.121120\pi$
$158$		0			0
$159$	−4.93667	−	15.1935i	−0.391503	−	1.20492i
$160$		0			0
$161$	2.24546			0.176967
$162$		0			0
$163$	12.9849			1.01705			0.508527	−	0.861046i	$-0.330190\pi$
$163$	12.9849			1.01705			0.508527	+	0.861046i	$0.330190\pi$
$164$		0			0
$165$	−1.71888			−0.133815
$166$		0			0
$167$	−12.9279			−1.00039			−0.500197	−	0.865911i	$-0.666739\pi$
$167$	−12.9279			−1.00039			−0.500197	+	0.865911i	$0.666739\pi$
$168$		0			0
$169$	9.59646	+	29.5349i	0.738189	+	2.27191i
$170$		0			0
$171$	−9.79367	+	7.11552i	−0.748941	+	0.544137i
$172$		0			0
$173$	−13.0690			−0.993616			−0.496808	−	0.867860i	$-0.665495\pi$
$173$	−13.0690			−0.993616			−0.496808	+	0.867860i	$0.665495\pi$
$174$		0			0
$175$	−1.48037	+	4.55610i	−0.111905	+	0.344409i
$176$		0			0
$177$	−32.6067	−	23.6901i	−2.45087	−	1.78066i
$178$		0			0
$179$	−6.85736	−	21.1048i	−0.512543	−	1.57745i	−0.787708	−	0.616049i	$-0.788732\pi$
$179$	−6.85736	−	21.1048i	−0.512543	−	1.57745i	0.275164	−	0.961397i	$-0.411268\pi$
$180$		0			0
$181$	−3.65796	+	11.2581i	−0.271894	+	0.836805i	0.718130	+	0.695909i	$0.244998\pi$
$181$	−3.65796	+	11.2581i	−0.271894	+	0.836805i	−0.990024	+	0.140896i	$0.955002\pi$
$182$		0			0
$183$	23.1031	−	16.7854i	1.70783	−	1.24081i
$184$		0			0
$185$	2.49280	−	1.81113i	0.183275	−	0.133157i
$186$		0			0
$187$	0.111516	+	0.0810211i	0.00815486	+	0.00592485i
$188$		0			0
$189$	13.8008	−	10.0269i	1.00386	−	0.729348i
$190$		0			0
$191$	−18.4700			−1.33644			−0.668222	−	0.743962i	$-0.732944\pi$
$191$	−18.4700			−1.33644			−0.668222	+	0.743962i	$0.732944\pi$
$192$		0			0
$193$	6.21916	+	19.1406i	0.447665	+	1.37777i	0.879535	+	0.475835i	$0.157854\pi$
$193$	6.21916	+	19.1406i	0.447665	+	1.37777i	−0.431870	+	0.901936i	$0.642146\pi$
$194$		0			0
$195$	3.12955	−	9.63175i	0.224111	−	0.689744i
$196$		0			0
$197$	−6.00785	+	18.4903i	−0.428041	+	1.31738i	0.472010	+	0.881593i	$0.343529\pi$
$197$	−6.00785	+	18.4903i	−0.428041	+	1.31738i	−0.900052	+	0.435783i	$0.856471\pi$
$198$		0			0
$199$	19.1041	+	13.8799i	1.35425	+	0.983922i	0.998787	+	0.0492330i	$0.0156777\pi$
$199$	19.1041	+	13.8799i	1.35425	+	0.983922i	0.355466	+	0.934689i	$0.384322\pi$
$200$		0			0
$201$	−9.94274	−	30.6006i	−0.701307	−	2.15840i
$202$		0			0
$203$	5.07901	+	3.69012i	0.356477	+	0.258995i
$204$		0			0
$205$	1.70653	−	2.38211i	0.119189	−	0.166374i
$206$		0			0
$207$	−14.7444	−	10.7124i	−1.02481	−	0.744565i
$208$		0			0
$209$	−0.519218	−	1.59799i	−0.0359150	−	0.110535i
$210$		0			0
$211$	−8.65862	−	6.29086i	−0.596084	−	0.433081i	0.248403	−	0.968657i	$-0.420094\pi$
$211$	−8.65862	−	6.29086i	−0.596084	−	0.433081i	−0.844487	+	0.535576i	$0.820094\pi$
$212$		0			0
$213$	11.0978	−	34.1555i	0.760409	−	2.34030i
$214$		0			0
$215$	−0.0749951	+	0.230811i	−0.00511462	+	0.0157412i
$216$		0			0
$217$	−0.240026	−	0.738725i	−0.0162940	−	0.0501479i
$218$		0			0
$219$	−26.4233			−1.78552
$220$		0			0
$221$	−0.657039	+	0.477366i	−0.0441972	+	0.0321111i
$222$		0			0
$223$	4.63653	+	3.36864i	0.310485	+	0.225581i	0.732105	−	0.681192i	$-0.238538\pi$
$223$	4.63653	+	3.36864i	0.310485	+	0.225581i	−0.421619	+	0.906773i	$0.638538\pi$
$224$		0			0
$225$	31.4563	−	22.8544i	2.09709	−	1.52362i
$226$		0			0
$227$	7.03066	−	5.10808i	0.466641	−	0.339035i	−0.329489	−	0.944159i	$-0.606877\pi$
$227$	7.03066	−	5.10808i	0.466641	−	0.339035i	0.796131	+	0.605124i	$0.206877\pi$
$228$		0			0
$229$	−3.53908	+	10.8922i	−0.233869	+	0.719774i	0.763401	+	0.645925i	$0.223528\pi$
$229$	−3.53908	+	10.8922i	−0.233869	+	0.719774i	−0.997269	+	0.0738489i	$0.976472\pi$
$230$		0			0
$231$	1.16067	+	3.57216i	0.0763662	+	0.235031i
$232$		0			0
$233$	2.80473	+	2.03776i	0.183744	+	0.133498i	0.675855	−	0.737035i	$-0.263775\pi$
$233$	2.80473	+	2.03776i	0.183744	+	0.133498i	−0.492111	+	0.870533i	$0.663775\pi$
$234$		0			0
$235$	0.00266323	−	0.00819659i	0.000173730	−	0.000534686i
$236$		0			0
$237$	−22.9772			−1.49253
$238$		0			0
$239$	21.0289	−	15.2784i	1.36025	−	0.988278i	0.361819	−	0.932248i	$-0.382156\pi$
$239$	21.0289	−	15.2784i	1.36025	−	0.988278i	0.998429	−	0.0560301i	$-0.0178443\pi$
$240$		0			0
$241$	2.72515	+	8.38714i	0.175542	+	0.540263i	0.999658	−	0.0261584i	$-0.00832742\pi$
$241$	2.72515	+	8.38714i	0.175542	+	0.540263i	−0.824116	+	0.566422i	$0.808327\pi$
$242$		0			0
$243$	−57.2722			−3.67401
$244$		0			0
$245$	−0.457636			−0.0292373
$246$		0			0
$247$	9.89967			0.629901
$248$		0			0
$249$	−15.9398			−1.01014
$250$		0			0
$251$	−4.78491	−	14.7264i	−0.302021	−	0.929525i	−0.980772	−	0.195157i	$-0.937478\pi$
$251$	−4.78491	−	14.7264i	−0.302021	−	0.929525i	0.678751	−	0.734368i	$-0.262522\pi$
$252$		0			0
$253$	2.04647	−	1.48685i	0.128661	−	0.0934774i
$254$		0			0
$255$	0.186698			0.0116915
$256$		0			0
$257$	7.69408	−	23.6799i	0.479943	−	1.47711i	−0.359230	−	0.933249i	$-0.616961\pi$
$257$	7.69408	−	23.6799i	0.479943	−	1.47711i	0.839173	−	0.543865i	$-0.183039\pi$
$258$		0			0
$259$	−5.44713	−	3.95757i	−0.338468	−	0.245912i
$260$		0			0
$261$	−15.7459	−	48.4609i	−0.974646	−	2.99965i
$262$		0			0
$263$	−2.15911	+	6.64505i	−0.133136	+	0.409751i	−0.995295	−	0.0968862i	$-0.969112\pi$
$263$	−2.15911	+	6.64505i	−0.133136	+	0.409751i	0.862159	+	0.506637i	$0.169112\pi$
$264$		0			0
$265$	1.77397	−	1.28887i	0.108974	−	0.0791745i
$266$		0			0
$267$	−42.7578	+	31.0654i	−2.61674	+	1.90117i
$268$		0			0
$269$	2.96650	+	2.15529i	0.180871	+	0.131410i	0.674537	−	0.738241i	$-0.264343\pi$
$269$	2.96650	+	2.15529i	0.180871	+	0.131410i	−0.493666	+	0.869652i	$0.664343\pi$
$270$		0			0
$271$	−3.60618	+	2.62004i	−0.219060	+	0.159156i	−0.691903	−	0.721990i	$-0.743228\pi$
$271$	−3.60618	+	2.62004i	−0.219060	+	0.159156i	0.472844	+	0.881146i	$0.343228\pi$
$272$		0			0
$273$	−22.1299			−1.33936
$274$		0			0
$275$	1.66768	+	5.13259i	0.100565	+	0.309507i
$276$		0			0
$277$	6.00174	−	18.4714i	0.360609	−	1.10984i	−0.592076	−	0.805882i	$-0.701691\pi$
$277$	6.00174	−	18.4714i	0.360609	−	1.10984i	0.952685	−	0.303959i	$-0.0983086\pi$
$278$		0			0
$279$	−1.94815	+	5.99579i	−0.116633	+	0.358958i
$280$		0			0
$281$	−13.0625	−	9.49046i	−0.779243	−	0.566153i	0.125508	−	0.992093i	$-0.459944\pi$
$281$	−13.0625	−	9.49046i	−0.779243	−	0.566153i	−0.904752	+	0.425939i	$0.859944\pi$
$282$		0			0
$283$	2.70542	+	8.32642i	0.160820	+	0.494954i	0.998704	−	0.0508945i	$-0.0162072\pi$
$283$	2.70542	+	8.32642i	0.160820	+	0.494954i	−0.837884	+	0.545849i	$0.816207\pi$
$284$		0			0
$285$	−1.84113	−	1.33766i	−0.109059	−	0.0792361i
$286$		0			0
$287$	−6.10280	−	1.93798i	−0.360237	−	0.114395i
$288$		0			0
$289$	13.7412	+	9.98355i	0.808304	+	0.587268i
$290$		0			0
$291$	−6.88447	−	21.1882i	−0.403575	−	1.24208i
$292$		0			0
$293$	13.5108	+	9.81618i	0.789310	+	0.573467i	0.907759	−	0.419493i	$-0.137792\pi$
$293$	13.5108	+	9.81618i	0.789310	+	0.573467i	−0.118449	+	0.992960i	$0.537792\pi$
$294$		0			0
$295$	1.70950	−	5.26130i	0.0995310	−	0.306325i
$296$		0			0
$297$	5.93843	−	18.2766i	0.344583	−	1.06052i
$298$		0			0
$299$	4.60558	+	14.1745i	0.266348	+	0.819733i
$300$		0			0
$301$	0.530310			0.0305666
$302$		0			0
$303$	10.9659	−	7.96722i	0.629976	−	0.457705i
$304$		0			0
$305$	3.17109	+	2.30393i	0.181576	+	0.131923i
$306$		0			0
$307$	1.68282	−	1.22264i	0.0960435	−	0.0697797i	−0.538727	−	0.842480i	$-0.681095\pi$
$307$	1.68282	−	1.22264i	0.0960435	−	0.0697797i	0.634771	+	0.772701i	$0.281095\pi$
$308$		0			0
$309$	50.0211	−	36.3425i	2.84560	−	2.06745i
$310$		0			0
$311$	−6.64315	+	20.4455i	−0.376698	+	1.15936i	0.565627	+	0.824661i	$0.308634\pi$
$311$	−6.64315	+	20.4455i	−0.376698	+	1.15936i	−0.942326	+	0.334697i	$0.891366\pi$
$312$		0			0
$313$	−0.176358	−	0.542773i	−0.00996832	−	0.0306793i	0.945949	−	0.324316i	$-0.105134\pi$
$313$	−0.176358	−	0.542773i	−0.00996832	−	0.0306793i	−0.955917	+	0.293637i	$0.905134\pi$
$314$		0			0
$315$	3.00498	+	2.18324i	0.169311	+	0.123012i
$316$		0			0
$317$	−0.0279135	+	0.0859089i	−0.00156778	+	0.00482512i	−0.951837	−	0.306603i	$-0.900807\pi$
$317$	−0.0279135	+	0.0859089i	−0.00156778	+	0.00482512i	0.950270	+	0.311429i	$0.100807\pi$
$318$		0			0
$319$	7.07236			0.395976
$320$		0			0
$321$	−3.00070	+	2.18014i	−0.167483	+	0.121683i
$322$		0			0
$323$	0.0563954	+	0.173567i	0.00313792	+	0.00965753i
$324$		0			0
$325$	−31.7968			−1.76377
$326$		0			0
$327$	−4.89268			−0.270566
$328$		0			0
$329$	−0.0188324			−0.00103827
$330$		0			0
$331$	−6.13432			−0.337173			−0.168586	−	0.985687i	$-0.553920\pi$
$331$	−6.13432			−0.337173			−0.168586	+	0.985687i	$0.553920\pi$
$332$		0			0
$333$	16.8871	+	51.9733i	0.925410	+	2.84812i
$334$		0			0
$335$	3.57289	−	2.59585i	0.195208	−	0.141827i
$336$		0			0
$337$	−21.8979			−1.19285			−0.596427	−	0.802668i	$-0.703413\pi$
$337$	−21.8979			−1.19285			−0.596427	+	0.802668i	$0.703413\pi$
$338$		0			0
$339$	−1.24011	+	3.81665i	−0.0673533	+	0.207292i
$340$		0			0
$341$	−0.707908	−	0.514325i	−0.0383354	−	0.0278523i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$		0			0
$345$	1.05874	−	3.25847i	0.0570007	−	0.175430i
$346$		0			0
$347$	21.1380	−	15.3577i	1.13475	−	0.824442i	0.148368	−	0.988932i	$-0.452598\pi$
$347$	21.1380	−	15.3577i	1.13475	−	0.824442i	0.986379	+	0.164490i	$0.0525979\pi$
$348$		0			0
$349$	−19.0358	+	13.8303i	−1.01896	+	0.740320i	−0.966070	−	0.258281i	$-0.916844\pi$
$349$	−19.0358	+	13.8303i	−1.01896	+	0.740320i	−0.0528925	+	0.998600i	$0.516844\pi$
$350$		0			0
$351$	91.6012	+	66.5521i	4.88931	+	3.55229i
$352$		0			0
$353$	−7.49277	+	5.44381i	−0.398800	+	0.289745i	−0.769052	−	0.639186i	$-0.779271\pi$
$353$	−7.49277	+	5.44381i	−0.398800	+	0.289745i	0.370252	+	0.928931i	$0.379271\pi$
$354$		0			0
$355$	4.92938			0.261625
$356$		0			0
$357$	−0.126067	−	0.387994i	−0.00667217	−	0.0205348i
$358$		0			0
$359$	6.93086	−	21.3310i	0.365797	−	1.12581i	−0.583684	−	0.811981i	$-0.698389\pi$
$359$	6.93086	−	21.3310i	0.365797	−	1.12581i	0.949481	−	0.313826i	$-0.101611\pi$
$360$		0			0
$361$	−5.18389	+	15.9544i	−0.272836	+	0.839704i
$362$		0			0
$363$	−26.2479	−	19.0702i	−1.37766	−	1.00093i
$364$		0			0
$365$	−1.12075	−	3.44930i	−0.0586626	−	0.180545i
$366$		0			0
$367$	−0.968073	−	0.703346i	−0.0505330	−	0.0367144i	0.562232	−	0.826980i	$-0.309943\pi$
$367$	−0.968073	−	0.703346i	−0.0505330	−	0.0367144i	−0.612765	+	0.790265i	$0.709943\pi$
$368$		0			0
$369$	30.8274	+	41.8400i	1.60481	+	2.17811i
$370$		0			0
$371$	−3.87639	−	2.81636i	−0.201252	−	0.146218i
$372$		0			0
$373$	10.0354	+	30.8857i	0.519613	+	1.59920i	0.774729	+	0.632293i	$0.217886\pi$
$373$	10.0354	+	30.8857i	0.519613	+	1.59920i	−0.255116	+	0.966910i	$0.582114\pi$
$374$		0			0
$375$	12.0856	+	8.78070i	0.624097	+	0.453433i
$376$		0			0
$377$	−12.8766	+	39.6300i	−0.663177	+	2.04105i
$378$		0			0
$379$	−7.82615	+	24.0864i	−0.402002	+	1.23724i	0.521370	+	0.853331i	$0.325421\pi$
$379$	−7.82615	+	24.0864i	−0.402002	+	1.23724i	−0.923372	+	0.383905i	$0.874579\pi$
$380$		0			0
$381$	9.20331	+	28.3249i	0.471500	+	1.45113i
$382$		0			0
$383$	25.6044			1.30833			0.654163	−	0.756354i	$-0.273021\pi$
$383$	25.6044			1.30833			0.654163	+	0.756354i	$0.273021\pi$
$384$		0			0
$385$	−0.417081	+	0.303027i	−0.0212564	+	0.0154437i
$386$		0			0
$387$	−3.48218	−	2.52995i	−0.177009	−	0.128605i
$388$		0			0
$389$	12.8919	−	9.36649i	0.653644	−	0.474900i	−0.210867	−	0.977515i	$-0.567629\pi$
$389$	12.8919	−	9.36649i	0.653644	−	0.474900i	0.864510	+	0.502615i	$0.167629\pi$
$390$		0			0
$391$	−0.222280	+	0.161496i	−0.0112412	+	0.00816718i
$392$		0			0
$393$	1.45091	−	4.46545i	0.0731889	−	0.225252i
$394$		0			0
$395$	−0.974580	−	2.99945i	−0.0490365	−	0.150919i
$396$		0			0
$397$	16.8148	+	12.2167i	0.843912	+	0.613138i	0.923461	−	0.383693i	$-0.125348\pi$
$397$	16.8148	+	12.2167i	0.843912	+	0.613138i	−0.0795489	+	0.996831i	$0.525348\pi$
$398$		0			0
$399$	−1.53670	+	4.72947i	−0.0769312	+	0.236770i
$400$		0			0
$401$	−5.38829			−0.269079			−0.134539	−	0.990908i	$-0.542955\pi$
$401$	−5.38829			−0.269079			−0.134539	+	0.990908i	$0.542955\pi$
$402$		0			0
$403$	4.17091	−	3.03034i	0.207768	−	0.150952i
$404$		0			0
$405$	−4.59985	−	14.1569i	−0.228568	−	0.703461i
$406$		0			0
$407$	−7.58496			−0.375972
$408$		0			0
$409$	16.4523			0.813513			0.406756	−	0.913537i	$-0.366660\pi$
$409$	16.4523			0.813513			0.406756	+	0.913537i	$0.366660\pi$
$410$		0			0
$411$	63.9387			3.15386
$412$		0			0
$413$	−12.0883			−0.594828
$414$		0			0
$415$	−0.676089	−	2.08079i	−0.0331879	−	0.102142i
$416$		0			0
$417$	−32.1006	+	23.3225i	−1.57197	+	1.14211i
$418$		0			0
$419$	−24.7202			−1.20766			−0.603831	−	0.797113i	$-0.706360\pi$
$419$	−24.7202			−1.20766			−0.603831	+	0.797113i	$0.706360\pi$
$420$		0			0
$421$	3.12458	−	9.61647i	0.152283	−	0.468678i	−0.845593	−	0.533829i	$-0.820753\pi$
$421$	3.12458	−	9.61647i	0.152283	−	0.468678i	0.997875	+	0.0651504i	$0.0207527\pi$
$422$		0			0
$423$	0.123660	+	0.0898439i	0.00601253	+	0.00436836i
$424$		0			0
$425$	−0.181137	−	0.557481i	−0.00878642	−	0.0270418i
$426$		0			0
$427$	2.64675	−	8.14585i	0.128085	−	0.394205i
$428$		0			0
$429$	−20.1688	+	14.6535i	−0.973757	+	0.707476i
$430$		0			0
$431$	−10.8706	+	7.89796i	−0.523619	+	0.380431i	−0.817965	−	0.575267i	$-0.804898\pi$
$431$	−10.8706	+	7.89796i	−0.523619	+	0.380431i	0.294347	+	0.955699i	$0.404898\pi$
$432$		0			0
$433$	−22.1203	−	16.0713i	−1.06303	−	0.772339i	−0.0883864	−	0.996086i	$-0.528171\pi$
$433$	−22.1203	−	16.0713i	−1.06303	−	0.772339i	−0.974647	+	0.223747i	$0.928171\pi$
$434$		0			0
$435$	7.74964	−	5.63044i	0.371567	−	0.269959i
$436$		0			0
$437$	3.34911			0.160210
$438$		0			0
$439$	−4.06843	−	12.5213i	−0.194176	−	0.597611i	−0.999985	−	0.00543650i	$-0.998270\pi$
$439$	−4.06843	−	12.5213i	−0.194176	−	0.597611i	0.805810	−	0.592175i	$-0.201730\pi$
$440$		0			0
$441$	2.50811	−	7.71916i	0.119434	−	0.367579i
$442$		0			0
$443$	8.55966	−	26.3439i	0.406682	−	1.25164i	−0.512801	−	0.858507i	$-0.671392\pi$
$443$	8.55966	−	26.3439i	0.406682	−	1.25164i	0.919483	−	0.393130i	$-0.128608\pi$
$444$		0			0
$445$	−5.86886	−	4.26398i	−0.278211	−	0.202132i
$446$		0			0
$447$	−16.8648	−	51.9045i	−0.797678	−	2.45500i
$448$		0			0
$449$	−8.90842	−	6.47235i	−0.420414	−	0.305449i	0.357390	−	0.933955i	$-0.383667\pi$
$449$	−8.90842	−	6.47235i	−0.420414	−	0.305449i	−0.777805	+	0.628506i	$0.783667\pi$
$450$		0			0
$451$	−6.84524	+	2.27478i	−0.322330	+	0.107115i
$452$		0			0
$453$	−9.03800	−	6.56649i	−0.424642	−	0.308521i
$454$		0			0
$455$	−0.938640	−	2.88884i	−0.0440041	−	0.135431i
$456$		0			0
$457$	16.6033	+	12.0630i	0.776670	+	0.564284i	0.903978	−	0.427579i	$-0.140634\pi$
$457$	16.6033	+	12.0630i	0.776670	+	0.564284i	−0.127307	+	0.991863i	$0.540634\pi$
$458$		0			0
$459$	−0.645009	+	1.98513i	−0.0301064	+	0.0926581i
$460$		0			0
$461$	0.398017	−	1.22497i	0.0185375	−	0.0570525i	−0.941360	−	0.337404i	$-0.890451\pi$
$461$	0.398017	−	1.22497i	0.0185375	−	0.0570525i	0.959897	+	0.280352i	$0.0904511\pi$
$462$		0			0
$463$	7.88541	+	24.2688i	0.366466	+	1.12787i	0.949058	+	0.315101i	$0.102039\pi$
$463$	7.88541	+	24.2688i	0.366466	+	1.12787i	−0.582592	+	0.812765i	$0.697961\pi$
$464$		0			0
$465$	−1.18516			−0.0549607
$466$		0			0
$467$	20.2702	−	14.7272i	0.937992	−	0.681491i	−0.00994420	−	0.999951i	$-0.503165\pi$
$467$	20.2702	−	14.7272i	0.937992	−	0.681491i	0.947937	+	0.318459i	$0.103165\pi$
$468$		0			0
$469$	−7.80727	−	5.67231i	−0.360506	−	0.261923i
$470$		0			0
$471$	−65.5309	+	47.6110i	−3.01950	+	2.19380i
$472$		0			0
$473$	0.483315	−	0.351149i	0.0222229	−	0.0161459i
$474$		0			0
$475$	−2.20797	+	6.79544i	−0.101309	+	0.311796i
$476$		0			0
$477$	12.0175	+	36.9862i	0.550245	+	1.69348i
$478$		0			0
$479$	−13.9454	−	10.1319i	−0.637182	−	0.462940i	0.221699	−	0.975115i	$-0.428840\pi$
$479$	−13.9454	−	10.1319i	−0.637182	−	0.462940i	−0.858881	+	0.512175i	$0.828840\pi$
$480$		0			0
$481$	13.8099	−	42.5024i	0.629675	−	1.93794i
$482$		0			0
$483$	−7.48665			−0.340654
$484$		0			0
$485$	2.47391	−	1.79740i	0.112334	−	0.0816158i
$486$		0			0
$487$	−3.28570	−	10.1123i	−0.148889	−	0.458234i	0.848601	−	0.529033i	$-0.177445\pi$
$487$	−3.28570	−	10.1123i	−0.148889	−	0.458234i	−0.997491	+	0.0707987i	$0.977445\pi$
$488$		0			0
$489$	−43.2933			−1.95779
$490$		0			0
$491$	8.95361			0.404071			0.202035	−	0.979378i	$-0.435244\pi$
$491$	8.95361			0.404071			0.202035	+	0.979378i	$0.435244\pi$
$492$		0			0
$493$	−0.768171			−0.0345967
$494$		0			0
$495$	4.18434			0.188072
$496$		0			0
$497$	−3.32855	−	10.2442i	−0.149306	−	0.459516i
$498$		0			0
$499$	11.0296	−	8.01348i	0.493753	−	0.358733i	−0.312873	−	0.949795i	$-0.601291\pi$
$499$	11.0296	−	8.01348i	0.493753	−	0.358733i	0.806626	+	0.591062i	$0.201291\pi$
$500$		0			0
$501$	43.1034			1.92572
$502$		0			0
$503$	9.71775	−	29.9082i	0.433293	−	1.33354i	−0.461533	−	0.887123i	$-0.652700\pi$
$503$	9.71775	−	29.9082i	0.433293	−	1.33354i	0.894826	−	0.446416i	$-0.147300\pi$
$504$		0			0
$505$	1.50516	+	1.09357i	0.0669789	+	0.0486630i
$506$		0			0
$507$	−31.9958	−	98.4730i	−1.42098	−	4.37334i
$508$		0			0
$509$	−10.9835	+	33.8036i	−0.486833	+	1.49832i	0.342475	+	0.939527i	$0.388735\pi$
$509$	−10.9835	+	33.8036i	−0.486833	+	1.49832i	−0.829308	+	0.558791i	$0.811265\pi$
$510$		0			0
$511$	−6.41154	+	4.65826i	−0.283630	+	0.206069i
$512$		0			0
$513$	20.5840	−	14.9551i	0.908804	−	0.660285i
$514$		0			0
$515$	6.86581	+	4.98830i	0.302544	+	0.219811i
$516$		0			0
$517$	−0.0171635	+	0.0124700i	−0.000754852	+	0.000548432i
$518$		0			0
$519$	43.5736			1.91267
$520$		0			0
$521$	7.19139	+	22.1328i	0.315061	+	0.969657i	0.975730	+	0.218979i	$0.0702727\pi$
$521$	7.19139	+	22.1328i	0.315061	+	0.969657i	−0.660669	+	0.750677i	$0.729727\pi$
$522$		0			0
$523$	−7.43200	+	22.8733i	−0.324979	+	1.00018i	0.646472	+	0.762938i	$0.276244\pi$
$523$	−7.43200	+	22.8733i	−0.324979	+	1.00018i	−0.971450	+	0.237243i	$0.923756\pi$
$524$		0			0
$525$	4.93573	−	15.1906i	0.215413	−	0.662973i
$526$		0			0
$527$	0.0768901	+	0.0558640i	0.00334939	+	0.00243347i
$528$		0			0
$529$	−5.54930	−	17.0790i	−0.241274	−	0.742565i
$530$		0			0
$531$	79.3758	+	57.6699i	3.44461	+	2.50266i
$532$		0			0
$533$	−0.283683	−	42.4990i	−0.0122877	−	1.84084i
$534$		0			0
$535$	−0.411871	−	0.299242i	−0.0178067	−	0.0129374i
$536$		0			0
$537$	22.8633	+	70.3661i	0.986625	+	3.03652i
$538$		0			0
$539$	0.911382	+	0.662158i	0.0392560	+	0.0285212i
$540$		0			0
$541$	0.672642	−	2.07018i	0.0289191	−	0.0890039i	−0.935555	−	0.353180i	$-0.885100\pi$
$541$	0.672642	−	2.07018i	0.0289191	−	0.0890039i	0.964474	+	0.264177i	$0.0851002\pi$
$542$		0			0
$543$	12.1961	−	37.5358i	0.523385	−	1.61081i
$544$		0			0
$545$	−0.207523	−	0.638691i	−0.00888933	−	0.0273585i
$546$		0			0
$547$	−30.6678			−1.31126			−0.655631	−	0.755082i	$-0.727597\pi$
$547$	−30.6678			−1.31126			−0.655631	+	0.755082i	$0.727597\pi$
$548$		0			0
$549$	−56.2408	+	40.8613i	−2.40030	+	1.74392i
$550$		0			0
$551$	7.57536	+	5.50382i	0.322721	+	0.234471i
$552$		0			0
$553$	−5.57536	+	4.05073i	−0.237088	+	0.172255i
$554$		0			0
$555$	−8.31132	+	6.03853i	−0.352796	+	0.256321i
$556$		0			0
$557$	−8.44865	+	26.0023i	−0.357981	+	1.10175i	0.596280	+	0.802776i	$0.296645\pi$
$557$	−8.44865	+	26.0023i	−0.357981	+	1.10175i	−0.954261	+	0.298975i	$0.903355\pi$
$558$		0			0
$559$	1.08770	+	3.34760i	0.0460048	+	0.141588i
$560$		0			0
$561$	−0.371808	−	0.270135i	−0.0156978	−	0.0114051i
$562$		0			0
$563$	4.53643	−	13.9617i	0.191188	−	0.588416i	−0.808812	−	0.588067i	$-0.799889\pi$
$563$	4.53643	−	13.9617i	0.191188	−	0.588416i	1.00000		0.000348433i	$-0.000110910\pi$
$564$		0			0
$565$	−0.550826			−0.0231734
$566$		0			0
$567$	−26.3147	+	19.1188i	−1.10511	+	0.802912i
$568$		0			0
$569$	−12.1703	−	37.4562i	−0.510204	−	1.57025i	−0.791843	−	0.610725i	$-0.790878\pi$
$569$	−12.1703	−	37.4562i	−0.510204	−	1.57025i	0.281639	−	0.959520i	$-0.409122\pi$
$570$		0			0
$571$	18.8277			0.787916			0.393958	−	0.919129i	$-0.371106\pi$
$571$	18.8277			0.787916			0.393958	+	0.919129i	$0.371106\pi$
$572$		0			0
$573$	61.5814			2.57260
$574$		0			0
$575$	−10.7570			−0.448599
$576$		0			0
$577$	15.2636			0.635432			0.317716	−	0.948186i	$-0.397084\pi$
$577$	15.2636			0.635432			0.317716	+	0.948186i	$0.397084\pi$
$578$		0			0
$579$	−20.7355	−	63.8172i	−0.861736	−	2.65215i
$580$		0			0
$581$	−3.86775	+	2.81009i	−0.160461	+	0.116582i
$582$		0			0
$583$	−5.39775			−0.223552
$584$		0			0
$585$	−7.61838	+	23.4470i	−0.314981	+	0.969413i
$586$		0			0
$587$	−32.0399	−	23.2783i	−1.32243	−	0.960800i	−0.999899	−	0.0142399i	$-0.995467\pi$
$587$	−32.0399	−	23.2783i	−1.32243	−	0.960800i	−0.322529	−	0.946560i	$-0.604533\pi$
$588$		0			0
$589$	−0.358000	−	1.10181i	−0.0147511	−	0.0453993i
$590$		0			0
$591$	20.0309	−	61.6489i	0.823962	−	2.53590i
$592$		0			0
$593$	−24.9925	+	18.1581i	−1.02632	+	0.745665i	−0.967569	−	0.252608i	$-0.918712\pi$
$593$	−24.9925	+	18.1581i	−1.02632	+	0.745665i	−0.0587510	+	0.998273i	$0.518712\pi$
$594$		0			0
$595$	0.0453017	−	0.0329136i	0.00185719	−	0.00134933i
$596$		0			0
$597$	−63.6955	−	46.2775i	−2.60688	−	1.89401i
$598$		0			0
$599$	6.15941	−	4.47507i	0.251667	−	0.182847i	−0.454798	−	0.890594i	$-0.650289\pi$
$599$	6.15941	−	4.47507i	0.251667	−	0.182847i	0.706465	+	0.707748i	$0.250289\pi$
$600$		0			0
$601$	22.9743			0.937143			0.468572	−	0.883426i	$-0.344769\pi$
$601$	22.9743			0.937143			0.468572	+	0.883426i	$0.344769\pi$
$602$		0			0
$603$	24.2040	+	74.4923i	0.985664	+	3.03356i
$604$		0			0
$605$	1.37612	−	4.23527i	0.0559473	−	0.172188i
$606$		0			0
$607$	−4.28142	+	13.1769i	−0.173777	+	0.534832i	−0.999576	−	0.0291339i	$-0.990725\pi$
$607$	−4.28142	+	13.1769i	−0.173777	+	0.534832i	0.825798	+	0.563966i	$0.190725\pi$
$608$		0			0
$609$	−16.9341	−	12.3033i	−0.686203	−	0.498555i
$610$		0			0
$611$	−0.0386265	−	0.118880i	−0.00156266	−	0.00480938i
$612$		0			0
$613$	−12.7924	−	9.29422i	−0.516680	−	0.375390i	0.298672	−	0.954356i	$-0.403456\pi$
$613$	−12.7924	−	9.29422i	−0.516680	−	0.375390i	−0.815352	+	0.578966i	$0.803456\pi$
$614$		0			0
$615$	−5.68977	+	7.94225i	−0.229434	+	0.320262i
$616$		0			0
$617$	−4.33614	−	3.15039i	−0.174566	−	0.126830i	0.497071	−	0.867710i	$-0.334409\pi$
$617$	−4.33614	−	3.15039i	−0.174566	−	0.126830i	−0.671638	+	0.740880i	$0.734409\pi$
$618$		0			0
$619$	12.5008	+	38.4736i	0.502451	+	1.54639i	0.805014	+	0.593256i	$0.202158\pi$
$619$	12.5008	+	38.4736i	0.502451	+	1.54639i	−0.302562	+	0.953130i	$0.597842\pi$
$620$		0			0
$621$	30.9892	+	22.5149i	1.24355	+	0.903493i
$622$		0			0
$623$	−4.89845	+	15.0759i	−0.196252	+	0.604002i
$624$		0			0
$625$	6.76821	−	20.8304i	0.270729	−	0.833217i
$626$		0			0
$627$	1.73114	+	5.32789i	0.0691350	+	0.212776i
$628$		0			0
$629$	0.823848			0.0328490
$630$		0			0
$631$	12.5243	−	9.09944i	0.498585	−	0.362243i	−0.309891	−	0.950772i	$-0.600293\pi$
$631$	12.5243	−	9.09944i	0.498585	−	0.362243i	0.808476	+	0.588529i	$0.200293\pi$
$632$		0			0
$633$	28.8690	+	20.9745i	1.14744	+	0.833662i
$634$		0			0
$635$	−3.30718	+	2.40280i	−0.131241	+	0.0953524i
$636$		0			0
$637$	−5.36975	+	3.90135i	−0.212757	+	0.154577i
$638$		0			0
$639$	−27.0158	+	83.1462i	−1.06873	+	3.28921i
$640$		0			0
$641$	−0.273061	−	0.840395i	−0.0107853	−	0.0331936i	0.945519	−	0.325567i	$-0.105555\pi$
$641$	−0.273061	−	0.840395i	−0.0107853	−	0.0331936i	−0.956304	+	0.292373i	$0.905555\pi$
$642$		0			0
$643$	36.9243	+	26.8271i	1.45615	+	1.05796i	0.984344	+	0.176257i	$0.0563989\pi$
$643$	36.9243	+	26.8271i	1.45615	+	1.05796i	0.471809	+	0.881701i	$0.343601\pi$
$644$		0			0
$645$	0.250043	−	0.769554i	0.00984544	−	0.0303011i
$646$		0			0
$647$	46.8551			1.84206			0.921032	−	0.389487i	$-0.127348\pi$
$647$	46.8551			1.84206			0.921032	+	0.389487i	$0.127348\pi$
$648$		0			0
$649$	−11.0171	+	8.00439i	−0.432459	+	0.314200i
$650$		0			0
$651$	0.800278	+	2.46300i	0.0313654	+	0.0965327i
$652$		0			0
$653$	4.78916			0.187414			0.0937072	−	0.995600i	$-0.470128\pi$
$653$	4.78916			0.187414			0.0937072	+	0.995600i	$0.470128\pi$
$654$		0			0
$655$	0.644462			0.0251812
$656$		0			0
$657$	64.3233			2.50949
$658$		0			0
$659$	−17.0786			−0.665287			−0.332643	−	0.943053i	$-0.607941\pi$
$659$	−17.0786			−0.665287			−0.332643	+	0.943053i	$0.607941\pi$
$660$		0			0
$661$	11.3911	+	35.0582i	0.443062	+	1.36361i	0.884595	+	0.466361i	$0.154435\pi$
$661$	11.3911	+	35.0582i	0.443062	+	1.36361i	−0.441532	+	0.897245i	$0.645565\pi$
$662$		0			0
$663$	2.19065	−	1.59160i	0.0850778	−	0.0618126i
$664$		0			0
$665$	−0.682566			−0.0264688
$666$		0			0
$667$	−4.35621	+	13.4070i	−0.168673	+	0.519123i
$668$		0			0
$669$	−15.4588	−	11.2315i	−0.597672	−	0.434234i
$670$		0			0
$671$	−2.98164	−	9.17655i	−0.115105	−	0.354257i
$672$		0			0
$673$	−3.35715	+	10.3322i	−0.129409	+	0.398279i	−0.994678	−	0.103028i	$-0.967147\pi$
$673$	−3.35715	+	10.3322i	−0.129409	+	0.398279i	0.865270	+	0.501306i	$0.167147\pi$
$674$		0			0
$675$	−66.1137	+	48.0344i	−2.54472	+	1.84885i
$676$		0			0
$677$	29.5425	−	21.4639i	1.13541	−	0.824924i	0.148937	−	0.988847i	$-0.452415\pi$
$677$	29.5425	−	21.4639i	1.13541	−	0.824924i	0.986473	+	0.163923i	$0.0524148\pi$
$678$		0			0
$679$	−5.40585	−	3.92758i	−0.207457	−	0.150727i
$680$		0			0
$681$	−23.4411	+	17.0310i	−0.898266	+	0.652628i
$682$		0			0
$683$	−41.1087			−1.57298			−0.786489	−	0.617604i	$-0.788104\pi$
$683$	−41.1087			−1.57298			−0.786489	+	0.617604i	$0.788104\pi$
$684$		0			0
$685$	2.71197	+	8.34658i	0.103619	+	0.318906i
$686$		0			0
$687$	11.7997	−	36.3158i	0.450188	−	1.38554i
$688$		0			0
$689$	9.82762	−	30.2463i	0.374403	−	1.15229i
$690$		0			0
$691$	24.8250	+	18.0364i	0.944387	+	0.686137i	0.949473	−	0.313850i	$-0.101619\pi$
$691$	24.8250	+	18.0364i	0.944387	+	0.686137i	−0.00508568	+	0.999987i	$0.501619\pi$
$692$		0			0
$693$	−2.82546	−	8.69586i	−0.107330	−	0.330329i
$694$		0			0
$695$	−4.40607	−	3.20120i	−0.167132	−	0.121428i
$696$		0			0
$697$	0.743502	−	0.247077i	0.0281622	−	0.00935872i
$698$		0			0
$699$	−9.35133	−	6.79414i	−0.353700	−	0.256978i
$700$		0			0
$701$	−3.94637	−	12.1457i	−0.149053	−	0.458736i	0.848457	−	0.529264i	$-0.177532\pi$
$701$	−3.94637	−	12.1457i	−0.149053	−	0.458736i	−0.997510	+	0.0705273i	$0.977532\pi$
$702$		0			0
$703$	−8.12442	−	5.90273i	−0.306418	−	0.222626i
$704$		0			0
$705$	−0.00887956	+	0.0273285i	−0.000334423	+	0.00102925i
$706$		0			0
$707$	1.25629	−	3.86645i	0.0472475	−	0.145413i
$708$		0			0
$709$	−4.78551	−	14.7283i	−0.179724	−	0.553132i	0.820094	−	0.572229i	$-0.193921\pi$
$709$	−4.78551	−	14.7283i	−0.179724	−	0.553132i	−0.999818	+	0.0190965i	$0.993921\pi$
$710$		0			0
$711$	55.9344			2.09770
$712$		0			0
$713$	1.41104	−	1.02518i	0.0528439	−	0.0383933i
$714$		0			0
$715$	−2.76833	−	2.01131i	−0.103530	−	0.0752186i
$716$		0			0
$717$	−70.1131	+	50.9402i	−2.61842	+	1.90240i
$718$		0			0
$719$	−8.06036	+	5.85619i	−0.300601	+	0.218399i	−0.727853	−	0.685733i	$-0.759482\pi$
$719$	−8.06036	+	5.85619i	−0.300601	+	0.218399i	0.427252	+	0.904132i	$0.359482\pi$
$720$		0			0
$721$	5.73055	−	17.6368i	0.213417	−	0.656829i
$722$		0			0
$723$	−9.08599	−	27.9638i	−0.337911	−	1.03998i
$724$		0			0
$725$	−24.3313	−	17.6778i	−0.903643	−	0.656535i
$726$		0			0
$727$	−10.6607	+	32.8104i	−0.395385	+	1.21687i	0.533276	+	0.845941i	$0.320961\pi$
$727$	−10.6607	+	32.8104i	−0.395385	+	1.21687i	−0.928661	+	0.370929i	$0.879039\pi$
$728$		0			0
$729$	93.3724			3.45824
$730$		0			0
$731$	−0.0524958	+	0.0381404i	−0.00194163	+	0.00141067i
$732$		0			0
$733$	−13.8346	−	42.5785i	−0.510992	−	1.57267i	−0.790457	−	0.612517i	$-0.790157\pi$
$733$	−13.8346	−	42.5785i	−0.510992	−	1.57267i	0.279465	−	0.960156i	$-0.409843\pi$
$734$		0			0
$735$	1.52582			0.0562806
$736$		0			0
$737$	−10.8714			−0.400452
$738$		0			0
$739$	−42.3397			−1.55749			−0.778746	−	0.627339i	$-0.784144\pi$
$739$	−42.3397			−1.55749			−0.778746	+	0.627339i	$0.784144\pi$
$740$		0			0
$741$	−33.0068			−1.21253
$742$		0			0
$743$	7.23484	+	22.2666i	0.265421	+	0.816881i	0.991596	+	0.129371i	$0.0412959\pi$
$743$	7.23484	+	22.2666i	0.265421	+	0.816881i	−0.726176	+	0.687509i	$0.758704\pi$
$744$		0			0
$745$	6.06031	−	4.40307i	0.222033	−	0.161316i
$746$		0			0
$747$	38.8029			1.41973
$748$		0			0
$749$	−0.343768	+	1.05801i	−0.0125610	+	0.0386588i
$750$		0			0
$751$	1.87495	+	1.36223i	0.0684178	+	0.0497084i	0.621468	−	0.783439i	$-0.286536\pi$
$751$	1.87495	+	1.36223i	0.0684178	+	0.0497084i	−0.553051	+	0.833148i	$0.686536\pi$
$752$		0			0
$753$	15.9535	+	49.0998i	0.581378	+	1.78930i
$754$		0			0
$755$	0.473844	−	1.45834i	0.0172449	−	0.0530745i
$756$		0			0
$757$	29.8035	−	21.6535i	1.08323	−	0.787010i	0.104984	−	0.994474i	$-0.466521\pi$
$757$	29.8035	−	21.6535i	1.08323	−	0.787010i	0.978243	+	0.207464i	$0.0665209\pi$
$758$		0			0
$759$	−6.82320	+	4.95734i	−0.247666	+	0.179940i
$760$		0			0
$761$	−11.0813	−	8.05106i	−0.401698	−	0.291851i	0.368534	−	0.929614i	$-0.379860\pi$
$761$	−11.0813	−	8.05106i	−0.401698	−	0.291851i	−0.770232	+	0.637763i	$0.779860\pi$
$762$		0			0
$763$	−1.18720	+	0.862548i	−0.0429794	+	0.0312263i
$764$		0			0
$765$	−0.454486			−0.0164320
$766$		0			0
$767$	−24.7939	−	76.3079i	−0.895257	−	2.75532i
$768$		0			0
$769$	14.7900	−	45.5188i	0.533340	−	1.64145i	−0.213870	−	0.976862i	$-0.568607\pi$
$769$	14.7900	−	45.5188i	0.533340	−	1.64145i	0.747209	−	0.664589i	$-0.231393\pi$
$770$		0			0
$771$	−25.6530	+	78.9519i	−0.923871	+	2.84338i
$772$		0			0
$773$	27.1727	+	19.7421i	0.977333	+	0.710074i	0.957111	−	0.289721i	$-0.0935627\pi$
$773$	27.1727	+	19.7421i	0.977333	+	0.710074i	0.0202221	+	0.999796i	$0.493563\pi$
$774$		0			0
$775$	1.14986	+	3.53891i	0.0413043	+	0.127121i
$776$		0			0
$777$	18.1614	+	13.1950i	0.651538	+	0.473370i
$778$		0			0
$779$	−9.10236	−	2.89051i	−0.326126	−	0.103563i
$780$		0			0
$781$	−9.81687	−	7.13237i	−0.351275	−	0.255216i
$782$		0			0
$783$	33.0941	+	101.853i	1.18269	+	3.63993i
$784$		0			0
$785$	−8.99465	−	6.53499i	−0.321033	−	0.233244i
$786$		0			0
$787$	11.4717	−	35.3063i	0.408923	−	1.25854i	−0.508652	−	0.860972i	$-0.669856\pi$
$787$	11.4717	−	35.3063i	0.408923	−	1.25854i	0.917575	−	0.397563i	$-0.130144\pi$
$788$		0			0
$789$	7.19874	−	22.1554i	0.256282	−	0.788754i
$790$		0			0
$791$	0.371943	+	1.14472i	0.0132248	+	0.0407017i
$792$		0			0
$793$	56.8495			2.01878
$794$		0			0
$795$	−5.91466	+	4.29725i	−0.209771	+	0.152408i
$796$		0			0
$797$	−21.2277	−	15.4228i	−0.751924	−	0.546304i	0.144499	−	0.989505i	$-0.453843\pi$
$797$	−21.2277	−	15.4228i	−0.751924	−	0.546304i	−0.896423	+	0.443200i	$0.853843\pi$
$798$		0			0
$799$	0.00186424	−	0.00135445i	6.59519e−5	−	4.79169e-5i
$800$		0			0
$801$	104.087	−	75.6237i	3.67774	−	2.67203i
$802$		0			0
$803$	−2.75886	+	8.49091i	−0.0973581	+	0.299638i
$804$		0			0
$805$	−0.317547	−	0.977309i	−0.0111921	−	0.0344456i
$806$		0			0
$807$	−9.89068	−	7.18600i	−0.348168	−	0.252959i
$808$		0			0
$809$	−15.9418	+	49.0637i	−0.560482	+	1.72499i	0.120525	+	0.992710i	$0.461542\pi$
$809$	−15.9418	+	49.0637i	−0.560482	+	1.72499i	−0.681007	+	0.732277i	$0.738458\pi$
$810$		0			0
$811$	16.9148			0.593961			0.296980	−	0.954884i	$-0.404020\pi$
$811$	16.9148			0.593961			0.296980	+	0.954884i	$0.404020\pi$
$812$		0			0
$813$	12.0234	−	8.73555i	0.421681	−	0.306369i
$814$		0			0
$815$	−1.83629	−	5.65151i	−0.0643223	−	0.197964i
$816$		0			0
$817$	0.790960			0.0276722
$818$		0			0
$819$	53.8716			1.88243
$820$		0			0
$821$	−14.2362			−0.496845			−0.248423	−	0.968652i	$-0.579912\pi$
$821$	−14.2362			−0.496845			−0.248423	+	0.968652i	$0.579912\pi$
$822$		0			0
$823$	−50.2779			−1.75258			−0.876288	−	0.481787i	$-0.839988\pi$
$823$	−50.2779			−1.75258			−0.876288	+	0.481787i	$0.839988\pi$
$824$		0			0
$825$	−5.56025	−	17.1127i	−0.193583	−	0.595788i
$826$		0			0
$827$	7.25134	−	5.26840i	0.252154	−	0.183200i	−0.454527	−	0.890733i	$-0.650192\pi$
$827$	7.25134	−	5.26840i	0.252154	−	0.183200i	0.706681	+	0.707533i	$0.250192\pi$
$828$		0			0
$829$	−26.2974			−0.913347			−0.456673	−	0.889634i	$-0.650959\pi$
$829$	−26.2974			−0.913347			−0.456673	+	0.889634i	$0.650959\pi$
$830$		0			0
$831$	−20.0105	+	61.5861i	−0.694158	+	2.13640i
$832$		0			0
$833$	−0.0989907	−	0.0719209i	−0.00342982	−	0.00249191i
$834$		0			0
$835$	1.82824	+	5.62673i	0.0632687	+	0.194721i
$836$		0			0
$837$	4.09454	−	12.6017i	0.141528	−	0.435579i
$838$		0			0
$839$	−36.3900	+	26.4389i	−1.25632	+	0.912771i	−0.998571	−	0.0534403i	$-0.982981\pi$
$839$	−36.3900	+	26.4389i	−1.25632	+	0.912771i	−0.257751	+	0.966211i	$0.582981\pi$
$840$		0			0
$841$	−8.42453	+	6.12078i	−0.290501	+	0.211061i
$842$		0			0
$843$	43.5520	+	31.6424i	1.50001	+	1.08982i
$844$		0			0
$845$	11.4976	−	8.35348i	0.395529	−	0.287368i
$846$		0			0
$847$	−9.73093			−0.334359
$848$		0			0
$849$	−9.02021	−	27.7613i	−0.309573	−	0.952767i
$850$		0			0
$851$	4.67195	−	14.3788i	0.160152	−	0.492898i
$852$		0			0
$853$	8.48162	−	26.1037i	0.290405	−	0.893775i	−0.694321	−	0.719665i	$-0.744295\pi$
$853$	8.48162	−	26.1037i	0.290405	−	0.893775i	0.984726	−	0.174110i	$-0.0557048\pi$
$854$		0			0
$855$	4.48194	+	3.25632i	0.153279	+	0.111364i
$856$		0			0
$857$	13.3875	+	41.2026i	0.457310	+	1.40745i	0.868402	+	0.495860i	$0.165147\pi$
$857$	13.3875	+	41.2026i	0.457310	+	1.40745i	−0.411093	+	0.911594i	$0.634853\pi$
$858$		0			0
$859$	39.1462	+	28.4414i	1.33565	+	0.970407i	0.999592	+	0.0285653i	$0.00909387\pi$
$859$	39.1462	+	28.4414i	1.33565	+	0.970407i	0.336058	+	0.941841i	$0.390906\pi$
$860$		0			0
$861$	20.3475	+	6.46148i	0.693442	+	0.220207i
$862$		0			0
$863$	44.9969	+	32.6922i	1.53171	+	1.11286i	0.955277	+	0.295714i	$0.0955575\pi$
$863$	44.9969	+	32.6922i	1.53171	+	1.11286i	0.576437	+	0.817141i	$0.304442\pi$
$864$		0			0
$865$	1.84818	+	5.68811i	0.0628400	+	0.193402i
$866$		0			0
$867$	−45.8148	−	33.2864i	−1.55595	−	1.13047i
$868$		0			0
$869$	−2.39906	+	7.38353i	−0.0813824	+	0.250469i
$870$		0			0
$871$	19.7934	−	60.9178i	0.670674	−	2.06412i
$872$		0			0
$873$	16.7592	+	51.5794i	0.567211	+	1.74570i
$874$		0			0
$875$	4.48052			0.151469
$876$		0			0
$877$	−41.6907	+	30.2901i	−1.40779	+	1.02282i	−0.414156	+	0.910206i	$0.635923\pi$
$877$	−41.6907	+	30.2901i	−1.40779	+	1.02282i	−0.993639	+	0.112616i	$0.964077\pi$
$878$		0			0
$879$	−45.0467	−	32.7284i	−1.51939	−	1.10390i
$880$		0			0
$881$	−35.3264	+	25.6662i	−1.19018	+	0.864715i	−0.993283	−	0.115710i	$-0.963086\pi$
$881$	−35.3264	+	25.6662i	−1.19018	+	0.864715i	−0.196895	+	0.980425i	$0.563086\pi$
$882$		0			0
$883$	18.6120	−	13.5224i	0.626343	−	0.455065i	−0.228788	−	0.973476i	$-0.573476\pi$
$883$	18.6120	−	13.5224i	0.626343	−	0.455065i	0.855131	+	0.518411i	$0.173476\pi$
$884$		0			0
$885$	−5.69969	+	17.5418i	−0.191593	+	0.589663i
$886$		0			0
$887$	−16.4756	−	50.7066i	−0.553195	−	1.70256i	−0.700663	−	0.713493i	$-0.747112\pi$
$887$	−16.4756	−	50.7066i	−0.553195	−	1.70256i	0.147468	−	0.989067i	$-0.452888\pi$
$888$		0			0
$889$	7.22665	+	5.25047i	0.242374	+	0.176095i
$890$		0			0
$891$	−11.3231	+	34.8490i	−0.379339	+	1.16748i
$892$		0			0
$893$	−0.0280887			−0.000939951
$894$		0			0
$895$	−8.21585	+	5.96917i	−0.274626	+	0.199527i
$896$		0			0
$897$	−15.3556	−	47.2596i	−0.512708	−	1.57795i
$898$		0			0
$899$	4.87638			0.162636
$900$		0			0
$901$	0.586282			0.0195319
$902$		0			0
$903$	−1.76812			−0.0588394
$904$		0			0
$905$	5.41723			0.180075
$906$		0			0
$907$	−6.24001	−	19.2048i	−0.207196	−	0.637684i	−0.999616	−	0.0277079i	$-0.991179\pi$
$907$	−6.24001	−	19.2048i	−0.207196	−	0.637684i	0.792420	−	0.609976i	$-0.208821\pi$
$908$		0			0
$909$	−26.6948	+	19.3949i	−0.885411	+	0.643289i
$910$		0			0
$911$	8.88663			0.294427			0.147214	−	0.989105i	$-0.452970\pi$
$911$	8.88663			0.294427			0.147214	+	0.989105i	$0.452970\pi$
$912$		0			0
$913$	−1.66428	+	5.12213i	−0.0550796	+	0.169518i
$914$		0			0
$915$	−10.5728	−	7.68159i	−0.349526	−	0.253946i
$916$		0			0
$917$	−0.435171	−	1.33932i	−0.0143706	−	0.0442281i
$918$		0			0
$919$	−0.0283070	+	0.0871200i	−0.000933762	+	0.00287382i	−0.951522	−	0.307580i	$-0.900481\pi$
$919$	−0.0283070	+	0.0871200i	−0.000933762	+	0.00287382i	0.950589	+	0.310454i	$0.100481\pi$
$920$		0			0
$921$	−5.61073	+	4.07643i	−0.184880	+	0.134323i
$922$		0			0
$923$	57.8398	−	42.0231i	1.90382	−	1.38321i
$924$		0			0
$925$	26.0949	+	18.9590i	0.857994	+	0.623369i
$926$		0			0
$927$	−121.769	+	88.4700i	−3.99940	+	2.90574i
$928$		0			0
$929$	2.55450			0.0838104			0.0419052	−	0.999122i	$-0.486657\pi$
$929$	2.55450			0.0838104			0.0419052	+	0.999122i	$0.486657\pi$
$930$		0			0
$931$	0.460900	+	1.41850i	0.0151054	+	0.0464896i
$932$		0			0
$933$	22.1491	−	68.1679i	0.725129	−	2.23172i
$934$		0			0
$935$	0.0194932	−	0.0599938i	0.000637494	−	0.00196201i
$936$		0			0
$937$	3.33219	+	2.42098i	0.108858	+	0.0790899i	0.640882	−	0.767639i	$-0.278569\pi$
$937$	3.33219	+	2.42098i	0.108858	+	0.0790899i	−0.532025	+	0.846729i	$0.678569\pi$
$938$		0			0
$939$	0.587998	+	1.80967i	0.0191886	+	0.0590565i
$940$		0			0
$941$	−21.6470	−	15.7275i	−0.705673	−	0.512702i	0.176102	−	0.984372i	$-0.443651\pi$
$941$	−21.6470	−	15.7275i	−0.705673	−	0.512702i	−0.881775	+	0.471670i	$0.843651\pi$
$942$		0			0
$943$	−0.0959715	−	14.3776i	−0.00312526	−	0.468200i
$944$		0			0
$945$	−6.31575	−	4.58866i	−0.205451	−	0.149269i
$946$		0			0
$947$	13.0278	+	40.0956i	0.423348	+	1.30293i	0.904568	+	0.426330i	$0.140194\pi$
$947$	13.0278	+	40.0956i	0.423348	+	1.30293i	−0.481220	+	0.876600i	$0.659806\pi$
$948$		0			0
$949$	−42.5558	−	30.9186i	−1.38142	−	1.00366i
$950$		0			0
$951$	0.0930671	−	0.286431i	0.00301791	−	0.00928816i
$952$		0			0
$953$	−12.1951	+	37.5326i	−0.395038	+	1.21580i	0.533895	+	0.845551i	$0.320728\pi$
$953$	−12.1951	+	37.5326i	−0.395038	+	1.21580i	−0.928932	+	0.370250i	$0.879272\pi$
$954$		0			0
$955$	2.61198	+	8.03885i	0.0845218	+	0.260131i
$956$		0			0
$957$	−23.5801			−0.762238
$958$		0			0
$959$	15.5146	−	11.2720i	0.500991	−	0.363991i
$960$		0			0
$961$	24.5914	+	17.8667i	0.793272	+	0.576346i
$962$		0			0
$963$	7.30474	−	5.30720i	0.235392	−	0.171022i
$964$		0			0
$965$	7.45121	−	5.41362i	0.239863	−	0.174271i
$966$		0			0
$967$	0.811611	−	2.49788i	0.0260996	−	0.0803264i	−0.937158	−	0.348905i	$-0.886554\pi$
$967$	0.811611	−	2.49788i	0.0260996	−	0.0803264i	0.963258	+	0.268578i	$0.0865537\pi$
$968$		0			0
$969$	−0.188029	−	0.578695i	−0.00604037	−	0.0185904i
$970$		0			0
$971$	−8.54447	−	6.20792i	−0.274205	−	0.199222i	0.442181	−	0.896926i	$-0.354205\pi$
$971$	−8.54447	−	6.20792i	−0.274205	−	0.199222i	−0.716386	+	0.697704i	$0.754205\pi$
$972$		0			0
$973$	−3.67753	+	11.3183i	−0.117896	+	0.362847i
$974$		0			0
$975$	106.015			3.39519
$976$		0			0
$977$	−38.6556	+	28.0850i	−1.23670	+	0.898518i	−0.997374	−	0.0724207i	$-0.976928\pi$
$977$	−38.6556	+	28.0850i	−1.23670	+	0.898518i	−0.239329	+	0.970938i	$0.576928\pi$
$978$		0			0
$979$	5.51825	+	16.9834i	0.176364	+	0.542792i
$980$		0			0
$981$	11.9104			0.380271
$982$		0			0
$983$	5.08417			0.162160			0.0810800	−	0.996708i	$-0.474163\pi$
$983$	5.08417			0.162160			0.0810800	+	0.996708i	$0.474163\pi$
$984$		0			0
$985$	8.89727			0.283491
$986$		0			0
$987$	0.0627897			0.00199862
$988$		0			0
$989$	0.367975	+	1.13251i	0.0117009	+	0.0360117i
$990$		0			0
$991$	−29.4753	+	21.4150i	−0.936313	+	0.680271i	−0.947530	−	0.319666i	$-0.896429\pi$
$991$	−29.4753	+	21.4150i	−0.936313	+	0.680271i	0.0112176	+	0.999937i	$0.496429\pi$
$992$		0			0
$993$	20.4526			0.649044
$994$		0			0
$995$	3.33942	−	10.2777i	0.105867	−	0.325824i
$996$		0			0
$997$	10.4800	+	7.61415i	0.331904	+	0.241142i	0.741238	−	0.671242i	$-0.234239\pi$
$997$	10.4800	+	7.61415i	0.331904	+	0.241142i	−0.409334	+	0.912385i	$0.634239\pi$
$998$		0			0
$999$	−35.4927	−	109.235i	−1.12294	−	3.45605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.953.1	yes	24
41.37	even	5	inner	1148.2.n.d.365.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.365.1	✓	24	41.37	even	5	inner
1148.2.n.d.953.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-3.33413 q^{3} +(-0.141417 - 0.435238i) q^{5} +(-0.809017 + 0.587785i) q^{7} +8.11640 q^{9} +O(q^{10})\)	\(q-3.33413 q^{3} +(-0.141417 - 0.435238i) q^{5} +(-0.809017 + 0.587785i) q^{7} +8.11640 q^{9} +(-0.348117 + 1.07139i) q^{11} +(-5.36975 - 3.90135i) q^{13} +(0.471503 + 1.45114i) q^{15} +(0.0378111 - 0.116371i) q^{17} +(-1.20665 + 0.876684i) q^{19} +(2.69737 - 1.95975i) q^{21} +(-1.81662 - 1.31985i) q^{23} +(3.87565 - 2.81583i) q^{25} -17.0587 q^{27} +(-1.94001 - 5.97073i) q^{29} +(-0.240026 + 0.738725i) q^{31} +(1.16067 - 3.57216i) q^{33} +(0.370235 + 0.268992i) q^{35} +(2.08062 + 6.40349i) q^{37} +(17.9034 + 13.0076i) q^{39} +(3.79816 + 5.15500i) q^{41} +(-0.429030 - 0.311709i) q^{43} +(-1.14780 - 3.53256i) q^{45} +(0.0152358 + 0.0110694i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.126067 + 0.387994i) q^{51} +(1.48065 + 4.55697i) q^{53} +0.515541 q^{55} +(4.02313 - 2.92298i) q^{57} +(9.77967 + 7.10535i) q^{59} +(-6.92927 + 5.03441i) q^{61} +(-6.56631 + 4.77070i) q^{63} +(-0.938640 + 2.88884i) q^{65} +(2.98211 + 9.17800i) q^{67} +(6.05683 + 4.40054i) q^{69} +(-3.32855 + 10.2442i) q^{71} +7.92510 q^{73} +(-12.9219 + 9.38832i) q^{75} +(-0.348117 - 1.07139i) q^{77} +6.89152 q^{79} +32.5268 q^{81} +4.78081 q^{83} -0.0559960 q^{85} +(6.46824 + 19.9072i) q^{87} +(12.8243 - 9.31740i) q^{89} +6.63738 q^{91} +(0.800278 - 2.46300i) q^{93} +(0.552207 + 0.401202i) q^{95} +(2.06485 + 6.35495i) q^{97} +(-2.82546 + 8.69586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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