LMFDB - Embedded newform 592.2.be.c.399.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.1234538496.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 24x^{6} - 58x^{5} + 167x^{4} - 242x^{3} + 394x^{2} - 282x + 241 $ x^8 - 4x^7 + 24x^6 - 58x^5 + 167x^4 - 242x^3 + 394x^2 - 282*x + 241
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.2
Root			$0.500000 - 1.27030i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.c.319.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 2.36603i) q^{3} +(0.702139 + 2.62042i) q^{5} +(2.97244 + 1.71614i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(1.36603 - 2.36603i) q^{3} +(0.702139 + 2.62042i) q^{5} +(2.97244 + 1.71614i) q^{7} +(-2.23205 - 3.86603i) q^{9} +0.327773 q^{11} +(1.36603 + 5.09808i) q^{13} +(7.15912 + 1.91828i) q^{15} +(-2.97053 - 0.795952i) q^{17} +(3.12042 - 0.836114i) q^{19} +(8.12086 - 4.68858i) q^{21} +(0.136329 + 0.136329i) q^{23} +(-2.04347 + 1.17980i) q^{25} -4.00000 q^{27} +(-5.38238 - 5.38238i) q^{29} +(-5.98454 + 5.98454i) q^{31} +(0.447746 - 0.775518i) q^{33} +(-2.40994 + 8.99401i) q^{35} +(1.81186 - 5.80665i) q^{37} +(13.9282 + 3.73205i) q^{39} +(1.50000 + 0.866025i) q^{41} +(-4.88003 - 4.88003i) q^{43} +(8.56340 - 8.56340i) q^{45} -10.1643i q^{47} +(2.39028 + 4.14008i) q^{49} +(-5.94107 + 5.94107i) q^{51} +(-5.43228 - 9.40899i) q^{53} +(0.230142 + 0.858902i) q^{55} +(2.28431 - 8.52514i) q^{57} +(2.55225 - 9.52514i) q^{59} +(-9.67503 + 2.59242i) q^{61} -15.3221i q^{63} +(-12.4000 + 7.15912i) q^{65} +(3.16389 - 5.48001i) q^{67} +(0.508787 - 0.136329i) q^{69} +(10.5807 + 6.10877i) q^{71} +9.81326i q^{73} +6.44653i q^{75} +(0.974285 + 0.562504i) q^{77} +(-0.649885 + 0.174136i) q^{79} +(1.23205 - 2.13397i) q^{81} +(9.32256 - 5.38238i) q^{83} -8.34291i q^{85} +(-20.0873 + 5.38238i) q^{87} +(-1.63773 + 6.11208i) q^{89} +(-4.68858 + 17.4980i) q^{91} +(5.98454 + 22.3346i) q^{93} +(4.38194 + 7.58974i) q^{95} +(-12.0710 + 12.0710i) q^{97} +(-0.731605 - 1.26718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 2 * q^5 + 6 * q^7 - 4 * q^9	$ 8 q + 4 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 20 q^{23} - 36 q^{25} - 32 q^{27} + 4 q^{29} - 4 q^{31} + 16 q^{33} + 10 q^{35} + 6 q^{37} + 56 q^{39} + 12 q^{41} - 20 q^{43} - 4 q^{45} + 24 q^{49} + 16 q^{51} - 12 q^{53} - 26 q^{55} - 8 q^{57} + 8 q^{59} - 14 q^{61} + 12 q^{65} + 22 q^{67} - 28 q^{69} + 6 q^{71} - 60 q^{77} - 14 q^{79} - 4 q^{81} + 48 q^{83} - 40 q^{87} + 16 q^{89} - 4 q^{91} + 4 q^{93} + 30 q^{95} - 16 q^{97} - 34 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 2 * q^5 + 6 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 20 * q^23 - 36 * q^25 - 32 * q^27 + 4 * q^29 - 4 * q^31 + 16 * q^33 + 10 * q^35 + 6 * q^37 + 56 * q^39 + 12 * q^41 - 20 * q^43 - 4 * q^45 + 24 * q^49 + 16 * q^51 - 12 * q^53 - 26 * q^55 - 8 * q^57 + 8 * q^59 - 14 * q^61 + 12 * q^65 + 22 * q^67 - 28 * q^69 + 6 * q^71 - 60 * q^77 - 14 * q^79 - 4 * q^81 + 48 * q^83 - 40 * q^87 + 16 * q^89 - 4 * q^91 + 4 * q^93 + 30 * q^95 - 16 * q^97 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	−0.138104	−	0.990418i	$-0.544101\pi$
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	0.926779	−	0.375608i	$-0.122566\pi$
$4$		0			0
$5$	0.702139	+	2.62042i	0.314006	+	1.17189i	0.924911	+	0.380183i	$0.124139\pi$
$5$	0.702139	+	2.62042i	0.314006	+	1.17189i	−0.610905	+	0.791704i	$0.709194\pi$
$6$		0			0
$7$	2.97244	+	1.71614i	1.12348	+	0.648640i	0.942286	−	0.334808i	$-0.108671\pi$
$7$	2.97244	+	1.71614i	1.12348	+	0.648640i	0.181191	+	0.983448i	$0.442005\pi$
$8$		0			0
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$		0			0
$11$	0.327773			0.0988272			0.0494136	−	0.998778i	$-0.484265\pi$
$11$	0.327773			0.0988272			0.0494136	+	0.998778i	$0.484265\pi$
$12$		0			0
$13$	1.36603	+	5.09808i	0.378867	+	1.41395i	0.847611	+	0.530618i	$0.178040\pi$
$13$	1.36603	+	5.09808i	0.378867	+	1.41395i	−0.468744	+	0.883334i	$0.655293\pi$
$14$		0			0
$15$	7.15912	+	1.91828i	1.84848	+	0.495298i
$16$		0			0
$17$	−2.97053	−	0.795952i	−0.720460	−	0.193047i	−0.120083	−	0.992764i	$-0.538316\pi$
$17$	−2.97053	−	0.795952i	−0.720460	−	0.193047i	−0.600377	+	0.799717i	$0.704983\pi$
$18$		0			0
$19$	3.12042	−	0.836114i	0.715873	−	0.191818i	0.117544	−	0.993068i	$-0.462498\pi$
$19$	3.12042	−	0.836114i	0.715873	−	0.191818i	0.598330	+	0.801250i	$0.295831\pi$
$20$		0			0
$21$	8.12086	−	4.68858i	1.77212	−	1.02313i
$22$		0			0
$23$	0.136329	+	0.136329i	0.0284265	+	0.0284265i	0.721177	−	0.692751i	$-0.243601\pi$
$23$	0.136329	+	0.136329i	0.0284265	+	0.0284265i	−0.692751	+	0.721177i	$0.743601\pi$
$24$		0			0
$25$	−2.04347	+	1.17980i	−0.408694	+	0.235959i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−5.38238	−	5.38238i	−0.999483	−	0.999483i	0.000516767	−	1.00000i	$-0.499836\pi$
$29$	−5.38238	−	5.38238i	−0.999483	−	0.999483i	−1.00000		0.000516767i	$0.999836\pi$
$30$		0			0
$31$	−5.98454	+	5.98454i	−1.07485	+	1.07485i	−0.0778925	+	0.996962i	$0.524819\pi$
$31$	−5.98454	+	5.98454i	−1.07485	+	1.07485i	−0.996962	+	0.0778925i	$0.975181\pi$
$32$		0			0
$33$	0.447746	−	0.775518i	0.0779425	−	0.135000i
$34$		0			0
$35$	−2.40994	+	8.99401i	−0.407354	+	1.52027i
$36$		0			0
$37$	1.81186	−	5.80665i	0.297868	−	0.954607i
$37$	1.81186	−	5.80665i	0.297868	−	0.954607i
$38$		0			0
$39$	13.9282	+	3.73205i	2.23030	+	0.597606i
$40$		0			0
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	0.612536	−	0.790443i	$-0.290149\pi$
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	−0.378275	+	0.925693i	$0.623483\pi$
$42$		0			0
$43$	−4.88003	−	4.88003i	−0.744197	−	0.744197i	0.229186	−	0.973383i	$-0.426394\pi$
$43$	−4.88003	−	4.88003i	−0.744197	−	0.744197i	−0.973383	+	0.229186i	$0.926394\pi$
$44$		0			0
$45$	8.56340	−	8.56340i	1.27656	−	1.27656i
$46$		0			0
$47$		−	10.1643i		−	1.48262i	−0.671163	−	0.741310i	$-0.734205\pi$
$47$		−	10.1643i		−	1.48262i	0.671163	−	0.741310i	$-0.265795\pi$
$48$		0			0
$49$	2.39028	+	4.14008i	0.341468	+	0.591440i
$50$		0			0
$51$	−5.94107	+	5.94107i	−0.831916	+	0.831916i
$52$		0			0
$53$	−5.43228	−	9.40899i	−0.746181	−	1.29242i	−0.949641	−	0.313340i	$-0.898552\pi$
$53$	−5.43228	−	9.40899i	−0.746181	−	1.29242i	0.203460	−	0.979083i	$-0.434781\pi$
$54$		0			0
$55$	0.230142	+	0.858902i	0.0310323	+	0.115814i
$56$		0			0
$57$	2.28431	−	8.52514i	0.302564	−	1.12918i
$58$		0			0
$59$	2.55225	−	9.52514i	0.332275	−	1.24007i	−0.574518	−	0.818492i	$-0.694810\pi$
$59$	2.55225	−	9.52514i	0.332275	−	1.24007i	0.906793	−	0.421576i	$-0.138523\pi$
$60$		0			0
$61$	−9.67503	+	2.59242i	−1.23876	+	0.331925i	−0.817985	−	0.575240i	$-0.804909\pi$
$61$	−9.67503	+	2.59242i	−1.23876	+	0.331925i	−0.420776	+	0.907165i	$0.638242\pi$
$62$		0			0
$63$		−	15.3221i		−	1.93040i
$64$		0			0
$65$	−12.4000	+	7.15912i	−1.53803	+	0.887979i
$66$		0			0
$67$	3.16389	−	5.48001i	0.386530	−	0.669490i	−0.605450	−	0.795883i	$-0.707007\pi$
$67$	3.16389	−	5.48001i	0.386530	−	0.669490i	0.991980	+	0.126393i	$0.0403402\pi$
$68$		0			0
$69$	0.508787	−	0.136329i	0.0612507	−	0.0164121i
$70$		0			0
$71$	10.5807	+	6.10877i	1.25570	+	0.724978i	0.972235	−	0.234005i	$-0.0751833\pi$
$71$	10.5807	+	6.10877i	1.25570	+	0.724978i	0.283463	+	0.958983i	$0.408517\pi$
$72$		0			0
$73$			9.81326i			1.14856i	0.818660	+	0.574278i	$0.194717\pi$
$73$			9.81326i			1.14856i	−0.818660	+	0.574278i	$0.805283\pi$
$74$		0			0
$75$			6.44653i			0.744381i
$76$		0			0
$77$	0.974285	+	0.562504i	0.111030	+	0.0641033i
$78$		0			0
$79$	−0.649885	+	0.174136i	−0.0731178	+	0.0195918i	−0.295192	−	0.955438i	$-0.595384\pi$
$79$	−0.649885	+	0.174136i	−0.0731178	+	0.0195918i	0.222075	+	0.975030i	$0.428717\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		0			0
$83$	9.32256	−	5.38238i	1.02328	−	0.590793i	0.108230	−	0.994126i	$-0.465482\pi$
$83$	9.32256	−	5.38238i	1.02328	−	0.590793i	0.915053	+	0.403333i	$0.132148\pi$
$84$		0			0
$85$		−	8.34291i		−	0.904916i
$86$		0			0
$87$	−20.0873	+	5.38238i	−2.15359	+	0.577052i
$88$		0			0
$89$	−1.63773	+	6.11208i	−0.173599	+	0.647879i	0.823187	+	0.567770i	$0.192194\pi$
$89$	−1.63773	+	6.11208i	−0.173599	+	0.647879i	−0.996786	+	0.0801092i	$0.974473\pi$
$90$		0			0
$91$	−4.68858	+	17.4980i	−0.491497	+	1.83429i
$92$		0			0
$93$	5.98454	+	22.3346i	0.620567	+	2.31599i
$94$		0			0
$95$	4.38194	+	7.58974i	0.449577	+	0.778690i
$96$		0			0
$97$	−12.0710	+	12.0710i	−1.22562	+	1.22562i	−0.260017	+	0.965604i	$0.583728\pi$
$97$	−12.0710	+	12.0710i	−1.22562	+	1.22562i	−0.965604	+	0.260017i	$0.916272\pi$
$98$		0			0
$99$	−0.731605	−	1.26718i	−0.0735291	−	0.127356i
$100$		0			0
$101$			7.16433i			0.712878i	0.934319	+	0.356439i	$0.116009\pi$
$101$			7.16433i			0.712878i	−0.934319	+	0.356439i	$0.883991\pi$
$102$		0			0
$103$	−8.72040	+	8.72040i	−0.859247	+	0.859247i	−0.991249	−	0.132002i	$-0.957859\pi$
$103$	−8.72040	+	8.72040i	−0.859247	+	0.859247i	0.132002	+	0.991249i	$0.457859\pi$
$104$		0			0
$105$	17.9880	+	17.9880i	1.75545	+	1.75545i
$106$		0			0
$107$	−15.2116	−	8.78240i	−1.47056	−	0.849026i	−0.471103	−	0.882078i	$-0.656144\pi$
$107$	−15.2116	−	8.78240i	−1.47056	−	0.849026i	−0.999454	+	0.0330519i	$0.989477\pi$
$108$		0			0
$109$	16.3306	+	4.37576i	1.56419	+	0.419122i	0.933985	−	0.357311i	$-0.116306\pi$
$109$	16.3306	+	4.37576i	1.56419	+	0.419122i	0.630200	+	0.776433i	$0.282973\pi$
$110$		0			0
$111$	−11.2636	−	12.2189i	−1.06910	−	1.15977i
$112$		0			0
$113$	−0.840377	+	3.13633i	−0.0790560	+	0.295041i	−0.994122	−	0.108262i	$-0.965471\pi$
$113$	−0.840377	+	3.13633i	−0.0790560	+	0.295041i	0.915066	+	0.403303i	$0.132138\pi$
$114$		0			0
$115$	−0.261517	+	0.452961i	−0.0243866	+	0.0422388i
$116$		0			0
$117$	16.6603	−	16.6603i	1.54024	−	1.54024i
$118$		0			0
$119$	−7.46378	−	7.46378i	−0.684203	−	0.684203i
$120$		0			0
$121$	−10.8926			−0.990233
$122$		0			0
$123$	4.09808	−	2.36603i	0.369511	−	0.213337i
$124$		0			0
$125$	5.06504	+	5.06504i	0.453031	+	0.453031i
$126$		0			0
$127$	11.5470	−	6.66669i	1.02463	−	0.591573i	0.109191	−	0.994021i	$-0.465174\pi$
$127$	11.5470	−	6.66669i	1.02463	−	0.591573i	0.915443	+	0.402448i	$0.131841\pi$
$128$		0			0
$129$	−18.2125	+	4.88003i	−1.60352	+	0.429662i
$130$		0			0
$131$	2.81377	+	0.753948i	0.245840	+	0.0658727i	0.379635	−	0.925136i	$-0.376050\pi$
$131$	2.81377	+	0.753948i	0.245840	+	0.0658727i	−0.133795	+	0.991009i	$0.542716\pi$
$132$		0			0
$133$	10.7102	+	2.86978i	0.928688	+	0.248841i
$134$		0			0
$135$	−2.80856	−	10.4817i	−0.241722	−	0.902119i
$136$		0			0
$137$	8.76005			0.748422			0.374211	−	0.927344i	$-0.377914\pi$
$137$	8.76005			0.748422			0.374211	+	0.927344i	$0.377914\pi$
$138$		0			0
$139$	4.11443	+	7.12641i	0.348982	+	0.604454i	0.986069	−	0.166338i	$-0.0531942\pi$
$139$	4.11443	+	7.12641i	0.348982	+	0.604454i	−0.637087	+	0.770792i	$0.719861\pi$
$140$		0			0
$141$	−24.0491	−	13.8847i	−2.02530	−	1.16931i
$142$		0			0
$143$	0.447746	+	1.67101i	0.0374424	+	0.139737i
$144$		0			0
$145$	10.3249	−	17.8833i	0.857437	−	1.48512i
$146$		0			0
$147$	13.0607			1.07723
$148$		0			0
$149$	−18.7814			−1.53864			−0.769318	−	0.638866i	$-0.779404\pi$
$149$	−18.7814			−1.53864			−0.769318	+	0.638866i	$0.779404\pi$
$150$		0			0
$151$	−1.07007	+	1.85342i	−0.0870813	+	0.150829i	−0.906276	−	0.422686i	$-0.861087\pi$
$151$	−1.07007	+	1.85342i	−0.0870813	+	0.150829i	0.819195	+	0.573515i	$0.194421\pi$
$152$		0			0
$153$	3.55321	+	13.2608i	0.287260	+	1.07207i
$154$		0			0
$155$	−19.8840	−	11.4800i	−1.59712	−	0.922097i
$156$		0			0
$157$	−1.83376	−	3.17616i	−0.146350	−	0.253486i	0.783526	−	0.621359i	$-0.213419\pi$
$157$	−1.83376	−	3.17616i	−0.146350	−	0.253486i	−0.929876	+	0.367874i	$0.880086\pi$
$158$		0			0
$159$	−29.6825			−2.35398
$160$		0			0
$161$	0.171270	+	0.639190i	0.0134980	+	0.0503752i
$162$		0			0
$163$	14.8624	+	3.98237i	1.16411	+	0.311923i	0.788607	−	0.614897i	$-0.210803\pi$
$163$	14.8624	+	3.98237i	1.16411	+	0.311923i	0.375505	+	0.926820i	$0.377469\pi$
$164$		0			0
$165$	2.34656	+	0.628760i	0.182680	+	0.0489489i
$166$		0			0
$167$	−1.46532	+	0.392631i	−0.113390	+	0.0303827i	−0.315068	−	0.949069i	$-0.602027\pi$
$167$	−1.46532	+	0.392631i	−0.113390	+	0.0303827i	0.201678	+	0.979452i	$0.435361\pi$
$168$		0			0
$169$	−12.8660	+	7.42820i	−0.989694	+	0.571400i
$170$		0			0
$171$	−10.1974	−	10.1974i	−0.779812	−	0.779812i
$172$		0			0
$173$	−14.1645	+	8.17789i	−1.07691	+	0.621753i	−0.930061	−	0.367406i	$-0.880246\pi$
$173$	−14.1645	+	8.17789i	−1.07691	+	0.621753i	−0.146848	+	0.989159i	$0.546913\pi$
$174$		0			0
$175$	−8.09879			−0.612211
$176$		0			0
$177$	−19.0503	−	19.0503i	−1.43191	−	1.43191i
$178$		0			0
$179$	7.77292	−	7.77292i	0.580975	−	0.580975i	−0.354196	−	0.935171i	$-0.615245\pi$
$179$	7.77292	−	7.77292i	0.580975	−	0.580975i	0.935171	+	0.354196i	$0.115245\pi$
$180$		0			0
$181$	6.01305	−	10.4149i	0.446946	−	0.774134i	−0.551239	−	0.834347i	$-0.685845\pi$
$181$	6.01305	−	10.4149i	0.446946	−	0.774134i	0.998186	+	0.0602134i	$0.0191781\pi$
$182$		0			0
$183$	−7.08261	+	26.4327i	−0.523562	+	1.95396i
$184$		0			0
$185$	16.4880	+	0.670764i	1.21222	+	0.0493156i
$186$		0			0
$187$	−0.973660	−	0.260891i	−0.0712011	−	0.0190783i
$188$		0			0
$189$	−11.8898	−	6.86456i	−0.864854	−	0.499323i
$190$		0			0
$191$	−9.07740	−	9.07740i	−0.656817	−	0.656817i	0.297808	−	0.954626i	$-0.403744\pi$
$191$	−9.07740	−	9.07740i	−0.656817	−	0.656817i	−0.954626	+	0.297808i	$0.903744\pi$
$192$		0			0
$193$	10.2662	−	10.2662i	0.738979	−	0.738979i	−0.233401	−	0.972380i	$-0.574986\pi$
$193$	10.2662	−	10.2662i	0.738979	−	0.738979i	0.972380	+	0.233401i	$0.0749856\pi$
$194$		0			0
$195$			39.1181i			2.80131i
$196$		0			0
$197$	8.38429	+	14.5220i	0.597356	+	1.03465i	0.993210	+	0.116337i	$0.0371154\pi$
$197$	8.38429	+	14.5220i	0.597356	+	1.03465i	−0.395854	+	0.918314i	$0.629551\pi$
$198$		0			0
$199$	2.34795	−	2.34795i	0.166441	−	0.166441i	−0.618972	−	0.785413i	$-0.712450\pi$
$199$	2.34795	−	2.34795i	0.166441	−	0.166441i	0.785413	+	0.618972i	$0.212450\pi$
$200$		0			0
$201$	−8.64390	−	14.9717i	−0.609694	−	1.05602i
$202$		0			0
$203$	−6.76190	−	25.2357i	−0.474592	−	1.77120i
$204$		0			0
$205$	−1.21614	+	4.53870i	−0.0849389	+	0.316996i
$206$		0			0
$207$	0.222758	−	0.831344i	0.0154828	−	0.0577824i
$208$		0			0
$209$	1.02279	−	0.274055i	0.0707477	−	0.0189568i
$210$		0			0
$211$		−	2.99618i		−	0.206266i	−0.994668	−	0.103133i	$-0.967113\pi$
$211$		−	2.99618i		−	0.206266i	0.994668	−	0.103133i	$-0.0328867\pi$
$212$		0			0
$213$	28.9070	−	16.6895i	1.98068	−	1.14354i
$214$		0			0
$215$	9.36126	−	16.2142i	0.638432	−	1.10580i
$216$		0			0
$217$	−28.0590	+	7.51838i	−1.90477	+	0.510381i
$218$		0			0
$219$	23.2184	+	13.4052i	1.56896	+	0.905837i
$220$		0			0
$221$		−	16.2313i		−	1.09184i
$222$		0			0
$223$			22.7975i			1.52663i	0.646025	+	0.763316i	$0.276430\pi$
$223$			22.7975i			1.52663i	−0.646025	+	0.763316i	$0.723570\pi$
$224$		0			0
$225$	9.12225	+	5.26673i	0.608150	+	0.351115i
$226$		0			0
$227$	−10.1978	+	2.73250i	−0.676853	+	0.181362i	−0.580840	−	0.814018i	$-0.697276\pi$
$227$	−10.1978	+	2.73250i	−0.676853	+	0.181362i	−0.0960130	+	0.995380i	$0.530609\pi$
$228$		0			0
$229$	7.63677	−	13.2273i	0.504652	−	0.874083i	−0.495333	−	0.868703i	$-0.664954\pi$
$229$	7.63677	−	13.2273i	0.504652	−	0.874083i	0.999986	−	0.00538033i	$-0.00171262\pi$
$230$		0			0
$231$	2.66180	−	1.53679i	0.175133	−	0.101113i
$232$		0			0
$233$			21.6674i			1.41948i	0.704465	+	0.709739i	$0.251187\pi$
$233$			21.6674i			1.41948i	−0.704465	+	0.709739i	$0.748813\pi$
$234$		0			0
$235$	26.6348	−	7.13677i	1.73746	−	0.465552i
$236$		0			0
$237$	−0.475749	+	1.77552i	−0.0309032	+	0.115332i
$238$		0			0
$239$	0.487841	−	1.82065i	0.0315558	−	0.117768i	−0.948351	−	0.317222i	$-0.897250\pi$
$239$	0.487841	−	1.82065i	0.0315558	−	0.117768i	0.979907	+	0.199454i	$0.0639167\pi$
$240$		0			0
$241$	1.05130	+	3.92349i	0.0677200	+	0.252735i	0.991484	−	0.130227i	$-0.0415707\pi$
$241$	1.05130	+	3.92349i	0.0677200	+	0.252735i	−0.923764	+	0.382962i	$0.874904\pi$
$242$		0			0
$243$	−9.36603	−	16.2224i	−0.600831	−	1.04067i
$244$		0			0
$245$	−9.17044	+	9.17044i	−0.585878	+	0.585878i
$246$		0			0
$247$	8.52514	+	14.7660i	0.542442	+	0.939537i
$248$		0			0
$249$		−	29.4099i		−	1.86378i
$250$		0			0
$251$	−4.43106	+	4.43106i	−0.279686	+	0.279686i	−0.832984	−	0.553297i	$-0.813369\pi$
$251$	−4.43106	+	4.43106i	−0.279686	+	0.279686i	0.553297	+	0.832984i	$0.313369\pi$
$252$		0			0
$253$	0.0446849	+	0.0446849i	0.00280932	+	0.00280932i
$254$		0			0
$255$	−19.7395	−	11.3966i	−1.23614	−	0.713685i
$256$		0			0
$257$	−21.9904	−	5.89230i	−1.37172	−	0.367552i	−0.503615	−	0.863928i	$-0.667997\pi$
$257$	−21.9904	−	5.89230i	−1.37172	−	0.367552i	−0.868107	+	0.496376i	$0.834664\pi$
$258$		0			0
$259$	15.3507	−	14.1505i	0.953845	−	0.879270i
$260$		0			0
$261$	−8.79467	+	32.8222i	−0.544377	+	2.03164i
$262$		0			0
$263$	4.49592	−	7.78717i	0.277230	−	0.480177i	−0.693465	−	0.720490i	$-0.743917\pi$
$263$	4.49592	−	7.78717i	0.277230	−	0.480177i	0.970695	+	0.240313i	$0.0772501\pi$
$264$		0			0
$265$	20.8413	−	20.8413i	1.28027	−	1.28027i
$266$		0			0
$267$	12.2242	+	12.2242i	0.748106	+	0.748106i
$268$		0			0
$269$	15.5966			0.950942			0.475471	−	0.879731i	$-0.342278\pi$
$269$	15.5966			0.950942			0.475471	+	0.879731i	$0.342278\pi$
$270$		0			0
$271$	−7.98670	+	4.61113i	−0.485158	+	0.280106i	−0.722563	−	0.691305i	$-0.757036\pi$
$271$	−7.98670	+	4.61113i	−0.485158	+	0.280106i	0.237406	+	0.971411i	$0.423703\pi$
$272$		0			0
$273$	34.9961	+	34.9961i	2.11806	+	2.11806i
$274$		0			0
$275$	−0.669793	+	0.386705i	−0.0403900	+	0.0233192i
$276$		0			0
$277$	19.7401	−	5.28933i	1.18607	−	0.317805i	0.388736	−	0.921349i	$-0.372912\pi$
$277$	19.7401	−	5.28933i	1.18607	−	0.317805i	0.797330	+	0.603544i	$0.206245\pi$
$278$		0			0
$279$	36.4942	+	9.77858i	2.18485	+	0.585428i
$280$		0			0
$281$	5.85438	+	1.56868i	0.349243	+	0.0935794i	0.429176	−	0.903221i	$-0.358804\pi$
$281$	5.85438	+	1.56868i	0.349243	+	0.0935794i	−0.0799331	+	0.996800i	$0.525471\pi$
$282$		0			0
$283$	−2.20526	−	8.23014i	−0.131089	−	0.489231i	0.868894	−	0.494998i	$-0.164831\pi$
$283$	−2.20526	−	8.23014i	−0.131089	−	0.489231i	−0.999983	+	0.00576655i	$0.998164\pi$
$284$		0			0
$285$	23.9433			1.41828
$286$		0			0
$287$	2.97244	+	5.14842i	0.175458	+	0.303902i
$288$		0			0
$289$	−6.53190	−	3.77119i	−0.384229	−	0.221835i
$290$		0			0
$291$	12.0710	+	45.0495i	0.707612	+	2.64085i
$292$		0			0
$293$	−8.99809	+	15.5852i	−0.525674	+	0.910494i	0.473879	+	0.880590i	$0.342854\pi$
$293$	−8.99809	+	15.5852i	−0.525674	+	0.910494i	−0.999553	+	0.0299041i	$0.990480\pi$
$294$		0			0
$295$	26.7519			1.55756
$296$		0			0
$297$	−1.31109			−0.0760772
$298$		0			0
$299$	−0.508787	+	0.881244i	−0.0294239	+	0.0509637i
$300$		0			0
$301$	−6.13079	−	22.8804i	−0.353373	−	1.31881i
$302$		0			0
$303$	16.9510	+	9.78666i	0.973809	+	0.562229i
$304$		0			0
$305$	−13.5864	−	23.5324i	−0.777957	−	1.34746i
$306$		0			0
$307$	−25.6844			−1.46589			−0.732944	−	0.680289i	$-0.761854\pi$
$307$	−25.6844			−1.46589			−0.732944	+	0.680289i	$0.761854\pi$
$308$		0			0
$309$	8.72040	+	32.5450i	0.496086	+	1.85142i
$310$		0			0
$311$	−17.4821	−	4.68432i	−0.991320	−	0.265623i	−0.273515	−	0.961868i	$-0.588186\pi$
$311$	−17.4821	−	4.68432i	−0.991320	−	0.265623i	−0.717805	+	0.696244i	$0.754853\pi$
$312$		0			0
$313$	21.1189	+	5.65879i	1.19371	+	0.319854i	0.800351	−	0.599531i	$-0.204646\pi$
$313$	21.1189	+	5.65879i	1.19371	+	0.319854i	0.393359	+	0.919385i	$0.371313\pi$
$314$		0			0
$315$	40.1502	−	10.7582i	2.26221	−	0.606157i
$316$		0			0
$317$	−11.8355	+	6.83325i	−0.664750	+	0.383794i	−0.794085	−	0.607807i	$-0.792049\pi$
$317$	−11.8355	+	6.83325i	−0.664750	+	0.383794i	0.129334	+	0.991601i	$0.458716\pi$
$318$		0			0
$319$	−1.76420	−	1.76420i	−0.0987761	−	0.0987761i
$320$		0			0
$321$	−41.5587	+	23.9940i	−2.31958	+	1.33921i
$322$		0			0
$323$	−9.93482			−0.552788
$324$		0			0
$325$	−8.80612	−	8.80612i	−0.488476	−	0.488476i
$326$		0			0
$327$	32.6611	−	32.6611i	1.80617	−	1.80617i
$328$		0			0
$329$	17.4434	−	30.2129i	0.961687	−	1.66569i
$330$		0			0
$331$	5.29628	−	19.7660i	0.291110	−	1.08644i	−0.653148	−	0.757230i	$-0.726552\pi$
$331$	5.29628	−	19.7660i	0.291110	−	1.08644i	0.944258	−	0.329206i	$-0.106781\pi$
$332$		0			0
$333$	−26.4928	+	5.95603i	−1.45180	+	0.326388i
$334$		0			0
$335$	16.5814	+	4.44298i	0.905939	+	0.242746i
$336$		0			0
$337$	12.9166	+	7.45742i	0.703614	+	0.406232i	0.808692	−	0.588232i	$-0.200176\pi$
$337$	12.9166	+	7.45742i	0.703614	+	0.406232i	−0.105078	+	0.994464i	$0.533509\pi$
$338$		0			0
$339$	6.27266	+	6.27266i	0.340684	+	0.340684i
$340$		0			0
$341$	−1.96157	+	1.96157i	−0.106225	+	0.106225i
$342$		0			0
$343$		−	7.61776i		−	0.411321i
$344$		0			0
$345$	0.714478	+	1.23751i	0.0384662	+	0.0666254i
$346$		0			0
$347$	−18.4537	+	18.4537i	−0.990645	+	0.990645i	−0.999957	−	0.00931164i	$-0.997036\pi$
$347$	−18.4537	+	18.4537i	−0.990645	+	0.990645i	0.00931164	+	0.999957i	$0.497036\pi$
$348$		0			0
$349$	−2.88715	−	5.00069i	−0.154546	−	0.267681i	0.778348	−	0.627833i	$-0.216058\pi$
$349$	−2.88715	−	5.00069i	−0.154546	−	0.267681i	−0.932893	+	0.360152i	$0.882725\pi$
$350$		0			0
$351$	−5.46410	−	20.3923i	−0.291652	−	1.08846i
$352$		0			0
$353$	2.44018	−	9.10686i	0.129877	−	0.484709i	−0.870089	−	0.492895i	$-0.835939\pi$
$353$	2.44018	−	9.10686i	0.129877	−	0.484709i	0.999967	+	0.00818523i	$0.00260547\pi$
$354$		0			0
$355$	−8.57841	+	32.0151i	−0.455295	+	1.69918i
$356$		0			0
$357$	−27.8552	+	7.46378i	−1.47425	+	0.395025i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−7.41656	+	4.28195i	−0.390345	+	0.225366i
$362$		0			0
$363$	−14.8795	+	25.7721i	−0.780972	+	1.35268i
$364$		0			0
$365$	−25.7149	+	6.89028i	−1.34598	+	0.360654i
$366$		0			0
$367$	10.9070	+	6.29717i	0.569342	+	0.328710i	0.756886	−	0.653547i	$-0.226720\pi$
$367$	10.9070	+	6.29717i	0.569342	+	0.328710i	−0.187545	+	0.982256i	$0.560053\pi$
$368$		0			0
$369$		−	7.73205i		−	0.402514i
$370$		0			0
$371$		−	37.2902i		−	1.93601i
$372$		0			0
$373$	15.7924	+	9.11774i	0.817699	+	0.472099i	0.849622	−	0.527392i	$-0.176830\pi$
$373$	15.7924	+	9.11774i	0.817699	+	0.472099i	−0.0319235	+	0.999490i	$0.510163\pi$
$374$		0			0
$375$	18.9030	−	5.06504i	0.976146	−	0.261557i
$376$		0			0
$377$	20.0873	−	34.7923i	1.03455	−	1.79189i
$378$		0			0
$379$	−9.03054	+	5.21379i	−0.463868	+	0.267814i	−0.713669	−	0.700483i	$-0.752968\pi$
$379$	−9.03054	+	5.21379i	−0.463868	+	0.267814i	0.249801	+	0.968297i	$0.419635\pi$
$380$		0			0
$381$		−	36.4275i		−	1.86623i
$382$		0			0
$383$	16.1978	−	4.34019i	0.827670	−	0.221773i	0.179973	−	0.983672i	$-0.442399\pi$
$383$	16.1978	−	4.34019i	0.827670	−	0.221773i	0.647697	+	0.761898i	$0.275732\pi$
$384$		0			0
$385$	−0.789912	+	2.94799i	−0.0402576	+	0.150244i
$386$		0			0
$387$	−7.97384	+	29.7588i	−0.405333	+	1.51272i
$388$		0			0
$389$	−8.79169	−	32.8110i	−0.445756	−	1.66359i	−0.713932	−	0.700215i	$-0.753087\pi$
$389$	−8.79169	−	32.8110i	−0.445756	−	1.66359i	0.268176	−	0.963370i	$-0.413579\pi$
$390$		0			0
$391$	−0.296458	−	0.513481i	−0.0149925	−	0.0259679i
$392$		0			0
$393$	5.62754	−	5.62754i	0.283872	−	0.283872i
$394$		0			0
$395$	−0.912619	−	1.58070i	−0.0459189	−	0.0795338i
$396$		0			0
$397$			15.6237i			0.784132i	0.919937	+	0.392066i	$0.128240\pi$
$397$			15.6237i			0.784132i	−0.919937	+	0.392066i	$0.871760\pi$
$398$		0			0
$399$	21.4203	−	21.4203i	1.07236	−	1.07236i
$400$		0			0
$401$	4.42668	+	4.42668i	0.221058	+	0.221058i	0.808944	−	0.587886i	$-0.200040\pi$
$401$	4.42668	+	4.42668i	0.221058	+	0.221058i	−0.587886	+	0.808944i	$0.700040\pi$
$402$		0			0
$403$	−38.6846	−	22.3346i	−1.92702	−	1.11257i
$404$		0			0
$405$	6.45698	+	1.73014i	0.320850	+	0.0859714i
$406$		0			0
$407$	0.593879	−	1.90326i	0.0294375	−	0.0943411i
$408$		0			0
$409$	2.66261	−	9.93699i	0.131658	−	0.491353i	−0.868332	−	0.495984i	$-0.834808\pi$
$409$	2.66261	−	9.93699i	0.131658	−	0.491353i	0.999989	+	0.00463130i	$0.00147419\pi$
$410$		0			0
$411$	11.9665	−	20.7265i	0.590262	−	1.02236i
$412$		0			0
$413$	23.9329	−	23.9329i	1.17766	−	1.17766i
$414$		0			0
$415$	20.6498	+	20.6498i	1.01366	+	1.01366i
$416$		0			0
$417$	22.4817			1.10093
$418$		0			0
$419$	28.2118	−	16.2881i	1.37823	−	0.795724i	0.386287	−	0.922378i	$-0.373757\pi$
$419$	28.2118	−	16.2881i	1.37823	−	0.795724i	0.991947	+	0.126655i	$0.0404240\pi$
$420$		0			0
$421$	12.9101	+	12.9101i	0.629201	+	0.629201i	0.947867	−	0.318666i	$-0.103235\pi$
$421$	12.9101	+	12.9101i	0.629201	+	0.629201i	−0.318666	+	0.947867i	$0.603235\pi$
$422$		0			0
$423$	−39.2956	+	22.6873i	−1.91062	+	1.10309i
$424$		0			0
$425$	7.00925	−	1.87812i	0.339999	−	0.0911024i
$426$		0			0
$427$	−33.2074	−	8.89790i	−1.60702	−	0.430600i
$428$		0			0
$429$	4.56528	+	1.22326i	0.220414	+	0.0590598i
$430$		0			0
$431$	7.05855	+	26.3429i	0.339998	+	1.26889i	0.898348	+	0.439285i	$0.144768\pi$
$431$	7.05855	+	26.3429i	0.339998	+	1.26889i	−0.558350	+	0.829606i	$0.688565\pi$
$432$		0			0
$433$	−9.15479			−0.439951			−0.219976	−	0.975505i	$-0.570598\pi$
$433$	−9.15479			−0.439951			−0.219976	+	0.975505i	$0.570598\pi$
$434$		0			0
$435$	−28.2082	−	48.8580i	−1.35248	−	2.34256i
$436$		0			0
$437$	0.539390	+	0.311417i	0.0258025	+	0.0148971i
$438$		0			0
$439$	0.503187	+	1.87792i	0.0240158	+	0.0896282i	0.976894	−	0.213726i	$-0.0685601\pi$
$439$	0.503187	+	1.87792i	0.0240158	+	0.0896282i	−0.952878	+	0.303354i	$0.901893\pi$
$440$		0			0
$441$	10.6704	−	18.4817i	0.508116	−	0.880083i
$442$		0			0
$443$	−8.60132			−0.408661			−0.204331	−	0.978902i	$-0.565502\pi$
$443$	−8.60132			−0.408661			−0.204331	+	0.978902i	$0.565502\pi$
$444$		0			0
$445$	−17.1661			−0.813752
$446$		0			0
$447$	−25.6559	+	44.4374i	−1.21348	+	2.10182i
$448$		0			0
$449$	−3.59764	−	13.4266i	−0.169783	−	0.633639i	−0.997382	−	0.0723183i	$-0.976960\pi$
$449$	−3.59764	−	13.4266i	−0.169783	−	0.633639i	0.827599	−	0.561320i	$-0.189706\pi$
$450$		0			0
$451$	0.491659	+	0.283859i	0.0231513	+	0.0133664i
$452$		0			0
$453$	2.92349	+	5.06364i	0.137358	+	0.237911i
$454$		0			0
$455$	−49.1442			−2.30392
$456$		0			0
$457$	2.56486	+	9.57218i	0.119979	+	0.447768i	0.999611	−	0.0278870i	$-0.00887785\pi$
$457$	2.56486	+	9.57218i	0.119979	+	0.447768i	−0.879632	+	0.475655i	$0.842211\pi$
$458$		0			0
$459$	11.8821	+	3.18381i	0.554611	+	0.148607i
$460$		0			0
$461$	−29.1484	−	7.81028i	−1.35757	−	0.363761i	−0.494649	−	0.869093i	$-0.664703\pi$
$461$	−29.1484	−	7.81028i	−1.35757	−	0.363761i	−0.862925	+	0.505332i	$0.831370\pi$
$462$		0			0
$463$	−15.7384	+	4.21710i	−0.731427	+	0.195985i	−0.605264	−	0.796024i	$-0.706933\pi$
$463$	−15.7384	+	4.21710i	−0.731427	+	0.195985i	−0.126162	+	0.992010i	$0.540266\pi$
$464$		0			0
$465$	−54.3240	+	31.3640i	−2.51922	+	1.45447i
$466$		0			0
$467$	11.1002	+	11.1002i	0.513655	+	0.513655i	0.915644	−	0.401990i	$-0.131681\pi$
$467$	11.1002	+	11.1002i	0.513655	+	0.513655i	−0.401990	+	0.915644i	$0.631681\pi$
$468$		0			0
$469$	18.8089	−	10.8593i	0.868516	−	0.501438i
$470$		0			0
$471$	−10.0198			−0.461690
$472$		0			0
$473$	−1.59954	−	1.59954i	−0.0735469	−	0.0735469i
$474$		0			0
$475$	−5.39003	+	5.39003i	−0.247312	+	0.247312i
$476$		0			0
$477$	−24.2503	+	42.0027i	−1.11034	+	1.92317i
$478$		0			0
$479$	−1.83344	+	6.84249i	−0.0837719	+	0.312641i	−0.995079	−	0.0990867i	$-0.968408\pi$
$479$	−1.83344	+	6.84249i	−0.0837719	+	0.312641i	0.911307	+	0.411728i	$0.135075\pi$
$480$		0			0
$481$	32.0778	+	1.30498i	1.46262	+	0.0595022i
$482$		0			0
$483$	1.74630	+	0.467919i	0.0794593	+	0.0212911i
$484$		0			0
$485$	−40.1065	−	23.1555i	−1.82114	−	1.05144i
$486$		0			0
$487$	−4.76769	−	4.76769i	−0.216045	−	0.216045i	0.590785	−	0.806829i	$-0.298818\pi$
$487$	−4.76769	−	4.76769i	−0.216045	−	0.216045i	−0.806829	+	0.590785i	$0.798818\pi$
$488$		0			0
$489$	29.7248	−	29.7248i	1.34420	−	1.34420i
$490$		0			0
$491$		−	20.5625i		−	0.927973i	−0.885842	−	0.463987i	$-0.846419\pi$
$491$		−	20.5625i		−	0.927973i	0.885842	−	0.463987i	$-0.153581\pi$
$492$		0			0
$493$	11.7044	+	20.2727i	0.527141	+	0.913035i
$494$		0			0
$495$	2.80685	−	2.80685i	0.126158	−	0.126158i
$496$		0			0
$497$	20.9670	+	36.3159i	0.940499	+	1.62899i
$498$		0			0
$499$	3.52782	+	13.1660i	0.157927	+	0.589391i	0.998837	+	0.0482161i	$0.0153536\pi$
$499$	3.52782	+	13.1660i	0.157927	+	0.589391i	−0.840910	+	0.541175i	$0.817980\pi$
$500$		0			0
$501$	−1.07269	+	4.00333i	−0.0479242	+	0.178855i
$502$		0			0
$503$	0.0103692	−	0.0386983i	0.000462338	−	0.00172547i	−0.965694	−	0.259682i	$-0.916382\pi$
$503$	0.0103692	−	0.0386983i	0.000462338	−	0.00172547i	0.966157	+	0.257956i	$0.0830490\pi$
$504$		0			0
$505$	−18.7735	+	5.03036i	−0.835412	+	0.223848i
$506$		0			0
$507$			40.5885i			1.80260i
$508$		0			0
$509$	−13.5321	+	7.81275i	−0.599799	+	0.346294i	−0.768963	−	0.639294i	$-0.779227\pi$
$509$	−13.5321	+	7.81275i	−0.599799	+	0.346294i	0.169163	+	0.985588i	$0.445893\pi$
$510$		0			0
$511$	−16.8409	+	29.1694i	−0.744999	+	1.29038i
$512$		0			0
$513$	−12.4817	+	3.34445i	−0.551079	+	0.147661i
$514$		0			0
$515$	−28.9740	−	16.7282i	−1.27675	−	0.737131i
$516$		0			0
$517$		−	3.33159i		−	0.146523i
$518$		0			0
$519$			44.6848i			1.96145i
$520$		0			0
$521$	21.7806	+	12.5750i	0.954226	+	0.550923i	0.894391	−	0.447286i	$-0.147609\pi$
$521$	21.7806	+	12.5750i	0.954226	+	0.550923i	0.0598348	+	0.998208i	$0.480943\pi$
$522$		0			0
$523$	29.8816	−	8.00676i	1.30663	−	0.350111i	0.462678	−	0.886526i	$-0.346889\pi$
$523$	29.8816	−	8.00676i	1.30663	−	0.350111i	0.843954	+	0.536415i	$0.180222\pi$
$524$		0			0
$525$	−11.0631	+	19.1619i	−0.482835	+	0.836295i
$526$		0			0
$527$	22.5407	−	13.0139i	0.981887	−	0.566893i
$528$		0			0
$529$		−	22.9628i		−	0.998384i
$530$		0			0
$531$	−42.5212	+	11.3935i	−1.84526	+	0.494437i
$532$		0			0
$533$	−2.36603	+	8.83013i	−0.102484	+	0.382475i
$534$		0			0
$535$	12.3329	−	46.0271i	0.533199	−	1.98993i
$536$		0			0
$537$	−7.77292	−	29.0089i	−0.335426	−	1.25183i
$538$		0			0
$539$	0.783467	+	1.35701i	0.0337463	+	0.0584504i
$540$		0			0
$541$	3.81900	−	3.81900i	0.164192	−	0.164192i	−0.620229	−	0.784421i	$-0.712960\pi$
$541$	3.81900	−	3.81900i	0.164192	−	0.164192i	0.784421	+	0.620229i	$0.212960\pi$
$542$		0			0
$543$	−16.4280	−	28.4541i	−0.704991	−	1.22108i
$544$		0			0
$545$			45.8653i			1.96465i
$546$		0			0
$547$	0.0639673	−	0.0639673i	0.00273504	−	0.00273504i	−0.705738	−	0.708473i	$-0.749384\pi$
$547$	0.0639673	−	0.0639673i	0.00273504	−	0.00273504i	0.708473	+	0.705738i	$0.249384\pi$
$548$		0			0
$549$	31.6175	+	31.6175i	1.34940	+	1.34940i
$550$		0			0
$551$	−21.2956	−	12.2950i	−0.907222	−	0.523785i
$552$		0			0
$553$	−2.23059	−	0.597684i	−0.0948542	−	0.0254161i
$554$		0			0
$555$	24.1101	−	38.0948i	1.02342	−	1.61703i
$556$		0			0
$557$	−7.57802	+	28.2816i	−0.321091	+	1.19833i	0.597092	+	0.802173i	$0.296323\pi$
$557$	−7.57802	+	28.2816i	−0.321091	+	1.19833i	−0.918183	+	0.396156i	$0.870344\pi$
$558$		0			0
$559$	18.2125	−	31.5450i	0.770307	−	1.33421i
$560$		0			0
$561$	−1.94732	+	1.94732i	−0.0822159	+	0.0822159i
$562$		0			0
$563$	5.21092	+	5.21092i	0.219614	+	0.219614i	0.808336	−	0.588722i	$-0.200369\pi$
$563$	5.21092	+	5.21092i	0.219614	+	0.219614i	−0.588722	+	0.808336i	$0.700369\pi$
$564$		0			0
$565$	−8.80856			−0.370579
$566$		0			0
$567$	7.32440	−	4.22874i	0.307596	−	0.177591i
$568$		0			0
$569$	9.38587	+	9.38587i	0.393476	+	0.393476i	0.875924	−	0.482448i	$-0.160252\pi$
$569$	9.38587	+	9.38587i	0.393476	+	0.393476i	−0.482448	+	0.875924i	$0.660252\pi$
$570$		0			0
$571$	−28.4170	+	16.4066i	−1.18921	+	0.686593i	−0.958128	−	0.286340i	$-0.907561\pi$
$571$	−28.4170	+	16.4066i	−1.18921	+	0.686593i	−0.231087	+	0.972933i	$0.574228\pi$
$572$		0			0
$573$	−33.8773	+	9.07740i	−1.41524	+	0.379214i
$574$		0			0
$575$	−0.439424	−	0.117743i	−0.0183253	−	0.00491024i
$576$		0			0
$577$	3.61208	+	0.967853i	0.150373	+	0.0402923i	0.333220	−	0.942849i	$-0.391865\pi$
$577$	3.61208	+	0.967853i	0.150373	+	0.0402923i	−0.182847	+	0.983141i	$0.558531\pi$
$578$		0			0
$579$	−10.2662	−	38.3141i	−0.426650	−	1.59228i
$580$		0			0
$581$	36.9477			1.53285
$582$		0			0
$583$	−1.78055	−	3.08401i	−0.0737430	−	0.127727i
$584$		0			0
$585$	55.3547	+	31.9590i	2.28863	+	1.32134i
$586$		0			0
$587$	−1.21367	−	4.52947i	−0.0500934	−	0.186951i	0.936346	−	0.351080i	$-0.114185\pi$
$587$	−1.21367	−	4.52947i	−0.0500934	−	0.186951i	−0.986439	+	0.164129i	$0.947519\pi$
$588$		0			0
$589$	−13.6705	+	23.6780i	−0.563283	+	0.975635i
$590$		0			0
$591$	45.8126			1.88448
$592$		0			0
$593$	−11.3662			−0.466755			−0.233377	−	0.972386i	$-0.574978\pi$
$593$	−11.3662			−0.466755			−0.233377	+	0.972386i	$0.574978\pi$
$594$		0			0
$595$	14.3176	−	24.7988i	0.586965	−	1.01665i
$596$		0			0
$597$	−2.34795	−	8.76265i	−0.0960950	−	0.358632i
$598$		0			0
$599$	3.65548	+	2.11050i	0.149359	+	0.0862325i	0.572817	−	0.819683i	$-0.305851\pi$
$599$	3.65548	+	2.11050i	0.149359	+	0.0862325i	−0.423458	+	0.905916i	$0.639184\pi$
$600$		0			0
$601$	−2.88932	−	5.00445i	−0.117858	−	0.204136i	0.801061	−	0.598583i	$-0.204269\pi$
$601$	−2.88932	−	5.00445i	−0.117858	−	0.204136i	−0.918919	+	0.394447i	$0.870936\pi$
$602$		0			0
$603$	−28.2478			−1.15034
$604$		0			0
$605$	−7.64810	−	28.5431i	−0.310939	−	1.16044i
$606$		0			0
$607$	13.7449	+	3.68292i	0.557886	+	0.149485i	0.526735	−	0.850029i	$-0.323416\pi$
$607$	13.7449	+	3.68292i	0.557886	+	0.149485i	0.0311513	+	0.999515i	$0.490083\pi$
$608$		0			0
$609$	−68.9453	−	18.4738i	−2.79381	−	0.748598i
$610$		0			0
$611$	51.8185	−	13.8847i	2.09635	−	0.561716i
$612$		0			0
$613$	10.5104	−	6.06816i	0.424510	−	0.245091i	−0.272495	−	0.962157i	$-0.587849\pi$
$613$	10.5104	−	6.06816i	0.424510	−	0.245091i	0.697005	+	0.717066i	$0.254516\pi$
$614$		0			0
$615$	9.07740	+	9.07740i	0.366036	+	0.366036i
$616$		0			0
$617$	21.0066	−	12.1282i	0.845694	−	0.488262i	−0.0135014	−	0.999909i	$-0.504298\pi$
$617$	21.0066	−	12.1282i	0.845694	−	0.488262i	0.859196	+	0.511647i	$0.170964\pi$
$618$		0			0
$619$	−28.3337			−1.13883			−0.569415	−	0.822050i	$-0.692830\pi$
$619$	−28.3337			−1.13883			−0.569415	+	0.822050i	$0.692830\pi$
$620$		0			0
$621$	−0.545316	−	0.545316i	−0.0218828	−	0.0218828i
$622$		0			0
$623$	−15.3572	+	15.3572i	−0.615274	+	0.615274i
$624$		0			0
$625$	−15.6151	+	27.0462i	−0.624606	+	1.08185i
$626$		0			0
$627$	0.748733	−	2.79431i	0.0299015	−	0.111594i
$628$		0			0
$629$	−10.0040	+	15.8067i	−0.398886	+	0.630254i
$630$		0			0
$631$	−29.7110	−	7.96105i	−1.18278	−	0.316924i	−0.386750	−	0.922184i	$-0.626402\pi$
$631$	−29.7110	−	7.96105i	−1.18278	−	0.316924i	−0.796028	+	0.605260i	$0.793069\pi$
$632$		0			0
$633$	−7.08904	−	4.09286i	−0.281764	−	0.162677i
$634$		0			0
$635$	25.5771	+	25.5771i	1.01500	+	1.01500i
$636$		0			0
$637$	−17.8413	+	17.8413i	−0.706897	+	0.706897i
$638$		0			0
$639$		−	54.5404i		−	2.15758i
$640$		0			0
$641$	9.82345	+	17.0147i	0.388003	+	0.672041i	0.992181	−	0.124809i	$-0.0398317\pi$
$641$	9.82345	+	17.0147i	0.388003	+	0.672041i	−0.604178	+	0.796849i	$0.706498\pi$
$642$		0			0
$643$	2.00820	−	2.00820i	0.0791957	−	0.0791957i	−0.666399	−	0.745595i	$-0.732165\pi$
$643$	2.00820	−	2.00820i	0.0791957	−	0.0791957i	0.745595	+	0.666399i	$0.232165\pi$
$644$		0			0
$645$	−25.5754	−	44.2979i	−1.00703	−	1.74423i
$646$		0			0
$647$	−1.14441	−	4.27100i	−0.0449914	−	0.167910i	0.939775	−	0.341795i	$-0.111035\pi$
$647$	−1.14441	−	4.27100i	−0.0449914	−	0.167910i	−0.984766	+	0.173884i	$0.944368\pi$
$648$		0			0
$649$	0.836559	−	3.12208i	0.0328378	−	0.122552i
$650$		0			0
$651$	−20.5406	+	76.6586i	−0.805050	+	3.00449i
$652$		0			0
$653$	−5.70303	+	1.52812i	−0.223177	+	0.0598000i	−0.368675	−	0.929559i	$-0.620188\pi$
$653$	−5.70303	+	1.52812i	−0.223177	+	0.0598000i	0.145498	+	0.989359i	$0.453522\pi$
$654$		0			0
$655$			7.90263i			0.308781i
$656$		0			0
$657$	37.9383	−	21.9037i	1.48012	−	0.854545i
$658$		0			0
$659$	18.5698	−	32.1639i	0.723378	−	1.25293i	−0.236260	−	0.971690i	$-0.575922\pi$
$659$	18.5698	−	32.1639i	0.723378	−	1.25293i	0.959638	−	0.281237i	$-0.0907448\pi$
$660$		0			0
$661$	23.8888	−	6.40097i	0.929165	−	0.248969i	0.237666	−	0.971347i	$-0.423618\pi$
$661$	23.8888	−	6.40097i	0.929165	−	0.248969i	0.691498	+	0.722378i	$0.256951\pi$
$662$		0			0
$663$	−38.4037	−	22.1724i	−1.49147	−	0.861103i
$664$		0			0
$665$			30.0801i			1.16646i
$666$		0			0
$667$		−	1.46755i		−	0.0568237i
$668$		0			0
$669$	53.9394	+	31.1419i	2.08542	+	1.20402i
$670$		0			0
$671$	−3.17121	+	0.849723i	−0.122423	+	0.0328032i
$672$		0			0
$673$	7.08765	−	12.2762i	0.273209	−	0.473211i	−0.696473	−	0.717583i	$-0.745248\pi$
$673$	7.08765	−	12.2762i	0.273209	−	0.473211i	0.969682	+	0.244372i	$0.0785817\pi$
$674$		0			0
$675$	8.17387	−	4.71919i	0.314612	−	0.181642i
$676$		0			0
$677$			26.6406i			1.02388i	0.859020	+	0.511942i	$0.171074\pi$
$677$			26.6406i			1.02388i	−0.859020	+	0.511942i	$0.828926\pi$
$678$		0			0
$679$	−56.5957	+	15.1648i	−2.17194	+	0.581971i
$680$		0			0
$681$	−7.46532	+	27.8609i	−0.286072	+	1.06763i
$682$		0			0
$683$	−6.58522	+	24.5764i	−0.251976	+	0.940389i	0.717771	+	0.696279i	$0.245162\pi$
$683$	−6.58522	+	24.5764i	−0.251976	+	0.940389i	−0.969748	+	0.244110i	$0.921504\pi$
$684$		0			0
$685$	6.15078	+	22.9550i	0.235009	+	0.877066i
$686$		0			0
$687$	−20.8641	−	36.1376i	−0.796013	−	1.37874i
$688$		0			0
$689$	40.5471	−	40.5471i	1.54472	−	1.54472i
$690$		0			0
$691$	8.25796	+	14.3032i	0.314148	+	0.544120i	0.979256	−	0.202627i	$-0.0649479\pi$
$691$	8.25796	+	14.3032i	0.314148	+	0.544120i	−0.665108	+	0.746747i	$0.731615\pi$
$692$		0			0
$693$		−	5.02215i		−	0.190776i
$694$		0			0
$695$	−15.7853	+	15.7853i	−0.598769	+	0.598769i
$696$		0			0
$697$	−3.76649	−	3.76649i	−0.142666	−	0.142666i
$698$		0			0
$699$	51.2656	+	29.5982i	1.93904	+	1.11951i
$700$		0			0
$701$	27.2697	+	7.30690i	1.02996	+	0.275978i	0.733948	−	0.679206i	$-0.237676\pi$
$701$	27.2697	+	7.30690i	1.02996	+	0.275978i	0.296015	+	0.955183i	$0.404342\pi$
$702$		0			0
$703$	0.798752	−	19.6341i	0.0301255	−	0.740514i
$704$		0			0
$705$	19.4980	−	72.7676i	0.734338	−	2.74059i
$706$		0			0
$707$	−12.2950	+	21.2956i	−0.462401	+	0.800902i
$708$		0			0
$709$	−26.1177	+	26.1177i	−0.980872	+	0.980872i	−0.999820	−	0.0189480i	$-0.993968\pi$
$709$	−26.1177	+	26.1177i	−0.980872	+	0.980872i	0.0189480	+	0.999820i	$0.493968\pi$
$710$		0			0
$711$	2.12379	+	2.12379i	0.0796484	+	0.0796484i
$712$		0			0
$713$	−1.63173			−0.0611088
$714$		0			0
$715$	−4.06437	+	2.34656i	−0.151999	+	0.0877565i
$716$		0			0
$717$	−3.64130	−	3.64130i	−0.135987	−	0.135987i
$718$		0			0
$719$	−32.7406	+	18.9028i	−1.22102	+	0.704956i	−0.965135	−	0.261751i	$-0.915700\pi$
$719$	−32.7406	+	18.9028i	−1.22102	+	0.704956i	−0.255884	+	0.966707i	$0.582367\pi$
$720$		0			0
$721$	−40.8863	+	10.9555i	−1.52269	+	0.408003i
$722$		0			0
$723$	10.7192	+	2.87220i	0.398651	+	0.106818i
$724$		0			0
$725$	17.3488	+	4.64861i	0.644320	+	0.172645i
$726$		0			0
$727$	4.85608	+	18.1231i	0.180102	+	0.672150i	0.995626	+	0.0934269i	$0.0297821\pi$
$727$	4.85608	+	18.1231i	0.180102	+	0.672150i	−0.815524	+	0.578723i	$0.803551\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$		0			0
$731$	10.6120	+	18.3806i	0.392500	+	0.679829i
$732$		0			0
$733$	−11.2245	−	6.48046i	−0.414586	−	0.239361i	0.278172	−	0.960531i	$-0.410271\pi$
$733$	−11.2245	−	6.48046i	−0.414586	−	0.239361i	−0.692758	+	0.721170i	$0.743605\pi$
$734$		0			0
$735$	9.17044	+	34.2245i	0.338257	+	1.26239i
$736$		0			0
$737$	1.03704	−	1.79620i	0.0381997	−	0.0661638i
$738$		0			0
$739$	−1.81707			−0.0668421			−0.0334210	−	0.999441i	$-0.510640\pi$
$739$	−1.81707			−0.0668421			−0.0334210	+	0.999441i	$0.510640\pi$
$740$		0			0
$741$	46.5822			1.71124
$742$		0			0
$743$	−3.73682	+	6.47236i	−0.137091	+	0.237448i	−0.926394	−	0.376555i	$-0.877108\pi$
$743$	−3.73682	+	6.47236i	−0.137091	+	0.237448i	0.789304	+	0.614003i	$0.210442\pi$
$744$		0			0
$745$	−13.1872	−	49.2152i	−0.483141	−	1.80311i
$746$		0			0
$747$	−41.6168	−	24.0275i	−1.52268	−	0.879120i
$748$		0			0
$749$	−30.1437	−	52.2103i	−1.10143	−	1.90772i
$750$		0			0
$751$	−5.47263			−0.199699			−0.0998495	−	0.995003i	$-0.531836\pi$
$751$	−5.47263			−0.199699			−0.0998495	+	0.995003i	$0.531836\pi$
$752$		0			0
$753$	4.43106	+	16.5370i	0.161477	+	0.602640i
$754$		0			0
$755$	−5.60808	−	1.50268i	−0.204099	−	0.0546881i
$756$		0			0
$757$	−30.4521	−	8.15963i	−1.10680	−	0.296567i	−0.341271	−	0.939965i	$-0.610857\pi$
$757$	−30.4521	−	8.15963i	−1.10680	−	0.296567i	−0.765532	+	0.643398i	$0.777524\pi$
$758$		0			0
$759$	0.166766	−	0.0446849i	0.00605323	−	0.00162196i
$760$		0			0
$761$	−6.66638	+	3.84884i	−0.241656	+	0.139520i	−0.615938	−	0.787795i	$-0.711223\pi$
$761$	−6.66638	+	3.84884i	−0.241656	+	0.139520i	0.374282	+	0.927315i	$0.377889\pi$
$762$		0			0
$763$	41.0323	+	41.0323i	1.48547	+	1.48547i
$764$		0			0
$765$	−32.2539	+	18.6218i	−1.16614	+	0.673273i
$766$		0			0
$767$	52.0463			1.87928
$768$		0			0
$769$	16.4911	+	16.4911i	0.594684	+	0.594684i	0.938893	−	0.344209i	$-0.111853\pi$
$769$	16.4911	+	16.4911i	0.594684	+	0.594684i	−0.344209	+	0.938893i	$0.611853\pi$
$770$		0			0
$771$	−43.9808	+	43.9808i	−1.58393	+	1.58393i
$772$		0			0
$773$	14.3916	−	24.9270i	0.517630	−	0.896562i	−0.482160	−	0.876083i	$-0.660148\pi$
$773$	14.3916	−	24.9270i	0.517630	−	0.896562i	0.999790	−	0.0204789i	$-0.00651908\pi$
$774$		0			0
$775$	5.16867	−	19.2897i	0.185664	−	0.692908i
$776$		0			0
$777$	−12.5111	−	55.6501i	−0.448832	−	1.99643i
$778$		0			0
$779$	5.40472	+	1.44819i	0.193644	+	0.0518868i
$780$		0			0
$781$	3.46807	+	2.00229i	0.124097	+	0.0716475i
$782$		0			0
$783$	21.5295	+	21.5295i	0.769402	+	0.769402i
$784$		0			0
$785$	7.03533	−	7.03533i	0.251102	−	0.251102i
$786$		0			0
$787$		−	39.5980i		−	1.41152i	−0.708452	−	0.705759i	$-0.750606\pi$
$787$		−	39.5980i		−	1.41152i	0.708452	−	0.705759i	$-0.249394\pi$
$788$		0			0
$789$	−12.2831	−	21.2749i	−0.437290	−	0.757408i
$790$		0			0
$791$	−7.88035	+	7.88035i	−0.280193	+	0.280193i
$792$		0			0
$793$	−26.4327	−	45.7827i	−0.938651	−	1.62579i
$794$		0			0
$795$	−20.8413	−	77.7807i	−0.739164	−	2.75860i
$796$		0			0
$797$	−0.529792	+	1.97721i	−0.0187662	+	0.0700364i	−0.974674	−	0.223631i	$-0.928209\pi$
$797$	−0.529792	+	1.97721i	−0.0187662	+	0.0700364i	0.955908	+	0.293667i	$0.0948757\pi$
$798$		0			0
$799$	−8.09032	+	30.1935i	−0.286215	+	1.06817i
$800$		0			0
$801$	27.2849	−	7.31098i	0.964066	−	0.258321i
$802$		0			0
$803$			3.21652i			0.113509i
$804$		0			0
$805$	−1.55469	+	0.897600i	−0.0547956	+	0.0316362i
$806$		0			0
$807$	21.3054	−	36.9020i	0.749985	−	1.29901i
$808$		0			0
$809$	−5.46670	+	1.46480i	−0.192199	+	0.0514996i	−0.353634	−	0.935384i	$-0.615054\pi$
$809$	−5.46670	+	1.46480i	−0.192199	+	0.0514996i	0.161435	+	0.986883i	$0.448388\pi$
$810$		0			0
$811$	48.6511	+	28.0887i	1.70837	+	0.986328i	0.936582	+	0.350450i	$0.113971\pi$
$811$	48.6511	+	28.0887i	1.70837	+	0.986328i	0.771789	+	0.635879i	$0.219362\pi$
$812$		0			0
$813$			25.1957i			0.883650i
$814$		0			0
$815$			41.7419i			1.46215i
$816$		0			0
$817$	−19.3080	−	11.1475i	−0.675501	−	0.390001i
$818$		0			0
$819$	78.1130	−	20.9303i	2.72949	−	0.731364i
$820$		0			0
$821$	−21.0111	+	36.3924i	−0.733294	+	1.27010i	0.222174	+	0.975007i	$0.428685\pi$
$821$	−21.0111	+	36.3924i	−0.733294	+	1.27010i	−0.955468	+	0.295095i	$0.904649\pi$
$822$		0			0
$823$	−36.9354	+	21.3247i	−1.28749	+	0.743331i	−0.978205	−	0.207639i	$-0.933422\pi$
$823$	−36.9354	+	21.3247i	−1.28749	+	0.743331i	−0.309282	+	0.950970i	$0.600089\pi$
$824$		0			0
$825$			2.11300i			0.0735651i
$826$		0			0
$827$	43.3497	−	11.6155i	1.50742	−	0.403911i	0.591841	−	0.806055i	$-0.298401\pi$
$827$	43.3497	−	11.6155i	1.50742	−	0.403911i	0.915577	+	0.402143i	$0.131735\pi$
$828$		0			0
$829$	7.70195	−	28.7441i	0.267500	−	0.998323i	−0.693203	−	0.720743i	$-0.743801\pi$
$829$	7.70195	−	28.7441i	0.267500	−	0.998323i	0.960702	−	0.277580i	$-0.0895325\pi$
$830$		0			0
$831$	14.4507	−	53.9309i	0.501290	−	1.87084i
$832$		0			0
$833$	−3.80509	−	14.2008i	−0.131839	−	0.492028i
$834$		0			0
$835$	−2.05772	−	3.56407i	−0.0712102	−	0.123340i
$836$		0			0
$837$	23.9381	−	23.9381i	0.827423	−	0.827423i
$838$		0			0
$839$	−23.8427	−	41.2967i	−0.823140	−	1.42572i	−0.903332	−	0.428941i	$-0.858887\pi$
$839$	−23.8427	−	41.2967i	−0.823140	−	1.42572i	0.0801922	−	0.996779i	$-0.474447\pi$
$840$		0			0
$841$			28.9401i			0.997933i
$842$		0			0
$843$	11.7088	−	11.7088i	0.403271	−	0.403271i
$844$		0			0
$845$	−28.4987	−	28.4987i	−0.980387	−	0.980387i
$846$		0			0
$847$	−32.3775	−	18.6932i	−1.11250	−	0.642305i
$848$		0			0
$849$	−22.4852	−	6.02488i	−0.771689	−	0.206773i
$850$		0			0
$851$	1.03862	−	0.544605i	0.0356035	−	0.0186688i
$852$		0			0
$853$	0.879277	−	3.28151i	0.0301059	−	0.112357i	−0.949238	−	0.314559i	$-0.898143\pi$
$853$	0.879277	−	3.28151i	0.0301059	−	0.112357i	0.979344	+	0.202203i	$0.0648100\pi$
$854$		0			0
$855$	19.5614	−	33.8813i	0.668986	−	1.15872i
$856$		0			0
$857$	−16.9084	+	16.9084i	−0.577580	+	0.577580i	−0.934236	−	0.356656i	$-0.883917\pi$
$857$	−16.9084	+	16.9084i	−0.577580	+	0.577580i	0.356656	+	0.934236i	$0.383917\pi$
$858$		0			0
$859$	7.90625	+	7.90625i	0.269758	+	0.269758i	0.829003	−	0.559245i	$-0.188909\pi$
$859$	7.90625	+	7.90625i	0.269758	+	0.269758i	−0.559245	+	0.829003i	$0.688909\pi$
$860$		0			0
$861$	16.2417			0.553517
$862$		0			0
$863$	−20.1073	+	11.6090i	−0.684461	+	0.395173i	−0.801534	−	0.597950i	$-0.795982\pi$
$863$	−20.1073	+	11.6090i	−0.684461	+	0.395173i	0.117073	+	0.993123i	$0.462649\pi$
$864$		0			0
$865$	−31.3750	−	31.3750i	−1.06678	−	1.06678i
$866$		0			0
$867$	−17.8455	+	10.3031i	−0.606064	+	0.349911i
$868$		0			0
$869$	−0.213015	+	0.0570771i	−0.00722602	+	0.00193621i
$870$		0			0
$871$	32.2595	+	8.64390i	1.09307	+	0.292887i
$872$		0			0
$873$	73.6097	+	19.7236i	2.49131	+	0.667544i
$874$		0			0
$875$	6.36322	+	23.7479i	0.215116	+	0.802824i
$876$		0			0
$877$	56.2234			1.89853			0.949264	−	0.314479i	$-0.101830\pi$
$877$	56.2234			1.89853			0.949264	+	0.314479i	$0.101830\pi$
$878$		0			0
$879$	24.5832	+	42.5794i	0.829172	+	1.43617i
$880$		0			0
$881$	−3.38021	−	1.95156i	−0.113882	−	0.0657498i	0.441977	−	0.897026i	$-0.354277\pi$
$881$	−3.38021	−	1.95156i	−0.113882	−	0.0657498i	−0.555859	+	0.831277i	$0.687611\pi$
$882$		0			0
$883$	−13.5593	−	50.6038i	−0.456305	−	1.70295i	−0.684222	−	0.729273i	$-0.739858\pi$
$883$	−13.5593	−	50.6038i	−0.456305	−	1.70295i	0.227917	−	0.973681i	$-0.426808\pi$
$884$		0			0
$885$	36.5438	−	63.2957i	1.22841	−	2.12766i
$886$		0			0
$887$	48.2501			1.62008			0.810040	−	0.586374i	$-0.199445\pi$
$887$	48.2501			1.62008			0.810040	+	0.586374i	$0.199445\pi$
$888$		0			0
$889$	45.7639			1.53487
$890$		0			0
$891$	0.403833	−	0.699459i	0.0135289	−	0.0234327i
$892$		0			0
$893$	−8.49854	−	31.7170i	−0.284393	−	1.06137i
$894$		0			0
$895$	25.8260	+	14.9106i	0.863267	+	0.498407i
$896$		0			0
$897$	1.39003	+	2.40760i	0.0464118	+	0.0803875i
$898$		0			0
$899$	64.4221			2.14860
$900$		0			0
$901$	8.64767	+	32.2735i	0.288096	+	1.07519i
$902$		0			0
$903$	−62.5104	−	16.7496i	−2.08022	−	0.557393i
$904$		0			0
$905$	31.5134	+	8.44399i	1.04754	+	0.280688i
$906$		0			0
$907$	12.7668	−	3.42084i	0.423913	−	0.113587i	−0.0405545	−	0.999177i	$-0.512912\pi$
$907$	12.7668	−	3.42084i	0.423913	−	0.113587i	0.464467	+	0.885590i	$0.346246\pi$
$908$		0			0
$909$	27.6975	−	15.9912i	0.918668	−	0.530393i
$910$		0			0
$911$	−24.4984	−	24.4984i	−0.811667	−	0.811667i	0.173217	−	0.984884i	$-0.444584\pi$
$911$	−24.4984	−	24.4984i	−0.811667	−	0.811667i	−0.984884	+	0.173217i	$0.944584\pi$
$912$		0			0
$913$	3.05568	−	1.76420i	0.101128	−	0.0583864i
$914$		0			0
$915$	−74.2376			−2.45422
$916$		0			0
$917$	7.06989	+	7.06989i	0.233468	+	0.233468i
$918$		0			0
$919$	13.6495	−	13.6495i	0.450254	−	0.450254i	−0.445185	−	0.895439i	$-0.646862\pi$
$919$	13.6495	−	13.6495i	0.450254	−	0.450254i	0.895439	+	0.445185i	$0.146862\pi$
$920$		0			0
$921$	−35.0856	+	60.7700i	−1.15611	+	2.00244i
$922$		0			0
$923$	−16.6895	+	62.2860i	−0.549341	+	2.05017i
$924$		0			0
$925$	3.14818	+	14.0033i	0.103512	+	0.460427i
$926$		0			0
$927$	53.1777	+	14.2489i	1.74658	+	0.467996i
$928$		0			0
$929$	26.4213	+	15.2543i	0.866854	+	0.500478i	0.866302	−	0.499521i	$-0.166491\pi$
$929$	26.4213	+	15.2543i	0.866854	+	0.500478i	0.000552515		1.00000i	$0.499824\pi$
$930$		0			0
$931$	10.9202	+	10.9202i	0.357896	+	0.357896i
$932$		0			0
$933$	−34.9642	+	34.9642i	−1.14468	+	1.14468i
$934$		0			0
$935$		−	2.73458i		−	0.0894303i
$936$		0			0
$937$	13.5026	+	23.3872i	0.441111	+	0.764027i	0.997772	−	0.0667127i	$-0.0212511\pi$
$937$	13.5026	+	23.3872i	0.441111	+	0.764027i	−0.556661	+	0.830740i	$0.687918\pi$
$938$		0			0
$939$	42.2378	−	42.2378i	1.37838	−	1.37838i
$940$		0			0
$941$	19.3612	+	33.5346i	0.631157	+	1.09320i	0.987316	+	0.158770i	$0.0507529\pi$
$941$	19.3612	+	33.5346i	0.631157	+	1.09320i	−0.356159	+	0.934425i	$0.615914\pi$
$942$		0			0
$943$	0.0864291	+	0.322558i	0.00281452	+	0.0105039i
$944$		0			0
$945$	9.63975	−	35.9761i	0.313581	−	1.17030i
$946$		0			0
$947$	−11.1694	+	41.6846i	−0.362956	+	1.35457i	0.507215	+	0.861819i	$0.330675\pi$
$947$	−11.1694	+	41.6846i	−0.362956	+	1.35457i	−0.870171	+	0.492750i	$0.835992\pi$
$948$		0			0
$949$	−50.0288	+	13.4052i	−1.62400	+	0.435150i
$950$		0			0
$951$			37.3376i			1.21075i
$952$		0			0
$953$	−25.9510	+	14.9828i	−0.840635	+	0.485341i	−0.857480	−	0.514517i	$-0.827971\pi$
$953$	−25.9510	+	14.9828i	−0.840635	+	0.485341i	0.0168450	+	0.999858i	$0.494638\pi$
$954$		0			0
$955$	17.4130	−	30.1602i	0.563471	−	0.975960i
$956$		0			0
$957$	−6.58407	+	1.76420i	−0.212833	+	0.0570284i
$958$		0			0
$959$	26.0388	+	15.0335i	0.840835	+	0.485456i
$960$		0			0
$961$		−	40.6293i		−	1.31062i
$962$		0			0
$963$			78.4110i			2.52676i
$964$		0			0
$965$	34.1101	+	19.6935i	1.09804	+	0.633956i
$966$		0			0
$967$	43.8924	−	11.7609i	1.41149	−	0.378206i	0.529031	−	0.848603i	$-0.322556\pi$
$967$	43.8924	−	11.7609i	1.41149	−	0.378206i	0.882455	+	0.470396i	$0.155889\pi$
$968$		0			0
$969$	−13.5712	+	23.5060i	−0.435970	+	0.755122i
$970$		0			0
$971$	7.67606	−	4.43177i	0.246336	−	0.142222i	−0.371749	−	0.928333i	$-0.621242\pi$
$971$	7.67606	−	4.43177i	0.246336	−	0.142222i	0.618086	+	0.786111i	$0.287909\pi$
$972$		0			0
$973$			28.2438i			0.905454i
$974$		0			0
$975$	−32.8649	+	8.80612i	−1.05252	+	0.282022i
$976$		0			0
$977$	−14.2289	+	53.1028i	−0.455222	+	1.69891i	0.232214	+	0.972665i	$0.425403\pi$
$977$	−14.2289	+	53.1028i	−0.455222	+	1.69891i	−0.687435	+	0.726246i	$0.741263\pi$
$978$		0			0
$979$	−0.536802	+	2.00337i	−0.0171563	+	0.0640280i
$980$		0			0
$981$	−19.5339	−	72.9013i	−0.623668	−	2.32756i
$982$		0			0
$983$	21.5148	+	37.2648i	0.686216	+	1.18856i	0.973053	+	0.230582i	$0.0740629\pi$
$983$	21.5148	+	37.2648i	0.686216	+	1.18856i	−0.286837	+	0.957979i	$0.592604\pi$
$984$		0			0
$985$	−32.1668	+	32.1668i	−1.02492	+	1.02492i
$986$		0			0
$987$	−47.6563	−	82.5432i	−1.51692	−	2.62738i
$988$		0			0
$989$		−	1.33058i		−	0.0423099i
$990$		0			0
$991$	18.4829	−	18.4829i	0.587128	−	0.587128i	−0.349724	−	0.936853i	$-0.613725\pi$
$991$	18.4829	−	18.4829i	0.587128	−	0.587128i	0.936853	+	0.349724i	$0.113725\pi$
$992$		0			0
$993$	−39.5320	−	39.5320i	−1.25451	−	1.25451i
$994$		0			0
$995$	7.80119	+	4.50402i	0.247314	+	0.142787i
$996$		0			0
$997$	−9.71608	−	2.60342i	−0.307711	−	0.0824510i	0.101659	−	0.994819i	$-0.467585\pi$
$997$	−9.71608	−	2.60342i	−0.307711	−	0.0824510i	−0.409370	+	0.912368i	$0.634252\pi$
$998$		0			0
$999$	−7.24745	+	23.2266i	−0.229299	+	0.734857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.c.399.2	yes	8
4.3	odd	2		592.2.be.b.399.2	yes	8
37.23	odd	12		592.2.be.b.319.2	✓	8
148.23	even	12	inner	592.2.be.c.319.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.b.319.2	✓	8	37.23	odd	12
592.2.be.b.399.2	yes	8	4.3	odd	2
592.2.be.c.319.2	yes	8	148.23	even	12	inner
592.2.be.c.399.2	yes	8	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 2.36603i) q^{3} +(0.702139 + 2.62042i) q^{5} +(2.97244 + 1.71614i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 2.36603i) q^{3} +(0.702139 + 2.62042i) q^{5} +(2.97244 + 1.71614i) q^{7} +(-2.23205 - 3.86603i) q^{9} +0.327773 q^{11} +(1.36603 + 5.09808i) q^{13} +(7.15912 + 1.91828i) q^{15} +(-2.97053 - 0.795952i) q^{17} +(3.12042 - 0.836114i) q^{19} +(8.12086 - 4.68858i) q^{21} +(0.136329 + 0.136329i) q^{23} +(-2.04347 + 1.17980i) q^{25} -4.00000 q^{27} +(-5.38238 - 5.38238i) q^{29} +(-5.98454 + 5.98454i) q^{31} +(0.447746 - 0.775518i) q^{33} +(-2.40994 + 8.99401i) q^{35} +(1.81186 - 5.80665i) q^{37} +(13.9282 + 3.73205i) q^{39} +(1.50000 + 0.866025i) q^{41} +(-4.88003 - 4.88003i) q^{43} +(8.56340 - 8.56340i) q^{45} -10.1643i q^{47} +(2.39028 + 4.14008i) q^{49} +(-5.94107 + 5.94107i) q^{51} +(-5.43228 - 9.40899i) q^{53} +(0.230142 + 0.858902i) q^{55} +(2.28431 - 8.52514i) q^{57} +(2.55225 - 9.52514i) q^{59} +(-9.67503 + 2.59242i) q^{61} -15.3221i q^{63} +(-12.4000 + 7.15912i) q^{65} +(3.16389 - 5.48001i) q^{67} +(0.508787 - 0.136329i) q^{69} +(10.5807 + 6.10877i) q^{71} +9.81326i q^{73} +6.44653i q^{75} +(0.974285 + 0.562504i) q^{77} +(-0.649885 + 0.174136i) q^{79} +(1.23205 - 2.13397i) q^{81} +(9.32256 - 5.38238i) q^{83} -8.34291i q^{85} +(-20.0873 + 5.38238i) q^{87} +(-1.63773 + 6.11208i) q^{89} +(-4.68858 + 17.4980i) q^{91} +(5.98454 + 22.3346i) q^{93} +(4.38194 + 7.58974i) q^{95} +(-12.0710 + 12.0710i) q^{97} +(-0.731605 - 1.26718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 2 * q^5 + 6 * q^7 - 4 * q^9	\( 8 q + 4 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 20 q^{23} - 36 q^{25} - 32 q^{27} + 4 q^{29} - 4 q^{31} + 16 q^{33} + 10 q^{35} + 6 q^{37} + 56 q^{39} + 12 q^{41} - 20 q^{43} - 4 q^{45} + 24 q^{49} + 16 q^{51} - 12 q^{53} - 26 q^{55} - 8 q^{57} + 8 q^{59} - 14 q^{61} + 12 q^{65} + 22 q^{67} - 28 q^{69} + 6 q^{71} - 60 q^{77} - 14 q^{79} - 4 q^{81} + 48 q^{83} - 40 q^{87} + 16 q^{89} - 4 q^{91} + 4 q^{93} + 30 q^{95} - 16 q^{97} - 34 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 2 * q^5 + 6 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 20 * q^23 - 36 * q^25 - 32 * q^27 + 4 * q^29 - 4 * q^31 + 16 * q^33 + 10 * q^35 + 6 * q^37 + 56 * q^39 + 12 * q^41 - 20 * q^43 - 4 * q^45 + 24 * q^49 + 16 * q^51 - 12 * q^53 - 26 * q^55 - 8 * q^57 + 8 * q^59 - 14 * q^61 + 12 * q^65 + 22 * q^67 - 28 * q^69 + 6 * q^71 - 60 * q^77 - 14 * q^79 - 4 * q^81 + 48 * q^83 - 40 * q^87 + 16 * q^89 - 4 * q^91 + 4 * q^93 + 30 * q^95 - 16 * q^97 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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