LMFDB - Embedded newform 592.2.be.b.399.1

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			399.1
Root			$0.500000 + 1.27030i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.b.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 2.36603i) q^{3} +(-1.06816 - 3.98644i) q^{5} +(2.33847 + 1.35012i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 2.36603i) q^{3} +(-1.06816 - 3.98644i) q^{5} +(2.33847 + 1.35012i) q^{7} +(-2.23205 - 3.86603i) q^{9} -3.86838 q^{11} +(1.36603 + 5.09808i) q^{13} +(10.8912 + 2.91828i) q^{15} +(6.70258 + 1.79595i) q^{17} +(3.48644 - 0.934190i) q^{19} +(-6.38881 + 3.68858i) q^{21} +(3.40428 + 3.40428i) q^{23} +(-10.4206 + 6.01636i) q^{25} +4.00000 q^{27} +(-0.545822 - 0.545822i) q^{29} +(-4.98454 + 4.98454i) q^{31} +(5.28431 - 9.15268i) q^{33} +(2.88429 - 10.7643i) q^{35} +(2.28621 + 5.63677i) q^{37} +(-13.9282 - 3.73205i) q^{39} +(1.50000 + 0.866025i) q^{41} +(3.58407 + 3.58407i) q^{43} +(-13.0275 + 13.0275i) q^{45} +4.03182i q^{47} +(0.145622 + 0.252224i) q^{49} +(-13.4052 + 13.4052i) q^{51} +(0.700230 + 1.21283i) q^{53} +(4.13207 + 15.4211i) q^{55} +(-2.55225 + 9.52514i) q^{57} +(2.28431 - 8.52514i) q^{59} +(5.30900 - 1.42254i) q^{61} -12.0541i q^{63} +(18.8641 - 10.8912i) q^{65} +(-4.93419 + 8.54627i) q^{67} +(-12.7049 + 3.40428i) q^{69} +(4.75058 + 2.74275i) q^{71} -4.34916i q^{73} -32.8740i q^{75} +(-9.04608 - 5.22276i) q^{77} +(3.71614 - 0.995737i) q^{79} +(1.23205 - 2.13397i) q^{81} +(-0.945391 + 0.545822i) q^{83} -28.6379i q^{85} +(2.03704 - 0.545822i) q^{87} +(-1.29048 + 4.81613i) q^{89} +(-3.68858 + 13.7660i) q^{91} +(-4.98454 - 18.6025i) q^{93} +(-7.44819 - 12.9006i) q^{95} +(1.14276 - 1.14276i) q^{97} +(8.63442 + 14.9553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.455899\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	−0.926779	+	0.375608i	$0.877434\pi$
$4$		0			0
$5$	−1.06816	−	3.98644i	−0.477698	−	1.78279i	−0.610905	−	0.791704i	$-0.709194\pi$
$5$	−1.06816	−	3.98644i	−0.477698	−	1.78279i	0.133207	−	0.991088i	$-0.457472\pi$
$6$		0			0
$7$	2.33847	+	1.35012i	0.883858	+	0.510296i	0.871928	−	0.489633i	$-0.162869\pi$
$7$	2.33847	+	1.35012i	0.883858	+	0.510296i	0.0119294	+	0.999929i	$0.496203\pi$
$8$		0			0
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$		0			0
$11$	−3.86838			−1.16636			−0.583180	−	0.812343i	$-0.698192\pi$
$11$	−3.86838			−1.16636			−0.583180	+	0.812343i	$0.698192\pi$
$12$		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
$15$	10.8912	+	2.91828i	2.81209	+	0.753497i
$16$		0			0
$17$	6.70258	+	1.79595i	1.62562	+	0.435582i	0.952644	−	0.304086i	$-0.0983512\pi$
$17$	6.70258	+	1.79595i	1.62562	+	0.435582i	0.672971	+	0.739669i	$0.265018\pi$
$18$		0			0
$19$	3.48644	−	0.934190i	0.799845	−	0.214318i	0.164329	−	0.986406i	$-0.447454\pi$
$19$	3.48644	−	0.934190i	0.799845	−	0.214318i	0.635516	+	0.772088i	$0.280787\pi$
$20$		0			0
$21$	−6.38881	+	3.68858i	−1.39415	+	0.804915i
$22$		0			0
$23$	3.40428	+	3.40428i	0.709841	+	0.709841i	0.966502	−	0.256661i	$-0.0826222\pi$
$23$	3.40428	+	3.40428i	0.709841	+	0.709841i	−0.256661	+	0.966502i	$0.582622\pi$
$24$		0			0
$25$	−10.4206	+	6.01636i	−2.08413	+	1.20327i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	−0.545822	−	0.545822i	−0.101357	−	0.101357i	0.654610	−	0.755967i	$-0.272833\pi$
$29$	−0.545822	−	0.545822i	−0.101357	−	0.101357i	−0.755967	+	0.654610i	$0.772833\pi$
$30$		0			0
$31$	−4.98454	+	4.98454i	−0.895249	+	0.895249i	−0.995011	−	0.0997623i	$-0.968192\pi$
$31$	−4.98454	+	4.98454i	−0.895249	+	0.895249i	0.0997623	+	0.995011i	$0.468192\pi$
$32$		0			0
$33$	5.28431	−	9.15268i	0.919879	−	1.59328i
$34$		0			0
$35$	2.88429	−	10.7643i	0.487534	−	1.81950i
$36$		0			0
$37$	2.28621	+	5.63677i	0.375851	+	0.926680i
$37$	2.28621	+	5.63677i	0.375851	+	0.926680i
$38$		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
$43$	3.58407	+	3.58407i	0.546566	+	0.546566i	0.925446	−	0.378880i	$-0.123691\pi$
$43$	3.58407	+	3.58407i	0.546566	+	0.546566i	−0.378880	+	0.925446i	$0.623691\pi$
$44$		0			0
$45$	−13.0275	+	13.0275i	−1.94202	+	1.94202i
$46$		0			0
$47$			4.03182i			0.588101i	0.955790	+	0.294051i	$0.0950035\pi$
$47$			4.03182i			0.588101i	−0.955790	+	0.294051i	$0.904997\pi$
$48$		0			0
$49$	0.145622	+	0.252224i	0.0208031	+	0.0360320i
$50$		0			0
$51$	−13.4052	+	13.4052i	−1.87710	+	1.87710i
$52$		0			0
$53$	0.700230	+	1.21283i	0.0961840	+	0.166596i	0.910102	−	0.414384i	$-0.136003\pi$
$53$	0.700230	+	1.21283i	0.0961840	+	0.166596i	−0.813918	+	0.580980i	$0.802670\pi$
$54$		0			0
$55$	4.13207	+	15.4211i	0.557168	+	2.07938i
$56$		0			0
$57$	−2.55225	+	9.52514i	−0.338054	+	1.26164i
$58$		0			0
$59$	2.28431	−	8.52514i	0.297391	−	1.10988i	−0.641909	−	0.766781i	$-0.721857\pi$
$59$	2.28431	−	8.52514i	0.297391	−	1.10988i	0.939300	−	0.343098i	$-0.111476\pi$
$60$		0			0
$61$	5.30900	−	1.42254i	0.679748	−	0.182138i	0.0976061	−	0.995225i	$-0.468881\pi$
$61$	5.30900	−	1.42254i	0.679748	−	0.182138i	0.582142	+	0.813087i	$0.302215\pi$
$62$		0			0
$63$		−	12.0541i		−	1.51867i
$64$		0			0
$65$	18.8641	−	10.8912i	2.33980	−	1.35088i
$66$		0			0
$67$	−4.93419	+	8.54627i	−0.602807	+	1.04409i	0.389587	+	0.920990i	$0.372618\pi$
$67$	−4.93419	+	8.54627i	−0.602807	+	1.04409i	−0.992394	+	0.123103i	$0.960715\pi$
$68$		0			0
$69$	−12.7049	+	3.40428i	−1.52949	+	0.409827i
$70$		0			0
$71$	4.75058	+	2.74275i	0.563790	+	0.325504i	0.754665	−	0.656110i	$-0.227799\pi$
$71$	4.75058	+	2.74275i	0.563790	+	0.325504i	−0.190876	+	0.981614i	$0.561133\pi$
$72$		0			0
$73$		−	4.34916i		−	0.509031i	−0.967069	−	0.254516i	$-0.918084\pi$
$73$		−	4.34916i		−	0.509031i	0.967069	−	0.254516i	$-0.0819160\pi$
$74$		0			0
$75$		−	32.8740i		−	3.79596i
$76$		0			0
$77$	−9.04608	−	5.22276i	−1.03090	−	0.595189i
$78$		0			0
$79$	3.71614	−	0.995737i	0.418098	−	0.112029i	−0.0436357	−	0.999048i	$-0.513894\pi$
$79$	3.71614	−	0.995737i	0.418098	−	0.112029i	0.461734	+	0.887018i	$0.347227\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		0			0
$83$	−0.945391	+	0.545822i	−0.103770	+	0.0599117i	−0.550987	−	0.834514i	$-0.685749\pi$
$83$	−0.945391	+	0.545822i	−0.103770	+	0.0599117i	0.447217	+	0.894426i	$0.352415\pi$
$84$		0			0
$85$		−	28.6379i		−	3.10621i
$86$		0			0
$87$	2.03704	−	0.545822i	0.218393	−	0.0585183i
$88$		0			0
$89$	−1.29048	+	4.81613i	−0.136790	+	0.510508i	0.863194	+	0.504873i	$0.168461\pi$
$89$	−1.29048	+	4.81613i	−0.136790	+	0.510508i	−0.999984	+	0.00563563i	$0.998206\pi$
$90$		0			0
$91$	−3.68858	+	13.7660i	−0.386669	+	1.44307i
$92$		0			0
$93$	−4.98454	−	18.6025i	−0.516872	−	1.92899i
$94$		0			0
$95$	−7.44819	−	12.9006i	−0.764168	−	1.32358i
$96$		0			0
$97$	1.14276	−	1.14276i	0.116030	−	0.116030i	−0.646708	−	0.762738i	$-0.723855\pi$
$97$	1.14276	−	1.14276i	0.116030	−	0.116030i	0.762738	+	0.646708i	$0.223855\pi$
$98$		0			0
$99$	8.63442	+	14.9553i	0.867792	+	1.50306i
$100$		0			0
$101$			1.03182i			0.102670i	0.998681	+	0.0513350i	$0.0163476\pi$
$101$			1.03182i			0.102670i	−0.998681	+	0.0513350i	$0.983652\pi$
$102$		0			0
$103$	6.47575	−	6.47575i	0.638074	−	0.638074i	−0.312006	−	0.950080i	$-0.601001\pi$
$103$	6.47575	−	6.47575i	0.638074	−	0.638074i	0.950080	+	0.312006i	$0.101001\pi$
$104$		0			0
$105$	21.5286	+	21.5286i	2.10098	+	2.10098i
$106$		0			0
$107$	−0.721175	−	0.416371i	−0.0697187	−	0.0402521i	0.464735	−	0.885450i	$-0.346149\pi$
$107$	−0.721175	−	0.416371i	−0.0697187	−	0.0402521i	−0.534454	+	0.845197i	$0.679483\pi$
$108$		0			0
$109$	8.42776	+	2.25821i	0.807233	+	0.216297i	0.638757	−	0.769408i	$-0.279449\pi$
$109$	8.42776	+	2.25821i	0.807233	+	0.216297i	0.168476	+	0.985706i	$0.446116\pi$
$110$		0			0
$111$	−16.4598	−	2.29074i	−1.56229	−	0.217427i
$112$		0			0
$113$	0.108326	−	0.404278i	0.0101905	−	0.0380313i	−0.960643	−	0.277785i	$-0.910400\pi$
$113$	0.108326	−	0.404278i	0.0101905	−	0.0380313i	0.970834	+	0.239753i	$0.0770665\pi$
$114$		0			0
$115$	9.93464	−	17.2073i	0.926410	−	1.60459i
$116$		0			0
$117$	16.6603	−	16.6603i	1.54024	−	1.54024i
$118$		0			0
$119$	13.2490	+	13.2490i	1.21454	+	1.21454i
$120$		0			0
$121$	3.96436			0.360397
$122$		0			0
$123$	−4.09808	+	2.36603i	−0.369511	+	0.213337i
$124$		0			0
$125$	20.5234	+	20.5234i	1.83567	+	1.83567i
$126$		0			0
$127$	5.20729	−	3.00643i	0.462073	−	0.266778i	−0.250843	−	0.968028i	$-0.580708\pi$
$127$	5.20729	−	3.00643i	0.462073	−	0.266778i	0.712915	+	0.701250i	$0.247374\pi$
$128$		0			0
$129$	−13.3759	+	3.58407i	−1.17769	+	0.315560i
$130$		0			0
$131$	−7.65033	−	2.04990i	−0.668412	−	0.179101i	−0.0913729	−	0.995817i	$-0.529126\pi$
$131$	−7.65033	−	2.04990i	−0.668412	−	0.179101i	−0.577040	+	0.816716i	$0.695792\pi$
$132$		0			0
$133$	9.41420	+	2.52253i	0.816315	+	0.218731i
$134$		0			0
$135$	−4.27266	−	15.9458i	−0.367732	−	1.37239i
$136$		0			0
$137$	6.16815			0.526981			0.263490	−	0.964662i	$-0.415126\pi$
$137$	6.16815			0.526981			0.263490	+	0.964662i	$0.415126\pi$
$138$		0			0
$139$	0.722127	+	1.25076i	0.0612500	+	0.106088i	0.895024	−	0.446017i	$-0.147158\pi$
$139$	0.722127	+	1.25076i	0.0612500	+	0.106088i	−0.833774	+	0.552105i	$0.813825\pi$
$140$		0			0
$141$	−9.53939	−	5.50757i	−0.803362	−	0.463821i
$142$		0			0
$143$	−5.28431	−	19.7213i	−0.441896	−	1.64918i
$144$		0			0
$145$	−1.59286	+	2.75892i	−0.132280	+	0.229116i
$146$		0			0
$147$	−0.795692			−0.0656276
$148$		0			0
$149$	1.51350			0.123990			0.0619952	−	0.998076i	$-0.480254\pi$
$149$	1.51350			0.123990			0.0619952	+	0.998076i	$0.480254\pi$
$150$		0			0
$151$	3.66198	−	6.34273i	0.298008	−	0.516164i	−0.677673	−	0.735364i	$-0.737011\pi$
$151$	3.66198	−	6.34273i	0.298008	−	0.516164i	0.975680	+	0.219200i	$0.0703446\pi$
$152$		0			0
$153$	−8.01731	−	29.9210i	−0.648161	−	2.41897i
$154$		0			0
$155$	25.1949	+	14.5463i	2.02370	+	1.16838i
$156$		0			0
$157$	−3.60406	−	6.24242i	−0.287636	−	0.498199i	0.685609	−	0.727970i	$-0.259536\pi$
$157$	−3.60406	−	6.24242i	−0.287636	−	0.498199i	−0.973245	+	0.229770i	$0.926203\pi$
$158$		0			0
$159$	−3.82613			−0.303432
$160$		0			0
$161$	3.36463	+	12.5570i	0.265170	+	0.989627i
$162$		0			0
$163$	−13.0921	−	3.50801i	−1.02545	−	0.274769i	−0.293379	−	0.955996i	$-0.594780\pi$
$163$	−13.0921	−	3.50801i	−1.02545	−	0.274769i	−0.732072	+	0.681227i	$0.761447\pi$
$164$		0			0
$165$	−42.1312	−	11.2890i	−3.27991	−	0.878849i
$166$		0			0
$167$	−20.1256	+	5.39263i	−1.55736	+	0.417294i	−0.931828	−	0.362901i	$-0.881786\pi$
$167$	−20.1256	+	5.39263i	−1.55736	+	0.417294i	−0.625536	+	0.780195i	$0.715120\pi$
$168$		0			0
$169$	−12.8660	+	7.42820i	−0.989694	+	0.571400i
$170$		0			0
$171$	−11.3935	−	11.3935i	−0.871284	−	0.871284i
$172$		0			0
$173$	−14.9861	+	8.65224i	−1.13937	+	0.657818i	−0.946275	−	0.323362i	$-0.895187\pi$
$173$	−14.9861	+	8.65224i	−1.13937	+	0.657818i	−0.193098	+	0.981179i	$0.561854\pi$
$174$		0			0
$175$	−32.4911			−2.45610
$176$		0			0
$177$	17.0503	+	17.0503i	1.28158	+	1.28158i
$178$		0			0
$179$	14.1652	−	14.1652i	1.05876	−	1.05876i	0.0605961	−	0.998162i	$-0.480700\pi$
$179$	14.1652	−	14.1652i	1.05876	−	1.05876i	0.998162	−	0.0605961i	$-0.0193002\pi$
$180$		0			0
$181$	−6.37908	+	11.0489i	−0.474153	+	0.821257i	−0.999562	−	0.0295928i	$-0.990579\pi$
$181$	−6.37908	+	11.0489i	−0.474153	+	0.821257i	0.525409	+	0.850850i	$0.323912\pi$
$182$		0			0
$183$	−3.88646	+	14.5045i	−0.287295	+	1.07220i
$184$		0			0
$185$	20.0286	−	15.1349i	1.47253	−	1.11274i
$186$		0			0
$187$	−25.9281	−	6.94742i	−1.89605	−	0.508046i
$188$		0			0
$189$	9.35387	+	5.40046i	0.680394	+	0.392826i
$190$		0			0
$191$	−13.8094	−	13.8094i	−0.999217	−	0.999217i	0.000783154	−	1.00000i	$-0.499751\pi$
$191$	−13.8094	−	13.8094i	−0.999217	−	0.999217i	−1.00000		0.000783154i	$0.999751\pi$
$192$		0			0
$193$	12.8581	−	12.8581i	0.925548	−	0.925548i	−0.0718659	−	0.997414i	$-0.522895\pi$
$193$	12.8581	−	12.8581i	0.925548	−	0.925548i	0.997414	+	0.0718659i	$0.0228954\pi$
$194$		0			0
$195$			59.5104i			4.26163i
$196$		0			0
$197$	7.90994	+	13.7004i	0.563560	+	0.976114i	0.997182	+	0.0750195i	$0.0239019\pi$
$197$	7.90994	+	13.7004i	0.563560	+	0.976114i	−0.433622	+	0.901095i	$0.642765\pi$
$198$		0			0
$199$	−9.77641	+	9.77641i	−0.693031	+	0.693031i	−0.962898	−	0.269866i	$-0.913020\pi$
$199$	−9.77641	+	9.77641i	−0.693031	+	0.693031i	0.269866	+	0.962898i	$0.413020\pi$
$200$		0			0
$201$	−13.4805	−	23.3488i	−0.950838	−	1.64690i
$202$		0			0
$203$	−0.539465	−	2.01331i	−0.0378630	−	0.141307i
$204$		0			0
$205$	1.85012	−	6.90472i	0.129218	−	0.482247i
$206$		0			0
$207$	5.56250	−	20.7595i	0.386621	−	1.44289i
$208$		0			0
$209$	−13.4869	+	3.61380i	−0.932908	+	0.249972i
$210$		0			0
$211$		−	5.72823i		−	0.394348i	−0.980369	−	0.197174i	$-0.936824\pi$
$211$		−	5.72823i		−	0.394348i	0.980369	−	0.197174i	$-0.0631764\pi$
$212$		0			0
$213$	−12.9788	+	7.49332i	−0.889294	+	0.513434i
$214$		0			0
$215$	10.4593	−	18.1161i	0.713321	−	1.23551i
$216$		0			0
$217$	−18.3859	+	4.92648i	−1.24811	+	0.334431i
$218$		0			0
$219$	10.2902	+	5.94107i	0.695349	+	0.401460i
$220$		0			0
$221$			36.6236i			2.46357i
$222$		0			0
$223$		−	3.45124i		−	0.231112i	−0.993301	−	0.115556i	$-0.963135\pi$
$223$		−	3.45124i		−	0.231112i	0.993301	−	0.115556i	$-0.0368650\pi$
$224$		0			0
$225$	46.5188	+	26.8576i	3.10125	+	1.79051i
$226$		0			0
$227$	−19.2959	+	5.17032i	−1.28071	+	0.343166i	−0.834126	−	0.551574i	$-0.814027\pi$
$227$	−19.2959	+	5.17032i	−1.28071	+	0.343166i	−0.446587	+	0.894740i	$0.647361\pi$
$228$		0			0
$229$	−3.80665	+	6.59331i	−0.251550	+	0.435698i	−0.963953	−	0.266073i	$-0.914274\pi$
$229$	−3.80665	+	6.59331i	−0.251550	+	0.435698i	0.712403	+	0.701771i	$0.247607\pi$
$230$		0			0
$231$	24.7144	−	14.2688i	1.62609	−	0.938821i
$232$		0			0
$233$		−	28.5956i		−	1.87336i	−0.350186	−	0.936680i	$-0.613882\pi$
$233$		−	28.5956i		−	1.87336i	0.350186	−	0.936680i	$-0.386118\pi$
$234$		0			0
$235$	16.0726	−	4.30665i	1.04846	−	0.280935i
$236$		0			0
$237$	−2.72040	+	10.1527i	−0.176709	+	0.659488i
$238$		0			0
$239$	2.92566	−	10.9187i	0.189245	−	0.706274i	−0.804436	−	0.594039i	$-0.797532\pi$
$239$	2.92566	−	10.9187i	0.189245	−	0.706274i	0.993682	−	0.112235i	$-0.0358008\pi$
$240$		0			0
$241$	2.94870	+	11.0047i	0.189943	+	0.708876i	0.993518	+	0.113673i	$0.0362616\pi$
$241$	2.94870	+	11.0047i	0.189943	+	0.708876i	−0.803576	+	0.595203i	$0.797072\pi$
$242$		0			0
$243$	9.36603	+	16.2224i	0.600831	+	1.04067i
$244$		0			0
$245$	0.849930	−	0.849930i	0.0543000	−	0.0543000i
$246$		0			0
$247$	9.52514	+	16.4980i	0.606070	+	1.04974i
$248$		0			0
$249$		−	2.98243i		−	0.189004i
$250$		0			0
$251$	19.8894	−	19.8894i	1.25541	−	1.25541i	0.302150	−	0.953260i	$-0.402296\pi$
$251$	19.8894	−	19.8894i	1.25541	−	1.25541i	0.953260	−	0.302150i	$-0.0977044\pi$
$252$		0			0
$253$	−13.1690	−	13.1690i	−0.827930	−	0.827930i
$254$		0			0
$255$	67.7579	+	39.1200i	4.24316	+	2.44979i
$256$		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
$259$	−2.26406	+	16.2681i	−0.140682	+	1.01085i
$260$		0			0
$261$	−0.891859	+	3.32846i	−0.0552047	+	0.206027i
$262$		0			0
$263$	−10.6284	+	18.4090i	−0.655377	+	1.13515i	0.326422	+	0.945224i	$0.394157\pi$
$263$	−10.6284	+	18.4090i	−0.655377	+	1.13515i	−0.981799	+	0.189923i	$0.939176\pi$
$264$		0			0
$265$	4.08694	−	4.08694i	0.251058	−	0.251058i
$266$		0			0
$267$	−9.63225	−	9.63225i	−0.589484	−	0.589484i
$268$		0			0
$269$	3.33159			0.203131			0.101565	−	0.994829i	$-0.467615\pi$
$269$	3.33159			0.203131			0.101565	+	0.994829i	$0.467615\pi$
$270$		0			0
$271$	−13.4771	+	7.78100i	−0.818675	+	0.472662i	−0.849959	−	0.526848i	$-0.823374\pi$
$271$	−13.4771	+	7.78100i	−0.818675	+	0.472662i	0.0312846	+	0.999511i	$0.490040\pi$
$272$		0			0
$273$	−27.5320	−	27.5320i	−1.66631	−	1.66631i
$274$		0			0
$275$	40.3110	−	23.2735i	2.43084	−	1.40345i
$276$		0			0
$277$	20.2144	−	5.41644i	1.21457	−	0.325442i	0.406014	−	0.913867i	$-0.366918\pi$
$277$	20.2144	−	5.41644i	1.21457	−	0.325442i	0.808552	+	0.588425i	$0.200252\pi$
$278$		0			0
$279$	30.3961	+	8.14460i	1.81977	+	0.487605i
$280$		0			0
$281$	3.60972	+	0.967222i	0.215338	+	0.0576997i	0.364875	−	0.931056i	$-0.381112\pi$
$281$	3.60972	+	0.967222i	0.215338	+	0.0576997i	−0.149537	+	0.988756i	$0.547778\pi$
$282$		0			0
$283$	1.03641	+	3.86793i	0.0616082	+	0.229925i	0.989864	−	0.142017i	$-0.0453588\pi$
$283$	1.03641	+	3.86793i	0.0616082	+	0.229925i	−0.928256	+	0.371942i	$0.878692\pi$
$284$		0			0
$285$	40.6977			2.41072
$286$		0			0
$287$	2.33847	+	4.05035i	0.138035	+	0.239084i
$288$		0			0
$289$	26.9768	+	15.5750i	1.58687	+	0.916179i
$290$		0			0
$291$	1.14276	+	4.26484i	0.0669898	+	0.250009i
$292$		0			0
$293$	−4.63588	+	8.02959i	−0.270831	+	0.469093i	−0.969075	−	0.246767i	$-0.920632\pi$
$293$	−4.63588	+	8.02959i	−0.270831	+	0.469093i	0.698244	+	0.715860i	$0.253965\pi$
$294$		0			0
$295$	−36.4250			−2.12075
$296$		0			0
$297$	−15.4735			−0.897865
$298$		0			0
$299$	−12.7049	+	22.0056i	−0.734746	+	1.27262i
$300$		0			0
$301$	3.54233	+	13.2202i	0.204177	+	0.761997i
$302$		0			0
$303$	−2.44131	−	1.40949i	−0.140250	−	0.0809733i
$304$		0			0
$305$	−11.3418	−	19.6445i	−0.649428	−	1.12484i
$306$		0			0
$307$	14.3681			0.820032			0.410016	−	0.912078i	$-0.365523\pi$
$307$	14.3681			0.820032			0.410016	+	0.912078i	$0.365523\pi$
$308$		0			0
$309$	6.47575	+	24.1678i	0.368392	+	1.37486i
$310$		0			0
$311$	−16.8481	−	4.51445i	−0.955371	−	0.255991i	−0.252731	−	0.967537i	$-0.581329\pi$
$311$	−16.8481	−	4.51445i	−0.955371	−	0.255991i	−0.702640	+	0.711546i	$0.747995\pi$
$312$		0			0
$313$	−24.6548	−	6.60623i	−1.39357	−	0.373406i	−0.517539	−	0.855659i	$-0.673152\pi$
$313$	−24.6548	−	6.60623i	−1.39357	−	0.373406i	−0.876032	+	0.482253i	$0.839819\pi$
$314$		0			0
$315$	−48.0530	+	12.8758i	−2.70748	+	0.725467i
$316$		0			0
$317$	18.0054	−	10.3954i	1.01128	−	0.583866i	0.0997172	−	0.995016i	$-0.468206\pi$
$317$	18.0054	−	10.3954i	1.01128	−	0.583866i	0.911568	+	0.411150i	$0.134873\pi$
$318$		0			0
$319$	2.11145	+	2.11145i	0.118218	+	0.118218i
$320$		0			0
$321$	1.97029	−	1.13755i	0.109971	−	0.0634916i
$322$		0			0
$323$	25.0459			1.39359
$324$		0			0
$325$	−44.9067	−	44.9067i	−2.49098	−	2.49098i
$326$		0			0
$327$	−16.8555	+	16.8555i	−0.932112	+	0.932112i
$328$		0			0
$329$	−5.44342	+	9.42828i	−0.300106	+	0.519798i
$330$		0			0
$331$	3.08089	−	11.4980i	0.169341	−	0.631989i	−0.828106	−	0.560572i	$-0.810581\pi$
$331$	3.08089	−	11.4980i	0.169341	−	0.631989i	0.997447	−	0.0714168i	$-0.0227521\pi$
$332$		0			0
$333$	16.6890	−	21.4201i	0.914550	−	1.17382i
$334$		0			0
$335$	39.3397	+	10.5411i	2.14936	+	0.575919i
$336$		0			0
$337$	−28.9692	−	16.7254i	−1.57805	−	0.911089i	−0.995131	−	0.0985607i	$-0.968576\pi$
$337$	−28.9692	−	16.7254i	−1.57805	−	0.911089i	−0.582922	−	0.812528i	$-0.698091\pi$
$338$		0			0
$339$	0.808556	+	0.808556i	0.0439147	+	0.0439147i
$340$		0			0
$341$	19.2821	−	19.2821i	1.04418	−	1.04418i
$342$		0			0
$343$		−	18.1152i		−	0.978128i
$344$		0			0
$345$	27.1419	+	47.0112i	1.46127	+	2.53100i
$346$		0			0
$347$	−5.38187	+	5.38187i	−0.288914	+	0.288914i	−0.836651	−	0.547737i	$-0.815490\pi$
$347$	−5.38187	+	5.38187i	−0.288914	+	0.288914i	0.547737	+	0.836651i	$0.315490\pi$
$348$		0			0
$349$	−17.8712	−	30.9538i	−0.956622	−	1.65692i	−0.730611	−	0.682794i	$-0.760765\pi$
$349$	−17.8712	−	30.9538i	−0.956622	−	1.65692i	−0.226011	−	0.974125i	$-0.572569\pi$
$350$		0			0
$351$	5.46410	+	20.3923i	0.291652	+	1.08846i
$352$		0			0
$353$	−1.10043	+	4.10686i	−0.0585700	+	0.218586i	−0.989008	−	0.147864i	$-0.952760\pi$
$353$	−1.10043	+	4.10686i	−0.0585700	+	0.218586i	0.930438	+	0.366450i	$0.119427\pi$
$354$		0			0
$355$	5.85941	−	21.8676i	0.310985	−	1.16061i
$356$		0			0
$357$	−49.4461	+	13.2490i	−2.61696	+	0.701213i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−5.17190	+	2.98600i	−0.272205	+	0.157158i
$362$		0			0
$363$	−5.41542	+	9.37978i	−0.284236	+	0.492311i
$364$		0			0
$365$	−17.3377	+	4.64562i	−0.907497	+	0.243163i
$366$		0			0
$367$	30.9788	+	17.8856i	1.61708	+	0.933622i	0.987670	+	0.156549i	$0.0500370\pi$
$367$	30.9788	+	17.8856i	1.61708	+	0.933622i	0.629411	+	0.777073i	$0.283296\pi$
$368$		0			0
$369$		−	7.73205i		−	0.402514i
$370$		0			0
$371$			3.78157i			0.196329i
$372$		0			0
$373$	20.5018	+	11.8367i	1.06155	+	0.612883i	0.925859	−	0.377869i	$-0.123343\pi$
$373$	20.5018	+	11.8367i	1.06155	+	0.612883i	0.135686	+	0.990752i	$0.456676\pi$
$374$		0			0
$375$	−76.5944	+	20.5234i	−3.95532	+	1.05982i
$376$		0			0
$377$	2.03704	−	3.52825i	0.104913	−	0.181714i
$378$		0			0
$379$	9.85214	−	5.68814i	0.506071	−	0.292180i	−0.225146	−	0.974325i	$-0.572286\pi$
$379$	9.85214	−	5.68814i	0.506071	−	0.292180i	0.731217	+	0.682145i	$0.238953\pi$
$380$		0			0
$381$			16.4275i			0.841604i
$382$		0			0
$383$	13.2959	−	3.56262i	0.679388	−	0.182042i	0.0974081	−	0.995245i	$-0.468945\pi$
$383$	13.2959	−	3.56262i	0.679388	−	0.182042i	0.581980	+	0.813203i	$0.302278\pi$
$384$		0			0
$385$	−11.1575	+	41.6405i	−0.568640	+	2.12219i
$386$		0			0
$387$	5.85629	−	21.8560i	0.297692	−	1.11100i
$388$		0			0
$389$	−5.37818	−	20.0717i	−0.272685	−	1.01767i	−0.957377	−	0.288841i	$-0.906730\pi$
$389$	−5.37818	−	20.0717i	−0.272685	−	1.01767i	0.684692	−	0.728832i	$-0.259937\pi$
$390$		0			0
$391$	16.7035	+	28.9314i	0.844734	+	1.46312i
$392$		0			0
$393$	15.3007	−	15.3007i	0.771816	−	0.771816i
$394$		0			0
$395$	−7.93890	−	13.7506i	−0.399449	−	0.691867i
$396$		0			0
$397$			16.5724i			0.831746i	0.909423	+	0.415873i	$0.136524\pi$
$397$			16.5724i			0.831746i	−0.909423	+	0.415873i	$0.863476\pi$
$398$		0			0
$399$	−18.8284	+	18.8284i	−0.942599	+	0.942599i
$400$		0			0
$401$	21.1810	+	21.1810i	1.05773	+	1.05773i	0.998228	+	0.0595011i	$0.0189510\pi$
$401$	21.1810	+	21.1810i	1.05773	+	1.05773i	0.0595011	+	0.998228i	$0.481049\pi$
$402$		0			0
$403$	−32.2205	−	18.6025i	−1.60502	−	0.926658i
$404$		0			0
$405$	−9.82300	−	2.63207i	−0.488109	−	0.130788i
$406$		0			0
$407$	−8.84394	−	21.8052i	−0.438378	−	1.08084i
$408$		0			0
$409$	−0.877999	+	3.27674i	−0.0434142	+	0.162024i	−0.984230	−	0.176895i	$-0.943395\pi$
$409$	−0.877999	+	3.27674i	−0.0434142	+	0.162024i	0.940815	+	0.338919i	$0.110061\pi$
$410$		0			0
$411$	−8.42585	+	14.5940i	−0.415616	+	0.719869i
$412$		0			0
$413$	16.8517	−	16.8517i	0.829218	−	0.829218i
$414$		0			0
$415$	3.18572	+	3.18572i	0.156381	+	0.156381i
$416$		0			0
$417$	−3.94578			−0.193225
$418$		0			0
$419$	11.6496	−	6.72588i	0.569119	−	0.328581i	−0.187678	−	0.982231i	$-0.560096\pi$
$419$	11.6496	−	6.72588i	0.569119	−	0.328581i	0.756797	+	0.653650i	$0.226763\pi$
$420$		0			0
$421$	20.3386	+	20.3386i	0.991242	+	0.991242i	0.999962	−	0.00871988i	$-0.00277566\pi$
$421$	20.3386	+	20.3386i	0.991242	+	0.991242i	−0.00871988	+	0.999962i	$0.502776\pi$
$422$		0			0
$423$	15.5871	−	8.99923i	0.757872	−	0.437557i
$424$		0			0
$425$	−80.6503	+	21.6102i	−3.91211	+	1.04825i
$426$		0			0
$427$	14.3355	+	3.84119i	0.693745	+	0.185888i
$428$		0			0
$429$	53.8796	+	14.4370i	2.60133	+	0.697024i
$430$		0			0
$431$	−5.28824	−	19.7360i	−0.254726	−	0.950649i	−0.968243	−	0.250011i	$-0.919566\pi$
$431$	−5.28824	−	19.7360i	−0.254726	−	0.950649i	0.713517	−	0.700638i	$-0.247101\pi$
$432$		0			0
$433$	36.6189			1.75979			0.879896	−	0.475167i	$-0.157612\pi$
$433$	36.6189			1.75979			0.879896	+	0.475167i	$0.157612\pi$
$434$		0			0
$435$	−4.35178	−	7.53750i	−0.208652	−	0.361395i
$436$		0			0
$437$	15.0491	+	8.68858i	0.719895	+	0.415631i
$438$		0			0
$439$	−10.1763	−	37.9785i	−0.485689	−	1.81261i	−0.576940	−	0.816786i	$-0.695753\pi$
$439$	−10.1763	−	37.9785i	−0.485689	−	1.81261i	0.0912516	−	0.995828i	$-0.470913\pi$
$440$		0			0
$441$	0.650070	−	1.12595i	0.0309557	−	0.0536169i
$442$		0			0
$443$	−10.7449			−0.510506			−0.255253	−	0.966874i	$-0.582159\pi$
$443$	−10.7449			−0.510506			−0.255253	+	0.966874i	$0.582159\pi$
$444$		0			0
$445$	20.5777			0.975474
$446$		0			0
$447$	−2.06747	+	3.58097i	−0.0977881	+	0.169374i
$448$		0			0
$449$	6.32969	+	23.6227i	0.298716	+	1.11482i	0.938221	+	0.346037i	$0.112473\pi$
$449$	6.32969	+	23.6227i	0.298716	+	1.11482i	−0.639504	+	0.768787i	$0.720860\pi$
$450$		0			0
$451$	−5.80257	−	3.35012i	−0.273232	−	0.157751i
$452$		0			0
$453$	10.0047	+	17.3287i	0.470062	+	0.814172i
$454$		0			0
$455$	58.8173			2.75740
$456$		0			0
$457$	−6.76101	−	25.2324i	−0.316267	−	1.18032i	−0.922804	−	0.385269i	$-0.874109\pi$
$457$	−6.76101	−	25.2324i	−0.316267	−	1.18032i	0.606538	−	0.795055i	$-0.292558\pi$
$458$		0			0
$459$	26.8103	+	7.18381i	1.25140	+	0.335311i
$460$		0			0
$461$	6.95221	+	1.86284i	0.323797	+	0.0867610i	0.417056	−	0.908881i	$-0.363062\pi$
$461$	6.95221	+	1.86284i	0.323797	+	0.0867610i	−0.0932593	+	0.995642i	$0.529729\pi$
$462$		0			0
$463$	−20.8365	+	5.58312i	−0.968354	+	0.259470i	−0.708133	−	0.706079i	$-0.750462\pi$
$463$	−20.8365	+	5.58312i	−0.968354	+	0.259470i	−0.260221	+	0.965549i	$0.583796\pi$
$464$		0			0
$465$	−68.8337	+	39.7411i	−3.19209	+	1.84295i
$466$		0			0
$467$	−22.4165	−	22.4165i	−1.03731	−	1.03731i	−0.999276	−	0.0380351i	$-0.987890\pi$
$467$	−22.4165	−	22.4165i	−1.03731	−	1.03731i	−0.0380351	−	0.999276i	$-0.512110\pi$
$468$		0			0
$469$	−23.0769	+	13.3234i	−1.06559	+	0.615220i
$470$		0			0
$471$	19.6930			0.907404
$472$		0			0
$473$	−13.8646	−	13.8646i	−0.637493	−	0.637493i
$474$		0			0
$475$	−30.7105	+	30.7105i	−1.40910	+	1.40910i
$476$		0			0
$477$	3.12590	−	5.41422i	0.143125	−	0.247900i
$478$		0			0
$479$	−8.44113	+	31.5027i	−0.385685	+	1.43940i	0.451399	+	0.892322i	$0.350925\pi$
$479$	−8.44113	+	31.5027i	−0.385685	+	1.43940i	−0.837084	+	0.547075i	$0.815741\pi$
$480$		0			0
$481$	−25.6137	+	19.3553i	−1.16788	+	0.882524i
$482$		0			0
$483$	−34.3063	−	9.19233i	−1.56099	−	0.418266i
$484$		0			0
$485$	−5.77621	−	3.33490i	−0.262284	−	0.151430i
$486$		0			0
$487$	19.6246	+	19.6246i	0.889276	+	0.889276i	0.994453	−	0.105177i	$-0.0335410\pi$
$487$	19.6246	+	19.6246i	0.889276	+	0.889276i	−0.105177	+	0.994453i	$0.533541\pi$
$488$		0			0
$489$	26.1842	−	26.1842i	1.18409	−	1.18409i
$490$		0			0
$491$		−	33.9356i		−	1.53149i	−0.643143	−	0.765746i	$-0.722370\pi$
$491$		−	33.9356i		−	1.53149i	0.643143	−	0.765746i	$-0.277630\pi$
$492$		0			0
$493$	−2.67815	−	4.63869i	−0.120618	−	0.208916i
$494$		0			0
$495$	50.3953	−	50.3953i	2.26510	−	2.26510i
$496$		0			0
$497$	7.40605	+	12.8276i	0.332207	+	0.575399i
$498$		0			0
$499$	6.01820	+	22.4602i	0.269412	+	1.00546i	0.959494	+	0.281727i	$0.0909074\pi$
$499$	6.01820	+	22.4602i	0.269412	+	1.00546i	−0.690083	+	0.723730i	$0.742426\pi$
$500$		0			0
$501$	14.7329	−	54.9841i	0.658219	−	2.45651i
$502$		0			0
$503$	3.05589	−	11.4047i	0.136255	−	0.508511i	−0.863734	−	0.503947i	$-0.831881\pi$
$503$	3.05589	−	11.4047i	0.136255	−	0.508511i	0.999990	−	0.00456409i	$-0.00145280\pi$
$504$		0			0
$505$	4.11329	−	1.10215i	0.183039	−	0.0490452i
$506$		0			0
$507$		−	40.5885i		−	1.80260i
$508$		0			0
$509$	13.0225	−	7.51852i	0.577211	−	0.333253i	−0.182813	−	0.983148i	$-0.558520\pi$
$509$	13.0225	−	7.51852i	0.577211	−	0.333253i	0.760024	+	0.649895i	$0.225187\pi$
$510$		0			0
$511$	5.87187	−	10.1704i	0.259756	−	0.449911i
$512$		0			0
$513$	13.9458	−	3.73676i	0.615721	−	0.164982i
$514$		0			0
$515$	−32.7324	−	18.8980i	−1.44236	−	0.832747i
$516$		0			0
$517$		−	15.5966i		−	0.685938i
$518$		0			0
$519$		−	47.2767i		−	2.07522i
$520$		0			0
$521$	−11.7281	−	6.77119i	−0.513815	−	0.296651i	0.220585	−	0.975368i	$-0.429203\pi$
$521$	−11.7281	−	6.77119i	−0.513815	−	0.296651i	−0.734401	+	0.678716i	$0.762537\pi$
$522$		0			0
$523$	27.8098	−	7.45162i	1.21604	−	0.325837i	0.406910	−	0.913468i	$-0.366606\pi$
$523$	27.8098	−	7.45162i	1.21604	−	0.325837i	0.809129	+	0.587631i	$0.199939\pi$
$524$		0			0
$525$	44.3837	−	76.8747i	1.93706	−	3.35509i
$526$		0			0
$527$	−42.3613	+	24.4573i	−1.84529	+	1.06538i
$528$		0			0
$529$			0.178219i			0.00774866i
$530$		0			0
$531$	−38.0571	+	10.1974i	−1.65154	+	0.442528i
$532$		0			0
$533$	−2.36603	+	8.83013i	−0.102484	+	0.382475i
$534$		0			0
$535$	−0.889505	+	3.31968i	−0.0384567	+	0.143522i
$536$		0			0
$537$	14.1652	+	52.8653i	0.611274	+	2.28131i
$538$		0			0
$539$	−0.563320	−	0.975699i	−0.0242639	−	0.0420263i
$540$		0			0
$541$	−28.1395	+	28.1395i	−1.20981	+	1.20981i	−0.238725	+	0.971087i	$0.576729\pi$
$541$	−28.1395	+	28.1395i	−1.20981	+	1.20981i	−0.971087	+	0.238725i	$0.923271\pi$
$542$		0			0
$543$	−17.4280	−	30.1861i	−0.747905	−	1.29541i
$544$		0			0
$545$		−	36.0089i		−	1.54245i
$546$		0			0
$547$	−6.54373	+	6.54373i	−0.279790	+	0.279790i	−0.833025	−	0.553235i	$-0.813393\pi$
$547$	−6.54373	+	6.54373i	−0.279790	+	0.279790i	0.553235	+	0.833025i	$0.313393\pi$
$548$		0			0
$549$	−17.3495	−	17.3495i	−0.740461	−	0.740461i
$550$		0			0
$551$	−2.41288	−	1.39308i	−0.102792	−	0.0593471i
$552$		0			0
$553$	10.0344	+	2.68872i	0.426708	+	0.114336i
$554$		0			0
$555$	8.44985	+	68.0629i	0.358676	+	2.88911i
$556$		0			0
$557$	−1.57261	+	5.86907i	−0.0666337	+	0.248681i	−0.991206	−	0.132325i	$-0.957756\pi$
$557$	−1.57261	+	5.86907i	−0.0666337	+	0.248681i	0.924573	+	0.381006i	$0.124422\pi$
$558$		0			0
$559$	−13.3759	+	23.1678i	−0.565742	+	0.979895i
$560$		0			0
$561$	51.8563	−	51.8563i	2.18937	−	2.18937i
$562$		0			0
$563$	−8.05703	−	8.05703i	−0.339563	−	0.339563i	0.516640	−	0.856203i	$-0.327183\pi$
$563$	−8.05703	−	8.05703i	−0.339563	−	0.339563i	−0.856203	+	0.516640i	$0.827183\pi$
$564$		0			0
$565$	−1.72734			−0.0726698
$566$		0			0
$567$	5.76222	−	3.32682i	0.241991	−	0.139713i
$568$		0			0
$569$	19.0590	+	19.0590i	0.798994	+	0.798994i	0.982937	−	0.183943i	$-0.0588860\pi$
$569$	19.0590	+	19.0590i	0.798994	+	0.798994i	−0.183943	+	0.982937i	$0.558886\pi$
$570$		0			0
$571$	0.439400	−	0.253687i	0.0183883	−	0.0106165i	−0.490778	−	0.871285i	$-0.663287\pi$
$571$	0.439400	−	0.253687i	0.0183883	−	0.0106165i	0.509166	+	0.860668i	$0.329954\pi$
$572$		0			0
$573$	51.5376	−	13.8094i	2.15301	−	0.576898i
$574$		0			0
$575$	−55.9561	−	14.9934i	−2.33353	−	0.625267i
$576$		0			0
$577$	2.31613	+	0.620604i	0.0964216	+	0.0258361i	0.306707	−	0.951804i	$-0.400773\pi$
$577$	2.31613	+	0.620604i	0.0964216	+	0.0258361i	−0.210286	+	0.977640i	$0.567439\pi$
$578$		0			0
$579$	12.8581	+	47.9872i	0.534366	+	1.99428i
$580$		0			0
$581$	−2.94769			−0.122291
$582$		0			0
$583$	−2.70876	−	4.69170i	−0.112185	−	0.194311i
$584$		0			0
$585$	−84.2111	−	48.6193i	−3.48170	−	2.01016i
$586$		0			0
$587$	3.80557	+	14.2026i	0.157073	+	0.586203i	0.998919	+	0.0464859i	$0.0148023\pi$
$587$	3.80557	+	14.2026i	0.157073	+	0.586203i	−0.841846	+	0.539717i	$0.818531\pi$
$588$		0			0
$589$	−12.7218	+	22.0348i	−0.524193	+	0.907928i
$590$		0			0
$591$	−43.2207			−1.77786
$592$		0			0
$593$	−0.490191			−0.0201297			−0.0100649	−	0.999949i	$-0.503204\pi$
$593$	−0.490191			−0.0201297			−0.0100649	+	0.999949i	$0.503204\pi$
$594$		0			0
$595$	38.6644	−	66.9687i	1.58509	−	2.74545i
$596$		0			0
$597$	−9.77641	−	36.4861i	−0.400122	−	1.49327i
$598$		0			0
$599$	16.1651	+	9.33293i	0.660488	+	0.381333i	0.792463	−	0.609920i	$-0.208798\pi$
$599$	16.1651	+	9.33293i	0.660488	+	0.381333i	−0.131975	+	0.991253i	$0.542132\pi$
$600$		0			0
$601$	−7.37863	−	12.7802i	−0.300981	−	0.521314i	0.675378	−	0.737472i	$-0.263981\pi$
$601$	−7.37863	−	12.7802i	−0.300981	−	0.521314i	−0.976358	+	0.216158i	$0.930647\pi$
$602$		0			0
$603$	44.0534			1.79400
$604$		0			0
$605$	−4.23459	−	15.8037i	−0.172161	−	0.642512i
$606$		0			0
$607$	32.5032	+	8.70920i	1.31926	+	0.353496i	0.848702	−	0.528872i	$-0.177385\pi$
$607$	32.5032	+	8.70920i	1.31926	+	0.353496i	0.470562	+	0.882367i	$0.344051\pi$
$608$		0			0
$609$	5.50046	+	1.47385i	0.222890	+	0.0597232i
$610$		0			0
$611$	−20.5545	+	5.50757i	−0.831547	+	0.222812i
$612$		0			0
$613$	7.44411	−	4.29786i	0.300665	−	0.173589i	−0.342077	−	0.939672i	$-0.611130\pi$
$613$	7.44411	−	4.29786i	0.300665	−	0.173589i	0.642742	+	0.766083i	$0.277797\pi$
$614$		0			0
$615$	13.8094	+	13.8094i	0.556851	+	0.556851i
$616$		0			0
$617$	36.1177	−	20.8526i	1.45405	−	0.839494i	0.455338	−	0.890319i	$-0.349518\pi$
$617$	36.1177	−	20.8526i	1.45405	−	0.839494i	0.998708	+	0.0508250i	$0.0161851\pi$
$618$		0			0
$619$	22.8957			0.920257			0.460129	−	0.887852i	$-0.347803\pi$
$619$	22.8957			0.920257			0.460129	+	0.887852i	$0.347803\pi$
$620$		0			0
$621$	13.6171	+	13.6171i	0.546436	+	0.546436i
$622$		0			0
$623$	−9.52006	+	9.52006i	−0.381413	+	0.381413i
$624$		0			0
$625$	29.8113	−	51.6347i	1.19245	−	2.06539i
$626$		0			0
$627$	9.87309	−	36.8469i	0.394293	−	1.47152i
$628$		0			0
$629$	5.20016	+	41.8869i	0.207344	+	1.67014i
$630$		0			0
$631$	12.6095	+	3.37870i	0.501975	+	0.134504i	0.500916	−	0.865496i	$-0.332996\pi$
$631$	12.6095	+	3.37870i	0.501975	+	0.134504i	0.00105844	+	0.999999i	$0.499663\pi$
$632$		0			0
$633$	13.5531	+	7.82491i	0.538689	+	0.311012i
$634$		0			0
$635$	−17.5472	−	17.5472i	−0.696340	−	0.696340i
$636$		0			0
$637$	−1.08694	+	1.08694i	−0.0430659	+	0.0430659i
$638$		0			0
$639$		−	24.4878i		−	0.968722i
$640$		0			0
$641$	−14.3593	−	24.8711i	−0.567160	−	0.982350i	−0.996845	−	0.0793713i	$-0.974709\pi$
$641$	−14.3593	−	24.8711i	−0.567160	−	0.982350i	0.429685	−	0.902979i	$-0.358625\pi$
$642$		0			0
$643$	−9.43666	+	9.43666i	−0.372146	+	0.372146i	−0.868258	−	0.496113i	$-0.834760\pi$
$643$	−9.43666	+	9.43666i	−0.372146	+	0.372146i	0.496113	+	0.868258i	$0.334760\pi$
$644$		0			0
$645$	28.5754	+	49.4941i	1.12516	+	1.94883i
$646$		0			0
$647$	7.14982	+	26.6835i	0.281088	+	1.04904i	0.951651	+	0.307183i	$0.0993863\pi$
$647$	7.14982	+	26.6835i	0.281088	+	1.04904i	−0.670562	+	0.741853i	$0.733947\pi$
$648$		0			0
$649$	−8.83656	+	32.9785i	−0.346865	+	1.29452i
$650$		0			0
$651$	13.4594	−	50.2311i	0.527515	−	1.96871i
$652$		0			0
$653$	11.8729	−	3.18133i	0.464623	−	0.124495i	−0.0189108	−	0.999821i	$-0.506020\pi$
$653$	11.8729	−	3.18133i	0.464623	−	0.124495i	0.483533	+	0.875326i	$0.339353\pi$
$654$		0			0
$655$			32.6872i			1.27720i
$656$		0			0
$657$	−16.8140	+	9.70755i	−0.655976	+	0.378728i
$658$		0			0
$659$	12.6942	−	21.9870i	0.494495	−	0.856491i	−0.505485	−	0.862836i	$-0.668686\pi$
$659$	12.6942	−	21.9870i	0.494495	−	0.856491i	0.999980	+	0.00634482i	$0.00201963\pi$
$660$		0			0
$661$	−17.5227	+	4.69520i	−0.681555	+	0.182622i	−0.582954	−	0.812505i	$-0.698103\pi$
$661$	−17.5227	+	4.69520i	−0.681555	+	0.182622i	−0.0986008	+	0.995127i	$0.531437\pi$
$662$		0			0
$663$	−86.6524	−	50.0288i	−3.36530	−	1.94296i
$664$		0			0
$665$		−	40.2237i		−	1.55981i
$666$		0			0
$667$		−	3.71626i		−	0.143894i
$668$		0			0
$669$	8.16572	+	4.71448i	0.315705	+	0.182272i
$670$		0			0
$671$	−20.5372	+	5.50294i	−0.792831	+	0.212438i
$672$		0			0
$673$	−16.7479	+	29.0082i	−0.645584	+	1.11818i	0.338582	+	0.940937i	$0.390053\pi$
$673$	−16.7479	+	29.0082i	−0.645584	+	1.11818i	−0.984166	+	0.177248i	$0.943281\pi$
$674$		0			0
$675$	−41.6825	+	24.0654i	−1.60436	+	0.926279i
$676$		0			0
$677$			12.7324i			0.489347i	0.969606	+	0.244673i	$0.0786807\pi$
$677$			12.7324i			0.489347i	−0.969606	+	0.244673i	$0.921319\pi$
$678$		0			0
$679$	4.21517	−	1.12945i	0.161763	−	0.0433444i
$680$		0			0
$681$	14.1256	−	52.7174i	0.541293	−	2.02013i
$682$		0			0
$683$	−4.95125	+	18.4783i	−0.189454	+	0.707053i	0.804179	+	0.594387i	$0.202605\pi$
$683$	−4.95125	+	18.4783i	−0.189454	+	0.707053i	−0.993633	+	0.112665i	$0.964061\pi$
$684$		0			0
$685$	−6.58860	−	24.5890i	−0.251737	−	0.939497i
$686$		0			0
$687$	−10.4000	−	18.0132i	−0.396783	−	0.687248i
$688$		0			0
$689$	−5.22659	+	5.22659i	−0.199117	+	0.199117i
$690$		0			0
$691$	23.4804	+	40.6692i	0.893236	+	1.54713i	0.835972	+	0.548772i	$0.184904\pi$
$691$	23.4804	+	40.6692i	0.893236	+	1.54713i	0.0572642	+	0.998359i	$0.481762\pi$
$692$		0			0
$693$			46.6298i			1.77132i
$694$		0			0
$695$	4.21474	−	4.21474i	0.159874	−	0.159874i
$696$		0			0
$697$	8.49854	+	8.49854i	0.321905	+	0.321905i
$698$		0			0
$699$	67.6579	+	39.0623i	2.55906	+	1.47747i
$700$		0			0
$701$	44.3713	+	11.8893i	1.67588	+	0.449051i	0.966687	−	0.255962i	$-0.0823923\pi$
$701$	44.3713	+	11.8893i	1.67588	+	0.449051i	0.709194	+	0.705013i	$0.249059\pi$
$702$		0			0
$703$	13.2366	+	17.5165i	0.499227	+	0.660649i
$704$		0			0
$705$	−11.7660	+	43.9112i	−0.443132	+	1.65379i
$706$		0			0
$707$	−1.39308	+	2.41288i	−0.0523920	+	0.0907457i
$708$		0			0
$709$	−11.0066	+	11.0066i	−0.413362	+	0.413362i	−0.882908	−	0.469546i	$-0.844418\pi$
$709$	−11.0066	+	11.0066i	−0.413362	+	0.413362i	0.469546	+	0.882908i	$0.344418\pi$
$710$		0			0
$711$	−12.1442	−	12.1442i	−0.455442	−	0.455442i
$712$		0			0
$713$	−33.9375			−1.27097
$714$		0			0
$715$	−72.9733	+	42.1312i	−2.72905	+	1.57562i
$716$		0			0
$717$	21.8375	+	21.8375i	0.815535	+	0.815535i
$718$		0			0
$719$	5.36448	−	3.09719i	0.200061	−	0.115506i	−0.396623	−	0.917982i	$-0.629818\pi$
$719$	5.36448	−	3.09719i	0.200061	−	0.115506i	0.596684	+	0.802476i	$0.296485\pi$
$720$		0			0
$721$	23.8863	−	6.40032i	0.889574	−	0.238361i
$722$		0			0
$723$	−30.0654	−	8.05601i	−1.11815	−	0.299606i
$724$		0			0
$725$	8.97167	+	2.40395i	0.333199	+	0.0892805i
$726$		0			0
$727$	−10.6413	−	39.7140i	−0.394666	−	1.47291i	−0.822349	−	0.568983i	$-0.807337\pi$
$727$	−10.6413	−	39.7140i	−0.394666	−	1.47291i	0.427684	−	0.903929i	$-0.359330\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$		0			0
$731$	17.5857	+	30.4594i	0.650432	+	1.12658i
$732$		0			0
$733$	−2.84732	−	1.64390i	−0.105168	−	0.0607188i	0.446493	−	0.894787i	$-0.352673\pi$
$733$	−2.84732	−	1.64390i	−0.105168	−	0.0607188i	−0.551661	+	0.834068i	$0.686006\pi$
$734$		0			0
$735$	0.849930	+	3.17198i	0.0313501	+	0.117000i
$736$		0			0
$737$	19.0873	−	33.0602i	0.703090	−	1.21779i
$738$		0			0
$739$	32.0393			1.17859			0.589293	−	0.807919i	$-0.299406\pi$
$739$	32.0393			1.17859			0.589293	+	0.807919i	$0.299406\pi$
$740$		0			0
$741$	−52.0463			−1.91197
$742$		0			0
$743$	23.5574	−	40.8026i	0.864237	−	1.49690i	−0.00356481	−	0.999994i	$-0.501135\pi$
$743$	23.5574	−	40.8026i	0.864237	−	1.49690i	0.867802	−	0.496910i	$-0.165532\pi$
$744$		0			0
$745$	−1.61666	−	6.03346i	−0.0592299	−	0.221049i
$746$		0			0
$747$	4.22032	+	2.43660i	0.154414	+	0.0891507i
$748$		0			0
$749$	−1.12430	−	1.94734i	−0.0410809	−	0.0711542i
$750$		0			0
$751$	7.11583			0.259660			0.129830	−	0.991536i	$-0.458557\pi$
$751$	7.11583			0.259660			0.129830	+	0.991536i	$0.458557\pi$
$752$		0			0
$753$	19.8894	+	74.2284i	0.724812	+	2.70503i
$754$		0			0
$755$	−29.1965	−	7.82319i	−1.06257	−	0.284715i
$756$		0			0
$757$	32.5502	+	8.72181i	1.18306	+	0.316999i	0.796139	−	0.605114i	$-0.206873\pi$
$757$	32.5502	+	8.72181i	1.18306	+	0.316999i	0.386919	+	0.922114i	$0.373539\pi$
$758$		0			0
$759$	49.1475	−	13.1690i	1.78394	−	0.478006i
$760$		0			0
$761$	7.84330	−	4.52833i	0.284319	−	0.164152i	−0.351058	−	0.936354i	$-0.614178\pi$
$761$	7.84330	−	4.52833i	0.284319	−	0.164152i	0.635377	+	0.772202i	$0.280845\pi$
$762$		0			0
$763$	16.6592	+	16.6592i	0.603103	+	0.603103i
$764$		0			0
$765$	−110.715	+	63.9211i	−4.00290	+	2.31107i
$766$		0			0
$767$	46.5822			1.68199
$768$		0			0
$769$	−24.0988	−	24.0988i	−0.869024	−	0.869024i	0.123340	−	0.992364i	$-0.460639\pi$
$769$	−24.0988	−	24.0988i	−0.869024	−	0.869024i	−0.992364	+	0.123340i	$0.960639\pi$
$770$		0			0
$771$	43.9808	−	43.9808i	1.58393	−	1.58393i
$772$		0			0
$773$	−11.5615	+	20.0251i	−0.415838	+	0.720252i	−0.995516	−	0.0945933i	$-0.969845\pi$
$773$	−11.5615	+	20.0251i	−0.415838	+	0.720252i	0.579678	+	0.814845i	$0.303178\pi$
$774$		0			0
$775$	21.9533	−	81.9308i	0.788585	−	2.94304i
$776$		0			0
$777$	−35.3979	−	27.5794i	−1.26989	−	0.989406i
$778$		0			0
$779$	6.03870	+	1.61806i	0.216359	+	0.0579732i
$780$		0			0
$781$	−18.3770	−	10.6100i	−0.657582	−	0.379655i
$782$		0			0
$783$	−2.18329	−	2.18329i	−0.0780244	−	0.0780244i
$784$		0			0
$785$	−21.0353	+	21.0353i	−0.750783	+	0.750783i
$786$		0			0
$787$		−	53.8467i		−	1.91943i	−0.280977	−	0.959715i	$-0.590658\pi$
$787$		−	53.8467i		−	1.91943i	0.280977	−	0.959715i	$-0.409342\pi$
$788$		0			0
$789$	−29.0374	−	50.2943i	−1.03376	−	1.79052i
$790$		0			0
$791$	0.799139	−	0.799139i	0.0284141	−	0.0284141i
$792$		0			0
$793$	14.5045	+	25.1225i	0.515069	+	0.892125i
$794$		0			0
$795$	4.08694	+	15.2527i	0.144949	+	0.540956i
$796$		0			0
$797$	−4.41765	+	16.4869i	−0.156481	+	0.583996i	0.842493	+	0.538708i	$0.181087\pi$
$797$	−4.41765	+	16.4869i	−0.156481	+	0.583996i	−0.998974	+	0.0452880i	$0.985579\pi$
$798$		0			0
$799$	−7.24096	+	27.0236i	−0.256167	+	0.956027i
$800$		0			0
$801$	21.4997	−	5.76082i	0.759654	−	0.203549i
$802$		0			0
$803$			16.8242i			0.593714i
$804$		0			0
$805$	46.4637	−	26.8258i	1.63763	−	0.945485i
$806$		0			0
$807$	−4.55104	+	7.88263i	−0.160204	+	0.277482i
$808$		0			0
$809$	−35.7820	+	9.58776i	−1.25803	+	0.337088i	−0.825433	−	0.564500i	$-0.809069\pi$
$809$	−35.7820	+	9.58776i	−1.25803	+	0.337088i	−0.432596	+	0.901588i	$0.642402\pi$
$810$		0			0
$811$	−22.9181	−	13.2318i	−0.804765	−	0.464631i	0.0403699	−	0.999185i	$-0.487146\pi$
$811$	−22.9181	−	13.2318i	−0.804765	−	0.464631i	−0.845134	+	0.534554i	$0.820480\pi$
$812$		0			0
$813$		−	42.5162i		−	1.49111i
$814$		0			0
$815$			55.9380i			1.95942i
$816$		0			0
$817$	15.8439	+	9.14747i	0.554307	+	0.320029i
$818$		0			0
$819$	61.4527	−	16.4662i	2.14733	−	0.575376i
$820$		0			0
$821$	−4.25681	+	7.37301i	−0.148564	+	0.257320i	−0.930697	−	0.365792i	$-0.880798\pi$
$821$	−4.25681	+	7.37301i	−0.148564	+	0.257320i	0.782133	+	0.623111i	$0.214132\pi$
$822$		0			0
$823$	−42.3469	+	24.4490i	−1.47612	+	0.852239i	−0.999637	−	0.0269434i	$-0.991423\pi$
$823$	−42.3469	+	24.4490i	−1.47612	+	0.852239i	−0.476485	+	0.879183i	$0.658089\pi$
$824$		0			0
$825$			127.169i			4.42746i
$826$		0			0
$827$	−19.1669	+	5.13576i	−0.666500	+	0.178588i	−0.576177	−	0.817325i	$-0.695456\pi$
$827$	−19.1669	+	5.13576i	−0.666500	+	0.178588i	−0.0903220	+	0.995913i	$0.528790\pi$
$828$		0			0
$829$	−1.02246	+	3.81588i	−0.0355116	+	0.132531i	−0.981406	−	0.191944i	$-0.938521\pi$
$829$	−1.02246	+	3.81588i	−0.0355116	+	0.132531i	0.945894	+	0.324475i	$0.105188\pi$
$830$		0			0
$831$	−14.7980	+	55.2268i	−0.513336	+	1.91580i
$832$		0			0
$833$	0.523059	+	1.95208i	0.0181229	+	0.0676357i
$834$		0			0
$835$	42.9948	+	74.4693i	1.48790	+	2.57711i
$836$		0			0
$837$	−19.9381	+	19.9381i	−0.689163	+	0.689163i
$838$		0			0
$839$	10.2817	+	17.8084i	0.354963	+	0.614815i	0.987112	−	0.160033i	$-0.0511600\pi$
$839$	10.2817	+	17.8084i	0.354963	+	0.614815i	−0.632148	+	0.774847i	$0.717827\pi$
$840$		0			0
$841$		−	28.4042i		−	0.979454i
$842$		0			0
$843$	−7.21945	+	7.21945i	−0.248651	+	0.248651i
$844$		0			0
$845$	43.3551	+	43.3551i	1.49146	+	1.49146i
$846$		0			0
$847$	9.27053	+	5.35234i	0.318539	+	0.183909i
$848$		0			0
$849$	−10.5674	−	2.83152i	−0.362672	−	0.0971777i
$850$		0			0
$851$	−11.4062	+	26.9721i	−0.391001	+	0.924590i
$852$		0			0
$853$	2.64958	−	9.88837i	0.0907199	−	0.338571i	−0.905616	−	0.424099i	$-0.860591\pi$
$853$	2.64958	−	9.88837i	0.0907199	−	0.338571i	0.996336	+	0.0855276i	$0.0272576\pi$
$854$		0			0
$855$	−33.2495	+	57.5898i	−1.13711	+	1.96953i
$856$		0			0
$857$	21.7841	−	21.7841i	0.744129	−	0.744129i	−0.229241	−	0.973370i	$-0.573624\pi$
$857$	21.7841	−	21.7841i	0.744129	−	0.744129i	0.973370	+	0.229241i	$0.0736242\pi$
$858$		0			0
$859$	−35.6297	−	35.6297i	−1.21567	−	1.21567i	−0.969134	−	0.246534i	$-0.920708\pi$
$859$	−35.6297	−	35.6297i	−1.21567	−	1.21567i	−0.246534	−	0.969134i	$-0.579292\pi$
$860$		0			0
$861$	−12.7776			−0.435460
$862$		0			0
$863$	16.8209	−	9.71155i	0.572590	−	0.330585i	−0.185593	−	0.982627i	$-0.559421\pi$
$863$	16.8209	−	9.71155i	0.572590	−	0.330585i	0.758183	+	0.652042i	$0.226087\pi$
$864$		0			0
$865$	50.4993	+	50.4993i	1.71703	+	1.71703i
$866$		0			0
$867$	−73.7019	+	42.5518i	−2.50305	+	1.44514i
$868$		0			0
$869$	−14.3754	+	3.85189i	−0.487653	+	0.130666i
$870$		0			0
$871$	−50.3098	−	13.4805i	−1.70468	−	0.456768i
$872$		0			0
$873$	−6.96864	−	1.86724i	−0.235853	−	0.0631966i
$874$		0			0
$875$	20.2844	+	75.7023i	0.685737	+	2.55921i
$876$		0			0
$877$	11.3984			0.384897			0.192448	−	0.981307i	$-0.438357\pi$
$877$	11.3984			0.384897			0.192448	+	0.981307i	$0.438357\pi$
$878$		0			0
$879$	−12.6655	−	21.9372i	−0.427196	−	0.739925i
$880$		0			0
$881$	−26.8685	−	15.5125i	−0.905223	−	0.522631i	−0.0263319	−	0.999653i	$-0.508383\pi$
$881$	−26.8685	−	15.5125i	−0.905223	−	0.522631i	−0.878891	+	0.477023i	$0.841716\pi$
$882$		0			0
$883$	−10.9708	−	40.9436i	−0.369197	−	1.37786i	−0.861642	−	0.507517i	$-0.830563\pi$
$883$	−10.9708	−	40.9436i	−0.369197	−	1.37786i	0.492445	−	0.870343i	$-0.336103\pi$
$884$		0			0
$885$	49.7575	−	86.1825i	1.67258	−	2.89699i
$886$		0			0
$887$	32.9296			1.10567			0.552834	−	0.833291i	$-0.313546\pi$
$887$	32.9296			1.10567			0.552834	+	0.833291i	$0.313546\pi$
$888$		0			0
$889$	16.2361			0.544542
$890$		0			0
$891$	−4.76604	+	8.25502i	−0.159668	+	0.276554i
$892$		0			0
$893$	3.76649	+	14.0567i	0.126041	+	0.470390i
$894$		0			0
$895$	−71.5997	−	41.3381i	−2.39331	−	1.38178i
$896$		0			0
$897$	−34.7105	−	60.1204i	−1.15895	−	2.00736i
$898$		0			0
$899$	5.44134			0.181479
$900$		0			0
$901$	2.51516	+	9.38671i	0.0837921	+	0.312716i
$902$		0			0
$903$	−36.1181	−	9.67783i	−1.20194	−	0.322058i
$904$		0			0
$905$	50.8597	+	13.6278i	1.69063	+	0.453003i
$906$		0			0
$907$	32.1853	−	8.62403i	1.06870	−	0.286356i	0.318739	−	0.947842i	$-0.396741\pi$
$907$	32.1853	−	8.62403i	1.06870	−	0.286356i	0.749957	+	0.661486i	$0.230074\pi$
$908$		0			0
$909$	3.98904	−	2.30308i	0.132308	−	0.0763882i
$910$		0			0
$911$	−12.5509	−	12.5509i	−0.415830	−	0.415830i	0.467933	−	0.883764i	$-0.344999\pi$
$911$	−12.5509	−	12.5509i	−0.415830	−	0.415830i	−0.883764	+	0.467933i	$0.844999\pi$
$912$		0			0
$913$	3.65713	−	2.11145i	0.121033	−	0.0698787i
$914$		0			0
$915$	61.9726			2.04875
$916$		0			0
$917$	−15.1225	−	15.1225i	−0.499387	−	0.499387i
$918$		0			0
$919$	24.0943	−	24.0943i	0.794798	−	0.794798i	−0.187472	−	0.982270i	$-0.560029\pi$
$919$	24.0943	−	24.0943i	0.794798	−	0.794798i	0.982270	+	0.187472i	$0.0600293\pi$
$920$		0			0
$921$	−19.6272	+	33.9953i	−0.646739	+	1.12018i
$922$		0			0
$923$	−7.49332	+	27.9655i	−0.246646	+	0.920494i
$924$		0			0
$925$	−57.7366	−	44.9841i	−1.89837	−	1.47907i
$926$		0			0
$927$	−39.4896	−	10.5812i	−1.29701	−	0.347532i
$928$		0			0
$929$	−31.6174	−	18.2543i	−1.03733	−	0.598905i	−0.118257	−	0.992983i	$-0.537731\pi$
$929$	−31.6174	−	18.2543i	−1.03733	−	0.598905i	−0.919077	+	0.394078i	$0.871064\pi$
$930$		0			0
$931$	0.743327	+	0.743327i	0.0243616	+	0.0243616i
$932$		0			0
$933$	33.6963	−	33.6963i	1.10317	−	1.10317i
$934$		0			0
$935$			110.782i			3.62296i
$936$		0			0
$937$	−4.89492	−	8.47825i	−0.159910	−	0.276972i	0.774926	−	0.632052i	$-0.217787\pi$
$937$	−4.89492	−	8.47825i	−0.159910	−	0.276972i	−0.934836	+	0.355080i	$0.884454\pi$
$938$		0			0
$939$	49.3096	−	49.3096i	1.60916	−	1.60916i
$940$		0			0
$941$	−9.53106	−	16.5083i	−0.310704	−	0.538155i	0.667811	−	0.744331i	$-0.267231\pi$
$941$	−9.53106	−	16.5083i	−0.310704	−	0.538155i	−0.978515	+	0.206176i	$0.933898\pi$
$942$		0			0
$943$	2.15823	+	8.05461i	0.0702815	+	0.262294i
$944$		0			0
$945$	11.5372	−	43.0573i	0.375304	−	1.40065i
$946$		0			0
$947$	−7.82962	+	29.2205i	−0.254428	+	0.949540i	0.713979	+	0.700167i	$0.246891\pi$
$947$	−7.82962	+	29.2205i	−0.254428	+	0.949540i	−0.968408	+	0.249373i	$0.919775\pi$
$948$		0			0
$949$	22.1724	−	5.94107i	0.719745	−	0.192855i
$950$		0			0
$951$			56.8017i			1.84192i
$952$		0			0
$953$	−11.4413	+	6.60565i	−0.370621	+	0.213978i	−0.673730	−	0.738978i	$-0.735309\pi$
$953$	−11.4413	+	6.60565i	−0.370621	+	0.213978i	0.303109	+	0.952956i	$0.401975\pi$
$954$		0			0
$955$	−40.2998	+	69.8014i	−1.30407	+	2.25872i
$956$		0			0
$957$	−7.88003	+	2.11145i	−0.254725	+	0.0682534i
$958$		0			0
$959$	14.4240	+	8.32771i	0.465776	+	0.268916i
$960$		0			0
$961$		−	18.6912i		−	0.602941i
$962$		0			0
$963$			3.71744i			0.119793i
$964$		0			0
$965$	−64.9928	−	37.5236i	−2.09219	−	1.20793i
$966$		0			0
$967$	24.7681	−	6.63659i	0.796488	−	0.213418i	0.162447	−	0.986717i	$-0.448062\pi$
$967$	24.7681	−	6.63659i	0.796488	−	0.213418i	0.634041	+	0.773299i	$0.281395\pi$
$968$		0			0
$969$	−34.2134	+	59.2593i	−1.09909	+	1.90368i
$970$		0			0
$971$	35.8530	−	20.6997i	1.15058	−	0.664286i	0.201549	−	0.979478i	$-0.435402\pi$
$971$	35.8530	−	20.6997i	1.15058	−	0.664286i	0.949028	+	0.315193i	$0.102069\pi$
$972$		0			0
$973$			3.89982i			0.125022i
$974$		0			0
$975$	167.594	−	44.9067i	5.36731	−	1.43817i
$976$		0			0
$977$	−4.55575	+	17.0023i	−0.145751	+	0.543951i	0.853970	+	0.520323i	$0.174188\pi$
$977$	−4.55575	+	17.0023i	−0.145751	+	0.543951i	−0.999721	+	0.0236280i	$0.992478\pi$
$978$		0			0
$979$	4.99205	−	18.6306i	0.159547	−	0.595437i
$980$		0			0
$981$	−10.0809	−	37.6224i	−0.321858	−	1.20119i
$982$		0			0
$983$	−26.2243	−	45.4218i	−0.836424	−	1.44873i	−0.892865	−	0.450324i	$-0.851309\pi$
$983$	−26.2243	−	45.4218i	−0.836424	−	1.44873i	0.0564409	−	0.998406i	$-0.482025\pi$
$984$		0			0
$985$	46.1668	−	46.1668i	1.47100	−	1.47100i
$986$		0			0
$987$	−14.8717	−	25.7585i	−0.473372	−	0.819904i
$988$		0			0
$989$			24.4024i			0.775950i
$990$		0			0
$991$	29.5355	−	29.5355i	0.938225	−	0.938225i	−0.0599753	−	0.998200i	$-0.519102\pi$
$991$	29.5355	−	29.5355i	0.938225	−	0.938225i	0.998200	+	0.0599753i	$0.0191022\pi$
$992$		0			0
$993$	22.9961	+	22.9961i	0.729758	+	0.729758i
$994$		0			0
$995$	49.4159	+	28.5303i	1.56659	+	0.904471i
$996$		0			0
$997$	20.2520	+	5.42650i	0.641387	+	0.171859i	0.564831	−	0.825206i	$-0.308941\pi$
$997$	20.2520	+	5.42650i	0.641387	+	0.171859i	0.0765552	+	0.997065i	$0.475608\pi$
$998$		0			0
$999$	9.14486	+	22.5471i	0.289330	+	0.713359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.b.399.1	yes	8
4.3	odd	2		592.2.be.c.399.1	yes	8
37.23	odd	12		592.2.be.c.319.1	yes	8
148.23	even	12	inner	592.2.be.b.319.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.b.319.1	✓	8	148.23	even	12	inner
592.2.be.b.399.1	yes	8	1.1	even	1	trivial
592.2.be.c.319.1	yes	8	37.23	odd	12
592.2.be.c.399.1	yes	8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.36603 + 2.36603i) q^{3} +(-1.06816 - 3.98644i) q^{5} +(2.33847 + 1.35012i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 2.36603i) q^{3} +(-1.06816 - 3.98644i) q^{5} +(2.33847 + 1.35012i) q^{7} +(-2.23205 - 3.86603i) q^{9} -3.86838 q^{11} +(1.36603 + 5.09808i) q^{13} +(10.8912 + 2.91828i) q^{15} +(6.70258 + 1.79595i) q^{17} +(3.48644 - 0.934190i) q^{19} +(-6.38881 + 3.68858i) q^{21} +(3.40428 + 3.40428i) q^{23} +(-10.4206 + 6.01636i) q^{25} +4.00000 q^{27} +(-0.545822 - 0.545822i) q^{29} +(-4.98454 + 4.98454i) q^{31} +(5.28431 - 9.15268i) q^{33} +(2.88429 - 10.7643i) q^{35} +(2.28621 + 5.63677i) q^{37} +(-13.9282 - 3.73205i) q^{39} +(1.50000 + 0.866025i) q^{41} +(3.58407 + 3.58407i) q^{43} +(-13.0275 + 13.0275i) q^{45} +4.03182i q^{47} +(0.145622 + 0.252224i) q^{49} +(-13.4052 + 13.4052i) q^{51} +(0.700230 + 1.21283i) q^{53} +(4.13207 + 15.4211i) q^{55} +(-2.55225 + 9.52514i) q^{57} +(2.28431 - 8.52514i) q^{59} +(5.30900 - 1.42254i) q^{61} -12.0541i q^{63} +(18.8641 - 10.8912i) q^{65} +(-4.93419 + 8.54627i) q^{67} +(-12.7049 + 3.40428i) q^{69} +(4.75058 + 2.74275i) q^{71} -4.34916i q^{73} -32.8740i q^{75} +(-9.04608 - 5.22276i) q^{77} +(3.71614 - 0.995737i) q^{79} +(1.23205 - 2.13397i) q^{81} +(-0.945391 + 0.545822i) q^{83} -28.6379i q^{85} +(2.03704 - 0.545822i) q^{87} +(-1.29048 + 4.81613i) q^{89} +(-3.68858 + 13.7660i) q^{91} +(-4.98454 - 18.6025i) q^{93} +(-7.44819 - 12.9006i) q^{95} +(1.14276 - 1.14276i) q^{97} +(8.63442 + 14.9553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 2 q^{5} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 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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