LMFDB - Embedded newform 592.2.be.c.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			$0.500000 + 2.27030i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.c.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	$-0.544101\pi$
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	0.926779	−	0.375608i	$-0.122566\pi$
$4$		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	−0.0119294	−	0.999929i	$-0.503797\pi$
$7$	−2.33847	−	1.35012i	−0.883858	−	0.510296i	−0.871928	+	0.489633i	$0.837131\pi$
$8$		0			0
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$		0			0
$11$	3.86838			1.16636			0.583180	−	0.812343i	$-0.301808\pi$
$11$	3.86838			1.16636			0.583180	+	0.812343i	$0.301808\pi$
$12$		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	−0.635516	−	0.772088i	$-0.719213\pi$
$19$	−3.48644	+	0.934190i	−0.799845	+	0.214318i	−0.164329	+	0.986406i	$0.552546\pi$
$20$		0			0
$21$	−6.38881	+	3.68858i	−1.39415	+	0.804915i
$22$		0			0
$23$	−3.40428	−	3.40428i	−0.709841	−	0.709841i	0.256661	−	0.966502i	$-0.417378\pi$
$23$	−3.40428	−	3.40428i	−0.709841	−	0.709841i	−0.966502	+	0.256661i	$0.917378\pi$
$24$		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	−0.0997623	−	0.995011i	$-0.531808\pi$
$31$	4.98454	−	4.98454i	0.895249	−	0.895249i	0.995011	+	0.0997623i	$0.0318082\pi$
$32$		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	0.378880	−	0.925446i	$-0.376309\pi$
$43$	−3.58407	−	3.58407i	−0.546566	−	0.546566i	−0.925446	+	0.378880i	$0.876309\pi$
$44$		0			0
$45$	−13.0275	+	13.0275i	−1.94202	+	1.94202i
$46$		0			0
$47$		−	4.03182i		−	0.588101i	−0.955790	−	0.294051i	$-0.904997\pi$
$47$		−	4.03182i		−	0.588101i	0.955790	−	0.294051i	$-0.0950035\pi$
$48$		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	$0.278143\pi$
$59$	−2.28431	+	8.52514i	−0.297391	+	1.10988i	−0.939300	+	0.343098i	$0.888524\pi$
$60$		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	$-0.627382\pi$
$67$	4.93419	−	8.54627i	0.602807	−	1.04409i	0.992394	−	0.123103i	$-0.0392845\pi$
$68$		0			0
$69$	−12.7049	+	3.40428i	−1.52949	+	0.409827i
$70$		0			0
$71$	−4.75058	−	2.74275i	−0.563790	−	0.325504i	0.190876	−	0.981614i	$-0.438867\pi$
$71$	−4.75058	−	2.74275i	−0.563790	−	0.325504i	−0.754665	+	0.656110i	$0.772201\pi$
$72$		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	−0.461734	−	0.887018i	$-0.652773\pi$
$79$	−3.71614	+	0.995737i	−0.418098	+	0.112029i	0.0436357	+	0.999048i	$0.486106\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		0			0
$83$	0.945391	−	0.545822i	0.103770	−	0.0599117i	−0.447217	−	0.894426i	$-0.647585\pi$
$83$	0.945391	−	0.545822i	0.103770	−	0.0599117i	0.550987	+	0.834514i	$0.314251\pi$
$84$		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	−0.950080	−	0.312006i	$-0.898999\pi$
$103$	−6.47575	+	6.47575i	−0.638074	+	0.638074i	0.312006	+	0.950080i	$0.398999\pi$
$104$		0			0
$105$	21.5286	+	21.5286i	2.10098	+	2.10098i
$106$		0			0
$107$	0.721175	+	0.416371i	0.0697187	+	0.0402521i	0.534454	−	0.845197i	$-0.320517\pi$
$107$	0.721175	+	0.416371i	0.0697187	+	0.0402521i	−0.464735	+	0.885450i	$0.653851\pi$
$108$		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	−0.712915	−	0.701250i	$-0.752626\pi$
$127$	−5.20729	+	3.00643i	−0.462073	+	0.266778i	0.250843	+	0.968028i	$0.419292\pi$
$128$		0			0
$129$	−13.3759	+	3.58407i	−1.17769	+	0.315560i
$130$		0			0
$131$	7.65033	+	2.04990i	0.668412	+	0.179101i	0.577040	−	0.816716i	$-0.304208\pi$
$131$	7.65033	+	2.04990i	0.668412	+	0.179101i	0.0913729	+	0.995817i	$0.470874\pi$
$132$		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	0.833774	−	0.552105i	$-0.186175\pi$
$139$	−0.722127	−	1.25076i	−0.0612500	−	0.106088i	−0.895024	+	0.446017i	$0.852842\pi$
$140$		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	−0.975680	−	0.219200i	$-0.929655\pi$
$151$	−3.66198	+	6.34273i	−0.298008	+	0.516164i	0.677673	+	0.735364i	$0.262989\pi$
$152$		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	0.732072	−	0.681227i	$-0.238553\pi$
$163$	13.0921	+	3.50801i	1.02545	+	0.274769i	0.293379	+	0.955996i	$0.405220\pi$
$164$		0			0
$165$	−42.1312	−	11.2890i	−3.27991	−	0.878849i
$166$		0			0
$167$	20.1256	−	5.39263i	1.55736	−	0.417294i	0.625536	−	0.780195i	$-0.284880\pi$
$167$	20.1256	−	5.39263i	1.55736	−	0.417294i	0.931828	+	0.362901i	$0.118214\pi$
$168$		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	$0.519300\pi$
$179$	−14.1652	+	14.1652i	−1.05876	+	1.05876i	−0.998162	+	0.0605961i	$0.980700\pi$
$180$		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	1.00000		0.000783154i	$-0.000249286\pi$
$191$	13.8094	+	13.8094i	0.999217	+	0.999217i	−0.000783154		1.00000i	$0.500249\pi$
$192$		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	−0.269866	−	0.962898i	$-0.586980\pi$
$199$	9.77641	−	9.77641i	0.693031	−	0.693031i	0.962898	+	0.269866i	$0.0869796\pi$
$200$		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	$0.0631764\pi$
$211$			5.72823i			0.394348i	−0.980369	+	0.197174i	$0.936824\pi$
$212$		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	$0.0368650\pi$
$223$			3.45124i			0.231112i	−0.993301	+	0.115556i	$0.963135\pi$
$224$		0			0
$225$	46.5188	+	26.8576i	3.10125	+	1.79051i
$226$		0			0
$227$	19.2959	−	5.17032i	1.28071	−	0.343166i	0.446587	−	0.894740i	$-0.352639\pi$
$227$	19.2959	−	5.17032i	1.28071	−	0.343166i	0.834126	+	0.551574i	$0.185973\pi$
$228$		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	$0.202468\pi$
$239$	−2.92566	+	10.9187i	−0.189245	+	0.706274i	−0.993682	+	0.112235i	$0.964199\pi$
$240$		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	$0.597704\pi$
$251$	−19.8894	+	19.8894i	−1.25541	+	1.25541i	−0.953260	+	0.302150i	$0.902296\pi$
$252$		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	$-0.605843\pi$
$263$	10.6284	−	18.4090i	0.655377	−	1.13515i	0.981799	−	0.189923i	$-0.0608237\pi$
$264$		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	−0.0312846	−	0.999511i	$-0.509960\pi$
$271$	13.4771	−	7.78100i	0.818675	−	0.472662i	0.849959	+	0.526848i	$0.176626\pi$
$272$		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	0.928256	−	0.371942i	$-0.121308\pi$
$283$	−1.03641	−	3.86793i	−0.0616082	−	0.229925i	−0.989864	+	0.142017i	$0.954641\pi$
$284$		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	$-0.634477\pi$
$307$	−14.3681			−0.820032			−0.410016	+	0.912078i	$0.634477\pi$
$308$		0			0
$309$	6.47575	+	24.1678i	0.368392	+	1.37486i
$310$		0			0
$311$	16.8481	+	4.51445i	0.955371	+	0.255991i	0.702640	−	0.711546i	$-0.252005\pi$
$311$	16.8481	+	4.51445i	0.955371	+	0.255991i	0.252731	+	0.967537i	$0.418671\pi$
$312$		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	$0.189419\pi$
$331$	−3.08089	+	11.4980i	−0.169341	+	0.631989i	−0.997447	+	0.0714168i	$0.977248\pi$
$332$		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	−0.547737	−	0.836651i	$-0.684510\pi$
$347$	5.38187	−	5.38187i	0.288914	−	0.288914i	0.836651	+	0.547737i	$0.184510\pi$
$348$		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	$-0.949963\pi$
$367$	−30.9788	−	17.8856i	−1.61708	−	0.933622i	−0.629411	−	0.777073i	$-0.716704\pi$
$368$		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	−0.731217	−	0.682145i	$-0.761047\pi$
$379$	−9.85214	+	5.68814i	−0.506071	+	0.292180i	0.225146	+	0.974325i	$0.427714\pi$
$380$		0			0
$381$			16.4275i			0.841604i
$382$		0			0
$383$	−13.2959	+	3.56262i	−0.679388	+	0.182042i	−0.581980	−	0.813203i	$-0.697722\pi$
$383$	−13.2959	+	3.56262i	−0.679388	+	0.182042i	−0.0974081	+	0.995245i	$0.531055\pi$
$384$		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	−0.756797	−	0.653650i	$-0.773237\pi$
$419$	−11.6496	+	6.72588i	−0.569119	+	0.328581i	0.187678	+	0.982231i	$0.439904\pi$
$420$		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	$0.0804344\pi$
$431$	5.28824	+	19.7360i	0.254726	+	0.950649i	−0.713517	+	0.700638i	$0.752899\pi$
$432$		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	$0.304247\pi$
$439$	10.1763	+	37.9785i	0.485689	+	1.81261i	−0.0912516	+	0.995828i	$0.529087\pi$
$440$		0			0
$441$	0.650070	−	1.12595i	0.0309557	−	0.0536169i
$442$		0			0
$443$	10.7449			0.510506			0.255253	−	0.966874i	$-0.417841\pi$
$443$	10.7449			0.510506			0.255253	+	0.966874i	$0.417841\pi$
$444$		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	0.260221	−	0.965549i	$-0.416204\pi$
$463$	20.8365	−	5.58312i	0.968354	−	0.259470i	0.708133	+	0.706079i	$0.249538\pi$
$464$		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	$0.0121099\pi$
$467$	22.4165	+	22.4165i	1.03731	+	1.03731i	0.0380351	+	0.999276i	$0.487890\pi$
$468$		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	$-0.649075\pi$
$479$	8.44113	−	31.5027i	0.385685	−	1.43940i	0.837084	−	0.547075i	$-0.184259\pi$
$480$		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	0.105177	−	0.994453i	$-0.466459\pi$
$487$	−19.6246	−	19.6246i	−0.889276	−	0.889276i	−0.994453	+	0.105177i	$0.966459\pi$
$488$		0			0
$489$	26.1842	−	26.1842i	1.18409	−	1.18409i
$490$		0			0
$491$			33.9356i			1.53149i	0.643143	+	0.765746i	$0.277630\pi$
$491$			33.9356i			1.53149i	−0.643143	+	0.765746i	$0.722370\pi$
$492$		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	$-0.909093\pi$
$499$	−6.01820	−	22.4602i	−0.269412	−	1.00546i	0.690083	−	0.723730i	$-0.257574\pi$
$500$		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	$0.168119\pi$
$503$	−3.05589	+	11.4047i	−0.136255	+	0.508511i	−0.999990	+	0.00456409i	$0.998547\pi$
$504$		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	−0.809129	−	0.587631i	$-0.800061\pi$
$523$	−27.8098	+	7.45162i	−1.21604	+	0.325837i	−0.406910	+	0.913468i	$0.633394\pi$
$524$		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	−0.553235	−	0.833025i	$-0.686607\pi$
$547$	6.54373	−	6.54373i	0.279790	−	0.279790i	0.833025	+	0.553235i	$0.186607\pi$
$548$		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	0.856203	−	0.516640i	$-0.172817\pi$
$563$	8.05703	+	8.05703i	0.339563	+	0.339563i	−0.516640	+	0.856203i	$0.672817\pi$
$564$		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	−0.509166	−	0.860668i	$-0.670046\pi$
$571$	−0.439400	+	0.253687i	−0.0183883	+	0.0106165i	0.490778	+	0.871285i	$0.336713\pi$
$572$		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	$-0.985198\pi$
$587$	−3.80557	−	14.2026i	−0.157073	−	0.586203i	0.841846	−	0.539717i	$-0.181469\pi$
$588$		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	0.131975	−	0.991253i	$-0.457868\pi$
$599$	−16.1651	−	9.33293i	−0.660488	−	0.381333i	−0.792463	+	0.609920i	$0.791202\pi$
$600$		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	−0.470562	−	0.882367i	$-0.655949\pi$
$607$	−32.5032	−	8.70920i	−1.31926	−	0.353496i	−0.848702	+	0.528872i	$0.822615\pi$
$608$		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	$-0.652197\pi$
$619$	−22.8957			−0.920257			−0.460129	+	0.887852i	$0.652197\pi$
$620$		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	−0.00105844	−	0.999999i	$-0.500337\pi$
$631$	−12.6095	−	3.37870i	−0.501975	−	0.134504i	−0.500916	+	0.865496i	$0.667004\pi$
$632$		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	−0.496113	−	0.868258i	$-0.665240\pi$
$643$	9.43666	−	9.43666i	0.372146	−	0.372146i	0.868258	+	0.496113i	$0.165240\pi$
$644$		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	$-0.900614\pi$
$647$	−7.14982	−	26.6835i	−0.281088	−	1.04904i	0.670562	−	0.741853i	$-0.266053\pi$
$648$		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	−0.999980	−	0.00634482i	$-0.997980\pi$
$659$	−12.6942	+	21.9870i	−0.494495	+	0.856491i	0.505485	+	0.862836i	$0.331314\pi$
$660$		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	$-0.797395\pi$
$683$	4.95125	−	18.4783i	0.189454	−	0.707053i	0.993633	−	0.112665i	$-0.0359387\pi$
$684$		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	$-0.815096\pi$
$691$	−23.4804	−	40.6692i	−0.893236	−	1.54713i	−0.0572642	−	0.998359i	$-0.518238\pi$
$692$		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	−0.596684	−	0.802476i	$-0.703515\pi$
$719$	−5.36448	+	3.09719i	−0.200061	+	0.115506i	0.396623	+	0.917982i	$0.370182\pi$
$720$		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	$0.192663\pi$
$727$	10.6413	+	39.7140i	0.394666	+	1.47291i	−0.427684	+	0.903929i	$0.640670\pi$
$728$		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	$-0.700594\pi$
$739$	−32.0393			−1.17859			−0.589293	+	0.807919i	$0.700594\pi$
$740$		0			0
$741$	−52.0463			−1.91197
$742$		0			0
$743$	−23.5574	+	40.8026i	−0.864237	+	1.49690i	0.00356481	+	0.999994i	$0.498865\pi$
$743$	−23.5574	+	40.8026i	−0.864237	+	1.49690i	−0.867802	+	0.496910i	$0.834468\pi$
$744$		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	$-0.541443\pi$
$751$	−7.11583			−0.259660			−0.129830	+	0.991536i	$0.541443\pi$
$752$		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	$0.409342\pi$
$787$			53.8467i			1.91943i	−0.280977	+	0.959715i	$0.590658\pi$
$788$		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	0.845134	−	0.534554i	$-0.179520\pi$
$811$	22.9181	+	13.2318i	0.804765	+	0.464631i	−0.0403699	+	0.999185i	$0.512854\pi$
$812$		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	0.476485	−	0.879183i	$-0.341911\pi$
$823$	42.3469	−	24.4490i	1.47612	−	0.852239i	0.999637	+	0.0269434i	$0.00857738\pi$
$824$		0			0
$825$			127.169i			4.42746i
$826$		0			0
$827$	19.1669	−	5.13576i	0.666500	−	0.178588i	0.0903220	−	0.995913i	$-0.471210\pi$
$827$	19.1669	−	5.13576i	0.666500	−	0.178588i	0.576177	+	0.817325i	$0.304544\pi$
$828$		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	0.632148	−	0.774847i	$-0.282173\pi$
$839$	−10.2817	−	17.8084i	−0.354963	−	0.614815i	−0.987112	+	0.160033i	$0.948840\pi$
$840$		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	$0.0792916\pi$
$859$	35.6297	+	35.6297i	1.21567	+	1.21567i	0.246534	+	0.969134i	$0.420708\pi$
$860$		0			0
$861$	−12.7776			−0.435460
$862$		0			0
$863$	−16.8209	+	9.71155i	−0.572590	+	0.330585i	−0.758183	−	0.652042i	$-0.773913\pi$
$863$	−16.8209	+	9.71155i	−0.572590	+	0.330585i	0.185593	+	0.982627i	$0.440579\pi$
$864$		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	$0.169437\pi$
$883$	10.9708	+	40.9436i	0.369197	+	1.37786i	−0.492445	+	0.870343i	$0.663897\pi$
$884$		0			0
$885$	49.7575	−	86.1825i	1.67258	−	2.89699i
$886$		0			0
$887$	−32.9296			−1.10567			−0.552834	−	0.833291i	$-0.686454\pi$
$887$	−32.9296			−1.10567			−0.552834	+	0.833291i	$0.686454\pi$
$888$		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	−0.749957	−	0.661486i	$-0.769926\pi$
$907$	−32.1853	+	8.62403i	−1.06870	+	0.286356i	−0.318739	+	0.947842i	$0.603259\pi$
$908$		0			0
$909$	3.98904	−	2.30308i	0.132308	−	0.0763882i
$910$		0			0
$911$	12.5509	+	12.5509i	0.415830	+	0.415830i	0.883764	−	0.467933i	$-0.155001\pi$
$911$	12.5509	+	12.5509i	0.415830	+	0.415830i	−0.467933	+	0.883764i	$0.655001\pi$
$912$		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	−0.982270	−	0.187472i	$-0.939971\pi$
$919$	−24.0943	+	24.0943i	−0.794798	+	0.794798i	0.187472	+	0.982270i	$0.439971\pi$
$920$		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	$-0.753109\pi$
$947$	7.82962	−	29.2205i	0.254428	−	0.949540i	0.968408	−	0.249373i	$-0.0802245\pi$
$948$		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	−0.634041	−	0.773299i	$-0.718605\pi$
$967$	−24.7681	+	6.63659i	−0.796488	+	0.213418i	−0.162447	+	0.986717i	$0.551938\pi$
$968$		0			0
$969$	−34.2134	+	59.2593i	−1.09909	+	1.90368i
$970$		0			0
$971$	−35.8530	+	20.6997i	−1.15058	+	0.664286i	−0.949028	−	0.315193i	$-0.897931\pi$
$971$	−35.8530	+	20.6997i	−1.15058	+	0.664286i	−0.201549	+	0.979478i	$0.564598\pi$
$972$		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	$0.148691\pi$
$983$	26.2243	+	45.4218i	0.836424	+	1.44873i	−0.0564409	+	0.998406i	$0.517975\pi$
$984$		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	−0.998200	−	0.0599753i	$-0.980898\pi$
$991$	−29.5355	+	29.5355i	−0.938225	+	0.938225i	0.0599753	+	0.998200i	$0.480898\pi$
$992$		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.c.399.1	yes	8
4.3	odd	2		592.2.be.b.399.1	yes	8
37.23	odd	12		592.2.be.b.319.1	✓	8
148.23	even	12	inner	592.2.be.c.319.1	yes	8

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

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