LMFDB - Embedded newform 1064.2.q.n.305.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.4
Root			$-0.342094 + 0.592525i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.n.457.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342094 + 0.592525i) q^{3} +(1.82548 + 3.16183i) q^{5} +(-1.95459 + 1.78314i) q^{7} +(1.26594 + 2.19268i) q^{9} +O(q^{10})$	\(q+(-0.342094 + 0.592525i) q^{3} +(1.82548 + 3.16183i) q^{5} +(-1.95459 + 1.78314i) q^{7} +(1.26594 + 2.19268i) q^{9} +(-1.18865 + 2.05880i) q^{11} +5.46860 q^{13} -2.49795 q^{15} +(2.43032 - 4.20943i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-0.387898 - 1.76814i) q^{21} +(0.887746 + 1.53762i) q^{23} +(-4.16477 + 7.21359i) q^{25} -3.78485 q^{27} -6.04283 q^{29} +(-0.849279 + 1.47099i) q^{31} +(-0.813260 - 1.40861i) q^{33} +(-9.20604 - 2.92500i) q^{35} +(-2.81318 - 4.87257i) q^{37} +(-1.87078 + 3.24028i) q^{39} -2.00000 q^{41} +3.10972 q^{43} +(-4.62191 + 8.00539i) q^{45} +(2.61508 + 4.52946i) q^{47} +(0.640854 - 6.97060i) q^{49} +(1.66280 + 2.88005i) q^{51} +(3.23257 - 5.59897i) q^{53} -8.67942 q^{55} +0.684189 q^{57} +(3.76133 - 6.51482i) q^{59} +(3.87796 + 6.71683i) q^{61} +(-6.38424 - 2.02844i) q^{63} +(9.98283 + 17.2908i) q^{65} +(1.31045 - 2.26977i) q^{67} -1.21477 q^{69} +11.1529 q^{71} +(-7.26525 + 12.5838i) q^{73} +(-2.84949 - 4.93546i) q^{75} +(-1.34780 - 6.14363i) q^{77} +(-0.480902 - 0.832946i) q^{79} +(-2.50305 + 4.33541i) q^{81} -15.0476 q^{83} +17.7460 q^{85} +(2.06722 - 3.58053i) q^{87} +(-6.01606 - 10.4201i) q^{89} +(-10.6889 + 9.75126i) q^{91} +(-0.581067 - 1.00644i) q^{93} +(1.82548 - 3.16183i) q^{95} -6.26438 q^{97} -6.01904 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.342094	+	0.592525i	−0.197508	+	0.342094i	−0.947720	−	0.319103i	$-0.896618\pi$
$3$	−0.342094	+	0.592525i	−0.197508	+	0.342094i	0.750212	+	0.661198i	$0.229952\pi$
$4$		0			0
$5$	1.82548	+	3.16183i	0.816380	+	1.41401i	0.908333	+	0.418249i	$0.137356\pi$
$5$	1.82548	+	3.16183i	0.816380	+	1.41401i	−0.0919522	+	0.995763i	$0.529311\pi$
$6$		0			0
$7$	−1.95459	+	1.78314i	−0.738766	+	0.673962i
$7$	−1.95459	+	1.78314i	−0.738766	+	0.673962i
$8$		0			0
$9$	1.26594	+	2.19268i	0.421981	+	0.730892i
$10$		0			0
$11$	−1.18865	+	2.05880i	−0.358391	+	0.620751i	−0.987692	−	0.156410i	$-0.950008\pi$
$11$	−1.18865	+	2.05880i	−0.358391	+	0.620751i	0.629301	+	0.777161i	$0.283341\pi$
$12$		0			0
$13$	5.46860			1.51672			0.758358	−	0.651838i	$-0.226002\pi$
$13$	5.46860			1.51672			0.758358	+	0.651838i	$0.226002\pi$
$14$		0			0
$15$	−2.49795			−0.644968
$16$		0			0
$17$	2.43032	−	4.20943i	0.589438	−	1.02094i	−0.404868	−	0.914375i	$-0.632682\pi$
$17$	2.43032	−	4.20943i	0.589438	−	1.02094i	0.994306	−	0.106562i	$-0.0339842\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$		0			0
$21$	−0.387898	−	1.76814i	−0.0846462	−	0.385841i
$22$		0			0
$23$	0.887746	+	1.53762i	0.185108	+	0.320616i	0.943613	−	0.331051i	$-0.107403\pi$
$23$	0.887746	+	1.53762i	0.185108	+	0.320616i	−0.758505	+	0.651667i	$0.774070\pi$
$24$		0			0
$25$	−4.16477	+	7.21359i	−0.832954	+	1.44272i
$26$		0			0
$27$	−3.78485			−0.728396
$28$		0			0
$29$	−6.04283			−1.12213			−0.561063	−	0.827773i	$-0.689607\pi$
$29$	−6.04283			−1.12213			−0.561063	+	0.827773i	$0.689607\pi$
$30$		0			0
$31$	−0.849279	+	1.47099i	−0.152535	+	0.264198i	−0.932159	−	0.362050i	$-0.882077\pi$
$31$	−0.849279	+	1.47099i	−0.152535	+	0.264198i	0.779624	+	0.626248i	$0.215410\pi$
$32$		0			0
$33$	−0.813260	−	1.40861i	−0.141570	−	0.245207i
$34$		0			0
$35$	−9.20604	−	2.92500i	−1.55610	−	0.494415i
$36$		0			0
$37$	−2.81318	−	4.87257i	−0.462483	−	0.801045i	0.536601	−	0.843836i	$-0.319708\pi$
$37$	−2.81318	−	4.87257i	−0.462483	−	0.801045i	−0.999084	+	0.0427915i	$0.986375\pi$
$38$		0			0
$39$	−1.87078	+	3.24028i	−0.299564	+	0.518860i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	3.10972			0.474227			0.237114	−	0.971482i	$-0.423799\pi$
$43$	3.10972			0.474227			0.237114	+	0.971482i	$0.423799\pi$
$44$		0			0
$45$	−4.62191	+	8.00539i	−0.688994	+	1.19337i
$46$		0			0
$47$	2.61508	+	4.52946i	0.381449	+	0.660689i	0.991270	−	0.131850i	$-0.0420918\pi$
$47$	2.61508	+	4.52946i	0.381449	+	0.660689i	−0.609820	+	0.792540i	$0.708758\pi$
$48$		0			0
$49$	0.640854	−	6.97060i	0.0915506	−	0.995800i
$50$		0			0
$51$	1.66280	+	2.88005i	0.232838	+	0.403287i
$52$		0			0
$53$	3.23257	−	5.59897i	0.444027	−	0.769077i	−0.553957	−	0.832545i	$-0.686883\pi$
$53$	3.23257	−	5.59897i	0.444027	−	0.769077i	0.997984	+	0.0634680i	$0.0202161\pi$
$54$		0			0
$55$	−8.67942			−1.17033
$56$		0			0
$57$	0.684189			0.0906230
$58$		0			0
$59$	3.76133	−	6.51482i	0.489684	−	0.848157i	−0.510246	−	0.860029i	$-0.670446\pi$
$59$	3.76133	−	6.51482i	0.489684	−	0.848157i	0.999930	+	0.0118716i	$0.00377892\pi$
$60$		0			0
$61$	3.87796	+	6.71683i	0.496522	+	0.860002i	0.999992	−	0.00401117i	$-0.00127680\pi$
$61$	3.87796	+	6.71683i	0.496522	+	0.860002i	−0.503470	+	0.864013i	$0.667943\pi$
$62$		0			0
$63$	−6.38424	−	2.02844i	−0.804339	−	0.255559i
$64$		0			0
$65$	9.98283	+	17.2908i	1.23822	+	2.14466i
$66$		0			0
$67$	1.31045	−	2.26977i	0.160097	−	0.277296i	−0.774806	−	0.632199i	$-0.782153\pi$
$67$	1.31045	−	2.26977i	0.160097	−	0.277296i	0.934903	+	0.354902i	$0.115486\pi$
$68$		0			0
$69$	−1.21477			−0.146241
$70$		0			0
$71$	11.1529			1.32361			0.661805	−	0.749676i	$-0.269791\pi$
$71$	11.1529			1.32361			0.661805	+	0.749676i	$0.269791\pi$
$72$		0			0
$73$	−7.26525	+	12.5838i	−0.850333	+	1.47282i	0.0305744	+	0.999532i	$0.490266\pi$
$73$	−7.26525	+	12.5838i	−0.850333	+	1.47282i	−0.880908	+	0.473288i	$0.843067\pi$
$74$		0			0
$75$	−2.84949	−	4.93546i	−0.329030	−	0.569898i
$76$		0			0
$77$	−1.34780	−	6.14363i	−0.153596	−	0.700132i
$78$		0			0
$79$	−0.480902	−	0.832946i	−0.0541057	−	0.0937138i	0.837704	−	0.546124i	$-0.183897\pi$
$79$	−0.480902	−	0.832946i	−0.0541057	−	0.0937138i	−0.891810	+	0.452411i	$0.850564\pi$
$80$		0			0
$81$	−2.50305	+	4.33541i	−0.278117	+	0.481712i
$82$		0			0
$83$	−15.0476			−1.65169			−0.825844	−	0.563898i	$-0.809301\pi$
$83$	−15.0476			−1.65169			−0.825844	+	0.563898i	$0.809301\pi$
$84$		0			0
$85$	17.7460			1.92482
$86$		0			0
$87$	2.06722	−	3.58053i	0.221629	−	0.383873i
$88$		0			0
$89$	−6.01606	−	10.4201i	−0.637701	−	1.10453i	−0.985936	−	0.167123i	$-0.946552\pi$
$89$	−6.01606	−	10.4201i	−0.637701	−	1.10453i	0.348235	−	0.937407i	$-0.386781\pi$
$90$		0			0
$91$	−10.6889	+	9.75126i	−1.12050	+	1.02221i
$92$		0			0
$93$	−0.581067	−	1.00644i	−0.0602539	−	0.104363i
$94$		0			0
$95$	1.82548	−	3.16183i	0.187290	−	0.324397i
$96$		0			0
$97$	−6.26438			−0.636052			−0.318026	−	0.948082i	$-0.603020\pi$
$97$	−6.26438			−0.636052			−0.318026	+	0.948082i	$0.603020\pi$
$98$		0			0
$99$	−6.01904			−0.604937
$100$		0			0
$101$	2.85798	−	4.95016i	0.284379	−	0.492559i	−0.688079	−	0.725636i	$-0.741546\pi$
$101$	2.85798	−	4.95016i	0.284379	−	0.492559i	0.972458	+	0.233076i	$0.0748792\pi$
$102$		0			0
$103$	0.849397	+	1.47120i	0.0836935	+	0.144961i	0.904834	−	0.425765i	$-0.139995\pi$
$103$	0.849397	+	1.47120i	0.0836935	+	0.144961i	−0.821140	+	0.570726i	$0.806662\pi$
$104$		0			0
$105$	4.88247	−	4.45418i	0.476480	−	0.434684i
$106$		0			0
$107$	−3.62921	−	6.28598i	−0.350849	−	0.607688i	0.635550	−	0.772060i	$-0.280774\pi$
$107$	−3.62921	−	6.28598i	−0.350849	−	0.607688i	−0.986398	+	0.164372i	$0.947440\pi$
$108$		0			0
$109$	−9.22246	+	15.9738i	−0.883351	+	1.53001i	−0.0357590	+	0.999360i	$0.511385\pi$
$109$	−9.22246	+	15.9738i	−0.883351	+	1.53001i	−0.847592	+	0.530648i	$0.821948\pi$
$110$		0			0
$111$	3.84949			0.365377
$112$		0			0
$113$	17.9243			1.68618			0.843090	−	0.537772i	$-0.180734\pi$
$113$	17.9243			1.68618			0.843090	+	0.537772i	$0.180734\pi$
$114$		0			0
$115$	−3.24113	+	5.61380i	−0.302237	+	0.523490i
$116$		0			0
$117$	6.92294	+	11.9909i	0.640026	+	1.10856i
$118$		0			0
$119$	2.75571	+	12.5613i	0.252616	+	1.15149i
$120$		0			0
$121$	2.67423	+	4.63190i	0.243112	+	0.421082i
$122$		0			0
$123$	0.684189	−	1.18505i	0.0616912	−	0.106852i
$124$		0			0
$125$	−12.1560			−1.08727
$126$		0			0
$127$	16.8044			1.49115			0.745575	−	0.666421i	$-0.232175\pi$
$127$	16.8044			1.49115			0.745575	+	0.666421i	$0.232175\pi$
$128$		0			0
$129$	−1.06382	+	1.84258i	−0.0936638	+	0.162230i
$130$		0			0
$131$	5.05319	+	8.75239i	0.441500	+	0.764700i	0.997801	−	0.0662810i	$-0.0211134\pi$
$131$	5.05319	+	8.75239i	0.441500	+	0.764700i	−0.556301	+	0.830981i	$0.687780\pi$
$132$		0			0
$133$	2.52154	+	0.801158i	0.218645	+	0.0694692i
$134$		0			0
$135$	−6.90918	−	11.9671i	−0.594648	−	1.02996i
$136$		0			0
$137$	2.77605	−	4.80826i	0.237174	−	0.410797i	−0.722728	−	0.691132i	$-0.757112\pi$
$137$	2.77605	−	4.80826i	0.237174	−	0.410797i	0.959902	+	0.280335i	$0.0904456\pi$
$138$		0			0
$139$	4.35122			0.369066			0.184533	−	0.982826i	$-0.440923\pi$
$139$	4.35122			0.369066			0.184533	+	0.982826i	$0.440923\pi$
$140$		0			0
$141$	−3.57842			−0.301357
$142$		0			0
$143$	−6.50024	+	11.2588i	−0.543578	+	0.941504i
$144$		0			0
$145$	−11.0311	−	19.1064i	−0.916081	−	1.58670i
$146$		0			0
$147$	3.91102	+	2.76433i	0.322576	+	0.227998i
$148$		0			0
$149$	−6.07213	−	10.5172i	−0.497448	−	0.861605i	0.502548	−	0.864549i	$-0.332396\pi$
$149$	−6.07213	−	10.5172i	−0.497448	−	0.861605i	−0.999996	+	0.00294443i	$0.999063\pi$
$150$		0			0
$151$	7.89604	−	13.6763i	0.642571	−	1.11297i	−0.342286	−	0.939596i	$-0.611201\pi$
$151$	7.89604	−	13.6763i	0.642571	−	1.11297i	0.984857	−	0.173370i	$-0.0554655\pi$
$152$		0			0
$153$	12.3066			0.994927
$154$		0			0
$155$	−6.20138			−0.498106
$156$		0			0
$157$	−3.91918	+	6.78822i	−0.312785	+	0.541759i	−0.978964	−	0.204033i	$-0.934595\pi$
$157$	−3.91918	+	6.78822i	−0.312785	+	0.541759i	0.666180	+	0.745791i	$0.267928\pi$
$158$		0			0
$159$	2.21169	+	3.83075i	0.175398	+	0.303798i
$160$		0			0
$161$	−4.47697	−	1.42245i	−0.352835	−	0.112105i
$162$		0			0
$163$	2.43233	+	4.21292i	0.190515	+	0.329982i	0.945421	−	0.325851i	$-0.105651\pi$
$163$	2.43233	+	4.21292i	0.190515	+	0.329982i	−0.754906	+	0.655833i	$0.772318\pi$
$164$		0			0
$165$	2.96918	−	5.14277i	0.231151	−	0.400364i
$166$		0			0
$167$	−13.6708			−1.05788			−0.528939	−	0.848660i	$-0.677410\pi$
$167$	−13.6708			−1.05788			−0.528939	+	0.848660i	$0.677410\pi$
$168$		0			0
$169$	16.9056			1.30043
$170$		0			0
$171$	1.26594	−	2.19268i	0.0968091	−	0.167678i
$172$		0			0
$173$	2.67454	+	4.63243i	0.203341	+	0.352197i	0.949603	−	0.313455i	$-0.101487\pi$
$173$	2.67454	+	4.63243i	0.203341	+	0.352197i	−0.746262	+	0.665653i	$0.768153\pi$
$174$		0			0
$175$	−4.72239	−	21.5260i	−0.356979	−	1.62721i
$176$		0			0
$177$	2.57346	+	4.45737i	0.193433	+	0.335036i
$178$		0			0
$179$	0.343912	−	0.595673i	0.0257052	−	0.0445227i	−0.852887	−	0.522096i	$-0.825150\pi$
$179$	0.343912	−	0.595673i	0.0257052	−	0.0445227i	0.878592	+	0.477573i	$0.158484\pi$
$180$		0			0
$181$	7.91388			0.588234			0.294117	−	0.955769i	$-0.404974\pi$
$181$	7.91388			0.588234			0.294117	+	0.955769i	$0.404974\pi$
$182$		0			0
$183$	−5.30652			−0.392269
$184$		0			0
$185$	10.2708	−	17.7896i	0.755125	−	1.30791i
$186$		0			0
$187$	5.77758	+	10.0071i	0.422499	+	0.731789i
$188$		0			0
$189$	7.39784	−	6.74891i	0.538114	−	0.490911i
$190$		0			0
$191$	−12.0448	−	20.8622i	−0.871530	−	1.50954i	−0.860413	−	0.509597i	$-0.829795\pi$
$191$	−12.0448	−	20.8622i	−0.871530	−	1.50954i	−0.0111172	−	0.999938i	$-0.503539\pi$
$192$		0			0
$193$	2.23886	−	3.87783i	0.161157	−	0.279132i	−0.774127	−	0.633030i	$-0.781811\pi$
$193$	2.23886	−	3.87783i	0.161157	−	0.279132i	0.935284	+	0.353898i	$0.115144\pi$
$194$		0			0
$195$	−13.6603			−0.978233
$196$		0			0
$197$	15.0277			1.07068			0.535339	−	0.844637i	$-0.320184\pi$
$197$	15.0277			1.07068			0.535339	+	0.844637i	$0.320184\pi$
$198$		0			0
$199$	13.6957	−	23.7217i	0.970866	−	1.68159i	0.277913	−	0.960606i	$-0.410357\pi$
$199$	13.6957	−	23.7217i	0.970866	−	1.68159i	0.692953	−	0.720983i	$-0.256309\pi$
$200$		0			0
$201$	0.896596	+	1.55295i	0.0632410	+	0.109537i
$202$		0			0
$203$	11.8113	−	10.7752i	0.828988	−	0.756270i
$204$		0			0
$205$	−3.65096	−	6.32365i	−0.254994	−	0.441663i
$206$		0			0
$207$	−2.24767	+	3.89308i	−0.156224	+	0.270588i
$208$		0			0
$209$	2.37730			0.164441
$210$		0			0
$211$	−1.37592			−0.0947219			−0.0473610	−	0.998878i	$-0.515081\pi$
$211$	−1.37592			−0.0947219			−0.0473610	+	0.998878i	$0.515081\pi$
$212$		0			0
$213$	−3.81535	+	6.60839i	−0.261424	+	0.452799i
$214$		0			0
$215$	5.67673	+	9.83239i	0.387150	+	0.670563i
$216$		0			0
$217$	−0.962990	−	4.38957i	−0.0653720	−	0.297984i
$218$		0			0
$219$	−4.97080	−	8.60968i	−0.335896	−	0.581789i
$220$		0			0
$221$	13.2904	−	23.0197i	0.894011	−	1.54847i
$222$		0			0
$223$	27.7782			1.86016			0.930082	−	0.367352i	$-0.119735\pi$
$223$	27.7782			1.86016			0.930082	+	0.367352i	$0.119735\pi$
$224$		0			0
$225$	−21.0894			−1.40596
$226$		0			0
$227$	−10.2953	+	17.8319i	−0.683320	+	1.18355i	0.290641	+	0.956832i	$0.406131\pi$
$227$	−10.2953	+	17.8319i	−0.683320	+	1.18355i	−0.973962	+	0.226713i	$0.927202\pi$
$228$		0			0
$229$	−13.0793	−	22.6541i	−0.864307	−	1.49702i	−0.867733	−	0.497030i	$-0.834424\pi$
$229$	−13.0793	−	22.6541i	−0.864307	−	1.49702i	0.00342574	−	0.999994i	$-0.498910\pi$
$230$		0			0
$231$	4.10133	+	1.30310i	0.269848	+	0.0857376i
$232$		0			0
$233$	6.29226	+	10.8985i	0.412219	+	0.713985i	0.995132	−	0.0985498i	$-0.0314204\pi$
$233$	6.29226	+	10.8985i	0.412219	+	0.713985i	−0.582913	+	0.812535i	$0.698087\pi$
$234$		0			0
$235$	−9.54758	+	16.5369i	−0.622815	+	1.07875i
$236$		0			0
$237$	0.658055			0.0427453
$238$		0			0
$239$	28.5846			1.84898			0.924492	−	0.381202i	$-0.124490\pi$
$239$	28.5846			1.84898			0.924492	+	0.381202i	$0.124490\pi$
$240$		0			0
$241$	−2.32273	+	4.02309i	−0.149620	+	0.259150i	−0.931087	−	0.364797i	$-0.881138\pi$
$241$	−2.32273	+	4.02309i	−0.149620	+	0.259150i	0.781467	+	0.623947i	$0.214472\pi$
$242$		0			0
$243$	−7.38984	−	12.7996i	−0.474059	−	0.821093i
$244$		0			0
$245$	23.2097	−	10.6984i	1.48281	−	0.683498i
$246$		0			0
$247$	−2.73430	−	4.73595i	−0.173979	−	0.301341i
$248$		0			0
$249$	5.14770	−	8.91608i	0.326222	−	0.565033i
$250$		0			0
$251$	−12.0953			−0.763446			−0.381723	−	0.924277i	$-0.624669\pi$
$251$	−12.0953			−0.763446			−0.381723	+	0.924277i	$0.624669\pi$
$252$		0			0
$253$	−4.22087			−0.265364
$254$		0			0
$255$	−6.07081	+	10.5149i	−0.380169	+	0.658471i
$256$		0			0
$257$	−0.946193	−	1.63885i	−0.0590219	−	0.102229i	0.835005	−	0.550243i	$-0.185465\pi$
$257$	−0.946193	−	1.63885i	−0.0590219	−	0.102229i	−0.894027	+	0.448014i	$0.852132\pi$
$258$		0			0
$259$	14.1871	+	4.50760i	0.881541	+	0.280088i
$260$		0			0
$261$	−7.64988	−	13.2500i	−0.473516	−	0.820153i
$262$		0			0
$263$	−11.5901	+	20.0746i	−0.714674	+	1.23785i	0.248411	+	0.968655i	$0.420092\pi$
$263$	−11.5901	+	20.0746i	−0.714674	+	1.23785i	−0.963085	+	0.269197i	$0.913242\pi$
$264$		0			0
$265$	23.6040			1.44998
$266$		0			0
$267$	8.23224			0.503805
$268$		0			0
$269$	−12.1491	+	21.0429i	−0.740744	+	1.28301i	0.211412	+	0.977397i	$0.432194\pi$
$269$	−12.1491	+	21.0429i	−0.740744	+	1.28301i	−0.952157	+	0.305610i	$0.901140\pi$
$270$		0			0
$271$	−6.20481	−	10.7470i	−0.376915	−	0.652836i	0.613696	−	0.789542i	$-0.289682\pi$
$271$	−6.20481	−	10.7470i	−0.376915	−	0.652836i	−0.990612	+	0.136706i	$0.956349\pi$
$272$		0			0
$273$	−2.12126	−	9.66928i	−0.128384	−	0.585211i
$274$		0			0
$275$	−9.90089	−	17.1488i	−0.597046	−	1.03411i
$276$		0			0
$277$	1.16899	−	2.02475i	0.0702377	−	0.121655i	−0.828768	−	0.559593i	$-0.810958\pi$
$277$	1.16899	−	2.02475i	0.0702377	−	0.121655i	0.899005	+	0.437938i	$0.144291\pi$
$278$		0			0
$279$	−4.30056			−0.257468
$280$		0			0
$281$	3.65566			0.218078			0.109039	−	0.994037i	$-0.465223\pi$
$281$	3.65566			0.218078			0.109039	+	0.994037i	$0.465223\pi$
$282$		0			0
$283$	−4.79237	+	8.30064i	−0.284877	+	0.493422i	−0.972579	−	0.232571i	$-0.925286\pi$
$283$	−4.79237	+	8.30064i	−0.284877	+	0.493422i	0.687702	+	0.725993i	$0.258619\pi$
$284$		0			0
$285$	1.24897	+	2.16329i	0.0739828	+	0.128142i
$286$		0			0
$287$	3.90918	−	3.56627i	0.230752	−	0.210510i
$288$		0			0
$289$	−3.31288	−	5.73807i	−0.194875	−	0.337534i
$290$		0			0
$291$	2.14301	−	3.71180i	0.125625	−	0.217590i
$292$		0			0
$293$	−10.0249			−0.585662			−0.292831	−	0.956164i	$-0.594597\pi$
$293$	−10.0249			−0.585662			−0.292831	+	0.956164i	$0.594597\pi$
$294$		0			0
$295$	27.4650			1.59907
$296$		0			0
$297$	4.49886	−	7.79226i	0.261050	−	0.452153i
$298$		0			0
$299$	4.85473	+	8.40864i	0.280756	+	0.486284i
$300$		0			0
$301$	−6.07822	+	5.54505i	−0.350343	+	0.319611i
$302$		0			0
$303$	1.95540	+	3.38684i	0.112335	+	0.194569i
$304$		0			0
$305$	−14.1583	+	24.5229i	−0.810702	+	1.40418i
$306$		0			0
$307$	31.0911			1.77446			0.887230	−	0.461327i	$-0.152627\pi$
$307$	31.0911			1.77446			0.887230	+	0.461327i	$0.152627\pi$
$308$		0			0
$309$	−1.16230			−0.0661207
$310$		0			0
$311$	1.29995	−	2.25158i	0.0737134	−	0.127675i	−0.826813	−	0.562477i	$-0.809848\pi$
$311$	1.29995	−	2.25158i	0.0737134	−	0.127675i	0.900526	+	0.434802i	$0.143182\pi$
$312$		0			0
$313$	7.28660	+	12.6208i	0.411863	+	0.713368i	0.995094	−	0.0989388i	$-0.0315448\pi$
$313$	7.28660	+	12.6208i	0.411863	+	0.713368i	−0.583230	+	0.812307i	$0.698211\pi$
$314$		0			0
$315$	−5.24074	−	23.8888i	−0.295282	−	1.34598i
$316$		0			0
$317$	−5.65025	−	9.78653i	−0.317350	−	0.549666i	0.662584	−	0.748987i	$-0.269460\pi$
$317$	−5.65025	−	9.78653i	−0.317350	−	0.549666i	−0.979934	+	0.199321i	$0.936126\pi$
$318$		0			0
$319$	7.18280	−	12.4410i	0.402160	−	0.696561i
$320$		0			0
$321$	4.96613			0.277182
$322$		0			0
$323$	−4.86063			−0.270453
$324$		0			0
$325$	−22.7755	+	39.4482i	−1.26335	+	2.18819i
$326$		0			0
$327$	−6.30990	−	10.9291i	−0.348938	−	0.604379i
$328$		0			0
$329$	−13.1881	−	4.19019i	−0.727081	−	0.231013i
$330$		0			0
$331$	7.66890	+	13.2829i	0.421521	+	0.730096i	0.996088	−	0.0883616i	$-0.0281631\pi$
$331$	7.66890	+	13.2829i	0.421521	+	0.730096i	−0.574568	+	0.818457i	$0.694830\pi$
$332$		0			0
$333$	7.12264	−	12.3368i	0.390318	−	0.676051i
$334$		0			0
$335$	9.56882			0.522801
$336$		0			0
$337$	7.62537			0.415380			0.207690	−	0.978195i	$-0.433405\pi$
$337$	7.62537			0.415380			0.207690	+	0.978195i	$0.433405\pi$
$338$		0			0
$339$	−6.13182	+	10.6206i	−0.333035	+	0.576833i
$340$		0			0
$341$	−2.01899	−	3.49699i	−0.109334	−	0.189373i
$342$		0			0
$343$	11.1769	+	14.7674i	0.603497	+	0.797365i
$344$		0			0
$345$	−2.21754	−	3.84090i	−0.119389	−	0.206787i
$346$		0			0
$347$	−12.4379	+	21.5430i	−0.667700	+	1.15649i	0.310846	+	0.950460i	$0.399388\pi$
$347$	−12.4379	+	21.5430i	−0.667700	+	1.15649i	−0.978546	+	0.206029i	$0.933946\pi$
$348$		0			0
$349$	31.0832			1.66384			0.831922	−	0.554893i	$-0.187241\pi$
$349$	31.0832			1.66384			0.831922	+	0.554893i	$0.187241\pi$
$350$		0			0
$351$	−20.6979			−1.10477
$352$		0			0
$353$	−7.35250	+	12.7349i	−0.391334	+	0.677810i	−0.992626	−	0.121219i	$-0.961320\pi$
$353$	−7.35250	+	12.7349i	−0.391334	+	0.677810i	0.601292	+	0.799029i	$0.294653\pi$
$354$		0			0
$355$	20.3595	+	35.2636i	1.08057	+	1.87160i
$356$		0			0
$357$	−8.38560	−	2.66432i	−0.443813	−	0.141011i
$358$		0			0
$359$	−10.0452	−	17.3988i	−0.530165	−	0.918272i	−0.999381	−	0.0351887i	$-0.988797\pi$
$359$	−10.0452	−	17.3988i	−0.530165	−	0.918272i	0.469216	−	0.883083i	$-0.344537\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	−3.65936			−0.192066
$364$		0			0
$365$	−53.0503			−2.77678
$366$		0			0
$367$	17.2569	−	29.8898i	0.900802	−	1.56023i	0.0743465	−	0.997232i	$-0.476313\pi$
$367$	17.2569	−	29.8898i	0.900802	−	1.56023i	0.826455	−	0.563002i	$-0.190354\pi$
$368$		0			0
$369$	−2.53189	−	4.38535i	−0.131805	−	0.228292i
$370$		0			0
$371$	3.66538	+	16.7078i	0.190297	+	0.867426i
$372$		0			0
$373$	13.7955	+	23.8944i	0.714301	+	1.23721i	0.963228	+	0.268684i	$0.0865888\pi$
$373$	13.7955	+	23.8944i	0.714301	+	1.23721i	−0.248927	+	0.968522i	$0.580078\pi$
$374$		0			0
$375$	4.15850	−	7.20274i	0.214744	−	0.371948i
$376$		0			0
$377$	−33.0458			−1.70195
$378$		0			0
$379$	9.40171			0.482933			0.241467	−	0.970409i	$-0.422372\pi$
$379$	9.40171			0.482933			0.241467	+	0.970409i	$0.422372\pi$
$380$		0			0
$381$	−5.74869	+	9.95703i	−0.294515	+	0.510114i
$382$		0			0
$383$	−7.16005	−	12.4016i	−0.365861	−	0.633691i	0.623053	−	0.782180i	$-0.285892\pi$
$383$	−7.16005	−	12.4016i	−0.365861	−	0.633691i	−0.988914	+	0.148489i	$0.952559\pi$
$384$		0			0
$385$	16.9647	−	15.4766i	0.864603	−	0.788760i
$386$		0			0
$387$	3.93672	+	6.81860i	0.200115	+	0.346609i
$388$		0			0
$389$	0.817066	−	1.41520i	0.0414269	−	0.0717535i	−0.844569	−	0.535448i	$-0.820143\pi$
$389$	0.817066	−	1.41520i	0.0414269	−	0.0717535i	0.885995	+	0.463694i	$0.153476\pi$
$390$		0			0
$391$	8.63002			0.436439
$392$		0			0
$393$	−6.91468			−0.348799
$394$		0			0
$395$	1.75575	−	3.04106i	0.0883416	−	0.153012i
$396$		0			0
$397$	−3.65489	−	6.33046i	−0.183434	−	0.317717i	0.759614	−	0.650374i	$-0.225388\pi$
$397$	−3.65489	−	6.33046i	−0.183434	−	0.317717i	−0.943048	+	0.332658i	$0.892055\pi$
$398$		0			0
$399$	−1.33731	+	1.22000i	−0.0669492	+	0.0610765i
$400$		0			0
$401$	−13.4986	−	23.3803i	−0.674088	−	1.16756i	−0.976734	−	0.214452i	$-0.931203\pi$
$401$	−13.4986	−	23.3803i	−0.674088	−	1.16756i	0.302646	−	0.953103i	$-0.402130\pi$
$402$		0			0
$403$	−4.64437	+	8.04428i	−0.231352	+	0.400714i
$404$		0			0
$405$	−18.2771			−0.908196
$406$		0			0
$407$	13.3755			0.663000
$408$		0			0
$409$	−12.6820	+	21.9658i	−0.627082	+	1.08614i	0.361052	+	0.932546i	$0.382418\pi$
$409$	−12.6820	+	21.9658i	−0.627082	+	1.08614i	−0.988134	+	0.153593i	$0.950916\pi$
$410$		0			0
$411$	1.89934	+	3.28976i	0.0936876	+	0.162272i
$412$		0			0
$413$	4.26494	+	19.4408i	0.209864	+	0.956618i
$414$		0			0
$415$	−27.4691	−	47.5779i	−1.34841	−	2.33551i
$416$		0			0
$417$	−1.48853	+	2.57821i	−0.0728935	+	0.126255i
$418$		0			0
$419$	8.43567			0.412109			0.206055	−	0.978540i	$-0.433938\pi$
$419$	8.43567			0.412109			0.206055	+	0.978540i	$0.433938\pi$
$420$		0			0
$421$	10.5892			0.516087			0.258044	−	0.966133i	$-0.416922\pi$
$421$	10.5892			0.516087			0.258044	+	0.966133i	$0.416922\pi$
$422$		0			0
$423$	−6.62109	+	11.4681i	−0.321929	+	0.557597i
$424$		0			0
$425$	20.2434	+	35.0626i	0.981950	+	1.70079i
$426$		0			0
$427$	−19.5568	−	6.21372i	−0.946422	−	0.300703i
$428$		0			0
$429$	−4.44739	−	7.70311i	−0.214722	−	0.371910i
$430$		0			0
$431$	14.5234	−	25.1553i	0.699567	−	1.21169i	−0.269049	−	0.963126i	$-0.586709\pi$
$431$	14.5234	−	25.1553i	0.699567	−	1.21169i	0.968617	−	0.248560i	$-0.0799573\pi$
$432$		0			0
$433$	−15.4759			−0.743725			−0.371862	−	0.928288i	$-0.621281\pi$
$433$	−15.4759			−0.743725			−0.371862	+	0.928288i	$0.621281\pi$
$434$		0			0
$435$	15.0947			0.723734
$436$		0			0
$437$	0.887746	−	1.53762i	0.0424667	−	0.0735544i
$438$		0			0
$439$	12.3095	+	21.3206i	0.587499	+	1.01758i	0.994559	+	0.104176i	$0.0332206\pi$
$439$	12.3095	+	21.3206i	0.587499	+	1.01758i	−0.407060	+	0.913401i	$0.633446\pi$
$440$		0			0
$441$	16.0956	−	7.41920i	0.766456	−	0.353295i
$442$		0			0
$443$	−4.22398	−	7.31614i	−0.200687	−	0.347600i	0.748063	−	0.663628i	$-0.230984\pi$
$443$	−4.22398	−	7.31614i	−0.200687	−	0.347600i	−0.948750	+	0.316027i	$0.897651\pi$
$444$		0			0
$445$	21.9644	−	38.0435i	1.04121	−	1.80343i
$446$		0			0
$447$	8.30896			0.393000
$448$		0			0
$449$	−12.8063			−0.604368			−0.302184	−	0.953250i	$-0.597716\pi$
$449$	−12.8063			−0.604368			−0.302184	+	0.953250i	$0.597716\pi$
$450$		0			0
$451$	2.37730	−	4.11760i	0.111943	−	0.193890i
$452$		0			0
$453$	5.40238	+	9.35720i	0.253826	+	0.439640i
$454$		0			0
$455$	−50.3441	−	15.9956i	−2.36017	−	0.749887i
$456$		0			0
$457$	14.2579	+	24.6953i	0.666954	+	1.15520i	0.978751	+	0.205050i	$0.0657358\pi$
$457$	14.2579	+	24.6953i	0.666954	+	1.15520i	−0.311797	+	0.950149i	$0.600931\pi$
$458$		0			0
$459$	−9.19839	+	15.9321i	−0.429344	+	0.743646i
$460$		0			0
$461$	−37.8648			−1.76354			−0.881771	−	0.471679i	$-0.843648\pi$
$461$	−37.8648			−1.76354			−0.881771	+	0.471679i	$0.843648\pi$
$462$		0			0
$463$	24.6922			1.14754			0.573772	−	0.819015i	$-0.305480\pi$
$463$	24.6922			1.14754			0.573772	+	0.819015i	$0.305480\pi$
$464$		0			0
$465$	2.12146	−	3.67447i	0.0983802	−	0.170399i
$466$		0			0
$467$	1.17249	+	2.03081i	0.0542563	+	0.0939747i	0.891878	−	0.452276i	$-0.149388\pi$
$467$	1.17249	+	2.03081i	0.0542563	+	0.0939747i	−0.837622	+	0.546251i	$0.816055\pi$
$468$		0			0
$469$	1.48591	+	6.77318i	0.0686129	+	0.312757i
$470$		0			0
$471$	−2.68146	−	4.64442i	−0.123555	−	0.214004i
$472$		0			0
$473$	−3.69636	+	6.40228i	−0.169959	+	0.294377i
$474$		0			0
$475$	8.32954			0.382185
$476$		0			0
$477$	16.3690			0.749484
$478$		0			0
$479$	−14.6564	+	25.3857i	−0.669670	+	1.15990i	0.308327	+	0.951281i	$0.400231\pi$
$479$	−14.6564	+	25.3857i	−0.669670	+	1.15990i	−0.977996	+	0.208621i	$0.933102\pi$
$480$		0			0
$481$	−15.3841	−	26.6461i	−0.701456	−	1.21496i
$482$		0			0
$483$	2.37438	−	2.16610i	0.108038	−	0.0985611i
$484$		0			0
$485$	−11.4355	−	19.8069i	−0.519260	−	0.899385i
$486$		0			0
$487$	−7.03223	+	12.1802i	−0.318661	+	0.551937i	−0.980209	−	0.197966i	$-0.936566\pi$
$487$	−7.03223	+	12.1802i	−0.318661	+	0.551937i	0.661548	+	0.749903i	$0.269900\pi$
$488$		0			0
$489$	−3.32835			−0.150513
$490$		0			0
$491$	33.8667			1.52838			0.764191	−	0.644991i	$-0.223139\pi$
$491$	33.8667			1.52838			0.764191	+	0.644991i	$0.223139\pi$
$492$		0			0
$493$	−14.6860	+	25.4369i	−0.661424	+	1.14562i
$494$		0			0
$495$	−10.9877	−	19.0312i	−0.493858	−	0.855388i
$496$		0			0
$497$	−21.7994	+	19.8872i	−0.977838	+	0.892062i
$498$		0			0
$499$	−13.1457	−	22.7690i	−0.588482	−	1.01928i	−0.994432	−	0.105385i	$-0.966393\pi$
$499$	−13.1457	−	22.7690i	−0.588482	−	1.01928i	0.405950	−	0.913895i	$-0.366941\pi$
$500$		0			0
$501$	4.67670	−	8.10028i	0.208940	−	0.361894i
$502$		0			0
$503$	36.7282			1.63763			0.818815	−	0.574058i	$-0.194632\pi$
$503$	36.7282			1.63763			0.818815	+	0.574058i	$0.194632\pi$
$504$		0			0
$505$	20.8687			0.928646
$506$		0			0
$507$	−5.78331	+	10.0170i	−0.256846	+	0.444870i
$508$		0			0
$509$	−3.38848	−	5.86901i	−0.150192	−	0.260139i	0.781106	−	0.624398i	$-0.214656\pi$
$509$	−3.38848	−	5.86901i	−0.150192	−	0.260139i	−0.931298	+	0.364259i	$0.881322\pi$
$510$		0			0
$511$	−8.23800	−	37.5511i	−0.364428	−	1.66116i
$512$		0			0
$513$	1.89243	+	3.27778i	0.0835527	+	0.144718i
$514$		0			0
$515$	−3.10112	+	5.37129i	−0.136651	+	0.236687i
$516$		0			0
$517$	−12.4337			−0.546832
$518$		0			0
$519$	−3.65977			−0.160646
$520$		0			0
$521$	15.6681	−	27.1379i	0.686431	−	1.18893i	−0.286554	−	0.958064i	$-0.592510\pi$
$521$	15.6681	−	27.1379i	0.686431	−	1.18893i	0.972985	−	0.230869i	$-0.0741569\pi$
$522$		0			0
$523$	15.9196	+	27.5735i	0.696114	+	1.20570i	0.969804	+	0.243887i	$0.0784225\pi$
$523$	15.9196	+	27.5735i	0.696114	+	1.20570i	−0.273690	+	0.961818i	$0.588244\pi$
$524$		0			0
$525$	14.3702	+	4.56578i	0.627166	+	0.199267i
$526$		0			0
$527$	4.12803	+	7.14997i	0.179820	+	0.311457i
$528$		0			0
$529$	9.92381	−	17.1885i	0.431470	−	0.747328i
$530$		0			0
$531$	19.0465			0.826549
$532$		0			0
$533$	−10.9372			−0.473743
$534$		0			0
$535$	13.2501	−	22.9499i	0.572852	−	0.992209i
$536$		0			0
$537$	0.235301	+	0.407553i	0.0101540	+	0.0175872i
$538$		0			0
$539$	13.5893	+	9.60499i	0.585334	+	0.413716i
$540$		0			0
$541$	−4.48383	−	7.76621i	−0.192775	−	0.333896i	0.753394	−	0.657569i	$-0.228415\pi$
$541$	−4.48383	−	7.76621i	−0.192775	−	0.333896i	−0.946169	+	0.323674i	$0.895082\pi$
$542$		0			0
$543$	−2.70729	+	4.68917i	−0.116181	+	0.201232i
$544$		0			0
$545$	−67.3417			−2.88460
$546$		0			0
$547$	−26.0700			−1.11467			−0.557337	−	0.830287i	$-0.688177\pi$
$547$	−26.0700			−1.11467			−0.557337	+	0.830287i	$0.688177\pi$
$548$		0			0
$549$	−9.81856	+	17.0062i	−0.419046	+	0.725809i
$550$		0			0
$551$	3.02142	+	5.23324i	0.128717	+	0.222944i
$552$		0			0
$553$	2.42522	+	0.770556i	0.103131	+	0.0327674i
$554$		0			0
$555$	7.02717	+	12.1714i	0.298287	+	0.516648i
$556$		0			0
$557$	−12.1375	+	21.0228i	−0.514284	+	0.890766i	0.485579	+	0.874193i	$0.338609\pi$
$557$	−12.1375	+	21.0228i	−0.514284	+	0.890766i	−0.999863	+	0.0165730i	$0.994724\pi$
$558$		0			0
$559$	17.0058			0.719268
$560$		0			0
$561$	−7.90592			−0.333788
$562$		0			0
$563$	−15.6075	+	27.0330i	−0.657779	+	1.13931i	0.323410	+	0.946259i	$0.395171\pi$
$563$	−15.6075	+	27.0330i	−0.657779	+	1.13931i	−0.981189	+	0.193048i	$0.938163\pi$
$564$		0			0
$565$	32.7206	+	56.6737i	1.37656	+	2.38428i
$566$		0			0
$567$	−2.83819	−	12.9372i	−0.119193	−	0.543313i
$568$		0			0
$569$	8.48242	+	14.6920i	0.355602	+	0.615920i	0.987221	−	0.159359i	$-0.0509426\pi$
$569$	8.48242	+	14.6920i	0.355602	+	0.615920i	−0.631619	+	0.775279i	$0.717609\pi$
$570$		0			0
$571$	−3.14069	+	5.43984i	−0.131434	+	0.227650i	−0.924230	−	0.381837i	$-0.875291\pi$
$571$	−3.14069	+	5.43984i	−0.131434	+	0.227650i	0.792796	+	0.609488i	$0.208625\pi$
$572$		0			0
$573$	16.4818			0.688538
$574$		0			0
$575$	−14.7890			−0.616745
$576$		0			0
$577$	8.12592	−	14.0745i	0.338287	−	0.585930i	−0.645824	−	0.763486i	$-0.723486\pi$
$577$	8.12592	−	14.0745i	0.338287	−	0.585930i	0.984111	+	0.177557i	$0.0568193\pi$
$578$		0			0
$579$	1.53181	+	2.65316i	0.0636597	+	0.110262i
$580$		0			0
$581$	29.4119	−	26.8319i	1.22021	−	1.11318i
$582$		0			0
$583$	7.68477	+	13.3104i	0.318271	+	0.551261i
$584$		0			0
$585$	−25.2754	+	43.7783i	−1.04501	+	1.81001i
$586$		0			0
$587$	−45.7490			−1.88826			−0.944131	−	0.329571i	$-0.893096\pi$
$587$	−45.7490			−1.88826			−0.944131	+	0.329571i	$0.893096\pi$
$588$		0			0
$589$	1.69856			0.0699879
$590$		0			0
$591$	−5.14089	+	8.90428i	−0.211468	+	0.366273i
$592$		0			0
$593$	−3.47092	−	6.01180i	−0.142533	−	0.246875i	0.785917	−	0.618333i	$-0.212192\pi$
$593$	−3.47092	−	6.01180i	−0.142533	−	0.246875i	−0.928450	+	0.371457i	$0.878858\pi$
$594$		0			0
$595$	−34.6862	+	31.6435i	−1.42199	+	1.29726i
$596$		0			0
$597$	9.37048	+	16.2301i	0.383508	+	0.664256i
$598$		0			0
$599$	−7.29513	+	12.6355i	−0.298071	+	0.516274i	−0.975695	−	0.219135i	$-0.929677\pi$
$599$	−7.29513	+	12.6355i	−0.298071	+	0.516274i	0.677624	+	0.735409i	$0.263010\pi$
$600$		0			0
$601$	−43.5586			−1.77679			−0.888396	−	0.459077i	$-0.848180\pi$
$601$	−43.5586			−1.77679			−0.888396	+	0.459077i	$0.848180\pi$
$602$		0			0
$603$	6.63583			0.270232
$604$		0			0
$605$	−9.76352	+	16.9109i	−0.396943	+	0.687526i
$606$		0			0
$607$	11.7216	+	20.3023i	0.475763	+	0.824046i	0.999615	−	0.0277638i	$-0.00883863\pi$
$607$	11.7216	+	20.3023i	0.475763	+	0.824046i	−0.523851	+	0.851810i	$0.675505\pi$
$608$		0			0
$609$	2.34400	+	10.6846i	0.0949836	+	0.432962i
$610$		0			0
$611$	14.3008	+	24.7698i	0.578550	+	1.00208i
$612$		0			0
$613$	1.79313	−	3.10580i	0.0724240	−	0.125442i	−0.827539	−	0.561408i	$-0.810260\pi$
$613$	1.79313	−	3.10580i	0.0724240	−	0.125442i	0.899963	+	0.435966i	$0.143593\pi$
$614$		0			0
$615$	4.99590			0.201454
$616$		0			0
$617$	5.93981			0.239128			0.119564	−	0.992827i	$-0.461850\pi$
$617$	5.93981			0.239128			0.119564	+	0.992827i	$0.461850\pi$
$618$		0			0
$619$	−13.7618	+	23.8361i	−0.553134	+	0.958055i	0.444913	+	0.895574i	$0.353235\pi$
$619$	−13.7618	+	23.8361i	−0.553134	+	0.958055i	−0.998046	+	0.0624814i	$0.980099\pi$
$620$		0			0
$621$	−3.35999	−	5.81967i	−0.134832	−	0.233535i
$622$		0			0
$623$	30.3394	+	9.63962i	1.21552	+	0.386203i
$624$		0			0
$625$	−1.36675	−	2.36727i	−0.0546698	−	0.0946909i
$626$		0			0
$627$	−0.813260	+	1.40861i	−0.0324785	+	0.0562544i
$628$		0			0
$629$	−27.3476			−1.09042
$630$		0			0
$631$	−45.2443			−1.80115			−0.900573	−	0.434705i	$-0.856853\pi$
$631$	−45.2443			−1.80115			−0.900573	+	0.434705i	$0.856853\pi$
$632$		0			0
$633$	0.470693	−	0.815264i	0.0187084	−	0.0324038i
$634$		0			0
$635$	30.6761	+	53.1326i	1.21735	+	2.10850i
$636$		0			0
$637$	3.50457	−	38.1194i	0.138856	−	1.51035i
$638$		0			0
$639$	14.1190	+	24.4548i	0.558538	+	0.967416i
$640$		0			0
$641$	14.2499	−	24.6816i	0.562838	−	0.974863i	−0.434410	−	0.900715i	$-0.643043\pi$
$641$	14.2499	−	24.6816i	0.562838	−	0.974863i	0.997247	−	0.0741480i	$-0.0236237\pi$
$642$		0			0
$643$	−22.8611			−0.901553			−0.450776	−	0.892637i	$-0.648853\pi$
$643$	−22.8611			−0.901553			−0.450776	+	0.892637i	$0.648853\pi$
$644$		0			0
$645$	−7.76791			−0.305861
$646$		0			0
$647$	12.0417	−	20.8568i	0.473408	−	0.819967i	−0.526129	−	0.850405i	$-0.676357\pi$
$647$	12.0417	−	20.8568i	0.473408	−	0.819967i	0.999537	+	0.0304384i	$0.00969034\pi$
$648$		0			0
$649$	8.94180	+	15.4877i	0.350996	+	0.607944i
$650$		0			0
$651$	2.93037	+	0.931053i	0.114850	+	0.0364909i
$652$		0			0
$653$	−2.02629	−	3.50964i	−0.0792950	−	0.137343i	0.823651	−	0.567097i	$-0.191934\pi$
$653$	−2.02629	−	3.50964i	−0.0792950	−	0.137343i	−0.902946	+	0.429754i	$0.858600\pi$
$654$		0			0
$655$	−18.4490	+	31.9546i	−0.720863	+	1.24857i
$656$		0			0
$657$	−36.7896			−1.43530
$658$		0			0
$659$	23.7165			0.923864			0.461932	−	0.886915i	$-0.347156\pi$
$659$	23.7165			0.923864			0.461932	+	0.886915i	$0.347156\pi$
$660$		0			0
$661$	8.60872	−	14.9107i	0.334840	−	0.579961i	−0.648614	−	0.761118i	$-0.724651\pi$
$661$	8.60872	−	14.9107i	0.334840	−	0.579961i	0.983454	+	0.181157i	$0.0579842\pi$
$662$		0			0
$663$	9.09316	+	15.7498i	0.353149	+	0.611672i
$664$		0			0
$665$	2.06990	+	9.43516i	0.0802671	+	0.365880i
$666$		0			0
$667$	−5.36450	−	9.29159i	−0.207714	−	0.359772i
$668$		0			0
$669$	−9.50276	+	16.4593i	−0.367398	+	0.636352i
$670$		0			0
$671$	−18.4381			−0.711796
$672$		0			0
$673$	−20.1890			−0.778229			−0.389115	−	0.921189i	$-0.627219\pi$
$673$	−20.1890			−0.778229			−0.389115	+	0.921189i	$0.627219\pi$
$674$		0			0
$675$	15.7630	−	27.3024i	0.606720	−	1.05087i
$676$		0			0
$677$	−11.7264	−	20.3107i	−0.450681	−	0.780602i	0.547747	−	0.836644i	$-0.315485\pi$
$677$	−11.7264	−	20.3107i	−0.450681	−	0.780602i	−0.998428	+	0.0560413i	$0.982152\pi$
$678$		0			0
$679$	12.2443	−	11.1702i	0.469893	−	0.428675i
$680$		0			0
$681$	−7.04390	−	12.2004i	−0.269923	−	0.467520i
$682$		0			0
$683$	−12.8619	+	22.2775i	−0.492148	+	0.852425i	−0.999959	−	0.00904340i	$-0.997121\pi$
$683$	−12.8619	+	22.2775i	−0.492148	+	0.852425i	0.507811	+	0.861468i	$0.330455\pi$
$684$		0			0
$685$	20.2705			0.774496
$686$		0			0
$687$	17.8975			0.682832
$688$		0			0
$689$	17.6776	−	30.6185i	0.673463	−	1.16647i
$690$		0			0
$691$	−25.4045	−	44.0019i	−0.966434	−	1.67391i	−0.705712	−	0.708499i	$-0.749373\pi$
$691$	−25.4045	−	44.0019i	−0.966434	−	1.67391i	−0.260722	−	0.965414i	$-0.583961\pi$
$692$		0			0
$693$	11.7648	−	10.7328i	0.446907	−	0.407704i
$694$		0			0
$695$	7.94307	+	13.7578i	0.301298	+	0.521863i
$696$		0			0
$697$	−4.86063	+	8.41886i	−0.184110	+	0.318887i
$698$		0			0
$699$	−8.61018			−0.325667
$700$		0			0
$701$	46.4663			1.75501			0.877504	−	0.479570i	$-0.159207\pi$
$701$	46.4663			1.75501			0.877504	+	0.479570i	$0.159207\pi$
$702$		0			0
$703$	−2.81318	+	4.87257i	−0.106101	+	0.183772i
$704$		0			0
$705$	−6.53234	−	11.3144i	−0.246022	−	0.426123i
$706$		0			0
$707$	3.24063	+	14.7717i	0.121876	+	0.555547i
$708$		0			0
$709$	−1.46179	−	2.53189i	−0.0548986	−	0.0950872i	0.837270	−	0.546790i	$-0.184150\pi$
$709$	−1.46179	−	2.53189i	−0.0548986	−	0.0950872i	−0.892169	+	0.451702i	$0.850817\pi$
$710$		0			0
$711$	1.21759	−	2.10892i	0.0456631	−	0.0790909i
$712$		0			0
$713$	−3.01578			−0.112942
$714$		0			0
$715$	−47.4643			−1.77506
$716$		0			0
$717$	−9.77863	+	16.9371i	−0.365190	+	0.632527i
$718$		0			0
$719$	−14.8003	−	25.6349i	−0.551959	−	0.956020i	−0.998133	−	0.0610745i	$-0.980547\pi$
$719$	−14.8003	−	25.6349i	−0.551959	−	0.956020i	0.446175	−	0.894946i	$-0.352786\pi$
$720$		0			0
$721$	−4.28357	−	1.36100i	−0.159528	−	0.0506863i
$722$		0			0
$723$	−1.58919	−	2.75255i	−0.0591025	−	0.102369i
$724$		0			0
$725$	25.1670	−	43.5905i	0.934678	−	1.61891i
$726$		0			0
$727$	39.1285			1.45119			0.725597	−	0.688120i	$-0.241564\pi$
$727$	39.1285			1.45119			0.725597	+	0.688120i	$0.241564\pi$
$728$		0			0
$729$	−4.90622			−0.181712
$730$		0			0
$731$	7.55759	−	13.0901i	0.279528	−	0.484156i
$732$		0			0
$733$	−7.34720	−	12.7257i	−0.271375	−	0.470035i	0.697839	−	0.716254i	$-0.254145\pi$
$733$	−7.34720	−	12.7257i	−0.271375	−	0.470035i	−0.969214	+	0.246219i	$0.920812\pi$
$734$		0			0
$735$	−1.60082	+	17.4122i	−0.0590471	+	0.642259i
$736$		0			0
$737$	3.11533	+	5.39591i	0.114755	+	0.198761i
$738$		0			0
$739$	−8.08118	+	13.9970i	−0.297271	+	0.514888i	−0.975511	−	0.219952i	$-0.929410\pi$
$739$	−8.08118	+	13.9970i	−0.297271	+	0.514888i	0.678240	+	0.734841i	$0.262743\pi$
$740$		0			0
$741$	3.74155			0.137449
$742$		0			0
$743$	21.2412			0.779265			0.389632	−	0.920971i	$-0.372602\pi$
$743$	21.2412			0.779265			0.389632	+	0.920971i	$0.372602\pi$
$744$		0			0
$745$	22.1691	−	38.3980i	0.812213	−	1.40679i
$746$		0			0
$747$	−19.0494	−	32.9945i	−0.696981	−	1.20721i
$748$		0			0
$749$	18.3024	+	5.81514i	0.668754	+	0.212481i
$750$		0			0
$751$	26.0177	+	45.0639i	0.949398	+	1.64441i	0.746696	+	0.665165i	$0.231639\pi$
$751$	26.0177	+	45.0639i	0.949398	+	1.64441i	0.202702	+	0.979240i	$0.435028\pi$
$752$		0			0
$753$	4.13772	−	7.16675i	0.150787	−	0.261171i
$754$		0			0
$755$	57.6563			2.09833
$756$		0			0
$757$	30.6379			1.11355			0.556777	−	0.830662i	$-0.312038\pi$
$757$	30.6379			1.11355			0.556777	+	0.830662i	$0.312038\pi$
$758$		0			0
$759$	1.44394	−	2.50097i	0.0524116	−	0.0907795i
$760$		0			0
$761$	9.79628	+	16.9677i	0.355115	+	0.615077i	0.987138	−	0.159873i	$-0.0511084\pi$
$761$	9.79628	+	16.9677i	0.355115	+	0.615077i	−0.632023	+	0.774950i	$0.717775\pi$
$762$		0			0
$763$	−10.4573	−	47.6671i	−0.378578	−	1.72566i
$764$		0			0
$765$	22.4654	+	38.9112i	0.812239	+	1.40684i
$766$		0			0
$767$	20.5692	−	35.6269i	0.742711	−	1.28641i
$768$		0			0
$769$	−6.70349			−0.241734			−0.120867	−	0.992669i	$-0.538567\pi$
$769$	−6.70349			−0.241734			−0.120867	+	0.992669i	$0.538567\pi$
$770$		0			0
$771$	1.29475			0.0466293
$772$		0			0
$773$	6.77547	−	11.7355i	0.243697	−	0.422095i	−0.718068	−	0.695973i	$-0.754973\pi$
$773$	6.77547	−	11.7355i	0.243697	−	0.422095i	0.961764	+	0.273878i	$0.0883065\pi$
$774$		0			0
$775$	−7.07410	−	12.2527i	−0.254109	−	0.440130i
$776$		0			0
$777$	−7.52418	+	6.86416i	−0.269928	+	0.246250i
$778$		0			0
$779$	1.00000	+	1.73205i	0.0358287	+	0.0620572i
$780$		0			0
$781$	−13.2569	+	22.9616i	−0.474370	+	0.821632i
$782$		0			0
$783$	22.8712			0.817351
$784$		0			0
$785$	−28.6176			−1.02140
$786$		0			0
$787$	18.1660	−	31.4644i	0.647547	−	1.12158i	−0.336160	−	0.941805i	$-0.609128\pi$
$787$	18.1660	−	31.4644i	0.647547	−	1.12158i	0.983707	−	0.179779i	$-0.0575383\pi$
$788$		0			0
$789$	−7.92980	−	13.7348i	−0.282308	−	0.488972i
$790$		0			0
$791$	−35.0348	+	31.9615i	−1.24569	+	1.13642i
$792$		0			0
$793$	21.2070	+	36.7316i	0.753084	+	1.30438i
$794$		0			0
$795$	−8.07478	+	13.9859i	−0.286383	+	0.496030i
$796$		0			0
$797$	−55.0232			−1.94902			−0.974511	−	0.224338i	$-0.927978\pi$
$797$	−55.0232			−1.94902			−0.974511	+	0.224338i	$0.927978\pi$
$798$		0			0
$799$	25.4219			0.899363
$800$		0			0
$801$	15.2320	−	26.3825i	0.538195	−	0.932181i
$802$		0			0
$803$	−17.2717	−	29.9154i	−0.609504	−	1.05569i
$804$		0			0
$805$	−3.67508	−	16.7521i	−0.129530	−	0.590432i
$806$		0			0
$807$	−8.31229	−	14.3973i	−0.292606	−	0.506809i
$808$		0			0
$809$	13.5581	−	23.4833i	0.476677	−	0.825629i	−0.522966	−	0.852354i	$-0.675174\pi$
$809$	13.5581	−	23.4833i	0.476677	−	0.825629i	0.999643	+	0.0267249i	$0.00850782\pi$
$810$		0			0
$811$	−20.7862			−0.729903			−0.364952	−	0.931027i	$-0.618914\pi$
$811$	−20.7862			−0.729903			−0.364952	+	0.931027i	$0.618914\pi$
$812$		0			0
$813$	8.49052			0.297776
$814$		0			0
$815$	−8.88035	+	15.3812i	−0.311065	+	0.538781i
$816$		0			0
$817$	−1.55486	−	2.69309i	−0.0543976	−	0.0942194i
$818$		0			0
$819$	−34.9129	−	11.0927i	−1.21995	−	0.387611i
$820$		0			0
$821$	−21.0837	−	36.5181i	−0.735826	−	1.27449i	−0.954360	−	0.298659i	$-0.903461\pi$
$821$	−21.0837	−	36.5181i	−0.735826	−	1.27449i	0.218533	−	0.975829i	$-0.429873\pi$
$822$		0			0
$823$	−13.9765	+	24.2079i	−0.487189	+	0.843836i	−0.999891	−	0.0147305i	$-0.995311\pi$
$823$	−13.9765	+	24.2079i	−0.487189	+	0.843836i	0.512703	+	0.858566i	$0.328644\pi$
$824$		0			0
$825$	13.5482			0.471686
$826$		0			0
$827$	−46.6553			−1.62236			−0.811182	−	0.584794i	$-0.801175\pi$
$827$	−46.6553			−1.62236			−0.811182	+	0.584794i	$0.801175\pi$
$828$		0			0
$829$	14.7908	−	25.6184i	0.513706	−	0.889764i	−0.486168	−	0.873865i	$-0.661606\pi$
$829$	14.7908	−	25.6184i	0.513706	−	0.889764i	0.999874	−	0.0158990i	$-0.00506101\pi$
$830$		0			0
$831$	0.799808	+	1.38531i	0.0277450	+	0.0480558i
$832$		0			0
$833$	−27.7848	−	19.6384i	−0.962686	−	0.680430i
$834$		0			0
$835$	−24.9558	−	43.2247i	−0.863630	−	1.49585i
$836$		0			0
$837$	3.21440	−	5.56750i	0.111106	−	0.192441i
$838$		0			0
$839$	−27.0614			−0.934263			−0.467132	−	0.884188i	$-0.654713\pi$
$839$	−27.0614			−0.934263			−0.467132	+	0.884188i	$0.654713\pi$
$840$		0			0
$841$	7.51580			0.259166
$842$		0			0
$843$	−1.25058	+	2.16607i	−0.0430723	+	0.0746034i
$844$		0			0
$845$	30.8608	+	53.4526i	1.06165	+	1.83882i
$846$		0			0
$847$	−13.4863	−	4.28496i	−0.463396	−	0.147233i
$848$		0			0
$849$	−3.27889	−	5.67920i	−0.112531	−	0.194910i
$850$		0			0
$851$	4.99477	−	8.65120i	0.171219	−	0.296559i
$852$		0			0
$853$	−1.19742			−0.0409989			−0.0204995	−	0.999790i	$-0.506526\pi$
$853$	−1.19742			−0.0409989			−0.0204995	+	0.999790i	$0.506526\pi$
$854$		0			0
$855$	9.24382			0.316132
$856$		0			0
$857$	−17.2208	+	29.8274i	−0.588253	+	1.01888i	0.406208	+	0.913780i	$0.366851\pi$
$857$	−17.2208	+	29.8274i	−0.588253	+	1.01888i	−0.994461	+	0.105103i	$0.966483\pi$
$858$		0			0
$859$	1.87274	+	3.24369i	0.0638972	+	0.110673i	0.896204	−	0.443642i	$-0.146314\pi$
$859$	1.87274	+	3.24369i	0.0638972	+	0.110673i	−0.832307	+	0.554315i	$0.812980\pi$
$860$		0			0
$861$	0.775795	+	3.53629i	0.0264390	+	0.120516i
$862$		0			0
$863$	14.9335	+	25.8656i	0.508343	+	0.880477i	0.999953	+	0.00966107i	$0.00307526\pi$
$863$	14.9335	+	25.8656i	0.508343	+	0.880477i	−0.491610	+	0.870816i	$0.663591\pi$
$864$		0			0
$865$	−9.76463	+	16.9128i	−0.332007	+	0.575054i
$866$		0			0
$867$	4.53327			0.153958
$868$		0			0
$869$	2.28649			0.0775639
$870$		0			0
$871$	7.16634	−	12.4125i	0.242822	−	0.420580i
$872$		0			0
$873$	−7.93035	−	13.7358i	−0.268402	−	0.464885i
$874$		0			0
$875$	23.7600	−	21.6758i	0.803236	−	0.732777i
$876$		0			0
$877$	4.74105	+	8.21174i	0.160094	+	0.277291i	0.934902	−	0.354906i	$-0.115487\pi$
$877$	4.74105	+	8.21174i	0.160094	+	0.277291i	−0.774808	+	0.632196i	$0.782154\pi$
$878$		0			0
$879$	3.42947	−	5.94002i	0.115673	−	0.200352i
$880$		0			0
$881$	33.1936			1.11832			0.559160	−	0.829060i	$-0.311124\pi$
$881$	33.1936			1.11832			0.559160	+	0.829060i	$0.311124\pi$
$882$		0			0
$883$	−27.9645			−0.941079			−0.470540	−	0.882379i	$-0.655941\pi$
$883$	−27.9645			−0.941079			−0.470540	+	0.882379i	$0.655941\pi$
$884$		0			0
$885$	−9.39561	+	16.2737i	−0.315830	+	0.547034i
$886$		0			0
$887$	−15.6812	−	27.1606i	−0.526523	−	0.911965i	−0.999522	−	0.0309023i	$-0.990162\pi$
$887$	−15.6812	−	27.1606i	−0.526523	−	0.911965i	0.472999	−	0.881063i	$-0.343171\pi$
$888$		0			0
$889$	−32.8458	+	29.9645i	−1.10161	+	1.00498i
$890$		0			0
$891$	−5.95050	−	10.3066i	−0.199349	−	0.345283i
$892$		0			0
$893$	2.61508	−	4.52946i	0.0875104	−	0.151573i
$894$		0			0
$895$	2.51122			0.0839409
$896$		0			0
$897$	−6.64310			−0.221807
$898$		0			0
$899$	5.13205	−	8.88897i	0.171163	−	0.296464i
$900$		0			0
$901$	−15.7123	−	27.2145i	−0.523453	−	0.906647i
$902$		0			0
$903$	−1.20625	−	5.49843i	−0.0401415	−	0.182976i
$904$		0			0
$905$	14.4466	+	25.0223i	0.480223	+	0.831770i
$906$		0			0
$907$	−4.36780	+	7.56526i	−0.145031	+	0.251200i	−0.929384	−	0.369113i	$-0.879661\pi$
$907$	−4.36780	+	7.56526i	−0.145031	+	0.251200i	0.784354	+	0.620314i	$0.212995\pi$
$908$		0			0
$909$	14.4721			0.480011
$910$		0			0
$911$	6.50534			0.215532			0.107766	−	0.994176i	$-0.465630\pi$
$911$	6.50534			0.215532			0.107766	+	0.994176i	$0.465630\pi$
$912$		0			0
$913$	17.8863	−	30.9800i	0.591950	−	1.02529i
$914$		0			0
$915$	−9.68695	−	16.7783i	−0.320241	−	0.554673i
$916$		0			0
$917$	−25.4836	−	8.09681i	−0.841543	−	0.267380i
$918$		0			0
$919$	−16.2251	−	28.1027i	−0.535216	−	0.927022i	−0.999153	−	0.0411532i	$-0.986897\pi$
$919$	−16.2251	−	28.1027i	−0.535216	−	0.927022i	0.463937	−	0.885868i	$-0.346437\pi$
$920$		0			0
$921$	−10.6361	+	18.4222i	−0.350471	+	0.607033i
$922$		0			0
$923$	60.9909			2.00754
$924$		0			0
$925$	46.8649			1.54091
$926$		0			0
$927$	−2.15057	+	3.72491i	−0.0706341	+	0.122342i
$928$		0			0
$929$	10.9756	+	19.0103i	0.360098	+	0.623708i	0.987977	−	0.154603i	$-0.0494099\pi$
$929$	10.9756	+	19.0103i	0.360098	+	0.623708i	−0.627879	+	0.778311i	$0.716077\pi$
$930$		0			0
$931$	−6.35715	+	2.93031i	−0.208347	+	0.0960369i
$932$		0			0
$933$	0.889411	+	1.54050i	0.0291180	+	0.0504339i
$934$		0			0
$935$	−21.0937	+	36.5354i	−0.689839	+	1.19484i
$936$		0			0
$937$	−20.0361			−0.654552			−0.327276	−	0.944929i	$-0.606131\pi$
$937$	−20.0361			−0.654552			−0.327276	+	0.944929i	$0.606131\pi$
$938$		0			0
$939$	−9.97083			−0.325386
$940$		0			0
$941$	3.25615	−	5.63981i	0.106147	−	0.183853i	−0.808059	−	0.589102i	$-0.799482\pi$
$941$	3.25615	−	5.63981i	0.106147	−	0.183853i	0.914206	+	0.405249i	$0.132815\pi$
$942$		0			0
$943$	−1.77549	−	3.07524i	−0.0578180	−	0.100144i
$944$		0			0
$945$	34.8435	+	11.0707i	1.13346	+	0.360130i
$946$		0			0
$947$	−28.0531	−	48.5893i	−0.911602	−	1.57894i	−0.811801	−	0.583934i	$-0.801513\pi$
$947$	−28.0531	−	48.5893i	−0.911602	−	1.57894i	−0.0998014	−	0.995007i	$-0.531821\pi$
$948$		0			0
$949$	−39.7308	+	68.8157i	−1.28971	+	2.23385i
$950$		0			0
$951$	7.73168			0.250717
$952$		0			0
$953$	23.9841			0.776920			0.388460	−	0.921466i	$-0.373007\pi$
$953$	23.9841			0.776920			0.388460	+	0.921466i	$0.373007\pi$
$954$		0			0
$955$	43.9751	−	76.1671i	1.42300	−	2.46471i
$956$		0			0
$957$	4.91439	+	8.51198i	0.158860	+	0.275153i
$958$		0			0
$959$	3.14774	+	14.3483i	0.101646	+	0.463329i
$960$		0			0
$961$	14.0574	+	24.3482i	0.453466	+	0.785426i
$962$		0			0
$963$	9.18874	−	15.9154i	0.296103	−	0.512866i
$964$		0			0
$965$	16.3480			0.526261
$966$		0			0
$967$	25.6539			0.824974			0.412487	−	0.910963i	$-0.364660\pi$
$967$	25.6539			0.824974			0.412487	+	0.910963i	$0.364660\pi$
$968$		0			0
$969$	1.66280	−	2.88005i	0.0534167	−	0.0925204i
$970$		0			0
$971$	−3.75173	−	6.49819i	−0.120399	−	0.208537i	0.799526	−	0.600631i	$-0.205084\pi$
$971$	−3.75173	−	6.49819i	−0.120399	−	0.208537i	−0.919925	+	0.392094i	$0.871751\pi$
$972$		0			0
$973$	−8.50486	+	7.75881i	−0.272653	+	0.248736i
$974$		0			0
$975$	−15.5827	−	26.9900i	−0.499046	−	0.864373i
$976$		0			0
$977$	29.3271	−	50.7959i	0.938255	−	1.62511i	0.169532	−	0.985525i	$-0.445774\pi$
$977$	29.3271	−	50.7959i	0.938255	−	1.62511i	0.768723	−	0.639581i	$-0.220892\pi$
$978$		0			0
$979$	28.6039			0.914185
$980$		0			0
$981$	−46.7004			−1.49103
$982$		0			0
$983$	8.19313	−	14.1909i	0.261320	−	0.452620i	−0.705273	−	0.708936i	$-0.749176\pi$
$983$	8.19313	−	14.1909i	0.261320	−	0.452620i	0.966593	+	0.256316i	$0.0825088\pi$
$984$		0			0
$985$	27.4328	+	47.5150i	0.874081	+	1.51395i
$986$		0			0
$987$	6.99435	−	6.38081i	0.222633	−	0.203103i
$988$		0			0
$989$	2.76064	+	4.78157i	0.0877832	+	0.152045i
$990$		0			0
$991$	22.5210	−	39.0075i	0.715402	−	1.23911i	−0.247402	−	0.968913i	$-0.579577\pi$
$991$	22.5210	−	39.0075i	0.715402	−	1.23911i	0.962804	−	0.270200i	$-0.0870899\pi$
$992$		0			0
$993$	−10.4940			−0.333015
$994$		0			0
$995$	100.005			3.17038
$996$		0			0
$997$	1.70418	−	2.95172i	0.0539719	−	0.0934821i	−0.837777	−	0.546012i	$-0.816145\pi$
$997$	1.70418	−	2.95172i	0.0539719	−	0.0934821i	0.891749	+	0.452530i	$0.149479\pi$
$998$		0			0
$999$	10.6475	+	18.4419i	0.336871	+	0.583477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.305.4	✓	16
7.2	even	3	inner	1064.2.q.n.457.4	yes	16
7.3	odd	6		7448.2.a.br.1.4		8
7.4	even	3		7448.2.a.bq.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.4	✓	16	1.1	even	1	trivial
1064.2.q.n.457.4	yes	16	7.2	even	3	inner
7448.2.a.bq.1.5		8	7.4	even	3
7448.2.a.br.1.4		8	7.3	odd	6

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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342094 + 0.592525i) q^{3} +(1.82548 + 3.16183i) q^{5} +(-1.95459 + 1.78314i) q^{7} +(1.26594 + 2.19268i) q^{9} +O(q^{10})\)	\(q+(-0.342094 + 0.592525i) q^{3} +(1.82548 + 3.16183i) q^{5} +(-1.95459 + 1.78314i) q^{7} +(1.26594 + 2.19268i) q^{9} +(-1.18865 + 2.05880i) q^{11} +5.46860 q^{13} -2.49795 q^{15} +(2.43032 - 4.20943i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-0.387898 - 1.76814i) q^{21} +(0.887746 + 1.53762i) q^{23} +(-4.16477 + 7.21359i) q^{25} -3.78485 q^{27} -6.04283 q^{29} +(-0.849279 + 1.47099i) q^{31} +(-0.813260 - 1.40861i) q^{33} +(-9.20604 - 2.92500i) q^{35} +(-2.81318 - 4.87257i) q^{37} +(-1.87078 + 3.24028i) q^{39} -2.00000 q^{41} +3.10972 q^{43} +(-4.62191 + 8.00539i) q^{45} +(2.61508 + 4.52946i) q^{47} +(0.640854 - 6.97060i) q^{49} +(1.66280 + 2.88005i) q^{51} +(3.23257 - 5.59897i) q^{53} -8.67942 q^{55} +0.684189 q^{57} +(3.76133 - 6.51482i) q^{59} +(3.87796 + 6.71683i) q^{61} +(-6.38424 - 2.02844i) q^{63} +(9.98283 + 17.2908i) q^{65} +(1.31045 - 2.26977i) q^{67} -1.21477 q^{69} +11.1529 q^{71} +(-7.26525 + 12.5838i) q^{73} +(-2.84949 - 4.93546i) q^{75} +(-1.34780 - 6.14363i) q^{77} +(-0.480902 - 0.832946i) q^{79} +(-2.50305 + 4.33541i) q^{81} -15.0476 q^{83} +17.7460 q^{85} +(2.06722 - 3.58053i) q^{87} +(-6.01606 - 10.4201i) q^{89} +(-10.6889 + 9.75126i) q^{91} +(-0.581067 - 1.00644i) q^{93} +(1.82548 - 3.16183i) q^{95} -6.26438 q^{97} -6.01904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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