LMFDB - Embedded newform 1456.2.r.p.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, 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("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.2
Root			$-0.862625 + 1.49411i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.p.417.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.673208 - 1.16603i) q^{3} +(-1.09358 + 1.89414i) q^{5} +(2.19729 - 1.47375i) q^{7} +(0.593582 - 1.02811i) q^{9} +(-0.524077 - 0.907729i) q^{11} +1.00000 q^{13} +2.94483 q^{15} +(2.64562 + 4.58236i) q^{17} +(0.378453 - 0.655500i) q^{19} +(-3.19767 - 1.56996i) q^{21} +(0.326792 - 0.566020i) q^{23} +(0.108157 + 0.187333i) q^{25} -5.63766 q^{27} -3.10408 q^{29} +(0.513956 + 0.890198i) q^{31} +(-0.705626 + 1.22218i) q^{33} +(0.388575 + 5.77363i) q^{35} +(5.44661 - 9.43381i) q^{37} +(-0.673208 - 1.16603i) q^{39} +7.32040 q^{41} -0.887771 q^{43} +(1.29826 + 2.24865i) q^{45} +(1.16875 - 2.02434i) q^{47} +(2.65613 - 6.47650i) q^{49} +(3.56211 - 6.16976i) q^{51} +(-2.44407 - 4.23325i) q^{53} +2.29249 q^{55} -1.01911 q^{57} +(-0.524077 - 0.907729i) q^{59} +(6.24989 - 10.8251i) q^{61} +(-0.210913 - 3.13385i) q^{63} +(-1.09358 + 1.89414i) q^{65} +(2.23944 + 3.87883i) q^{67} -0.879996 q^{69} +6.60274 q^{71} +(4.14174 + 7.17370i) q^{73} +(0.145624 - 0.252229i) q^{75} +(-2.48931 - 1.22218i) q^{77} +(1.07007 - 1.85342i) q^{79} +(2.01457 + 3.48935i) q^{81} +6.66558 q^{83} -11.5728 q^{85} +(2.08969 + 3.61946i) q^{87} +(2.88388 - 4.99503i) q^{89} +(2.19729 - 1.47375i) q^{91} +(0.691998 - 1.19858i) q^{93} +(0.827739 + 1.43369i) q^{95} -2.88777 q^{97} -1.24433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.673208	−	1.16603i	−0.388677	−	0.673208i	0.603595	−	0.797291i	$-0.293734\pi$
$3$	−0.673208	−	1.16603i	−0.388677	−	0.673208i	−0.992272	+	0.124083i	$0.960401\pi$
$4$		0			0
$5$	−1.09358	+	1.89414i	−0.489065	+	0.847085i	−0.999921	−	0.0125813i	$-0.995995\pi$
$5$	−1.09358	+	1.89414i	−0.489065	+	0.847085i	0.510856	+	0.859666i	$0.329328\pi$
$6$		0			0
$7$	2.19729	−	1.47375i	0.830496	−	0.557025i
$7$	2.19729	−	1.47375i	0.830496	−	0.557025i
$8$		0			0
$9$	0.593582	−	1.02811i	0.197861	−	0.342705i
$10$		0			0
$11$	−0.524077	−	0.907729i	−0.158015	−	0.273691i	0.776138	−	0.630564i	$-0.217176\pi$
$11$	−0.524077	−	0.907729i	−0.158015	−	0.273691i	−0.934153	+	0.356873i	$0.883843\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	2.94483			0.760352
$16$		0			0
$17$	2.64562	+	4.58236i	0.641658	+	1.11138i	0.985063	+	0.172197i	$0.0550865\pi$
$17$	2.64562	+	4.58236i	0.641658	+	1.11138i	−0.343404	+	0.939188i	$0.611580\pi$
$18$		0			0
$19$	0.378453	−	0.655500i	0.0868231	−	0.150382i	−0.819344	−	0.573303i	$-0.805662\pi$
$19$	0.378453	−	0.655500i	0.0868231	−	0.150382i	0.906167	+	0.422921i	$0.138995\pi$
$20$		0			0
$21$	−3.19767	−	1.56996i	−0.697788	−	0.342594i
$22$		0			0
$23$	0.326792	−	0.566020i	0.0681408	−	0.118023i	−0.829942	−	0.557850i	$-0.811627\pi$
$23$	0.326792	−	0.566020i	0.0681408	−	0.118023i	0.898083	+	0.439826i	$0.144960\pi$
$24$		0			0
$25$	0.108157	+	0.187333i	0.0216314	+	0.0374667i
$26$		0			0
$27$	−5.63766			−1.08497
$28$		0			0
$29$	−3.10408			−0.576414			−0.288207	−	0.957568i	$-0.593059\pi$
$29$	−3.10408			−0.576414			−0.288207	+	0.957568i	$0.593059\pi$
$30$		0			0
$31$	0.513956	+	0.890198i	0.0923092	+	0.159884i	0.908482	−	0.417923i	$-0.137242\pi$
$31$	0.513956	+	0.890198i	0.0923092	+	0.159884i	−0.816173	+	0.577807i	$0.803909\pi$
$32$		0			0
$33$	−0.705626	+	1.22218i	−0.122834	+	0.212754i
$34$		0			0
$35$	0.388575	+	5.77363i	0.0656811	+	0.975922i
$36$		0			0
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.0621309	−	0.998068i	$-0.480210\pi$
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.833287	−	0.552841i	$-0.186456\pi$
$38$		0			0
$39$	−0.673208	−	1.16603i	−0.107800	−	0.186714i
$40$		0			0
$41$	7.32040			1.14325			0.571627	−	0.820514i	$-0.306312\pi$
$41$	7.32040			1.14325			0.571627	+	0.820514i	$0.306312\pi$
$42$		0			0
$43$	−0.887771			−0.135384			−0.0676919	−	0.997706i	$-0.521563\pi$
$43$	−0.887771			−0.135384			−0.0676919	+	0.997706i	$0.521563\pi$
$44$		0			0
$45$	1.29826	+	2.24865i	0.193533	+	0.335210i
$46$		0			0
$47$	1.16875	−	2.02434i	0.170480	−	0.295281i	−0.768108	−	0.640321i	$-0.778801\pi$
$47$	1.16875	−	2.02434i	0.170480	−	0.295281i	0.938588	+	0.345040i	$0.112135\pi$
$48$		0			0
$49$	2.65613	−	6.47650i	0.379447	−	0.925214i
$50$		0			0
$51$	3.56211	−	6.16976i	0.498795	−	0.863939i
$52$		0			0
$53$	−2.44407	−	4.23325i	−0.335719	−	0.581482i	0.647904	−	0.761722i	$-0.275646\pi$
$53$	−2.44407	−	4.23325i	−0.335719	−	0.581482i	−0.983623	+	0.180240i	$0.942313\pi$
$54$		0			0
$55$	2.29249			0.309119
$56$		0			0
$57$	−1.01911			−0.134985
$58$		0			0
$59$	−0.524077	−	0.907729i	−0.0682291	−	0.118176i	0.829893	−	0.557923i	$-0.188402\pi$
$59$	−0.524077	−	0.907729i	−0.0682291	−	0.118176i	−0.898122	+	0.439747i	$0.855068\pi$
$60$		0			0
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	−0.119256	−	0.992864i	$-0.538051\pi$
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	0.919473	−	0.393153i	$-0.128616\pi$
$62$		0			0
$63$	−0.210913	−	3.13385i	−0.0265726	−	0.394828i
$64$		0			0
$65$	−1.09358	+	1.89414i	−0.135642	+	0.234939i
$66$		0			0
$67$	2.23944	+	3.87883i	0.273592	+	0.473875i	0.969779	−	0.243986i	$-0.0784550\pi$
$67$	2.23944	+	3.87883i	0.273592	+	0.473875i	−0.696187	+	0.717860i	$0.745122\pi$
$68$		0			0
$69$	−0.879996			−0.105939
$70$		0			0
$71$	6.60274			0.783601			0.391801	−	0.920050i	$-0.371852\pi$
$71$	6.60274			0.783601			0.391801	+	0.920050i	$0.371852\pi$
$72$		0			0
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	0.999847	−	0.0175164i	$-0.00557593\pi$
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	−0.515093	+	0.857134i	$0.672243\pi$
$74$		0			0
$75$	0.145624	−	0.252229i	0.0168152	−	0.0291249i
$76$		0			0
$77$	−2.48931	−	1.22218i	−0.283683	−	0.139280i
$78$		0			0
$79$	1.07007	−	1.85342i	0.120392	−	0.208526i	−0.799530	−	0.600626i	$-0.794918\pi$
$79$	1.07007	−	1.85342i	0.120392	−	0.208526i	0.919922	+	0.392100i	$0.128251\pi$
$80$		0			0
$81$	2.01457	+	3.48935i	0.223842	+	0.387705i
$82$		0			0
$83$	6.66558			0.731642			0.365821	−	0.930685i	$-0.380788\pi$
$83$	6.66558			0.731642			0.365821	+	0.930685i	$0.380788\pi$
$84$		0			0
$85$	−11.5728			−1.25525
$86$		0			0
$87$	2.08969	+	3.61946i	0.224039	+	0.388047i
$88$		0			0
$89$	2.88388	−	4.99503i	0.305691	−	0.529472i	−0.671724	−	0.740802i	$-0.734446\pi$
$89$	2.88388	−	4.99503i	0.305691	−	0.529472i	0.977415	+	0.211329i	$0.0677792\pi$
$90$		0			0
$91$	2.19729	−	1.47375i	0.230338	−	0.154491i
$92$		0			0
$93$	0.691998	−	1.19858i	0.0717569	−	0.124287i
$94$		0			0
$95$	0.827739	+	1.43369i	0.0849242	+	0.147093i
$96$		0			0
$97$	−2.88777			−0.293209			−0.146604	−	0.989195i	$-0.546834\pi$
$97$	−2.88777			−0.293209			−0.146604	+	0.989195i	$0.546834\pi$
$98$		0			0
$99$	−1.24433			−0.125060
$100$		0			0
$101$	5.62716	+	9.74653i	0.559924	+	0.969816i	0.997502	+	0.0706359i	$0.0225028\pi$
$101$	5.62716	+	9.74653i	0.559924	+	0.969816i	−0.437579	+	0.899180i	$0.644164\pi$
$102$		0			0
$103$	10.1167	−	17.5226i	0.996828	−	1.72656i	0.429487	−	0.903073i	$-0.358694\pi$
$103$	10.1167	−	17.5226i	0.996828	−	1.72656i	0.567341	−	0.823483i	$-0.307972\pi$
$104$		0			0
$105$	6.47064	−	4.33994i	0.631470	−	0.423535i
$106$		0			0
$107$	4.52758	−	7.84201i	0.437698	−	0.758115i	−0.559813	−	0.828619i	$-0.689127\pi$
$107$	4.52758	−	7.84201i	0.437698	−	0.758115i	0.997512	+	0.0705034i	$0.0224606\pi$
$108$		0			0
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	−0.959700	−	0.281026i	$-0.909325\pi$
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	0.236474	−	0.971638i	$-0.424008\pi$
$110$		0			0
$111$	−14.6668			−1.39211
$112$		0			0
$113$	3.10408			0.292008			0.146004	−	0.989284i	$-0.453359\pi$
$113$	3.10408			0.292008			0.146004	+	0.989284i	$0.453359\pi$
$114$		0			0
$115$	0.714748	+	1.23798i	0.0666506	+	0.115442i
$116$		0			0
$117$	0.593582	−	1.02811i	0.0548767	−	0.0950492i
$118$		0			0
$119$	12.5664	+	6.16976i	1.15196	+	0.565581i
$120$		0			0
$121$	4.95069	−	8.57484i	0.450062	−	0.779531i
$122$		0			0
$123$	−4.92815	−	8.53581i	−0.444356	−	0.769648i
$124$		0			0
$125$	−11.4089			−1.02045
$126$		0			0
$127$	−8.78914			−0.779910			−0.389955	−	0.920834i	$-0.627509\pi$
$127$	−8.78914			−0.779910			−0.389955	+	0.920834i	$0.627509\pi$
$128$		0			0
$129$	0.597654	+	1.03517i	0.0526205	+	0.0911414i
$130$		0			0
$131$	−5.25723	+	9.10580i	−0.459327	+	0.795577i	−0.998925	−	0.0463451i	$-0.985243\pi$
$131$	−5.25723	+	9.10580i	−0.459327	+	0.795577i	0.539599	+	0.841922i	$0.318576\pi$
$132$		0			0
$133$	−0.134473	−	1.99807i	−0.0116603	−	0.173254i
$134$		0			0
$135$	6.16525	−	10.6785i	0.530620	−	0.919061i
$136$		0			0
$137$	−4.36583	−	7.56183i	−0.372998	−	0.646051i	0.617028	−	0.786942i	$-0.288337\pi$
$137$	−4.36583	−	7.56183i	−0.372998	−	0.646051i	−0.990025	+	0.140891i	$0.955003\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−3.14726			−0.265047
$142$		0			0
$143$	−0.524077	−	0.907729i	−0.0438256	−	0.0759081i
$144$		0			0
$145$	3.39457	−	5.87957i	0.281904	−	0.488272i
$146$		0			0
$147$	−9.33992	+	1.26290i	−0.770343	+	0.104163i
$148$		0			0
$149$	−7.69632	+	13.3304i	−0.630507	+	1.09207i	0.356941	+	0.934127i	$0.383820\pi$
$149$	−7.69632	+	13.3304i	−0.630507	+	1.09207i	−0.987448	+	0.157944i	$0.949514\pi$
$150$		0			0
$151$	−6.83786	−	11.8435i	−0.556457	−	0.963812i	−0.997789	−	0.0664680i	$-0.978827\pi$
$151$	−6.83786	−	11.8435i	−0.556457	−	0.963812i	0.441331	−	0.897344i	$-0.354506\pi$
$152$		0			0
$153$	6.28158			0.507836
$154$		0			0
$155$	−2.24821			−0.180581
$156$		0			0
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	0.790487	−	0.612478i	$-0.209827\pi$
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	−0.925666	+	0.378343i	$0.876494\pi$
$158$		0			0
$159$	−3.29074	+	5.69972i	−0.260972	+	0.452017i
$160$		0			0
$161$	−0.116117	−	1.72532i	−0.00915128	−	0.135974i
$162$		0			0
$163$	−6.90502	+	11.9598i	−0.540843	+	0.936767i	0.458013	+	0.888946i	$0.348561\pi$
$163$	−6.90502	+	11.9598i	−0.540843	+	0.936767i	−0.998856	+	0.0478219i	$0.984772\pi$
$164$		0			0
$165$	−1.54332	−	2.67311i	−0.120147	−	0.208101i
$166$		0			0
$167$	−16.3783			−1.26739			−0.633695	−	0.773583i	$-0.718462\pi$
$167$	−16.3783			−1.26739			−0.633695	+	0.773583i	$0.718462\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−0.449286	−	0.778186i	−0.0343578	−	0.0595094i
$172$		0			0
$173$	−2.06273	+	3.57275i	−0.156826	+	0.271631i	−0.933723	−	0.357997i	$-0.883460\pi$
$173$	−2.06273	+	3.57275i	−0.156826	+	0.271631i	0.776896	+	0.629629i	$0.216793\pi$
$174$		0			0
$175$	0.513734	+	0.252229i	0.0388346	+	0.0190667i
$176$		0			0
$177$	−0.705626	+	1.22218i	−0.0530381	+	0.0918647i
$178$		0			0
$179$	7.20679	+	12.4825i	0.538661	+	0.932988i	0.998976	+	0.0452324i	$0.0144028\pi$
$179$	7.20679	+	12.4825i	0.538661	+	0.932988i	−0.460316	+	0.887755i	$0.652264\pi$
$180$		0			0
$181$	18.1014			1.34547			0.672733	−	0.739885i	$-0.265120\pi$
$181$	18.1014			1.34547			0.672733	+	0.739885i	$0.265120\pi$
$182$		0			0
$183$	−16.8299			−1.24410
$184$		0			0
$185$	11.9126	+	20.6333i	0.875834	+	1.51699i
$186$		0			0
$187$	2.77302	−	4.80302i	0.202784	−	0.351232i
$188$		0			0
$189$	−12.3876	+	8.30850i	−0.901062	+	0.604355i
$190$		0			0
$191$	2.77068	−	4.79895i	0.200479	−	0.347240i	−0.748204	−	0.663469i	$-0.769083\pi$
$191$	2.77068	−	4.79895i	0.200479	−	0.347240i	0.948683	+	0.316229i	$0.102417\pi$
$192$		0			0
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	0.979351	−	0.202170i	$-0.0647992\pi$
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	−0.664759	+	0.747058i	$0.731466\pi$
$194$		0			0
$195$	2.94483			0.210884
$196$		0			0
$197$	−5.46874			−0.389632			−0.194816	−	0.980840i	$-0.562411\pi$
$197$	−5.46874			−0.389632			−0.194816	+	0.980840i	$0.562411\pi$
$198$		0			0
$199$	9.76839	+	16.9193i	0.692463	+	1.19938i	0.971029	+	0.238963i	$0.0768075\pi$
$199$	9.76839	+	16.9193i	0.692463	+	1.19938i	−0.278566	+	0.960417i	$0.589859\pi$
$200$		0			0
$201$	3.01522	−	5.22252i	0.212677	−	0.368368i
$202$		0			0
$203$	−6.82056	+	4.57464i	−0.478709	+	0.321077i
$204$		0			0
$205$	−8.00546	+	13.8659i	−0.559125	+	0.968433i
$206$		0			0
$207$	−0.387956	−	0.671959i	−0.0269648	−	0.0467044i
$208$		0			0
$209$	−0.793355			−0.0548775
$210$		0			0
$211$	−16.6905			−1.14902			−0.574511	−	0.818497i	$-0.694808\pi$
$211$	−16.6905			−1.14902			−0.574511	+	0.818497i	$0.694808\pi$
$212$		0			0
$213$	−4.44502	−	7.69900i	−0.304568	−	0.527527i
$214$		0			0
$215$	0.970850	−	1.68156i	0.0662114	−	0.114682i
$216$		0			0
$217$	2.44124	+	1.19858i	0.165722	+	0.0813647i
$218$		0			0
$219$	5.57650	−	9.65878i	0.376825	−	0.652680i
$220$		0			0
$221$	2.64562	+	4.58236i	0.177964	+	0.308243i
$222$		0			0
$223$	5.34217			0.357738			0.178869	−	0.983873i	$-0.442756\pi$
$223$	5.34217			0.357738			0.178869	+	0.983873i	$0.442756\pi$
$224$		0			0
$225$	0.256800			0.0171200
$226$		0			0
$227$	10.0608	+	17.4258i	0.667757	+	1.15659i	0.978530	+	0.206104i	$0.0660786\pi$
$227$	10.0608	+	17.4258i	0.667757	+	1.15659i	−0.310774	+	0.950484i	$0.600588\pi$
$228$		0			0
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	0.0603445	+	0.998178i	$0.480780\pi$
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	−0.894619	+	0.446829i	$0.852553\pi$
$230$		0			0
$231$	0.250725	+	3.72540i	0.0164965	+	0.245113i
$232$		0			0
$233$	0.396678	−	0.687066i	0.0259872	−	0.0450112i	−0.852739	−	0.522337i	$-0.825060\pi$
$233$	0.396678	−	0.687066i	0.0259872	−	0.0450112i	0.878727	+	0.477326i	$0.158394\pi$
$234$		0			0
$235$	2.55626	+	4.42757i	0.166752	+	0.288823i
$236$		0			0
$237$	−2.88152			−0.187175
$238$		0			0
$239$	−20.0488			−1.29685			−0.648425	−	0.761279i	$-0.724572\pi$
$239$	−20.0488			−1.29685			−0.648425	+	0.761279i	$0.724572\pi$
$240$		0			0
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	0.553186	−	0.833058i	$-0.313412\pi$
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	−0.998042	+	0.0625446i	$0.980078\pi$
$242$		0			0
$243$	−5.74404	+	9.94897i	−0.368480	+	0.638227i
$244$		0			0
$245$	9.36269	+	12.1137i	0.598161	+	0.773913i
$246$		0			0
$247$	0.378453	−	0.655500i	0.0240804	−	0.0417085i
$248$		0			0
$249$	−4.48732	−	7.77227i	−0.284372	−	0.492547i
$250$		0			0
$251$	26.1095			1.64802			0.824010	−	0.566576i	$-0.191732\pi$
$251$	26.1095			1.64802			0.824010	+	0.566576i	$0.191732\pi$
$252$		0			0
$253$	−0.685057			−0.0430692
$254$		0			0
$255$	7.79092	+	13.4943i	0.487886	+	0.845044i
$256$		0			0
$257$	−5.30990	+	9.19701i	−0.331222	+	0.573694i	−0.982752	−	0.184930i	$-0.940794\pi$
$257$	−5.30990	+	9.19701i	−0.331222	+	0.573694i	0.651530	+	0.758623i	$0.274128\pi$
$258$		0			0
$259$	−1.93531	−	28.7557i	−0.120254	−	1.78679i
$260$		0			0
$261$	−1.84253	+	3.19135i	−0.114050	+	0.197540i
$262$		0			0
$263$	5.17888	+	8.97008i	0.319343	+	0.553119i	0.980351	−	0.197260i	$-0.0632044\pi$
$263$	5.17888	+	8.97008i	0.319343	+	0.553119i	−0.661008	+	0.750379i	$0.729871\pi$
$264$		0			0
$265$	10.6912			0.656753
$266$		0			0
$267$	−7.76581			−0.475260
$268$		0			0
$269$	−5.98503	−	10.3664i	−0.364914	−	0.632049i	0.623849	−	0.781545i	$-0.285568\pi$
$269$	−5.98503	−	10.3664i	−0.364914	−	0.632049i	−0.988762	+	0.149496i	$0.952235\pi$
$270$		0			0
$271$	−1.37845	+	2.38755i	−0.0837351	+	0.145033i	−0.904852	−	0.425727i	$-0.860018\pi$
$271$	−1.37845	+	2.38755i	−0.0837351	+	0.145033i	0.821116	+	0.570761i	$0.193352\pi$
$272$		0			0
$273$	−3.19767	−	1.56996i	−0.193532	−	0.0950184i
$274$		0			0
$275$	0.113365	−	0.196354i	0.00683618	−	0.0118406i
$276$		0			0
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	0.961463	+	0.274933i	$0.0886558\pi$
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	−0.242632	+	0.970118i	$0.578011\pi$
$278$		0			0
$279$	1.22030			0.0730574
$280$		0			0
$281$	−3.87870			−0.231384			−0.115692	−	0.993285i	$-0.536909\pi$
$281$	−3.87870			−0.231384			−0.115692	+	0.993285i	$0.536909\pi$
$282$		0			0
$283$	−3.10499	−	5.37801i	−0.184573	−	0.319689i	0.758860	−	0.651254i	$-0.225757\pi$
$283$	−3.10499	−	5.37801i	−0.184573	−	0.319689i	−0.943432	+	0.331565i	$0.892423\pi$
$284$		0			0
$285$	1.11448	−	1.93034i	0.0660162	−	0.114343i
$286$		0			0
$287$	16.0850	−	10.7884i	0.949468	−	0.636821i
$288$		0			0
$289$	−5.49866	+	9.52395i	−0.323450	+	0.560232i
$290$		0			0
$291$	1.94407	+	3.36723i	0.113963	+	0.197390i
$292$		0			0
$293$	16.5754			0.968347			0.484174	−	0.874972i	$-0.339120\pi$
$293$	16.5754			0.968347			0.484174	+	0.874972i	$0.339120\pi$
$294$		0			0
$295$	2.29249			0.133474
$296$		0			0
$297$	2.95457	+	5.11747i	0.171442	+	0.296946i
$298$		0			0
$299$	0.326792	−	0.566020i	0.0188989	−	0.0327338i
$300$		0			0
$301$	−1.95069	+	1.30835i	−0.112436	+	0.0754121i
$302$		0			0
$303$	7.57650	−	13.1229i	0.435259	−	0.753890i
$304$		0			0
$305$	13.6695	+	23.6763i	0.782716	+	1.35570i
$306$		0			0
$307$	7.05788			0.402815			0.201407	−	0.979508i	$-0.435449\pi$
$307$	7.05788			0.402815			0.201407	+	0.979508i	$0.435449\pi$
$308$		0			0
$309$	−27.2426			−1.54978
$310$		0			0
$311$	10.5551	+	18.2820i	0.598525	+	1.03668i	0.993039	+	0.117785i	$0.0375795\pi$
$311$	10.5551	+	18.2820i	0.598525	+	1.03668i	−0.394514	+	0.918890i	$0.629087\pi$
$312$		0			0
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	−0.892654	−	0.450742i	$-0.851159\pi$
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	0.836681	+	0.547690i	$0.184493\pi$
$314$		0			0
$315$	6.16660	+	3.02762i	0.347449	+	0.170587i
$316$		0			0
$317$	9.02297	−	15.6282i	0.506781	−	0.877770i	−0.493189	−	0.869922i	$-0.664169\pi$
$317$	9.02297	−	15.6282i	0.506781	−	0.877770i	0.999969	−	0.00784727i	$-0.00249789\pi$
$318$		0			0
$319$	1.62678	+	2.81767i	0.0910822	+	0.157759i
$320$		0			0
$321$	−12.1920			−0.680492
$322$		0			0
$323$	4.00498			0.222843
$324$		0			0
$325$	0.108157	+	0.187333i	0.00599947	+	0.0103914i
$326$		0			0
$327$	−10.1664	+	17.6087i	−0.562202	+	0.973763i
$328$		0			0
$329$	−0.415285	−	6.17051i	−0.0228954	−	0.340191i
$330$		0			0
$331$	−7.33689	+	12.7079i	−0.403272	+	0.698488i	−0.994119	−	0.108296i	$-0.965460\pi$
$331$	−7.33689	+	12.7079i	−0.403272	+	0.698488i	0.590847	+	0.806784i	$0.298794\pi$
$332$		0			0
$333$	−6.46602	−	11.1995i	−0.354336	−	0.613728i
$334$		0			0
$335$	−9.79606			−0.535216
$336$		0			0
$337$	12.8080			0.697698			0.348849	−	0.937179i	$-0.386573\pi$
$337$	12.8080			0.697698			0.348849	+	0.937179i	$0.386573\pi$
$338$		0			0
$339$	−2.08969	−	3.61946i	−0.113497	−	0.196582i
$340$		0			0
$341$	0.538705	−	0.933065i	0.0291725	−	0.0505283i
$342$		0			0
$343$	−3.70846	−	18.1452i	−0.200238	−	0.979747i
$344$		0			0
$345$	0.962348	−	1.66684i	0.0518111	−	0.0897394i
$346$		0			0
$347$	10.1027	+	17.4984i	0.542342	+	0.939363i	0.998769	+	0.0496025i	$0.0157954\pi$
$347$	10.1027	+	17.4984i	0.542342	+	0.939363i	−0.456428	+	0.889761i	$0.650871\pi$
$348$		0			0
$349$	−18.4434			−0.987252			−0.493626	−	0.869674i	$-0.664329\pi$
$349$	−18.4434			−0.987252			−0.493626	+	0.869674i	$0.664329\pi$
$350$		0			0
$351$	−5.63766			−0.300916
$352$		0			0
$353$	4.07218	+	7.05322i	0.216740	+	0.375405i	0.953810	−	0.300412i	$-0.0971242\pi$
$353$	4.07218	+	7.05322i	0.216740	+	0.375405i	−0.737069	+	0.675817i	$0.763791\pi$
$354$		0			0
$355$	−7.22064	+	12.5065i	−0.383232	+	0.663777i
$356$		0			0
$357$	−1.26570	−	18.8064i	−0.0669879	−	0.995339i
$358$		0			0
$359$	−16.3050	+	28.2411i	−0.860545	+	1.49051i	0.0108595	+	0.999941i	$0.496543\pi$
$359$	−16.3050	+	28.2411i	−0.860545	+	1.49051i	−0.871404	+	0.490566i	$0.836790\pi$
$360$		0			0
$361$	9.21355	+	15.9583i	0.484923	+	0.839912i
$362$		0			0
$363$	−13.3314			−0.699715
$364$		0			0
$365$	−18.1173			−0.948304
$366$		0			0
$367$	−1.58006	−	2.73675i	−0.0824786	−	0.142857i	0.821835	−	0.569725i	$-0.192950\pi$
$367$	−1.58006	−	2.73675i	−0.0824786	−	0.142857i	−0.904314	+	0.426868i	$0.859617\pi$
$368$		0			0
$369$	4.34526	−	7.52621i	0.226205	−	0.391799i
$370$		0			0
$371$	−11.6091	−	5.69972i	−0.602713	−	0.295915i
$372$		0			0
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	−0.846263	−	0.532765i	$-0.821153\pi$
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	0.884520	+	0.466503i	$0.154486\pi$
$374$		0			0
$375$	7.68059	+	13.3032i	0.396624	+	0.686972i
$376$		0			0
$377$	−3.10408			−0.159868
$378$		0			0
$379$	−10.7254			−0.550927			−0.275463	−	0.961312i	$-0.588831\pi$
$379$	−10.7254			−0.550927			−0.275463	+	0.961312i	$0.588831\pi$
$380$		0			0
$381$	5.91692	+	10.2484i	0.303133	+	0.525042i
$382$		0			0
$383$	−10.7054	+	18.5424i	−0.547023	+	0.947471i	0.451454	+	0.892294i	$0.350906\pi$
$383$	−10.7054	+	18.5424i	−0.547023	+	0.947471i	−0.998477	+	0.0551766i	$0.982428\pi$
$384$		0			0
$385$	5.03725	−	3.37855i	0.256722	−	0.172187i
$386$		0			0
$387$	−0.526965	+	0.912730i	−0.0267871	+	0.0463967i
$388$		0			0
$389$	−17.3909	−	30.1220i	−0.881755	−	1.52725i	−0.849388	−	0.527769i	$-0.823029\pi$
$389$	−17.3909	−	30.1220i	−0.881755	−	1.52725i	−0.0323675	−	0.999476i	$-0.510305\pi$
$390$		0			0
$391$	3.45828			0.174893
$392$		0			0
$393$	14.1568			0.714119
$394$		0			0
$395$	2.34042	+	4.05373i	0.117759	+	0.203965i
$396$		0			0
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	−0.916465	−	0.400115i	$-0.868970\pi$
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	0.804742	+	0.593624i	$0.202303\pi$
$398$		0			0
$399$	−2.23928	+	1.50191i	−0.112104	+	0.0751897i
$400$		0			0
$401$	6.87687	−	11.9111i	0.343415	−	0.594811i	−0.641650	−	0.766998i	$-0.721750\pi$
$401$	6.87687	−	11.9111i	0.343415	−	0.594811i	0.985064	+	0.172186i	$0.0550831\pi$
$402$		0			0
$403$	0.513956	+	0.890198i	0.0256020	+	0.0443439i
$404$		0			0
$405$	−8.81241			−0.437892
$406$		0			0
$407$	−11.4178			−0.565959
$408$		0			0
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	0.905960	−	0.423364i	$-0.139151\pi$
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	−0.819624	+	0.572902i	$0.805818\pi$
$410$		0			0
$411$	−5.87822	+	10.1814i	−0.289951	+	0.502210i
$412$		0			0
$413$	−2.48931	−	1.22218i	−0.122491	−	0.0601396i
$414$		0			0
$415$	−7.28935	+	12.6255i	−0.357820	+	0.619763i
$416$		0			0
$417$	−2.69283	−	4.66412i	−0.131869	−	0.228403i
$418$		0			0
$419$	3.56737			0.174278			0.0871388	−	0.996196i	$-0.472228\pi$
$419$	3.56737			0.174278			0.0871388	+	0.996196i	$0.472228\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	−1.38750	−	2.40323i	−0.0674627	−	0.116849i
$424$		0			0
$425$	−0.572285	+	0.991227i	−0.0277599	+	0.0480816i
$426$		0			0
$427$	−2.22073	−	32.9967i	−0.107469	−	1.59682i
$428$		0			0
$429$	−0.705626	+	1.22218i	−0.0340680	+	0.0590074i
$430$		0			0
$431$	−5.68211	−	9.84171i	−0.273698	−	0.474059i	0.696108	−	0.717937i	$-0.254913\pi$
$431$	−5.68211	−	9.84171i	−0.273698	−	0.474059i	−0.969806	+	0.243879i	$0.921580\pi$
$432$		0			0
$433$	−21.2136			−1.01946			−0.509731	−	0.860334i	$-0.670255\pi$
$433$	−21.2136			−1.01946			−0.509731	+	0.860334i	$0.670255\pi$
$434$		0			0
$435$	−9.14101			−0.438278
$436$		0			0
$437$	−0.247351	−	0.428424i	−0.0118324	−	0.0204943i
$438$		0			0
$439$	−12.2503	+	21.2182i	−0.584676	+	1.01269i	0.410239	+	0.911978i	$0.365445\pi$
$439$	−12.2503	+	21.2182i	−0.584676	+	1.01269i	−0.994916	+	0.100711i	$0.967888\pi$
$440$		0			0
$441$	−5.08195	−	6.57513i	−0.241997	−	0.313102i
$442$		0			0
$443$	20.2344	−	35.0470i	0.961366	−	1.66513i	0.242288	−	0.970204i	$-0.422102\pi$
$443$	20.2344	−	35.0470i	0.961366	−	1.66513i	0.719077	−	0.694930i	$-0.244565\pi$
$444$		0			0
$445$	6.30753	+	10.9250i	0.299005	+	0.517893i
$446$		0			0
$447$	20.7249			0.980254
$448$		0			0
$449$	−27.7638			−1.31025			−0.655127	−	0.755519i	$-0.727385\pi$
$449$	−27.7638			−1.31025			−0.655127	+	0.755519i	$0.727385\pi$
$450$		0			0
$451$	−3.83646	−	6.64494i	−0.180652	−	0.312898i
$452$		0			0
$453$	−9.20661	+	15.9463i	−0.432564	+	0.749223i
$454$		0			0
$455$	0.388575	+	5.77363i	0.0182167	+	0.270672i
$456$		0			0
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	−0.704910	−	0.709297i	$-0.749012\pi$
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	0.966724	+	0.255821i	$0.0823457\pi$
$458$		0			0
$459$	−14.9151	−	25.8338i	−0.696179	−	1.20582i
$460$		0			0
$461$	−9.29773			−0.433038			−0.216519	−	0.976278i	$-0.569470\pi$
$461$	−9.29773			−0.433038			−0.216519	+	0.976278i	$0.569470\pi$
$462$		0			0
$463$	−28.2439			−1.31260			−0.656302	−	0.754499i	$-0.727880\pi$
$463$	−28.2439			−1.31260			−0.656302	+	0.754499i	$0.727880\pi$
$464$		0			0
$465$	1.51351	+	2.62148i	0.0701875	+	0.121568i
$466$		0			0
$467$	11.1303	−	19.2783i	0.515050	−	0.892093i	−0.484797	−	0.874626i	$-0.661107\pi$
$467$	11.1303	−	19.2783i	0.515050	−	0.892093i	0.999847	−	0.0174663i	$-0.00555997\pi$
$468$		0			0
$469$	10.6371	+	5.22252i	0.491177	+	0.241154i
$470$		0			0
$471$	−2.28053	+	3.95000i	−0.105081	+	0.182006i
$472$		0			0
$473$	0.465261	+	0.805855i	0.0213927	+	0.0370533i
$474$		0			0
$475$	0.163729			0.00751242
$476$		0			0
$477$	−5.80302			−0.265702
$478$		0			0
$479$	−16.4382	−	28.4718i	−0.751081	−	1.30091i	−0.947299	−	0.320350i	$-0.896200\pi$
$479$	−16.4382	−	28.4718i	−0.751081	−	1.30091i	0.196219	−	0.980560i	$-0.437134\pi$
$480$		0			0
$481$	5.44661	−	9.43381i	0.248344	−	0.430145i
$482$		0			0
$483$	−1.93360	+	1.29689i	−0.0879820	+	0.0590107i
$484$		0			0
$485$	3.15801	−	5.46984i	0.143398	−	0.248373i
$486$		0			0
$487$	−13.9462	−	24.1555i	−0.631962	−	1.09459i	−0.987150	−	0.159796i	$-0.948916\pi$
$487$	−13.9462	−	24.1555i	−0.631962	−	1.09459i	0.355188	−	0.934795i	$-0.384417\pi$
$488$		0			0
$489$	18.5941			0.840852
$490$		0			0
$491$	−10.6571			−0.480948			−0.240474	−	0.970656i	$-0.577303\pi$
$491$	−10.6571			−0.480948			−0.240474	+	0.970656i	$0.577303\pi$
$492$		0			0
$493$	−8.21224	−	14.2240i	−0.369861	−	0.640618i
$494$		0			0
$495$	1.36078	−	2.35694i	0.0611625	−	0.105936i
$496$		0			0
$497$	14.5081	−	9.73078i	0.650777	−	0.436485i
$498$		0			0
$499$	−12.2557	+	21.2275i	−0.548641	+	0.950274i	0.449727	+	0.893166i	$0.351521\pi$
$499$	−12.2557	+	21.2275i	−0.548641	+	0.950274i	−0.998368	+	0.0571077i	$0.981812\pi$
$500$		0			0
$501$	11.0260	+	19.0976i	0.492605	+	0.853217i
$502$		0			0
$503$	38.0054			1.69458			0.847288	−	0.531134i	$-0.178234\pi$
$503$	38.0054			1.69458			0.847288	+	0.531134i	$0.178234\pi$
$504$		0			0
$505$	−24.6151			−1.09536
$506$		0			0
$507$	−0.673208	−	1.16603i	−0.0298982	−	0.0517852i
$508$		0			0
$509$	−19.9250	+	34.5112i	−0.883161	+	1.52968i	−0.0353545	+	0.999375i	$0.511256\pi$
$509$	−19.9250	+	34.5112i	−0.883161	+	1.52968i	−0.847807	+	0.530305i	$0.822077\pi$
$510$		0			0
$511$	19.6728	+	9.65878i	0.870274	+	0.427279i
$512$		0			0
$513$	−2.13359	+	3.69549i	−0.0942004	+	0.163160i
$514$		0			0
$515$	22.1269	+	38.3249i	0.975027	+	1.68880i
$516$		0			0
$517$	−2.45007			−0.107754
$518$		0			0
$519$	5.55459			0.243819
$520$		0			0
$521$	9.81670	+	17.0030i	0.430077	+	0.744916i	0.996880	−	0.0789382i	$-0.0251530\pi$
$521$	9.81670	+	17.0030i	0.430077	+	0.744916i	−0.566802	+	0.823854i	$0.691820\pi$
$522$		0			0
$523$	11.4162	−	19.7734i	0.499195	−	0.864632i	−0.500804	−	0.865561i	$-0.666962\pi$
$523$	11.4162	−	19.7734i	0.499195	−	0.864632i	1.00000		0.000928862i	$0.000295666\pi$
$524$		0			0
$525$	−0.0517436	−	0.768832i	−0.00225828	−	0.0335546i
$526$		0			0
$527$	−2.71947	+	4.71026i	−0.118462	+	0.205182i
$528$		0			0
$529$	11.2864	+	19.5486i	0.490714	+	0.849941i
$530$		0			0
$531$	−1.24433			−0.0539994
$532$		0			0
$533$	7.32040			0.317082
$534$		0			0
$535$	9.90257	+	17.1518i	0.428125	+	0.741535i
$536$		0			0
$537$	9.70333	−	16.8067i	0.418730	−	0.725261i
$538$		0			0
$539$	−7.27092	+	0.983142i	−0.313181	+	0.0423469i
$540$		0			0
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	−0.743514	−	0.668720i	$-0.766842\pi$
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	0.950886	+	0.309542i	$0.100176\pi$
$542$		0			0
$543$	−12.1860	−	21.1068i	−0.522952	−	0.905779i
$544$		0			0
$545$	33.0292			1.41482
$546$		0			0
$547$	43.8570			1.87519			0.937596	−	0.347728i	$-0.113047\pi$
$547$	43.8570			1.87519			0.937596	+	0.347728i	$0.113047\pi$
$548$		0			0
$549$	−7.41965	−	12.8512i	−0.316663	−	0.548476i
$550$		0			0
$551$	−1.17475	+	2.03473i	−0.0500461	+	0.0866823i
$552$		0			0
$553$	−0.380221	−	5.64950i	−0.0161686	−	0.240241i
$554$		0			0
$555$	16.0394	−	27.7810i	0.680833	−	1.17924i
$556$		0			0
$557$	−7.45977	−	12.9207i	−0.316080	−	0.547467i	0.663586	−	0.748100i	$-0.269034\pi$
$557$	−7.45977	−	12.9207i	−0.316080	−	0.547467i	−0.979667	+	0.200633i	$0.935700\pi$
$558$		0			0
$559$	−0.887771			−0.0375487
$560$		0			0
$561$	−7.46729			−0.315269
$562$		0			0
$563$	−8.63486	−	14.9560i	−0.363916	−	0.630321i	0.624686	−	0.780876i	$-0.285227\pi$
$563$	−8.63486	−	14.9560i	−0.363916	−	0.630321i	−0.988602	+	0.150555i	$0.951894\pi$
$564$		0			0
$565$	−3.39457	+	5.87957i	−0.142811	+	0.247355i
$566$		0			0
$567$	9.56902	+	4.69811i	0.401861	+	0.197302i
$568$		0			0
$569$	−13.2662	+	22.9777i	−0.556148	+	0.963277i	0.441665	+	0.897180i	$0.354388\pi$
$569$	−13.2662	+	22.9777i	−0.556148	+	0.963277i	−0.997813	+	0.0660972i	$0.978945\pi$
$570$		0			0
$571$	−0.992844	−	1.71966i	−0.0415492	−	0.0719654i	0.844503	−	0.535551i	$-0.179896\pi$
$571$	−0.992844	−	1.71966i	−0.0415492	−	0.0719654i	−0.886052	+	0.463586i	$0.846563\pi$
$572$		0			0
$573$	−7.46097			−0.311686
$574$		0			0
$575$	0.141379			0.00589593
$576$		0			0
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	0.715212	−	0.698908i	$-0.246330\pi$
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	−0.962878	+	0.269937i	$0.912997\pi$
$578$		0			0
$579$	5.88443	−	10.1921i	0.244549	−	0.423571i
$580$		0			0
$581$	14.6462	−	9.82339i	0.607626	−	0.407543i
$582$		0			0
$583$	−2.56176	+	4.43711i	−0.106097	+	0.183766i
$584$		0			0
$585$	1.29826	+	2.24865i	0.0536765	+	0.0929704i
$586$		0			0
$587$	−33.5122			−1.38320			−0.691598	−	0.722283i	$-0.743093\pi$
$587$	−33.5122			−1.38320			−0.691598	+	0.722283i	$0.743093\pi$
$588$		0			0
$589$	0.778033			0.0320583
$590$		0			0
$591$	3.68160	+	6.37672i	0.151441	+	0.262303i
$592$		0			0
$593$	−17.6408	+	30.5547i	−0.724419	+	1.25473i	0.234793	+	0.972045i	$0.424559\pi$
$593$	−17.6408	+	30.5547i	−0.724419	+	1.25473i	−0.959213	+	0.282686i	$0.908775\pi$
$594$		0			0
$595$	−25.4288	+	17.0554i	−1.04248	+	0.699205i
$596$		0			0
$597$	13.1523	−	22.7805i	0.538288	−	0.932343i
$598$		0			0
$599$	−12.5034	−	21.6565i	−0.510876	−	0.884863i	−0.999921	−	0.0126040i	$-0.995988\pi$
$599$	−12.5034	−	21.6565i	−0.510876	−	0.884863i	0.489045	−	0.872259i	$-0.337345\pi$
$600$		0			0
$601$	−28.4688			−1.16127			−0.580634	−	0.814165i	$-0.697195\pi$
$601$	−28.4688			−1.16127			−0.580634	+	0.814165i	$0.697195\pi$
$602$		0			0
$603$	5.31717			0.216532
$604$		0			0
$605$	10.8280	+	18.7546i	0.440219	+	0.762482i
$606$		0			0
$607$	18.0234	−	31.2175i	0.731549	−	1.26708i	−0.224672	−	0.974434i	$-0.572131\pi$
$607$	18.0234	−	31.2175i	0.731549	−	1.26708i	0.956221	−	0.292646i	$-0.0945356\pi$
$608$		0			0
$609$	9.92583	+	4.87330i	0.402215	+	0.197476i
$610$		0			0
$611$	1.16875	−	2.02434i	0.0472827	−	0.0818961i
$612$		0			0
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	0.619501	−	0.784996i	$-0.287335\pi$
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	−0.989577	+	0.144006i	$0.954001\pi$
$614$		0			0
$615$	21.5573			0.869276
$616$		0			0
$617$	44.3782			1.78660			0.893299	−	0.449463i	$-0.148385\pi$
$617$	44.3782			1.78660			0.893299	+	0.449463i	$0.148385\pi$
$618$		0			0
$619$	−12.5043	−	21.6580i	−0.502588	−	0.870509i	−0.999996	−	0.00299144i	$-0.999048\pi$
$619$	−12.5043	−	21.6580i	−0.502588	−	0.870509i	0.497407	−	0.867517i	$-0.334286\pi$
$620$		0			0
$621$	−1.84234	+	3.19103i	−0.0739307	+	0.128052i
$622$		0			0
$623$	−1.02471	−	15.2256i	−0.0410541	−	0.610002i
$624$		0			0
$625$	11.9358	−	20.6734i	0.477433	−	0.826938i
$626$		0			0
$627$	0.534093	+	0.925076i	0.0213296	+	0.0369440i
$628$		0			0
$629$	57.6388			2.29821
$630$		0			0
$631$	18.4638			0.735032			0.367516	−	0.930017i	$-0.380208\pi$
$631$	18.4638			0.735032			0.367516	+	0.930017i	$0.380208\pi$
$632$		0			0
$633$	11.2362	+	19.4616i	0.446598	+	0.773531i
$634$		0			0
$635$	9.61165	−	16.6479i	0.381427	−	0.660650i
$636$		0			0
$637$	2.65613	−	6.47650i	0.105240	−	0.256608i
$638$		0			0
$639$	3.91927	−	6.78837i	0.155044	−	0.268544i
$640$		0			0
$641$	10.6284	+	18.4088i	0.419795	+	0.727106i	0.995919	−	0.0902567i	$-0.0287687\pi$
$641$	10.6284	+	18.4088i	0.419795	+	0.727106i	−0.576124	+	0.817362i	$0.695435\pi$
$642$		0			0
$643$	36.0554			1.42188			0.710942	−	0.703251i	$-0.248269\pi$
$643$	36.0554			1.42188			0.710942	+	0.703251i	$0.248269\pi$
$644$		0			0
$645$	−2.61434			−0.102939
$646$		0			0
$647$	19.9117	+	34.4881i	0.782809	+	1.35587i	0.930299	+	0.366802i	$0.119547\pi$
$647$	19.9117	+	34.4881i	0.782809	+	1.35587i	−0.147490	+	0.989064i	$0.547119\pi$
$648$		0			0
$649$	−0.549314	+	0.951440i	−0.0215625	+	0.0373473i
$650$		0			0
$651$	−0.245883	−	3.65345i	−0.00963691	−	0.143190i
$652$		0			0
$653$	16.2335	−	28.1172i	0.635265	−	1.10031i	−0.351195	−	0.936303i	$-0.614224\pi$
$653$	16.2335	−	28.1172i	0.635265	−	1.10031i	0.986459	−	0.164008i	$-0.0524423\pi$
$654$		0			0
$655$	−11.4984	−	19.9159i	−0.449281	−	0.778177i
$656$		0			0
$657$	9.83384			0.383655
$658$		0			0
$659$	−23.5230			−0.916327			−0.458164	−	0.888868i	$-0.651493\pi$
$659$	−23.5230			−0.916327			−0.458164	+	0.888868i	$0.651493\pi$
$660$		0			0
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	0.696610	−	0.717450i	$-0.254691\pi$
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	−0.969635	+	0.244557i	$0.921357\pi$
$662$		0			0
$663$	3.56211	−	6.16976i	0.138341	−	0.239614i
$664$		0			0
$665$	3.93167	+	1.93034i	0.152464	+	0.0748553i
$666$		0			0
$667$	−1.01439	+	1.75698i	−0.0392773	+	0.0680303i
$668$		0			0
$669$	−3.59639	−	6.22913i	−0.139044	−	0.240832i
$670$		0			0
$671$	−13.1017			−0.505786
$672$		0			0
$673$	−47.1937			−1.81918			−0.909592	−	0.415502i	$-0.863606\pi$
$673$	−47.1937			−1.81918			−0.909592	+	0.415502i	$0.863606\pi$
$674$		0			0
$675$	−0.609753	−	1.05612i	−0.0234694	−	0.0406502i
$676$		0			0
$677$	4.79438	−	8.30411i	0.184263	−	0.319153i	−0.759065	−	0.651015i	$-0.774344\pi$
$677$	4.79438	−	8.30411i	0.184263	−	0.319153i	0.943328	+	0.331862i	$0.107677\pi$
$678$		0			0
$679$	−6.34526	+	4.25585i	−0.243509	+	0.163325i
$680$		0			0
$681$	13.5460	−	23.4623i	0.519083	−	0.899078i
$682$		0			0
$683$	23.6581	+	40.9769i	0.905250	+	1.56794i	0.820581	+	0.571530i	$0.193650\pi$
$683$	23.6581	+	40.9769i	0.905250	+	1.56794i	0.0846691	+	0.996409i	$0.473017\pi$
$684$		0			0
$685$	19.0976			0.729680
$686$		0			0
$687$	33.9967			1.29705
$688$		0			0
$689$	−2.44407	−	4.23325i	−0.0931117	−	0.161274i
$690$		0			0
$691$	−13.5559	+	23.4796i	−0.515692	+	0.893205i	0.484142	+	0.874990i	$0.339132\pi$
$691$	−13.5559	+	23.4796i	−0.515692	+	0.893205i	−0.999834	+	0.0182158i	$0.994201\pi$
$692$		0			0
$693$	−2.73415	+	1.83383i	−0.103862	+	0.0696615i
$694$		0			0
$695$	−4.37433	+	7.57656i	−0.165928	+	0.287395i
$696$		0			0
$697$	19.3670	+	33.5447i	0.733578	+	1.27059i
$698$		0			0
$699$	−1.06819			−0.0404025
$700$		0			0
$701$	−1.79821			−0.0679176			−0.0339588	−	0.999423i	$-0.510811\pi$
$701$	−1.79821			−0.0679176			−0.0339588	+	0.999423i	$0.510811\pi$
$702$		0			0
$703$	−4.12258	−	7.14051i	−0.155486	−	0.269310i
$704$		0			0
$705$	3.44179	−	5.96135i	0.129625	−	0.224517i
$706$		0			0
$707$	26.7284	+	13.1229i	1.00523	+	0.493537i
$708$		0			0
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	−0.467462	−	0.884013i	$-0.654832\pi$
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	0.999309	−	0.0371721i	$-0.0118350\pi$
$710$		0			0
$711$	−1.27035	−	2.20031i	−0.0476418	−	0.0825180i
$712$		0			0
$713$	0.671827			0.0251601
$714$		0			0
$715$	2.29249			0.0857341
$716$		0			0
$717$	13.4970	+	23.3775i	0.504055	+	0.873050i
$718$		0			0
$719$	−20.9485	+	36.2839i	−0.781249	+	1.35316i	0.149966	+	0.988691i	$0.452084\pi$
$719$	−20.9485	+	36.2839i	−0.781249	+	1.35316i	−0.931215	+	0.364471i	$0.881250\pi$
$720$		0			0
$721$	−3.59469	−	53.4117i	−0.133873	−	1.98916i
$722$		0			0
$723$	−9.29838	+	16.1053i	−0.345810	+	0.598961i
$724$		0			0
$725$	−0.335728	−	0.581499i	−0.0124686	−	0.0215963i
$726$		0			0
$727$	−19.5123			−0.723670			−0.361835	−	0.932242i	$-0.617850\pi$
$727$	−19.5123			−0.723670			−0.361835	+	0.932242i	$0.617850\pi$
$728$		0			0
$729$	27.5552			1.02056
$730$		0			0
$731$	−2.34871	−	4.06808i	−0.0868701	−	0.150463i
$732$		0			0
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	−0.982091	−	0.188409i	$-0.939667\pi$
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	0.654212	+	0.756311i	$0.273000\pi$
$734$		0			0
$735$	7.82185	−	19.0722i	0.288513	−	0.703488i
$736$		0			0
$737$	2.34728	−	4.06562i	0.0864633	−	0.149759i
$738$		0			0
$739$	22.1571	+	38.3772i	0.815061	+	1.41173i	0.909284	+	0.416176i	$0.136630\pi$
$739$	22.1571	+	38.3772i	0.815061	+	1.41173i	−0.0942227	+	0.995551i	$0.530037\pi$
$740$		0			0
$741$	−1.01911			−0.0374380
$742$		0			0
$743$	7.16727			0.262941			0.131471	−	0.991320i	$-0.458030\pi$
$743$	7.16727			0.262941			0.131471	+	0.991320i	$0.458030\pi$
$744$		0			0
$745$	−16.8331	−	29.1558i	−0.616718	−	1.06819i
$746$		0			0
$747$	3.95657	−	6.85297i	0.144763	−	0.250737i
$748$		0			0
$749$	−1.60875	−	23.9036i	−0.0587826	−	0.873420i
$750$		0			0
$751$	−16.9532	+	29.3639i	−0.618632	+	1.07150i	0.371103	+	0.928592i	$0.378980\pi$
$751$	−16.9532	+	29.3639i	−0.618632	+	1.07150i	−0.989736	+	0.142911i	$0.954354\pi$
$752$		0			0
$753$	−17.5772	−	30.4445i	−0.640547	−	1.10946i
$754$		0			0
$755$	29.9110			1.08857
$756$		0			0
$757$	−0.906670			−0.0329535			−0.0164767	−	0.999864i	$-0.505245\pi$
$757$	−0.906670			−0.0329535			−0.0164767	+	0.999864i	$0.505245\pi$
$758$		0			0
$759$	0.461186	+	0.798798i	0.0167400	+	0.0289945i
$760$		0			0
$761$	−10.1247	+	17.5365i	−0.367020	+	0.635697i	−0.989098	−	0.147258i	$-0.952955\pi$
$761$	−10.1247	+	17.5365i	−0.367020	+	0.635697i	0.622079	+	0.782955i	$0.286288\pi$
$762$		0			0
$763$	−35.8650	−	17.6087i	−1.29840	−	0.637477i
$764$		0			0
$765$	−6.86942	+	11.8982i	−0.248364	+	0.430180i
$766$		0			0
$767$	−0.524077	−	0.907729i	−0.0189233	−	0.0327762i
$768$		0			0
$769$	−36.9094			−1.33099			−0.665494	−	0.746403i	$-0.731779\pi$
$769$	−36.9094			−1.33099			−0.665494	+	0.746403i	$0.731779\pi$
$770$		0			0
$771$	14.2987			0.514954
$772$		0			0
$773$	4.94018	+	8.55665i	0.177686	+	0.307761i	0.941088	−	0.338163i	$-0.109806\pi$
$773$	4.94018	+	8.55665i	0.177686	+	0.307761i	−0.763402	+	0.645924i	$0.776472\pi$
$774$		0			0
$775$	−0.111176	+	0.192562i	−0.00399355	+	0.00691704i
$776$		0			0
$777$	−32.2272	+	21.6152i	−1.15614	+	0.775441i
$778$		0			0
$779$	2.77043	−	4.79852i	0.0992609	−	0.171925i
$780$		0			0
$781$	−3.46035	−	5.99350i	−0.123821	−	0.214464i
$782$		0			0
$783$	17.4998			0.625391
$784$		0			0
$785$	7.40915			0.264444
$786$		0			0
$787$	18.8411	+	32.6337i	0.671611	+	1.16326i	0.977447	+	0.211180i	$0.0677307\pi$
$787$	18.8411	+	32.6337i	0.671611	+	1.16326i	−0.305836	+	0.952084i	$0.598936\pi$
$788$		0			0
$789$	6.97292	−	12.0775i	0.248243	−	0.429969i
$790$		0			0
$791$	6.82056	−	4.57464i	0.242511	−	0.162656i
$792$		0			0
$793$	6.24989	−	10.8251i	0.221940	−	0.384412i
$794$		0			0
$795$	−7.19738	−	12.4662i	−0.255265	−	0.442131i
$796$		0			0
$797$	28.3837			1.00540			0.502701	−	0.864460i	$-0.332340\pi$
$797$	28.3837			1.00540			0.502701	+	0.864460i	$0.332340\pi$
$798$		0			0
$799$	12.3683			0.437560
$800$		0			0
$801$	−3.42364	−	5.92992i	−0.120968	−	0.209524i
$802$		0			0
$803$	4.34118	−	7.51915i	0.153197	−	0.265345i
$804$		0			0
$805$	3.39498	+	1.66684i	0.119657	+	0.0587482i
$806$		0			0
$807$	−8.05834	+	13.9574i	−0.283667	+	0.491325i
$808$		0			0
$809$	5.87327	+	10.1728i	0.206493	+	0.357657i	0.950607	−	0.310396i	$-0.100461\pi$
$809$	5.87327	+	10.1728i	0.206493	+	0.357657i	−0.744114	+	0.668052i	$0.767128\pi$
$810$		0			0
$811$	−2.01940			−0.0709108			−0.0354554	−	0.999371i	$-0.511288\pi$
$811$	−2.01940			−0.0709108			−0.0354554	+	0.999371i	$0.511288\pi$
$812$		0			0
$813$	3.71194			0.130184
$814$		0			0
$815$	−15.1024	−	26.1581i	−0.529014	−	0.916280i
$816$		0			0
$817$	−0.335980	+	0.581934i	−0.0117544	+	0.0203593i
$818$		0			0
$819$	−0.210913	−	3.13385i	−0.00736991	−	0.109506i
$820$		0			0
$821$	7.54208	−	13.0633i	0.263220	−	0.455911i	−0.703875	−	0.710323i	$-0.748549\pi$
$821$	7.54208	−	13.0633i	0.263220	−	0.455911i	0.967096	+	0.254412i	$0.0818820\pi$
$822$		0			0
$823$	−7.38828	−	12.7969i	−0.257539	−	0.446071i	0.708043	−	0.706170i	$-0.249578\pi$
$823$	−7.38828	−	12.7969i	−0.257539	−	0.446071i	−0.965582	+	0.260098i	$0.916245\pi$
$824$		0			0
$825$	−0.305274			−0.0106283
$826$		0			0
$827$	−13.0407			−0.453471			−0.226736	−	0.973956i	$-0.572805\pi$
$827$	−13.0407			−0.453471			−0.226736	+	0.973956i	$0.572805\pi$
$828$		0			0
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	0.997845	−	0.0656144i	$-0.0209007\pi$
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	−0.555746	+	0.831352i	$0.687567\pi$
$830$		0			0
$831$	16.1082	−	27.9002i	0.558786	−	0.967845i
$832$		0			0
$833$	36.7047	−	4.96305i	1.27174	−	0.171960i
$834$		0			0
$835$	17.9110	−	31.0228i	0.619835	−	1.07359i
$836$		0			0
$837$	−2.89751	−	5.01864i	−0.100153	−	0.173469i
$838$		0			0
$839$	−32.1703			−1.11064			−0.555321	−	0.831636i	$-0.687404\pi$
$839$	−32.1703			−1.11064			−0.555321	+	0.831636i	$0.687404\pi$
$840$		0			0
$841$	−19.3647			−0.667747
$842$		0			0
$843$	2.61117	+	4.52268i	0.0899335	+	0.155769i
$844$		0			0
$845$	−1.09358	+	1.89414i	−0.0376204	+	0.0651604i
$846$		0			0
$847$	−1.75909	−	26.1374i	−0.0604431	−	0.898093i
$848$		0			0
$849$	−4.18061	+	7.24104i	−0.143478	+	0.248512i
$850$		0			0
$851$	−3.55982	−	6.16579i	−0.122029	−	0.211360i
$852$		0			0
$853$	−19.3910			−0.663934			−0.331967	−	0.943291i	$-0.607712\pi$
$853$	−19.3910			−0.663934			−0.331967	+	0.943291i	$0.607712\pi$
$854$		0			0
$855$	1.96532			0.0672127
$856$		0			0
$857$	−8.71210	−	15.0898i	−0.297600	−	0.515458i	0.677987	−	0.735074i	$-0.262853\pi$
$857$	−8.71210	−	15.0898i	−0.297600	−	0.515458i	−0.975586	+	0.219616i	$0.929519\pi$
$858$		0			0
$859$	−17.7459	+	30.7367i	−0.605481	+	1.04872i	0.386495	+	0.922292i	$0.373686\pi$
$859$	−17.7459	+	30.7367i	−0.605481	+	1.04872i	−0.991975	+	0.126432i	$0.959648\pi$
$860$		0			0
$861$	−23.4082	−	11.4927i	−0.797749	−	0.391672i
$862$		0			0
$863$	28.0010	−	48.4991i	0.953164	−	1.65093i	0.214648	−	0.976691i	$-0.431140\pi$
$863$	28.0010	−	48.4991i	0.953164	−	1.65093i	0.738516	−	0.674236i	$-0.235527\pi$
$864$		0			0
$865$	−4.51153	−	7.81420i	−0.153397	−	0.265691i
$866$		0			0
$867$	14.8070			0.502871
$868$		0			0
$869$	−2.24320			−0.0760953
$870$		0			0
$871$	2.23944	+	3.87883i	0.0758807	+	0.131429i
$872$		0			0
$873$	−1.71413	+	2.96896i	−0.0580145	+	0.100484i
$874$		0			0
$875$	−25.0687	+	16.8139i	−0.847476	+	0.568414i
$876$		0			0
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	−0.996474	−	0.0839011i	$-0.973262\pi$
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	0.570898	+	0.821021i	$0.306595\pi$
$878$		0			0
$879$	−11.1587	−	19.3275i	−0.376374	−	0.651899i
$880$		0			0
$881$	−18.6082			−0.626925			−0.313463	−	0.949601i	$-0.601489\pi$
$881$	−18.6082			−0.626925			−0.313463	+	0.949601i	$0.601489\pi$
$882$		0			0
$883$	11.2552			0.378768			0.189384	−	0.981903i	$-0.439351\pi$
$883$	11.2552			0.378768			0.189384	+	0.981903i	$0.439351\pi$
$884$		0			0
$885$	−1.54332	−	2.67311i	−0.0518781	−	0.0898556i
$886$		0			0
$887$	−19.6056	+	33.9579i	−0.658292	+	1.14020i	0.322765	+	0.946479i	$0.395388\pi$
$887$	−19.6056	+	33.9579i	−0.658292	+	1.14020i	−0.981057	+	0.193717i	$0.937946\pi$
$888$		0			0
$889$	−19.3123	+	12.9530i	−0.647712	+	0.434429i
$890$		0			0
$891$	2.11159	−	3.65738i	0.0707408	−	0.122527i
$892$		0			0
$893$	−0.884638	−	1.53224i	−0.0296033	−	0.0512744i
$894$		0			0
$895$	−31.5249			−1.05376
$896$		0			0
$897$	−0.879996			−0.0293822
$898$		0			0
$899$	−1.59536	−	2.76325i	−0.0532083	−	0.0921595i
$900$		0			0
$901$	12.9322	−	22.3992i	0.430834	−	0.746226i
$902$		0			0
$903$	2.83879	+	1.39377i	0.0944692	+	0.0463816i
$904$		0			0
$905$	−19.7954	+	34.2866i	−0.658020	+	1.13972i
$906$		0			0
$907$	10.7985	+	18.7035i	0.358558	+	0.621040i	0.987720	−	0.156234i	$-0.0499353\pi$
$907$	10.7985	+	18.7035i	0.358558	+	0.621040i	−0.629162	+	0.777274i	$0.716602\pi$
$908$		0			0
$909$	13.3607			0.443147
$910$		0			0
$911$	32.4434			1.07490			0.537449	−	0.843297i	$-0.319388\pi$
$911$	32.4434			1.07490			0.537449	+	0.843297i	$0.319388\pi$
$912$		0			0
$913$	−3.49328	−	6.05054i	−0.115611	−	0.200244i
$914$		0			0
$915$	18.4049	−	31.8782i	0.608447	−	1.05386i
$916$		0			0
$917$	1.86802	+	27.7559i	0.0616873	+	0.916580i
$918$		0			0
$919$	17.8686	−	30.9493i	0.589430	−	1.02092i	−0.404877	−	0.914371i	$-0.632686\pi$
$919$	17.8686	−	30.9493i	0.589430	−	1.02092i	0.994307	−	0.106552i	$-0.0339811\pi$
$920$		0			0
$921$	−4.75142	−	8.22971i	−0.156565	−	0.271178i
$922$		0			0
$923$	6.60274			0.217332
$924$		0			0
$925$	2.35636			0.0774765
$926$		0			0
$927$	−12.0102	−	20.8022i	−0.394466	−	0.683235i
$928$		0			0
$929$	−5.88847	+	10.1991i	−0.193194	+	0.334622i	−0.946307	−	0.323269i	$-0.895218\pi$
$929$	−5.88847	+	10.1991i	−0.193194	+	0.334622i	0.753113	+	0.657891i	$0.228551\pi$
$930$		0			0
$931$	−3.24012	−	4.19214i	−0.106191	−	0.137392i
$932$		0			0
$933$	14.2116	−	24.6151i	0.465265	−	0.805863i
$934$		0			0
$935$	6.06506	+	10.5050i	0.198349	+	0.343550i
$936$		0			0
$937$	18.9937			0.620497			0.310248	−	0.950655i	$-0.399588\pi$
$937$	18.9937			0.620497			0.310248	+	0.950655i	$0.399588\pi$
$938$		0			0
$939$	2.66660			0.0870213
$940$		0			0
$941$	−3.40932	−	5.90511i	−0.111141	−	0.192501i	0.805090	−	0.593153i	$-0.202117\pi$
$941$	−3.40932	−	5.90511i	−0.111141	−	0.192501i	−0.916230	+	0.400652i	$0.868784\pi$
$942$		0			0
$943$	2.39225	−	4.14349i	0.0779023	−	0.134931i
$944$		0			0
$945$	−2.19065	−	32.5498i	−0.0712620	−	1.05884i
$946$		0			0
$947$	0.529958	−	0.917914i	0.0172213	−	0.0298282i	−0.857286	−	0.514840i	$-0.827851\pi$
$947$	0.529958	−	0.917914i	0.0172213	−	0.0298282i	0.874508	+	0.485012i	$0.161185\pi$
$948$		0			0
$949$	4.14174	+	7.17370i	0.134446	+	0.232868i
$950$		0			0
$951$	−24.2973			−0.787895
$952$		0			0
$953$	−40.4127			−1.30910			−0.654548	−	0.756020i	$-0.727141\pi$
$953$	−40.4127			−1.30910			−0.654548	+	0.756020i	$0.727141\pi$
$954$		0			0
$955$	6.05993	+	10.4961i	0.196095	+	0.339646i
$956$		0			0
$957$	2.19032	−	3.79375i	0.0708031	−	0.122635i
$958$		0			0
$959$	−20.7372	−	10.1814i	−0.669639	−	0.328774i
$960$		0			0
$961$	14.9717	−	25.9317i	0.482958	−	0.836508i
$962$		0			0
$963$	−5.37498	−	9.30975i	−0.173206	−	0.300002i
$964$		0			0
$965$	−19.1177			−0.615422
$966$		0			0
$967$	36.2949			1.16717			0.583583	−	0.812053i	$-0.301650\pi$
$967$	36.2949			1.16717			0.583583	+	0.812053i	$0.301650\pi$
$968$		0			0
$969$	−2.69618	−	4.66993i	−0.0866139	−	0.150020i
$970$		0			0
$971$	−10.7218	+	18.5708i	−0.344080	+	0.595964i	−0.985186	−	0.171488i	$-0.945142\pi$
$971$	−10.7218	+	18.5708i	−0.344080	+	0.595964i	0.641106	+	0.767452i	$0.278476\pi$
$972$		0			0
$973$	8.78914	−	5.89500i	0.281767	−	0.188985i
$974$		0			0
$975$	0.145624	−	0.252229i	0.00466371	−	0.00807778i
$976$		0			0
$977$	19.9138	+	34.4918i	0.637100	+	1.10349i	0.986066	+	0.166354i	$0.0531994\pi$
$977$	19.9138	+	34.4918i	0.637100	+	1.10349i	−0.348966	+	0.937135i	$0.613467\pi$
$978$		0			0
$979$	−6.04551			−0.193215
$980$		0			0
$981$	−17.9278			−0.572392
$982$		0			0
$983$	7.94071	+	13.7537i	0.253269	+	0.438675i	0.964424	−	0.264360i	$-0.0851608\pi$
$983$	7.94071	+	13.7537i	0.253269	+	0.438675i	−0.711155	+	0.703036i	$0.751827\pi$
$984$		0			0
$985$	5.98052	−	10.3586i	0.190555	−	0.330051i
$986$		0			0
$987$	−6.91543	+	4.63827i	−0.220120	+	0.147638i
$988$		0			0
$989$	−0.290116	+	0.502496i	−0.00922516	+	0.0159785i
$990$		0			0
$991$	−8.83435	−	15.3016i	−0.280633	−	0.486070i	0.690908	−	0.722943i	$-0.257211\pi$
$991$	−8.83435	−	15.3016i	−0.280633	−	0.486070i	−0.971541	+	0.236873i	$0.923878\pi$
$992$		0			0
$993$	19.7570			0.626970
$994$		0			0
$995$	−42.7301			−1.35464
$996$		0			0
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	0.992931	−	0.118692i	$-0.0378701\pi$
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	−0.599256	+	0.800558i	$0.704537\pi$
$998$		0			0
$999$	−30.7062	+	53.1847i	−0.971500	+	1.68269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.p.625.2		10
4.3	odd	2		91.2.e.c.79.1	yes	10
7.4	even	3	inner	1456.2.r.p.417.2		10
12.11	even	2		819.2.j.h.352.5		10
28.3	even	6		637.2.e.m.508.1		10
28.11	odd	6		91.2.e.c.53.1	✓	10
28.19	even	6		637.2.a.k.1.5		5
28.23	odd	6		637.2.a.l.1.5		5
28.27	even	2		637.2.e.m.79.1		10
52.51	odd	2		1183.2.e.f.170.5		10
84.11	even	6		819.2.j.h.235.5		10
84.23	even	6		5733.2.a.bl.1.1		5
84.47	odd	6		5733.2.a.bm.1.1		5
364.51	odd	6		8281.2.a.bw.1.1		5
364.103	even	6		8281.2.a.bx.1.1		5
364.207	odd	6		1183.2.e.f.508.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	28.11	odd	6
91.2.e.c.79.1	yes	10	4.3	odd	2
637.2.a.k.1.5		5	28.19	even	6
637.2.a.l.1.5		5	28.23	odd	6
637.2.e.m.79.1		10	28.27	even	2
637.2.e.m.508.1		10	28.3	even	6
819.2.j.h.235.5		10	84.11	even	6
819.2.j.h.352.5		10	12.11	even	2
1183.2.e.f.170.5		10	52.51	odd	2
1183.2.e.f.508.5		10	364.207	odd	6
1456.2.r.p.417.2		10	7.4	even	3	inner
1456.2.r.p.625.2		10	1.1	even	1	trivial
5733.2.a.bl.1.1		5	84.23	even	6
5733.2.a.bm.1.1		5	84.47	odd	6
8281.2.a.bw.1.1		5	364.51	odd	6
8281.2.a.bx.1.1		5	364.103	even	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.673208 - 1.16603i) q^{3} +(-1.09358 + 1.89414i) q^{5} +(2.19729 - 1.47375i) q^{7} +(0.593582 - 1.02811i) q^{9} +(-0.524077 - 0.907729i) q^{11} +1.00000 q^{13} +2.94483 q^{15} +(2.64562 + 4.58236i) q^{17} +(0.378453 - 0.655500i) q^{19} +(-3.19767 - 1.56996i) q^{21} +(0.326792 - 0.566020i) q^{23} +(0.108157 + 0.187333i) q^{25} -5.63766 q^{27} -3.10408 q^{29} +(0.513956 + 0.890198i) q^{31} +(-0.705626 + 1.22218i) q^{33} +(0.388575 + 5.77363i) q^{35} +(5.44661 - 9.43381i) q^{37} +(-0.673208 - 1.16603i) q^{39} +7.32040 q^{41} -0.887771 q^{43} +(1.29826 + 2.24865i) q^{45} +(1.16875 - 2.02434i) q^{47} +(2.65613 - 6.47650i) q^{49} +(3.56211 - 6.16976i) q^{51} +(-2.44407 - 4.23325i) q^{53} +2.29249 q^{55} -1.01911 q^{57} +(-0.524077 - 0.907729i) q^{59} +(6.24989 - 10.8251i) q^{61} +(-0.210913 - 3.13385i) q^{63} +(-1.09358 + 1.89414i) q^{65} +(2.23944 + 3.87883i) q^{67} -0.879996 q^{69} +6.60274 q^{71} +(4.14174 + 7.17370i) q^{73} +(0.145624 - 0.252229i) q^{75} +(-2.48931 - 1.22218i) q^{77} +(1.07007 - 1.85342i) q^{79} +(2.01457 + 3.48935i) q^{81} +6.66558 q^{83} -11.5728 q^{85} +(2.08969 + 3.61946i) q^{87} +(2.88388 - 4.99503i) q^{89} +(2.19729 - 1.47375i) q^{91} +(0.691998 - 1.19858i) q^{93} +(0.827739 + 1.43369i) q^{95} -2.88777 q^{97} -1.24433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

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Database

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