LMFDB - Embedded newform 560.2.ci.c.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.4
Root			$0.587308 - 2.01725i$ of defining polynomial
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.c.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.80762 - 0.752300i) q^{3} +(-2.21323 + 0.318742i) q^{5} +(-0.559876 - 2.58583i) q^{7} +(4.71872 - 2.72435i) q^{9} +O(q^{10})$	\(q+(2.80762 - 0.752300i) q^{3} +(-2.21323 + 0.318742i) q^{5} +(-0.559876 - 2.58583i) q^{7} +(4.71872 - 2.72435i) q^{9} +(1.83557 - 3.17930i) q^{11} +(0.830578 + 0.830578i) q^{13} +(-5.97414 + 2.55992i) q^{15} +(-0.204036 - 0.761471i) q^{17} +(-1.09461 - 1.89593i) q^{19} +(-3.51725 - 6.83885i) q^{21} +(4.54529 + 1.21791i) q^{23} +(4.79681 - 1.41090i) q^{25} +(5.03288 - 5.03288i) q^{27} +2.62236i q^{29} +(-0.0359651 - 0.0207644i) q^{31} +(2.76180 - 10.3072i) q^{33} +(2.06335 + 5.54460i) q^{35} +(0.0664979 - 0.248174i) q^{37} +(2.95680 + 1.70711i) q^{39} +8.98026i q^{41} +(0.474569 - 0.474569i) q^{43} +(-9.57526 + 7.53368i) q^{45} +(-6.18205 - 1.65648i) q^{47} +(-6.37308 + 2.89549i) q^{49} +(-1.14571 - 1.98443i) q^{51} +(2.04824 + 7.64413i) q^{53} +(-3.04917 + 7.62161i) q^{55} +(-4.49957 - 4.49957i) q^{57} +(-5.35616 + 9.27713i) q^{59} +(1.72539 - 0.996157i) q^{61} +(-9.68662 - 10.6765i) q^{63} +(-2.10300 - 1.57352i) q^{65} +(-6.39671 + 1.71399i) q^{67} +13.6777 q^{69} -8.11777 q^{71} +(9.52910 - 2.55331i) q^{73} +(12.4062 - 7.56992i) q^{75} +(-9.24884 - 2.96647i) q^{77} +(11.6145 - 6.70563i) q^{79} +(2.17114 - 3.76053i) q^{81} +(9.73033 + 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(1.97280 + 7.36260i) q^{87} +(0.715130 + 1.23864i) q^{89} +(1.68272 - 2.61276i) q^{91} +(-0.116597 - 0.0312422i) q^{93} +(3.02695 + 3.84723i) q^{95} +(-3.16693 + 3.16693i) q^{97} -20.0030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.80762	−	0.752300i	1.62098	−	0.434341i	0.669692	−	0.742639i	$-0.266426\pi$
$3$	2.80762	−	0.752300i	1.62098	−	0.434341i	0.951290	+	0.308298i	$0.0997593\pi$
$4$		0			0
$5$	−2.21323	+	0.318742i	−0.989788	+	0.142546i
$5$	−2.21323	+	0.318742i	−0.989788	+	0.142546i
$6$		0			0
$7$	−0.559876	−	2.58583i	−0.211613	−	0.977353i
$7$	−0.559876	−	2.58583i	−0.211613	−	0.977353i
$8$		0			0
$9$	4.71872	−	2.72435i	1.57291	−	0.908118i
$10$		0			0
$11$	1.83557	−	3.17930i	0.553445	−	0.958596i	−0.444577	−	0.895741i	$-0.646646\pi$
$11$	1.83557	−	3.17930i	0.553445	−	0.958596i	0.998023	−	0.0628551i	$-0.0200206\pi$
$12$		0			0
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	0.812843	−	0.582482i	$-0.197918\pi$
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	−0.582482	+	0.812843i	$0.697918\pi$
$14$		0			0
$15$	−5.97414	+	2.55992i	−1.54252	+	0.660970i
$16$		0			0
$17$	−0.204036	−	0.761471i	−0.0494859	−	0.184684i	0.936759	−	0.349976i	$-0.113810\pi$
$17$	−0.204036	−	0.761471i	−0.0494859	−	0.184684i	−0.986245	+	0.165292i	$0.947143\pi$
$18$		0			0
$19$	−1.09461	−	1.89593i	−0.251122	−	0.434955i	0.712713	−	0.701455i	$-0.247466\pi$
$19$	−1.09461	−	1.89593i	−0.251122	−	0.434955i	−0.963835	+	0.266500i	$0.914133\pi$
$20$		0			0
$21$	−3.51725	−	6.83885i	−0.767526	−	1.49236i
$22$		0			0
$23$	4.54529	+	1.21791i	0.947759	+	0.253951i	0.699411	−	0.714719i	$-0.253446\pi$
$23$	4.54529	+	1.21791i	0.947759	+	0.253951i	0.248348	+	0.968671i	$0.420112\pi$
$24$		0			0
$25$	4.79681	−	1.41090i	0.959361	−	0.282180i
$26$		0			0
$27$	5.03288	−	5.03288i	0.968579	−	0.968579i
$28$		0			0
$29$			2.62236i			0.486960i	0.969906	+	0.243480i	$0.0782891\pi$
$29$			2.62236i			0.486960i	−0.969906	+	0.243480i	$0.921711\pi$
$30$		0			0
$31$	−0.0359651	−	0.0207644i	−0.00645952	−	0.00372940i	0.496767	−	0.867884i	$-0.334520\pi$
$31$	−0.0359651	−	0.0207644i	−0.00645952	−	0.00372940i	−0.503226	+	0.864155i	$0.667854\pi$
$32$		0			0
$33$	2.76180	−	10.3072i	0.480768	−	1.79425i
$34$		0			0
$35$	2.06335	+	5.54460i	0.348770	+	0.937208i
$36$		0			0
$37$	0.0664979	−	0.248174i	0.0109322	−	0.0407995i	−0.960244	−	0.279161i	$-0.909944\pi$
$37$	0.0664979	−	0.248174i	0.0109322	−	0.0407995i	0.971176	+	0.238362i	$0.0766103\pi$
$38$		0			0
$39$	2.95680	+	1.70711i	0.473466	+	0.273356i
$40$		0			0
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$		0			0
$43$	0.474569	−	0.474569i	0.0723711	−	0.0723711i	−0.669995	−	0.742366i	$-0.733704\pi$
$43$	0.474569	−	0.474569i	0.0723711	−	0.0723711i	0.742366	+	0.669995i	$0.233704\pi$
$44$		0			0
$45$	−9.57526	+	7.53368i	−1.42740	+	1.12306i
$46$		0			0
$47$	−6.18205	−	1.65648i	−0.901745	−	0.241622i	−0.221980	−	0.975051i	$-0.571252\pi$
$47$	−6.18205	−	1.65648i	−0.901745	−	0.241622i	−0.679766	+	0.733429i	$0.737919\pi$
$48$		0			0
$49$	−6.37308	+	2.89549i	−0.910440	+	0.413642i
$50$		0			0
$51$	−1.14571	−	1.98443i	−0.160432	−	0.277876i
$52$		0			0
$53$	2.04824	+	7.64413i	0.281347	+	1.05000i	0.951468	+	0.307749i	$0.0995758\pi$
$53$	2.04824	+	7.64413i	0.281347	+	1.05000i	−0.670120	+	0.742252i	$0.733758\pi$
$54$		0			0
$55$	−3.04917	+	7.62161i	−0.411150	+	1.02770i
$56$		0			0
$57$	−4.49957	−	4.49957i	−0.595982	−	0.595982i
$58$		0			0
$59$	−5.35616	+	9.27713i	−0.697312	+	1.20778i	0.272083	+	0.962274i	$0.412287\pi$
$59$	−5.35616	+	9.27713i	−0.697312	+	1.20778i	−0.969395	+	0.245506i	$0.921046\pi$
$60$		0			0
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	−0.385459	−	0.922725i	$-0.625957\pi$
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	0.606373	+	0.795180i	$0.292624\pi$
$62$		0			0
$63$	−9.68662	−	10.6765i	−1.22040	−	1.34512i
$64$		0			0
$65$	−2.10300	−	1.57352i	−0.260846	−	0.195172i
$66$		0			0
$67$	−6.39671	+	1.71399i	−0.781482	+	0.209398i	−0.627438	−	0.778666i	$-0.715897\pi$
$67$	−6.39671	+	1.71399i	−0.781482	+	0.209398i	−0.154044	+	0.988064i	$0.549230\pi$
$68$		0			0
$69$	13.6777			1.64660
$70$		0			0
$71$	−8.11777			−0.963402			−0.481701	−	0.876336i	$-0.659981\pi$
$71$	−8.11777			−0.963402			−0.481701	+	0.876336i	$0.659981\pi$
$72$		0			0
$73$	9.52910	−	2.55331i	1.11530	−	0.298843i	0.346318	−	0.938117i	$-0.387432\pi$
$73$	9.52910	−	2.55331i	1.11530	−	0.298843i	0.768979	+	0.639274i	$0.220765\pi$
$74$		0			0
$75$	12.4062	−	7.56992i	1.43255	−	0.874099i
$76$		0			0
$77$	−9.24884	−	2.96647i	−1.05400	−	0.338060i
$78$		0			0
$79$	11.6145	−	6.70563i	1.30673	−	0.754443i	0.325184	−	0.945651i	$-0.394574\pi$
$79$	11.6145	−	6.70563i	1.30673	−	0.754443i	0.981550	+	0.191208i	$0.0612405\pi$
$80$		0			0
$81$	2.17114	−	3.76053i	0.241238	−	0.417836i
$82$		0			0
$83$	9.73033	+	9.73033i	1.06804	+	1.06804i	0.997509	+	0.0705331i	$0.0224700\pi$
$83$	9.73033	+	9.73033i	1.06804	+	1.06804i	0.0705331	+	0.997509i	$0.477530\pi$
$84$		0			0
$85$	0.694291	+	1.62028i	0.0753065	+	0.175744i
$86$		0			0
$87$	1.97280	+	7.36260i	0.211507	+	0.789354i
$88$		0			0
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	0.901435	−	0.432914i	$-0.142514\pi$
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	−0.825632	+	0.564209i	$0.809181\pi$
$90$		0			0
$91$	1.68272	−	2.61276i	0.176397	−	0.273892i
$92$		0			0
$93$	−0.116597	−	0.0312422i	−0.0120906	−	0.00323967i
$94$		0			0
$95$	3.02695	+	3.84723i	0.310558	+	0.394717i
$96$		0			0
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	−0.849363	−	0.527810i	$-0.823013\pi$
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	0.527810	+	0.849363i	$0.323013\pi$
$98$		0			0
$99$		−	20.0030i		−	2.01037i
$100$		0			0
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	0.496899	−	0.867809i	$-0.334472\pi$
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	−0.503095	+	0.864231i	$0.667805\pi$
$102$		0			0
$103$	4.29116	−	16.0148i	0.422820	−	1.57799i	−0.345817	−	0.938302i	$-0.612398\pi$
$103$	4.29116	−	16.0148i	0.422820	−	1.57799i	0.768638	−	0.639685i	$-0.220935\pi$
$104$		0			0
$105$	9.96432	+	14.0149i	0.972418	+	1.36771i
$106$		0			0
$107$	−1.18265	+	4.41372i	−0.114331	+	0.426690i	−0.999236	−	0.0390819i	$-0.987557\pi$
$107$	−1.18265	+	4.41372i	−0.114331	+	0.426690i	0.884905	+	0.465772i	$0.154223\pi$
$108$		0			0
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.999998	−	0.00186842i	$-0.999405\pi$
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.501617	−	0.865090i	$-0.667261\pi$
$110$		0			0
$111$		−	0.746804i		−	0.0708835i
$112$		0			0
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	−0.631955	−	0.775005i	$-0.717747\pi$
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	0.775005	+	0.631955i	$0.217747\pi$
$114$		0			0
$115$	−10.4480	−	1.24674i	−0.974281	−	0.116259i
$116$		0			0
$117$	6.18205	+	1.65648i	0.571531	+	0.153141i
$118$		0			0
$119$	−1.85480	+	0.953932i	−0.170030	+	0.0874468i
$120$		0			0
$121$	−1.23864	−	2.14539i	−0.112604	−	0.195035i
$122$		0			0
$123$	6.75585	+	25.2132i	0.609155	+	2.27340i
$124$		0			0
$125$	−10.1667	+	4.65160i	−0.909341	+	0.416051i
$126$		0			0
$127$	13.2527	+	13.2527i	1.17599	+	1.17599i	0.980757	+	0.195234i	$0.0625467\pi$
$127$	13.2527	+	13.2527i	1.17599	+	1.17599i	0.195234	+	0.980757i	$0.437453\pi$
$128$		0			0
$129$	0.975392	−	1.68943i	0.0858785	−	0.148746i
$130$		0			0
$131$	−12.2929	+	7.09731i	−1.07404	+	0.620095i	−0.929281	−	0.369372i	$-0.879573\pi$
$131$	−12.2929	+	7.09731i	−1.07404	+	0.620095i	−0.144755	+	0.989468i	$0.546239\pi$
$132$		0			0
$133$	−4.28970	+	3.89197i	−0.371964	+	0.337477i
$134$		0			0
$135$	−9.53476	+	12.7431i	−0.820621	+	1.09675i
$136$		0			0
$137$	18.3201	−	4.90887i	1.56519	−	0.419393i	0.630891	−	0.775871i	$-0.282689\pi$
$137$	18.3201	−	4.90887i	1.56519	−	0.419393i	0.934303	+	0.356479i	$0.116023\pi$
$138$		0			0
$139$	−8.23706			−0.698658			−0.349329	−	0.937000i	$-0.613591\pi$
$139$	−8.23706			−0.698658			−0.349329	+	0.937000i	$0.613591\pi$
$140$		0			0
$141$	−18.6030			−1.56666
$142$		0			0
$143$	4.16524	−	1.11607i	0.348315	−	0.0933308i
$144$		0			0
$145$	−0.835856	−	5.80390i	−0.0694141	−	0.481988i
$146$		0			0
$147$	−15.7149	+	12.9239i	−1.29614	+	1.06595i
$148$		0			0
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	−0.318309	−	0.947987i	$-0.603115\pi$
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	0.661826	+	0.749657i	$0.269782\pi$
$150$		0			0
$151$	5.02292	−	8.69995i	0.408759	−	0.707992i	−0.585992	−	0.810317i	$-0.699295\pi$
$151$	5.02292	−	8.69995i	0.408759	−	0.707992i	0.994751	+	0.102325i	$0.0326282\pi$
$152$		0			0
$153$	−3.03730	−	3.03730i	−0.245551	−	0.245551i
$154$		0			0
$155$	0.0862176	+	0.0344930i	0.00692516	+	0.00277054i
$156$		0			0
$157$	6.33762	+	23.6523i	0.505797	+	1.88766i	0.458320	+	0.888788i	$0.348452\pi$
$157$	6.33762	+	23.6523i	0.505797	+	1.88766i	0.0474774	+	0.998872i	$0.484882\pi$
$158$		0			0
$159$	11.5014	+	19.9209i	0.912117	+	1.57983i
$160$		0			0
$161$	0.604505	−	12.4353i	0.0476417	−	0.980035i
$162$		0			0
$163$	−21.2171	−	5.68510i	−1.66185	−	0.445291i	−0.698954	−	0.715166i	$-0.746351\pi$
$163$	−21.2171	−	5.68510i	−1.66185	−	0.445291i	−0.962895	+	0.269875i	$0.913018\pi$
$164$		0			0
$165$	−2.82718	+	23.6925i	−0.220096	+	1.84446i
$166$		0			0
$167$	3.14616	−	3.14616i	0.243457	−	0.243457i	−0.574821	−	0.818279i	$-0.694928\pi$
$167$	3.14616	−	3.14616i	0.243457	−	0.243457i	0.818279	+	0.574821i	$0.194928\pi$
$168$		0			0
$169$		−	11.6203i		−	0.893868i
$170$		0			0
$171$	−10.3303	−	5.96423i	−0.789981	−	0.456096i
$172$		0			0
$173$	−1.35273	+	5.04844i	−0.102846	+	0.383826i	−0.998092	−	0.0617463i	$-0.980333\pi$
$173$	−1.35273	+	5.04844i	−0.102846	+	0.383826i	0.895246	+	0.445572i	$0.147000\pi$
$174$		0			0
$175$	−6.33397	−	11.6138i	−0.478803	−	0.877922i
$176$		0			0
$177$	−8.05888	+	30.0761i	−0.605742	+	2.26066i
$178$		0			0
$179$	−10.8847	−	6.28428i	−0.813560	−	0.469709i	0.0346308	−	0.999400i	$-0.488974\pi$
$179$	−10.8847	−	6.28428i	−0.813560	−	0.469709i	−0.848191	+	0.529691i	$0.822308\pi$
$180$		0			0
$181$		−	11.6742i		−	0.867740i	−0.900976	−	0.433870i	$-0.857148\pi$
$181$		−	11.6742i		−	0.867740i	0.900976	−	0.433870i	$-0.142852\pi$
$182$		0			0
$183$	4.09485	−	4.09485i	0.302700	−	0.302700i
$184$		0			0
$185$	−0.0680721	+	0.570462i	−0.00500476	+	0.0419412i
$186$		0			0
$187$	−2.79547	−	0.749044i	−0.204425	−	0.0547755i
$188$		0			0
$189$	−15.8320	−	10.1964i	−1.15161	−	0.741680i
$190$		0			0
$191$	7.75170	+	13.4263i	0.560894	+	0.971496i	0.997419	+	0.0718040i	$0.0228756\pi$
$191$	7.75170	+	13.4263i	0.560894	+	0.971496i	−0.436525	+	0.899692i	$0.643791\pi$
$192$		0			0
$193$	2.32883	+	8.69132i	0.167633	+	0.625615i	0.997690	+	0.0679359i	$0.0216413\pi$
$193$	2.32883	+	8.69132i	0.167633	+	0.625615i	−0.830057	+	0.557679i	$0.811692\pi$
$194$		0			0
$195$	−7.08821	−	2.83577i	−0.507597	−	0.203074i
$196$		0			0
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	0.992347	−	0.123482i	$-0.0394061\pi$
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	−0.123482	+	0.992347i	$0.539406\pi$
$198$		0			0
$199$	−4.36557	+	7.56140i	−0.309467	+	0.536013i	−0.978246	−	0.207448i	$-0.933484\pi$
$199$	−4.36557	+	7.56140i	−0.309467	+	0.536013i	0.668779	+	0.743462i	$0.266817\pi$
$200$		0			0
$201$	−16.6701	+	9.62450i	−1.17582	+	0.678860i
$202$		0			0
$203$	6.78099	−	1.46820i	0.475932	−	0.103047i
$204$		0			0
$205$	−2.86239	−	19.8754i	−0.199918	−	1.38816i
$206$		0			0
$207$	24.7660	−	6.63602i	1.72135	−	0.461235i
$208$		0			0
$209$	−8.03696			−0.555928
$210$		0			0
$211$	11.1745			0.769288			0.384644	−	0.923065i	$-0.374324\pi$
$211$	11.1745			0.769288			0.384644	+	0.923065i	$0.374324\pi$
$212$		0			0
$213$	−22.7916	+	6.10700i	−1.56166	+	0.418445i
$214$		0			0
$215$	−0.899067	+	1.20160i	−0.0613158	+	0.0819482i
$216$		0			0
$217$	−0.0335574	+	0.104625i	−0.00227803	+	0.00710242i
$218$		0			0
$219$	24.8333	−	14.3375i	1.67808	−	0.968838i
$220$		0			0
$221$	0.462994	−	0.801929i	0.0311443	−	0.0539436i
$222$		0			0
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	0.681660	−	0.731669i	$-0.261258\pi$
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	−0.731669	+	0.681660i	$0.761258\pi$
$224$		0			0
$225$	18.7910	−	19.7258i	1.25273	−	1.31506i
$226$		0			0
$227$	0.807609	+	3.01404i	0.0536029	+	0.200049i	0.987534	−	0.157403i	$-0.0503122\pi$
$227$	0.807609	+	3.01404i	0.0536029	+	0.200049i	−0.933932	+	0.357452i	$0.883646\pi$
$228$		0			0
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	0.970954	−	0.239268i	$-0.0769075\pi$
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	−0.692689	+	0.721236i	$0.743574\pi$
$230$		0			0
$231$	−28.1989	−	1.37081i	−1.85535	−	0.0901928i
$232$		0			0
$233$	22.0201	+	5.90027i	1.44259	+	0.386540i	0.893439	−	0.449186i	$-0.148286\pi$
$233$	22.0201	+	5.90027i	1.44259	+	0.386540i	0.549148	+	0.835725i	$0.314952\pi$
$234$		0			0
$235$	14.2103	+	1.69569i	0.926979	+	0.110615i
$236$		0			0
$237$	27.5645	−	27.5645i	1.79051	−	1.79051i
$238$		0			0
$239$		−	23.9971i		−	1.55224i	−0.630585	−	0.776120i	$-0.717185\pi$
$239$		−	23.9971i		−	1.55224i	0.630585	−	0.776120i	$-0.282815\pi$
$240$		0			0
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.390295	−	0.920690i	$-0.627627\pi$
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.992488	+	0.122340i	$0.960960\pi$
$242$		0			0
$243$	−2.25979	+	8.43364i	−0.144965	+	0.541018i
$244$		0			0
$245$	13.1822	−	8.43977i	0.842179	−	0.539197i
$246$		0			0
$247$	0.665553	−	2.48388i	0.0423481	−	0.158045i
$248$		0			0
$249$	34.6392	+	19.9990i	2.19517	+	1.26738i
$250$		0			0
$251$		−	11.1158i		−	0.701623i	−0.936446	−	0.350811i	$-0.885906\pi$
$251$		−	11.1158i		−	0.701623i	0.936446	−	0.350811i	$-0.114094\pi$
$252$		0			0
$253$	12.2153	−	12.2153i	0.767970	−	0.767970i
$254$		0			0
$255$	3.16825	+	4.02682i	0.198403	+	0.252169i
$256$		0			0
$257$	−24.4314	−	6.54637i	−1.52399	−	0.408351i	−0.602935	−	0.797790i	$-0.706002\pi$
$257$	−24.4314	−	6.54637i	−1.52399	−	0.408351i	−0.921052	+	0.389439i	$0.872669\pi$
$258$		0			0
$259$	−0.678966	−	0.0330060i	−0.0421889	−	0.00205090i
$260$		0			0
$261$	7.14424	+	12.3742i	0.442217	+	0.765943i
$262$		0			0
$263$	−2.93659	−	10.9595i	−0.181078	−	0.675792i	−0.995436	−	0.0954297i	$-0.969577\pi$
$263$	−2.93659	−	10.9595i	−0.181078	−	0.675792i	0.814358	−	0.580363i	$-0.197089\pi$
$264$		0			0
$265$	−6.96973	−	16.2654i	−0.428147	−	0.999174i
$266$		0			0
$267$	2.93964	+	2.93964i	0.179903	+	0.179903i
$268$		0			0
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	−0.962391	−	0.271668i	$-0.912425\pi$
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	0.716467	+	0.697621i	$0.245758\pi$
$270$		0			0
$271$	−7.27419	+	4.19976i	−0.441876	+	0.255117i	−0.704393	−	0.709810i	$-0.748781\pi$
$271$	−7.27419	+	4.19976i	−0.441876	+	0.255117i	0.262517	+	0.964927i	$0.415447\pi$
$272$		0			0
$273$	2.75885	−	8.60155i	0.166974	−	0.520590i
$274$		0			0
$275$	4.31920	−	17.8403i	0.260458	−	1.07581i
$276$		0			0
$277$	−5.48646	+	1.47009i	−0.329650	+	0.0883293i	−0.419848	−	0.907594i	$-0.637917\pi$
$277$	−5.48646	+	1.47009i	−0.329650	+	0.0883293i	0.0901983	+	0.995924i	$0.471250\pi$
$278$		0			0
$279$	−0.226279			−0.0135470
$280$		0			0
$281$	7.27627			0.434066			0.217033	−	0.976164i	$-0.430362\pi$
$281$	7.27627			0.434066			0.217033	+	0.976164i	$0.430362\pi$
$282$		0			0
$283$	7.44729	−	1.99550i	0.442696	−	0.118620i	−0.0305840	−	0.999532i	$-0.509737\pi$
$283$	7.44729	−	1.99550i	0.442696	−	0.118620i	0.473280	+	0.880912i	$0.343070\pi$
$284$		0			0
$285$	11.3928	+	8.52440i	0.674851	+	0.504942i
$286$		0			0
$287$	23.2215	−	5.02784i	1.37072	−	0.296784i
$288$		0			0
$289$	14.1842	−	8.18927i	0.834366	−	0.481721i
$290$		0			0
$291$	−6.50906	+	11.2740i	−0.381568	+	0.660895i
$292$		0			0
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	0.798207	−	0.602383i	$-0.205782\pi$
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	−0.602383	+	0.798207i	$0.705782\pi$
$294$		0			0
$295$	8.89741	−	22.2397i	0.518027	−	1.29485i
$296$		0			0
$297$	−6.76284	−	25.2393i	−0.392420	−	1.46453i
$298$		0			0
$299$	2.76365	+	4.78679i	0.159826	+	0.276827i
$300$		0			0
$301$	−1.49286	−	0.961456i	−0.0860468	−	0.0554174i
$302$		0			0
$303$	−0.201888	−	0.0540958i	−0.0115982	−	0.00310772i
$304$		0			0
$305$	−3.50118	+	2.75468i	−0.200477	+	0.157733i
$306$		0			0
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	−0.676048	−	0.736857i	$-0.736309\pi$
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	0.736857	+	0.676048i	$0.236309\pi$
$308$		0			0
$309$		−	48.1918i		−	2.74154i
$310$		0			0
$311$	−11.9584	−	6.90417i	−0.678097	−	0.391500i	0.121040	−	0.992648i	$-0.461377\pi$
$311$	−11.9584	−	6.90417i	−0.678097	−	0.391500i	−0.799138	+	0.601148i	$0.794710\pi$
$312$		0			0
$313$	6.04266	−	22.5515i	0.341551	−	1.27469i	−0.555038	−	0.831825i	$-0.687296\pi$
$313$	6.04266	−	22.5515i	0.341551	−	1.27469i	0.896590	−	0.442863i	$-0.146037\pi$
$314$		0			0
$315$	24.8418	+	20.5421i	1.39968	+	1.15742i
$316$		0			0
$317$	3.41352	−	12.7394i	0.191722	−	0.715518i	−0.801369	−	0.598171i	$-0.795894\pi$
$317$	3.41352	−	12.7394i	0.191722	−	0.715518i	0.993091	−	0.117347i	$-0.0374390\pi$
$318$		0			0
$319$	8.33728	+	4.81353i	0.466798	+	0.269506i
$320$		0			0
$321$			13.2818i			0.741316i
$322$		0			0
$323$	−1.22035	+	1.22035i	−0.0679023	+	0.0679023i
$324$		0			0
$325$	5.15599	+	2.81226i	0.286003	+	0.155996i
$326$		0			0
$327$	−50.8253	−	13.6186i	−2.81065	−	0.753111i
$328$		0			0
$329$	−0.822187	+	16.9132i	−0.0453286	+	0.932454i
$330$		0			0
$331$	−9.54799	−	16.5376i	−0.524805	−	0.908989i	−0.999583	−	0.0288830i	$-0.990805\pi$
$331$	−9.54799	−	16.5376i	−0.524805	−	0.908989i	0.474778	−	0.880106i	$-0.342528\pi$
$332$		0			0
$333$	−0.362328	−	1.35222i	−0.0198554	−	0.0741015i
$334$		0			0
$335$	13.6111	−	5.83237i	0.743653	−	0.318656i
$336$		0			0
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	0.720279	−	0.693684i	$-0.244014\pi$
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	−0.693684	+	0.720279i	$0.744014\pi$
$338$		0			0
$339$	3.12540	−	5.41335i	0.169748	−	0.294013i
$340$		0			0
$341$	−0.132033	+	0.0762292i	−0.00714998	+	0.00412804i
$342$		0			0
$343$	11.0554	+	14.8586i	0.596936	+	0.802289i
$344$		0			0
$345$	−30.2720	+	4.35966i	−1.62979	+	0.234716i
$346$		0			0
$347$	3.68015	−	0.986094i	0.197561	−	0.0529363i	−0.158682	−	0.987330i	$-0.550724\pi$
$347$	3.68015	−	0.986094i	0.197561	−	0.0529363i	0.356243	+	0.934393i	$0.384058\pi$
$348$		0			0
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$		0			0
$351$	8.36041			0.446246
$352$		0			0
$353$	−24.9004	+	6.67203i	−1.32531	+	0.355116i	−0.850965	−	0.525222i	$-0.823982\pi$
$353$	−24.9004	+	6.67203i	−1.32531	+	0.355116i	−0.474347	+	0.880338i	$0.657316\pi$
$354$		0			0
$355$	17.9665	−	2.58747i	0.953564	−	0.137329i
$356$		0			0
$357$	−4.48995	+	4.07365i	−0.237633	+	0.215601i
$358$		0			0
$359$	−8.99497	+	5.19325i	−0.474737	+	0.274089i	−0.718220	−	0.695816i	$-0.755043\pi$
$359$	−8.99497	+	5.19325i	−0.474737	+	0.274089i	0.243484	+	0.969905i	$0.421710\pi$
$360$		0			0
$361$	7.10364	−	12.3039i	0.373876	−	0.647572i
$362$		0			0
$363$	−5.09161	−	5.09161i	−0.267240	−	0.267240i
$364$		0			0
$365$	−20.2763	+	8.68840i	−1.06131	+	0.454772i
$366$		0			0
$367$	2.24811	+	8.39004i	0.117350	+	0.437957i	0.999452	−	0.0331020i	$-0.0105386\pi$
$367$	2.24811	+	8.39004i	0.117350	+	0.437957i	−0.882102	+	0.471059i	$0.843872\pi$
$368$		0			0
$369$	24.4654	+	42.3753i	1.27362	+	2.20597i
$370$		0			0
$371$	18.6197	−	9.57617i	0.966686	−	0.497170i
$372$		0			0
$373$	−12.8560	−	3.44476i	−0.665660	−	0.178363i	−0.0898611	−	0.995954i	$-0.528642\pi$
$373$	−12.8560	−	3.44476i	−0.665660	−	0.178363i	−0.575799	+	0.817591i	$0.695309\pi$
$374$		0			0
$375$	−25.0450	+	20.7084i	−1.29332	+	1.06938i
$376$		0			0
$377$	−2.17808	+	2.17808i	−0.112177	+	0.112177i
$378$		0			0
$379$			25.3453i			1.30190i	0.759121	+	0.650949i	$0.225629\pi$
$379$			25.3453i			1.30190i	−0.759121	+	0.650949i	$0.774371\pi$
$380$		0			0
$381$	47.1788	+	27.2387i	2.41704	+	1.39548i
$382$		0			0
$383$	−4.76251	+	17.7739i	−0.243353	+	0.908205i	0.730851	+	0.682537i	$0.239123\pi$
$383$	−4.76251	+	17.7739i	−0.243353	+	0.908205i	−0.974204	+	0.225668i	$0.927543\pi$
$384$		0			0
$385$	21.4154	+	3.61749i	1.09143	+	0.184364i
$386$		0			0
$387$	0.946464	−	3.53225i	0.0481114	−	0.179554i
$388$		0			0
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.0789164	−	0.996881i	$-0.525146\pi$
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.902783	+	0.430097i	$0.858479\pi$
$390$		0			0
$391$		−	3.70961i		−	0.187603i
$392$		0			0
$393$	−29.1745	+	29.1745i	−1.47166	+	1.47166i
$394$		0			0
$395$	−23.5682	+	18.5432i	−1.18585	+	0.933008i
$396$		0			0
$397$	−15.2461	−	4.08518i	−0.765181	−	0.205029i	−0.144939	−	0.989441i	$-0.546299\pi$
$397$	−15.2461	−	4.08518i	−0.765181	−	0.205029i	−0.620241	+	0.784411i	$0.712965\pi$
$398$		0			0
$399$	−9.11594	+	14.1543i	−0.456368	+	0.708603i
$400$		0			0
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$		0			0
$403$	−0.0126253	−	0.0471183i	−0.000628911	−	0.00234713i
$404$		0			0
$405$	−3.60661	+	9.01496i	−0.179214	+	0.447957i
$406$		0			0
$407$	−0.666957	−	0.666957i	−0.0330598	−	0.0330598i
$408$		0			0
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	−0.869873	−	0.493276i	$-0.835799\pi$
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	0.862126	+	0.506694i	$0.169133\pi$
$410$		0			0
$411$	47.7431	−	27.5645i	2.35499	−	1.35966i
$412$		0			0
$413$	26.9879	+	8.65608i	1.32799	+	0.425938i
$414$		0			0
$415$	−24.6370	−	18.4340i	−1.20938	−	0.904891i
$416$		0			0
$417$	−23.1266	+	6.19675i	−1.13251	+	0.303456i
$418$		0			0
$419$	−31.6254			−1.54500			−0.772501	−	0.635014i	$-0.780994\pi$
$419$	−31.6254			−1.54500			−0.772501	+	0.635014i	$0.780994\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$		0			0
$423$	−33.6842	+	9.02565i	−1.63778	+	0.438842i
$424$		0			0
$425$	−2.05308	−	3.36476i	−0.0995890	−	0.163215i
$426$		0			0
$427$	−3.54190	−	3.90386i	−0.171405	−	0.188921i
$428$		0			0
$429$	10.8548	−	6.26703i	0.524075	−	0.302575i
$430$		0			0
$431$	0.779037	−	1.34933i	0.0375249	−	0.0649950i	−0.846653	−	0.532145i	$-0.821386\pi$
$431$	0.779037	−	1.34933i	0.0375249	−	0.0649950i	0.884178	+	0.467150i	$0.154719\pi$
$432$		0			0
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	0.841748	−	0.539871i	$-0.181527\pi$
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	−0.539871	+	0.841748i	$0.681527\pi$
$434$		0			0
$435$	−6.71305	−	15.6663i	−0.321866	−	0.751144i
$436$		0			0
$437$	−2.66628	−	9.95068i	−0.127545	−	0.476006i
$438$		0			0
$439$	−11.9571	−	20.7103i	−0.570681	−	0.988449i	−0.996496	−	0.0836389i	$-0.973346\pi$
$439$	−11.9571	−	20.7103i	−0.570681	−	0.988449i	0.425815	−	0.904810i	$-0.359988\pi$
$440$		0			0
$441$	−22.1844	+	31.0255i	−1.05640	+	1.47741i
$442$		0			0
$443$	12.4238	+	3.32895i	0.590272	+	0.158163i	0.541578	−	0.840651i	$-0.317827\pi$
$443$	12.4238	+	3.32895i	0.590272	+	0.158163i	0.0486946	+	0.998814i	$0.484494\pi$
$444$		0			0
$445$	−1.97756	−	2.51346i	−0.0937451	−	0.119149i
$446$		0			0
$447$	9.95157	−	9.95157i	0.470693	−	0.470693i
$448$		0			0
$449$			17.8932i			0.844435i	0.906495	+	0.422217i	$0.138748\pi$
$449$			17.8932i			0.844435i	−0.906495	+	0.422217i	$0.861252\pi$
$450$		0			0
$451$	28.5510	+	16.4839i	1.34441	+	0.776197i
$452$		0			0
$453$	7.55749	−	28.2049i	0.355082	−	1.32518i
$454$		0			0
$455$	−2.89145	+	6.31900i	−0.135553	+	0.296239i
$456$		0			0
$457$	8.85449	−	33.0454i	0.414196	−	1.54580i	−0.372246	−	0.928134i	$-0.621412\pi$
$457$	8.85449	−	33.0454i	0.414196	−	1.54580i	0.786442	−	0.617665i	$-0.211921\pi$
$458$		0			0
$459$	−4.85928	−	2.80551i	−0.226812	−	0.130950i
$460$		0			0
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$		0			0
$463$	−3.98510	+	3.98510i	−0.185203	+	0.185203i	−0.793619	−	0.608415i	$-0.791805\pi$
$463$	−3.98510	+	3.98510i	−0.185203	+	0.185203i	0.608415	+	0.793619i	$0.291805\pi$
$464$		0			0
$465$	0.268016	+	0.0319818i	0.0124289	+	0.00148312i
$466$		0			0
$467$	4.71932	+	1.26454i	0.218384	+	0.0585159i	0.366352	−	0.930476i	$-0.380607\pi$
$467$	4.71932	+	1.26454i	0.218384	+	0.0585159i	−0.147968	+	0.988992i	$0.547273\pi$
$468$		0			0
$469$	8.01347	+	15.5812i	0.370028	+	0.719473i
$470$		0			0
$471$	35.5873	+	61.6390i	1.63978	+	2.84017i
$472$		0			0
$473$	−0.637693	−	2.37990i	−0.0293212	−	0.109428i
$474$		0			0
$475$	−7.92561	−	7.55000i	−0.363652	−	0.346418i
$476$		0			0
$477$	30.4904	+	30.4904i	1.39606	+	1.39606i
$478$		0			0
$479$	8.55572	−	14.8189i	0.390921	−	0.677094i	−0.601651	−	0.798759i	$-0.705490\pi$
$479$	8.55572	−	14.8189i	0.390921	−	0.677094i	0.992571	+	0.121665i	$0.0388234\pi$
$480$		0			0
$481$	0.261359	−	0.150896i	0.0119170	−	0.00688026i
$482$		0			0
$483$	−7.65783	−	35.3683i	−0.348443	−	1.60931i
$484$		0			0
$485$	5.99972	−	8.01859i	0.272433	−	0.364105i
$486$		0			0
$487$	0.125860	−	0.0337240i	0.00570325	−	0.00152818i	−0.255966	−	0.966686i	$-0.582394\pi$
$487$	0.125860	−	0.0337240i	0.00570325	−	0.00152818i	0.261670	+	0.965158i	$0.415727\pi$
$488$		0			0
$489$	−63.8465			−2.88724
$490$		0			0
$491$	−26.9895			−1.21802			−0.609011	−	0.793162i	$-0.708433\pi$
$491$	−26.9895			−1.21802			−0.609011	+	0.793162i	$0.708433\pi$
$492$		0			0
$493$	1.99685	−	0.535055i	0.0899337	−	0.0240977i
$494$		0			0
$495$	6.37579	+	44.2713i	0.286570	+	1.98985i
$496$		0			0
$497$	4.54495	+	20.9912i	0.203869	+	0.941584i
$498$		0			0
$499$	0.0833977	−	0.0481497i	0.00373339	−	0.00215548i	−0.498132	−	0.867101i	$-0.665981\pi$
$499$	0.0833977	−	0.0481497i	0.00373339	−	0.00215548i	0.501866	+	0.864946i	$0.332647\pi$
$500$		0			0
$501$	6.46638	−	11.2001i	0.288897	−	0.500384i
$502$		0			0
$503$	13.6334	+	13.6334i	0.607883	+	0.607883i	0.942392	−	0.334509i	$-0.108571\pi$
$503$	13.6334	+	13.6334i	0.607883	+	0.607883i	−0.334509	+	0.942392i	$0.608571\pi$
$504$		0			0
$505$	0.149286	+	0.0597245i	0.00664312	+	0.00265771i
$506$		0			0
$507$	−8.74194	−	32.6254i	−0.388243	−	1.44894i
$508$		0			0
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	0.696480	−	0.717576i	$-0.254749\pi$
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	−0.969679	+	0.244381i	$0.921415\pi$
$510$		0			0
$511$	−11.9376	−	23.2111i	−0.528087	−	1.02680i
$512$		0			0
$513$	−15.0510	−	4.03291i	−0.664520	−	0.178057i
$514$		0			0
$515$	−4.39274	+	36.8123i	−0.193567	+	1.62214i
$516$		0			0
$517$	−16.6140	+	16.6140i	−0.730684	+	0.730684i
$518$		0			0
$519$			15.1918i			0.666845i
$520$		0			0
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	0.776694	−	0.629878i	$-0.216895\pi$
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	−0.157143	+	0.987576i	$0.550228\pi$
$522$		0			0
$523$	7.09270	−	26.4703i	0.310142	−	1.15747i	−0.618286	−	0.785953i	$-0.712173\pi$
$523$	7.09270	−	26.4703i	0.310142	−	1.15747i	0.928428	−	0.371512i	$-0.121161\pi$
$524$		0			0
$525$	−26.5205	−	27.8422i	−1.15745	−	1.21513i
$526$		0			0
$527$	−0.00847337	+	0.0316231i	−0.000369106	+	0.00137752i
$528$		0			0
$529$	−0.742186	−	0.428501i	−0.0322689	−	0.0186305i
$530$		0			0
$531$			58.3682i			2.53297i
$532$		0			0
$533$	−7.45881	+	7.45881i	−0.323077	+	0.323077i
$534$		0			0
$535$	1.21065	−	10.1456i	0.0523409	−	0.438630i
$536$		0			0
$537$	−35.2878	−	9.45533i	−1.52278	−	0.408028i
$538$		0			0
$539$	−2.49258	+	25.5768i	−0.107363	+	1.10167i
$540$		0			0
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.846069	+	0.533073i	$0.178963\pi$
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.0386200	+	0.999254i	$0.487704\pi$
$542$		0			0
$543$	−8.78254	−	32.7769i	−0.376895	−	1.40659i
$544$		0			0
$545$	37.5826	+	15.0356i	1.60986	+	0.644056i
$546$		0			0
$547$	−8.06541	−	8.06541i	−0.344852	−	0.344852i	0.513336	−	0.858188i	$-0.328410\pi$
$547$	−8.06541	−	8.06541i	−0.344852	−	0.344852i	−0.858188	+	0.513336i	$0.828410\pi$
$548$		0			0
$549$	5.42777	−	9.40117i	0.231651	−	0.401232i
$550$		0			0
$551$	4.97180	−	2.87047i	0.211806	−	0.122286i
$552$		0			0
$553$	−23.8423	−	26.2788i	−1.01388	−	1.11749i
$554$		0			0
$555$	0.238038	+	1.65285i	0.0101041	+	0.0701597i
$556$		0			0
$557$	24.7826	−	6.64049i	1.05007	−	0.281367i	0.307792	−	0.951454i	$-0.400410\pi$
$557$	24.7826	−	6.64049i	1.05007	−	0.281367i	0.742282	+	0.670087i	$0.233743\pi$
$558$		0			0
$559$	0.788333			0.0333429
$560$		0			0
$561$	−8.41213			−0.355160
$562$		0			0
$563$	12.3749	−	3.31584i	0.521539	−	0.139746i	0.0115606	−	0.999933i	$-0.496320\pi$
$563$	12.3749	−	3.31584i	0.521539	−	0.139746i	0.509978	+	0.860187i	$0.329653\pi$
$564$		0			0
$565$	−2.88083	+	3.85022i	−0.121198	+	0.161980i
$566$		0			0
$567$	−10.9397	−	3.50878i	−0.459423	−	0.147355i
$568$		0			0
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.971209	−	0.238229i	$-0.923433\pi$
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.279292	+	0.960206i	$0.590100\pi$
$570$		0			0
$571$	−4.11985	+	7.13579i	−0.172410	+	0.298623i	−0.939262	−	0.343201i	$-0.888489\pi$
$571$	−4.11985	+	7.13579i	−0.172410	+	0.298623i	0.766852	+	0.641824i	$0.221822\pi$
$572$		0			0
$573$	31.8645	+	31.8645i	1.33116	+	1.33116i
$574$		0			0
$575$	23.5212	−	0.570889i	0.980904	−	0.0238077i
$576$		0			0
$577$	−0.910086	−	3.39649i	−0.0378874	−	0.141398i	0.944391	−	0.328824i	$-0.106652\pi$
$577$	−0.910086	−	3.39649i	−0.0378874	−	0.141398i	−0.982279	+	0.187426i	$0.939985\pi$
$578$		0			0
$579$	13.0770	+	22.6500i	0.543460	+	0.941301i
$580$		0			0
$581$	19.7132	−	30.6088i	0.817843	−	1.26987i
$582$		0			0
$583$	28.0627	+	7.51937i	1.16224	+	0.311421i
$584$		0			0
$585$	−14.2103	−	1.69569i	−0.587524	−	0.0701081i
$586$		0			0
$587$	5.37485	−	5.37485i	0.221844	−	0.221844i	−0.587431	−	0.809275i	$-0.699861\pi$
$587$	5.37485	−	5.37485i	0.221844	−	0.221844i	0.809275	+	0.587431i	$0.199861\pi$
$588$		0			0
$589$			0.0909162i			0.00374613i
$590$		0			0
$591$	43.4136	+	25.0649i	1.78580	+	1.03103i
$592$		0			0
$593$	0.190155	−	0.709668i	0.00780872	−	0.0291426i	−0.961912	−	0.273361i	$-0.911865\pi$
$593$	0.190155	−	0.709668i	0.00780872	−	0.0291426i	0.969720	+	0.244218i	$0.0785314\pi$
$594$		0			0
$595$	3.80106	−	2.70248i	0.155828	−	0.110791i
$596$		0			0
$597$	−6.56845	+	24.5138i	−0.268829	+	1.00328i
$598$		0			0
$599$	−7.23778	−	4.17873i	−0.295727	−	0.170738i	0.344794	−	0.938678i	$-0.387949\pi$
$599$	−7.23778	−	4.17873i	−0.295727	−	0.170738i	−0.640522	+	0.767940i	$0.721282\pi$
$600$		0			0
$601$			39.9236i			1.62852i	0.580501	+	0.814259i	$0.302857\pi$
$601$			39.9236i			1.62852i	−0.580501	+	0.814259i	$0.697143\pi$
$602$		0			0
$603$	−25.5147	+	25.5147i	−1.03904	+	1.03904i
$604$		0			0
$605$	3.42523	+	4.35344i	0.139255	+	0.176993i
$606$		0			0
$607$	−33.2758	−	8.91623i	−1.35062	−	0.361899i	−0.490259	−	0.871577i	$-0.663098\pi$
$607$	−33.2758	−	8.91623i	−1.35062	−	0.361899i	−0.860365	+	0.509678i	$0.829765\pi$
$608$		0			0
$609$	17.9339	−	9.22349i	0.726720	−	0.373755i
$610$		0			0
$611$	−3.75885	−	6.51051i	−0.152067	−	0.263387i
$612$		0			0
$613$	−8.46832	−	31.6042i	−0.342032	−	1.27648i	−0.896041	−	0.443971i	$-0.853569\pi$
$613$	−8.46832	−	31.6042i	−0.342032	−	1.27648i	0.554009	−	0.832510i	$-0.313097\pi$
$614$		0			0
$615$	−22.9888	−	53.6493i	−0.926997	−	2.16335i
$616$		0			0
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	0.322533	−	0.946558i	$-0.395466\pi$
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	−0.946558	+	0.322533i	$0.895466\pi$
$618$		0			0
$619$	−4.31138	+	7.46752i	−0.173289	+	0.300145i	−0.939568	−	0.342363i	$-0.888773\pi$
$619$	−4.31138	+	7.46752i	−0.173289	+	0.300145i	0.766279	+	0.642508i	$0.222106\pi$
$620$		0			0
$621$	29.0055	−	16.7463i	1.16395	−	0.672008i
$622$		0			0
$623$	2.80254	−	2.54269i	0.112281	−	0.101871i
$624$		0			0
$625$	21.0187	−	13.5356i	0.840749	−	0.541425i
$626$		0			0
$627$	−22.5648	+	6.04621i	−0.901150	+	0.241462i
$628$		0			0
$629$	−0.202545			−0.00807600
$630$		0			0
$631$	4.13675			0.164682			0.0823408	−	0.996604i	$-0.473760\pi$
$631$	4.13675			0.164682			0.0823408	+	0.996604i	$0.473760\pi$
$632$		0			0
$633$	31.3739	−	8.40662i	1.24700	−	0.334133i
$634$		0			0
$635$	−33.5556	−	25.1072i	−1.33161	−	0.996349i
$636$		0			0
$637$	−7.69827	−	2.88840i	−0.305017	−	0.114443i
$638$		0			0
$639$	−38.3055	+	22.1157i	−1.51534	+	0.874882i
$640$		0			0
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	−0.953086	−	0.302701i	$-0.902112\pi$
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	0.738690	+	0.674046i	$0.235445\pi$
$642$		0			0
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	0.847978	−	0.530032i	$-0.177820\pi$
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	−0.530032	+	0.847978i	$0.677820\pi$
$644$		0			0
$645$	−1.62028	+	4.05000i	−0.0637984	+	0.159469i
$646$		0			0
$647$	2.69865	+	10.0715i	0.106095	+	0.395951i	0.998467	−	0.0553490i	$-0.0176271\pi$
$647$	2.69865	+	10.0715i	0.106095	+	0.395951i	−0.892372	+	0.451300i	$0.850960\pi$
$648$		0			0
$649$	19.6632	+	34.0577i	0.771848	+	1.33688i
$650$		0			0
$651$	−0.0155070	+	0.318994i	−0.000607766	+	0.0125023i
$652$		0			0
$653$	6.41946	+	1.72009i	0.251213	+	0.0673123i	0.382228	−	0.924068i	$-0.375157\pi$
$653$	6.41946	+	1.72009i	0.251213	+	0.0673123i	−0.131015	+	0.991380i	$0.541824\pi$
$654$		0			0
$655$	24.9449	−	19.6263i	0.974677	−	0.766862i
$656$		0			0
$657$	38.0090	−	38.0090i	1.48287	−	1.48287i
$658$		0			0
$659$			22.0345i			0.858343i	0.903223	+	0.429172i	$0.141194\pi$
$659$			22.0345i			0.858343i	−0.903223	+	0.429172i	$0.858806\pi$
$660$		0			0
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	0.294013	−	0.955802i	$-0.405009\pi$
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	−0.680742	+	0.732523i	$0.738343\pi$
$662$		0			0
$663$	0.696621	−	2.59983i	0.0270545	−	0.100969i
$664$		0			0
$665$	8.25358	−	9.98115i	0.320060	−	0.387053i
$666$		0			0
$667$	−3.19379	+	11.9194i	−0.123664	+	0.461521i
$668$		0			0
$669$	−2.65857	−	1.53492i	−0.102786	−	0.0593436i
$670$		0			0
$671$		−	7.31407i		−	0.282356i
$672$		0			0
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	−0.936600	−	0.350402i	$-0.886045\pi$
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	0.350402	+	0.936600i	$0.386045\pi$
$674$		0			0
$675$	17.0409	−	31.2427i	0.655903	−	1.20253i
$676$		0			0
$677$	−5.54296	−	1.48523i	−0.213033	−	0.0570821i	0.150724	−	0.988576i	$-0.451840\pi$
$677$	−5.54296	−	1.48523i	−0.213033	−	0.0570821i	−0.363757	+	0.931494i	$0.618506\pi$
$678$		0			0
$679$	9.96224	+	6.41606i	0.382316	+	0.246226i
$680$		0			0
$681$	4.53492	+	7.85472i	0.173779	+	0.300993i
$682$		0			0
$683$	−5.02900	−	18.7685i	−0.192430	−	0.718157i	−0.992917	−	0.118808i	$-0.962093\pi$
$683$	−5.02900	−	18.7685i	−0.192430	−	0.718157i	0.800488	−	0.599349i	$-0.204574\pi$
$684$		0			0
$685$	−38.9821	+	16.7039i	−1.48943	+	0.638222i
$686$		0			0
$687$	17.3095	+	17.3095i	0.660400	+	0.660400i
$688$		0			0
$689$	−4.64782	+	8.05027i	−0.177068	+	0.306691i
$690$		0			0
$691$	−19.0914	+	11.0224i	−0.726270	+	0.419312i	−0.817056	−	0.576558i	$-0.804395\pi$
$691$	−19.0914	+	11.0224i	−0.726270	+	0.419312i	0.0907861	+	0.995870i	$0.471062\pi$
$692$		0			0
$693$	−51.7244	+	11.1992i	−1.96485	+	0.425422i
$694$		0			0
$695$	18.2305	−	2.62550i	0.691524	−	0.0995908i
$696$		0			0
$697$	6.83821	−	1.83229i	0.259016	−	0.0694031i
$698$		0			0
$699$	66.2630			2.50630
$700$		0			0
$701$	−18.0270			−0.680870			−0.340435	−	0.940268i	$-0.610574\pi$
$701$	−18.0270			−0.680870			−0.340435	+	0.940268i	$0.610574\pi$
$702$		0			0
$703$	−0.543308	+	0.145579i	−0.0204913	+	0.00549062i
$704$		0			0
$705$	41.1729	−	5.92957i	1.55066	−	0.223321i
$706$		0			0
$707$	−0.0581046	+	0.181158i	−0.00218525	+	0.00681316i
$708$		0			0
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.993522	−	0.113637i	$-0.963750\pi$
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.398349	+	0.917234i	$0.630417\pi$
$710$		0			0
$711$	36.5370	−	63.2840i	1.37025	−	2.37334i
$712$		0			0
$713$	−0.138183	−	0.138183i	−0.00517498	−	0.00517498i
$714$		0			0
$715$	−8.86292	+	3.79777i	−0.331454	+	0.142029i
$716$		0			0
$717$	−18.0530	−	67.3747i	−0.674202	−	2.51615i
$718$		0			0
$719$	2.72691	+	4.72315i	0.101697	+	0.176144i	0.912384	−	0.409336i	$-0.134240\pi$
$719$	2.72691	+	4.72315i	0.101697	+	0.176144i	−0.810687	+	0.585480i	$0.800906\pi$
$720$		0			0
$721$	−43.8142	−	2.12990i	−1.63172	−	0.0793217i
$722$		0			0
$723$	−69.5938	−	18.6476i	−2.58822	−	0.693512i
$724$		0			0
$725$	3.69989	+	12.5790i	0.137411	+	0.467171i
$726$		0			0
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	−0.945161	−	0.326606i	$-0.894095\pi$
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	0.326606	+	0.945161i	$0.394095\pi$
$728$		0			0
$729$			38.4054i			1.42242i
$730$		0			0
$731$	−0.458200	−	0.264542i	−0.0169471	−	0.00978443i
$732$		0			0
$733$	−8.79960	+	32.8405i	−0.325021	+	1.21299i	0.589271	+	0.807936i	$0.299415\pi$
$733$	−8.79960	+	32.8405i	−0.325021	+	1.21299i	−0.914291	+	0.405057i	$0.867252\pi$
$734$		0			0
$735$	30.6614	−	33.6127i	1.13096	−	1.23982i
$736$		0			0
$737$	−6.29231	+	23.4832i	−0.231780	+	0.865016i
$738$		0			0
$739$	−25.0733	−	14.4761i	−0.922335	−	0.532510i	−0.0379557	−	0.999279i	$-0.512085\pi$
$739$	−25.0733	−	14.4761i	−0.922335	−	0.532510i	−0.884379	+	0.466769i	$0.845418\pi$
$740$		0			0
$741$		−	7.47449i		−	0.274582i
$742$		0			0
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.292300	+	0.956327i	$0.594421\pi$
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.956327	+	0.292300i	$0.905579\pi$
$744$		0			0
$745$	−8.50881	+	6.69461i	−0.311739	+	0.245272i
$746$		0			0
$747$	72.4235	+	19.4058i	2.64984	+	0.710022i
$748$		0			0
$749$	12.0753	+	0.587006i	0.441221	+	0.0214487i
$750$		0			0
$751$	−9.30569	−	16.1179i	−0.339569	−	0.588151i	0.644782	−	0.764366i	$-0.276948\pi$
$751$	−9.30569	−	16.1179i	−0.339569	−	0.588151i	−0.984352	+	0.176215i	$0.943615\pi$
$752$		0			0
$753$	−8.36242	−	31.2090i	−0.304743	−	1.13732i
$754$		0			0
$755$	−8.34385	+	20.8560i	−0.303664	+	0.759029i
$756$		0			0
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.996416	+	0.0845825i	$0.0269557\pi$
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.0845825	+	0.996416i	$0.473044\pi$
$758$		0			0
$759$	25.1064	−	43.4856i	0.911305	−	1.57843i
$760$		0			0
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	−0.144788	−	0.989463i	$-0.546250\pi$
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	0.784506	+	0.620122i	$0.212917\pi$
$762$		0			0
$763$	−14.6278	+	45.6066i	−0.529563	+	1.65107i
$764$		0			0
$765$	7.69038	+	5.75415i	0.278046	+	0.208042i
$766$		0			0
$767$	−12.1541	+	3.25668i	−0.438859	+	0.117592i
$768$		0			0
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$		0			0
$771$	−73.5189			−2.64772
$772$		0			0
$773$	23.8577	−	6.39265i	0.858101	−	0.229928i	0.197166	−	0.980370i	$-0.436826\pi$
$773$	23.8577	−	6.39265i	0.858101	−	0.229928i	0.660936	+	0.750443i	$0.270160\pi$
$774$		0			0
$775$	−0.201814	−	0.0488599i	−0.00724938	−	0.00175510i
$776$		0			0
$777$	−1.93111	+	0.418118i	−0.0692783	+	0.0149999i
$778$		0			0
$779$	17.0259	−	9.82991i	0.610017	−	0.352193i
$780$		0			0
$781$	−14.9007	+	25.8088i	−0.533190	+	0.923513i
$782$		0			0
$783$	13.1980	+	13.1980i	0.471659	+	0.471659i
$784$		0			0
$785$	−21.5656	−	50.3280i	−0.769710	−	1.79628i
$786$		0			0
$787$	−2.12442	−	7.92843i	−0.0757273	−	0.282618i	0.917670	−	0.397343i	$-0.130068\pi$
$787$	−2.12442	−	7.92843i	−0.0757273	−	0.282618i	−0.993397	+	0.114725i	$0.963401\pi$
$788$		0			0
$789$	−16.4897	−	28.5610i	−0.587048	−	1.01680i
$790$		0			0
$791$	−4.78348	−	3.08075i	−0.170081	−	0.109539i
$792$		0			0
$793$	2.26046	+	0.605689i	0.0802713	+	0.0215086i
$794$		0			0
$795$	−31.8048	−	40.4237i	−1.12800	−	1.43368i
$796$		0			0
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	−0.466696	−	0.884418i	$-0.654556\pi$
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	0.884418	+	0.466696i	$0.154556\pi$
$798$		0			0
$799$			5.04544i			0.178495i
$800$		0			0
$801$	6.74899	+	3.89653i	0.238464	+	0.137677i
$802$		0			0
$803$	9.37358	−	34.9827i	0.330786	−	1.23451i
$804$		0			0
$805$	2.62573	+	27.7148i	0.0925447	+	0.976819i
$806$		0			0
$807$	−6.06875	+	22.6489i	−0.213630	+	0.797278i
$808$		0			0
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.101855	−	0.994799i	$-0.532478\pi$
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.912449	+	0.409191i	$0.865811\pi$
$810$		0			0
$811$			55.2368i			1.93963i	0.243850	+	0.969813i	$0.421590\pi$
$811$			55.2368i			1.93963i	−0.243850	+	0.969813i	$0.578410\pi$
$812$		0			0
$813$	−17.2637	+	17.2637i	−0.605465	+	0.605465i
$814$		0			0
$815$	48.7704	+	5.81968i	1.70835	+	0.203855i
$816$		0			0
$817$	−1.41922	−	0.380278i	−0.0496521	−	0.0133042i
$818$		0			0
$819$	0.822187	−	16.9132i	0.0287295	−	0.590995i
$820$		0			0
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	0.656448	−	0.754371i	$-0.272058\pi$
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	−0.981529	+	0.191315i	$0.938725\pi$
$822$		0			0
$823$	4.37130	+	16.3139i	0.152374	+	0.568668i	0.999316	+	0.0369821i	$0.0117745\pi$
$823$	4.37130	+	16.3139i	0.152374	+	0.568668i	−0.846942	+	0.531685i	$0.821559\pi$
$824$		0			0
$825$	−1.29458	−	53.3382i	−0.0450716	−	1.85700i
$826$		0			0
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	0.798143	−	0.602468i	$-0.205816\pi$
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	−0.602468	+	0.798143i	$0.705816\pi$
$828$		0			0
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	−0.803062	−	0.595895i	$-0.796797\pi$
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	0.917591	+	0.397525i	$0.130131\pi$
$830$		0			0
$831$	−14.2980	+	8.25494i	−0.495991	+	0.286361i
$832$		0			0
$833$	3.50517	+	4.26213i	0.121447	+	0.147674i
$834$		0			0
$835$	−5.96038	+	7.96601i	−0.206268	+	0.275675i
$836$		0			0
$837$	−0.285513	+	0.0765030i	−0.00986877	+	0.00264433i
$838$		0			0
$839$	−46.0930			−1.59131			−0.795654	−	0.605752i	$-0.792872\pi$
$839$	−46.0930			−1.59131			−0.795654	+	0.605752i	$0.792872\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$		0			0
$843$	20.4290	−	5.47394i	0.703613	−	0.188533i
$844$		0			0
$845$	3.70387	+	25.7184i	0.127417	+	0.884740i
$846$		0			0
$847$	−4.85413	+	4.40407i	−0.166790	+	0.151326i
$848$		0			0
$849$	19.4080	−	11.2052i	0.666080	−	0.384562i
$850$		0			0
$851$	0.604505	−	1.04703i	0.0207222	−	0.0358918i
$852$		0			0
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	0.915200	−	0.403000i	$-0.132032\pi$
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	−0.403000	+	0.915200i	$0.632032\pi$
$854$		0			0
$855$	24.7645	+	9.90752i	0.846929	+	0.338830i
$856$		0			0
$857$	3.12136	+	11.6491i	0.106623	+	0.397924i	0.998524	−	0.0543068i	$-0.0172949\pi$
$857$	3.12136	+	11.6491i	0.106623	+	0.397924i	−0.891901	+	0.452231i	$0.850628\pi$
$858$		0			0
$859$	2.90061	+	5.02401i	0.0989677	+	0.171417i	0.911258	−	0.411837i	$-0.135113\pi$
$859$	2.90061	+	5.02401i	0.0989677	+	0.171417i	−0.812290	+	0.583254i	$0.801779\pi$
$860$		0			0
$861$	61.4147	−	31.5858i	2.09301	−	1.07644i
$862$		0			0
$863$	−2.90586	−	0.778623i	−0.0989167	−	0.0265046i	0.209021	−	0.977911i	$-0.432972\pi$
$863$	−2.90586	−	0.778623i	−0.0989167	−	0.0265046i	−0.307938	+	0.951406i	$0.599639\pi$
$864$		0			0
$865$	1.38475	−	11.6046i	0.0470829	−	0.394567i
$866$		0			0
$867$	33.6632	−	33.6632i	1.14326	−	1.14326i
$868$		0			0
$869$		−	49.2347i		−	1.67017i
$870$		0			0
$871$	−6.73657	−	3.88936i	−0.228260	−	0.131786i
$872$		0			0
$873$	−6.31601	+	23.5717i	−0.213765	+	0.797780i
$874$		0			0
$875$	17.7204	+	23.6852i	0.599058	+	0.800706i
$876$		0			0
$877$	9.07228	−	33.8582i	0.306349	−	1.14331i	−0.625428	−	0.780282i	$-0.715076\pi$
$877$	9.07228	−	33.8582i	0.306349	−	1.14331i	0.931778	−	0.363030i	$-0.118258\pi$
$878$		0			0
$879$	11.9328	+	6.88939i	0.402483	+	0.232373i
$880$		0			0
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$		0			0
$883$	7.95370	−	7.95370i	0.267663	−	0.267663i	−0.560495	−	0.828158i	$-0.689389\pi$
$883$	7.95370	−	7.95370i	0.267663	−	0.267663i	0.828158	+	0.560495i	$0.189389\pi$
$884$		0			0
$885$	8.24965	−	69.1342i	0.277309	−	2.32392i
$886$		0			0
$887$	19.6954	+	5.27738i	0.661308	+	0.177197i	0.573836	−	0.818970i	$-0.305455\pi$
$887$	19.6954	+	5.27738i	0.661308	+	0.177197i	0.0874718	+	0.996167i	$0.472121\pi$
$888$		0			0
$889$	26.8495	−	41.6893i	0.900503	−	1.39821i
$890$		0			0
$891$	−7.97057	−	13.8054i	−0.267024	−	0.462499i
$892$		0			0
$893$	3.62640	+	13.5339i	0.121353	+	0.452895i
$894$		0			0
$895$	26.0934	+	10.4392i	0.872207	+	0.348943i
$896$		0			0
$897$	11.3604	+	11.3604i	0.379313	+	0.379313i
$898$		0			0
$899$	0.0544519	−	0.0943134i	0.00181607	−	0.00314553i
$900$		0			0
$901$	5.40287	−	3.11935i	0.179996	−	0.103921i
$902$		0			0
$903$	−4.91468	−	1.57633i	−0.163550	−	0.0524570i
$904$		0			0
$905$	3.72107	+	25.8378i	0.123693	+	0.858879i
$906$		0			0
$907$	−6.29276	+	1.68614i	−0.208948	+	0.0559874i	−0.361775	−	0.932266i	$-0.617829\pi$
$907$	−6.29276	+	1.68614i	−0.208948	+	0.0559874i	0.152827	+	0.988253i	$0.451162\pi$
$908$		0			0
$909$	−0.391801			−0.0129952
$910$		0			0
$911$	24.2528			0.803531			0.401765	−	0.915743i	$-0.368397\pi$
$911$	24.2528			0.803531			0.401765	+	0.915743i	$0.368397\pi$
$912$		0			0
$913$	48.7964	−	13.0749i	1.61492	−	0.432718i
$914$		0			0
$915$	−7.75766	+	10.3681i	−0.256460	+	0.342757i
$916$		0			0
$917$	25.2350	+	27.8138i	0.833333	+	0.918493i
$918$		0			0
$919$	31.2542	−	18.0446i	1.03098	−	0.595236i	0.113714	−	0.993513i	$-0.463725\pi$
$919$	31.2542	−	18.0446i	1.03098	−	0.595236i	0.917265	+	0.398277i	$0.130392\pi$
$920$		0			0
$921$	2.18986	−	3.79295i	0.0721583	−	0.124982i
$922$		0			0
$923$	−6.74244	−	6.74244i	−0.221930	−	0.221930i
$924$		0			0
$925$	−0.0311706	−	1.28426i	−0.00102488	−	0.0422263i
$926$		0			0
$927$	−23.3813	−	87.2600i	−0.767941	−	2.86600i
$928$		0			0
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	−0.969949	−	0.243307i	$-0.921768\pi$
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	0.274264	−	0.961654i	$-0.411566\pi$
$930$		0			0
$931$	12.4657	+	8.91344i	0.408547	+	0.292126i
$932$		0			0
$933$	−38.7686	−	10.3880i	−1.26923	−	0.340089i
$934$		0			0
$935$	6.42578	+	0.766776i	0.210145	+	0.0250762i
$936$		0			0
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	−0.637546	−	0.770412i	$-0.720050\pi$
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	0.770412	+	0.637546i	$0.220050\pi$
$938$		0			0
$939$		−	67.8621i		−	2.21460i
$940$		0			0
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	0.188677	−	0.982039i	$-0.439580\pi$
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	−0.756132	+	0.654419i	$0.772913\pi$
$942$		0			0
$943$	−10.9371	+	40.8179i	−0.356162	+	1.32921i
$944$		0			0
$945$	38.2899	+	17.5207i	1.24557	+	0.569949i
$946$		0			0
$947$	15.2583	−	56.9449i	0.495830	−	1.85046i	−0.0295030	−	0.999565i	$-0.509392\pi$
$947$	15.2583	−	56.9449i	0.495830	−	1.85046i	0.525333	−	0.850897i	$-0.323941\pi$
$948$		0			0
$949$	10.0354	+	5.79393i	0.325762	+	0.188079i
$950$		0			0
$951$		−	38.3355i		−	1.24311i
$952$		0			0
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.00759828	+	0.999971i	$0.502419\pi$
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.999971	+	0.00759828i	$0.997581\pi$
$954$		0			0
$955$	−21.4359	−	27.2448i	−0.693648	−	0.881622i
$956$		0			0
$957$	27.0292	+	7.24244i	0.873729	+	0.234115i
$958$		0			0
$959$	−22.9505	−	44.6245i	−0.741111	−	1.44100i
$960$		0			0
$961$	−15.4991	−	26.8453i	−0.499972	−	0.865977i
$962$		0			0
$963$	6.44392	+	24.0491i	0.207653	+	0.774970i
$964$		0			0
$965$	−7.92454	−	18.4936i	−0.255100	−	0.595331i
$966$		0			0
$967$	21.5036	+	21.5036i	0.691510	+	0.691510i	0.962564	−	0.271054i	$-0.0873721\pi$
$967$	21.5036	+	21.5036i	0.691510	+	0.691510i	−0.271054	+	0.962564i	$0.587372\pi$
$968$		0			0
$969$	−2.50822	+	4.34437i	−0.0805756	+	0.139561i
$970$		0			0
$971$	45.3034	−	26.1559i	1.45385	−	0.839384i	0.455158	−	0.890411i	$-0.349583\pi$
$971$	45.3034	−	26.1559i	1.45385	−	0.839384i	0.998697	+	0.0510273i	$0.0162496\pi$
$972$		0			0
$973$	4.61174	+	21.2997i	0.147845	+	0.682836i
$974$		0			0
$975$	16.5917	+	4.01692i	0.531361	+	0.128644i
$976$		0			0
$977$	−54.6658	+	14.6477i	−1.74891	+	0.468620i	−0.984394	−	0.175979i	$-0.943691\pi$
$977$	−54.6658	+	14.6477i	−1.74891	+	0.468620i	−0.764520	+	0.644599i	$0.777024\pi$
$978$		0			0
$979$	5.25068			0.167813
$980$		0			0
$981$	−98.6358			−3.14920
$982$		0			0
$983$	−14.9514	+	4.00621i	−0.476875	+	0.127778i	−0.489247	−	0.872145i	$-0.662728\pi$
$983$	−14.9514	+	4.00621i	−0.476875	+	0.127778i	0.0123723	+	0.999923i	$0.496062\pi$
$984$		0			0
$985$	−30.8777	−	23.1035i	−0.983845	−	0.736139i
$986$		0			0
$987$	10.4154	+	48.1044i	0.331526	+	1.53118i
$988$		0			0
$989$	2.73504	−	1.57907i	0.0869691	−	0.0502116i
$990$		0			0
$991$	−26.8648	+	46.5311i	−0.853388	+	1.47811i	0.0247453	+	0.999694i	$0.492123\pi$
$991$	−26.8648	+	46.5311i	−0.853388	+	1.47811i	−0.878133	+	0.478417i	$0.841211\pi$
$992$		0			0
$993$	−39.2484	−	39.2484i	−1.24551	−	1.24551i
$994$		0			0
$995$	7.25190	−	18.1266i	0.229901	−	0.574653i
$996$		0			0
$997$	9.97217	+	37.2167i	0.315822	+	1.17866i	0.923222	+	0.384267i	$0.125546\pi$
$997$	9.97217	+	37.2167i	0.315822	+	1.17866i	−0.607400	+	0.794396i	$0.707787\pi$
$998$		0			0
$999$	−0.914352	−	1.58370i	−0.0289288	−	0.0501062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.17.4		16
4.3	odd	2		70.2.k.a.17.1	yes	16
5.3	odd	4	inner	560.2.ci.c.353.4		16
7.5	odd	6	inner	560.2.ci.c.257.4		16
12.11	even	2		630.2.bv.c.577.4		16
20.3	even	4		70.2.k.a.3.3	✓	16
20.7	even	4		350.2.o.c.143.2		16
20.19	odd	2		350.2.o.c.157.4		16
28.3	even	6		490.2.g.c.97.1		16
28.11	odd	6		490.2.g.c.97.4		16
28.19	even	6		70.2.k.a.47.3	yes	16
28.23	odd	6		490.2.l.c.117.4		16
28.27	even	2		490.2.l.c.227.2		16
35.33	even	12	inner	560.2.ci.c.33.4		16
60.23	odd	4		630.2.bv.c.73.1		16
84.47	odd	6		630.2.bv.c.397.1		16
140.3	odd	12		490.2.g.c.293.4		16
140.19	even	6		350.2.o.c.257.2		16
140.23	even	12		490.2.l.c.313.2		16
140.47	odd	12		350.2.o.c.243.4		16
140.83	odd	4		490.2.l.c.423.4		16
140.103	odd	12		70.2.k.a.33.1	yes	16
140.123	even	12		490.2.g.c.293.1		16
420.383	even	12		630.2.bv.c.523.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	20.3	even	4
70.2.k.a.17.1	yes	16	4.3	odd	2
70.2.k.a.33.1	yes	16	140.103	odd	12
70.2.k.a.47.3	yes	16	28.19	even	6
350.2.o.c.143.2		16	20.7	even	4
350.2.o.c.157.4		16	20.19	odd	2
350.2.o.c.243.4		16	140.47	odd	12
350.2.o.c.257.2		16	140.19	even	6
490.2.g.c.97.1		16	28.3	even	6
490.2.g.c.97.4		16	28.11	odd	6
490.2.g.c.293.1		16	140.123	even	12
490.2.g.c.293.4		16	140.3	odd	12
490.2.l.c.117.4		16	28.23	odd	6
490.2.l.c.227.2		16	28.27	even	2
490.2.l.c.313.2		16	140.23	even	12
490.2.l.c.423.4		16	140.83	odd	4
560.2.ci.c.17.4		16	1.1	even	1	trivial
560.2.ci.c.33.4		16	35.33	even	12	inner
560.2.ci.c.257.4		16	7.5	odd	6	inner
560.2.ci.c.353.4		16	5.3	odd	4	inner
630.2.bv.c.73.1		16	60.23	odd	4
630.2.bv.c.397.1		16	84.47	odd	6
630.2.bv.c.523.4		16	420.383	even	12
630.2.bv.c.577.4		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.80762 - 0.752300i) q^{3} +(-2.21323 + 0.318742i) q^{5} +(-0.559876 - 2.58583i) q^{7} +(4.71872 - 2.72435i) q^{9} +O(q^{10})\)	\(q+(2.80762 - 0.752300i) q^{3} +(-2.21323 + 0.318742i) q^{5} +(-0.559876 - 2.58583i) q^{7} +(4.71872 - 2.72435i) q^{9} +(1.83557 - 3.17930i) q^{11} +(0.830578 + 0.830578i) q^{13} +(-5.97414 + 2.55992i) q^{15} +(-0.204036 - 0.761471i) q^{17} +(-1.09461 - 1.89593i) q^{19} +(-3.51725 - 6.83885i) q^{21} +(4.54529 + 1.21791i) q^{23} +(4.79681 - 1.41090i) q^{25} +(5.03288 - 5.03288i) q^{27} +2.62236i q^{29} +(-0.0359651 - 0.0207644i) q^{31} +(2.76180 - 10.3072i) q^{33} +(2.06335 + 5.54460i) q^{35} +(0.0664979 - 0.248174i) q^{37} +(2.95680 + 1.70711i) q^{39} +8.98026i q^{41} +(0.474569 - 0.474569i) q^{43} +(-9.57526 + 7.53368i) q^{45} +(-6.18205 - 1.65648i) q^{47} +(-6.37308 + 2.89549i) q^{49} +(-1.14571 - 1.98443i) q^{51} +(2.04824 + 7.64413i) q^{53} +(-3.04917 + 7.62161i) q^{55} +(-4.49957 - 4.49957i) q^{57} +(-5.35616 + 9.27713i) q^{59} +(1.72539 - 0.996157i) q^{61} +(-9.68662 - 10.6765i) q^{63} +(-2.10300 - 1.57352i) q^{65} +(-6.39671 + 1.71399i) q^{67} +13.6777 q^{69} -8.11777 q^{71} +(9.52910 - 2.55331i) q^{73} +(12.4062 - 7.56992i) q^{75} +(-9.24884 - 2.96647i) q^{77} +(11.6145 - 6.70563i) q^{79} +(2.17114 - 3.76053i) q^{81} +(9.73033 + 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(1.97280 + 7.36260i) q^{87} +(0.715130 + 1.23864i) q^{89} +(1.68272 - 2.61276i) q^{91} +(-0.116597 - 0.0312422i) q^{93} +(3.02695 + 3.84723i) q^{95} +(-3.16693 + 3.16693i) q^{97} -20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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