LMFDB - Embedded newform 528.2.y.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(49,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("528.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.y (of order $5$, 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:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	528.97
Dual form			528.2.y.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(0.881966 + 2.71441i) q^{5} +(3.73607 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(0.881966 + 2.71441i) q^{5} +(3.73607 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.23607 - 3.07768i) q^{11} +(-1.00000 + 3.07768i) q^{13} +(-2.30902 - 1.67760i) q^{15} +(-0.763932 - 2.35114i) q^{17} +(-2.61803 + 1.90211i) q^{19} -4.61803 q^{21} +3.23607 q^{23} +(-2.54508 + 1.84911i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.309017 + 0.224514i) q^{29} +(-2.66312 + 8.19624i) q^{31} +(2.80902 + 1.76336i) q^{33} +(-4.07295 + 12.5352i) q^{35} +(-1.23607 - 0.898056i) q^{37} +(-1.00000 - 3.07768i) q^{39} +(2.61803 - 1.90211i) q^{41} +3.23607 q^{43} +2.85410 q^{45} +(2.00000 - 1.45309i) q^{47} +(4.42705 + 13.6251i) q^{49} +(2.00000 + 1.45309i) q^{51} +(-1.19098 + 3.66547i) q^{53} +(7.26393 - 6.06961i) q^{55} +(1.00000 - 3.07768i) q^{57} +(-3.11803 - 2.26538i) q^{59} +(-2.09017 - 6.43288i) q^{61} +(3.73607 - 2.71441i) q^{63} -9.23607 q^{65} -4.00000 q^{67} +(-2.61803 + 1.90211i) q^{69} +(-3.85410 - 11.8617i) q^{71} +(9.16312 + 6.65740i) q^{73} +(0.972136 - 2.99193i) q^{75} +(3.73607 - 14.8536i) q^{77} +(2.88197 - 8.86978i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.208204 + 0.640786i) q^{83} +(5.70820 - 4.14725i) q^{85} -0.381966 q^{87} -11.7082 q^{89} +(-12.0902 + 8.78402i) q^{91} +(-2.66312 - 8.19624i) q^{93} +(-7.47214 - 5.42882i) q^{95} +(3.50000 - 10.7719i) q^{97} +(-3.30902 + 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9	$ 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9} + 4 q^{11} - 4 q^{13} - 7 q^{15} - 12 q^{17} - 6 q^{19} - 14 q^{21} + 4 q^{23} + q^{25} - q^{27} - q^{29} + 5 q^{31} + 9 q^{33} - 23 q^{35} + 4 q^{37} - 4 q^{39} + 6 q^{41} + 4 q^{43} - 2 q^{45} + 8 q^{47} + 11 q^{49} + 8 q^{51} - 7 q^{53} + 38 q^{55} + 4 q^{57} - 8 q^{59} + 14 q^{61} + 6 q^{63} - 28 q^{65} - 16 q^{67} - 6 q^{69} - 2 q^{71} + 21 q^{73} - 14 q^{75} + 6 q^{77} + 16 q^{79} - q^{81} - 26 q^{83} - 4 q^{85} - 6 q^{87} - 20 q^{89} - 26 q^{91} + 5 q^{93} - 12 q^{95} + 14 q^{97} - 11 q^{99}+O(q^{100}) $ 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9 + 4 * q^11 - 4 * q^13 - 7 * q^15 - 12 * q^17 - 6 * q^19 - 14 * q^21 + 4 * q^23 + q^25 - q^27 - q^29 + 5 * q^31 + 9 * q^33 - 23 * q^35 + 4 * q^37 - 4 * q^39 + 6 * q^41 + 4 * q^43 - 2 * q^45 + 8 * q^47 + 11 * q^49 + 8 * q^51 - 7 * q^53 + 38 * q^55 + 4 * q^57 - 8 * q^59 + 14 * q^61 + 6 * q^63 - 28 * q^65 - 16 * q^67 - 6 * q^69 - 2 * q^71 + 21 * q^73 - 14 * q^75 + 6 * q^77 + 16 * q^79 - q^81 - 26 * q^83 - 4 * q^85 - 6 * q^87 - 20 * q^89 - 26 * q^91 + 5 * q^93 - 12 * q^95 + 14 * q^97 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	0.881966	+	2.71441i	0.394427	+	1.21392i	0.929407	+	0.369057i	$0.120319\pi$
$5$	0.881966	+	2.71441i	0.394427	+	1.21392i	−0.534980	+	0.844865i	$0.679681\pi$
$6$		0			0
$7$	3.73607	+	2.71441i	1.41210	+	1.02595i	0.993013	+	0.118006i	$0.0376501\pi$
$7$	3.73607	+	2.71441i	1.41210	+	1.02595i	0.419088	+	0.907946i	$0.362350\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$12$		0			0
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	0.711238	+	0.702951i	$0.248135\pi$
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	−0.988588	+	0.150644i	$0.951865\pi$
$14$		0			0
$15$	−2.30902	−	1.67760i	−0.596186	−	0.433154i
$16$		0			0
$17$	−0.763932	−	2.35114i	−0.185281	−	0.570235i	0.814672	−	0.579922i	$-0.196917\pi$
$17$	−0.763932	−	2.35114i	−0.185281	−	0.570235i	−0.999953	+	0.00968605i	$0.996917\pi$
$18$		0			0
$19$	−2.61803	+	1.90211i	−0.600618	+	0.436375i	−0.846098	−	0.533027i	$-0.821054\pi$
$19$	−2.61803	+	1.90211i	−0.600618	+	0.436375i	0.245480	+	0.969402i	$0.421054\pi$
$20$		0			0
$21$	−4.61803			−1.00774
$22$		0			0
$23$	3.23607			0.674767			0.337383	−	0.941367i	$-0.390458\pi$
$23$	3.23607			0.674767			0.337383	+	0.941367i	$0.390458\pi$
$24$		0			0
$25$	−2.54508	+	1.84911i	−0.509017	+	0.369822i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	0.309017	+	0.224514i	0.0573830	+	0.0416912i	0.616107	−	0.787662i	$-0.288709\pi$
$29$	0.309017	+	0.224514i	0.0573830	+	0.0416912i	−0.558724	+	0.829354i	$0.688709\pi$
$30$		0			0
$31$	−2.66312	+	8.19624i	−0.478310	+	1.47209i	0.363130	+	0.931738i	$0.381708\pi$
$31$	−2.66312	+	8.19624i	−0.478310	+	1.47209i	−0.841441	+	0.540349i	$0.818292\pi$
$32$		0			0
$33$	2.80902	+	1.76336i	0.488987	+	0.306961i
$34$		0			0
$35$	−4.07295	+	12.5352i	−0.688454	+	2.11884i
$36$		0			0
$37$	−1.23607	−	0.898056i	−0.203208	−	0.147639i	0.481527	−	0.876431i	$-0.340082\pi$
$37$	−1.23607	−	0.898056i	−0.203208	−	0.147639i	−0.684735	+	0.728792i	$0.740082\pi$
$38$		0			0
$39$	−1.00000	−	3.07768i	−0.160128	−	0.492824i
$40$		0			0
$41$	2.61803	−	1.90211i	0.408868	−	0.297060i	−0.364275	−	0.931291i	$-0.618683\pi$
$41$	2.61803	−	1.90211i	0.408868	−	0.297060i	0.773143	+	0.634231i	$0.218683\pi$
$42$		0			0
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$		0			0
$45$	2.85410			0.425464
$46$		0			0
$47$	2.00000	−	1.45309i	0.291730	−	0.211954i	−0.432288	−	0.901736i	$-0.642293\pi$
$47$	2.00000	−	1.45309i	0.291730	−	0.211954i	0.724018	+	0.689782i	$0.242293\pi$
$48$		0			0
$49$	4.42705	+	13.6251i	0.632436	+	1.94644i
$50$		0			0
$51$	2.00000	+	1.45309i	0.280056	+	0.203473i
$52$		0			0
$53$	−1.19098	+	3.66547i	−0.163594	+	0.503491i	−0.998930	−	0.0462491i	$-0.985273\pi$
$53$	−1.19098	+	3.66547i	−0.163594	+	0.503491i	0.835336	+	0.549740i	$0.185273\pi$
$54$		0			0
$55$	7.26393	−	6.06961i	0.979468	−	0.818426i
$56$		0			0
$57$	1.00000	−	3.07768i	0.132453	−	0.407649i
$58$		0			0
$59$	−3.11803	−	2.26538i	−0.405933	−	0.294928i	0.366020	−	0.930607i	$-0.380720\pi$
$59$	−3.11803	−	2.26538i	−0.405933	−	0.294928i	−0.771953	+	0.635679i	$0.780720\pi$
$60$		0			0
$61$	−2.09017	−	6.43288i	−0.267619	−	0.823646i	−0.991078	−	0.133279i	$-0.957449\pi$
$61$	−2.09017	−	6.43288i	−0.267619	−	0.823646i	0.723460	−	0.690367i	$-0.242551\pi$
$62$		0			0
$63$	3.73607	−	2.71441i	0.470700	−	0.341984i
$64$		0			0
$65$	−9.23607			−1.14559
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	−2.61803	+	1.90211i	−0.315174	+	0.228988i
$70$		0			0
$71$	−3.85410	−	11.8617i	−0.457398	−	1.40773i	−0.868297	−	0.496045i	$-0.834785\pi$
$71$	−3.85410	−	11.8617i	−0.457398	−	1.40773i	0.410899	−	0.911681i	$-0.365215\pi$
$72$		0			0
$73$	9.16312	+	6.65740i	1.07246	+	0.779189i	0.976353	−	0.216182i	$-0.0693603\pi$
$73$	9.16312	+	6.65740i	1.07246	+	0.779189i	0.0961088	+	0.995371i	$0.469360\pi$
$74$		0			0
$75$	0.972136	−	2.99193i	0.112253	−	0.345478i
$76$		0			0
$77$	3.73607	−	14.8536i	0.425764	−	1.69273i
$78$		0			0
$79$	2.88197	−	8.86978i	0.324247	−	0.997928i	−0.647533	−	0.762037i	$-0.724199\pi$
$79$	2.88197	−	8.86978i	0.324247	−	0.997928i	0.971780	−	0.235891i	$-0.0758008\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	0.208204	+	0.640786i	0.0228534	+	0.0703354i	0.961833	−	0.273638i	$-0.0882270\pi$
$83$	0.208204	+	0.640786i	0.0228534	+	0.0703354i	−0.938979	+	0.343973i	$0.888227\pi$
$84$		0			0
$85$	5.70820	−	4.14725i	0.619142	−	0.449833i
$86$		0			0
$87$	−0.381966			−0.0409511
$88$		0			0
$89$	−11.7082			−1.24107			−0.620534	−	0.784180i	$-0.713084\pi$
$89$	−11.7082			−1.24107			−0.620534	+	0.784180i	$0.713084\pi$
$90$		0			0
$91$	−12.0902	+	8.78402i	−1.26739	+	0.920816i
$92$		0			0
$93$	−2.66312	−	8.19624i	−0.276153	−	0.849910i
$94$		0			0
$95$	−7.47214	−	5.42882i	−0.766625	−	0.556986i
$96$		0			0
$97$	3.50000	−	10.7719i	0.355371	−	1.09372i	−0.600423	−	0.799683i	$-0.705001\pi$
$97$	3.50000	−	10.7719i	0.355371	−	1.09372i	0.955794	−	0.294037i	$-0.0949990\pi$
$98$		0			0
$99$	−3.30902	+	0.224514i	−0.332569	+	0.0225645i
$100$		0			0
$101$	−3.82624	+	11.7759i	−0.380725	+	1.17175i	0.558809	+	0.829296i	$0.311258\pi$
$101$	−3.82624	+	11.7759i	−0.380725	+	1.17175i	−0.939534	+	0.342455i	$0.888742\pi$
$102$		0			0
$103$	9.73607	+	7.07367i	0.959323	+	0.696989i	0.952993	−	0.302991i	$-0.0979851\pi$
$103$	9.73607	+	7.07367i	0.959323	+	0.696989i	0.00632980	+	0.999980i	$0.497985\pi$
$104$		0			0
$105$	−4.07295	−	12.5352i	−0.397479	−	1.22331i
$106$		0			0
$107$	4.35410	−	3.16344i	0.420927	−	0.305821i	−0.357084	−	0.934072i	$-0.616229\pi$
$107$	4.35410	−	3.16344i	0.420927	−	0.305821i	0.778011	+	0.628251i	$0.216229\pi$
$108$		0			0
$109$	17.4164			1.66819			0.834095	−	0.551621i	$-0.185991\pi$
$109$	17.4164			1.66819			0.834095	+	0.551621i	$0.185991\pi$
$110$		0			0
$111$	1.52786			0.145018
$112$		0			0
$113$	10.0902	−	7.33094i	0.949203	−	0.689637i	−0.00141497	−	0.999999i	$-0.500450\pi$
$113$	10.0902	−	7.33094i	0.949203	−	0.689637i	0.950618	+	0.310362i	$0.100450\pi$
$114$		0			0
$115$	2.85410	+	8.78402i	0.266146	+	0.819114i
$116$		0			0
$117$	2.61803	+	1.90211i	0.242037	+	0.175850i
$118$		0			0
$119$	3.52786	−	10.8576i	0.323399	−	0.995319i
$120$		0			0
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$		0			0
$123$	−1.00000	+	3.07768i	−0.0901670	+	0.277505i
$124$		0			0
$125$	4.28115	+	3.11044i	0.382918	+	0.278206i
$126$		0			0
$127$	−3.70820	−	11.4127i	−0.329050	−	1.01271i	−0.969579	−	0.244778i	$-0.921285\pi$
$127$	−3.70820	−	11.4127i	−0.329050	−	1.01271i	0.640529	−	0.767934i	$-0.278715\pi$
$128$		0			0
$129$	−2.61803	+	1.90211i	−0.230505	+	0.167472i
$130$		0			0
$131$	15.2705			1.33419			0.667095	−	0.744972i	$-0.267537\pi$
$131$	15.2705			1.33419			0.667095	+	0.744972i	$0.267537\pi$
$132$		0			0
$133$	−14.9443			−1.29583
$134$		0			0
$135$	−2.30902	+	1.67760i	−0.198729	+	0.144385i
$136$		0			0
$137$	−7.14590	−	21.9928i	−0.610515	−	1.87897i	−0.453156	−	0.891431i	$-0.649702\pi$
$137$	−7.14590	−	21.9928i	−0.610515	−	1.87897i	−0.157360	−	0.987541i	$-0.550298\pi$
$138$		0			0
$139$	10.7082	+	7.77997i	0.908258	+	0.659888i	0.940574	−	0.339590i	$-0.110288\pi$
$139$	10.7082	+	7.77997i	0.908258	+	0.659888i	−0.0323157	+	0.999478i	$0.510288\pi$
$140$		0			0
$141$	−0.763932	+	2.35114i	−0.0643347	+	0.198002i
$142$		0			0
$143$	10.7082	−	0.726543i	0.895465	−	0.0607565i
$144$		0			0
$145$	−0.336881	+	1.03681i	−0.0279764	+	0.0861027i
$146$		0			0
$147$	−11.5902	−	8.42075i	−0.955941	−	0.694532i
$148$		0			0
$149$	0.427051	+	1.31433i	0.0349854	+	0.107674i	0.967024	−	0.254685i	$-0.0819716\pi$
$149$	0.427051	+	1.31433i	0.0349854	+	0.107674i	−0.932039	+	0.362358i	$0.881972\pi$
$150$		0			0
$151$	7.54508	−	5.48183i	0.614010	−	0.446105i	−0.236814	−	0.971555i	$-0.576103\pi$
$151$	7.54508	−	5.48183i	0.614010	−	0.446105i	0.850824	+	0.525450i	$0.176103\pi$
$152$		0			0
$153$	−2.47214			−0.199860
$154$		0			0
$155$	−24.5967			−1.97566
$156$		0			0
$157$	−3.61803	+	2.62866i	−0.288751	+	0.209790i	−0.722725	−	0.691136i	$-0.757111\pi$
$157$	−3.61803	+	2.62866i	−0.288751	+	0.209790i	0.433975	+	0.900925i	$0.357111\pi$
$158$		0			0
$159$	−1.19098	−	3.66547i	−0.0944511	−	0.290691i
$160$		0			0
$161$	12.0902	+	8.78402i	0.952839	+	0.692278i
$162$		0			0
$163$	4.14590	−	12.7598i	0.324732	−	0.999422i	−0.646830	−	0.762634i	$-0.723906\pi$
$163$	4.14590	−	12.7598i	0.324732	−	0.999422i	0.971562	−	0.236787i	$-0.0760944\pi$
$164$		0			0
$165$	−2.30902	+	9.18005i	−0.179757	+	0.714666i
$166$		0			0
$167$	−2.23607	+	6.88191i	−0.173032	+	0.532538i	−0.999538	−	0.0303898i	$-0.990325\pi$
$167$	−2.23607	+	6.88191i	−0.173032	+	0.532538i	0.826506	+	0.562928i	$0.190325\pi$
$168$		0			0
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$		0			0
$171$	1.00000	+	3.07768i	0.0764719	+	0.235356i
$172$		0			0
$173$	3.35410	−	2.43690i	0.255008	−	0.185274i	−0.452936	−	0.891543i	$-0.649623\pi$
$173$	3.35410	−	2.43690i	0.255008	−	0.185274i	0.707943	+	0.706269i	$0.249623\pi$
$174$		0			0
$175$	−14.5279			−1.09820
$176$		0			0
$177$	3.85410			0.289692
$178$		0			0
$179$	−5.16312	+	3.75123i	−0.385910	+	0.280380i	−0.763777	−	0.645480i	$-0.776657\pi$
$179$	−5.16312	+	3.75123i	−0.385910	+	0.280380i	0.377868	+	0.925860i	$0.376657\pi$
$180$		0			0
$181$	−5.09017	−	15.6659i	−0.378349	−	1.16444i	−0.941191	−	0.337875i	$-0.890292\pi$
$181$	−5.09017	−	15.6659i	−0.378349	−	1.16444i	0.562842	−	0.826565i	$-0.309708\pi$
$182$		0			0
$183$	5.47214	+	3.97574i	0.404512	+	0.293895i
$184$		0			0
$185$	1.34752	−	4.14725i	0.0990719	−	0.304912i
$186$		0			0
$187$	−6.29180	+	5.25731i	−0.460102	+	0.384453i
$188$		0			0
$189$	−1.42705	+	4.39201i	−0.103803	+	0.319472i
$190$		0			0
$191$	18.1803	+	13.2088i	1.31548	+	0.955755i	0.999977	+	0.00683111i	$0.00217443\pi$
$191$	18.1803	+	13.2088i	1.31548	+	0.955755i	0.315507	+	0.948923i	$0.397826\pi$
$192$		0			0
$193$	0.100813	+	0.310271i	0.00725668	+	0.0223338i	0.954619	−	0.297829i	$-0.0962625\pi$
$193$	0.100813	+	0.310271i	0.00725668	+	0.0223338i	−0.947363	+	0.320163i	$0.896262\pi$
$194$		0			0
$195$	7.47214	−	5.42882i	0.535091	−	0.388766i
$196$		0			0
$197$	6.09017			0.433907			0.216953	−	0.976182i	$-0.430388\pi$
$197$	6.09017			0.433907			0.216953	+	0.976182i	$0.430388\pi$
$198$		0			0
$199$	−13.1459			−0.931888			−0.465944	−	0.884814i	$-0.654285\pi$
$199$	−13.1459			−0.931888			−0.465944	+	0.884814i	$0.654285\pi$
$200$		0			0
$201$	3.23607	−	2.35114i	0.228255	−	0.165837i
$202$		0			0
$203$	0.545085	+	1.67760i	0.0382575	+	0.117744i
$204$		0			0
$205$	7.47214	+	5.42882i	0.521877	+	0.379166i
$206$		0			0
$207$	1.00000	−	3.07768i	0.0695048	−	0.213914i
$208$		0			0
$209$	9.09017	+	5.70634i	0.628780	+	0.394716i
$210$		0			0
$211$	1.43769	−	4.42477i	0.0989749	−	0.304614i	−0.889294	−	0.457335i	$-0.848804\pi$
$211$	1.43769	−	4.42477i	0.0989749	−	0.304614i	0.988269	+	0.152722i	$0.0488039\pi$
$212$		0			0
$213$	10.0902	+	7.33094i	0.691367	+	0.502308i
$214$		0			0
$215$	2.85410	+	8.78402i	0.194648	+	0.599065i
$216$		0			0
$217$	−32.1976	+	23.3929i	−2.18571	+	1.58801i
$218$		0			0
$219$	−11.3262			−0.765356
$220$		0			0
$221$	8.00000			0.538138
$222$		0			0
$223$	−1.54508	+	1.12257i	−0.103467	+	0.0751728i	−0.638316	−	0.769775i	$-0.720368\pi$
$223$	−1.54508	+	1.12257i	−0.103467	+	0.0751728i	0.534849	+	0.844948i	$0.320368\pi$
$224$		0			0
$225$	0.972136	+	2.99193i	0.0648091	+	0.199462i
$226$		0			0
$227$	−5.78115	−	4.20025i	−0.383709	−	0.278781i	0.379164	−	0.925330i	$-0.376212\pi$
$227$	−5.78115	−	4.20025i	−0.383709	−	0.278781i	−0.762873	+	0.646549i	$0.776212\pi$
$228$		0			0
$229$	7.09017	−	21.8213i	0.468532	−	1.44199i	−0.385954	−	0.922518i	$-0.626128\pi$
$229$	7.09017	−	21.8213i	0.468532	−	1.44199i	0.854486	−	0.519474i	$-0.173872\pi$
$230$		0			0
$231$	5.70820	+	14.2128i	0.375572	+	0.935137i
$232$		0			0
$233$	−2.76393	+	8.50651i	−0.181071	+	0.557280i	−0.999859	−	0.0168170i	$-0.994647\pi$
$233$	−2.76393	+	8.50651i	−0.181071	+	0.557280i	0.818787	+	0.574097i	$0.194647\pi$
$234$		0			0
$235$	5.70820	+	4.14725i	0.372362	+	0.270537i
$236$		0			0
$237$	2.88197	+	8.86978i	0.187204	+	0.576154i
$238$		0			0
$239$	−13.3262	+	9.68208i	−0.862003	+	0.626282i	−0.928429	−	0.371510i	$-0.878840\pi$
$239$	−13.3262	+	9.68208i	−0.862003	+	0.626282i	0.0664264	+	0.997791i	$0.478840\pi$
$240$		0			0
$241$	−2.43769			−0.157026			−0.0785128	−	0.996913i	$-0.525017\pi$
$241$	−2.43769			−0.157026			−0.0785128	+	0.996913i	$0.525017\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−33.0795	+	24.0337i	−2.11337	+	1.53546i
$246$		0			0
$247$	−3.23607	−	9.95959i	−0.205906	−	0.633714i
$248$		0			0
$249$	−0.545085	−	0.396027i	−0.0345434	−	0.0250972i
$250$		0			0
$251$	5.97214	−	18.3803i	0.376958	−	1.16016i	−0.565190	−	0.824961i	$-0.691197\pi$
$251$	5.97214	−	18.3803i	0.376958	−	1.16016i	0.942148	−	0.335197i	$-0.108803\pi$
$252$		0			0
$253$	−4.00000	−	9.95959i	−0.251478	−	0.626154i
$254$		0			0
$255$	−2.18034	+	6.71040i	−0.136538	+	0.420221i
$256$		0			0
$257$	1.47214	+	1.06957i	0.0918293	+	0.0667179i	0.632753	−	0.774354i	$-0.281925\pi$
$257$	1.47214	+	1.06957i	0.0918293	+	0.0667179i	−0.540923	+	0.841072i	$0.681925\pi$
$258$		0			0
$259$	−2.18034	−	6.71040i	−0.135480	−	0.416964i
$260$		0			0
$261$	0.309017	−	0.224514i	0.0191277	−	0.0138971i
$262$		0			0
$263$	−7.70820			−0.475308			−0.237654	−	0.971350i	$-0.576378\pi$
$263$	−7.70820			−0.475308			−0.237654	+	0.971350i	$0.576378\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$		0			0
$267$	9.47214	−	6.88191i	0.579685	−	0.421166i
$268$		0			0
$269$	−0.909830	−	2.80017i	−0.0554733	−	0.170729i	0.919481	−	0.393134i	$-0.128609\pi$
$269$	−0.909830	−	2.80017i	−0.0554733	−	0.170729i	−0.974954	+	0.222405i	$0.928609\pi$
$270$		0			0
$271$	18.9443	+	13.7638i	1.15078	+	0.836092i	0.988585	−	0.150666i	$-0.0481417\pi$
$271$	18.9443	+	13.7638i	1.15078	+	0.836092i	0.162198	+	0.986758i	$0.448142\pi$
$272$		0			0
$273$	4.61803	−	14.2128i	0.279496	−	0.860201i
$274$		0			0
$275$	8.83688	+	5.54734i	0.532884	+	0.334517i
$276$		0			0
$277$	3.43769	−	10.5801i	0.206551	−	0.635699i	−0.793095	−	0.609098i	$-0.791532\pi$
$277$	3.43769	−	10.5801i	0.206551	−	0.635699i	0.999646	−	0.0266009i	$-0.00846832\pi$
$278$		0			0
$279$	6.97214	+	5.06555i	0.417411	+	0.303267i
$280$		0			0
$281$	7.14590	+	21.9928i	0.426289	+	1.31198i	0.901755	+	0.432247i	$0.142279\pi$
$281$	7.14590	+	21.9928i	0.426289	+	1.31198i	−0.475467	+	0.879734i	$0.657721\pi$
$282$		0			0
$283$	−19.3262	+	14.0413i	−1.14883	+	0.834671i	−0.988324	−	0.152365i	$-0.951311\pi$
$283$	−19.3262	+	14.0413i	−1.14883	+	0.834671i	−0.160501	+	0.987036i	$0.551311\pi$
$284$		0			0
$285$	9.23607			0.547097
$286$		0			0
$287$	14.9443			0.882132
$288$		0			0
$289$	8.80902	−	6.40013i	0.518177	−	0.376478i
$290$		0			0
$291$	3.50000	+	10.7719i	0.205174	+	0.631460i
$292$		0			0
$293$	−18.5902	−	13.5065i	−1.08605	−	0.789061i	−0.107322	−	0.994224i	$-0.534227\pi$
$293$	−18.5902	−	13.5065i	−1.08605	−	0.789061i	−0.978728	+	0.205163i	$0.934227\pi$
$294$		0			0
$295$	3.39919	−	10.4616i	0.197908	−	0.609099i
$296$		0			0
$297$	2.54508	−	2.12663i	0.147681	−	0.123399i
$298$		0			0
$299$	−3.23607	+	9.95959i	−0.187147	+	0.575978i
$300$		0			0
$301$	12.0902	+	8.78402i	0.696866	+	0.506303i
$302$		0			0
$303$	−3.82624	−	11.7759i	−0.219812	−	0.676511i
$304$		0			0
$305$	15.6180	−	11.3472i	0.894286	−	0.649737i
$306$		0			0
$307$	16.6525			0.950407			0.475203	−	0.879876i	$-0.342374\pi$
$307$	16.6525			0.950407			0.475203	+	0.879876i	$0.342374\pi$
$308$		0			0
$309$	−12.0344			−0.684615
$310$		0			0
$311$	−19.3262	+	14.0413i	−1.09589	+	0.796211i	−0.980384	−	0.197096i	$-0.936849\pi$
$311$	−19.3262	+	14.0413i	−1.09589	+	0.796211i	−0.115506	+	0.993307i	$0.536849\pi$
$312$		0			0
$313$	4.68034	+	14.4046i	0.264548	+	0.814196i	0.991797	+	0.127822i	$0.0407987\pi$
$313$	4.68034	+	14.4046i	0.264548	+	0.814196i	−0.727249	+	0.686374i	$0.759201\pi$
$314$		0			0
$315$	10.6631	+	7.74721i	0.600799	+	0.436506i
$316$		0			0
$317$	−6.14590	+	18.9151i	−0.345188	+	1.06238i	0.616295	+	0.787515i	$0.288633\pi$
$317$	−6.14590	+	18.9151i	−0.345188	+	1.06238i	−0.961483	+	0.274864i	$0.911367\pi$
$318$		0			0
$319$	0.309017	−	1.22857i	0.0173016	−	0.0687868i
$320$		0			0
$321$	−1.66312	+	5.11855i	−0.0928262	+	0.285690i
$322$		0			0
$323$	6.47214	+	4.70228i	0.360119	+	0.261642i
$324$		0			0
$325$	−3.14590	−	9.68208i	−0.174503	−	0.537065i
$326$		0			0
$327$	−14.0902	+	10.2371i	−0.779188	+	0.566113i
$328$		0			0
$329$	11.4164			0.629407
$330$		0			0
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$		0			0
$333$	−1.23607	+	0.898056i	−0.0677361	+	0.0492132i
$334$		0			0
$335$	−3.52786	−	10.8576i	−0.192748	−	0.593217i
$336$		0			0
$337$	−5.61803	−	4.08174i	−0.306034	−	0.222347i	0.424159	−	0.905588i	$-0.360570\pi$
$337$	−5.61803	−	4.08174i	−0.306034	−	0.222347i	−0.730193	+	0.683241i	$0.760570\pi$
$338$		0			0
$339$	−3.85410	+	11.8617i	−0.209326	+	0.644239i
$340$		0			0
$341$	28.5172	−	1.93487i	1.54429	−	0.104779i
$342$		0			0
$343$	−10.4549	+	32.1769i	−0.564512	+	1.73739i
$344$		0			0
$345$	−7.47214	−	5.42882i	−0.402286	−	0.292278i
$346$		0			0
$347$	−3.66312	−	11.2739i	−0.196647	−	0.605216i	−0.999953	−	0.00965049i	$-0.996928\pi$
$347$	−3.66312	−	11.2739i	−0.196647	−	0.605216i	0.803307	−	0.595565i	$-0.203072\pi$
$348$		0			0
$349$	10.7082	−	7.77997i	0.573197	−	0.416452i	−0.263068	−	0.964777i	$-0.584734\pi$
$349$	10.7082	−	7.77997i	0.573197	−	0.416452i	0.836265	+	0.548325i	$0.184734\pi$
$350$		0			0
$351$	−3.23607			−0.172729
$352$		0			0
$353$	−21.5967			−1.14948			−0.574739	−	0.818336i	$-0.694897\pi$
$353$	−21.5967			−1.14948			−0.574739	+	0.818336i	$0.694897\pi$
$354$		0			0
$355$	28.7984	−	20.9232i	1.52846	−	1.11049i
$356$		0			0
$357$	3.52786	+	10.8576i	0.186714	+	0.574648i
$358$		0			0
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	0.825938	−	0.563761i	$-0.190646\pi$
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	−0.280940	+	0.959725i	$0.590646\pi$
$360$		0			0
$361$	−2.63525	+	8.11048i	−0.138698	+	0.426867i
$362$		0			0
$363$	1.95492	−	10.8249i	0.102606	−	0.568160i
$364$		0			0
$365$	−9.98936	+	30.7441i	−0.522867	+	1.60922i
$366$		0			0
$367$	−30.3435	−	22.0458i	−1.58392	−	1.15078i	−0.912027	−	0.410130i	$-0.865483\pi$
$367$	−30.3435	−	22.0458i	−1.58392	−	1.15078i	−0.671888	−	0.740652i	$-0.734517\pi$
$368$		0			0
$369$	−1.00000	−	3.07768i	−0.0520579	−	0.160218i
$370$		0			0
$371$	−14.3992	+	10.4616i	−0.747569	+	0.543140i
$372$		0			0
$373$	−9.52786			−0.493334			−0.246667	−	0.969100i	$-0.579335\pi$
$373$	−9.52786			−0.493334			−0.246667	+	0.969100i	$0.579335\pi$
$374$		0			0
$375$	−5.29180			−0.273267
$376$		0			0
$377$	−1.00000	+	0.726543i	−0.0515026	+	0.0374188i
$378$		0			0
$379$	−1.14590	−	3.52671i	−0.0588608	−	0.181155i	0.917303	−	0.398190i	$-0.130361\pi$
$379$	−1.14590	−	3.52671i	−0.0588608	−	0.181155i	−0.976164	+	0.217035i	$0.930361\pi$
$380$		0			0
$381$	9.70820	+	7.05342i	0.497366	+	0.361358i
$382$		0			0
$383$	−4.09017	+	12.5882i	−0.208998	+	0.643229i	0.790528	+	0.612426i	$0.209806\pi$
$383$	−4.09017	+	12.5882i	−0.208998	+	0.643229i	−0.999525	+	0.0308030i	$0.990194\pi$
$384$		0			0
$385$	43.6140	−	2.95917i	2.22277	−	0.150813i
$386$		0			0
$387$	1.00000	−	3.07768i	0.0508329	−	0.156447i
$388$		0			0
$389$	−31.5066	−	22.8909i	−1.59745	−	1.16061i	−0.892189	−	0.451662i	$-0.850831\pi$
$389$	−31.5066	−	22.8909i	−1.59745	−	1.16061i	−0.705258	−	0.708951i	$-0.749169\pi$
$390$		0			0
$391$	−2.47214	−	7.60845i	−0.125021	−	0.384776i
$392$		0			0
$393$	−12.3541	+	8.97578i	−0.623182	+	0.452768i
$394$		0			0
$395$	26.6180			1.33930
$396$		0			0
$397$	9.88854			0.496292			0.248146	−	0.968723i	$-0.420179\pi$
$397$	9.88854			0.496292			0.248146	+	0.968723i	$0.420179\pi$
$398$		0			0
$399$	12.0902	−	8.78402i	0.605266	−	0.439751i
$400$		0			0
$401$	3.18034	+	9.78808i	0.158819	+	0.488793i	0.998528	−	0.0542430i	$-0.0172746\pi$
$401$	3.18034	+	9.78808i	0.158819	+	0.488793i	−0.839709	+	0.543036i	$0.817275\pi$
$402$		0			0
$403$	−22.5623	−	16.3925i	−1.12391	−	0.816567i
$404$		0			0
$405$	0.881966	−	2.71441i	0.0438252	−	0.134880i
$406$		0			0
$407$	−1.23607	+	4.91428i	−0.0612696	+	0.243592i
$408$		0			0
$409$	−3.73607	+	11.4984i	−0.184737	+	0.568561i	−0.999944	−	0.0106086i	$-0.996623\pi$
$409$	−3.73607	+	11.4984i	−0.184737	+	0.568561i	0.815207	+	0.579170i	$0.196623\pi$
$410$		0			0
$411$	18.7082	+	13.5923i	0.922808	+	0.670459i
$412$		0			0
$413$	−5.50000	−	16.9273i	−0.270637	−	0.832936i
$414$		0			0
$415$	−1.55573	+	1.13030i	−0.0763677	+	0.0554844i
$416$		0			0
$417$	−13.2361			−0.648173
$418$		0			0
$419$	17.9787			0.878318			0.439159	−	0.898409i	$-0.355277\pi$
$419$	17.9787			0.878318			0.439159	+	0.898409i	$0.355277\pi$
$420$		0			0
$421$	−28.4164	+	20.6457i	−1.38493	+	1.00621i	−0.388531	+	0.921436i	$0.627017\pi$
$421$	−28.4164	+	20.6457i	−1.38493	+	1.00621i	−0.996400	+	0.0847756i	$0.972983\pi$
$422$		0			0
$423$	−0.763932	−	2.35114i	−0.0371436	−	0.114316i
$424$		0			0
$425$	6.29180	+	4.57126i	0.305197	+	0.221739i
$426$		0			0
$427$	9.65248	−	29.7073i	0.467116	−	1.43764i
$428$		0			0
$429$	−8.23607	+	6.88191i	−0.397641	+	0.332262i
$430$		0			0
$431$	2.23607	−	6.88191i	0.107708	−	0.331490i	−0.882649	−	0.470033i	$-0.844242\pi$
$431$	2.23607	−	6.88191i	0.107708	−	0.331490i	0.990356	+	0.138543i	$0.0442420\pi$
$432$		0			0
$433$	−9.97214	−	7.24518i	−0.479230	−	0.348181i	0.321797	−	0.946809i	$-0.395713\pi$
$433$	−9.97214	−	7.24518i	−0.479230	−	0.348181i	−0.801028	+	0.598627i	$0.795713\pi$
$434$		0			0
$435$	−0.336881	−	1.03681i	−0.0161522	−	0.0497114i
$436$		0			0
$437$	−8.47214	+	6.15537i	−0.405277	+	0.294451i
$438$		0			0
$439$	−16.0344			−0.765282			−0.382641	−	0.923897i	$-0.624985\pi$
$439$	−16.0344			−0.765282			−0.382641	+	0.923897i	$0.624985\pi$
$440$		0			0
$441$	14.3262			0.682202
$442$		0			0
$443$	−1.35410	+	0.983813i	−0.0643353	+	0.0467424i	−0.619488	−	0.785006i	$-0.712660\pi$
$443$	−1.35410	+	0.983813i	−0.0643353	+	0.0467424i	0.555153	+	0.831748i	$0.312660\pi$
$444$		0			0
$445$	−10.3262	−	31.7809i	−0.489511	−	1.50656i
$446$		0			0
$447$	−1.11803	−	0.812299i	−0.0528812	−	0.0384204i
$448$		0			0
$449$	11.0902	−	34.1320i	0.523377	−	1.61079i	−0.244125	−	0.969744i	$-0.578501\pi$
$449$	11.0902	−	34.1320i	0.523377	−	1.61079i	0.767502	−	0.641046i	$-0.221499\pi$
$450$		0			0
$451$	−9.09017	−	5.70634i	−0.428039	−	0.268701i
$452$		0			0
$453$	−2.88197	+	8.86978i	−0.135407	+	0.416739i
$454$		0			0
$455$	−34.5066	−	25.0705i	−1.61769	−	1.17532i
$456$		0			0
$457$	−6.79180	−	20.9030i	−0.317707	−	0.977801i	−0.974626	−	0.223840i	$-0.928141\pi$
$457$	−6.79180	−	20.9030i	−0.317707	−	0.977801i	0.656919	−	0.753961i	$-0.271859\pi$
$458$		0			0
$459$	2.00000	−	1.45309i	0.0933520	−	0.0678242i
$460$		0			0
$461$	40.8328			1.90177			0.950887	−	0.309538i	$-0.100175\pi$
$461$	40.8328			1.90177			0.950887	+	0.309538i	$0.100175\pi$
$462$		0			0
$463$	−19.0902			−0.887195			−0.443598	−	0.896226i	$-0.646298\pi$
$463$	−19.0902			−0.887195			−0.443598	+	0.896226i	$0.646298\pi$
$464$		0			0
$465$	19.8992	−	14.4576i	0.922803	−	0.670455i
$466$		0			0
$467$	−6.04508	−	18.6049i	−0.279733	−	0.860930i	−0.987928	−	0.154913i	$-0.950490\pi$
$467$	−6.04508	−	18.6049i	−0.279733	−	0.860930i	0.708195	−	0.706017i	$-0.249510\pi$
$468$		0			0
$469$	−14.9443	−	10.8576i	−0.690062	−	0.501360i
$470$		0			0
$471$	1.38197	−	4.25325i	0.0636776	−	0.195980i
$472$		0			0
$473$	−4.00000	−	9.95959i	−0.183920	−	0.457943i
$474$		0			0
$475$	3.14590	−	9.68208i	0.144344	−	0.444244i
$476$		0			0
$477$	3.11803	+	2.26538i	0.142765	+	0.103725i
$478$		0			0
$479$	2.23607	+	6.88191i	0.102169	+	0.314442i	0.989055	−	0.147544i	$-0.0471368\pi$
$479$	2.23607	+	6.88191i	0.102169	+	0.314442i	−0.886887	+	0.461987i	$0.847137\pi$
$480$		0			0
$481$	4.00000	−	2.90617i	0.182384	−	0.132510i
$482$		0			0
$483$	−14.9443			−0.679988
$484$		0			0
$485$	32.3262			1.46786
$486$		0			0
$487$	20.2082	−	14.6821i	0.915721	−	0.665310i	−0.0267342	−	0.999643i	$-0.508511\pi$
$487$	20.2082	−	14.6821i	0.915721	−	0.665310i	0.942455	+	0.334332i	$0.108511\pi$
$488$		0			0
$489$	4.14590	+	12.7598i	0.187484	+	0.577016i
$490$		0			0
$491$	34.1803	+	24.8335i	1.54254	+	1.12072i	0.948719	+	0.316119i	$0.102380\pi$
$491$	34.1803	+	24.8335i	1.54254	+	1.12072i	0.593818	+	0.804600i	$0.297620\pi$
$492$		0			0
$493$	0.291796	−	0.898056i	0.0131418	−	0.0404464i
$494$		0			0
$495$	−3.52786	−	8.78402i	−0.158566	−	0.394812i
$496$		0			0
$497$	17.7984	−	54.7778i	0.798366	−	2.45712i
$498$		0			0
$499$	−6.00000	−	4.35926i	−0.268597	−	0.195147i	0.445332	−	0.895366i	$-0.353086\pi$
$499$	−6.00000	−	4.35926i	−0.268597	−	0.195147i	−0.713928	+	0.700219i	$0.753086\pi$
$500$		0			0
$501$	−2.23607	−	6.88191i	−0.0999001	−	0.307461i
$502$		0			0
$503$	3.52786	−	2.56314i	0.157300	−	0.114285i	−0.506351	−	0.862327i	$-0.669006\pi$
$503$	3.52786	−	2.56314i	0.157300	−	0.114285i	0.663651	+	0.748042i	$0.269006\pi$
$504$		0			0
$505$	−35.3394			−1.57258
$506$		0			0
$507$	−2.52786			−0.112266
$508$		0			0
$509$	−2.59017	+	1.88187i	−0.114807	+	0.0834124i	−0.643707	−	0.765272i	$-0.722605\pi$
$509$	−2.59017	+	1.88187i	−0.114807	+	0.0834124i	0.528900	+	0.848684i	$0.322605\pi$
$510$		0			0
$511$	16.1631	+	49.7450i	0.715014	+	2.20059i
$512$		0			0
$513$	−2.61803	−	1.90211i	−0.115589	−	0.0839803i
$514$		0			0
$515$	−10.6140	+	32.6664i	−0.467707	+	1.43946i
$516$		0			0
$517$	−6.94427	−	4.35926i	−0.305409	−	0.191720i
$518$		0			0
$519$	−1.28115	+	3.94298i	−0.0562364	+	0.173078i
$520$		0			0
$521$	−25.4164	−	18.4661i	−1.11351	−	0.809015i	−0.130300	−	0.991475i	$-0.541594\pi$
$521$	−25.4164	−	18.4661i	−1.11351	−	0.809015i	−0.983213	+	0.182460i	$0.941594\pi$
$522$		0			0
$523$	−6.05573	−	18.6376i	−0.264799	−	0.814966i	−0.991740	−	0.128266i	$-0.959059\pi$
$523$	−6.05573	−	18.6376i	−0.264799	−	0.814966i	0.726941	−	0.686700i	$-0.240941\pi$
$524$		0			0
$525$	11.7533	−	8.53926i	0.512956	−	0.372684i
$526$		0			0
$527$	21.3050			0.928058
$528$		0			0
$529$	−12.5279			−0.544690
$530$		0			0
$531$	−3.11803	+	2.26538i	−0.135311	+	0.0983093i
$532$		0			0
$533$	3.23607	+	9.95959i	0.140170	+	0.431398i
$534$		0			0
$535$	12.4271	+	9.02878i	0.537268	+	0.390348i
$536$		0			0
$537$	1.97214	−	6.06961i	0.0851039	−	0.261923i
$538$		0			0
$539$	36.4615	−	30.4666i	1.57051	−	1.31229i
$540$		0			0
$541$	2.32624	−	7.15942i	0.100013	−	0.307808i	−0.888515	−	0.458848i	$-0.848262\pi$
$541$	2.32624	−	7.15942i	0.100013	−	0.307808i	0.988528	+	0.151040i	$0.0482623\pi$
$542$		0			0
$543$	13.3262	+	9.68208i	0.571884	+	0.415498i
$544$		0			0
$545$	15.3607	+	47.2753i	0.657979	+	2.02505i
$546$		0			0
$547$	14.7082	−	10.6861i	0.628877	−	0.456906i	−0.227134	−	0.973864i	$-0.572935\pi$
$547$	14.7082	−	10.6861i	0.628877	−	0.456906i	0.856011	+	0.516957i	$0.172935\pi$
$548$		0			0
$549$	−6.76393			−0.288678
$550$		0			0
$551$	−1.23607			−0.0526583
$552$		0			0
$553$	34.8435	−	25.3153i	1.48169	−	1.07651i
$554$		0			0
$555$	1.34752	+	4.14725i	0.0571992	+	0.176041i
$556$		0			0
$557$	34.0066	+	24.7072i	1.44090	+	1.04688i	0.987852	+	0.155395i	$0.0496650\pi$
$557$	34.0066	+	24.7072i	1.44090	+	1.04688i	0.453053	+	0.891484i	$0.350335\pi$
$558$		0			0
$559$	−3.23607	+	9.95959i	−0.136871	+	0.421246i
$560$		0			0
$561$	2.00000	−	7.95148i	0.0844401	−	0.335712i
$562$		0			0
$563$	14.4721	−	44.5407i	0.609928	−	1.87716i	0.151433	−	0.988467i	$-0.451611\pi$
$563$	14.4721	−	44.5407i	0.609928	−	1.87716i	0.458494	−	0.888697i	$-0.348389\pi$
$564$		0			0
$565$	28.7984	+	20.9232i	1.21156	+	0.880247i
$566$		0			0
$567$	−1.42705	−	4.39201i	−0.0599305	−	0.184447i
$568$		0			0
$569$	−29.7984	+	21.6498i	−1.24921	+	0.907606i	−0.998176	−	0.0603713i	$-0.980772\pi$
$569$	−29.7984	+	21.6498i	−1.24921	+	0.907606i	−0.251037	+	0.967978i	$0.580772\pi$
$570$		0			0
$571$	−9.59675			−0.401611			−0.200806	−	0.979631i	$-0.564356\pi$
$571$	−9.59675			−0.401611			−0.200806	+	0.979631i	$0.564356\pi$
$572$		0			0
$573$	−22.4721			−0.938787
$574$		0			0
$575$	−8.23607	+	5.98385i	−0.343468	+	0.249544i
$576$		0			0
$577$	2.19098	+	6.74315i	0.0912118	+	0.280721i	0.986248	−	0.165273i	$-0.0528504\pi$
$577$	2.19098	+	6.74315i	0.0912118	+	0.280721i	−0.895036	+	0.445994i	$0.852850\pi$
$578$		0			0
$579$	−0.263932	−	0.191758i	−0.0109686	−	0.00796918i
$580$		0			0
$581$	−0.961493	+	2.95917i	−0.0398894	+	0.122767i
$582$		0			0
$583$	12.7533	−	0.865300i	0.528187	−	0.0358371i
$584$		0			0
$585$	−2.85410	+	8.78402i	−0.118003	+	0.363175i
$586$		0			0
$587$	−19.4894	−	14.1598i	−0.804412	−	0.584439i	0.107793	−	0.994173i	$-0.465622\pi$
$587$	−19.4894	−	14.1598i	−0.804412	−	0.584439i	−0.912205	+	0.409734i	$0.865622\pi$
$588$		0			0
$589$	−8.61803	−	26.5236i	−0.355100	−	1.09289i
$590$		0			0
$591$	−4.92705	+	3.57971i	−0.202672	+	0.147250i
$592$		0			0
$593$	24.4721			1.00495			0.502475	−	0.864592i	$-0.332423\pi$
$593$	24.4721			1.00495			0.502475	+	0.864592i	$0.332423\pi$
$594$		0			0
$595$	32.5836			1.33580
$596$		0			0
$597$	10.6353	−	7.72696i	0.435272	−	0.316244i
$598$		0			0
$599$	−2.58359	−	7.95148i	−0.105563	−	0.324889i	0.884299	−	0.466920i	$-0.154637\pi$
$599$	−2.58359	−	7.95148i	−0.105563	−	0.324889i	−0.989862	+	0.142032i	$0.954637\pi$
$600$		0			0
$601$	19.2082	+	13.9556i	0.783519	+	0.569260i	0.906033	−	0.423207i	$-0.139096\pi$
$601$	19.2082	+	13.9556i	0.783519	+	0.569260i	−0.122514	+	0.992467i	$0.539096\pi$
$602$		0			0
$603$	−1.23607	+	3.80423i	−0.0503366	+	0.154920i
$604$		0			0
$605$	−27.6591	−	14.8536i	−1.12450	−	0.603886i
$606$		0			0
$607$	−7.34752	+	22.6134i	−0.298227	+	0.917848i	0.683892	+	0.729584i	$0.260286\pi$
$607$	−7.34752	+	22.6134i	−0.298227	+	0.917848i	−0.982118	+	0.188264i	$0.939714\pi$
$608$		0			0
$609$	−1.42705	−	1.03681i	−0.0578270	−	0.0420138i
$610$		0			0
$611$	2.47214	+	7.60845i	0.100012	+	0.307805i
$612$		0			0
$613$	11.5623	−	8.40051i	0.466997	−	0.339293i	−0.329273	−	0.944235i	$-0.606804\pi$
$613$	11.5623	−	8.40051i	0.466997	−	0.339293i	0.796270	+	0.604942i	$0.206804\pi$
$614$		0			0
$615$	−9.23607			−0.372434
$616$		0			0
$617$	−30.2918			−1.21950			−0.609751	−	0.792593i	$-0.708731\pi$
$617$	−30.2918			−1.21950			−0.609751	+	0.792593i	$0.708731\pi$
$618$		0			0
$619$	−20.4721	+	14.8739i	−0.822845	+	0.597832i	−0.917526	−	0.397676i	$-0.869817\pi$
$619$	−20.4721	+	14.8739i	−0.822845	+	0.597832i	0.0946813	+	0.995508i	$0.469817\pi$
$620$		0			0
$621$	1.00000	+	3.07768i	0.0401286	+	0.123503i
$622$		0			0
$623$	−43.7426	−	31.7809i	−1.75251	−	1.27327i
$624$		0			0
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$		0			0
$627$	−10.7082	+	0.726543i	−0.427644	+	0.0290153i
$628$		0			0
$629$	−1.16718	+	3.59222i	−0.0465387	+	0.143231i
$630$		0			0
$631$	−13.8713	−	10.0781i	−0.552209	−	0.401203i	0.276390	−	0.961045i	$-0.410862\pi$
$631$	−13.8713	−	10.0781i	−0.552209	−	0.401203i	−0.828599	+	0.559842i	$0.810862\pi$
$632$		0			0
$633$	1.43769	+	4.42477i	0.0571432	+	0.175869i
$634$		0			0
$635$	27.7082	−	20.1312i	1.09957	−	0.798882i
$636$		0			0
$637$	−46.3607			−1.83688
$638$		0			0
$639$	−12.4721			−0.493390
$640$		0			0
$641$	−38.1246	+	27.6992i	−1.50583	+	1.09405i	−0.537847	+	0.843043i	$0.680762\pi$
$641$	−38.1246	+	27.6992i	−1.50583	+	1.09405i	−0.967985	+	0.251008i	$0.919238\pi$
$642$		0			0
$643$	−3.38197	−	10.4086i	−0.133372	−	0.410476i	0.861961	−	0.506974i	$-0.169236\pi$
$643$	−3.38197	−	10.4086i	−0.133372	−	0.410476i	−0.995333	+	0.0964978i	$0.969236\pi$
$644$		0			0
$645$	−7.47214	−	5.42882i	−0.294215	−	0.213760i
$646$		0			0
$647$	0.888544	−	2.73466i	0.0349323	−	0.107510i	−0.932070	−	0.362278i	$-0.881999\pi$
$647$	0.888544	−	2.73466i	0.0349323	−	0.107510i	0.967002	+	0.254768i	$0.0819990\pi$
$648$		0			0
$649$	−3.11803	+	12.3965i	−0.122394	+	0.486605i
$650$		0			0
$651$	12.2984	−	37.8505i	0.482011	−	1.48348i
$652$		0			0
$653$	17.1074	+	12.4292i	0.669464	+	0.486394i	0.869846	−	0.493324i	$-0.164218\pi$
$653$	17.1074	+	12.4292i	0.669464	+	0.486394i	−0.200382	+	0.979718i	$0.564218\pi$
$654$		0			0
$655$	13.4681	+	41.4505i	0.526241	+	1.61960i
$656$		0			0
$657$	9.16312	−	6.65740i	0.357487	−	0.259730i
$658$		0			0
$659$	−43.1459			−1.68073			−0.840363	−	0.542024i	$-0.817658\pi$
$659$	−43.1459			−1.68073			−0.840363	+	0.542024i	$0.817658\pi$
$660$		0			0
$661$	5.81966			0.226359			0.113179	−	0.993575i	$-0.463897\pi$
$661$	5.81966			0.226359			0.113179	+	0.993575i	$0.463897\pi$
$662$		0			0
$663$	−6.47214	+	4.70228i	−0.251357	+	0.182622i
$664$		0			0
$665$	−13.1803	−	40.5649i	−0.511112	−	1.57304i
$666$		0			0
$667$	1.00000	+	0.726543i	0.0387202	+	0.0281318i
$668$		0			0
$669$	0.590170	−	1.81636i	0.0228173	−	0.0702244i
$670$		0			0
$671$	−17.2148	+	14.3844i	−0.664569	+	0.555302i
$672$		0			0
$673$	−2.15248	+	6.62464i	−0.0829718	+	0.255361i	−0.983933	−	0.178539i	$-0.942863\pi$
$673$	−2.15248	+	6.62464i	−0.0829718	+	0.255361i	0.900961	+	0.433900i	$0.142863\pi$
$674$		0			0
$675$	−2.54508	−	1.84911i	−0.0979604	−	0.0711724i
$676$		0			0
$677$	−12.5172	−	38.5240i	−0.481076	−	1.48060i	−0.837585	−	0.546307i	$-0.816033\pi$
$677$	−12.5172	−	38.5240i	−0.481076	−	1.48060i	0.356509	−	0.934292i	$-0.383967\pi$
$678$		0			0
$679$	42.3156	−	30.7441i	1.62392	−	1.17985i
$680$		0			0
$681$	7.14590			0.273831
$682$		0			0
$683$	−45.7426			−1.75029			−0.875147	−	0.483857i	$-0.839235\pi$
$683$	−45.7426			−1.75029			−0.875147	+	0.483857i	$0.839235\pi$
$684$		0			0
$685$	53.3951	−	38.7938i	2.04012	−	1.48224i
$686$		0			0
$687$	7.09017	+	21.8213i	0.270507	+	0.832534i
$688$		0			0
$689$	−10.0902	−	7.33094i	−0.384405	−	0.279286i
$690$		0			0
$691$	0.0901699	−	0.277515i	0.00343023	−	0.0105572i	−0.949327	−	0.314291i	$-0.898233\pi$
$691$	0.0901699	−	0.277515i	0.00343023	−	0.0105572i	0.952757	+	0.303734i	$0.0982333\pi$
$692$		0			0
$693$	−12.9721	−	8.14324i	−0.492771	−	0.309336i
$694$		0			0
$695$	−11.6738	+	35.9281i	−0.442811	+	1.36283i
$696$		0			0
$697$	−6.47214	−	4.70228i	−0.245150	−	0.178112i
$698$		0			0
$699$	−2.76393	−	8.50651i	−0.104542	−	0.321746i
$700$		0			0
$701$	−0.854102	+	0.620541i	−0.0322590	+	0.0234375i	−0.603798	−	0.797137i	$-0.706347\pi$
$701$	−0.854102	+	0.620541i	−0.0322590	+	0.0234375i	0.571539	+	0.820575i	$0.306347\pi$
$702$		0			0
$703$	4.94427			0.186477
$704$		0			0
$705$	−7.05573			−0.265734
$706$		0			0
$707$	−46.2599	+	33.6098i	−1.73978	+	1.26403i
$708$		0			0
$709$	10.8197	+	33.2995i	0.406341	+	1.25059i	0.919770	+	0.392457i	$0.128375\pi$
$709$	10.8197	+	33.2995i	0.406341	+	1.25059i	−0.513430	+	0.858132i	$0.671625\pi$
$710$		0			0
$711$	−7.54508	−	5.48183i	−0.282963	−	0.205585i
$712$		0			0
$713$	−8.61803	+	26.5236i	−0.322748	+	0.993316i
$714$		0			0
$715$	11.4164	+	28.4257i	0.426949	+	1.06306i
$716$		0			0
$717$	5.09017	−	15.6659i	0.190096	−	0.585055i
$718$		0			0
$719$	8.85410	+	6.43288i	0.330202	+	0.239906i	0.740516	−	0.672038i	$-0.234581\pi$
$719$	8.85410	+	6.43288i	0.330202	+	0.239906i	−0.410314	+	0.911944i	$0.634581\pi$
$720$		0			0
$721$	17.1738	+	52.8554i	0.639584	+	1.96844i
$722$		0			0
$723$	1.97214	−	1.43284i	0.0733445	−	0.0532879i
$724$		0			0
$725$	−1.20163			−0.0446273
$726$		0			0
$727$	−3.41641			−0.126708			−0.0633538	−	0.997991i	$-0.520180\pi$
$727$	−3.41641			−0.126708			−0.0633538	+	0.997991i	$0.520180\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−2.47214	−	7.60845i	−0.0914353	−	0.281409i
$732$		0			0
$733$	35.3607	+	25.6910i	1.30608	+	0.948920i	0.999995	−	0.00308526i	$-0.000982070\pi$
$733$	35.3607	+	25.6910i	1.30608	+	0.948920i	0.306081	+	0.952005i	$0.400982\pi$
$734$		0			0
$735$	12.6353	−	38.8873i	0.466058	−	1.43438i
$736$		0			0
$737$	4.94427	+	12.3107i	0.182125	+	0.453472i
$738$		0			0
$739$	−4.65248	+	14.3188i	−0.171144	+	0.526727i	−0.999436	−	0.0335689i	$-0.989313\pi$
$739$	−4.65248	+	14.3188i	−0.171144	+	0.526727i	0.828292	+	0.560296i	$0.189313\pi$
$740$		0			0
$741$	8.47214	+	6.15537i	0.311232	+	0.226123i
$742$		0			0
$743$	11.6738	+	35.9281i	0.428269	+	1.31808i	0.899829	+	0.436242i	$0.143691\pi$
$743$	11.6738	+	35.9281i	0.428269	+	1.31808i	−0.471561	+	0.881834i	$0.656309\pi$
$744$		0			0
$745$	−3.19098	+	2.31838i	−0.116909	+	0.0849390i
$746$		0			0
$747$	0.673762			0.0246517
$748$		0			0
$749$	24.8541			0.908149
$750$		0			0
$751$	−8.18034	+	5.94336i	−0.298505	+	0.216876i	−0.726948	−	0.686692i	$-0.759062\pi$
$751$	−8.18034	+	5.94336i	−0.298505	+	0.216876i	0.428444	+	0.903569i	$0.359062\pi$
$752$		0			0
$753$	5.97214	+	18.3803i	0.217637	+	0.669817i
$754$		0			0
$755$	21.5344	+	15.6457i	0.783719	+	0.569405i
$756$		0			0
$757$	−9.43769	+	29.0462i	−0.343019	+	1.05570i	0.619617	+	0.784904i	$0.287288\pi$
$757$	−9.43769	+	29.0462i	−0.343019	+	1.05570i	−0.962636	+	0.270799i	$0.912712\pi$
$758$		0			0
$759$	9.09017	+	5.70634i	0.329952	+	0.207127i
$760$		0			0
$761$	3.18034	−	9.78808i	0.115287	−	0.354818i	−0.876720	−	0.481002i	$-0.840273\pi$
$761$	3.18034	−	9.78808i	0.115287	−	0.354818i	0.992007	+	0.126184i	$0.0402730\pi$
$762$		0			0
$763$	65.0689	+	47.2753i	2.35565	+	1.71148i
$764$		0			0
$765$	−2.18034	−	6.71040i	−0.0788304	−	0.242615i
$766$		0			0
$767$	10.0902	−	7.33094i	0.364335	−	0.264705i
$768$		0			0
$769$	−4.27051			−0.153999			−0.0769993	−	0.997031i	$-0.524534\pi$
$769$	−4.27051			−0.153999			−0.0769993	+	0.997031i	$0.524534\pi$
$770$		0			0
$771$	−1.81966			−0.0655335
$772$		0			0
$773$	−7.69098	+	5.58783i	−0.276625	+	0.200980i	−0.717444	−	0.696616i	$-0.754688\pi$
$773$	−7.69098	+	5.58783i	−0.276625	+	0.200980i	0.440819	+	0.897596i	$0.354688\pi$
$774$		0			0
$775$	−8.37790	−	25.7845i	−0.300943	−	0.926208i
$776$		0			0
$777$	5.70820	+	4.14725i	0.204781	+	0.148782i
$778$		0			0
$779$	−3.23607	+	9.95959i	−0.115944	+	0.356839i
$780$		0			0
$781$	−31.7426	+	26.5236i	−1.13584	+	0.949088i
$782$		0			0
$783$	−0.118034	+	0.363271i	−0.00421819	+	0.0129823i
$784$		0			0
$785$	−10.3262	−	7.50245i	−0.368559	−	0.267774i
$786$		0			0
$787$	11.5836	+	35.6506i	0.412910	+	1.27081i	0.914107	+	0.405474i	$0.132894\pi$
$787$	11.5836	+	35.6506i	0.412910	+	1.27081i	−0.501196	+	0.865334i	$0.667106\pi$
$788$		0			0
$789$	6.23607	−	4.53077i	0.222010	−	0.161300i
$790$		0			0
$791$	57.5967			2.04790
$792$		0			0
$793$	21.8885			0.777285
$794$		0			0
$795$	8.89919	−	6.46564i	0.315622	−	0.229313i
$796$		0			0
$797$	−6.98936	−	21.5110i	−0.247576	−	0.761960i	−0.995202	−	0.0978402i	$-0.968807\pi$
$797$	−6.98936	−	21.5110i	−0.247576	−	0.761960i	0.747626	−	0.664120i	$-0.231193\pi$
$798$		0			0
$799$	−4.94427	−	3.59222i	−0.174916	−	0.127084i
$800$		0			0
$801$	−3.61803	+	11.1352i	−0.127837	+	0.393442i
$802$		0			0
$803$	9.16312	−	36.4302i	0.323359	−	1.28559i
$804$		0			0
$805$	−13.1803	+	40.5649i	−0.464546	+	1.42973i
$806$		0			0
$807$	2.38197	+	1.73060i	0.0838492	+	0.0609200i
$808$		0			0
$809$	9.34752	+	28.7687i	0.328641	+	1.01145i	0.969770	+	0.244021i	$0.0784665\pi$
$809$	9.34752	+	28.7687i	0.328641	+	1.01145i	−0.641129	+	0.767434i	$0.721533\pi$
$810$		0			0
$811$	−32.9787	+	23.9604i	−1.15804	+	0.841365i	−0.989529	−	0.144335i	$-0.953896\pi$
$811$	−32.9787	+	23.9604i	−1.15804	+	0.841365i	−0.168510	+	0.985700i	$0.553896\pi$
$812$		0			0
$813$	−23.4164			−0.821249
$814$		0			0
$815$	38.2918			1.34130
$816$		0			0
$817$	−8.47214	+	6.15537i	−0.296403	+	0.215349i
$818$		0			0
$819$	4.61803	+	14.2128i	0.161367	+	0.496637i
$820$		0			0
$821$	−17.0623	−	12.3965i	−0.595479	−	0.432641i	0.248793	−	0.968557i	$-0.419966\pi$
$821$	−17.0623	−	12.3965i	−0.595479	−	0.432641i	−0.844271	+	0.535916i	$0.819966\pi$
$822$		0			0
$823$	0.993422	−	3.05744i	0.0346285	−	0.106576i	−0.932248	−	0.361819i	$-0.882156\pi$
$823$	0.993422	−	3.05744i	0.0346285	−	0.106576i	0.966877	+	0.255244i	$0.0821557\pi$
$824$		0			0
$825$	−10.4098	+	0.706298i	−0.362424	+	0.0245901i
$826$		0			0
$827$	−3.30244	+	10.1639i	−0.114837	+	0.353432i	−0.991913	−	0.126920i	$-0.959491\pi$
$827$	−3.30244	+	10.1639i	−0.114837	+	0.353432i	0.877076	+	0.480352i	$0.159491\pi$
$828$		0			0
$829$	−5.90983	−	4.29374i	−0.205257	−	0.149128i	0.480408	−	0.877045i	$-0.340489\pi$
$829$	−5.90983	−	4.29374i	−0.205257	−	0.149128i	−0.685665	+	0.727917i	$0.740489\pi$
$830$		0			0
$831$	3.43769	+	10.5801i	0.119252	+	0.367021i
$832$		0			0
$833$	28.6525	−	20.8172i	0.992749	−	0.721275i
$834$		0			0
$835$	−20.6525			−0.714708
$836$		0			0
$837$	−8.61803			−0.297883
$838$		0			0
$839$	−2.52786	+	1.83660i	−0.0872716	+	0.0634065i	−0.630565	−	0.776136i	$-0.717177\pi$
$839$	−2.52786	+	1.83660i	−0.0872716	+	0.0634065i	0.543294	+	0.839543i	$0.317177\pi$
$840$		0			0
$841$	−8.91641	−	27.4419i	−0.307462	−	0.946272i
$842$		0			0
$843$	−18.7082	−	13.5923i	−0.644345	−	0.468144i
$844$		0			0
$845$	−2.22949	+	6.86167i	−0.0766968	+	0.236048i
$846$		0			0
$847$	−50.3328	+	6.86167i	−1.72946	+	0.235770i
$848$		0			0
$849$	7.38197	−	22.7194i	0.253348	−	0.779726i
$850$		0			0
$851$	−4.00000	−	2.90617i	−0.137118	−	0.0996222i
$852$		0			0
$853$	4.65248	+	14.3188i	0.159298	+	0.490268i	0.998571	−	0.0534419i	$-0.0170192\pi$
$853$	4.65248	+	14.3188i	0.159298	+	0.490268i	−0.839273	+	0.543710i	$0.817019\pi$
$854$		0			0
$855$	−7.47214	+	5.42882i	−0.255542	+	0.185662i
$856$		0			0
$857$	8.76393			0.299370			0.149685	−	0.988734i	$-0.452174\pi$
$857$	8.76393			0.299370			0.149685	+	0.988734i	$0.452174\pi$
$858$		0			0
$859$	−4.40325			−0.150237			−0.0751185	−	0.997175i	$-0.523934\pi$
$859$	−4.40325			−0.150237			−0.0751185	+	0.997175i	$0.523934\pi$
$860$		0			0
$861$	−12.0902	+	8.78402i	−0.412032	+	0.299359i
$862$		0			0
$863$	−0.854102	−	2.62866i	−0.0290740	−	0.0894805i	0.935467	−	0.353415i	$-0.114980\pi$
$863$	−0.854102	−	2.62866i	−0.0290740	−	0.0894805i	−0.964541	+	0.263935i	$0.914980\pi$
$864$		0			0
$865$	9.57295	+	6.95515i	0.325490	+	0.236482i
$866$		0			0
$867$	−3.36475	+	10.3556i	−0.114273	+	0.351695i
$868$		0			0
$869$	−30.8607	+	2.09387i	−1.04688	+	0.0710297i
$870$		0			0
$871$	4.00000	−	12.3107i	0.135535	−	0.417133i
$872$		0			0
$873$	−9.16312	−	6.65740i	−0.310125	−	0.225319i
$874$		0			0
$875$	7.55166	+	23.2416i	0.255293	+	0.785710i
$876$		0			0
$877$	24.5623	−	17.8456i	0.829410	−	0.602602i	−0.0899822	−	0.995943i	$-0.528681\pi$
$877$	24.5623	−	17.8456i	0.829410	−	0.602602i	0.919392	+	0.393342i	$0.128681\pi$
$878$		0			0
$879$	22.9787			0.775053
$880$		0			0
$881$	−12.2918			−0.414121			−0.207061	−	0.978328i	$-0.566390\pi$
$881$	−12.2918			−0.414121			−0.207061	+	0.978328i	$0.566390\pi$
$882$		0			0
$883$	22.5066	−	16.3520i	0.757407	−	0.550288i	−0.140707	−	0.990051i	$-0.544938\pi$
$883$	22.5066	−	16.3520i	0.757407	−	0.550288i	0.898114	+	0.439763i	$0.144938\pi$
$884$		0			0
$885$	3.39919	+	10.4616i	0.114262	+	0.351664i
$886$		0			0
$887$	−23.0902	−	16.7760i	−0.775292	−	0.563283i	0.128270	−	0.991739i	$-0.459057\pi$
$887$	−23.0902	−	16.7760i	−0.775292	−	0.563283i	−0.903562	+	0.428457i	$0.859057\pi$
$888$		0			0
$889$	17.1246	−	52.7041i	0.574341	−	1.76764i
$890$		0			0
$891$	−0.809017	+	3.21644i	−0.0271031	+	0.107755i
$892$		0			0
$893$	−2.47214	+	7.60845i	−0.0827269	+	0.254607i
$894$		0			0
$895$	−14.7361	−	10.7064i	−0.492572	−	0.357875i
$896$		0			0
$897$	−3.23607	−	9.95959i	−0.108049	−	0.332541i
$898$		0			0
$899$	−2.66312	+	1.93487i	−0.0888200	+	0.0645315i
$900$		0			0
$901$	9.52786			0.317419
$902$		0			0
$903$	−14.9443			−0.497314
$904$		0			0
$905$	38.0344	−	27.6336i	1.26431	−	0.918573i
$906$		0			0
$907$	2.52786	+	7.77997i	0.0839363	+	0.258330i	0.984213	−	0.176989i	$-0.0566357\pi$
$907$	2.52786	+	7.77997i	0.0839363	+	0.258330i	−0.900276	+	0.435319i	$0.856636\pi$
$908$		0			0
$909$	10.0172	+	7.27794i	0.332250	+	0.241394i
$910$		0			0
$911$	−13.5066	+	41.5690i	−0.447493	+	1.37724i	0.432234	+	0.901762i	$0.357726\pi$
$911$	−13.5066	+	41.5690i	−0.447493	+	1.37724i	−0.879727	+	0.475480i	$0.842274\pi$
$912$		0			0
$913$	1.71478	−	1.43284i	0.0567510	−	0.0474201i
$914$		0			0
$915$	−5.96556	+	18.3601i	−0.197215	+	0.606966i
$916$		0			0
$917$	57.0517	+	41.4505i	1.88401	+	1.36881i
$918$		0			0
$919$	−15.5344	−	47.8101i	−0.512434	−	1.57711i	−0.787903	−	0.615800i	$-0.788833\pi$
$919$	−15.5344	−	47.8101i	−0.512434	−	1.57711i	0.275469	−	0.961310i	$-0.411167\pi$
$920$		0			0
$921$	−13.4721	+	9.78808i	−0.443922	+	0.322528i
$922$		0			0
$923$	40.3607			1.32849
$924$		0			0
$925$	4.80650			0.158037
$926$		0			0
$927$	9.73607	−	7.07367i	0.319774	−	0.232330i
$928$		0			0
$929$	−7.14590	−	21.9928i	−0.234449	−	0.721561i	−0.997194	−	0.0748610i	$-0.976149\pi$
$929$	−7.14590	−	21.9928i	−0.234449	−	0.721561i	0.762745	−	0.646700i	$-0.223851\pi$
$930$		0			0
$931$	−37.5066	−	27.2501i	−1.22923	−	0.893087i
$932$		0			0
$933$	7.38197	−	22.7194i	0.241675	−	0.743798i
$934$		0			0
$935$	−19.8197	−	12.4418i	−0.648172	−	0.406889i
$936$		0			0
$937$	8.48278	−	26.1073i	0.277120	−	0.852889i	−0.711530	−	0.702655i	$-0.751998\pi$
$937$	8.48278	−	26.1073i	0.277120	−	0.852889i	0.988651	−	0.150233i	$-0.0480024\pi$
$938$		0			0
$939$	−12.2533	−	8.90254i	−0.399871	−	0.290523i
$940$		0			0
$941$	−2.72949	−	8.40051i	−0.0889788	−	0.273849i	0.896659	−	0.442722i	$-0.145987\pi$
$941$	−2.72949	−	8.40051i	−0.0889788	−	0.273849i	−0.985638	+	0.168873i	$0.945987\pi$
$942$		0			0
$943$	8.47214	−	6.15537i	0.275891	−	0.200446i
$944$		0			0
$945$	−13.1803			−0.428756
$946$		0			0
$947$	−2.32624			−0.0755926			−0.0377963	−	0.999285i	$-0.512034\pi$
$947$	−2.32624			−0.0755926			−0.0377963	+	0.999285i	$0.512034\pi$
$948$		0			0
$949$	−29.6525	+	21.5438i	−0.962560	+	0.699341i
$950$		0			0
$951$	−6.14590	−	18.9151i	−0.199294	−	0.613365i
$952$		0			0
$953$	−39.4164	−	28.6377i	−1.27682	−	0.927666i	−0.277371	−	0.960763i	$-0.589463\pi$
$953$	−39.4164	−	28.6377i	−1.27682	−	0.927666i	−0.999452	+	0.0330970i	$0.989463\pi$
$954$		0			0
$955$	−19.8197	+	60.9986i	−0.641349	+	1.97387i
$956$		0			0
$957$	0.472136	+	1.17557i	0.0152620	+	0.0380008i
$958$		0			0
$959$	33.0000	−	101.564i	1.06563	−	3.27966i
$960$		0			0
$961$	−35.0066	−	25.4338i	−1.12924	−	0.820444i
$962$		0			0
$963$	−1.66312	−	5.11855i	−0.0535933	−	0.164943i
$964$		0			0
$965$	−0.753289	+	0.547296i	−0.0242492	+	0.0176181i
$966$		0			0
$967$	−13.6869			−0.440142			−0.220071	−	0.975484i	$-0.570629\pi$
$967$	−13.6869			−0.440142			−0.220071	+	0.975484i	$0.570629\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$		0			0
$971$	−7.52786	+	5.46931i	−0.241581	+	0.175519i	−0.701987	−	0.712190i	$-0.747704\pi$
$971$	−7.52786	+	5.46931i	−0.241581	+	0.175519i	0.460407	+	0.887708i	$0.347704\pi$
$972$		0			0
$973$	18.8885	+	58.1330i	0.605539	+	1.86366i
$974$		0			0
$975$	8.23607	+	5.98385i	0.263765	+	0.191637i
$976$		0			0
$977$	−11.3607	+	34.9646i	−0.363460	+	1.11862i	0.587479	+	0.809239i	$0.300120\pi$
$977$	−11.3607	+	34.9646i	−0.363460	+	1.11862i	−0.950940	+	0.309377i	$0.899880\pi$
$978$		0			0
$979$	14.4721	+	36.0341i	0.462531	+	1.15166i
$980$		0			0
$981$	5.38197	−	16.5640i	0.171833	−	0.528847i
$982$		0			0
$983$	−7.38197	−	5.36331i	−0.235448	−	0.171063i	0.463805	−	0.885937i	$-0.346484\pi$
$983$	−7.38197	−	5.36331i	−0.235448	−	0.171063i	−0.699253	+	0.714874i	$0.746484\pi$
$984$		0			0
$985$	5.37132	+	16.5312i	0.171145	+	0.526729i
$986$		0			0
$987$	−9.23607	+	6.71040i	−0.293987	+	0.213594i
$988$		0			0
$989$	10.4721			0.332995
$990$		0			0
$991$	45.6869			1.45129			0.725646	−	0.688068i	$-0.241541\pi$
$991$	45.6869			1.45129			0.725646	+	0.688068i	$0.241541\pi$
$992$		0			0
$993$	7.23607	−	5.25731i	0.229630	−	0.166836i
$994$		0			0
$995$	−11.5942	−	35.6834i	−0.367562	−	1.13124i
$996$		0			0
$997$	−46.8885	−	34.0665i	−1.48498	−	1.07890i	−0.975911	−	0.218169i	$-0.929992\pi$
$997$	−46.8885	−	34.0665i	−1.48498	−	1.07890i	−0.509064	−	0.860729i	$-0.670008\pi$
$998$		0			0
$999$	0.472136	−	1.45309i	0.0149377	−	0.0459736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.y.d.97.1		4
4.3	odd	2		66.2.e.a.31.1	✓	4
11.4	even	5		5808.2.a.cb.1.2		2
11.5	even	5	inner	528.2.y.d.49.1		4
11.7	odd	10		5808.2.a.cg.1.2		2
12.11	even	2		198.2.f.c.163.1		4
44.3	odd	10		726.2.e.f.565.1		4
44.7	even	10		726.2.a.j.1.2		2
44.15	odd	10		726.2.a.l.1.2		2
44.19	even	10		726.2.e.n.565.1		4
44.27	odd	10		66.2.e.a.49.1	yes	4
44.31	odd	10		726.2.e.f.487.1		4
44.35	even	10		726.2.e.n.487.1		4
44.39	even	10		726.2.e.r.511.1		4
44.43	even	2		726.2.e.r.493.1		4
132.59	even	10		2178.2.a.t.1.1		2
132.71	even	10		198.2.f.c.181.1		4
132.95	odd	10		2178.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.31.1	✓	4	4.3	odd	2
66.2.e.a.49.1	yes	4	44.27	odd	10
198.2.f.c.163.1		4	12.11	even	2
198.2.f.c.181.1		4	132.71	even	10
528.2.y.d.49.1		4	11.5	even	5	inner
528.2.y.d.97.1		4	1.1	even	1	trivial
726.2.a.j.1.2		2	44.7	even	10
726.2.a.l.1.2		2	44.15	odd	10
726.2.e.f.487.1		4	44.31	odd	10
726.2.e.f.565.1		4	44.3	odd	10
726.2.e.n.487.1		4	44.35	even	10
726.2.e.n.565.1		4	44.19	even	10
726.2.e.r.493.1		4	44.43	even	2
726.2.e.r.511.1		4	44.39	even	10
2178.2.a.t.1.1		2	132.59	even	10
2178.2.a.bb.1.1		2	132.95	odd	10
5808.2.a.cb.1.2		2	11.4	even	5
5808.2.a.cg.1.2		2	11.7	odd	10

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.y (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(0.881966 + 2.71441i) q^{5} +(3.73607 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(0.881966 + 2.71441i) q^{5} +(3.73607 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.23607 - 3.07768i) q^{11} +(-1.00000 + 3.07768i) q^{13} +(-2.30902 - 1.67760i) q^{15} +(-0.763932 - 2.35114i) q^{17} +(-2.61803 + 1.90211i) q^{19} -4.61803 q^{21} +3.23607 q^{23} +(-2.54508 + 1.84911i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.309017 + 0.224514i) q^{29} +(-2.66312 + 8.19624i) q^{31} +(2.80902 + 1.76336i) q^{33} +(-4.07295 + 12.5352i) q^{35} +(-1.23607 - 0.898056i) q^{37} +(-1.00000 - 3.07768i) q^{39} +(2.61803 - 1.90211i) q^{41} +3.23607 q^{43} +2.85410 q^{45} +(2.00000 - 1.45309i) q^{47} +(4.42705 + 13.6251i) q^{49} +(2.00000 + 1.45309i) q^{51} +(-1.19098 + 3.66547i) q^{53} +(7.26393 - 6.06961i) q^{55} +(1.00000 - 3.07768i) q^{57} +(-3.11803 - 2.26538i) q^{59} +(-2.09017 - 6.43288i) q^{61} +(3.73607 - 2.71441i) q^{63} -9.23607 q^{65} -4.00000 q^{67} +(-2.61803 + 1.90211i) q^{69} +(-3.85410 - 11.8617i) q^{71} +(9.16312 + 6.65740i) q^{73} +(0.972136 - 2.99193i) q^{75} +(3.73607 - 14.8536i) q^{77} +(2.88197 - 8.86978i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.208204 + 0.640786i) q^{83} +(5.70820 - 4.14725i) q^{85} -0.381966 q^{87} -11.7082 q^{89} +(-12.0902 + 8.78402i) q^{91} +(-2.66312 - 8.19624i) q^{93} +(-7.47214 - 5.42882i) q^{95} +(3.50000 - 10.7719i) q^{97} +(-3.30902 + 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9	\( 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9} + 4 q^{11} - 4 q^{13} - 7 q^{15} - 12 q^{17} - 6 q^{19} - 14 q^{21} + 4 q^{23} + q^{25} - q^{27} - q^{29} + 5 q^{31} + 9 q^{33} - 23 q^{35} + 4 q^{37} - 4 q^{39} + 6 q^{41} + 4 q^{43} - 2 q^{45} + 8 q^{47} + 11 q^{49} + 8 q^{51} - 7 q^{53} + 38 q^{55} + 4 q^{57} - 8 q^{59} + 14 q^{61} + 6 q^{63} - 28 q^{65} - 16 q^{67} - 6 q^{69} - 2 q^{71} + 21 q^{73} - 14 q^{75} + 6 q^{77} + 16 q^{79} - q^{81} - 26 q^{83} - 4 q^{85} - 6 q^{87} - 20 q^{89} - 26 q^{91} + 5 q^{93} - 12 q^{95} + 14 q^{97} - 11 q^{99}+O(q^{100}) \) 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9 + 4 * q^11 - 4 * q^13 - 7 * q^15 - 12 * q^17 - 6 * q^19 - 14 * q^21 + 4 * q^23 + q^25 - q^27 - q^29 + 5 * q^31 + 9 * q^33 - 23 * q^35 + 4 * q^37 - 4 * q^39 + 6 * q^41 + 4 * q^43 - 2 * q^45 + 8 * q^47 + 11 * q^49 + 8 * q^51 - 7 * q^53 + 38 * q^55 + 4 * q^57 - 8 * q^59 + 14 * q^61 + 6 * q^63 - 28 * q^65 - 16 * q^67 - 6 * q^69 - 2 * q^71 + 21 * q^73 - 14 * q^75 + 6 * q^77 + 16 * q^79 - q^81 - 26 * q^83 - 4 * q^85 - 6 * q^87 - 20 * q^89 - 26 * q^91 + 5 * q^93 - 12 * q^95 + 14 * q^97 - 11 * q^99

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