LMFDB - Embedded newform 804.2.q.a.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			241.2
Character	$\chi$	$=$	804.241
Dual form			804.2.q.a.397.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(-1.26159 - 0.370436i) q^{5} +(-2.70108 - 3.11721i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(-1.26159 - 0.370436i) q^{5} +(-2.70108 - 3.11721i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(2.75858 + 0.809991i) q^{11} +(0.609479 + 0.391688i) q^{13} +(-0.861044 + 0.993698i) q^{15} +(-0.382271 - 2.65875i) q^{17} +(-2.81192 + 3.24513i) q^{19} +(-3.95759 + 1.16205i) q^{21} +(-0.335049 + 0.733656i) q^{23} +(-2.75188 - 1.76853i) q^{25} +(-0.959493 + 0.281733i) q^{27} -10.3394 q^{29} +(-5.38078 + 3.45802i) q^{31} +(1.88275 - 2.17281i) q^{33} +(2.25293 + 4.93322i) q^{35} -7.84985 q^{37} +(0.609479 - 0.391688i) q^{39} +(-0.409955 - 2.85130i) q^{41} +(0.293738 + 2.04299i) q^{43} +(0.546209 + 1.19603i) q^{45} +(4.79668 - 10.5033i) q^{47} +(-1.42498 + 9.91093i) q^{49} +(-2.57729 - 0.756760i) q^{51} +(1.11509 - 7.75560i) q^{53} +(-3.18014 - 2.04375i) q^{55} +(1.78376 + 3.90589i) q^{57} +(2.33513 - 1.50070i) q^{59} +(9.21537 - 2.70588i) q^{61} +(-0.587001 + 4.08268i) q^{63} +(-0.623817 - 0.719923i) q^{65} +(-3.28782 + 7.49601i) q^{67} +(0.528172 + 0.609543i) q^{69} +(0.160284 - 1.11480i) q^{71} +(15.5125 - 4.55487i) q^{73} +(-2.75188 + 1.76853i) q^{75} +(-4.92622 - 10.7869i) q^{77} +(4.24287 + 2.72673i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(3.71544 + 1.09095i) q^{83} +(-0.502629 + 3.49586i) q^{85} +(-4.29514 + 9.40504i) q^{87} +(-3.33899 - 7.31137i) q^{89} +(-0.425276 - 2.95786i) q^{91} +(0.910266 + 6.33104i) q^{93} +(4.74961 - 3.05239i) q^{95} -7.38619 q^{97} +(-1.19433 - 2.61522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	−1.26159	−	0.370436i	−0.564200	−	0.165664i	−0.0128195	−	0.999918i	$-0.504081\pi$
$5$	−1.26159	−	0.370436i	−0.564200	−	0.165664i	−0.551381	+	0.834254i	$0.685899\pi$
$6$		0			0
$7$	−2.70108	−	3.11721i	−1.02091	−	1.17820i	−0.983871	−	0.178882i	$-0.942752\pi$
$7$	−2.70108	−	3.11721i	−1.02091	−	1.17820i	−0.0370418	−	0.999314i	$-0.511793\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	2.75858	+	0.809991i	0.831742	+	0.244221i	0.669765	−	0.742573i	$-0.266395\pi$
$11$	2.75858	+	0.809991i	0.831742	+	0.244221i	0.161977	+	0.986795i	$0.448213\pi$
$12$		0			0
$13$	0.609479	+	0.391688i	0.169039	+	0.108635i	0.622425	−	0.782680i	$-0.286148\pi$
$13$	0.609479	+	0.391688i	0.169039	+	0.108635i	−0.453386	+	0.891314i	$0.649784\pi$
$14$		0			0
$15$	−0.861044	+	0.993698i	−0.222321	+	0.256572i
$16$		0			0
$17$	−0.382271	−	2.65875i	−0.0927143	−	0.644842i	−0.982194	−	0.187868i	$-0.939842\pi$
$17$	−0.382271	−	2.65875i	−0.0927143	−	0.644842i	0.889480	−	0.456974i	$-0.151067\pi$
$18$		0			0
$19$	−2.81192	+	3.24513i	−0.645100	+	0.744485i	−0.980268	−	0.197673i	$-0.936661\pi$
$19$	−2.81192	+	3.24513i	−0.645100	+	0.744485i	0.335168	+	0.942158i	$0.391207\pi$
$20$		0			0
$21$	−3.95759	+	1.16205i	−0.863616	+	0.253581i
$22$		0			0
$23$	−0.335049	+	0.733656i	−0.0698626	+	0.152978i	−0.941342	−	0.337455i	$-0.890434\pi$
$23$	−0.335049	+	0.733656i	−0.0698626	+	0.152978i	0.871479	+	0.490433i	$0.163161\pi$
$24$		0			0
$25$	−2.75188	−	1.76853i	−0.550376	−	0.353705i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	−10.3394			−1.91998			−0.959989	−	0.280039i	$-0.909653\pi$
$29$	−10.3394			−1.91998			−0.959989	+	0.280039i	$0.909653\pi$
$30$		0			0
$31$	−5.38078	+	3.45802i	−0.966416	+	0.621078i	−0.925767	−	0.378095i	$-0.876579\pi$
$31$	−5.38078	+	3.45802i	−0.966416	+	0.621078i	−0.0406497	+	0.999173i	$0.512943\pi$
$32$		0			0
$33$	1.88275	−	2.17281i	0.327744	−	0.378237i
$34$		0			0
$35$	2.25293	+	4.93322i	0.380814	+	0.833867i
$36$		0			0
$37$	−7.84985			−1.29051			−0.645254	−	0.763968i	$-0.723248\pi$
$37$	−7.84985			−1.29051			−0.645254	+	0.763968i	$0.723248\pi$
$38$		0			0
$39$	0.609479	−	0.391688i	0.0975947	−	0.0627203i
$40$		0			0
$41$	−0.409955	−	2.85130i	−0.0640243	−	0.445299i	−0.996467	−	0.0839816i	$-0.973236\pi$
$41$	−0.409955	−	2.85130i	−0.0640243	−	0.445299i	0.932443	−	0.361317i	$-0.117673\pi$
$42$		0			0
$43$	0.293738	+	2.04299i	0.0447946	+	0.311553i	0.999884	+	0.0152352i	$0.00484969\pi$
$43$	0.293738	+	2.04299i	0.0447946	+	0.311553i	−0.955089	+	0.296318i	$0.904241\pi$
$44$		0			0
$45$	0.546209	+	1.19603i	0.0814240	+	0.178294i
$46$		0			0
$47$	4.79668	−	10.5033i	0.699667	−	1.53206i	−0.140707	−	0.990051i	$-0.544938\pi$
$47$	4.79668	−	10.5033i	0.699667	−	1.53206i	0.840374	−	0.542006i	$-0.182335\pi$
$48$		0			0
$49$	−1.42498	+	9.91093i	−0.203568	+	1.41585i
$50$		0			0
$51$	−2.57729	−	0.756760i	−0.360893	−	0.105968i
$52$		0			0
$53$	1.11509	−	7.75560i	0.153169	−	1.06531i	−0.757695	−	0.652608i	$-0.773675\pi$
$53$	1.11509	−	7.75560i	0.153169	−	1.06531i	0.910864	−	0.412706i	$-0.135416\pi$
$54$		0			0
$55$	−3.18014	−	2.04375i	−0.428810	−	0.275580i
$56$		0			0
$57$	1.78376	+	3.90589i	0.236265	+	0.517348i
$58$		0			0
$59$	2.33513	−	1.50070i	0.304008	−	0.195374i	−0.379738	−	0.925094i	$-0.623986\pi$
$59$	2.33513	−	1.50070i	0.304008	−	0.195374i	0.683746	+	0.729720i	$0.260350\pi$
$60$		0			0
$61$	9.21537	−	2.70588i	1.17991	−	0.346452i	0.367769	−	0.929917i	$-0.380122\pi$
$61$	9.21537	−	2.70588i	1.17991	−	0.346452i	0.812138	+	0.583465i	$0.198304\pi$
$62$		0			0
$63$	−0.587001	+	4.08268i	−0.0739552	+	0.514369i
$64$		0			0
$65$	−0.623817	−	0.719923i	−0.0773750	−	0.0892955i
$66$		0			0
$67$	−3.28782	+	7.49601i	−0.401671	+	0.915784i
$67$	−3.28782	+	7.49601i	−0.401671	+	0.915784i
$68$		0			0
$69$	0.528172	+	0.609543i	0.0635845	+	0.0733804i
$70$		0			0
$71$	0.160284	−	1.11480i	0.0190222	−	0.132302i	−0.978097	−	0.208148i	$-0.933257\pi$
$71$	0.160284	−	1.11480i	0.0190222	−	0.132302i	0.997120	+	0.0758456i	$0.0241656\pi$
$72$		0			0
$73$	15.5125	−	4.55487i	1.81560	−	0.533107i	0.816570	−	0.577246i	$-0.195873\pi$
$73$	15.5125	−	4.55487i	1.81560	−	0.533107i	0.999025	+	0.0441392i	$0.0140545\pi$
$74$		0			0
$75$	−2.75188	+	1.76853i	−0.317760	+	0.204212i
$76$		0			0
$77$	−4.92622	−	10.7869i	−0.561395	−	1.22928i
$78$		0			0
$79$	4.24287	+	2.72673i	0.477360	+	0.306781i	0.757104	−	0.653294i	$-0.226613\pi$
$79$	4.24287	+	2.72673i	0.477360	+	0.306781i	−0.279744	+	0.960074i	$0.590250\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	3.71544	+	1.09095i	0.407822	+	0.119747i	0.479208	−	0.877701i	$-0.340924\pi$
$83$	3.71544	+	1.09095i	0.407822	+	0.119747i	−0.0713858	+	0.997449i	$0.522742\pi$
$84$		0			0
$85$	−0.502629	+	3.49586i	−0.0545178	+	0.379180i
$86$		0			0
$87$	−4.29514	+	9.40504i	−0.460487	+	1.00833i
$88$		0			0
$89$	−3.33899	−	7.31137i	−0.353933	−	0.775004i	−0.999932	−	0.0116662i	$-0.996286\pi$
$89$	−3.33899	−	7.31137i	−0.353933	−	0.775004i	0.645999	−	0.763338i	$-0.276441\pi$
$90$		0			0
$91$	−0.425276	−	2.95786i	−0.0445810	−	0.310068i
$92$		0			0
$93$	0.910266	+	6.33104i	0.0943902	+	0.656498i
$94$		0			0
$95$	4.74961	−	3.05239i	0.487300	−	0.313169i
$96$		0			0
$97$	−7.38619			−0.749954			−0.374977	−	0.927034i	$-0.622349\pi$
$97$	−7.38619			−0.749954			−0.374977	+	0.927034i	$0.622349\pi$
$98$		0			0
$99$	−1.19433	−	2.61522i	−0.120035	−	0.262840i
$100$		0			0
$101$	−6.05979	+	6.99338i	−0.602972	+	0.695867i	−0.972381	−	0.233400i	$-0.925015\pi$
$101$	−6.05979	+	6.99338i	−0.602972	+	0.695867i	0.369409	+	0.929267i	$0.379560\pi$
$102$		0			0
$103$	−8.41219	+	5.40618i	−0.828877	+	0.532687i	−0.884921	−	0.465741i	$-0.845788\pi$
$103$	−8.41219	+	5.40618i	−0.828877	+	0.532687i	0.0560436	+	0.998428i	$0.482151\pi$
$104$		0			0
$105$	5.42332			0.529262
$106$		0			0
$107$	5.49964	−	1.61484i	0.531670	−	0.156113i	−0.00486837	−	0.999988i	$-0.501550\pi$
$107$	5.49964	−	1.61484i	0.531670	−	0.156113i	0.536539	+	0.843876i	$0.319731\pi$
$108$		0			0
$109$	−9.46271	−	6.08132i	−0.906363	−	0.582484i	0.00230763	−	0.999997i	$-0.499265\pi$
$109$	−9.46271	−	6.08132i	−0.906363	−	0.582484i	−0.908671	+	0.417513i	$0.862902\pi$
$110$		0			0
$111$	−3.26095	+	7.14047i	−0.309515	+	0.677744i
$112$		0			0
$113$	13.0263	−	3.82486i	1.22541	−	0.359813i	0.395894	−	0.918296i	$-0.370435\pi$
$113$	13.0263	−	3.82486i	1.22541	−	0.359813i	0.829516	+	0.558483i	$0.188617\pi$
$114$		0			0
$115$	0.694468	−	0.801459i	0.0647595	−	0.0747364i
$116$		0			0
$117$	−0.103105	−	0.717114i	−0.00953211	−	0.0662973i
$118$		0			0
$119$	−7.25535	+	8.37313i	−0.665097	+	0.767563i
$120$		0			0
$121$	−2.30014	−	1.47821i	−0.209103	−	0.134383i
$122$		0			0
$123$	−2.76394	−	0.811565i	−0.249216	−	0.0731764i
$124$		0			0
$125$	7.12184	+	8.21904i	0.636997	+	0.735134i
$126$		0			0
$127$	3.64828	+	4.21034i	0.323733	+	0.373607i	0.894165	−	0.447737i	$-0.147770\pi$
$127$	3.64828	+	4.21034i	0.323733	+	0.373607i	−0.570433	+	0.821344i	$0.693224\pi$
$128$		0			0
$129$	1.98039	+	0.581496i	0.174364	+	0.0511978i
$130$		0			0
$131$	3.16749	−	6.93584i	0.276745	−	0.605987i	−0.719313	−	0.694686i	$-0.755543\pi$
$131$	3.16749	−	6.93584i	0.276745	−	0.605987i	0.996059	+	0.0886983i	$0.0282707\pi$
$132$		0			0
$133$	17.7110			1.53574
$134$		0			0
$135$	1.31485			0.113164
$136$		0			0
$137$	3.33728	−	7.30763i	0.285123	−	0.624333i	−0.711829	−	0.702353i	$-0.752133\pi$
$137$	3.33728	−	7.30763i	0.285123	−	0.624333i	0.996952	+	0.0780206i	$0.0248600\pi$
$138$		0			0
$139$	−16.4024	−	4.81618i	−1.39123	−	0.408503i	−0.501569	−	0.865118i	$-0.667244\pi$
$139$	−16.4024	−	4.81618i	−1.39123	−	0.408503i	−0.889665	+	0.456615i	$0.849062\pi$
$140$		0			0
$141$	−7.56149	−	8.72642i	−0.636792	−	0.734897i
$142$		0			0
$143$	1.36403	+	1.57417i	0.114066	+	0.131639i
$144$		0			0
$145$	13.0441	+	3.83009i	1.08325	+	0.318071i
$146$		0			0
$147$	8.42335	+	5.41336i	0.694746	+	0.446486i
$148$		0			0
$149$	14.6840	−	16.9462i	1.20296	−	1.38829i	0.302608	−	0.953115i	$-0.402143\pi$
$149$	14.6840	−	16.9462i	1.20296	−	1.38829i	0.900348	−	0.435171i	$-0.143312\pi$
$150$		0			0
$151$	−1.32842	−	9.23934i	−0.108105	−	0.751887i	−0.969702	−	0.244293i	$-0.921444\pi$
$151$	−1.32842	−	9.23934i	−0.108105	−	0.751887i	0.861597	−	0.507594i	$-0.169465\pi$
$152$		0			0
$153$	−1.75902	+	2.03001i	−0.142208	+	0.164117i
$154$		0			0
$155$	8.06931	−	2.36936i	0.648143	−	0.190312i
$156$		0			0
$157$	1.40043	−	3.06651i	0.111766	−	0.244734i	−0.845481	−	0.534006i	$-0.820686\pi$
$157$	1.40043	−	3.06651i	0.111766	−	0.244734i	0.957247	+	0.289272i	$0.0934132\pi$
$158$		0			0
$159$	−6.59152	−	4.23611i	−0.522742	−	0.335946i
$160$		0			0
$161$	3.19196	−	0.937243i	0.251561	−	0.0738651i
$162$		0			0
$163$	19.7408			1.54622			0.773111	−	0.634271i	$-0.218700\pi$
$163$	19.7408			1.54622			0.773111	+	0.634271i	$0.218700\pi$
$164$		0			0
$165$	−3.18014	+	2.04375i	−0.247574	+	0.159106i
$166$		0			0
$167$	−2.43535	+	2.81054i	−0.188453	+	0.217486i	−0.842112	−	0.539303i	$-0.818688\pi$
$167$	−2.43535	+	2.81054i	−0.188453	+	0.217486i	0.653659	+	0.756789i	$0.273233\pi$
$168$		0			0
$169$	−5.18235	−	11.3478i	−0.398642	−	0.872905i
$170$		0			0
$171$	4.29393			0.328365
$172$		0			0
$173$	−8.55354	+	5.49702i	−0.650313	+	0.417931i	−0.823781	−	0.566909i	$-0.808139\pi$
$173$	−8.55354	+	5.49702i	−0.650313	+	0.417931i	0.173467	+	0.984840i	$0.444503\pi$
$174$		0			0
$175$	1.92018	+	13.3551i	0.145152	+	1.00955i
$176$		0			0
$177$	−0.395034	−	2.74752i	−0.0296925	−	0.206516i
$178$		0			0
$179$	9.08025	+	19.8830i	0.678690	+	1.48612i	0.864026	+	0.503448i	$0.167935\pi$
$179$	9.08025	+	19.8830i	0.678690	+	1.48612i	−0.185336	+	0.982675i	$0.559337\pi$
$180$		0			0
$181$	0.400334	−	0.876609i	0.0297566	−	0.0651579i	−0.894170	−	0.447727i	$-0.852233\pi$
$181$	0.400334	−	0.876609i	0.0297566	−	0.0651579i	0.923927	+	0.382570i	$0.124961\pi$
$182$		0			0
$183$	1.36685	−	9.50665i	0.101040	−	0.702752i
$184$		0			0
$185$	9.90329	+	2.90787i	0.728105	+	0.213791i
$186$		0			0
$187$	1.09904	−	7.64401i	0.0803699	−	0.558985i
$188$		0			0
$189$	3.46989	+	2.22996i	0.252397	+	0.162206i
$190$		0			0
$191$	−4.90422	−	10.7387i	−0.354857	−	0.777028i	−0.999917	−	0.0128962i	$-0.995895\pi$
$191$	−4.90422	−	10.7387i	−0.354857	−	0.777028i	0.645060	−	0.764132i	$-0.276832\pi$
$192$		0			0
$193$	−6.83659	+	4.39361i	−0.492108	+	0.316259i	−0.763053	−	0.646336i	$-0.776300\pi$
$193$	−6.83659	+	4.39361i	−0.492108	+	0.316259i	0.270945	+	0.962595i	$0.412664\pi$
$194$		0			0
$195$	−0.914008	+	0.268377i	−0.0654535	+	0.0192189i
$196$		0			0
$197$	3.33711	−	23.2101i	0.237760	−	1.65365i	−0.425274	−	0.905065i	$-0.639822\pi$
$197$	3.33711	−	23.2101i	0.237760	−	1.65365i	0.663034	−	0.748590i	$-0.269269\pi$
$198$		0			0
$199$	−2.60563	−	3.00706i	−0.184708	−	0.213165i	0.655842	−	0.754898i	$-0.272314\pi$
$199$	−2.60563	−	3.00706i	−0.184708	−	0.213165i	−0.840550	+	0.541733i	$0.817768\pi$
$200$		0			0
$201$	5.45280	+	6.10466i	0.384611	+	0.430590i
$202$		0			0
$203$	27.9275	+	32.2301i	1.96013	+	2.26211i
$204$		0			0
$205$	−0.539030	+	3.74904i	−0.0376475	+	0.261844i
$206$		0			0
$207$	0.773871	−	0.227229i	0.0537877	−	0.0157935i
$208$		0			0
$209$	−10.3854	+	6.67431i	−0.718376	+	0.461672i
$210$		0			0
$211$	4.55959	+	9.98411i	0.313895	+	0.687334i	0.999161	−	0.0409587i	$-0.0130412\pi$
$211$	4.55959	+	9.98411i	0.313895	+	0.687334i	−0.685266	+	0.728293i	$0.740314\pi$
$212$		0			0
$213$	−0.947472	−	0.608903i	−0.0649197	−	0.0417214i
$214$		0			0
$215$	0.386221	−	2.68623i	0.0263401	−	0.183199i
$216$		0			0
$217$	25.3133	+	7.43265i	1.71838	+	0.504561i
$218$		0			0
$219$	2.30085	−	16.0028i	0.155477	−	1.08137i
$220$		0			0
$221$	0.808416	−	1.77018i	0.0543800	−	0.119075i
$222$		0			0
$223$	2.04120	+	4.46959i	0.136689	+	0.299306i	0.965581	−	0.260101i	$-0.0837560\pi$
$223$	2.04120	+	4.46959i	0.136689	+	0.299306i	−0.828893	+	0.559408i	$0.811029\pi$
$224$		0			0
$225$	0.465536	+	3.23787i	0.0310357	+	0.215858i
$226$		0			0
$227$	1.91801	+	13.3400i	0.127303	+	0.885409i	0.948953	+	0.315417i	$0.102144\pi$
$227$	1.91801	+	13.3400i	0.127303	+	0.885409i	−0.821650	+	0.569992i	$0.806946\pi$
$228$		0			0
$229$	1.73884	−	1.11749i	0.114906	−	0.0738457i	−0.481925	−	0.876212i	$-0.660062\pi$
$229$	1.73884	−	1.11749i	0.114906	−	0.0738457i	0.596832	+	0.802367i	$0.296426\pi$
$230$		0			0
$231$	−11.8585			−0.780235
$232$		0			0
$233$	−9.33327	−	20.4370i	−0.611443	−	1.33887i	−0.921582	−	0.388183i	$-0.873103\pi$
$233$	−9.33327	−	20.4370i	−0.611443	−	1.33887i	0.310139	−	0.950691i	$-0.399624\pi$
$234$		0			0
$235$	−9.94223	+	11.4739i	−0.648560	+	0.748478i
$236$		0			0
$237$	4.24287	−	2.72673i	0.275604	−	0.177120i
$238$		0			0
$239$	−21.4577			−1.38798			−0.693990	−	0.719984i	$-0.744149\pi$
$239$	−21.4577			−1.38798			−0.693990	+	0.719984i	$0.744149\pi$
$240$		0			0
$241$	−20.8778	+	6.13027i	−1.34486	+	0.394885i	−0.873400	−	0.487004i	$-0.838090\pi$
$241$	−20.8778	+	6.13027i	−1.34486	+	0.394885i	−0.471456	+	0.881890i	$0.656271\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	5.46911	−	11.9757i	0.349408	−	0.765098i
$246$		0			0
$247$	−2.98489	+	0.876443i	−0.189924	+	0.0557667i
$248$		0			0
$249$	2.53581	−	2.92648i	0.160701	−	0.185458i
$250$		0			0
$251$	−0.510120	−	3.54796i	−0.0321985	−	0.223945i	0.967368	−	0.253374i	$-0.0815403\pi$
$251$	−0.510120	−	3.54796i	−0.0321985	−	0.223945i	−0.999567	+	0.0294286i	$0.990631\pi$
$252$		0			0
$253$	−1.51851	+	1.75246i	−0.0954681	+	0.110176i
$254$		0			0
$255$	2.97115	+	1.90944i	0.186061	+	0.119574i
$256$		0			0
$257$	−3.16901	−	0.930505i	−0.197677	−	0.0580433i	0.181395	−	0.983410i	$-0.441939\pi$
$257$	−3.16901	−	0.930505i	−0.197677	−	0.0580433i	−0.379073	+	0.925367i	$0.623757\pi$
$258$		0			0
$259$	21.2031	+	24.4696i	1.31749	+	1.52047i
$260$		0			0
$261$	6.77086	+	7.81399i	0.419106	+	0.483674i
$262$		0			0
$263$	−2.94954	−	0.866063i	−0.181876	−	0.0534037i	0.189526	−	0.981876i	$-0.439305\pi$
$263$	−2.94954	−	0.866063i	−0.181876	−	0.0534037i	−0.371403	+	0.928472i	$0.621123\pi$
$264$		0			0
$265$	−4.27974	+	9.37133i	−0.262902	+	0.575676i
$266$		0			0
$267$	−8.03773			−0.491901
$268$		0			0
$269$	29.0615			1.77191			0.885956	−	0.463769i	$-0.153503\pi$
$269$	29.0615			1.77191			0.885956	+	0.463769i	$0.153503\pi$
$270$		0			0
$271$	−0.592590	+	1.29759i	−0.0359973	+	0.0788231i	−0.926776	−	0.375613i	$-0.877432\pi$
$271$	−0.592590	+	1.29759i	−0.0359973	+	0.0788231i	0.890779	+	0.454436i	$0.150159\pi$
$272$		0			0
$273$	−2.86723	−	0.841894i	−0.173532	−	0.0509537i
$274$		0			0
$275$	−6.15878	−	7.10761i	−0.371388	−	0.428605i
$276$		0			0
$277$	−5.81477	−	6.71061i	−0.349376	−	0.403201i	0.553676	−	0.832732i	$-0.313224\pi$
$277$	−5.81477	−	6.71061i	−0.349376	−	0.403201i	−0.903052	+	0.429531i	$0.858679\pi$
$278$		0			0
$279$	6.13706	+	1.80200i	0.367416	+	0.107883i
$280$		0			0
$281$	13.6681	+	8.78397i	0.815372	+	0.524008i	0.880599	−	0.473863i	$-0.157141\pi$
$281$	13.6681	+	8.78397i	0.815372	+	0.524008i	−0.0652269	+	0.997870i	$0.520777\pi$
$282$		0			0
$283$	7.77496	−	8.97279i	0.462174	−	0.533377i	−0.476045	−	0.879421i	$-0.657930\pi$
$283$	7.77496	−	8.97279i	0.462174	−	0.533377i	0.938218	+	0.346044i	$0.112475\pi$
$284$		0			0
$285$	−0.803492	−	5.58841i	−0.0475948	−	0.331029i
$286$		0			0
$287$	−7.78079	+	8.97952i	−0.459286	+	0.530044i
$288$		0			0
$289$	9.38854	−	2.75673i	0.552267	−	0.162160i
$290$		0			0
$291$	−3.06833	+	6.71871i	−0.179869	+	0.393858i
$292$		0			0
$293$	9.21396	+	5.92145i	0.538285	+	0.345935i	0.781368	−	0.624071i	$-0.214522\pi$
$293$	9.21396	+	5.92145i	0.538285	+	0.345935i	−0.243083	+	0.970006i	$0.578159\pi$
$294$		0			0
$295$	−3.50189	+	1.02825i	−0.203888	+	0.0598669i
$296$		0			0
$297$	−2.87503			−0.166826
$298$		0			0
$299$	−0.491570	+	0.315913i	−0.0284282	+	0.0182697i
$300$		0			0
$301$	5.57503	−	6.43392i	0.321339	−	0.370845i
$302$		0			0
$303$	3.84407	+	8.41734i	0.220836	+	0.483563i
$304$		0			0
$305$	−12.6284			−0.723098
$306$		0			0
$307$	−6.29642	+	4.04646i	−0.359356	+	0.230944i	−0.707843	−	0.706370i	$-0.750332\pi$
$307$	−6.29642	+	4.04646i	−0.359356	+	0.230944i	0.348488	+	0.937313i	$0.386695\pi$
$308$		0			0
$309$	1.42309	+	9.89780i	0.0809567	+	0.563066i
$310$		0			0
$311$	1.08256	+	7.52934i	0.0613861	+	0.426950i	0.997220	+	0.0745092i	$0.0237390\pi$
$311$	1.08256	+	7.52934i	0.0613861	+	0.426950i	−0.935834	+	0.352440i	$0.885352\pi$
$312$		0			0
$313$	−4.82109	−	10.5567i	−0.272504	−	0.596701i	0.723060	−	0.690785i	$-0.242735\pi$
$313$	−4.82109	−	10.5567i	−0.272504	−	0.596701i	−0.995564	+	0.0940845i	$0.970008\pi$
$314$		0			0
$315$	2.25293	−	4.93322i	0.126938	−	0.277956i
$316$		0			0
$317$	3.29800	−	22.9381i	0.185234	−	1.28833i	−0.658913	−	0.752219i	$-0.728984\pi$
$317$	3.29800	−	22.9381i	0.185234	−	1.28833i	0.844147	−	0.536111i	$-0.180107\pi$
$318$		0			0
$319$	−28.5220	−	8.37481i	−1.59693	−	0.468900i
$320$		0			0
$321$	0.815723	−	5.67348i	0.0455292	−	0.316663i
$322$		0			0
$323$	9.70293	+	6.23569i	0.539885	+	0.346963i
$324$		0			0
$325$	−0.984502	−	2.15576i	−0.0546103	−	0.119580i
$326$		0			0
$327$	−9.46271	+	6.08132i	−0.523289	+	0.336297i
$328$		0			0
$329$	−45.6971	+	13.4179i	−2.51936	+	0.739752i
$330$		0			0
$331$	2.46868	−	17.1700i	0.135691	−	0.943750i	−0.802258	−	0.596977i	$-0.796368\pi$
$331$	2.46868	−	17.1700i	0.135691	−	0.943750i	0.937949	−	0.346773i	$-0.112723\pi$
$332$		0			0
$333$	5.14056	+	5.93252i	0.281701	+	0.325100i
$334$		0			0
$335$	6.92468	−	8.23897i	0.378336	−	0.450143i
$336$		0			0
$337$	−3.47159	−	4.00643i	−0.189110	−	0.218244i	0.653275	−	0.757121i	$-0.273394\pi$
$337$	−3.47159	−	4.00643i	−0.189110	−	0.218244i	−0.842385	+	0.538876i	$0.818849\pi$
$338$		0			0
$339$	1.93210	−	13.4380i	0.104937	−	0.729854i
$340$		0			0
$341$	−17.6442	+	5.18082i	−0.955489	+	0.280557i
$342$		0			0
$343$	10.4543	−	6.71854i	0.564477	−	0.362767i
$344$		0			0
$345$	−0.440540	−	0.964648i	−0.0237179	−	0.0519349i
$346$		0			0
$347$	−10.6217	−	6.82617i	−0.570204	−	0.366448i	0.223545	−	0.974694i	$-0.428237\pi$
$347$	−10.6217	−	6.82617i	−0.570204	−	0.366448i	−0.793749	+	0.608246i	$0.791874\pi$
$348$		0			0
$349$	2.61963	−	18.2200i	0.140226	−	0.975292i	−0.791251	−	0.611491i	$-0.790570\pi$
$349$	2.61963	−	18.2200i	0.140226	−	0.975292i	0.931477	−	0.363801i	$-0.118521\pi$
$350$		0			0
$351$	−0.695142	−	0.204112i	−0.0371039	−	0.0108947i
$352$		0			0
$353$	−0.421879	+	2.93423i	−0.0224543	+	0.156173i	−0.997964	−	0.0637846i	$-0.979683\pi$
$353$	−0.421879	+	2.93423i	−0.0224543	+	0.156173i	0.975509	+	0.219958i	$0.0705920\pi$
$354$		0			0
$355$	−0.615174	+	1.34704i	−0.0326501	+	0.0714937i
$356$		0			0
$357$	4.60248	+	10.0780i	0.243589	+	0.533386i
$358$		0			0
$359$	−4.63491	−	32.2365i	−0.244621	−	1.70138i	−0.628350	−	0.777930i	$-0.716270\pi$
$359$	−4.63491	−	32.2365i	−0.244621	−	1.70138i	0.383729	−	0.923446i	$-0.374640\pi$
$360$		0			0
$361$	0.0800068	+	0.556459i	0.00421088	+	0.0292873i
$362$		0			0
$363$	−2.30014	+	1.47821i	−0.120726	+	0.0775858i
$364$		0			0
$365$	−21.2577			−1.11268
$366$		0			0
$367$	1.58665	+	3.47428i	0.0828226	+	0.181356i	0.946512	−	0.322668i	$-0.104580\pi$
$367$	1.58665	+	3.47428i	0.0828226	+	0.181356i	−0.863690	+	0.504024i	$0.831852\pi$
$368$		0			0
$369$	−1.88641	+	2.17703i	−0.0982024	+	0.113332i
$370$		0			0
$371$	−27.1878	+	17.4725i	−1.41152	+	0.907129i
$372$		0			0
$373$	−28.3650			−1.46868			−0.734342	−	0.678779i	$-0.762509\pi$
$373$	−28.3650			−1.46868			−0.734342	+	0.678779i	$0.762509\pi$
$374$		0			0
$375$	10.4348	−	3.06394i	0.538852	−	0.158221i
$376$		0			0
$377$	−6.30164	−	4.04982i	−0.324551	−	0.208576i
$378$		0			0
$379$	11.9127	−	26.0852i	0.611915	−	1.33991i	−0.309342	−	0.950951i	$-0.600109\pi$
$379$	11.9127	−	26.0852i	0.611915	−	1.33991i	0.921256	−	0.388956i	$-0.127164\pi$
$380$		0			0
$381$	5.34541	−	1.56955i	0.273854	−	0.0804107i
$382$		0			0
$383$	−10.7165	+	12.3675i	−0.547587	+	0.631949i	−0.960319	−	0.278903i	$-0.910029\pi$
$383$	−10.7165	+	12.3675i	−0.547587	+	0.631949i	0.412732	+	0.910852i	$0.364575\pi$
$384$		0			0
$385$	2.21901	+	15.4335i	0.113091	+	0.786565i
$386$		0			0
$387$	1.35163	−	1.55987i	0.0687073	−	0.0792924i
$388$		0			0
$389$	20.9528	+	13.4655i	1.06235	+	0.682729i	0.950414	−	0.310987i	$-0.100659\pi$
$389$	20.9528	+	13.4655i	1.06235	+	0.682729i	0.111933	+	0.993716i	$0.464296\pi$
$390$		0			0
$391$	2.07869	+	0.610358i	0.105124	+	0.0308671i
$392$		0			0
$393$	−4.99324	−	5.76251i	−0.251876	−	0.290680i
$394$		0			0
$395$	−4.34268	−	5.01172i	−0.218504	−	0.252167i
$396$		0			0
$397$	31.6433	+	9.29131i	1.58813	+	0.466317i	0.952212	−	0.305439i	$-0.0988031\pi$
$397$	31.6433	+	9.29131i	1.58813	+	0.466317i	0.635919	+	0.771756i	$0.280621\pi$
$398$		0			0
$399$	7.35742	−	16.1105i	0.368332	−	0.806534i
$400$		0			0
$401$	−6.08236			−0.303739			−0.151869	−	0.988401i	$-0.548529\pi$
$401$	−6.08236			−0.303739			−0.151869	+	0.988401i	$0.548529\pi$
$402$		0			0
$403$	−4.63393			−0.230833
$404$		0			0
$405$	0.546209	−	1.19603i	0.0271413	−	0.0594312i
$406$		0			0
$407$	−21.6544	−	6.35830i	−1.07337	−	0.315169i
$408$		0			0
$409$	3.80417	+	4.39025i	0.188104	+	0.217084i	0.841967	−	0.539530i	$-0.181398\pi$
$409$	3.80417	+	4.39025i	0.188104	+	0.217084i	−0.653862	+	0.756613i	$0.726852\pi$
$410$		0			0
$411$	−5.26089	−	6.07140i	−0.259501	−	0.299480i
$412$		0			0
$413$	−10.9854	−	3.22559i	−0.540554	−	0.158721i
$414$		0			0
$415$	−4.28323	−	2.75267i	−0.210256	−	0.135123i
$416$		0			0
$417$	−11.1948	+	12.9194i	−0.548210	+	0.632668i
$418$		0			0
$419$	0.258487	+	1.79782i	0.0126279	+	0.0878291i	0.995161	−	0.0982601i	$-0.0313277\pi$
$419$	0.258487	+	1.79782i	0.0126279	+	0.0878291i	−0.982533	+	0.186089i	$0.940419\pi$
$420$		0			0
$421$	−25.8484	+	29.8307i	−1.25978	+	1.45386i	−0.423174	+	0.906048i	$0.639084\pi$
$421$	−25.8484	+	29.8307i	−1.25978	+	1.45386i	−0.836602	+	0.547811i	$0.815461\pi$
$422$		0			0
$423$	−11.0790	+	3.25308i	−0.538679	+	0.158170i
$424$		0			0
$425$	−3.65011	+	7.99263i	−0.177056	+	0.387699i
$426$		0			0
$427$	−33.3262	−	21.4175i	−1.61277	−	1.03646i
$428$		0			0
$429$	1.99856	−	0.586829i	0.0964912	−	0.0283324i
$430$		0			0
$431$	16.6079			0.799972			0.399986	−	0.916521i	$-0.369015\pi$
$431$	16.6079			0.799972			0.399986	+	0.916521i	$0.369015\pi$
$432$		0			0
$433$	−1.96127	+	1.26043i	−0.0942528	+	0.0605726i	−0.586918	−	0.809646i	$-0.699659\pi$
$433$	−1.96127	+	1.26043i	−0.0942528	+	0.0605726i	0.492665	+	0.870219i	$0.336023\pi$
$434$		0			0
$435$	8.90268	−	10.2742i	0.426851	−	0.492612i
$436$		0			0
$437$	−1.43868	−	3.15027i	−0.0688213	−	0.150698i
$438$		0			0
$439$	−2.82762			−0.134955			−0.0674774	−	0.997721i	$-0.521495\pi$
$439$	−2.82762			−0.134955			−0.0674774	+	0.997721i	$0.521495\pi$
$440$		0			0
$441$	8.42335	−	5.41336i	0.401112	−	0.257779i
$442$		0			0
$443$	2.36415	+	16.4430i	0.112324	+	0.781233i	0.965648	+	0.259852i	$0.0836737\pi$
$443$	2.36415	+	16.4430i	0.112324	+	0.781233i	−0.853324	+	0.521381i	$0.825417\pi$
$444$		0			0
$445$	1.50404	+	10.4608i	0.0712984	+	0.495892i
$446$		0			0
$447$	−9.31486	−	20.3967i	−0.440578	−	0.964731i
$448$		0			0
$449$	−12.8347	+	28.1042i	−0.605709	+	1.32632i	0.319761	+	0.947498i	$0.396397\pi$
$449$	−12.8347	+	28.1042i	−0.605709	+	1.32632i	−0.925470	+	0.378820i	$0.876330\pi$
$450$		0			0
$451$	1.17864	−	8.19759i	0.0554998	−	0.386010i
$452$		0			0
$453$	−8.95624	−	2.62979i	−0.420801	−	0.123558i
$454$		0			0
$455$	−0.559174	+	3.88914i	−0.0262145	+	0.182326i
$456$		0			0
$457$	−27.9150	−	17.9399i	−1.30581	−	0.839194i	−0.311979	−	0.950089i	$-0.600992\pi$
$457$	−27.9150	−	17.9399i	−1.30581	−	0.839194i	−0.993832	+	0.110895i	$0.964628\pi$
$458$		0			0
$459$	1.11584	+	2.44336i	0.0520831	+	0.114046i
$460$		0			0
$461$	−2.37403	+	1.52570i	−0.110570	+	0.0710588i	−0.594757	−	0.803906i	$-0.702752\pi$
$461$	−2.37403	+	1.52570i	−0.110570	+	0.0710588i	0.484187	+	0.874964i	$0.339115\pi$
$462$		0			0
$463$	−4.22991	+	1.24201i	−0.196581	+	0.0577213i	−0.378541	−	0.925585i	$-0.623574\pi$
$463$	−4.22991	+	1.24201i	−0.196581	+	0.0577213i	0.181960	+	0.983306i	$0.441756\pi$
$464$		0			0
$465$	1.19686	−	8.32438i	0.0555033	−	0.386034i
$466$		0			0
$467$	11.5643	+	13.3459i	0.535130	+	0.617573i	0.957354	−	0.288919i	$-0.0932957\pi$
$467$	11.5643	+	13.3459i	0.535130	+	0.617573i	−0.422224	+	0.906492i	$0.638750\pi$
$468$		0			0
$469$	32.2473	−	9.99850i	1.48904	−	0.461688i
$470$		0			0
$471$	−2.20764	−	2.54775i	−0.101723	−	0.117394i
$472$		0			0
$473$	−0.844506	+	5.87367i	−0.0388304	+	0.270071i
$474$		0			0
$475$	13.4772	−	3.95726i	0.618376	−	0.181571i
$476$		0			0
$477$	−6.59152	+	4.23611i	−0.301805	+	0.193958i
$478$		0			0
$479$	8.83706	+	19.3505i	0.403776	+	0.884145i	0.996873	+	0.0790149i	$0.0251775\pi$
$479$	8.83706	+	19.3505i	0.403776	+	0.884145i	−0.593098	+	0.805130i	$0.702095\pi$
$480$		0			0
$481$	−4.78432	−	3.07469i	−0.218146	−	0.140194i
$482$		0			0
$483$	0.473440	−	3.29285i	0.0215423	−	0.149830i
$484$		0			0
$485$	9.31835	+	2.73611i	0.423124	+	0.124241i
$486$		0			0
$487$	5.46291	−	37.9954i	0.247548	−	1.72173i	−0.364748	−	0.931106i	$-0.618845\pi$
$487$	5.46291	−	37.9954i	0.247548	−	1.72173i	0.612296	−	0.790629i	$-0.290246\pi$
$488$		0			0
$489$	8.20064	−	17.9569i	0.370846	−	0.812039i
$490$		0			0
$491$	2.10531	+	4.60999i	0.0950115	+	0.208046i	0.951170	−	0.308667i	$-0.0998828\pi$
$491$	2.10531	+	4.60999i	0.0950115	+	0.208046i	−0.856159	+	0.516713i	$0.827155\pi$
$492$		0			0
$493$	3.95245	+	27.4899i	0.178009	+	1.23808i
$494$		0			0
$495$	0.537985	+	3.74176i	0.0241806	+	0.168180i
$496$		0			0
$497$	−3.90800	+	2.51152i	−0.175298	+	0.112657i
$498$		0			0
$499$	7.41336			0.331868			0.165934	−	0.986137i	$-0.446936\pi$
$499$	7.41336			0.331868			0.165934	+	0.986137i	$0.446936\pi$
$500$		0			0
$501$	1.54488	+	3.38281i	0.0690200	+	0.151133i
$502$		0			0
$503$	−0.252307	+	0.291178i	−0.0112498	+	0.0129830i	−0.761347	−	0.648345i	$-0.775461\pi$
$503$	−0.252307	+	0.291178i	−0.0112498	+	0.0129830i	0.750097	+	0.661328i	$0.230007\pi$
$504$		0			0
$505$	10.2356	−	6.57801i	0.455477	−	0.292717i
$506$		0			0
$507$	−12.4751			−0.554039
$508$		0			0
$509$	−42.0701	+	12.3529i	−1.86473	+	0.547533i	−0.865841	+	0.500319i	$0.833216\pi$
$509$	−42.0701	+	12.3529i	−1.86473	+	0.547533i	−0.998885	+	0.0472137i	$0.984966\pi$
$510$		0			0
$511$	−56.0989	−	36.0526i	−2.48167	−	1.59487i
$512$		0			0
$513$	1.78376	−	3.90589i	0.0787550	−	0.172449i
$514$		0			0
$515$	12.6154	−	3.70421i	0.555900	−	0.163227i
$516$		0			0
$517$	21.7395	−	25.0888i	0.956104	−	1.10340i
$518$		0			0
$519$	1.44700	+	10.0641i	0.0635163	+	0.441766i
$520$		0			0
$521$	−28.2067	+	32.5522i	−1.23576	+	1.42614i	−0.367501	+	0.930023i	$0.619787\pi$
$521$	−28.2067	+	32.5522i	−1.23576	+	1.42614i	−0.868256	+	0.496116i	$0.834759\pi$
$522$		0			0
$523$	−3.79762	−	2.44058i	−0.166058	−	0.106719i	0.454972	−	0.890506i	$-0.349649\pi$
$523$	−3.79762	−	2.44058i	−0.166058	−	0.106719i	−0.621030	+	0.783787i	$0.713286\pi$
$524$		0			0
$525$	12.9459	+	3.80127i	0.565006	+	0.165901i
$526$		0			0
$527$	11.2509	+	12.9843i	0.490098	+	0.565603i
$528$		0			0
$529$	14.6358	+	16.8906i	0.636339	+	0.734375i
$530$		0			0
$531$	−2.66333	−	0.782026i	−0.115579	−	0.0339370i
$532$		0			0
$533$	0.866962	−	1.89838i	0.0375523	−	0.0822281i
$534$		0			0
$535$	−7.53649			−0.325831
$536$		0			0
$537$	21.8583			0.943253
$538$		0			0
$539$	−11.9587	+	26.1858i	−0.515096	+	1.12790i
$540$		0			0
$541$	−19.3619	−	5.68516i	−0.832432	−	0.244424i	−0.162370	−	0.986730i	$-0.551914\pi$
$541$	−19.3619	−	5.68516i	−0.832432	−	0.244424i	−0.670061	+	0.742306i	$0.733732\pi$
$542$		0			0
$543$	−0.631087	−	0.728313i	−0.0270825	−	0.0312549i
$544$		0			0
$545$	9.68533	+	11.1775i	0.414874	+	0.478790i
$546$		0			0
$547$	28.2146	+	8.28455i	1.20637	+	0.354222i	0.822285	−	0.569076i	$-0.192699\pi$
$547$	28.2146	+	8.28455i	1.20637	+	0.354222i	0.384084	+	0.923298i	$0.374517\pi$
$548$		0			0
$549$	−8.07975	−	5.19254i	−0.344835	−	0.221612i
$550$		0			0
$551$	29.0736	−	33.5527i	1.23858	−	1.42939i
$552$		0			0
$553$	−2.96054	−	20.5910i	−0.125895	−	0.875619i
$554$		0			0
$555$	6.75907	−	7.80038i	0.286906	−	0.331108i
$556$		0			0
$557$	1.33301	−	0.391407i	0.0564815	−	0.0165845i	−0.253370	−	0.967370i	$-0.581539\pi$
$557$	1.33301	−	0.391407i	0.0564815	−	0.0165845i	0.309851	+	0.950785i	$0.399721\pi$
$558$		0			0
$559$	−0.621188	+	1.36021i	−0.0262735	+	0.0575309i
$560$		0			0
$561$	−6.49667	−	4.17516i	−0.274290	−	0.176275i
$562$		0			0
$563$	−4.06824	+	1.19454i	−0.171456	+	0.0503439i	−0.366334	−	0.930484i	$-0.619387\pi$
$563$	−4.06824	+	1.19454i	−0.171456	+	0.0503439i	0.194878	+	0.980828i	$0.437569\pi$
$564$		0			0
$565$	−17.8507			−0.750985
$566$		0			0
$567$	3.46989	−	2.22996i	0.145722	−	0.0936496i
$568$		0			0
$569$	4.79043	−	5.52845i	0.200825	−	0.231765i	−0.646400	−	0.762999i	$-0.723726\pi$
$569$	4.79043	−	5.52845i	0.200825	−	0.231765i	0.847225	+	0.531234i	$0.178272\pi$
$570$		0			0
$571$	11.5773	+	25.3507i	0.484494	+	1.06089i	0.981203	+	0.192977i	$0.0618143\pi$
$571$	11.5773	+	25.3507i	0.484494	+	1.06089i	−0.496709	+	0.867917i	$0.665458\pi$
$572$		0			0
$573$	−11.8056			−0.493186
$574$		0			0
$575$	2.21951	−	1.42639i	0.0925598	−	0.0594846i
$576$		0			0
$577$	5.18740	+	36.0792i	0.215954	+	1.50200i	0.752763	+	0.658292i	$0.228721\pi$
$577$	5.18740	+	36.0792i	0.215954	+	1.50200i	−0.536808	+	0.843704i	$0.680370\pi$
$578$		0			0
$579$	1.15654	+	8.04395i	0.0480644	+	0.334295i
$580$		0			0
$581$	−6.63497	−	14.5286i	−0.275265	−	0.602746i
$582$		0			0
$583$	9.35802	−	20.4912i	0.387570	−	0.848659i
$584$		0			0
$585$	−0.135568	+	0.942899i	−0.00560506	+	0.0389841i
$586$		0			0
$587$	9.25219	+	2.71669i	0.381879	+	0.112130i	0.467037	−	0.884238i	$-0.345321\pi$
$587$	9.25219	+	2.71669i	0.381879	+	0.112130i	−0.0851585	+	0.996367i	$0.527140\pi$
$588$		0			0
$589$	3.90862	−	27.1850i	0.161052	−	1.12014i
$590$		0			0
$591$	−19.7264	−	12.6774i	−0.811436	−	0.521478i
$592$		0			0
$593$	16.3058	+	35.7047i	0.669599	+	1.46622i	0.873299	+	0.487185i	$0.161976\pi$
$593$	16.3058	+	35.7047i	0.669599	+	1.46622i	−0.203700	+	0.979033i	$0.565297\pi$
$594$		0			0
$595$	12.2550	−	7.87581i	0.502406	−	0.322877i
$596$		0			0
$597$	−3.81773	+	1.12099i	−0.156249	+	0.0458790i
$598$		0			0
$599$	−1.51251	+	10.5198i	−0.0617996	+	0.429826i	0.935309	+	0.353833i	$0.115122\pi$
$599$	−1.51251	+	10.5198i	−0.0617996	+	0.429826i	−0.997108	+	0.0759930i	$0.975787\pi$
$600$		0			0
$601$	11.1776	+	12.8996i	0.455943	+	0.526186i	0.936448	−	0.350806i	$-0.114092\pi$
$601$	11.1776	+	12.8996i	0.455943	+	0.526186i	−0.480505	+	0.876992i	$0.659547\pi$
$602$		0			0
$603$	7.81817	−	2.42408i	0.318381	−	0.0987160i
$604$		0			0
$605$	2.35425	+	2.71695i	0.0957138	+	0.110460i
$606$		0			0
$607$	−1.65952	+	11.5422i	−0.0673580	+	0.468485i	0.928026	+	0.372515i	$0.121504\pi$
$607$	−1.65952	+	11.5422i	−0.0673580	+	0.468485i	−0.995384	+	0.0959702i	$0.969405\pi$
$608$		0			0
$609$	40.9190	−	12.0149i	1.65812	−	0.486869i
$610$		0			0
$611$	7.03747	−	4.52271i	0.284706	−	0.182969i
$612$		0			0
$613$	5.31669	+	11.6419i	0.214739	+	0.470213i	0.986093	−	0.166193i	$-0.0531475\pi$
$613$	5.31669	+	11.6419i	0.214739	+	0.470213i	−0.771354	+	0.636406i	$0.780420\pi$
$614$		0			0
$615$	3.18632	+	2.04773i	0.128485	+	0.0825723i
$616$		0			0
$617$	3.87523	−	26.9528i	0.156011	−	1.08508i	−0.749882	−	0.661572i	$-0.769890\pi$
$617$	3.87523	−	26.9528i	0.156011	−	1.08508i	0.905893	−	0.423507i	$-0.139201\pi$
$618$		0			0
$619$	17.9957	+	5.28400i	0.723306	+	0.212382i	0.622607	−	0.782535i	$-0.286074\pi$
$619$	17.9957	+	5.28400i	0.723306	+	0.212382i	0.100700	+	0.994917i	$0.467892\pi$
$620$		0			0
$621$	0.114783	−	0.798332i	0.00460608	−	0.0320360i
$622$		0			0
$623$	−13.7722	+	30.1570i	−0.551772	+	1.20821i
$624$		0			0
$625$	0.854244	+	1.87053i	0.0341697	+	0.0748213i
$626$		0			0
$627$	1.75690	+	12.2195i	0.0701640	+	0.488001i
$628$		0			0
$629$	3.00077	+	20.8708i	0.119649	+	0.832174i
$630$		0			0
$631$	−7.67878	+	4.93486i	−0.305688	+	0.196453i	−0.684487	−	0.729026i	$-0.739974\pi$
$631$	−7.67878	+	4.93486i	−0.305688	+	0.196453i	0.378799	+	0.925479i	$0.376337\pi$
$632$		0			0
$633$	10.9760			0.436256
$634$		0			0
$635$	−3.04297	−	6.66318i	−0.120757	−	0.264420i
$636$		0			0
$637$	−4.75049	+	5.48236i	−0.188221	+	0.217219i
$638$		0			0
$639$	−0.947472	+	0.608903i	−0.0374814	+	0.0240878i
$640$		0			0
$641$	−40.7260			−1.60858			−0.804291	−	0.594236i	$-0.797454\pi$
$641$	−40.7260			−1.60858			−0.804291	+	0.594236i	$0.797454\pi$
$642$		0			0
$643$	13.9394	−	4.09299i	0.549717	−	0.161412i	0.00493317	−	0.999988i	$-0.498430\pi$
$643$	13.9394	−	4.09299i	0.549717	−	0.161412i	0.544784	+	0.838576i	$0.316612\pi$
$644$		0			0
$645$	−2.28304	−	1.46722i	−0.0898945	−	0.0577717i
$646$		0			0
$647$	4.25038	−	9.30703i	0.167100	−	0.365897i	−0.807495	−	0.589875i	$-0.799177\pi$
$647$	4.25038	−	9.30703i	0.167100	−	0.365897i	0.974594	+	0.223978i	$0.0719043\pi$
$648$		0			0
$649$	7.65718	−	2.24835i	0.300570	−	0.0882555i
$650$		0			0
$651$	17.2765	−	19.9381i	0.677119	−	0.781437i
$652$		0			0
$653$	1.27434	+	8.86324i	0.0498688	+	0.346845i	0.999445	+	0.0333091i	$0.0106046\pi$
$653$	1.27434	+	8.86324i	0.0498688	+	0.346845i	−0.949576	+	0.313536i	$0.898486\pi$
$654$		0			0
$655$	−6.56537	+	7.57684i	−0.256530	+	0.296052i
$656$		0			0
$657$	−13.6008	−	8.74073i	−0.530619	−	0.341008i
$658$		0			0
$659$	−12.2387	−	3.59360i	−0.476751	−	0.139987i	0.0345238	−	0.999404i	$-0.489009\pi$
$659$	−12.2387	−	3.59360i	−0.476751	−	0.139987i	−0.511275	+	0.859417i	$0.670827\pi$
$660$		0			0
$661$	−24.8095	−	28.6317i	−0.964977	−	1.11364i	−0.993475	−	0.114049i	$-0.963618\pi$
$661$	−24.8095	−	28.6317i	−0.964977	−	1.11364i	0.0284978	−	0.999594i	$-0.490928\pi$
$662$		0			0
$663$	−1.27439	−	1.47072i	−0.0494931	−	0.0571181i
$664$		0			0
$665$	−22.3440	−	6.56080i	−0.866465	−	0.254417i
$666$		0			0
$667$	3.46421	−	7.58556i	0.134135	−	0.293714i
$668$		0			0
$669$	4.91363			0.189972
$670$		0			0
$671$	27.6130			1.06599
$672$		0			0
$673$	2.33293	−	5.10841i	0.0899280	−	0.196915i	−0.859324	−	0.511432i	$-0.829115\pi$
$673$	2.33293	−	5.10841i	0.0899280	−	0.196915i	0.949252	+	0.314517i	$0.101843\pi$
$674$		0			0
$675$	3.13866	+	0.921594i	0.120807	+	0.0354722i
$676$		0			0
$677$	−22.4800	−	25.9433i	−0.863976	−	0.997081i	−0.999980	−	0.00637273i	$-0.997971\pi$
$677$	−22.4800	−	25.9433i	−0.863976	−	0.997081i	0.136004	−	0.990708i	$-0.456574\pi$
$678$		0			0
$679$	19.9507	+	23.0243i	0.765637	+	0.883592i
$680$		0			0
$681$	12.9313	+	3.79697i	0.495528	+	0.145500i
$682$		0			0
$683$	−14.8258	−	9.52796i	−0.567294	−	0.364577i	0.225336	−	0.974281i	$-0.427652\pi$
$683$	−14.8258	−	9.52796i	−0.567294	−	0.364577i	−0.792629	+	0.609704i	$0.791288\pi$
$684$		0			0
$685$	−6.91729	+	7.98298i	−0.264296	+	0.305014i
$686$		0			0
$687$	−0.294160	−	2.04593i	−0.0112229	−	0.0780571i
$688$		0			0
$689$	3.71740	−	4.29011i	0.141622	−	0.163440i
$690$		0			0
$691$	11.1148	−	3.26361i	0.422828	−	0.124153i	−0.0633947	−	0.997989i	$-0.520193\pi$
$691$	11.1148	−	3.26361i	0.422828	−	0.124153i	0.486222	+	0.873835i	$0.338375\pi$
$692$		0			0
$693$	−4.92622	+	10.7869i	−0.187132	+	0.409761i
$694$		0			0
$695$	18.9090	+	12.1521i	0.717260	+	0.460955i
$696$		0			0
$697$	−7.42420	+	2.17994i	−0.281211	+	0.0825711i
$698$		0			0
$699$	−22.4674			−0.849793
$700$		0			0
$701$	−3.50645	+	2.25346i	−0.132437	+	0.0851120i	−0.605182	−	0.796087i	$-0.706900\pi$
$701$	−3.50645	+	2.25346i	−0.132437	+	0.0851120i	0.472745	+	0.881199i	$0.343263\pi$
$702$		0			0
$703$	22.0732	−	25.4738i	0.832506	−	0.960763i
$704$		0			0
$705$	6.30692	+	13.8102i	0.237532	+	0.520123i
$706$		0			0
$707$	38.1678			1.43545
$708$		0			0
$709$	19.3640	−	12.4445i	0.727229	−	0.467362i	−0.123916	−	0.992293i	$-0.539545\pi$
$709$	19.3640	−	12.4445i	0.727229	−	0.467362i	0.851145	+	0.524931i	$0.175909\pi$
$710$		0			0
$711$	−0.717766	−	4.99217i	−0.0269183	−	0.187221i
$712$		0			0
$713$	−0.734167	−	5.10625i	−0.0274948	−	0.191230i
$714$		0			0
$715$	−1.13771	−	2.49125i	−0.0425481	−	0.0931674i
$716$		0			0
$717$	−8.91383	+	19.5186i	−0.332893	+	0.728934i
$718$		0			0
$719$	−3.31416	+	23.0505i	−0.123597	+	0.859639i	0.829830	+	0.558016i	$0.188437\pi$
$719$	−3.31416	+	23.0505i	−0.123597	+	0.859639i	−0.953427	+	0.301623i	$0.902472\pi$
$720$		0			0
$721$	39.5742	+	11.6200i	1.47382	+	0.432753i
$722$		0			0
$723$	−3.09665	+	21.5377i	−0.115166	+	0.800996i
$724$		0			0
$725$	28.4528	+	18.2855i	1.05671	+	0.679106i
$726$		0			0
$727$	22.2434	+	48.7063i	0.824963	+	1.80642i	0.520388	+	0.853930i	$0.325787\pi$
$727$	22.2434	+	48.7063i	0.824963	+	1.80642i	0.304575	+	0.952488i	$0.401485\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	5.31952	−	1.56195i	0.196750	−	0.0577709i
$732$		0			0
$733$	−4.67323	+	32.5030i	−0.172610	+	1.20053i	0.700734	+	0.713422i	$0.252856\pi$
$733$	−4.67323	+	32.5030i	−0.172610	+	1.20053i	−0.873344	+	0.487104i	$0.838053\pi$
$734$		0			0
$735$	−8.62151	−	9.94975i	−0.318009	−	0.367002i
$736$		0			0
$737$	−15.1414	+	18.0152i	−0.557741	+	0.663599i
$738$		0			0
$739$	−21.7024	−	25.0459i	−0.798335	−	0.921328i	0.199954	−	0.979805i	$-0.435921\pi$
$739$	−21.7024	−	25.0459i	−0.798335	−	0.921328i	−0.998289	+	0.0584776i	$0.981375\pi$
$740$		0			0
$741$	−0.442728	+	3.07924i	−0.0162640	+	0.113119i
$742$		0			0
$743$	28.2701	−	8.30086i	1.03713	−	0.304529i	0.281524	−	0.959554i	$-0.409160\pi$
$743$	28.2701	−	8.30086i	1.03713	−	0.304529i	0.755607	+	0.655025i	$0.227342\pi$
$744$		0			0
$745$	−24.8026	+	15.9397i	−0.908698	+	0.583985i
$746$		0			0
$747$	−1.60861	−	3.52236i	−0.0588559	−	0.128876i
$748$		0			0
$749$	−19.8888	−	12.7817i	−0.726720	−	0.467035i
$750$		0			0
$751$	1.76737	−	12.2923i	0.0644921	−	0.448552i	−0.931832	−	0.362890i	$-0.881790\pi$
$751$	1.76737	−	12.2923i	0.0644921	−	0.448552i	0.996324	−	0.0856626i	$-0.0273007\pi$
$752$		0			0
$753$	−3.43925	−	1.00986i	−0.125333	−	0.0368012i
$754$		0			0
$755$	−1.74667	+	12.1484i	−0.0635678	+	0.442124i
$756$		0			0
$757$	−2.92546	+	6.40587i	−0.106328	+	0.232825i	−0.955316	−	0.295586i	$-0.904485\pi$
$757$	−2.92546	+	6.40587i	−0.106328	+	0.232825i	0.848988	+	0.528412i	$0.177212\pi$
$758$		0			0
$759$	0.963279	+	2.10929i	0.0349648	+	0.0765622i
$760$		0			0
$761$	−5.40272	−	37.5767i	−0.195848	−	1.36216i	−0.816172	−	0.577809i	$-0.803908\pi$
$761$	−5.40272	−	37.5767i	−0.195848	−	1.36216i	0.620324	−	0.784346i	$-0.287001\pi$
$762$		0			0
$763$	6.60279	+	45.9234i	0.239037	+	1.66254i
$764$		0			0
$765$	2.97115	−	1.90944i	0.107422	−	0.0690360i
$766$		0			0
$767$	2.01102			0.0726136
$768$		0			0
$769$	−16.7392	−	36.6538i	−0.603632	−	1.32177i	−0.926845	−	0.375444i	$-0.877490\pi$
$769$	−16.7392	−	36.6538i	−0.603632	−	1.32177i	0.323213	−	0.946326i	$-0.395237\pi$
$770$		0			0
$771$	−2.16287	+	2.49609i	−0.0778939	+	0.0898944i
$772$		0			0
$773$	38.4729	−	24.7250i	1.38377	−	0.889296i	0.384347	−	0.923189i	$-0.374427\pi$
$773$	38.4729	−	24.7250i	1.38377	−	0.889296i	0.999425	+	0.0338923i	$0.0107903\pi$
$774$		0			0
$775$	20.9229			0.751571
$776$		0			0
$777$	31.0665	−	9.12193i	1.11450	−	0.327248i
$778$		0			0
$779$	10.4056	+	6.68729i	0.372820	+	0.239597i
$780$		0			0
$781$	1.34513	−	2.94543i	0.0481326	−	0.105396i
$782$		0			0
$783$	9.92058	−	2.91294i	0.354532	−	0.104100i
$784$		0			0
$785$	−2.90271	+	3.34991i	−0.103602	+	0.119563i
$786$		0			0
$787$	−6.30897	−	43.8798i	−0.224890	−	1.56415i	−0.719164	−	0.694841i	$-0.755475\pi$
$787$	−6.30897	−	43.8798i	−0.224890	−	1.56415i	0.494273	−	0.869307i	$-0.335434\pi$
$788$		0			0
$789$	−2.01308	+	2.32322i	−0.0716676	+	0.0827088i
$790$		0			0
$791$	−47.1079	−	30.2744i	−1.67497	−	1.07644i
$792$		0			0
$793$	6.67643	+	1.96038i	0.237087	+	0.0696150i
$794$		0			0
$795$	6.74659	+	7.78598i	0.239277	+	0.276140i
$796$		0			0
$797$	−11.2091	−	12.9360i	−0.397047	−	0.458217i	0.521662	−	0.853153i	$-0.325312\pi$
$797$	−11.2091	−	12.9360i	−0.397047	−	0.458217i	−0.918709	+	0.394936i	$0.870767\pi$
$798$		0			0
$799$	−29.7592	−	8.73809i	−1.05280	−	0.309131i
$800$		0			0
$801$	−3.33899	+	7.31137i	−0.117978	+	0.258335i
$802$		0			0
$803$	46.4817			1.64030
$804$		0			0
$805$	−4.37413			−0.154168
$806$		0			0
$807$	12.0726	−	26.4353i	0.424975	−	0.930566i
$808$		0			0
$809$	2.87282	+	0.843535i	0.101003	+	0.0296571i	0.331843	−	0.943334i	$-0.392329\pi$
$809$	2.87282	+	0.843535i	0.101003	+	0.0296571i	−0.230841	+	0.972992i	$0.574148\pi$
$810$		0			0
$811$	9.74637	+	11.2479i	0.342241	+	0.394967i	0.900612	−	0.434624i	$-0.143119\pi$
$811$	9.74637	+	11.2479i	0.342241	+	0.394967i	−0.558371	+	0.829592i	$0.688573\pi$
$812$		0			0
$813$	0.934160	+	1.07808i	0.0327624	+	0.0378098i
$814$		0			0
$815$	−24.9048	−	7.31272i	−0.872379	−	0.256153i
$816$		0			0
$817$	−7.45575	−	4.79152i	−0.260844	−	0.167634i
$818$		0			0
$819$	−1.95690	+	2.25839i	−0.0683797	+	0.0789144i
$820$		0			0
$821$	3.13480	+	21.8030i	0.109405	+	0.760931i	0.968482	+	0.249084i	$0.0801295\pi$
$821$	3.13480	+	21.8030i	0.109405	+	0.760931i	−0.859076	+	0.511847i	$0.828961\pi$
$822$		0			0
$823$	−17.3723	+	20.0487i	−0.605561	+	0.698854i	−0.972898	−	0.231233i	$-0.925724\pi$
$823$	−17.3723	+	20.0487i	−0.605561	+	0.698854i	0.367338	+	0.930088i	$0.380269\pi$
$824$		0			0
$825$	−9.02376	+	2.64961i	−0.314167	+	0.0922477i
$826$		0			0
$827$	19.6671	−	43.0649i	0.683891	−	1.49751i	−0.174576	−	0.984644i	$-0.555855\pi$
$827$	19.6671	−	43.0649i	0.683891	−	1.49751i	0.858467	−	0.512869i	$-0.171417\pi$
$828$		0			0
$829$	39.0799	+	25.1151i	1.35730	+	0.872284i	0.998138	−	0.0609920i	$-0.0194264\pi$
$829$	39.0799	+	25.1151i	1.35730	+	0.872284i	0.359161	+	0.933275i	$0.383063\pi$
$830$		0			0
$831$	−8.51973	+	2.50162i	−0.295546	+	0.0867801i
$832$		0			0
$833$	26.8955			0.931872
$834$		0			0
$835$	4.11354	−	2.64361i	0.142355	−	0.0914859i
$836$		0			0
$837$	4.18858	−	4.83388i	0.144779	−	0.167083i
$838$		0			0
$839$	−15.3380	−	33.5856i	−0.529528	−	1.15950i	−0.965705	−	0.259643i	$-0.916395\pi$
$839$	−15.3380	−	33.5856i	−0.529528	−	1.15950i	0.436177	−	0.899861i	$-0.356332\pi$
$840$		0			0
$841$	77.9031			2.68631
$842$		0			0
$843$	13.6681	−	8.78397i	0.470755	−	0.302536i
$844$		0			0
$845$	2.33438	+	16.2360i	0.0803051	+	0.558534i
$846$		0			0
$847$	1.60497	+	11.1628i	0.0551473	+	0.383558i
$848$		0			0
$849$	−4.93210	−	10.7998i	−0.169269	−	0.370648i
$850$		0			0
$851$	2.63009	−	5.75909i	0.0901582	−	0.197419i
$852$		0			0
$853$	−2.84441	+	19.7833i	−0.0973908	+	0.677368i	0.881380	+	0.472408i	$0.156615\pi$
$853$	−2.84441	+	19.7833i	−0.0973908	+	0.677368i	−0.978771	+	0.204959i	$0.934294\pi$
$854$		0			0
$855$	−5.41718	−	1.59063i	−0.185264	−	0.0543983i
$856$		0			0
$857$	1.48524	−	10.3301i	0.0507347	−	0.352868i	−0.948603	−	0.316470i	$-0.897502\pi$
$857$	1.48524	−	10.3301i	0.0507347	−	0.352868i	0.999337	−	0.0363982i	$-0.0115885\pi$
$858$		0			0
$859$	17.3639	+	11.1591i	0.592449	+	0.380744i	0.802239	−	0.597002i	$-0.203642\pi$
$859$	17.3639	+	11.1591i	0.592449	+	0.380744i	−0.209790	+	0.977746i	$0.567278\pi$
$860$		0			0
$861$	4.93580	+	10.8079i	0.168211	+	0.368332i
$862$		0			0
$863$	31.8619	−	20.4764i	1.08459	−	0.697024i	0.128978	−	0.991647i	$-0.458830\pi$
$863$	31.8619	−	20.4764i	1.08459	−	0.697024i	0.955614	+	0.294623i	$0.0951941\pi$
$864$		0			0
$865$	12.8274	−	3.76645i	0.436143	−	0.128063i
$866$		0			0
$867$	1.39254	−	9.68530i	0.0472930	−	0.328930i
$868$		0			0
$869$	9.49565	+	10.9586i	0.322118	+	0.371744i
$870$		0			0
$871$	−4.93996	+	3.28086i	−0.167384	+	0.111168i
$872$		0			0
$873$	4.83693	+	5.58211i	0.163705	+	0.188926i
$874$		0			0
$875$	6.38384	−	44.4006i	0.215813	−	1.50101i
$876$		0			0
$877$	−32.0607	+	9.41388i	−1.08261	+	0.317884i	−0.773924	−	0.633279i	$-0.781709\pi$
$877$	−32.0607	+	9.41388i	−1.08261	+	0.317884i	−0.308690	+	0.951163i	$0.599891\pi$
$878$		0			0
$879$	9.21396	−	5.92145i	0.310779	−	0.199726i
$880$		0			0
$881$	−14.2250	−	31.1484i	−0.479253	−	1.04942i	−0.982668	−	0.185373i	$-0.940651\pi$
$881$	−14.2250	−	31.1484i	−0.479253	−	1.04942i	0.503415	−	0.864044i	$-0.332077\pi$
$882$		0			0
$883$	−10.0471	−	6.45690i	−0.338113	−	0.217292i	0.360555	−	0.932738i	$-0.382587\pi$
$883$	−10.0471	−	6.45690i	−0.338113	−	0.217292i	−0.698668	+	0.715446i	$0.746224\pi$
$884$		0			0
$885$	−0.519410	+	3.61258i	−0.0174598	+	0.121436i
$886$		0			0
$887$	20.9660	+	6.15618i	0.703970	+	0.206704i	0.614076	−	0.789247i	$-0.289529\pi$
$887$	20.9660	+	6.15618i	0.703970	+	0.206704i	0.0898943	+	0.995951i	$0.471347\pi$
$888$		0			0
$889$	3.27023	−	22.7449i	0.109680	−	0.762841i
$890$		0			0
$891$	−1.19433	+	2.61522i	−0.0400116	+	0.0876133i
$892$		0			0
$893$	20.5966	+	45.1002i	0.689238	+	1.50922i
$894$		0			0
$895$	−4.09018	−	28.4478i	−0.136720	−	0.950906i
$896$		0			0
$897$	0.0831589	+	0.578383i	0.00277659	+	0.0193116i
$898$		0			0
$899$	55.6340	−	35.7538i	1.85550	−	1.19246i
$900$		0			0
$901$	−21.0465			−0.701161
$902$		0			0
$903$	−3.53655	−	7.74397i	−0.117689	−	0.257703i
$904$		0			0
$905$	−0.829786	+	0.957624i	−0.0275830	+	0.0318325i
$906$		0			0
$907$	−40.1019	+	25.7719i	−1.33156	+	0.855743i	−0.996263	−	0.0863685i	$-0.972474\pi$
$907$	−40.1019	+	25.7719i	−1.33156	+	0.855743i	−0.335299	+	0.942112i	$0.608837\pi$
$908$		0			0
$909$	9.25356			0.306921
$910$		0			0
$911$	−38.5138	+	11.3087i	−1.27602	+	0.374673i	−0.848434	−	0.529301i	$-0.822454\pi$
$911$	−38.5138	+	11.3087i	−1.27602	+	0.374673i	−0.427586	+	0.903975i	$0.640636\pi$
$912$		0			0
$913$	9.36565	+	6.01894i	0.309958	+	0.199198i
$914$		0			0
$915$	−5.24602	+	11.4872i	−0.173428	+	0.379754i
$916$		0			0
$917$	−30.1762	+	8.86052i	−0.996504	+	0.292600i
$918$		0			0
$919$	33.4258	−	38.5754i	1.10261	−	1.27248i	0.143443	−	0.989659i	$-0.454183\pi$
$919$	33.4258	−	38.5754i	1.10261	−	1.27248i	0.959171	−	0.282826i	$-0.0912720\pi$
$920$		0			0
$921$	1.06516	+	7.40838i	0.0350984	+	0.244115i
$922$		0			0
$923$	0.534343	−	0.616665i	0.0175881	−	0.0202978i
$924$		0			0
$925$	21.6018	+	13.8827i	0.710264	+	0.456459i
$926$		0			0
$927$	9.59453	+	2.81721i	0.315126	+	0.0925293i
$928$		0			0
$929$	10.5320	+	12.1545i	0.345542	+	0.398777i	0.901744	−	0.432270i	$-0.142287\pi$
$929$	10.5320	+	12.1545i	0.345542	+	0.398777i	−0.556202	+	0.831047i	$0.687742\pi$
$930$		0			0
$931$	−28.1554	−	32.4930i	−0.922755	−	1.06492i
$932$		0			0
$933$	7.29864	+	2.14307i	0.238947	+	0.0701611i
$934$		0			0
$935$	−4.21816	+	9.23648i	−0.137949	+	0.302065i
$936$		0			0
$937$	−9.68910			−0.316529			−0.158265	−	0.987397i	$-0.550590\pi$
$937$	−9.68910			−0.316529			−0.158265	+	0.987397i	$0.550590\pi$
$938$		0			0
$939$	−11.6055			−0.378730
$940$		0			0
$941$	−10.5603	+	23.1239i	−0.344256	+	0.753816i	−0.999999	−	0.00116782i	$-0.999628\pi$
$941$	−10.5603	+	23.1239i	−0.344256	+	0.753816i	0.655743	+	0.754984i	$0.272356\pi$
$942$		0			0
$943$	2.22923	+	0.654561i	0.0725937	+	0.0213154i
$944$		0			0
$945$	−3.55152	−	4.09867i	−0.115531	−	0.133330i
$946$		0			0
$947$	21.1813	+	24.4445i	0.688299	+	0.794340i	0.987122	−	0.159969i	$-0.0511394\pi$
$947$	21.1813	+	24.4445i	0.688299	+	0.794340i	−0.298823	+	0.954309i	$0.596594\pi$
$948$		0			0
$949$	11.2386	+	3.29995i	0.364820	+	0.107121i
$950$		0			0
$951$	−19.4952	−	12.5288i	−0.632174	−	0.406273i
$952$		0			0
$953$	8.17018	−	9.42889i	0.264658	−	0.305432i	−0.607830	−	0.794067i	$-0.707960\pi$
$953$	8.17018	−	9.42889i	0.264658	−	0.305432i	0.872488	+	0.488635i	$0.162505\pi$
$954$		0			0
$955$	2.20910	+	15.3646i	0.0714847	+	0.497187i
$956$		0			0
$957$	−19.4665	+	22.4655i	−0.629261	+	0.726206i
$958$		0			0
$959$	−31.7937	+	9.33547i	−1.02667	+	0.301458i
$960$		0			0
$961$	4.11704	−	9.01505i	0.132808	−	0.290808i
$962$		0			0
$963$	−4.82192	−	3.09886i	−0.155384	−	0.0998593i
$964$		0			0
$965$	10.2525	−	3.01041i	0.330040	−	0.0969086i
$966$		0			0
$967$	−59.6244			−1.91739			−0.958695	−	0.284436i	$-0.908194\pi$
$967$	−59.6244			−1.91739			−0.958695	+	0.284436i	$0.908194\pi$
$968$		0			0
$969$	9.70293	−	6.23569i	0.311703	−	0.200319i
$970$		0			0
$971$	−31.0700	+	35.8567i	−0.997085	+	1.15070i	−0.00851035	+	0.999964i	$0.502709\pi$
$971$	−31.0700	+	35.8567i	−0.997085	+	1.15070i	−0.988574	+	0.150733i	$0.951836\pi$
$972$		0			0
$973$	29.2911	+	64.1387i	0.939031	+	2.05619i
$974$		0			0
$975$	−2.36992			−0.0758983
$976$		0			0
$977$	−44.0888	+	28.3342i	−1.41053	+	0.906490i	−0.999986	−	0.00535176i	$-0.998296\pi$
$977$	−44.0888	+	28.3342i	−1.41053	+	0.906490i	−0.410541	+	0.911842i	$0.634660\pi$
$978$		0			0
$979$	−3.28872	−	22.8735i	−0.105108	−	0.731041i
$980$		0			0
$981$	1.60081	+	11.1339i	0.0511098	+	0.355477i
$982$		0			0
$983$	11.9386	+	26.1419i	0.380782	+	0.833797i	0.998863	+	0.0476821i	$0.0151834\pi$
$983$	11.9386	+	26.1419i	0.380782	+	0.833797i	−0.618080	+	0.786115i	$0.712089\pi$
$984$		0			0
$985$	−12.8080	+	28.0455i	−0.408095	+	0.893604i
$986$		0			0
$987$	−6.77793	+	47.1415i	−0.215744	+	1.50053i
$988$		0			0
$989$	−1.59727	−	0.469000i	−0.0507902	−	0.0149133i
$990$		0			0
$991$	4.53537	−	31.5442i	0.144071	−	1.00203i	−0.781620	−	0.623754i	$-0.785607\pi$
$991$	4.53537	−	31.5442i	0.144071	−	1.00203i	0.925691	−	0.378280i	$-0.123484\pi$
$992$		0			0
$993$	−14.5929	−	9.37828i	−0.463091	−	0.297611i
$994$		0			0
$995$	2.17331	+	4.75889i	0.0688987	+	0.150867i
$996$		0			0
$997$	−0.732070	+	0.470473i	−0.0231849	+	0.0149000i	−0.552182	−	0.833724i	$-0.686205\pi$
$997$	−0.732070	+	0.470473i	−0.0231849	+	0.0149000i	0.528997	+	0.848624i	$0.322568\pi$
$998$		0			0
$999$	7.53187	−	2.21156i	0.238298	−	0.0699706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.241.2	✓	60
67.62	even	11	inner	804.2.q.a.397.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.241.2	✓	60	1.1	even	1	trivial
804.2.q.a.397.2	yes	60	67.62	even	11	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(-1.26159 - 0.370436i) q^{5} +(-2.70108 - 3.11721i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(-1.26159 - 0.370436i) q^{5} +(-2.70108 - 3.11721i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(2.75858 + 0.809991i) q^{11} +(0.609479 + 0.391688i) q^{13} +(-0.861044 + 0.993698i) q^{15} +(-0.382271 - 2.65875i) q^{17} +(-2.81192 + 3.24513i) q^{19} +(-3.95759 + 1.16205i) q^{21} +(-0.335049 + 0.733656i) q^{23} +(-2.75188 - 1.76853i) q^{25} +(-0.959493 + 0.281733i) q^{27} -10.3394 q^{29} +(-5.38078 + 3.45802i) q^{31} +(1.88275 - 2.17281i) q^{33} +(2.25293 + 4.93322i) q^{35} -7.84985 q^{37} +(0.609479 - 0.391688i) q^{39} +(-0.409955 - 2.85130i) q^{41} +(0.293738 + 2.04299i) q^{43} +(0.546209 + 1.19603i) q^{45} +(4.79668 - 10.5033i) q^{47} +(-1.42498 + 9.91093i) q^{49} +(-2.57729 - 0.756760i) q^{51} +(1.11509 - 7.75560i) q^{53} +(-3.18014 - 2.04375i) q^{55} +(1.78376 + 3.90589i) q^{57} +(2.33513 - 1.50070i) q^{59} +(9.21537 - 2.70588i) q^{61} +(-0.587001 + 4.08268i) q^{63} +(-0.623817 - 0.719923i) q^{65} +(-3.28782 + 7.49601i) q^{67} +(0.528172 + 0.609543i) q^{69} +(0.160284 - 1.11480i) q^{71} +(15.5125 - 4.55487i) q^{73} +(-2.75188 + 1.76853i) q^{75} +(-4.92622 - 10.7869i) q^{77} +(4.24287 + 2.72673i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(3.71544 + 1.09095i) q^{83} +(-0.502629 + 3.49586i) q^{85} +(-4.29514 + 9.40504i) q^{87} +(-3.33899 - 7.31137i) q^{89} +(-0.425276 - 2.95786i) q^{91} +(0.910266 + 6.33104i) q^{93} +(4.74961 - 3.05239i) q^{95} -7.38619 q^{97} +(-1.19433 - 2.61522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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