LMFDB - Embedded newform 804.2.q.b.25.6

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			25.6
Character	$\chi$	$=$	804.25
Dual form			804.2.q.b.193.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(4.04726 - 2.60101i) q^{11} +(-2.03230 + 4.45011i) q^{13} +(0.438719 - 3.05136i) q^{15} +(3.53314 + 1.03742i) q^{17} +(0.417152 - 2.90136i) q^{19} +(1.06979 + 0.687514i) q^{21} +(-1.78008 + 2.05432i) q^{23} +(1.87072 - 4.09630i) q^{25} +(-0.841254 - 0.540641i) q^{27} +1.04126 q^{29} +(-1.99390 - 4.36603i) q^{31} +(0.684674 - 4.76201i) q^{33} +(2.56719 + 2.96269i) q^{35} -7.59300 q^{37} +(2.03230 + 4.45011i) q^{39} +(-4.78280 - 1.40436i) q^{41} +(10.2741 + 3.01674i) q^{43} +(-2.01876 - 2.32977i) q^{45} +(-0.421438 + 0.486365i) q^{47} +(5.16482 - 1.51653i) q^{49} +(3.09774 - 1.99080i) q^{51} +(-13.4486 + 3.94887i) q^{53} +(6.16101 - 13.4907i) q^{55} +(-1.91952 - 2.21525i) q^{57} +(-1.53624 - 3.36389i) q^{59} +(-0.360924 - 0.231952i) q^{61} +(1.22015 - 0.358269i) q^{63} +(2.14630 + 14.9279i) q^{65} +(-5.33324 - 6.20939i) q^{67} +(0.386848 + 2.69059i) q^{69} +(9.46015 - 2.77775i) q^{71} +(-0.916042 - 0.588705i) q^{73} +(-1.87072 - 4.09630i) q^{75} +(4.00641 + 4.62365i) q^{77} +(1.64183 - 3.59510i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-4.80142 + 3.08568i) q^{83} +(10.8917 - 3.19810i) q^{85} +(0.681883 - 0.786935i) q^{87} +(8.42570 + 9.72377i) q^{89} +(-5.96924 - 1.75273i) q^{91} +(-4.60536 - 1.35225i) q^{93} +(-3.75372 - 8.21951i) q^{95} -5.06821 q^{97} +(-3.15052 - 3.63590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$		0			0
$5$	2.59336	−	1.66665i	1.15979	−	0.745349i	0.188222	−	0.982126i	$-0.439728\pi$
$5$	2.59336	−	1.66665i	1.15979	−	0.745349i	0.971564	+	0.236777i	$0.0760912\pi$
$6$		0			0
$7$	0.180977	+	1.25872i	0.0684028	+	0.475752i	0.995014	+	0.0997319i	$0.0317985\pi$
$7$	0.180977	+	1.25872i	0.0684028	+	0.475752i	−0.926612	+	0.376020i	$0.877292\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	4.04726	−	2.60101i	1.22029	−	0.784235i	0.237942	−	0.971279i	$-0.423527\pi$
$11$	4.04726	−	2.60101i	1.22029	−	0.784235i	0.982352	+	0.187044i	$0.0598907\pi$
$12$		0			0
$13$	−2.03230	+	4.45011i	−0.563658	+	1.23424i	0.386449	+	0.922311i	$0.373702\pi$
$13$	−2.03230	+	4.45011i	−0.563658	+	1.23424i	−0.950106	+	0.311927i	$0.899026\pi$
$14$		0			0
$15$	0.438719	−	3.05136i	0.113277	−	0.787857i
$16$		0			0
$17$	3.53314	+	1.03742i	0.856911	+	0.251612i	0.680539	−	0.732712i	$-0.261746\pi$
$17$	3.53314	+	1.03742i	0.856911	+	0.251612i	0.176372	+	0.984324i	$0.443564\pi$
$18$		0			0
$19$	0.417152	−	2.90136i	0.0957013	−	0.665617i	−0.884343	−	0.466838i	$-0.845393\pi$
$19$	0.417152	−	2.90136i	0.0957013	−	0.665617i	0.980044	−	0.198779i	$-0.0636977\pi$
$20$		0			0
$21$	1.06979	+	0.687514i	0.233448	+	0.150028i
$22$		0			0
$23$	−1.78008	+	2.05432i	−0.371172	+	0.428355i	−0.910352	−	0.413836i	$-0.864189\pi$
$23$	−1.78008	+	2.05432i	−0.371172	+	0.428355i	0.539180	+	0.842191i	$0.318734\pi$
$24$		0			0
$25$	1.87072	−	4.09630i	0.374143	−	0.819259i
$26$		0			0
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$		0			0
$29$	1.04126			0.193358			0.0966790	−	0.995316i	$-0.469178\pi$
$29$	1.04126			0.193358			0.0966790	+	0.995316i	$0.469178\pi$
$30$		0			0
$31$	−1.99390	−	4.36603i	−0.358115	−	0.784163i	−0.999851	−	0.0172375i	$-0.994513\pi$
$31$	−1.99390	−	4.36603i	−0.358115	−	0.784163i	0.641736	−	0.766925i	$-0.278214\pi$
$32$		0			0
$33$	0.684674	−	4.76201i	0.119187	−	0.828960i
$34$		0			0
$35$	2.56719	+	2.96269i	0.433934	+	0.500786i
$36$		0			0
$37$	−7.59300			−1.24828			−0.624141	−	0.781312i	$-0.714551\pi$
$37$	−7.59300			−1.24828			−0.624141	+	0.781312i	$0.714551\pi$
$38$		0			0
$39$	2.03230	+	4.45011i	0.325428	+	0.712588i
$40$		0			0
$41$	−4.78280	−	1.40436i	−0.746948	−	0.219324i	−0.113960	−	0.993485i	$-0.536354\pi$
$41$	−4.78280	−	1.40436i	−0.746948	−	0.219324i	−0.632988	+	0.774162i	$0.718172\pi$
$42$		0			0
$43$	10.2741	+	3.01674i	1.56678	+	0.460049i	0.946063	−	0.323983i	$-0.105022\pi$
$43$	10.2741	+	3.01674i	1.56678	+	0.460049i	0.620721	+	0.784032i	$0.286840\pi$
$44$		0			0
$45$	−2.01876	−	2.32977i	−0.300939	−	0.347302i
$46$		0			0
$47$	−0.421438	+	0.486365i	−0.0614731	+	0.0709437i	−0.785653	−	0.618667i	$-0.787673\pi$
$47$	−0.421438	+	0.486365i	−0.0614731	+	0.0709437i	0.724180	+	0.689611i	$0.242218\pi$
$48$		0			0
$49$	5.16482	−	1.51653i	0.737832	−	0.216647i
$50$		0			0
$51$	3.09774	−	1.99080i	0.433771	−	0.278768i
$52$		0			0
$53$	−13.4486	+	3.94887i	−1.84731	+	0.542418i	−0.847373	+	0.530998i	$0.821817\pi$
$53$	−13.4486	+	3.94887i	−1.84731	+	0.542418i	−0.999935	+	0.0114203i	$0.996365\pi$
$54$		0			0
$55$	6.16101	−	13.4907i	0.830751	−	1.81909i
$56$		0			0
$57$	−1.91952	−	2.21525i	−0.254247	−	0.293417i
$58$		0			0
$59$	−1.53624	−	3.36389i	−0.200001	−	0.437941i	0.782883	−	0.622170i	$-0.213749\pi$
$59$	−1.53624	−	3.36389i	−0.200001	−	0.437941i	−0.982883	+	0.184229i	$0.941021\pi$
$60$		0			0
$61$	−0.360924	−	0.231952i	−0.0462116	−	0.0296984i	0.517331	−	0.855785i	$-0.326926\pi$
$61$	−0.360924	−	0.231952i	−0.0462116	−	0.0296984i	−0.563543	+	0.826087i	$0.690562\pi$
$62$		0			0
$63$	1.22015	−	0.358269i	0.153725	−	0.0451377i
$64$		0			0
$65$	2.14630	+	14.9279i	0.266216	+	1.85157i
$66$		0			0
$67$	−5.33324	−	6.20939i	−0.651559	−	0.758598i
$67$	−5.33324	−	6.20939i	−0.651559	−	0.758598i
$68$		0			0
$69$	0.386848	+	2.69059i	0.0465710	+	0.323908i
$70$		0			0
$71$	9.46015	−	2.77775i	1.12271	−	0.329658i	0.332874	−	0.942971i	$-0.391982\pi$
$71$	9.46015	−	2.77775i	1.12271	−	0.329658i	0.789840	+	0.613313i	$0.210164\pi$
$72$		0			0
$73$	−0.916042	−	0.588705i	−0.107215	−	0.0689027i	0.485935	−	0.873995i	$-0.338479\pi$
$73$	−0.916042	−	0.588705i	−0.107215	−	0.0689027i	−0.593149	+	0.805092i	$0.702116\pi$
$74$		0			0
$75$	−1.87072	−	4.09630i	−0.216012	−	0.473000i
$76$		0			0
$77$	4.00641	+	4.62365i	0.456573	+	0.526913i
$78$		0			0
$79$	1.64183	−	3.59510i	0.184720	−	0.404480i	−0.794505	−	0.607258i	$-0.792270\pi$
$79$	1.64183	−	3.59510i	0.184720	−	0.404480i	0.979225	+	0.202778i	$0.0649969\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−4.80142	+	3.08568i	−0.527024	+	0.338698i	−0.776945	−	0.629568i	$-0.783232\pi$
$83$	−4.80142	+	3.08568i	−0.527024	+	0.338698i	0.249921	+	0.968266i	$0.419595\pi$
$84$		0			0
$85$	10.8917	−	3.19810i	1.18137	−	0.346882i
$86$		0			0
$87$	0.681883	−	0.786935i	0.0731056	−	0.0843683i
$88$		0			0
$89$	8.42570	+	9.72377i	0.893122	+	1.03072i	0.999338	+	0.0363747i	$0.0115810\pi$
$89$	8.42570	+	9.72377i	0.893122	+	1.03072i	−0.106216	+	0.994343i	$0.533874\pi$
$90$		0			0
$91$	−5.96924	−	1.75273i	−0.625747	−	0.183736i
$92$		0			0
$93$	−4.60536	−	1.35225i	−0.477553	−	0.140222i
$94$		0			0
$95$	−3.75372	−	8.21951i	−0.385124	−	0.843304i
$96$		0			0
$97$	−5.06821			−0.514598			−0.257299	−	0.966332i	$-0.582833\pi$
$97$	−5.06821			−0.514598			−0.257299	+	0.966332i	$0.582833\pi$
$98$		0			0
$99$	−3.15052	−	3.63590i	−0.316640	−	0.365422i
$100$		0			0
$101$	1.61568	−	11.2373i	0.160766	−	1.11815i	−0.736429	−	0.676515i	$-0.763489\pi$
$101$	1.61568	−	11.2373i	0.160766	−	1.11815i	0.897195	−	0.441635i	$-0.145601\pi$
$102$		0			0
$103$	3.99109	+	8.73926i	0.393253	+	0.861105i	0.997910	+	0.0646185i	$0.0205830\pi$
$103$	3.99109	+	8.73926i	0.393253	+	0.861105i	−0.604657	+	0.796486i	$0.706690\pi$
$104$		0			0
$105$	3.92020			0.382573
$106$		0			0
$107$	1.67901	+	1.07903i	0.162316	+	0.104314i	0.619277	−	0.785173i	$-0.287426\pi$
$107$	1.67901	+	1.07903i	0.162316	+	0.104314i	−0.456961	+	0.889487i	$0.651062\pi$
$108$		0			0
$109$	−6.37773	+	13.9653i	−0.610876	+	1.33763i	0.311097	+	0.950378i	$0.399304\pi$
$109$	−6.37773	+	13.9653i	−0.610876	+	1.33763i	−0.921973	+	0.387254i	$0.873424\pi$
$110$		0			0
$111$	−4.97236	+	5.73841i	−0.471955	+	0.544666i
$112$		0			0
$113$	10.4150	+	6.69331i	0.979760	+	0.629654i	0.929399	−	0.369077i	$-0.120326\pi$
$113$	10.4150	+	6.69331i	0.979760	+	0.629654i	0.0503616	+	0.998731i	$0.483963\pi$
$114$		0			0
$115$	−1.19255	+	8.29436i	−0.111206	+	0.773453i
$116$		0			0
$117$	4.69404	+	1.37829i	0.433964	+	0.127423i
$118$		0			0
$119$	−0.666410	+	4.63498i	−0.0610897	+	0.424888i
$120$		0			0
$121$	5.04545	−	11.0480i	0.458677	−	1.00436i
$122$		0			0
$123$	−4.19341	+	2.69494i	−0.378107	+	0.242995i
$124$		0			0
$125$	0.217935	+	1.51577i	0.0194927	+	0.135575i
$126$		0			0
$127$	−2.42585	−	16.8721i	−0.215259	−	1.49716i	−0.755221	−	0.655470i	$-0.772471\pi$
$127$	−2.42585	−	16.8721i	−0.215259	−	1.49716i	0.539962	−	0.841689i	$-0.318439\pi$
$128$		0			0
$129$	9.00800	−	5.78909i	0.793110	−	0.509701i
$130$		0			0
$131$	−7.73740	+	8.92944i	−0.676020	+	0.780169i	−0.985306	−	0.170801i	$-0.945365\pi$
$131$	−7.73740	+	8.92944i	−0.676020	+	0.780169i	0.309286	+	0.950969i	$0.399910\pi$
$132$		0			0
$133$	3.72749			0.323215
$134$		0			0
$135$	−3.08273			−0.265319
$136$		0			0
$137$	−14.9842	+	17.2927i	−1.28019	+	1.47742i	−0.480512	+	0.876988i	$0.659549\pi$
$137$	−14.9842	+	17.2927i	−1.28019	+	1.47742i	−0.799678	+	0.600429i	$0.794996\pi$
$138$		0			0
$139$	7.20148	−	4.62811i	0.610822	−	0.392551i	−0.198344	−	0.980133i	$-0.563556\pi$
$139$	7.20148	−	4.62811i	0.610822	−	0.392551i	0.809165	+	0.587581i	$0.199920\pi$
$140$		0			0
$141$	0.0915872	+	0.637003i	0.00771304	+	0.0536454i
$142$		0			0
$143$	3.34957	+	23.2968i	0.280105	+	1.94817i
$144$		0			0
$145$	2.70038	−	1.73543i	0.224254	−	0.144119i
$146$		0			0
$147$	2.23612	−	4.89643i	0.184432	−	0.403851i
$148$		0			0
$149$	−1.62615	+	11.3101i	−0.133220	+	0.926563i	0.808100	+	0.589046i	$0.200496\pi$
$149$	−1.62615	+	11.3101i	−0.133220	+	0.926563i	−0.941319	+	0.337517i	$0.890413\pi$
$150$		0			0
$151$	−10.0782	−	2.95922i	−0.820150	−	0.240818i	−0.155369	−	0.987856i	$-0.549657\pi$
$151$	−10.0782	−	2.95922i	−0.820150	−	0.240818i	−0.664781	+	0.747039i	$0.731475\pi$
$152$		0			0
$153$	0.524045	−	3.64481i	0.0423665	−	0.294666i
$154$		0			0
$155$	−12.4476	−	7.99956i	−0.999812	−	0.642540i
$156$		0			0
$157$	−10.8095	+	12.4749i	−0.862694	+	0.995602i	0.137293	+	0.990530i	$0.456160\pi$
$157$	−10.8095	+	12.4749i	−0.862694	+	0.995602i	−0.999987	+	0.00507169i	$0.998386\pi$
$158$		0			0
$159$	−5.82261	+	12.7497i	−0.461763	+	1.01112i
$160$		0			0
$161$	−2.90797	−	1.86884i	−0.229180	−	0.147285i
$162$		0			0
$163$	−23.8950			−1.87160			−0.935798	−	0.352535i	$-0.885320\pi$
$163$	−23.8950			−1.87160			−0.935798	+	0.352535i	$0.885320\pi$
$164$		0			0
$165$	−6.16101	−	13.4907i	−0.479634	−	1.05025i
$166$		0			0
$167$	0.111829	−	0.777790i	0.00865361	−	0.0601872i	−0.985037	−	0.172343i	$-0.944866\pi$
$167$	0.111829	−	0.777790i	0.00865361	−	0.0601872i	0.993691	+	0.112155i	$0.0357755\pi$
$168$		0			0
$169$	−7.16004	−	8.26313i	−0.550772	−	0.635625i
$170$		0			0
$171$	−2.93119			−0.224154
$172$		0			0
$173$	4.29923	+	9.41400i	0.326864	+	0.715733i	0.999711	−	0.0240491i	$-0.00765580\pi$
$173$	4.29923	+	9.41400i	0.326864	+	0.715733i	−0.672846	+	0.739782i	$0.734929\pi$
$174$		0			0
$175$	5.49465	+	1.61338i	0.415357	+	0.121960i
$176$		0			0
$177$	−3.54828	−	1.04187i	−0.266705	−	0.0783116i
$178$		0			0
$179$	−3.23301	−	3.73109i	−0.241647	−	0.278875i	0.621952	−	0.783056i	$-0.286340\pi$
$179$	−3.23301	−	3.73109i	−0.241647	−	0.278875i	−0.863598	+	0.504181i	$0.831795\pi$
$180$		0			0
$181$	−7.78046	+	8.97913i	−0.578317	+	0.667413i	−0.967242	−	0.253856i	$-0.918301\pi$
$181$	−7.78046	+	8.97913i	−0.578317	+	0.667413i	0.388925	+	0.921269i	$0.372846\pi$
$182$		0			0
$183$	−0.411653	+	0.120872i	−0.0304303	+	0.00893513i
$184$		0			0
$185$	−19.6914	+	12.6549i	−1.44774	+	0.930406i
$186$		0			0
$187$	16.9979	−	4.99102i	1.24301	−	0.364980i
$188$		0			0
$189$	0.528269	−	1.15675i	0.0384259	−	0.0841410i
$190$		0			0
$191$	−8.72050	−	10.0640i	−0.630993	−	0.728205i	0.346762	−	0.937953i	$-0.387281\pi$
$191$	−8.72050	−	10.0640i	−0.630993	−	0.728205i	−0.977755	+	0.209748i	$0.932736\pi$
$192$		0			0
$193$	0.745307	+	1.63200i	0.0536484	+	0.117474i	0.934558	−	0.355811i	$-0.115795\pi$
$193$	0.745307	+	1.63200i	0.0536484	+	0.117474i	−0.880909	+	0.473285i	$0.843068\pi$
$194$		0			0
$195$	12.6873	+	8.15360i	0.908553	+	0.583892i
$196$		0			0
$197$	2.10277	−	0.617430i	0.149816	−	0.0439900i	−0.205965	−	0.978559i	$-0.566033\pi$
$197$	2.10277	−	0.617430i	0.149816	−	0.0439900i	0.355781	+	0.934569i	$0.384215\pi$
$198$		0			0
$199$	−0.277162	−	1.92770i	−0.0196475	−	0.136651i	0.977637	−	0.210301i	$-0.0674444\pi$
$199$	−0.277162	−	1.92770i	−0.0196475	−	0.136651i	−0.997284	+	0.0736498i	$0.976535\pi$
$200$		0			0
$201$	−8.18527	−	0.0356889i	−0.577345	−	0.00251730i
$202$		0			0
$203$	0.188445	+	1.31066i	0.0132262	+	0.0919905i
$204$		0			0
$205$	−14.7441	+	4.32926i	−1.02977	+	0.302369i
$206$		0			0
$207$	2.28674	+	1.46960i	0.158939	+	0.102144i
$208$		0			0
$209$	−5.85815	−	12.8276i	−0.405217	−	0.887300i
$210$		0			0
$211$	14.5033	+	16.7377i	0.998450	+	1.15227i	0.988331	+	0.152324i	$0.0486756\pi$
$211$	14.5033	+	16.7377i	0.998450	+	1.15227i	0.0101191	+	0.999949i	$0.496779\pi$
$212$		0			0
$213$	4.09580	−	8.96855i	0.280639	−	0.614515i
$214$		0			0
$215$	31.6723	−	9.29982i	2.16003	−	0.634242i
$216$		0			0
$217$	5.13477	−	3.29992i	0.348571	−	0.224013i
$218$		0			0
$219$	−1.04479	+	0.306779i	−0.0706006	+	0.0207302i
$220$		0			0
$221$	−11.7970	+	13.6145i	−0.793554	+	0.915810i
$222$		0			0
$223$	4.00925	+	4.62692i	0.268479	+	0.309842i	0.873940	−	0.486033i	$-0.161557\pi$
$223$	4.00925	+	4.62692i	0.268479	+	0.309842i	−0.605461	+	0.795875i	$0.707011\pi$
$224$		0			0
$225$	−4.32083	−	1.26871i	−0.288056	−	0.0845807i
$226$		0			0
$227$	−17.9113	−	5.25922i	−1.18881	−	0.349067i	−0.373247	−	0.927732i	$-0.621756\pi$
$227$	−17.9113	−	5.25922i	−1.18881	−	0.349067i	−0.815565	+	0.578666i	$0.803574\pi$
$228$		0			0
$229$	−6.31208	−	13.8215i	−0.417114	−	0.913352i	−0.995245	−	0.0974077i	$-0.968945\pi$
$229$	−6.31208	−	13.8215i	−0.417114	−	0.913352i	0.578131	−	0.815944i	$-0.303782\pi$
$230$		0			0
$231$	6.11796			0.402532
$232$		0			0
$233$	13.6117	+	15.7088i	0.891734	+	1.02912i	0.999390	+	0.0349282i	$0.0111202\pi$
$233$	13.6117	+	15.7088i	0.891734	+	1.02912i	−0.107655	+	0.994188i	$0.534334\pi$
$234$		0			0
$235$	−0.282339	+	1.96371i	−0.0184178	+	0.128098i
$236$		0			0
$237$	−1.64183	−	3.59510i	−0.106648	−	0.233527i
$238$		0			0
$239$	14.7158			0.951884			0.475942	−	0.879477i	$-0.342107\pi$
$239$	14.7158			0.951884			0.475942	+	0.879477i	$0.342107\pi$
$240$		0			0
$241$	8.08049	+	5.19301i	0.520510	+	0.334511i	0.774374	−	0.632729i	$-0.218065\pi$
$241$	8.08049	+	5.19301i	0.520510	+	0.334511i	−0.253864	+	0.967240i	$0.581701\pi$
$242$		0			0
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$		0			0
$245$	10.8667	−	12.5409i	0.694250	−	0.801207i
$246$		0			0
$247$	12.0636	+	7.75279i	0.767587	+	0.493298i
$248$		0			0
$249$	−0.812256	+	5.64936i	−0.0514746	+	0.358014i
$250$		0			0
$251$	17.5860	+	5.16370i	1.11002	+	0.325930i	0.784824	−	0.619718i	$-0.212753\pi$
$251$	17.5860	+	5.16370i	1.11002	+	0.325930i	0.325191	+	0.945648i	$0.394571\pi$
$252$		0			0
$253$	−1.86112	+	12.9444i	−0.117008	+	0.813805i
$254$		0			0
$255$	4.71560	−	10.3257i	0.295302	−	0.646622i
$256$		0			0
$257$	14.2898	−	9.18347i	0.891370	−	0.572849i	−0.0128490	−	0.999917i	$-0.504090\pi$
$257$	14.2898	−	9.18347i	0.891370	−	0.572849i	0.904219	+	0.427069i	$0.140454\pi$
$258$		0			0
$259$	−1.37416	−	9.55747i	−0.0853860	−	0.593872i
$260$		0			0
$261$	−0.148187	−	1.03067i	−0.00917257	−	0.0637966i
$262$		0			0
$263$	−2.84893	+	1.83089i	−0.175672	+	0.112898i	−0.625522	−	0.780207i	$-0.715114\pi$
$263$	−2.84893	+	1.83089i	−0.175672	+	0.112898i	0.449850	+	0.893104i	$0.351478\pi$
$264$		0			0
$265$	−28.2957	+	32.6550i	−1.73819	+	2.00598i
$266$		0			0
$267$	12.8664			0.787411
$268$		0			0
$269$	−14.2503			−0.868854			−0.434427	−	0.900707i	$-0.643049\pi$
$269$	−14.2503			−0.868854			−0.434427	+	0.900707i	$0.643049\pi$
$270$		0			0
$271$	−12.8182	+	14.7930i	−0.778652	+	0.898612i	−0.997011	−	0.0772562i	$-0.975384\pi$
$271$	−12.8182	+	14.7930i	−0.778652	+	0.898612i	0.218359	+	0.975868i	$0.429930\pi$
$272$		0			0
$273$	−5.23365	+	3.36346i	−0.316755	+	0.203566i
$274$		0			0
$275$	−3.08326	−	21.4445i	−0.185927	−	1.29315i
$276$		0			0
$277$	−2.33591	−	16.2466i	−0.140351	−	0.976164i	−0.931293	−	0.364272i	$-0.881318\pi$
$277$	−2.33591	−	16.2466i	−0.140351	−	0.976164i	0.790942	−	0.611892i	$-0.209591\pi$
$278$		0			0
$279$	−4.03783	+	2.59496i	−0.241739	+	0.155356i
$280$		0			0
$281$	−9.90941	+	21.6986i	−0.591146	+	1.29443i	0.343601	+	0.939116i	$0.388353\pi$
$281$	−9.90941	+	21.6986i	−0.591146	+	1.29443i	−0.934747	+	0.355313i	$0.884374\pi$
$282$		0			0
$283$	1.59471	−	11.0915i	0.0947957	−	0.659318i	−0.885914	−	0.463849i	$-0.846468\pi$
$283$	1.59471	−	11.0915i	0.0947957	−	0.659318i	0.980710	−	0.195469i	$-0.0626230\pi$
$284$		0			0
$285$	−8.67006	−	2.54576i	−0.513570	−	0.150798i
$286$		0			0
$287$	0.902118	−	6.27437i	0.0532504	−	0.370364i
$288$		0			0
$289$	−2.89450	−	1.86018i	−0.170265	−	0.109423i
$290$		0			0
$291$	−3.31897	+	3.83030i	−0.194561	+	0.224536i
$292$		0			0
$293$	0.510917	−	1.11875i	0.0298481	−	0.0653582i	−0.894121	−	0.447826i	$-0.852198\pi$
$293$	0.510917	−	1.11875i	0.0298481	−	0.0653582i	0.923969	+	0.382468i	$0.124926\pi$
$294$		0			0
$295$	−9.59044	−	6.16340i	−0.558377	−	0.358847i
$296$		0			0
$297$	−4.81098			−0.279162
$298$		0			0
$299$	−5.52430	−	12.0965i	−0.319478	−	0.699560i
$300$		0			0
$301$	−1.93787	+	13.4782i	−0.111697	+	0.776869i
$302$		0			0
$303$	−7.43452	−	8.57989i	−0.427102	−	0.492902i
$304$		0			0
$305$	−1.32259			−0.0757313
$306$		0			0
$307$	1.31587	+	2.88135i	0.0751006	+	0.164447i	0.943458	−	0.331491i	$-0.107552\pi$
$307$	1.31587	+	2.88135i	0.0751006	+	0.164447i	−0.868358	+	0.495938i	$0.834824\pi$
$308$		0			0
$309$	9.21830	+	2.70674i	0.524410	+	0.153981i
$310$		0			0
$311$	−1.69351	−	0.497260i	−0.0960303	−	0.0281970i	0.233364	−	0.972389i	$-0.425026\pi$
$311$	−1.69351	−	0.497260i	−0.0960303	−	0.0281970i	−0.329395	+	0.944192i	$0.606845\pi$
$312$		0			0
$313$	−14.5048	−	16.7394i	−0.819860	−	0.946169i	0.179433	−	0.983770i	$-0.442574\pi$
$313$	−14.5048	−	16.7394i	−0.819860	−	0.946169i	−0.999293	+	0.0376013i	$0.988028\pi$
$314$		0			0
$315$	2.56719	−	2.96269i	0.144645	−	0.166929i
$316$		0			0
$317$	17.9688	−	5.27612i	1.00923	−	0.296336i	0.264991	−	0.964251i	$-0.414631\pi$
$317$	17.9688	−	5.27612i	1.00923	−	0.296336i	0.744238	+	0.667915i	$0.232813\pi$
$318$		0			0
$319$	4.21427	−	2.70834i	0.235954	−	0.151638i
$320$		0			0
$321$	1.91500	−	0.562294i	0.106885	−	0.0313842i
$322$		0			0
$323$	4.48379	−	9.81813i	0.249485	−	0.546295i
$324$		0			0
$325$	14.4271	+	16.6498i	0.800272	+	0.923563i
$326$		0			0
$327$	6.37773	+	13.9653i	0.352690	+	0.772282i
$328$		0			0
$329$	−0.688469	−	0.442452i	−0.0379565	−	0.0243932i
$330$		0			0
$331$	−16.7690	+	4.92382i	−0.921707	+	0.270638i	−0.707961	−	0.706252i	$-0.750385\pi$
$331$	−16.7690	+	4.92382i	−0.921707	+	0.270638i	−0.213746	+	0.976889i	$0.568567\pi$
$332$		0			0
$333$	1.08060	+	7.51572i	0.0592163	+	0.411859i
$334$		0			0
$335$	−24.1799	−	7.21453i	−1.32109	−	0.394172i
$336$		0			0
$337$	−4.04964	−	28.1659i	−0.220598	−	1.53429i	−0.735786	−	0.677214i	$-0.763187\pi$
$337$	−4.04964	−	28.1659i	−0.220598	−	1.53429i	0.515188	−	0.857077i	$-0.327722\pi$
$338$		0			0
$339$	11.8788	−	3.48794i	0.645170	−	0.189439i
$340$		0			0
$341$	−19.4259	−	12.4843i	−1.05197	−	0.676063i
$342$		0			0
$343$	6.54148	+	14.3238i	0.353207	+	0.773415i
$344$		0			0
$345$	5.48750	+	6.33292i	0.295437	+	0.340953i
$346$		0			0
$347$	14.4794	−	31.7054i	0.777294	−	1.70204i	0.0674033	−	0.997726i	$-0.478529\pi$
$347$	14.4794	−	31.7054i	0.777294	−	1.70204i	0.709891	−	0.704311i	$-0.248744\pi$
$348$		0			0
$349$	−2.45689	+	0.721408i	−0.131514	+	0.0386161i	−0.346827	−	0.937929i	$-0.612741\pi$
$349$	−2.45689	+	0.721408i	−0.131514	+	0.0386161i	0.215313	+	0.976545i	$0.430923\pi$
$350$		0			0
$351$	4.11559	−	2.64493i	0.219674	−	0.141176i
$352$		0			0
$353$	14.6377	−	4.29803i	0.779088	−	0.228761i	0.132075	−	0.991240i	$-0.457836\pi$
$353$	14.6377	−	4.29803i	0.779088	−	0.228761i	0.647013	+	0.762479i	$0.276018\pi$
$354$		0			0
$355$	19.9040	−	22.9705i	1.05640	−	1.21915i
$356$		0			0
$357$	3.06648	+	3.53891i	0.162295	+	0.187299i
$358$		0			0
$359$	2.91575	+	0.856143i	0.153888	+	0.0451855i	0.357769	−	0.933810i	$-0.383538\pi$
$359$	2.91575	+	0.856143i	0.153888	+	0.0451855i	−0.203881	+	0.978996i	$0.565356\pi$
$360$		0			0
$361$	9.98651	+	2.93230i	0.525606	+	0.154332i
$362$		0			0
$363$	−5.04545	−	11.0480i	−0.264817	−	0.579869i
$364$		0			0
$365$	−3.35679			−0.175703
$366$		0			0
$367$	23.2388	+	26.8190i	1.21305	+	1.39994i	0.891484	+	0.453052i	$0.149665\pi$
$367$	23.2388	+	26.8190i	1.21305	+	1.39994i	0.321570	+	0.946886i	$0.395790\pi$
$368$		0			0
$369$	−0.709399	+	4.93398i	−0.0369299	+	0.256853i
$370$		0			0
$371$	−7.40441	−	16.2134i	−0.384418	−	0.841757i
$372$		0			0
$373$	11.9975			0.621208			0.310604	−	0.950539i	$-0.399469\pi$
$373$	11.9975			0.621208			0.310604	+	0.950539i	$0.399469\pi$
$374$		0			0
$375$	1.28826	+	0.827915i	0.0665255	+	0.0427534i
$376$		0			0
$377$	−2.11616	+	4.63374i	−0.108988	+	0.238650i
$378$		0			0
$379$	−4.01398	+	4.63237i	−0.206184	+	0.237949i	−0.849418	−	0.527721i	$-0.823047\pi$
$379$	−4.01398	+	4.63237i	−0.206184	+	0.237949i	0.643234	+	0.765670i	$0.277592\pi$
$380$		0			0
$381$	−14.3397	−	9.21556i	−0.734645	−	0.472128i
$382$		0			0
$383$	−2.01495	+	14.0143i	−0.102959	+	0.716098i	0.871314	+	0.490727i	$0.163269\pi$
$383$	−2.01495	+	14.0143i	−0.102959	+	0.716098i	−0.974273	+	0.225371i	$0.927640\pi$
$384$		0			0
$385$	18.0961	+	5.31349i	0.922261	+	0.270800i
$386$		0			0
$387$	1.52388	−	10.5988i	0.0774633	−	0.538769i
$388$		0			0
$389$	5.25897	−	11.5155i	0.266640	−	0.583861i	−0.728194	−	0.685371i	$-0.759640\pi$
$389$	5.25897	−	11.5155i	0.266640	−	0.583861i	0.994835	+	0.101510i	$0.0323674\pi$
$390$		0			0
$391$	−8.42045	+	5.41150i	−0.425841	+	0.273671i
$392$		0			0
$393$	1.68150	+	11.6951i	0.0848204	+	0.589939i
$394$		0			0
$395$	−1.73393	−	12.0597i	−0.0872434	−	0.606791i
$396$		0			0
$397$	12.8115	−	8.23348i	0.642993	−	0.413227i	−0.178107	−	0.984011i	$-0.556997\pi$
$397$	12.8115	−	8.23348i	0.642993	−	0.413227i	0.821100	+	0.570785i	$0.193361\pi$
$398$		0			0
$399$	2.44099	−	2.81705i	0.122202	−	0.141029i
$400$		0			0
$401$	24.5289			1.22492			0.612458	−	0.790503i	$-0.290181\pi$
$401$	24.5289			1.22492			0.612458	+	0.790503i	$0.290181\pi$
$402$		0			0
$403$	23.4815			1.16970
$404$		0			0
$405$	−2.01876	+	2.32977i	−0.100313	+	0.115767i
$406$		0			0
$407$	−30.7308	+	19.7495i	−1.52327	+	0.978947i
$408$		0			0
$409$	−5.43426	−	37.7961i	−0.268707	−	1.86890i	−0.460778	−	0.887515i	$-0.652430\pi$
$409$	−5.43426	−	37.7961i	−0.268707	−	1.86890i	0.192072	−	0.981381i	$-0.438479\pi$
$410$		0			0
$411$	3.25639	+	22.6487i	0.160626	+	1.11718i
$412$		0			0
$413$	3.95617	−	2.54248i	0.194671	−	0.125107i
$414$		0			0
$415$	−7.30905	+	16.0046i	−0.358787	+	0.785634i
$416$		0			0
$417$	1.21827	−	8.47328i	0.0596591	−	0.414938i
$418$		0			0
$419$	27.2080	+	7.98899i	1.32920	+	0.390288i	0.867804	−	0.496907i	$-0.165531\pi$
$419$	27.2080	+	7.98899i	1.32920	+	0.390288i	0.461395	+	0.887195i	$0.347349\pi$
$420$		0			0
$421$	4.22583	−	29.3913i	0.205954	−	1.43244i	−0.580231	−	0.814452i	$-0.697038\pi$
$421$	4.22583	−	29.3913i	0.205954	−	1.43244i	0.786185	−	0.617991i	$-0.212053\pi$
$422$		0			0
$423$	0.541392	+	0.347931i	0.0263234	+	0.0169170i
$424$		0			0
$425$	10.8591	−	12.5321i	0.526743	−	0.607894i
$426$		0			0
$427$	0.226644	−	0.496281i	0.0109681	−	0.0240167i
$428$		0			0
$429$	19.8000	+	12.7247i	0.955954	+	0.614354i
$430$		0			0
$431$	6.47892			0.312079			0.156039	−	0.987751i	$-0.450127\pi$
$431$	6.47892			0.312079			0.156039	+	0.987751i	$0.450127\pi$
$432$		0			0
$433$	−2.39442	−	5.24305i	−0.115069	−	0.251965i	0.843331	−	0.537394i	$-0.180591\pi$
$433$	−2.39442	−	5.24305i	−0.115069	−	0.251965i	−0.958400	+	0.285429i	$0.907864\pi$
$434$		0			0
$435$	0.456822	−	3.17727i	0.0219030	−	0.152338i
$436$		0			0
$437$	5.21775	+	6.02160i	0.249599	+	0.288052i
$438$		0			0
$439$	−4.65641			−0.222238			−0.111119	−	0.993807i	$-0.535444\pi$
$439$	−4.65641			−0.222238			−0.111119	+	0.993807i	$0.535444\pi$
$440$		0			0
$441$	−2.23612	−	4.89643i	−0.106482	−	0.233163i
$442$		0			0
$443$	8.51652	+	2.50068i	0.404632	+	0.118811i	0.477714	−	0.878515i	$-0.341465\pi$
$443$	8.51652	+	2.50068i	0.404632	+	0.118811i	−0.0730823	+	0.997326i	$0.523284\pi$
$444$		0			0
$445$	38.0570	+	11.1745i	1.80408	+	0.529724i
$446$		0			0
$447$	7.48273	+	8.63553i	0.353921	+	0.408446i
$448$		0			0
$449$	−17.9050	+	20.6634i	−0.844987	+	0.975167i	−0.999919	−	0.0127581i	$-0.995939\pi$
$449$	−17.9050	+	20.6634i	−0.844987	+	0.975167i	0.154932	+	0.987925i	$0.450484\pi$
$450$		0			0
$451$	−23.0100	+	6.75634i	−1.08350	+	0.318144i
$452$		0			0
$453$	−8.83623	+	5.67870i	−0.415162	+	0.266809i
$454$		0			0
$455$	−18.4016	+	5.40319i	−0.862680	+	0.253306i
$456$		0			0
$457$	9.62141	−	21.0680i	0.450071	−	0.985517i	−0.539569	−	0.841942i	$-0.681413\pi$
$457$	9.62141	−	21.0680i	0.450071	−	0.985517i	0.989639	−	0.143576i	$-0.0458601\pi$
$458$		0			0
$459$	−2.41139	−	2.78289i	−0.112554	−	0.129894i
$460$		0			0
$461$	−4.96332	−	10.8681i	−0.231165	−	0.506180i	0.758131	−	0.652102i	$-0.226113\pi$
$461$	−4.96332	−	10.8681i	−0.231165	−	0.506180i	−0.989296	+	0.145922i	$0.953385\pi$
$462$		0			0
$463$	32.4444	+	20.8508i	1.50782	+	0.969018i	0.993793	+	0.111245i	$0.0354837\pi$
$463$	32.4444	+	20.8508i	1.50782	+	0.969018i	0.514028	+	0.857773i	$0.328153\pi$
$464$		0			0
$465$	−14.1971	+	4.16864i	−0.658374	+	0.193316i
$466$		0			0
$467$	−5.19324	−	36.1198i	−0.240315	−	1.67142i	−0.650564	−	0.759451i	$-0.725468\pi$
$467$	−5.19324	−	36.1198i	−0.240315	−	1.67142i	0.410250	−	0.911973i	$-0.365442\pi$
$468$		0			0
$469$	6.85070	−	7.83682i	0.316336	−	0.361871i
$470$		0			0
$471$	2.34913	+	16.3386i	0.108242	+	0.752843i
$472$		0			0
$473$	49.4285	−	14.5135i	2.27272	−	0.667332i
$474$		0			0
$475$	−11.1044	−	7.13639i	−0.509507	−	0.327440i
$476$		0			0
$477$	5.82261	+	12.7497i	0.266599	+	0.583770i
$478$		0			0
$479$	−22.2276	−	25.6520i	−1.01560	−	1.17207i	−0.985003	−	0.172536i	$-0.944804\pi$
$479$	−22.2276	−	25.6520i	−1.01560	−	1.17207i	−0.0305996	−	0.999532i	$-0.509742\pi$
$480$		0			0
$481$	15.4312	−	33.7897i	0.703603	−	1.54068i
$482$		0			0
$483$	−3.31669	+	0.973867i	−0.150914	+	0.0443125i
$484$		0			0
$485$	−13.1437	+	8.44694i	−0.596824	+	0.383556i
$486$		0			0
$487$	−24.6310	+	7.23233i	−1.11614	+	0.327728i	−0.787246	−	0.616639i	$-0.788494\pi$
$487$	−24.6310	+	7.23233i	−1.11614	+	0.327728i	−0.328893	+	0.944367i	$0.606676\pi$
$488$		0			0
$489$	−15.6479	+	18.0586i	−0.707621	+	0.816638i
$490$		0			0
$491$	−9.24794	−	10.6727i	−0.417354	−	0.481652i	0.507675	−	0.861549i	$-0.330505\pi$
$491$	−9.24794	−	10.6727i	−0.417354	−	0.481652i	−0.925029	+	0.379897i	$0.875960\pi$
$492$		0			0
$493$	3.67893	+	1.08023i	0.165691	+	0.0486512i
$494$		0			0
$495$	−14.2302	−	4.17837i	−0.639601	−	0.187804i
$496$		0			0
$497$	5.20848	+	11.4050i	0.233632	+	0.511584i
$498$		0			0
$499$	40.7494			1.82419			0.912096	−	0.409977i	$-0.134463\pi$
$499$	40.7494			1.82419			0.912096	+	0.409977i	$0.134463\pi$
$500$		0			0
$501$	−0.514582	−	0.593859i	−0.0229898	−	0.0265317i
$502$		0			0
$503$	2.37212	−	16.4985i	0.105768	−	0.735631i	−0.866060	−	0.499940i	$-0.833355\pi$
$503$	2.37212	−	16.4985i	0.105768	−	0.735631i	0.971828	−	0.235691i	$-0.0757354\pi$
$504$		0			0
$505$	−14.5386	−	31.8351i	−0.646958	−	1.41664i
$506$		0			0
$507$	−10.9337			−0.485582
$508$		0			0
$509$	11.1243	+	7.14915i	0.493076	+	0.316880i	0.763441	−	0.645877i	$-0.223508\pi$
$509$	11.1243	+	7.14915i	0.493076	+	0.316880i	−0.270366	+	0.962758i	$0.587145\pi$
$510$		0			0
$511$	0.575233	−	1.25958i	0.0254468	−	0.0557207i
$512$		0			0
$513$	−1.91952	+	2.21525i	−0.0847490	+	0.0978055i
$514$		0			0
$515$	24.9156	+	16.0123i	1.09791	+	0.705586i
$516$		0			0
$517$	−0.440625	+	3.06461i	−0.0193787	+	0.134781i
$518$		0			0
$519$	9.93002	+	2.91572i	0.435880	+	0.127986i
$520$		0			0
$521$	5.40923	−	37.6220i	0.236983	−	1.64825i	−0.429745	−	0.902950i	$-0.641397\pi$
$521$	5.40923	−	37.6220i	0.236983	−	1.64825i	0.666728	−	0.745301i	$-0.267694\pi$
$522$		0			0
$523$	5.04096	−	11.0382i	0.220426	−	0.482665i	−0.766821	−	0.641861i	$-0.778163\pi$
$523$	5.04096	−	11.0382i	0.220426	−	0.482665i	0.987247	+	0.159196i	$0.0508901\pi$
$524$		0			0
$525$	4.81754	−	3.09604i	0.210255	−	0.135122i
$526$		0			0
$527$	−2.51530	−	17.4943i	−0.109568	−	0.762064i
$528$		0			0
$529$	2.22169	+	15.4522i	0.0965953	+	0.671835i
$530$		0			0
$531$	−3.11102	+	1.99933i	−0.135007	+	0.0867635i
$532$		0			0
$533$	15.9696	−	18.4299i	0.691721	−	0.798288i
$534$		0			0
$535$	6.15265			0.266002
$536$		0			0
$537$	−4.93694			−0.213045
$538$		0			0
$539$	16.9589	−	19.5716i	0.730470	−	0.843007i
$540$		0			0
$541$	−2.11613	+	1.35995i	−0.0909795	+	0.0584690i	−0.585340	−	0.810788i	$-0.699039\pi$
$541$	−2.11613	+	1.35995i	−0.0909795	+	0.0584690i	0.494360	+	0.869257i	$0.335402\pi$
$542$		0			0
$543$	1.69085	+	11.7602i	0.0725615	+	0.504677i
$544$		0			0
$545$	6.73551	+	46.8465i	0.288518	+	2.00668i
$546$		0			0
$547$	9.88371	−	6.35187i	0.422597	−	0.271586i	−0.312011	−	0.950078i	$-0.601003\pi$
$547$	9.88371	−	6.35187i	0.422597	−	0.271586i	0.734608	+	0.678492i	$0.237366\pi$
$548$		0			0
$549$	−0.178226	+	0.390261i	−0.00760651	+	0.0166559i
$550$		0			0
$551$	0.434366	−	3.02108i	0.0185046	−	0.128702i
$552$		0			0
$553$	4.82236	+	1.41597i	0.205067	+	0.0602132i
$554$		0			0
$555$	−3.33119	+	23.1689i	−0.141401	+	0.983467i
$556$		0			0
$557$	2.00543	+	1.28881i	0.0849730	+	0.0546088i	0.582437	−	0.812876i	$-0.302099\pi$
$557$	2.00543	+	1.28881i	0.0849730	+	0.0546088i	−0.497464	+	0.867484i	$0.665735\pi$
$558$		0			0
$559$	−34.3048	+	39.5899i	−1.45094	+	1.67447i
$560$		0			0
$561$	7.35927	−	16.1146i	0.310709	−	0.680357i
$562$		0			0
$563$	−8.96275	−	5.76001i	−0.377735	−	0.242756i	0.337972	−	0.941156i	$-0.390259\pi$
$563$	−8.96275	−	5.76001i	−0.377735	−	0.242756i	−0.715707	+	0.698401i	$0.753895\pi$
$564$		0			0
$565$	38.1653			1.60562
$566$		0			0
$567$	−0.528269	−	1.15675i	−0.0221852	−	0.0485788i
$568$		0			0
$569$	−2.18735	+	15.2134i	−0.0916986	+	0.637778i	0.891197	+	0.453616i	$0.149866\pi$
$569$	−2.18735	+	15.2134i	−0.0916986	+	0.637778i	−0.982896	+	0.184162i	$0.941043\pi$
$570$		0			0
$571$	−1.60634	−	1.85382i	−0.0672233	−	0.0775799i	0.721142	−	0.692788i	$-0.243618\pi$
$571$	−1.60634	−	1.85382i	−0.0672233	−	0.0775799i	−0.788365	+	0.615208i	$0.789072\pi$
$572$		0			0
$573$	−13.3166			−0.556308
$574$		0			0
$575$	5.08508	+	11.1348i	0.212063	+	0.464352i
$576$		0			0
$577$	−43.6503	−	12.8169i	−1.81719	−	0.533574i	−0.818051	−	0.575146i	$-0.804945\pi$
$577$	−43.6503	−	12.8169i	−1.81719	−	0.533574i	−0.999135	+	0.0415724i	$0.986763\pi$
$578$		0			0
$579$	1.72145	+	0.505464i	0.0715411	+	0.0210064i
$580$		0			0
$581$	−4.75296	−	5.48521i	−0.197186	−	0.227565i
$582$		0			0
$583$	−44.1589	+	50.9621i	−1.82887	+	2.11063i
$584$		0			0
$585$	14.4705	−	4.24891i	0.598280	−	0.175671i
$586$		0			0
$587$	14.3865	−	9.24563i	0.593794	−	0.381608i	−0.208955	−	0.977925i	$-0.567006\pi$
$587$	14.3865	−	9.24563i	0.593794	−	0.381608i	0.802749	+	0.596317i	$0.203370\pi$
$588$		0			0
$589$	−13.4992	+	3.96372i	−0.556224	+	0.163322i
$590$		0			0
$591$	0.910401	−	1.99350i	0.0374489	−	0.0820016i
$592$		0			0
$593$	3.52838	+	4.07196i	0.144893	+	0.167216i	0.823557	−	0.567233i	$-0.191986\pi$
$593$	3.52838	+	4.07196i	0.144893	+	0.167216i	−0.678664	+	0.734449i	$0.737441\pi$
$594$		0			0
$595$	5.99666	+	13.1309i	0.245839	+	0.538313i
$596$		0			0
$597$	−1.63836	−	1.05291i	−0.0670537	−	0.0430928i
$598$		0			0
$599$	−21.7579	+	6.38868i	−0.889002	+	0.261035i	−0.694178	−	0.719804i	$-0.744232\pi$
$599$	−21.7579	+	6.38868i	−0.889002	+	0.261035i	−0.194824	+	0.980838i	$0.562414\pi$
$600$		0			0
$601$	−2.39915	−	16.6864i	−0.0978632	−	0.680653i	−0.978407	−	0.206688i	$-0.933731\pi$
$601$	−2.39915	−	16.6864i	−0.0978632	−	0.680653i	0.880544	−	0.473965i	$-0.157178\pi$
$602$		0			0
$603$	−5.38719	+	6.16265i	−0.219383	+	0.250962i
$604$		0			0
$605$	−5.32849	−	37.0604i	−0.216634	−	1.50672i
$606$		0			0
$607$	−35.1356	+	10.3167i	−1.42611	+	0.418743i	−0.901566	−	0.432641i	$-0.857582\pi$
$607$	−35.1356	+	10.3167i	−1.42611	+	0.418743i	−0.524542	+	0.851384i	$0.675764\pi$
$608$		0			0
$609$	1.11394	+	0.715884i	0.0451390	+	0.0290091i
$610$		0			0
$611$	−1.30789	−	2.86388i	−0.0529116	−	0.115860i
$612$		0			0
$613$	−23.5183	−	27.1416i	−0.949895	−	1.09624i	−0.995258	−	0.0972665i	$-0.968990\pi$
$613$	−23.5183	−	27.1416i	−0.949895	−	1.09624i	0.0453636	−	0.998971i	$-0.485555\pi$
$614$		0			0
$615$	−6.38350	+	13.9779i	−0.257408	+	0.563644i
$616$		0			0
$617$	−15.6019	+	4.58113i	−0.628109	+	0.184429i	−0.580268	−	0.814426i	$-0.697052\pi$
$617$	−15.6019	+	4.58113i	−0.628109	+	0.184429i	−0.0478407	+	0.998855i	$0.515234\pi$
$618$		0			0
$619$	−22.4566	+	14.4319i	−0.902605	+	0.580069i	−0.907562	−	0.419919i	$-0.862059\pi$
$619$	−22.4566	+	14.4319i	−0.902605	+	0.580069i	0.00495671	+	0.999988i	$0.498422\pi$
$620$		0			0
$621$	2.60814	−	0.765820i	0.104661	−	0.0307313i
$622$		0			0
$623$	−10.7147	+	12.3654i	−0.429274	+	0.495408i
$624$		0			0
$625$	17.8364	+	20.5844i	0.713458	+	0.823374i
$626$		0			0
$627$	−13.5307	−	3.97297i	−0.540364	−	0.158665i
$628$		0			0
$629$	−26.8271	−	7.87715i	−1.06967	−	0.314083i
$630$		0			0
$631$	−7.12104	−	15.5929i	−0.283484	−	0.620744i	0.713301	−	0.700857i	$-0.247199\pi$
$631$	−7.12104	−	15.5929i	−0.283484	−	0.620744i	−0.996786	+	0.0801133i	$0.974472\pi$
$632$		0			0
$633$	22.1472			0.880271
$634$		0			0
$635$	−34.4111	−	39.7125i	−1.36556	−	1.57594i
$636$		0			0
$637$	−3.74773	+	26.0661i	−0.148491	+	1.03277i
$638$		0			0
$639$	−4.09580	−	8.96855i	−0.162027	−	0.354790i
$640$		0			0
$641$	−24.9820			−0.986730			−0.493365	−	0.869823i	$-0.664233\pi$
$641$	−24.9820			−0.986730			−0.493365	+	0.869823i	$0.664233\pi$
$642$		0			0
$643$	−2.60332	−	1.67305i	−0.102665	−	0.0659787i	0.488301	−	0.872675i	$-0.337617\pi$
$643$	−2.60332	−	1.67305i	−0.102665	−	0.0659787i	−0.590966	+	0.806697i	$0.701253\pi$
$644$		0			0
$645$	13.7126	−	30.0264i	0.539933	−	1.18229i
$646$		0			0
$647$	−4.46857	+	5.15700i	−0.175678	+	0.202743i	−0.836759	−	0.547572i	$-0.815552\pi$
$647$	−4.46857	+	5.15700i	−0.175678	+	0.202743i	0.661081	+	0.750314i	$0.270098\pi$
$648$		0			0
$649$	−14.9671	−	9.61875i	−0.587508	−	0.377569i
$650$		0			0
$651$	0.868649	−	6.04159i	0.0340450	−	0.236788i
$652$		0			0
$653$	−31.3221	−	9.19699i	−1.22573	−	0.359906i	−0.396091	−	0.918211i	$-0.629634\pi$
$653$	−31.3221	−	9.19699i	−1.22573	−	0.359906i	−0.829636	+	0.558305i	$0.811452\pi$
$654$		0			0
$655$	−5.18361	+	36.0528i	−0.202540	+	1.40870i
$656$		0			0
$657$	−0.452346	+	0.990500i	−0.0176477	+	0.0386431i
$658$		0			0
$659$	−2.57002	+	1.65165i	−0.100114	+	0.0643391i	−0.589740	−	0.807593i	$-0.700770\pi$
$659$	−2.57002	+	1.65165i	−0.100114	+	0.0643391i	0.489626	+	0.871933i	$0.337133\pi$
$660$		0			0
$661$	0.336948	+	2.34352i	0.0131058	+	0.0911526i	0.995324	−	0.0965876i	$-0.0307928\pi$
$661$	0.336948	+	2.34352i	0.0131058	+	0.0911526i	−0.982219	+	0.187740i	$0.939884\pi$
$662$		0			0
$663$	2.56374	+	17.8312i	0.0995673	+	0.692506i
$664$		0			0
$665$	9.66674	−	6.21243i	0.374860	−	0.240908i
$666$		0			0
$667$	−1.85353	+	2.13909i	−0.0717690	+	0.0828259i
$668$		0			0
$669$	6.12230			0.236702
$670$		0			0
$671$	−2.06406			−0.0796823
$672$		0			0
$673$	−8.44622	+	9.74746i	−0.325578	+	0.375737i	−0.894815	−	0.446436i	$-0.852693\pi$
$673$	−8.44622	+	9.74746i	−0.325578	+	0.375737i	0.569238	+	0.822173i	$0.307238\pi$
$674$		0			0
$675$	−3.78837	+	2.43464i	−0.145814	+	0.0937093i
$676$		0			0
$677$	4.82467	+	33.5563i	0.185427	+	1.28968i	0.843667	+	0.536867i	$0.180392\pi$
$677$	4.82467	+	33.5563i	0.185427	+	1.28968i	−0.658240	+	0.752808i	$0.728699\pi$
$678$		0			0
$679$	−0.917228	−	6.37946i	−0.0352000	−	0.244821i
$680$		0			0
$681$	−15.7040	+	10.0924i	−0.601780	+	0.386740i
$682$		0			0
$683$	−14.9751	+	32.7909i	−0.573006	+	1.25471i	0.372175	+	0.928163i	$0.378612\pi$
$683$	−14.9751	+	32.7909i	−0.573006	+	1.25471i	−0.945181	+	0.326546i	$0.894115\pi$
$684$		0			0
$685$	−10.0386	+	69.8198i	−0.383554	+	2.66768i
$686$		0			0
$687$	−14.5791	−	4.28082i	−0.556229	−	0.163324i
$688$		0			0
$689$	9.75866	−	67.8730i	0.371775	−	2.58576i
$690$		0			0
$691$	−21.4045	−	13.7558i	−0.814266	−	0.523297i	0.0659768	−	0.997821i	$-0.478984\pi$
$691$	−21.4045	−	13.7558i	−0.814266	−	0.523297i	−0.880242	+	0.474524i	$0.842620\pi$
$692$		0			0
$693$	4.00641	−	4.62365i	0.152191	−	0.175638i
$694$		0			0
$695$	10.9626	−	24.0047i	0.415835	−	0.910551i
$696$		0			0
$697$	−15.4414	−	9.92357i	−0.584884	−	0.375882i
$698$		0			0
$699$	20.7857			0.786187
$700$		0			0
$701$	2.60479	+	5.70369i	0.0983816	+	0.215426i	0.952423	−	0.304780i	$-0.0985828\pi$
$701$	2.60479	+	5.70369i	0.0983816	+	0.215426i	−0.854041	+	0.520205i	$0.825856\pi$
$702$		0			0
$703$	−3.16744	+	22.0300i	−0.119462	+	0.830877i
$704$		0			0
$705$	1.29918	+	1.49934i	0.0489300	+	0.0564682i
$706$		0			0
$707$	14.4370			0.542959
$708$		0			0
$709$	15.2067	+	33.2979i	0.571098	+	1.25053i	0.946211	+	0.323551i	$0.104877\pi$
$709$	15.2067	+	33.2979i	0.571098	+	1.25053i	−0.375113	+	0.926979i	$0.622396\pi$
$710$		0			0
$711$	−3.79216	−	1.11348i	−0.142217	−	0.0417587i
$712$		0			0
$713$	12.5185	+	3.67577i	0.468822	+	0.137659i
$714$		0			0
$715$	47.5142	+	54.8343i	1.77693	+	2.05069i
$716$		0			0
$717$	9.63678	−	11.1214i	0.359892	−	0.415338i
$718$		0			0
$719$	−17.9803	+	5.27949i	−0.670552	+	0.196892i	−0.599249	−	0.800563i	$-0.704534\pi$
$719$	−17.9803	+	5.27949i	−0.670552	+	0.196892i	−0.0713030	+	0.997455i	$0.522716\pi$
$720$		0			0
$721$	−10.2780	+	6.60527i	−0.382773	+	0.245993i
$722$		0			0
$723$	9.21621	−	2.70612i	0.342755	−	0.100642i
$724$		0			0
$725$	1.94791	−	4.26533i	0.0723436	−	0.158410i
$726$		0			0
$727$	25.1188	+	28.9887i	0.931606	+	1.07513i	0.997010	+	0.0772723i	$0.0246211\pi$
$727$	25.1188	+	28.9887i	0.931606	+	1.07513i	−0.0654035	+	0.997859i	$0.520833\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	33.1701	+	21.3171i	1.22684	+	0.788443i
$732$		0			0
$733$	22.1942	−	6.51682i	0.819763	−	0.240704i	0.155149	−	0.987891i	$-0.450414\pi$
$733$	22.1942	−	6.51682i	0.819763	−	0.240704i	0.664614	+	0.747187i	$0.268596\pi$
$734$		0			0
$735$	−2.36157	−	16.4250i	−0.0871076	−	0.605847i
$736$		0			0
$737$	−37.7357	−	11.2592i	−1.39001	−	0.414736i
$738$		0			0
$739$	−5.56160	−	38.6818i	−0.204587	−	1.42293i	−0.790452	−	0.612524i	$-0.790154\pi$
$739$	−5.56160	−	38.6818i	−0.204587	−	1.42293i	0.585865	−	0.810409i	$-0.300755\pi$
$740$		0			0
$741$	13.7591	−	4.04004i	0.505454	−	0.148415i
$742$		0			0
$743$	29.5955	+	19.0199i	1.08575	+	0.697771i	0.955879	−	0.293760i	$-0.0949065\pi$
$743$	29.5955	+	19.0199i	1.08575	+	0.697771i	0.129874	+	0.991531i	$0.458543\pi$
$744$		0			0
$745$	14.6329	+	32.0415i	0.536106	+	1.17391i
$746$		0			0
$747$	3.73759	+	4.31341i	0.136751	+	0.157819i
$748$		0			0
$749$	−1.05434	+	2.30868i	−0.0385248	+	0.0843575i
$750$		0			0
$751$	−13.3387	+	3.91658i	−0.486735	+	0.142918i	−0.515887	−	0.856657i	$-0.672537\pi$
$751$	−13.3387	+	3.91658i	−0.486735	+	0.142918i	0.0291521	+	0.999575i	$0.490719\pi$
$752$		0			0
$753$	15.4188	−	9.90907i	0.561893	−	0.361107i
$754$		0			0
$755$	−31.0683	+	9.12248i	−1.13069	+	0.332001i
$756$		0			0
$757$	26.9948	−	31.1536i	0.981142	−	1.13230i	−0.0100617	−	0.999949i	$-0.503203\pi$
$757$	26.9948	−	31.1536i	0.981142	−	1.13230i	0.991203	−	0.132348i	$-0.0422518\pi$
$758$		0			0
$759$	8.56392	+	9.88329i	0.310851	+	0.358741i
$760$		0			0
$761$	44.2559	+	12.9947i	1.60428	+	0.471058i	0.956732	−	0.290970i	$-0.0939779\pi$
$761$	44.2559	+	12.9947i	1.60428	+	0.471058i	0.647544	+	0.762028i	$0.275796\pi$
$762$		0			0
$763$	−18.7326	−	5.50040i	−0.678167	−	0.199128i
$764$		0			0
$765$	−4.71560	−	10.3257i	−0.170493	−	0.373327i
$766$		0			0
$767$	18.0917			0.653255
$768$		0			0
$769$	21.6397	+	24.9735i	0.780347	+	0.900569i	0.997134	−	0.0756500i	$-0.0241032\pi$
$769$	21.6397	+	24.9735i	0.780347	+	0.900569i	−0.216787	+	0.976219i	$0.569558\pi$
$770$		0			0
$771$	2.41740	−	16.8134i	0.0870604	−	0.605519i
$772$		0			0
$773$	0.726752	+	1.59136i	0.0261394	+	0.0572374i	0.922251	−	0.386591i	$-0.126347\pi$
$773$	0.726752	+	1.59136i	0.0261394	+	0.0572374i	−0.896112	+	0.443828i	$0.853620\pi$
$774$		0			0
$775$	−21.6146			−0.776419
$776$		0			0
$777$	−8.12294	−	5.22030i	−0.291409	−	0.187277i
$778$		0			0
$779$	−6.06970	+	13.2908i	−0.217469	+	0.476192i
$780$		0			0
$781$	31.0627	−	35.8483i	1.11151	−	1.28275i
$782$		0			0
$783$	−0.875968	−	0.562950i	−0.0313045	−	0.0201182i
$784$		0			0
$785$	−7.24176	+	50.3675i	−0.258469	+	1.79769i
$786$		0			0
$787$	−2.18289	−	0.640954i	−0.0778115	−	0.0228475i	0.242595	−	0.970128i	$-0.422001\pi$
$787$	−2.18289	−	0.640954i	−0.0778115	−	0.0228475i	−0.320407	+	0.947280i	$0.603820\pi$
$788$		0			0
$789$	−0.481953	+	3.35206i	−0.0171580	+	0.119336i
$790$		0			0
$791$	−6.54014	+	14.3209i	−0.232541	+	0.509193i
$792$		0			0
$793$	1.76572	−	1.13476i	0.0627024	−	0.0402964i
$794$		0			0
$795$	6.14924	+	42.7689i	0.218091	+	1.51686i
$796$		0			0
$797$	−5.25766	−	36.5678i	−0.186236	−	1.29530i	−0.841648	−	0.540026i	$-0.818414\pi$
$797$	−5.25766	−	36.5678i	−0.186236	−	1.29530i	0.655412	−	0.755271i	$-0.272495\pi$
$798$		0			0
$799$	−1.99356	+	1.28119i	−0.0705273	+	0.0453251i
$800$		0			0
$801$	8.42570	−	9.72377i	0.297707	−	0.343573i
$802$		0			0
$803$	−5.23869			−0.184869
$804$		0			0
$805$	−10.6561			−0.375578
$806$		0			0
$807$	−9.33193	+	10.7696i	−0.328500	+	0.379109i
$808$		0			0
$809$	1.58564	−	1.01903i	0.0557482	−	0.0358272i	−0.512470	−	0.858705i	$-0.671269\pi$
$809$	1.58564	−	1.01903i	0.0557482	−	0.0358272i	0.568218	+	0.822878i	$0.307633\pi$
$810$		0			0
$811$	−6.93887	−	48.2609i	−0.243657	−	1.69467i	−0.633463	−	0.773773i	$-0.718367\pi$
$811$	−6.93887	−	48.2609i	−0.243657	−	1.69467i	0.389806	−	0.920897i	$-0.372542\pi$
$812$		0			0
$813$	2.78567	+	19.3747i	0.0976976	+	0.679502i
$814$		0			0
$815$	−61.9682	+	39.8246i	−2.17065	+	1.39499i
$816$		0			0
$817$	13.0385	−	28.5504i	0.456160	−	0.998850i
$818$		0			0
$819$	−0.885376	+	6.15792i	−0.0309375	+	0.215175i
$820$		0			0
$821$	38.6539	+	11.3498i	1.34903	+	0.396111i	0.874883	−	0.484334i	$-0.160938\pi$
$821$	38.6539	+	11.3498i	1.34903	+	0.396111i	0.474148	+	0.880445i	$0.342756\pi$
$822$		0			0
$823$	5.64560	−	39.2660i	0.196793	−	1.36873i	−0.616721	−	0.787182i	$-0.711539\pi$
$823$	5.64560	−	39.2660i	0.196793	−	1.36873i	0.813514	−	0.581545i	$-0.197551\pi$
$824$		0			0
$825$	−18.2258	−	11.7130i	−0.634541	−	0.407795i
$826$		0			0
$827$	5.34097	−	6.16381i	0.185724	−	0.214337i	−0.655251	−	0.755411i	$-0.727437\pi$
$827$	5.34097	−	6.16381i	0.185724	−	0.214337i	0.840974	+	0.541075i	$0.181982\pi$
$828$		0			0
$829$	−11.1507	+	24.4167i	−0.387280	+	0.848026i	0.611123	+	0.791536i	$0.290718\pi$
$829$	−11.1507	+	24.4167i	−0.387280	+	0.848026i	−0.998403	+	0.0564899i	$0.982009\pi$
$830$		0			0
$831$	−13.8081	−	8.87390i	−0.478996	−	0.307832i
$832$		0			0
$833$	19.8213			0.686768
$834$		0			0
$835$	−1.00629	−	2.20347i	−0.0348242	−	0.0762543i
$836$		0			0
$837$	−0.683080	+	4.75093i	−0.0236107	+	0.164216i
$838$		0			0
$839$	−35.5876	−	41.0703i	−1.22862	−	1.41790i	−0.876120	−	0.482093i	$-0.839877\pi$
$839$	−35.5876	−	41.0703i	−1.22862	−	1.41790i	−0.352502	−	0.935811i	$-0.614669\pi$
$840$		0			0
$841$	−27.9158			−0.962613
$842$		0			0
$843$	9.90941	+	21.6986i	0.341298	+	0.747339i
$844$		0			0
$845$	−32.3403	−	9.49598i	−1.11254	−	0.326672i
$846$		0			0
$847$	14.8195	+	4.35138i	0.509202	+	0.149515i
$848$		0			0
$849$	−7.33805	−	8.46856i	−0.251841	−	0.290640i
$850$		0			0
$851$	13.5161	−	15.5984i	0.463327	−	0.534708i
$852$		0			0
$853$	−38.1292	+	11.1957i	−1.30552	+	0.383335i	−0.859246	−	0.511563i	$-0.829067\pi$
$853$	−38.1292	+	11.1957i	−1.30552	+	0.383335i	−0.446272	+	0.894897i	$0.647249\pi$
$854$		0			0
$855$	−7.60164	+	4.88528i	−0.259970	+	0.167073i
$856$		0			0
$857$	55.4586	−	16.2841i	1.89443	−	0.556255i	0.902289	−	0.431131i	$-0.141885\pi$
$857$	55.4586	−	16.2841i	1.89443	−	0.556255i	0.992141	−	0.125124i	$-0.0399327\pi$
$858$		0			0
$859$	11.8610	−	25.9721i	0.404693	−	0.886155i	−0.592079	−	0.805880i	$-0.701693\pi$
$859$	11.8610	−	25.9721i	0.404693	−	0.886155i	0.996773	−	0.0802753i	$-0.0255799\pi$
$860$		0			0
$861$	−4.15109	−	4.79061i	−0.141469	−	0.163264i
$862$		0			0
$863$	14.9414	+	32.7171i	0.508611	+	1.11370i	0.973574	+	0.228372i	$0.0733402\pi$
$863$	14.9414	+	32.7171i	0.508611	+	1.11370i	−0.464963	+	0.885330i	$0.653933\pi$
$864$		0			0
$865$	26.8393	+	17.2486i	0.912564	+	0.586469i
$866$		0			0
$867$	−3.30133	+	0.969357i	−0.112119	+	0.0329211i
$868$		0			0
$869$	−2.70601	−	18.8207i	−0.0917950	−	0.638448i
$870$		0			0
$871$	38.4712	−	11.1142i	1.30355	−	0.376590i
$872$		0			0
$873$	0.721281	+	5.01662i	0.0244117	+	0.169787i
$874$		0			0
$875$	−1.86849	+	0.548639i	−0.0631666	+	0.0185474i
$876$		0			0
$877$	−26.9014	−	17.2885i	−0.908396	−	0.583791i	0.000872724	−	1.00000i	$-0.499722\pi$
$877$	−26.9014	−	17.2885i	−0.908396	−	0.583791i	−0.909269	+	0.416209i	$0.863359\pi$
$878$		0			0
$879$	−0.510917	−	1.11875i	−0.0172328	−	0.0377346i
$880$		0			0
$881$	−31.8395	−	36.7448i	−1.07270	−	1.23796i	−0.969962	−	0.243255i	$-0.921785\pi$
$881$	−31.8395	−	36.7448i	−1.07270	−	1.23796i	−0.102739	−	0.994708i	$-0.532761\pi$
$882$		0			0
$883$	−22.4067	+	49.0638i	−0.754045	+	1.65113i	0.00491281	+	0.999988i	$0.498436\pi$
$883$	−22.4067	+	49.0638i	−0.754045	+	1.65113i	−0.758958	+	0.651140i	$0.774291\pi$
$884$		0			0
$885$	−10.9384	+	3.21180i	−0.367690	+	0.107964i
$886$		0			0
$887$	−12.1550	+	7.81157i	−0.408126	+	0.262287i	−0.728557	−	0.684985i	$-0.759809\pi$
$887$	−12.1550	+	7.81157i	−0.408126	+	0.262287i	0.320431	+	0.947272i	$0.396172\pi$
$888$		0			0
$889$	20.7983	−	6.10693i	0.697552	−	0.204820i
$890$		0			0
$891$	−3.15052	+	3.63590i	−0.105547	+	0.121807i
$892$		0			0
$893$	1.23532	+	1.42563i	0.0413383	+	0.0477069i
$894$		0			0
$895$	−14.6028	−	4.28777i	−0.488118	−	0.143324i
$896$		0			0
$897$	−12.7596	−	3.74655i	−0.426030	−	0.125094i
$898$		0			0
$899$	−2.07618	−	4.54620i	−0.0692444	−	0.151624i
$900$		0			0
$901$	−51.6124			−1.71946
$902$		0			0
$903$	8.91709	+	10.2909i	0.296742	+	0.342459i
$904$		0			0
$905$	−5.21245	+	36.2534i	−0.173268	+	1.20510i
$906$		0			0
$907$	−15.4916	−	33.9218i	−0.514389	−	1.12635i	−0.971520	−	0.236956i	$-0.923850\pi$
$907$	−15.4916	−	33.9218i	−0.514389	−	1.12635i	0.457132	−	0.889399i	$-0.348877\pi$
$908$		0			0
$909$	−11.3528			−0.376549
$910$		0			0
$911$	29.8283	+	19.1695i	0.988255	+	0.635113i	0.931678	−	0.363285i	$-0.118345\pi$
$911$	29.8283	+	19.1695i	0.988255	+	0.635113i	0.0565771	+	0.998398i	$0.481981\pi$
$912$		0			0
$913$	−11.4067	+	24.9771i	−0.377505	+	0.826622i
$914$		0			0
$915$	−0.866112	+	0.999547i	−0.0286328	+	0.0330440i
$916$		0			0
$917$	−12.6400	−	8.12321i	−0.417408	−	0.268252i
$918$		0			0
$919$	−0.783313	+	5.44806i	−0.0258391	+	0.179715i	−0.998654	−	0.0518697i	$-0.983482\pi$
$919$	−0.783313	+	5.44806i	−0.0258391	+	0.179715i	0.972815	+	0.231585i	$0.0743910\pi$
$920$		0			0
$921$	3.03929	+	0.892416i	0.100148	+	0.0294061i
$922$		0			0
$923$	−6.86454	+	47.7439i	−0.225949	+	1.57151i
$924$		0			0
$925$	−14.2044	+	31.1032i	−0.467036	+	1.02267i
$926$		0			0
$927$	8.08231	−	5.19419i	0.265458	−	0.170600i
$928$		0			0
$929$	5.29260	+	36.8108i	0.173644	+	1.20772i	0.871104	+	0.491099i	$0.163405\pi$
$929$	5.29260	+	36.8108i	0.173644	+	1.20772i	−0.697459	+	0.716624i	$0.745686\pi$
$930$		0			0
$931$	−2.24547	−	15.6176i	−0.0735925	−	0.511847i
$932$		0			0
$933$	−1.48482	+	0.954235i	−0.0486108	+	0.0312403i
$934$		0			0
$935$	35.7633	−	41.2730i	1.16958	−	1.34977i
$936$		0			0
$937$	−18.6089			−0.607926			−0.303963	−	0.952684i	$-0.598310\pi$
$937$	−18.6089			−0.607926			−0.303963	+	0.952684i	$0.598310\pi$
$938$		0			0
$939$	−22.1495			−0.722820
$940$		0			0
$941$	−6.28343	+	7.25147i	−0.204834	+	0.236391i	−0.848867	−	0.528607i	$-0.822715\pi$
$941$	−6.28343	+	7.25147i	−0.204834	+	0.236391i	0.644033	+	0.764998i	$0.277260\pi$
$942$		0			0
$943$	11.3988	−	7.32554i	0.371195	−	0.238552i
$944$		0			0
$945$	−0.557903	−	3.88030i	−0.0181486	−	0.126226i
$946$		0			0
$947$	0.0851825	+	0.592457i	0.00276806	+	0.0192523i	0.991159	−	0.132682i	$-0.0423589\pi$
$947$	0.0851825	+	0.592457i	0.00276806	+	0.0192523i	−0.988391	+	0.151934i	$0.951450\pi$
$948$		0			0
$949$	4.48147	−	2.88006i	0.145475	−	0.0934908i
$950$		0			0
$951$	7.77964	−	17.0350i	0.252272	−	0.552399i
$952$		0			0
$953$	−1.42290	+	9.89646i	−0.0460921	+	0.320578i	0.953711	+	0.300725i	$0.0972288\pi$
$953$	−1.42290	+	9.89646i	−0.0460921	+	0.320578i	−0.999803	+	0.0198525i	$0.993680\pi$
$954$		0			0
$955$	−39.3886	−	11.5655i	−1.27458	−	0.374252i
$956$		0			0
$957$	0.712927	−	4.95852i	0.0230457	−	0.160286i
$958$		0			0
$959$	−24.4785	−	15.7314i	−0.790453	−	0.507993i
$960$		0			0
$961$	5.21407	−	6.01736i	0.168196	−	0.194108i
$962$		0			0
$963$	0.829103	−	1.81548i	0.0267175	−	0.0585031i
$964$		0			0
$965$	4.65282	+	2.99018i	0.149780	+	0.0962575i
$966$		0			0
$967$	57.2815			1.84205			0.921024	−	0.389505i	$-0.127354\pi$
$967$	57.2815			1.84205			0.921024	+	0.389505i	$0.127354\pi$
$968$		0			0
$969$	−4.48379	−	9.81813i	−0.144040	−	0.315404i
$970$		0			0
$971$	−1.16890	+	8.12990i	−0.0375119	+	0.260901i	−0.999944	−	0.0106230i	$-0.996619\pi$
$971$	−1.16890	+	8.12990i	−0.0375119	+	0.260901i	0.962432	+	0.271524i	$0.0875276\pi$
$972$		0			0
$973$	7.12880	+	8.22708i	0.228539	+	0.263748i
$974$		0			0
$975$	22.0308			0.705551
$976$		0			0
$977$	5.02986	+	11.0139i	0.160919	+	0.352364i	0.972867	−	0.231366i	$-0.0743196\pi$
$977$	5.02986	+	11.0139i	0.160919	+	0.352364i	−0.811947	+	0.583731i	$0.801592\pi$
$978$		0			0
$979$	59.3926	+	17.4392i	1.89820	+	0.557361i
$980$		0			0
$981$	14.7308	+	4.32535i	0.470318	+	0.138098i
$982$		0			0
$983$	35.9893	+	41.5338i	1.14788	+	1.32472i	0.937855	+	0.347028i	$0.112809\pi$
$983$	35.9893	+	41.5338i	1.14788	+	1.32472i	0.210025	+	0.977696i	$0.432646\pi$
$984$		0			0
$985$	4.42421	−	5.10581i	0.140967	−	0.162685i
$986$		0			0
$987$	−0.785234	+	0.230566i	−0.0249943	+	0.00733899i
$988$		0			0
$989$	−24.4860	+	15.7362i	−0.778610	+	0.500382i
$990$		0			0
$991$	43.4428	−	12.7559i	1.38000	−	0.405206i	0.494234	−	0.869329i	$-0.335449\pi$
$991$	43.4428	−	12.7559i	1.38000	−	0.405206i	0.885771	+	0.464123i	$0.153630\pi$
$992$		0			0
$993$	−7.26018	+	15.8976i	−0.230395	+	0.504494i
$994$		0			0
$995$	−3.93159	−	4.53729i	−0.124640	−	0.143842i
$996$		0			0
$997$	−19.9331	−	43.6475i	−0.631289	−	1.38233i	−0.907017	−	0.421094i	$-0.861646\pi$
$997$	−19.9331	−	43.6475i	−0.631289	−	1.38233i	0.275728	−	0.961236i	$-0.411081\pi$
$998$		0			0
$999$	6.38764	+	4.10509i	0.202096	+	0.129879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.25.6	✓	60
67.59	even	11	inner	804.2.q.b.193.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.6	✓	60	1.1	even	1	trivial
804.2.q.b.193.6	yes	60	67.59	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)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(4.04726 - 2.60101i) q^{11} +(-2.03230 + 4.45011i) q^{13} +(0.438719 - 3.05136i) q^{15} +(3.53314 + 1.03742i) q^{17} +(0.417152 - 2.90136i) q^{19} +(1.06979 + 0.687514i) q^{21} +(-1.78008 + 2.05432i) q^{23} +(1.87072 - 4.09630i) q^{25} +(-0.841254 - 0.540641i) q^{27} +1.04126 q^{29} +(-1.99390 - 4.36603i) q^{31} +(0.684674 - 4.76201i) q^{33} +(2.56719 + 2.96269i) q^{35} -7.59300 q^{37} +(2.03230 + 4.45011i) q^{39} +(-4.78280 - 1.40436i) q^{41} +(10.2741 + 3.01674i) q^{43} +(-2.01876 - 2.32977i) q^{45} +(-0.421438 + 0.486365i) q^{47} +(5.16482 - 1.51653i) q^{49} +(3.09774 - 1.99080i) q^{51} +(-13.4486 + 3.94887i) q^{53} +(6.16101 - 13.4907i) q^{55} +(-1.91952 - 2.21525i) q^{57} +(-1.53624 - 3.36389i) q^{59} +(-0.360924 - 0.231952i) q^{61} +(1.22015 - 0.358269i) q^{63} +(2.14630 + 14.9279i) q^{65} +(-5.33324 - 6.20939i) q^{67} +(0.386848 + 2.69059i) q^{69} +(9.46015 - 2.77775i) q^{71} +(-0.916042 - 0.588705i) q^{73} +(-1.87072 - 4.09630i) q^{75} +(4.00641 + 4.62365i) q^{77} +(1.64183 - 3.59510i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-4.80142 + 3.08568i) q^{83} +(10.8917 - 3.19810i) q^{85} +(0.681883 - 0.786935i) q^{87} +(8.42570 + 9.72377i) q^{89} +(-5.96924 - 1.75273i) q^{91} +(-4.60536 - 1.35225i) q^{93} +(-3.75372 - 8.21951i) q^{95} -5.06821 q^{97} +(-3.15052 - 3.63590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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