LMFDB - Embedded newform 804.2.q.a.193.3

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			193.3
Character	$\chi$	$=$	804.193
Dual form			804.2.q.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{3} +(0.361898 + 0.232578i) q^{5} +(-0.272618 + 1.89610i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{3} +(0.361898 + 0.232578i) q^{5} +(-0.272618 + 1.89610i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-5.24182 - 3.36871i) q^{11} +(-0.0671701 - 0.147082i) q^{13} +(-0.0612223 - 0.425811i) q^{15} +(1.41191 - 0.414574i) q^{17} +(-0.295838 - 2.05760i) q^{19} +(1.61150 - 1.03565i) q^{21} +(-4.42111 - 5.10223i) q^{23} +(-2.00020 - 4.37982i) q^{25} +(0.841254 - 0.540641i) q^{27} -2.66238 q^{29} +(-0.427955 + 0.937091i) q^{31} +(0.886758 + 6.16754i) q^{33} +(-0.539650 + 0.622790i) q^{35} -5.68964 q^{37} +(-0.0671701 + 0.147082i) q^{39} +(8.57030 - 2.51647i) q^{41} +(-2.75355 + 0.808514i) q^{43} +(-0.281714 + 0.325115i) q^{45} +(-0.851908 - 0.983154i) q^{47} +(3.19559 + 0.938309i) q^{49} +(-1.23792 - 0.795562i) q^{51} +(-10.6967 - 3.14083i) q^{53} +(-1.11352 - 2.43826i) q^{55} +(-1.36130 + 1.57102i) q^{57} +(1.41246 - 3.09285i) q^{59} +(-7.24942 + 4.65892i) q^{61} +(-1.83800 - 0.539685i) q^{63} +(0.00989928 - 0.0688510i) q^{65} +(-6.64901 + 4.77396i) q^{67} +(-0.960798 + 6.68250i) q^{69} +(-10.8103 - 3.17418i) q^{71} +(-3.07398 + 1.97553i) q^{73} +(-2.00020 + 4.37982i) q^{75} +(7.81641 - 9.02062i) q^{77} +(0.219732 + 0.481145i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.38878 - 0.892512i) q^{83} +(0.607389 + 0.178345i) q^{85} +(1.74349 + 2.01209i) q^{87} +(-0.568270 + 0.655819i) q^{89} +(0.297193 - 0.0872638i) q^{91} +(0.988458 - 0.290237i) q^{93} +(0.371489 - 0.813447i) q^{95} +18.1778 q^{97} +(4.08041 - 4.70904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

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
$5$	0.361898	+	0.232578i	0.161846	+	0.104012i	0.619057	−	0.785346i	$-0.287515\pi$
$5$	0.361898	+	0.232578i	0.161846	+	0.104012i	−0.457211	+	0.889358i	$0.651151\pi$
$6$		0			0
$7$	−0.272618	+	1.89610i	−0.103040	+	0.716657i	0.871165	+	0.490991i	$0.163365\pi$
$7$	−0.272618	+	1.89610i	−0.103040	+	0.716657i	−0.974205	+	0.225667i	$0.927544\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−5.24182	−	3.36871i	−1.58047	−	1.01570i	−0.975648	−	0.219341i	$-0.929609\pi$
$11$	−5.24182	−	3.36871i	−1.58047	−	1.01570i	−0.604819	−	0.796363i	$-0.706755\pi$
$12$		0			0
$13$	−0.0671701	−	0.147082i	−0.0186296	−	0.0407932i	0.900088	−	0.435707i	$-0.143502\pi$
$13$	−0.0671701	−	0.147082i	−0.0186296	−	0.0407932i	−0.918718	+	0.394914i	$0.870774\pi$
$14$		0			0
$15$	−0.0612223	−	0.425811i	−0.0158075	−	0.109944i
$16$		0			0
$17$	1.41191	−	0.414574i	0.342438	−	0.100549i	−0.105991	−	0.994367i	$-0.533802\pi$
$17$	1.41191	−	0.414574i	0.342438	−	0.100549i	0.448430	+	0.893818i	$0.351983\pi$
$18$		0			0
$19$	−0.295838	−	2.05760i	−0.0678699	−	0.472046i	−0.995205	−	0.0978131i	$-0.968815\pi$
$19$	−0.295838	−	2.05760i	−0.0678699	−	0.472046i	0.927335	−	0.374233i	$-0.122094\pi$
$20$		0			0
$21$	1.61150	−	1.03565i	0.351658	−	0.225997i
$22$		0			0
$23$	−4.42111	−	5.10223i	−0.921865	−	1.06389i	−0.997768	−	0.0667733i	$-0.978730\pi$
$23$	−4.42111	−	5.10223i	−0.921865	−	1.06389i	0.0759036	−	0.997115i	$-0.475816\pi$
$24$		0			0
$25$	−2.00020	−	4.37982i	−0.400039	−	0.875964i
$26$		0			0
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$		0			0
$29$	−2.66238			−0.494392			−0.247196	−	0.968966i	$-0.579509\pi$
$29$	−2.66238			−0.494392			−0.247196	+	0.968966i	$0.579509\pi$
$30$		0			0
$31$	−0.427955	+	0.937091i	−0.0768630	+	0.168307i	−0.944162	−	0.329480i	$-0.893127\pi$
$31$	−0.427955	+	0.937091i	−0.0768630	+	0.168307i	0.867299	+	0.497787i	$0.165854\pi$
$32$		0			0
$33$	0.886758	+	6.16754i	0.154365	+	1.07363i
$34$		0			0
$35$	−0.539650	+	0.622790i	−0.0912175	+	0.105271i
$36$		0			0
$37$	−5.68964			−0.935371			−0.467685	−	0.883895i	$-0.654912\pi$
$37$	−5.68964			−0.935371			−0.467685	+	0.883895i	$0.654912\pi$
$38$		0			0
$39$	−0.0671701	+	0.147082i	−0.0107558	+	0.0235520i
$40$		0			0
$41$	8.57030	−	2.51647i	1.33846	−	0.393006i	0.467337	−	0.884079i	$-0.345213\pi$
$41$	8.57030	−	2.51647i	1.33846	−	0.393006i	0.871118	+	0.491073i	$0.163395\pi$
$42$		0			0
$43$	−2.75355	+	0.808514i	−0.419912	+	0.123297i	−0.484861	−	0.874591i	$-0.661130\pi$
$43$	−2.75355	+	0.808514i	−0.419912	+	0.123297i	0.0649489	+	0.997889i	$0.479312\pi$
$44$		0			0
$45$	−0.281714	+	0.325115i	−0.0419955	+	0.0484654i
$46$		0			0
$47$	−0.851908	−	0.983154i	−0.124264	−	0.143408i	0.690209	−	0.723610i	$-0.257519\pi$
$47$	−0.851908	−	0.983154i	−0.124264	−	0.143408i	−0.814472	+	0.580203i	$0.802973\pi$
$48$		0			0
$49$	3.19559	+	0.938309i	0.456513	+	0.134044i
$50$		0			0
$51$	−1.23792	−	0.795562i	−0.173343	−	0.111401i
$52$		0			0
$53$	−10.6967	−	3.14083i	−1.46930	−	0.431426i	−0.553429	−	0.832896i	$-0.686681\pi$
$53$	−10.6967	−	3.14083i	−1.46930	−	0.431426i	−0.915872	+	0.401471i	$0.868499\pi$
$54$		0			0
$55$	−1.11352	−	2.43826i	−0.150147	−	0.328775i
$56$		0			0
$57$	−1.36130	+	1.57102i	−0.180308	+	0.208087i
$58$		0			0
$59$	1.41246	−	3.09285i	0.183886	−	0.402655i	−0.795129	−	0.606440i	$-0.792597\pi$
$59$	1.41246	−	3.09285i	0.183886	−	0.402655i	0.979016	+	0.203785i	$0.0653244\pi$
$60$		0			0
$61$	−7.24942	+	4.65892i	−0.928193	+	0.596513i	−0.915024	−	0.403400i	$-0.867828\pi$
$61$	−7.24942	+	4.65892i	−0.928193	+	0.596513i	−0.0131692	+	0.999913i	$0.504192\pi$
$62$		0			0
$63$	−1.83800	−	0.539685i	−0.231566	−	0.0679940i
$64$		0			0
$65$	0.00989928	−	0.0688510i	0.00122785	−	0.00853991i
$66$		0			0
$67$	−6.64901	+	4.77396i	−0.812306	+	0.583232i
$67$	−6.64901	+	4.77396i	−0.812306	+	0.583232i
$68$		0			0
$69$	−0.960798	+	6.68250i	−0.115667	+	0.804478i
$70$		0			0
$71$	−10.8103	−	3.17418i	−1.28294	−	0.376706i	−0.431956	−	0.901895i	$-0.642176\pi$
$71$	−10.8103	−	3.17418i	−1.28294	−	0.376706i	−0.850985	+	0.525189i	$0.823995\pi$
$72$		0			0
$73$	−3.07398	+	1.97553i	−0.359782	+	0.231218i	−0.708027	−	0.706186i	$-0.750414\pi$
$73$	−3.07398	+	1.97553i	−0.359782	+	0.231218i	0.348244	+	0.937404i	$0.386778\pi$
$74$		0			0
$75$	−2.00020	+	4.37982i	−0.230963	+	0.505738i
$76$		0			0
$77$	7.81641	−	9.02062i	0.890763	−	1.02800i
$78$		0			0
$79$	0.219732	+	0.481145i	0.0247217	+	0.0541330i	0.921590	−	0.388165i	$-0.126891\pi$
$79$	0.219732	+	0.481145i	0.0247217	+	0.0541330i	−0.896868	+	0.442298i	$0.854164\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−1.38878	−	0.892512i	−0.152438	−	0.0979659i	0.462198	−	0.886777i	$-0.347061\pi$
$83$	−1.38878	−	0.892512i	−0.152438	−	0.0979659i	−0.614636	+	0.788811i	$0.710697\pi$
$84$		0			0
$85$	0.607389	+	0.178345i	0.0658806	+	0.0193443i
$86$		0			0
$87$	1.74349	+	2.01209i	0.186922	+	0.215719i
$88$		0			0
$89$	−0.568270	+	0.655819i	−0.0602365	+	0.0695167i	−0.785068	−	0.619409i	$-0.787372\pi$
$89$	−0.568270	+	0.655819i	−0.0602365	+	0.0695167i	0.724832	+	0.688926i	$0.241918\pi$
$90$		0			0
$91$	0.297193	−	0.0872638i	0.0311543	−	0.00914774i
$92$		0			0
$93$	0.988458	−	0.290237i	0.102498	−	0.0300962i
$94$		0			0
$95$	0.371489	−	0.813447i	0.0381140	−	0.0834579i
$96$		0			0
$97$	18.1778			1.84567			0.922836	−	0.385192i	$-0.125865\pi$
$97$	18.1778			1.84567			0.922836	+	0.385192i	$0.125865\pi$
$98$		0			0
$99$	4.08041	−	4.70904i	0.410097	−	0.473277i
$100$		0			0
$101$	−0.323359	−	2.24901i	−0.0321755	−	0.223785i	0.967389	−	0.253295i	$-0.0815144\pi$
$101$	−0.323359	−	2.24901i	−0.0321755	−	0.223785i	−0.999564	+	0.0295100i	$0.990605\pi$
$102$		0			0
$103$	5.18565	−	11.3550i	0.510957	−	1.11884i	−0.461794	−	0.886987i	$-0.652794\pi$
$103$	5.18565	−	11.3550i	0.510957	−	1.11884i	0.972751	−	0.231853i	$-0.0744787\pi$
$104$		0			0
$105$	0.824069			0.0804209
$106$		0			0
$107$	6.36325	−	4.08941i	0.615159	−	0.395339i	−0.195630	−	0.980678i	$-0.562675\pi$
$107$	6.36325	−	4.08941i	0.615159	−	0.395339i	0.810788	+	0.585339i	$0.199039\pi$
$108$		0			0
$109$	4.31433	+	9.44707i	0.413238	+	0.904866i	0.995755	+	0.0920466i	$0.0293409\pi$
$109$	4.31433	+	9.44707i	0.413238	+	0.904866i	−0.582516	+	0.812819i	$0.697932\pi$
$110$		0			0
$111$	3.72592	+	4.29994i	0.353649	+	0.408132i
$112$		0			0
$113$	11.6511	−	7.48770i	1.09604	−	0.704384i	0.137835	−	0.990455i	$-0.455986\pi$
$113$	11.6511	−	7.48770i	1.09604	−	0.704384i	0.958208	+	0.286071i	$0.0923494\pi$
$114$		0			0
$115$	−0.413325	−	2.87474i	−0.0385428	−	0.268071i
$116$		0			0
$117$	0.155144	−	0.0455544i	0.0143431	−	0.00421151i
$118$		0			0
$119$	0.401161	+	2.79014i	0.0367744	+	0.255772i
$120$		0			0
$121$	11.5589	+	25.3104i	1.05081	+	2.30094i
$122$		0			0
$123$	−7.51417	−	4.82906i	−0.677530	−	0.435422i
$124$		0			0
$125$	0.600893	−	4.17931i	0.0537455	−	0.373808i
$126$		0			0
$127$	−1.73374	+	12.0584i	−0.153844	+	1.07001i	0.755853	+	0.654741i	$0.227222\pi$
$127$	−1.73374	+	12.0584i	−0.153844	+	1.07001i	−0.909698	+	0.415271i	$0.863687\pi$
$128$		0			0
$129$	2.41422	+	1.55153i	0.212561	+	0.136604i
$130$		0			0
$131$	−9.02458	−	10.4149i	−0.788481	−	0.909956i	0.209210	−	0.977871i	$-0.432911\pi$
$131$	−9.02458	−	10.4149i	−0.788481	−	0.909956i	−0.997691	+	0.0679151i	$0.978365\pi$
$132$		0			0
$133$	3.98206			0.345288
$134$		0			0
$135$	0.430189			0.0370248
$136$		0			0
$137$	−2.69335	−	3.10830i	−0.230109	−	0.265560i	0.628940	−	0.777454i	$-0.283489\pi$
$137$	−2.69335	−	3.10830i	−0.230109	−	0.265560i	−0.859048	+	0.511895i	$0.828944\pi$
$138$		0			0
$139$	5.57830	+	3.58496i	0.473145	+	0.304072i	0.755396	−	0.655269i	$-0.227445\pi$
$139$	5.57830	+	3.58496i	0.473145	+	0.304072i	−0.282250	+	0.959341i	$0.591081\pi$
$140$		0			0
$141$	−0.185137	+	1.28766i	−0.0155914	+	0.108440i
$142$		0			0
$143$	−0.143383	+	0.997253i	−0.0119903	+	0.0833945i
$144$		0			0
$145$	−0.963511	−	0.619211i	−0.0800153	−	0.0514227i
$146$		0			0
$147$	−1.38354	−	3.02953i	−0.114112	−	0.249871i
$148$		0			0
$149$	−0.326514	−	2.27095i	−0.0267490	−	0.186044i	0.972066	−	0.234707i	$-0.0754130\pi$
$149$	−0.326514	−	2.27095i	−0.0267490	−	0.186044i	−0.998815	+	0.0486632i	$0.984504\pi$
$150$		0			0
$151$	5.81882	−	1.70856i	0.473529	−	0.139041i	−0.0362560	−	0.999343i	$-0.511543\pi$
$151$	5.81882	−	1.70856i	0.473529	−	0.139041i	0.509785	+	0.860302i	$0.329725\pi$
$152$		0			0
$153$	0.209419	+	1.45654i	0.0169305	+	0.117754i
$154$		0			0
$155$	−0.372823	+	0.239599i	−0.0299459	+	0.0192450i
$156$		0			0
$157$	7.98360	+	9.21357i	0.637161	+	0.735323i	0.978870	−	0.204483i	$-0.0655513\pi$
$157$	7.98360	+	9.21357i	0.637161	+	0.735323i	−0.341709	+	0.939806i	$0.611006\pi$
$158$		0			0
$159$	4.63115	+	10.1408i	0.367274	+	0.804219i
$160$		0			0
$161$	10.8796	−	6.99189i	0.857432	−	0.551038i
$162$		0			0
$163$	−7.46283			−0.584534			−0.292267	−	0.956337i	$-0.594410\pi$
$163$	−7.46283			−0.584534			−0.292267	+	0.956337i	$0.594410\pi$
$164$		0			0
$165$	−1.11352	+	2.43826i	−0.0866872	+	0.189818i
$166$		0			0
$167$	2.94190	+	20.4614i	0.227651	+	1.58335i	0.707962	+	0.706251i	$0.249615\pi$
$167$	2.94190	+	20.4614i	0.227651	+	1.58335i	−0.480310	+	0.877099i	$0.659476\pi$
$168$		0			0
$169$	8.49607	−	9.80499i	0.653544	−	0.754230i
$170$		0			0
$171$	2.07876			0.158967
$172$		0			0
$173$	−5.44500	+	11.9229i	−0.413975	+	0.906480i	0.581685	+	0.813414i	$0.302394\pi$
$173$	−5.44500	+	11.9229i	−0.413975	+	0.906480i	−0.995660	+	0.0930652i	$0.970334\pi$
$174$		0			0
$175$	8.84985	−	2.59855i	0.668986	−	0.196432i
$176$		0			0
$177$	−3.26238	+	0.957922i	−0.245216	+	0.0720018i
$178$		0			0
$179$	2.21800	−	2.55971i	0.165781	−	0.191321i	−0.666780	−	0.745254i	$-0.732328\pi$
$179$	2.21800	−	2.55971i	0.165781	−	0.191321i	0.832561	+	0.553933i	$0.186874\pi$
$180$		0			0
$181$	−6.00678	−	6.93220i	−0.446481	−	0.515266i	0.487240	−	0.873268i	$-0.338004\pi$
$181$	−6.00678	−	6.93220i	−0.446481	−	0.515266i	−0.933721	+	0.358002i	$0.883458\pi$
$182$		0			0
$183$	8.26834	+	2.42780i	0.611213	+	0.179468i
$184$		0			0
$185$	−2.05907	−	1.32328i	−0.151386	−	0.0972898i
$186$		0			0
$187$	−8.79755	−	2.58319i	−0.643341	−	0.188902i
$188$		0			0
$189$	0.795767	+	1.74249i	0.0578835	+	0.126747i
$190$		0			0
$191$	−1.19552	+	1.37970i	−0.0865045	+	0.0998315i	−0.797352	−	0.603515i	$-0.793766\pi$
$191$	−1.19552	+	1.37970i	−0.0865045	+	0.0998315i	0.710847	+	0.703347i	$0.248312\pi$
$192$		0			0
$193$	−9.91190	+	21.7040i	−0.713475	+	1.56229i	0.109355	+	0.994003i	$0.465122\pi$
$193$	−9.91190	+	21.7040i	−0.713475	+	1.56229i	−0.822829	+	0.568289i	$0.807606\pi$
$194$		0			0
$195$	−0.0585167	+	0.0376064i	−0.00419047	+	0.00269305i
$196$		0			0
$197$	19.5966	+	5.75407i	1.39620	+	0.409961i	0.891377	−	0.453263i	$-0.149740\pi$
$197$	19.5966	+	5.75407i	1.39620	+	0.409961i	0.504821	+	0.863224i	$0.331558\pi$
$198$		0			0
$199$	2.71425	−	18.8780i	0.192408	−	1.33823i	−0.633202	−	0.773987i	$-0.718260\pi$
$199$	2.71425	−	18.8780i	0.192408	−	1.33823i	0.825610	−	0.564241i	$-0.190831\pi$
$200$		0			0
$201$	7.96209	+	1.89871i	0.561603	+	0.133925i
$202$		0			0
$203$	0.725812	−	5.04813i	0.0509420	−	0.354310i
$204$		0			0
$205$	3.68685	+	1.08256i	0.257501	+	0.0756091i
$206$		0			0
$207$	5.67949	−	3.64998i	0.394752	−	0.253691i
$208$		0			0
$209$	−5.38073	+	11.7822i	−0.372193	+	0.814988i
$210$		0			0
$211$	8.88653	−	10.2556i	0.611774	−	0.706024i	−0.362349	−	0.932042i	$-0.618025\pi$
$211$	8.88653	−	10.2556i	0.611774	−	0.706024i	0.974123	+	0.226018i	$0.0725708\pi$
$212$		0			0
$213$	4.68033	+	10.2485i	0.320691	+	0.702215i
$214$		0			0
$215$	−1.18455	−	0.347814i	−0.0807854	−	0.0237207i
$216$		0			0
$217$	−1.66015	−	1.06691i	−0.112698	−	0.0724267i
$218$		0			0
$219$	3.50603	+	1.02946i	0.236916	+	0.0695647i
$220$		0			0
$221$	−0.155814	−	0.179819i	−0.0104812	−	0.0120960i
$222$		0			0
$223$	−7.22419	+	8.33716i	−0.483767	+	0.558297i	−0.944189	−	0.329403i	$-0.893153\pi$
$223$	−7.22419	+	8.33716i	−0.483767	+	0.558297i	0.460422	+	0.887700i	$0.347698\pi$
$224$		0			0
$225$	4.61990	−	1.35652i	0.307993	−	0.0904350i
$226$		0			0
$227$	4.20511	−	1.23473i	0.279103	−	0.0819520i	−0.139185	−	0.990266i	$-0.544448\pi$
$227$	4.20511	−	1.23473i	0.279103	−	0.0819520i	0.418288	+	0.908314i	$0.362630\pi$
$228$		0			0
$229$	8.05735	−	17.6431i	0.532444	−	1.16589i	−0.432065	−	0.901842i	$-0.642215\pi$
$229$	8.05735	−	17.6431i	0.532444	−	1.16589i	0.964509	−	0.264048i	$-0.0850578\pi$
$230$		0			0
$231$	−11.9360			−0.785331
$232$		0			0
$233$	8.68730	−	10.0257i	0.569124	−	0.656804i	−0.396107	−	0.918204i	$-0.629639\pi$
$233$	8.68730	−	10.0257i	0.569124	−	0.656804i	0.965230	+	0.261401i	$0.0841844\pi$
$234$		0			0
$235$	−0.0796441	−	0.553937i	−0.00519541	−	0.0361348i
$236$		0			0
$237$	0.219732	−	0.481145i	0.0142731	−	0.0312537i
$238$		0			0
$239$	2.70011			0.174656			0.0873278	−	0.996180i	$-0.472167\pi$
$239$	2.70011			0.174656			0.0873278	+	0.996180i	$0.472167\pi$
$240$		0			0
$241$	−15.8902	+	10.2120i	−1.02358	+	0.657814i	−0.940873	−	0.338760i	$-0.889993\pi$
$241$	−15.8902	+	10.2120i	−1.02358	+	0.657814i	−0.0827057	+	0.996574i	$0.526356\pi$
$242$		0			0
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$		0			0
$245$	0.938248	+	1.08280i	0.0599425	+	0.0691773i
$246$		0			0
$247$	−0.282764	+	0.181722i	−0.0179919	+	0.0115627i
$248$		0			0
$249$	0.234939	+	1.63404i	0.0148887	+	0.103553i
$250$		0			0
$251$	12.1003	−	3.55296i	0.763762	−	0.224261i	0.123424	−	0.992354i	$-0.460612\pi$
$251$	12.1003	−	3.55296i	0.763762	−	0.224261i	0.640338	+	0.768093i	$0.278794\pi$
$252$		0			0
$253$	5.98670	+	41.6384i	0.376380	+	2.61778i
$254$		0			0
$255$	−0.262971	−	0.575825i	−0.0164679	−	0.0360596i
$256$		0			0
$257$	−22.7305	−	14.6080i	−1.41789	−	0.911222i	−0.999996	−	0.00272532i	$-0.999133\pi$
$257$	−22.7305	−	14.6080i	−1.41789	−	0.911222i	−0.417893	−	0.908496i	$-0.637231\pi$
$258$		0			0
$259$	1.55110	−	10.7881i	0.0963804	−	0.670340i
$260$		0			0
$261$	0.378896	−	2.63528i	0.0234531	−	0.163120i
$262$		0			0
$263$	6.23679	+	4.00814i	0.384577	+	0.247152i	0.718617	−	0.695406i	$-0.244776\pi$
$263$	6.23679	+	4.00814i	0.384577	+	0.247152i	−0.334040	+	0.942559i	$0.608412\pi$
$264$		0			0
$265$	−3.14062	−	3.62447i	−0.192927	−	0.222649i
$266$		0			0
$267$	0.867773			0.0531068
$268$		0			0
$269$	−18.5341			−1.13004			−0.565022	−	0.825076i	$-0.691132\pi$
$269$	−18.5341			−1.13004			−0.565022	+	0.825076i	$0.691132\pi$
$270$		0			0
$271$	−17.5999	−	20.3114i	−1.06912	−	1.23383i	−0.971107	−	0.238643i	$-0.923297\pi$
$271$	−17.5999	−	20.3114i	−1.06912	−	1.23383i	−0.0980113	−	0.995185i	$-0.531248\pi$
$272$		0			0
$273$	−0.260570	−	0.167458i	−0.0157704	−	0.0101350i
$274$		0			0
$275$	−4.26968	+	29.6963i	−0.257472	+	1.79075i
$276$		0			0
$277$	2.99492	−	20.8301i	0.179947	−	1.25156i	−0.676934	−	0.736044i	$-0.736692\pi$
$277$	2.99492	−	20.8301i	0.179947	−	1.25156i	0.856881	−	0.515515i	$-0.172399\pi$
$278$		0			0
$279$	−0.866649	−	0.556961i	−0.0518849	−	0.0333444i
$280$		0			0
$281$	−8.92691	−	19.5472i	−0.532535	−	1.16609i	−0.964472	−	0.264185i	$-0.914897\pi$
$281$	−8.92691	−	19.5472i	−0.532535	−	1.16609i	0.431937	−	0.901904i	$-0.357830\pi$
$282$		0			0
$283$	1.79730	+	12.5005i	0.106838	+	0.743076i	0.970864	+	0.239629i	$0.0770260\pi$
$283$	1.79730	+	12.5005i	0.106838	+	0.743076i	−0.864026	+	0.503447i	$0.832065\pi$
$284$		0			0
$285$	−0.858036	+	0.251942i	−0.0508257	+	0.0149238i
$286$		0			0
$287$	2.43505	+	16.9361i	0.143736	+	0.999709i
$288$		0			0
$289$	−12.4797	+	8.02021i	−0.734100	+	0.471777i
$290$		0			0
$291$	−11.9039	−	13.7378i	−0.697819	−	0.805326i
$292$		0			0
$293$	3.55397	+	7.78211i	0.207625	+	0.454636i	0.984583	−	0.174917i	$-0.0559656\pi$
$293$	3.55397	+	7.78211i	0.207625	+	0.454636i	−0.776958	+	0.629552i	$0.783238\pi$
$294$		0			0
$295$	1.23049	−	0.790791i	0.0716421	−	0.0460416i
$296$		0			0
$297$	−6.23096			−0.361557
$298$		0			0
$299$	−0.453480	+	0.992982i	−0.0262254	+	0.0574256i
$300$		0			0
$301$	−0.782356	−	5.44141i	−0.0450943	−	0.313638i
$302$		0			0
$303$	−1.48794	+	1.71717i	−0.0854797	+	0.0986488i
$304$		0			0
$305$	−3.70711			−0.212269
$306$		0			0
$307$	3.78721	−	8.29282i	0.216147	−	0.473297i	−0.770236	−	0.637759i	$-0.779862\pi$
$307$	3.78721	−	8.29282i	0.216147	−	0.473297i	0.986383	+	0.164462i	$0.0525889\pi$
$308$		0			0
$309$	−11.9774	+	3.51688i	−0.681371	+	0.200068i
$310$		0			0
$311$	12.4188	−	3.64649i	0.704205	−	0.206773i	0.0900255	−	0.995939i	$-0.471305\pi$
$311$	12.4188	−	3.64649i	0.704205	−	0.206773i	0.614180	+	0.789166i	$0.289487\pi$
$312$		0			0
$313$	−9.75630	+	11.2594i	−0.551459	+	0.636418i	−0.961222	−	0.275774i	$-0.911066\pi$
$313$	−9.75630	+	11.2594i	−0.551459	+	0.636418i	0.409764	+	0.912192i	$0.365611\pi$
$314$		0			0
$315$	−0.539650	−	0.622790i	−0.0304058	−	0.0350902i
$316$		0			0
$317$	−4.30957	−	1.26540i	−0.242049	−	0.0710721i	0.158458	−	0.987366i	$-0.449348\pi$
$317$	−4.30957	−	1.26540i	−0.242049	−	0.0710721i	−0.400507	+	0.916294i	$0.631166\pi$
$318$		0			0
$319$	13.9557	+	8.96879i	0.781370	+	0.502156i
$320$		0			0
$321$	−7.25762	−	2.13103i	−0.405081	−	0.118942i
$322$		0			0
$323$	−1.27072	−	2.78250i	−0.0707050	−	0.154822i
$324$		0			0
$325$	−0.509839	+	0.588386i	−0.0282808	+	0.0326378i
$326$		0			0
$327$	4.31433	−	9.44707i	0.238583	−	0.522424i
$328$		0			0
$329$	2.09640	−	1.34727i	0.115578	−	0.0742777i
$330$		0			0
$331$	7.31617	+	2.14822i	0.402133	+	0.118077i	0.476544	−	0.879151i	$-0.341889\pi$
$331$	7.31617	+	2.14822i	0.402133	+	0.118077i	−0.0744107	+	0.997228i	$0.523708\pi$
$332$		0			0
$333$	0.809720	−	5.63173i	0.0443724	−	0.308617i
$334$		0			0
$335$	−3.51658	+	0.181275i	−0.192131	+	0.00990409i
$336$		0			0
$337$	1.24544	−	8.66219i	0.0678432	−	0.471860i	−0.927371	−	0.374143i	$-0.877937\pi$
$337$	1.24544	−	8.66219i	0.0678432	−	0.471860i	0.995214	−	0.0977168i	$-0.0311539\pi$
$338$		0			0
$339$	−13.2887	−	3.90191i	−0.721742	−	0.211922i
$340$		0			0
$341$	5.40005	−	3.47040i	0.292429	−	0.187933i
$342$		0			0
$343$	−8.22067	+	18.0007i	−0.443874	+	0.971949i
$344$		0			0
$345$	−1.90191	+	2.19493i	−0.102396	+	0.118171i
$346$		0			0
$347$	−8.07560	−	17.6831i	−0.433521	−	0.949279i	−0.992742	−	0.120260i	$-0.961627\pi$
$347$	−8.07560	−	17.6831i	−0.433521	−	0.949279i	0.559221	−	0.829018i	$-0.311100\pi$
$348$		0			0
$349$	24.3730	+	7.15655i	1.30466	+	0.383081i	0.858932	−	0.512089i	$-0.171128\pi$
$349$	24.3730	+	7.15655i	1.30466	+	0.383081i	0.445723	+	0.895171i	$0.352947\pi$
$350$		0			0
$351$	−0.136026	−	0.0874183i	−0.00726051	−	0.00466604i
$352$		0			0
$353$	3.83223	+	1.12524i	0.203969	+	0.0598907i	0.382121	−	0.924112i	$-0.375194\pi$
$353$	3.83223	+	1.12524i	0.203969	+	0.0598907i	−0.178152	+	0.984003i	$0.557012\pi$
$354$		0			0
$355$	−3.17397	−	3.66296i	−0.168457	−	0.194410i
$356$		0			0
$357$	1.84594	−	2.13033i	0.0976976	−	0.112749i
$358$		0			0
$359$	−3.83986	+	1.12748i	−0.202660	+	0.0595063i	−0.381487	−	0.924374i	$-0.624588\pi$
$359$	−3.83986	+	1.12748i	−0.202660	+	0.0595063i	0.178827	+	0.983881i	$0.442770\pi$
$360$		0			0
$361$	14.0842	−	4.13549i	0.741272	−	0.217657i
$362$		0			0
$363$	11.5589	−	25.3104i	0.606683	−	1.32845i
$364$		0			0
$365$	−1.57193			−0.0822787
$366$		0			0
$367$	−5.76072	+	6.64823i	−0.300707	+	0.347035i	−0.885914	−	0.463849i	$-0.846468\pi$
$367$	−5.76072	+	6.64823i	−0.300707	+	0.347035i	0.585207	+	0.810884i	$0.301013\pi$
$368$		0			0
$369$	1.27117	+	8.84120i	0.0661746	+	0.460254i
$370$		0			0
$371$	8.87141	−	19.4257i	0.460581	−	1.00853i
$372$		0			0
$373$	−8.59176			−0.444865			−0.222432	−	0.974948i	$-0.571400\pi$
$373$	−8.59176			−0.444865			−0.222432	+	0.974948i	$0.571400\pi$
$374$		0			0
$375$	−3.55201	+	2.28274i	−0.183425	+	0.117880i
$376$		0			0
$377$	0.178832	+	0.391588i	0.00921033	+	0.0201678i
$378$		0			0
$379$	−7.06292	−	8.15105i	−0.362798	−	0.418691i	0.544777	−	0.838581i	$-0.316614\pi$
$379$	−7.06292	−	8.15105i	−0.362798	−	0.418691i	−0.907575	+	0.419890i	$0.862069\pi$
$380$		0			0
$381$	10.2485	−	6.58631i	0.525047	−	0.337427i
$382$		0			0
$383$	3.86259	+	26.8649i	0.197369	+	1.37273i	0.811880	+	0.583824i	$0.198444\pi$
$383$	3.86259	+	26.8649i	0.197369	+	1.37273i	−0.614511	+	0.788908i	$0.710647\pi$
$384$		0			0
$385$	4.92674	−	1.44662i	0.251090	−	0.0737267i
$386$		0			0
$387$	−0.408414	−	2.84058i	−0.0207609	−	0.144395i
$388$		0			0
$389$	1.72630	+	3.78006i	0.0875266	+	0.191657i	0.948334	−	0.317275i	$-0.102768\pi$
$389$	1.72630	+	3.78006i	0.0875266	+	0.191657i	−0.860807	+	0.508932i	$0.830041\pi$
$390$		0			0
$391$	−8.35746	−	5.37101i	−0.422655	−	0.271624i
$392$		0			0
$393$	−1.96123	+	13.6406i	−0.0989309	+	0.688079i
$394$		0			0
$395$	−0.0323832	+	0.225230i	−0.00162938	+	0.0113326i
$396$		0			0
$397$	−26.2942	−	16.8983i	−1.31967	−	0.848101i	−0.324464	−	0.945898i	$-0.605184\pi$
$397$	−26.2942	−	16.8983i	−1.31967	−	0.848101i	−0.995206	+	0.0977976i	$0.968820\pi$
$398$		0			0
$399$	−2.60769	−	3.00944i	−0.130548	−	0.150660i
$400$		0			0
$401$	−8.28811			−0.413888			−0.206944	−	0.978353i	$-0.566352\pi$
$401$	−8.28811			−0.413888			−0.206944	+	0.978353i	$0.566352\pi$
$402$		0			0
$403$	0.166575			0.00829769
$404$		0			0
$405$	−0.281714	−	0.325115i	−0.0139985	−	0.0161551i
$406$		0			0
$407$	29.8240	+	19.1667i	1.47832	+	0.950060i
$408$		0			0
$409$	5.20867	−	36.2271i	0.257552	−	1.79132i	−0.292583	−	0.956240i	$-0.594515\pi$
$409$	5.20867	−	36.2271i	0.257552	−	1.79132i	0.550135	−	0.835075i	$-0.314576\pi$
$410$		0			0
$411$	−0.585322	+	4.07100i	−0.0288718	+	0.200808i
$412$		0			0
$413$	5.47928	+	3.52132i	0.269618	+	0.173273i
$414$		0			0
$415$	−0.295017	−	0.645997i	−0.0144818	−	0.0317107i
$416$		0			0
$417$	−0.943681	−	6.56345i	−0.0462123	−	0.321413i
$418$		0			0
$419$	−30.3455	+	8.91025i	−1.48248	+	0.435294i	−0.920132	−	0.391609i	$-0.871918\pi$
$419$	−30.3455	+	8.91025i	−1.48248	+	0.435294i	−0.562344	+	0.826903i	$0.690100\pi$
$420$		0			0
$421$	−3.53724	−	24.6020i	−0.172394	−	1.19903i	−0.873807	−	0.486273i	$-0.838356\pi$
$421$	−3.53724	−	24.6020i	−0.172394	−	1.19903i	0.701413	−	0.712756i	$-0.252553\pi$
$422$		0			0
$423$	1.09439	−	0.703319i	0.0532109	−	0.0341965i
$424$		0			0
$425$	−4.63986	−	5.35468i	−0.225066	−	0.259740i
$426$		0			0
$427$	−6.85744	−	15.0157i	−0.331855	−	0.726661i
$428$		0			0
$429$	0.847570	−	0.544700i	0.0409210	−	0.0262984i
$430$		0			0
$431$	−38.3923			−1.84929			−0.924645	−	0.380829i	$-0.875639\pi$
$431$	−38.3923			−1.84929			−0.924645	+	0.380829i	$0.875639\pi$
$432$		0			0
$433$	−6.28447	+	13.7611i	−0.302012	+	0.661315i	−0.998412	−	0.0563396i	$-0.982057\pi$
$433$	−6.28447	+	13.7611i	−0.302012	+	0.661315i	0.696399	+	0.717655i	$0.254784\pi$
$434$		0			0
$435$	0.162997	+	1.13367i	0.00781512	+	0.0543553i
$436$		0			0
$437$	−9.19041	+	10.6063i	−0.439637	+	0.507368i
$438$		0			0
$439$	−10.5837			−0.505134			−0.252567	−	0.967579i	$-0.581275\pi$
$439$	−10.5837			−0.505134			−0.252567	+	0.967579i	$0.581275\pi$
$440$		0			0
$441$	−1.38354	+	3.02953i	−0.0658828	+	0.144263i
$442$		0			0
$443$	8.00479	−	2.35042i	0.380319	−	0.111672i	−0.0859845	−	0.996296i	$-0.527404\pi$
$443$	8.00479	−	2.35042i	0.380319	−	0.111672i	0.466304	+	0.884625i	$0.345585\pi$
$444$		0			0
$445$	−0.358185	+	0.105173i	−0.0169796	+	0.00498566i
$446$		0			0
$447$	−1.50245	+	1.73392i	−0.0710634	+	0.0820116i
$448$		0			0
$449$	6.82406	+	7.87539i	0.322047	+	0.371663i	0.893570	−	0.448924i	$-0.148193\pi$
$449$	6.82406	+	7.87539i	0.322047	+	0.371663i	−0.571523	+	0.820586i	$0.693647\pi$
$450$		0			0
$451$	−53.4012	−	15.6800i	−2.51456	−	0.738342i
$452$		0			0
$453$	−5.10176	−	3.27870i	−0.239702	−	0.154047i
$454$		0			0
$455$	0.127849	+	0.0375400i	0.00599367	+	0.00175990i
$456$		0			0
$457$	−0.516122	−	1.13015i	−0.0241431	−	0.0528661i	0.897176	−	0.441673i	$-0.145615\pi$
$457$	−0.516122	−	1.13015i	−0.0241431	−	0.0528661i	−0.921319	+	0.388807i	$0.872887\pi$
$458$		0			0
$459$	0.963638	−	1.11210i	0.0449788	−	0.0519083i
$460$		0			0
$461$	11.6387	−	25.4853i	0.542070	−	1.18697i	−0.418318	−	0.908301i	$-0.637380\pi$
$461$	11.6387	−	25.4853i	0.542070	−	1.18697i	0.960388	−	0.278667i	$-0.0898925\pi$
$462$		0			0
$463$	23.7057	−	15.2347i	1.10170	−	0.708019i	0.142230	−	0.989834i	$-0.454573\pi$
$463$	23.7057	−	15.2347i	1.10170	−	0.708019i	0.959469	+	0.281815i	$0.0909365\pi$
$464$		0			0
$465$	0.425224	+	0.124857i	0.0197193	+	0.00579011i
$466$		0			0
$467$	−2.68090	+	18.6461i	−0.124057	+	0.862837i	0.828827	+	0.559504i	$0.189008\pi$
$467$	−2.68090	+	18.6461i	−0.124057	+	0.862837i	−0.952885	+	0.303333i	$0.901901\pi$
$468$		0			0
$469$	−7.23925	−	13.9086i	−0.334278	−	0.642241i
$470$		0			0
$471$	1.73500	−	12.0672i	0.0799447	−	0.556027i
$472$		0			0
$473$	17.1572	+	5.03782i	0.788891	+	0.231639i
$474$		0			0
$475$	−8.42018	+	5.41132i	−0.386344	+	0.248289i
$476$		0			0
$477$	4.63115	−	10.1408i	0.212046	−	0.464316i
$478$		0			0
$479$	−5.99392	+	6.91736i	−0.273869	+	0.316062i	−0.875977	−	0.482353i	$-0.839782\pi$
$479$	−5.99392	+	6.91736i	−0.273869	+	0.316062i	0.602108	+	0.798415i	$0.294328\pi$
$480$		0			0
$481$	0.382173	+	0.836843i	0.0174256	+	0.0381568i
$482$		0			0
$483$	−12.4087	−	3.64353i	−0.564617	−	0.165787i
$484$		0			0
$485$	6.57850	+	4.22775i	0.298715	+	0.191972i
$486$		0			0
$487$	5.04691	+	1.48191i	0.228697	+	0.0671516i	0.394073	−	0.919079i	$-0.371066\pi$
$487$	5.04691	+	1.48191i	0.228697	+	0.0671516i	−0.165376	+	0.986231i	$0.552884\pi$
$488$		0			0
$489$	4.88712	+	5.64003i	0.221003	+	0.255051i
$490$		0			0
$491$	−19.6823	+	22.7146i	−0.888250	+	1.02510i	0.111260	+	0.993791i	$0.464511\pi$
$491$	−19.6823	+	22.7146i	−0.888250	+	1.02510i	−0.999510	+	0.0313038i	$0.990034\pi$
$492$		0			0
$493$	−3.75904	+	1.10375i	−0.169299	+	0.0497106i
$494$		0			0
$495$	2.57191	−	0.755182i	0.115599	−	0.0339429i
$496$		0			0
$497$	8.96561	−	19.6320i	0.402163	−	0.880614i
$498$		0			0
$499$	31.3330			1.40266			0.701330	−	0.712837i	$-0.252590\pi$
$499$	31.3330			1.40266			0.701330	+	0.712837i	$0.252590\pi$
$500$		0			0
$501$	13.5371	−	15.6227i	0.604795	−	0.697971i
$502$		0			0
$503$	4.91219	+	34.1650i	0.219024	+	1.52334i	0.741653	+	0.670784i	$0.234042\pi$
$503$	4.91219	+	34.1650i	0.219024	+	1.52334i	−0.522629	+	0.852560i	$0.675049\pi$
$504$		0			0
$505$	0.406048	−	0.889121i	0.0180689	−	0.0395654i
$506$		0			0
$507$	−12.9739			−0.576189
$508$		0			0
$509$	−21.6534	+	13.9158i	−0.959771	+	0.616808i	−0.923935	−	0.382550i	$-0.875046\pi$
$509$	−21.6534	+	13.9158i	−0.959771	+	0.616808i	−0.0358366	+	0.999358i	$0.511410\pi$
$510$		0			0
$511$	−2.90777	−	6.36713i	−0.128632	−	0.281665i
$512$		0			0
$513$	−1.36130	−	1.57102i	−0.0601027	−	0.0693623i
$514$		0			0
$515$	4.51760	−	2.90328i	0.199069	−	0.127934i
$516$		0			0
$517$	1.15358	+	8.02334i	0.0507345	+	0.352866i
$518$		0			0
$519$	12.5764	−	3.69277i	0.552044	−	0.162095i
$520$		0			0
$521$	−1.43683	−	9.99339i	−0.0629488	−	0.437818i	−0.996785	−	0.0801183i	$-0.974470\pi$
$521$	−1.43683	−	9.99339i	−0.0629488	−	0.437818i	0.933837	−	0.357700i	$-0.116439\pi$
$522$		0			0
$523$	−1.49968	−	3.28383i	−0.0655762	−	0.143592i	0.874006	−	0.485915i	$-0.161514\pi$
$523$	−1.49968	−	3.28383i	−0.0655762	−	0.143592i	−0.939582	+	0.342323i	$0.888786\pi$
$524$		0			0
$525$	−7.75928	−	4.98658i	−0.338643	−	0.217632i
$526$		0			0
$527$	−0.215740	+	1.50051i	−0.00939780	+	0.0653632i
$528$		0			0
$529$	−3.21332	+	22.3491i	−0.139709	+	0.971701i
$530$		0			0
$531$	2.86035	+	1.83824i	0.124129	+	0.0797727i
$532$		0			0
$533$	−0.945794	−	1.09150i	−0.0409669	−	0.0472783i
$534$		0			0
$535$	3.25396			0.140681
$536$		0			0
$537$	−3.38698			−0.146159
$538$		0			0
$539$	−13.5898	−	15.6835i	−0.585354	−	0.675534i
$540$		0			0
$541$	−37.7012	−	24.2291i	−1.62090	−	1.04169i	−0.955409	−	0.295285i	$-0.904585\pi$
$541$	−37.7012	−	24.2291i	−1.62090	−	1.04169i	−0.665492	−	0.746405i	$-0.731778\pi$
$542$		0			0
$543$	−1.30540	+	9.07925i	−0.0560200	+	0.389628i
$544$		0			0
$545$	−0.635831	+	4.42230i	−0.0272360	+	0.189430i
$546$		0			0
$547$	−5.59574	−	3.59616i	−0.239256	−	0.153761i	0.415518	−	0.909585i	$-0.363600\pi$
$547$	−5.59574	−	3.59616i	−0.239256	−	0.153761i	−0.654775	+	0.755824i	$0.727237\pi$
$548$		0			0
$549$	−3.57980	−	7.83866i	−0.152782	−	0.334546i
$550$		0			0
$551$	0.787634	+	5.47811i	0.0335543	+	0.233376i
$552$		0			0
$553$	−0.972200	+	0.285464i	−0.0413422	+	0.0121392i
$554$		0			0
$555$	0.348333	+	2.42271i	0.0147859	+	0.102838i
$556$		0			0
$557$	−3.89750	+	2.50477i	−0.165142	+	0.106131i	−0.620602	−	0.784126i	$-0.713112\pi$
$557$	−3.89750	+	2.50477i	−0.165142	+	0.106131i	0.455459	+	0.890257i	$0.349475\pi$
$558$		0			0
$559$	0.303874	+	0.350689i	0.0128525	+	0.0148326i
$560$		0			0
$561$	3.80892	+	8.34038i	0.160813	+	0.352131i
$562$		0			0
$563$	−18.1620	+	11.6720i	−0.765438	+	0.491917i	−0.864172	−	0.503197i	$-0.832157\pi$
$563$	−18.1620	+	11.6720i	−0.765438	+	0.491917i	0.0987338	+	0.995114i	$0.468521\pi$
$564$		0			0
$565$	5.95799			0.250654
$566$		0			0
$567$	0.795767	−	1.74249i	0.0334191	−	0.0731776i
$568$		0			0
$569$	1.49690	+	10.4112i	0.0627533	+	0.436459i	0.996842	+	0.0794166i	$0.0253057\pi$
$569$	1.49690	+	10.4112i	0.0627533	+	0.436459i	−0.934088	+	0.357042i	$0.883785\pi$
$570$		0			0
$571$	28.4601	−	32.8447i	1.19102	−	1.37451i	0.281123	−	0.959672i	$-0.409293\pi$
$571$	28.4601	−	32.8447i	1.19102	−	1.37451i	0.909896	−	0.414837i	$-0.136161\pi$
$572$		0			0
$573$	1.82560			0.0762656
$574$		0			0
$575$	−13.5038	+	29.5691i	−0.563146	+	1.23312i
$576$		0			0
$577$	2.03816	−	0.598459i	0.0848499	−	0.0249142i	−0.239032	−	0.971012i	$-0.576830\pi$
$577$	2.03816	−	0.598459i	0.0848499	−	0.0249142i	0.323882	+	0.946097i	$0.395012\pi$
$578$		0			0
$579$	22.8937	−	6.72221i	0.951431	−	0.279365i
$580$		0			0
$581$	2.07089	−	2.38994i	0.0859151	−	0.0991513i
$582$		0			0
$583$	45.4895	+	52.4976i	1.88398	+	2.17423i
$584$		0			0
$585$	0.0667414	+	0.0195970i	0.00275942	+	0.000810238i
$586$		0			0
$587$	27.2669	+	17.5234i	1.12543	+	0.723267i	0.964601	−	0.263715i	$-0.0849480\pi$
$587$	27.2669	+	17.5234i	1.12543	+	0.723267i	0.160825	+	0.986983i	$0.448584\pi$
$588$		0			0
$589$	2.05476	+	0.603333i	0.0846651	+	0.0248599i
$590$		0			0
$591$	−8.48439	−	18.5782i	−0.349001	−	0.764206i
$592$		0			0
$593$	17.7903	−	20.5311i	0.730559	−	0.843110i	−0.261975	−	0.965075i	$-0.584374\pi$
$593$	17.7903	−	20.5311i	0.730559	−	0.843110i	0.992535	+	0.121964i	$0.0389193\pi$
$594$		0			0
$595$	−0.503745	+	1.10305i	−0.0206515	+	0.0452205i
$596$		0			0
$597$	−16.0445	+	10.3112i	−0.656658	+	0.422009i
$598$		0			0
$599$	33.7369	+	9.90605i	1.37845	+	0.404750i	0.885230	−	0.465153i	$-0.154001\pi$
$599$	33.7369	+	9.90605i	1.37845	+	0.404750i	0.493223	+	0.869903i	$0.335819\pi$
$600$		0			0
$601$	1.24425	−	8.65397i	0.0507542	−	0.353003i	−0.948581	−	0.316535i	$-0.897480\pi$
$601$	1.24425	−	8.65397i	0.0507542	−	0.353003i	0.999335	−	0.0364675i	$-0.0116105\pi$
$602$		0			0
$603$	−3.77911	−	7.26074i	−0.153897	−	0.295680i
$604$		0			0
$605$	−1.70350	+	11.8481i	−0.0692572	+	0.481695i
$606$		0			0
$607$	21.8123	+	6.40468i	0.885336	+	0.259958i	0.692625	−	0.721298i	$-0.256454\pi$
$607$	21.8123	+	6.40468i	0.885336	+	0.259958i	0.192711	+	0.981256i	$0.438272\pi$
$608$		0			0
$609$	−4.29043	+	2.75729i	−0.173857	+	0.111731i
$610$		0			0
$611$	−0.0873815	+	0.191339i	−0.00353508	+	0.00774074i
$612$		0			0
$613$	−4.89911	+	5.65388i	−0.197873	+	0.228358i	−0.846011	−	0.533165i	$-0.821003\pi$
$613$	−4.89911	+	5.65388i	−0.197873	+	0.228358i	0.648138	+	0.761523i	$0.275548\pi$
$614$		0			0
$615$	−1.59623	−	3.49526i	−0.0643663	−	0.140943i
$616$		0			0
$617$	−20.3463	−	5.97420i	−0.819109	−	0.240512i	−0.154777	−	0.987949i	$-0.549466\pi$
$617$	−20.3463	−	5.97420i	−0.819109	−	0.240512i	−0.664332	+	0.747437i	$0.731284\pi$
$618$		0			0
$619$	−23.4974	−	15.1009i	−0.944440	−	0.606955i	−0.0247895	−	0.999693i	$-0.507892\pi$
$619$	−23.4974	−	15.1009i	−0.944440	−	0.606955i	−0.919650	+	0.392738i	$0.871528\pi$
$620$		0			0
$621$	−6.47775	−	1.90204i	−0.259943	−	0.0763261i
$622$		0			0
$623$	−1.08858	−	1.25628i	−0.0436129	−	0.0503319i
$624$		0			0
$625$	−14.5761	+	16.8217i	−0.583044	+	0.672868i
$626$		0			0
$627$	12.4280	−	3.64919i	0.496326	−	0.145734i
$628$		0			0
$629$	−8.03326	+	2.35878i	−0.320307	+	0.0940506i
$630$		0			0
$631$	−10.2502	+	22.4449i	−0.408055	+	0.893516i	0.588335	+	0.808618i	$0.299784\pi$
$631$	−10.2502	+	22.4449i	−0.408055	+	0.893516i	−0.996390	+	0.0848983i	$0.972943\pi$
$632$		0			0
$633$	−13.5701			−0.539363
$634$		0			0
$635$	−3.43196	+	3.96069i	−0.136193	+	0.157175i
$636$		0			0
$637$	−0.0766395	−	0.533039i	−0.00303657	−	0.0211198i
$638$		0			0
$639$	4.68033	−	10.2485i	0.185151	−	0.405424i
$640$		0			0
$641$	−2.59790			−0.102611			−0.0513055	−	0.998683i	$-0.516338\pi$
$641$	−2.59790			−0.102611			−0.0513055	+	0.998683i	$0.516338\pi$
$642$		0			0
$643$	−5.32848	+	3.42440i	−0.210135	+	0.135045i	−0.641475	−	0.767144i	$-0.721677\pi$
$643$	−5.32848	+	3.42440i	−0.210135	+	0.135045i	0.431340	+	0.902189i	$0.358041\pi$
$644$		0			0
$645$	0.512853	+	1.12299i	0.0201936	+	0.0442177i
$646$		0			0
$647$	−13.2935	−	15.3415i	−0.522621	−	0.603137i	0.431664	−	0.902035i	$-0.357927\pi$
$647$	−13.2935	−	15.3415i	−0.522621	−	0.603137i	−0.954285	+	0.298897i	$0.903381\pi$
$648$		0			0
$649$	−17.8228	+	11.4540i	−0.699604	+	0.449608i
$650$		0			0
$651$	0.280847	+	1.95334i	0.0110073	+	0.0765572i
$652$		0			0
$653$	−21.4974	+	6.31221i	−0.841259	+	0.247016i	−0.673847	−	0.738871i	$-0.735359\pi$
$653$	−21.4974	+	6.31221i	−0.841259	+	0.247016i	−0.167412	+	0.985887i	$0.553541\pi$
$654$		0			0
$655$	−0.843700	−	5.86806i	−0.0329661	−	0.229284i
$656$		0			0
$657$	−1.51795	−	3.32384i	−0.0592207	−	0.129675i
$658$		0			0
$659$	5.70057	+	3.66353i	0.222063	+	0.142711i	0.646943	−	0.762539i	$-0.276047\pi$
$659$	5.70057	+	3.66353i	0.222063	+	0.142711i	−0.424880	+	0.905250i	$0.639684\pi$
$660$		0			0
$661$	4.47209	−	31.1041i	0.173944	−	1.20981i	−0.696505	−	0.717552i	$-0.745263\pi$
$661$	4.47209	−	31.1041i	0.173944	−	1.20981i	0.870450	−	0.492257i	$-0.163828\pi$
$662$		0			0
$663$	−0.0338617	+	0.235513i	−0.00131508	+	0.00914658i
$664$		0			0
$665$	1.44110	+	0.926139i	0.0558835	+	0.0359141i
$666$		0			0
$667$	11.7707	+	13.5841i	0.455762	+	0.525978i
$668$		0			0
$669$	11.0316			0.426508
$670$		0			0
$671$	53.6947			2.07286
$672$		0			0
$673$	−11.2380	−	12.9693i	−0.433193	−	0.499931i	0.496618	−	0.867969i	$-0.334575\pi$
$673$	−11.2380	−	12.9693i	−0.433193	−	0.499931i	−0.929811	+	0.368038i	$0.880030\pi$
$674$		0			0
$675$	−4.05058	−	2.60315i	−0.155907	−	0.100195i
$676$		0			0
$677$	−1.64919	+	11.4704i	−0.0633835	+	0.440842i	0.933275	+	0.359162i	$0.116938\pi$
$677$	−1.64919	+	11.4704i	−0.0633835	+	0.440842i	−0.996659	+	0.0816798i	$0.973972\pi$
$678$		0			0
$679$	−4.95558	+	34.4668i	−0.190178	+	1.32271i
$680$		0			0
$681$	−3.68691	−	2.36943i	−0.141283	−	0.0907969i
$682$		0			0
$683$	12.7855	+	27.9964i	0.489224	+	1.07125i	0.979823	+	0.199866i	$0.0640506\pi$
$683$	12.7855	+	27.9964i	0.489224	+	1.07125i	−0.490599	+	0.871385i	$0.663222\pi$
$684$		0			0
$685$	−0.251799	−	1.75130i	−0.00962076	−	0.0669138i
$686$		0			0
$687$	−18.6102	+	5.46445i	−0.710024	+	0.208482i
$688$		0			0
$689$	0.256537	+	1.78426i	0.00977330	+	0.0679748i
$690$		0			0
$691$	22.4080	−	14.4007i	0.852439	−	0.547829i	−0.0398958	−	0.999204i	$-0.512703\pi$
$691$	22.4080	−	14.4007i	0.852439	−	0.547829i	0.892334	+	0.451375i	$0.149066\pi$
$692$		0			0
$693$	7.81641	+	9.02062i	0.296921	+	0.342665i
$694$		0			0
$695$	1.18500	+	2.59478i	0.0449495	+	0.0984256i
$696$		0			0
$697$	11.0572	−	7.10605i	0.418822	−	0.269161i
$698$		0			0
$699$	−13.2659			−0.501761
$700$		0			0
$701$	9.63911	−	21.1067i	0.364064	−	0.797189i	−0.635619	−	0.772003i	$-0.719255\pi$
$701$	9.63911	−	21.1067i	0.364064	−	0.797189i	0.999683	−	0.0251861i	$-0.00801783\pi$
$702$		0			0
$703$	1.68321	+	11.7070i	0.0634835	+	0.441538i
$704$		0			0
$705$	−0.366482	+	0.422942i	−0.0138025	+	0.0159289i
$706$		0			0
$707$	4.35250			0.163693
$708$		0			0
$709$	2.92092	−	6.39591i	0.109697	−	0.240204i	−0.846820	−	0.531880i	$-0.821486\pi$
$709$	2.92092	−	6.39591i	0.109697	−	0.240204i	0.956517	+	0.291676i	$0.0942130\pi$
$710$		0			0
$711$	−0.507519	+	0.149021i	−0.0190334	+	0.00558872i
$712$		0			0
$713$	6.67329	−	1.95946i	0.249917	−	0.0733822i
$714$		0			0
$715$	−0.283829	+	0.327556i	−0.0106146	+	0.0122499i
$716$		0			0
$717$	−1.76820	−	2.04061i	−0.0660345	−	0.0762079i
$718$		0			0
$719$	1.86210	+	0.546761i	0.0694445	+	0.0203907i	0.316270	−	0.948669i	$-0.397569\pi$
$719$	1.86210	+	0.546761i	0.0694445	+	0.0203907i	−0.246826	+	0.969060i	$0.579388\pi$
$720$		0			0
$721$	20.1165	+	12.9281i	0.749176	+	0.481466i
$722$		0			0
$723$	18.1236	+	5.32157i	0.674024	+	0.197911i
$724$		0			0
$725$	5.32529	+	11.6608i	0.197776	+	0.433070i
$726$		0			0
$727$	22.9628	−	26.5005i	0.851643	−	0.982848i	−0.148339	−	0.988937i	$-0.547393\pi$
$727$	22.9628	−	26.5005i	0.851643	−	0.982848i	0.999981	+	0.00608860i	$0.00193807\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−3.55257	+	2.28310i	−0.131397	+	0.0844435i
$732$		0			0
$733$	18.2497	+	5.35858i	0.674067	+	0.197924i	0.600813	−	0.799390i	$-0.294844\pi$
$733$	18.2497	+	5.35858i	0.674067	+	0.197924i	0.0732536	+	0.997313i	$0.476662\pi$
$734$		0			0
$735$	0.203901	−	1.41816i	0.00752099	−	0.0523097i
$736$		0			0
$737$	50.9350	−	2.62562i	1.87621	−	0.0967160i
$738$		0			0
$739$	2.12273	−	14.7639i	0.0780858	−	0.543098i	−0.912801	−	0.408404i	$-0.866086\pi$
$739$	2.12273	−	14.7639i	0.0780858	−	0.543098i	0.990887	−	0.134695i	$-0.0430054\pi$
$740$		0			0
$741$	0.322507	+	0.0946966i	0.0118476	+	0.00347877i
$742$		0			0
$743$	9.55233	−	6.13891i	0.350441	−	0.225215i	−0.353563	−	0.935411i	$-0.615030\pi$
$743$	9.55233	−	6.13891i	0.350441	−	0.225215i	0.704004	+	0.710196i	$0.251394\pi$
$744$		0			0
$745$	0.410009	−	0.897793i	0.0150215	−	0.0328926i
$746$		0			0
$747$	1.08107	−	1.24762i	0.0395543	−	0.0456481i
$748$		0			0
$749$	6.01919	+	13.1802i	0.219936	+	0.481594i
$750$		0			0
$751$	38.1313	+	11.1964i	1.39143	+	0.408561i	0.889733	−	0.456482i	$-0.150891\pi$
$751$	38.1313	+	11.1964i	1.39143	+	0.408561i	0.501698	+	0.865043i	$0.332709\pi$
$752$		0			0
$753$	−10.6091	−	6.81808i	−0.386618	−	0.248465i
$754$		0			0
$755$	2.50319	+	0.735004i	0.0911006	+	0.0267495i
$756$		0			0
$757$	−21.4272	−	24.7283i	−0.778785	−	0.898765i	0.218236	−	0.975896i	$-0.429970\pi$
$757$	−21.4272	−	24.7283i	−0.778785	−	0.898765i	−0.997021	+	0.0771305i	$0.975424\pi$
$758$		0			0
$759$	27.5477	−	31.7918i	0.999920	−	1.15397i
$760$		0			0
$761$	48.4940	−	14.2391i	1.75790	−	0.516167i	0.765965	−	0.642882i	$-0.222261\pi$
$761$	48.4940	−	14.2391i	1.75790	−	0.516167i	0.991939	+	0.126714i	$0.0404432\pi$
$762$		0			0
$763$	−19.0887	+	5.60496i	−0.691058	+	0.202913i
$764$		0			0
$765$	−0.262971	+	0.575825i	−0.00950772	+	0.0208190i
$766$		0			0
$767$	−0.549777			−0.0198513
$768$		0			0
$769$	−4.74691	+	5.47823i	−0.171178	+	0.197550i	−0.834856	−	0.550468i	$-0.814449\pi$
$769$	−4.74691	+	5.47823i	−0.171178	+	0.197550i	0.663678	+	0.748019i	$0.268995\pi$
$770$		0			0
$771$	3.84532	+	26.7448i	0.138486	+	0.963189i
$772$		0			0
$773$	−5.46458	+	11.9658i	−0.196547	+	0.430379i	−0.982086	−	0.188434i	$-0.939659\pi$
$773$	−5.46458	+	11.9658i	−0.196547	+	0.430379i	0.785538	+	0.618813i	$0.212386\pi$
$774$		0			0
$775$	4.96029			0.178179
$776$		0			0
$777$	−9.16886	+	5.89247i	−0.328931	+	0.211391i
$778$		0			0
$779$	−7.71330	−	16.8898i	−0.276358	−	0.605139i
$780$		0			0
$781$	45.9725	+	53.0551i	1.64502	+	1.89846i
$782$		0			0
$783$	−2.23974	+	1.43939i	−0.0800417	+	0.0514397i
$784$		0			0
$785$	0.746379	+	5.19118i	0.0266394	+	0.185281i
$786$		0			0
$787$	4.91819	−	1.44411i	0.175314	−	0.0514770i	−0.192897	−	0.981219i	$-0.561788\pi$
$787$	4.91819	−	1.44411i	0.175314	−	0.0514770i	0.368212	+	0.929742i	$0.379970\pi$
$788$		0			0
$789$	−1.05508	−	7.33822i	−0.0375617	−	0.261248i
$790$		0			0
$791$	11.0211	+	24.1329i	0.391866	+	0.858067i
$792$		0			0
$793$	1.17219	+	0.753319i	0.0416256	+	0.0267511i
$794$		0			0
$795$	−0.682522	+	4.74705i	−0.0242066	+	0.168360i
$796$		0			0
$797$	5.38054	−	37.4225i	0.190588	−	1.32557i	−0.639867	−	0.768486i	$-0.721010\pi$
$797$	5.38054	−	37.4225i	0.190588	−	1.32557i	0.830455	−	0.557085i	$-0.188080\pi$
$798$		0			0
$799$	−1.61041	−	1.03495i	−0.0569721	−	0.0366138i
$800$		0			0
$801$	−0.568270	−	0.655819i	−0.0200788	−	0.0231722i
$802$		0			0
$803$	22.7682			0.803473
$804$		0			0
$805$	5.56347			0.196086
$806$		0			0
$807$	12.1372	+	14.0071i	0.427251	+	0.493074i
$808$		0			0
$809$	−20.4534	−	13.1446i	−0.719103	−	0.462139i	0.129222	−	0.991616i	$-0.458752\pi$
$809$	−20.4534	−	13.1446i	−0.719103	−	0.462139i	−0.848325	+	0.529477i	$0.822388\pi$
$810$		0			0
$811$	5.40398	−	37.5855i	0.189759	−	1.31981i	−0.642870	−	0.765975i	$-0.722256\pi$
$811$	5.40398	−	37.5855i	0.189759	−	1.31981i	0.832629	−	0.553831i	$-0.186835\pi$
$812$		0			0
$813$	−3.82483	+	26.6023i	−0.134143	+	0.932982i
$814$		0			0
$815$	−2.70079	−	1.73569i	−0.0946045	−	0.0607986i
$816$		0			0
$817$	2.47820	+	5.42651i	0.0867013	+	0.189849i
$818$		0			0
$819$	0.0440806	+	0.306587i	0.00154030	+	0.0107130i
$820$		0			0
$821$	−28.2143	+	8.28447i	−0.984687	+	0.289130i	−0.734158	−	0.678979i	$-0.762423\pi$
$821$	−28.2143	+	8.28447i	−0.984687	+	0.289130i	−0.250529	+	0.968109i	$0.580605\pi$
$822$		0			0
$823$	0.0939554	+	0.653474i	0.00327508	+	0.0227787i	0.991393	−	0.130916i	$-0.0417918\pi$
$823$	0.0939554	+	0.653474i	0.00327508	+	0.0227787i	−0.988118	+	0.153695i	$0.950883\pi$
$824$		0			0
$825$	25.2390	−	16.2201i	0.878710	−	0.564712i
$826$		0			0
$827$	20.7256	+	23.9186i	0.720699	+	0.831731i	0.991391	−	0.130935i	$-0.0417980\pi$
$827$	20.7256	+	23.9186i	0.720699	+	0.831731i	−0.270692	+	0.962666i	$0.587253\pi$
$828$		0			0
$829$	5.86533	+	12.8433i	0.203711	+	0.446065i	0.983721	−	0.179702i	$-0.0575133\pi$
$829$	5.86533	+	12.8433i	0.203711	+	0.446065i	−0.780010	+	0.625767i	$0.784786\pi$
$830$		0			0
$831$	−17.7036	+	11.3774i	−0.614131	+	0.394678i
$832$		0			0
$833$	4.90088			0.169805
$834$		0			0
$835$	−3.69420	+	8.08916i	−0.127843	+	0.279937i
$836$		0			0
$837$	0.146611	+	1.01970i	0.00506762	+	0.0352460i
$838$		0			0
$839$	−17.8505	+	20.6006i	−0.616267	+	0.711210i	−0.974994	−	0.222233i	$-0.928666\pi$
$839$	−17.8505	+	20.6006i	−0.616267	+	0.711210i	0.358727	+	0.933443i	$0.383211\pi$
$840$		0			0
$841$	−21.9117			−0.755577
$842$		0			0
$843$	−8.92691	+	19.5472i	−0.307459	+	0.673242i
$844$		0			0
$845$	5.35514	−	1.57241i	0.184222	−	0.0540925i
$846$		0			0
$847$	−51.1421	+	15.0167i	−1.75726	+	0.515979i
$848$		0			0
$849$	8.27025	−	9.54438i	0.283834	−	0.327562i
$850$		0			0
$851$	25.1545	+	29.0298i	0.862285	+	0.995130i
$852$		0			0
$853$	13.1985	+	3.87543i	0.451908	+	0.132692i	0.499763	−	0.866162i	$-0.333420\pi$
$853$	13.1985	+	3.87543i	0.451908	+	0.132692i	−0.0478552	+	0.998854i	$0.515239\pi$
$854$		0			0
$855$	0.752299	+	0.483473i	0.0257281	+	0.0165344i
$856$		0			0
$857$	−55.2541	−	16.2241i	−1.88745	−	0.554204i	−0.994592	−	0.103856i	$-0.966882\pi$
$857$	−55.2541	−	16.2241i	−1.88745	−	0.554204i	−0.892853	−	0.450348i	$-0.851300\pi$
$858$		0			0
$859$	−16.8768	−	36.9550i	−0.575828	−	1.26089i	−0.943636	−	0.330986i	$-0.892619\pi$
$859$	−16.8768	−	36.9550i	−0.575828	−	1.26089i	0.367808	−	0.929902i	$-0.380109\pi$
$860$		0			0
$861$	11.2049	−	12.9311i	0.381861	−	0.440691i
$862$		0			0
$863$	11.9532	−	26.1739i	0.406892	−	0.890969i	−0.589633	−	0.807671i	$-0.700728\pi$
$863$	11.9532	−	26.1739i	0.406892	−	0.890969i	0.996525	−	0.0832976i	$-0.0265452\pi$
$864$		0			0
$865$	−4.74353	+	3.04848i	−0.161285	+	0.103652i
$866$		0			0
$867$	14.2337	+	4.17940i	0.483403	+	0.141940i
$868$		0			0
$869$	0.469046	−	3.26229i	0.0159113	−	0.110665i
$870$		0			0
$871$	1.14878	+	0.657282i	0.0389248	+	0.0222712i
$872$		0			0
$873$	−2.58697	+	17.9927i	−0.0875555	+	0.608962i
$874$		0			0
$875$	7.76055	+	2.27870i	0.262355	+	0.0770343i
$876$		0			0
$877$	25.7608	−	16.5555i	0.869880	−	0.559038i	−0.0278361	−	0.999613i	$-0.508862\pi$
$877$	25.7608	−	16.5555i	0.869880	−	0.559038i	0.897716	+	0.440575i	$0.145225\pi$
$878$		0			0
$879$	3.55397	−	7.78211i	0.119873	−	0.262484i
$880$		0			0
$881$	−33.6334	+	38.8150i	−1.13314	+	1.30771i	−0.187584	+	0.982249i	$0.560066\pi$
$881$	−33.6334	+	38.8150i	−1.13314	+	1.30771i	−0.945555	+	0.325463i	$0.894480\pi$
$882$		0			0
$883$	−8.58206	−	18.7921i	−0.288809	−	0.632404i	0.708500	−	0.705711i	$-0.249372\pi$
$883$	−8.58206	−	18.7921i	−0.288809	−	0.632404i	−0.997309	+	0.0733065i	$0.976645\pi$
$884$		0			0
$885$	−1.40344	−	0.412088i	−0.0471762	−	0.0138522i
$886$		0			0
$887$	−12.1307	−	7.79595i	−0.407310	−	0.261762i	0.320904	−	0.947112i	$-0.396013\pi$
$887$	−12.1307	−	7.79595i	−0.407310	−	0.261762i	−0.728215	+	0.685349i	$0.759650\pi$
$888$		0			0
$889$	−22.3913	−	6.57468i	−0.750980	−	0.220508i
$890$		0			0
$891$	4.08041	+	4.70904i	0.136699	+	0.157759i
$892$		0			0
$893$	−1.77091	+	2.04374i	−0.0592612	+	0.0683911i
$894$		0			0
$895$	1.39802	−	0.410496i	0.0467307	−	0.0137214i
$896$		0			0
$897$	1.04741	−	0.307548i	0.0349721	−	0.0102687i
$898$		0			0
$899$	1.13938	−	2.49489i	0.0380005	−	0.0832094i
$900$		0			0
$901$	−16.4048			−0.546525
$902$		0			0
$903$	−3.60001	+	4.15463i	−0.119801	+	0.138257i
$904$		0			0
$905$	−0.561569	−	3.90580i	−0.0186672	−	0.129833i
$906$		0			0
$907$	−2.62226	+	5.74194i	−0.0870706	+	0.190658i	−0.948158	−	0.317798i	$-0.897056\pi$
$907$	−2.62226	+	5.74194i	−0.0870706	+	0.190658i	0.861088	+	0.508457i	$0.169784\pi$
$908$		0			0
$909$	2.27214			0.0753622
$910$		0			0
$911$	13.1031	−	8.42086i	0.434126	−	0.278996i	−0.305271	−	0.952265i	$-0.598747\pi$
$911$	13.1031	−	8.42086i	0.434126	−	0.278996i	0.739397	+	0.673270i	$0.235111\pi$
$912$		0			0
$913$	4.27309	+	9.35676i	0.141419	+	0.309664i
$914$		0			0
$915$	2.42764	+	2.80165i	0.0802554	+	0.0926197i
$916$		0			0
$917$	22.2080	−	14.2722i	0.733371	−	0.471309i
$918$		0			0
$919$	8.58293	+	59.6956i	0.283125	+	1.96918i	0.243211	+	0.969973i	$0.421799\pi$
$919$	8.58293	+	59.6956i	0.283125	+	1.96918i	0.0399140	+	0.999203i	$0.487292\pi$
$920$		0			0
$921$	−8.74739	+	2.56847i	−0.288236	+	0.0846338i
$922$		0			0
$923$	0.259261	+	1.80320i	0.00853369	+	0.0593531i
$924$		0			0
$925$	11.3804	+	24.9196i	0.374185	+	0.819351i
$926$		0			0
$927$	10.5014	+	6.74885i	0.344912	+	0.221661i
$928$		0			0
$929$	4.08249	−	28.3943i	0.133942	−	0.931587i	−0.806403	−	0.591366i	$-0.798589\pi$
$929$	4.08249	−	28.3943i	0.133942	−	0.931587i	0.940345	−	0.340221i	$-0.110502\pi$
$930$		0			0
$931$	0.985288	−	6.85283i	0.0322915	−	0.224592i
$932$		0			0
$933$	−10.8884	−	6.99756i	−0.356471	−	0.229090i
$934$		0			0
$935$	−2.58303	−	2.98097i	−0.0844740	−	0.0974882i
$936$		0			0
$937$	−27.2711			−0.890907			−0.445454	−	0.895305i	$-0.646958\pi$
$937$	−27.2711			−0.890907			−0.445454	+	0.895305i	$0.646958\pi$
$938$		0			0
$939$	14.8983			0.486187
$940$		0			0
$941$	27.6169	+	31.8716i	0.900285	+	1.03898i	0.999037	+	0.0438726i	$0.0139696\pi$
$941$	27.6169	+	31.8716i	0.900285	+	1.03898i	−0.0987518	+	0.995112i	$0.531485\pi$
$942$		0			0
$943$	−50.7298	−	32.6021i	−1.65199	−	1.06167i
$944$		0			0
$945$	−0.117277	+	0.815681i	−0.00381503	+	0.0265341i
$946$		0			0
$947$	−4.57679	+	31.8322i	−0.148726	+	1.03441i	0.769584	+	0.638546i	$0.220464\pi$
$947$	−4.57679	+	31.8322i	−0.148726	+	1.03441i	−0.918309	+	0.395863i	$0.870445\pi$
$948$		0			0
$949$	0.497044	+	0.319431i	0.0161347	+	0.0103692i
$950$		0			0
$951$	1.86584	+	4.08562i	0.0605040	+	0.132485i
$952$		0			0
$953$	−5.19695	−	36.1456i	−0.168346	−	1.17087i	−0.882304	−	0.470681i	$-0.844008\pi$
$953$	−5.19695	−	36.1456i	−0.168346	−	1.17087i	0.713958	−	0.700189i	$-0.246901\pi$
$954$		0			0
$955$	−0.753543	+	0.221260i	−0.0243841	+	0.00715981i
$956$		0			0
$957$	−2.36089	−	16.4203i	−0.0763167	−	0.530794i
$958$		0			0
$959$	6.62789	−	4.25948i	0.214026	−	0.137546i
$960$		0			0
$961$	19.6057	+	22.6262i	0.632442	+	0.729876i
$962$		0			0
$963$	3.14220	+	6.88047i	0.101256	+	0.221720i
$964$		0			0
$965$	−8.63498	+	5.54937i	−0.277970	+	0.178640i
$966$		0			0
$967$	48.8043			1.56944			0.784721	−	0.619850i	$-0.212806\pi$
$967$	48.8043			1.56944			0.784721	+	0.619850i	$0.212806\pi$
$968$		0			0
$969$	−1.27072	+	2.78250i	−0.0408215	+	0.0893867i
$970$		0			0
$971$	−6.04795	−	42.0644i	−0.194088	−	1.34991i	−0.821047	−	0.570860i	$-0.806610\pi$
$971$	−6.04795	−	42.0644i	−0.194088	−	1.34991i	0.626959	−	0.779052i	$-0.284299\pi$
$972$		0			0
$973$	−8.31817	+	9.59968i	−0.266668	+	0.307752i
$974$		0			0
$975$	0.778546			0.0249334
$976$		0			0
$977$	23.1957	−	50.7914i	0.742095	−	1.62496i	−0.0379834	−	0.999278i	$-0.512093\pi$
$977$	23.1957	−	50.7914i	0.742095	−	1.62496i	0.780078	−	0.625682i	$-0.215179\pi$
$978$		0			0
$979$	5.18803	−	1.52334i	0.165810	−	0.0486863i
$980$		0			0
$981$	−9.96491	+	2.92596i	−0.318155	+	0.0934188i
$982$		0			0
$983$	−31.0433	+	35.8259i	−0.990128	+	1.14267i	−0.000356925		1.00000i	$0.500114\pi$
$983$	−31.0433	+	35.8259i	−0.990128	+	1.14267i	−0.989771	+	0.142668i	$0.954432\pi$
$984$		0			0
$985$	5.75370	+	6.64012i	0.183328	+	0.211572i
$986$		0			0
$987$	−2.39105	−	0.702076i	−0.0761080	−	0.0223473i
$988$		0			0
$989$	16.2990	+	10.4747i	0.518277	+	0.333076i
$990$		0			0
$991$	3.05357	+	0.896608i	0.0969997	+	0.0284817i	0.329872	−	0.944026i	$-0.392994\pi$
$991$	3.05357	+	0.896608i	0.0969997	+	0.0284817i	−0.232873	+	0.972507i	$0.574812\pi$
$992$		0			0
$993$	−3.16755	−	6.93598i	−0.100519	−	0.220107i
$994$		0			0
$995$	5.37290	−	6.20065i	0.170332	−	0.196574i
$996$		0			0
$997$	12.9061	−	28.2604i	0.408740	−	0.895017i	−0.587568	−	0.809175i	$-0.699915\pi$
$997$	12.9061	−	28.2604i	0.408740	−	0.895017i	0.996309	−	0.0858421i	$-0.0273581\pi$
$998$		0			0
$999$	−4.78643	+	3.07605i	−0.151436	+	0.0973219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.193.3	yes	60
67.25	even	11	inner	804.2.q.a.25.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.25.3	✓	60	67.25	even	11	inner
804.2.q.a.193.3	yes	60	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.361898 + 0.232578i) q^{5} +(-0.272618 + 1.89610i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.361898 + 0.232578i) q^{5} +(-0.272618 + 1.89610i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-5.24182 - 3.36871i) q^{11} +(-0.0671701 - 0.147082i) q^{13} +(-0.0612223 - 0.425811i) q^{15} +(1.41191 - 0.414574i) q^{17} +(-0.295838 - 2.05760i) q^{19} +(1.61150 - 1.03565i) q^{21} +(-4.42111 - 5.10223i) q^{23} +(-2.00020 - 4.37982i) q^{25} +(0.841254 - 0.540641i) q^{27} -2.66238 q^{29} +(-0.427955 + 0.937091i) q^{31} +(0.886758 + 6.16754i) q^{33} +(-0.539650 + 0.622790i) q^{35} -5.68964 q^{37} +(-0.0671701 + 0.147082i) q^{39} +(8.57030 - 2.51647i) q^{41} +(-2.75355 + 0.808514i) q^{43} +(-0.281714 + 0.325115i) q^{45} +(-0.851908 - 0.983154i) q^{47} +(3.19559 + 0.938309i) q^{49} +(-1.23792 - 0.795562i) q^{51} +(-10.6967 - 3.14083i) q^{53} +(-1.11352 - 2.43826i) q^{55} +(-1.36130 + 1.57102i) q^{57} +(1.41246 - 3.09285i) q^{59} +(-7.24942 + 4.65892i) q^{61} +(-1.83800 - 0.539685i) q^{63} +(0.00989928 - 0.0688510i) q^{65} +(-6.64901 + 4.77396i) q^{67} +(-0.960798 + 6.68250i) q^{69} +(-10.8103 - 3.17418i) q^{71} +(-3.07398 + 1.97553i) q^{73} +(-2.00020 + 4.37982i) q^{75} +(7.81641 - 9.02062i) q^{77} +(0.219732 + 0.481145i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.38878 - 0.892512i) q^{83} +(0.607389 + 0.178345i) q^{85} +(1.74349 + 2.01209i) q^{87} +(-0.568270 + 0.655819i) q^{89} +(0.297193 - 0.0872638i) q^{91} +(0.988458 - 0.290237i) q^{93} +(0.371489 - 0.813447i) q^{95} +18.1778 q^{97} +(4.08041 - 4.70904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 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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