LMFDB - Embedded newform 525.2.j.c.218.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.10
Character	$\chi$	$=$	525.218
Dual form			525.2.j.c.407.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723969 + 0.723969i) q^{2} +(-0.994020 + 1.41842i) q^{3} -0.951738i q^{4} +(-1.74653 + 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.13697 - 2.13697i) q^{8} +(-1.02385 - 2.81988i) q^{9} +O(q^{10})$	\(q+(0.723969 + 0.723969i) q^{2} +(-0.994020 + 1.41842i) q^{3} -0.951738i q^{4} +(-1.74653 + 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.13697 - 2.13697i) q^{8} +(-1.02385 - 2.81988i) q^{9} +3.63664i q^{11} +(1.34997 + 0.946047i) q^{12} +(4.19487 + 4.19487i) q^{13} +1.02385 q^{14} +1.19072 q^{16} +(4.61300 + 4.61300i) q^{17} +(1.30027 - 2.78274i) q^{18} -3.77162i q^{19} +(0.300098 + 1.70586i) q^{21} +(-2.63281 + 2.63281i) q^{22} +(1.81887 - 1.81887i) q^{23} +(0.906934 + 5.15531i) q^{24} +6.07391i q^{26} +(5.01751 + 1.35077i) q^{27} +(-0.672980 - 0.672980i) q^{28} -1.13909 q^{29} +3.62492 q^{31} +(-3.41189 - 3.41189i) q^{32} +(-5.15829 - 3.61489i) q^{33} +6.67933i q^{34} +(-2.68379 + 0.974434i) q^{36} +(-7.24824 + 7.24824i) q^{37} +(2.73054 - 2.73054i) q^{38} +(-10.1199 + 1.78031i) q^{39} -0.314852i q^{41} +(-1.01772 + 1.45225i) q^{42} +(1.06556 + 1.06556i) q^{43} +3.46112 q^{44} +2.63362 q^{46} +(-4.48582 - 4.48582i) q^{47} +(-1.18360 + 1.68894i) q^{48} -1.00000i q^{49} +(-11.1286 + 1.95777i) q^{51} +(3.99242 - 3.99242i) q^{52} +(-1.44794 + 1.44794i) q^{53} +(2.65460 + 4.61044i) q^{54} -3.02213i q^{56} +(5.34975 + 3.74907i) q^{57} +(-0.824666 - 0.824666i) q^{58} +8.70646 q^{59} +3.08903 q^{61} +(2.62433 + 2.62433i) q^{62} +(-2.71793 - 1.26999i) q^{63} -7.32164i q^{64} +(-1.11737 - 6.35151i) q^{66} +(9.67044 - 9.67044i) q^{67} +(4.39036 - 4.39036i) q^{68} +(0.771934 + 4.38793i) q^{69} -10.4601i q^{71} +(-8.21392 - 3.83807i) q^{72} +(-0.710104 - 0.710104i) q^{73} -10.4950 q^{74} -3.58959 q^{76} +(2.57149 + 2.57149i) q^{77} +(-8.61538 - 6.03759i) q^{78} -7.30426i q^{79} +(-6.90348 + 5.77426i) q^{81} +(0.227943 - 0.227943i) q^{82} +(-9.58225 + 9.58225i) q^{83} +(1.62353 - 0.285614i) q^{84} +1.54287i q^{86} +(1.13228 - 1.61571i) q^{87} +(7.77137 + 7.77137i) q^{88} -15.5299 q^{89} +5.93244 q^{91} +(-1.73109 - 1.73109i) q^{92} +(-3.60325 + 5.14167i) q^{93} -6.49519i q^{94} +(8.23099 - 1.44801i) q^{96} +(-5.28841 + 5.28841i) q^{97} +(0.723969 - 0.723969i) q^{98} +(10.2549 - 3.72336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{6}+O(q^{10}) $ 32 * q - 16 * q^6	$ 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) $ 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.723969	+	0.723969i	0.511923	+	0.511923i	0.915115	−	0.403192i	$-0.132099\pi$
$2$	0.723969	+	0.723969i	0.511923	+	0.511923i	−0.403192	+	0.915115i	$0.632099\pi$
$3$	−0.994020	+	1.41842i	−0.573898	+	0.818927i
$3$	−0.994020	+	1.41842i	−0.573898	+	0.818927i
$4$		−	0.951738i		−	0.475869i
$5$		0			0
$5$		0			0
$6$	−1.74653	+	0.307254i	−0.713020	+	0.125436i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	2.13697	−	2.13697i	0.755532	−	0.755532i
$9$	−1.02385	−	2.81988i	−0.341282	−	0.939961i
$10$		0			0
$11$			3.63664i			1.09649i	0.836319	+	0.548243i	$0.184703\pi$
$11$			3.63664i			1.09649i	−0.836319	+	0.548243i	$0.815297\pi$
$12$	1.34997	+	0.946047i	0.389702	+	0.273100i
$13$	4.19487	+	4.19487i	1.16345	+	1.16345i	0.983716	+	0.179732i	$0.0575231\pi$
$13$	4.19487	+	4.19487i	1.16345	+	1.16345i	0.179732	+	0.983716i	$0.442477\pi$
$14$	1.02385			0.273635
$15$		0			0
$16$	1.19072			0.297680
$17$	4.61300	+	4.61300i	1.11882	+	1.11882i	0.991915	+	0.126901i	$0.0405030\pi$
$17$	4.61300	+	4.61300i	1.11882	+	1.11882i	0.126901	+	0.991915i	$0.459497\pi$
$18$	1.30027	−	2.78274i	0.306478	−	0.655898i
$19$		−	3.77162i		−	0.865269i	−0.901569	−	0.432635i	$-0.857584\pi$
$19$		−	3.77162i		−	0.865269i	0.901569	−	0.432635i	$-0.142416\pi$
$20$		0			0
$21$	0.300098	+	1.70586i	0.0654867	+	0.372248i
$22$	−2.63281	+	2.63281i	−0.561317	+	0.561317i
$23$	1.81887	−	1.81887i	0.379261	−	0.379261i	−0.491574	−	0.870836i	$-0.663578\pi$
$23$	1.81887	−	1.81887i	0.379261	−	0.379261i	0.870836	+	0.491574i	$0.163578\pi$
$24$	0.906934	+	5.15531i	0.185127	+	1.05232i
$25$		0			0
$26$			6.07391i			1.19119i
$27$	5.01751	+	1.35077i	0.965620	+	0.259956i
$28$	−0.672980	−	0.672980i	−0.127181	−	0.127181i
$29$	−1.13909			−0.211524			−0.105762	−	0.994391i	$-0.533728\pi$
$29$	−1.13909			−0.211524			−0.105762	+	0.994391i	$0.533728\pi$
$30$		0			0
$31$	3.62492			0.651055			0.325528	−	0.945532i	$-0.394458\pi$
$31$	3.62492			0.651055			0.325528	+	0.945532i	$0.394458\pi$
$32$	−3.41189	−	3.41189i	−0.603142	−	0.603142i
$33$	−5.15829	−	3.61489i	−0.897943	−	0.629272i
$34$			6.67933i			1.14550i
$35$		0			0
$36$	−2.68379	+	0.974434i	−0.447298	+	0.162406i
$37$	−7.24824	+	7.24824i	−1.19160	+	1.19160i	−0.214987	+	0.976617i	$0.568971\pi$
$37$	−7.24824	+	7.24824i	−1.19160	+	1.19160i	−0.976617	+	0.214987i	$0.931029\pi$
$38$	2.73054	−	2.73054i	0.442951	−	0.442951i
$39$	−10.1199	+	1.78031i	−1.62048	+	0.285078i
$40$		0			0
$41$		−	0.314852i		−	0.0491716i	−0.999698	−	0.0245858i	$-0.992173\pi$
$41$		−	0.314852i		−	0.0491716i	0.999698	−	0.0245858i	$-0.00782669\pi$
$42$	−1.01772	+	1.45225i	−0.157038	+	0.224087i
$43$	1.06556	+	1.06556i	0.162497	+	0.162497i	0.783672	−	0.621175i	$-0.213344\pi$
$43$	1.06556	+	1.06556i	0.162497	+	0.162497i	−0.621175	+	0.783672i	$0.713344\pi$
$44$	3.46112			0.521784
$45$		0			0
$46$	2.63362			0.388306
$47$	−4.48582	−	4.48582i	−0.654324	−	0.654324i	0.299707	−	0.954031i	$-0.403111\pi$
$47$	−4.48582	−	4.48582i	−0.654324	−	0.654324i	−0.954031	+	0.299707i	$0.903111\pi$
$48$	−1.18360	+	1.68894i	−0.170838	+	0.243778i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−11.1286	+	1.95777i	−1.55831	+	0.274142i
$52$	3.99242	−	3.99242i	0.553648	−	0.553648i
$53$	−1.44794	+	1.44794i	−0.198890	+	0.198890i	−0.799524	−	0.600634i	$-0.794915\pi$
$53$	−1.44794	+	1.44794i	−0.198890	+	0.198890i	0.600634	+	0.799524i	$0.294915\pi$
$54$	2.65460	+	4.61044i	0.361246	+	0.627401i
$55$		0			0
$56$		−	3.02213i		−	0.403849i
$57$	5.34975	+	3.74907i	0.708592	+	0.496576i
$58$	−0.824666	−	0.824666i	−0.108284	−	0.108284i
$59$	8.70646			1.13348			0.566742	−	0.823895i	$-0.308204\pi$
$59$	8.70646			1.13348			0.566742	+	0.823895i	$0.308204\pi$
$60$		0			0
$61$	3.08903			0.395509			0.197755	−	0.980252i	$-0.436635\pi$
$61$	3.08903			0.395509			0.197755	+	0.980252i	$0.436635\pi$
$62$	2.62433	+	2.62433i	0.333291	+	0.333291i
$63$	−2.71793	−	1.26999i	−0.342427	−	0.160004i
$64$		−	7.32164i		−	0.915205i
$65$		0			0
$66$	−1.11737	−	6.35151i	−0.137539	−	0.781817i
$67$	9.67044	−	9.67044i	1.18143	−	1.18143i	0.202060	−	0.979373i	$-0.435237\pi$
$67$	9.67044	−	9.67044i	1.18143	−	1.18143i	0.979373	−	0.202060i	$-0.0647635\pi$
$68$	4.39036	−	4.39036i	0.532410	−	0.532410i
$69$	0.771934	+	4.38793i	0.0929300	+	0.528245i
$70$		0			0
$71$		−	10.4601i		−	1.24138i	−0.784056	−	0.620690i	$-0.786853\pi$
$71$		−	10.4601i		−	1.24138i	0.784056	−	0.620690i	$-0.213147\pi$
$72$	−8.21392	−	3.83807i	−0.968020	−	0.452321i
$73$	−0.710104	−	0.710104i	−0.0831114	−	0.0831114i	0.664329	−	0.747440i	$-0.268717\pi$
$73$	−0.710104	−	0.710104i	−0.0831114	−	0.0831114i	−0.747440	+	0.664329i	$0.768717\pi$
$74$	−10.4950			−1.22002
$75$		0			0
$76$	−3.58959			−0.411755
$77$	2.57149	+	2.57149i	0.293048	+	0.293048i
$78$	−8.61538	−	6.03759i	−0.975499	−	0.683623i
$79$		−	7.30426i		−	0.821793i	−0.911682	−	0.410897i	$-0.865216\pi$
$79$		−	7.30426i		−	0.821793i	0.911682	−	0.410897i	$-0.134784\pi$
$80$		0			0
$81$	−6.90348	+	5.77426i	−0.767053	+	0.641584i
$82$	0.227943	−	0.227943i	0.0251721	−	0.0251721i
$83$	−9.58225	+	9.58225i	−1.05179	+	1.05179i	−0.0532053	+	0.998584i	$0.516944\pi$
$83$	−9.58225	+	9.58225i	−1.05179	+	1.05179i	−0.998584	+	0.0532053i	$0.983056\pi$
$84$	1.62353	−	0.285614i	0.177141	−	0.0311631i
$85$		0			0
$86$			1.54287i			0.166372i
$87$	1.13228	−	1.61571i	0.121393	−	0.173223i
$88$	7.77137	+	7.77137i	0.828431	+	0.828431i
$89$	−15.5299			−1.64616			−0.823082	−	0.567923i	$-0.807747\pi$
$89$	−15.5299			−1.64616			−0.823082	+	0.567923i	$0.807747\pi$
$90$		0			0
$91$	5.93244			0.621889
$92$	−1.73109	−	1.73109i	−0.180479	−	0.180479i
$93$	−3.60325	+	5.14167i	−0.373639	+	0.533167i
$94$		−	6.49519i		−	0.669928i
$95$		0			0
$96$	8.23099	−	1.44801i	0.840072	−	0.147787i
$97$	−5.28841	+	5.28841i	−0.536957	+	0.536957i	−0.922634	−	0.385677i	$-0.873968\pi$
$97$	−5.28841	+	5.28841i	−0.536957	+	0.536957i	0.385677	+	0.922634i	$0.373968\pi$
$98$	0.723969	−	0.723969i	0.0731319	−	0.0731319i
$99$	10.2549	−	3.72336i	1.03065	−	0.374212i
$100$		0			0
$101$		−	5.52857i		−	0.550114i	−0.961428	−	0.275057i	$-0.911303\pi$
$101$		−	5.52857i		−	0.550114i	0.961428	−	0.275057i	$-0.0886966\pi$
$102$	−9.47412	−	6.63939i	−0.938078	−	0.657398i
$103$	1.67893	+	1.67893i	0.165430	+	0.165430i	0.784967	−	0.619538i	$-0.212680\pi$
$103$	1.67893	+	1.67893i	0.165430	+	0.165430i	−0.619538	+	0.784967i	$0.712680\pi$
$104$	17.9286			1.75804
$105$		0			0
$106$	−2.09652			−0.203632
$107$	−6.33012	−	6.33012i	−0.611956	−	0.611956i	0.331500	−	0.943455i	$-0.392445\pi$
$107$	−6.33012	−	6.33012i	−0.611956	−	0.611956i	−0.943455	+	0.331500i	$0.892445\pi$
$108$	1.28558	−	4.77535i	0.123705	−	0.459509i
$109$			6.19191i			0.593078i	0.955021	+	0.296539i	$0.0958324\pi$
$109$			6.19191i			0.593078i	−0.955021	+	0.296539i	$0.904168\pi$
$110$		0			0
$111$	−3.07617	−	17.4860i	−0.291977	−	1.65970i
$112$	0.841966	−	0.841966i	0.0795583	−	0.0795583i
$113$	−1.87617	+	1.87617i	−0.176495	+	0.176495i	−0.789826	−	0.613331i	$-0.789829\pi$
$113$	−1.87617	+	1.87617i	−0.176495	+	0.176495i	0.613331	+	0.789826i	$0.289829\pi$
$114$	1.15885	+	6.58726i	0.108536	+	0.616954i
$115$		0			0
$116$			1.08412i			0.100658i
$117$	7.53414	−	16.1239i	0.696531	−	1.49066i
$118$	6.30320	+	6.30320i	0.580257	+	0.580257i
$119$	6.52376			0.598032
$120$		0			0
$121$	−2.22512			−0.202284
$122$	2.23636	+	2.23636i	0.202470	+	0.202470i
$123$	0.446593	+	0.312969i	0.0402680	+	0.0282195i
$124$		−	3.44998i		−	0.309817i
$125$		0			0
$126$	−1.04826	−	2.88713i	−0.0933866	−	0.257206i
$127$	−3.43180	+	3.43180i	−0.304523	+	0.304523i	−0.842781	−	0.538257i	$-0.819083\pi$
$127$	−3.43180	+	3.43180i	−0.304523	+	0.304523i	0.538257	+	0.842781i	$0.319083\pi$
$128$	−1.52313	+	1.52313i	−0.134627	+	0.134627i
$129$	−2.57061	+	0.452227i	−0.226329	+	0.0398164i
$130$		0			0
$131$		−	3.84637i		−	0.336059i	−0.985782	−	0.168029i	$-0.946260\pi$
$131$		−	3.84637i		−	0.336059i	0.985782	−	0.168029i	$-0.0537403\pi$
$132$	−3.44043	+	4.90934i	−0.299451	+	0.427303i
$133$	−2.66694	−	2.66694i	−0.231253	−	0.231253i
$134$	14.0022			1.20961
$135$		0			0
$136$	19.7156			1.69060
$137$	−13.6056	−	13.6056i	−1.16241	−	1.16241i	−0.983947	−	0.178459i	$-0.942889\pi$
$137$	−13.6056	−	13.6056i	−1.16241	−	1.16241i	−0.178459	−	0.983947i	$-0.557111\pi$
$138$	−2.61787	+	3.73558i	−0.222848	+	0.317994i
$139$		−	9.05369i		−	0.767924i	−0.923349	−	0.383962i	$-0.874559\pi$
$139$		−	9.05369i		−	0.767924i	0.923349	−	0.383962i	$-0.125441\pi$
$140$		0			0
$141$	10.8218	−	1.90379i	0.911359	−	0.160328i
$142$	7.57276	−	7.57276i	0.635492	−	0.635492i
$143$	−15.2552	+	15.2552i	−1.27571	+	1.27571i
$144$	−1.21911	−	3.35769i	−0.101593	−	0.279808i
$145$		0			0
$146$		−	1.02819i		−	0.0850934i
$147$	1.41842	+	0.994020i	0.116990	+	0.0819854i
$148$	6.89843	+	6.89843i	0.567047	+	0.567047i
$149$	−20.5997			−1.68759			−0.843796	−	0.536663i	$-0.819685\pi$
$149$	−20.5997			−1.68759			−0.843796	+	0.536663i	$0.819685\pi$
$150$		0			0
$151$	15.9282			1.29622			0.648109	−	0.761547i	$-0.275560\pi$
$151$	15.9282			1.29622			0.648109	+	0.761547i	$0.275560\pi$
$152$	−8.05983	−	8.05983i	−0.653738	−	0.653738i
$153$	8.28511	−	17.7311i	0.669811	−	1.43348i
$154$			3.72336i			0.300037i
$155$		0			0
$156$	1.69439	+	9.63148i	0.135660	+	0.771135i
$157$	−4.00609	+	4.00609i	−0.319721	+	0.319721i	−0.848660	−	0.528939i	$-0.822590\pi$
$157$	−4.00609	+	4.00609i	−0.319721	+	0.319721i	0.528939	+	0.848660i	$0.322590\pi$
$158$	5.28806	−	5.28806i	0.420695	−	0.420695i
$159$	−0.614508	−	3.49307i	−0.0487337	−	0.277018i
$160$		0			0
$161$		−	2.57228i		−	0.202724i
$162$	−9.17828	−	0.817520i	−0.721114	−	0.0642304i
$163$	5.18238	+	5.18238i	0.405915	+	0.405915i	0.880311	−	0.474396i	$-0.157334\pi$
$163$	5.18238	+	5.18238i	0.405915	+	0.405915i	−0.474396	+	0.880311i	$0.657334\pi$
$164$	−0.299656			−0.0233992
$165$		0			0
$166$	−13.8745			−1.07687
$167$	7.76731	+	7.76731i	0.601053	+	0.601053i	0.940592	−	0.339539i	$-0.110271\pi$
$167$	7.76731	+	7.76731i	0.601053	+	0.601053i	−0.339539	+	0.940592i	$0.610271\pi$
$168$	4.28665	+	3.00406i	0.330723	+	0.231768i
$169$			22.1939i			1.70722i
$170$		0			0
$171$	−10.6355	+	3.86156i	−0.813319	+	0.295301i
$172$	1.01414	−	1.01414i	0.0773271	−	0.0773271i
$173$	−0.953760	+	0.953760i	−0.0725131	+	0.0725131i	−0.742433	−	0.669920i	$-0.766328\pi$
$173$	−0.953760	+	0.953760i	−0.0725131	+	0.0725131i	0.669920	+	0.742433i	$0.266328\pi$
$174$	1.98946	−	0.349990i	0.150821	−	0.0265327i
$175$		0			0
$176$			4.33021i			0.326402i
$177$	−8.65440	+	12.3494i	−0.650504	+	0.928241i
$178$	−11.2431	−	11.2431i	−0.842710	−	0.842710i
$179$	−19.1906			−1.43437			−0.717187	−	0.696881i	$-0.754571\pi$
$179$	−19.1906			−1.43437			−0.717187	+	0.696881i	$0.754571\pi$
$180$		0			0
$181$	6.81119			0.506272			0.253136	−	0.967431i	$-0.418538\pi$
$181$	6.81119			0.506272			0.253136	+	0.967431i	$0.418538\pi$
$182$	4.29490	+	4.29490i	0.318359	+	0.318359i
$183$	−3.07055	+	4.38154i	−0.226982	+	0.323893i
$184$		−	7.77374i		−	0.573088i
$185$		0			0
$186$	−6.33105	+	1.11377i	−0.464215	+	0.0816658i
$187$	−16.7758	+	16.7758i	−1.22677	+	1.22677i
$188$	−4.26933	+	4.26933i	−0.311373	+	0.311373i
$189$	4.50306	−	2.59277i	0.327549	−	0.188597i
$190$		0			0
$191$		−	24.6052i		−	1.78037i	−0.455602	−	0.890183i	$-0.650576\pi$
$191$		−	24.6052i		−	1.78037i	0.455602	−	0.890183i	$-0.349424\pi$
$192$	10.3852	+	7.27786i	0.749486	+	0.525235i
$193$	−16.1551	−	16.1551i	−1.16287	−	1.16287i	−0.983844	−	0.179026i	$-0.942705\pi$
$193$	−16.1551	−	16.1551i	−1.16287	−	1.16287i	−0.179026	−	0.983844i	$-0.557295\pi$
$194$	−7.65729			−0.549762
$195$		0			0
$196$	−0.951738			−0.0679813
$197$	17.2478	+	17.2478i	1.22886	+	1.22886i	0.964397	+	0.264459i	$0.0851933\pi$
$197$	17.2478	+	17.2478i	1.22886	+	1.22886i	0.264459	+	0.964397i	$0.414807\pi$
$198$	10.1198	+	4.72862i	0.719184	+	0.336049i
$199$			17.1682i			1.21702i	0.793547	+	0.608509i	$0.208232\pi$
$199$			17.1682i			1.21702i	−0.793547	+	0.608509i	$0.791768\pi$
$200$		0			0
$201$	4.10416	+	23.3294i	0.289485	+	1.64553i
$202$	4.00252	−	4.00252i	0.281616	−	0.281616i
$203$	−0.805459	+	0.805459i	−0.0565321	+	0.0565321i
$204$	1.86328	+	10.5915i	0.130456	+	0.741554i
$205$		0			0
$206$			2.43098i			0.169374i
$207$	−6.99126	−	3.26676i	−0.485926	−	0.227056i
$208$	4.99492	+	4.99492i	0.346335	+	0.346335i
$209$	13.7160			0.948756
$210$		0			0
$211$	−12.4888			−0.859766			−0.429883	−	0.902884i	$-0.641445\pi$
$211$	−12.4888			−0.859766			−0.429883	+	0.902884i	$0.641445\pi$
$212$	1.37806	+	1.37806i	0.0946454	+	0.0946454i
$213$	14.8368	+	10.3975i	1.01660	+	0.712426i
$214$		−	9.16562i		−	0.626549i
$215$		0			0
$216$	13.6088	−	7.83570i	0.925962	−	0.533152i
$217$	2.56321	−	2.56321i	0.174002	−	0.174002i
$218$	−4.48275	+	4.48275i	−0.303610	+	0.303610i
$219$	1.71309	−	0.301370i	0.115760	−	0.0203647i
$220$		0			0
$221$			38.7018i			2.60337i
$222$	10.4323	−	14.8864i	0.700167	−	0.999107i
$223$	−14.6702	−	14.6702i	−0.982386	−	0.982386i	0.0174612	−	0.999848i	$-0.494442\pi$
$223$	−14.6702	−	14.6702i	−0.982386	−	0.982386i	−0.999848	+	0.0174612i	$0.994442\pi$
$224$	−4.82514			−0.322393
$225$		0			0
$226$	−2.71657			−0.180704
$227$	−1.58995	−	1.58995i	−0.105528	−	0.105528i	0.652371	−	0.757900i	$-0.273774\pi$
$227$	−1.58995	−	1.58995i	−0.105528	−	0.105528i	−0.757900	+	0.652371i	$0.773774\pi$
$228$	3.56813	−	5.09156i	0.236305	−	0.337197i
$229$			1.35671i			0.0896541i	0.998995	+	0.0448270i	$0.0142737\pi$
$229$			1.35671i			0.0896541i	−0.998995	+	0.0448270i	$0.985726\pi$
$230$		0			0
$231$	−6.20357	+	1.09135i	−0.408165	+	0.0718053i
$232$	−2.43420	+	2.43420i	−0.159813	+	0.159813i
$233$	15.1279	−	15.1279i	0.991061	−	0.991061i	−0.00889977	−	0.999960i	$-0.502833\pi$
$233$	15.1279	−	15.1279i	0.991061	−	0.991061i	0.999960	+	0.00889977i	$0.00283292\pi$
$234$	17.1277	−	6.21876i	1.11967	−	0.406533i
$235$		0			0
$236$		−	8.28626i		−	0.539390i
$237$	10.3605	+	7.26058i	0.672989	+	0.471625i
$238$	4.72300	+	4.72300i	0.306147	+	0.306147i
$239$	−12.4988			−0.808483			−0.404242	−	0.914652i	$-0.632465\pi$
$239$	−12.4988			−0.808483			−0.404242	+	0.914652i	$0.632465\pi$
$240$		0			0
$241$	−18.0373			−1.16188			−0.580942	−	0.813945i	$-0.697316\pi$
$241$	−18.0373			−1.16188			−0.580942	+	0.813945i	$0.697316\pi$
$242$	−1.61092	−	1.61092i	−0.103554	−	0.103554i
$243$	−1.32814	−	15.5318i	−0.0852003	−	0.996364i
$244$		−	2.93994i		−	0.188210i
$245$		0			0
$246$	0.0967396	+	0.549900i	0.00616789	+	0.0350603i
$247$	15.8215	−	15.8215i	1.00670	−	1.00670i
$248$	7.74634	−	7.74634i	0.491893	−	0.491893i
$249$	−4.06673	−	23.1166i	−0.257719	−	1.46496i
$250$		0			0
$251$			5.34538i			0.337398i	0.985668	+	0.168699i	$0.0539565\pi$
$251$			5.34538i			0.337398i	−0.985668	+	0.168699i	$0.946043\pi$
$252$	−1.20870	+	2.58675i	−0.0761407	+	0.162950i
$253$	6.61458	+	6.61458i	0.415855	+	0.415855i
$254$	−4.96904			−0.311785
$255$		0			0
$256$	−16.8487			−1.05304
$257$	11.6091	+	11.6091i	0.724155	+	0.724155i	0.969449	−	0.245294i	$-0.0788845\pi$
$257$	11.6091	+	11.6091i	0.724155	+	0.724155i	−0.245294	+	0.969449i	$0.578885\pi$
$258$	−2.18844	−	1.53364i	−0.136246	−	0.0954803i
$259$			10.2506i			0.636939i
$260$		0			0
$261$	1.16625	+	3.21210i	0.0721893	+	0.198824i
$262$	2.78465	−	2.78465i	0.172036	−	0.172036i
$263$	−3.90300	+	3.90300i	−0.240669	+	0.240669i	−0.817127	−	0.576458i	$-0.804435\pi$
$263$	−3.90300	+	3.90300i	−0.240669	+	0.240669i	0.576458	+	0.817127i	$0.304435\pi$
$264$	−18.7480	+	3.29819i	−1.15386	+	0.202989i
$265$		0			0
$266$		−	3.86156i		−	0.236768i
$267$	15.4370	−	22.0279i	0.944730	−	1.34809i
$268$	−9.20373	−	9.20373i	−0.562207	−	0.562207i
$269$	31.1948			1.90198			0.950989	−	0.309225i	$-0.100070\pi$
$269$	31.1948			1.90198			0.950989	+	0.309225i	$0.100070\pi$
$270$		0			0
$271$	−19.4757			−1.18306			−0.591532	−	0.806282i	$-0.701477\pi$
$271$	−19.4757			−1.18306			−0.591532	+	0.806282i	$0.701477\pi$
$272$	5.49279	+	5.49279i	0.333049	+	0.333049i
$273$	−5.89697	+	8.41471i	−0.356901	+	0.509282i
$274$		−	19.7001i		−	1.19013i
$275$		0			0
$276$	4.17616	−	0.734679i	0.251375	−	0.0442225i
$277$	−1.91736	+	1.91736i	−0.115203	+	0.115203i	−0.762358	−	0.647155i	$-0.775959\pi$
$277$	−1.91736	+	1.91736i	−0.115203	+	0.115203i	0.647155	+	0.762358i	$0.275959\pi$
$278$	6.55459	−	6.55459i	0.393118	−	0.393118i
$279$	−3.71137	−	10.2219i	−0.222194	−	0.611967i
$280$		0			0
$281$			0.320414i			0.0191143i	0.999954	+	0.00955715i	$0.00304218\pi$
$281$			0.320414i			0.0191143i	−0.999954	+	0.00955715i	$0.996958\pi$
$282$	9.21293	+	6.45635i	0.548622	+	0.384470i
$283$	−1.20675	−	1.20675i	−0.0717340	−	0.0717340i	0.670330	−	0.742064i	$-0.266153\pi$
$283$	−1.20675	−	1.20675i	−0.0717340	−	0.0717340i	−0.742064	+	0.670330i	$0.766153\pi$
$284$	−9.95523			−0.590734
$285$		0			0
$286$	−22.0886			−1.30613
$287$	−0.222634	−	0.222634i	−0.0131417	−	0.0131417i
$288$	−6.12787	+	13.1144i	−0.361088	+	0.772772i
$289$			25.5595i			1.50350i
$290$		0			0
$291$	−2.24441	−	12.7580i	−0.131570	−	0.747887i
$292$	−0.675833	+	0.675833i	−0.0395501	+	0.0395501i
$293$	11.2016	−	11.2016i	0.654402	−	0.654402i	−0.299648	−	0.954050i	$-0.596869\pi$
$293$	11.2016	−	11.2016i	0.654402	−	0.654402i	0.954050	+	0.299648i	$0.0968692\pi$
$294$	0.307254	+	1.74653i	0.0179194	+	0.101860i
$295$		0			0
$296$			30.9785i			1.80059i
$297$	−4.91227	+	18.2469i	−0.285039	+	1.05879i
$298$	−14.9135	−	14.9135i	−0.863918	−	0.863918i
$299$	15.2599			0.882502
$300$		0			0
$301$	1.50693			0.0868581
$302$	11.5315	+	11.5315i	0.663565	+	0.663565i
$303$	7.84185	+	5.49551i	0.450503	+	0.315709i
$304$		−	4.49094i		−	0.257573i
$305$		0			0
$306$	18.8349	−	6.83862i	1.07672	−	0.390938i
$307$	−16.0589	+	16.0589i	−0.916529	+	0.916529i	−0.996775	−	0.0802463i	$-0.974429\pi$
$307$	−16.0589	+	16.0589i	−0.916529	+	0.916529i	0.0802463	+	0.996775i	$0.474429\pi$
$308$	2.44738	−	2.44738i	0.139453	−	0.139453i
$309$	−4.05031	+	0.712540i	−0.230414	+	0.0405350i
$310$		0			0
$311$		−	0.709997i		−	0.0402602i	−0.999797	−	0.0201301i	$-0.993592\pi$
$311$		−	0.709997i		−	0.0402602i	0.999797	−	0.0201301i	$-0.00640805\pi$
$312$	−17.8214	+	25.4303i	−1.00894	+	1.43971i
$313$	14.9431	+	14.9431i	0.844632	+	0.844632i	0.989457	−	0.144826i	$-0.0462621\pi$
$313$	14.9431	+	14.9431i	0.844632	+	0.844632i	−0.144826	+	0.989457i	$0.546262\pi$
$314$	−5.80057			−0.327345
$315$		0			0
$316$	−6.95174			−0.391066
$317$	3.83925	+	3.83925i	0.215634	+	0.215634i	0.806656	−	0.591022i	$-0.201275\pi$
$317$	3.83925	+	3.83925i	0.215634	+	0.215634i	−0.591022	+	0.806656i	$0.701275\pi$
$318$	2.08399	−	2.97376i	0.116864	−	0.166760i
$319$		−	4.14246i		−	0.231933i
$320$		0			0
$321$	15.2711	−	2.68652i	0.852347	−	0.149947i
$322$	1.86225	−	1.86225i	0.103779	−	0.103779i
$323$	17.3985	−	17.3985i	0.968077	−	0.968077i
$324$	5.49558	+	6.57030i	0.305310	+	0.365017i
$325$		0			0
$326$			7.50376i			0.415595i
$327$	−8.78275	−	6.15489i	−0.485687	−	0.340366i
$328$	−0.672828	−	0.672828i	−0.0371507	−	0.0371507i
$329$	−6.34391			−0.349751
$330$		0			0
$331$	31.8078			1.74831			0.874157	−	0.485644i	$-0.161415\pi$
$331$	31.8078			1.74831			0.874157	+	0.485644i	$0.161415\pi$
$332$	9.11979	+	9.11979i	0.500514	+	0.500514i
$333$	27.8603	+	13.0181i	1.52673	+	0.713388i
$334$			11.2466i			0.615386i
$335$		0			0
$336$	0.357333	+	2.03120i	0.0194941	+	0.110811i
$337$	12.8338	−	12.8338i	0.699104	−	0.699104i	−0.265113	−	0.964217i	$-0.585409\pi$
$337$	12.8338	−	12.8338i	0.699104	−	0.699104i	0.964217	+	0.265113i	$0.0854093\pi$
$338$	−16.0677	+	16.0677i	−0.873966	+	0.873966i
$339$	−0.796250	−	4.52615i	−0.0432464	−	0.245827i
$340$		0			0
$341$			13.1825i			0.713874i
$342$	−10.4954	−	4.90414i	−0.567529	−	0.265186i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	4.55414			0.245543
$345$		0			0
$346$	−1.38099			−0.0742423
$347$	−17.4728	−	17.4728i	−0.937989	−	0.937989i	0.0601971	−	0.998187i	$-0.480827\pi$
$347$	−17.4728	−	17.4728i	−0.937989	−	0.937989i	−0.998187	+	0.0601971i	$0.980827\pi$
$348$	−1.53773	−	1.07763i	−0.0824312	−	0.0577672i
$349$			2.27784i			0.121930i	0.998140	+	0.0609649i	$0.0194178\pi$
$349$			2.27784i			0.121930i	−0.998140	+	0.0609649i	$0.980582\pi$
$350$		0			0
$351$	15.3815	+	26.7141i	0.821003	+	1.42589i
$352$	12.4078	−	12.4078i	0.661338	−	0.661338i
$353$	0.992444	−	0.992444i	0.0528225	−	0.0528225i	−0.680202	−	0.733025i	$-0.738108\pi$
$353$	0.992444	−	0.992444i	0.0528225	−	0.0528225i	0.733025	+	0.680202i	$0.238108\pi$
$354$	−15.2061	+	2.67510i	−0.808196	+	0.142180i
$355$		0			0
$356$			14.7804i			0.783358i
$357$	−6.48475	+	9.25346i	−0.343210	+	0.489745i
$358$	−13.8934	−	13.8934i	−0.734289	−	0.734289i
$359$	4.68580			0.247307			0.123654	−	0.992325i	$-0.460539\pi$
$359$	4.68580			0.247307			0.123654	+	0.992325i	$0.460539\pi$
$360$		0			0
$361$	4.77488			0.251310
$362$	4.93109	+	4.93109i	0.259172	+	0.259172i
$363$	2.21181	−	3.15616i	0.116090	−	0.165655i
$364$		−	5.64613i		−	0.295938i
$365$		0			0
$366$	−5.39509	+	0.949116i	−0.282006	+	0.0496111i
$367$	−8.68225	+	8.68225i	−0.453210	+	0.453210i	−0.896418	−	0.443209i	$-0.853840\pi$
$367$	−8.68225	+	8.68225i	−0.453210	+	0.453210i	0.443209	+	0.896418i	$0.353840\pi$
$368$	2.16577	−	2.16577i	0.112899	−	0.112899i
$369$	−0.887846	+	0.322360i	−0.0462194	+	0.0167814i
$370$		0			0
$371$			2.04769i			0.106311i
$372$	4.89353	+	3.42935i	0.253717	+	0.177803i
$373$	−14.4089	−	14.4089i	−0.746062	−	0.746062i	0.227675	−	0.973737i	$-0.426888\pi$
$373$	−14.4089	−	14.4089i	−0.746062	−	0.746062i	−0.973737	+	0.227675i	$0.926888\pi$
$374$	−24.2903			−1.25602
$375$		0			0
$376$	−19.1721			−0.988726
$377$	−4.77834	−	4.77834i	−0.246097	−	0.246097i
$378$	5.13716	+	1.38298i	0.264227	+	0.0711331i
$379$			14.3572i			0.737482i	0.929532	+	0.368741i	$0.120211\pi$
$379$			14.3572i			0.737482i	−0.929532	+	0.368741i	$0.879789\pi$
$380$		0			0
$381$	−1.45647	−	8.27903i	−0.0746170	−	0.424148i
$382$	17.8134	−	17.8134i	0.911411	−	0.911411i
$383$	−10.9175	+	10.9175i	−0.557860	+	0.557860i	−0.928698	−	0.370838i	$-0.879071\pi$
$383$	−10.9175	+	10.9175i	−0.557860	+	0.557860i	0.370838	+	0.928698i	$0.379071\pi$
$384$	−0.646422	−	3.67448i	−0.0329876	−	0.187512i
$385$		0			0
$386$		−	23.3916i		−	1.19060i
$387$	1.91379	−	4.09573i	0.0972832	−	0.208198i
$388$	5.03318	+	5.03318i	0.255521	+	0.255521i
$389$	14.3250			0.726304			0.363152	−	0.931730i	$-0.381701\pi$
$389$	14.3250			0.726304			0.363152	+	0.931730i	$0.381701\pi$
$390$		0			0
$391$	16.7809			0.848648
$392$	−2.13697	−	2.13697i	−0.107933	−	0.107933i
$393$	5.45577	+	3.82337i	0.275207	+	0.192863i
$394$			24.9738i			1.25816i
$395$		0			0
$396$	−3.54366	−	9.75996i	−0.178076	−	0.490456i
$397$	−21.0767	+	21.0767i	−1.05781	+	1.05781i	−0.0595859	+	0.998223i	$0.518978\pi$
$397$	−21.0767	+	21.0767i	−1.05781	+	1.05781i	−0.998223	+	0.0595859i	$0.981022\pi$
$398$	−12.4292	+	12.4292i	−0.623020	+	0.623020i
$399$	6.43384	−	1.13186i	0.322095	−	0.0566636i
$400$		0			0
$401$		−	10.9494i		−	0.546788i	−0.961902	−	0.273394i	$-0.911854\pi$
$401$		−	10.9494i		−	0.546788i	0.961902	−	0.273394i	$-0.0881463\pi$
$402$	−13.9185	+	19.8610i	−0.694191	+	0.990579i
$403$	15.2061	+	15.2061i	0.757469	+	0.757469i
$404$	−5.26175			−0.261782
$405$		0			0
$406$	−1.16625			−0.0578802
$407$	−26.3592	−	26.3592i	−1.30658	−	1.30658i
$408$	−19.5978	+	27.9651i	−0.970233	+	1.38448i
$409$		−	19.4500i		−	0.961739i	−0.876792	−	0.480870i	$-0.840321\pi$
$409$		−	19.4500i		−	0.961739i	0.876792	−	0.480870i	$-0.159679\pi$
$410$		0			0
$411$	32.8228	−	5.77426i	1.61903	−	0.284823i
$412$	1.59790	−	1.59790i	0.0787227	−	0.0787227i
$413$	6.15639	−	6.15639i	0.302936	−	0.302936i
$414$	−2.69642	−	7.42649i	−0.132522	−	0.364992i
$415$		0			0
$416$		−	28.6249i		−	1.40345i
$417$	12.8420	+	8.99956i	0.628874	+	0.440710i
$418$	9.92997	+	9.92997i	0.485690	+	0.485690i
$419$	25.9297			1.26675			0.633373	−	0.773846i	$-0.281670\pi$
$419$	25.9297			1.26675			0.633373	+	0.773846i	$0.281670\pi$
$420$		0			0
$421$	−5.79961			−0.282656			−0.141328	−	0.989963i	$-0.545137\pi$
$421$	−5.79961			−0.282656			−0.141328	+	0.989963i	$0.545137\pi$
$422$	−9.04153	−	9.04153i	−0.440135	−	0.440135i
$423$	−8.05670	+	17.2423i	−0.391730	+	0.838349i
$424$			6.18839i			0.300535i
$425$		0			0
$426$	3.21390	+	18.2688i	0.155714	+	0.885128i
$427$	2.18427	−	2.18427i	0.105704	−	0.105704i
$428$	−6.02461	+	6.02461i	−0.291211	+	0.291211i
$429$	−6.47435	−	36.8023i	−0.312585	−	1.77683i
$430$		0			0
$431$		−	14.8759i		−	0.716545i	−0.933617	−	0.358272i	$-0.883366\pi$
$431$		−	14.8759i		−	0.716545i	0.933617	−	0.358272i	$-0.116634\pi$
$432$	5.97445	+	1.60839i	0.287446	+	0.0773838i
$433$	−18.5862	−	18.5862i	−0.893198	−	0.893198i	0.101625	−	0.994823i	$-0.467596\pi$
$433$	−18.5862	−	18.5862i	−0.893198	−	0.893198i	−0.994823	+	0.101625i	$0.967596\pi$
$434$	3.71137			0.178151
$435$		0			0
$436$	5.89308			0.282227
$437$	−6.86010	−	6.86010i	−0.328163	−	0.328163i
$438$	1.45840	+	1.02204i	0.0696852	+	0.0488349i
$439$		−	15.6687i		−	0.747828i	−0.927463	−	0.373914i	$-0.878016\pi$
$439$		−	15.6687i		−	0.747828i	0.927463	−	0.373914i	$-0.121984\pi$
$440$		0			0
$441$	−2.81988	+	1.02385i	−0.134280	+	0.0487546i
$442$	−28.0189	+	28.0189i	−1.33273	+	1.33273i
$443$	17.4278	−	17.4278i	0.828021	−	0.828021i	−0.159222	−	0.987243i	$-0.550898\pi$
$443$	17.4278	−	17.4278i	0.828021	−	0.828021i	0.987243	+	0.159222i	$0.0508985\pi$
$444$	−16.6421	+	2.92771i	−0.789797	+	0.138943i
$445$		0			0
$446$		−	21.2415i		−	1.00581i
$447$	20.4765	−	29.2191i	0.968506	−	1.38202i
$448$	−5.17718	−	5.17718i	−0.244599	−	0.244599i
$449$	0.620804			0.0292975			0.0146488	−	0.999893i	$-0.495337\pi$
$449$	0.620804			0.0292975			0.0146488	+	0.999893i	$0.495337\pi$
$450$		0			0
$451$	1.14500			0.0539160
$452$	1.78562	+	1.78562i	0.0839885	+	0.0839885i
$453$	−15.8330	+	22.5929i	−0.743897	+	1.06151i
$454$		−	2.30214i		−	0.108045i
$455$		0			0
$456$	19.4439	−	3.42061i	0.910543	−	0.160185i
$457$	9.10965	−	9.10965i	0.426131	−	0.426131i	−0.461177	−	0.887308i	$-0.652573\pi$
$457$	9.10965	−	9.10965i	0.426131	−	0.426131i	0.887308	+	0.461177i	$0.152573\pi$
$458$	−0.982218	+	0.982218i	−0.0458960	+	0.0458960i
$459$	16.9147	+	29.3769i	0.789508	+	1.37120i
$460$		0			0
$461$		−	2.78274i		−	0.129605i	−0.997898	−	0.0648025i	$-0.979358\pi$
$461$		−	2.78274i		−	0.129605i	0.997898	−	0.0648025i	$-0.0206418\pi$
$462$	−5.28130	−	3.70109i	−0.245708	−	0.172190i
$463$	10.4466	+	10.4466i	0.485495	+	0.485495i	0.906881	−	0.421386i	$-0.138456\pi$
$463$	10.4466	+	10.4466i	0.485495	+	0.485495i	−0.421386	+	0.906881i	$0.638456\pi$
$464$	−1.35634			−0.0629664
$465$		0			0
$466$	21.9042			1.01469
$467$	−15.9720	−	15.9720i	−0.739097	−	0.739097i	0.233306	−	0.972403i	$-0.425046\pi$
$467$	−15.9720	−	15.9720i	−0.739097	−	0.739097i	−0.972403	+	0.233306i	$0.925046\pi$
$468$	−15.3458	−	7.17052i	−0.709358	−	0.331457i
$469$		−	13.6761i		−	0.631502i
$470$		0			0
$471$	−1.70020	−	9.66447i	−0.0783409	−	0.445315i
$472$	18.6054	−	18.6054i	0.856383	−	0.856383i
$473$	−3.87506	+	3.87506i	−0.178175	+	0.178175i
$474$	2.24426	+	12.7571i	0.103082	+	0.585955i
$475$		0			0
$476$		−	6.20891i		−	0.284585i
$477$	5.56548	+	2.60055i	0.254826	+	0.119071i
$478$	−9.04878	−	9.04878i	−0.413882	−	0.413882i
$479$	−10.8945			−0.497782			−0.248891	−	0.968531i	$-0.580066\pi$
$479$	−10.8945			−0.497782			−0.248891	+	0.968531i	$0.580066\pi$
$480$		0			0
$481$	−60.8109			−2.77274
$482$	−13.0584	−	13.0584i	−0.594796	−	0.594796i
$483$	3.64857	+	2.55689i	0.166016	+	0.116343i
$484$			2.11773i			0.0962604i
$485$		0			0
$486$	10.2830	−	12.2061i	0.466446	−	0.553678i
$487$	5.03387	−	5.03387i	0.228107	−	0.228107i	−0.583795	−	0.811901i	$-0.698433\pi$
$487$	5.03387	−	5.03387i	0.228107	−	0.228107i	0.811901	+	0.583795i	$0.198433\pi$
$488$	6.60114	−	6.60114i	0.298820	−	0.298820i
$489$	−12.5022	+	2.19941i	−0.565368	+	0.0994609i
$490$		0			0
$491$		−	11.9196i		−	0.537922i	−0.963151	−	0.268961i	$-0.913320\pi$
$491$		−	11.9196i		−	0.537922i	0.963151	−	0.268961i	$-0.0866803\pi$
$492$	0.297865	−	0.425040i	0.0134288	−	0.0191623i
$493$	−5.25462	−	5.25462i	−0.236656	−	0.236656i
$494$	22.9085			1.03070
$495$		0			0
$496$	4.31627			0.193806
$497$	−7.39638	−	7.39638i	−0.331773	−	0.331773i
$498$	13.7915	−	19.6799i	0.618014	−	0.881878i
$499$		−	0.966794i		−	0.0432797i	−0.999766	−	0.0216398i	$-0.993111\pi$
$499$		−	0.966794i		−	0.0432797i	0.999766	−	0.0216398i	$-0.00688871\pi$
$500$		0			0
$501$	−18.7382	+	3.29647i	−0.837161	+	0.147275i
$502$	−3.86989	+	3.86989i	−0.172722	+	0.172722i
$503$	−3.21397	+	3.21397i	−0.143304	+	0.143304i	−0.775119	−	0.631815i	$-0.782310\pi$
$503$	−3.21397	+	3.21397i	−0.143304	+	0.143304i	0.631815	+	0.775119i	$0.282310\pi$
$504$	−8.52204	+	3.09420i	−0.379602	+	0.137826i
$505$		0			0
$506$			9.57750i			0.425772i
$507$	−31.4803	−	22.0612i	−1.39809	−	0.979771i
$508$	3.26618	+	3.26618i	0.144913	+	0.144913i
$509$	24.1223			1.06920			0.534601	−	0.845104i	$-0.320462\pi$
$509$	24.1223			1.06920			0.534601	+	0.845104i	$0.320462\pi$
$510$		0			0
$511$	−1.00424			−0.0444249
$512$	−9.15166	−	9.15166i	−0.404450	−	0.404450i
$513$	5.09460	−	18.9241i	0.224932	−	0.835521i
$514$			16.8092i			0.741423i
$515$		0			0
$516$	0.430401	+	2.44654i	0.0189474	+	0.107703i
$517$	16.3133	−	16.3133i	0.717458	−	0.717458i
$518$	−7.42109	+	7.42109i	−0.326064	+	0.326064i
$519$	−0.404778	−	2.30089i	−0.0177678	−	0.100998i
$520$		0			0
$521$			43.5258i			1.90690i	0.301554	+	0.953449i	$0.402495\pi$
$521$			43.5258i			1.90690i	−0.301554	+	0.953449i	$0.597505\pi$
$522$	−1.48113	+	3.16979i	−0.0648273	+	0.138738i
$523$	−7.55731	−	7.55731i	−0.330458	−	0.330458i	0.522302	−	0.852760i	$-0.325073\pi$
$523$	−7.55731	−	7.55731i	−0.330458	−	0.330458i	−0.852760	+	0.522302i	$0.825073\pi$
$524$	−3.66073			−0.159920
$525$		0			0
$526$	−5.65130			−0.246408
$527$	16.7218	+	16.7218i	0.728411	+	0.728411i
$528$	−6.14208	−	4.30432i	−0.267300	−	0.187322i
$529$			16.3834i			0.712322i
$530$		0			0
$531$	−8.91408	−	24.5512i	−0.386838	−	1.06543i
$532$	−2.53823	+	2.53823i	−0.110046	+	0.110046i
$533$	1.32076	−	1.32076i	0.0572086	−	0.0572086i
$534$	27.1235	−	4.77162i	1.17375	−	0.206488i
$535$		0			0
$536$		−	41.3308i		−	1.78522i
$537$	19.0759	−	27.2204i	0.823184	−	1.17465i
$538$	22.5840	+	22.5840i	0.973667	+	0.973667i
$539$	3.63664			0.156641
$540$		0			0
$541$	21.5120			0.924873			0.462436	−	0.886652i	$-0.346975\pi$
$541$	21.5120			0.924873			0.462436	+	0.886652i	$0.346975\pi$
$542$	−14.0998	−	14.0998i	−0.605638	−	0.605638i
$543$	−6.77046	+	9.66115i	−0.290548	+	0.414600i
$544$		−	31.4781i		−	1.34961i
$545$		0			0
$546$	−10.3612	+	1.82277i	−0.443419	+	0.0780073i
$547$	−4.12772	+	4.12772i	−0.176489	+	0.176489i	−0.789823	−	0.613335i	$-0.789828\pi$
$547$	−4.12772	+	4.12772i	−0.176489	+	0.176489i	0.613335	+	0.789823i	$0.289828\pi$
$548$	−12.9490	+	12.9490i	−0.553153	+	0.553153i
$549$	−3.16269	−	8.71069i	−0.134980	−	0.371763i
$550$		0			0
$551$			4.29622i			0.183025i
$552$	11.0265	+	7.72726i	0.469317	+	0.328894i
$553$	−5.16489	−	5.16489i	−0.219633	−	0.219633i
$554$	−2.77622			−0.117950
$555$		0			0
$556$	−8.61674			−0.365431
$557$	30.3025	+	30.3025i	1.28396	+	1.28396i	0.938396	+	0.345560i	$0.112311\pi$
$557$	30.3025	+	30.3025i	1.28396	+	1.28396i	0.345560	+	0.938396i	$0.387689\pi$
$558$	4.71339	−	10.0872i	0.199534	−	0.427026i
$559$			8.93978i			0.378113i
$560$		0			0
$561$	−7.11969	−	40.4706i	−0.300593	−	1.70867i
$562$	−0.231970	+	0.231970i	−0.00978505	+	0.00978505i
$563$	8.67504	−	8.67504i	0.365609	−	0.365609i	−0.500264	−	0.865873i	$-0.666764\pi$
$563$	8.67504	−	8.67504i	0.365609	−	0.365609i	0.865873	+	0.500264i	$0.166764\pi$
$564$	−1.81191	−	10.2995i	−0.0762953	−	0.433687i
$565$		0			0
$566$		−	1.74730i		−	0.0734447i
$567$	−0.798479	+	8.96451i	−0.0335330	+	0.376474i
$568$	−22.3528	−	22.3528i	−0.937902	−	0.937902i
$569$	7.88148			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$569$	7.88148			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$570$		0			0
$571$	−11.5764			−0.484459			−0.242230	−	0.970219i	$-0.577879\pi$
$571$	−11.5764			−0.484459			−0.242230	+	0.970219i	$0.577879\pi$
$572$	14.5190	+	14.5190i	0.607068	+	0.607068i
$573$	34.9005	+	24.4580i	1.45799	+	1.02175i
$574$		−	0.322360i		−	0.0134551i
$575$		0			0
$576$	−20.6462	+	7.49624i	−0.860257	+	0.312343i
$577$	15.8784	−	15.8784i	0.661027	−	0.661027i	−0.294595	−	0.955622i	$-0.595185\pi$
$577$	15.8784	−	15.8784i	0.661027	−	0.661027i	0.955622	+	0.294595i	$0.0951849\pi$
$578$	−18.5043	+	18.5043i	−0.769677	+	0.769677i
$579$	38.9733	−	6.85627i	1.61967	−	0.284937i
$580$		0			0
$581$			13.5514i			0.562205i
$582$	7.61150	−	10.8613i	0.315507	−	0.450214i
$583$	−5.26562	−	5.26562i	−0.218080	−	0.218080i
$584$	−3.03494			−0.125587
$585$		0			0
$586$	16.2192			0.670007
$587$	−9.87937	−	9.87937i	−0.407765	−	0.407765i	0.473193	−	0.880959i	$-0.343101\pi$
$587$	−9.87937	−	9.87937i	−0.407765	−	0.407765i	−0.880959	+	0.473193i	$0.843101\pi$
$588$	0.946047	−	1.34997i	0.0390143	−	0.0556717i
$589$		−	13.6718i		−	0.563338i
$590$		0			0
$591$	−41.6094	+	7.32001i	−1.71158	+	0.301105i
$592$	−8.63063	+	8.63063i	−0.354717	+	0.354717i
$593$	−0.614696	+	0.614696i	−0.0252426	+	0.0252426i	−0.719615	−	0.694373i	$-0.755682\pi$
$593$	−0.614696	+	0.614696i	−0.0252426	+	0.0252426i	0.694373	+	0.719615i	$0.255682\pi$
$594$	−16.7665	+	9.65383i	−0.687937	+	0.396101i
$595$		0			0
$596$			19.6055i			0.803073i
$597$	−24.3517	−	17.0655i	−0.996649	−	0.698445i
$598$	11.0477	+	11.0477i	0.451773	+	0.451773i
$599$	15.3650			0.627797			0.313898	−	0.949457i	$-0.398365\pi$
$599$	15.3650			0.627797			0.313898	+	0.949457i	$0.398365\pi$
$600$		0			0
$601$	−26.6232			−1.08598			−0.542991	−	0.839738i	$-0.682708\pi$
$601$	−26.6232			−1.08598			−0.542991	+	0.839738i	$0.682708\pi$
$602$	1.09097	+	1.09097i	0.0444647	+	0.0444647i
$603$	−37.1706	−	17.3685i	−1.51370	−	0.707299i
$604$		−	15.1595i		−	0.616830i
$605$		0			0
$606$	1.69868	+	9.65584i	0.0690040	+	0.392242i
$607$	−12.5800	+	12.5800i	−0.510606	+	0.510606i	−0.914712	−	0.404106i	$-0.867583\pi$
$607$	−12.5800	+	12.5800i	−0.510606	+	0.510606i	0.404106	+	0.914712i	$0.367583\pi$
$608$	−12.8683	+	12.8683i	−0.521880	+	0.521880i
$609$	−0.341839	−	1.94312i	−0.0138520	−	0.0787393i
$610$		0			0
$611$		−	37.6349i		−	1.52254i
$612$	−16.8754	−	7.88525i	−0.682146	−	0.318742i
$613$	−26.4562	−	26.4562i	−1.06856	−	1.06856i	−0.997470	−	0.0710867i	$-0.977353\pi$
$613$	−26.4562	−	26.4562i	−1.06856	−	1.06856i	−0.0710867	−	0.997470i	$-0.522647\pi$
$614$	−23.2523			−0.938385
$615$		0			0
$616$	10.9904			0.442815
$617$	8.96074	+	8.96074i	0.360746	+	0.360746i	0.864088	−	0.503342i	$-0.167896\pi$
$617$	8.96074	+	8.96074i	0.360746	+	0.360746i	−0.503342	+	0.864088i	$0.667896\pi$
$618$	−3.44816	−	2.41644i	−0.138705	−	0.0972037i
$619$			23.8205i			0.957426i	0.877971	+	0.478713i	$0.158897\pi$
$619$			23.8205i			0.957426i	−0.877971	+	0.478713i	$0.841103\pi$
$620$		0			0
$621$	11.5831	−	6.66933i	0.464814	−	0.267631i
$622$	0.514016	−	0.514016i	0.0206101	−	0.0206101i
$623$	−10.9813	+	10.9813i	−0.439956	+	0.439956i
$624$	−12.0500	+	2.11985i	−0.482384	+	0.0848621i
$625$		0			0
$626$			21.6366i			0.864773i
$627$	−13.6340	+	19.4551i	−0.544489	+	0.776962i
$628$	3.81275	+	3.81275i	0.152145	+	0.152145i
$629$	−66.8723			−2.66637
$630$		0			0
$631$	20.2819			0.807410			0.403705	−	0.914889i	$-0.367722\pi$
$631$	20.2819			0.807410			0.403705	+	0.914889i	$0.367722\pi$
$632$	−15.6090	−	15.6090i	−0.620891	−	0.620891i
$633$	12.4142	−	17.7144i	0.493418	−	0.704086i
$634$			5.55900i			0.220776i
$635$		0			0
$636$	−3.32448	+	0.584851i	−0.131824	+	0.0231908i
$637$	4.19487	−	4.19487i	0.166207	−	0.166207i
$638$	2.99901	−	2.99901i	0.118732	−	0.118732i
$639$	−29.4961	+	10.7095i	−1.16685	+	0.423661i
$640$		0			0
$641$		−	27.5041i		−	1.08635i	−0.839620	−	0.543174i	$-0.817222\pi$
$641$		−	27.5041i		−	1.08635i	0.839620	−	0.543174i	$-0.182778\pi$
$642$	13.0007	+	9.11081i	0.513098	+	0.359575i
$643$	17.2643	+	17.2643i	0.680839	+	0.680839i	0.960189	−	0.279350i	$-0.0901190\pi$
$643$	17.2643	+	17.2643i	0.680839	+	0.680839i	−0.279350	+	0.960189i	$0.590119\pi$
$644$	−2.44813			−0.0964699
$645$		0			0
$646$	25.1919			0.991163
$647$	−2.92523	−	2.92523i	−0.115003	−	0.115003i	0.647264	−	0.762266i	$-0.275913\pi$
$647$	−2.92523	−	2.92523i	−0.115003	−	0.115003i	−0.762266	+	0.647264i	$0.775913\pi$
$648$	−2.41310	+	27.0919i	−0.0947957	+	1.06427i
$649$			31.6622i			1.24285i
$650$		0			0
$651$	1.08783	+	6.18359i	0.0426355	+	0.242354i
$652$	4.93226	−	4.93226i	0.193162	−	0.193162i
$653$	25.2123	−	25.2123i	0.986635	−	0.986635i	−0.0132769	−	0.999912i	$-0.504226\pi$
$653$	25.2123	−	25.2123i	0.986635	−	0.986635i	0.999912	+	0.0132769i	$0.00422630\pi$
$654$	−1.90249	−	10.8144i	−0.0743933	−	0.422876i
$655$		0			0
$656$		−	0.374901i		−	0.0146374i
$657$	−1.27537	+	2.72945i	−0.0497570	+	0.106486i
$658$	−4.59280	−	4.59280i	−0.179046	−	0.179046i
$659$	−20.3603			−0.793125			−0.396563	−	0.918008i	$-0.629797\pi$
$659$	−20.3603			−0.793125			−0.396563	+	0.918008i	$0.629797\pi$
$660$		0			0
$661$	17.8508			0.694314			0.347157	−	0.937807i	$-0.387147\pi$
$661$	17.8508			0.694314			0.347157	+	0.937807i	$0.387147\pi$
$662$	23.0278	+	23.0278i	0.895002	+	0.895002i
$663$	−54.8956	−	38.4704i	−2.13197	−	1.49407i
$664$			40.9539i			1.58932i
$665$		0			0
$666$	10.7453	+	29.5947i	0.416371	+	1.14677i
$667$	−2.07186	+	2.07186i	−0.0802228	+	0.0802228i
$668$	7.39244	−	7.39244i	0.286022	−	0.286022i
$669$	35.3909	−	6.22605i	1.36829	−	0.240713i
$670$		0			0
$671$			11.2337i			0.433671i
$672$	4.79629	−	6.84409i	0.185021	−	0.264016i
$673$	22.7637	+	22.7637i	0.877476	+	0.877476i	0.993273	−	0.115797i	$-0.0369421\pi$
$673$	22.7637	+	22.7637i	0.877476	+	0.877476i	−0.115797	+	0.993273i	$0.536942\pi$
$674$	18.5826			0.715776
$675$		0			0
$676$	21.1227			0.812413
$677$	−10.9347	−	10.9347i	−0.420256	−	0.420256i	0.465036	−	0.885292i	$-0.346041\pi$
$677$	−10.9347	−	10.9347i	−0.420256	−	0.420256i	−0.885292	+	0.465036i	$0.846041\pi$
$678$	2.70033	−	3.85325i	0.103706	−	0.147983i
$679$			7.47894i			0.287015i
$680$		0			0
$681$	3.83566	−	0.674777i	0.146983	−	0.0258575i
$682$	−9.54374	+	9.54374i	−0.365449	+	0.365449i
$683$	6.50227	−	6.50227i	0.248802	−	0.248802i	−0.571677	−	0.820479i	$-0.693707\pi$
$683$	6.50227	−	6.50227i	0.248802	−	0.248802i	0.820479	+	0.571677i	$0.193707\pi$
$684$	3.67519	+	10.1222i	0.140525	+	0.387033i
$685$		0			0
$686$		−	1.02385i		−	0.0390907i
$687$	−1.92439	−	1.34860i	−0.0734201	−	0.0514523i
$688$	1.26879	+	1.26879i	0.0483720	+	0.0483720i
$689$	−12.1478			−0.462795
$690$		0			0
$691$	27.4621			1.04471			0.522353	−	0.852729i	$-0.325054\pi$
$691$	27.4621			1.04471			0.522353	+	0.852729i	$0.325054\pi$
$692$	0.907730	+	0.907730i	0.0345067	+	0.0345067i
$693$	4.61849	−	9.88411i	0.175442	−	0.375466i
$694$		−	25.2995i		−	0.960357i
$695$		0			0
$696$	−1.03308	−	5.87237i	−0.0391588	−	0.222591i
$697$	1.45241	−	1.45241i	0.0550140	−	0.0550140i
$698$	−1.64908	+	1.64908i	−0.0624187	+	0.0624187i
$699$	6.42031	+	36.4952i	0.242838	+	1.38037i
$700$		0			0
$701$			22.1998i			0.838473i	0.907877	+	0.419237i	$0.137702\pi$
$701$			22.1998i			0.838473i	−0.907877	+	0.419237i	$0.862298\pi$
$702$	−8.20448	+	30.4759i	−0.309658	+	1.15024i
$703$	27.3376	+	27.3376i	1.03106	+	1.03106i
$704$	26.6262			1.00351
$705$		0			0
$706$	1.43700			0.0540821
$707$	−3.90929	−	3.90929i	−0.147024	−	0.147024i
$708$	11.7534	+	8.23671i	0.441721	+	0.309555i
$709$		−	29.2448i		−	1.09831i	−0.835721	−	0.549155i	$-0.814950\pi$
$709$		−	29.2448i		−	1.09831i	0.835721	−	0.549155i	$-0.185050\pi$
$710$		0			0
$711$	−20.5972	+	7.47844i	−0.772453	+	0.280463i
$712$	−33.1868	+	33.1868i	−1.24373	+	1.24373i
$713$	6.59328	−	6.59328i	0.246920	−	0.246920i
$714$	−11.3940	+	2.00445i	−0.426409	+	0.0750148i
$715$		0			0
$716$			18.2644i			0.682574i
$717$	12.4241	−	17.7287i	0.463987	−	0.662089i
$718$	3.39237	+	3.39237i	0.126602	+	0.126602i
$719$	20.4862			0.764006			0.382003	−	0.924161i	$-0.375234\pi$
$719$	20.4862			0.764006			0.382003	+	0.924161i	$0.375234\pi$
$720$		0			0
$721$	2.37436			0.0884258
$722$	3.45687	+	3.45687i	0.128651	+	0.128651i
$723$	17.9294	−	25.5845i	0.666803	−	0.951498i
$724$		−	6.48247i		−	0.240919i
$725$		0			0
$726$	3.88625	−	0.683677i	0.144232	−	0.0253736i
$727$	−17.3682	+	17.3682i	−0.644150	+	0.644150i	−0.951573	−	0.307423i	$-0.900533\pi$
$727$	−17.3682	+	17.3682i	−0.644150	+	0.644150i	0.307423	+	0.951573i	$0.400533\pi$
$728$	12.6774	−	12.6774i	0.469857	−	0.469857i
$729$	23.3508	+	13.5550i	0.864845	+	0.502038i
$730$		0			0
$731$			9.83087i			0.363608i
$732$	4.17008	+	2.92236i	0.154131	+	0.108014i
$733$	7.68183	+	7.68183i	0.283735	+	0.283735i	0.834597	−	0.550862i	$-0.185701\pi$
$733$	7.68183	+	7.68183i	0.283735	+	0.283735i	−0.550862	+	0.834597i	$0.685701\pi$
$734$	−12.5714			−0.464017
$735$		0			0
$736$	−12.4116			−0.457497
$737$	35.1679	+	35.1679i	1.29543	+	1.29543i
$738$	−0.876152	−	0.409394i	−0.0322516	−	0.0150700i
$739$		−	9.51894i		−	0.350160i	−0.984554	−	0.175080i	$-0.943982\pi$
$739$		−	9.51894i		−	0.350160i	0.984554	−	0.175080i	$-0.0560184\pi$
$740$		0			0
$741$	6.71467	+	38.1684i	0.246669	+	1.40215i
$742$	−1.48247	+	1.48247i	−0.0544231	+	0.0544231i
$743$	−3.56000	+	3.56000i	−0.130604	+	0.130604i	−0.769387	−	0.638783i	$-0.779438\pi$
$743$	−3.56000	+	3.56000i	−0.130604	+	0.130604i	0.638783	+	0.769387i	$0.279438\pi$
$744$	3.28757	+	18.6876i	0.120528	+	0.685121i
$745$		0			0
$746$		−	20.8631i		−	0.763854i
$747$	36.8316	+	17.2101i	1.34760	+	0.629683i
$748$	15.9662	+	15.9662i	0.583780	+	0.583780i
$749$	−8.95214			−0.327104
$750$		0			0
$751$	−27.8113			−1.01485			−0.507424	−	0.861696i	$-0.669402\pi$
$751$	−27.8113			−1.01485			−0.507424	+	0.861696i	$0.669402\pi$
$752$	−5.34136	−	5.34136i	−0.194779	−	0.194779i
$753$	−7.58201	−	5.31342i	−0.276304	−	0.193632i
$754$		−	6.91874i		−	0.251966i
$755$		0			0
$756$	−2.46764	−	4.28573i	−0.0897473	−	0.155870i
$757$	−17.0932	+	17.0932i	−0.621262	+	0.621262i	−0.945854	−	0.324592i	$-0.894773\pi$
$757$	−17.0932	+	17.0932i	−0.621262	+	0.621262i	0.324592	+	0.945854i	$0.394773\pi$
$758$	−10.3942	+	10.3942i	−0.377534	+	0.377534i
$759$	−15.9573	+	2.80724i	−0.579213	+	0.101897i
$760$		0			0
$761$			19.0016i			0.688809i	0.938821	+	0.344404i	$0.111919\pi$
$761$			19.0016i			0.688809i	−0.938821	+	0.344404i	$0.888081\pi$
$762$	4.93933	−	7.04820i	0.178933	−	0.255329i
$763$	4.37834	+	4.37834i	0.158507	+	0.158507i
$764$	−23.4177			−0.847221
$765$		0			0
$766$	−15.8079			−0.571163
$767$	36.5225	+	36.5225i	1.31875	+	1.31875i
$768$	16.7479	−	23.8986i	0.604339	−	0.862365i
$769$		−	45.4833i		−	1.64017i	−0.572242	−	0.820085i	$-0.693926\pi$
$769$		−	45.4833i		−	1.64017i	0.572242	−	0.820085i	$-0.306074\pi$
$770$		0			0
$771$	−28.0063	+	4.92692i	−1.00862	+	0.177439i
$772$	−15.3754	+	15.3754i	−0.553374	+	0.553374i
$773$	−31.5448	+	31.5448i	−1.13459	+	1.13459i	−0.145183	+	0.989405i	$0.546377\pi$
$773$	−31.5448	+	31.5448i	−1.13459	+	1.13459i	−0.989405	+	0.145183i	$0.953623\pi$
$774$	4.35070	−	1.57966i	0.156383	−	0.0567797i
$775$		0			0
$776$			22.6023i			0.811376i
$777$	−14.5396	−	10.1893i	−0.521606	−	0.365538i
$778$	10.3708	+	10.3708i	0.371812	+	0.371812i
$779$	−1.18750			−0.0425467
$780$		0			0
$781$	38.0394			1.36116
$782$	12.1489	+	12.1489i	0.434443	+	0.434443i
$783$	−5.71540	−	1.53865i	−0.204252	−	0.0549870i
$784$		−	1.19072i		−	0.0425257i
$785$		0			0
$786$	1.18181	+	6.71781i	0.0421538	+	0.239616i
$787$	29.4500	−	29.4500i	1.04978	−	1.04978i	0.0510863	−	0.998694i	$-0.483732\pi$
$787$	29.4500	−	29.4500i	1.04978	−	1.04978i	0.998694	−	0.0510863i	$-0.0162683\pi$
$788$	16.4154	−	16.4154i	0.584774	−	0.584774i
$789$	−1.65644	−	9.41576i	−0.0589709	−	0.335210i
$790$		0			0
$791$			2.65330i			0.0943406i
$792$	13.9577	−	29.8710i	0.495964	−	1.06142i
$793$	12.9581	+	12.9581i	0.460154	+	0.460154i
$794$	−30.5178			−1.08303
$795$		0			0
$796$	16.3396			0.579141
$797$	−12.4688	−	12.4688i	−0.441668	−	0.441668i	0.450905	−	0.892572i	$-0.351101\pi$
$797$	−12.4688	−	12.4688i	−0.441668	−	0.441668i	−0.892572	+	0.450905i	$0.851101\pi$
$798$	5.47733	+	3.83847i	0.193895	+	0.135880i
$799$		−	41.3862i		−	1.46414i
$800$		0			0
$801$	15.9002	+	43.7924i	0.561806	+	1.54733i
$802$	7.92704	−	7.92704i	0.279914	−	0.279914i
$803$	2.58239	−	2.58239i	0.0911306	−	0.0911306i
$804$	22.2035	−	3.90608i	0.783056	−	0.137757i
$805$		0			0
$806$			22.0175i			0.775532i
$807$	−31.0082	+	44.2474i	−1.09154	+	1.55758i
$808$	−11.8144	−	11.8144i	−0.415628	−	0.415628i
$809$	24.8749			0.874556			0.437278	−	0.899326i	$-0.355943\pi$
$809$	24.8749			0.874556			0.437278	+	0.899326i	$0.355943\pi$
$810$		0			0
$811$	6.91973			0.242984			0.121492	−	0.992592i	$-0.461232\pi$
$811$	6.91973			0.242984			0.121492	+	0.992592i	$0.461232\pi$
$812$	0.766585	+	0.766585i	0.0269019	+	0.0269019i
$813$	19.3592	−	27.6248i	0.678958	−	0.968842i
$814$		−	38.1665i		−	1.33774i
$815$		0			0
$816$	−13.2510	+	2.33115i	−0.463879	+	0.0816067i
$817$	4.01889	−	4.01889i	0.140603	−	0.140603i
$818$	14.0812	−	14.0812i	0.492337	−	0.492337i
$819$	−6.07391	−	16.7288i	−0.212240	−	0.584551i
$820$		0			0
$821$		−	3.31823i		−	0.115807i	−0.998322	−	0.0579034i	$-0.981558\pi$
$821$		−	3.31823i		−	0.115807i	0.998322	−	0.0579034i	$-0.0184415\pi$
$822$	27.9431	+	19.5823i	0.974626	+	0.683011i
$823$	8.02010	+	8.02010i	0.279563	+	0.279563i	0.832935	−	0.553371i	$-0.186659\pi$
$823$	8.02010	+	8.02010i	0.279563	+	0.279563i	−0.553371	+	0.832935i	$0.686659\pi$
$824$	7.17562			0.249975
$825$		0			0
$826$	8.91408			0.310160
$827$	−26.6136	−	26.6136i	−0.925444	−	0.925444i	0.0719628	−	0.997407i	$-0.477074\pi$
$827$	−26.6136	−	26.6136i	−0.925444	−	0.925444i	−0.997407	+	0.0719628i	$0.977074\pi$
$828$	−3.10910	+	6.65384i	−0.108049	+	0.231237i
$829$			16.8759i			0.586125i	0.956093	+	0.293062i	$0.0946744\pi$
$829$			16.8759i			0.586125i	−0.956093	+	0.293062i	$0.905326\pi$
$830$		0			0
$831$	−0.813734	−	4.62553i	−0.0282281	−	0.160458i
$832$	30.7133	−	30.7133i	1.06479	−	1.06479i
$833$	4.61300	−	4.61300i	0.159831	−	0.159831i
$834$	2.78179	+	15.8126i	0.0963254	+	0.547545i
$835$		0			0
$836$		−	13.0540i		−	0.451483i
$837$	18.1881	+	4.89645i	0.628672	+	0.169246i
$838$	18.7723	+	18.7723i	0.648477	+	0.648477i
$839$	−38.5483			−1.33084			−0.665418	−	0.746471i	$-0.731747\pi$
$839$	−38.5483			−1.33084			−0.665418	+	0.746471i	$0.731747\pi$
$840$		0			0
$841$	−27.7025			−0.955258
$842$	−4.19874	−	4.19874i	−0.144698	−	0.144698i
$843$	−0.454482	−	0.318498i	−0.0156532	−	0.0109697i
$844$			11.8861i			0.409136i
$845$		0			0
$846$	−18.3157	+	6.65008i	−0.629706	+	0.228635i
$847$	−1.57340	+	1.57340i	−0.0540626	+	0.0540626i
$848$	−1.72409	+	1.72409i	−0.0592055	+	0.0592055i
$849$	2.91122	−	0.512149i	0.0999129	−	0.0175769i
$850$		0			0
$851$			26.3673i			0.903859i
$852$	9.89570	−	14.1207i	0.339021	−	0.483768i
$853$	18.1797	+	18.1797i	0.622462	+	0.622462i	0.946160	−	0.323699i	$-0.104926\pi$
$853$	18.1797	+	18.1797i	0.622462	+	0.622462i	−0.323699	+	0.946160i	$0.604926\pi$
$854$	3.16269			0.108225
$855$		0			0
$856$	−27.0545			−0.924704
$857$	32.6389	+	32.6389i	1.11492	+	1.11492i	0.992475	+	0.122447i	$0.0390742\pi$
$857$	32.6389	+	32.6389i	1.11492	+	1.11492i	0.122447	+	0.992475i	$0.460926\pi$
$858$	21.9565	−	31.3310i	0.749583	−	1.06962i
$859$		−	22.2340i		−	0.758615i	−0.925271	−	0.379308i	$-0.876162\pi$
$859$		−	22.2340i		−	0.758615i	0.925271	−	0.379308i	$-0.123838\pi$
$860$		0			0
$861$	0.537092	−	0.0944864i	0.0183040	−	0.00322009i
$862$	10.7697	−	10.7697i	0.366816	−	0.366816i
$863$	−41.1315	+	41.1315i	−1.40013	+	1.40013i	−0.600534	+	0.799599i	$0.705045\pi$
$863$	−41.1315	+	41.1315i	−1.40013	+	1.40013i	−0.799599	+	0.600534i	$0.794955\pi$
$864$	−12.5105	−	21.7279i	−0.425616	−	0.739197i
$865$		0			0
$866$		−	26.9117i		−	0.914498i
$867$	−36.2542	−	25.4067i	−1.23126	−	0.862855i
$868$	−2.43950	−	2.43950i	−0.0828021	−	0.0828021i
$869$	26.5629			0.901086
$870$		0			0
$871$	81.1325			2.74907
$872$	13.2319	+	13.2319i	0.448089	+	0.448089i
$873$	20.3272	+	9.49818i	0.687972	+	0.321465i
$874$		−	9.93300i		−	0.335989i
$875$		0			0
$876$	−0.286825	−	1.63041i	−0.00969092	−	0.0550864i
$877$	11.3627	−	11.3627i	0.383690	−	0.383690i	−0.488740	−	0.872430i	$-0.662543\pi$
$877$	11.3627	−	11.3627i	0.383690	−	0.383690i	0.872430	+	0.488740i	$0.162543\pi$
$878$	11.3437	−	11.3437i	0.382831	−	0.382831i
$879$	4.75397	+	27.0231i	0.160347	+	0.911467i
$880$		0			0
$881$		−	15.3402i		−	0.516823i	−0.966035	−	0.258412i	$-0.916801\pi$
$881$		−	15.3402i		−	0.516823i	0.966035	−	0.258412i	$-0.0831991\pi$
$882$	−2.78274	−	1.30027i	−0.0936998	−	0.0437825i
$883$	−0.509152	−	0.509152i	−0.0171343	−	0.0171343i	0.698488	−	0.715622i	$-0.253857\pi$
$883$	−0.509152	−	0.509152i	−0.0171343	−	0.0171343i	−0.715622	+	0.698488i	$0.753857\pi$
$884$	36.8340			1.23886
$885$		0			0
$886$	25.2344			0.847767
$887$	35.3019	+	35.3019i	1.18532	+	1.18532i	0.978346	+	0.206974i	$0.0663617\pi$
$887$	35.3019	+	35.3019i	1.18532	+	1.18532i	0.206974	+	0.978346i	$0.433638\pi$
$888$	−43.9406	−	30.7933i	−1.47455	−	1.03335i
$889$			4.85330i			0.162775i
$890$		0			0
$891$	−20.9989	−	25.1054i	−0.703488	−	0.841063i
$892$	−13.9621	+	13.9621i	−0.467487	+	0.467487i
$893$	−16.9188	+	16.9188i	−0.566167	+	0.566167i
$894$	35.9781	−	6.32934i	1.20329	−	0.211685i
$895$		0			0
$896$			2.15404i			0.0719613i
$897$	−15.1686	+	21.6450i	−0.506466	+	0.722704i
$898$	0.449443	+	0.449443i	0.0149981	+	0.0149981i
$899$	−4.12912			−0.137714
$900$		0			0
$901$	−13.3587			−0.445042
$902$	0.828946	+	0.828946i	0.0276009	+	0.0276009i
$903$	−1.49792	+	2.13747i	−0.0498477	+	0.0711304i
$904$			8.01862i			0.266695i
$905$		0			0
$906$	−27.8192	+	4.89401i	−0.924229	+	0.162593i
$907$	6.84363	−	6.84363i	0.227239	−	0.227239i	−0.584299	−	0.811538i	$-0.698631\pi$
$907$	6.84363	−	6.84363i	0.227239	−	0.227239i	0.811538	+	0.584299i	$0.198631\pi$
$908$	−1.51321	+	1.51321i	−0.0502177	+	0.0502177i
$909$	−15.5899	+	5.66041i	−0.517085	+	0.187744i
$910$		0			0
$911$			33.2065i			1.10018i	0.835105	+	0.550090i	$0.185407\pi$
$911$			33.2065i			1.10018i	−0.835105	+	0.550090i	$0.814593\pi$
$912$	6.37006	+	4.46409i	0.210934	+	0.147821i
$913$	−34.8472	−	34.8472i	−1.15327	−	1.15327i
$914$	13.1902			0.436293
$915$		0			0
$916$	1.29123			0.0426636
$917$	−2.71979	−	2.71979i	−0.0898154	−	0.0898154i
$918$	−9.02227	+	33.5136i	−0.297779	+	1.10611i
$919$			48.0196i			1.58402i	0.610507	+	0.792011i	$0.290966\pi$
$919$			48.0196i			1.58402i	−0.610507	+	0.792011i	$0.709034\pi$
$920$		0			0
$921$	−6.81543	−	38.7411i	−0.224576	−	1.27656i
$922$	2.01462	−	2.01462i	0.0663479	−	0.0663479i
$923$	43.8786	−	43.8786i	1.44428	−	1.44428i
$924$	1.03868	+	5.90417i	0.0341699	+	0.194233i
$925$		0			0
$926$			15.1261i			0.497073i
$927$	3.01541	−	6.45334i	0.0990391	−	0.211955i
$928$	3.88645	+	3.88645i	0.127579	+	0.127579i
$929$	−29.7649			−0.976555			−0.488277	−	0.872688i	$-0.662375\pi$
$929$	−29.7649			−0.976555			−0.488277	+	0.872688i	$0.662375\pi$
$930$		0			0
$931$	−3.77162			−0.123610
$932$	−14.3978	−	14.3978i	−0.471615	−	0.471615i
$933$	1.00708	+	0.705751i	0.0329702	+	0.0231053i
$934$		−	23.1265i		−	0.756722i
$935$		0			0
$936$	−18.3561	−	50.5565i	−0.599989	−	1.65249i
$937$	−16.2931	+	16.2931i	−0.532273	+	0.532273i	−0.921248	−	0.388975i	$-0.872829\pi$
$937$	−16.2931	+	16.2931i	−0.532273	+	0.532273i	0.388975	+	0.921248i	$0.372829\pi$
$938$	9.90105	−	9.90105i	0.323281	−	0.323281i
$939$	−36.0493	+	6.34187i	−1.17642	+	0.206959i
$940$		0			0
$941$		−	38.9179i		−	1.26869i	−0.773052	−	0.634343i	$-0.781271\pi$
$941$		−	38.9179i		−	1.26869i	0.773052	−	0.634343i	$-0.218729\pi$
$942$	5.76589	−	8.22767i	0.187863	−	0.268072i
$943$	−0.572676	−	0.572676i	−0.0186489	−	0.0186489i
$944$	10.3670			0.337416
$945$		0			0
$946$	−5.61085			−0.182424
$947$	2.32343	+	2.32343i	0.0755014	+	0.0755014i	0.743849	−	0.668348i	$-0.232998\pi$
$947$	2.32343	+	2.32343i	0.0755014	+	0.0755014i	−0.668348	+	0.743849i	$0.732998\pi$
$948$	6.91017	−	9.86050i	0.224432	−	0.320254i
$949$		−	5.95759i		−	0.193392i
$950$		0			0
$951$	−9.26198	+	1.62939i	−0.300340	+	0.0528366i
$952$	13.9411	−	13.9411i	0.451833	−	0.451833i
$953$	−4.77849	+	4.77849i	−0.154791	+	0.154791i	−0.780254	−	0.625463i	$-0.784910\pi$
$953$	−4.77849	+	4.77849i	−0.154791	+	0.154791i	0.625463	+	0.780254i	$0.284910\pi$
$954$	2.14652	+	5.91195i	0.0694962	+	0.191407i
$955$		0			0
$956$			11.8956i			0.384732i
$957$	5.87576	+	4.11769i	0.189936	+	0.133106i
$958$	−7.88727	−	7.88727i	−0.254826	−	0.254826i
$959$	−19.2412			−0.621332
$960$		0			0
$961$	−17.8599			−0.576127
$962$	−44.0252	−	44.0252i	−1.41943	−	1.41943i
$963$	−11.3691	+	24.3313i	−0.366365	+	0.784064i
$964$			17.1668i			0.552904i
$965$		0			0
$966$	0.790343	+	4.49257i	0.0254289	+	0.144546i
$967$	−26.7726	+	26.7726i	−0.860949	+	0.860949i	−0.991448	−	0.130499i	$-0.958342\pi$
$967$	−26.7726	+	26.7726i	−0.860949	+	0.860949i	0.130499	+	0.991448i	$0.458342\pi$
$968$	−4.75501	+	4.75501i	−0.152832	+	0.152832i
$969$	7.38396	+	41.9728i	0.237207	+	1.34836i
$970$		0			0
$971$			10.3583i			0.332413i	0.986091	+	0.166206i	$0.0531518\pi$
$971$			10.3583i			0.332413i	−0.986091	+	0.166206i	$0.946848\pi$
$972$	−14.7822	+	1.26404i	−0.474139	+	0.0405442i
$973$	−6.40193	−	6.40193i	−0.205236	−	0.205236i
$974$	7.28874			0.233546
$975$		0			0
$976$	3.67816			0.117735
$977$	−11.0435	−	11.0435i	−0.353311	−	0.353311i	0.508029	−	0.861340i	$-0.330374\pi$
$977$	−11.0435	−	11.0435i	−0.353311	−	0.353311i	−0.861340	+	0.508029i	$0.830374\pi$
$978$	−10.6435	−	7.45889i	−0.340342	−	0.238509i
$979$		−	56.4765i		−	1.80500i
$980$		0			0
$981$	17.4605	−	6.33957i	0.557470	−	0.202407i
$982$	8.62939	−	8.62939i	0.275375	−	0.275375i
$983$	9.03917	−	9.03917i	0.288305	−	0.288305i	−0.548105	−	0.836410i	$-0.684651\pi$
$983$	9.03917	−	9.03917i	0.288305	−	0.288305i	0.836410	+	0.548105i	$0.184651\pi$
$984$	1.62316	−	0.285550i	0.0517444	−	0.00910300i
$985$		0			0
$986$		−	7.60837i		−	0.242300i
$987$	6.30598	−	8.99835i	0.200721	−	0.286421i
$988$	−15.0579	−	15.0579i	−0.479055	−	0.479055i
$989$	3.87624			0.123257
$990$		0			0
$991$	9.41165			0.298971			0.149485	−	0.988764i	$-0.452238\pi$
$991$	9.41165			0.298971			0.149485	+	0.988764i	$0.452238\pi$
$992$	−12.3678	−	12.3678i	−0.392679	−	0.392679i
$993$	−31.6176	+	45.1169i	−1.00335	+	1.43174i
$994$		−	10.7095i		−	0.339685i
$995$		0			0
$996$	−22.0010	+	3.87046i	−0.697128	+	0.122640i
$997$	−14.3463	+	14.3463i	−0.454351	+	0.454351i	−0.896796	−	0.442445i	$-0.854111\pi$
$997$	−14.3463	+	14.3463i	−0.454351	+	0.454351i	0.442445	+	0.896796i	$0.354111\pi$
$998$	0.699929	−	0.699929i	0.0221559	−	0.0221559i
$999$	−46.1589	+	26.5774i	−1.46040	+	0.840872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.c.218.10	yes	32
3.2	odd	2	inner	525.2.j.c.218.8	yes	32
5.2	odd	4	inner	525.2.j.c.407.8	yes	32
5.3	odd	4	inner	525.2.j.c.407.9	yes	32
5.4	even	2	inner	525.2.j.c.218.7	✓	32
15.2	even	4	inner	525.2.j.c.407.10	yes	32
15.8	even	4	inner	525.2.j.c.407.7	yes	32
15.14	odd	2	inner	525.2.j.c.218.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.j.c.218.7	✓	32	5.4	even	2	inner
525.2.j.c.218.8	yes	32	3.2	odd	2	inner
525.2.j.c.218.9	yes	32	15.14	odd	2	inner
525.2.j.c.218.10	yes	32	1.1	even	1	trivial
525.2.j.c.407.7	yes	32	15.8	even	4	inner
525.2.j.c.407.8	yes	32	5.2	odd	4	inner
525.2.j.c.407.9	yes	32	5.3	odd	4	inner
525.2.j.c.407.10	yes	32	15.2	even	4	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723969 + 0.723969i) q^{2} +(-0.994020 + 1.41842i) q^{3} -0.951738i q^{4} +(-1.74653 + 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.13697 - 2.13697i) q^{8} +(-1.02385 - 2.81988i) q^{9} +O(q^{10})\)	\(q+(0.723969 + 0.723969i) q^{2} +(-0.994020 + 1.41842i) q^{3} -0.951738i q^{4} +(-1.74653 + 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.13697 - 2.13697i) q^{8} +(-1.02385 - 2.81988i) q^{9} +3.63664i q^{11} +(1.34997 + 0.946047i) q^{12} +(4.19487 + 4.19487i) q^{13} +1.02385 q^{14} +1.19072 q^{16} +(4.61300 + 4.61300i) q^{17} +(1.30027 - 2.78274i) q^{18} -3.77162i q^{19} +(0.300098 + 1.70586i) q^{21} +(-2.63281 + 2.63281i) q^{22} +(1.81887 - 1.81887i) q^{23} +(0.906934 + 5.15531i) q^{24} +6.07391i q^{26} +(5.01751 + 1.35077i) q^{27} +(-0.672980 - 0.672980i) q^{28} -1.13909 q^{29} +3.62492 q^{31} +(-3.41189 - 3.41189i) q^{32} +(-5.15829 - 3.61489i) q^{33} +6.67933i q^{34} +(-2.68379 + 0.974434i) q^{36} +(-7.24824 + 7.24824i) q^{37} +(2.73054 - 2.73054i) q^{38} +(-10.1199 + 1.78031i) q^{39} -0.314852i q^{41} +(-1.01772 + 1.45225i) q^{42} +(1.06556 + 1.06556i) q^{43} +3.46112 q^{44} +2.63362 q^{46} +(-4.48582 - 4.48582i) q^{47} +(-1.18360 + 1.68894i) q^{48} -1.00000i q^{49} +(-11.1286 + 1.95777i) q^{51} +(3.99242 - 3.99242i) q^{52} +(-1.44794 + 1.44794i) q^{53} +(2.65460 + 4.61044i) q^{54} -3.02213i q^{56} +(5.34975 + 3.74907i) q^{57} +(-0.824666 - 0.824666i) q^{58} +8.70646 q^{59} +3.08903 q^{61} +(2.62433 + 2.62433i) q^{62} +(-2.71793 - 1.26999i) q^{63} -7.32164i q^{64} +(-1.11737 - 6.35151i) q^{66} +(9.67044 - 9.67044i) q^{67} +(4.39036 - 4.39036i) q^{68} +(0.771934 + 4.38793i) q^{69} -10.4601i q^{71} +(-8.21392 - 3.83807i) q^{72} +(-0.710104 - 0.710104i) q^{73} -10.4950 q^{74} -3.58959 q^{76} +(2.57149 + 2.57149i) q^{77} +(-8.61538 - 6.03759i) q^{78} -7.30426i q^{79} +(-6.90348 + 5.77426i) q^{81} +(0.227943 - 0.227943i) q^{82} +(-9.58225 + 9.58225i) q^{83} +(1.62353 - 0.285614i) q^{84} +1.54287i q^{86} +(1.13228 - 1.61571i) q^{87} +(7.77137 + 7.77137i) q^{88} -15.5299 q^{89} +5.93244 q^{91} +(-1.73109 - 1.73109i) q^{92} +(-3.60325 + 5.14167i) q^{93} -6.49519i q^{94} +(8.23099 - 1.44801i) q^{96} +(-5.28841 + 5.28841i) q^{97} +(0.723969 - 0.723969i) q^{98} +(10.2549 - 3.72336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{6}+O(q^{10}) \) 32 * q - 16 * q^6	\( 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) \) 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

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