LMFDB - Embedded newform 432.2.v.a.395.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("432.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			395.11
Character	$\chi$	$=$	432.395
Dual form			432.2.v.a.35.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0381759 - 1.41370i) q^{2} +(-1.99709 + 0.107938i) q^{4} +(0.642590 + 2.39818i) q^{5} +(-1.93190 - 3.34616i) q^{7} +(0.228833 + 2.81916i) q^{8} +O(q^{10})$	\(q+(-0.0381759 - 1.41370i) q^{2} +(-1.99709 + 0.107938i) q^{4} +(0.642590 + 2.39818i) q^{5} +(-1.93190 - 3.34616i) q^{7} +(0.228833 + 2.81916i) q^{8} +(3.36577 - 0.999982i) q^{10} +(1.07665 - 4.01810i) q^{11} +(-0.850284 - 3.17330i) q^{13} +(-4.65670 + 2.85887i) q^{14} +(3.97670 - 0.431125i) q^{16} -1.33161i q^{17} +(-6.09021 - 6.09021i) q^{19} +(-1.54216 - 4.72001i) q^{20} +(-5.72148 - 1.36866i) q^{22} +(-0.521462 - 0.301066i) q^{23} +(-1.00822 + 0.582095i) q^{25} +(-4.45363 + 1.32319i) q^{26} +(4.21936 + 6.47403i) q^{28} +(-0.0730837 + 0.272752i) q^{29} +(5.84901 + 3.37693i) q^{31} +(-0.761294 - 5.60539i) q^{32} +(-1.88250 + 0.0508355i) q^{34} +(6.78326 - 6.78326i) q^{35} +(0.00346351 + 0.00346351i) q^{37} +(-8.37722 + 8.84221i) q^{38} +(-6.61380 + 2.36034i) q^{40} +(-0.614318 + 1.06403i) q^{41} +(0.563698 + 0.151042i) q^{43} +(-1.71645 + 8.14070i) q^{44} +(-0.405710 + 0.748684i) q^{46} +(1.24972 + 2.16458i) q^{47} +(-3.96450 + 6.86672i) q^{49} +(0.861396 + 1.40309i) q^{50} +(2.04061 + 6.24558i) q^{52} +(-3.24883 + 3.24883i) q^{53} +10.3280 q^{55} +(8.99125 - 6.21205i) q^{56} +(0.388379 + 0.0929058i) q^{58} +(-5.40194 + 1.44745i) q^{59} +(-1.97301 - 0.528668i) q^{61} +(4.55067 - 8.39766i) q^{62} +(-7.89527 + 1.29023i) q^{64} +(7.06377 - 4.07827i) q^{65} +(9.90429 - 2.65385i) q^{67} +(0.143732 + 2.65934i) q^{68} +(-9.84844 - 9.33053i) q^{70} +7.85052i q^{71} -7.41855i q^{73} +(0.00476414 - 0.00502859i) q^{74} +(12.8200 + 11.5053i) q^{76} +(-15.5252 + 4.15995i) q^{77} +(0.839597 - 0.484742i) q^{79} +(3.58930 + 9.25980i) q^{80} +(1.52767 + 0.827840i) q^{82} +(0.639302 + 0.171300i) q^{83} +(3.19344 - 0.855680i) q^{85} +(0.192009 - 0.802665i) q^{86} +(11.5740 + 2.11576i) q^{88} +11.2223 q^{89} +(-8.97570 + 8.97570i) q^{91} +(1.07390 + 0.544969i) q^{92} +(3.01235 - 1.84936i) q^{94} +(10.6919 - 18.5189i) q^{95} +(-3.24710 - 5.62414i) q^{97} +(9.85882 + 5.34247i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.0381759	−	1.41370i	−0.0269945	−	0.999636i
$2$	−0.0381759	−	1.41370i	−0.0269945	−	0.999636i
$3$		0			0
$3$		0			0
$4$	−1.99709	+	0.107938i	−0.998543	+	0.0539692i
$5$	0.642590	+	2.39818i	0.287375	+	1.07250i	0.947086	+	0.320979i	$0.104012\pi$
$5$	0.642590	+	2.39818i	0.287375	+	1.07250i	−0.659711	+	0.751519i	$0.729321\pi$
$6$		0			0
$7$	−1.93190	−	3.34616i	−0.730191	−	1.26473i	−0.956801	−	0.290742i	$-0.906098\pi$
$7$	−1.93190	−	3.34616i	−0.730191	−	1.26473i	0.226610	−	0.973985i	$-0.427236\pi$
$8$	0.228833	+	2.81916i	0.0809047	+	0.996722i
$9$		0			0
$10$	3.36577	−	0.999982i	1.06435	−	0.316222i
$11$	1.07665	−	4.01810i	0.324621	−	1.21150i	−0.590071	−	0.807351i	$-0.700900\pi$
$11$	1.07665	−	4.01810i	0.324621	−	1.21150i	0.914692	−	0.404151i	$-0.132433\pi$
$12$		0			0
$13$	−0.850284	−	3.17330i	−0.235826	−	0.880116i	−0.977775	−	0.209659i	$-0.932765\pi$
$13$	−0.850284	−	3.17330i	−0.235826	−	0.880116i	0.741948	−	0.670457i	$-0.233902\pi$
$14$	−4.65670	+	2.85887i	−1.24456	+	0.764066i
$15$		0			0
$16$	3.97670	−	0.431125i	0.994175	−	0.107781i
$17$		−	1.33161i		−	0.322963i	−0.986876	−	0.161482i	$-0.948373\pi$
$17$		−	1.33161i		−	0.322963i	0.986876	−	0.161482i	$-0.0516272\pi$
$18$		0			0
$19$	−6.09021	−	6.09021i	−1.39719	−	1.39719i	−0.807981	−	0.589208i	$-0.799440\pi$
$19$	−6.09021	−	6.09021i	−1.39719	−	1.39719i	−0.589208	−	0.807981i	$-0.700560\pi$
$20$	−1.54216	−	4.72001i	−0.344838	−	1.05543i
$21$		0			0
$22$	−5.72148	−	1.36866i	−1.21982	−	0.291799i
$23$	−0.521462	−	0.301066i	−0.108732	−	0.0627767i	0.444648	−	0.895706i	$-0.353329\pi$
$23$	−0.521462	−	0.301066i	−0.108732	−	0.0627767i	−0.553380	+	0.832929i	$0.686662\pi$
$24$		0			0
$25$	−1.00822	+	0.582095i	−0.201643	+	0.116419i
$26$	−4.45363	+	1.32319i	−0.873429	+	0.259499i
$27$		0			0
$28$	4.21936	+	6.47403i	0.797383	+	1.22348i
$29$	−0.0730837	+	0.272752i	−0.0135713	+	0.0506488i	−0.972379	−	0.233406i	$-0.925013\pi$
$29$	−0.0730837	+	0.272752i	−0.0135713	+	0.0506488i	0.958808	+	0.284054i	$0.0916797\pi$
$30$		0			0
$31$	5.84901	+	3.37693i	1.05051	+	0.606514i	0.922793	−	0.385296i	$-0.125901\pi$
$31$	5.84901	+	3.37693i	1.05051	+	0.606514i	0.127721	+	0.991810i	$0.459234\pi$
$32$	−0.761294	−	5.60539i	−0.134579	−	0.990903i
$33$		0			0
$34$	−1.88250	+	0.0508355i	−0.322845	+	0.00871821i
$35$	6.78326	−	6.78326i	1.14658	−	1.14658i
$36$		0			0
$37$	0.00346351	+	0.00346351i	0.000569398	+	0.000569398i	0.707391	−	0.706822i	$-0.249872\pi$
$37$	0.00346351	+	0.00346351i	0.000569398	+	0.000569398i	−0.706822	+	0.707391i	$0.749872\pi$
$38$	−8.37722	+	8.84221i	−1.35896	+	1.43440i
$39$		0			0
$40$	−6.61380	+	2.36034i	−1.04573	+	0.373203i
$41$	−0.614318	+	1.06403i	−0.0959403	+	0.166174i	−0.910001	−	0.414607i	$-0.863919\pi$
$41$	−0.614318	+	1.06403i	−0.0959403	+	0.166174i	0.814060	+	0.580780i	$0.197252\pi$
$42$		0			0
$43$	0.563698	+	0.151042i	0.0859631	+	0.0230337i	0.301544	−	0.953452i	$-0.402498\pi$
$43$	0.563698	+	0.151042i	0.0859631	+	0.0230337i	−0.215581	+	0.976486i	$0.569165\pi$
$44$	−1.71645	+	8.14070i	−0.258764	+	1.22726i
$45$		0			0
$46$	−0.405710	+	0.748684i	−0.0598186	+	0.110387i
$47$	1.24972	+	2.16458i	0.182290	+	0.315736i	0.942660	−	0.333754i	$-0.108316\pi$
$47$	1.24972	+	2.16458i	0.182290	+	0.315736i	−0.760370	+	0.649490i	$0.774982\pi$
$48$		0			0
$49$	−3.96450	+	6.86672i	−0.566358	+	0.980960i
$50$	0.861396	+	1.40309i	0.121820	+	0.198427i
$51$		0			0
$52$	2.04061	+	6.24558i	0.282982	+	0.866106i
$53$	−3.24883	+	3.24883i	−0.446262	+	0.446262i	−0.894110	−	0.447848i	$-0.852191\pi$
$53$	−3.24883	+	3.24883i	−0.446262	+	0.446262i	0.447848	+	0.894110i	$0.352191\pi$
$54$		0			0
$55$	10.3280			1.39262
$56$	8.99125	−	6.21205i	1.20151	−	0.830120i
$57$		0			0
$58$	0.388379	+	0.0929058i	0.0509967	+	0.0121991i
$59$	−5.40194	+	1.44745i	−0.703273	+	0.188441i	−0.592696	−	0.805426i	$-0.701936\pi$
$59$	−5.40194	+	1.44745i	−0.703273	+	0.188441i	−0.110577	+	0.993868i	$0.535270\pi$
$60$		0			0
$61$	−1.97301	−	0.528668i	−0.252619	−	0.0676890i	0.130287	−	0.991476i	$-0.458410\pi$
$61$	−1.97301	−	0.528668i	−0.252619	−	0.0676890i	−0.382906	+	0.923787i	$0.625077\pi$
$62$	4.55067	−	8.39766i	0.577935	−	1.06650i
$63$		0			0
$64$	−7.89527	+	1.29023i	−0.986909	+	0.161279i
$65$	7.06377	−	4.07827i	0.876153	−	0.505847i
$66$		0			0
$67$	9.90429	−	2.65385i	1.21000	−	0.324219i	0.403239	−	0.915095i	$-0.367884\pi$
$67$	9.90429	−	2.65385i	1.21000	−	0.324219i	0.806763	+	0.590876i	$0.201218\pi$
$68$	0.143732	+	2.65934i	0.0174301	+	0.322492i
$69$		0			0
$70$	−9.84844	−	9.33053i	−1.17711	−	1.11521i
$71$			7.85052i			0.931685i	0.884868	+	0.465843i	$0.154249\pi$
$71$			7.85052i			0.931685i	−0.884868	+	0.465843i	$0.845751\pi$
$72$		0			0
$73$		−	7.41855i		−	0.868275i	−0.900847	−	0.434138i	$-0.857053\pi$
$73$		−	7.41855i		−	0.868275i	0.900847	−	0.434138i	$-0.142947\pi$
$74$	0.00476414	−	0.00502859i	0.000553820	−	0.000584561i
$75$		0			0
$76$	12.8200	+	11.5053i	1.47056	+	1.31975i
$77$	−15.5252	+	4.15995i	−1.76926	+	0.474071i
$78$		0			0
$79$	0.839597	−	0.484742i	0.0944620	−	0.0545377i	−0.452025	−	0.892005i	$-0.649298\pi$
$79$	0.839597	−	0.484742i	0.0944620	−	0.0545377i	0.546487	+	0.837468i	$0.315965\pi$
$80$	3.58930	+	9.25980i	0.401296	+	1.03528i
$81$		0			0
$82$	1.52767	+	0.827840i	0.168703	+	0.0914196i
$83$	0.639302	+	0.171300i	0.0701725	+	0.0188027i	0.293735	−	0.955887i	$-0.405102\pi$
$83$	0.639302	+	0.171300i	0.0701725	+	0.0188027i	−0.223562	+	0.974690i	$0.571769\pi$
$84$		0			0
$85$	3.19344	−	0.855680i	0.346378	−	0.0928116i
$86$	0.192009	−	0.802665i	0.0207048	−	0.0865535i
$87$		0			0
$88$	11.5740	+	2.11576i	1.23379	+	0.225541i
$89$	11.2223			1.18956			0.594781	−	0.803887i	$-0.297239\pi$
$89$	11.2223			1.18956			0.594781	+	0.803887i	$0.297239\pi$
$90$		0			0
$91$	−8.97570	+	8.97570i	−0.940909	+	0.940909i
$92$	1.07390	+	0.544969i	0.111962	+	0.0568170i
$93$		0			0
$94$	3.01235	−	1.84936i	0.310700	−	0.190747i
$95$	10.6919	−	18.5189i	1.09697	−	1.90000i
$96$		0			0
$97$	−3.24710	−	5.62414i	−0.329693	−	0.571045i	0.652758	−	0.757567i	$-0.273612\pi$
$97$	−3.24710	−	5.62414i	−0.329693	−	0.571045i	−0.982451	+	0.186521i	$0.940279\pi$
$98$	9.85882	+	5.34247i	0.995891	+	0.539671i
$99$		0			0
$100$	1.95067	−	1.27132i	0.195067	−	0.127132i
$101$	5.78490	+	1.55006i	0.575619	+	0.154237i	0.534872	−	0.844933i	$-0.320360\pi$
$101$	5.78490	+	1.55006i	0.575619	+	0.154237i	0.0407464	+	0.999170i	$0.487026\pi$
$102$		0			0
$103$	6.06520	−	10.5052i	0.597622	−	1.03511i	−0.395549	−	0.918445i	$-0.629446\pi$
$103$	6.06520	−	10.5052i	0.597622	−	1.03511i	0.993171	−	0.116667i	$-0.0372211\pi$
$104$	8.75146	−	3.12324i	0.858151	−	0.306259i
$105$		0			0
$106$	4.71690	+	4.46884i	0.458146	+	0.434052i
$107$	−3.78971	−	3.78971i	−0.366365	−	0.366365i	0.499785	−	0.866150i	$-0.333412\pi$
$107$	−3.78971	−	3.78971i	−0.366365	−	0.366365i	−0.866150	+	0.499785i	$0.833412\pi$
$108$		0			0
$109$	−6.42830	+	6.42830i	−0.615719	+	0.615719i	−0.944430	−	0.328711i	$-0.893386\pi$
$109$	−6.42830	+	6.42830i	−0.615719	+	0.615719i	0.328711	+	0.944430i	$0.393386\pi$
$110$	−0.394280	−	14.6006i	−0.0375931	−	1.39211i
$111$		0			0
$112$	−9.12521	−	12.4738i	−0.862251	−	1.17866i
$113$	8.09791	+	4.67533i	0.761788	+	0.439818i	0.829937	−	0.557857i	$-0.188376\pi$
$113$	8.09791	+	4.67533i	0.761788	+	0.439818i	−0.0681497	+	0.997675i	$0.521710\pi$
$114$		0			0
$115$	0.386925	−	1.44402i	0.0360809	−	0.134656i
$116$	0.116514	−	0.552598i	0.0108181	−	0.0513074i
$117$		0			0
$118$	2.25247	+	7.58145i	0.207357	+	0.697930i
$119$	−4.45578	+	2.57254i	−0.408460	+	0.235825i
$120$		0			0
$121$	−5.45967	−	3.15214i	−0.496333	−	0.286558i
$122$	−0.672055	+	2.80943i	−0.0608450	+	0.254354i
$123$		0			0
$124$	−12.0455	−	6.11268i	−1.08172	−	0.548935i
$125$	6.73411	+	6.73411i	0.602317	+	0.602317i
$126$		0			0
$127$		−	10.4883i		−	0.930687i	−0.885130	−	0.465343i	$-0.845931\pi$
$127$		−	10.4883i		−	0.930687i	0.885130	−	0.465343i	$-0.154069\pi$
$128$	2.12541	+	11.1123i	0.187861	+	0.982196i
$129$		0			0
$130$	−6.03511	−	9.83034i	−0.529314	−	0.862178i
$131$	−4.83728	−	18.0530i	−0.422635	−	1.57730i	−0.769034	−	0.639208i	$-0.779262\pi$
$131$	−4.83728	−	18.0530i	−0.422635	−	1.57730i	0.346399	−	0.938087i	$-0.387404\pi$
$132$		0			0
$133$	−8.61309	+	32.1445i	−0.746849	+	2.78728i
$134$	−4.12984	−	13.9004i	−0.356764	−	1.20081i
$135$		0			0
$136$	3.75402	−	0.304716i	0.321904	−	0.0261292i
$137$	−5.65739	−	9.79888i	−0.483343	−	0.837175i	0.516474	−	0.856303i	$-0.327244\pi$
$137$	−5.65739	−	9.79888i	−0.483343	−	0.837175i	−0.999817	+	0.0191280i	$0.993911\pi$
$138$		0			0
$139$	1.71664	+	6.40659i	0.145603	+	0.543399i	0.999728	+	0.0233307i	$0.00742705\pi$
$139$	1.71664	+	6.40659i	0.145603	+	0.543399i	−0.854124	+	0.520069i	$0.825906\pi$
$140$	−12.8146	+	14.2789i	−1.08303	+	1.20679i
$141$		0			0
$142$	11.0983	−	0.299701i	0.931346	−	0.0251503i
$143$	−13.6661			−1.14282
$144$		0			0
$145$	−0.701072			−0.0582208
$146$	−10.4876	+	0.283210i	−0.867959	+	0.0234386i
$147$		0			0
$148$	−0.00729078	−	0.00654309i	−0.000599298	−	0.000537838i
$149$	5.88059	+	21.9467i	0.481757	+	1.79794i	0.594240	+	0.804288i	$0.297453\pi$
$149$	5.88059	+	21.9467i	0.481757	+	1.79794i	−0.112483	+	0.993654i	$0.535880\pi$
$150$		0			0
$151$	7.60398	+	13.1705i	0.618803	+	1.07180i	0.989704	+	0.143126i	$0.0457154\pi$
$151$	7.60398	+	13.1705i	0.618803	+	1.07180i	−0.370902	+	0.928672i	$0.620951\pi$
$152$	15.7756	−	18.5629i	1.27957	−	1.50565i
$153$		0			0
$154$	6.47361	+	21.7891i	0.521658	+	1.75581i
$155$	−4.33996	+	16.1970i	−0.348594	+	1.30097i
$156$		0			0
$157$	3.05749	+	11.4107i	0.244015	+	0.910675i	0.973876	+	0.227080i	$0.0729179\pi$
$157$	3.05749	+	11.4107i	0.244015	+	0.910675i	−0.729862	+	0.683595i	$0.760415\pi$
$158$	−0.717331	−	1.16843i	−0.0570678	−	0.0929554i
$159$		0			0
$160$	12.9535	−	5.42769i	1.02407	−	0.429097i
$161$			2.32652i			0.183356i
$162$		0			0
$163$	−2.65630	−	2.65630i	−0.208057	−	0.208057i	0.595384	−	0.803441i	$-0.297000\pi$
$163$	−2.65630	−	2.65630i	−0.208057	−	0.208057i	−0.803441	+	0.595384i	$0.797000\pi$
$164$	1.11200	−	2.19127i	0.0868323	−	0.171109i
$165$		0			0
$166$	0.217761	−	0.910320i	0.0169015	−	0.0706545i
$167$	9.93169	+	5.73407i	0.768538	+	0.443715i	0.832353	−	0.554246i	$-0.186993\pi$
$167$	9.93169	+	5.73407i	0.768538	+	0.443715i	−0.0638151	+	0.997962i	$0.520327\pi$
$168$		0			0
$169$	1.91146	−	1.10358i	0.147035	−	0.0848909i
$170$	−1.33159	−	4.48190i	−0.102128	−	0.343746i
$171$		0			0
$172$	−1.14206	−	0.240800i	−0.0870809	−	0.0183608i
$173$	5.86908	−	21.9037i	0.446218	−	1.66531i	−0.266483	−	0.963840i	$-0.585862\pi$
$173$	5.86908	−	21.9037i	0.446218	−	1.66531i	0.712701	−	0.701468i	$-0.247472\pi$
$174$		0			0
$175$	3.89556	+	2.24910i	0.294476	+	0.170016i
$176$	2.54920	−	16.4429i	0.192153	−	1.23943i
$177$		0			0
$178$	−0.428422	−	15.8650i	−0.0321116	−	1.18913i
$179$	−7.29427	+	7.29427i	−0.545199	+	0.545199i	−0.925048	−	0.379849i	$-0.875976\pi$
$179$	−7.29427	+	7.29427i	−0.545199	+	0.545199i	0.379849	+	0.925048i	$0.375976\pi$
$180$		0			0
$181$	−2.73737	−	2.73737i	−0.203467	−	0.203467i	0.598016	−	0.801484i	$-0.295956\pi$
$181$	−2.73737	−	2.73737i	−0.203467	−	0.203467i	−0.801484	+	0.598016i	$0.795956\pi$
$182$	13.0316	+	12.3463i	0.965965	+	0.915167i
$183$		0			0
$184$	0.729425	−	1.53898i	0.0537739	−	0.113455i
$185$	−0.00608051	+	0.0105317i	−0.000447048	+	0.000774310i
$186$		0			0
$187$	−5.35054	−	1.43367i	−0.391271	−	0.104841i
$188$	−2.72944	−	4.18795i	−0.199065	−	0.305438i
$189$		0			0
$190$	−26.5883	−	14.4081i	−1.92892	−	1.04528i
$191$	2.98376	+	5.16802i	0.215897	+	0.373945i	0.953550	−	0.301236i	$-0.0973991\pi$
$191$	2.98376	+	5.16802i	0.215897	+	0.373945i	−0.737653	+	0.675180i	$0.764066\pi$
$192$		0			0
$193$	1.79816	−	3.11450i	0.129434	−	0.224187i	−0.794023	−	0.607887i	$-0.792017\pi$
$193$	1.79816	−	3.11450i	0.129434	−	0.224187i	0.923458	+	0.383701i	$0.125351\pi$
$194$	−7.82688	+	4.80513i	−0.561937	+	0.344988i
$195$		0			0
$196$	7.17627	−	14.1414i	0.512591	−	1.01010i
$197$	−9.60375	+	9.60375i	−0.684239	+	0.684239i	−0.960952	−	0.276713i	$-0.910755\pi$
$197$	−9.60375	+	9.60375i	−0.684239	+	0.684239i	0.276713	+	0.960952i	$0.410755\pi$
$198$		0			0
$199$	11.8548			0.840363			0.420182	−	0.907440i	$-0.361966\pi$
$199$	11.8548			0.840363			0.420182	+	0.907440i	$0.361966\pi$
$200$	−1.87173	−	2.70912i	−0.132351	−	0.191564i
$201$		0			0
$202$	1.97047	−	8.23727i	0.138642	−	0.579572i
$203$	1.05386	−	0.282381i	0.0739666	−	0.0198193i
$204$		0			0
$205$	−2.94649	−	0.789510i	−0.205792	−	0.0551417i
$206$	−15.0828	−	8.17332i	−1.05087	−	0.569462i
$207$		0			0
$208$	−4.74941	−	12.2527i	−0.329312	−	0.849571i
$209$	−31.0280	+	17.9141i	−2.14626	+	1.23914i
$210$		0			0
$211$	−15.8165	+	4.23802i	−1.08885	+	0.291757i	−0.758218	−	0.652001i	$-0.773930\pi$
$211$	−15.8165	+	4.23802i	−1.08885	+	0.291757i	−0.330635	+	0.943759i	$0.607263\pi$
$212$	6.13752	−	6.83887i	0.421527	−	0.469696i
$213$		0			0
$214$	−5.21283	+	5.50218i	−0.356342	+	0.376121i
$215$			1.44891i			0.0988146i
$216$		0			0
$217$		−	26.0956i		−	1.77149i
$218$	9.33308	+	8.84226i	0.632116	+	0.598874i
$219$		0			0
$220$	−20.6258	+	1.11478i	−1.39059	+	0.0751588i
$221$	−4.22561	+	1.13225i	−0.284245	+	0.0761632i
$222$		0			0
$223$	−15.9088	+	9.18497i	−1.06533	+	0.615071i	−0.926903	−	0.375301i	$-0.877539\pi$
$223$	−15.9088	+	9.18497i	−1.06533	+	0.615071i	−0.138431	+	0.990372i	$0.544206\pi$
$224$	−17.2858	+	13.3765i	−1.15495	+	0.893754i
$225$		0			0
$226$	6.30036	−	11.6265i	0.419094	−	0.773383i
$227$	−5.38000	−	1.44157i	−0.357083	−	0.0956802i	0.0758175	−	0.997122i	$-0.475843\pi$
$227$	−5.38000	−	1.44157i	−0.357083	−	0.0956802i	−0.432901	+	0.901441i	$0.642510\pi$
$228$		0			0
$229$	25.8093	−	6.91557i	1.70552	−	0.456994i	0.731204	−	0.682159i	$-0.238959\pi$
$229$	25.8093	−	6.91557i	1.70552	−	0.456994i	0.974321	+	0.225165i	$0.0722923\pi$
$230$	−2.05618	−	0.491868i	−0.135581	−	0.0324328i
$231$		0			0
$232$	−0.785655	−	0.143620i	−0.0515808	−	0.00942909i
$233$	16.7979			1.10047			0.550233	−	0.835011i	$-0.314539\pi$
$233$	16.7979			1.10047			0.550233	+	0.835011i	$0.314539\pi$
$234$		0			0
$235$	−4.38799	+	4.38799i	−0.286241	+	0.286241i
$236$	10.6319	−	3.47375i	0.692078	−	0.226122i
$237$		0			0
$238$	3.80690	+	6.20092i	0.246765	+	0.401946i
$239$	−7.79074	+	13.4940i	−0.503941	+	0.872851i	0.496049	+	0.868295i	$0.334784\pi$
$239$	−7.79074	+	13.4940i	−0.503941	+	0.872851i	−0.999990	+	0.00455666i	$0.998550\pi$
$240$		0			0
$241$	7.24520	+	12.5490i	0.466704	+	0.808355i	0.999277	−	0.0380291i	$-0.0121080\pi$
$241$	7.24520	+	12.5490i	0.466704	+	0.808355i	−0.532573	+	0.846384i	$0.678775\pi$
$242$	−4.24775	+	7.83866i	−0.273056	+	0.503888i
$243$		0			0
$244$	3.99734	+	0.842830i	0.255904	+	0.0539567i
$245$	−19.0152	−	5.09510i	−1.21484	−	0.325514i
$246$		0			0
$247$	−14.1477	+	24.5045i	−0.900195	+	1.55918i
$248$	−8.18164	+	17.2620i	−0.519535	+	1.09614i
$249$		0			0
$250$	9.26292	−	9.77708i	0.585838	−	0.618357i
$251$	−19.7766	−	19.7766i	−1.24829	−	1.24829i	−0.956475	−	0.291815i	$-0.905741\pi$
$251$	−19.7766	−	19.7766i	−1.24829	−	1.24829i	−0.291815	−	0.956475i	$-0.594259\pi$
$252$		0			0
$253$	−1.77114	+	1.77114i	−0.111351	+	0.111351i
$254$	−14.8273	+	0.400401i	−0.930348	+	0.0251234i
$255$		0			0
$256$	15.6283	−	3.42891i	0.976766	−	0.214307i
$257$	−17.3273	−	10.0039i	−1.08085	−	0.624028i	−0.149723	−	0.988728i	$-0.547838\pi$
$257$	−17.3273	−	10.0039i	−1.08085	−	0.624028i	−0.931125	+	0.364700i	$0.881172\pi$
$258$		0			0
$259$	0.00489828	−	0.0182806i	0.000304364	−	0.00113590i
$260$	−13.6667	+	8.90710i	−0.847575	+	0.552395i
$261$		0			0
$262$	−25.3368	+	7.52764i	−1.56531	+	0.465059i
$263$	5.23357	−	3.02160i	0.322716	−	0.186320i	−0.329887	−	0.944021i	$-0.607011\pi$
$263$	5.23357	−	3.02160i	0.322716	−	0.186320i	0.652602	+	0.757700i	$0.273677\pi$
$264$		0			0
$265$	−9.87896	−	5.70362i	−0.606859	−	0.350370i
$266$	45.7714	+	10.9492i	2.80642	+	0.671336i
$267$		0			0
$268$	−19.4933	+	6.36901i	−1.19074	+	0.389049i
$269$	−16.3593	−	16.3593i	−0.997443	−	0.997443i	0.00255337	−	0.999997i	$-0.499187\pi$
$269$	−16.3593	−	16.3593i	−0.997443	−	0.997443i	−0.999997	+	0.00255337i	$0.999187\pi$
$270$		0			0
$271$		−	12.7820i		−	0.776454i	−0.921564	−	0.388227i	$-0.873088\pi$
$271$		−	12.7820i		−	0.776454i	0.921564	−	0.388227i	$-0.126912\pi$
$272$	−0.574090	−	5.29542i	−0.0348093	−	0.321082i
$273$		0			0
$274$	−13.6367	+	8.37192i	−0.823822	+	0.505766i
$275$	1.25342	+	4.67783i	0.0755841	+	0.282084i
$276$		0			0
$277$	2.96015	−	11.0474i	0.177858	−	0.663776i	−0.818189	−	0.574949i	$-0.805022\pi$
$277$	2.96015	−	11.0474i	0.177858	−	0.663776i	0.996047	−	0.0888264i	$-0.0283116\pi$
$278$	8.99144	−	2.67139i	0.539271	−	0.160219i
$279$		0			0
$280$	20.6753	+	17.5708i	1.23559	+	1.05006i
$281$	3.53089	+	6.11568i	0.210635	+	0.364831i	0.951914	−	0.306367i	$-0.0991134\pi$
$281$	3.53089	+	6.11568i	0.210635	+	0.364831i	−0.741278	+	0.671198i	$0.765780\pi$
$282$		0			0
$283$	−7.56336	−	28.2269i	−0.449595	−	1.67791i	−0.703510	−	0.710686i	$-0.748385\pi$
$283$	−7.56336	−	28.2269i	−0.449595	−	1.67791i	0.253915	−	0.967227i	$-0.418282\pi$
$284$	−0.847373	−	15.6782i	−0.0502823	−	0.930328i
$285$		0			0
$286$	0.521716	+	19.3197i	0.0308497	+	1.14240i
$287$	4.74721			0.280219
$288$		0			0
$289$	15.2268			0.895695
$290$	0.0267641	+	0.991104i	0.00157164	+	0.0581996i
$291$		0			0
$292$	0.800746	+	14.8155i	0.0468601	+	0.867010i
$293$	−6.43469	−	24.0146i	−0.375919	−	1.40295i	−0.851998	−	0.523545i	$-0.824609\pi$
$293$	−6.43469	−	24.0146i	−0.375919	−	1.40295i	0.476080	−	0.879402i	$-0.342057\pi$
$294$		0			0
$295$	−6.94247	−	12.0247i	−0.404206	−	0.700106i
$296$	−0.00897162	+	0.0105567i	−0.000521465	+	0.000613598i
$297$		0			0
$298$	30.8015	−	9.15122i	1.78428	−	0.530116i
$299$	−0.511984	+	1.91075i	−0.0296088	+	0.110501i
$300$		0			0
$301$	−0.583598	−	2.17802i	−0.0336381	−	0.125539i
$302$	18.3288	−	11.2525i	1.05470	−	0.647510i
$303$		0			0
$304$	−26.8446	−	21.5933i	−1.53964	−	1.23846i
$305$		−	5.07136i		−	0.290385i
$306$		0			0
$307$	13.0736	+	13.0736i	0.746147	+	0.746147i	0.973753	−	0.227606i	$-0.0730898\pi$
$307$	13.0736	+	13.0736i	0.746147	+	0.746147i	−0.227606	+	0.973753i	$0.573090\pi$
$308$	30.5560	−	9.98354i	1.74109	−	0.568865i
$309$		0			0
$310$	23.0633	+	5.51707i	1.30991	+	0.313348i
$311$	24.9978	+	14.4325i	1.41749	+	0.818390i	0.996078	−	0.0884785i	$-0.0282005\pi$
$311$	24.9978	+	14.4325i	1.41749	+	0.818390i	0.421414	+	0.906868i	$0.361534\pi$
$312$		0			0
$313$	17.2743	−	9.97334i	0.976403	−	0.563727i	0.0752210	−	0.997167i	$-0.476034\pi$
$313$	17.2743	−	9.97334i	0.976403	−	0.563727i	0.901182	+	0.433440i	$0.142700\pi$
$314$	16.0146	−	4.75799i	0.903756	−	0.268509i
$315$		0			0
$316$	−1.62442	+	1.05869i	−0.0913810	+	0.0595562i
$317$	−3.28240	+	12.2501i	−0.184358	+	0.688034i	0.810409	+	0.585865i	$0.199245\pi$
$317$	−3.28240	+	12.2501i	−0.184358	+	0.688034i	−0.994767	+	0.102169i	$0.967422\pi$
$318$		0			0
$319$	1.01726	+	0.587315i	0.0569556	+	0.0328833i
$320$	−8.16763	−	18.1052i	−0.456584	−	1.01211i
$321$		0			0
$322$	3.28900	−	0.0888172i	0.183289	−	0.00494959i
$323$	−8.10979	+	8.10979i	−0.451241	+	0.451241i
$324$		0			0
$325$	2.70443	+	2.70443i	0.150015	+	0.150015i
$326$	−3.65380	+	3.85661i	−0.202365	+	0.213598i
$327$		0			0
$328$	−3.14024	−	1.48837i	−0.173391	−	0.0821816i
$329$	4.82867	−	8.36351i	0.266213	−	0.461095i
$330$		0			0
$331$	26.0714	+	6.98582i	1.43302	+	0.383975i	0.890082	−	0.455800i	$-0.150647\pi$
$331$	26.0714	+	6.98582i	1.43302	+	0.383975i	0.542934	+	0.839776i	$0.317313\pi$
$332$	−1.29523	−	0.273096i	−0.0710850	−	0.0149881i
$333$		0			0
$334$	7.72709	−	14.2593i	0.422807	−	0.780235i
$335$	12.7288	+	22.0469i	0.695449	+	1.20455i
$336$		0			0
$337$	−1.19472	+	2.06931i	−0.0650805	+	0.112723i	−0.896730	−	0.442579i	$-0.854064\pi$
$337$	−1.19472	+	2.06931i	−0.0650805	+	0.112723i	0.831649	+	0.555301i	$0.187397\pi$
$338$	−1.63310	−	2.66010i	−0.0888291	−	0.144690i
$339$		0			0
$340$	−6.28522	+	2.05356i	−0.340864	+	0.111370i
$341$	19.8662	−	19.8662i	1.07581	−	1.07581i
$342$		0			0
$343$	3.58951			0.193815
$344$	−0.296819	+	1.62371i	−0.0160034	+	0.0875448i
$345$		0			0
$346$	−31.1893	−	7.46091i	−1.67675	−	0.401101i
$347$	30.9839	−	8.30210i	1.66330	−	0.445680i	0.700009	−	0.714134i	$-0.253179\pi$
$347$	30.9839	−	8.30210i	1.66330	−	0.445680i	0.963292	+	0.268454i	$0.0865128\pi$
$348$		0			0
$349$	−4.24471	−	1.13737i	−0.227214	−	0.0608818i	0.143416	−	0.989663i	$-0.454191\pi$
$349$	−4.24471	−	1.13737i	−0.227214	−	0.0608818i	−0.370630	+	0.928781i	$0.620858\pi$
$350$	3.03083	−	5.59300i	0.162005	−	0.298959i
$351$		0			0
$352$	−23.3427	−	2.97607i	−1.24417	−	0.158625i
$353$	30.3229	−	17.5069i	1.61393	−	0.931800i	0.625477	−	0.780243i	$-0.284904\pi$
$353$	30.3229	−	17.5069i	1.61393	−	0.931800i	0.988448	−	0.151558i	$-0.0484290\pi$
$354$		0			0
$355$	−18.8270	+	5.04467i	−0.999231	+	0.267743i
$356$	−22.4119	+	1.21132i	−1.18783	+	0.0641998i
$357$		0			0
$358$	10.5904	+	10.0334i	0.559718	+	0.530283i
$359$			3.80659i			0.200904i	0.994942	+	0.100452i	$0.0320289\pi$
$359$			3.80659i			0.200904i	−0.994942	+	0.100452i	$0.967971\pi$
$360$		0			0
$361$			55.1813i			2.90428i
$362$	−3.76532	+	3.97432i	−0.197901	+	0.208886i
$363$		0			0
$364$	16.9564	−	18.8941i	0.888757	−	0.990318i
$365$	17.7910	−	4.76709i	0.931224	−	0.249521i
$366$		0			0
$367$	−5.70033	+	3.29109i	−0.297555	+	0.171793i	−0.641344	−	0.767253i	$-0.721623\pi$
$367$	−5.70033	+	3.29109i	−0.297555	+	0.171793i	0.343789	+	0.939047i	$0.388289\pi$
$368$	−2.20349	−	0.972435i	−0.114865	−	0.0506917i
$369$		0			0
$370$	0.0151208	+	0.00819394i	0.000786095	+	0.000425983i
$371$	17.1475	+	4.59467i	0.890256	+	0.238543i
$372$		0			0
$373$	8.46055	−	2.26700i	0.438071	−	0.117381i	−0.0330416	−	0.999454i	$-0.510519\pi$
$373$	8.46055	−	2.26700i	0.438071	−	0.117381i	0.471112	+	0.882073i	$0.343853\pi$
$374$	−1.82252	+	7.61879i	−0.0942403	+	0.393958i
$375$		0			0
$376$	−5.81630	+	4.01848i	−0.299953	+	0.207237i
$377$	0.927667			0.0477773
$378$		0			0
$379$	−17.4765	+	17.4765i	−0.897706	+	0.897706i	−0.995233	−	0.0975266i	$-0.968907\pi$
$379$	−17.4765	+	17.4765i	−0.897706	+	0.897706i	0.0975266	+	0.995233i	$0.468907\pi$
$380$	−19.3537	+	38.1379i	−0.992826	+	1.95643i
$381$		0			0
$382$	7.19211	−	4.41543i	0.367980	−	0.225913i
$383$	−4.06922	+	7.04809i	−0.207927	+	0.360140i	−0.951061	−	0.309002i	$-0.900005\pi$
$383$	−4.06922	+	7.04809i	−0.207927	+	0.360140i	0.743134	+	0.669142i	$0.233338\pi$
$384$		0			0
$385$	−19.9526	−	34.5590i	−1.01688	−	1.76129i
$386$	−4.47161	−	2.42315i	−0.227599	−	0.123335i
$387$		0			0
$388$	7.09180	+	10.8814i	0.360031	+	0.552420i
$389$	−8.98924	−	2.40866i	−0.455772	−	0.122124i	0.0236267	−	0.999721i	$-0.492479\pi$
$389$	−8.98924	−	2.40866i	−0.455772	−	0.122124i	−0.479399	+	0.877597i	$0.659145\pi$
$390$		0			0
$391$	−0.400903	+	0.694385i	−0.0202745	+	0.0351165i
$392$	−20.2656	−	9.60522i	−1.02357	−	0.485137i
$393$		0			0
$394$	13.9434	+	13.2102i	0.702460	+	0.665519i
$395$	1.70201	+	1.70201i	0.0856376	+	0.0856376i
$396$		0			0
$397$	7.15374	−	7.15374i	0.359036	−	0.359036i	−0.504422	−	0.863458i	$-0.668294\pi$
$397$	7.15374	−	7.15374i	0.359036	−	0.359036i	0.863458	+	0.504422i	$0.168294\pi$
$398$	−0.452567	−	16.7591i	−0.0226851	−	0.840057i
$399$		0			0
$400$	−3.75842	+	2.74948i	−0.187921	+	0.137474i
$401$	3.93575	+	2.27231i	0.196542	+	0.113474i	0.595041	−	0.803695i	$-0.297136\pi$
$401$	3.93575	+	2.27231i	0.196542	+	0.113474i	−0.398500	+	0.917169i	$0.630469\pi$
$402$		0			0
$403$	5.74270	−	21.4320i	0.286064	−	1.06761i
$404$	−11.7202	−	2.47119i	−0.583104	−	0.122946i
$405$		0			0
$406$	−0.439434	−	1.47906i	−0.0218088	−	0.0734046i
$407$	0.0176457	−	0.0101878i	0.000874666	−	0.000504988i
$408$		0			0
$409$	−3.62043	−	2.09026i	−0.179019	−	0.103356i	0.407813	−	0.913066i	$-0.366292\pi$
$409$	−3.62043	−	2.09026i	−0.179019	−	0.103356i	−0.586832	+	0.809709i	$0.699625\pi$
$410$	−1.00364	+	4.19559i	−0.0495664	+	0.207205i
$411$		0			0
$412$	−10.9788	+	21.6345i	−0.540887	+	1.06586i
$413$	15.2794	+	15.2794i	0.751850	+	0.751850i
$414$		0			0
$415$			1.64324i			0.0806634i
$416$	−17.1403	+	7.18199i	−0.840372	+	0.352126i
$417$		0			0
$418$	26.5096	+	43.1804i	1.29663	+	2.11202i
$419$	1.68551	+	6.29040i	0.0823425	+	0.307306i	0.994798	−	0.101870i	$-0.0324827\pi$
$419$	1.68551	+	6.29040i	0.0823425	+	0.307306i	−0.912455	+	0.409177i	$0.865816\pi$
$420$		0			0
$421$	5.43340	−	20.2777i	0.264808	−	0.988275i	−0.697560	−	0.716526i	$-0.745731\pi$
$421$	5.43340	−	20.2777i	0.264808	−	0.988275i	0.962368	−	0.271749i	$-0.0876022\pi$
$422$	6.59509	+	22.1980i	0.321044	+	1.08058i
$423$		0			0
$424$	−9.90241	−	8.41553i	−0.480903	−	0.408694i
$425$	0.775124	+	1.34255i	0.0375990	+	0.0651234i
$426$		0			0
$427$	2.04267	+	7.62335i	0.0988517	+	0.368920i
$428$	7.97743	+	7.15931i	0.385603	+	0.346059i
$429$		0			0
$430$	2.04832	−	0.0553133i	0.0987786	−	0.00266745i
$431$	0.0435385			0.00209718			0.00104859	−	0.999999i	$-0.499666\pi$
$431$	0.0435385			0.00209718			0.00104859	+	0.999999i	$0.499666\pi$
$432$		0			0
$433$	2.44457			0.117479			0.0587393	−	0.998273i	$-0.481292\pi$
$433$	2.44457			0.117479			0.0587393	+	0.998273i	$0.481292\pi$
$434$	−36.8913	+	0.996224i	−1.77084	+	0.0478203i
$435$		0			0
$436$	12.1440	−	13.5317i	0.581592	−	0.648052i
$437$	1.34226	+	5.00937i	0.0642088	+	0.239631i
$438$		0			0
$439$	−8.44077	−	14.6199i	−0.402856	−	0.697767i	0.591213	−	0.806515i	$-0.298649\pi$
$439$	−8.44077	−	14.6199i	−0.402856	−	0.697767i	−0.994069	+	0.108748i	$0.965316\pi$
$440$	2.36338	+	29.1161i	0.112670	+	1.38806i
$441$		0			0
$442$	1.76197	+	5.93051i	0.0838085	+	0.282085i
$443$	1.95722	−	7.30446i	0.0929905	−	0.347045i	−0.903717	−	0.428131i	$-0.859172\pi$
$443$	1.95722	−	7.30446i	0.0929905	−	0.347045i	0.996707	+	0.0810858i	$0.0258388\pi$
$444$		0			0
$445$	7.21135	+	26.9131i	0.341851	+	1.27580i
$446$	13.5921	+	22.1396i	0.643605	+	1.04834i
$447$		0			0
$448$	19.5702	+	23.9262i	0.924606	+	1.13041i
$449$		−	1.51444i		−	0.0714709i	−0.999361	−	0.0357355i	$-0.988623\pi$
$449$		−	1.51444i		−	0.0714709i	0.999361	−	0.0357355i	$-0.0113774\pi$
$450$		0			0
$451$	3.61397	+	3.61397i	0.170175	+	0.170175i
$452$	−16.6769	−	8.46296i	−0.784414	−	0.398064i
$453$		0			0
$454$	−1.83256	+	7.66074i	−0.0860061	+	0.359536i
$455$	−27.2930	−	15.7576i	−1.27952	−	0.738730i
$456$		0			0
$457$	28.8273	−	16.6435i	1.34848	−	0.778548i	0.360450	−	0.932779i	$-0.382623\pi$
$457$	28.8273	−	16.6435i	1.34848	−	0.778548i	0.988035	+	0.154230i	$0.0492898\pi$
$458$	−10.7618	−	36.2225i	−0.502867	−	1.69257i
$459$		0			0
$460$	−0.616856	+	2.92560i	−0.0287611	+	0.136407i
$461$	−4.54777	+	16.9725i	−0.211811	+	0.790488i	0.775454	+	0.631404i	$0.217521\pi$
$461$	−4.54777	+	16.9725i	−0.211811	+	0.790488i	−0.987265	+	0.159084i	$0.949146\pi$
$462$		0			0
$463$	−9.07067	−	5.23695i	−0.421550	−	0.243382i	0.274190	−	0.961675i	$-0.411590\pi$
$463$	−9.07067	−	5.23695i	−0.421550	−	0.243382i	−0.695740	+	0.718294i	$0.744923\pi$
$464$	−0.173042	+	1.11616i	−0.00803326	+	0.0518165i
$465$		0			0
$466$	−0.641275	−	23.7472i	−0.0297065	−	1.10007i
$467$	2.14028	−	2.14028i	0.0990405	−	0.0990405i	−0.655850	−	0.754891i	$-0.727690\pi$
$467$	2.14028	−	2.14028i	0.0990405	−	0.0990405i	0.754891	+	0.655850i	$0.227690\pi$
$468$		0			0
$469$	−28.0143	−	28.0143i	−1.29358	−	1.29358i
$470$	6.37081	+	6.03578i	0.293863	+	0.278410i
$471$		0			0
$472$	−5.31671	−	14.8977i	−0.244722	−	0.685721i
$473$	1.21381	−	2.10237i	0.0558109	−	0.0966672i
$474$		0			0
$475$	9.68533	+	2.59518i	0.444393	+	0.119075i
$476$	8.62089	−	5.61854i	0.395138	−	0.257525i
$477$		0			0
$478$	19.3738	+	10.4986i	0.886137	+	0.480195i
$479$	−8.05687	−	13.9549i	−0.368128	−	0.637616i	0.621145	−	0.783696i	$-0.286668\pi$
$479$	−8.05687	−	13.9549i	−0.368128	−	0.637616i	−0.989273	+	0.146080i	$0.953334\pi$
$480$		0			0
$481$	0.00804581	−	0.0139357i	0.000366857	−	0.000635415i
$482$	17.4640	−	10.7216i	0.795462	−	0.488355i
$483$		0			0
$484$	11.2437	+	5.70578i	0.511075	+	0.259354i
$485$	11.4012	−	11.4012i	0.517700	−	0.517700i
$486$		0			0
$487$	−31.5803			−1.43104			−0.715520	−	0.698593i	$-0.753810\pi$
$487$	−31.5803			−1.43104			−0.715520	+	0.698593i	$0.753810\pi$
$488$	1.03891	−	5.68321i	0.0470290	−	0.257267i
$489$		0			0
$490$	−6.47702	+	27.0762i	−0.292602	+	1.22318i
$491$	−37.5248	+	10.0547i	−1.69347	+	0.453764i	−0.971282	−	0.237931i	$-0.923531\pi$
$491$	−37.5248	+	10.0547i	−1.69347	+	0.453764i	−0.722190	+	0.691695i	$0.756864\pi$
$492$		0			0
$493$	0.363200	+	0.0973191i	0.0163577	+	0.00438303i
$494$	35.1820	+	19.0651i	1.58291	+	0.857777i
$495$		0			0
$496$	24.7156	+	10.9074i	1.10977	+	0.489756i
$497$	26.2691	−	15.1665i	1.17833	−	0.680308i
$498$		0			0
$499$	18.4149	−	4.93425i	0.824362	−	0.220887i	0.178110	−	0.984011i	$-0.443002\pi$
$499$	18.4149	−	4.93425i	0.824362	−	0.220887i	0.646253	+	0.763123i	$0.276335\pi$
$500$	−14.1755	−	12.7217i	−0.633946	−	0.568933i
$501$		0			0
$502$	−27.2032	+	28.7132i	−1.21414	+	1.28153i
$503$		−	29.5143i		−	1.31598i	−0.753028	−	0.657988i	$-0.771408\pi$
$503$		−	29.5143i		−	1.31598i	0.753028	−	0.657988i	$-0.228592\pi$
$504$		0			0
$505$			14.8693i			0.661674i
$506$	2.57148	+	2.43625i	0.114316	+	0.108304i
$507$		0			0
$508$	1.13209	+	20.9460i	0.0502285	+	0.929331i
$509$	−3.05007	+	0.817265i	−0.135192	+	0.0362246i	−0.325781	−	0.945445i	$-0.605627\pi$
$509$	−3.05007	+	0.817265i	−0.135192	+	0.0362246i	0.190588	+	0.981670i	$0.438960\pi$
$510$		0			0
$511$	−24.8236	+	14.3319i	−1.09813	+	0.634007i
$512$	−5.44406	−	21.9627i	−0.240596	−	0.970625i
$513$		0			0
$514$	−13.4811	+	24.8775i	−0.594624	+	1.09730i
$515$	29.0909	+	7.79488i	1.28190	+	0.343484i
$516$		0			0
$517$	10.0430	−	2.69101i	0.441690	−	0.118351i
$518$	−0.0260303	−	0.00622681i	−0.00114371	−	0.000273590i
$519$		0			0
$520$	13.1137	+	18.9806i	0.575073	+	0.832355i
$521$	10.0508			0.440334			0.220167	−	0.975462i	$-0.429340\pi$
$521$	10.0508			0.440334			0.220167	+	0.975462i	$0.429340\pi$
$522$		0			0
$523$	10.1827	−	10.1827i	0.445258	−	0.445258i	−0.448516	−	0.893775i	$-0.648047\pi$
$523$	10.1827	−	10.1827i	0.445258	−	0.445258i	0.893775	+	0.448516i	$0.148047\pi$
$524$	11.6091	+	35.5312i	0.507144	+	1.55219i
$525$		0			0
$526$	−4.47143	−	7.28334i	−0.194964	−	0.317569i
$527$	4.49676	−	7.78861i	0.195882	−	0.339277i
$528$		0			0
$529$	−11.3187	−	19.6046i	−0.492118	−	0.852374i
$530$	−7.68606	+	14.1836i	−0.333861	+	0.616096i
$531$		0			0
$532$	13.7314	−	65.1249i	0.595334	−	2.82352i
$533$	3.89883	+	1.04469i	0.168877	+	0.0452505i
$534$		0			0
$535$	6.65317	−	11.5236i	0.287642	−	0.498210i
$536$	9.74803	+	27.3144i	0.421051	+	1.17980i
$537$		0			0
$538$	−22.5026	+	23.7516i	−0.970154	+	1.02401i
$539$	23.3228	+	23.3228i	1.00458	+	1.00458i
$540$		0			0
$541$	−2.24130	+	2.24130i	−0.0963612	+	0.0963612i	−0.753644	−	0.657283i	$-0.771706\pi$
$541$	−2.24130	+	2.24130i	−0.0963612	+	0.0963612i	0.657283	+	0.753644i	$0.271706\pi$
$542$	−18.0700	+	0.487966i	−0.776171	+	0.0209599i
$543$		0			0
$544$	−7.46420	+	1.01375i	−0.320025	+	0.0434641i
$545$	−19.5470	−	11.2854i	−0.837300	−	0.483415i
$546$		0			0
$547$	−8.53649	+	31.8586i	−0.364994	+	1.36218i	0.502435	+	0.864615i	$0.332437\pi$
$547$	−8.53649	+	31.8586i	−0.364994	+	1.36218i	−0.867429	+	0.497561i	$0.834229\pi$
$548$	12.3560	+	18.9586i	0.527820	+	0.809869i
$549$		0			0
$550$	6.56518	−	1.95054i	0.279940	−	0.0831712i
$551$	2.10621	−	1.21602i	0.0897277	−	0.0518043i
$552$		0			0
$553$	−3.24404	−	1.87295i	−0.137951	−	0.0796458i
$554$	−15.7307	−	3.76301i	−0.668335	−	0.159875i
$555$		0			0
$556$	−4.11979	−	12.6092i	−0.174718	−	0.534749i
$557$	−13.3242	−	13.3242i	−0.564566	−	0.564566i	0.366035	−	0.930601i	$-0.380715\pi$
$557$	−13.3242	−	13.3242i	−0.564566	−	0.564566i	−0.930601	+	0.366035i	$0.880715\pi$
$558$		0			0
$559$		−	1.91721i		−	0.0810894i
$560$	24.0505	−	29.8994i	1.01632	−	1.26348i
$561$		0			0
$562$	8.51094	−	5.22509i	0.359012	−	0.220407i
$563$	6.87376	+	25.6532i	0.289695	+	1.08115i	0.945340	+	0.326086i	$0.105730\pi$
$563$	6.87376	+	25.6532i	0.289695	+	1.08115i	−0.655646	+	0.755069i	$0.727603\pi$
$564$		0			0
$565$	−6.00865	+	22.4246i	−0.252786	+	0.943409i
$566$	−39.6155	+	11.7699i	−1.66516	+	0.494726i
$567$		0			0
$568$	−22.1318	+	1.79646i	−0.928631	+	0.0753777i
$569$	−15.0997	−	26.1535i	−0.633013	−	1.09641i	−0.986932	−	0.161135i	$-0.948484\pi$
$569$	−15.0997	−	26.1535i	−0.633013	−	1.09641i	0.353919	−	0.935276i	$-0.384849\pi$
$570$		0			0
$571$	−7.88159	−	29.4145i	−0.329834	−	1.23096i	−0.909362	−	0.416006i	$-0.863430\pi$
$571$	−7.88159	−	29.4145i	−0.329834	−	1.23096i	0.579528	−	0.814953i	$-0.303237\pi$
$572$	27.2924	−	1.47510i	1.14115	−	0.0616769i
$573$		0			0
$574$	−0.181229	−	6.71113i	−0.00756436	−	0.280117i
$575$	0.700996			0.0292336
$576$		0			0
$577$	25.2709			1.05204			0.526021	−	0.850472i	$-0.323683\pi$
$577$	25.2709			1.05204			0.526021	+	0.850472i	$0.323683\pi$
$578$	−0.581298	−	21.5261i	−0.0241788	−	0.895368i
$579$		0			0
$580$	1.40010	−	0.0756726i	0.0581360	−	0.00314213i
$581$	−0.661872	−	2.47014i	−0.0274591	−	0.102479i
$582$		0			0
$583$	9.55629	+	16.5520i	0.395781	+	0.685513i
$584$	20.9140	−	1.69761i	0.865429	−	0.0702475i
$585$		0			0
$586$	−33.7037	+	10.0135i	−1.39229	+	0.413653i
$587$	−3.42026	+	12.7646i	−0.141169	+	0.526851i	0.858727	+	0.512434i	$0.171256\pi$
$587$	−3.42026	+	12.7646i	−0.141169	+	0.526851i	−0.999896	+	0.0144172i	$0.995411\pi$
$588$		0			0
$589$	−15.0555	−	56.1879i	−0.620351	−	2.31518i
$590$	−16.7343	+	10.2736i	−0.688939	+	0.422958i
$591$		0			0
$592$	0.0152666	+	0.0122801i	0.000627452	+	0.000504711i
$593$			41.0718i			1.68662i	0.537429	+	0.843309i	$0.319396\pi$
$593$			41.0718i			1.68662i	−0.537429	+	0.843309i	$0.680604\pi$
$594$		0			0
$595$	−9.03266	−	9.03266i	−0.370303	−	0.370303i
$596$	−14.1129	−	43.1946i	−0.578088	−	1.76932i
$597$		0			0
$598$	2.72077	+	0.650846i	0.111260	+	0.0266151i
$599$	−28.2975	−	16.3376i	−1.15621	−	0.667536i	−0.205814	−	0.978591i	$-0.565984\pi$
$599$	−28.2975	−	16.3376i	−1.15621	−	0.667536i	−0.950392	+	0.311055i	$0.899318\pi$
$600$		0			0
$601$	6.48334	−	3.74316i	0.264461	−	0.152687i	−0.361907	−	0.932214i	$-0.617874\pi$
$601$	6.48334	−	3.74316i	0.264461	−	0.152687i	0.626368	+	0.779528i	$0.284541\pi$
$602$	−3.05678	+	0.908180i	−0.124585	+	0.0370147i
$603$		0			0
$604$	−16.6074	−	25.4818i	−0.675745	−	1.03684i
$605$	4.05107	−	15.1188i	0.164699	−	0.614667i
$606$		0			0
$607$	28.1639	+	16.2604i	1.14314	+	0.659991i	0.947206	−	0.320627i	$-0.103893\pi$
$607$	28.1639	+	16.2604i	1.14314	+	0.659991i	0.195932	+	0.980617i	$0.437227\pi$
$608$	−29.5016	+	38.7744i	−1.19645	+	1.57251i
$609$		0			0
$610$	−7.16937	+	0.193604i	−0.290279	+	0.00783879i
$611$	5.80624	−	5.80624i	0.234895	−	0.234895i
$612$		0			0
$613$	−8.73063	−	8.73063i	−0.352627	−	0.352627i	0.508459	−	0.861086i	$-0.330215\pi$
$613$	−8.73063	−	8.73063i	−0.352627	−	0.352627i	−0.861086	+	0.508459i	$0.830215\pi$
$614$	17.9830	−	18.9812i	0.725734	−	0.766017i
$615$		0			0
$616$	−15.2802	−	42.8159i	−0.615658	−	1.72510i
$617$	−16.0423	+	27.7861i	−0.645839	+	1.11863i	0.338268	+	0.941050i	$0.390159\pi$
$617$	−16.0423	+	27.7861i	−0.645839	+	1.11863i	−0.984107	+	0.177576i	$0.943174\pi$
$618$		0			0
$619$	0.225364	+	0.0603861i	0.00905814	+	0.00242712i	0.263345	−	0.964702i	$-0.415174\pi$
$619$	0.225364	+	0.0603861i	0.00905814	+	0.00242712i	−0.254287	+	0.967129i	$0.581841\pi$
$620$	6.91900	−	32.8152i	0.277874	−	1.31789i
$621$		0			0
$622$	19.4488	−	35.8902i	0.779827	−	1.43907i
$623$	−21.6804	−	37.5516i	−0.868608	−	1.50447i
$624$		0			0
$625$	−14.7328	+	25.5180i	−0.589312	+	1.02072i
$626$	−14.7588	−	24.0400i	−0.589879	−	0.960830i
$627$		0			0
$628$	−7.33773	−	22.4582i	−0.292807	−	0.896178i
$629$	0.00461205	−	0.00461205i	0.000183895	−	0.000183895i
$630$		0			0
$631$	43.7263			1.74071			0.870357	−	0.492421i	$-0.163888\pi$
$631$	43.7263			1.74071			0.870357	+	0.492421i	$0.163888\pi$
$632$	1.55869	+	2.25603i	0.0620013	+	0.0897400i
$633$		0			0
$634$	17.4432	+	4.17267i	0.692760	+	0.165718i
$635$	25.1529	−	6.73969i	0.998160	−	0.267456i
$636$		0			0
$637$	25.1611	+	6.74191i	0.996921	+	0.267124i
$638$	0.791452	−	1.46052i	0.0313339	−	0.0578225i
$639$		0			0
$640$	−25.2835	+	12.2377i	−0.999417	+	0.483739i
$641$	−13.8843	+	8.01611i	−0.548398	+	0.316617i	−0.748475	−	0.663163i	$-0.769214\pi$
$641$	−13.8843	+	8.01611i	−0.548398	+	0.316617i	0.200078	+	0.979780i	$0.435880\pi$
$642$		0			0
$643$	−14.8089	+	3.96803i	−0.584006	+	0.156484i	−0.538712	−	0.842490i	$-0.681089\pi$
$643$	−14.8089	+	3.96803i	−0.584006	+	0.156484i	−0.0452937	+	0.998974i	$0.514422\pi$
$644$	−0.251121	−	4.64627i	−0.00989557	−	0.183089i
$645$		0			0
$646$	11.7744	+	11.1552i	0.463257	+	0.438895i
$647$			25.9667i			1.02086i	0.859920	+	0.510428i	$0.170513\pi$
$647$			25.9667i			1.02086i	−0.859920	+	0.510428i	$0.829487\pi$
$648$		0			0
$649$			23.2639i			0.913188i
$650$	3.72001	−	3.92650i	0.145911	−	0.154010i
$651$		0			0
$652$	5.59157	+	5.01814i	0.218983	+	0.196526i
$653$	19.6002	−	5.25185i	0.767014	−	0.205521i	0.145962	−	0.989290i	$-0.453372\pi$
$653$	19.6002	−	5.25185i	0.767014	−	0.205521i	0.621052	+	0.783769i	$0.286706\pi$
$654$		0			0
$655$	40.1859	−	23.2013i	1.57019	−	0.906551i
$656$	−1.98423	+	4.49617i	−0.0774711	+	0.175546i
$657$		0			0
$658$	−12.0078	−	6.50700i	−0.468113	−	0.253669i
$659$	−20.5292	−	5.50079i	−0.799706	−	0.214281i	−0.164251	−	0.986419i	$-0.552521\pi$
$659$	−20.5292	−	5.50079i	−0.799706	−	0.214281i	−0.635455	+	0.772138i	$0.719187\pi$
$660$		0			0
$661$	−36.6676	+	9.82504i	−1.42620	+	0.382150i	−0.887680	−	0.460461i	$-0.847684\pi$
$661$	−36.6676	+	9.82504i	−1.42620	+	0.382150i	−0.538523	+	0.842611i	$0.681017\pi$
$662$	8.88054	−	37.1238i	0.345152	−	1.44286i
$663$		0			0
$664$	−0.336629	+	1.84149i	−0.0130637	+	0.0714637i
$665$	−82.6229			−3.20398
$666$		0			0
$667$	0.120227	−	0.120227i	0.00465520	−	0.00465520i
$668$	−20.4534	−	10.3794i	−0.791364	−	0.401591i
$669$		0			0
$670$	30.6818	−	18.8363i	1.18534	−	0.727712i
$671$	−4.24848	+	7.35858i	−0.164011	+	0.284075i
$672$		0			0
$673$	13.2270	+	22.9098i	0.509863	+	0.883108i	0.999935	+	0.0114260i	$0.00363709\pi$
$673$	13.2270	+	22.9098i	0.509863	+	0.883108i	−0.490072	+	0.871682i	$0.663030\pi$
$674$	2.97099	+	1.60997i	0.114438	+	0.0620139i
$675$		0			0
$676$	−3.69823	+	2.41027i	−0.142240	+	0.0927026i
$677$	38.2162	+	10.2400i	1.46877	+	0.393556i	0.902509	−	0.430671i	$-0.141723\pi$
$677$	38.2162	+	10.2400i	1.46877	+	0.393556i	0.566260	+	0.824226i	$0.308390\pi$
$678$		0			0
$679$	−12.5462	+	21.7306i	−0.481478	+	0.833944i
$680$	3.14306	+	8.80700i	0.120531	+	0.337733i
$681$		0			0
$682$	−28.8432	−	27.3263i	−1.10446	−	1.04638i
$683$	−8.25500	−	8.25500i	−0.315869	−	0.315869i	0.531309	−	0.847178i	$-0.321700\pi$
$683$	−8.25500	−	8.25500i	−0.315869	−	0.315869i	−0.847178	+	0.531309i	$0.821700\pi$
$684$		0			0
$685$	19.8641	−	19.8641i	0.758968	−	0.758968i
$686$	−0.137033	−	5.07448i	−0.00523193	−	0.193745i
$687$		0			0
$688$	2.30677	+	0.357626i	0.0879449	+	0.0136344i
$689$	13.0720	+	7.54710i	0.498002	+	0.287522i
$690$		0			0
$691$	2.28570	−	8.53034i	0.0869520	−	0.324509i	−0.908725	−	0.417396i	$-0.862943\pi$
$691$	2.28570	−	8.53034i	0.0869520	−	0.324509i	0.995677	+	0.0928867i	$0.0296094\pi$
$692$	−9.35680	+	44.3771i	−0.355692	+	1.68696i
$693$		0			0
$694$	−12.9195	−	43.4849i	−0.490418	−	1.65066i
$695$	−14.2610	+	8.23362i	−0.540952	+	0.312319i
$696$		0			0
$697$	1.41687	+	0.818033i	0.0536679	+	0.0309852i
$698$	−1.44585	+	6.04415i	−0.0547261	+	0.228775i
$699$		0			0
$700$	−8.02253	−	4.07117i	−0.303223	−	0.153876i
$701$	33.2403	+	33.2403i	1.25547	+	1.25547i	0.953233	+	0.302237i	$0.0977333\pi$
$701$	33.2403	+	33.2403i	1.25547	+	1.25547i	0.302237	+	0.953233i	$0.402267\pi$
$702$		0			0
$703$		−	0.0421870i		−	0.00159111i
$704$	−3.31614	+	33.1131i	−0.124982	+	1.24800i
$705$		0			0
$706$	−25.9071	−	42.1991i	−0.975028	−	1.58818i
$707$	−5.98913	−	22.3517i	−0.225244	−	0.840623i
$708$		0			0
$709$	2.25784	−	8.42638i	0.0847950	−	0.316459i	−0.910480	−	0.413553i	$-0.864288\pi$
$709$	2.25784	−	8.42638i	0.0847950	−	0.316459i	0.995275	+	0.0970932i	$0.0309545\pi$
$710$	7.85038	+	26.4231i	0.294619	+	0.991640i
$711$		0			0
$712$	2.56804	+	31.6374i	0.0962412	+	1.18566i
$713$	−2.03336	−	3.52188i	−0.0761499	−	0.131896i
$714$		0			0
$715$	−8.78170	−	32.7738i	−0.328417	−	1.22567i
$716$	13.7799	−	15.3546i	0.514981	−	0.573829i
$717$		0			0
$718$	5.38136	−	0.145320i	0.200831	−	0.00542329i
$719$	−28.3359			−1.05675			−0.528375	−	0.849011i	$-0.677199\pi$
$719$	−28.3359			−1.05675			−0.528375	+	0.849011i	$0.677199\pi$
$720$		0			0
$721$	−46.8696			−1.74551
$722$	78.0096	−	2.10660i	2.90322	−	0.0783993i
$723$		0			0
$724$	5.76224	+	5.17130i	0.214152	+	0.192190i
$725$	−0.0850833	−	0.317535i	−0.00315991	−	0.0117930i
$726$		0			0
$727$	−23.7175	−	41.0800i	−0.879635	−	1.52357i	−0.851742	−	0.523962i	$-0.824453\pi$
$727$	−23.7175	−	41.0800i	−0.879635	−	1.52357i	−0.0278935	−	0.999611i	$-0.508880\pi$
$728$	−27.3578	−	23.2500i	−1.01395	−	0.861701i
$729$		0			0
$730$	−7.41841	−	24.9691i	−0.274568	−	0.924149i
$731$	0.201130	−	0.750626i	0.00743905	−	0.0277629i
$732$		0			0
$733$	−10.5330	−	39.3098i	−0.389046	−	1.45194i	−0.831689	−	0.555241i	$-0.812626\pi$
$733$	−10.5330	−	39.3098i	−0.389046	−	1.45194i	0.442643	−	0.896698i	$-0.354041\pi$
$734$	4.87022	+	7.93291i	0.179763	+	0.292809i
$735$		0			0
$736$	−1.29061	+	3.15220i	−0.0475725	+	0.116192i
$737$		−	42.6537i		−	1.57117i
$738$		0			0
$739$	2.25483	+	2.25483i	0.0829451	+	0.0829451i	0.747362	−	0.664417i	$-0.231320\pi$
$739$	2.25483	+	2.25483i	0.0829451	+	0.0829451i	−0.664417	+	0.747362i	$0.731320\pi$
$740$	0.0110065	−	0.0216891i	0.000404607	−	0.000797308i
$741$		0			0
$742$	5.84085	−	24.4168i	0.214424	−	0.896371i
$743$	17.9150	+	10.3432i	0.657238	+	0.379456i	0.791224	−	0.611527i	$-0.209444\pi$
$743$	17.9150	+	10.3432i	0.657238	+	0.379456i	−0.133986	+	0.990983i	$0.542778\pi$
$744$		0			0
$745$	−48.8533	+	28.2054i	−1.78985	+	1.03337i
$746$	−3.52784	−	11.8741i	−0.129163	−	0.434742i
$747$		0			0
$748$	10.8402	+	2.28564i	0.396358	+	0.0835713i
$749$	−5.35960	+	20.0023i	−0.195836	+	0.730868i
$750$		0			0
$751$	6.17369	+	3.56438i	0.225281	+	0.130066i	0.608393	−	0.793636i	$-0.291814\pi$
$751$	6.17369	+	3.56438i	0.225281	+	0.130066i	−0.383112	+	0.923702i	$0.625148\pi$
$752$	5.90296	+	8.06909i	0.215259	+	0.294249i
$753$		0			0
$754$	−0.0354146	−	1.31144i	−0.00128972	−	0.0477599i
$755$	−26.6989	+	26.6989i	−0.971673	+	0.971673i
$756$		0			0
$757$	18.4928	+	18.4928i	0.672132	+	0.672132i	0.958207	−	0.286075i	$-0.0923507\pi$
$757$	18.4928	+	18.4928i	0.672132	+	0.672132i	−0.286075	+	0.958207i	$0.592351\pi$
$758$	25.3736	+	24.0393i	0.921612	+	0.873146i
$759$		0			0
$760$	54.6544	+	25.9044i	1.98252	+	0.939651i
$761$	−15.5559	+	26.9436i	−0.563900	+	0.976704i	0.433251	+	0.901273i	$0.357366\pi$
$761$	−15.5559	+	26.9436i	−0.563900	+	0.976704i	−0.997151	+	0.0754303i	$0.975967\pi$
$762$		0			0
$763$	33.9289	+	9.09123i	1.22831	+	0.329125i
$764$	−6.51664	−	9.99891i	−0.235764	−	0.361748i
$765$		0			0
$766$	10.1192	+	5.48358i	0.365622	+	0.198130i
$767$	9.18637	+	15.9113i	0.331700	+	0.574522i
$768$		0			0
$769$	−18.6655	+	32.3296i	−0.673094	+	1.16583i	0.303928	+	0.952695i	$0.401702\pi$
$769$	−18.6655	+	32.3296i	−0.673094	+	1.16583i	−0.977022	+	0.213138i	$0.931631\pi$
$770$	−48.0943	+	29.5263i	−1.73320	+	1.06405i
$771$		0			0
$772$	−3.25490	+	6.41401i	−0.117146	+	0.230845i
$773$	17.6571	−	17.6571i	0.635082	−	0.635082i	−0.314256	−	0.949338i	$-0.601755\pi$
$773$	17.6571	−	17.6571i	0.635082	−	0.635082i	0.949338	+	0.314256i	$0.101755\pi$
$774$		0			0
$775$	−7.86277			−0.282439
$776$	15.1123	−	10.4411i	0.542500	−	0.374813i
$777$		0			0
$778$	−3.06194	+	12.8000i	−0.109776	+	0.458903i
$779$	10.2215	−	2.73884i	0.366223	−	0.0981291i
$780$		0			0
$781$	31.5442	+	8.45223i	1.12874	+	0.302445i
$782$	0.996955	+	0.540247i	0.0356510	+	0.0193192i
$783$		0			0
$784$	−12.8052	+	29.0161i	−0.457329	+	1.03629i
$785$	−25.4003	+	14.6648i	−0.906574	+	0.523411i
$786$		0			0
$787$	−3.55437	+	0.952391i	−0.126700	+	0.0339491i	−0.321612	−	0.946872i	$-0.604225\pi$
$787$	−3.55437	+	0.952391i	−0.126700	+	0.0339491i	0.194912	+	0.980821i	$0.437558\pi$
$788$	18.1429	−	20.2161i	0.646314	−	0.720170i
$789$		0			0
$790$	2.34116	−	2.47111i	0.0832947	−	0.0879182i
$791$		−	36.1292i		−	1.28461i
$792$		0			0
$793$			6.71049i			0.238297i
$794$	−10.3863	−	9.84013i	−0.368597	−	0.349213i
$795$		0			0
$796$	−23.6750	+	1.27959i	−0.839138	+	0.0453537i
$797$	−14.1028	+	3.77883i	−0.499546	+	0.133853i	−0.499789	−	0.866147i	$-0.666589\pi$
$797$	−14.1028	+	3.77883i	−0.499546	+	0.133853i	0.000243208		1.00000i	$0.499923\pi$
$798$		0			0
$799$	2.88237	−	1.66414i	0.101971	−	0.0588730i
$800$	4.03042	+	5.20831i	0.142497	+	0.184142i
$801$		0			0
$802$	3.06210	−	5.65071i	0.108127	−	0.199533i
$803$	−29.8084	−	7.98715i	−1.05192	−	0.281860i
$804$		0			0
$805$	−5.57942	+	1.49500i	−0.196649	+	0.0526919i
$806$	−30.5177	−	7.30025i	−1.07494	−	0.257140i
$807$		0			0
$808$	−3.04608	+	16.6632i	−0.107161	+	0.586210i
$809$	39.7873			1.39885			0.699423	−	0.714708i	$-0.253440\pi$
$809$	39.7873			1.39885			0.699423	+	0.714708i	$0.253440\pi$
$810$		0			0
$811$	1.19344	−	1.19344i	0.0419073	−	0.0419073i	−0.685843	−	0.727750i	$-0.740566\pi$
$811$	1.19344	−	1.19344i	0.0419073	−	0.0419073i	0.727750	+	0.685843i	$0.240566\pi$
$812$	−2.07417	+	0.677692i	−0.0727892	+	0.0237823i
$813$		0			0
$814$	−0.0150761	−	0.0245568i	−0.000528416	−	0.000860715i
$815$	4.66337	−	8.07720i	0.163351	−	0.282932i
$816$		0			0
$817$	−2.51316	−	4.35291i	−0.0879242	−	0.152289i
$818$	−2.81678	+	5.19799i	−0.0984863	+	0.181743i
$819$		0			0
$820$	5.96961	+	1.25868i	0.208468	+	0.0439550i
$821$	−37.8783	−	10.1495i	−1.32196	−	0.354218i	−0.472249	−	0.881465i	$-0.656558\pi$
$821$	−37.8783	−	10.1495i	−1.32196	−	0.354218i	−0.849712	+	0.527247i	$0.823224\pi$
$822$		0			0
$823$	−15.1207	+	26.1898i	−0.527075	+	0.912921i	0.472427	+	0.881370i	$0.343378\pi$
$823$	−15.1207	+	26.1898i	−0.527075	+	0.912921i	−0.999502	+	0.0315509i	$0.989955\pi$
$824$	31.0038	+	14.6948i	1.08007	+	0.511918i
$825$		0			0
$826$	21.0172	−	22.1838i	0.731281	−	0.771872i
$827$	30.5628	+	30.5628i	1.06277	+	1.06277i	0.997893	+	0.0648812i	$0.0206668\pi$
$827$	30.5628	+	30.5628i	1.06277	+	1.06277i	0.0648812	+	0.997893i	$0.479333\pi$
$828$		0			0
$829$	−30.0006	+	30.0006i	−1.04196	+	1.04196i	−0.0428841	+	0.999080i	$0.513655\pi$
$829$	−30.0006	+	30.0006i	−1.04196	+	1.04196i	−0.999080	+	0.0428841i	$0.986345\pi$
$830$	2.32304	−	0.0627321i	0.0806340	−	0.00217746i
$831$		0			0
$832$	10.8075	+	23.9570i	0.374683	+	0.830560i
$833$	9.14380	+	5.27918i	0.316814	+	0.182913i
$834$		0			0
$835$	−7.36931	+	27.5026i	−0.255026	+	0.951768i
$836$	60.0320	−	39.1250i	2.07625	−	1.35317i
$837$		0			0
$838$	8.82839	−	2.62294i	0.304972	−	0.0906080i
$839$	9.52850	−	5.50128i	0.328960	−	0.189925i	−0.326419	−	0.945225i	$-0.605842\pi$
$839$	9.52850	−	5.50128i	0.328960	−	0.189925i	0.655379	+	0.755300i	$0.272509\pi$
$840$		0			0
$841$	25.0457	+	14.4601i	0.863644	+	0.498625i
$842$	−28.8740	−	6.90706i	−0.995064	−	0.238033i
$843$		0			0
$844$	31.1295	−	10.1709i	1.07152	−	0.350097i
$845$	3.87487	+	3.87487i	0.133300	+	0.133300i
$846$		0			0
$847$			24.3585i			0.836969i
$848$	−11.5190	+	14.3203i	−0.395563	+	0.491761i
$849$		0			0
$850$	1.86837	−	1.14704i	0.0640847	−	0.0393433i
$851$	−0.000763344	−	0.00284884i	−2.61671e−5	−	9.76569e-5i
$852$		0			0
$853$	−2.31959	+	8.65682i	−0.0794212	+	0.296404i	−0.994199	−	0.107553i	$-0.965699\pi$
$853$	−2.31959	+	8.65682i	−0.0794212	+	0.296404i	0.914778	+	0.403956i	$0.132365\pi$
$854$	10.6991	−	3.17875i	0.366117	−	0.108774i
$855$		0			0
$856$	9.81656	−	11.5510i	0.335523	−	0.394805i
$857$	7.80951	+	13.5265i	0.266768	+	0.462055i	0.968025	−	0.250853i	$-0.0807110\pi$
$857$	7.80951	+	13.5265i	0.266768	+	0.462055i	−0.701257	+	0.712908i	$0.747378\pi$
$858$		0			0
$859$	6.98915	+	26.0839i	0.238467	+	0.889970i	0.976555	+	0.215266i	$0.0690619\pi$
$859$	6.98915	+	26.0839i	0.238467	+	0.889970i	−0.738089	+	0.674704i	$0.764271\pi$
$860$	−0.156393	−	2.89359i	−0.00533295	−	0.0986706i
$861$		0			0
$862$	−0.00166212	−	0.0615503i	−5.66121e−5	−	0.00209641i
$863$	56.2955			1.91632			0.958161	−	0.286231i	$-0.0924026\pi$
$863$	56.2955			1.91632			0.958161	+	0.286231i	$0.0924026\pi$
$864$		0			0
$865$	56.3004			1.91427
$866$	−0.0933238	−	3.45589i	−0.00317127	−	0.117436i
$867$		0			0
$868$	2.81672	+	52.1152i	0.0956057	+	1.76890i
$869$	−1.04379	−	3.89548i	−0.0354082	−	0.132145i
$870$		0			0
$871$	−16.8429	−	29.1728i	−0.570701	−	0.988482i
$872$	−19.5934	−	16.6514i	−0.663515	−	0.563886i
$873$		0			0
$874$	7.03049	−	2.08878i	0.237810	−	0.0706541i
$875$	9.52373	−	35.5430i	0.321961	−	1.20157i
$876$		0			0
$877$	1.37947	+	5.14826i	0.0465815	+	0.173845i	0.985298	−	0.170847i	$-0.0546503\pi$
$877$	1.37947	+	5.14826i	0.0465815	+	0.173845i	−0.938716	+	0.344691i	$0.887984\pi$
$878$	−20.3458	+	12.4908i	−0.686638	+	0.421545i
$879$		0			0
$880$	41.0712	−	4.45264i	1.38451	−	0.150098i
$881$			25.7797i			0.868540i	0.900783	+	0.434270i	$0.142994\pi$
$881$			25.7797i			0.868540i	−0.900783	+	0.434270i	$0.857006\pi$
$882$		0			0
$883$	33.2893	+	33.2893i	1.12028	+	1.12028i	0.991700	+	0.128576i	$0.0410407\pi$
$883$	33.2893	+	33.2893i	1.12028	+	1.12028i	0.128576	+	0.991700i	$0.458959\pi$
$884$	8.31668	−	2.71730i	0.279720	−	0.0913927i
$885$		0			0
$886$	−10.4010	−	2.48807i	−0.349429	−	0.0835883i
$887$	−44.7029	−	25.8093i	−1.50098	−	0.866590i	−0.999999	−	0.00112995i	$-0.999640\pi$
$887$	−44.7029	−	25.8093i	−1.50098	−	0.866590i	−0.500978	−	0.865460i	$-0.667026\pi$
$888$		0			0
$889$	−35.0955	+	20.2624i	−1.17707	+	0.679579i
$890$	37.7717	−	11.2221i	1.26611	−	0.376166i
$891$		0			0
$892$	30.7799	−	20.0603i	1.03059	−	0.671670i
$893$	5.57167	−	20.7938i	0.186449	−	0.695837i
$894$		0			0
$895$	−22.1802	−	12.8057i	−0.741402	−	0.428049i
$896$	33.0773	−	28.5798i	1.10504	−	0.954784i
$897$		0			0
$898$	−2.14096	+	0.0578152i	−0.0714449	+	0.00192932i
$899$	−1.34853	+	1.34853i	−0.0449761	+	0.0449761i
$900$		0			0
$901$	4.32618	+	4.32618i	0.144126	+	0.144126i
$902$	4.97110	−	5.24703i	0.165520	−	0.174707i
$903$		0			0
$904$	−11.3274	+	23.8991i	−0.376744	+	0.794874i
$905$	4.80571	−	8.32373i	0.159747	−	0.276690i
$906$		0			0
$907$	−6.40970	−	1.71747i	−0.212831	−	0.0570278i	0.150828	−	0.988560i	$-0.451806\pi$
$907$	−6.40970	−	1.71747i	−0.212831	−	0.0570278i	−0.363659	+	0.931532i	$0.618473\pi$
$908$	10.8999	+	2.29822i	0.361727	+	0.0762692i
$909$		0			0
$910$	−21.2346	+	39.1857i	−0.703921	+	1.29899i
$911$	0.858615	+	1.48716i	0.0284472	+	0.0492719i	0.879899	−	0.475162i	$-0.157610\pi$
$911$	0.858615	+	1.48716i	0.0284472	+	0.0492719i	−0.851451	+	0.524434i	$0.824277\pi$
$912$		0			0
$913$	1.37660	−	2.38435i	0.0455590	−	0.0789104i
$914$	−24.6293	−	40.1177i	−0.814666	−	1.32698i
$915$		0			0
$916$	−50.7968	+	16.5968i	−1.67837	+	0.548374i
$917$	−51.0629	+	51.0629i	−1.68625	+	1.68625i
$918$		0			0
$919$	−36.4439			−1.20217			−0.601087	−	0.799184i	$-0.705266\pi$
$919$	−36.4439			−1.20217			−0.601087	+	0.799184i	$0.705266\pi$
$920$	4.15946	+	0.760361i	0.137133	+	0.0250683i
$921$		0			0
$922$	24.1676	+	5.78123i	0.795917	+	0.190395i
$923$	24.9121	−	6.67517i	0.819991	−	0.219716i
$924$		0			0
$925$	−0.00550807	−	0.00147588i	−0.000181104	−	4.85267e-5i
$926$	−7.05719	+	13.0231i	−0.231914	+	0.427966i
$927$		0			0
$928$	1.58452	+	0.202018i	0.0520145	+	0.00663158i
$929$	−11.6134	+	6.70498i	−0.381022	+	0.219983i	−0.678263	−	0.734819i	$-0.737267\pi$
$929$	−11.6134	+	6.70498i	−0.381022	+	0.219983i	0.297241	+	0.954803i	$0.403934\pi$
$930$		0			0
$931$	65.9644	−	17.6751i	2.16190	−	0.579278i
$932$	−33.5468	+	1.81314i	−1.09886	+	0.0593913i
$933$		0			0
$934$	−3.10742	−	2.94401i	−0.101678	−	0.0963308i
$935$		−	13.7528i		−	0.449766i
$936$		0			0
$937$		−	7.84860i		−	0.256403i	−0.991748	−	0.128201i	$-0.959080\pi$
$937$		−	7.84860i		−	0.256403i	0.991748	−	0.128201i	$-0.0409204\pi$
$938$	−38.5343	+	40.6733i	−1.25819	+	1.32803i
$939$		0			0
$940$	8.28955	−	9.23682i	0.270375	−	0.301272i
$941$	−17.7200	+	4.74807i	−0.577657	+	0.154783i	−0.535806	−	0.844341i	$-0.679992\pi$
$941$	−17.7200	+	4.74807i	−0.577657	+	0.154783i	−0.0418508	+	0.999124i	$0.513325\pi$
$942$		0			0
$943$	0.640687	−	0.369901i	0.0208636	−	0.0120456i
$944$	−20.8579	+	8.08496i	−0.678865	+	0.263143i
$945$		0			0
$946$	−3.01846	−	1.63570i	−0.0981386	−	0.0531810i
$947$	−14.5681	−	3.90352i	−0.473401	−	0.126847i	0.0142275	−	0.999899i	$-0.495471\pi$
$947$	−14.5681	−	3.90352i	−0.473401	−	0.126847i	−0.487628	+	0.873051i	$0.662138\pi$
$948$		0			0
$949$	−23.5413	+	6.30787i	−0.764183	+	0.204762i
$950$	3.29905	−	13.7912i	0.107035	−	0.447446i
$951$		0			0
$952$	−8.27203	−	11.9728i	−0.268098	−	0.388042i
$953$	−57.0251			−1.84722			−0.923612	−	0.383329i	$-0.874778\pi$
$953$	−57.0251			−1.84722			−0.923612	+	0.383329i	$0.874778\pi$
$954$		0			0
$955$	−10.4765	+	10.4765i	−0.339012	+	0.339012i
$956$	14.1023	−	27.7895i	0.456099	−	0.898777i
$957$		0			0
$958$	−19.4204	+	11.9227i	−0.627446	+	0.385206i
$959$	−21.8591	+	37.8610i	−0.705866	+	1.22260i
$960$		0			0
$961$	7.30730	+	12.6566i	0.235720	+	0.408278i
$962$	−0.0200081	−	0.0108423i	−0.000645087	−	0.000349571i
$963$		0			0
$964$	−15.8238	−	24.2795i	−0.509650	−	0.781990i
$965$	8.62461	+	2.31096i	0.277636	+	0.0743924i
$966$		0			0
$967$	−12.8293	+	22.2210i	−0.412562	+	0.714578i	−0.995169	−	0.0981760i	$-0.968699\pi$
$967$	−12.8293	+	22.2210i	−0.412562	+	0.714578i	0.582607	+	0.812754i	$0.302033\pi$
$968$	7.63702	−	16.1130i	0.245463	−	0.517890i
$969$		0			0
$970$	−16.5530	−	15.6825i	−0.531486	−	0.503536i
$971$	28.3253	+	28.3253i	0.909001	+	0.909001i	0.996192	−	0.0871907i	$-0.0277889\pi$
$971$	28.3253	+	28.3253i	0.909001	+	0.909001i	−0.0871907	+	0.996192i	$0.527789\pi$
$972$		0			0
$973$	18.1210	−	18.1210i	0.580934	−	0.580934i
$974$	1.20561	+	44.6450i	0.0386301	+	1.43052i
$975$		0			0
$976$	−8.07401	−	1.25174i	−0.258443	−	0.0400671i
$977$	22.8095	+	13.1691i	0.729742	+	0.421317i	0.818328	−	0.574752i	$-0.194901\pi$
$977$	22.8095	+	13.1691i	0.729742	+	0.421317i	−0.0885859	+	0.996069i	$0.528235\pi$
$978$		0			0
$979$	12.0825	−	45.0924i	0.386157	−	1.44116i
$980$	38.5249	+	8.12289i	1.23063	+	0.259476i
$981$		0			0
$982$	15.6469	+	52.6649i	0.499313	+	1.68061i
$983$	0.336455	−	0.194253i	0.0107313	−	0.00619570i	−0.494625	−	0.869107i	$-0.664695\pi$
$983$	0.336455	−	0.194253i	0.0107313	−	0.00619570i	0.505356	+	0.862911i	$0.331361\pi$
$984$		0			0
$985$	−29.2028	−	16.8602i	−0.930479	−	0.537212i
$986$	0.123714	−	0.517170i	0.00393987	−	0.0164701i
$987$		0			0
$988$	25.6091	−	50.4646i	0.814735	−	1.60549i
$989$	−0.248473	−	0.248473i	−0.00790099	−	0.00790099i
$990$		0			0
$991$			3.59863i			0.114314i	0.998365	+	0.0571571i	$0.0182036\pi$
$991$			3.59863i			0.114314i	−0.998365	+	0.0571571i	$0.981796\pi$
$992$	14.4762	−	35.3569i	0.459620	−	1.12258i
$993$		0			0
$994$	−22.4436	−	36.5575i	−0.711869	−	1.15953i
$995$	7.61777	+	28.4299i	0.241499	+	0.901288i
$996$		0			0
$997$	−9.05536	+	33.7951i	−0.286786	+	1.07030i	0.660738	+	0.750616i	$0.270243\pi$
$997$	−9.05536	+	33.7951i	−0.286786	+	1.07030i	−0.947524	+	0.319684i	$0.896423\pi$
$998$	−7.67854	−	25.8447i	−0.243060	−	0.818099i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.395.11		88
3.2	odd	2		144.2.u.a.59.12	yes	88
4.3	odd	2		1728.2.z.a.719.17		88
9.2	odd	6	inner	432.2.v.a.251.20		88
9.7	even	3		144.2.u.a.11.3	✓	88
12.11	even	2		576.2.y.a.527.19		88
16.3	odd	4	inner	432.2.v.a.179.20		88
16.13	even	4		1728.2.z.a.1583.17		88
36.7	odd	6		576.2.y.a.335.14		88
36.11	even	6		1728.2.z.a.143.17		88
48.29	odd	4		576.2.y.a.239.14		88
48.35	even	4		144.2.u.a.131.3	yes	88
144.29	odd	12		1728.2.z.a.1007.17		88
144.61	even	12		576.2.y.a.47.19		88
144.83	even	12	inner	432.2.v.a.35.11		88
144.115	odd	12		144.2.u.a.83.12	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.3	✓	88	9.7	even	3
144.2.u.a.59.12	yes	88	3.2	odd	2
144.2.u.a.83.12	yes	88	144.115	odd	12
144.2.u.a.131.3	yes	88	48.35	even	4
432.2.v.a.35.11		88	144.83	even	12	inner
432.2.v.a.179.20		88	16.3	odd	4	inner
432.2.v.a.251.20		88	9.2	odd	6	inner
432.2.v.a.395.11		88	1.1	even	1	trivial
576.2.y.a.47.19		88	144.61	even	12
576.2.y.a.239.14		88	48.29	odd	4
576.2.y.a.335.14		88	36.7	odd	6
576.2.y.a.527.19		88	12.11	even	2
1728.2.z.a.143.17		88	36.11	even	6
1728.2.z.a.719.17		88	4.3	odd	2
1728.2.z.a.1007.17		88	144.29	odd	12
1728.2.z.a.1583.17		88	16.13	even	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0381759 - 1.41370i) q^{2} +(-1.99709 + 0.107938i) q^{4} +(0.642590 + 2.39818i) q^{5} +(-1.93190 - 3.34616i) q^{7} +(0.228833 + 2.81916i) q^{8} +O(q^{10})\)	\(q+(-0.0381759 - 1.41370i) q^{2} +(-1.99709 + 0.107938i) q^{4} +(0.642590 + 2.39818i) q^{5} +(-1.93190 - 3.34616i) q^{7} +(0.228833 + 2.81916i) q^{8} +(3.36577 - 0.999982i) q^{10} +(1.07665 - 4.01810i) q^{11} +(-0.850284 - 3.17330i) q^{13} +(-4.65670 + 2.85887i) q^{14} +(3.97670 - 0.431125i) q^{16} -1.33161i q^{17} +(-6.09021 - 6.09021i) q^{19} +(-1.54216 - 4.72001i) q^{20} +(-5.72148 - 1.36866i) q^{22} +(-0.521462 - 0.301066i) q^{23} +(-1.00822 + 0.582095i) q^{25} +(-4.45363 + 1.32319i) q^{26} +(4.21936 + 6.47403i) q^{28} +(-0.0730837 + 0.272752i) q^{29} +(5.84901 + 3.37693i) q^{31} +(-0.761294 - 5.60539i) q^{32} +(-1.88250 + 0.0508355i) q^{34} +(6.78326 - 6.78326i) q^{35} +(0.00346351 + 0.00346351i) q^{37} +(-8.37722 + 8.84221i) q^{38} +(-6.61380 + 2.36034i) q^{40} +(-0.614318 + 1.06403i) q^{41} +(0.563698 + 0.151042i) q^{43} +(-1.71645 + 8.14070i) q^{44} +(-0.405710 + 0.748684i) q^{46} +(1.24972 + 2.16458i) q^{47} +(-3.96450 + 6.86672i) q^{49} +(0.861396 + 1.40309i) q^{50} +(2.04061 + 6.24558i) q^{52} +(-3.24883 + 3.24883i) q^{53} +10.3280 q^{55} +(8.99125 - 6.21205i) q^{56} +(0.388379 + 0.0929058i) q^{58} +(-5.40194 + 1.44745i) q^{59} +(-1.97301 - 0.528668i) q^{61} +(4.55067 - 8.39766i) q^{62} +(-7.89527 + 1.29023i) q^{64} +(7.06377 - 4.07827i) q^{65} +(9.90429 - 2.65385i) q^{67} +(0.143732 + 2.65934i) q^{68} +(-9.84844 - 9.33053i) q^{70} +7.85052i q^{71} -7.41855i q^{73} +(0.00476414 - 0.00502859i) q^{74} +(12.8200 + 11.5053i) q^{76} +(-15.5252 + 4.15995i) q^{77} +(0.839597 - 0.484742i) q^{79} +(3.58930 + 9.25980i) q^{80} +(1.52767 + 0.827840i) q^{82} +(0.639302 + 0.171300i) q^{83} +(3.19344 - 0.855680i) q^{85} +(0.192009 - 0.802665i) q^{86} +(11.5740 + 2.11576i) q^{88} +11.2223 q^{89} +(-8.97570 + 8.97570i) q^{91} +(1.07390 + 0.544969i) q^{92} +(3.01235 - 1.84936i) q^{94} +(10.6919 - 18.5189i) q^{95} +(-3.24710 - 5.62414i) q^{97} +(9.85882 + 5.34247i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

L-functions

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