LMFDB - Embedded newform 325.2.s.c.32.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(32,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("325.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.9
Character	$\chi$	$=$	325.32
Dual form			325.2.s.c.193.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14665 - 1.98606i) q^{2} +(-0.483980 - 1.80624i) q^{3} +(-1.62962 - 2.82258i) q^{4} +(-4.14225 - 1.10991i) q^{6} +(2.78443 - 1.60759i) q^{7} -2.88781 q^{8} +(-0.430177 + 0.248363i) q^{9} +O(q^{10})$	\(q+(1.14665 - 1.98606i) q^{2} +(-0.483980 - 1.80624i) q^{3} +(-1.62962 - 2.82258i) q^{4} +(-4.14225 - 1.10991i) q^{6} +(2.78443 - 1.60759i) q^{7} -2.88781 q^{8} +(-0.430177 + 0.248363i) q^{9} +(-3.45476 + 0.925701i) q^{11} +(-4.30955 + 4.30955i) q^{12} +(-1.87639 + 3.07882i) q^{13} -7.37338i q^{14} +(-0.0520747 + 0.0901960i) q^{16} +(5.80109 + 1.55440i) q^{17} +1.13914i q^{18} +(-2.03669 + 7.60104i) q^{19} +(-4.25130 - 4.25130i) q^{21} +(-2.12291 + 7.92281i) q^{22} +(1.10778 - 0.296828i) q^{23} +(1.39764 + 5.21607i) q^{24} +(3.96315 + 7.25696i) q^{26} +(-3.30997 - 3.30997i) q^{27} +(-9.07511 - 5.23952i) q^{28} +(-0.877436 - 0.506588i) q^{29} +(4.47451 - 4.47451i) q^{31} +(-2.76839 - 4.79499i) q^{32} +(3.34407 + 5.79210i) q^{33} +(9.73895 - 9.73895i) q^{34} +(1.40205 + 0.809474i) q^{36} +(-0.645511 - 0.372686i) q^{37} +(12.7607 + 12.7607i) q^{38} +(6.46922 + 1.89912i) q^{39} +(1.65312 + 6.16954i) q^{41} +(-13.3181 + 3.56857i) q^{42} +(0.335632 - 1.25260i) q^{43} +(8.24281 + 8.24281i) q^{44} +(0.680717 - 2.54047i) q^{46} -8.22199i q^{47} +(0.188118 + 0.0504062i) q^{48} +(1.66870 - 2.89027i) q^{49} -11.2304i q^{51} +(11.7480 + 0.278965i) q^{52} +(3.01886 - 3.01886i) q^{53} +(-10.3692 + 2.77841i) q^{54} +(-8.04090 + 4.64242i) q^{56} +14.7150 q^{57} +(-2.01223 + 1.16176i) q^{58} +(-6.45324 - 1.72914i) q^{59} +(0.928497 + 1.60820i) q^{61} +(-3.75593 - 14.0173i) q^{62} +(-0.798532 + 1.38310i) q^{63} -12.9058 q^{64} +15.3379 q^{66} +(-4.17633 + 7.23362i) q^{67} +(-5.06615 - 18.9071i) q^{68} +(-1.07228 - 1.85725i) q^{69} +(-9.01343 - 2.41514i) q^{71} +(1.24227 - 0.717225i) q^{72} +7.93972 q^{73} +(-1.48035 + 0.854682i) q^{74} +(24.7736 - 6.63806i) q^{76} +(-8.13139 + 8.13139i) q^{77} +(11.1897 - 10.6706i) q^{78} +10.1869i q^{79} +(-5.12172 + 8.87108i) q^{81} +(14.1486 + 3.79111i) q^{82} -9.01936i q^{83} +(-5.07164 + 18.9276i) q^{84} +(-2.10288 - 2.10288i) q^{86} +(-0.490356 + 1.83003i) q^{87} +(9.97670 - 2.67325i) q^{88} +(-0.176147 - 0.657390i) q^{89} +(-0.275194 + 11.5892i) q^{91} +(-2.64308 - 2.64308i) q^{92} +(-10.2476 - 5.91645i) q^{93} +(-16.3294 - 9.42776i) q^{94} +(-7.32104 + 7.32104i) q^{96} +(6.80414 + 11.7851i) q^{97} +(-3.82682 - 6.62825i) q^{98} +(1.25625 - 1.25625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9}+O(q^{10}) $ 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9	$ 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46} + 28 q^{49} - 68 q^{54} + 72 q^{56} - 72 q^{59} + 144 q^{64} + 24 q^{66} - 80 q^{69} - 52 q^{71} + 168 q^{74} + 8 q^{76} - 20 q^{81} - 248 q^{84} - 168 q^{86} + 60 q^{89} - 100 q^{91} - 156 q^{94} - 36 q^{96} + 208 q^{99}+O(q^{100}) $ 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	1.14665	−	1.98606i	0.810805	−	1.40436i	−0.101497	−	0.994836i	$-0.532363\pi$
$2$	1.14665	−	1.98606i	0.810805	−	1.40436i	0.912301	−	0.409519i	$-0.134304\pi$
$3$	−0.483980	−	1.80624i	−0.279426	−	1.04283i	−0.952817	−	0.303545i	$-0.901830\pi$
$3$	−0.483980	−	1.80624i	−0.279426	−	1.04283i	0.673391	−	0.739286i	$-0.264837\pi$
$4$	−1.62962	−	2.82258i	−0.814809	−	1.41129i
$5$		0			0
$5$		0			0
$6$	−4.14225	−	1.10991i	−1.69107	−	0.453120i
$7$	2.78443	−	1.60759i	1.05242	−	0.607612i	0.129091	−	0.991633i	$-0.458794\pi$
$7$	2.78443	−	1.60759i	1.05242	−	0.607612i	0.923325	+	0.384021i	$0.125461\pi$
$8$	−2.88781			−1.02100
$9$	−0.430177	+	0.248363i	−0.143392	+	0.0827877i
$10$		0			0
$11$	−3.45476	+	0.925701i	−1.04165	+	0.279109i	−0.738797	−	0.673928i	$-0.764606\pi$
$11$	−3.45476	+	0.925701i	−1.04165	+	0.279109i	−0.302853	+	0.953037i	$0.597939\pi$
$12$	−4.30955	+	4.30955i	−1.24406	+	1.24406i
$13$	−1.87639	+	3.07882i	−0.520418	+	0.853912i
$13$	−1.87639	+	3.07882i	−0.520418	+	0.853912i
$14$		−	7.37338i		−	1.97062i
$15$		0			0
$16$	−0.0520747	+	0.0901960i	−0.0130187	+	0.0225490i
$17$	5.80109	+	1.55440i	1.40697	+	0.376997i	0.880843	−	0.473409i	$-0.156977\pi$
$17$	5.80109	+	1.55440i	1.40697	+	0.376997i	0.526128	+	0.850405i	$0.323643\pi$
$18$			1.13914i			0.268499i
$19$	−2.03669	+	7.60104i	−0.467249	+	1.74380i	0.182075	+	0.983285i	$0.441719\pi$
$19$	−2.03669	+	7.60104i	−0.467249	+	1.74380i	−0.649324	+	0.760512i	$0.724948\pi$
$20$		0			0
$21$	−4.25130	−	4.25130i	−0.927709	−	0.927709i
$22$	−2.12291	+	7.92281i	−0.452606	+	1.68915i
$23$	1.10778	−	0.296828i	0.230988	−	0.0618930i	−0.141468	−	0.989943i	$-0.545182\pi$
$23$	1.10778	−	0.296828i	0.230988	−	0.0618930i	0.372456	+	0.928050i	$0.378516\pi$
$24$	1.39764	+	5.21607i	0.285292	+	1.06473i
$25$		0			0
$26$	3.96315	+	7.25696i	0.777238	+	1.42321i
$27$	−3.30997	−	3.30997i	−0.637004	−	0.637004i
$28$	−9.07511	−	5.23952i	−1.71503	−	0.990176i
$29$	−0.877436	−	0.506588i	−0.162936	−	0.0940710i	0.416315	−	0.909221i	$-0.363321\pi$
$29$	−0.877436	−	0.506588i	−0.162936	−	0.0940710i	−0.579251	+	0.815150i	$0.696655\pi$
$30$		0			0
$31$	4.47451	−	4.47451i	0.803645	−	0.803645i	−0.180018	−	0.983663i	$-0.557616\pi$
$31$	4.47451	−	4.47451i	0.803645	−	0.803645i	0.983663	+	0.180018i	$0.0576156\pi$
$32$	−2.76839	−	4.79499i	−0.489386	−	0.847642i
$33$	3.34407	+	5.79210i	0.582128	+	1.00827i
$34$	9.73895	−	9.73895i	1.67022	−	1.67022i
$35$		0			0
$36$	1.40205	+	0.809474i	0.233675	+	0.134912i
$37$	−0.645511	−	0.372686i	−0.106121	−	0.0612692i	0.446000	−	0.895033i	$-0.352848\pi$
$37$	−0.645511	−	0.372686i	−0.106121	−	0.0612692i	−0.552121	+	0.833764i	$0.686181\pi$
$38$	12.7607	+	12.7607i	2.07006	+	2.07006i
$39$	6.46922	+	1.89912i	1.03590	+	0.304103i
$40$		0			0
$41$	1.65312	+	6.16954i	0.258175	+	0.963521i	0.966297	+	0.257431i	$0.0828759\pi$
$41$	1.65312	+	6.16954i	0.258175	+	0.963521i	−0.708122	+	0.706090i	$0.750457\pi$
$42$	−13.3181	+	3.56857i	−2.05502	+	0.550642i
$43$	0.335632	−	1.25260i	0.0511834	−	0.191019i	−0.935601	−	0.353060i	$-0.885141\pi$
$43$	0.335632	−	1.25260i	0.0511834	−	0.191019i	0.986784	+	0.162041i	$0.0518077\pi$
$44$	8.24281	+	8.24281i	1.24265	+	1.24265i
$45$		0			0
$46$	0.680717	−	2.54047i	0.100366	−	0.374572i
$47$		−	8.22199i		−	1.19930i	−0.800262	−	0.599650i	$-0.795306\pi$
$47$		−	8.22199i		−	1.19930i	0.800262	−	0.599650i	$-0.204694\pi$
$48$	0.188118	+	0.0504062i	0.0271526	+	0.00727551i
$49$	1.66870	−	2.89027i	0.238385	−	0.412895i
$50$		0			0
$51$		−	11.2304i		−	1.57258i
$52$	11.7480	+	0.278965i	1.62916	+	0.0386854i
$53$	3.01886	−	3.01886i	0.414672	−	0.414672i	−0.468690	−	0.883363i	$-0.655274\pi$
$53$	3.01886	−	3.01886i	0.414672	−	0.414672i	0.883363	+	0.468690i	$0.155274\pi$
$54$	−10.3692	+	2.77841i	−1.41107	+	0.378094i
$55$		0			0
$56$	−8.04090	+	4.64242i	−1.07451	+	0.620369i
$57$	14.7150			1.94905
$58$	−2.01223	+	1.16176i	−0.264218	+	0.152546i
$59$	−6.45324	−	1.72914i	−0.840141	−	0.225115i	−0.187008	−	0.982358i	$-0.559879\pi$
$59$	−6.45324	−	1.72914i	−0.840141	−	0.225115i	−0.653133	+	0.757243i	$0.726546\pi$
$60$		0			0
$61$	0.928497	+	1.60820i	0.118882	+	0.205909i	0.919325	−	0.393500i	$-0.128736\pi$
$61$	0.928497	+	1.60820i	0.118882	+	0.205909i	−0.800443	+	0.599409i	$0.795402\pi$
$62$	−3.75593	−	14.0173i	−0.477004	−	1.78020i
$63$	−0.798532	+	1.38310i	−0.100606	+	0.174254i
$64$	−12.9058			−1.61322
$65$		0			0
$66$	15.3379			1.88797
$67$	−4.17633	+	7.23362i	−0.510220	+	0.883727i	0.489710	+	0.871885i	$0.337103\pi$
$67$	−4.17633	+	7.23362i	−0.510220	+	0.883727i	−0.999930	+	0.0118416i	$0.996231\pi$
$68$	−5.06615	−	18.9071i	−0.614361	−	2.29283i
$69$	−1.07228	−	1.85725i	−0.129088	−	0.223587i
$70$		0			0
$71$	−9.01343	−	2.41514i	−1.06970	−	0.286625i	−0.319329	−	0.947644i	$-0.603457\pi$
$71$	−9.01343	−	2.41514i	−1.06970	−	0.286625i	−0.750369	+	0.661019i	$0.770124\pi$
$72$	1.24227	−	0.717225i	0.146403	−	0.0845258i
$73$	7.93972			0.929274			0.464637	−	0.885501i	$-0.346185\pi$
$73$	7.93972			0.929274			0.464637	+	0.885501i	$0.346185\pi$
$74$	−1.48035	+	0.854682i	−0.172088	+	0.0993548i
$75$		0			0
$76$	24.7736	−	6.63806i	2.84172	−	0.761438i
$77$	−8.13139	+	8.13139i	−0.926658	+	0.926658i
$78$	11.1897	−	10.6706i	1.26698	−	1.20821i
$79$			10.1869i			1.14611i	0.819517	+	0.573056i	$0.194242\pi$
$79$			10.1869i			1.14611i	−0.819517	+	0.573056i	$0.805758\pi$
$80$		0			0
$81$	−5.12172	+	8.87108i	−0.569080	+	0.985676i
$82$	14.1486	+	3.79111i	1.56245	+	0.418658i
$83$		−	9.01936i		−	0.990003i	−0.868892	−	0.495002i	$-0.835167\pi$
$83$		−	9.01936i		−	0.990003i	0.868892	−	0.495002i	$-0.164833\pi$
$84$	−5.07164	+	18.9276i	−0.553361	+	2.06517i
$85$		0			0
$86$	−2.10288	−	2.10288i	−0.226759	−	0.226759i
$87$	−0.490356	+	1.83003i	−0.0525717	+	0.196200i
$88$	9.97670	−	2.67325i	1.06352	−	0.284969i
$89$	−0.176147	−	0.657390i	−0.0186716	−	0.0696832i	0.955961	−	0.293492i	$-0.0948175\pi$
$89$	−0.176147	−	0.657390i	−0.0186716	−	0.0696832i	−0.974633	+	0.223809i	$0.928151\pi$
$90$		0			0
$91$	−0.275194	+	11.5892i	−0.0288481	+	1.21488i
$92$	−2.64308	−	2.64308i	−0.275560	−	0.275560i
$93$	−10.2476	−	5.91645i	−1.06263	−	0.613507i
$94$	−16.3294	−	9.42776i	−1.68424	−	0.972399i
$95$		0			0
$96$	−7.32104	+	7.32104i	−0.747200	+	0.747200i
$97$	6.80414	+	11.7851i	0.690856	+	1.19660i	0.971558	+	0.236803i	$0.0760996\pi$
$97$	6.80414	+	11.7851i	0.690856	+	1.19660i	−0.280702	+	0.959795i	$0.590567\pi$
$98$	−3.82682	−	6.62825i	−0.386568	−	0.669555i
$99$	1.25625	−	1.25625i	0.126258	−	0.126258i
$100$		0			0
$101$	7.78812	+	4.49648i	0.774947	+	0.447416i	0.834637	−	0.550801i	$-0.185678\pi$
$101$	7.78812	+	4.49648i	0.774947	+	0.447416i	−0.0596893	+	0.998217i	$0.519011\pi$
$102$	−22.3043	−	12.8774i	−2.20845	−	1.27505i
$103$	1.73771	+	1.73771i	0.171222	+	0.171222i	0.787516	−	0.616294i	$-0.211367\pi$
$103$	1.73771	+	1.73771i	0.171222	+	0.171222i	−0.616294	+	0.787516i	$0.711367\pi$
$104$	5.41867	−	8.89106i	0.531344	−	0.871840i
$105$		0			0
$106$	−2.53405	−	9.45721i	−0.246129	−	0.918566i
$107$	9.50358	−	2.54648i	0.918745	−	0.246177i	0.231696	−	0.972788i	$-0.425572\pi$
$107$	9.50358	−	2.54648i	0.918745	−	0.246177i	0.687049	+	0.726611i	$0.258906\pi$
$108$	−3.94867	+	14.7367i	−0.379961	+	1.41804i
$109$	6.16709	+	6.16709i	0.590700	+	0.590700i	0.937820	−	0.347121i	$-0.112841\pi$
$109$	6.16709	+	6.16709i	0.590700	+	0.590700i	−0.347121	+	0.937820i	$0.612841\pi$
$110$		0			0
$111$	−0.360745	+	1.34632i	−0.0342404	+	0.127787i
$112$			0.334859i			0.0316412i
$113$	−14.6563	−	3.92715i	−1.37875	−	0.369435i	−0.508084	−	0.861307i	$-0.669646\pi$
$113$	−14.6563	−	3.92715i	−1.37875	−	0.369435i	−0.870668	+	0.491872i	$0.836313\pi$
$114$	16.8730	−	29.2248i	1.58030	−	2.73715i
$115$		0			0
$116$			3.30218i			0.306600i
$117$	0.0425158	−	1.79047i	0.00393058	−	0.165529i
$118$	−10.8338	+	10.8338i	−0.997332	+	0.997332i
$119$	18.6516	−	4.99767i	1.70979	−	0.458136i
$120$		0			0
$121$	1.55218	−	0.896149i	0.141107	−	0.0814681i
$122$	4.25865			0.385560
$123$	10.3436	−	5.97187i	0.932649	−	0.538465i
$124$	−19.9214	−	5.33792i	−1.78900	−	0.479360i
$125$		0			0
$126$	1.83128	+	3.17186i	0.163143	+	0.282572i
$127$	3.13461	+	11.6985i	0.278151	+	1.03807i	0.953700	+	0.300759i	$0.0972401\pi$
$127$	3.13461	+	11.6985i	0.278151	+	1.03807i	−0.675549	+	0.737315i	$0.736093\pi$
$128$	−9.26167	+	16.0417i	−0.818624	+	1.41790i
$129$	−2.42492			−0.213503
$130$		0			0
$131$	0.0696124			0.00608206			0.00304103	−	0.999995i	$-0.499032\pi$
$131$	0.0696124			0.00608206			0.00304103	+	0.999995i	$0.499032\pi$
$132$	10.8991	−	18.8778i	0.948646	−	1.64310i
$133$	6.54833	+	24.4387i	0.567812	+	2.11910i
$134$	9.57759	+	16.5889i	0.827378	+	1.43306i
$135$		0			0
$136$	−16.7524	−	4.48880i	−1.43651	−	0.384912i
$137$	−9.14097	+	5.27754i	−0.780966	+	0.450891i	−0.836773	−	0.547551i	$-0.815560\pi$
$137$	−9.14097	+	5.27754i	−0.780966	+	0.450891i	0.0558064	+	0.998442i	$0.482227\pi$
$138$	−4.91814			−0.418660
$139$	8.01918	−	4.62988i	0.680178	−	0.392701i	−0.119744	−	0.992805i	$-0.538207\pi$
$139$	8.01918	−	4.62988i	0.680178	−	0.392701i	0.799922	+	0.600104i	$0.204874\pi$
$140$		0			0
$141$	−14.8509	+	3.97928i	−1.25067	+	0.335116i
$142$	−15.1319	+	15.1319i	−1.26984	+	1.26984i
$143$	3.63242	−	12.3736i	0.303758	−	1.03473i
$144$		−	0.0517337i		−	0.00431114i
$145$		0			0
$146$	9.10409	−	15.7687i	0.753460	−	1.30503i
$147$	−6.02812	−	1.61523i	−0.497191	−	0.133222i
$148$			2.42934i			0.199691i
$149$	−3.85291	+	14.3792i	−0.315642	+	1.17799i	0.607748	+	0.794130i	$0.292073\pi$
$149$	−3.85291	+	14.3792i	−0.315642	+	1.17799i	−0.923390	+	0.383863i	$0.874593\pi$
$150$		0			0
$151$	10.3382	+	10.3382i	0.841308	+	0.841308i	0.989029	−	0.147721i	$-0.0471937\pi$
$151$	10.3382	+	10.3382i	0.841308	+	0.841308i	−0.147721	+	0.989029i	$0.547194\pi$
$152$	5.88158	−	21.9503i	0.477059	−	1.78041i
$153$	−2.88155	+	0.772110i	−0.232960	+	0.0624214i
$154$	6.82555	+	25.4733i	0.550018	+	2.05270i
$155$		0			0
$156$	−5.18193	−	21.3547i	−0.414887	−	1.70975i
$157$	−15.9216	−	15.9216i	−1.27068	−	1.27068i	−0.945733	−	0.324946i	$-0.894654\pi$
$157$	−15.9216	−	15.9216i	−1.27068	−	1.27068i	−0.324946	−	0.945733i	$-0.605346\pi$
$158$	20.2317	+	11.6808i	1.60955	+	0.929272i
$159$	−6.91384	−	3.99171i	−0.548303	−	0.316563i
$160$		0			0
$161$	2.60735	−	2.60735i	0.205488	−	0.205488i
$162$	11.7457	+	20.3441i	0.922826	+	1.59838i
$163$	−4.34865	−	7.53208i	−0.340612	−	0.589958i	0.643934	−	0.765081i	$-0.277301\pi$
$163$	−4.34865	−	7.53208i	−0.340612	−	0.589958i	−0.984547	+	0.175123i	$0.943968\pi$
$164$	14.7201	−	14.7201i	1.14944	−	1.14944i
$165$		0			0
$166$	−17.9130	−	10.3421i	−1.39032	−	0.802699i
$167$	−2.89467	−	1.67124i	−0.223996	−	0.129324i	0.383803	−	0.923415i	$-0.374614\pi$
$167$	−2.89467	−	1.67124i	−0.223996	−	0.129324i	−0.607799	+	0.794091i	$0.707947\pi$
$168$	12.2769	+	12.2769i	0.947186	+	0.947186i
$169$	−5.95830	−	11.5542i	−0.458331	−	0.888782i
$170$		0			0
$171$	−1.01168	−	3.77563i	−0.0773649	−	0.288730i
$172$	−4.08251	+	1.09390i	−0.311288	+	0.0834094i
$173$	−1.24898	+	4.66127i	−0.0949585	+	0.354390i	−0.997013	−	0.0772319i	$-0.975392\pi$
$173$	−1.24898	+	4.66127i	−0.0949585	+	0.354390i	0.902055	+	0.431622i	$0.142058\pi$
$174$	3.07229	+	3.07229i	0.232910	+	0.232910i
$175$		0			0
$176$	0.0964112	−	0.359811i	0.00726727	−	0.0271218i
$177$			12.4930i			0.939028i
$178$	−1.50760	−	0.403959i	−0.112999	−	0.0302780i
$179$	−1.57907	+	2.73504i	−0.118025	+	0.204426i	−0.918985	−	0.394292i	$-0.870990\pi$
$179$	−1.57907	+	2.73504i	−0.118025	+	0.204426i	0.800960	+	0.598718i	$0.204323\pi$
$180$		0			0
$181$			1.80661i			0.134284i	0.997743	+	0.0671422i	$0.0213881\pi$
$181$			1.80661i			0.134284i	−0.997743	+	0.0671422i	$0.978612\pi$
$182$	22.7013	+	13.8354i	1.68274	+	1.02555i
$183$	2.45542	−	2.45542i	0.181510	−	0.181510i
$184$	−3.19905	+	0.857184i	−0.235837	+	0.0631924i
$185$		0			0
$186$	−23.5008	+	13.5682i	−1.72316	+	0.994869i
$187$	−21.4803			−1.57079
$188$	−23.2072	+	13.3987i	−1.69256	+	0.977201i
$189$	−14.5375	−	3.89530i	−1.05744	−	0.283341i
$190$		0			0
$191$	−11.0167	−	19.0815i	−0.797142	−	1.38069i	−0.921470	−	0.388449i	$-0.873011\pi$
$191$	−11.0167	−	19.0815i	−0.797142	−	1.38069i	0.124328	−	0.992241i	$-0.460322\pi$
$192$	6.24614	+	23.3109i	0.450776	+	1.68232i
$193$	−8.32256	+	14.4151i	−0.599071	+	1.03762i	0.393887	+	0.919159i	$0.371130\pi$
$193$	−8.32256	+	14.4151i	−0.599071	+	1.03762i	−0.992958	+	0.118463i	$0.962203\pi$
$194$	31.2079			2.24060
$195$		0			0
$196$	−10.8773			−0.776953
$197$	1.40602	−	2.43530i	0.100175	−	0.173508i	−0.811582	−	0.584239i	$-0.801393\pi$
$197$	1.40602	−	2.43530i	0.100175	−	0.173508i	0.911757	+	0.410731i	$0.134726\pi$
$198$	−1.05451	−	3.93547i	−0.0749404	−	0.279682i
$199$	9.27945	+	16.0725i	0.657803	+	1.13935i	0.981183	+	0.193079i	$0.0618473\pi$
$199$	9.27945	+	16.0725i	0.657803	+	1.13935i	−0.323380	+	0.946269i	$0.604819\pi$
$200$		0			0
$201$	15.0869	+	4.04252i	1.06415	+	0.285137i
$202$	17.8605	−	10.3118i	1.25666	−	0.725534i
$203$	−3.25754			−0.228635
$204$	−31.6988	+	18.3013i	−2.21936	+	1.28135i
$205$		0			0
$206$	5.44375	−	1.45865i	0.379284	−	0.101629i
$207$	−0.402820	+	0.402820i	−0.0279979	+	0.0279979i
$208$	−0.179985	−	0.329572i	−0.0124797	−	0.0228517i
$209$		−	28.1451i		−	1.94684i
$210$		0			0
$211$	10.1084	−	17.5083i	0.695892	−	1.20532i	−0.273987	−	0.961733i	$-0.588343\pi$
$211$	10.1084	−	17.5083i	0.695892	−	1.20532i	0.969879	−	0.243587i	$-0.0783241\pi$
$212$	−13.4406	−	3.60139i	−0.923102	−	0.247345i
$213$			17.4493i			1.19560i
$214$	5.83984	−	21.7946i	0.399203	−	1.48985i
$215$		0			0
$216$	9.55857	+	9.55857i	0.650378	+	0.650378i
$217$	5.26577	−	19.6521i	0.357464	−	1.33407i
$218$	19.3197	−	5.17670i	1.30849	−	0.350610i
$219$	−3.84266	−	14.3410i	−0.259663	−	0.969075i
$220$		0			0
$221$	−15.6708	+	14.9439i	−1.05413	+	1.00523i
$222$	2.26022	+	2.26022i	0.151696	+	0.151696i
$223$	−17.6466	−	10.1883i	−1.18170	−	0.682257i	−0.225296	−	0.974290i	$-0.572335\pi$
$223$	−17.6466	−	10.1883i	−1.18170	−	0.682257i	−0.956408	+	0.292033i	$0.905668\pi$
$224$	−15.4168	−	8.90087i	−1.03008	−	0.594714i
$225$		0			0
$226$	−24.6053	+	24.6053i	−1.63672	+	1.63672i
$227$	3.40059	+	5.88999i	0.225705	+	0.390932i	0.956531	−	0.291632i	$-0.0941981\pi$
$227$	3.40059	+	5.88999i	0.225705	+	0.390932i	−0.730826	+	0.682564i	$0.760865\pi$
$228$	−23.9798	−	41.5342i	−1.58810	−	2.75067i
$229$	−6.74680	+	6.74680i	−0.445841	+	0.445841i	−0.893969	−	0.448128i	$-0.852091\pi$
$229$	−6.74680	+	6.74680i	−0.445841	+	0.445841i	0.448128	+	0.893969i	$0.352091\pi$
$230$		0			0
$231$	18.6226	+	10.7518i	1.22528	+	0.707416i
$232$	2.53387	+	1.46293i	0.166357	+	0.0960460i
$233$	−15.0352	−	15.0352i	−0.984989	−	0.984989i	0.0148998	−	0.999889i	$-0.495257\pi$
$233$	−15.0352	−	15.0352i	−0.984989	−	0.984989i	−0.999889	+	0.0148998i	$0.995257\pi$
$234$	−3.50722	−	2.13748i	−0.229274	−	0.139731i
$235$		0			0
$236$	5.63568	+	21.0326i	0.366852	+	1.36911i
$237$	18.3999	−	4.93023i	1.19520	−	0.320253i
$238$	11.4612	−	42.7737i	0.742917	−	2.77260i
$239$	−8.18783	−	8.18783i	−0.529627	−	0.529627i	0.390834	−	0.920461i	$-0.372187\pi$
$239$	−8.18783	−	8.18783i	−0.529627	−	0.529627i	−0.920461	+	0.390834i	$0.872187\pi$
$240$		0			0
$241$	−4.74605	+	17.7125i	−0.305720	+	1.14096i	0.626604	+	0.779338i	$0.284444\pi$
$241$	−4.74605	+	17.7125i	−0.305720	+	1.14096i	−0.932324	+	0.361624i	$0.882222\pi$
$242$		−	4.11028i		−	0.264219i
$243$	4.93756	+	1.32302i	0.316745	+	0.0848715i
$244$	3.02619	−	5.24152i	0.193732	−	0.335554i
$245$		0			0
$246$		−	27.3906i		−	1.74636i
$247$	−19.5806	−	20.5331i	−1.24588	−	1.30649i
$248$	−12.9215	+	12.9215i	−0.820518	+	0.820518i
$249$	−16.2911	+	4.36518i	−1.03241	+	0.276632i
$250$		0			0
$251$	22.6574	−	13.0812i	1.43012	−	0.825681i	0.432992	−	0.901398i	$-0.357458\pi$
$251$	22.6574	−	13.0812i	1.43012	−	0.825681i	0.997129	+	0.0757168i	$0.0241245\pi$
$252$	5.20521			0.327897
$253$	−3.55234	+	2.05094i	−0.223333	+	0.128942i
$254$	26.8282	+	7.18860i	1.68335	+	0.451053i
$255$		0			0
$256$	8.33402	+	14.4350i	0.520877	+	0.902185i
$257$	−2.14065	−	7.98901i	−0.133530	−	0.498341i	0.866470	−	0.499230i	$-0.166384\pi$
$257$	−2.14065	−	7.98901i	−0.133530	−	0.498341i	−1.00000		0.000888947i	$0.999717\pi$
$258$	−2.78054	+	4.81604i	−0.173109	+	0.299833i
$259$	−2.39651			−0.148912
$260$		0			0
$261$	0.503271			0.0311517
$262$	0.0798211	−	0.138254i	0.00493136	−	0.00854137i
$263$	−3.42140	−	12.7688i	−0.210972	−	0.787360i	−0.987546	−	0.157333i	$-0.949710\pi$
$263$	−3.42140	−	12.7688i	−0.210972	−	0.787360i	0.776573	−	0.630027i	$-0.216956\pi$
$264$	−9.65703	−	16.7265i	−0.594349	−	1.02944i
$265$		0			0
$266$	56.0453	+	15.0173i	3.43636	+	0.920770i
$267$	−1.10215	+	0.636327i	−0.0674505	+	0.0389426i
$268$	27.2233			1.66293
$269$	4.88179	−	2.81850i	0.297648	−	0.171847i	−0.343738	−	0.939066i	$-0.611693\pi$
$269$	4.88179	−	2.81850i	0.297648	−	0.171847i	0.641386	+	0.767218i	$0.278360\pi$
$270$		0			0
$271$	−7.32435	+	1.96255i	−0.444922	+	0.119217i	−0.474323	−	0.880351i	$-0.657307\pi$
$271$	−7.32435	+	1.96255i	−0.444922	+	0.119217i	0.0294001	+	0.999568i	$0.490640\pi$
$272$	−0.442291	+	0.442291i	−0.0268178	+	0.0268178i
$273$	21.0661	−	5.11189i	1.27498	−	0.309386i
$274$			24.2060i			1.46234i
$275$		0			0
$276$	−3.49483	+	6.05322i	−0.210364	+	0.364361i
$277$	−11.2688	−	3.01947i	−0.677078	−	0.181422i	−0.0961367	−	0.995368i	$-0.530649\pi$
$277$	−11.2688	−	3.01947i	−0.677078	−	0.181422i	−0.580941	+	0.813946i	$0.697315\pi$
$278$		−	21.2354i		−	1.27362i
$279$	−0.813530	+	3.03613i	−0.0487048	+	0.181769i
$280$		0			0
$281$	−9.46111	−	9.46111i	−0.564402	−	0.564402i	0.366153	−	0.930555i	$-0.380675\pi$
$281$	−9.46111	−	9.46111i	−0.564402	−	0.564402i	−0.930555	+	0.366153i	$0.880675\pi$
$282$	−9.12569	+	34.0575i	−0.543427	+	2.02810i
$283$	3.87586	−	1.03853i	0.230396	−	0.0617344i	−0.141774	−	0.989899i	$-0.545281\pi$
$283$	3.87586	−	1.03853i	0.230396	−	0.0617344i	0.372170	+	0.928165i	$0.378614\pi$
$284$	7.87152	+	29.3769i	0.467089	+	1.74320i
$285$		0			0
$286$	−20.4095	−	21.4024i	−1.20684	−	1.26555i
$287$	14.5211	+	14.5211i	0.857154	+	0.857154i
$288$	2.38180	+	1.37513i	0.140349	+	0.0810303i
$289$	16.5141	+	9.53440i	0.971415	+	0.560847i
$290$		0			0
$291$	17.9937	−	17.9937i	1.05481	−	1.05481i
$292$	−12.9387	−	22.4105i	−0.757181	−	1.31148i
$293$	12.3375	+	21.3692i	0.720766	+	1.24840i	0.960693	+	0.277613i	$0.0895432\pi$
$293$	12.3375	+	21.3692i	0.720766	+	1.24840i	−0.239927	+	0.970791i	$0.577123\pi$
$294$	−10.1201	+	10.1201i	−0.590215	+	0.590215i
$295$		0			0
$296$	1.86411	+	1.07625i	0.108349	+	0.0625556i
$297$	14.4992	+	8.37112i	0.841329	+	0.485742i
$298$	24.1401	+	24.1401i	1.39840	+	1.39840i
$299$	−1.16474	+	3.96762i	−0.0673589	+	0.229453i
$300$		0			0
$301$	−1.07912	−	4.02732i	−0.0621993	−	0.232131i
$302$	32.3865	−	8.67793i	1.86363	−	0.499359i
$303$	4.35240	−	16.2434i	0.250039	−	0.933159i
$304$	−0.579523	−	0.579523i	−0.0332379	−	0.0332379i
$305$		0			0
$306$	−1.77068	+	6.60827i	−0.101223	+	0.377770i
$307$			7.41296i			0.423080i	0.977369	+	0.211540i	$0.0678478\pi$
$307$			7.41296i			0.423080i	−0.977369	+	0.211540i	$0.932152\pi$
$308$	36.2026	+	9.70045i	2.06283	+	0.552734i
$309$	2.29770	−	3.97974i	0.130712	−	0.226399i
$310$		0			0
$311$			1.67111i			0.0947601i	0.998877	+	0.0473800i	$0.0150872\pi$
$311$			1.67111i			0.0947601i	−0.998877	+	0.0473800i	$0.984913\pi$
$312$	−18.6819	−	5.48430i	−1.05765	−	0.310487i
$313$	15.8540	−	15.8540i	0.896123	−	0.896123i	−0.0989679	−	0.995091i	$-0.531554\pi$
$313$	15.8540	−	15.8540i	0.896123	−	0.896123i	0.995091	+	0.0989679i	$0.0315541\pi$
$314$	−49.8776	+	13.3647i	−2.81476	+	0.754212i
$315$		0			0
$316$	28.7532	−	16.6007i	1.61750	−	0.933862i
$317$	−1.50512			−0.0845357			−0.0422679	−	0.999106i	$-0.513458\pi$
$317$	−1.50512			−0.0845357			−0.0422679	+	0.999106i	$0.513458\pi$
$318$	−15.8555	+	9.15420i	−0.889134	+	0.513342i
$319$	3.50028	+	0.937897i	0.195978	+	0.0525122i
$320$		0			0
$321$	−9.19907	−	15.9333i	−0.513442	−	0.889308i
$322$	−2.18863	−	8.16807i	−0.121968	−	0.455189i
$323$	−23.6301	+	40.9285i	−1.31481	+	2.27732i
$324$	33.3858			1.85477
$325$		0			0
$326$	−19.9455			−1.10468
$327$	8.15447	−	14.1240i	0.450943	−	0.781057i
$328$	−4.77391	−	17.8165i	−0.263595	−	0.983750i
$329$	−13.2176	−	22.8936i	−0.728710	−	1.26216i
$330$		0			0
$331$	2.29629	+	0.615289i	0.126215	+	0.0338193i	0.321374	−	0.946952i	$-0.395855\pi$
$331$	2.29629	+	0.615289i	0.126215	+	0.0338193i	−0.195158	+	0.980772i	$0.562522\pi$
$332$	−25.4579	+	14.6981i	−1.39718	+	0.806663i
$333$	0.370246			0.0202894
$334$	−6.63834	+	3.83265i	−0.363234	+	0.209713i
$335$		0			0
$336$	0.604835	−	0.162065i	0.0329965	−	0.00884137i
$337$	−3.02028	+	3.02028i	−0.164525	+	0.164525i	−0.784568	−	0.620043i	$-0.787115\pi$
$337$	−3.02028	+	3.02028i	−0.164525	+	0.164525i	0.620043	+	0.784568i	$0.287115\pi$
$338$	−29.7793	−	1.41506i	−1.61978	−	0.0769689i
$339$			28.3735i			1.54104i
$340$		0			0
$341$	−11.3163	+	19.6004i	−0.612812	+	1.06142i
$342$	−8.65867	−	2.32008i	−0.468207	−	0.125456i
$343$			11.7760i			0.635842i
$344$	−0.969242	+	3.61726i	−0.0522580	+	0.195030i
$345$		0			0
$346$	7.82541	+	7.82541i	0.420697	+	0.420697i
$347$	0.952998	−	3.55664i	0.0511596	−	0.190930i	−0.935617	−	0.353017i	$-0.885156\pi$
$347$	0.952998	−	3.55664i	0.0511596	−	0.190930i	0.986777	+	0.162087i	$0.0518224\pi$
$348$	5.96452	−	1.59819i	0.319732	−	0.0856718i
$349$	−2.60923	−	9.73777i	−0.139669	−	0.521251i	−0.999935	−	0.0114057i	$-0.996369\pi$
$349$	−2.60923	−	9.73777i	−0.139669	−	0.521251i	0.860266	−	0.509845i	$-0.170297\pi$
$350$		0			0
$351$	16.4016	−	3.98001i	0.875454	−	0.212437i
$352$	14.0028	+	14.0028i	0.746354	+	0.746354i
$353$	23.4823	+	13.5575i	1.24984	+	0.721593i	0.971077	−	0.238768i	$-0.0767435\pi$
$353$	23.4823	+	13.5575i	1.24984	+	0.721593i	0.278759	+	0.960361i	$0.410077\pi$
$354$	24.8117	+	14.3251i	1.31873	+	0.761368i
$355$		0			0
$356$	−1.56849	+	1.56849i	−0.0831296	+	0.0831296i
$357$	−18.0539	−	31.2703i	−0.955516	−	1.65500i
$358$	3.62129	+	6.27226i	0.191391	+	0.331499i
$359$	0.894231	−	0.894231i	0.0471957	−	0.0471957i	−0.683115	−	0.730311i	$-0.739375\pi$
$359$	0.894231	−	0.894231i	0.0471957	−	0.0471957i	0.730311	+	0.683115i	$0.239375\pi$
$360$		0			0
$361$	−37.1731	−	21.4619i	−1.95648	−	1.12957i
$362$	3.58804	+	2.07155i	0.188583	+	0.108879i
$363$	−2.36988	−	2.36988i	−0.124386	−	0.124386i
$364$	33.1600	−	18.1093i	1.73806	−	0.949184i
$365$		0			0
$366$	−2.06110	−	7.69212i	−0.107735	−	0.402074i
$367$	12.5755	−	3.36959i	0.656436	−	0.175891i	0.0847988	−	0.996398i	$-0.472975\pi$
$367$	12.5755	−	3.36959i	0.656436	−	0.175891i	0.571637	+	0.820507i	$0.306309\pi$
$368$	−0.0309145	+	0.115374i	−0.00161153	+	0.00601431i
$369$	−2.24342	−	2.24342i	−0.116788	−	0.116788i
$370$		0			0
$371$	3.55271	−	13.2589i	0.184448	−	0.688368i
$372$			38.5662i			1.99957i
$373$	10.1385	+	2.71659i	0.524950	+	0.140660i	0.511555	−	0.859250i	$-0.329070\pi$
$373$	10.1385	+	2.71659i	0.524950	+	0.140660i	0.0133946	+	0.999910i	$0.495736\pi$
$374$	−24.6304	+	42.6611i	−1.27361	+	2.20595i
$375$		0			0
$376$			23.7436i			1.22448i
$377$	3.20611	−	1.75091i	0.165123	−	0.0901766i
$378$	−24.4057	+	24.4057i	−1.25529	+	1.25529i
$379$	−9.74593	+	2.61141i	−0.500615	+	0.134139i	−0.500285	−	0.865861i	$-0.666772\pi$
$379$	−9.74593	+	2.61141i	−0.500615	+	0.134139i	−0.000329419		1.00000i	$0.500105\pi$
$380$		0			0
$381$	19.6132	−	11.3237i	1.00481	−	0.580130i
$382$	−50.5293			−2.58531
$383$	9.31368	−	5.37726i	0.475907	−	0.274765i	−0.242802	−	0.970076i	$-0.578067\pi$
$383$	9.31368	−	5.37726i	0.475907	−	0.274765i	0.718709	+	0.695311i	$0.244733\pi$
$384$	33.4575	+	8.96492i	1.70737	+	0.457489i
$385$		0			0
$386$	19.0862	+	33.0582i	0.971460	+	1.68262i
$387$	0.166717	+	0.622197i	0.00847471	+	0.0316281i
$388$	22.1763	−	38.4105i	1.12583	−	1.95000i
$389$	34.9585			1.77247			0.886234	−	0.463238i	$-0.153313\pi$
$389$	34.9585			1.77247			0.886234	+	0.463238i	$0.153313\pi$
$390$		0			0
$391$	6.88771			0.348326
$392$	−4.81888	+	8.34654i	−0.243390	+	0.421564i
$393$	−0.0336910	−	0.125736i	−0.00169948	−	0.00634256i
$394$	−3.22443	−	5.58487i	−0.162444	−	0.281362i
$395$		0			0
$396$	−5.59308	−	1.49866i	−0.281063	−	0.0753105i
$397$	−5.28828	+	3.05319i	−0.265411	+	0.153235i	−0.626801	−	0.779180i	$-0.715636\pi$
$397$	−5.28828	+	3.05319i	−0.265411	+	0.153235i	0.361389	+	0.932415i	$0.382303\pi$
$398$	42.5612			2.13340
$399$	40.9728	−	23.6557i	2.05121	−	1.18426i
$400$		0			0
$401$	0.267716	−	0.0717343i	0.0133691	−	0.00358224i	−0.252128	−	0.967694i	$-0.581130\pi$
$401$	0.267716	−	0.0717343i	0.0133691	−	0.00358224i	0.265497	+	0.964112i	$0.414464\pi$
$402$	25.3281	−	25.3281i	1.26325	−	1.26325i
$403$	5.38029	+	22.1722i	0.268011	+	1.10447i
$404$		−	29.3102i		−	1.45823i
$405$		0			0
$406$	−3.73527	+	6.46967i	−0.185378	+	0.321084i
$407$	2.57508	+	0.689992i	0.127642	+	0.0342016i
$408$			32.4314i			1.60559i
$409$	3.90517	−	14.5743i	0.193098	−	0.720653i	−0.799653	−	0.600463i	$-0.794983\pi$
$409$	3.90517	−	14.5743i	0.193098	−	0.720653i	0.992751	−	0.120190i	$-0.0383504\pi$
$410$		0			0
$411$	13.9565	+	13.9565i	0.688425	+	0.688425i
$412$	2.07303	−	7.73665i	0.102131	−	0.381157i
$413$	−20.7483	+	5.55950i	−1.02096	+	0.273565i
$414$	0.338130	+	1.26192i	0.0166182	+	0.0620199i
$415$		0			0
$416$	19.9575	+	0.473904i	0.978497	+	0.0232350i
$417$	−12.2438	−	12.2438i	−0.599580	−	0.599580i
$418$	−55.8979	−	32.2726i	−2.73405	−	1.57851i
$419$	−7.65847	−	4.42162i	−0.374141	−	0.216010i	0.301125	−	0.953585i	$-0.402638\pi$
$419$	−7.65847	−	4.42162i	−0.374141	−	0.216010i	−0.675266	+	0.737574i	$0.735971\pi$
$420$		0			0
$421$	6.58165	−	6.58165i	0.320770	−	0.320770i	−0.528292	−	0.849062i	$-0.677168\pi$
$421$	6.58165	−	6.58165i	0.320770	−	0.320770i	0.849062	+	0.528292i	$0.177168\pi$
$422$	−23.1816	−	40.1518i	−1.12847	−	1.95456i
$423$	2.04204	+	3.53692i	0.0992873	+	0.171971i
$424$	−8.71790	+	8.71790i	−0.423379	+	0.423379i
$425$		0			0
$426$	34.6553	+	20.0082i	1.67905	+	0.969402i
$427$	5.17067	+	2.98529i	0.250226	+	0.144468i
$428$	−22.6748	−	22.6748i	−1.09603	−	1.09603i
$429$	−24.1076	−	0.572451i	−1.16393	−	0.0276382i
$430$		0			0
$431$	1.88510	+	7.03529i	0.0908021	+	0.338878i	0.996350	−	0.0853669i	$-0.0272062\pi$
$431$	1.88510	+	7.03529i	0.0908021	+	0.338878i	−0.905547	+	0.424245i	$0.860540\pi$
$432$	0.470912	−	0.126180i	0.0226568	−	0.00607086i
$433$	2.83990	−	10.5986i	0.136477	−	0.509338i	−0.863511	−	0.504330i	$-0.831739\pi$
$433$	2.83990	−	10.5986i	0.136477	−	0.509338i	0.999987	−	0.00500749i	$-0.00159394\pi$
$434$	−32.9923	−	32.9923i	−1.58368	−	1.58368i
$435$		0			0
$436$	7.35711	−	27.4571i	0.352342	−	1.31496i
$437$			9.02481i			0.431715i
$438$	−32.8883	−	8.81238i	−1.57146	−	0.421072i
$439$	−5.86048	+	10.1506i	−0.279705	+	0.484464i	−0.971311	−	0.237811i	$-0.923570\pi$
$439$	−5.86048	+	10.1506i	−0.279705	+	0.484464i	0.691606	+	0.722275i	$0.256903\pi$
$440$		0			0
$441$			1.65777i			0.0789414i
$442$	11.7104	+	48.2586i	0.557007	+	2.29543i
$443$	19.3277	−	19.3277i	0.918288	−	0.918288i	−0.0786170	−	0.996905i	$-0.525050\pi$
$443$	19.3277	−	19.3277i	0.918288	−	0.918288i	0.996905	+	0.0786170i	$0.0250504\pi$
$444$	4.38797	−	1.17575i	0.208244	−	0.0557988i
$445$		0			0
$446$	−40.4690	+	23.3648i	−1.91626	+	1.10635i
$447$	27.8370			1.31665
$448$	−35.9353	+	20.7472i	−1.69778	+	0.980215i
$449$	−19.9671	−	5.35017i	−0.942306	−	0.252490i	−0.245212	−	0.969470i	$-0.578858\pi$
$449$	−19.9671	−	5.35017i	−0.942306	−	0.252490i	−0.697094	+	0.716979i	$0.745524\pi$
$450$		0			0
$451$	−11.4223	−	19.7840i	−0.537855	−	0.931592i
$452$	12.7995	+	47.7685i	0.602039	+	2.24684i
$453$	13.6697	−	23.6766i	0.642259	−	1.11243i
$454$	15.5972			0.732011
$455$		0			0
$456$	−42.4941			−1.98997
$457$	1.28025	−	2.21747i	0.0598878	−	0.103729i	−0.834527	−	0.550967i	$-0.814259\pi$
$457$	1.28025	−	2.21747i	0.0598878	−	0.103729i	0.894415	+	0.447238i	$0.147592\pi$
$458$	5.66331	+	21.1358i	0.264629	+	0.987610i
$459$	−14.0564	−	24.3464i	−0.656098	−	1.13639i
$460$		0			0
$461$	−9.77044	−	2.61798i	−0.455055	−	0.121932i	0.0240087	−	0.999712i	$-0.492357\pi$
$461$	−9.77044	−	2.61798i	−0.455055	−	0.121932i	−0.479064	+	0.877780i	$0.659024\pi$
$462$	42.7073	−	24.6571i	1.98693	−	1.14715i
$463$	−12.2556			−0.569565			−0.284782	−	0.958592i	$-0.591921\pi$
$463$	−12.2556			−0.569565			−0.284782	+	0.958592i	$0.591921\pi$
$464$	0.0913844	−	0.0527608i	0.00424242	−	0.00244936i
$465$		0			0
$466$	−47.1009	+	12.6207i	−2.18191	+	0.584641i
$467$	−16.2946	+	16.2946i	−0.754023	+	0.754023i	−0.975227	−	0.221205i	$-0.929001\pi$
$467$	−16.2946	+	16.2946i	−0.754023	+	0.754023i	0.221205	+	0.975227i	$0.429001\pi$
$468$	−5.12302	+	2.79777i	−0.236812	+	0.129327i
$469$			26.8553i			1.24006i
$470$		0			0
$471$	−21.0524	+	36.4638i	−0.970043	+	1.68016i
$472$	18.6357	+	4.99343i	0.857780	+	0.229841i
$473$			4.63811i			0.213261i
$474$	11.3065	−	42.1965i	0.519325	−	1.93815i
$475$		0			0
$476$	−44.5012	−	44.5012i	−2.03971	−	2.03971i
$477$	−0.548872	+	2.04842i	−0.0251311	+	0.0937907i
$478$	−25.6501	+	6.87292i	−1.17321	+	0.314360i
$479$	3.58854	+	13.3926i	0.163965	+	0.611924i	0.998170	+	0.0604705i	$0.0192601\pi$
$479$	3.58854	+	13.3926i	0.163965	+	0.611924i	−0.834205	+	0.551454i	$0.814073\pi$
$480$		0			0
$481$	2.35867	−	1.28811i	0.107546	−	0.0587328i
$482$	29.7360	+	29.7360i	1.35444	+	1.35444i
$483$	−5.97140	−	3.44759i	−0.271708	−	0.156871i
$484$	−5.05891	−	2.92076i	−0.229950	−	0.132762i
$485$		0			0
$486$	8.28925	−	8.28925i	0.376008	−	0.376008i
$487$	−4.12568	−	7.14590i	−0.186953	−	0.323811i	0.757280	−	0.653090i	$-0.226528\pi$
$487$	−4.12568	−	7.14590i	−0.186953	−	0.323811i	−0.944233	+	0.329279i	$0.893194\pi$
$488$	−2.68132	−	4.64419i	−0.121378	−	0.210232i
$489$	−11.5001	+	11.5001i	−0.520051	+	0.520051i
$490$		0			0
$491$	−32.4891	−	18.7576i	−1.46621	−	0.846519i	−0.466928	−	0.884295i	$-0.654639\pi$
$491$	−32.4891	−	18.7576i	−1.46621	−	0.846519i	−0.999286	+	0.0377764i	$0.987973\pi$
$492$	−33.7122	−	19.4637i	−1.51986	−	0.877492i
$493$	−4.30265	−	4.30265i	−0.193781	−	0.193781i
$494$	−63.2321	+	15.3439i	−2.84495	+	0.690354i
$495$		0			0
$496$	0.170574	+	0.636592i	0.00765901	+	0.0285838i
$497$	−28.9798	+	7.76512i	−1.29992	+	0.348313i
$498$	−10.0107	+	37.3604i	−0.448590	+	1.67416i
$499$	−26.3014	−	26.3014i	−1.17741	−	1.17741i	−0.980401	−	0.197011i	$-0.936876\pi$
$499$	−26.3014	−	26.3014i	−1.17741	−	1.17741i	−0.197011	−	0.980401i	$-0.563124\pi$
$500$		0			0
$501$	−1.61769	+	6.03729i	−0.0722730	+	0.269726i
$502$		−	59.9985i		−	2.67786i
$503$	−32.8830	−	8.81098i	−1.46618	−	0.392862i	−0.564562	−	0.825391i	$-0.690955\pi$
$503$	−32.8830	−	8.81098i	−1.46618	−	0.392862i	−0.901620	+	0.432528i	$0.857622\pi$
$504$	2.30601	−	3.99413i	0.102718	−	0.177912i
$505$		0			0
$506$			9.40686i			0.418186i
$507$	−17.9858	+	16.3541i	−0.798780	+	0.726310i
$508$	27.9118	−	27.9118i	1.23839	−	1.23839i
$509$	33.8235	−	9.06297i	1.49920	−	0.401709i	0.586367	−	0.810046i	$-0.300558\pi$
$509$	33.8235	−	9.06297i	1.49920	−	0.401709i	0.912831	+	0.408337i	$0.133891\pi$
$510$		0			0
$511$	22.1076	−	12.7638i	0.977982	−	0.564638i
$512$	1.17818			0.0520687
$513$	31.9006	−	18.4178i	1.40845	−	0.813166i
$514$	−18.3212	−	4.90916i	−0.808115	−	0.216534i
$515$		0			0
$516$	3.95170	+	6.84454i	0.173964	+	0.301314i
$517$	7.61110	+	28.4050i	0.334736	+	1.24925i
$518$	−2.74796	+	4.75960i	−0.120738	+	0.209125i
$519$	9.02384			0.396103
$520$		0			0
$521$	7.65467			0.335357			0.167679	−	0.985842i	$-0.446373\pi$
$521$	7.65467			0.335357			0.167679	+	0.985842i	$0.446373\pi$
$522$	0.577076	−	0.999525i	0.0252579	−	0.0437480i
$523$	−5.45483	−	20.3577i	−0.238523	−	0.890180i	−0.976529	−	0.215386i	$-0.930899\pi$
$523$	−5.45483	−	20.3577i	−0.238523	−	0.890180i	0.738006	−	0.674794i	$-0.235768\pi$
$524$	−0.113442	−	0.196487i	−0.00495572	−	0.00858356i
$525$		0			0
$526$	−29.2828	−	7.84630i	−1.27679	−	0.342115i
$527$	32.9122	−	19.0019i	1.43368	−	0.827734i
$528$	−0.696565			−0.0303141
$529$	−18.7795	+	10.8424i	−0.816501	+	0.471407i
$530$		0			0
$531$	3.20549	−	0.858910i	0.139107	−	0.0372735i
$532$	58.3090	−	58.3090i	2.52801	−	2.52801i
$533$	−22.0968	−	6.48681i	−0.957120	−	0.280975i
$534$			2.91858i			0.126299i
$535$		0			0
$536$	12.0605	−	20.8893i	0.520932	−	0.902281i
$537$	5.70436	+	1.52848i	0.246161	+	0.0659587i
$538$		−	12.9274i		−	0.557338i
$539$	−3.08942	+	11.5299i	−0.133071	+	0.496628i
$540$		0			0
$541$	15.4272	+	15.4272i	0.663267	+	0.663267i	0.956149	−	0.292882i	$-0.0946142\pi$
$541$	15.4272	+	15.4272i	0.663267	+	0.663267i	−0.292882	+	0.956149i	$0.594614\pi$
$542$	−4.50073	+	16.7969i	−0.193323	+	0.721491i
$543$	3.26317	−	0.874364i	0.140036	−	0.0375225i
$544$	−8.60635	−	32.1193i	−0.368994	−	1.37710i
$545$		0			0
$546$	14.0029	−	47.7000i	0.599271	−	2.04137i
$547$	−5.79215	−	5.79215i	−0.247654	−	0.247654i	0.572353	−	0.820007i	$-0.306031\pi$
$547$	−5.79215	−	5.79215i	−0.247654	−	0.247654i	−0.820007	+	0.572353i	$0.806031\pi$
$548$	29.7926	+	17.2008i	1.27268	+	0.734780i
$549$	−0.798837	−	0.461209i	−0.0340935	−	0.0196839i
$550$		0			0
$551$	5.63766	−	5.63766i	0.240172	−	0.240172i
$552$	3.09655	+	5.36339i	0.131798	+	0.228281i
$553$	16.3763	+	28.3646i	0.696391	+	1.20618i
$554$	−18.9182	+	18.9182i	−0.803759	+	0.803759i
$555$		0			0
$556$	−26.1364	−	15.0899i	−1.10843	−	0.639953i
$557$	19.9488	+	11.5174i	0.845256	+	0.488009i	0.859047	−	0.511896i	$-0.171057\pi$
$557$	19.9488	+	11.5174i	0.845256	+	0.488009i	−0.0137912	+	0.999905i	$0.504390\pi$
$558$	5.09711	+	5.09711i	0.215778	+	0.215778i
$559$	3.22674	+	3.38371i	0.136477	+	0.143116i
$560$		0			0
$561$	10.3960	+	38.7985i	0.438920	+	1.63807i
$562$	−29.6389	+	7.94172i	−1.25024	+	0.335001i
$563$	−1.56919	+	5.85629i	−0.0661334	+	0.246813i	−0.991077	−	0.133291i	$-0.957445\pi$
$563$	−1.56919	+	5.85629i	−0.0661334	+	0.246813i	0.924943	+	0.380105i	$0.124112\pi$
$564$	35.4331	+	35.4331i	1.49200	+	1.49200i
$565$		0			0
$566$	2.38167	−	8.88851i	0.100109	−	0.373612i
$567$			32.9345i			1.38312i
$568$	26.0291	+	6.97447i	1.09216	+	0.292642i
$569$	11.2211	−	19.4355i	0.470413	−	0.814779i	−0.529015	−	0.848613i	$-0.677438\pi$
$569$	11.2211	−	19.4355i	0.470413	−	0.814779i	0.999427	+	0.0338340i	$0.0107718\pi$
$570$		0			0
$571$			41.7374i			1.74665i	0.487135	+	0.873327i	$0.338042\pi$
$571$			41.7374i			1.74665i	−0.487135	+	0.873327i	$0.661958\pi$
$572$	−40.8449	+	9.91140i	−1.70781	+	0.414417i
$573$	−29.1339	+	29.1339i	−1.21708	+	1.21708i
$574$	45.4904	−	12.1891i	1.89873	−	0.508764i
$575$		0			0
$576$	5.55178	−	3.20532i	0.231324	−	0.133555i
$577$	10.4937			0.436859			0.218429	−	0.975853i	$-0.429907\pi$
$577$	10.4937			0.436859			0.218429	+	0.975853i	$0.429907\pi$
$578$	37.8717	−	21.8653i	1.57526	−	0.909475i
$579$	30.0650	+	8.05590i	1.24946	+	0.334792i
$580$		0			0
$581$	−14.4994	−	25.1138i	−0.601538	−	1.04189i
$582$	−15.1040	−	56.3689i	−0.626081	−	2.33657i
$583$	−7.63488	+	13.2240i	−0.316205	+	0.547682i
$584$	−22.9284			−0.948784
$585$		0			0
$586$	56.5874			2.33760
$587$	−23.4529	+	40.6217i	−0.968006	+	1.67664i	−0.266693	+	0.963782i	$0.585931\pi$
$587$	−23.4529	+	40.6217i	−0.968006	+	1.67664i	−0.701313	+	0.712853i	$0.747402\pi$
$588$	5.26441	+	19.6471i	0.217101	+	0.810231i
$589$	24.8977	+	43.1241i	1.02589	+	1.77690i
$590$		0			0
$591$	−5.07921	−	1.36097i	−0.208931	−	0.0559828i
$592$	0.0672296	−	0.0388150i	0.00276312	−	0.00159529i
$593$	−24.0105			−0.985994			−0.492997	−	0.870031i	$-0.664099\pi$
$593$	−24.0105			−0.985994			−0.492997	+	0.870031i	$0.664099\pi$
$594$	33.2511	−	19.1975i	1.36431	−	0.787683i
$595$		0			0
$596$	46.8653	−	12.5575i	1.91968	−	0.514377i
$597$	24.5396	−	24.5396i	1.00434	−	1.00434i
$598$	6.54437	+	6.86273i	0.267619	+	0.280638i
$599$			2.24349i			0.0916664i	0.998949	+	0.0458332i	$0.0145943\pi$
$599$			2.24349i			0.0916664i	−0.998949	+	0.0458332i	$0.985406\pi$
$600$		0			0
$601$	−19.5199	+	33.8095i	−0.796234	+	1.37912i	0.125818	+	0.992053i	$0.459845\pi$
$601$	−19.5199	+	33.8095i	−0.796234	+	1.37912i	−0.922052	+	0.387065i	$0.873489\pi$
$602$	−9.23587	−	2.47474i	−0.376426	−	0.100863i
$603$		−	4.14899i		−	0.168960i
$604$	12.3331	−	46.0276i	0.501825	−	1.87284i
$605$		0			0
$606$	−27.2696	−	27.2696i	−1.10775	−	1.10775i
$607$	5.82801	−	21.7504i	0.236552	−	0.882823i	−0.740892	−	0.671625i	$-0.765597\pi$
$607$	5.82801	−	21.7504i	0.236552	−	0.882823i	0.977443	−	0.211198i	$-0.0677366\pi$
$608$	42.0852	−	11.2767i	1.70678	−	0.457331i
$609$	1.57658	+	5.88389i	0.0638864	+	0.238427i
$610$		0			0
$611$	25.3141	+	15.4277i	1.02410	+	0.624137i
$612$	6.87517	+	6.87517i	0.277912	+	0.277912i
$613$	−2.80523	−	1.61960i	−0.113302	−	0.0654151i	0.442278	−	0.896878i	$-0.354170\pi$
$613$	−2.80523	−	1.61960i	−0.113302	−	0.0654151i	−0.555580	+	0.831463i	$0.687504\pi$
$614$	14.7226	+	8.50008i	0.594154	+	0.343035i
$615$		0			0
$616$	23.4819	−	23.4819i	0.946113	−	0.946113i
$617$	−17.4002	−	30.1380i	−0.700504	−	1.21331i	−0.968290	−	0.249830i	$-0.919625\pi$
$617$	−17.4002	−	30.1380i	−0.700504	−	1.21331i	0.267786	−	0.963478i	$-0.413708\pi$
$618$	−5.26933	−	9.12674i	−0.211963	−	0.367131i
$619$	−5.38094	+	5.38094i	−0.216278	+	0.216278i	−0.806928	−	0.590650i	$-0.798871\pi$
$619$	−5.38094	+	5.38094i	−0.216278	+	0.216278i	0.590650	+	0.806928i	$0.298871\pi$
$620$		0			0
$621$	−4.64921	−	2.68422i	−0.186566	−	0.107714i
$622$	3.31893	+	1.91618i	0.133077	+	0.0768319i
$623$	−1.54728	−	1.54728i	−0.0619906	−	0.0619906i
$624$	−0.508176	+	0.484602i	−0.0203433	+	0.0193996i
$625$		0			0
$626$	−13.3080	−	49.6661i	−0.531894	−	1.98506i
$627$	−50.8368	+	13.6217i	−2.03022	+	0.543997i
$628$	−18.9938	+	70.8859i	−0.757936	+	2.82866i
$629$	−3.16537	−	3.16537i	−0.126211	−	0.126211i
$630$		0			0
$631$	−10.4197	+	38.8868i	−0.414801	+	1.54806i	0.370433	+	0.928859i	$0.379209\pi$
$631$	−10.4197	+	38.8868i	−0.414801	+	1.54806i	−0.785234	+	0.619199i	$0.787457\pi$
$632$		−	29.4177i		−	1.17017i
$633$	−36.5164	−	9.78453i	−1.45140	−	0.388900i
$634$	−1.72584	+	2.98925i	−0.0685420	+	0.118718i
$635$		0			0
$636$			26.0198i			1.03175i
$637$	5.76749	+	10.5609i	0.228516	+	0.418438i
$638$	5.87632	−	5.87632i	0.232646	−	0.232646i
$639$	4.47721	−	1.19966i	0.177116	−	0.0474580i
$640$		0			0
$641$	−31.1015	+	17.9565i	−1.22844	+	0.709239i	−0.966703	−	0.255901i	$-0.917628\pi$
$641$	−31.1015	+	17.9565i	−1.22844	+	0.709239i	−0.261734	+	0.965140i	$0.584294\pi$
$642$	−42.1925			−1.66521
$643$	5.24544	−	3.02845i	0.206860	−	0.119431i	−0.392991	−	0.919542i	$-0.628560\pi$
$643$	5.24544	−	3.02845i	0.206860	−	0.119431i	0.599851	+	0.800112i	$0.295226\pi$
$644$	−11.6084	−	3.11047i	−0.457437	−	0.122570i
$645$		0			0
$646$	54.1909	+	93.8613i	2.13211	+	3.69292i
$647$	−5.09717	−	19.0229i	−0.200390	−	0.747867i	−0.990805	−	0.135295i	$-0.956802\pi$
$647$	−5.09717	−	19.0229i	−0.200390	−	0.747867i	0.790415	−	0.612572i	$-0.209865\pi$
$648$	14.7906	−	25.6180i	0.581028	−	1.00637i
$649$	23.8951			0.937964
$650$		0			0
$651$	−38.0449			−1.49110
$652$	−14.1733	+	24.5488i	−0.555068	+	0.961406i
$653$	−3.46867	−	12.9452i	−0.135739	−	0.506587i	−0.999994	−	0.00353138i	$-0.998876\pi$
$653$	−3.46867	−	12.9452i	−0.135739	−	0.506587i	0.864254	−	0.503055i	$-0.167791\pi$
$654$	−18.7007	−	32.3905i	−0.731254	−	1.26657i
$655$		0			0
$656$	−0.642554	−	0.172172i	−0.0250875	−	0.00672218i
$657$	−3.41549	+	1.97193i	−0.133251	+	0.0769324i
$658$	−60.6239			−2.36337
$659$	−12.2454	+	7.06989i	−0.477013	+	0.275404i	−0.719171	−	0.694833i	$-0.755478\pi$
$659$	−12.2454	+	7.06989i	−0.477013	+	0.275404i	0.242158	+	0.970237i	$0.422145\pi$
$660$		0			0
$661$	43.7807	−	11.7310i	1.70287	−	0.456283i	0.729213	−	0.684287i	$-0.239886\pi$
$661$	43.7807	−	11.7310i	1.70287	−	0.456283i	0.973660	+	0.228004i	$0.0732198\pi$
$662$	3.85504	−	3.85504i	0.149830	−	0.149830i
$663$	34.5765	+	21.0727i	1.34284	+	0.818396i
$664$			26.0462i			1.01079i
$665$		0			0
$666$	0.424543	−	0.735330i	0.0164507	−	0.0284935i
$667$	−1.12237	−	0.300739i	−0.0434585	−	0.0116447i
$668$			10.8939i			0.421498i
$669$	−9.86183	+	36.8049i	−0.381280	+	1.42296i
$670$		0			0
$671$	−4.69645	−	4.69645i	−0.181304	−	0.181304i
$672$	−8.61568	+	32.1541i	−0.332357	+	1.24037i
$673$	22.0353	−	5.90434i	0.849399	−	0.227596i	0.192240	−	0.981348i	$-0.438425\pi$
$673$	22.0353	−	5.90434i	0.849399	−	0.227596i	0.657159	+	0.753752i	$0.271758\pi$
$674$	2.53524	+	9.46165i	0.0976539	+	0.364449i
$675$		0			0
$676$	−22.9028	+	35.6467i	−0.880877	+	1.37103i
$677$	21.3802	+	21.3802i	0.821709	+	0.821709i	0.986353	−	0.164644i	$-0.0526474\pi$
$677$	21.3802	+	21.3802i	0.821709	+	0.821709i	−0.164644	+	0.986353i	$0.552647\pi$
$678$	56.3514	+	32.5345i	2.16416	+	1.24948i
$679$	37.8913	+	21.8766i	1.45414	+	0.839545i
$680$		0			0
$681$	8.99290	−	8.99290i	0.344609	−	0.344609i
$682$	25.9517	+	44.9497i	0.993742	+	1.72121i
$683$	−19.6502	−	34.0351i	−0.751894	−	1.30232i	−0.946904	−	0.321517i	$-0.895807\pi$
$683$	−19.6502	−	34.0351i	−0.751894	−	1.30232i	0.195010	−	0.980801i	$-0.437526\pi$
$684$	−9.00838	+	9.00838i	−0.344444	+	0.344444i
$685$		0			0
$686$	23.3877	+	13.5029i	0.892948	+	0.515543i
$687$	15.4516	+	8.92101i	0.589517	+	0.340358i
$688$	0.0955012	+	0.0955012i	0.00364095	+	0.00364095i
$689$	3.62997	+	14.9591i	0.138291	+	0.569897i
$690$		0			0
$691$	−10.4916	−	39.1552i	−0.399119	−	1.48953i	−0.814650	−	0.579953i	$-0.803071\pi$
$691$	−10.4916	−	39.1552i	−0.399119	−	1.48953i	0.415531	−	0.909579i	$-0.363596\pi$
$692$	15.1922	−	4.07073i	0.577520	−	0.154746i
$693$	1.47840	−	5.51748i	0.0561599	−	0.209592i
$694$	−5.97093	−	5.97093i	−0.226653	−	0.226653i
$695$		0			0
$696$	1.41606	−	5.28479i	0.0536755	−	0.200320i
$697$			38.3597i			1.45298i
$698$	−22.3316	−	5.98375i	−0.845265	−	0.226488i
$699$	−19.8804	+	34.4339i	−0.751946	+	1.30241i
$700$		0			0
$701$		−	34.8480i		−	1.31619i	−0.752935	−	0.658094i	$-0.771363\pi$
$701$		−	34.8480i		−	1.31619i	0.752935	−	0.658094i	$-0.228637\pi$
$702$	10.9024	−	37.1383i	0.411485	−	1.40169i
$703$	4.14751	−	4.14751i	0.156426	−	0.156426i
$704$	44.5865	−	11.9469i	1.68042	−	0.450266i
$705$		0			0
$706$	53.8520	−	31.0915i	2.02675	−	1.17014i
$707$	28.9140			1.08742
$708$	35.2624	−	20.3587i	1.32524	−	0.765128i
$709$	−36.3341	−	9.73570i	−1.36456	−	0.365632i	−0.499069	−	0.866562i	$-0.666325\pi$
$709$	−36.3341	−	9.73570i	−1.36456	−	0.365632i	−0.865488	+	0.500930i	$0.832991\pi$
$710$		0			0
$711$	−2.53004	−	4.38216i	−0.0948839	−	0.164344i
$712$	0.508680	+	1.89842i	0.0190636	+	0.0711463i
$713$	3.62860	−	6.28492i	0.135892	−	0.235372i
$714$	−82.8063			−3.09895
$715$		0			0
$716$	10.2931			0.384673
$717$	−10.8264	+	18.7519i	−0.404320	+	0.700303i
$718$	−0.750624	−	2.80137i	−0.0280130	−	0.104546i
$719$	17.9827	+	31.1470i	0.670642	+	1.16159i	0.977722	+	0.209902i	$0.0673146\pi$
$719$	17.9827	+	31.1470i	0.670642	+	1.16159i	−0.307080	+	0.951684i	$0.599352\pi$
$720$		0			0
$721$	7.63207	+	2.04501i	0.284233	+	0.0761600i
$722$	−85.2493	+	49.2187i	−3.17265	+	1.83173i
$723$	34.2899			1.27526
$724$	5.09931	−	2.94409i	0.189514	−	0.109416i
$725$		0			0
$726$	−7.42414	+	1.98929i	−0.275536	+	0.0738296i
$727$	2.50307	−	2.50307i	0.0928336	−	0.0928336i	−0.659165	−	0.751998i	$-0.729090\pi$
$727$	2.50307	−	2.50307i	0.0928336	−	0.0928336i	0.751998	+	0.659165i	$0.229090\pi$
$728$	0.794707	−	33.4675i	0.0294538	−	1.24039i
$729$			21.1716i			0.784134i
$730$		0			0
$731$	3.89406	−	6.74472i	0.144027	−	0.249462i
$732$	−10.9320	−	2.92923i	−0.404059	−	0.108267i
$733$		−	1.25540i		−	0.0463694i	−0.999731	−	0.0231847i	$-0.992619\pi$
$733$		−	1.25540i		−	0.0463694i	0.999731	−	0.0231847i	$-0.00738058\pi$
$734$	7.72750	−	28.8394i	0.285227	−	1.06448i
$735$		0			0
$736$	−4.49005	−	4.49005i	−0.165505	−	0.165505i
$737$	7.73206	−	28.8565i	0.284814	−	1.06294i
$738$	−7.02799	+	1.88314i	−0.258704	+	0.0693195i
$739$	−5.60031	−	20.9006i	−0.206011	−	0.768842i	−0.989139	−	0.146982i	$-0.953044\pi$
$739$	−5.60031	−	20.9006i	−0.206011	−	0.768842i	0.783129	−	0.621860i	$-0.213623\pi$
$740$		0			0
$741$	−27.6111	+	45.3048i	−1.01432	+	1.66431i
$742$	−22.2592	−	22.2592i	−0.817162	−	0.817162i
$743$	9.49772	+	5.48351i	0.348438	+	0.201171i	0.663997	−	0.747735i	$-0.268859\pi$
$743$	9.49772	+	5.48351i	0.348438	+	0.201171i	−0.315559	+	0.948906i	$0.602192\pi$
$744$	29.5931	+	17.0856i	1.08494	+	0.626388i
$745$		0			0
$746$	17.0206	−	17.0206i	0.623168	−	0.623168i
$747$	2.24007	+	3.87992i	0.0819601	+	0.141959i
$748$	35.0047	+	60.6299i	1.27990	+	2.21685i
$749$	22.3683	−	22.3683i	0.817321	−	0.817321i
$750$		0			0
$751$	27.9580	+	16.1416i	1.02020	+	0.589015i	0.914163	−	0.405347i	$-0.132849\pi$
$751$	27.9580	+	16.1416i	1.02020	+	0.589015i	0.106041	+	0.994362i	$0.466183\pi$
$752$	0.741591	+	0.428158i	0.0270430	+	0.0156133i
$753$	−34.5935	−	34.5935i	−1.26066	−	1.26066i
$754$	0.198875	−	8.37520i	0.00724259	−	0.305007i
$755$		0			0
$756$	12.6957	+	47.3810i	0.461738	+	1.72323i
$757$	31.0370	−	8.31633i	1.12806	−	0.302262i	0.353918	−	0.935277i	$-0.384849\pi$
$757$	31.0370	−	8.31633i	1.12806	−	0.302262i	0.774140	+	0.633014i	$0.218183\pi$
$758$	−5.98876	+	22.3504i	−0.217522	+	0.811802i
$759$	5.42374	+	5.42374i	0.196869	+	0.196869i
$760$		0			0
$761$	10.3043	−	38.4564i	0.373532	−	1.39404i	−0.481945	−	0.876201i	$-0.660069\pi$
$761$	10.3043	−	38.4564i	0.373532	−	1.39404i	0.855477	−	0.517840i	$-0.173264\pi$
$762$		−	51.9372i		−	1.88149i
$763$	27.0860	+	7.25766i	0.980578	+	0.262745i
$764$	−35.9061	+	62.1912i	−1.29904	+	2.25000i
$765$		0			0
$766$		−	24.6634i		−	0.891123i
$767$	17.4325	−	16.6238i	0.629452	−	0.600252i
$768$	22.0394	−	22.0394i	0.795280	−	0.795280i
$769$	−18.0132	+	4.82663i	−0.649573	+	0.174053i	−0.568536	−	0.822658i	$-0.692490\pi$
$769$	−18.0132	+	4.82663i	−0.649573	+	0.174053i	−0.0810373	+	0.996711i	$0.525823\pi$
$770$		0			0
$771$	−13.3940	+	7.73304i	−0.482374	+	0.278499i
$772$	54.2504			1.95251
$773$	−8.83684	+	5.10195i	−0.317839	+	0.183504i	−0.650429	−	0.759567i	$-0.725411\pi$
$773$	−8.83684	+	5.10195i	−0.317839	+	0.183504i	0.332590	+	0.943072i	$0.392077\pi$
$774$	1.42689	+	0.382333i	0.0512884	+	0.0137427i
$775$		0			0
$776$	−19.6491	−	34.0332i	−0.705361	−	1.22172i
$777$	1.15986	+	4.32866i	0.0416098	+	0.155290i
$778$	40.0852	−	69.4297i	1.43713	−	2.48917i
$779$	−50.2618			−1.80082
$780$		0			0
$781$	33.3750			1.19425
$782$	7.89780	−	13.6794i	0.282425	−	0.489174i
$783$	1.22750	+	4.58108i	0.0438671	+	0.163714i
$784$	0.173794	+	0.301019i	0.00620692	+	0.0107507i
$785$		0			0
$786$	−0.288352	−	0.0772636i	−0.0102852	−	0.00275590i
$787$	18.3010	−	10.5661i	0.652360	−	0.376640i	−0.137000	−	0.990571i	$-0.543746\pi$
$787$	18.3010	−	10.5661i	0.652360	−	0.376640i	0.789360	+	0.613931i	$0.210413\pi$
$788$	−9.16510			−0.326493
$789$	−21.4076	+	12.3597i	−0.762132	+	0.440017i
$790$		0			0
$791$	−47.1228	+	12.6265i	−1.67549	+	0.448947i
$792$	−3.62781	+	3.62781i	−0.128909	+	0.128909i
$793$	−6.69360	−	0.158944i	−0.237697	−	0.00564426i
$794$			14.0038i			0.496976i
$795$		0			0
$796$	30.2439	−	52.3840i	1.07197	−	1.85670i
$797$	−24.4507	−	6.55155i	−0.866089	−	0.232068i	−0.201693	−	0.979449i	$-0.564644\pi$
$797$	−24.4507	−	6.55155i	−0.866089	−	0.232068i	−0.664396	+	0.747381i	$0.731311\pi$
$798$		−	108.499i		−	3.84083i
$799$	12.7802	−	47.6965i	0.452133	−	1.68738i
$800$		0			0
$801$	0.239046	+	0.239046i	0.00844628	+	0.00844628i
$802$	0.164508	−	0.613954i	0.00580900	−	0.0216795i
$803$	−27.4298	+	7.34980i	−0.967978	+	0.259369i
$804$	−13.1755	−	49.1717i	−0.464665	−	1.73415i
$805$		0			0
$806$	50.2045	+	14.7382i	1.76838	+	0.519130i
$807$	−7.45357	−	7.45357i	−0.262378	−	0.262378i
$808$	−22.4906	−	12.9850i	−0.791217	−	0.456810i
$809$	−3.76608	−	2.17435i	−0.132408	−	0.0764459i	0.432333	−	0.901714i	$-0.357691\pi$
$809$	−3.76608	−	2.17435i	−0.132408	−	0.0764459i	−0.564741	+	0.825268i	$0.691024\pi$
$810$		0			0
$811$	−21.7750	+	21.7750i	−0.764623	+	0.764623i	−0.977154	−	0.212531i	$-0.931829\pi$
$811$	−21.7750	+	21.7750i	−0.764623	+	0.764623i	0.212531	+	0.977154i	$0.431829\pi$
$812$	5.30855	+	9.19468i	0.186294	+	0.322670i
$813$	7.08967	+	12.2797i	0.248646	+	0.430667i
$814$	4.32309	−	4.32309i	0.151524	−	0.151524i
$815$		0			0
$816$	1.01294	+	0.584822i	0.0354600	+	0.0204729i
$817$	8.83745	+	5.10230i	0.309183	+	0.178507i
$818$	−24.4675	−	24.4675i	−0.855488	−	0.855488i
$819$	−2.75996	−	5.05377i	−0.0964406	−	0.176593i
$820$		0			0
$821$	2.18315	+	8.14764i	0.0761926	+	0.284355i	0.993501	−	0.113823i	$-0.0363096\pi$
$821$	2.18315	+	8.14764i	0.0761926	+	0.284355i	−0.917309	+	0.398177i	$0.869643\pi$
$822$	43.7218	−	11.7152i	1.52497	−	0.408615i
$823$	5.05067	−	18.8493i	0.176055	−	0.657047i	−0.820314	−	0.571913i	$-0.806202\pi$
$823$	5.05067	−	18.8493i	0.176055	−	0.657047i	0.996370	−	0.0851339i	$-0.0271318\pi$
$824$	−5.01819	−	5.01819i	−0.174817	−	0.174817i
$825$		0			0
$826$	−12.7496	+	47.5822i	−0.443616	+	1.65560i
$827$		−	6.08198i		−	0.211491i	−0.994393	−	0.105745i	$-0.966277\pi$
$827$		−	6.08198i		−	0.211491i	0.994393	−	0.105745i	$-0.0337229\pi$
$828$	1.79343	+	0.480549i	0.0623262	+	0.0167002i
$829$	24.8232	−	42.9950i	0.862145	−	1.49328i	−0.00771009	−	0.999970i	$-0.502454\pi$
$829$	24.8232	−	42.9950i	0.862145	−	1.49328i	0.869855	−	0.493308i	$-0.164212\pi$
$830$		0			0
$831$			21.8155i			0.756772i
$832$	24.2163	−	39.7347i	0.839551	−	1.37755i
$833$	14.1729	−	14.1729i	0.491061	−	0.491061i
$834$	−38.3562	+	10.2775i	−1.32817	+	0.355881i
$835$		0			0
$836$	−79.4419	+	45.8658i	−2.74756	+	1.58630i
$837$	−29.6210			−1.02385
$838$	−17.5632	+	10.1401i	−0.606710	+	0.350284i
$839$	−2.83726	−	0.760241i	−0.0979530	−	0.0262464i	0.209510	−	0.977807i	$-0.432813\pi$
$839$	−2.83726	−	0.760241i	−0.0979530	−	0.0262464i	−0.307463	+	0.951560i	$0.599480\pi$
$840$		0			0
$841$	−13.9867	−	24.2257i	−0.482301	−	0.835370i
$842$	−5.52468	−	20.6184i	−0.190393	−	0.710557i
$843$	−12.5100	+	21.6680i	−0.430868	+	0.746285i
$844$	−65.8914			−2.26808
$845$		0			0
$846$	9.36603			0.322011
$847$	2.88128	−	4.99053i	0.0990020	−	0.171477i
$848$	0.115083	+	0.429496i	0.00395197	+	0.0147489i
$849$	−3.75167	−	6.49808i	−0.128757	−	0.223014i
$850$		0			0
$851$	−0.825707	−	0.221248i	−0.0283049	−	0.00758427i
$852$	49.2520	−	28.4356i	1.68734	−	0.974189i
$853$	−52.5348			−1.79876			−0.899378	−	0.437171i	$-0.855980\pi$
$853$	−52.5348			−1.79876			−0.899378	+	0.437171i	$0.855980\pi$
$854$	11.8579	−	6.84616i	0.405769	−	0.234271i
$855$		0			0
$856$	−27.4445	+	7.35374i	−0.938034	+	0.251346i
$857$	−21.4029	+	21.4029i	−0.731110	+	0.731110i	−0.970840	−	0.239730i	$-0.922941\pi$
$857$	−21.4029	+	21.4029i	−0.731110	+	0.731110i	0.239730	+	0.970840i	$0.422941\pi$
$858$	−28.7800	+	47.2227i	−0.982531	+	1.61216i
$859$		−	44.8260i		−	1.52944i	−0.644360	−	0.764722i	$-0.722876\pi$
$859$		−	44.8260i		−	1.52944i	0.644360	−	0.764722i	$-0.277124\pi$
$860$		0			0
$861$	19.2006	−	33.2565i	0.654356	−	1.13338i
$862$	16.1341	+	4.32311i	0.549528	+	0.147246i
$863$			17.5619i			0.597815i	0.954282	+	0.298907i	$0.0966222\pi$
$863$			17.5619i			0.597815i	−0.954282	+	0.298907i	$0.903378\pi$
$864$	−6.70799	+	25.0345i	−0.228210	+	0.851693i
$865$		0			0
$866$	−17.7931	−	17.7931i	−0.604635	−	0.604635i
$867$	9.22891	−	34.4427i	0.313430	−	1.16974i
$868$	−64.0509	+	17.1624i	−2.17403	+	0.582530i
$869$	−9.42998	−	35.1932i	−0.319890	−	1.19385i
$870$		0			0
$871$	−14.4346	−	26.4313i	−0.489098	−	0.895590i
$872$	−17.8094	−	17.8094i	−0.603102	−	0.603102i
$873$	−5.85398	−	3.37980i	−0.198127	−	0.114389i
$874$	17.9238	+	10.3483i	0.606281	+	0.350037i
$875$		0			0
$876$	−34.2166	+	34.2166i	−1.15607	+	1.15607i
$877$	4.27420	+	7.40312i	0.144329	+	0.249986i	0.929123	−	0.369772i	$-0.120564\pi$
$877$	4.27420	+	7.40312i	0.144329	+	0.249986i	−0.784793	+	0.619758i	$0.787231\pi$
$878$	13.4398	+	23.2785i	0.453573	+	0.785611i
$879$	32.6268	−	32.6268i	1.10047	−	1.10047i
$880$		0			0
$881$	37.8333	+	21.8430i	1.27464	+	0.735911i	0.975857	−	0.218411i	$-0.0700875\pi$
$881$	37.8333	+	21.8430i	1.27464	+	0.735911i	0.298779	+	0.954322i	$0.403421\pi$
$882$	3.29243	+	1.90088i	0.110862	+	0.0640061i
$883$	26.5027	+	26.5027i	0.891887	+	0.891887i	0.994701	−	0.102814i	$-0.0327846\pi$
$883$	26.5027	+	26.5027i	0.891887	+	0.891887i	−0.102814	+	0.994701i	$0.532785\pi$
$884$	67.7178	+	19.8794i	2.27760	+	0.668617i
$885$		0			0
$886$	−16.2238	−	60.5481i	−0.545050	−	2.03415i
$887$	−17.7822	+	4.76472i	−0.597067	+	0.159984i	−0.544681	−	0.838643i	$-0.683349\pi$
$887$	−17.7822	+	4.76472i	−0.597067	+	0.159984i	−0.0523860	+	0.998627i	$0.516683\pi$
$888$	1.04176	−	3.88791i	0.0349593	−	0.130470i
$889$	27.5345	+	27.5345i	0.923478	+	0.923478i
$890$		0			0
$891$	9.48236	−	35.3886i	0.317671	−	1.18556i
$892$			66.4120i			2.22364i
$893$	62.4957	+	16.7457i	2.09134	+	0.560372i
$894$	31.9194	−	55.2860i	1.06754	−	1.84904i
$895$		0			0
$896$			59.5559i			1.98962i
$897$	7.73017	+	0.183558i	0.258103	+	0.00612882i
$898$	−33.5211	+	33.5211i	−1.11861	+	1.11861i
$899$	−6.19283	+	1.65936i	−0.206542	+	0.0553428i
$900$		0			0
$901$	22.2052	−	12.8202i	0.739762	−	0.427102i
$902$	−52.3896			−1.74438
$903$	−6.75203	+	3.89828i	−0.224693	+	0.129727i
$904$	42.3247	+	11.3409i	1.40770	+	0.377192i
$905$		0			0
$906$	−31.3488	−	54.2977i	−1.04149	−	1.80392i
$907$	−3.37350	−	12.5901i	−0.112015	−	0.418046i	0.887031	−	0.461710i	$-0.152764\pi$
$907$	−3.37350	−	12.5901i	−0.112015	−	0.418046i	−0.999046	+	0.0436633i	$0.986097\pi$
$908$	11.0833	−	19.1969i	0.367813	−	0.637071i
$909$	−4.46703			−0.148162
$910$		0			0
$911$	−38.7946			−1.28532			−0.642662	−	0.766150i	$-0.722170\pi$
$911$	−38.7946			−1.28532			−0.642662	+	0.766150i	$0.722170\pi$
$912$	−0.766278	+	1.32723i	−0.0253740	+	0.0439491i
$913$	8.34922	+	31.1597i	0.276319	+	1.03124i
$914$	−2.93601	−	5.08532i	−0.0971146	−	0.168207i
$915$		0			0
$916$	30.0381	+	8.04869i	0.992487	+	0.265936i
$917$	0.193831	−	0.111908i	0.00640085	−	0.00369553i
$918$	−64.4713			−2.12787
$919$	−21.9085	+	12.6489i	−0.722695	+	0.417248i	−0.815744	−	0.578414i	$-0.803672\pi$
$919$	−21.9085	+	12.6489i	−0.722695	+	0.417248i	0.0930490	+	0.995662i	$0.470339\pi$
$920$		0			0
$921$	13.3896	−	3.58772i	0.441201	−	0.118219i
$922$	−16.4028	+	16.4028i	−0.540196	+	0.540196i
$923$	24.3485	−	23.2190i	0.801442	−	0.764263i
$924$		−	70.0852i		−	2.30563i
$925$		0			0
$926$	−14.0529	+	24.3403i	−0.461806	+	0.799871i
$927$	−1.17911	−	0.315941i	−0.0387270	−	0.0103769i
$928$			5.60973i			0.184148i
$929$	−10.0323	+	37.4412i	−0.329150	+	1.22841i	0.580923	+	0.813959i	$0.302692\pi$
$929$	−10.0323	+	37.4412i	−0.329150	+	1.22841i	−0.910073	+	0.414448i	$0.863975\pi$
$930$		0			0
$931$	18.5704	+	18.5704i	0.608620	+	0.608620i
$932$	−17.9365	+	66.9398i	−0.587528	+	2.19268i
$933$	3.01842	−	0.808784i	0.0988188	−	0.0264784i
$934$	13.6778	+	51.0462i	0.447551	+	1.67028i
$935$		0			0
$936$	−0.122777	+	5.17053i	−0.00401311	+	0.169004i
$937$	−18.4851	−	18.4851i	−0.603883	−	0.603883i	0.337457	−	0.941341i	$-0.390433\pi$
$937$	−18.4851	−	18.4851i	−0.603883	−	0.603883i	−0.941341	+	0.337457i	$0.890433\pi$
$938$	53.3362	+	30.7937i	1.74149	+	1.00545i
$939$	−36.3091	−	20.9631i	−1.18490	−	0.684105i
$940$		0			0
$941$	13.1581	−	13.1581i	0.428942	−	0.428942i	−0.459326	−	0.888268i	$-0.651909\pi$
$941$	13.1581	−	13.1581i	0.428942	−	0.428942i	0.888268	+	0.459326i	$0.151909\pi$
$942$	48.2795	+	83.6225i	1.57303	+	2.72457i
$943$	3.66259	+	6.34379i	0.119270	+	0.206582i
$944$	0.492012	−	0.492012i	0.0160136	−	0.0160136i
$945$		0			0
$946$	9.21157	+	5.31830i	0.299494	+	0.172913i
$947$	21.7601	+	12.5632i	0.707109	+	0.408249i	0.809990	−	0.586444i	$-0.199473\pi$
$947$	21.7601	+	12.5632i	0.707109	+	0.408249i	−0.102881	+	0.994694i	$0.532806\pi$
$948$	−43.9007	−	43.9007i	−1.42583	−	1.42583i
$949$	−14.8980	+	24.4450i	−0.483610	+	0.793518i
$950$		0			0
$951$	0.728445	+	2.71859i	0.0236215	+	0.0881565i
$952$	−53.8622	+	14.4323i	−1.74568	+	0.467754i
$953$	4.34536	−	16.2171i	0.140760	−	0.525324i	−0.859147	−	0.511728i	$-0.829006\pi$
$953$	4.34536	−	16.2171i	0.140760	−	0.525324i	0.999908	−	0.0135958i	$-0.00432781\pi$
$954$	3.43891	+	3.43891i	0.111339	+	0.111339i
$955$		0			0
$956$	−9.76778	+	36.4539i	−0.315913	+	1.17900i
$957$		−	6.77626i		−	0.219045i
$958$	30.7133	+	8.22961i	0.992303	+	0.265887i
$959$	−16.9683	+	29.3899i	−0.547934	+	0.949049i
$960$		0			0
$961$		−	9.04245i		−	0.291692i
$962$	0.146308	−	6.16146i	0.00471716	−	0.198654i
$963$	−3.45577	+	3.45577i	−0.111361	+	0.111361i
$964$	57.7292	−	15.4685i	1.85933	−	0.498207i
$965$		0			0
$966$	−13.6942	+	7.90636i	−0.440604	+	0.254383i
$967$	58.5376			1.88244			0.941222	−	0.337790i	$-0.109679\pi$
$967$	58.5376			1.88244			0.941222	+	0.337790i	$0.109679\pi$
$968$	−4.48239	+	2.58791i	−0.144069	+	0.0831785i
$969$	85.3629	+	22.8729i	2.74225	+	0.734784i
$970$		0			0
$971$	−15.3457	−	26.5795i	−0.492467	−	0.852977i	0.507496	−	0.861654i	$-0.330571\pi$
$971$	−15.3457	−	26.5795i	−0.492467	−	0.852977i	−0.999962	+	0.00867714i	$0.997238\pi$
$972$	−4.31202	−	16.0927i	−0.138308	−	0.516173i
$973$	14.8859	−	25.7831i	0.477220	−	0.826569i
$974$	−18.9229			−0.606328
$975$		0			0
$976$	−0.193405			−0.00619074
$977$	13.4383	−	23.2758i	0.429929	−	0.744659i	−0.566938	−	0.823761i	$-0.691872\pi$
$977$	13.4383	−	23.2758i	0.429929	−	0.744659i	0.996867	+	0.0791020i	$0.0252053\pi$
$978$	9.65323	+	36.0263i	0.308676	+	1.15200i
$979$	1.21709	+	2.10807i	0.0388985	+	0.0673741i
$980$		0			0
$981$	−4.18462	−	1.12126i	−0.133605	−	0.0357992i
$982$	−74.5074	+	43.0169i	−2.37763	+	1.37272i
$983$	10.4201			0.332350			0.166175	−	0.986096i	$-0.446858\pi$
$983$	10.4201			0.332350			0.166175	+	0.986096i	$0.446858\pi$
$984$	−29.8703	+	17.2456i	−0.952230	+	0.549770i
$985$		0			0
$986$	−13.4789	+	3.61167i	−0.429257	+	0.115019i
$987$	−34.9541	+	34.9541i	−1.11260	+	1.11260i
$988$	−26.0475	+	88.7290i	−0.828682	+	2.82285i
$989$		−	1.48722i		−	0.0472910i
$990$		0			0
$991$	19.1088	−	33.0974i	0.607011	−	1.05137i	−0.384719	−	0.923034i	$-0.625702\pi$
$991$	19.1088	−	33.0974i	0.607011	−	1.05137i	0.991730	−	0.128341i	$-0.0409651\pi$
$992$	−33.8424	−	9.06804i	−1.07450	−	0.287911i
$993$		−	4.44543i		−	0.141071i
$994$	−17.8078	+	66.4595i	−0.564828	+	2.10797i
$995$		0			0
$996$	38.8693	+	38.8693i	1.23162	+	1.23162i
$997$	−7.84331	+	29.2716i	−0.248400	+	0.927042i	0.723244	+	0.690593i	$0.242650\pi$
$997$	−7.84331	+	29.2716i	−0.248400	+	0.927042i	−0.971644	+	0.236449i	$0.924016\pi$
$998$	−82.3947	+	22.0776i	−2.60816	+	0.698854i
$999$	0.903044	+	3.37020i	0.0285710	+	0.106629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.s.c.32.9	yes	40
5.2	odd	4		325.2.x.c.318.9	yes	40
5.3	odd	4		325.2.x.c.318.2	yes	40
5.4	even	2	inner	325.2.s.c.32.2	✓	40
13.11	odd	12		325.2.x.c.232.2	yes	40
65.24	odd	12		325.2.x.c.232.9	yes	40
65.37	even	12	inner	325.2.s.c.193.2	yes	40
65.63	even	12	inner	325.2.s.c.193.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.32.2	✓	40	5.4	even	2	inner
325.2.s.c.32.9	yes	40	1.1	even	1	trivial
325.2.s.c.193.2	yes	40	65.37	even	12	inner
325.2.s.c.193.9	yes	40	65.63	even	12	inner
325.2.x.c.232.2	yes	40	13.11	odd	12
325.2.x.c.232.9	yes	40	65.24	odd	12
325.2.x.c.318.2	yes	40	5.3	odd	4
325.2.x.c.318.9	yes	40	5.2	odd	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14665 - 1.98606i) q^{2} +(-0.483980 - 1.80624i) q^{3} +(-1.62962 - 2.82258i) q^{4} +(-4.14225 - 1.10991i) q^{6} +(2.78443 - 1.60759i) q^{7} -2.88781 q^{8} +(-0.430177 + 0.248363i) q^{9} +O(q^{10})\)	\(q+(1.14665 - 1.98606i) q^{2} +(-0.483980 - 1.80624i) q^{3} +(-1.62962 - 2.82258i) q^{4} +(-4.14225 - 1.10991i) q^{6} +(2.78443 - 1.60759i) q^{7} -2.88781 q^{8} +(-0.430177 + 0.248363i) q^{9} +(-3.45476 + 0.925701i) q^{11} +(-4.30955 + 4.30955i) q^{12} +(-1.87639 + 3.07882i) q^{13} -7.37338i q^{14} +(-0.0520747 + 0.0901960i) q^{16} +(5.80109 + 1.55440i) q^{17} +1.13914i q^{18} +(-2.03669 + 7.60104i) q^{19} +(-4.25130 - 4.25130i) q^{21} +(-2.12291 + 7.92281i) q^{22} +(1.10778 - 0.296828i) q^{23} +(1.39764 + 5.21607i) q^{24} +(3.96315 + 7.25696i) q^{26} +(-3.30997 - 3.30997i) q^{27} +(-9.07511 - 5.23952i) q^{28} +(-0.877436 - 0.506588i) q^{29} +(4.47451 - 4.47451i) q^{31} +(-2.76839 - 4.79499i) q^{32} +(3.34407 + 5.79210i) q^{33} +(9.73895 - 9.73895i) q^{34} +(1.40205 + 0.809474i) q^{36} +(-0.645511 - 0.372686i) q^{37} +(12.7607 + 12.7607i) q^{38} +(6.46922 + 1.89912i) q^{39} +(1.65312 + 6.16954i) q^{41} +(-13.3181 + 3.56857i) q^{42} +(0.335632 - 1.25260i) q^{43} +(8.24281 + 8.24281i) q^{44} +(0.680717 - 2.54047i) q^{46} -8.22199i q^{47} +(0.188118 + 0.0504062i) q^{48} +(1.66870 - 2.89027i) q^{49} -11.2304i q^{51} +(11.7480 + 0.278965i) q^{52} +(3.01886 - 3.01886i) q^{53} +(-10.3692 + 2.77841i) q^{54} +(-8.04090 + 4.64242i) q^{56} +14.7150 q^{57} +(-2.01223 + 1.16176i) q^{58} +(-6.45324 - 1.72914i) q^{59} +(0.928497 + 1.60820i) q^{61} +(-3.75593 - 14.0173i) q^{62} +(-0.798532 + 1.38310i) q^{63} -12.9058 q^{64} +15.3379 q^{66} +(-4.17633 + 7.23362i) q^{67} +(-5.06615 - 18.9071i) q^{68} +(-1.07228 - 1.85725i) q^{69} +(-9.01343 - 2.41514i) q^{71} +(1.24227 - 0.717225i) q^{72} +7.93972 q^{73} +(-1.48035 + 0.854682i) q^{74} +(24.7736 - 6.63806i) q^{76} +(-8.13139 + 8.13139i) q^{77} +(11.1897 - 10.6706i) q^{78} +10.1869i q^{79} +(-5.12172 + 8.87108i) q^{81} +(14.1486 + 3.79111i) q^{82} -9.01936i q^{83} +(-5.07164 + 18.9276i) q^{84} +(-2.10288 - 2.10288i) q^{86} +(-0.490356 + 1.83003i) q^{87} +(9.97670 - 2.67325i) q^{88} +(-0.176147 - 0.657390i) q^{89} +(-0.275194 + 11.5892i) q^{91} +(-2.64308 - 2.64308i) q^{92} +(-10.2476 - 5.91645i) q^{93} +(-16.3294 - 9.42776i) q^{94} +(-7.32104 + 7.32104i) q^{96} +(6.80414 + 11.7851i) q^{97} +(-3.82682 - 6.62825i) q^{98} +(1.25625 - 1.25625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9}+O(q^{10}) \) 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9	\( 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46} + 28 q^{49} - 68 q^{54} + 72 q^{56} - 72 q^{59} + 144 q^{64} + 24 q^{66} - 80 q^{69} - 52 q^{71} + 168 q^{74} + 8 q^{76} - 20 q^{81} - 248 q^{84} - 168 q^{86} + 60 q^{89} - 100 q^{91} - 156 q^{94} - 36 q^{96} + 208 q^{99}+O(q^{100}) \) 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Introduction

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