LMFDB - Embedded newform 325.2.x.c.232.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(7,325)]

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, 11]))

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

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

chi := DirichletCharacter("325.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (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			232.2
Character	$\chi$	$=$	325.232
Dual form			325.2.x.c.318.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98606 + 1.14665i) q^{2} +(1.80624 + 0.483980i) q^{3} +(1.62962 - 2.82258i) q^{4} +(-4.14225 + 1.10991i) q^{6} +(-1.60759 + 2.78443i) q^{7} +2.88781i q^{8} +(0.430177 + 0.248363i) q^{9} +O(q^{10})$	\(q+(-1.98606 + 1.14665i) q^{2} +(1.80624 + 0.483980i) q^{3} +(1.62962 - 2.82258i) q^{4} +(-4.14225 + 1.10991i) q^{6} +(-1.60759 + 2.78443i) q^{7} +2.88781i q^{8} +(0.430177 + 0.248363i) q^{9} +(-3.45476 - 0.925701i) q^{11} +(4.30955 - 4.30955i) q^{12} +(-3.07882 + 1.87639i) q^{13} -7.37338i q^{14} +(-0.0520747 - 0.0901960i) q^{16} +(1.55440 + 5.80109i) q^{17} -1.13914 q^{18} +(2.03669 + 7.60104i) q^{19} +(-4.25130 + 4.25130i) q^{21} +(7.92281 - 2.12291i) q^{22} +(0.296828 - 1.10778i) q^{23} +(-1.39764 + 5.21607i) q^{24} +(3.96315 - 7.25696i) q^{26} +(-3.30997 - 3.30997i) q^{27} +(5.23952 + 9.07511i) q^{28} +(0.877436 - 0.506588i) q^{29} +(4.47451 + 4.47451i) q^{31} +(-4.79499 - 2.76839i) q^{32} +(-5.79210 - 3.34407i) q^{33} +(-9.73895 - 9.73895i) q^{34} +(1.40205 - 0.809474i) q^{36} +(-0.372686 - 0.645511i) q^{37} +(-12.7607 - 12.7607i) q^{38} +(-6.46922 + 1.89912i) q^{39} +(1.65312 - 6.16954i) q^{41} +(3.56857 - 13.3181i) q^{42} +(1.25260 - 0.335632i) q^{43} +(-8.24281 + 8.24281i) q^{44} +(0.680717 + 2.54047i) q^{46} -8.22199 q^{47} +(-0.0504062 - 0.188118i) q^{48} +(-1.66870 - 2.89027i) q^{49} +11.2304i q^{51} +(0.278965 + 11.7480i) q^{52} +(3.01886 - 3.01886i) q^{53} +(10.3692 + 2.77841i) q^{54} +(-8.04090 - 4.64242i) q^{56} +14.7150i q^{57} +(-1.16176 + 2.01223i) q^{58} +(6.45324 - 1.72914i) q^{59} +(0.928497 - 1.60820i) q^{61} +(-14.0173 - 3.75593i) q^{62} +(-1.38310 + 0.798532i) q^{63} +12.9058 q^{64} +15.3379 q^{66} +(7.23362 - 4.17633i) q^{67} +(18.9071 + 5.06615i) q^{68} +(1.07228 - 1.85725i) q^{69} +(-9.01343 + 2.41514i) q^{71} +(-0.717225 + 1.24227i) q^{72} -7.93972i q^{73} +(1.48035 + 0.854682i) q^{74} +(24.7736 + 6.63806i) q^{76} +(8.13139 - 8.13139i) q^{77} +(10.6706 - 11.1897i) q^{78} +10.1869i q^{79} +(-5.12172 - 8.87108i) q^{81} +(3.79111 + 14.1486i) q^{82} +9.01936 q^{83} +(5.07164 + 18.9276i) q^{84} +(-2.10288 + 2.10288i) q^{86} +(1.83003 - 0.490356i) q^{87} +(2.67325 - 9.97670i) q^{88} +(0.176147 - 0.657390i) q^{89} +(-0.275194 - 11.5892i) q^{91} +(-2.64308 - 2.64308i) q^{92} +(5.91645 + 10.2476i) q^{93} +(16.3294 - 9.42776i) q^{94} +(-7.32104 - 7.32104i) q^{96} +(11.7851 + 6.80414i) q^{97} +(6.62825 + 3.82682i) 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−1.98606	+	1.14665i	−1.40436	+	0.810805i	−0.994836	−	0.101497i	$-0.967637\pi$
$2$	−1.98606	+	1.14665i	−1.40436	+	0.810805i	−0.409519	+	0.912301i	$0.634304\pi$
$3$	1.80624	+	0.483980i	1.04283	+	0.279426i	0.739286	−	0.673391i	$-0.235163\pi$
$3$	1.80624	+	0.483980i	1.04283	+	0.279426i	0.303545	+	0.952817i	$0.401830\pi$
$4$	1.62962	−	2.82258i	0.814809	−	1.41129i
$5$		0			0
$5$		0			0
$6$	−4.14225	+	1.10991i	−1.69107	+	0.453120i
$7$	−1.60759	+	2.78443i	−0.607612	+	1.05242i	0.384021	+	0.923325i	$0.374539\pi$
$7$	−1.60759	+	2.78443i	−0.607612	+	1.05242i	−0.991633	+	0.129091i	$0.958794\pi$
$8$			2.88781i			1.02100i
$9$	0.430177	+	0.248363i	0.143392	+	0.0827877i
$10$		0			0
$11$	−3.45476	−	0.925701i	−1.04165	−	0.279109i	−0.302853	−	0.953037i	$-0.597939\pi$
$11$	−3.45476	−	0.925701i	−1.04165	−	0.279109i	−0.738797	+	0.673928i	$0.764606\pi$
$12$	4.30955	−	4.30955i	1.24406	−	1.24406i
$13$	−3.07882	+	1.87639i	−0.853912	+	0.520418i
$13$	−3.07882	+	1.87639i	−0.853912	+	0.520418i
$14$		−	7.37338i		−	1.97062i
$15$		0			0
$16$	−0.0520747	−	0.0901960i	−0.0130187	−	0.0225490i
$17$	1.55440	+	5.80109i	0.376997	+	1.40697i	0.850405	+	0.526128i	$0.176357\pi$
$17$	1.55440	+	5.80109i	0.376997	+	1.40697i	−0.473409	+	0.880843i	$0.656977\pi$
$18$	−1.13914			−0.268499
$19$	2.03669	+	7.60104i	0.467249	+	1.74380i	0.649324	+	0.760512i	$0.275052\pi$
$19$	2.03669	+	7.60104i	0.467249	+	1.74380i	−0.182075	+	0.983285i	$0.558281\pi$
$20$		0			0
$21$	−4.25130	+	4.25130i	−0.927709	+	0.927709i
$22$	7.92281	−	2.12291i	1.68915	−	0.452606i
$23$	0.296828	−	1.10778i	0.0618930	−	0.230988i	−0.928050	−	0.372456i	$-0.878516\pi$
$23$	0.296828	−	1.10778i	0.0618930	−	0.230988i	0.989943	+	0.141468i	$0.0451824\pi$
$24$	−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
$28$	5.23952	+	9.07511i	0.990176	+	1.71503i
$29$	0.877436	−	0.506588i	0.162936	−	0.0940710i	−0.416315	−	0.909221i	$-0.636679\pi$
$29$	0.877436	−	0.506588i	0.162936	−	0.0940710i	0.579251	+	0.815150i	$0.303345\pi$
$30$		0			0
$31$	4.47451	+	4.47451i	0.803645	+	0.803645i	0.983663	−	0.180018i	$-0.0576156\pi$
$31$	4.47451	+	4.47451i	0.803645	+	0.803645i	−0.180018	+	0.983663i	$0.557616\pi$
$32$	−4.79499	−	2.76839i	−0.847642	−	0.489386i
$33$	−5.79210	−	3.34407i	−1.00827	−	0.582128i
$34$	−9.73895	−	9.73895i	−1.67022	−	1.67022i
$35$		0			0
$36$	1.40205	−	0.809474i	0.233675	−	0.134912i
$37$	−0.372686	−	0.645511i	−0.0612692	−	0.106121i	0.833764	−	0.552121i	$-0.186181\pi$
$37$	−0.372686	−	0.645511i	−0.0612692	−	0.106121i	−0.895033	+	0.446000i	$0.852848\pi$
$38$	−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	−0.708122	−	0.706090i	$-0.750457\pi$
$41$	1.65312	−	6.16954i	0.258175	−	0.963521i	0.966297	−	0.257431i	$-0.0828759\pi$
$42$	3.56857	−	13.3181i	0.550642	−	2.05502i
$43$	1.25260	−	0.335632i	0.191019	−	0.0511834i	−0.162041	−	0.986784i	$-0.551808\pi$
$43$	1.25260	−	0.335632i	0.191019	−	0.0511834i	0.353060	+	0.935601i	$0.385141\pi$
$44$	−8.24281	+	8.24281i	−1.24265	+	1.24265i
$45$		0			0
$46$	0.680717	+	2.54047i	0.100366	+	0.374572i
$47$	−8.22199			−1.19930			−0.599650	−	0.800262i	$-0.704694\pi$
$47$	−8.22199			−1.19930			−0.599650	+	0.800262i	$0.704694\pi$
$48$	−0.0504062	−	0.188118i	−0.00727551	−	0.0271526i
$49$	−1.66870	−	2.89027i	−0.238385	−	0.412895i
$50$		0			0
$51$			11.2304i			1.57258i
$52$	0.278965	+	11.7480i	0.0386854	+	1.62916i
$53$	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
$57$			14.7150i			1.94905i
$58$	−1.16176	+	2.01223i	−0.152546	+	0.264218i
$59$	6.45324	−	1.72914i	0.840141	−	0.225115i	0.187008	−	0.982358i	$-0.440121\pi$
$59$	6.45324	−	1.72914i	0.840141	−	0.225115i	0.653133	+	0.757243i	$0.273454\pi$
$60$		0			0
$61$	0.928497	−	1.60820i	0.118882	−	0.205909i	−0.800443	−	0.599409i	$-0.795402\pi$
$61$	0.928497	−	1.60820i	0.118882	−	0.205909i	0.919325	+	0.393500i	$0.128736\pi$
$62$	−14.0173	−	3.75593i	−1.78020	−	0.477004i
$63$	−1.38310	+	0.798532i	−0.174254	+	0.100606i
$64$	12.9058			1.61322
$65$		0			0
$66$	15.3379			1.88797
$67$	7.23362	−	4.17633i	0.883727	−	0.510220i	0.0118416	−	0.999930i	$-0.496231\pi$
$67$	7.23362	−	4.17633i	0.883727	−	0.510220i	0.871885	+	0.489710i	$0.162897\pi$
$68$	18.9071	+	5.06615i	2.29283	+	0.614361i
$69$	1.07228	−	1.85725i	0.129088	−	0.223587i
$70$		0			0
$71$	−9.01343	+	2.41514i	−1.06970	+	0.286625i	−0.750369	−	0.661019i	$-0.770124\pi$
$71$	−9.01343	+	2.41514i	−1.06970	+	0.286625i	−0.319329	+	0.947644i	$0.603457\pi$
$72$	−0.717225	+	1.24227i	−0.0845258	+	0.146403i
$73$		−	7.93972i		−	0.929274i	−0.885501	−	0.464637i	$-0.846185\pi$
$73$		−	7.93972i		−	0.929274i	0.885501	−	0.464637i	$-0.153815\pi$
$74$	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
$78$	10.6706	−	11.1897i	1.20821	−	1.26698i
$79$			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
$82$	3.79111	+	14.1486i	0.418658	+	1.56245i
$83$	9.01936			0.990003			0.495002	−	0.868892i	$-0.335167\pi$
$83$	9.01936			0.990003			0.495002	+	0.868892i	$0.335167\pi$
$84$	5.07164	+	18.9276i	0.553361	+	2.06517i
$85$		0			0
$86$	−2.10288	+	2.10288i	−0.226759	+	0.226759i
$87$	1.83003	−	0.490356i	0.196200	−	0.0525717i
$88$	2.67325	−	9.97670i	0.284969	−	1.06352i
$89$	0.176147	−	0.657390i	0.0186716	−	0.0696832i	−0.955961	−	0.293492i	$-0.905183\pi$
$89$	0.176147	−	0.657390i	0.0186716	−	0.0696832i	0.974633	+	0.223809i	$0.0718492\pi$
$90$		0			0
$91$	−0.275194	−	11.5892i	−0.0288481	−	1.21488i
$92$	−2.64308	−	2.64308i	−0.275560	−	0.275560i
$93$	5.91645	+	10.2476i	0.613507	+	1.06263i
$94$	16.3294	−	9.42776i	1.68424	−	0.972399i
$95$		0			0
$96$	−7.32104	−	7.32104i	−0.747200	−	0.747200i
$97$	11.7851	+	6.80414i	1.19660	+	0.690856i	0.959795	−	0.280702i	$-0.0905671\pi$
$97$	11.7851	+	6.80414i	1.19660	+	0.690856i	0.236803	+	0.971558i	$0.423900\pi$
$98$	6.62825	+	3.82682i	0.669555	+	0.386568i
$99$	−1.25625	−	1.25625i	−0.126258	−	0.126258i
$100$		0			0
$101$	7.78812	−	4.49648i	0.774947	−	0.447416i	−0.0596893	−	0.998217i	$-0.519011\pi$
$101$	7.78812	−	4.49648i	0.774947	−	0.447416i	0.834637	+	0.550801i	$0.185678\pi$
$102$	−12.8774	−	22.3043i	−1.27505	−	2.20845i
$103$	−1.73771	−	1.73771i	−0.171222	−	0.171222i	0.616294	−	0.787516i	$-0.288633\pi$
$103$	−1.73771	−	1.73771i	−0.171222	−	0.171222i	−0.787516	+	0.616294i	$0.788633\pi$
$104$	−5.41867	−	8.89106i	−0.531344	−	0.871840i
$105$		0			0
$106$	−2.53405	+	9.45721i	−0.246129	+	0.918566i
$107$	−2.54648	+	9.50358i	−0.246177	+	0.918745i	0.726611	+	0.687049i	$0.241094\pi$
$107$	−2.54648	+	9.50358i	−0.246177	+	0.918745i	−0.972788	+	0.231696i	$0.925572\pi$
$108$	−14.7367	+	3.94867i	−1.41804	+	0.379961i
$109$	−6.16709	+	6.16709i	−0.590700	+	0.590700i	−0.937820	−	0.347121i	$-0.887159\pi$
$109$	−6.16709	+	6.16709i	−0.590700	+	0.590700i	0.347121	+	0.937820i	$0.387159\pi$
$110$		0			0
$111$	−0.360745	−	1.34632i	−0.0342404	−	0.127787i
$112$	0.334859			0.0316412
$113$	3.92715	+	14.6563i	0.369435	+	1.37875i	0.861307	+	0.508084i	$0.169646\pi$
$113$	3.92715	+	14.6563i	0.369435	+	1.37875i	−0.491872	+	0.870668i	$0.663687\pi$
$114$	−16.8730	−	29.2248i	−1.58030	−	2.73715i
$115$		0			0
$116$		−	3.30218i		−	0.306600i
$117$	−1.79047	+	0.0425158i	−0.165529	+	0.00393058i
$118$	−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
$122$			4.25865i			0.385560i
$123$	5.97187	−	10.3436i	0.538465	−	0.932649i
$124$	19.9214	−	5.33792i	1.78900	−	0.479360i
$125$		0			0
$126$	1.83128	−	3.17186i	0.163143	−	0.282572i
$127$	11.6985	+	3.13461i	1.03807	+	0.278151i	0.737315	−	0.675549i	$-0.236093\pi$
$127$	11.6985	+	3.13461i	1.03807	+	0.278151i	0.300759	+	0.953700i	$0.402760\pi$
$128$	−16.0417	+	9.26167i	−1.41790	+	0.818624i
$129$	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	$0.499032\pi$
$132$	−18.8778	+	10.8991i	−1.64310	+	0.948646i
$133$	−24.4387	−	6.54833i	−2.11910	−	0.567812i
$134$	−9.57759	+	16.5889i	−0.827378	+	1.43306i
$135$		0			0
$136$	−16.7524	+	4.48880i	−1.43651	+	0.384912i
$137$	5.27754	−	9.14097i	0.450891	−	0.780966i	−0.547551	−	0.836773i	$-0.684440\pi$
$137$	5.27754	−	9.14097i	0.450891	−	0.780966i	0.998442	+	0.0558064i	$0.0177730\pi$
$138$			4.91814i			0.418660i
$139$	−8.01918	−	4.62988i	−0.680178	−	0.392701i	0.119744	−	0.992805i	$-0.461793\pi$
$139$	−8.01918	−	4.62988i	−0.680178	−	0.392701i	−0.799922	+	0.600104i	$0.795126\pi$
$140$		0			0
$141$	−14.8509	−	3.97928i	−1.25067	−	0.335116i
$142$	15.1319	−	15.1319i	1.26984	−	1.26984i
$143$	12.3736	−	3.63242i	1.03473	−	0.303758i
$144$		−	0.0517337i		−	0.00431114i
$145$		0			0
$146$	9.10409	+	15.7687i	0.753460	+	1.30503i
$147$	−1.61523	−	6.02812i	−0.133222	−	0.497191i
$148$	−2.42934			−0.199691
$149$	3.85291	+	14.3792i	0.315642	+	1.17799i	0.923390	+	0.383863i	$0.125407\pi$
$149$	3.85291	+	14.3792i	0.315642	+	1.17799i	−0.607748	+	0.794130i	$0.707927\pi$
$150$		0			0
$151$	10.3382	−	10.3382i	0.841308	−	0.841308i	−0.147721	−	0.989029i	$-0.547194\pi$
$151$	10.3382	−	10.3382i	0.841308	−	0.841308i	0.989029	+	0.147721i	$0.0471937\pi$
$152$	−21.9503	+	5.88158i	−1.78041	+	0.477059i
$153$	−0.772110	+	2.88155i	−0.0624214	+	0.232960i
$154$	−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	$-0.605346\pi$
$158$	−11.6808	−	20.2317i	−0.929272	−	1.60955i
$159$	6.91384	−	3.99171i	0.548303	−	0.316563i
$160$		0			0
$161$	2.60735	+	2.60735i	0.205488	+	0.205488i
$162$	20.3441	+	11.7457i	1.59838	+	0.922826i
$163$	7.53208	+	4.34865i	0.589958	+	0.340612i	0.765081	−	0.643934i	$-0.222699\pi$
$163$	7.53208	+	4.34865i	0.589958	+	0.340612i	−0.175123	+	0.984547i	$0.556032\pi$
$164$	−14.7201	−	14.7201i	−1.14944	−	1.14944i
$165$		0			0
$166$	−17.9130	+	10.3421i	−1.39032	+	0.802699i
$167$	−1.67124	−	2.89467i	−0.129324	−	0.223996i	0.794091	−	0.607799i	$-0.207947\pi$
$167$	−1.67124	−	2.89467i	−0.129324	−	0.223996i	−0.923415	+	0.383803i	$0.874614\pi$
$168$	−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
$172$	1.09390	−	4.08251i	0.0834094	−	0.311288i
$173$	−4.66127	+	1.24898i	−0.354390	+	0.0949585i	−0.431622	−	0.902055i	$-0.642058\pi$
$173$	−4.66127	+	1.24898i	−0.354390	+	0.0949585i	0.0772319	+	0.997013i	$0.475392\pi$
$174$	−3.07229	+	3.07229i	−0.232910	+	0.232910i
$175$		0			0
$176$	0.0964112	+	0.359811i	0.00726727	+	0.0271218i
$177$	12.4930			0.939028
$178$	0.403959	+	1.50760i	0.0302780	+	0.112999i
$179$	1.57907	+	2.73504i	0.118025	+	0.204426i	0.918985	−	0.394292i	$-0.129010\pi$
$179$	1.57907	+	2.73504i	0.118025	+	0.204426i	−0.800960	+	0.598718i	$0.795677\pi$
$180$		0			0
$181$		−	1.80661i		−	0.134284i	−0.997743	−	0.0671422i	$-0.978612\pi$
$181$		−	1.80661i		−	0.134284i	0.997743	−	0.0671422i	$-0.0213881\pi$
$182$	13.8354	+	22.7013i	1.02555	+	1.68274i
$183$	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
$187$		−	21.4803i		−	1.57079i
$188$	−13.3987	+	23.2072i	−0.977201	+	1.69256i
$189$	14.5375	−	3.89530i	1.05744	−	0.283341i
$190$		0			0
$191$	−11.0167	+	19.0815i	−0.797142	+	1.38069i	0.124328	+	0.992241i	$0.460322\pi$
$191$	−11.0167	+	19.0815i	−0.797142	+	1.38069i	−0.921470	+	0.388449i	$0.873011\pi$
$192$	23.3109	+	6.24614i	1.68232	+	0.450776i
$193$	−14.4151	+	8.32256i	−1.03762	+	0.599071i	−0.919159	−	0.393887i	$-0.871130\pi$
$193$	−14.4151	+	8.32256i	−1.03762	+	0.599071i	−0.118463	+	0.992958i	$0.537797\pi$
$194$	−31.2079			−2.24060
$195$		0			0
$196$	−10.8773			−0.776953
$197$	−2.43530	+	1.40602i	−0.173508	+	0.100175i	−0.584239	−	0.811582i	$-0.698607\pi$
$197$	−2.43530	+	1.40602i	−0.173508	+	0.100175i	0.410731	+	0.911757i	$0.365274\pi$
$198$	3.93547	+	1.05451i	0.279682	+	0.0749404i
$199$	−9.27945	+	16.0725i	−0.657803	+	1.13935i	0.323380	+	0.946269i	$0.395181\pi$
$199$	−9.27945	+	16.0725i	−0.657803	+	1.13935i	−0.981183	+	0.193079i	$0.938153\pi$
$200$		0			0
$201$	15.0869	−	4.04252i	1.06415	−	0.285137i
$202$	−10.3118	+	17.8605i	−0.725534	+	1.25666i
$203$			3.25754i			0.228635i
$204$	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
$208$	0.329572	+	0.179985i	0.0228517	+	0.0124797i
$209$		−	28.1451i		−	1.94684i
$210$		0			0
$211$	10.1084	+	17.5083i	0.695892	+	1.20532i	0.969879	+	0.243587i	$0.0783241\pi$
$211$	10.1084	+	17.5083i	0.695892	+	1.20532i	−0.273987	+	0.961733i	$0.588343\pi$
$212$	−3.60139	−	13.4406i	−0.247345	−	0.923102i
$213$	−17.4493			−1.19560
$214$	−5.83984	−	21.7946i	−0.399203	−	1.48985i
$215$		0			0
$216$	9.55857	−	9.55857i	0.650378	−	0.650378i
$217$	−19.6521	+	5.26577i	−1.33407	+	0.357464i
$218$	5.17670	−	19.3197i	0.350610	−	1.30849i
$219$	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
$223$	10.1883	+	17.6466i	0.682257	+	1.18170i	0.974290	+	0.225296i	$0.0723349\pi$
$223$	10.1883	+	17.6466i	0.682257	+	1.18170i	−0.292033	+	0.956408i	$0.594332\pi$
$224$	15.4168	−	8.90087i	1.03008	−	0.594714i
$225$		0			0
$226$	−24.6053	−	24.6053i	−1.63672	−	1.63672i
$227$	5.88999	+	3.40059i	0.390932	+	0.225705i	0.682564	−	0.730826i	$-0.260865\pi$
$227$	5.88999	+	3.40059i	0.390932	+	0.225705i	−0.291632	+	0.956531i	$0.594198\pi$
$228$	41.5342	+	23.9798i	2.75067	+	1.58810i
$229$	6.74680	+	6.74680i	0.445841	+	0.445841i	0.893969	−	0.448128i	$-0.147909\pi$
$229$	6.74680	+	6.74680i	0.445841	+	0.445841i	−0.448128	+	0.893969i	$0.647909\pi$
$230$		0			0
$231$	18.6226	−	10.7518i	1.22528	−	0.707416i
$232$	1.46293	+	2.53387i	0.0960460	+	0.166357i
$233$	15.0352	+	15.0352i	0.984989	+	0.984989i	0.999889	−	0.0148998i	$-0.00474292\pi$
$233$	15.0352	+	15.0352i	0.984989	+	0.984989i	−0.0148998	+	0.999889i	$0.504743\pi$
$234$	3.50722	−	2.13748i	0.229274	−	0.139731i
$235$		0			0
$236$	5.63568	−	21.0326i	0.366852	−	1.36911i
$237$	−4.93023	+	18.3999i	−0.320253	+	1.19520i
$238$	42.7737	−	11.4612i	2.77260	−	0.742917i
$239$	8.18783	−	8.18783i	0.529627	−	0.529627i	−0.390834	−	0.920461i	$-0.627813\pi$
$239$	8.18783	−	8.18783i	0.529627	−	0.529627i	0.920461	+	0.390834i	$0.127813\pi$
$240$		0			0
$241$	−4.74605	−	17.7125i	−0.305720	−	1.14096i	−0.932324	−	0.361624i	$-0.882222\pi$
$241$	−4.74605	−	17.7125i	−0.305720	−	1.14096i	0.626604	−	0.779338i	$-0.284444\pi$
$242$	−4.11028			−0.264219
$243$	−1.32302	−	4.93756i	−0.0848715	−	0.316745i
$244$	−3.02619	−	5.24152i	−0.193732	−	0.335554i
$245$		0			0
$246$			27.3906i			1.74636i
$247$	−20.5331	−	19.5806i	−1.30649	−	1.24588i
$248$	−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	0.997129	−	0.0757168i	$-0.0241245\pi$
$251$	22.6574	+	13.0812i	1.43012	+	0.825681i	0.432992	+	0.901398i	$0.357458\pi$
$252$			5.20521i			0.327897i
$253$	−2.05094	+	3.55234i	−0.128942	+	0.223333i
$254$	−26.8282	+	7.18860i	−1.68335	+	0.451053i
$255$		0			0
$256$	8.33402	−	14.4350i	0.520877	−	0.902185i
$257$	−7.98901	−	2.14065i	−0.498341	−	0.133530i	0.000888947	−	1.00000i	$-0.499717\pi$
$257$	−7.98901	−	2.14065i	−0.498341	−	0.133530i	−0.499230	+	0.866470i	$0.666384\pi$
$258$	−4.81604	+	2.78054i	−0.299833	+	0.173109i
$259$	2.39651			0.148912
$260$		0			0
$261$	0.503271			0.0311517
$262$	−0.138254	+	0.0798211i	−0.00854137	+	0.00493136i
$263$	12.7688	+	3.42140i	0.787360	+	0.210972i	0.630027	−	0.776573i	$-0.283044\pi$
$263$	12.7688	+	3.42140i	0.787360	+	0.210972i	0.157333	+	0.987546i	$0.449710\pi$
$264$	9.65703	−	16.7265i	0.594349	−	1.02944i
$265$		0			0
$266$	56.0453	−	15.0173i	3.43636	−	0.920770i
$267$	0.636327	−	1.10215i	0.0389426	−	0.0674505i
$268$		−	27.2233i		−	1.66293i
$269$	−4.88179	−	2.81850i	−0.297648	−	0.171847i	0.343738	−	0.939066i	$-0.388307\pi$
$269$	−4.88179	−	2.81850i	−0.297648	−	0.171847i	−0.641386	+	0.767218i	$0.721640\pi$
$270$		0			0
$271$	−7.32435	−	1.96255i	−0.444922	−	0.119217i	0.0294001	−	0.999568i	$-0.490640\pi$
$271$	−7.32435	−	1.96255i	−0.444922	−	0.119217i	−0.474323	+	0.880351i	$0.657307\pi$
$272$	0.442291	−	0.442291i	0.0268178	−	0.0268178i
$273$	5.11189	−	21.0661i	0.309386	−	1.27498i
$274$			24.2060i			1.46234i
$275$		0			0
$276$	−3.49483	−	6.05322i	−0.210364	−	0.364361i
$277$	−3.01947	−	11.2688i	−0.181422	−	0.677078i	−0.995368	−	0.0961367i	$-0.969351\pi$
$277$	−3.01947	−	11.2688i	−0.181422	−	0.677078i	0.813946	−	0.580941i	$-0.197315\pi$
$278$	21.2354			1.27362
$279$	0.813530	+	3.03613i	0.0487048	+	0.181769i
$280$		0			0
$281$	−9.46111	+	9.46111i	−0.564402	+	0.564402i	−0.930555	−	0.366153i	$-0.880675\pi$
$281$	−9.46111	+	9.46111i	−0.564402	+	0.564402i	0.366153	+	0.930555i	$0.380675\pi$
$282$	34.0575	−	9.12569i	2.02810	−	0.543427i
$283$	1.03853	−	3.87586i	0.0617344	−	0.230396i	−0.928165	−	0.372170i	$-0.878614\pi$
$283$	1.03853	−	3.87586i	0.0617344	−	0.230396i	0.989899	+	0.141774i	$0.0452806\pi$
$284$	−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
$288$	−1.37513	−	2.38180i	−0.0810303	−	0.140349i
$289$	−16.5141	+	9.53440i	−0.971415	+	0.560847i
$290$		0			0
$291$	17.9937	+	17.9937i	1.05481	+	1.05481i
$292$	−22.4105	−	12.9387i	−1.31148	−	0.757181i
$293$	−21.3692	−	12.3375i	−1.24840	−	0.720766i	−0.277613	−	0.960693i	$-0.589543\pi$
$293$	−21.3692	−	12.3375i	−1.24840	−	0.720766i	−0.970791	+	0.239927i	$0.922877\pi$
$294$	10.1201	+	10.1201i	0.590215	+	0.590215i
$295$		0			0
$296$	1.86411	−	1.07625i	0.108349	−	0.0625556i
$297$	8.37112	+	14.4992i	0.485742	+	0.841329i
$298$	−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
$302$	−8.67793	+	32.3865i	−0.499359	+	1.86363i
$303$	16.2434	−	4.35240i	0.933159	−	0.250039i
$304$	0.579523	−	0.579523i	0.0332379	−	0.0332379i
$305$		0			0
$306$	−1.77068	−	6.60827i	−0.101223	−	0.377770i
$307$	7.41296			0.423080			0.211540	−	0.977369i	$-0.432152\pi$
$307$	7.41296			0.423080			0.211540	+	0.977369i	$0.432152\pi$
$308$	−9.70045	−	36.2026i	−0.552734	−	2.06283i
$309$	−2.29770	−	3.97974i	−0.130712	−	0.226399i
$310$		0			0
$311$		−	1.67111i		−	0.0947601i	−0.998877	−	0.0473800i	$-0.984913\pi$
$311$		−	1.67111i		−	0.0947601i	0.998877	−	0.0473800i	$-0.0150872\pi$
$312$	−5.48430	−	18.6819i	−0.310487	−	1.05765i
$313$	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
$317$		−	1.50512i		−	0.0845357i	−0.999106	−	0.0422679i	$-0.986542\pi$
$317$		−	1.50512i		−	0.0845357i	0.999106	−	0.0422679i	$-0.0134583\pi$
$318$	−9.15420	+	15.8555i	−0.513342	+	0.889134i
$319$	−3.50028	+	0.937897i	−0.195978	+	0.0525122i
$320$		0			0
$321$	−9.19907	+	15.9333i	−0.513442	+	0.889308i
$322$	−8.16807	−	2.18863i	−0.455189	−	0.121968i
$323$	−40.9285	+	23.6301i	−2.27732	+	1.31481i
$324$	−33.3858			−1.85477
$325$		0			0
$326$	−19.9455			−1.10468
$327$	−14.1240	+	8.15447i	−0.781057	+	0.450943i
$328$	17.8165	+	4.77391i	0.983750	+	0.263595i
$329$	13.2176	−	22.8936i	0.728710	−	1.26216i
$330$		0			0
$331$	2.29629	−	0.615289i	0.126215	−	0.0338193i	−0.195158	−	0.980772i	$-0.562522\pi$
$331$	2.29629	−	0.615289i	0.126215	−	0.0338193i	0.321374	+	0.946952i	$0.395855\pi$
$332$	14.6981	−	25.4579i	0.806663	−	1.39718i
$333$		−	0.370246i		−	0.0202894i
$334$	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	−0.620043	−	0.784568i	$-0.712885\pi$
$337$	3.02028	−	3.02028i	0.164525	−	0.164525i	0.784568	+	0.620043i	$0.212885\pi$
$338$	1.41506	+	29.7793i	0.0769689	+	1.61978i
$339$			28.3735i			1.54104i
$340$		0			0
$341$	−11.3163	−	19.6004i	−0.612812	−	1.06142i
$342$	−2.32008	−	8.65867i	−0.125456	−	0.468207i
$343$	−11.7760			−0.635842
$344$	0.969242	+	3.61726i	0.0522580	+	0.195030i
$345$		0			0
$346$	7.82541	−	7.82541i	0.420697	−	0.420697i
$347$	−3.55664	+	0.952998i	−0.190930	+	0.0511596i	−0.353017	−	0.935617i	$-0.614844\pi$
$347$	−3.55664	+	0.952998i	−0.190930	+	0.0511596i	0.162087	+	0.986777i	$0.448178\pi$
$348$	1.59819	−	5.96452i	0.0856718	−	0.319732i
$349$	2.60923	−	9.73777i	0.139669	−	0.521251i	−0.860266	−	0.509845i	$-0.829703\pi$
$349$	2.60923	−	9.73777i	0.139669	−	0.521251i	0.999935	−	0.0114057i	$-0.00363061\pi$
$350$		0			0
$351$	16.4016	+	3.98001i	0.875454	+	0.212437i
$352$	14.0028	+	14.0028i	0.746354	+	0.746354i
$353$	−13.5575	−	23.4823i	−0.721593	−	1.24984i	−0.960361	−	0.278759i	$-0.910077\pi$
$353$	−13.5575	−	23.4823i	−0.721593	−	1.24984i	0.238768	−	0.971077i	$-0.423257\pi$
$354$	−24.8117	+	14.3251i	−1.31873	+	0.761368i
$355$		0			0
$356$	−1.56849	−	1.56849i	−0.0831296	−	0.0831296i
$357$	−31.2703	−	18.0539i	−1.65500	−	0.955516i
$358$	−6.27226	−	3.62129i	−0.331499	−	0.191391i
$359$	−0.894231	−	0.894231i	−0.0471957	−	0.0471957i	0.683115	−	0.730311i	$-0.260625\pi$
$359$	−0.894231	−	0.894231i	−0.0471957	−	0.0471957i	−0.730311	+	0.683115i	$0.760625\pi$
$360$		0			0
$361$	−37.1731	+	21.4619i	−1.95648	+	1.12957i
$362$	2.07155	+	3.58804i	0.108879	+	0.188583i
$363$	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
$367$	−3.36959	+	12.5755i	−0.175891	+	0.656436i	0.820507	+	0.571637i	$0.193691\pi$
$367$	−3.36959	+	12.5755i	−0.175891	+	0.656436i	−0.996398	+	0.0847988i	$0.972975\pi$
$368$	−0.115374	+	0.0309145i	−0.00601431	+	0.00161153i
$369$	2.24342	−	2.24342i	0.116788	−	0.116788i
$370$		0			0
$371$	3.55271	+	13.2589i	0.184448	+	0.688368i
$372$	38.5662			1.99957
$373$	−2.71659	−	10.1385i	−0.140660	−	0.524950i	−0.999910	−	0.0133946i	$-0.995736\pi$
$373$	−2.71659	−	10.1385i	−0.140660	−	0.524950i	0.859250	−	0.511555i	$-0.170930\pi$
$374$	24.6304	+	42.6611i	1.27361	+	2.20595i
$375$		0			0
$376$		−	23.7436i		−	1.22448i
$377$	−1.75091	+	3.20611i	−0.0901766	+	0.165123i
$378$	−24.4057	+	24.4057i	−1.25529	+	1.25529i
$379$	9.74593	+	2.61141i	0.500615	+	0.134139i	0.500285	−	0.865861i	$-0.333228\pi$
$379$	9.74593	+	2.61141i	0.500615	+	0.134139i	0.000329419		1.00000i	$0.499895\pi$
$380$		0			0
$381$	19.6132	+	11.3237i	1.00481	+	0.580130i
$382$		−	50.5293i		−	2.58531i
$383$	5.37726	−	9.31368i	0.274765	−	0.475907i	−0.695311	−	0.718709i	$-0.744733\pi$
$383$	5.37726	−	9.31368i	0.274765	−	0.475907i	0.970076	+	0.242802i	$0.0780666\pi$
$384$	−33.4575	+	8.96492i	−1.70737	+	0.457489i
$385$		0			0
$386$	19.0862	−	33.0582i	0.971460	−	1.68262i
$387$	0.622197	+	0.166717i	0.0316281	+	0.00847471i
$388$	38.4105	−	22.1763i	1.95000	−	1.12583i
$389$	−34.9585			−1.77247			−0.886234	−	0.463238i	$-0.846687\pi$
$389$	−34.9585			−1.77247			−0.886234	+	0.463238i	$0.846687\pi$
$390$		0			0
$391$	6.88771			0.348326
$392$	8.34654	−	4.81888i	0.421564	−	0.243390i
$393$	0.125736	+	0.0336910i	0.00634256	+	0.00169948i
$394$	3.22443	−	5.58487i	0.162444	−	0.281362i
$395$		0			0
$396$	−5.59308	+	1.49866i	−0.281063	+	0.0753105i
$397$	3.05319	−	5.28828i	0.153235	−	0.265411i	−0.779180	−	0.626801i	$-0.784364\pi$
$397$	3.05319	−	5.28828i	0.153235	−	0.265411i	0.932415	+	0.361389i	$0.117697\pi$
$398$		−	42.5612i		−	2.13340i
$399$	−40.9728	−	23.6557i	−2.05121	−	1.18426i
$400$		0			0
$401$	0.267716	+	0.0717343i	0.0133691	+	0.00358224i	0.265497	−	0.964112i	$-0.414464\pi$
$401$	0.267716	+	0.0717343i	0.0133691	+	0.00358224i	−0.252128	+	0.967694i	$0.581130\pi$
$402$	−25.3281	+	25.3281i	−1.26325	+	1.26325i
$403$	−22.1722	−	5.38029i	−1.10447	−	0.268011i
$404$		−	29.3102i		−	1.45823i
$405$		0			0
$406$	−3.73527	−	6.46967i	−0.185378	−	0.321084i
$407$	0.689992	+	2.57508i	0.0342016	+	0.127642i
$408$	−32.4314			−1.60559
$409$	−3.90517	−	14.5743i	−0.193098	−	0.720653i	−0.992751	−	0.120190i	$-0.961650\pi$
$409$	−3.90517	−	14.5743i	−0.193098	−	0.720653i	0.799653	−	0.600463i	$-0.205017\pi$
$410$		0			0
$411$	13.9565	−	13.9565i	0.688425	−	0.688425i
$412$	−7.73665	+	2.07303i	−0.381157	+	0.102131i
$413$	−5.55950	+	20.7483i	−0.273565	+	1.02096i
$414$	−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
$418$	32.2726	+	55.8979i	1.57851	+	2.73405i
$419$	7.65847	−	4.42162i	0.374141	−	0.216010i	−0.301125	−	0.953585i	$-0.597362\pi$
$419$	7.65847	−	4.42162i	0.374141	−	0.216010i	0.675266	+	0.737574i	$0.264029\pi$
$420$		0			0
$421$	6.58165	+	6.58165i	0.320770	+	0.320770i	0.849062	−	0.528292i	$-0.177168\pi$
$421$	6.58165	+	6.58165i	0.320770	+	0.320770i	−0.528292	+	0.849062i	$0.677168\pi$
$422$	−40.1518	−	23.1816i	−1.95456	−	1.12847i
$423$	−3.53692	−	2.04204i	−0.171971	−	0.0992873i
$424$	8.71790	+	8.71790i	0.423379	+	0.423379i
$425$		0			0
$426$	34.6553	−	20.0082i	1.67905	−	0.969402i
$427$	2.98529	+	5.17067i	0.144468	+	0.250226i
$428$	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	−0.905547	−	0.424245i	$-0.860540\pi$
$431$	1.88510	−	7.03529i	0.0908021	−	0.338878i	0.996350	+	0.0853669i	$0.0272062\pi$
$432$	−0.126180	+	0.470912i	−0.00607086	+	0.0226568i
$433$	10.5986	−	2.83990i	0.509338	−	0.136477i	0.00500749	−	0.999987i	$-0.498406\pi$
$433$	10.5986	−	2.83990i	0.509338	−	0.136477i	0.504330	+	0.863511i	$0.331739\pi$
$434$	32.9923	−	32.9923i	1.58368	−	1.58368i
$435$		0			0
$436$	7.35711	+	27.4571i	0.352342	+	1.31496i
$437$	9.02481			0.431715
$438$	8.81238	+	32.8883i	0.421072	+	1.57146i
$439$	5.86048	+	10.1506i	0.279705	+	0.484464i	0.971311	−	0.237811i	$-0.0764299\pi$
$439$	5.86048	+	10.1506i	0.279705	+	0.484464i	−0.691606	+	0.722275i	$0.743097\pi$
$440$		0			0
$441$		−	1.65777i		−	0.0789414i
$442$	48.2586	+	11.7104i	2.29543	+	0.557007i
$443$	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
$447$			27.8370i			1.31665i
$448$	−20.7472	+	35.9353i	−0.980215	+	1.69778i
$449$	19.9671	−	5.35017i	0.942306	−	0.252490i	0.245212	−	0.969470i	$-0.421142\pi$
$449$	19.9671	−	5.35017i	0.942306	−	0.252490i	0.697094	+	0.716979i	$0.254476\pi$
$450$		0			0
$451$	−11.4223	+	19.7840i	−0.537855	+	0.931592i
$452$	47.7685	+	12.7995i	2.24684	+	0.602039i
$453$	23.6766	−	13.6697i	1.11243	−	0.642259i
$454$	−15.5972			−0.732011
$455$		0			0
$456$	−42.4941			−1.98997
$457$	−2.21747	+	1.28025i	−0.103729	+	0.0598878i	−0.550967	−	0.834527i	$-0.685741\pi$
$457$	−2.21747	+	1.28025i	−0.103729	+	0.0598878i	0.447238	+	0.894415i	$0.352408\pi$
$458$	−21.1358	−	5.66331i	−0.987610	−	0.264629i
$459$	14.0564	−	24.3464i	0.656098	−	1.13639i
$460$		0			0
$461$	−9.77044	+	2.61798i	−0.455055	+	0.121932i	−0.479064	−	0.877780i	$-0.659024\pi$
$461$	−9.77044	+	2.61798i	−0.455055	+	0.121932i	0.0240087	+	0.999712i	$0.492357\pi$
$462$	−24.6571	+	42.7073i	−1.14715	+	1.98693i
$463$			12.2556i			0.569565i	0.958592	+	0.284782i	$0.0919213\pi$
$463$			12.2556i			0.569565i	−0.958592	+	0.284782i	$0.908079\pi$
$464$	−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	−0.221205	−	0.975227i	$-0.570999\pi$
$467$	16.2946	−	16.2946i	0.754023	−	0.754023i	0.975227	+	0.221205i	$0.0709988\pi$
$468$	−2.79777	+	5.12302i	−0.129327	+	0.236812i
$469$			26.8553i			1.24006i
$470$		0			0
$471$	−21.0524	−	36.4638i	−0.970043	−	1.68016i
$472$	4.99343	+	18.6357i	0.229841	+	0.857780i
$473$	−4.63811			−0.213261
$474$	−11.3065	−	42.1965i	−0.519325	−	1.93815i
$475$		0			0
$476$	−44.5012	+	44.5012i	−2.03971	+	2.03971i
$477$	2.04842	−	0.548872i	0.0937907	−	0.0251311i
$478$	−6.87292	+	25.6501i	−0.314360	+	1.17321i
$479$	−3.58854	+	13.3926i	−0.163965	+	0.611924i	0.834205	+	0.551454i	$0.185927\pi$
$479$	−3.58854	+	13.3926i	−0.163965	+	0.611924i	−0.998170	+	0.0604705i	$0.980740\pi$
$480$		0			0
$481$	2.35867	+	1.28811i	0.107546	+	0.0587328i
$482$	29.7360	+	29.7360i	1.35444	+	1.35444i
$483$	3.44759	+	5.97140i	0.156871	+	0.271708i
$484$	5.05891	−	2.92076i	0.229950	−	0.132762i
$485$		0			0
$486$	8.28925	+	8.28925i	0.376008	+	0.376008i
$487$	−7.14590	−	4.12568i	−0.323811	−	0.186953i	0.329279	−	0.944233i	$-0.393194\pi$
$487$	−7.14590	−	4.12568i	−0.323811	−	0.186953i	−0.653090	+	0.757280i	$0.726528\pi$
$488$	4.64419	+	2.68132i	0.210232	+	0.121378i
$489$	11.5001	+	11.5001i	0.520051	+	0.520051i
$490$		0			0
$491$	−32.4891	+	18.7576i	−1.46621	+	0.846519i	−0.999286	−	0.0377764i	$-0.987973\pi$
$491$	−32.4891	+	18.7576i	−1.46621	+	0.846519i	−0.466928	+	0.884295i	$0.654639\pi$
$492$	−19.4637	−	33.7122i	−0.877492	−	1.51986i
$493$	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
$497$	7.76512	−	28.9798i	0.348313	−	1.29992i
$498$	−37.3604	+	10.0107i	−1.67416	+	0.448590i
$499$	26.3014	−	26.3014i	1.17741	−	1.17741i	0.197011	−	0.980401i	$-0.436876\pi$
$499$	26.3014	−	26.3014i	1.17741	−	1.17741i	0.980401	−	0.197011i	$-0.0631235\pi$
$500$		0			0
$501$	−1.61769	−	6.03729i	−0.0722730	−	0.269726i
$502$	−59.9985			−2.67786
$503$	8.81098	+	32.8830i	0.392862	+	1.46618i	0.825391	+	0.564562i	$0.190955\pi$
$503$	8.81098	+	32.8830i	0.392862	+	1.46618i	−0.432528	+	0.901620i	$0.642378\pi$
$504$	−2.30601	−	3.99413i	−0.102718	−	0.177912i
$505$		0			0
$506$		−	9.40686i		−	0.418186i
$507$	16.3541	−	17.9858i	0.726310	−	0.798780i
$508$	27.9118	−	27.9118i	1.23839	−	1.23839i
$509$	−33.8235	−	9.06297i	−1.49920	−	0.401709i	−0.586367	−	0.810046i	$-0.699442\pi$
$509$	−33.8235	−	9.06297i	−1.49920	−	0.401709i	−0.912831	+	0.408337i	$0.866109\pi$
$510$		0			0
$511$	22.1076	+	12.7638i	0.977982	+	0.564638i
$512$			1.17818i			0.0520687i
$513$	18.4178	−	31.9006i	0.813166	−	1.40845i
$514$	18.3212	−	4.90916i	0.808115	−	0.216534i
$515$		0			0
$516$	3.95170	−	6.84454i	0.173964	−	0.301314i
$517$	28.4050	+	7.61110i	1.24925	+	0.334736i
$518$	−4.75960	+	2.74796i	−0.209125	+	0.120738i
$519$	−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	$0.446373\pi$
$522$	−0.999525	+	0.577076i	−0.0437480	+	0.0252579i
$523$	20.3577	+	5.45483i	0.890180	+	0.238523i	0.674794	−	0.738006i	$-0.264232\pi$
$523$	20.3577	+	5.45483i	0.890180	+	0.238523i	0.215386	+	0.976529i	$0.430899\pi$
$524$	0.113442	−	0.196487i	0.00495572	−	0.00858356i
$525$		0			0
$526$	−29.2828	+	7.84630i	−1.27679	+	0.342115i
$527$	−19.0019	+	32.9122i	−0.827734	+	1.43368i
$528$			0.696565i			0.0303141i
$529$	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
$533$	6.48681	+	22.0968i	0.280975	+	0.957120i
$534$			2.91858i			0.126299i
$535$		0			0
$536$	12.0605	+	20.8893i	0.520932	+	0.902281i
$537$	1.52848	+	5.70436i	0.0659587	+	0.246161i
$538$	12.9274			0.557338
$539$	3.08942	+	11.5299i	0.133071	+	0.496628i
$540$		0			0
$541$	15.4272	−	15.4272i	0.663267	−	0.663267i	−0.292882	−	0.956149i	$-0.594614\pi$
$541$	15.4272	−	15.4272i	0.663267	−	0.663267i	0.956149	+	0.292882i	$0.0946142\pi$
$542$	16.7969	−	4.50073i	0.721491	−	0.193323i
$543$	0.874364	−	3.26317i	0.0375225	−	0.140036i
$544$	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	$0.806031\pi$
$548$	−17.2008	−	29.7926i	−0.734780	−	1.27268i
$549$	0.798837	−	0.461209i	0.0340935	−	0.0196839i
$550$		0			0
$551$	5.63766	+	5.63766i	0.240172	+	0.240172i
$552$	5.36339	+	3.09655i	0.228281	+	0.131798i
$553$	−28.3646	−	16.3763i	−1.20618	−	0.696391i
$554$	18.9182	+	18.9182i	0.803759	+	0.803759i
$555$		0			0
$556$	−26.1364	+	15.0899i	−1.10843	+	0.639953i
$557$	11.5174	+	19.9488i	0.488009	+	0.845256i	0.999905	−	0.0137912i	$-0.00439001\pi$
$557$	11.5174	+	19.9488i	0.488009	+	0.845256i	−0.511896	+	0.859047i	$0.671057\pi$
$558$	−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
$562$	7.94172	−	29.6389i	0.335001	−	1.25024i
$563$	−5.85629	+	1.56919i	−0.246813	+	0.0661334i	−0.380105	−	0.924943i	$-0.624112\pi$
$563$	−5.85629	+	1.56919i	−0.246813	+	0.0661334i	0.133291	+	0.991077i	$0.457445\pi$
$564$	−35.4331	+	35.4331i	−1.49200	+	1.49200i
$565$		0			0
$566$	2.38167	+	8.88851i	0.100109	+	0.373612i
$567$	32.9345			1.38312
$568$	−6.97447	−	26.0291i	−0.292642	−	1.09216i
$569$	−11.2211	−	19.4355i	−0.470413	−	0.814779i	0.529015	−	0.848613i	$-0.322562\pi$
$569$	−11.2211	−	19.4355i	−0.470413	−	0.814779i	−0.999427	+	0.0338340i	$0.989228\pi$
$570$		0			0
$571$		−	41.7374i		−	1.74665i	−0.487135	−	0.873327i	$-0.661958\pi$
$571$		−	41.7374i		−	1.74665i	0.487135	−	0.873327i	$-0.338042\pi$
$572$	9.91140	−	40.8449i	0.414417	−	1.70781i
$573$	−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
$577$			10.4937i			0.436859i	0.975853	+	0.218429i	$0.0700933\pi$
$577$			10.4937i			0.436859i	−0.975853	+	0.218429i	$0.929907\pi$
$578$	21.8653	−	37.8717i	0.909475	−	1.57526i
$579$	−30.0650	+	8.05590i	−1.24946	+	0.334792i
$580$		0			0
$581$	−14.4994	+	25.1138i	−0.601538	+	1.04189i
$582$	−56.3689	−	15.1040i	−2.33657	−	0.626081i
$583$	−13.2240	+	7.63488i	−0.547682	+	0.316205i
$584$	22.9284			0.948784
$585$		0			0
$586$	56.5874			2.33760
$587$	40.6217	−	23.4529i	1.67664	−	0.968006i	0.712853	−	0.701313i	$-0.247402\pi$
$587$	40.6217	−	23.4529i	1.67664	−	0.968006i	0.963782	−	0.266693i	$-0.0859308\pi$
$588$	−19.6471	−	5.26441i	−0.810231	−	0.217101i
$589$	−24.8977	+	43.1241i	−1.02589	+	1.77690i
$590$		0			0
$591$	−5.07921	+	1.36097i	−0.208931	+	0.0559828i
$592$	−0.0388150	+	0.0672296i	−0.00159529	+	0.00276312i
$593$			24.0105i			0.985994i	0.870031	+	0.492997i	$0.164099\pi$
$593$			24.0105i			0.985994i	−0.870031	+	0.492997i	$0.835901\pi$
$594$	−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
$598$	−6.86273	−	6.54437i	−0.280638	−	0.267619i
$599$			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	−0.922052	−	0.387065i	$-0.873489\pi$
$601$	−19.5199	−	33.8095i	−0.796234	−	1.37912i	0.125818	−	0.992053i	$-0.459845\pi$
$602$	−2.47474	−	9.23587i	−0.100863	−	0.376426i
$603$	4.14899			0.168960
$604$	−12.3331	−	46.0276i	−0.501825	−	1.87284i
$605$		0			0
$606$	−27.2696	+	27.2696i	−1.10775	+	1.10775i
$607$	−21.7504	+	5.82801i	−0.882823	+	0.236552i	−0.671625	−	0.740892i	$-0.734403\pi$
$607$	−21.7504	+	5.82801i	−0.882823	+	0.236552i	−0.211198	+	0.977443i	$0.567737\pi$
$608$	11.2767	−	42.0852i	0.457331	−	1.70678i
$609$	−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
$613$	1.61960	+	2.80523i	0.0654151	+	0.113302i	0.896878	−	0.442278i	$-0.145830\pi$
$613$	1.61960	+	2.80523i	0.0654151	+	0.113302i	−0.831463	+	0.555580i	$0.812496\pi$
$614$	−14.7226	+	8.50008i	−0.594154	+	0.343035i
$615$		0			0
$616$	23.4819	+	23.4819i	0.946113	+	0.946113i
$617$	−30.1380	−	17.4002i	−1.21331	−	0.700504i	−0.249830	−	0.968290i	$-0.580375\pi$
$617$	−30.1380	−	17.4002i	−1.21331	−	0.700504i	−0.963478	+	0.267786i	$0.913708\pi$
$618$	9.12674	+	5.26933i	0.367131	+	0.211963i
$619$	5.38094	+	5.38094i	0.216278	+	0.216278i	0.806928	−	0.590650i	$-0.201129\pi$
$619$	5.38094	+	5.38094i	0.216278	+	0.216278i	−0.590650	+	0.806928i	$0.701129\pi$
$620$		0			0
$621$	−4.64921	+	2.68422i	−0.186566	+	0.107714i
$622$	1.91618	+	3.31893i	0.0768319	+	0.133077i
$623$	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
$627$	13.6217	−	50.8368i	0.543997	−	2.03022i
$628$	−70.8859	+	18.9938i	−2.82866	+	0.757936i
$629$	3.16537	−	3.16537i	0.126211	−	0.126211i
$630$		0			0
$631$	−10.4197	−	38.8868i	−0.414801	−	1.54806i	−0.785234	−	0.619199i	$-0.787457\pi$
$631$	−10.4197	−	38.8868i	−0.414801	−	1.54806i	0.370433	−	0.928859i	$-0.379209\pi$
$632$	−29.4177			−1.17017
$633$	9.78453	+	36.5164i	0.388900	+	1.45140i
$634$	1.72584	+	2.98925i	0.0685420	+	0.118718i
$635$		0			0
$636$		−	26.0198i		−	1.03175i
$637$	10.5609	+	5.76749i	0.418438	+	0.228516i
$638$	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	−0.261734	−	0.965140i	$-0.584294\pi$
$641$	−31.1015	−	17.9565i	−1.22844	−	0.709239i	−0.966703	+	0.255901i	$0.917628\pi$
$642$		−	42.1925i		−	1.66521i
$643$	3.02845	−	5.24544i	0.119431	−	0.206860i	−0.800112	−	0.599851i	$-0.795226\pi$
$643$	3.02845	−	5.24544i	0.119431	−	0.206860i	0.919542	+	0.392991i	$0.128560\pi$
$644$	11.6084	−	3.11047i	0.457437	−	0.122570i
$645$		0			0
$646$	54.1909	−	93.8613i	2.13211	−	3.69292i
$647$	−19.0229	−	5.09717i	−0.747867	−	0.200390i	−0.135295	−	0.990805i	$-0.543198\pi$
$647$	−19.0229	−	5.09717i	−0.747867	−	0.200390i	−0.612572	+	0.790415i	$0.709865\pi$
$648$	25.6180	−	14.7906i	1.00637	−	0.581028i
$649$	−23.8951			−0.937964
$650$		0			0
$651$	−38.0449			−1.49110
$652$	24.5488	−	14.1733i	0.961406	−	0.555068i
$653$	12.9452	+	3.46867i	0.506587	+	0.135739i	0.503055	−	0.864254i	$-0.332209\pi$
$653$	12.9452	+	3.46867i	0.506587	+	0.135739i	0.00353138	+	0.999994i	$0.498876\pi$
$654$	18.7007	−	32.3905i	0.731254	−	1.26657i
$655$		0			0
$656$	−0.642554	+	0.172172i	−0.0250875	+	0.00672218i
$657$	1.97193	−	3.41549i	0.0769324	−	0.133251i
$658$			60.6239i			2.36337i
$659$	12.2454	+	7.06989i	0.477013	+	0.275404i	0.719171	−	0.694833i	$-0.244522\pi$
$659$	12.2454	+	7.06989i	0.477013	+	0.275404i	−0.242158	+	0.970237i	$0.577855\pi$
$660$		0			0
$661$	43.7807	+	11.7310i	1.70287	+	0.456283i	0.973660	−	0.228004i	$-0.0732198\pi$
$661$	43.7807	+	11.7310i	1.70287	+	0.456283i	0.729213	+	0.684287i	$0.239886\pi$
$662$	−3.85504	+	3.85504i	−0.149830	+	0.149830i
$663$	−21.0727	−	34.5765i	−0.818396	−	1.34284i
$664$			26.0462i			1.01079i
$665$		0			0
$666$	0.424543	+	0.735330i	0.0164507	+	0.0284935i
$667$	−0.300739	−	1.12237i	−0.0116447	−	0.0434585i
$668$	−10.8939			−0.421498
$669$	9.86183	+	36.8049i	0.381280	+	1.42296i
$670$		0			0
$671$	−4.69645	+	4.69645i	−0.181304	+	0.181304i
$672$	32.1541	−	8.61568i	1.24037	−	0.332357i
$673$	5.90434	−	22.0353i	0.227596	−	0.849399i	−0.753752	−	0.657159i	$-0.771758\pi$
$673$	5.90434	−	22.0353i	0.227596	−	0.849399i	0.981348	−	0.192240i	$-0.0615752\pi$
$674$	−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	$0.552647\pi$
$678$	−32.5345	−	56.3514i	−1.24948	−	2.16416i
$679$	−37.8913	+	21.8766i	−1.45414	+	0.839545i
$680$		0			0
$681$	8.99290	+	8.99290i	0.344609	+	0.344609i
$682$	44.9497	+	25.9517i	1.72121	+	0.993742i
$683$	34.0351	+	19.6502i	1.30232	+	0.751894i	0.980801	−	0.195010i	$-0.0624740\pi$
$683$	34.0351	+	19.6502i	1.30232	+	0.751894i	0.321517	+	0.946904i	$0.395807\pi$
$684$	9.00838	+	9.00838i	0.344444	+	0.344444i
$685$		0			0
$686$	23.3877	−	13.5029i	0.892948	−	0.515543i
$687$	8.92101	+	15.4516i	0.340358	+	0.589517i
$688$	−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	0.415531	+	0.909579i	$0.363596\pi$
$691$	−10.4916	+	39.1552i	−0.399119	+	1.48953i	−0.814650	+	0.579953i	$0.803071\pi$
$692$	−4.07073	+	15.1922i	−0.154746	+	0.577520i
$693$	5.51748	−	1.47840i	0.209592	−	0.0561599i
$694$	5.97093	−	5.97093i	0.226653	−	0.226653i
$695$		0			0
$696$	1.41606	+	5.28479i	0.0536755	+	0.200320i
$697$	38.3597			1.45298
$698$	5.98375	+	22.3316i	0.226488	+	0.845265i
$699$	19.8804	+	34.4339i	0.751946	+	1.30241i
$700$		0			0
$701$			34.8480i			1.31619i	0.752935	+	0.658094i	$0.228637\pi$
$701$			34.8480i			1.31619i	−0.752935	+	0.658094i	$0.771363\pi$
$702$	−37.1383	+	10.9024i	−1.40169	+	0.411485i
$703$	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
$707$			28.9140i			1.08742i
$708$	20.3587	−	35.2624i	0.765128	−	1.32524i
$709$	36.3341	−	9.73570i	1.36456	−	0.365632i	0.499069	−	0.866562i	$-0.333675\pi$
$709$	36.3341	−	9.73570i	1.36456	−	0.365632i	0.865488	+	0.500930i	$0.167009\pi$
$710$		0			0
$711$	−2.53004	+	4.38216i	−0.0948839	+	0.164344i
$712$	1.89842	+	0.508680i	0.0711463	+	0.0190636i
$713$	6.28492	−	3.62860i	0.235372	−	0.135892i
$714$	82.8063			3.09895
$715$		0			0
$716$	10.2931			0.384673
$717$	18.7519	−	10.8264i	0.700303	−	0.404320i
$718$	2.80137	+	0.750624i	0.104546	+	0.0280130i
$719$	−17.9827	+	31.1470i	−0.670642	+	1.16159i	0.307080	+	0.951684i	$0.400648\pi$
$719$	−17.9827	+	31.1470i	−0.670642	+	1.16159i	−0.977722	+	0.209902i	$0.932685\pi$
$720$		0			0
$721$	7.63207	−	2.04501i	0.284233	−	0.0761600i
$722$	49.2187	−	85.2493i	1.83173	−	3.17265i
$723$		−	34.2899i		−	1.27526i
$724$	−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	−0.751998	−	0.659165i	$-0.770910\pi$
$727$	−2.50307	+	2.50307i	−0.0928336	+	0.0928336i	0.659165	+	0.751998i	$0.270910\pi$
$728$	33.4675	−	0.794707i	1.24039	−	0.0294538i
$729$			21.1716i			0.784134i
$730$		0			0
$731$	3.89406	+	6.74472i	0.144027	+	0.249462i
$732$	−2.92923	−	10.9320i	−0.108267	−	0.404059i
$733$	1.25540			0.0463694			0.0231847	−	0.999731i	$-0.492619\pi$
$733$	1.25540			0.0463694			0.0231847	+	0.999731i	$0.492619\pi$
$734$	−7.72750	−	28.8394i	−0.285227	−	1.06448i
$735$		0			0
$736$	−4.49005	+	4.49005i	−0.165505	+	0.165505i
$737$	−28.8565	+	7.73206i	−1.06294	+	0.284814i
$738$	−1.88314	+	7.02799i	−0.0693195	+	0.258704i
$739$	5.60031	−	20.9006i	0.206011	−	0.768842i	−0.783129	−	0.621860i	$-0.786377\pi$
$739$	5.60031	−	20.9006i	0.206011	−	0.768842i	0.989139	−	0.146982i	$-0.0469560\pi$
$740$		0			0
$741$	−27.6111	−	45.3048i	−1.01432	−	1.66431i
$742$	−22.2592	−	22.2592i	−0.817162	−	0.817162i
$743$	−5.48351	−	9.49772i	−0.201171	−	0.348438i	0.747735	−	0.663997i	$-0.231141\pi$
$743$	−5.48351	−	9.49772i	−0.201171	−	0.348438i	−0.948906	+	0.315559i	$0.897808\pi$
$744$	−29.5931	+	17.0856i	−1.08494	+	0.626388i
$745$		0			0
$746$	17.0206	+	17.0206i	0.623168	+	0.623168i
$747$	3.87992	+	2.24007i	0.141959	+	0.0819601i
$748$	−60.6299	−	35.0047i	−2.21685	−	1.27990i
$749$	−22.3683	−	22.3683i	−0.817321	−	0.817321i
$750$		0			0
$751$	27.9580	−	16.1416i	1.02020	−	0.589015i	0.106041	−	0.994362i	$-0.466183\pi$
$751$	27.9580	−	16.1416i	1.02020	−	0.589015i	0.914163	+	0.405347i	$0.132849\pi$
$752$	0.428158	+	0.741591i	0.0156133	+	0.0270430i
$753$	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
$757$	−8.31633	+	31.0370i	−0.302262	+	1.12806i	0.633014	+	0.774140i	$0.281817\pi$
$757$	−8.31633	+	31.0370i	−0.302262	+	1.12806i	−0.935277	+	0.353918i	$0.884849\pi$
$758$	−22.3504	+	5.98876i	−0.811802	+	0.217522i
$759$	−5.42374	+	5.42374i	−0.196869	+	0.196869i
$760$		0			0
$761$	10.3043	+	38.4564i	0.373532	+	1.39404i	0.855477	+	0.517840i	$0.173264\pi$
$761$	10.3043	+	38.4564i	0.373532	+	1.39404i	−0.481945	+	0.876201i	$0.660069\pi$
$762$	−51.9372			−1.88149
$763$	−7.25766	−	27.0860i	−0.262745	−	0.980578i
$764$	35.9061	+	62.1912i	1.29904	+	2.25000i
$765$		0			0
$766$			24.6634i			0.891123i
$767$	−16.6238	+	17.4325i	−0.600252	+	0.629452i
$768$	22.0394	−	22.0394i	0.795280	−	0.795280i
$769$	18.0132	+	4.82663i	0.649573	+	0.174053i	0.568536	−	0.822658i	$-0.307510\pi$
$769$	18.0132	+	4.82663i	0.649573	+	0.174053i	0.0810373	+	0.996711i	$0.474177\pi$
$770$		0			0
$771$	−13.3940	−	7.73304i	−0.482374	−	0.278499i
$772$			54.2504i			1.95251i
$773$	−5.10195	+	8.83684i	−0.183504	+	0.317839i	−0.943072	−	0.332590i	$-0.892077\pi$
$773$	−5.10195	+	8.83684i	−0.183504	+	0.317839i	0.759567	+	0.650429i	$0.225411\pi$
$774$	−1.42689	+	0.382333i	−0.0512884	+	0.0137427i
$775$		0			0
$776$	−19.6491	+	34.0332i	−0.705361	+	1.22172i
$777$	4.32866	+	1.15986i	0.155290	+	0.0416098i
$778$	69.4297	−	40.0852i	2.48917	−	1.43713i
$779$	50.2618			1.80082
$780$		0			0
$781$	33.3750			1.19425
$782$	−13.6794	+	7.89780i	−0.489174	+	0.282425i
$783$	−4.58108	−	1.22750i	−0.163714	−	0.0438671i
$784$	−0.173794	+	0.301019i	−0.00620692	+	0.0107507i
$785$		0			0
$786$	−0.288352	+	0.0772636i	−0.0102852	+	0.00275590i
$787$	−10.5661	+	18.3010i	−0.376640	+	0.652360i	−0.990571	−	0.137000i	$-0.956254\pi$
$787$	−10.5661	+	18.3010i	−0.376640	+	0.652360i	0.613931	+	0.789360i	$0.289587\pi$
$788$			9.16510i			0.326493i
$789$	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
$793$	0.158944	+	6.69360i	0.00564426	+	0.237697i
$794$			14.0038i			0.496976i
$795$		0			0
$796$	30.2439	+	52.3840i	1.07197	+	1.85670i
$797$	−6.55155	−	24.4507i	−0.232068	−	0.866089i	−0.979449	−	0.201693i	$-0.935356\pi$
$797$	−6.55155	−	24.4507i	−0.232068	−	0.866089i	0.747381	−	0.664396i	$-0.231311\pi$
$798$	108.499			3.84083
$799$	−12.7802	−	47.6965i	−0.452133	−	1.68738i
$800$		0			0
$801$	0.239046	−	0.239046i	0.00844628	−	0.00844628i
$802$	−0.613954	+	0.164508i	−0.0216795	+	0.00580900i
$803$	−7.34980	+	27.4298i	−0.259369	+	0.967978i
$804$	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
$808$	12.9850	+	22.4906i	0.456810	+	0.791217i
$809$	3.76608	−	2.17435i	0.132408	−	0.0764459i	−0.432333	−	0.901714i	$-0.642309\pi$
$809$	3.76608	−	2.17435i	0.132408	−	0.0764459i	0.564741	+	0.825268i	$0.308976\pi$
$810$		0			0
$811$	−21.7750	−	21.7750i	−0.764623	−	0.764623i	0.212531	−	0.977154i	$-0.431829\pi$
$811$	−21.7750	−	21.7750i	−0.764623	−	0.764623i	−0.977154	+	0.212531i	$0.931829\pi$
$812$	9.19468	+	5.30855i	0.322670	+	0.186294i
$813$	−12.2797	−	7.08967i	−0.430667	−	0.248646i
$814$	−4.32309	−	4.32309i	−0.151524	−	0.151524i
$815$		0			0
$816$	1.01294	−	0.584822i	0.0354600	−	0.0204729i
$817$	5.10230	+	8.83745i	0.178507	+	0.309183i
$818$	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	−0.917309	−	0.398177i	$-0.869643\pi$
$821$	2.18315	−	8.14764i	0.0761926	−	0.284355i	0.993501	+	0.113823i	$0.0363096\pi$
$822$	−11.7152	+	43.7218i	−0.408615	+	1.52497i
$823$	18.8493	−	5.05067i	0.657047	−	0.176055i	0.0851339	−	0.996370i	$-0.472868\pi$
$823$	18.8493	−	5.05067i	0.657047	−	0.176055i	0.571913	+	0.820314i	$0.306202\pi$
$824$	5.01819	−	5.01819i	0.174817	−	0.174817i
$825$		0			0
$826$	−12.7496	−	47.5822i	−0.443616	−	1.65560i
$827$	−6.08198			−0.211491			−0.105745	−	0.994393i	$-0.533723\pi$
$827$	−6.08198			−0.211491			−0.105745	+	0.994393i	$0.533723\pi$
$828$	−0.480549	−	1.79343i	−0.0167002	−	0.0623262i
$829$	−24.8232	−	42.9950i	−0.862145	−	1.49328i	−0.869855	−	0.493308i	$-0.835788\pi$
$829$	−24.8232	−	42.9950i	−0.862145	−	1.49328i	0.00771009	−	0.999970i	$-0.497546\pi$
$830$		0			0
$831$		−	21.8155i		−	0.756772i
$832$	−39.7347	+	24.2163i	−1.37755	+	0.839551i
$833$	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
$837$		−	29.6210i		−	1.02385i
$838$	−10.1401	+	17.5632i	−0.350284	+	0.606710i
$839$	2.83726	−	0.760241i	0.0979530	−	0.0262464i	−0.209510	−	0.977807i	$-0.567187\pi$
$839$	2.83726	−	0.760241i	0.0979530	−	0.0262464i	0.307463	+	0.951560i	$0.400520\pi$
$840$		0			0
$841$	−13.9867	+	24.2257i	−0.482301	+	0.835370i
$842$	−20.6184	−	5.52468i	−0.710557	−	0.190393i
$843$	−21.6680	+	12.5100i	−0.746285	+	0.430868i
$844$	65.8914			2.26808
$845$		0			0
$846$	9.36603			0.322011
$847$	−4.99053	+	2.88128i	−0.171477	+	0.0990020i
$848$	−0.429496	−	0.115083i	−0.0147489	−	0.00395197i
$849$	3.75167	−	6.49808i	0.128757	−	0.223014i
$850$		0			0
$851$	−0.825707	+	0.221248i	−0.0283049	+	0.00758427i
$852$	−28.4356	+	49.2520i	−0.974189	+	1.68734i
$853$			52.5348i			1.79876i	0.437171	+	0.899378i	$0.355980\pi$
$853$			52.5348i			1.79876i	−0.437171	+	0.899378i	$0.644020\pi$
$854$	−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	−0.239730	−	0.970840i	$-0.577059\pi$
$857$	21.4029	−	21.4029i	0.731110	−	0.731110i	0.970840	+	0.239730i	$0.0770588\pi$
$858$	−47.2227	+	28.7800i	−1.61216	+	0.982531i
$859$		−	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
$862$	4.32311	+	16.1341i	0.147246	+	0.549528i
$863$	−17.5619			−0.597815			−0.298907	−	0.954282i	$-0.596622\pi$
$863$	−17.5619			−0.597815			−0.298907	+	0.954282i	$0.596622\pi$
$864$	6.70799	+	25.0345i	0.228210	+	0.851693i
$865$		0			0
$866$	−17.7931	+	17.7931i	−0.604635	+	0.604635i
$867$	−34.4427	+	9.22891i	−1.16974	+	0.313430i
$868$	−17.1624	+	64.0509i	−0.582530	+	2.17403i
$869$	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
$873$	3.37980	+	5.85398i	0.114389	+	0.198127i
$874$	−17.9238	+	10.3483i	−0.606281	+	0.350037i
$875$		0			0
$876$	−34.2166	−	34.2166i	−1.15607	−	1.15607i
$877$	7.40312	+	4.27420i	0.249986	+	0.144329i	0.619758	−	0.784793i	$-0.287231\pi$
$877$	7.40312	+	4.27420i	0.249986	+	0.144329i	−0.369772	+	0.929123i	$0.620564\pi$
$878$	−23.2785	−	13.4398i	−0.785611	−	0.453573i
$879$	−32.6268	−	32.6268i	−1.10047	−	1.10047i
$880$		0			0
$881$	37.8333	−	21.8430i	1.27464	−	0.735911i	0.298779	−	0.954322i	$-0.403421\pi$
$881$	37.8333	−	21.8430i	1.27464	−	0.735911i	0.975857	+	0.218411i	$0.0700875\pi$
$882$	1.90088	+	3.29243i	0.0640061	+	0.110862i
$883$	−26.5027	−	26.5027i	−0.891887	−	0.891887i	0.102814	−	0.994701i	$-0.467215\pi$
$883$	−26.5027	−	26.5027i	−0.891887	−	0.891887i	−0.994701	+	0.102814i	$0.967215\pi$
$884$	−67.7178	+	19.8794i	−2.27760	+	0.668617i
$885$		0			0
$886$	−16.2238	+	60.5481i	−0.545050	+	2.03415i
$887$	4.76472	−	17.7822i	0.159984	−	0.597067i	−0.838643	−	0.544681i	$-0.816651\pi$
$887$	4.76472	−	17.7822i	0.159984	−	0.597067i	0.998627	−	0.0523860i	$-0.0166826\pi$
$888$	3.88791	−	1.04176i	0.130470	−	0.0349593i
$889$	−27.5345	+	27.5345i	−0.923478	+	0.923478i
$890$		0			0
$891$	9.48236	+	35.3886i	0.317671	+	1.18556i
$892$	66.4120			2.22364
$893$	−16.7457	−	62.4957i	−0.560372	−	2.09134i
$894$	−31.9194	−	55.2860i	−1.06754	−	1.84904i
$895$		0			0
$896$		−	59.5559i		−	1.98962i
$897$	0.183558	+	7.73017i	0.00612882	+	0.258103i
$898$	−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
$902$		−	52.3896i		−	1.74438i
$903$	−3.89828	+	6.75203i	−0.129727	+	0.224693i
$904$	−42.3247	+	11.3409i	−1.40770	+	0.377192i
$905$		0			0
$906$	−31.3488	+	54.2977i	−1.04149	+	1.80392i
$907$	−12.5901	−	3.37350i	−0.418046	−	0.112015i	0.0436633	−	0.999046i	$-0.486097\pi$
$907$	−12.5901	−	3.37350i	−0.418046	−	0.112015i	−0.461710	+	0.887031i	$0.652764\pi$
$908$	19.1969	−	11.0833i	0.637071	−	0.367813i
$909$	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	$0.722170\pi$
$912$	1.32723	−	0.766278i	0.0439491	−	0.0253740i
$913$	−31.1597	−	8.34922i	−1.03124	−	0.276319i
$914$	2.93601	−	5.08532i	0.0971146	−	0.168207i
$915$		0			0
$916$	30.0381	−	8.04869i	0.992487	−	0.265936i
$917$	−0.111908	+	0.193831i	−0.00369553	+	0.00640085i
$918$			64.4713i			2.12787i
$919$	21.9085	+	12.6489i	0.722695	+	0.417248i	0.815744	−	0.578414i	$-0.196328\pi$
$919$	21.9085	+	12.6489i	0.722695	+	0.417248i	−0.0930490	+	0.995662i	$0.529661\pi$
$920$		0			0
$921$	13.3896	+	3.58772i	0.441201	+	0.118219i
$922$	16.4028	−	16.4028i	0.540196	−	0.540196i
$923$	23.2190	−	24.3485i	0.764263	−	0.801442i
$924$		−	70.0852i		−	2.30563i
$925$		0			0
$926$	−14.0529	−	24.3403i	−0.461806	−	0.799871i
$927$	−0.315941	−	1.17911i	−0.0103769	−	0.0387270i
$928$	−5.60973			−0.184148
$929$	10.0323	+	37.4412i	0.329150	+	1.22841i	0.910073	+	0.414448i	$0.136025\pi$
$929$	10.0323	+	37.4412i	0.329150	+	1.22841i	−0.580923	+	0.813959i	$0.697308\pi$
$930$		0			0
$931$	18.5704	−	18.5704i	0.608620	−	0.608620i
$932$	66.9398	−	17.9365i	2.19268	−	0.587528i
$933$	0.808784	−	3.01842i	0.0264784	−	0.0988188i
$934$	−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	$0.890433\pi$
$938$	−30.7937	−	53.3362i	−1.00545	−	1.74149i
$939$	36.3091	−	20.9631i	1.18490	−	0.684105i
$940$		0			0
$941$	13.1581	+	13.1581i	0.428942	+	0.428942i	0.888268	−	0.459326i	$-0.151909\pi$
$941$	13.1581	+	13.1581i	0.428942	+	0.428942i	−0.459326	+	0.888268i	$0.651909\pi$
$942$	83.6225	+	48.2795i	2.72457	+	1.57303i
$943$	−6.34379	−	3.66259i	−0.206582	−	0.119270i
$944$	−0.492012	−	0.492012i	−0.0160136	−	0.0160136i
$945$		0			0
$946$	9.21157	−	5.31830i	0.299494	−	0.172913i
$947$	12.5632	+	21.7601i	0.408249	+	0.707109i	0.994694	−	0.102881i	$-0.0328061\pi$
$947$	12.5632	+	21.7601i	0.408249	+	0.707109i	−0.586444	+	0.809990i	$0.699473\pi$
$948$	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
$952$	14.4323	−	53.8622i	0.467754	−	1.74568i
$953$	16.2171	−	4.34536i	0.525324	−	0.140760i	0.0135958	−	0.999908i	$-0.495672\pi$
$953$	16.2171	−	4.34536i	0.525324	−	0.140760i	0.511728	+	0.859147i	$0.329006\pi$
$954$	−3.43891	+	3.43891i	−0.111339	+	0.111339i
$955$		0			0
$956$	−9.76778	−	36.4539i	−0.315913	−	1.17900i
$957$	−6.77626			−0.219045
$958$	−8.22961	−	30.7133i	−0.265887	−	0.992303i
$959$	16.9683	+	29.3899i	0.547934	+	0.949049i
$960$		0			0
$961$			9.04245i			0.291692i
$962$	−6.16146	+	0.146308i	−0.198654	+	0.00471716i
$963$	−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
$967$			58.5376i			1.88244i	0.337790	+	0.941222i	$0.390321\pi$
$967$			58.5376i			1.88244i	−0.337790	+	0.941222i	$0.609679\pi$
$968$	−2.58791	+	4.48239i	−0.0831785	+	0.144069i
$969$	−85.3629	+	22.8729i	−2.74225	+	0.734784i
$970$		0			0
$971$	−15.3457	+	26.5795i	−0.492467	+	0.852977i	−0.999962	−	0.00867714i	$-0.997238\pi$
$971$	−15.3457	+	26.5795i	−0.492467	+	0.852977i	0.507496	+	0.861654i	$0.330571\pi$
$972$	−16.0927	−	4.31202i	−0.516173	−	0.138308i
$973$	25.7831	−	14.8859i	0.826569	−	0.477220i
$974$	18.9229			0.606328
$975$		0			0
$976$	−0.193405			−0.00619074
$977$	−23.2758	+	13.4383i	−0.744659	+	0.429929i	−0.823761	−	0.566938i	$-0.808128\pi$
$977$	−23.2758	+	13.4383i	−0.744659	+	0.429929i	0.0791020	+	0.996867i	$0.474795\pi$
$978$	−36.0263	−	9.65323i	−1.15200	−	0.308676i
$979$	−1.21709	+	2.10807i	−0.0388985	+	0.0673741i
$980$		0			0
$981$	−4.18462	+	1.12126i	−0.133605	+	0.0357992i
$982$	43.0169	−	74.5074i	1.37272	−	2.37763i
$983$		−	10.4201i		−	0.332350i	−0.986096	−	0.166175i	$-0.946858\pi$
$983$		−	10.4201i		−	0.332350i	0.986096	−	0.166175i	$-0.0531417\pi$
$984$	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
$988$	−88.7290	+	26.0475i	−2.82285	+	0.828682i
$989$		−	1.48722i		−	0.0472910i
$990$		0			0
$991$	19.1088	+	33.0974i	0.607011	+	1.05137i	0.991730	+	0.128341i	$0.0409651\pi$
$991$	19.1088	+	33.0974i	0.607011	+	1.05137i	−0.384719	+	0.923034i	$0.625702\pi$
$992$	−9.06804	−	33.8424i	−0.287911	−	1.07450i
$993$	4.44543			0.141071
$994$	17.8078	+	66.4595i	0.564828	+	2.10797i
$995$		0			0
$996$	38.8693	−	38.8693i	1.23162	−	1.23162i
$997$	29.2716	−	7.84331i	0.927042	−	0.248400i	0.236449	−	0.971644i	$-0.424016\pi$
$997$	29.2716	−	7.84331i	0.927042	−	0.248400i	0.690593	+	0.723244i	$0.257350\pi$
$998$	−22.0776	+	82.3947i	−0.698854	+	2.60816i
$999$	−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.x.c.232.2	yes	40
5.2	odd	4		325.2.s.c.193.2	yes	40
5.3	odd	4		325.2.s.c.193.9	yes	40
5.4	even	2	inner	325.2.x.c.232.9	yes	40
13.6	odd	12		325.2.s.c.32.9	yes	40
65.19	odd	12		325.2.s.c.32.2	✓	40
65.32	even	12	inner	325.2.x.c.318.9	yes	40
65.58	even	12	inner	325.2.x.c.318.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.32.2	✓	40	65.19	odd	12
325.2.s.c.32.9	yes	40	13.6	odd	12
325.2.s.c.193.2	yes	40	5.2	odd	4
325.2.s.c.193.9	yes	40	5.3	odd	4
325.2.x.c.232.2	yes	40	1.1	even	1	trivial
325.2.x.c.232.9	yes	40	5.4	even	2	inner
325.2.x.c.318.2	yes	40	65.58	even	12	inner
325.2.x.c.318.9	yes	40	65.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

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

L-functions

Modular forms

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