LMFDB - Embedded newform 387.2.h.d.208.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(208,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("387.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			208.2
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	387.208
Dual form			387.2.h.d.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.61803 q^{2} +4.85410 q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.118034 + 0.204441i) q^{7} +7.47214 q^{8} +O(q^{10})$	\(q+2.61803 q^{2} +4.85410 q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.118034 + 0.204441i) q^{7} +7.47214 q^{8} +(-4.23607 - 7.33708i) q^{10} +1.38197 q^{11} +(-1.80902 + 3.13331i) q^{13} +(-0.309017 + 0.535233i) q^{14} +9.85410 q^{16} +(-2.54508 + 4.40822i) q^{17} +(-1.61803 - 2.80252i) q^{19} +(-7.85410 - 13.6037i) q^{20} +3.61803 q^{22} +(3.30902 + 5.73139i) q^{23} +(-2.73607 + 4.73901i) q^{25} +(-4.73607 + 8.20311i) q^{26} +(-0.572949 + 0.992377i) q^{28} +(1.50000 - 2.59808i) q^{29} +10.8541 q^{32} +(-6.66312 + 11.5409i) q^{34} +0.763932 q^{35} +(-0.927051 - 1.60570i) q^{37} +(-4.23607 - 7.33708i) q^{38} +(-12.0902 - 20.9408i) q^{40} -0.527864 q^{41} +(-6.50000 - 0.866025i) q^{43} +6.70820 q^{44} +(8.66312 + 15.0050i) q^{46} -7.85410 q^{47} +(3.47214 + 6.01392i) q^{49} +(-7.16312 + 12.4069i) q^{50} +(-8.78115 + 15.2094i) q^{52} +(-1.80902 - 3.13331i) q^{53} +(-2.23607 - 3.87298i) q^{55} +(-0.881966 + 1.52761i) q^{56} +(3.92705 - 6.80185i) q^{58} +6.09017 q^{59} +(1.92705 - 3.33775i) q^{61} +8.70820 q^{64} +11.7082 q^{65} +(-1.42705 - 2.47172i) q^{67} +(-12.3541 + 21.3979i) q^{68} +2.00000 q^{70} +(6.89919 - 11.9497i) q^{71} +(2.42705 - 4.20378i) q^{73} +(-2.42705 - 4.20378i) q^{74} +(-7.85410 - 13.6037i) q^{76} +(-0.163119 + 0.282530i) q^{77} +(1.80902 - 3.13331i) q^{79} +(-15.9443 - 27.6163i) q^{80} -1.38197 q^{82} +(-6.51722 - 11.2882i) q^{83} +16.4721 q^{85} +(-17.0172 - 2.26728i) q^{86} +10.3262 q^{88} +(2.42705 + 4.20378i) q^{89} +(-0.427051 - 0.739674i) q^{91} +(16.0623 + 27.8207i) q^{92} -20.5623 q^{94} +(-5.23607 + 9.06914i) q^{95} -4.76393 q^{97} +(9.09017 + 15.7446i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	$ 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} - 8 q^{10} + 10 q^{11} - 5 q^{13} + q^{14} + 26 q^{16} + q^{17} - 2 q^{19} - 18 q^{20} + 10 q^{22} + 11 q^{23} - 2 q^{25} - 10 q^{26} - 9 q^{28} + 6 q^{29} + 30 q^{32} - 11 q^{34} + 12 q^{35} + 3 q^{37} - 8 q^{38} - 26 q^{40} - 20 q^{41} - 26 q^{43} + 19 q^{46} - 18 q^{47} - 4 q^{49} - 13 q^{50} - 15 q^{52} - 5 q^{53} - 8 q^{56} + 9 q^{58} + 2 q^{59} + q^{61} + 8 q^{64} + 20 q^{65} + q^{67} - 36 q^{68} + 8 q^{70} + 3 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{76} + 15 q^{77} + 5 q^{79} - 28 q^{80} - 10 q^{82} + 3 q^{83} + 48 q^{85} - 39 q^{86} + 10 q^{88} + 3 q^{89} + 5 q^{91} + 24 q^{92} - 42 q^{94} - 12 q^{95} - 28 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 - 8 * q^10 + 10 * q^11 - 5 * q^13 + q^14 + 26 * q^16 + q^17 - 2 * q^19 - 18 * q^20 + 10 * q^22 + 11 * q^23 - 2 * q^25 - 10 * q^26 - 9 * q^28 + 6 * q^29 + 30 * q^32 - 11 * q^34 + 12 * q^35 + 3 * q^37 - 8 * q^38 - 26 * q^40 - 20 * q^41 - 26 * q^43 + 19 * q^46 - 18 * q^47 - 4 * q^49 - 13 * q^50 - 15 * q^52 - 5 * q^53 - 8 * q^56 + 9 * q^58 + 2 * q^59 + q^61 + 8 * q^64 + 20 * q^65 + q^67 - 36 * q^68 + 8 * q^70 + 3 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^76 + 15 * q^77 + 5 * q^79 - 28 * q^80 - 10 * q^82 + 3 * q^83 + 48 * q^85 - 39 * q^86 + 10 * q^88 + 3 * q^89 + 5 * q^91 + 24 * q^92 - 42 * q^94 - 12 * q^95 - 28 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.61803			1.85123			0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803			1.85123			0.925615	+	0.378467i	$0.123549\pi$
$3$		0			0
$3$		0			0
$4$	4.85410			2.42705
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	−0.959545	−	0.281556i	$-0.909150\pi$
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	0.235938	−	0.971768i	$-0.424184\pi$
$6$		0			0
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	−0.887469	−	0.460866i	$-0.847539\pi$
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	0.842857	+	0.538138i	$0.180872\pi$
$8$	7.47214			2.64180
$9$		0			0
$10$	−4.23607	−	7.33708i	−1.33956	−	2.32019i
$11$	1.38197			0.416678			0.208339	−	0.978057i	$-0.433194\pi$
$11$	1.38197			0.416678			0.208339	+	0.978057i	$0.433194\pi$
$12$		0			0
$13$	−1.80902	+	3.13331i	−0.501731	+	0.869024i	0.498267	+	0.867024i	$0.333970\pi$
$13$	−1.80902	+	3.13331i	−0.501731	+	0.869024i	−0.999998	+	0.00199999i	$0.999363\pi$
$14$	−0.309017	+	0.535233i	−0.0825883	+	0.143047i
$15$		0			0
$16$	9.85410			2.46353
$17$	−2.54508	+	4.40822i	−0.617274	+	1.06915i	0.372707	+	0.927949i	$0.378430\pi$
$17$	−2.54508	+	4.40822i	−0.617274	+	1.06915i	−0.989981	+	0.141201i	$0.954904\pi$
$18$		0			0
$19$	−1.61803	−	2.80252i	−0.371202	−	0.642942i	0.618548	−	0.785747i	$-0.287721\pi$
$19$	−1.61803	−	2.80252i	−0.371202	−	0.642942i	−0.989751	+	0.142805i	$0.954388\pi$
$20$	−7.85410	−	13.6037i	−1.75623	−	3.04188i
$21$		0			0
$22$	3.61803			0.771367
$23$	3.30902	+	5.73139i	0.689978	+	1.19508i	0.971845	+	0.235623i	$0.0757130\pi$
$23$	3.30902	+	5.73139i	0.689978	+	1.19508i	−0.281867	+	0.959454i	$0.590954\pi$
$24$		0			0
$25$	−2.73607	+	4.73901i	−0.547214	+	0.947802i
$26$	−4.73607	+	8.20311i	−0.928819	+	1.60876i
$27$		0			0
$28$	−0.572949	+	0.992377i	−0.108277	+	0.187542i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	10.8541			1.91875
$33$		0			0
$34$	−6.66312	+	11.5409i	−1.14272	+	1.97924i
$35$	0.763932			0.129128
$36$		0			0
$37$	−0.927051	−	1.60570i	−0.152406	−	0.263975i	0.779705	−	0.626147i	$-0.215369\pi$
$37$	−0.927051	−	1.60570i	−0.152406	−	0.263975i	−0.932112	+	0.362171i	$0.882036\pi$
$38$	−4.23607	−	7.33708i	−0.687181	−	1.19023i
$39$		0			0
$40$	−12.0902	−	20.9408i	−1.91162	−	3.31103i
$41$	−0.527864			−0.0824385			−0.0412193	−	0.999150i	$-0.513124\pi$
$41$	−0.527864			−0.0824385			−0.0412193	+	0.999150i	$0.513124\pi$
$42$		0			0
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$44$	6.70820			1.01130
$45$		0			0
$46$	8.66312	+	15.0050i	1.27731	+	2.21236i
$47$	−7.85410			−1.14564			−0.572819	−	0.819682i	$-0.694150\pi$
$47$	−7.85410			−1.14564			−0.572819	+	0.819682i	$0.694150\pi$
$48$		0			0
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$	−7.16312	+	12.4069i	−1.01302	+	1.75460i
$51$		0			0
$52$	−8.78115	+	15.2094i	−1.21773	+	2.10916i
$53$	−1.80902	−	3.13331i	−0.248488	−	0.430393i	0.714619	−	0.699514i	$-0.246600\pi$
$53$	−1.80902	−	3.13331i	−0.248488	−	0.430393i	−0.963106	+	0.269121i	$0.913267\pi$
$54$		0			0
$55$	−2.23607	−	3.87298i	−0.301511	−	0.522233i
$56$	−0.881966	+	1.52761i	−0.117858	+	0.204135i
$57$		0			0
$58$	3.92705	−	6.80185i	0.515647	−	0.893127i
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$		0			0
$61$	1.92705	−	3.33775i	0.246734	−	0.427355i	−0.715884	−	0.698219i	$-0.753976\pi$
$61$	1.92705	−	3.33775i	0.246734	−	0.427355i	0.962618	+	0.270864i	$0.0873094\pi$
$62$		0			0
$63$		0			0
$64$	8.70820			1.08853
$65$	11.7082			1.45222
$66$		0			0
$67$	−1.42705	−	2.47172i	−0.174342	−	0.301969i	0.765591	−	0.643327i	$-0.222447\pi$
$67$	−1.42705	−	2.47172i	−0.174342	−	0.301969i	−0.939933	+	0.341358i	$0.889113\pi$
$68$	−12.3541	+	21.3979i	−1.49815	+	2.59488i
$69$		0			0
$70$	2.00000			0.239046
$71$	6.89919	−	11.9497i	0.818783	−	1.41817i	−0.0877966	−	0.996138i	$-0.527983\pi$
$71$	6.89919	−	11.9497i	0.818783	−	1.41817i	0.906580	−	0.422035i	$-0.138684\pi$
$72$		0			0
$73$	2.42705	−	4.20378i	0.284065	−	0.492015i	−0.688317	−	0.725410i	$-0.741650\pi$
$73$	2.42705	−	4.20378i	0.284065	−	0.492015i	0.972382	+	0.233395i	$0.0749836\pi$
$74$	−2.42705	−	4.20378i	−0.282139	−	0.488679i
$75$		0			0
$76$	−7.85410	−	13.6037i	−0.900927	−	1.56045i
$77$	−0.163119	+	0.282530i	−0.0185891	+	0.0321973i
$78$		0			0
$79$	1.80902	−	3.13331i	0.203530	−	0.352525i	−0.746133	−	0.665797i	$-0.768092\pi$
$79$	1.80902	−	3.13331i	0.203530	−	0.352525i	0.949663	+	0.313272i	$0.101425\pi$
$80$	−15.9443	−	27.6163i	−1.78262	−	3.08759i
$81$		0			0
$82$	−1.38197			−0.152613
$83$	−6.51722	−	11.2882i	−0.715358	−	1.23904i	−0.962821	−	0.270139i	$-0.912930\pi$
$83$	−6.51722	−	11.2882i	−0.715358	−	1.23904i	0.247463	−	0.968897i	$-0.420403\pi$
$84$		0			0
$85$	16.4721			1.78665
$86$	−17.0172	−	2.26728i	−1.83501	−	0.244488i
$87$		0			0
$88$	10.3262			1.10078
$89$	2.42705	+	4.20378i	0.257267	+	0.445599i	0.965509	−	0.260371i	$-0.0838447\pi$
$89$	2.42705	+	4.20378i	0.257267	+	0.445599i	−0.708242	+	0.705970i	$0.750511\pi$
$90$		0			0
$91$	−0.427051	−	0.739674i	−0.0447671	−	0.0775389i
$92$	16.0623	+	27.8207i	1.67461	+	2.90051i
$93$		0			0
$94$	−20.5623			−2.12084
$95$	−5.23607	+	9.06914i	−0.537209	+	0.930474i
$96$		0			0
$97$	−4.76393			−0.483704			−0.241852	−	0.970313i	$-0.577755\pi$
$97$	−4.76393			−0.483704			−0.241852	+	0.970313i	$0.577755\pi$
$98$	9.09017	+	15.7446i	0.918246	+	1.59045i
$99$		0			0
$100$	−13.2812	+	23.0036i	−1.32812	+	2.30036i
$101$	4.11803	−	7.13264i	0.409760	−	0.709725i	−0.585103	−	0.810959i	$-0.698946\pi$
$101$	4.11803	−	7.13264i	0.409760	−	0.709725i	0.994863	+	0.101234i	$0.0322792\pi$
$102$		0			0
$103$	−5.20820	+	9.02087i	−0.513180	+	0.888853i	0.486704	+	0.873567i	$0.338199\pi$
$103$	−5.20820	+	9.02087i	−0.513180	+	0.888853i	−0.999883	+	0.0152859i	$0.995134\pi$
$104$	−13.5172	+	23.4125i	−1.32547	+	2.29579i
$105$		0			0
$106$	−4.73607	−	8.20311i	−0.460008	−	0.796757i
$107$	−16.4721			−1.59242			−0.796211	−	0.605019i	$-0.793165\pi$
$107$	−16.4721			−1.59242			−0.796211	+	0.605019i	$0.793165\pi$
$108$		0			0
$109$	3.57295	+	6.18853i	0.342226	+	0.592754i	0.984846	−	0.173432i	$-0.0554857\pi$
$109$	3.57295	+	6.18853i	0.342226	+	0.592754i	−0.642619	+	0.766186i	$0.722152\pi$
$110$	−5.85410	−	10.1396i	−0.558167	−	0.966773i
$111$		0			0
$112$	−1.16312	+	2.01458i	−0.109904	+	0.190360i
$113$	13.3820			1.25887			0.629435	−	0.777053i	$-0.283286\pi$
$113$	13.3820			1.25887			0.629435	+	0.777053i	$0.283286\pi$
$114$		0			0
$115$	10.7082	−	18.5472i	0.998545	−	1.72953i
$116$	7.28115	−	12.6113i	0.676038	−	1.17093i
$117$		0			0
$118$	15.9443			1.46779
$119$	−0.600813	−	1.04064i	−0.0550764	−	0.0953952i
$120$		0			0
$121$	−9.09017			−0.826379
$122$	5.04508	−	8.73834i	0.456761	−	0.791132i
$123$		0			0
$124$		0			0
$125$	1.52786			0.136656
$126$		0			0
$127$	16.6525			1.47767			0.738834	−	0.673887i	$-0.235377\pi$
$127$	16.6525			1.47767			0.738834	+	0.673887i	$0.235377\pi$
$128$	1.09017			0.0963583
$129$		0			0
$130$	30.6525			2.68840
$131$	7.94427			0.694094			0.347047	−	0.937848i	$-0.387184\pi$
$131$	7.94427			0.694094			0.347047	+	0.937848i	$0.387184\pi$
$132$		0			0
$133$	0.763932			0.0662413
$134$	−3.73607	−	6.47106i	−0.322747	−	0.559014i
$135$		0			0
$136$	−19.0172	+	32.9388i	−1.63071	+	2.82448i
$137$	9.70820			0.829428			0.414714	−	0.909952i	$-0.363882\pi$
$137$	9.70820			0.829428			0.414714	+	0.909952i	$0.363882\pi$
$138$		0			0
$139$	9.35410	+	16.2018i	0.793405	+	1.37422i	0.923847	+	0.382761i	$0.125027\pi$
$139$	9.35410	+	16.2018i	0.793405	+	1.37422i	−0.130443	+	0.991456i	$0.541640\pi$
$140$	3.70820			0.313400
$141$		0			0
$142$	18.0623	−	31.2848i	1.51576	−	2.62536i
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$		0			0
$145$	−9.70820			−0.806222
$146$	6.35410	−	11.0056i	0.525869	−	0.910832i
$147$		0			0
$148$	−4.50000	−	7.79423i	−0.369898	−	0.640682i
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	−2.14590			−0.174631			−0.0873154	−	0.996181i	$-0.527829\pi$
$151$	−2.14590			−0.174631			−0.0873154	+	0.996181i	$0.527829\pi$
$152$	−12.0902	−	20.9408i	−0.980642	−	1.69852i
$153$		0			0
$154$	−0.427051	+	0.739674i	−0.0344127	+	0.0596046i
$155$		0			0
$156$		0			0
$157$	5.92705	−	10.2660i	0.473030	−	0.819312i	−0.526493	−	0.850179i	$-0.676493\pi$
$157$	5.92705	−	10.2660i	0.473030	−	0.819312i	0.999524	+	0.0308670i	$0.00982682\pi$
$158$	4.73607	−	8.20311i	0.376781	−	0.652604i
$159$		0			0
$160$	−17.5623	−	30.4188i	−1.38842	−	2.40482i
$161$	−1.56231			−0.123127
$162$		0			0
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$	−2.56231			−0.200082
$165$		0			0
$166$	−17.0623	−	29.5528i	−1.32429	−	2.29374i
$167$	4.88197	+	8.45581i	0.377778	+	0.654330i	0.990739	−	0.135783i	$-0.0433550\pi$
$167$	4.88197	+	8.45581i	0.377778	+	0.654330i	−0.612961	+	0.790113i	$0.710022\pi$
$168$		0			0
$169$	−0.0450850	−	0.0780895i	−0.00346807	−	0.00600688i
$170$	43.1246			3.30751
$171$		0			0
$172$	−31.5517	−	4.20378i	−2.40579	−	0.320535i
$173$	8.23607			0.626177			0.313088	−	0.949724i	$-0.398636\pi$
$173$	8.23607			0.626177			0.313088	+	0.949724i	$0.398636\pi$
$174$		0			0
$175$	−0.645898	−	1.11873i	−0.0488253	−	0.0845679i
$176$	13.6180			1.02650
$177$		0			0
$178$	6.35410	+	11.0056i	0.476260	+	0.824907i
$179$	−10.8262	+	18.7516i	−0.809191	+	1.40156i	0.104234	+	0.994553i	$0.466761\pi$
$179$	−10.8262	+	18.7516i	−0.809191	+	1.40156i	−0.913425	+	0.407007i	$0.866572\pi$
$180$		0			0
$181$	10.8090	−	18.7218i	0.803428	−	1.39158i	−0.113919	−	0.993490i	$-0.536341\pi$
$181$	10.8090	−	18.7218i	0.803428	−	1.39158i	0.917347	−	0.398088i	$-0.130326\pi$
$182$	−1.11803	−	1.93649i	−0.0828742	−	0.143542i
$183$		0			0
$184$	24.7254	+	42.8257i	1.82278	+	3.15715i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	−3.51722	+	6.09201i	−0.257205	+	0.445492i
$188$	−38.1246			−2.78052
$189$		0			0
$190$	−13.7082	+	23.7433i	−0.994498	+	1.72252i
$191$	−11.7361	−	20.3275i	−0.849192	−	1.47084i	−0.881930	−	0.471380i	$-0.843756\pi$
$191$	−11.7361	−	20.3275i	−0.849192	−	1.47084i	0.0327382	−	0.999464i	$-0.489577\pi$
$192$		0			0
$193$	−10.7082			−0.770793			−0.385397	−	0.922751i	$-0.625935\pi$
$193$	−10.7082			−0.770793			−0.385397	+	0.922751i	$0.625935\pi$
$194$	−12.4721			−0.895447
$195$		0			0
$196$	16.8541	+	29.1922i	1.20386	+	2.08515i
$197$	7.47214	−	12.9421i	0.532368	−	0.922088i	−0.466918	−	0.884301i	$-0.654636\pi$
$197$	7.47214	−	12.9421i	0.532368	−	0.922088i	0.999286	−	0.0377873i	$-0.0120309\pi$
$198$		0			0
$199$	−15.9443			−1.13026			−0.565130	−	0.825002i	$-0.691174\pi$
$199$	−15.9443			−1.13026			−0.565130	+	0.825002i	$0.691174\pi$
$200$	−20.4443	+	35.4105i	−1.44563	+	2.50390i
$201$		0			0
$202$	10.7812	−	18.6735i	0.758559	−	1.31386i
$203$	0.354102	+	0.613323i	0.0248531	+	0.0430468i
$204$		0			0
$205$	0.854102	+	1.47935i	0.0596531	+	0.103322i
$206$	−13.6353	+	23.6170i	−0.950013	+	1.64547i
$207$		0			0
$208$	−17.8262	+	30.8759i	−1.23603	+	2.14086i
$209$	−2.23607	−	3.87298i	−0.154672	−	0.267900i
$210$		0			0
$211$	−4.76393			−0.327963			−0.163981	−	0.986463i	$-0.552434\pi$
$211$	−4.76393			−0.327963			−0.163981	+	0.986463i	$0.552434\pi$
$212$	−8.78115	−	15.2094i	−0.603092	−	1.04459i
$213$		0			0
$214$	−43.1246			−2.94794
$215$	8.09017	+	19.6176i	0.551745	+	1.33791i
$216$		0			0
$217$		0			0
$218$	9.35410	+	16.2018i	0.633540	+	1.09732i
$219$		0			0
$220$	−10.8541	−	18.7999i	−0.731783	−	1.26749i
$221$	−9.20820	−	15.9491i	−0.619411	−	1.07285i
$222$		0			0
$223$	7.23607			0.484563			0.242281	−	0.970206i	$-0.422104\pi$
$223$	7.23607			0.484563			0.242281	+	0.970206i	$0.422104\pi$
$224$	−1.28115	+	2.21902i	−0.0856006	+	0.148265i
$225$		0			0
$226$	35.0344			2.33046
$227$	3.73607	+	6.47106i	0.247972	+	0.429499i	0.962963	−	0.269634i	$-0.0869027\pi$
$227$	3.73607	+	6.47106i	0.247972	+	0.429499i	−0.714991	+	0.699133i	$0.753569\pi$
$228$		0			0
$229$	7.85410	−	13.6037i	0.519014	−	0.898958i	−0.480742	−	0.876862i	$-0.659633\pi$
$229$	7.85410	−	13.6037i	0.519014	−	0.898958i	0.999756	−	0.0220961i	$-0.00703396\pi$
$230$	28.0344	−	48.5571i	1.84854	−	3.20176i
$231$		0			0
$232$	11.2082	−	19.4132i	0.735855	−	1.27454i
$233$	−5.51722	+	9.55611i	−0.361445	+	0.626041i	−0.988199	−	0.153176i	$-0.951050\pi$
$233$	−5.51722	+	9.55611i	−0.361445	+	0.626041i	0.626754	+	0.779217i	$0.284383\pi$
$234$		0			0
$235$	12.7082	+	22.0113i	0.828992	+	1.43586i
$236$	29.5623			1.92434
$237$		0			0
$238$	−1.57295	−	2.72443i	−0.101959	−	0.176598i
$239$	−10.8541	−	18.7999i	−0.702093	−	1.21606i	−0.967730	−	0.251988i	$-0.918916\pi$
$239$	−10.8541	−	18.7999i	−0.702093	−	1.21606i	0.265637	−	0.964073i	$-0.414418\pi$
$240$		0			0
$241$	14.6353	−	25.3490i	0.942740	−	1.63287i	0.182525	−	0.983201i	$-0.441573\pi$
$241$	14.6353	−	25.3490i	0.942740	−	1.63287i	0.760215	−	0.649672i	$-0.225094\pi$
$242$	−23.7984			−1.52982
$243$		0			0
$244$	9.35410	−	16.2018i	0.598835	−	1.03721i
$245$	11.2361	−	19.4614i	0.717846	−	1.24335i
$246$		0			0
$247$	11.7082			0.744975
$248$		0			0
$249$		0			0
$250$	4.00000			0.252982
$251$	−3.40983	+	5.90600i	−0.215227	+	0.372783i	−0.953343	−	0.301890i	$-0.902382\pi$
$251$	−3.40983	+	5.90600i	−0.215227	+	0.372783i	0.738116	+	0.674674i	$0.235716\pi$
$252$		0			0
$253$	4.57295	+	7.92058i	0.287499	+	0.497963i
$254$	43.5967			2.73550
$255$		0			0
$256$	−14.5623			−0.910144
$257$	−23.5623			−1.46978			−0.734888	−	0.678188i	$-0.762765\pi$
$257$	−23.5623			−1.46978			−0.734888	+	0.678188i	$0.762765\pi$
$258$		0			0
$259$	0.437694			0.0271970
$260$	56.8328			3.52462
$261$		0			0
$262$	20.7984			1.28493
$263$	−5.25329	−	9.09896i	−0.323932	−	0.561066i	0.657364	−	0.753573i	$-0.271671\pi$
$263$	−5.25329	−	9.09896i	−0.323932	−	0.561066i	−0.981296	+	0.192507i	$0.938338\pi$
$264$		0			0
$265$	−5.85410	+	10.1396i	−0.359615	+	0.622871i
$266$	2.00000			0.122628
$267$		0			0
$268$	−6.92705	−	11.9980i	−0.423137	−	0.732895i
$269$	8.56231			0.522053			0.261027	−	0.965332i	$-0.415939\pi$
$269$	8.56231			0.522053			0.261027	+	0.965332i	$0.415939\pi$
$270$		0			0
$271$	−3.57295	+	6.18853i	−0.217041	+	0.375926i	−0.953902	−	0.300118i	$-0.902974\pi$
$271$	−3.57295	+	6.18853i	−0.217041	+	0.375926i	0.736861	+	0.676044i	$0.236307\pi$
$272$	−25.0795	+	43.4390i	−1.52067	+	2.63388i
$273$		0			0
$274$	25.4164			1.53546
$275$	−3.78115	+	6.54915i	−0.228012	+	0.394929i
$276$		0			0
$277$	1.76393	+	3.05522i	0.105984	+	0.183570i	0.914140	−	0.405399i	$-0.132867\pi$
$277$	1.76393	+	3.05522i	0.105984	+	0.183570i	−0.808156	+	0.588969i	$0.799534\pi$
$278$	24.4894	+	42.4168i	1.46877	+	2.54399i
$279$		0			0
$280$	5.70820			0.341130
$281$	−0.736068	−	1.27491i	−0.0439101	−	0.0760546i	0.843235	−	0.537545i	$-0.180648\pi$
$281$	−0.736068	−	1.27491i	−0.0439101	−	0.0760546i	−0.887145	+	0.461490i	$0.847315\pi$
$282$		0			0
$283$	−7.61803	+	13.1948i	−0.452845	+	0.784351i	−0.998561	−	0.0536192i	$-0.982924\pi$
$283$	−7.61803	+	13.1948i	−0.452845	+	0.784351i	0.545716	+	0.837970i	$0.316258\pi$
$284$	33.4894	−	58.0053i	1.98723	−	3.44198i
$285$		0			0
$286$	−6.54508	+	11.3364i	−0.387019	+	0.670337i
$287$	0.0623059	−	0.107917i	0.00367780	−	0.00637014i
$288$		0			0
$289$	−4.45492	−	7.71614i	−0.262054	−	0.453891i
$290$	−25.4164			−1.49250
$291$		0			0
$292$	11.7812	−	20.4056i	0.689440	−	1.19414i
$293$	0.909830			0.0531528			0.0265764	−	0.999647i	$-0.491539\pi$
$293$	0.909830			0.0531528			0.0265764	+	0.999647i	$0.491539\pi$
$294$		0			0
$295$	−9.85410	−	17.0678i	−0.573728	−	0.993726i
$296$	−6.92705	−	11.9980i	−0.402627	−	0.697370i
$297$		0			0
$298$	11.7812	+	20.4056i	0.682464	+	1.18206i
$299$	−23.9443			−1.38473
$300$		0			0
$301$	0.944272	−	1.22665i	0.0544269	−	0.0707027i
$302$	−5.61803			−0.323282
$303$		0			0
$304$	−15.9443	−	27.6163i	−0.914467	−	1.58390i
$305$	−12.4721			−0.714152
$306$		0			0
$307$	−14.1074	−	24.4347i	−0.805151	−	1.39456i	−0.916189	−	0.400747i	$-0.868751\pi$
$307$	−14.1074	−	24.4347i	−0.805151	−	1.39456i	0.111038	−	0.993816i	$-0.464583\pi$
$308$	−0.791796	+	1.37143i	−0.0451168	+	0.0781445i
$309$		0			0
$310$		0			0
$311$	11.9164	+	20.6398i	0.675717	+	1.17038i	0.976259	+	0.216608i	$0.0694994\pi$
$311$	11.9164	+	20.6398i	0.675717	+	1.17038i	−0.300541	+	0.953769i	$0.597167\pi$
$312$		0			0
$313$	13.5623	+	23.4906i	0.766587	+	1.32777i	0.939404	+	0.342813i	$0.111380\pi$
$313$	13.5623	+	23.4906i	0.766587	+	1.32777i	−0.172817	+	0.984954i	$0.555287\pi$
$314$	15.5172	−	26.8766i	0.875687	−	1.51674i
$315$		0			0
$316$	8.78115	−	15.2094i	0.493978	−	0.855596i
$317$	29.3050			1.64593			0.822965	−	0.568092i	$-0.192318\pi$
$317$	29.3050			1.64593			0.822965	+	0.568092i	$0.192318\pi$
$318$		0			0
$319$	2.07295	−	3.59045i	0.116063	−	0.201027i
$320$	−14.0902	−	24.4049i	−0.787664	−	1.36427i
$321$		0			0
$322$	−4.09017			−0.227936
$323$	16.4721			0.916534
$324$		0			0
$325$	−9.89919	−	17.1459i	−0.549108	−	0.951083i
$326$	−18.3262	+	31.7420i	−1.01500	+	1.75803i
$327$		0			0
$328$	−3.94427			−0.217786
$329$	0.927051	−	1.60570i	0.0511100	−	0.0885251i
$330$		0			0
$331$	−1.73607	+	3.00696i	−0.0954229	+	0.165277i	−0.909785	−	0.415080i	$-0.863754\pi$
$331$	−1.73607	+	3.00696i	−0.0954229	+	0.165277i	0.814362	+	0.580357i	$0.197087\pi$
$332$	−31.6353	−	54.7939i	−1.73621	−	3.00720i
$333$		0			0
$334$	12.7812	+	22.1376i	0.699354	+	1.21132i
$335$	−4.61803	+	7.99867i	−0.252310	+	0.437014i
$336$		0			0
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	0.178863	+	0.983874i	$0.442758\pi$
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	−0.941491	+	0.337037i	$0.890575\pi$
$338$	−0.118034	−	0.204441i	−0.00642020	−	0.0111201i
$339$		0			0
$340$	79.9574			4.33630
$341$		0			0
$342$		0			0
$343$	−3.29180			−0.177740
$344$	−48.5689	−	6.47106i	−2.61866	−	0.348896i
$345$		0			0
$346$	21.5623			1.15920
$347$	−0.545085	−	0.944115i	−0.0292617	−	0.0506827i	0.851024	−	0.525127i	$-0.175982\pi$
$347$	−0.545085	−	0.944115i	−0.0292617	−	0.0506827i	−0.880285	+	0.474445i	$0.842649\pi$
$348$		0			0
$349$	−3.64590	−	6.31488i	−0.195160	−	0.338028i	0.751793	−	0.659400i	$-0.229189\pi$
$349$	−3.64590	−	6.31488i	−0.195160	−	0.338028i	−0.946953	+	0.321372i	$0.895856\pi$
$350$	−1.69098	−	2.92887i	−0.0903868	−	0.156555i
$351$		0			0
$352$	15.0000			0.799503
$353$	−6.38197	+	11.0539i	−0.339678	+	0.588339i	−0.984372	−	0.176101i	$-0.943651\pi$
$353$	−6.38197	+	11.0539i	−0.339678	+	0.588339i	0.644694	+	0.764441i	$0.276985\pi$
$354$		0			0
$355$	−44.6525			−2.36991
$356$	11.7812	+	20.4056i	0.624400	+	1.08149i
$357$		0			0
$358$	−28.3435	+	49.0923i	−1.49800	+	2.59461i
$359$	−18.3262	+	31.7420i	−0.967222	+	1.67528i	−0.263699	+	0.964605i	$0.584942\pi$
$359$	−18.3262	+	31.7420i	−0.967222	+	1.67528i	−0.703523	+	0.710672i	$0.748391\pi$
$360$		0			0
$361$	4.26393	−	7.38535i	0.224417	−	0.388702i
$362$	28.2984	−	49.0142i	1.48733	−	2.57613i
$363$		0			0
$364$	−2.07295	−	3.59045i	−0.108652	−	0.188191i
$365$	−15.7082			−0.822205
$366$		0			0
$367$	1.59017	+	2.75426i	0.0830062	+	0.143771i	0.904540	−	0.426389i	$-0.140215\pi$
$367$	1.59017	+	2.75426i	0.0830062	+	0.143771i	−0.821534	+	0.570160i	$0.806881\pi$
$368$	32.6074	+	56.4777i	1.69978	+	2.94410i
$369$		0			0
$370$	−7.85410	+	13.6037i	−0.408315	+	0.707223i
$371$	0.854102			0.0443428
$372$		0			0
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	−9.20820	+	15.9491i	−0.476145	+	0.824707i
$375$		0			0
$376$	−58.6869			−3.02655
$377$	5.42705	+	9.39993i	0.279507	+	0.484121i
$378$		0			0
$379$	17.3607			0.891758			0.445879	−	0.895093i	$-0.352891\pi$
$379$	17.3607			0.891758			0.445879	+	0.895093i	$0.352891\pi$
$380$	−25.4164	+	44.0225i	−1.30383	+	2.25831i
$381$		0			0
$382$	−30.7254	−	53.2180i	−1.57205	−	2.72287i
$383$	2.12461			0.108563			0.0542813	−	0.998526i	$-0.482713\pi$
$383$	2.12461			0.108563			0.0542813	+	0.998526i	$0.482713\pi$
$384$		0			0
$385$	1.05573			0.0538049
$386$	−28.0344			−1.42692
$387$		0			0
$388$	−23.1246			−1.17397
$389$	−23.0689			−1.16964			−0.584819	−	0.811164i	$-0.698835\pi$
$389$	−23.0689			−1.16964			−0.584819	+	0.811164i	$0.698835\pi$
$390$		0			0
$391$	−33.6869			−1.70362
$392$	25.9443	+	44.9368i	1.31038	+	2.26965i
$393$		0			0
$394$	19.5623	−	33.8829i	0.985535	−	1.70700i
$395$	−11.7082			−0.589104
$396$		0			0
$397$	−2.79180	−	4.83553i	−0.140116	−	0.242688i	0.787424	−	0.616412i	$-0.211414\pi$
$397$	−2.79180	−	4.83553i	−0.140116	−	0.242688i	−0.927540	+	0.373723i	$0.878081\pi$
$398$	−41.7426			−2.09237
$399$		0			0
$400$	−26.9615	+	46.6987i	−1.34807	+	2.33493i
$401$	0.708204	−	1.22665i	0.0353660	−	0.0612557i	−0.847801	−	0.530315i	$-0.822074\pi$
$401$	0.708204	−	1.22665i	0.0353660	−	0.0612557i	0.883167	+	0.469059i	$0.155407\pi$
$402$		0			0
$403$		0			0
$404$	19.9894	−	34.6226i	0.994508	−	1.72254i
$405$		0			0
$406$	0.927051	+	1.60570i	0.0460088	+	0.0796895i
$407$	−1.28115	−	2.21902i	−0.0635044	−	0.109993i
$408$		0			0
$409$	20.0902			0.993395			0.496697	−	0.867924i	$-0.334546\pi$
$409$	20.0902			0.993395			0.496697	+	0.867924i	$0.334546\pi$
$410$	2.23607	+	3.87298i	0.110432	+	0.191273i
$411$		0			0
$412$	−25.2812	+	43.7882i	−1.24551	+	2.15729i
$413$	−0.718847	+	1.24508i	−0.0353722	+	0.0612664i
$414$		0			0
$415$	−21.0902	+	36.5292i	−1.03528	+	1.79315i
$416$	−19.6353	+	34.0093i	−0.962698	+	1.66744i
$417$		0			0
$418$	−5.85410	−	10.1396i	−0.286333	−	0.495944i
$419$	5.76393			0.281587			0.140793	−	0.990039i	$-0.455035\pi$
$419$	5.76393			0.281587			0.140793	+	0.990039i	$0.455035\pi$
$420$		0			0
$421$	−11.8262	+	20.4836i	−0.576376	+	0.998312i	0.419515	+	0.907748i	$0.362200\pi$
$421$	−11.8262	+	20.4836i	−0.576376	+	0.998312i	−0.995891	+	0.0905634i	$0.971133\pi$
$422$	−12.4721			−0.607134
$423$		0			0
$424$	−13.5172	−	23.4125i	−0.656454	−	1.13701i
$425$	−13.9271	−	24.1224i	−0.675561	−	1.17011i
$426$		0			0
$427$	0.454915	+	0.787936i	0.0220149	+	0.0381309i
$428$	−79.9574			−3.86489
$429$		0			0
$430$	21.1803	+	51.3596i	1.02141	+	2.47678i
$431$	0.201626			0.00971199			0.00485599	−	0.999988i	$-0.498454\pi$
$431$	0.201626			0.00971199			0.00485599	+	0.999988i	$0.498454\pi$
$432$		0			0
$433$	10.6459	+	18.4392i	0.511609	+	0.886133i	0.999909	+	0.0134574i	$0.00428377\pi$
$433$	10.6459	+	18.4392i	0.511609	+	0.886133i	−0.488300	+	0.872676i	$0.662383\pi$
$434$		0			0
$435$		0			0
$436$	17.3435	+	30.0398i	0.830601	+	1.43864i
$437$	10.7082	−	18.5472i	0.512243	−	0.887231i
$438$		0			0
$439$	−3.92705	+	6.80185i	−0.187428	+	0.324635i	−0.944392	−	0.328822i	$-0.893348\pi$
$439$	−3.92705	+	6.80185i	−0.187428	+	0.324635i	0.756964	+	0.653457i	$0.226682\pi$
$440$	−16.7082	−	28.9395i	−0.796532	−	1.37963i
$441$		0			0
$442$	−24.1074	−	41.7552i	−1.14667	−	1.98609i
$443$	−3.23607	+	5.60503i	−0.153750	+	0.266303i	−0.932603	−	0.360903i	$-0.882468\pi$
$443$	−3.23607	+	5.60503i	−0.153750	+	0.266303i	0.778853	+	0.627206i	$0.215802\pi$
$444$		0			0
$445$	7.85410	−	13.6037i	0.372320	−	0.644877i
$446$	18.9443			0.897037
$447$		0			0
$448$	−1.02786	+	1.78031i	−0.0485620	+	0.0841119i
$449$	10.4164	+	18.0417i	0.491581	+	0.851443i	0.999953	−	0.00969466i	$-0.00308595\pi$
$449$	10.4164	+	18.0417i	0.491581	+	0.851443i	−0.508372	+	0.861137i	$0.669753\pi$
$450$		0			0
$451$	−0.729490			−0.0343504
$452$	64.9574			3.05534
$453$		0			0
$454$	9.78115	+	16.9415i	0.459052	+	0.795102i
$455$	−1.38197	+	2.39364i	−0.0647876	+	0.112215i
$456$		0			0
$457$	−2.29180			−0.107206			−0.0536028	−	0.998562i	$-0.517070\pi$
$457$	−2.29180			−0.107206			−0.0536028	+	0.998562i	$0.517070\pi$
$458$	20.5623	−	35.6150i	0.960813	−	1.66418i
$459$		0			0
$460$	51.9787	−	90.0298i	2.42352	−	4.19766i
$461$	8.79837	+	15.2392i	0.409781	+	0.709762i	0.994865	−	0.101211i	$-0.0322717\pi$
$461$	8.79837	+	15.2392i	0.409781	+	0.709762i	−0.585084	+	0.810973i	$0.698938\pi$
$462$		0			0
$463$	−11.9164	−	20.6398i	−0.553802	−	0.959214i	−0.997996	−	0.0632829i	$-0.979843\pi$
$463$	−11.9164	−	20.6398i	−0.553802	−	0.959214i	0.444193	−	0.895931i	$-0.353490\pi$
$464$	14.7812	−	25.6017i	0.686198	−	1.18853i
$465$		0			0
$466$	−14.4443	+	25.0182i	−0.669118	+	1.15895i
$467$	−16.4721	−	28.5306i	−0.762240	−	1.32024i	−0.941694	−	0.336471i	$-0.890766\pi$
$467$	−16.4721	−	28.5306i	−0.762240	−	1.32024i	0.179454	−	0.983766i	$-0.442567\pi$
$468$		0			0
$469$	0.673762			0.0311114
$470$	33.2705	+	57.6262i	1.53465	+	2.65810i
$471$		0			0
$472$	45.5066			2.09461
$473$	−8.98278	−	1.19682i	−0.413029	−	0.0550297i
$474$		0			0
$475$	17.7082			0.812508
$476$	−2.91641	−	5.05137i	−0.133673	−	0.231529i
$477$		0			0
$478$	−28.4164	−	49.2187i	−1.29974	−	2.25121i
$479$	−18.0902	−	31.3331i	−0.826561	−	1.43165i	−0.900720	−	0.434399i	$-0.856961\pi$
$479$	−18.0902	−	31.3331i	−0.826561	−	1.43165i	0.0741595	−	0.997246i	$-0.476373\pi$
$480$		0			0
$481$	6.70820			0.305868
$482$	38.3156	−	66.3646i	1.74523	−	3.02282i
$483$		0			0
$484$	−44.1246			−2.00566
$485$	7.70820	+	13.3510i	0.350012	+	0.606238i
$486$		0			0
$487$	7.16312	−	12.4069i	0.324592	−	0.562210i	−0.656838	−	0.754032i	$-0.728106\pi$
$487$	7.16312	−	12.4069i	0.324592	−	0.562210i	0.981430	+	0.191822i	$0.0614397\pi$
$488$	14.3992	−	24.9401i	0.651821	−	1.12899i
$489$		0			0
$490$	29.4164	−	50.9507i	1.32890	−	2.30172i
$491$	−4.82624	+	8.35929i	−0.217805	+	0.377249i	−0.954137	−	0.299371i	$-0.903223\pi$
$491$	−4.82624	+	8.35929i	−0.217805	+	0.377249i	0.736332	+	0.676621i	$0.236556\pi$
$492$		0			0
$493$	7.63525	+	13.2246i	0.343875	+	0.595608i
$494$	30.6525			1.37912
$495$		0			0
$496$		0			0
$497$	1.62868	+	2.82095i	0.0730562	+	0.126537i
$498$		0			0
$499$	−3.57295	+	6.18853i	−0.159947	+	0.277037i	−0.934849	−	0.355044i	$-0.884466\pi$
$499$	−3.57295	+	6.18853i	−0.159947	+	0.277037i	0.774902	+	0.632081i	$0.217799\pi$
$500$	7.41641			0.331672
$501$		0			0
$502$	−8.92705	+	15.4621i	−0.398434	+	0.690108i
$503$	−2.26393	+	3.92125i	−0.100944	+	0.174840i	−0.912074	−	0.410026i	$-0.865520\pi$
$503$	−2.26393	+	3.92125i	−0.100944	+	0.174840i	0.811130	+	0.584866i	$0.198853\pi$
$504$		0			0
$505$	−26.6525			−1.18602
$506$	11.9721	+	20.7363i	0.532226	+	0.921843i
$507$		0			0
$508$	80.8328			3.58638
$509$	2.64590	−	4.58283i	0.117277	−	0.203130i	−0.801410	−	0.598115i	$-0.795917\pi$
$509$	2.64590	−	4.58283i	0.117277	−	0.203130i	0.918688	+	0.394984i	$0.129250\pi$
$510$		0			0
$511$	0.572949	+	0.992377i	0.0253458	+	0.0439002i
$512$	−40.3050			−1.78124
$513$		0			0
$514$	−61.6869			−2.72089
$515$	33.7082			1.48536
$516$		0			0
$517$	−10.8541			−0.477363
$518$	1.14590			0.0503479
$519$		0			0
$520$	87.4853			3.83648
$521$	3.51722	+	6.09201i	0.154092	+	0.266896i	0.932728	−	0.360580i	$-0.117421\pi$
$521$	3.51722	+	6.09201i	0.154092	+	0.266896i	−0.778636	+	0.627476i	$0.784088\pi$
$522$		0			0
$523$	8.91641	−	15.4437i	0.389887	−	0.675305i	−0.602547	−	0.798084i	$-0.705847\pi$
$523$	8.91641	−	15.4437i	0.389887	−	0.675305i	0.992434	+	0.122779i	$0.0391806\pi$
$524$	38.5623			1.68460
$525$		0			0
$526$	−13.7533	−	23.8214i	−0.599672	−	1.03866i
$527$		0			0
$528$		0			0
$529$	−10.3992	+	18.0119i	−0.452139	+	0.783127i
$530$	−15.3262	+	26.5458i	−0.665729	+	1.15308i
$531$		0			0
$532$	3.70820			0.160771
$533$	0.954915	−	1.65396i	0.0413620	−	0.0716410i
$534$		0			0
$535$	26.6525	+	46.1634i	1.15229	+	1.99582i
$536$	−10.6631	−	18.4691i	−0.460577	−	0.797742i
$537$		0			0
$538$	22.4164			0.966440
$539$	4.79837	+	8.31103i	0.206681	+	0.357981i
$540$		0			0
$541$	10.0279	−	17.3688i	0.431132	−	0.746742i	−0.565839	−	0.824515i	$-0.691448\pi$
$541$	10.0279	−	17.3688i	0.431132	−	0.746742i	0.996971	+	0.0777737i	$0.0247812\pi$
$542$	−9.35410	+	16.2018i	−0.401793	+	0.695926i
$543$		0			0
$544$	−27.6246	+	47.8472i	−1.18440	+	2.05143i
$545$	11.5623	−	20.0265i	0.495275	−	0.857841i
$546$		0			0
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	0.549370	−	0.835579i	$-0.314868\pi$
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	−0.998318	+	0.0579790i	$0.981534\pi$
$548$	47.1246			2.01306
$549$		0			0
$550$	−9.89919	+	17.1459i	−0.422103	+	0.731103i
$551$	−9.70820			−0.413583
$552$		0			0
$553$	0.427051	+	0.739674i	0.0181601	+	0.0314541i
$554$	4.61803	+	7.99867i	0.196201	+	0.339831i
$555$		0			0
$556$	45.4058	+	78.6451i	1.92563	+	3.33529i
$557$	18.4377			0.781230			0.390615	−	0.920554i	$-0.372262\pi$
$557$	18.4377			0.781230			0.390615	+	0.920554i	$0.372262\pi$
$558$		0			0
$559$	14.4721	−	18.7999i	0.612106	−	0.795149i
$560$	7.52786			0.318110
$561$		0			0
$562$	−1.92705	−	3.33775i	−0.0812877	−	0.140794i
$563$	−14.3262			−0.603779			−0.301889	−	0.953343i	$-0.597617\pi$
$563$	−14.3262			−0.603779			−0.301889	+	0.953343i	$0.597617\pi$
$564$		0			0
$565$	−21.6525	−	37.5032i	−0.910927	−	1.57777i
$566$	−19.9443	+	34.5445i	−0.838320	+	1.45201i
$567$		0			0
$568$	51.5517	−	89.2901i	2.16306	−	3.74653i
$569$	−4.02786	−	6.97647i	−0.168857	−	0.292469i	0.769161	−	0.639055i	$-0.220674\pi$
$569$	−4.02786	−	6.97647i	−0.168857	−	0.292469i	−0.938018	+	0.346586i	$0.887341\pi$
$570$		0			0
$571$	10.4098	+	18.0304i	0.435638	+	0.754547i	0.997347	−	0.0727876i	$-0.0231895\pi$
$571$	10.4098	+	18.0304i	0.435638	+	0.754547i	−0.561710	+	0.827334i	$0.689856\pi$
$572$	−12.1353	+	21.0189i	−0.507400	+	0.878843i
$573$		0			0
$574$	0.163119	−	0.282530i	0.00680845	−	0.0117926i
$575$	−36.2148			−1.51026
$576$		0			0
$577$	−11.6074	+	20.1046i	−0.483222	+	0.836965i	−0.999814	−	0.0192664i	$-0.993867\pi$
$577$	−11.6074	+	20.1046i	−0.483222	+	0.836965i	0.516592	+	0.856231i	$0.327200\pi$
$578$	−11.6631	−	20.2011i	−0.485122	−	0.840256i
$579$		0			0
$580$	−47.1246			−1.95674
$581$	3.07701			0.127656
$582$		0			0
$583$	−2.50000	−	4.33013i	−0.103539	−	0.179336i
$584$	18.1353	−	31.4112i	0.750442	−	1.29980i
$585$		0			0
$586$	2.38197			0.0983981
$587$	−13.3713	+	23.1598i	−0.551894	+	0.955908i	0.446244	+	0.894911i	$0.352761\pi$
$587$	−13.3713	+	23.1598i	−0.551894	+	0.955908i	−0.998138	+	0.0609966i	$0.980572\pi$
$588$		0			0
$589$		0			0
$590$	−25.7984	−	44.6841i	−1.06210	−	1.83962i
$591$		0			0
$592$	−9.13525	−	15.8227i	−0.375457	−	0.650310i
$593$	−10.7639	+	18.6437i	−0.442022	+	0.765604i	−0.997839	−	0.0657001i	$-0.979072\pi$
$593$	−10.7639	+	18.6437i	−0.442022	+	0.765604i	0.555818	+	0.831304i	$0.312405\pi$
$594$		0			0
$595$	−1.94427	+	3.36758i	−0.0797074	+	0.138057i
$596$	21.8435	+	37.8340i	0.894743	+	1.54974i
$597$		0			0
$598$	−62.6869			−2.56346
$599$	15.8820	+	27.5084i	0.648920	+	1.12396i	0.983381	+	0.181552i	$0.0581122\pi$
$599$	15.8820	+	27.5084i	0.648920	+	1.12396i	−0.334462	+	0.942409i	$0.608555\pi$
$600$		0			0
$601$	2.58359			0.105387			0.0526935	−	0.998611i	$-0.483219\pi$
$601$	2.58359			0.105387			0.0526935	+	0.998611i	$0.483219\pi$
$602$	2.47214	−	3.21140i	0.100757	−	0.130887i
$603$		0			0
$604$	−10.4164			−0.423838
$605$	14.7082	+	25.4754i	0.597974	+	1.03572i
$606$		0			0
$607$	8.57295	+	14.8488i	0.347965	+	0.602694i	0.985888	−	0.167407i	$-0.0535394\pi$
$607$	8.57295	+	14.8488i	0.347965	+	0.602694i	−0.637923	+	0.770100i	$0.720206\pi$
$608$	−17.5623	−	30.4188i	−0.712246	−	1.23365i
$609$		0			0
$610$	−32.6525			−1.32206
$611$	14.2082	−	24.6093i	0.574802	−	0.995587i
$612$		0			0
$613$	29.7984			1.20354			0.601772	−	0.798668i	$-0.294461\pi$
$613$	29.7984			1.20354			0.601772	+	0.798668i	$0.294461\pi$
$614$	−36.9336	−	63.9709i	−1.49052	−	2.58166i
$615$		0			0
$616$	−1.21885	+	2.11111i	−0.0491087	+	0.0850588i
$617$	−1.85410	+	3.21140i	−0.0746433	+	0.129286i	−0.900931	−	0.433962i	$-0.857115\pi$
$617$	−1.85410	+	3.21140i	−0.0746433	+	0.129286i	0.826288	+	0.563248i	$0.190448\pi$
$618$		0			0
$619$	−1.63525	+	2.83234i	−0.0657264	+	0.113842i	−0.897016	−	0.441998i	$-0.854270\pi$
$619$	−1.63525	+	2.83234i	−0.0657264	+	0.113842i	0.831290	+	0.555840i	$0.187603\pi$
$620$		0			0
$621$		0			0
$622$	31.1976	+	54.0358i	1.25091	+	2.16664i
$623$	−1.14590			−0.0459094
$624$		0			0
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$	35.5066	+	61.4992i	1.41913	+	2.45800i
$627$		0			0
$628$	28.7705	−	49.8320i	1.14807	−	1.98851i
$629$	9.43769			0.376306
$630$		0			0
$631$	7.95492	−	13.7783i	0.316680	−	0.548506i	−0.663113	−	0.748519i	$-0.730765\pi$
$631$	7.95492	−	13.7783i	0.316680	−	0.548506i	0.979793	+	0.200013i	$0.0640985\pi$
$632$	13.5172	−	23.4125i	0.537686	−	0.931300i
$633$		0			0
$634$	76.7214			3.04699
$635$	−26.9443	−	46.6688i	−1.06925	−	1.85200i
$636$		0			0
$637$	−25.1246			−0.995473
$638$	5.42705	−	9.39993i	0.214859	−	0.372147i
$639$		0			0
$640$	−1.76393	−	3.05522i	−0.0697255	−	0.120768i
$641$	−33.1803			−1.31054			−0.655272	−	0.755393i	$-0.727446\pi$
$641$	−33.1803			−1.31054			−0.655272	+	0.755393i	$0.727446\pi$
$642$		0			0
$643$	29.5623			1.16582			0.582912	−	0.812535i	$-0.301913\pi$
$643$	29.5623			1.16582			0.582912	+	0.812535i	$0.301913\pi$
$644$	−7.58359			−0.298835
$645$		0			0
$646$	43.1246			1.69672
$647$	37.3262			1.46745			0.733723	−	0.679449i	$-0.237781\pi$
$647$	37.3262			1.46745			0.733723	+	0.679449i	$0.237781\pi$
$648$		0			0
$649$	8.41641			0.330373
$650$	−25.9164	−	44.8885i	−1.01653	−	1.76067i
$651$		0			0
$652$	−33.9787	+	58.8529i	−1.33071	+	2.30486i
$653$	−2.88854			−0.113037			−0.0565187	−	0.998402i	$-0.518000\pi$
$653$	−2.88854			−0.113037			−0.0565187	+	0.998402i	$0.518000\pi$
$654$		0			0
$655$	−12.8541	−	22.2640i	−0.502251	−	0.869925i
$656$	−5.20163			−0.203089
$657$		0			0
$658$	2.42705	−	4.20378i	0.0946163	−	0.163880i
$659$	7.68034	−	13.3027i	0.299184	−	0.518201i	−0.676766	−	0.736198i	$-0.736619\pi$
$659$	7.68034	−	13.3027i	0.299184	−	0.518201i	0.975949	+	0.217997i	$0.0699524\pi$
$660$		0			0
$661$	30.3951			1.18223			0.591117	−	0.806586i	$-0.298687\pi$
$661$	30.3951			1.18223			0.591117	+	0.806586i	$0.298687\pi$
$662$	−4.54508	+	7.87232i	−0.176650	+	0.305966i
$663$		0			0
$664$	−48.6976	−	84.3466i	−1.88983	−	3.27328i
$665$	−1.23607	−	2.14093i	−0.0479327	−	0.0830218i
$666$		0			0
$667$	19.8541			0.768754
$668$	23.6976	+	41.0454i	0.916886	+	1.58809i
$669$		0			0
$670$	−12.0902	+	20.9408i	−0.467084	+	0.809013i
$671$	2.66312	−	4.61266i	0.102809	−	0.178070i
$672$		0			0
$673$	19.9164	−	34.4962i	0.767721	−	1.32973i	−0.171075	−	0.985258i	$-0.554724\pi$
$673$	19.9164	−	34.4962i	0.767721	−	1.32973i	0.938796	−	0.344474i	$-0.111943\pi$
$674$	−36.6525	+	63.4840i	−1.41180	+	2.44531i
$675$		0			0
$676$	−0.218847	−	0.379054i	−0.00841719	−	0.0145790i
$677$	36.2361			1.39267			0.696333	−	0.717719i	$-0.254814\pi$
$677$	36.2361			1.39267			0.696333	+	0.717719i	$0.254814\pi$
$678$		0			0
$679$	0.562306	−	0.973942i	0.0215793	−	0.0373765i
$680$	123.082			4.71998
$681$		0			0
$682$		0			0
$683$	14.5623	+	25.2227i	0.557211	+	0.965118i	0.997728	+	0.0673736i	$0.0214619\pi$
$683$	14.5623	+	25.2227i	0.557211	+	0.965118i	−0.440517	+	0.897744i	$0.645205\pi$
$684$		0			0
$685$	−15.7082	−	27.2074i	−0.600180	−	1.03954i
$686$	−8.61803			−0.329038
$687$		0			0
$688$	−64.0517	−	8.53390i	−2.44195	−	0.325352i
$689$	13.0902			0.498696
$690$		0			0
$691$	−24.6353	−	42.6695i	−0.937169	−	1.62322i	−0.770719	−	0.637175i	$-0.780103\pi$
$691$	−24.6353	−	42.6695i	−0.937169	−	1.62322i	−0.166450	−	0.986050i	$-0.553230\pi$
$692$	39.9787			1.51976
$693$		0			0
$694$	−1.42705	−	2.47172i	−0.0541701	−	0.0938254i
$695$	30.2705	−	52.4301i	1.14823	−	1.98879i
$696$		0			0
$697$	1.34346	−	2.32694i	0.0508871	−	0.0881391i
$698$	−9.54508	−	16.5326i	−0.361287	−	0.625767i
$699$		0			0
$700$	−3.13525	−	5.43042i	−0.118501	−	0.205251i
$701$	11.7533	−	20.3573i	0.443916	−	0.768884i	−0.554060	−	0.832476i	$-0.686922\pi$
$701$	11.7533	−	20.3573i	0.443916	−	0.768884i	0.997976	+	0.0635921i	$0.0202557\pi$
$702$		0			0
$703$	−3.00000	+	5.19615i	−0.113147	+	0.195977i
$704$	12.0344			0.453565
$705$		0			0
$706$	−16.7082	+	28.9395i	−0.628822	+	1.08915i
$707$	0.972136	+	1.68379i	0.0365609	+	0.0633254i
$708$		0			0
$709$	−6.88854			−0.258705			−0.129352	−	0.991599i	$-0.541290\pi$
$709$	−6.88854			−0.258705			−0.129352	+	0.991599i	$0.541290\pi$
$710$	−116.902			−4.38724
$711$		0			0
$712$	18.1353	+	31.4112i	0.679647	+	1.17718i
$713$		0			0
$714$		0			0
$715$	16.1803			0.605110
$716$	−52.5517	+	91.0221i	−1.96395	+	3.40166i
$717$		0			0
$718$	−47.9787	+	83.1016i	−1.79055	+	3.10132i
$719$	6.89919	+	11.9497i	0.257296	+	0.445650i	0.965517	−	0.260341i	$-0.0838350\pi$
$719$	6.89919	+	11.9497i	0.257296	+	0.445650i	−0.708220	+	0.705991i	$0.750502\pi$
$720$		0			0
$721$	−1.22949	−	2.12954i	−0.0457886	−	0.0793082i
$722$	11.1631	−	19.3351i	0.415448	−	0.719578i
$723$		0			0
$724$	52.4681	−	90.8774i	1.94996	−	3.37743i
$725$	8.20820	+	14.2170i	0.304845	+	0.528007i
$726$		0			0
$727$	28.9787			1.07476			0.537381	−	0.843340i	$-0.319414\pi$
$727$	28.9787			1.07476			0.537381	+	0.843340i	$0.319414\pi$
$728$	−3.19098	−	5.52694i	−0.118266	−	0.204842i
$729$		0			0
$730$	−41.1246			−1.52209
$731$	20.3607	−	26.4493i	0.753067	−	0.978263i
$732$		0			0
$733$	−42.5410			−1.57129			−0.785644	−	0.618679i	$-0.787668\pi$
$733$	−42.5410			−1.57129			−0.785644	+	0.618679i	$0.787668\pi$
$734$	4.16312	+	7.21073i	0.153664	+	0.266153i
$735$		0			0
$736$	35.9164	+	62.2090i	1.32390	+	2.29306i
$737$	−1.97214	−	3.41584i	−0.0726446	−	0.125824i
$738$		0			0
$739$	−17.5410			−0.645257			−0.322628	−	0.946526i	$-0.604566\pi$
$739$	−17.5410			−0.645257			−0.322628	+	0.946526i	$0.604566\pi$
$740$	−14.5623	+	25.2227i	−0.535321	+	0.927203i
$741$		0			0
$742$	2.23607			0.0820886
$743$	−5.68034	−	9.83864i	−0.208391	−	0.360945i	0.742817	−	0.669495i	$-0.233489\pi$
$743$	−5.68034	−	9.83864i	−0.208391	−	0.360945i	−0.951208	+	0.308550i	$0.900156\pi$
$744$		0			0
$745$	14.5623	−	25.2227i	0.533522	−	0.924087i
$746$	−7.85410	+	13.6037i	−0.287559	+	0.498067i
$747$		0			0
$748$	−17.0729	+	29.5712i	−0.624249	+	1.08123i
$749$	1.94427	−	3.36758i	0.0710421	−	0.123049i
$750$		0			0
$751$	−4.48936	−	7.77579i	−0.163819	−	0.283743i	0.772416	−	0.635117i	$-0.219048\pi$
$751$	−4.48936	−	7.77579i	−0.163819	−	0.283743i	−0.936235	+	0.351374i	$0.885715\pi$
$752$	−77.3951			−2.82231
$753$		0			0
$754$	14.2082	+	24.6093i	0.517432	+	0.896219i
$755$	3.47214	+	6.01392i	0.126364	+	0.218869i
$756$		0			0
$757$	−7.98936	+	13.8380i	−0.290378	+	0.502950i	−0.973899	−	0.226981i	$-0.927114\pi$
$757$	−7.98936	+	13.8380i	−0.290378	+	0.502950i	0.683521	+	0.729931i	$0.260448\pi$
$758$	45.4508			1.65085
$759$		0			0
$760$	−39.1246	+	67.7658i	−1.41920	+	2.45812i
$761$	−5.04508	+	8.73834i	−0.182884	+	0.316765i	−0.942862	−	0.333185i	$-0.891877\pi$
$761$	−5.04508	+	8.73834i	−0.182884	+	0.316765i	0.759977	+	0.649950i	$0.225210\pi$
$762$		0			0
$763$	−1.68692			−0.0610705
$764$	−56.9681	−	98.6716i	−2.06103	−	3.56981i
$765$		0			0
$766$	5.56231			0.200974
$767$	−11.0172	+	19.0824i	−0.397809	+	0.689025i
$768$		0			0
$769$	7.94427	+	13.7599i	0.286478	+	0.496194i	0.972966	−	0.230946i	$-0.0741822\pi$
$769$	7.94427	+	13.7599i	0.286478	+	0.496194i	−0.686489	+	0.727140i	$0.740849\pi$
$770$	2.76393			0.0996052
$771$		0			0
$772$	−51.9787			−1.87075
$773$	33.5967			1.20839			0.604196	−	0.796836i	$-0.293495\pi$
$773$	33.5967			1.20839			0.604196	+	0.796836i	$0.293495\pi$
$774$		0			0
$775$		0			0
$776$	−35.5967			−1.27785
$777$		0			0
$778$	−60.3951			−2.16527
$779$	0.854102	+	1.47935i	0.0306014	+	0.0530031i
$780$		0			0
$781$	9.53444	−	16.5141i	0.341169	−	0.590922i
$782$	−88.1935			−3.15379
$783$		0			0
$784$	34.2148	+	59.2617i	1.22196	+	2.11649i
$785$	−38.3607			−1.36915
$786$		0			0
$787$	22.7254	−	39.3616i	0.810074	−	1.40309i	−0.102738	−	0.994708i	$-0.532760\pi$
$787$	22.7254	−	39.3616i	0.810074	−	1.40309i	0.912812	−	0.408381i	$-0.133906\pi$
$788$	36.2705	−	62.8224i	1.29208	−	2.23795i
$789$		0			0
$790$	−30.6525			−1.09057
$791$	−1.57953	+	2.73582i	−0.0561615	+	0.0972746i
$792$		0			0
$793$	6.97214	+	12.0761i	0.247588	+	0.428835i
$794$	−7.30902	−	12.6596i	−0.259387	−	0.449272i
$795$		0			0
$796$	−77.3951			−2.74320
$797$	−1.88197	−	3.25966i	−0.0666627	−	0.115463i	0.830768	−	0.556619i	$-0.187902\pi$
$797$	−1.88197	−	3.25966i	−0.0666627	−	0.115463i	−0.897430	+	0.441156i	$0.854568\pi$
$798$		0			0
$799$	19.9894	−	34.6226i	0.707173	−	1.22486i
$800$	−29.6976	+	51.4377i	−1.04997	+	1.81860i
$801$		0			0
$802$	1.85410	−	3.21140i	0.0654706	−	0.113398i
$803$	3.35410	−	5.80948i	0.118364	−	0.205012i
$804$		0			0
$805$	2.52786	+	4.37839i	0.0890955	+	0.154318i
$806$		0			0
$807$		0			0
$808$	30.7705	−	53.2961i	1.08250	−	1.87495i
$809$	37.7426			1.32696			0.663480	−	0.748194i	$-0.269079\pi$
$809$	37.7426			1.32696			0.663480	+	0.748194i	$0.269079\pi$
$810$		0			0
$811$	13.1976	+	22.8588i	0.463429	+	0.802683i	0.999129	−	0.0417257i	$-0.0132856\pi$
$811$	13.1976	+	22.8588i	0.463429	+	0.802683i	−0.535700	+	0.844408i	$0.679952\pi$
$812$	1.71885	+	2.97713i	0.0603197	+	0.104477i
$813$		0			0
$814$	−3.35410	−	5.80948i	−0.117561	−	0.203622i
$815$	45.3050			1.58696
$816$		0			0
$817$	8.09017	+	19.6176i	0.283039	+	0.686334i
$818$	52.5967			1.83900
$819$		0			0
$820$	4.14590	+	7.18091i	0.144781	+	0.250768i
$821$	15.3262			0.534889			0.267445	−	0.963573i	$-0.413821\pi$
$821$	15.3262			0.534889			0.267445	+	0.963573i	$0.413821\pi$
$822$		0			0
$823$	12.0066	+	20.7960i	0.418523	+	0.724903i	0.995791	−	0.0916516i	$-0.0292146\pi$
$823$	12.0066	+	20.7960i	0.418523	+	0.724903i	−0.577268	+	0.816555i	$0.695881\pi$
$824$	−38.9164	+	67.4052i	−1.35572	+	2.34817i
$825$		0			0
$826$	−1.88197	+	3.25966i	−0.0654820	+	0.113418i
$827$	−6.59017	−	11.4145i	−0.229163	−	0.396921i	0.728398	−	0.685155i	$-0.240265\pi$
$827$	−6.59017	−	11.4145i	−0.229163	−	0.396921i	−0.957560	+	0.288233i	$0.906932\pi$
$828$		0			0
$829$	20.5795	+	35.6448i	0.714757	+	1.23799i	0.963053	+	0.269311i	$0.0867958\pi$
$829$	20.5795	+	35.6448i	0.714757	+	1.23799i	−0.248297	+	0.968684i	$0.579871\pi$
$830$	−55.2148	+	95.6348i	−1.91653	+	3.31953i
$831$		0			0
$832$	−15.7533	+	27.2855i	−0.546147	+	0.945954i
$833$	−35.3475			−1.22472
$834$		0			0
$835$	15.7984	−	27.3636i	0.546725	−	0.946956i
$836$	−10.8541	−	18.7999i	−0.375397	−	0.650207i
$837$		0			0
$838$	15.0902			0.521281
$839$	9.88854			0.341390			0.170695	−	0.985324i	$-0.445399\pi$
$839$	9.88854			0.341390			0.170695	+	0.985324i	$0.445399\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−30.9615	+	53.6269i	−1.06700	+	1.84810i
$843$		0			0
$844$	−23.1246			−0.795982
$845$	−0.145898	+	0.252703i	−0.00501904	+	0.00869324i
$846$		0			0
$847$	1.07295	−	1.85840i	0.0368670	−	0.0638555i
$848$	−17.8262	−	30.8759i	−0.612156	−	1.06028i
$849$		0			0
$850$	−36.4615	−	63.1532i	−1.25062	−	2.16614i
$851$	6.13525	−	10.6266i	0.210314	−	0.364274i
$852$		0			0
$853$	−26.8713	+	46.5425i	−0.920057	+	1.59358i	−0.120732	+	0.992685i	$0.538524\pi$
$853$	−26.8713	+	46.5425i	−0.920057	+	1.59358i	−0.799325	+	0.600900i	$0.794809\pi$
$854$	1.19098	+	2.06284i	0.0407546	+	0.0705890i
$855$		0			0
$856$	−123.082			−4.20686
$857$	−6.90983	−	11.9682i	−0.236035	−	0.408825i	0.723538	−	0.690285i	$-0.242515\pi$
$857$	−6.90983	−	11.9682i	−0.236035	−	0.408825i	−0.959573	+	0.281460i	$0.909181\pi$
$858$		0			0
$859$	−22.5836			−0.770542			−0.385271	−	0.922803i	$-0.625892\pi$
$859$	−22.5836			−0.770542			−0.385271	+	0.922803i	$0.625892\pi$
$860$	39.2705	+	95.2259i	1.33911	+	3.24718i
$861$		0			0
$862$	0.527864			0.0179791
$863$	−14.2533	−	24.6874i	−0.485188	−	0.840370i	0.514668	−	0.857390i	$-0.327915\pi$
$863$	−14.2533	−	24.6874i	−0.485188	−	0.840370i	−0.999855	+	0.0170203i	$0.994582\pi$
$864$		0			0
$865$	−13.3262	−	23.0817i	−0.453106	−	0.784802i
$866$	27.8713	+	48.2745i	0.947106	+	1.64044i
$867$		0			0
$868$		0			0
$869$	2.50000	−	4.33013i	0.0848067	−	0.146889i
$870$		0			0
$871$	10.3262			0.349891
$872$	26.6976	+	46.2415i	0.904093	+	1.56594i
$873$		0			0
$874$	28.0344	−	48.5571i	0.948279	−	1.64247i
$875$	−0.180340	+	0.312358i	−0.00609660	+	0.0105596i
$876$		0			0
$877$	−11.8262	+	20.4836i	−0.399344	+	0.691684i	−0.993645	−	0.112559i	$-0.964095\pi$
$877$	−11.8262	+	20.4836i	−0.399344	+	0.691684i	0.594301	+	0.804242i	$0.297429\pi$
$878$	−10.2812	+	17.8075i	−0.346972	+	0.600973i
$879$		0			0
$880$	−22.0344	−	38.1648i	−0.742781	−	1.28653i
$881$	−38.2361			−1.28821			−0.644103	−	0.764939i	$-0.722769\pi$
$881$	−38.2361			−1.28821			−0.644103	+	0.764939i	$0.722769\pi$
$882$		0			0
$883$	13.5623	+	23.4906i	0.456408	+	0.790522i	0.998768	−	0.0496245i	$-0.0158024\pi$
$883$	13.5623	+	23.4906i	0.456408	+	0.790522i	−0.542360	+	0.840146i	$0.682469\pi$
$884$	−44.6976	−	77.4184i	−1.50334	−	2.60386i
$885$		0			0
$886$	−8.47214	+	14.6742i	−0.284627	+	0.492988i
$887$	−40.9574			−1.37522			−0.687608	−	0.726082i	$-0.741339\pi$
$887$	−40.9574			−1.37522			−0.687608	+	0.726082i	$0.741339\pi$
$888$		0			0
$889$	−1.96556	+	3.40445i	−0.0659227	+	0.114181i
$890$	20.5623	−	35.6150i	0.689250	−	1.19382i
$891$		0			0
$892$	35.1246			1.17606
$893$	12.7082	+	22.0113i	0.425264	+	0.736579i
$894$		0			0
$895$	70.0689			2.34214
$896$	−0.128677	+	0.222875i	−0.00429880	+	0.00744574i
$897$		0			0
$898$	27.2705	+	47.2339i	0.910029	+	1.57622i
$899$		0			0
$900$		0			0
$901$	18.4164			0.613540
$902$	−1.90983			−0.0635904
$903$		0			0
$904$	99.9919			3.32568
$905$	−69.9574			−2.32546
$906$		0			0
$907$	−8.29180			−0.275325			−0.137662	−	0.990479i	$-0.543959\pi$
$907$	−8.29180			−0.275325			−0.137662	+	0.990479i	$0.543959\pi$
$908$	18.1353	+	31.4112i	0.601840	+	1.04242i
$909$		0			0
$910$	−3.61803	+	6.26662i	−0.119937	+	0.207736i
$911$	−3.97871			−0.131821			−0.0659103	−	0.997826i	$-0.520995\pi$
$911$	−3.97871			−0.131821			−0.0659103	+	0.997826i	$0.520995\pi$
$912$		0			0
$913$	−9.00658	−	15.5999i	−0.298074	−	0.516280i
$914$	−6.00000			−0.198462
$915$		0			0
$916$	38.1246	−	66.0338i	1.25967	−	2.18182i
$917$	−0.937694	+	1.62413i	−0.0309654	+	0.0536336i
$918$		0			0
$919$	−44.3951			−1.46446			−0.732230	−	0.681057i	$-0.761520\pi$
$919$	−44.3951			−1.46446			−0.732230	+	0.681057i	$0.761520\pi$
$920$	80.0132	−	138.587i	2.63796	−	4.56907i
$921$		0			0
$922$	23.0344	+	39.8968i	0.758599	+	1.31393i
$923$	24.9615	+	43.2346i	0.821618	+	1.42308i
$924$		0			0
$925$	10.1459			0.333595
$926$	−31.1976	−	54.0358i	−1.02522	−	1.77573i
$927$		0			0
$928$	16.2812	−	28.1998i	0.534455	−	0.925703i
$929$	15.3820	−	26.6423i	0.504666	−	0.874107i	−0.495320	−	0.868711i	$-0.664949\pi$
$929$	15.3820	−	26.6423i	0.504666	−	0.874107i	0.999985	−	0.00539616i	$-0.00171766\pi$
$930$		0			0
$931$	11.2361	−	19.4614i	0.368247	−	0.637823i
$932$	−26.7812	+	46.3863i	−0.877246	+	1.51943i
$933$		0			0
$934$	−43.1246	−	74.6940i	−1.41108	−	2.44406i
$935$	22.7639			0.744460
$936$		0			0
$937$	19.8369	−	34.3585i	0.648043	−	1.12244i	−0.335547	−	0.942023i	$-0.608921\pi$
$937$	19.8369	−	34.3585i	0.648043	−	1.12244i	0.983590	−	0.180419i	$-0.0577455\pi$
$938$	1.76393			0.0575944
$939$		0			0
$940$	61.6869	+	106.845i	2.01201	+	3.48490i
$941$	−10.8820	−	18.8481i	−0.354742	−	0.614431i	0.632332	−	0.774698i	$-0.282098\pi$
$941$	−10.8820	−	18.8481i	−0.354742	−	0.614431i	−0.987074	+	0.160267i	$0.948765\pi$
$942$		0			0
$943$	−1.74671	−	3.02539i	−0.0568807	−	0.0985203i
$944$	60.0132			1.95326
$945$		0			0
$946$	−23.5172	−	3.13331i	−0.764611	−	0.101873i
$947$	19.3607			0.629138			0.314569	−	0.949235i	$-0.398140\pi$
$947$	19.3607			0.629138			0.314569	+	0.949235i	$0.398140\pi$
$948$		0			0
$949$	8.78115	+	15.2094i	0.285048	+	0.493718i
$950$	46.3607			1.50414
$951$		0			0
$952$	−4.48936	−	7.77579i	−0.145501	−	0.252015i
$953$	−1.55573	+	2.69460i	−0.0503950	+	0.0872867i	−0.890122	−	0.455721i	$-0.849381\pi$
$953$	−1.55573	+	2.69460i	−0.0503950	+	0.0872867i	0.839728	+	0.543008i	$0.182715\pi$
$954$		0			0
$955$	−37.9787	+	65.7811i	−1.22896	+	2.12863i
$956$	−52.6869	−	91.2564i	−1.70402	−	2.95144i
$957$		0			0
$958$	−47.3607	−	82.0311i	−1.53015	−	2.65030i
$959$	−1.14590	+	1.98475i	−0.0370030	+	0.0640910i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	17.5623			0.566231
$963$		0			0
$964$	71.0410	−	123.047i	2.28808	−	3.96307i
$965$	17.3262	+	30.0099i	0.557751	+	0.966054i
$966$		0			0
$967$	−49.1033			−1.57906			−0.789528	−	0.613714i	$-0.789675\pi$
$967$	−49.1033			−1.57906			−0.789528	+	0.613714i	$0.789675\pi$
$968$	−67.9230			−2.18313
$969$		0			0
$970$	20.1803	+	34.9534i	0.647952	+	1.12229i
$971$	13.6803	−	23.6950i	0.439023	−	0.760410i	−0.558591	−	0.829443i	$-0.688658\pi$
$971$	13.6803	−	23.6950i	0.439023	−	0.760410i	0.997614	+	0.0690328i	$0.0219913\pi$
$972$		0			0
$973$	−4.41641			−0.141584
$974$	18.7533	−	32.4816i	0.600894	−	1.04078i
$975$		0			0
$976$	18.9894	−	32.8905i	0.607835	−	1.05280i
$977$	18.3820	+	31.8385i	0.588091	+	1.01860i	0.994482	+	0.104905i	$0.0334537\pi$
$977$	18.3820	+	31.8385i	0.588091	+	1.01860i	−0.406391	+	0.913699i	$0.633213\pi$
$978$		0			0
$979$	3.35410	+	5.80948i	0.107198	+	0.185672i
$980$	54.5410	−	94.4678i	1.74225	−	3.01766i
$981$		0			0
$982$	−12.6353	+	21.8849i	−0.403207	+	0.698375i
$983$	−0.763932	−	1.32317i	−0.0243656	−	0.0422025i	0.853585	−	0.520953i	$-0.174423\pi$
$983$	−0.763932	−	1.32317i	−0.0243656	−	0.0422025i	−0.877951	+	0.478750i	$0.841090\pi$
$984$		0			0
$985$	−48.3607			−1.54090
$986$	19.9894	+	34.6226i	0.636591	+	1.10261i
$987$		0			0
$988$	56.8328			1.80809
$989$	−16.5451	−	40.1197i	−0.526103	−	1.27573i
$990$		0			0
$991$	−33.1803			−1.05401			−0.527004	−	0.849863i	$-0.676685\pi$
$991$	−33.1803			−1.05401			−0.527004	+	0.849863i	$0.676685\pi$
$992$		0			0
$993$		0			0
$994$	4.26393	+	7.38535i	0.135244	+	0.234249i
$995$	25.7984	+	44.6841i	0.817863	+	1.41658i
$996$		0			0
$997$	36.4508			1.15441			0.577205	−	0.816599i	$-0.304143\pi$
$997$	36.4508			1.15441			0.577205	+	0.816599i	$0.304143\pi$
$998$	−9.35410	+	16.2018i	−0.296099	+	0.512858i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.h.d.208.2		4
3.2	odd	2		43.2.c.b.36.1	yes	4
12.11	even	2		688.2.i.e.337.2		4
43.6	even	3	inner	387.2.h.d.307.2		4
129.50	even	6		1849.2.a.h.1.2		2
129.92	odd	6		43.2.c.b.6.1	✓	4
129.122	odd	6		1849.2.a.e.1.1		2
516.479	even	6		688.2.i.e.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.1	✓	4	129.92	odd	6
43.2.c.b.36.1	yes	4	3.2	odd	2
387.2.h.d.208.2		4	1.1	even	1	trivial
387.2.h.d.307.2		4	43.6	even	3	inner
688.2.i.e.49.2		4	516.479	even	6
688.2.i.e.337.2		4	12.11	even	2
1849.2.a.e.1.1		2	129.122	odd	6
1849.2.a.h.1.2		2	129.50	even	6

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} +4.85410 q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.118034 + 0.204441i) q^{7} +7.47214 q^{8} +O(q^{10})\)	\(q+2.61803 q^{2} +4.85410 q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.118034 + 0.204441i) q^{7} +7.47214 q^{8} +(-4.23607 - 7.33708i) q^{10} +1.38197 q^{11} +(-1.80902 + 3.13331i) q^{13} +(-0.309017 + 0.535233i) q^{14} +9.85410 q^{16} +(-2.54508 + 4.40822i) q^{17} +(-1.61803 - 2.80252i) q^{19} +(-7.85410 - 13.6037i) q^{20} +3.61803 q^{22} +(3.30902 + 5.73139i) q^{23} +(-2.73607 + 4.73901i) q^{25} +(-4.73607 + 8.20311i) q^{26} +(-0.572949 + 0.992377i) q^{28} +(1.50000 - 2.59808i) q^{29} +10.8541 q^{32} +(-6.66312 + 11.5409i) q^{34} +0.763932 q^{35} +(-0.927051 - 1.60570i) q^{37} +(-4.23607 - 7.33708i) q^{38} +(-12.0902 - 20.9408i) q^{40} -0.527864 q^{41} +(-6.50000 - 0.866025i) q^{43} +6.70820 q^{44} +(8.66312 + 15.0050i) q^{46} -7.85410 q^{47} +(3.47214 + 6.01392i) q^{49} +(-7.16312 + 12.4069i) q^{50} +(-8.78115 + 15.2094i) q^{52} +(-1.80902 - 3.13331i) q^{53} +(-2.23607 - 3.87298i) q^{55} +(-0.881966 + 1.52761i) q^{56} +(3.92705 - 6.80185i) q^{58} +6.09017 q^{59} +(1.92705 - 3.33775i) q^{61} +8.70820 q^{64} +11.7082 q^{65} +(-1.42705 - 2.47172i) q^{67} +(-12.3541 + 21.3979i) q^{68} +2.00000 q^{70} +(6.89919 - 11.9497i) q^{71} +(2.42705 - 4.20378i) q^{73} +(-2.42705 - 4.20378i) q^{74} +(-7.85410 - 13.6037i) q^{76} +(-0.163119 + 0.282530i) q^{77} +(1.80902 - 3.13331i) q^{79} +(-15.9443 - 27.6163i) q^{80} -1.38197 q^{82} +(-6.51722 - 11.2882i) q^{83} +16.4721 q^{85} +(-17.0172 - 2.26728i) q^{86} +10.3262 q^{88} +(2.42705 + 4.20378i) q^{89} +(-0.427051 - 0.739674i) q^{91} +(16.0623 + 27.8207i) q^{92} -20.5623 q^{94} +(-5.23607 + 9.06914i) q^{95} -4.76393 q^{97} +(9.09017 + 15.7446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	\( 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} - 8 q^{10} + 10 q^{11} - 5 q^{13} + q^{14} + 26 q^{16} + q^{17} - 2 q^{19} - 18 q^{20} + 10 q^{22} + 11 q^{23} - 2 q^{25} - 10 q^{26} - 9 q^{28} + 6 q^{29} + 30 q^{32} - 11 q^{34} + 12 q^{35} + 3 q^{37} - 8 q^{38} - 26 q^{40} - 20 q^{41} - 26 q^{43} + 19 q^{46} - 18 q^{47} - 4 q^{49} - 13 q^{50} - 15 q^{52} - 5 q^{53} - 8 q^{56} + 9 q^{58} + 2 q^{59} + q^{61} + 8 q^{64} + 20 q^{65} + q^{67} - 36 q^{68} + 8 q^{70} + 3 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{76} + 15 q^{77} + 5 q^{79} - 28 q^{80} - 10 q^{82} + 3 q^{83} + 48 q^{85} - 39 q^{86} + 10 q^{88} + 3 q^{89} + 5 q^{91} + 24 q^{92} - 42 q^{94} - 12 q^{95} - 28 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 - 8 * q^10 + 10 * q^11 - 5 * q^13 + q^14 + 26 * q^16 + q^17 - 2 * q^19 - 18 * q^20 + 10 * q^22 + 11 * q^23 - 2 * q^25 - 10 * q^26 - 9 * q^28 + 6 * q^29 + 30 * q^32 - 11 * q^34 + 12 * q^35 + 3 * q^37 - 8 * q^38 - 26 * q^40 - 20 * q^41 - 26 * q^43 + 19 * q^46 - 18 * q^47 - 4 * q^49 - 13 * q^50 - 15 * q^52 - 5 * q^53 - 8 * q^56 + 9 * q^58 + 2 * q^59 + q^61 + 8 * q^64 + 20 * q^65 + q^67 - 36 * q^68 + 8 * q^70 + 3 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^76 + 15 * q^77 + 5 * q^79 - 28 * q^80 - 10 * q^82 + 3 * q^83 + 48 * q^85 - 39 * q^86 + 10 * q^88 + 3 * q^89 + 5 * q^91 + 24 * q^92 - 42 * q^94 - 12 * q^95 - 28 * q^97 + 14 * q^98

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