LMFDB - Embedded newform 688.2.i.e.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [688,2,Mod(49,688)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(688, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("688.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 688 = 2^{4} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	688.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.49370765906$
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			337.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	688.337
Dual form			688.2.i.e.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +O(q^{10})$	\(q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +1.38197 q^{11} +(-1.80902 + 3.13331i) q^{13} +(0.618034 - 1.07047i) q^{15} +(2.54508 - 4.40822i) q^{17} +(1.61803 + 2.80252i) q^{19} -0.0901699 q^{21} +(3.30902 + 5.73139i) q^{23} +(-2.73607 + 4.73901i) q^{25} -2.23607 q^{27} +(-1.50000 + 2.59808i) q^{29} +(-0.263932 - 0.457144i) q^{33} +0.763932 q^{35} +(-0.927051 - 1.60570i) q^{37} +1.38197 q^{39} +0.527864 q^{41} +(6.50000 + 0.866025i) q^{43} +9.23607 q^{45} -7.85410 q^{47} +(3.47214 + 6.01392i) q^{49} -1.94427 q^{51} +(1.80902 + 3.13331i) q^{53} +(2.23607 + 3.87298i) q^{55} +(0.618034 - 1.07047i) q^{57} +6.09017 q^{59} +(1.92705 - 3.33775i) q^{61} +(-0.336881 - 0.583495i) q^{63} -11.7082 q^{65} +(1.42705 + 2.47172i) q^{67} +(1.26393 - 2.18919i) q^{69} +(6.89919 - 11.9497i) q^{71} +(2.42705 - 4.20378i) q^{73} +2.09017 q^{75} +(0.163119 - 0.282530i) q^{77} +(-1.80902 + 3.13331i) q^{79} +(-3.85410 - 6.67550i) q^{81} +(-6.51722 - 11.2882i) q^{83} +16.4721 q^{85} +1.14590 q^{87} +(-2.42705 - 4.20378i) q^{89} +(0.427051 + 0.739674i) q^{91} +(-5.23607 + 9.06914i) q^{95} -4.76393 q^{97} +(1.97214 - 3.41584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} + 2 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 + 2 * q^5 - 4 * q^7 - q^9	$ 4 q - 3 q^{3} + 2 q^{5} - 4 q^{7} - q^{9} + 10 q^{11} - 5 q^{13} - 2 q^{15} - q^{17} + 2 q^{19} + 22 q^{21} + 11 q^{23} - 2 q^{25} - 6 q^{29} - 10 q^{33} + 12 q^{35} + 3 q^{37} + 10 q^{39} + 20 q^{41} + 26 q^{43} + 28 q^{45} - 18 q^{47} - 4 q^{49} + 28 q^{51} + 5 q^{53} - 2 q^{57} + 2 q^{59} + q^{61} - 17 q^{63} - 20 q^{65} - q^{67} + 14 q^{69} + 3 q^{71} + 3 q^{73} - 14 q^{75} - 15 q^{77} - 5 q^{79} - 2 q^{81} + 3 q^{83} + 48 q^{85} + 18 q^{87} - 3 q^{89} - 5 q^{91} - 12 q^{95} - 28 q^{97} - 10 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 + 2 * q^5 - 4 * q^7 - q^9 + 10 * q^11 - 5 * q^13 - 2 * q^15 - q^17 + 2 * q^19 + 22 * q^21 + 11 * q^23 - 2 * q^25 - 6 * q^29 - 10 * q^33 + 12 * q^35 + 3 * q^37 + 10 * q^39 + 20 * q^41 + 26 * q^43 + 28 * q^45 - 18 * q^47 - 4 * q^49 + 28 * q^51 + 5 * q^53 - 2 * q^57 + 2 * q^59 + q^61 - 17 * q^63 - 20 * q^65 - q^67 + 14 * q^69 + 3 * q^71 + 3 * q^73 - 14 * q^75 - 15 * q^77 - 5 * q^79 - 2 * q^81 + 3 * q^83 + 48 * q^85 + 18 * q^87 - 3 * q^89 - 5 * q^91 - 12 * q^95 - 28 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/688\mathbb{Z}\right)^\times$.

$n$	$431$	$433$	$517$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	0.805613	−	0.592443i	$-0.201836\pi$
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	−0.915877	+	0.401460i	$0.868503\pi$
$4$		0			0
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	0.959545	+	0.281556i	$0.0908504\pi$
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	−0.235938	+	0.971768i	$0.575816\pi$
$6$		0			0
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	−0.842857	−	0.538138i	$-0.819128\pi$
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	0.887469	+	0.460866i	$0.152461\pi$
$8$		0			0
$9$	1.42705	−	2.47172i	0.475684	−	0.823908i
$10$		0			0
$11$	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			0
$15$	0.618034	−	1.07047i	0.159576	−	0.276393i
$16$		0			0
$17$	2.54508	−	4.40822i	0.617274	−	1.06915i	−0.372707	−	0.927949i	$-0.621570\pi$
$17$	2.54508	−	4.40822i	0.617274	−	1.06915i	0.989981	−	0.141201i	$-0.0450962\pi$
$18$		0			0
$19$	1.61803	+	2.80252i	0.371202	+	0.642942i	0.989751	−	0.142805i	$-0.0456123\pi$
$19$	1.61803	+	2.80252i	0.371202	+	0.642942i	−0.618548	+	0.785747i	$0.712279\pi$
$20$		0			0
$21$	−0.0901699			−0.0196767
$22$		0			0
$23$	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
$26$		0			0
$27$	−2.23607			−0.430331
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$		0			0
$33$	−0.263932	−	0.457144i	−0.0459447	−	0.0795785i
$34$		0			0
$35$	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	$0.882036\pi$
$38$		0			0
$39$	1.38197			0.221292
$40$		0			0
$41$	0.527864			0.0824385			0.0412193	−	0.999150i	$-0.486876\pi$
$41$	0.527864			0.0824385			0.0412193	+	0.999150i	$0.486876\pi$
$42$		0			0
$43$	6.50000	+	0.866025i	0.991241	+	0.132068i
$43$	6.50000	+	0.866025i	0.991241	+	0.132068i
$44$		0			0
$45$	9.23607			1.37683
$46$		0			0
$47$	−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
$50$		0			0
$51$	−1.94427			−0.272253
$52$		0			0
$53$	1.80902	+	3.13331i	0.248488	+	0.430393i	0.963106	−	0.269121i	$-0.0867331\pi$
$53$	1.80902	+	3.13331i	0.248488	+	0.430393i	−0.714619	+	0.699514i	$0.753400\pi$
$54$		0			0
$55$	2.23607	+	3.87298i	0.301511	+	0.522233i
$56$		0			0
$57$	0.618034	−	1.07047i	0.0818606	−	0.141787i
$58$		0			0
$59$	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
$63$	−0.336881	−	0.583495i	−0.0424430	−	0.0735135i
$64$		0			0
$65$	−11.7082			−1.45222
$66$		0			0
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	0.939933	−	0.341358i	$-0.110887\pi$
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	−0.765591	+	0.643327i	$0.777553\pi$
$68$		0			0
$69$	1.26393	−	2.18919i	0.152160	−	0.263548i
$70$		0			0
$71$	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	$0.0749836\pi$
$74$		0			0
$75$	2.09017			0.241352
$76$		0			0
$77$	0.163119	−	0.282530i	0.0185891	−	0.0321973i
$78$		0			0
$79$	−1.80902	+	3.13331i	−0.203530	+	0.352525i	−0.949663	−	0.313272i	$-0.898575\pi$
$79$	−1.80902	+	3.13331i	−0.203530	+	0.352525i	0.746133	+	0.665797i	$0.231908\pi$
$80$		0			0
$81$	−3.85410	−	6.67550i	−0.428234	−	0.741722i
$82$		0			0
$83$	−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
$86$		0			0
$87$	1.14590			0.122853
$88$		0			0
$89$	−2.42705	−	4.20378i	−0.257267	−	0.445599i	0.708242	−	0.705970i	$-0.249489\pi$
$89$	−2.42705	−	4.20378i	−0.257267	−	0.445599i	−0.965509	+	0.260371i	$0.916155\pi$
$90$		0			0
$91$	0.427051	+	0.739674i	0.0447671	+	0.0775389i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−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	$0.577755\pi$
$98$		0			0
$99$	1.97214	−	3.41584i	0.198207	−	0.343305i
$100$		0			0
$101$	−4.11803	+	7.13264i	−0.409760	+	0.709725i	−0.994863	−	0.101234i	$-0.967721\pi$
$101$	−4.11803	+	7.13264i	−0.409760	+	0.709725i	0.585103	+	0.810959i	$0.301054\pi$
$102$		0			0
$103$	5.20820	−	9.02087i	0.513180	−	0.888853i	−0.486704	−	0.873567i	$-0.661801\pi$
$103$	5.20820	−	9.02087i	0.513180	−	0.888853i	0.999883	−	0.0152859i	$-0.00486585\pi$
$104$		0			0
$105$	−0.145898	−	0.252703i	−0.0142382	−	0.0246613i
$106$		0			0
$107$	−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	$0.722152\pi$
$110$		0			0
$111$	−0.354102	+	0.613323i	−0.0336099	+	0.0582140i
$112$		0			0
$113$	−13.3820			−1.25887			−0.629435	−	0.777053i	$-0.716714\pi$
$113$	−13.3820			−1.25887			−0.629435	+	0.777053i	$0.716714\pi$
$114$		0			0
$115$	−10.7082	+	18.5472i	−0.998545	+	1.72953i
$116$		0			0
$117$	5.16312	+	8.94278i	0.477331	+	0.826761i
$118$		0			0
$119$	−0.600813	−	1.04064i	−0.0550764	−	0.0953952i
$120$		0			0
$121$	−9.09017			−0.826379
$122$		0			0
$123$	−0.100813	−	0.174613i	−0.00909001	−	0.0157444i
$124$		0			0
$125$	−1.52786			−0.136656
$126$		0			0
$127$	−16.6525			−1.47767			−0.738834	−	0.673887i	$-0.764623\pi$
$127$	−16.6525			−1.47767			−0.738834	+	0.673887i	$0.764623\pi$
$128$		0			0
$129$	−0.954915	−	2.31555i	−0.0840756	−	0.203872i
$130$		0			0
$131$	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
$134$		0			0
$135$	−3.61803	−	6.26662i	−0.311391	−	0.539345i
$136$		0			0
$137$	−9.70820			−0.829428			−0.414714	−	0.909952i	$-0.636118\pi$
$137$	−9.70820			−0.829428			−0.414714	+	0.909952i	$0.636118\pi$
$138$		0			0
$139$	−9.35410	−	16.2018i	−0.793405	−	1.37422i	−0.923847	−	0.382761i	$-0.874973\pi$
$139$	−9.35410	−	16.2018i	−0.793405	−	1.37422i	0.130443	−	0.991456i	$-0.458360\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$		0			0
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$		0			0
$145$	−9.70820			−0.806222
$146$		0			0
$147$	1.32624	−	2.29711i	0.109386	−	0.189463i
$148$		0			0
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$		0			0
$151$	2.14590			0.174631			0.0873154	−	0.996181i	$-0.472171\pi$
$151$	2.14590			0.174631			0.0873154	+	0.996181i	$0.472171\pi$
$152$		0			0
$153$	−7.26393	−	12.5815i	−0.587254	−	1.01715i
$154$		0			0
$155$		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	$0.00982682\pi$
$158$		0			0
$159$	0.690983	−	1.19682i	0.0547985	−	0.0949138i
$160$		0			0
$161$	1.56231			0.123127
$162$		0			0
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	−0.450110	−	0.892973i	$-0.648615\pi$
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	0.998392	−	0.0566798i	$-0.0180514\pi$
$164$		0			0
$165$	0.854102	−	1.47935i	0.0664917	−	0.115167i
$166$		0			0
$167$	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
$170$		0			0
$171$	9.23607			0.706300
$172$		0			0
$173$	−8.23607			−0.626177			−0.313088	−	0.949724i	$-0.601364\pi$
$173$	−8.23607			−0.626177			−0.313088	+	0.949724i	$0.601364\pi$
$174$		0			0
$175$	0.645898	+	1.11873i	0.0488253	+	0.0845679i
$176$		0			0
$177$	−1.16312	−	2.01458i	−0.0874254	−	0.151425i
$178$		0			0
$179$	−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	$-0.130326\pi$
$182$		0			0
$183$	−1.47214			−0.108823
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	3.51722	−	6.09201i	0.257205	−	0.445492i
$188$		0			0
$189$	−0.263932	+	0.457144i	−0.0191982	+	0.0332523i
$190$		0			0
$191$	−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	$0.625935\pi$
$194$		0			0
$195$	2.23607	+	3.87298i	0.160128	+	0.277350i
$196$		0			0
$197$	−7.47214	+	12.9421i	−0.532368	+	0.922088i	0.466918	+	0.884301i	$0.345364\pi$
$197$	−7.47214	+	12.9421i	−0.532368	+	0.922088i	−0.999286	+	0.0377873i	$0.987969\pi$
$198$		0			0
$199$	15.9443			1.13026			0.565130	−	0.825002i	$-0.308826\pi$
$199$	15.9443			1.13026			0.565130	+	0.825002i	$0.308826\pi$
$200$		0			0
$201$	0.545085	−	0.944115i	0.0384473	−	0.0665927i
$202$		0			0
$203$	0.354102	+	0.613323i	0.0248531	+	0.0430468i
$204$		0			0
$205$	0.854102	+	1.47935i	0.0596531	+	0.103322i
$206$		0			0
$207$	18.8885			1.31284
$208$		0			0
$209$	2.23607	+	3.87298i	0.154672	+	0.267900i
$210$		0			0
$211$	4.76393			0.327963			0.163981	−	0.986463i	$-0.447566\pi$
$211$	4.76393			0.327963			0.163981	+	0.986463i	$0.447566\pi$
$212$		0			0
$213$	−5.27051			−0.361129
$214$		0			0
$215$	8.09017	+	19.6176i	0.551745	+	1.33791i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.85410			−0.125289
$220$		0			0
$221$	9.20820	+	15.9491i	0.619411	+	1.07285i
$222$		0			0
$223$	−7.23607			−0.484563			−0.242281	−	0.970206i	$-0.577896\pi$
$223$	−7.23607			−0.484563			−0.242281	+	0.970206i	$0.577896\pi$
$224$		0			0
$225$	7.80902	+	13.5256i	0.520601	+	0.901708i
$226$		0			0
$227$	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	$-0.00703396\pi$
$230$		0			0
$231$	−0.124612			−0.00819885
$232$		0			0
$233$	5.51722	−	9.55611i	0.361445	−	0.626041i	−0.626754	−	0.779217i	$-0.715617\pi$
$233$	5.51722	−	9.55611i	0.361445	−	0.626041i	0.988199	+	0.153176i	$0.0489501\pi$
$234$		0			0
$235$	−12.7082	−	22.0113i	−0.828992	−	1.43586i
$236$		0			0
$237$	1.38197			0.0897683
$238$		0			0
$239$	−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	$-0.225094\pi$
$242$		0			0
$243$	−4.82624	+	8.35929i	−0.309603	+	0.536249i
$244$		0			0
$245$	−11.2361	+	19.4614i	−0.717846	+	1.24335i
$246$		0			0
$247$	−11.7082			−0.744975
$248$		0			0
$249$	−2.48936	+	4.31169i	−0.157757	+	0.273242i
$250$		0			0
$251$	−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
$254$		0			0
$255$	−3.14590	−	5.44886i	−0.197004	−	0.341221i
$256$		0			0
$257$	23.5623			1.46978			0.734888	−	0.678188i	$-0.237235\pi$
$257$	23.5623			1.46978			0.734888	+	0.678188i	$0.237235\pi$
$258$		0			0
$259$	−0.437694			−0.0271970
$260$		0			0
$261$	4.28115	+	7.41517i	0.264997	+	0.458988i
$262$		0			0
$263$	−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
$266$		0			0
$267$	−0.927051	+	1.60570i	−0.0567346	+	0.0982672i
$268$		0			0
$269$	−8.56231			−0.522053			−0.261027	−	0.965332i	$-0.584061\pi$
$269$	−8.56231			−0.522053			−0.261027	+	0.965332i	$0.584061\pi$
$270$		0			0
$271$	3.57295	−	6.18853i	0.217041	−	0.375926i	−0.736861	−	0.676044i	$-0.763693\pi$
$271$	3.57295	−	6.18853i	0.217041	−	0.375926i	0.953902	+	0.300118i	$0.0970261\pi$
$272$		0			0
$273$	0.163119	−	0.282530i	0.00987241	−	0.0170995i
$274$		0			0
$275$	−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	$0.799534\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.736068	+	1.27491i	0.0439101	+	0.0760546i	0.887145	−	0.461490i	$-0.152685\pi$
$281$	0.736068	+	1.27491i	0.0439101	+	0.0760546i	−0.843235	+	0.537545i	$0.819352\pi$
$282$		0			0
$283$	7.61803	−	13.1948i	0.452845	−	0.784351i	−0.545716	−	0.837970i	$-0.683742\pi$
$283$	7.61803	−	13.1948i	0.452845	−	0.784351i	0.998561	+	0.0536192i	$0.0170757\pi$
$284$		0			0
$285$	4.00000			0.236940
$286$		0			0
$287$	0.0623059	−	0.107917i	0.00367780	−	0.00637014i
$288$		0			0
$289$	−4.45492	−	7.71614i	−0.262054	−	0.453891i
$290$		0			0
$291$	0.909830	+	1.57587i	0.0533352	+	0.0923792i
$292$		0			0
$293$	−0.909830			−0.0531528			−0.0265764	−	0.999647i	$-0.508461\pi$
$293$	−0.909830			−0.0531528			−0.0265764	+	0.999647i	$0.508461\pi$
$294$		0			0
$295$	9.85410	+	17.0678i	0.573728	+	0.993726i
$296$		0			0
$297$	−3.09017			−0.179310
$298$		0			0
$299$	−23.9443			−1.38473
$300$		0			0
$301$	0.944272	−	1.22665i	0.0544269	−	0.0707027i
$302$		0			0
$303$	3.14590			0.180727
$304$		0			0
$305$	12.4721			0.714152
$306$		0			0
$307$	14.1074	+	24.4347i	0.805151	+	1.39456i	0.916189	+	0.400747i	$0.131249\pi$
$307$	14.1074	+	24.4347i	0.805151	+	1.39456i	−0.111038	+	0.993816i	$0.535417\pi$
$308$		0			0
$309$	−3.97871			−0.226341
$310$		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	$0.555287\pi$
$314$		0			0
$315$	1.09017	−	1.88823i	0.0614241	−	0.106390i
$316$		0			0
$317$	−29.3050			−1.64593			−0.822965	−	0.568092i	$-0.807682\pi$
$317$	−29.3050			−1.64593			−0.822965	+	0.568092i	$0.807682\pi$
$318$		0			0
$319$	−2.07295	+	3.59045i	−0.116063	+	0.201027i
$320$		0			0
$321$	3.14590	+	5.44886i	0.175587	+	0.304125i
$322$		0			0
$323$	16.4721			0.916534
$324$		0			0
$325$	−9.89919	−	17.1459i	−0.549108	−	0.951083i
$326$		0			0
$327$	1.36475	−	2.36381i	0.0754706	−	0.130719i
$328$		0			0
$329$	−0.927051	+	1.60570i	−0.0511100	+	0.0885251i
$330$		0			0
$331$	1.73607	−	3.00696i	0.0954229	−	0.165277i	−0.814362	−	0.580357i	$-0.802913\pi$
$331$	1.73607	−	3.00696i	0.0954229	−	0.165277i	0.909785	+	0.415080i	$0.136246\pi$
$332$		0			0
$333$	−5.29180			−0.289989
$334$		0			0
$335$	−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			0
$339$	2.55573	+	4.42665i	0.138808	+	0.240423i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	3.29180			0.177740
$344$		0			0
$345$	8.18034			0.440415
$346$		0			0
$347$	−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	$0.895856\pi$
$350$		0			0
$351$	4.04508	−	7.00629i	0.215911	−	0.373968i
$352$		0			0
$353$	6.38197	−	11.0539i	0.339678	−	0.588339i	−0.644694	−	0.764441i	$-0.723015\pi$
$353$	6.38197	−	11.0539i	0.339678	−	0.588339i	0.984372	+	0.176101i	$0.0563486\pi$
$354$		0			0
$355$	44.6525			2.36991
$356$		0			0
$357$	−0.229490	+	0.397489i	−0.0121459	+	0.0210373i
$358$		0			0
$359$	−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
$362$		0			0
$363$	1.73607	+	3.00696i	0.0911199	+	0.157824i
$364$		0			0
$365$	15.7082			0.822205
$366$		0			0
$367$	−1.59017	−	2.75426i	−0.0830062	−	0.143771i	0.821534	−	0.570160i	$-0.193119\pi$
$367$	−1.59017	−	2.75426i	−0.0830062	−	0.143771i	−0.904540	+	0.426389i	$0.859785\pi$
$368$		0			0
$369$	0.753289	−	1.30473i	0.0392147	−	0.0679218i
$370$		0			0
$371$	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	$0.216312\pi$
$374$		0			0
$375$	0.291796	+	0.505406i	0.0150683	+	0.0260990i
$376$		0			0
$377$	−5.42705	−	9.39993i	−0.279507	−	0.484121i
$378$		0			0
$379$	−17.3607			−0.891758			−0.445879	−	0.895093i	$-0.647109\pi$
$379$	−17.3607			−0.891758			−0.445879	+	0.895093i	$0.647109\pi$
$380$		0			0
$381$	3.18034	+	5.50851i	0.162934	+	0.282210i
$382$		0			0
$383$	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
$386$		0			0
$387$	11.4164	−	14.8303i	0.580329	−	0.753869i
$388$		0			0
$389$	23.0689			1.16964			0.584819	−	0.811164i	$-0.301165\pi$
$389$	23.0689			1.16964			0.584819	+	0.811164i	$0.301165\pi$
$390$		0			0
$391$	33.6869			1.70362
$392$		0			0
$393$	−1.51722	−	2.62790i	−0.0765337	−	0.132560i
$394$		0			0
$395$	−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	$0.878081\pi$
$398$		0			0
$399$	−0.145898	−	0.252703i	−0.00730404	−	0.0126510i
$400$		0			0
$401$	−0.708204	+	1.22665i	−0.0353660	+	0.0612557i	−0.883167	−	0.469059i	$-0.844593\pi$
$401$	−0.708204	+	1.22665i	−0.0353660	+	0.0612557i	0.847801	+	0.530315i	$0.177926\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	12.4721	−	21.6024i	0.619745	−	1.07343i
$406$		0			0
$407$	−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	$0.334546\pi$
$410$		0			0
$411$	1.85410	+	3.21140i	0.0914561	+	0.158407i
$412$		0			0
$413$	0.718847	−	1.24508i	0.0353722	−	0.0612664i
$414$		0			0
$415$	21.0902	−	36.5292i	1.03528	−	1.79315i
$416$		0			0
$417$	−3.57295	+	6.18853i	−0.174968	+	0.303054i
$418$		0			0
$419$	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	$0.971133\pi$
$422$		0			0
$423$	−11.2082	+	19.4132i	−0.544962	+	0.943901i
$424$		0			0
$425$	13.9271	+	24.1224i	0.675561	+	1.17011i
$426$		0			0
$427$	−0.454915	−	0.787936i	−0.0220149	−	0.0381309i
$428$		0			0
$429$	1.90983			0.0922075
$430$		0			0
$431$	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
$435$	1.85410	+	3.21140i	0.0888974	+	0.153975i
$436$		0			0
$437$	−10.7082	+	18.5472i	−0.512243	+	0.887231i
$438$		0			0
$439$	3.92705	−	6.80185i	0.187428	−	0.324635i	−0.756964	−	0.653457i	$-0.773318\pi$
$439$	3.92705	−	6.80185i	0.187428	−	0.324635i	0.944392	+	0.328822i	$0.106652\pi$
$440$		0			0
$441$	19.8197			0.943793
$442$		0			0
$443$	−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
$446$		0			0
$447$	−1.71885	+	2.97713i	−0.0812987	+	0.140813i
$448$		0			0
$449$	−10.4164	−	18.0417i	−0.491581	−	0.851443i	0.508372	−	0.861137i	$-0.330247\pi$
$449$	−10.4164	−	18.0417i	−0.491581	−	0.851443i	−0.999953	+	0.00969466i	$0.996914\pi$
$450$		0			0
$451$	0.729490			0.0343504
$452$		0			0
$453$	−0.409830	−	0.709846i	−0.0192555	−	0.0333515i
$454$		0			0
$455$	−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	$0.517070\pi$
$458$		0			0
$459$	−5.69098	+	9.85707i	−0.265632	+	0.460089i
$460$		0			0
$461$	−8.79837	−	15.2392i	−0.409781	−	0.709762i	0.585084	−	0.810973i	$-0.301062\pi$
$461$	−8.79837	−	15.2392i	−0.409781	−	0.709762i	−0.994865	+	0.101211i	$0.967728\pi$
$462$		0			0
$463$	11.9164	+	20.6398i	0.553802	+	0.959214i	0.997996	+	0.0632829i	$0.0201571\pi$
$463$	11.9164	+	20.6398i	0.553802	+	0.959214i	−0.444193	+	0.895931i	$0.646510\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−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
$470$		0			0
$471$	−4.52786			−0.208633
$472$		0			0
$473$	8.98278	+	1.19682i	0.413029	+	0.0550297i
$474$		0			0
$475$	−17.7082			−0.812508
$476$		0			0
$477$	10.3262			0.472806
$478$		0			0
$479$	−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
$482$		0			0
$483$	−0.298374	−	0.516799i	−0.0135765	−	0.0235152i
$484$		0			0
$485$	−7.70820	−	13.3510i	−0.350012	−	0.606238i
$486$		0			0
$487$	−7.16312	+	12.4069i	−0.324592	+	0.562210i	−0.981430	−	0.191822i	$-0.938560\pi$
$487$	−7.16312	+	12.4069i	−0.324592	+	0.562210i	0.656838	+	0.754032i	$0.271894\pi$
$488$		0			0
$489$	−5.34752			−0.241823
$490$		0			0
$491$	−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
$494$		0			0
$495$	12.7639			0.573696
$496$		0			0
$497$	−1.62868	−	2.82095i	−0.0730562	−	0.126537i
$498$		0			0
$499$	3.57295	−	6.18853i	0.159947	−	0.277037i	−0.774902	−	0.632081i	$-0.782201\pi$
$499$	3.57295	−	6.18853i	0.159947	−	0.277037i	0.934849	+	0.355044i	$0.115534\pi$
$500$		0			0
$501$	1.86475	−	3.22983i	0.0833107	−	0.144298i
$502$		0			0
$503$	−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
$506$		0			0
$507$	−0.0172209	+	0.0298275i	−0.000764808	+	0.00132469i
$508$		0			0
$509$	−2.64590	+	4.58283i	−0.117277	+	0.203130i	−0.918688	−	0.394984i	$-0.870750\pi$
$509$	−2.64590	+	4.58283i	−0.117277	+	0.203130i	0.801410	+	0.598115i	$0.204083\pi$
$510$		0			0
$511$	−0.572949	−	0.992377i	−0.0253458	−	0.0439002i
$512$		0			0
$513$	−3.61803	−	6.26662i	−0.159740	−	0.276678i
$514$		0			0
$515$	33.7082			1.48536
$516$		0			0
$517$	−10.8541			−0.477363
$518$		0			0
$519$	1.57295	+	2.72443i	0.0690448	+	0.119589i
$520$		0			0
$521$	−3.51722	−	6.09201i	−0.154092	−	0.266896i	0.778636	−	0.627476i	$-0.215912\pi$
$521$	−3.51722	−	6.09201i	−0.154092	−	0.266896i	−0.932728	+	0.360580i	$0.882579\pi$
$522$		0			0
$523$	−8.91641	+	15.4437i	−0.389887	+	0.675305i	−0.992434	−	0.122779i	$-0.960819\pi$
$523$	−8.91641	+	15.4437i	−0.389887	+	0.675305i	0.602547	+	0.798084i	$0.294153\pi$
$524$		0			0
$525$	0.246711	−	0.427316i	0.0107674	−	0.0186496i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−10.3992	+	18.0119i	−0.452139	+	0.783127i
$530$		0			0
$531$	8.69098	−	15.0532i	0.377157	−	0.653254i
$532$		0			0
$533$	−0.954915	+	1.65396i	−0.0413620	+	0.0716410i
$534$		0			0
$535$	−26.6525	−	46.1634i	−1.15229	−	1.99582i
$536$		0			0
$537$	8.27051			0.356899
$538$		0			0
$539$	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	$0.0247812\pi$
$542$		0			0
$543$	−8.25735			−0.354357
$544$		0			0
$545$	−11.5623	+	20.0265i	−0.495275	+	0.857841i
$546$		0			0
$547$	10.5000	+	18.1865i	0.448948	+	0.777600i	0.998318	−	0.0579790i	$-0.0184657\pi$
$547$	10.5000	+	18.1865i	0.448948	+	0.777600i	−0.549370	+	0.835579i	$0.685132\pi$
$548$		0			0
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$	−9.70820			−0.413583
$552$		0			0
$553$	0.427051	+	0.739674i	0.0181601	+	0.0314541i
$554$		0			0
$555$	−2.29180			−0.0972813
$556$		0			0
$557$	−18.4377			−0.781230			−0.390615	−	0.920554i	$-0.627738\pi$
$557$	−18.4377			−0.781230			−0.390615	+	0.920554i	$0.627738\pi$
$558$		0			0
$559$	−14.4721	+	18.7999i	−0.612106	+	0.795149i
$560$		0			0
$561$	−2.68692			−0.113442
$562$		0			0
$563$	−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
$566$		0			0
$567$	−1.81966			−0.0764185
$568$		0			0
$569$	4.02786	+	6.97647i	0.168857	+	0.292469i	0.938018	−	0.346586i	$-0.112659\pi$
$569$	4.02786	+	6.97647i	0.168857	+	0.292469i	−0.769161	+	0.639055i	$0.779326\pi$
$570$		0			0
$571$	−10.4098	−	18.0304i	−0.435638	−	0.754547i	0.561710	−	0.827334i	$-0.310144\pi$
$571$	−10.4098	−	18.0304i	−0.435638	−	0.754547i	−0.997347	+	0.0727876i	$0.976810\pi$
$572$		0			0
$573$	−4.48278	+	7.76440i	−0.187271	+	0.324363i
$574$		0			0
$575$	−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	$0.327200\pi$
$578$		0			0
$579$	2.04508	+	3.54219i	0.0849908	+	0.147208i
$580$		0			0
$581$	−3.07701			−0.127656
$582$		0			0
$583$	2.50000	+	4.33013i	0.103539	+	0.179336i
$584$		0			0
$585$	−16.7082	+	28.9395i	−0.690799	+	1.19650i
$586$		0			0
$587$	−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
$590$		0			0
$591$	5.70820			0.234804
$592$		0			0
$593$	10.7639	−	18.6437i	0.442022	−	0.765604i	−0.555818	−	0.831304i	$-0.687595\pi$
$593$	10.7639	−	18.6437i	0.442022	−	0.765604i	0.997839	+	0.0657001i	$0.0209281\pi$
$594$		0			0
$595$	1.94427	−	3.36758i	0.0797074	−	0.138057i
$596$		0			0
$597$	−3.04508	−	5.27424i	−0.124627	−	0.215860i
$598$		0			0
$599$	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	$0.483219\pi$
$602$		0			0
$603$	8.14590			0.331727
$604$		0			0
$605$	−14.7082	−	25.4754i	−0.597974	−	1.03572i
$606$		0			0
$607$	−8.57295	−	14.8488i	−0.347965	−	0.602694i	0.637923	−	0.770100i	$-0.279794\pi$
$607$	−8.57295	−	14.8488i	−0.347965	−	0.602694i	−0.985888	+	0.167407i	$0.946461\pi$
$608$		0			0
$609$	0.135255	−	0.234268i	0.00548081	−	0.00949303i
$610$		0			0
$611$	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	$0.294461\pi$
$614$		0			0
$615$	0.326238	−	0.565061i	0.0131552	−	0.0227854i
$616$		0			0
$617$	1.85410	−	3.21140i	0.0746433	−	0.129286i	−0.826288	−	0.563248i	$-0.809552\pi$
$617$	1.85410	−	3.21140i	0.0746433	−	0.129286i	0.900931	+	0.433962i	$0.142885\pi$
$618$		0			0
$619$	1.63525	−	2.83234i	0.0657264	−	0.113842i	−0.831290	−	0.555840i	$-0.812397\pi$
$619$	1.63525	−	2.83234i	0.0657264	−	0.113842i	0.897016	+	0.441998i	$0.145730\pi$
$620$		0			0
$621$	−7.39919	−	12.8158i	−0.296919	−	0.514279i
$622$		0			0
$623$	−1.14590			−0.0459094
$624$		0			0
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$		0			0
$627$	0.854102	−	1.47935i	0.0341095	−	0.0590795i
$628$		0			0
$629$	−9.43769			−0.376306
$630$		0			0
$631$	−7.95492	+	13.7783i	−0.316680	+	0.548506i	−0.979793	−	0.200013i	$-0.935902\pi$
$631$	−7.95492	+	13.7783i	−0.316680	+	0.548506i	0.663113	+	0.748519i	$0.269235\pi$
$632$		0			0
$633$	−0.909830	−	1.57587i	−0.0361625	−	0.0626353i
$634$		0			0
$635$	−26.9443	−	46.6688i	−1.06925	−	1.85200i
$636$		0			0
$637$	−25.1246			−0.995473
$638$		0			0
$639$	−19.6910	−	34.1058i	−0.778963	−	1.34920i
$640$		0			0
$641$	33.1803			1.31054			0.655272	−	0.755393i	$-0.272554\pi$
$641$	33.1803			1.31054			0.655272	+	0.755393i	$0.272554\pi$
$642$		0			0
$643$	−29.5623			−1.16582			−0.582912	−	0.812535i	$-0.698087\pi$
$643$	−29.5623			−1.16582			−0.582912	+	0.812535i	$0.698087\pi$
$644$		0			0
$645$	4.94427	−	6.42280i	0.194681	−	0.252897i
$646$		0			0
$647$	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
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.88854			0.113037			0.0565187	−	0.998402i	$-0.482000\pi$
$653$	2.88854			0.113037			0.0565187	+	0.998402i	$0.482000\pi$
$654$		0			0
$655$	12.8541	+	22.2640i	0.502251	+	0.869925i
$656$		0			0
$657$	−6.92705	−	11.9980i	−0.270250	−	0.468087i
$658$		0			0
$659$	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	$0.298687\pi$
$662$		0			0
$663$	3.51722	−	6.09201i	0.136598	−	0.236594i
$664$		0			0
$665$	1.23607	+	2.14093i	0.0479327	+	0.0830218i
$666$		0			0
$667$	−19.8541			−0.768754
$668$		0			0
$669$	1.38197	+	2.39364i	0.0534299	+	0.0925433i
$670$		0			0
$671$	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	$-0.111943\pi$
$674$		0			0
$675$	6.11803	−	10.5967i	0.235483	−	0.407869i
$676$		0			0
$677$	−36.2361			−1.39267			−0.696333	−	0.717719i	$-0.745186\pi$
$677$	−36.2361			−1.39267			−0.696333	+	0.717719i	$0.745186\pi$
$678$		0			0
$679$	−0.562306	+	0.973942i	−0.0215793	+	0.0373765i
$680$		0			0
$681$	1.42705	−	2.47172i	0.0546847	−	0.0947167i
$682$		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
$686$		0			0
$687$	−6.00000			−0.228914
$688$		0			0
$689$	−13.0902			−0.498696
$690$		0			0
$691$	24.6353	+	42.6695i	0.937169	+	1.62322i	0.770719	+	0.637175i	$0.219897\pi$
$691$	24.6353	+	42.6695i	0.937169	+	1.62322i	0.166450	+	0.986050i	$0.446770\pi$
$692$		0			0
$693$	−0.465558	−	0.806370i	−0.0176851	−	0.0306315i
$694$		0			0
$695$	30.2705	−	52.4301i	1.14823	−	1.98879i
$696$		0			0
$697$	1.34346	−	2.32694i	0.0508871	−	0.0881391i
$698$		0			0
$699$	−4.21478			−0.159418
$700$		0			0
$701$	−11.7533	+	20.3573i	−0.443916	+	0.768884i	−0.997976	−	0.0635921i	$-0.979744\pi$
$701$	−11.7533	+	20.3573i	−0.443916	+	0.768884i	0.554060	+	0.832476i	$0.313078\pi$
$702$		0			0
$703$	3.00000	−	5.19615i	0.113147	−	0.195977i
$704$		0			0
$705$	−4.85410	+	8.40755i	−0.182816	+	0.316647i
$706$		0			0
$707$	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	$0.541290\pi$
$710$		0			0
$711$	5.16312	+	8.94278i	0.193632	+	0.335381i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−16.1803			−0.605110
$716$		0			0
$717$	−4.14590	+	7.18091i	−0.154831	+	0.268176i
$718$		0			0
$719$	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
$722$		0			0
$723$	−11.1803			−0.415801
$724$		0			0
$725$	−8.20820	−	14.2170i	−0.304845	−	0.528007i
$726$		0			0
$727$	−28.9787			−1.07476			−0.537381	−	0.843340i	$-0.680586\pi$
$727$	−28.9787			−1.07476			−0.537381	+	0.843340i	$0.680586\pi$
$728$		0			0
$729$	−19.4377			−0.719915
$730$		0			0
$731$	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	$0.787668\pi$
$734$		0			0
$735$	8.58359			0.316611
$736$		0			0
$737$	1.97214	+	3.41584i	0.0726446	+	0.125824i
$738$		0			0
$739$	17.5410			0.645257			0.322628	−	0.946526i	$-0.395434\pi$
$739$	17.5410			0.645257			0.322628	+	0.946526i	$0.395434\pi$
$740$		0			0
$741$	2.23607	+	3.87298i	0.0821440	+	0.142278i
$742$		0			0
$743$	−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
$746$		0			0
$747$	−37.2016			−1.36114
$748$		0			0
$749$	−1.94427	+	3.36758i	−0.0710421	+	0.123049i
$750$		0			0
$751$	4.48936	+	7.77579i	0.163819	+	0.283743i	0.936235	−	0.351374i	$-0.114285\pi$
$751$	4.48936	+	7.77579i	0.163819	+	0.283743i	−0.772416	+	0.635117i	$0.780952\pi$
$752$		0			0
$753$	2.60488			0.0949270
$754$		0			0
$755$	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	$0.260448\pi$
$758$		0			0
$759$	1.74671	−	3.02539i	0.0634016	−	0.109815i
$760$		0			0
$761$	5.04508	−	8.73834i	0.182884	−	0.316765i	−0.759977	−	0.649950i	$-0.774790\pi$
$761$	5.04508	−	8.73834i	0.182884	−	0.316765i	0.942862	+	0.333185i	$0.108123\pi$
$762$		0			0
$763$	1.68692			0.0610705
$764$		0			0
$765$	23.5066	−	40.7146i	0.849882	−	1.47204i
$766$		0			0
$767$	−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	$0.740849\pi$
$770$		0			0
$771$	−4.50000	−	7.79423i	−0.162064	−	0.280702i
$772$		0			0
$773$	−33.5967			−1.20839			−0.604196	−	0.796836i	$-0.706505\pi$
$773$	−33.5967			−1.20839			−0.604196	+	0.796836i	$0.706505\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0835921	+	0.144786i	0.00299885	+	0.00519416i
$778$		0			0
$779$	0.854102	+	1.47935i	0.0306014	+	0.0530031i
$780$		0			0
$781$	9.53444	−	16.5141i	0.341169	−	0.590922i
$782$		0			0
$783$	3.35410	−	5.80948i	0.119866	−	0.207614i
$784$		0			0
$785$	38.3607			1.36915
$786$		0			0
$787$	−22.7254	+	39.3616i	−0.810074	+	1.40309i	0.102738	+	0.994708i	$0.467240\pi$
$787$	−22.7254	+	39.3616i	−0.810074	+	1.40309i	−0.912812	+	0.408381i	$0.866094\pi$
$788$		0			0
$789$	−2.00658	+	3.47549i	−0.0714361	+	0.123731i
$790$		0			0
$791$	−1.57953	+	2.73582i	−0.0561615	+	0.0972746i
$792$		0			0
$793$	6.97214	+	12.0761i	0.247588	+	0.428835i
$794$		0			0
$795$	4.47214			0.158610
$796$		0			0
$797$	1.88197	+	3.25966i	0.0666627	+	0.115463i	0.897430	−	0.441156i	$-0.145432\pi$
$797$	1.88197	+	3.25966i	0.0666627	+	0.115463i	−0.830768	+	0.556619i	$0.812098\pi$
$798$		0			0
$799$	−19.9894	+	34.6226i	−0.707173	+	1.22486i
$800$		0			0
$801$	−13.8541			−0.489511
$802$		0			0
$803$	3.35410	−	5.80948i	0.118364	−	0.205012i
$804$		0			0
$805$	2.52786	+	4.37839i	0.0890955	+	0.154318i
$806$		0			0
$807$	1.63525	+	2.83234i	0.0575637	+	0.0997033i
$808$		0			0
$809$	−37.7426			−1.32696			−0.663480	−	0.748194i	$-0.730921\pi$
$809$	−37.7426			−1.32696			−0.663480	+	0.748194i	$0.730921\pi$
$810$		0			0
$811$	−13.1976	−	22.8588i	−0.463429	−	0.802683i	0.535700	−	0.844408i	$-0.320048\pi$
$811$	−13.1976	−	22.8588i	−0.463429	−	0.802683i	−0.999129	+	0.0417257i	$0.986714\pi$
$812$		0			0
$813$	−2.72949			−0.0957274
$814$		0			0
$815$	45.3050			1.58696
$816$		0			0
$817$	8.09017	+	19.6176i	0.283039	+	0.686334i
$818$		0			0
$819$	2.43769			0.0851799
$820$		0			0
$821$	−15.3262			−0.534889			−0.267445	−	0.963573i	$-0.586179\pi$
$821$	−15.3262			−0.534889			−0.267445	+	0.963573i	$0.586179\pi$
$822$		0			0
$823$	−12.0066	−	20.7960i	−0.418523	−	0.724903i	0.577268	−	0.816555i	$-0.304119\pi$
$823$	−12.0066	−	20.7960i	−0.418523	−	0.724903i	−0.995791	+	0.0916516i	$0.970785\pi$
$824$		0			0
$825$	2.88854			0.100566
$826$		0			0
$827$	−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	$0.579871\pi$
$830$		0			0
$831$	0.673762	−	1.16699i	0.0233725	−	0.0404824i
$832$		0			0
$833$	35.3475			1.22472
$834$		0			0
$835$	−15.7984	+	27.3636i	−0.546725	+	0.946956i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	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
$842$		0			0
$843$	0.281153	−	0.486971i	0.00968342	−	0.0167722i
$844$		0			0
$845$	0.145898	−	0.252703i	0.00501904	−	0.00869324i
$846$		0			0
$847$	−1.07295	+	1.85840i	−0.0368670	+	0.0638555i
$848$		0			0
$849$	−5.81966			−0.199730
$850$		0			0
$851$	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	$0.794809\pi$
$854$		0			0
$855$	14.9443	+	25.8842i	0.511083	+	0.885222i
$856$		0			0
$857$	6.90983	+	11.9682i	0.236035	+	0.408825i	0.959573	−	0.281460i	$-0.0908186\pi$
$857$	6.90983	+	11.9682i	0.236035	+	0.408825i	−0.723538	+	0.690285i	$0.757485\pi$
$858$		0			0
$859$	22.5836			0.770542			0.385271	−	0.922803i	$-0.374108\pi$
$859$	22.5836			0.770542			0.385271	+	0.922803i	$0.374108\pi$
$860$		0			0
$861$	−0.0475975			−0.00162212
$862$		0			0
$863$	−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
$866$		0			0
$867$	−1.70163	+	2.94730i	−0.0577903	+	0.100096i
$868$		0			0
$869$	−2.50000	+	4.33013i	−0.0848067	+	0.146889i
$870$		0			0
$871$	−10.3262			−0.349891
$872$		0			0
$873$	−6.79837	+	11.7751i	−0.230090	+	0.398528i
$874$		0			0
$875$	−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	$0.297429\pi$
$878$		0			0
$879$	0.173762	+	0.300965i	0.00586085	+	0.0101513i
$880$		0			0
$881$	38.2361			1.28821			0.644103	−	0.764939i	$-0.277231\pi$
$881$	38.2361			1.28821			0.644103	+	0.764939i	$0.277231\pi$
$882$		0			0
$883$	−13.5623	−	23.4906i	−0.456408	−	0.790522i	0.542360	−	0.840146i	$-0.317531\pi$
$883$	−13.5623	−	23.4906i	−0.456408	−	0.790522i	−0.998768	+	0.0496245i	$0.984198\pi$
$884$		0			0
$885$	3.76393	−	6.51932i	0.126523	−	0.219145i
$886$		0			0
$887$	−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
$890$		0			0
$891$	−5.32624	−	9.22531i	−0.178436	−	0.309060i
$892$		0			0
$893$	−12.7082	−	22.0113i	−0.425264	−	0.736579i
$894$		0			0
$895$	−70.0689			−2.34214
$896$		0			0
$897$	4.57295	+	7.92058i	0.152686	+	0.264460i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	18.4164			0.613540
$902$		0			0
$903$	−0.586105	−	0.0780895i	−0.0195043	−	0.00259865i
$904$		0			0
$905$	69.9574			2.32546
$906$		0			0
$907$	8.29180			0.275325			0.137662	−	0.990479i	$-0.456041\pi$
$907$	8.29180			0.275325			0.137662	+	0.990479i	$0.456041\pi$
$908$		0			0
$909$	11.7533	+	20.3573i	0.389832	+	0.675209i
$910$		0			0
$911$	−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
$914$		0			0
$915$	−2.38197	−	4.12569i	−0.0787454	−	0.136391i
$916$		0			0
$917$	0.937694	−	1.62413i	0.0309654	−	0.0536336i
$918$		0			0
$919$	44.3951			1.46446			0.732230	−	0.681057i	$-0.238480\pi$
$919$	44.3951			1.46446			0.732230	+	0.681057i	$0.238480\pi$
$920$		0			0
$921$	5.38854	−	9.33323i	0.177559	−	0.307540i
$922$		0			0
$923$	24.9615	+	43.2346i	0.821618	+	1.42308i
$924$		0			0
$925$	10.1459			0.333595
$926$		0			0
$927$	−14.8647	−	25.7465i	−0.488222	−	0.845626i
$928$		0			0
$929$	−15.3820	+	26.6423i	−0.504666	+	0.874107i	0.495320	+	0.868711i	$0.335051\pi$
$929$	−15.3820	+	26.6423i	−0.504666	+	0.874107i	−0.999985	+	0.00539616i	$0.998282\pi$
$930$		0			0
$931$	−11.2361	+	19.4614i	−0.368247	+	0.637823i
$932$		0			0
$933$	4.55166	−	7.88371i	0.149015	−	0.258101i
$934$		0			0
$935$	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	$-0.0577455\pi$
$938$		0			0
$939$	5.18034	−	8.97261i	0.169054	−	0.292810i
$940$		0			0
$941$	10.8820	+	18.8481i	0.354742	+	0.614431i	0.987074	−	0.160267i	$-0.0512354\pi$
$941$	10.8820	+	18.8481i	0.354742	+	0.614431i	−0.632332	+	0.774698i	$0.717902\pi$
$942$		0			0
$943$	1.74671	+	3.02539i	0.0568807	+	0.0985203i
$944$		0			0
$945$	−1.70820			−0.0555679
$946$		0			0
$947$	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
$950$		0			0
$951$	5.59675	+	9.69385i	0.181487	+	0.314345i
$952$		0			0
$953$	1.55573	−	2.69460i	0.0503950	−	0.0872867i	−0.839728	−	0.543008i	$-0.817285\pi$
$953$	1.55573	−	2.69460i	0.0503950	−	0.0872867i	0.890122	+	0.455721i	$0.150619\pi$
$954$		0			0
$955$	37.9787	−	65.7811i	1.22896	−	2.12863i
$956$		0			0
$957$	1.58359			0.0511903
$958$		0			0
$959$	−1.14590	+	1.98475i	−0.0370030	+	0.0640910i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	−23.5066	+	40.7146i	−0.757489	+	1.31201i
$964$		0			0
$965$	−17.3262	−	30.0099i	−0.557751	−	0.966054i
$966$		0			0
$967$	49.1033			1.57906			0.789528	−	0.613714i	$-0.210325\pi$
$967$	49.1033			1.57906			0.789528	+	0.613714i	$0.210325\pi$
$968$		0			0
$969$	−3.14590	−	5.44886i	−0.101061	−	0.175042i
$970$		0			0
$971$	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
$974$		0			0
$975$	−3.78115	+	6.54915i	−0.121094	+	0.209741i
$976$		0			0
$977$	−18.3820	−	31.8385i	−0.588091	−	1.01860i	−0.994482	−	0.104905i	$-0.966546\pi$
$977$	−18.3820	−	31.8385i	−0.588091	−	1.01860i	0.406391	−	0.913699i	$-0.366787\pi$
$978$		0			0
$979$	−3.35410	−	5.80948i	−0.107198	−	0.185672i
$980$		0			0
$981$	20.3951			0.651166
$982$		0			0
$983$	−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
$986$		0			0
$987$	0.708204			0.0225424
$988$		0			0
$989$	16.5451	+	40.1197i	0.526103	+	1.27573i
$990$		0			0
$991$	33.1803			1.05401			0.527004	−	0.849863i	$-0.323315\pi$
$991$	33.1803			1.05401			0.527004	+	0.849863i	$0.323315\pi$
$992$		0			0
$993$	−1.32624			−0.0420869
$994$		0			0
$995$	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	$0.304143\pi$
$998$		0			0
$999$	2.07295	+	3.59045i	0.0655852	+	0.113597i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.1	✓	4	172.135	odd	6
43.2.c.b.36.1	yes	4	4.3	odd	2
387.2.h.d.208.2		4	12.11	even	2
387.2.h.d.307.2		4	516.479	even	6
688.2.i.e.49.2		4	43.6	even	3	inner
688.2.i.e.337.2		4	1.1	even	1	trivial
1849.2.a.e.1.1		2	172.79	odd	6
1849.2.a.h.1.2		2	172.7	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:	\( N \)	\(=\)	\( 688 = 2^{4} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	688.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\)	\(q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +1.38197 q^{11} +(-1.80902 + 3.13331i) q^{13} +(0.618034 - 1.07047i) q^{15} +(2.54508 - 4.40822i) q^{17} +(1.61803 + 2.80252i) q^{19} -0.0901699 q^{21} +(3.30902 + 5.73139i) q^{23} +(-2.73607 + 4.73901i) q^{25} -2.23607 q^{27} +(-1.50000 + 2.59808i) q^{29} +(-0.263932 - 0.457144i) q^{33} +0.763932 q^{35} +(-0.927051 - 1.60570i) q^{37} +1.38197 q^{39} +0.527864 q^{41} +(6.50000 + 0.866025i) q^{43} +9.23607 q^{45} -7.85410 q^{47} +(3.47214 + 6.01392i) q^{49} -1.94427 q^{51} +(1.80902 + 3.13331i) q^{53} +(2.23607 + 3.87298i) q^{55} +(0.618034 - 1.07047i) q^{57} +6.09017 q^{59} +(1.92705 - 3.33775i) q^{61} +(-0.336881 - 0.583495i) q^{63} -11.7082 q^{65} +(1.42705 + 2.47172i) q^{67} +(1.26393 - 2.18919i) q^{69} +(6.89919 - 11.9497i) q^{71} +(2.42705 - 4.20378i) q^{73} +2.09017 q^{75} +(0.163119 - 0.282530i) q^{77} +(-1.80902 + 3.13331i) q^{79} +(-3.85410 - 6.67550i) q^{81} +(-6.51722 - 11.2882i) q^{83} +16.4721 q^{85} +1.14590 q^{87} +(-2.42705 - 4.20378i) q^{89} +(0.427051 + 0.739674i) q^{91} +(-5.23607 + 9.06914i) q^{95} -4.76393 q^{97} +(1.97214 - 3.41584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} + 2 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 + 2 * q^5 - 4 * q^7 - q^9	\( 4 q - 3 q^{3} + 2 q^{5} - 4 q^{7} - q^{9} + 10 q^{11} - 5 q^{13} - 2 q^{15} - q^{17} + 2 q^{19} + 22 q^{21} + 11 q^{23} - 2 q^{25} - 6 q^{29} - 10 q^{33} + 12 q^{35} + 3 q^{37} + 10 q^{39} + 20 q^{41} + 26 q^{43} + 28 q^{45} - 18 q^{47} - 4 q^{49} + 28 q^{51} + 5 q^{53} - 2 q^{57} + 2 q^{59} + q^{61} - 17 q^{63} - 20 q^{65} - q^{67} + 14 q^{69} + 3 q^{71} + 3 q^{73} - 14 q^{75} - 15 q^{77} - 5 q^{79} - 2 q^{81} + 3 q^{83} + 48 q^{85} + 18 q^{87} - 3 q^{89} - 5 q^{91} - 12 q^{95} - 28 q^{97} - 10 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 + 2 * q^5 - 4 * q^7 - q^9 + 10 * q^11 - 5 * q^13 - 2 * q^15 - q^17 + 2 * q^19 + 22 * q^21 + 11 * q^23 - 2 * q^25 - 6 * q^29 - 10 * q^33 + 12 * q^35 + 3 * q^37 + 10 * q^39 + 20 * q^41 + 26 * q^43 + 28 * q^45 - 18 * q^47 - 4 * q^49 + 28 * q^51 + 5 * q^53 - 2 * q^57 + 2 * q^59 + q^61 - 17 * q^63 - 20 * q^65 - q^67 + 14 * q^69 + 3 * q^71 + 3 * q^73 - 14 * q^75 - 15 * q^77 - 5 * q^79 - 2 * q^81 + 3 * q^83 + 48 * q^85 + 18 * q^87 - 3 * q^89 - 5 * q^91 - 12 * q^95 - 28 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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