LMFDB - Embedded newform 945.2.bl.i.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(251,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 3]))

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

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

chi := DirichletCharacter("945.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bl (of order $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.7
Character	$\chi$	$=$	945.251
Dual form			945.2.bl.i.881.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.552767 - 0.319140i) q^{2} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.58723 + 0.553395i) q^{7} +2.29308i q^{8} +O(q^{10})$	\(q+(-0.552767 - 0.319140i) q^{2} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.58723 + 0.553395i) q^{7} +2.29308i q^{8} +0.638280i q^{10} +(2.22872 + 1.28675i) q^{11} +(2.91218 - 1.68135i) q^{13} +(-1.25352 - 1.13159i) q^{14} +(-0.860783 + 1.49092i) q^{16} +2.60840 q^{17} +3.95039i q^{19} +(-0.796299 + 1.37923i) q^{20} +(-0.821308 - 1.42255i) q^{22} +(-4.63797 + 2.67773i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.14634 q^{26} +(-1.29695 - 4.00905i) q^{28} +(2.59976 + 1.50097i) q^{29} +(5.64874 - 3.26130i) q^{31} +(4.92336 - 2.84251i) q^{32} +(-1.44184 - 0.832444i) q^{34} +(-0.814360 - 2.51730i) q^{35} +7.47777 q^{37} +(1.26073 - 2.18365i) q^{38} +(1.98587 - 1.14654i) q^{40} +(-2.74102 - 4.74759i) q^{41} +(-4.78957 + 8.29578i) q^{43} -4.09855i q^{44} +3.41829 q^{46} +(5.53943 - 9.59457i) q^{47} +(6.38751 + 2.86352i) q^{49} +(0.552767 - 0.319140i) q^{50} +(-4.63793 - 2.67771i) q^{52} -8.57614i q^{53} -2.57350i q^{55} +(-1.26898 + 5.93274i) q^{56} +(-0.958039 - 1.65937i) q^{58} +(-4.28361 - 7.41944i) q^{59} +(3.81680 + 2.20363i) q^{61} -4.16325 q^{62} -0.185501 q^{64} +(-2.91218 - 1.68135i) q^{65} +(-4.92473 - 8.52989i) q^{67} +(-2.07706 - 3.59758i) q^{68} +(-0.353221 + 1.65138i) q^{70} +6.71360i q^{71} -6.51892i q^{73} +(-4.13346 - 2.38646i) q^{74} +(5.44850 - 3.14569i) q^{76} +(5.05412 + 4.56248i) q^{77} +(-1.07209 + 1.85691i) q^{79} +1.72157 q^{80} +3.49908i q^{82} +(3.62867 - 6.28503i) q^{83} +(-1.30420 - 2.25894i) q^{85} +(5.29503 - 3.05709i) q^{86} +(-2.95063 + 5.11064i) q^{88} +11.8056 q^{89} +(8.46492 - 2.73844i) q^{91} +(7.38642 + 4.26455i) q^{92} +(-6.12403 + 3.53571i) q^{94} +(3.42114 - 1.97520i) q^{95} +(0.235631 + 0.136041i) q^{97} +(-2.61694 - 3.62137i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 18 q^{4} - 12 q^{5}+O(q^{10}) $ 24 * q - 6 * q^2 + 18 * q^4 - 12 * q^5	$ 24 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 9 q^{11} - 3 q^{13} - 9 q^{14} - 18 q^{16} + 18 q^{17} + 18 q^{20} - 9 q^{22} - 9 q^{23} - 12 q^{25} - 18 q^{26} - 9 q^{28} - 9 q^{29} + 42 q^{31} - 18 q^{32} + 39 q^{34} - 9 q^{35} - 12 q^{38} + 6 q^{40} - 33 q^{41} + 18 q^{43} - 30 q^{46} + 6 q^{50} - 129 q^{52} - 6 q^{56} - 15 q^{58} + 12 q^{59} + 15 q^{61} + 12 q^{62} - 60 q^{64} + 3 q^{65} - 15 q^{67} + 9 q^{68} + 18 q^{70} + 18 q^{74} - 54 q^{76} + 57 q^{77} + 21 q^{79} + 36 q^{80} - 30 q^{83} - 9 q^{85} + 102 q^{86} - 9 q^{88} + 102 q^{89} + 42 q^{91} + 3 q^{92} + 156 q^{94} + 18 q^{95} + 45 q^{97} + 3 q^{98}+O(q^{100}) $ 24 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 9 * q^11 - 3 * q^13 - 9 * q^14 - 18 * q^16 + 18 * q^17 + 18 * q^20 - 9 * q^22 - 9 * q^23 - 12 * q^25 - 18 * q^26 - 9 * q^28 - 9 * q^29 + 42 * q^31 - 18 * q^32 + 39 * q^34 - 9 * q^35 - 12 * q^38 + 6 * q^40 - 33 * q^41 + 18 * q^43 - 30 * q^46 + 6 * q^50 - 129 * q^52 - 6 * q^56 - 15 * q^58 + 12 * q^59 + 15 * q^61 + 12 * q^62 - 60 * q^64 + 3 * q^65 - 15 * q^67 + 9 * q^68 + 18 * q^70 + 18 * q^74 - 54 * q^76 + 57 * q^77 + 21 * q^79 + 36 * q^80 - 30 * q^83 - 9 * q^85 + 102 * q^86 - 9 * q^88 + 102 * q^89 + 42 * q^91 + 3 * q^92 + 156 * q^94 + 18 * q^95 + 45 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.552767	−	0.319140i	−0.390865	−	0.225666i	0.291670	−	0.956519i	$-0.405789\pi$
$2$	−0.552767	−	0.319140i	−0.390865	−	0.225666i	−0.682535	+	0.730853i	$0.739123\pi$
$3$		0			0
$3$		0			0
$4$	−0.796299	−	1.37923i	−0.398150	−	0.689615i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.58723	+	0.553395i	0.977881	+	0.209164i
$7$	2.58723	+	0.553395i	0.977881	+	0.209164i
$8$			2.29308i			0.810728i
$9$		0			0
$10$			0.638280i			0.201842i
$11$	2.22872	+	1.28675i	0.671984	+	0.387970i	0.796828	−	0.604206i	$-0.206510\pi$
$11$	2.22872	+	1.28675i	0.671984	+	0.387970i	−0.124844	+	0.992176i	$0.539843\pi$
$12$		0			0
$13$	2.91218	−	1.68135i	0.807692	−	0.466321i	−0.0384614	−	0.999260i	$-0.512246\pi$
$13$	2.91218	−	1.68135i	0.807692	−	0.466321i	0.846154	+	0.532939i	$0.178912\pi$
$14$	−1.25352	−	1.13159i	−0.335018	−	0.302429i
$15$		0			0
$16$	−0.860783	+	1.49092i	−0.215196	+	0.372730i
$17$	2.60840			0.632629			0.316315	−	0.948654i	$-0.397554\pi$
$17$	2.60840			0.632629			0.316315	+	0.948654i	$0.397554\pi$
$18$		0			0
$19$			3.95039i			0.906282i	0.891439	+	0.453141i	$0.149697\pi$
$19$			3.95039i			0.906282i	−0.891439	+	0.453141i	$0.850303\pi$
$20$	−0.796299	+	1.37923i	−0.178058	+	0.308405i
$21$		0			0
$22$	−0.821308	−	1.42255i	−0.175103	−	0.303288i
$23$	−4.63797	+	2.67773i	−0.967084	+	0.558346i	−0.898346	−	0.439289i	$-0.855230\pi$
$23$	−4.63797	+	2.67773i	−0.967084	+	0.558346i	−0.0687376	+	0.997635i	$0.521897\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.14634			−0.420932
$27$		0			0
$28$	−1.29695	−	4.00905i	−0.245100	−	0.757640i
$29$	2.59976	+	1.50097i	0.482762	+	0.278723i	0.721567	−	0.692345i	$-0.243422\pi$
$29$	2.59976	+	1.50097i	0.482762	+	0.278723i	−0.238805	+	0.971068i	$0.576756\pi$
$30$		0			0
$31$	5.64874	−	3.26130i	1.01454	−	0.585747i	0.102025	−	0.994782i	$-0.467468\pi$
$31$	5.64874	−	3.26130i	1.01454	−	0.585747i	0.912519	+	0.409035i	$0.134134\pi$
$32$	4.92336	−	2.84251i	0.870336	−	0.502489i
$33$		0			0
$34$	−1.44184	−	0.832444i	−0.247273	−	0.142763i
$35$	−0.814360	−	2.51730i	−0.137652	−	0.425502i
$36$		0			0
$37$	7.47777			1.22934			0.614669	−	0.788785i	$-0.289290\pi$
$37$	7.47777			1.22934			0.614669	+	0.788785i	$0.289290\pi$
$38$	1.26073	−	2.18365i	0.204517	−	0.354234i
$39$		0			0
$40$	1.98587	−	1.14654i	0.313994	−	0.181284i
$41$	−2.74102	−	4.74759i	−0.428076	−	0.741449i	0.568626	−	0.822596i	$-0.307475\pi$
$41$	−2.74102	−	4.74759i	−0.428076	−	0.741449i	−0.996702	+	0.0811468i	$0.974142\pi$
$42$		0			0
$43$	−4.78957	+	8.29578i	−0.730403	+	1.26509i	0.226308	+	0.974056i	$0.427334\pi$
$43$	−4.78957	+	8.29578i	−0.730403	+	1.26509i	−0.956711	+	0.291039i	$0.905999\pi$
$44$		−	4.09855i		−	0.617880i
$45$		0			0
$46$	3.41829			0.503999
$47$	5.53943	−	9.59457i	0.808009	−	1.39951i	−0.106232	−	0.994341i	$-0.533879\pi$
$47$	5.53943	−	9.59457i	0.808009	−	1.39951i	0.914241	−	0.405171i	$-0.132788\pi$
$48$		0			0
$49$	6.38751	+	2.86352i	0.912501	+	0.409074i
$50$	0.552767	−	0.319140i	0.0781731	−	0.0451332i
$51$		0			0
$52$	−4.63793	−	2.67771i	−0.643165	−	0.371331i
$53$		−	8.57614i		−	1.17802i	−0.808124	−	0.589012i	$-0.799517\pi$
$53$		−	8.57614i		−	1.17802i	0.808124	−	0.589012i	$-0.200483\pi$
$54$		0			0
$55$		−	2.57350i		−	0.347011i
$56$	−1.26898	+	5.93274i	−0.169575	+	0.792795i
$57$		0			0
$58$	−0.958039	−	1.65937i	−0.125797	−	0.217886i
$59$	−4.28361	−	7.41944i	−0.557679	−	0.965928i	−0.997690	−	0.0679359i	$-0.978359\pi$
$59$	−4.28361	−	7.41944i	−0.557679	−	0.965928i	0.440011	−	0.897993i	$-0.354975\pi$
$60$		0			0
$61$	3.81680	+	2.20363i	0.488691	+	0.282146i	0.724031	−	0.689767i	$-0.242287\pi$
$61$	3.81680	+	2.20363i	0.488691	+	0.282146i	−0.235340	+	0.971913i	$0.575620\pi$
$62$	−4.16325			−0.528733
$63$		0			0
$64$	−0.185501			−0.0231876
$65$	−2.91218	−	1.68135i	−0.361211	−	0.208545i
$66$		0			0
$67$	−4.92473	−	8.52989i	−0.601652	−	1.04209i	−0.992571	−	0.121666i	$-0.961176\pi$
$67$	−4.92473	−	8.52989i	−0.601652	−	1.04209i	0.390919	−	0.920425i	$-0.372157\pi$
$68$	−2.07706	−	3.59758i	−0.251881	−	0.436271i
$69$		0			0
$70$	−0.353221	+	1.65138i	−0.0422180	+	0.197377i
$71$			6.71360i			0.796758i	0.917221	+	0.398379i	$0.130427\pi$
$71$			6.71360i			0.796758i	−0.917221	+	0.398379i	$0.869573\pi$
$72$		0			0
$73$		−	6.51892i		−	0.762982i	−0.924373	−	0.381491i	$-0.875411\pi$
$73$		−	6.51892i		−	0.762982i	0.924373	−	0.381491i	$-0.124589\pi$
$74$	−4.13346	−	2.38646i	−0.480505	−	0.277420i
$75$		0			0
$76$	5.44850	−	3.14569i	0.624986	−	0.360836i
$77$	5.05412	+	4.56248i	0.575971	+	0.519943i
$78$		0			0
$79$	−1.07209	+	1.85691i	−0.120619	+	0.208918i	−0.920012	−	0.391890i	$-0.871821\pi$
$79$	−1.07209	+	1.85691i	−0.120619	+	0.208918i	0.799393	+	0.600809i	$0.205155\pi$
$80$	1.72157			0.192477
$81$		0			0
$82$			3.49908i			0.386409i
$83$	3.62867	−	6.28503i	0.398298	−	0.689872i	−0.595218	−	0.803564i	$-0.702934\pi$
$83$	3.62867	−	6.28503i	0.398298	−	0.689872i	0.993516	+	0.113692i	$0.0362677\pi$
$84$		0			0
$85$	−1.30420	−	2.25894i	−0.141460	−	0.245016i
$86$	5.29503	−	3.05709i	0.570978	−	0.329654i
$87$		0			0
$88$	−2.95063	+	5.11064i	−0.314538	+	0.544796i
$89$	11.8056			1.25139			0.625696	−	0.780067i	$-0.284815\pi$
$89$	11.8056			1.25139			0.625696	+	0.780067i	$0.284815\pi$
$90$		0			0
$91$	8.46492	−	2.73844i	0.887364	−	0.287067i
$92$	7.38642	+	4.26455i	0.770088	+	0.444610i
$93$		0			0
$94$	−6.12403	+	3.53571i	−0.631645	+	0.364681i
$95$	3.42114	−	1.97520i	0.351002	−	0.202651i
$96$		0			0
$97$	0.235631	+	0.136041i	0.0239247	+	0.0138129i	0.511915	−	0.859036i	$-0.328936\pi$
$97$	0.235631	+	0.136041i	0.0239247	+	0.0138129i	−0.487990	+	0.872849i	$0.662270\pi$
$98$	−2.61694	−	3.62137i	−0.264351	−	0.365814i
$99$		0			0
$100$	1.59260			0.159260
$101$	−1.41899	+	2.45776i	−0.141195	+	0.244556i	−0.927947	−	0.372713i	$-0.878428\pi$
$101$	−1.41899	+	2.45776i	−0.141195	+	0.244556i	0.786752	+	0.617269i	$0.211761\pi$
$102$		0			0
$103$	−10.5034	+	6.06412i	−1.03493	+	0.597516i	−0.918392	−	0.395671i	$-0.870512\pi$
$103$	−10.5034	+	6.06412i	−1.03493	+	0.597516i	−0.116535	+	0.993187i	$0.537179\pi$
$104$	3.85547	+	6.67787i	0.378060	+	0.654819i
$105$		0			0
$106$	−2.73699	+	4.74061i	−0.265840	+	0.460449i
$107$			10.2861i			0.994392i	0.867638	+	0.497196i	$0.165637\pi$
$107$			10.2861i			0.994392i	−0.867638	+	0.497196i	$0.834363\pi$
$108$		0			0
$109$	17.9601			1.72026			0.860132	−	0.510071i	$-0.170381\pi$
$109$	17.9601			1.72026			0.860132	+	0.510071i	$0.170381\pi$
$110$	−0.821308	+	1.42255i	−0.0783086	+	0.135635i
$111$		0			0
$112$	−3.05211	+	3.38100i	−0.288397	+	0.319474i
$113$	−15.6229	+	9.01990i	−1.46968	+	0.848521i	−0.999422	−	0.0340066i	$-0.989173\pi$
$113$	−15.6229	+	9.01990i	−1.46968	+	0.848521i	−0.470260	+	0.882528i	$0.655840\pi$
$114$		0			0
$115$	4.63797	+	2.67773i	0.432493	+	0.249700i
$116$		−	4.78088i		−	0.443894i
$117$		0			0
$118$			5.46829i			0.503397i
$119$	6.74852	+	1.44348i	0.618636	+	0.132323i
$120$		0			0
$121$	−2.18854	−	3.79067i	−0.198959	−	0.344606i
$122$	−1.40653	−	2.43619i	−0.127342	−	0.220562i
$123$		0			0
$124$	−8.99618	−	5.19394i	−0.807880	−	0.466430i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−15.6765			−1.39107			−0.695534	−	0.718494i	$-0.744832\pi$
$127$	−15.6765			−1.39107			−0.695534	+	0.718494i	$0.744832\pi$
$128$	−9.74419	−	5.62581i	−0.861273	−	0.497256i
$129$		0			0
$130$	1.07317	+	1.85879i	0.0941233	+	0.163026i
$131$	3.07279	+	5.32223i	0.268471	+	0.465005i	0.968467	−	0.249141i	$-0.0801483\pi$
$131$	3.07279	+	5.32223i	0.268471	+	0.465005i	−0.699996	+	0.714147i	$0.746815\pi$
$132$		0			0
$133$	−2.18613	+	10.2206i	−0.189561	+	0.886236i
$134$			6.28672i			0.543090i
$135$		0			0
$136$			5.98128i			0.512890i
$137$	7.67620	+	4.43186i	0.655822	+	0.378639i	0.790683	−	0.612225i	$-0.209726\pi$
$137$	7.67620	+	4.43186i	0.655822	+	0.378639i	−0.134861	+	0.990865i	$0.543059\pi$
$138$		0			0
$139$	8.24478	−	4.76013i	0.699313	−	0.403749i	−0.107778	−	0.994175i	$-0.534374\pi$
$139$	8.24478	−	4.76013i	0.699313	−	0.403749i	0.807092	+	0.590426i	$0.201040\pi$
$140$	−2.82347	+	3.12772i	−0.238627	+	0.264340i
$141$		0			0
$142$	2.14258	−	3.71106i	0.179801	−	0.311425i
$143$	8.65389			0.723675
$144$		0			0
$145$		−	3.00194i		−	0.249297i
$146$	−2.08045	+	3.60344i	−0.172179	+	0.298223i
$147$		0			0
$148$	−5.95454	−	10.3136i	−0.489460	−	0.847770i
$149$	1.86456	−	1.07650i	0.152750	−	0.0881904i	−0.421677	−	0.906746i	$-0.638558\pi$
$149$	1.86456	−	1.07650i	0.152750	−	0.0881904i	0.574427	+	0.818556i	$0.305225\pi$
$150$		0			0
$151$	10.8088	−	18.7214i	0.879608	−	1.52353i	0.0278368	−	0.999612i	$-0.491138\pi$
$151$	10.8088	−	18.7214i	0.879608	−	1.52353i	0.851771	−	0.523914i	$-0.175529\pi$
$152$	−9.05859			−0.734748
$153$		0			0
$154$	−1.33768	−	4.13496i	−0.107793	−	0.333205i
$155$	−5.64874	−	3.26130i	−0.453718	−	0.261954i
$156$		0			0
$157$	−2.85973	+	1.65107i	−0.228232	+	0.131770i	−0.609756	−	0.792589i	$-0.708733\pi$
$157$	−2.85973	+	1.65107i	−0.228232	+	0.131770i	0.381524	+	0.924359i	$0.375399\pi$
$158$	1.18523	−	0.684291i	0.0942916	−	0.0544393i
$159$		0			0
$160$	−4.92336	−	2.84251i	−0.389226	−	0.224720i
$161$	−13.4813	+	4.36128i	−1.06248	+	0.343717i
$162$		0			0
$163$	−22.1660			−1.73618			−0.868089	−	0.496408i	$-0.834652\pi$
$163$	−22.1660			−1.73618			−0.868089	+	0.496408i	$0.834652\pi$
$164$	−4.36535	+	7.56100i	−0.340876	+	0.590415i
$165$		0			0
$166$	−4.01161	+	2.31611i	−0.311362	+	0.179765i
$167$	9.71593	+	16.8285i	0.751841	+	1.30223i	0.946929	+	0.321442i	$0.104167\pi$
$167$	9.71593	+	16.8285i	0.751841	+	1.30223i	−0.195088	+	0.980786i	$0.562499\pi$
$168$		0			0
$169$	−0.846151	+	1.46558i	−0.0650886	+	0.112737i
$170$			1.66489i			0.127691i
$171$		0			0
$172$	15.2557			1.16324
$173$	0.906004	−	1.56925i	0.0688822	−	0.119307i	−0.829527	−	0.558466i	$-0.811390\pi$
$173$	0.906004	−	1.56925i	0.0688822	−	0.119307i	0.898410	+	0.439159i	$0.144723\pi$
$174$		0			0
$175$	−1.77287	+	1.96391i	−0.134016	+	0.148458i
$176$	−3.83688	+	2.21523i	−0.289216	+	0.166979i
$177$		0			0
$178$	−6.52575	−	3.76765i	−0.489126	−	0.282397i
$179$		−	6.19083i		−	0.462725i	−0.972868	−	0.231362i	$-0.925682\pi$
$179$		−	6.19083i		−	0.462725i	0.972868	−	0.231362i	$-0.0743183\pi$
$180$		0			0
$181$			11.8291i			0.879249i	0.898182	+	0.439625i	$0.144889\pi$
$181$			11.8291i			0.879249i	−0.898182	+	0.439625i	$0.855111\pi$
$182$	−5.55307	−	1.18777i	−0.411621	−	0.0880437i
$183$		0			0
$184$	−6.14027	−	10.6353i	−0.452667	−	0.784042i
$185$	−3.73888	−	6.47594i	−0.274888	−	0.476120i
$186$		0			0
$187$	5.81338	+	3.35636i	0.425117	+	0.245441i
$188$	−17.6442			−1.28683
$189$		0			0
$190$	−2.52146			−0.182926
$191$	8.65572	+	4.99738i	0.626306	+	0.361598i	0.779320	−	0.626626i	$-0.215565\pi$
$191$	8.65572	+	4.99738i	0.626306	+	0.361598i	−0.153014	+	0.988224i	$0.548898\pi$
$192$		0			0
$193$	2.05829	+	3.56507i	0.148159	+	0.256619i	0.930547	−	0.366172i	$-0.119332\pi$
$193$	2.05829	+	3.56507i	0.148159	+	0.256619i	−0.782388	+	0.622791i	$0.785999\pi$
$194$	−0.0868325	−	0.150398i	−0.00623421	−	0.0107980i
$195$		0			0
$196$	−1.13691	−	11.0901i	−0.0812079	−	0.792147i
$197$		−	3.98010i		−	0.283570i	−0.989897	−	0.141785i	$-0.954716\pi$
$197$		−	3.98010i		−	0.283570i	0.989897	−	0.141785i	$-0.0452842\pi$
$198$		0			0
$199$			25.1000i			1.77929i	0.456649	+	0.889647i	$0.349049\pi$
$199$			25.1000i			1.77929i	−0.456649	+	0.889647i	$0.650951\pi$
$200$	−1.98587	−	1.14654i	−0.140422	−	0.0810728i
$201$		0			0
$202$	1.56874	−	0.905713i	0.110376	−	0.0637257i
$203$	5.89553	+	5.32204i	0.413785	+	0.373534i
$204$		0			0
$205$	−2.74102	+	4.74759i	−0.191441	+	0.331586i
$206$	7.74122			0.539356
$207$		0			0
$208$			5.78909i			0.401401i
$209$	−5.08317	+	8.80431i	−0.351610	+	0.609007i
$210$		0			0
$211$	−6.14184	−	10.6380i	−0.422822	−	0.732349i	0.573392	−	0.819281i	$-0.305627\pi$
$211$	−6.14184	−	10.6380i	−0.422822	−	0.732349i	−0.996214	+	0.0869318i	$0.972294\pi$
$212$	−11.8285	+	6.82917i	−0.812383	+	0.469029i
$213$		0			0
$214$	3.28270	−	5.68580i	0.224401	−	0.388673i
$215$	9.57914			0.653292
$216$		0			0
$217$	16.4194	−	5.31175i	1.11462	−	0.360585i
$218$	−9.92775	−	5.73179i	−0.672392	−	0.388206i
$219$		0			0
$220$	−3.54945	+	2.04928i	−0.239304	+	0.138162i
$221$	7.59611	−	4.38562i	0.510970	−	0.295009i
$222$		0			0
$223$	−16.5774	−	9.57096i	−1.11010	−	0.640919i	−0.171248	−	0.985228i	$-0.554780\pi$
$223$	−16.5774	−	9.57096i	−1.11010	−	0.640919i	−0.938856	+	0.344309i	$0.888113\pi$
$224$	14.3109	−	4.62965i	0.956187	−	0.309331i
$225$		0			0
$226$	11.5145			0.765930
$227$	−5.39780	+	9.34927i	−0.358265	+	0.620533i	−0.987671	−	0.156544i	$-0.949965\pi$
$227$	−5.39780	+	9.34927i	−0.358265	+	0.620533i	0.629406	+	0.777076i	$0.283298\pi$
$228$		0			0
$229$	−1.09578	+	0.632652i	−0.0724115	+	0.0418068i	−0.535769	−	0.844365i	$-0.679978\pi$
$229$	−1.09578	+	0.632652i	−0.0724115	+	0.0418068i	0.463357	+	0.886172i	$0.346645\pi$
$230$	−1.70914	−	2.96033i	−0.112698	−	0.195198i
$231$		0			0
$232$	−3.44185	+	5.96146i	−0.225969	+	0.391389i
$233$		−	2.66444i		−	0.174553i	−0.996184	−	0.0872766i	$-0.972184\pi$
$233$		−	2.66444i		−	0.174553i	0.996184	−	0.0872766i	$-0.0278164\pi$
$234$		0			0
$235$	−11.0789			−0.722705
$236$	−6.82208	+	11.8162i	−0.444079	+	0.769168i
$237$		0			0
$238$	−3.26969	−	2.95163i	−0.211942	−	0.191326i
$239$	−4.50900	+	2.60327i	−0.291663	+	0.168392i	−0.638692	−	0.769463i	$-0.720524\pi$
$239$	−4.50900	+	2.60327i	−0.291663	+	0.168392i	0.347028	+	0.937855i	$0.387191\pi$
$240$		0			0
$241$	−1.11798	−	0.645468i	−0.0720157	−	0.0415783i	0.463560	−	0.886066i	$-0.346572\pi$
$241$	−1.11798	−	0.645468i	−0.0720157	−	0.0415783i	−0.535575	+	0.844487i	$0.679905\pi$
$242$			2.79381i			0.179593i
$243$		0			0
$244$		−	7.01899i		−	0.449345i
$245$	−0.713871	−	6.96350i	−0.0456076	−	0.444882i
$246$		0			0
$247$	6.64198	+	11.5042i	0.422619	+	0.731997i
$248$	7.47844	+	12.9530i	0.474882	+	0.822519i
$249$		0			0
$250$	−0.552767	−	0.319140i	−0.0349601	−	0.0201842i
$251$	10.1130			0.638328			0.319164	−	0.947700i	$-0.396598\pi$
$251$	10.1130			0.638328			0.319164	+	0.947700i	$0.396598\pi$
$252$		0			0
$253$	−13.7823			−0.866486
$254$	8.66547	+	5.00301i	0.543720	+	0.313917i
$255$		0			0
$256$	3.77635	+	6.54082i	0.236022	+	0.408801i
$257$	−6.49877	−	11.2562i	−0.405382	−	0.702143i	0.588984	−	0.808145i	$-0.299528\pi$
$257$	−6.49877	−	11.2562i	−0.405382	−	0.702143i	−0.994366	+	0.106002i	$0.966195\pi$
$258$		0			0
$259$	19.3467	+	4.13816i	1.20215	+	0.257133i
$260$			5.35542i			0.332129i
$261$		0			0
$262$		−	3.92260i		−	0.242339i
$263$	−16.4072	−	9.47268i	−1.01171	−	0.584110i	−0.100017	−	0.994986i	$-0.531890\pi$
$263$	−16.4072	−	9.47268i	−1.01171	−	0.584110i	−0.911692	+	0.410875i	$0.865223\pi$
$264$		0			0
$265$	−7.42716	+	4.28807i	−0.456247	+	0.263414i
$266$	4.47022	−	4.95191i	0.274087	−	0.303621i
$267$		0			0
$268$	−7.84312	+	13.5847i	−0.479095	+	0.829816i
$269$	−15.1728			−0.925103			−0.462552	−	0.886592i	$-0.653066\pi$
$269$	−15.1728			−0.925103			−0.462552	+	0.886592i	$0.653066\pi$
$270$		0			0
$271$			0.872890i			0.0530243i	0.999648	+	0.0265121i	$0.00844006\pi$
$271$			0.872890i			0.0530243i	−0.999648	+	0.0265121i	$0.991560\pi$
$272$	−2.24526	+	3.88891i	−0.136139	+	0.235800i
$273$		0			0
$274$	−2.82877	−	4.89957i	−0.170892	−	0.295994i
$275$	−2.22872	+	1.28675i	−0.134397	+	0.0775940i
$276$		0			0
$277$	−4.56721	+	7.91063i	−0.274417	+	0.475304i	−0.969988	−	0.243153i	$-0.921818\pi$
$277$	−4.56721	+	7.91063i	−0.274417	+	0.475304i	0.695571	+	0.718457i	$0.255151\pi$
$278$	−6.07659			−0.364450
$279$		0			0
$280$	5.77239	−	1.86740i	0.344966	−	0.111598i
$281$	16.8697	+	9.73975i	1.00636	+	0.581025i	0.910125	−	0.414334i	$-0.135985\pi$
$281$	16.8697	+	9.73975i	1.00636	+	0.581025i	0.0962390	+	0.995358i	$0.469319\pi$
$282$		0			0
$283$	18.1140	−	10.4581i	1.07676	−	0.621669i	0.146742	−	0.989175i	$-0.453121\pi$
$283$	18.1140	−	10.4581i	1.07676	−	0.621669i	0.930021	+	0.367505i	$0.119788\pi$
$284$	9.25961	−	5.34604i	0.549457	−	0.317229i
$285$		0			0
$286$	−4.78359	−	2.76181i	−0.282859	−	0.163309i
$287$	−4.46436	−	13.8000i	−0.263523	−	0.814587i
$288$		0			0
$289$	−10.1963			−0.599780
$290$	−0.958039	+	1.65937i	−0.0562580	+	0.0974417i
$291$		0			0
$292$	−8.99109	+	5.19101i	−0.526164	+	0.303781i
$293$	3.70009	+	6.40874i	0.216161	+	0.374403i	0.953631	−	0.300978i	$-0.0973129\pi$
$293$	3.70009	+	6.40874i	0.216161	+	0.374403i	−0.737470	+	0.675380i	$0.763980\pi$
$294$		0			0
$295$	−4.28361	+	7.41944i	−0.249402	+	0.431976i
$296$			17.1472i			0.996658i
$297$		0			0
$298$	−1.37422			−0.0796064
$299$	−9.00439	+	15.5961i	−0.520737	+	0.901944i
$300$		0			0
$301$	−16.9826	+	18.8126i	−0.978859	+	1.08434i
$302$	−11.9495	+	6.89905i	−0.687617	+	0.396996i
$303$		0			0
$304$	−5.88972	−	3.40043i	−0.337798	−	0.195028i
$305$		−	4.40726i		−	0.252359i
$306$		0			0
$307$			14.9146i			0.851222i	0.904906	+	0.425611i	$0.139941\pi$
$307$			14.9146i			0.851222i	−0.904906	+	0.425611i	$0.860059\pi$
$308$	2.26812	−	10.6039i	0.129238	−	0.604213i
$309$		0			0
$310$	2.08163	+	3.60548i	0.118228	+	0.204778i
$311$	12.8802	+	22.3091i	0.730369	+	1.26504i	0.956726	+	0.290991i	$0.0939851\pi$
$311$	12.8802	+	22.3091i	0.730369	+	1.26504i	−0.226357	+	0.974044i	$0.572682\pi$
$312$		0			0
$313$	−3.95612	−	2.28407i	−0.223613	−	0.129103i	0.384009	−	0.923329i	$-0.374543\pi$
$313$	−3.95612	−	2.28407i	−0.223613	−	0.129103i	−0.607622	+	0.794226i	$0.707877\pi$
$314$	2.10769			0.118944
$315$		0			0
$316$	3.41480			0.192098
$317$	−21.7653	−	12.5662i	−1.22246	−	0.705790i	−0.257021	−	0.966406i	$-0.582741\pi$
$317$	−21.7653	−	12.5662i	−1.22246	−	0.705790i	−0.965443	+	0.260616i	$0.916074\pi$
$318$		0			0
$319$	3.86275	+	6.69047i	0.216272	+	0.374595i
$320$	0.0927504	+	0.160648i	0.00518491	+	0.00898052i
$321$		0			0
$322$	8.84390	+	1.89167i	0.492851	+	0.105418i
$323$			10.3042i			0.573341i
$324$		0			0
$325$			3.36269i			0.186529i
$326$	12.2527	+	7.07407i	0.678612	+	0.391797i
$327$		0			0
$328$	10.8866	−	6.28540i	0.601114	−	0.347053i
$329$	19.6414	−	21.7579i	1.08286	−	1.19955i
$330$		0			0
$331$	−9.30506	+	16.1168i	−0.511453	+	0.885862i	0.488459	+	0.872587i	$0.337559\pi$
$331$	−9.30506	+	16.1168i	−0.511453	+	0.885862i	−0.999912	+	0.0132751i	$0.995774\pi$
$332$	−11.5580			−0.634328
$333$		0			0
$334$		−	12.4030i		−	0.678661i
$335$	−4.92473	+	8.52989i	−0.269067	+	0.466037i
$336$		0			0
$337$	−3.96789	−	6.87259i	−0.216145	−	0.374374i	0.737481	−	0.675367i	$-0.236015\pi$
$337$	−3.96789	−	6.87259i	−0.216145	−	0.374374i	−0.953626	+	0.300994i	$0.902682\pi$
$338$	0.935449	−	0.540082i	0.0508817	−	0.0293766i
$339$		0			0
$340$	−2.07706	+	3.59758i	−0.112645	+	0.195106i
$341$	16.7859			0.909009
$342$		0			0
$343$	14.9413	+	10.9434i	0.806753	+	0.590888i
$344$	−19.0229	−	10.9829i	−1.02565	−	0.592158i
$345$		0			0
$346$	−1.00162	+	0.578285i	−0.0538473	+	0.0310888i
$347$	24.5808	−	14.1917i	1.31957	−	0.761853i	0.335909	−	0.941894i	$-0.390957\pi$
$347$	24.5808	−	14.1917i	1.31957	−	0.761853i	0.983659	+	0.180041i	$0.0576232\pi$
$348$		0			0
$349$	−4.22045	−	2.43668i	−0.225916	−	0.130433i	0.382771	−	0.923843i	$-0.374970\pi$
$349$	−4.22045	−	2.43668i	−0.225916	−	0.130433i	−0.608686	+	0.793411i	$0.708303\pi$
$350$	1.60675	−	0.519790i	0.0858842	−	0.0277839i
$351$		0			0
$352$	14.6304			0.779802
$353$	11.3820	−	19.7142i	0.605802	−	1.04928i	−0.386122	−	0.922448i	$-0.626186\pi$
$353$	11.3820	−	19.7142i	0.605802	−	1.04928i	0.991924	−	0.126833i	$-0.0404811\pi$
$354$		0			0
$355$	5.81415	−	3.35680i	0.308583	−	0.178161i
$356$	−9.40080	−	16.2827i	−0.498241	−	0.862979i
$357$		0			0
$358$	−1.97574	+	3.42209i	−0.104421	+	0.180863i
$359$			17.2003i			0.907799i	0.891053	+	0.453900i	$0.149968\pi$
$359$			17.2003i			0.907799i	−0.891053	+	0.453900i	$0.850032\pi$
$360$		0			0
$361$	3.39439			0.178652
$362$	3.77514	−	6.53873i	0.198417	−	0.343668i
$363$		0			0
$364$	−10.5175	−	9.49445i	−0.551269	−	0.497645i
$365$	−5.64555	+	3.25946i	−0.295502	+	0.170608i
$366$		0			0
$367$	2.88343	+	1.66475i	0.150514	+	0.0868992i	0.573365	−	0.819300i	$-0.305638\pi$
$367$	2.88343	+	1.66475i	0.150514	+	0.0868992i	−0.422852	+	0.906199i	$0.638971\pi$
$368$		−	9.21978i		−	0.480614i
$369$		0			0
$370$			4.77291i			0.248132i
$371$	4.74600	−	22.1884i	0.246400	−	1.15197i
$372$		0			0
$373$	8.03809	+	13.9224i	0.416197	+	0.720874i	0.995553	−	0.0942003i	$-0.0300294\pi$
$373$	8.03809	+	13.9224i	0.416197	+	0.720874i	−0.579357	+	0.815074i	$0.696696\pi$
$374$	−2.14230	−	3.71057i	−0.110776	−	0.191869i
$375$		0			0
$376$	22.0012	+	12.7024i	1.13462	+	0.655075i
$377$	10.0946			0.519898
$378$		0			0
$379$	−16.9619			−0.871275			−0.435638	−	0.900122i	$-0.643477\pi$
$379$	−16.9619			−0.871275			−0.435638	+	0.900122i	$0.643477\pi$
$380$	−5.44850	−	3.14569i	−0.279502	−	0.161371i
$381$		0			0
$382$	−3.18973	−	5.52478i	−0.163201	−	0.282672i
$383$	1.61770	+	2.80195i	0.0826608	+	0.143173i	0.904392	−	0.426703i	$-0.140325\pi$
$383$	1.61770	+	2.80195i	0.0826608	+	0.143173i	−0.821731	+	0.569875i	$0.806992\pi$
$384$		0			0
$385$	1.42416	−	6.65824i	0.0725821	−	0.339335i
$386$		−	2.62754i		−	0.133738i
$387$		0			0
$388$		−	0.433318i		−	0.0219984i
$389$	−14.1105	−	8.14671i	−0.715431	−	0.413054i	0.0976375	−	0.995222i	$-0.468871\pi$
$389$	−14.1105	−	8.14671i	−0.715431	−	0.413054i	−0.813069	+	0.582168i	$0.802205\pi$
$390$		0			0
$391$	−12.0977	+	6.98459i	−0.611805	+	0.353226i
$392$	−6.56630	+	14.6471i	−0.331648	+	0.739790i
$393$		0			0
$394$	−1.27021	+	2.20007i	−0.0639922	+	0.110838i
$395$	2.14417			0.107885
$396$		0			0
$397$		−	35.9834i		−	1.80596i	−0.429686	−	0.902978i	$-0.641376\pi$
$397$		−	35.9834i		−	1.80596i	0.429686	−	0.902978i	$-0.358624\pi$
$398$	8.01043	−	13.8745i	0.401526	−	0.695464i
$399$		0			0
$400$	−0.860783	−	1.49092i	−0.0430391	−	0.0745460i
$401$	1.55394	−	0.897167i	0.0776000	−	0.0448024i	−0.460698	−	0.887557i	$-0.652401\pi$
$401$	1.55394	−	0.897167i	0.0776000	−	0.0448024i	0.538298	+	0.842755i	$0.319068\pi$
$402$		0			0
$403$	10.9668	−	18.9950i	0.546293	−	0.946207i
$404$	4.51976			0.224866
$405$		0			0
$406$	−1.56038	−	4.82335i	−0.0774402	−	0.239379i
$407$	16.6658	+	9.62203i	0.826095	+	0.476946i
$408$		0			0
$409$	5.48011	−	3.16395i	0.270974	−	0.156447i	−0.358356	−	0.933585i	$-0.616663\pi$
$409$	5.48011	−	3.16395i	0.270974	−	0.156447i	0.629330	+	0.777138i	$0.283329\pi$
$410$	3.03029	−	1.74954i	0.149656	−	0.0864037i
$411$		0			0
$412$	16.7276	+	9.65771i	0.824112	+	0.475801i
$413$	−6.97681	−	21.5663i	−0.343306	−	1.06121i
$414$		0			0
$415$	−7.25733			−0.356248
$416$	9.55847	−	16.5558i	0.468643	−	0.811713i
$417$		0			0
$418$	5.61962	−	3.24449i	0.274865	−	0.158693i
$419$	−9.78420	−	16.9467i	−0.477990	−	0.827902i	0.521692	−	0.853134i	$-0.325301\pi$
$419$	−9.78420	−	16.9467i	−0.477990	−	0.827902i	−0.999682	+	0.0252316i	$0.991968\pi$
$420$		0			0
$421$	11.6203	−	20.1269i	0.566338	−	0.980926i	−0.430586	−	0.902550i	$-0.641693\pi$
$421$	11.6203	−	20.1269i	0.566338	−	0.980926i	0.996924	−	0.0783764i	$-0.0249736\pi$
$422$			7.84044i			0.381667i
$423$		0			0
$424$	19.6658			0.955057
$425$	−1.30420	+	2.25894i	−0.0632629	+	0.109575i
$426$		0			0
$427$	8.65545	+	7.81349i	0.418867	+	0.378121i
$428$	14.1869	−	8.19079i	0.685748	−	0.395917i
$429$		0			0
$430$	−5.29503	−	3.05709i	−0.255349	−	0.147426i
$431$			8.50547i			0.409694i	0.978794	+	0.204847i	$0.0656697\pi$
$431$			8.50547i			0.409694i	−0.978794	+	0.204847i	$0.934330\pi$
$432$		0			0
$433$		−	7.10048i		−	0.341228i	−0.985338	−	0.170614i	$-0.945425\pi$
$433$		−	7.10048i		−	0.341228i	0.985338	−	0.170614i	$-0.0545750\pi$
$434$	−10.7713	−	2.30392i	−0.517038	−	0.110592i
$435$		0			0
$436$	−14.3016	−	24.7711i	−0.684923	−	1.18632i
$437$	−10.5781	−	18.3218i	−0.506019	−	0.876451i
$438$		0			0
$439$	6.36593	+	3.67537i	0.303829	+	0.175416i	0.644162	−	0.764889i	$-0.277206\pi$
$439$	6.36593	+	3.67537i	0.303829	+	0.175416i	−0.340332	+	0.940305i	$0.610540\pi$
$440$	5.90126			0.281331
$441$		0			0
$442$	−5.59851			−0.266294
$443$	26.6244	+	15.3716i	1.26496	+	0.730328i	0.974031	−	0.226416i	$-0.0727007\pi$
$443$	26.6244	+	15.3716i	1.26496	+	0.730328i	0.290934	+	0.956743i	$0.406034\pi$
$444$		0			0
$445$	−5.90281	−	10.2240i	−0.279820	−	0.484662i
$446$	6.10896	+	10.5810i	0.289267	+	0.501026i
$447$		0			0
$448$	−0.479933	−	0.102655i	−0.0226747	−	0.00485001i
$449$			31.4977i			1.48647i	0.669031	+	0.743234i	$0.266709\pi$
$449$			31.4977i			1.48647i	−0.669031	+	0.743234i	$0.733291\pi$
$450$		0			0
$451$		−	14.1081i		−	0.664322i
$452$	24.8811	+	14.3651i	1.17031	+	0.675677i
$453$		0			0
$454$	5.96745	−	3.44531i	0.280066	−	0.161696i
$455$	−6.60402	−	5.96161i	−0.309601	−	0.279485i
$456$		0			0
$457$	5.54440	−	9.60319i	0.259356	−	0.449218i	−0.706713	−	0.707500i	$-0.749823\pi$
$457$	5.54440	−	9.60319i	0.259356	−	0.449218i	0.966070	+	0.258282i	$0.0831563\pi$
$458$	0.807618			0.0377375
$459$		0			0
$460$		−	8.52911i		−	0.397672i
$461$	19.3153	−	33.4552i	0.899605	−	1.55816i	0.0716059	−	0.997433i	$-0.477188\pi$
$461$	19.3153	−	33.4552i	0.899605	−	1.55816i	0.827999	−	0.560729i	$-0.189479\pi$
$462$		0			0
$463$	3.99332	+	6.91664i	0.185585	+	0.321444i	0.943774	−	0.330592i	$-0.107249\pi$
$463$	3.99332	+	6.91664i	0.185585	+	0.321444i	−0.758188	+	0.652036i	$0.773915\pi$
$464$	−4.47565	+	2.58402i	−0.207777	+	0.119960i
$465$		0			0
$466$	−0.850330	+	1.47281i	−0.0393908	+	0.0682268i
$467$	−11.2412			−0.520179			−0.260089	−	0.965585i	$-0.583752\pi$
$467$	−11.2412			−0.520179			−0.260089	+	0.965585i	$0.583752\pi$
$468$		0			0
$469$	−8.02101	−	24.7941i	−0.370376	−	1.14488i
$470$	6.12403	+	3.53571i	0.282480	+	0.163090i
$471$		0			0
$472$	17.0134	−	9.82269i	0.783105	−	0.452126i
$473$	−21.3492	+	12.3260i	−0.981637	+	0.566749i
$474$		0			0
$475$	−3.42114	−	1.97520i	−0.156973	−	0.0906282i
$476$	−3.38296	−	10.4572i	−0.155058	−	0.479305i
$477$		0			0
$478$	3.32324			0.152001
$479$	−7.35486	+	12.7390i	−0.336052	+	0.582059i	−0.983686	−	0.179892i	$-0.942425\pi$
$479$	−7.35486	+	12.7390i	−0.336052	+	0.582059i	0.647634	+	0.761951i	$0.275758\pi$
$480$		0			0
$481$	21.7766	−	12.5727i	0.992927	−	0.573267i
$482$	0.411990	+	0.713587i	0.0187656	+	0.0325030i
$483$		0			0
$484$	−3.48547	+	6.03701i	−0.158431	+	0.274410i
$485$		−	0.272083i		−	0.0123546i
$486$		0			0
$487$	−36.6576			−1.66112			−0.830558	−	0.556932i	$-0.811978\pi$
$487$	−36.6576			−1.66112			−0.830558	+	0.556932i	$0.811978\pi$
$488$	−5.05311	+	8.75224i	−0.228744	+	0.396195i
$489$		0			0
$490$	−1.82773	+	4.07702i	−0.0825684	+	0.184181i
$491$	−27.7690	+	16.0325i	−1.25320	+	0.723535i	−0.971743	−	0.236039i	$-0.924151\pi$
$491$	−27.7690	+	16.0325i	−1.25320	+	0.723535i	−0.281456	+	0.959574i	$0.590817\pi$
$492$		0			0
$493$	6.78119	+	3.91512i	0.305410	+	0.176328i
$494$		−	8.47889i		−	0.381483i
$495$		0			0
$496$			11.2291i			0.504201i
$497$	−3.71528	+	17.3696i	−0.166653	+	0.779134i
$498$		0			0
$499$	13.9529	+	24.1672i	0.624620	+	1.08187i	0.988614	+	0.150472i	$0.0480794\pi$
$499$	13.9529	+	24.1672i	0.624620	+	1.08187i	−0.363994	+	0.931401i	$0.618587\pi$
$500$	−0.796299	−	1.37923i	−0.0356116	−	0.0616811i
$501$		0			0
$502$	−5.59014	−	3.22747i	−0.249500	−	0.144049i
$503$	−1.50267			−0.0670006			−0.0335003	−	0.999439i	$-0.510665\pi$
$503$	−1.50267			−0.0670006			−0.0335003	+	0.999439i	$0.510665\pi$
$504$		0			0
$505$	2.83798			0.126288
$506$	7.61840	+	4.39849i	0.338679	+	0.195537i
$507$		0			0
$508$	12.4832	+	21.6215i	0.553853	+	0.959301i
$509$	−18.0390	−	31.2444i	−0.799563	−	1.38488i	−0.919901	−	0.392151i	$-0.871731\pi$
$509$	−18.0390	−	31.2444i	−0.799563	−	1.38488i	0.120338	−	0.992733i	$-0.461602\pi$
$510$		0			0
$511$	3.60754	−	16.8659i	0.159588	−	0.746105i
$512$			17.6825i			0.781464i
$513$		0			0
$514$			8.29608i			0.365924i
$515$	10.5034	+	6.06412i	0.462834	+	0.267217i
$516$		0			0
$517$	24.6916	−	14.2557i	1.08594	−	0.626966i
$518$	−9.37356	−	8.46175i	−0.411851	−	0.371788i
$519$		0			0
$520$	3.85547	−	6.67787i	0.169074	−	0.292844i
$521$	−40.0264			−1.75359			−0.876794	−	0.480866i	$-0.840322\pi$
$521$	−40.0264			−1.75359			−0.876794	+	0.480866i	$0.840322\pi$
$522$		0			0
$523$		−	22.6116i		−	0.988737i	−0.869252	−	0.494369i	$-0.835399\pi$
$523$		−	22.6116i		−	0.988737i	0.869252	−	0.494369i	$-0.164601\pi$
$524$	4.89372	−	8.47617i	0.213783	−	0.370283i
$525$		0			0
$526$	6.04622	+	10.4724i	0.263628	+	0.456617i
$527$	14.7342	−	8.50677i	0.641830	−	0.370561i
$528$		0			0
$529$	2.84051	−	4.91990i	0.123500	−	0.213909i
$530$	5.47398			0.237775
$531$		0			0
$532$	15.8373	−	5.12346i	0.686636	−	0.222130i
$533$	−15.9647	−	9.21722i	−0.691507	−	0.399242i
$534$		0			0
$535$	8.90800	−	5.14303i	0.385126	−	0.222353i
$536$	19.5598	−	11.2928i	0.844853	−	0.487776i
$537$		0			0
$538$	8.38703	+	4.84226i	0.361591	+	0.208764i
$539$	10.5513	+	14.6011i	0.454477	+	0.628914i
$540$		0			0
$541$	−0.766443			−0.0329520			−0.0164760	−	0.999864i	$-0.505245\pi$
$541$	−0.766443			−0.0329520			−0.0164760	+	0.999864i	$0.505245\pi$
$542$	0.278574	−	0.482505i	0.0119658	−	0.0207254i
$543$		0			0
$544$	12.8421	−	7.41438i	0.550600	−	0.317889i
$545$	−8.98004	−	15.5539i	−0.384663	−	0.666256i
$546$		0			0
$547$	9.59685	−	16.6222i	0.410332	−	0.710715i	−0.584594	−	0.811326i	$-0.698746\pi$
$547$	9.59685	−	16.6222i	0.410332	−	0.710715i	0.994926	+	0.100610i	$0.0320796\pi$
$548$		−	14.1163i		−	0.603020i
$549$		0			0
$550$	1.64262			0.0700414
$551$	−5.92942	+	10.2701i	−0.252602	+	0.437519i
$552$		0			0
$553$	−3.80133	+	4.21095i	−0.161649	+	0.179068i
$554$	5.04920	−	2.91516i	0.214520	−	0.123853i
$555$		0			0
$556$	−13.1306	−	7.58097i	−0.556863	−	0.321505i
$557$		−	24.8020i		−	1.05090i	−0.850826	−	0.525448i	$-0.823898\pi$
$557$		−	24.8020i		−	1.05090i	0.850826	−	0.525448i	$-0.176102\pi$
$558$		0			0
$559$			32.2117i			1.36241i
$560$	4.45408	+	0.952706i	0.188219	+	0.0402592i
$561$		0			0
$562$	−6.21669	−	10.7676i	−0.262235	−	0.454205i
$563$	5.29797	+	9.17636i	0.223283	+	0.386737i	0.955803	−	0.294008i	$-0.0949893\pi$
$563$	5.29797	+	9.17636i	0.223283	+	0.386737i	−0.732520	+	0.680746i	$0.761656\pi$
$564$		0			0
$565$	15.6229	+	9.01990i	0.657262	+	0.379470i
$566$	−13.3504			−0.561159
$567$		0			0
$568$	−15.3949			−0.645954
$569$	15.7502	+	9.09337i	0.660282	+	0.381214i	0.792384	−	0.610022i	$-0.208839\pi$
$569$	15.7502	+	9.09337i	0.660282	+	0.381214i	−0.132103	+	0.991236i	$0.542173\pi$
$570$		0			0
$571$	17.0719	+	29.5693i	0.714435	+	1.23744i	0.963177	+	0.268868i	$0.0866495\pi$
$571$	17.0719	+	29.5693i	0.714435	+	1.23744i	−0.248742	+	0.968570i	$0.580017\pi$
$572$	−6.89109	−	11.9357i	−0.288131	−	0.499057i
$573$		0			0
$574$	−1.93638	+	9.05293i	−0.0808228	+	0.377862i
$575$		−	5.35547i		−	0.223338i
$576$		0			0
$577$			8.14778i			0.339196i	0.985513	+	0.169598i	$0.0542470\pi$
$577$			8.14778i			0.339196i	−0.985513	+	0.169598i	$0.945753\pi$
$578$	5.63616	+	3.25404i	0.234433	+	0.135350i
$579$		0			0
$580$	−4.14037	+	2.39044i	−0.171919	+	0.0992577i
$581$	12.8663	−	14.2527i	0.533784	−	0.591303i
$582$		0			0
$583$	11.0354	−	19.1138i	0.457038	−	0.791613i
$584$	14.9484			0.618571
$585$		0			0
$586$		−	4.72339i		−	0.195121i
$587$	16.3555	−	28.3286i	0.675066	−	1.16925i	−0.301384	−	0.953503i	$-0.597449\pi$
$587$	16.3555	−	28.3286i	0.675066	−	1.16925i	0.976450	−	0.215745i	$-0.0692181\pi$
$588$		0			0
$589$	12.8834	+	22.3148i	0.530852	+	0.919463i
$590$	4.73568	−	2.73415i	0.194965	−	0.112563i
$591$		0			0
$592$	−6.43673	+	11.1487i	−0.264548	+	0.458211i
$593$	−40.6769			−1.67040			−0.835201	−	0.549945i	$-0.814649\pi$
$593$	−40.6769			−1.67040			−0.835201	+	0.549945i	$0.814649\pi$
$594$		0			0
$595$	−2.12417	−	6.56613i	−0.0870827	−	0.269185i
$596$	−2.96949	−	1.71443i	−0.121635	−	0.0702260i
$597$		0			0
$598$	9.95466	−	5.74733i	0.407076	−	0.235026i
$599$	−41.6861	+	24.0675i	−1.70325	+	0.983370i	−0.760816	+	0.648968i	$0.775201\pi$
$599$	−41.6861	+	24.0675i	−1.70325	+	0.983370i	−0.942430	+	0.334402i	$0.891466\pi$
$600$		0			0
$601$	−11.4167	−	6.59141i	−0.465695	−	0.268869i	0.248741	−	0.968570i	$-0.419983\pi$
$601$	−11.4167	−	6.59141i	−0.465695	−	0.268869i	−0.714436	+	0.699701i	$0.753317\pi$
$602$	15.3912	−	4.97914i	0.627300	−	0.202935i
$603$		0			0
$604$	−34.4282			−1.40086
$605$	−2.18854	+	3.79067i	−0.0889770	+	0.154113i
$606$		0			0
$607$	−41.2641	+	23.8238i	−1.67486	+	0.966979i	−0.710001	+	0.704200i	$0.751306\pi$
$607$	−41.2641	+	23.8238i	−1.67486	+	0.966979i	−0.964856	+	0.262779i	$0.915361\pi$
$608$	11.2290	+	19.4492i	0.455397	+	0.788770i
$609$		0			0
$610$	−1.40653	+	2.43619i	−0.0569489	+	0.0986384i
$611$		−	37.2548i		−	1.50717i
$612$		0			0
$613$	17.6569			0.713155			0.356578	−	0.934266i	$-0.383943\pi$
$613$	17.6569			0.713155			0.356578	+	0.934266i	$0.383943\pi$
$614$	4.75985	−	8.24431i	0.192092	−	0.332713i
$615$		0			0
$616$	−10.4622	+	11.5895i	−0.421532	+	0.466955i
$617$	−5.32696	+	3.07552i	−0.214455	+	0.123816i	−0.603380	−	0.797454i	$-0.706180\pi$
$617$	−5.32696	+	3.07552i	−0.214455	+	0.123816i	0.388925	+	0.921269i	$0.372847\pi$
$618$		0			0
$619$	−29.8898	−	17.2569i	−1.20137	−	0.693612i	−0.240511	−	0.970646i	$-0.577315\pi$
$619$	−29.8898	−	17.2569i	−1.20137	−	0.693612i	−0.960860	+	0.277035i	$0.910648\pi$
$620$			10.3879i			0.417188i
$621$		0			0
$622$		−	16.4423i		−	0.659278i
$623$	30.5438	+	6.53317i	1.22371	+	0.261746i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.45788	+	2.52512i	0.0582684	+	0.100924i
$627$		0			0
$628$	4.55441	+	2.62949i	0.181741	+	0.104928i
$629$	19.5050			0.777715
$630$		0			0
$631$	−14.8371			−0.590657			−0.295329	−	0.955396i	$-0.595429\pi$
$631$	−14.8371			−0.590657			−0.295329	+	0.955396i	$0.595429\pi$
$632$	−4.25804	−	2.45838i	−0.169376	−	0.0977892i
$633$		0			0
$634$	8.02078	+	13.8924i	0.318546	+	0.551737i
$635$	7.83826	+	13.5763i	0.311052	+	0.538758i
$636$		0			0
$637$	23.4161	−	2.40053i	0.927780	−	0.0951124i
$638$		−	4.93103i		−	0.195221i
$639$		0			0
$640$			11.2516i			0.444759i
$641$	−38.8970	−	22.4572i	−1.53634	−	0.887007i	−0.999049	−	0.0436106i	$-0.986114\pi$
$641$	−38.8970	−	22.4572i	−1.53634	−	0.887007i	−0.537292	−	0.843396i	$-0.680553\pi$
$642$		0			0
$643$	−29.7285	+	17.1637i	−1.17238	+	0.676872i	−0.954239	−	0.299046i	$-0.903331\pi$
$643$	−29.7285	+	17.1637i	−1.17238	+	0.676872i	−0.218138	+	0.975918i	$0.569998\pi$
$644$	16.7504	+	15.1210i	0.660057	+	0.595850i
$645$		0			0
$646$	3.28848	−	5.69582i	0.129384	−	0.224099i
$647$	31.2211			1.22743			0.613714	−	0.789528i	$-0.289675\pi$
$647$	31.2211			1.22743			0.613714	+	0.789528i	$0.289675\pi$
$648$		0			0
$649$		−	22.0478i		−	0.865451i
$650$	1.07317	−	1.85879i	0.0420932	−	0.0729076i
$651$		0			0
$652$	17.6508	+	30.5721i	0.691259	+	1.19729i
$653$	−9.41757	+	5.43723i	−0.368538	+	0.212775i	−0.672819	−	0.739807i	$-0.734917\pi$
$653$	−9.41757	+	5.43723i	−0.368538	+	0.212775i	0.304282	+	0.952582i	$0.401584\pi$
$654$		0			0
$655$	3.07279	−	5.32223i	0.120064	−	0.207957i
$656$	9.43770			0.368480
$657$		0			0
$658$	−17.8009	+	5.75868i	−0.693952	+	0.224497i
$659$	−10.0790	−	5.81909i	−0.392620	−	0.226679i	0.290675	−	0.956822i	$-0.406120\pi$
$659$	−10.0790	−	5.81909i	−0.392620	−	0.226679i	−0.683295	+	0.730143i	$0.739454\pi$
$660$		0			0
$661$	25.1880	−	14.5423i	0.979700	−	0.565630i	0.0775208	−	0.996991i	$-0.475300\pi$
$661$	25.1880	−	14.5423i	0.979700	−	0.565630i	0.902180	+	0.431360i	$0.141966\pi$
$662$	10.2871	−	5.93924i	0.399818	−	0.230835i
$663$		0			0
$664$	14.4121	+	8.32084i	0.559299	+	0.322911i
$665$	9.94434	−	3.21704i	0.385625	−	0.124752i
$666$		0			0
$667$	−16.0768			−0.622495
$668$	15.4736	−	26.8010i	0.598691	−	1.03696i
$669$		0			0
$670$	5.44446	−	3.14336i	0.210338	−	0.121439i
$671$	5.67104	+	9.82254i	0.218928	+	0.379195i
$672$		0			0
$673$	−0.591588	+	1.02466i	−0.0228040	+	0.0394977i	−0.877202	−	0.480121i	$-0.840593\pi$
$673$	−0.591588	+	1.02466i	−0.0228040	+	0.0394977i	0.854398	+	0.519619i	$0.173926\pi$
$674$			5.06525i			0.195106i
$675$		0			0
$676$	2.69516			0.103660
$677$	−20.4807	+	35.4736i	−0.787137	+	1.36336i	0.140577	+	0.990070i	$0.455104\pi$
$677$	−20.4807	+	35.4736i	−0.787137	+	1.36336i	−0.927714	+	0.373291i	$0.878229\pi$
$678$		0			0
$679$	0.534346	+	0.482367i	0.0205063	+	0.0185115i
$680$	5.17994	−	2.99064i	0.198642	−	0.114686i
$681$		0			0
$682$	−9.27871	−	5.35707i	−0.355300	−	0.205133i
$683$			2.27228i			0.0869463i	0.999055	+	0.0434731i	$0.0138423\pi$
$683$			2.27228i			0.0869463i	−0.999055	+	0.0434731i	$0.986158\pi$
$684$		0			0
$685$		−	8.86371i		−	0.338665i
$686$	−4.76657	−	10.8175i	−0.181988	−	0.413015i
$687$		0			0
$688$	−8.24556	−	14.2817i	−0.314359	−	0.544486i
$689$	−14.4195	−	24.9752i	−0.549338	−	0.951481i
$690$		0			0
$691$	42.1997	+	24.3640i	1.60535	+	0.926851i	0.990391	+	0.138293i	$0.0441617\pi$
$691$	42.1997	+	24.3640i	1.60535	+	0.926851i	0.614961	+	0.788557i	$0.289172\pi$
$692$	−2.88580			−0.109702
$693$		0			0
$694$	−18.1166			−0.687698
$695$	−8.24478	−	4.76013i	−0.312742	−	0.180562i
$696$		0			0
$697$	−7.14968	−	12.3836i	−0.270813	−	0.469062i
$698$	1.55529	+	2.69383i	0.0588684	+	0.101963i
$699$		0			0
$700$	4.12042	+	0.881337i	0.155737	+	0.0333114i
$701$		−	4.12119i		−	0.155655i	−0.996967	−	0.0778276i	$-0.975202\pi$
$701$		−	4.12119i		−	0.155655i	0.996967	−	0.0778276i	$-0.0247984\pi$
$702$		0			0
$703$			29.5401i			1.11413i
$704$	−0.413429	−	0.238693i	−0.0155817	−	0.00899610i
$705$		0			0
$706$	−12.5832	+	7.26490i	−0.473574	+	0.273418i
$707$	−5.03136	+	5.57353i	−0.189224	+	0.209614i
$708$		0			0
$709$	6.53830	−	11.3247i	0.245551	−	0.425307i	−0.716735	−	0.697345i	$-0.754364\pi$
$709$	6.53830	−	11.3247i	0.245551	−	0.425307i	0.962286	+	0.272038i	$0.0876978\pi$
$710$	−4.28516			−0.160819
$711$		0			0
$712$			27.0713i			1.01454i
$713$	−17.4658	+	30.2516i	−0.654099	+	1.13293i
$714$		0			0
$715$	−4.32695	−	7.49449i	−0.161819	−	0.280278i
$716$	−8.53859	+	4.92976i	−0.319102	+	0.184234i
$717$		0			0
$718$	5.48932	−	9.50778i	0.204860	−	0.354827i
$719$	30.0774			1.12170			0.560849	−	0.827918i	$-0.310475\pi$
$719$	30.0774			1.12170			0.560849	+	0.827918i	$0.310475\pi$
$720$		0			0
$721$	−30.5305	+	9.87676i	−1.13701	+	0.367830i
$722$	−1.87631	−	1.08329i	−0.0698289	−	0.0403158i
$723$		0			0
$724$	16.3150	−	9.41949i	0.606344	−	0.350073i
$725$	−2.59976	+	1.50097i	−0.0965525	+	0.0557446i
$726$		0			0
$727$	4.91269	+	2.83634i	0.182202	+	0.105194i	0.588327	−	0.808623i	$-0.299787\pi$
$727$	4.91269	+	2.83634i	0.182202	+	0.105194i	−0.406125	+	0.913818i	$0.633120\pi$
$728$	6.27948	+	19.4108i	0.232733	+	0.719411i
$729$		0			0
$730$	4.16090			0.154002
$731$	−12.4931	+	21.6387i	−0.462074	+	0.800336i
$732$		0			0
$733$	−33.7147	+	19.4652i	−1.24528	+	0.718963i	−0.970165	−	0.242447i	$-0.922050\pi$
$733$	−33.7147	+	19.4652i	−1.24528	+	0.718963i	−0.275117	+	0.961411i	$0.588716\pi$
$734$	−1.06258	−	1.84044i	−0.0392204	−	0.0679317i
$735$		0			0
$736$	−15.2229	+	26.3669i	−0.561125	+	0.971897i
$737$		−	25.3476i		−	0.933691i
$738$		0			0
$739$	11.1939			0.411773			0.205886	−	0.978576i	$-0.433992\pi$
$739$	11.1939			0.411773			0.205886	+	0.978576i	$0.433992\pi$
$740$	−5.95454	+	10.3136i	−0.218893	+	0.379134i
$741$		0			0
$742$	−9.70465	+	10.7504i	−0.356269	+	0.394660i
$743$	32.7743	−	18.9223i	1.20237	−	0.694191i	0.241291	−	0.970453i	$-0.422429\pi$
$743$	32.7743	−	18.9223i	1.20237	−	0.694191i	0.961082	+	0.276262i	$0.0890957\pi$
$744$		0			0
$745$	−1.86456	−	1.07650i	−0.0683120	−	0.0394400i
$746$		−	10.2611i		−	0.375686i
$747$		0			0
$748$		−	10.6907i		−	0.390889i
$749$	−5.69226	+	26.6124i	−0.207991	+	0.972396i
$750$		0			0
$751$	13.4719	+	23.3340i	0.491596	+	0.851468i	0.999953	−	0.00967764i	$-0.00308054\pi$
$751$	13.4719	+	23.3340i	0.491596	+	0.851468i	−0.508358	+	0.861146i	$0.669747\pi$
$752$	9.53649	+	16.5177i	0.347760	+	0.602338i
$753$		0			0
$754$	−5.57996	−	3.22159i	−0.203210	−	0.117323i
$755$	−21.6176			−0.786745
$756$		0			0
$757$	−24.7154			−0.898295			−0.449147	−	0.893458i	$-0.648272\pi$
$757$	−24.7154			−0.898295			−0.449147	+	0.893458i	$0.648272\pi$
$758$	9.37599	+	5.41323i	0.340551	+	0.196617i
$759$		0			0
$760$	4.52929	+	7.84497i	0.164295	+	0.284567i
$761$	24.6236	+	42.6493i	0.892604	+	1.54604i	0.836743	+	0.547596i	$0.184457\pi$
$761$	24.6236	+	42.6493i	0.892604	+	1.54604i	0.0558612	+	0.998439i	$0.482210\pi$
$762$		0			0
$763$	46.4669	+	9.93903i	1.68221	+	0.359817i
$764$		−	15.9177i		−	0.575880i
$765$		0			0
$766$		−	2.06510i		−	0.0746150i
$767$	−24.9493	−	14.4045i	−0.900866	−	0.520115i
$768$		0			0
$769$	−14.9460	+	8.62908i	−0.538967	+	0.311173i	−0.744660	−	0.667444i	$-0.767388\pi$
$769$	−14.9460	+	8.62908i	−0.538967	+	0.311173i	0.205693	+	0.978617i	$0.434055\pi$
$770$	−2.91214	+	3.22595i	−0.104946	+	0.116255i
$771$		0			0
$772$	3.27803	−	5.67772i	0.117979	−	0.204346i
$773$	−8.12844			−0.292360			−0.146180	−	0.989258i	$-0.546698\pi$
$773$	−8.12844			−0.292360			−0.146180	+	0.989258i	$0.546698\pi$
$774$		0			0
$775$			6.52261i			0.234299i
$776$	−0.311954	+	0.540321i	−0.0111985	+	0.0193964i
$777$		0			0
$778$	5.19988	+	9.00646i	0.186425	+	0.322897i
$779$	18.7549	−	10.8281i	0.671962	−	0.387958i
$780$		0			0
$781$	−8.63874	+	14.9627i	−0.309118	+	0.535409i
$782$	8.91626			0.318845
$783$		0			0
$784$	−9.76753	+	7.05839i	−0.348840	+	0.252085i
$785$	2.85973	+	1.65107i	0.102068	+	0.0589291i
$786$		0			0
$787$	−23.3372	+	13.4737i	−0.831880	+	0.480286i	−0.854496	−	0.519458i	$-0.826134\pi$
$787$	−23.3372	+	13.4737i	−0.831880	+	0.480286i	0.0226158	+	0.999744i	$0.492801\pi$
$788$	−5.48947	+	3.16935i	−0.195554	+	0.112903i
$789$		0			0
$790$	−1.18523	−	0.684291i	−0.0421685	−	0.0243460i
$791$	−45.4117	+	14.6909i	−1.61465	+	0.522348i
$792$		0			0
$793$	14.8203			0.526283
$794$	−11.4838	+	19.8905i	−0.407543	+	0.705886i
$795$		0			0
$796$	34.6187	−	19.9871i	1.22703	−	0.708425i
$797$	13.5679	+	23.5003i	0.480601	+	0.832425i	0.999752	−	0.0222575i	$-0.00708535\pi$
$797$	13.5679	+	23.5003i	0.480601	+	0.832425i	−0.519152	+	0.854682i	$0.673752\pi$
$798$		0			0
$799$	14.4490	−	25.0265i	0.511170	−	0.885372i
$800$			5.68501i			0.200995i
$801$		0			0
$802$	−1.14529			−0.0404415
$803$	8.38823	−	14.5288i	0.296014	−	0.512711i
$804$		0			0
$805$	10.5176	+	9.49454i	0.370698	+	0.334639i
$806$	−12.1241	+	6.99987i	−0.427054	+	0.246560i
$807$		0			0
$808$	−5.63585	−	3.25386i	−0.198269	−	0.114470i
$809$			34.5525i			1.21480i	0.794395	+	0.607401i	$0.207788\pi$
$809$			34.5525i			1.21480i	−0.794395	+	0.607401i	$0.792212\pi$
$810$		0			0
$811$		−	24.0030i		−	0.842859i	−0.906861	−	0.421430i	$-0.861528\pi$
$811$		−	24.0030i		−	0.842859i	0.906861	−	0.421430i	$-0.138472\pi$
$812$	2.64572	−	12.3692i	0.0928465	−	0.434075i
$813$		0			0
$814$	−6.14155	−	10.6375i	−0.215261	−	0.372843i
$815$	11.0830	+	19.1964i	0.388221	+	0.672419i
$816$		0			0
$817$	−32.7716	−	18.9207i	−1.14653	−	0.661951i
$818$	−4.03897			−0.141219
$819$		0			0
$820$	8.73070			0.304889
$821$	−7.98520	−	4.61026i	−0.278685	−	0.160899i	0.354143	−	0.935191i	$-0.384773\pi$
$821$	−7.98520	−	4.61026i	−0.278685	−	0.160899i	−0.632828	+	0.774292i	$0.718106\pi$
$822$		0			0
$823$	−0.276082	−	0.478188i	−0.00962362	−	0.0166686i	0.861173	−	0.508311i	$-0.169730\pi$
$823$	−0.276082	−	0.478188i	−0.00962362	−	0.0166686i	−0.870797	+	0.491643i	$0.836397\pi$
$824$	−13.9055	−	24.0851i	−0.484423	−	0.839045i
$825$		0			0
$826$	−3.02613	+	14.1477i	−0.105292	+	0.492262i
$827$		−	27.9487i		−	0.971871i	−0.873995	−	0.485935i	$-0.838479\pi$
$827$		−	27.9487i		−	0.971871i	0.873995	−	0.485935i	$-0.161521\pi$
$828$		0			0
$829$		−	7.35170i		−	0.255335i	−0.991817	−	0.127668i	$-0.959251\pi$
$829$		−	7.35170i		−	0.255335i	0.991817	−	0.127668i	$-0.0407491\pi$
$830$	4.01161	+	2.31611i	0.139245	+	0.0803932i
$831$		0			0
$832$	−0.540211	+	0.311891i	−0.0187285	+	0.0108129i
$833$	16.6612	+	7.46920i	0.577275	+	0.258792i
$834$		0			0
$835$	9.71593	−	16.8285i	0.336234	−	0.582374i
$836$	16.1909			0.559974
$837$		0			0
$838$			12.4901i			0.431464i
$839$	−16.1284	+	27.9352i	−0.556815	+	0.964431i	0.440945	+	0.897534i	$0.354643\pi$
$839$	−16.1284	+	27.9352i	−0.556815	+	0.964431i	−0.997760	+	0.0668972i	$0.978690\pi$
$840$		0			0
$841$	−9.99418	−	17.3104i	−0.344627	−	0.596911i
$842$	−12.8466	+	7.41700i	−0.442724	+	0.255607i
$843$		0			0
$844$	−9.78149	+	16.9420i	−0.336693	+	0.583169i
$845$	1.69230			0.0582170
$846$		0			0
$847$	−3.56453	−	11.0185i	−0.122479	−	0.378599i
$848$	12.7863	+	7.38219i	0.439084	+	0.253506i
$849$		0			0
$850$	1.44184	−	0.832444i	0.0494546	−	0.0285526i
$851$	−34.6817	+	20.0235i	−1.18887	+	0.686396i
$852$		0			0
$853$	−31.9904	−	18.4696i	−1.09533	−	0.632389i	−0.160339	−	0.987062i	$-0.551259\pi$
$853$	−31.9904	−	18.4696i	−1.09533	−	0.632389i	−0.934990	+	0.354674i	$0.884592\pi$
$854$	−2.29085	−	7.08134i	−0.0783912	−	0.242319i
$855$		0			0
$856$	−23.5868			−0.806181
$857$	9.79305	−	16.9621i	0.334524	−	0.579413i	−0.648869	−	0.760900i	$-0.724758\pi$
$857$	9.79305	−	16.9621i	0.334524	−	0.579413i	0.983393	+	0.181487i	$0.0580910\pi$
$858$		0			0
$859$	−49.4732	+	28.5634i	−1.68800	+	0.974570i	−0.731960	+	0.681348i	$0.761394\pi$
$859$	−49.4732	+	28.5634i	−1.68800	+	0.974570i	−0.956044	+	0.293222i	$0.905272\pi$
$860$	−7.62786	−	13.2118i	−0.260108	−	0.450520i
$861$		0			0
$862$	2.71444	−	4.70154i	0.0924541	−	0.160135i
$863$			11.2281i			0.382208i	0.981570	+	0.191104i	$0.0612067\pi$
$863$			11.2281i			0.382208i	−0.981570	+	0.191104i	$0.938793\pi$
$864$		0			0
$865$	−1.81201			−0.0616101
$866$	−2.26605	+	3.92491i	−0.0770035	+	0.133374i
$867$		0			0
$868$	−20.4009	−	18.4164i	−0.692450	−	0.625092i
$869$	−4.77875	+	2.75901i	−0.162108	+	0.0935931i
$870$		0			0
$871$	−28.6834	−	16.5604i	−0.971899	−	0.561126i
$872$			41.1840i			1.39467i
$873$		0			0
$874$			13.5036i			0.456766i
$875$	2.58723	+	0.553395i	0.0874643	+	0.0187082i
$876$		0			0
$877$	−1.20428	−	2.08587i	−0.0406656	−	0.0704348i	0.844976	−	0.534804i	$-0.179614\pi$
$877$	−1.20428	−	2.08587i	−0.0406656	−	0.0704348i	−0.885642	+	0.464369i	$0.846281\pi$
$878$	−2.34592	−	4.06325i	−0.0791709	−	0.137128i
$879$		0			0
$880$	3.83688	+	2.21523i	0.129341	+	0.0746752i
$881$	−44.5262			−1.50013			−0.750063	−	0.661367i	$-0.769977\pi$
$881$	−44.5262			−1.50013			−0.750063	+	0.661367i	$0.769977\pi$
$882$		0			0
$883$	36.5403			1.22968			0.614840	−	0.788652i	$-0.289221\pi$
$883$	36.5403			1.22968			0.614840	+	0.788652i	$0.289221\pi$
$884$	−12.0976	−	6.98453i	−0.406885	−	0.234915i
$885$		0			0
$886$	−9.81140	−	16.9938i	−0.329621	−	0.570920i
$887$	−25.4468	−	44.0752i	−0.854421	−	1.47990i	−0.877182	−	0.480159i	$-0.840579\pi$
$887$	−25.4468	−	44.0752i	−0.854421	−	1.47990i	0.0227610	−	0.999741i	$-0.492754\pi$
$888$		0			0
$889$	−40.5588	−	8.67532i	−1.36030	−	0.290961i
$890$			7.53529i			0.252584i
$891$		0			0
$892$			30.4854i			1.02073i
$893$	37.9023	+	21.8829i	1.26835	+	0.732284i
$894$		0			0
$895$	−5.36142	+	3.09542i	−0.179212	+	0.103468i
$896$	−22.0972	−	19.9476i	−0.738214	−	0.666404i
$897$		0			0
$898$	10.0522	−	17.4109i	0.335446	−	0.581009i
$899$	19.5805			0.653045
$900$		0			0
$901$		−	22.3700i		−	0.745252i
$902$	−4.50245	+	7.79847i	−0.149915	+	0.259661i
$903$		0			0
$904$	−20.6834	−	35.8247i	−0.687920	−	1.19151i
$905$	10.2443	−	5.91455i	0.340532	−	0.196606i
$906$		0			0
$907$	3.82592	−	6.62669i	0.127038	−	0.220036i	−0.795490	−	0.605967i	$-0.792786\pi$
$907$	3.82592	−	6.62669i	0.127038	−	0.220036i	0.922528	+	0.385931i	$0.126120\pi$
$908$	17.1931			0.570572
$909$		0			0
$910$	1.74789	+	5.40299i	0.0579421	+	0.179107i
$911$	−7.28269	−	4.20466i	−0.241286	−	0.139307i	0.374482	−	0.927234i	$-0.377821\pi$
$911$	−7.28269	−	4.20466i	−0.241286	−	0.139307i	−0.615768	+	0.787928i	$0.711154\pi$
$912$		0			0
$913$	16.1745	−	9.33838i	0.535299	−	0.309055i
$914$	−6.12953	+	3.53888i	−0.202747	+	0.117056i
$915$		0			0
$916$	1.74514	+	1.00756i	0.0576612	+	0.0332907i
$917$	5.00472	+	15.4703i	0.165270	+	0.510874i
$918$		0			0
$919$	5.71809			0.188622			0.0943112	−	0.995543i	$-0.469935\pi$
$919$	5.71809			0.188622			0.0943112	+	0.995543i	$0.469935\pi$
$920$	−6.14027	+	10.6353i	−0.202439	+	0.350634i
$921$		0			0
$922$	−21.3538	+	12.3286i	−0.703249	+	0.406021i
$923$	11.2879	+	19.5512i	0.371545	+	0.643536i
$924$		0			0
$925$	−3.73888	+	6.47594i	−0.122934	+	0.212928i
$926$		−	5.09772i		−	0.167521i
$927$		0			0
$928$	17.0661			0.560221
$929$	−6.63177	+	11.4866i	−0.217581	+	0.376862i	−0.954068	−	0.299590i	$-0.903150\pi$
$929$	−6.63177	+	11.4866i	−0.217581	+	0.376862i	0.736487	+	0.676452i	$0.236483\pi$
$930$		0			0
$931$	−11.3120	+	25.2332i	−0.370737	+	0.826984i
$932$	−3.67488	+	2.12169i	−0.120375	+	0.0694983i
$933$		0			0
$934$	6.21374	+	3.58751i	0.203320	+	0.117387i
$935$		−	6.71271i		−	0.219529i
$936$		0			0
$937$		−	10.8468i		−	0.354349i	−0.984179	−	0.177174i	$-0.943304\pi$
$937$		−	10.8468i		−	0.354349i	0.984179	−	0.177174i	$-0.0566957\pi$
$938$	−3.47904	+	16.2652i	−0.113595	+	0.531077i
$939$		0			0
$940$	8.82208	+	15.2803i	0.287745	+	0.498388i
$941$	2.15398	+	3.73079i	0.0702176	+	0.121620i	0.898997	−	0.437956i	$-0.144297\pi$
$941$	2.15398	+	3.73079i	0.0702176	+	0.121620i	−0.828779	+	0.559576i	$0.810964\pi$
$942$		0			0
$943$	25.4256	+	14.6795i	0.827970	+	0.478029i
$944$	14.7490			0.480040
$945$		0			0
$946$	15.7348			0.511584
$947$	−33.1900	−	19.1623i	−1.07853	−	0.622690i	−0.148031	−	0.988983i	$-0.547294\pi$
$947$	−33.1900	−	19.1623i	−1.07853	−	0.622690i	−0.930500	+	0.366293i	$0.880627\pi$
$948$		0			0
$949$	−10.9606	−	18.9842i	−0.355795	−	0.616255i
$950$	1.26073	+	2.18365i	0.0409035	+	0.0708469i
$951$		0			0
$952$	−3.31001	+	15.4749i	−0.107278	+	0.501545i
$953$			44.4892i			1.44115i	0.693379	+	0.720573i	$0.256121\pi$
$953$			44.4892i			1.44115i	−0.693379	+	0.720573i	$0.743879\pi$
$954$		0			0
$955$		−	9.99477i		−	0.323423i
$956$	7.18103	+	4.14597i	0.232251	+	0.134090i
$957$		0			0
$958$	8.13104	−	4.69446i	0.262702	−	0.151671i
$959$	17.4075	+	15.7142i	0.562118	+	0.507438i
$960$		0			0
$961$	5.77219	−	9.99773i	0.186200	−	0.322507i
$962$	−16.0498			−0.517468
$963$		0			0
$964$			2.05594i			0.0662175i
$965$	2.05829	−	3.56507i	0.0662588	−	0.114764i
$966$		0			0
$967$	−11.5983	−	20.0889i	−0.372977	−	0.646016i	0.617045	−	0.786928i	$-0.288330\pi$
$967$	−11.5983	−	20.0889i	−0.372977	−	0.646016i	−0.990022	+	0.140912i	$0.954996\pi$
$968$	8.69233	−	5.01852i	0.279382	−	0.161301i
$969$		0			0
$970$	−0.0868325	+	0.150398i	−0.00278802	+	0.00482900i
$971$	17.7740			0.570394			0.285197	−	0.958469i	$-0.407941\pi$
$971$	17.7740			0.570394			0.285197	+	0.958469i	$0.407941\pi$
$972$		0			0
$973$	23.9654	−	7.75292i	0.768295	−	0.248547i
$974$	20.2631	+	11.6989i	0.649273	+	0.374858i
$975$		0			0
$976$	−6.57087	+	3.79369i	−0.210328	+	0.121433i
$977$	−15.8434	+	9.14717i	−0.506874	+	0.292644i	−0.731548	−	0.681790i	$-0.761202\pi$
$977$	−15.8434	+	9.14717i	−0.506874	+	0.292644i	0.224674	+	0.974434i	$0.427868\pi$
$978$		0			0
$979$	26.3114	+	15.1909i	0.840915	+	0.485503i
$980$	−9.03582	+	6.52962i	−0.288639	+	0.208581i
$981$		0			0
$982$	20.4664			0.653109
$983$	−5.38132	+	9.32072i	−0.171637	+	0.297285i	−0.938992	−	0.343938i	$-0.888239\pi$
$983$	−5.38132	+	9.32072i	−0.171637	+	0.297285i	0.767355	+	0.641222i	$0.221572\pi$
$984$		0			0
$985$	−3.44687	+	1.99005i	−0.109826	+	0.0634082i
$986$	−2.49895	−	4.32830i	−0.0795827	−	0.137841i
$987$		0			0
$988$	10.5780	−	18.3216i	0.336531	−	0.582889i
$989$		−	51.3008i		−	1.63127i
$990$		0			0
$991$	−50.4106			−1.60135			−0.800673	−	0.599101i	$-0.795525\pi$
$991$	−50.4106			−1.60135			−0.800673	+	0.599101i	$0.795525\pi$
$992$	18.5405	−	32.1132i	0.588663	−	1.01959i
$993$		0			0
$994$	7.59703	−	8.41566i	0.240963	−	0.266929i
$995$	21.7373	−	12.5500i	0.689117	−	0.397862i
$996$		0			0
$997$	−47.9386	−	27.6774i	−1.51823	−	0.876551i	−0.999770	−	0.0214505i	$-0.993172\pi$
$997$	−47.9386	−	27.6774i	−1.51823	−	0.876551i	−0.518462	−	0.855101i	$-0.673495\pi$
$998$		−	17.8118i		−	0.563822i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bl.i.251.7		24
3.2	odd	2		315.2.bl.i.146.6	yes	24
7.6	odd	2		945.2.bl.j.251.7		24
9.4	even	3		315.2.bl.j.41.6	yes	24
9.5	odd	6		945.2.bl.j.881.7		24
21.20	even	2		315.2.bl.j.146.6	yes	24
63.13	odd	6		315.2.bl.i.41.6	✓	24
63.41	even	6	inner	945.2.bl.i.881.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.6	✓	24	63.13	odd	6
315.2.bl.i.146.6	yes	24	3.2	odd	2
315.2.bl.j.41.6	yes	24	9.4	even	3
315.2.bl.j.146.6	yes	24	21.20	even	2
945.2.bl.i.251.7		24	1.1	even	1	trivial
945.2.bl.i.881.7		24	63.41	even	6	inner
945.2.bl.j.251.7		24	7.6	odd	2
945.2.bl.j.881.7		24	9.5	odd	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.552767 - 0.319140i) q^{2} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.58723 + 0.553395i) q^{7} +2.29308i q^{8} +O(q^{10})\)	\(q+(-0.552767 - 0.319140i) q^{2} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.58723 + 0.553395i) q^{7} +2.29308i q^{8} +0.638280i q^{10} +(2.22872 + 1.28675i) q^{11} +(2.91218 - 1.68135i) q^{13} +(-1.25352 - 1.13159i) q^{14} +(-0.860783 + 1.49092i) q^{16} +2.60840 q^{17} +3.95039i q^{19} +(-0.796299 + 1.37923i) q^{20} +(-0.821308 - 1.42255i) q^{22} +(-4.63797 + 2.67773i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.14634 q^{26} +(-1.29695 - 4.00905i) q^{28} +(2.59976 + 1.50097i) q^{29} +(5.64874 - 3.26130i) q^{31} +(4.92336 - 2.84251i) q^{32} +(-1.44184 - 0.832444i) q^{34} +(-0.814360 - 2.51730i) q^{35} +7.47777 q^{37} +(1.26073 - 2.18365i) q^{38} +(1.98587 - 1.14654i) q^{40} +(-2.74102 - 4.74759i) q^{41} +(-4.78957 + 8.29578i) q^{43} -4.09855i q^{44} +3.41829 q^{46} +(5.53943 - 9.59457i) q^{47} +(6.38751 + 2.86352i) q^{49} +(0.552767 - 0.319140i) q^{50} +(-4.63793 - 2.67771i) q^{52} -8.57614i q^{53} -2.57350i q^{55} +(-1.26898 + 5.93274i) q^{56} +(-0.958039 - 1.65937i) q^{58} +(-4.28361 - 7.41944i) q^{59} +(3.81680 + 2.20363i) q^{61} -4.16325 q^{62} -0.185501 q^{64} +(-2.91218 - 1.68135i) q^{65} +(-4.92473 - 8.52989i) q^{67} +(-2.07706 - 3.59758i) q^{68} +(-0.353221 + 1.65138i) q^{70} +6.71360i q^{71} -6.51892i q^{73} +(-4.13346 - 2.38646i) q^{74} +(5.44850 - 3.14569i) q^{76} +(5.05412 + 4.56248i) q^{77} +(-1.07209 + 1.85691i) q^{79} +1.72157 q^{80} +3.49908i q^{82} +(3.62867 - 6.28503i) q^{83} +(-1.30420 - 2.25894i) q^{85} +(5.29503 - 3.05709i) q^{86} +(-2.95063 + 5.11064i) q^{88} +11.8056 q^{89} +(8.46492 - 2.73844i) q^{91} +(7.38642 + 4.26455i) q^{92} +(-6.12403 + 3.53571i) q^{94} +(3.42114 - 1.97520i) q^{95} +(0.235631 + 0.136041i) q^{97} +(-2.61694 - 3.62137i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 18 q^{4} - 12 q^{5}+O(q^{10}) \) 24 * q - 6 * q^2 + 18 * q^4 - 12 * q^5	\( 24 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 9 q^{11} - 3 q^{13} - 9 q^{14} - 18 q^{16} + 18 q^{17} + 18 q^{20} - 9 q^{22} - 9 q^{23} - 12 q^{25} - 18 q^{26} - 9 q^{28} - 9 q^{29} + 42 q^{31} - 18 q^{32} + 39 q^{34} - 9 q^{35} - 12 q^{38} + 6 q^{40} - 33 q^{41} + 18 q^{43} - 30 q^{46} + 6 q^{50} - 129 q^{52} - 6 q^{56} - 15 q^{58} + 12 q^{59} + 15 q^{61} + 12 q^{62} - 60 q^{64} + 3 q^{65} - 15 q^{67} + 9 q^{68} + 18 q^{70} + 18 q^{74} - 54 q^{76} + 57 q^{77} + 21 q^{79} + 36 q^{80} - 30 q^{83} - 9 q^{85} + 102 q^{86} - 9 q^{88} + 102 q^{89} + 42 q^{91} + 3 q^{92} + 156 q^{94} + 18 q^{95} + 45 q^{97} + 3 q^{98}+O(q^{100}) \) 24 * q - 6 * q^2 + 18 * q^4 - 12 * q^5 - 9 * q^11 - 3 * q^13 - 9 * q^14 - 18 * q^16 + 18 * q^17 + 18 * q^20 - 9 * q^22 - 9 * q^23 - 12 * q^25 - 18 * q^26 - 9 * q^28 - 9 * q^29 + 42 * q^31 - 18 * q^32 + 39 * q^34 - 9 * q^35 - 12 * q^38 + 6 * q^40 - 33 * q^41 + 18 * q^43 - 30 * q^46 + 6 * q^50 - 129 * q^52 - 6 * q^56 - 15 * q^58 + 12 * q^59 + 15 * q^61 + 12 * q^62 - 60 * q^64 + 3 * q^65 - 15 * q^67 + 9 * q^68 + 18 * q^70 + 18 * q^74 - 54 * q^76 + 57 * q^77 + 21 * q^79 + 36 * q^80 - 30 * q^83 - 9 * q^85 + 102 * q^86 - 9 * q^88 + 102 * q^89 + 42 * q^91 + 3 * q^92 + 156 * q^94 + 18 * q^95 + 45 * q^97 + 3 * q^98

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