LMFDB - Embedded newform 276.2.i.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$-0.0616736 + 0.0396352i$ of defining polynomial
Character	$\chi$	$=$	276.49
Dual form			276.2.i.a.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(-2.38152 + 2.74842i) q^{5} +(-3.67577 + 2.36227i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(-2.38152 + 2.74842i) q^{5} +(-3.67577 + 2.36227i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.389333 + 2.70787i) q^{11} +(-5.17334 - 3.32470i) q^{13} +(1.51073 + 3.30804i) q^{15} +(1.26223 + 0.370623i) q^{17} +(5.16792 - 1.51744i) q^{19} +(0.621829 + 4.32492i) q^{21} +(0.596495 + 4.75859i) q^{23} +(-1.17061 - 8.14175i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(6.27083 + 1.84128i) q^{29} +(1.69960 + 3.72161i) q^{31} +(2.30143 + 1.47904i) q^{33} +(2.26140 - 15.7284i) q^{35} +(-3.77633 - 4.35811i) q^{37} +(-5.17334 + 3.32470i) q^{39} +(-5.09298 + 5.87761i) q^{41} +(-3.90999 + 8.56169i) q^{43} +3.63668 q^{45} -5.07522 q^{47} +(5.02302 - 10.9989i) q^{49} +(0.861478 - 0.994198i) q^{51} +(3.43531 - 2.20774i) q^{53} +(-6.51516 - 7.51890i) q^{55} +(0.766521 - 5.33127i) q^{57} +(-2.90665 - 1.86799i) q^{59} +(-1.10276 - 2.41471i) q^{61} +(4.19240 + 1.23100i) q^{63} +(21.4581 - 6.30067i) q^{65} +(0.627040 + 4.36116i) q^{67} +(4.57636 + 1.43420i) q^{69} +(1.45569 + 10.1245i) q^{71} +(6.23284 - 1.83013i) q^{73} +(-7.89228 - 2.31738i) q^{75} +(-4.96562 - 10.8732i) q^{77} +(-2.84247 - 1.82675i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(4.71120 + 5.43702i) q^{83} +(-4.02464 + 2.58648i) q^{85} +(4.27989 - 4.93925i) q^{87} +(-4.07521 + 8.92347i) q^{89} +26.8698 q^{91} +4.09134 q^{93} +(-8.13695 + 17.8174i) q^{95} +(-1.60428 + 1.85144i) q^{97} +(2.30143 - 1.47904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$	$1$

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
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	−2.38152	+	2.74842i	−1.06505	+	1.22913i	−0.0926766	+	0.995696i	$0.529542\pi$
$5$	−2.38152	+	2.74842i	−1.06505	+	1.22913i	−0.972372	+	0.233436i	$0.925003\pi$
$6$		0			0
$7$	−3.67577	+	2.36227i	−1.38931	+	0.892855i	−0.999606	−	0.0280858i	$-0.991059\pi$
$7$	−3.67577	+	2.36227i	−1.38931	+	0.892855i	−0.389703	+	0.920940i	$0.627422\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−0.389333	+	2.70787i	−0.117388	+	0.816453i	0.843025	+	0.537874i	$0.180772\pi$
$11$	−0.389333	+	2.70787i	−0.117388	+	0.816453i	−0.960413	+	0.278579i	$0.910137\pi$
$12$		0			0
$13$	−5.17334	−	3.32470i	−1.43483	−	0.922107i	−0.999764	−	0.0217064i	$-0.993090\pi$
$13$	−5.17334	−	3.32470i	−1.43483	−	0.922107i	−0.435062	−	0.900401i	$-0.643274\pi$
$14$		0			0
$15$	1.51073	+	3.30804i	0.390070	+	0.854133i
$16$		0			0
$17$	1.26223	+	0.370623i	0.306135	+	0.0898892i	0.431192	−	0.902260i	$-0.358093\pi$
$17$	1.26223	+	0.370623i	0.306135	+	0.0898892i	−0.125057	+	0.992150i	$0.539911\pi$
$18$		0			0
$19$	5.16792	−	1.51744i	1.18560	−	0.348124i	0.371271	−	0.928525i	$-0.378922\pi$
$19$	5.16792	−	1.51744i	1.18560	−	0.348124i	0.814331	+	0.580400i	$0.197104\pi$
$20$		0			0
$21$	0.621829	+	4.32492i	0.135694	+	0.943774i
$22$		0			0
$23$	0.596495	+	4.75859i	0.124378	+	0.992235i
$23$	0.596495	+	4.75859i	0.124378	+	0.992235i
$24$		0			0
$25$	−1.17061	−	8.14175i	−0.234121	−	1.62835i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	6.27083	+	1.84128i	1.16446	+	0.341917i	0.806166	−	0.591690i	$-0.201539\pi$
$29$	6.27083	+	1.84128i	1.16446	+	0.341917i	0.358298	+	0.933607i	$0.383357\pi$
$30$		0			0
$31$	1.69960	+	3.72161i	0.305258	+	0.668422i	0.998639	−	0.0521491i	$-0.0166071\pi$
$31$	1.69960	+	3.72161i	0.305258	+	0.668422i	−0.693381	+	0.720571i	$0.743880\pi$
$32$		0			0
$33$	2.30143	+	1.47904i	0.400627	+	0.257468i
$34$		0			0
$35$	2.26140	−	15.7284i	0.382246	−	2.65858i
$36$		0			0
$37$	−3.77633	−	4.35811i	−0.620824	−	0.716469i	0.355039	−	0.934851i	$-0.384467\pi$
$37$	−3.77633	−	4.35811i	−0.620824	−	0.716469i	−0.975863	+	0.218382i	$0.929922\pi$
$38$		0			0
$39$	−5.17334	+	3.32470i	−0.828397	+	0.532379i
$40$		0			0
$41$	−5.09298	+	5.87761i	−0.795389	+	0.917928i	−0.998119	−	0.0613065i	$-0.980473\pi$
$41$	−5.09298	+	5.87761i	−0.795389	+	0.917928i	0.202730	+	0.979235i	$0.435019\pi$
$42$		0			0
$43$	−3.90999	+	8.56169i	−0.596268	+	1.30565i	0.335311	+	0.942107i	$0.391159\pi$
$43$	−3.90999	+	8.56169i	−0.596268	+	1.30565i	−0.931579	+	0.363538i	$0.881569\pi$
$44$		0			0
$45$	3.63668			0.542125
$46$		0			0
$47$	−5.07522			−0.740297			−0.370148	−	0.928973i	$-0.620693\pi$
$47$	−5.07522			−0.740297			−0.370148	+	0.928973i	$0.620693\pi$
$48$		0			0
$49$	5.02302	−	10.9989i	0.717575	−	1.57127i
$50$		0			0
$51$	0.861478	−	0.994198i	0.120631	−	0.139216i
$52$		0			0
$53$	3.43531	−	2.20774i	0.471877	−	0.303257i	−0.283004	−	0.959119i	$-0.591331\pi$
$53$	3.43531	−	2.20774i	0.471877	−	0.303257i	0.754881	+	0.655862i	$0.227695\pi$
$54$		0			0
$55$	−6.51516	−	7.51890i	−0.878504	−	1.01385i
$56$		0			0
$57$	0.766521	−	5.33127i	0.101528	−	0.706144i
$58$		0			0
$59$	−2.90665	−	1.86799i	−0.378414	−	0.243192i	0.337582	−	0.941296i	$-0.390391\pi$
$59$	−2.90665	−	1.86799i	−0.378414	−	0.243192i	−0.715996	+	0.698104i	$0.754027\pi$
$60$		0			0
$61$	−1.10276	−	2.41471i	−0.141194	−	0.309172i	0.825803	−	0.563958i	$-0.190722\pi$
$61$	−1.10276	−	2.41471i	−0.141194	−	0.309172i	−0.966997	+	0.254786i	$0.917995\pi$
$62$		0			0
$63$	4.19240	+	1.23100i	0.528193	+	0.155091i
$64$		0			0
$65$	21.4581	−	6.30067i	2.66155	−	0.781502i
$66$		0			0
$67$	0.627040	+	4.36116i	0.0766052	+	0.532801i	0.991601	+	0.129337i	$0.0412848\pi$
$67$	0.627040	+	4.36116i	0.0766052	+	0.532801i	−0.914996	+	0.403464i	$0.867806\pi$
$68$		0			0
$69$	4.57636	+	1.43420i	0.550929	+	0.172657i
$70$		0			0
$71$	1.45569	+	10.1245i	0.172759	+	1.20156i	0.873023	+	0.487679i	$0.162156\pi$
$71$	1.45569	+	10.1245i	0.172759	+	1.20156i	−0.700264	+	0.713884i	$0.746934\pi$
$72$		0			0
$73$	6.23284	−	1.83013i	0.729499	−	0.214200i	0.104168	−	0.994560i	$-0.466782\pi$
$73$	6.23284	−	1.83013i	0.729499	−	0.214200i	0.625331	+	0.780360i	$0.284964\pi$
$74$		0			0
$75$	−7.89228	−	2.31738i	−0.911322	−	0.267588i
$76$		0			0
$77$	−4.96562	−	10.8732i	−0.565885	−	1.23912i
$78$		0			0
$79$	−2.84247	−	1.82675i	−0.319803	−	0.205525i	0.370883	−	0.928680i	$-0.379055\pi$
$79$	−2.84247	−	1.82675i	−0.319803	−	0.205525i	−0.690686	+	0.723155i	$0.742691\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	4.71120	+	5.43702i	0.517122	+	0.596790i	0.952908	−	0.303260i	$-0.0980751\pi$
$83$	4.71120	+	5.43702i	0.517122	+	0.596790i	−0.435786	+	0.900050i	$0.643530\pi$
$84$		0			0
$85$	−4.02464	+	2.58648i	−0.436534	+	0.280543i
$86$		0			0
$87$	4.27989	−	4.93925i	0.458852	−	0.529543i
$88$		0			0
$89$	−4.07521	+	8.92347i	−0.431972	+	0.945886i	0.561031	+	0.827795i	$0.310405\pi$
$89$	−4.07521	+	8.92347i	−0.431972	+	0.945886i	−0.993003	+	0.118091i	$0.962322\pi$
$90$		0			0
$91$	26.8698			2.81672
$92$		0			0
$93$	4.09134			0.424252
$94$		0			0
$95$	−8.13695	+	17.8174i	−0.834834	+	1.82803i
$96$		0			0
$97$	−1.60428	+	1.85144i	−0.162890	+	0.187985i	−0.831327	−	0.555784i	$-0.812418\pi$
$97$	−1.60428	+	1.85144i	−0.162890	+	0.187985i	0.668437	+	0.743769i	$0.266964\pi$
$98$		0			0
$99$	2.30143	−	1.47904i	0.231302	−	0.148649i
$100$		0			0
$101$	−10.7712	−	12.4307i	−1.07178	−	1.23690i	−0.970261	−	0.242063i	$-0.922176\pi$
$101$	−10.7712	−	12.4307i	−1.07178	−	1.23690i	−0.101516	−	0.994834i	$-0.532369\pi$
$102$		0			0
$103$	0.732867	−	5.09720i	0.0722115	−	0.502242i	−0.921331	−	0.388780i	$-0.872897\pi$
$103$	0.732867	−	5.09720i	0.0722115	−	0.502242i	0.993542	−	0.113463i	$-0.0361942\pi$
$104$		0			0
$105$	−13.3676	−	8.59083i	−1.30454	−	0.838380i
$106$		0			0
$107$	−3.77368	−	8.26320i	−0.364815	−	0.798833i	−0.999657	−	0.0261913i	$-0.991662\pi$
$107$	−3.77368	−	8.26320i	−0.364815	−	0.798833i	0.634842	−	0.772642i	$-0.281065\pi$
$108$		0			0
$109$	3.02983	+	0.889638i	0.290205	+	0.0852119i	0.423595	−	0.905852i	$-0.360768\pi$
$109$	3.02983	+	0.889638i	0.290205	+	0.0852119i	−0.133390	+	0.991064i	$0.542586\pi$
$110$		0			0
$111$	−5.53302	+	1.62464i	−0.525171	+	0.154204i
$112$		0			0
$113$	1.95433	+	13.5927i	0.183848	+	1.27869i	0.847559	+	0.530702i	$0.178072\pi$
$113$	1.95433	+	13.5927i	0.183848	+	1.27869i	−0.663711	+	0.747990i	$0.731019\pi$
$114$		0			0
$115$	−14.4992	−	9.69327i	−1.35206	−	0.903902i
$116$		0			0
$117$	0.875174	+	6.08697i	0.0809098	+	0.562740i
$118$		0			0
$119$	−5.51516	+	1.61940i	−0.505574	+	0.148450i
$120$		0			0
$121$	3.37345	+	0.990535i	0.306677	+	0.0900486i
$122$		0			0
$123$	3.23076	+	7.07438i	0.291308	+	0.637875i
$124$		0			0
$125$	9.86792	+	6.34173i	0.882614	+	0.567222i
$126$		0			0
$127$	−1.39341	+	9.69141i	−0.123646	+	0.859974i	0.829725	+	0.558172i	$0.188497\pi$
$127$	−1.39341	+	9.69141i	−0.123646	+	0.859974i	−0.953371	+	0.301802i	$0.902412\pi$
$128$		0			0
$129$	6.16372	+	7.11331i	0.542685	+	0.626292i
$130$		0			0
$131$	4.15454	−	2.66996i	0.362984	−	0.233275i	−0.346417	−	0.938080i	$-0.612602\pi$
$131$	4.15454	−	2.66996i	0.362984	−	0.233275i	0.709401	+	0.704805i	$0.248966\pi$
$132$		0			0
$133$	−15.4115	+	17.7858i	−1.33634	+	1.54222i
$134$		0			0
$135$	1.51073	−	3.30804i	0.130023	−	0.284711i
$136$		0			0
$137$	−21.0333			−1.79699			−0.898496	−	0.438982i	$-0.855339\pi$
$137$	−21.0333			−1.79699			−0.898496	+	0.438982i	$0.855339\pi$
$138$		0			0
$139$	−8.52288			−0.722901			−0.361451	−	0.932391i	$-0.617718\pi$
$139$	−8.52288			−0.722901			−0.361451	+	0.932391i	$0.617718\pi$
$140$		0			0
$141$	−2.10832	+	4.61658i	−0.177553	+	0.388786i
$142$		0			0
$143$	11.0170	−	12.7143i	0.921289	−	1.06322i
$144$		0			0
$145$	−19.9947	+	12.8498i	−1.66047	+	1.06712i
$146$		0			0
$147$	−7.91830	−	9.13821i	−0.653090	−	0.753707i
$148$		0			0
$149$	0.416644	−	2.89782i	0.0341328	−	0.237399i	−0.965612	−	0.259987i	$-0.916282\pi$
$149$	0.416644	−	2.89782i	0.0341328	−	0.237399i	0.999745	+	0.0225883i	$0.00719069\pi$
$150$		0			0
$151$	14.9062	+	9.57967i	1.21305	+	0.779582i	0.981167	−	0.193161i	$-0.0618739\pi$
$151$	14.9062	+	9.57967i	1.21305	+	0.779582i	0.231886	+	0.972743i	$0.425510\pi$
$152$		0			0
$153$	−0.546484	−	1.19663i	−0.0441806	−	0.0967420i
$154$		0			0
$155$	−14.2762	−	4.19188i	−1.14669	−	0.336700i
$156$		0			0
$157$	6.80773	−	1.99893i	0.543316	−	0.159532i	0.00145328	−	0.999999i	$-0.499537\pi$
$157$	6.80773	−	1.99893i	0.543316	−	0.159532i	0.541863	+	0.840467i	$0.317719\pi$
$158$		0			0
$159$	−0.581152	−	4.04200i	−0.0460883	−	0.320551i
$160$		0			0
$161$	−13.4337	−	16.0824i	−1.05872	−	1.26747i
$162$		0			0
$163$	−0.120072	−	0.835116i	−0.00940473	−	0.0654113i	0.984579	−	0.174943i	$-0.0559740\pi$
$163$	−0.120072	−	0.835116i	−0.00940473	−	0.0654113i	−0.993983	+	0.109531i	$0.965065\pi$
$164$		0			0
$165$	−9.54593	+	2.80294i	−0.743149	+	0.218208i
$166$		0			0
$167$	18.2940	+	5.37161i	1.41563	+	0.415668i	0.898023	−	0.439948i	$-0.145003\pi$
$167$	18.2940	+	5.37161i	1.41563	+	0.415668i	0.517612	+	0.855616i	$0.326821\pi$
$168$		0			0
$169$	10.3094	+	22.5744i	0.793031	+	1.73649i
$170$		0			0
$171$	−4.53107	−	2.91194i	−0.346500	−	0.222682i
$172$		0			0
$173$	2.19624	−	15.2752i	0.166977	−	1.16135i	−0.718111	−	0.695929i	$-0.754993\pi$
$173$	2.19624	−	15.2752i	0.166977	−	1.16135i	0.885088	−	0.465424i	$-0.154098\pi$
$174$		0			0
$175$	23.5359	+	27.1619i	1.77915	+	2.05324i
$176$		0			0
$177$	−2.90665	+	1.86799i	−0.218477	+	0.140407i
$178$		0			0
$179$	7.96069	−	9.18713i	0.595010	−	0.686678i	−0.375753	−	0.926720i	$-0.622616\pi$
$179$	7.96069	−	9.18713i	0.595010	−	0.686678i	0.970763	+	0.240042i	$0.0771612\pi$
$180$		0			0
$181$	−3.09564	+	6.77850i	−0.230097	+	0.503842i	−0.989100	−	0.147245i	$-0.952959\pi$
$181$	−3.09564	+	6.77850i	−0.230097	+	0.503842i	0.759003	+	0.651087i	$0.225687\pi$
$182$		0			0
$183$	−2.65460			−0.196234
$184$		0			0
$185$	20.9713			1.54184
$186$		0			0
$187$	−1.49502	+	3.27364i	−0.109327	+	0.239393i
$188$		0			0
$189$	2.86134	−	3.30217i	0.208132	−	0.240197i
$190$		0			0
$191$	−6.49183	+	4.17204i	−0.469732	+	0.301878i	−0.754009	−	0.656864i	$-0.771883\pi$
$191$	−6.49183	+	4.17204i	−0.469732	+	0.301878i	0.284277	+	0.958742i	$0.408246\pi$
$192$		0			0
$193$	5.64707	+	6.51706i	0.406485	+	0.469108i	0.921672	−	0.387969i	$-0.126823\pi$
$193$	5.64707	+	6.51706i	0.406485	+	0.469108i	−0.515188	+	0.857077i	$0.672278\pi$
$194$		0			0
$195$	3.18273	−	22.1364i	0.227920	−	1.58522i
$196$		0			0
$197$	8.19376	+	5.26581i	0.583781	+	0.375173i	0.798944	−	0.601405i	$-0.205392\pi$
$197$	8.19376	+	5.26581i	0.583781	+	0.375173i	−0.215164	+	0.976578i	$0.569028\pi$
$198$		0			0
$199$	6.61876	+	14.4931i	0.469191	+	1.02739i	0.985295	+	0.170860i	$0.0546546\pi$
$199$	6.61876	+	14.4931i	0.469191	+	1.02739i	−0.516104	+	0.856526i	$0.672618\pi$
$200$		0			0
$201$	4.22753	+	1.24132i	0.298187	+	0.0875557i
$202$		0			0
$203$	−27.3997	+	8.04528i	−1.92308	+	0.564668i
$204$		0			0
$205$	−4.02512	−	27.9953i	−0.281126	−	1.95528i
$206$		0			0
$207$	3.20568	−	3.56702i	0.222810	−	0.247925i
$208$		0			0
$209$	2.09698	+	14.5848i	0.145051	+	1.00885i
$210$		0			0
$211$	−4.96850	+	1.45888i	−0.342046	+	0.100434i	−0.448244	−	0.893911i	$-0.647950\pi$
$211$	−4.96850	+	1.45888i	−0.342046	+	0.100434i	0.106198	+	0.994345i	$0.466132\pi$
$212$		0			0
$213$	9.81433	+	2.88175i	0.672467	+	0.197454i
$214$		0			0
$215$	−14.2194	−	31.1362i	−0.969755	−	2.12347i
$216$		0			0
$217$	−15.0388	−	9.66486i	−1.02090	−	0.656093i
$218$		0			0
$219$	0.924473	−	6.42985i	0.0624701	−	0.434489i
$220$		0			0
$221$	−5.29771	−	6.11388i	−0.356363	−	0.411264i
$222$		0			0
$223$	10.9141	−	7.01405i	0.730860	−	0.469695i	−0.121539	−	0.992587i	$-0.538783\pi$
$223$	10.9141	−	7.01405i	0.730860	−	0.469695i	0.852399	+	0.522891i	$0.175147\pi$
$224$		0			0
$225$	−5.38654	+	6.21640i	−0.359103	+	0.414426i
$226$		0			0
$227$	−3.94877	+	8.64661i	−0.262089	+	0.573896i	−0.994231	−	0.107256i	$-0.965793\pi$
$227$	−3.94877	+	8.64661i	−0.262089	+	0.573896i	0.732142	+	0.681152i	$0.238521\pi$
$228$		0			0
$229$	16.4978			1.09020			0.545102	−	0.838370i	$-0.316491\pi$
$229$	16.4978			1.09020			0.545102	+	0.838370i	$0.316491\pi$
$230$		0			0
$231$	−11.9534			−0.786476
$232$		0			0
$233$	0.696931	−	1.52607i	0.0456574	−	0.0999759i	−0.885429	−	0.464775i	$-0.846135\pi$
$233$	0.696931	−	1.52607i	0.0456574	−	0.0999759i	0.931086	+	0.364799i	$0.118862\pi$
$234$		0			0
$235$	12.0867	−	13.9488i	0.788452	−	0.909922i
$236$		0			0
$237$	−2.84247	+	1.82675i	−0.184638	+	0.118660i
$238$		0			0
$239$	−0.289779	−	0.334423i	−0.0187443	−	0.0216320i	0.746300	−	0.665610i	$-0.231828\pi$
$239$	−0.289779	−	0.334423i	−0.0187443	−	0.0216320i	−0.765044	+	0.643978i	$0.777283\pi$
$240$		0			0
$241$	4.13843	−	28.7834i	0.266580	−	1.85410i	−0.213586	−	0.976924i	$-0.568514\pi$
$241$	4.13843	−	28.7834i	0.266580	−	1.85410i	0.480165	−	0.877178i	$-0.340577\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	18.2672	+	39.9995i	1.16705	+	2.55547i
$246$		0			0
$247$	−31.7804	−	9.33158i	−2.02214	−	0.593754i
$248$		0			0
$249$	6.90279	−	2.02684i	0.437446	−	0.128446i
$250$		0			0
$251$	−1.09678	−	7.62826i	−0.0692280	−	0.481491i	−0.994712	−	0.102704i	$-0.967250\pi$
$251$	−1.09678	−	7.62826i	−0.0692280	−	0.481491i	0.925484	−	0.378787i	$-0.123659\pi$
$252$		0			0
$253$	−13.1179	−	0.237447i	−0.824714	−	0.0149281i
$254$		0			0
$255$	0.680849	+	4.73541i	0.0426364	+	0.296543i
$256$		0			0
$257$	−19.2008	+	5.63786i	−1.19771	+	0.351680i	−0.818978	−	0.573825i	$-0.805459\pi$
$257$	−19.2008	+	5.63786i	−1.19771	+	0.351680i	−0.378735	+	0.925505i	$0.623641\pi$
$258$		0			0
$259$	24.1759	+	7.09869i	1.50222	+	0.441091i
$260$		0			0
$261$	−2.71497	−	5.94496i	−0.168053	−	0.367984i
$262$		0			0
$263$	10.8503	+	6.97308i	0.669059	+	0.429978i	0.830586	−	0.556890i	$-0.188006\pi$
$263$	10.8503	+	6.97308i	0.669059	+	0.429978i	−0.161527	+	0.986868i	$0.551642\pi$
$264$		0			0
$265$	−2.11347	+	14.6995i	−0.129829	+	0.902982i
$266$		0			0
$267$	6.42417	+	7.41389i	0.393153	+	0.453723i
$268$		0			0
$269$	12.9289	−	8.30888i	0.788287	−	0.506601i	−0.0834876	−	0.996509i	$-0.526606\pi$
$269$	12.9289	−	8.30888i	0.788287	−	0.506601i	0.871774	+	0.489908i	$0.162970\pi$
$270$		0			0
$271$	13.2251	−	15.2626i	0.803370	−	0.927139i	−0.195191	−	0.980765i	$-0.562533\pi$
$271$	13.2251	−	15.2626i	0.803370	−	0.927139i	0.998561	+	0.0536265i	$0.0170780\pi$
$272$		0			0
$273$	11.1621	−	24.4417i	0.675563	−	1.47928i
$274$		0			0
$275$	22.5025			1.35695
$276$		0			0
$277$	22.7999			1.36991			0.684957	−	0.728584i	$-0.259821\pi$
$277$	22.7999			1.36991			0.684957	+	0.728584i	$0.259821\pi$
$278$		0			0
$279$	1.69960	−	3.72161i	0.101753	−	0.222807i
$280$		0			0
$281$	−9.75419	+	11.2569i	−0.581886	+	0.671533i	−0.968009	−	0.250915i	$-0.919269\pi$
$281$	−9.75419	+	11.2569i	−0.581886	+	0.671533i	0.386123	+	0.922447i	$0.373814\pi$
$282$		0			0
$283$	0.530368	−	0.340847i	0.0315271	−	0.0202612i	−0.524782	−	0.851236i	$-0.675853\pi$
$283$	0.530368	−	0.340847i	0.0315271	−	0.0202612i	0.556309	+	0.830975i	$0.312217\pi$
$284$		0			0
$285$	12.8271	+	14.8033i	0.759812	+	0.876870i
$286$		0			0
$287$	4.83608	−	33.6357i	0.285465	−	1.98545i
$288$		0			0
$289$	−12.8455	−	8.25528i	−0.755615	−	0.485604i
$290$		0			0
$291$	1.01768	+	2.22842i	0.0596577	+	0.130632i
$292$		0			0
$293$	−12.4802	−	3.66452i	−0.729101	−	0.214083i	−0.103945	−	0.994583i	$-0.533147\pi$
$293$	−12.4802	−	3.66452i	−0.729101	−	0.214083i	−0.625156	+	0.780500i	$0.714965\pi$
$294$		0			0
$295$	12.0563	−	3.54005i	0.701944	−	0.206109i
$296$		0			0
$297$	−0.389333	−	2.70787i	−0.0225914	−	0.157126i
$298$		0			0
$299$	12.7350	−	26.6010i	0.736486	−	1.53837i
$300$		0			0
$301$	−5.85281	−	40.7072i	−0.337351	−	2.34633i
$302$		0			0
$303$	−15.7819	+	4.63397i	−0.906644	+	0.266215i
$304$		0			0
$305$	9.26290	+	2.71983i	0.530392	+	0.155737i
$306$		0			0
$307$	−4.34960	−	9.52429i	−0.248245	−	0.543580i	0.743956	−	0.668228i	$-0.232947\pi$
$307$	−4.34960	−	9.52429i	−0.248245	−	0.543580i	−0.992201	+	0.124648i	$0.960220\pi$
$308$		0			0
$309$	−4.33213	−	2.78409i	−0.246447	−	0.158382i
$310$		0			0
$311$	−0.934480	+	6.49945i	−0.0529895	+	0.368550i	0.946022	+	0.324102i	$0.105062\pi$
$311$	−0.934480	+	6.49945i	−0.0529895	+	0.368550i	−0.999012	+	0.0444482i	$0.985847\pi$
$312$		0			0
$313$	6.05372	+	6.98637i	0.342177	+	0.394893i	0.900590	−	0.434670i	$-0.143135\pi$
$313$	6.05372	+	6.98637i	0.342177	+	0.394893i	−0.558413	+	0.829563i	$0.688590\pi$
$314$		0			0
$315$	−13.3676	+	8.59083i	−0.753179	+	0.484039i
$316$		0			0
$317$	−17.1993	+	19.8491i	−0.966009	+	1.11483i	0.0273323	+	0.999626i	$0.491299\pi$
$317$	−17.1993	+	19.8491i	−0.966009	+	1.11483i	−0.993341	+	0.115208i	$0.963247\pi$
$318$		0			0
$319$	−7.42739	+	16.2637i	−0.415854	+	0.910593i
$320$		0			0
$321$	−9.08411			−0.507026
$322$		0			0
$323$	7.08548			0.394246
$324$		0			0
$325$	−21.0130	+	46.0120i	−1.16559	+	2.55228i
$326$		0			0
$327$	2.06788	−	2.38646i	0.114354	−	0.131972i
$328$		0			0
$329$	18.6553	−	11.9890i	1.02850	−	0.660977i
$330$		0			0
$331$	8.65360	+	9.98678i	0.475645	+	0.548923i	0.941973	−	0.335689i	$-0.108969\pi$
$331$	8.65360	+	9.98678i	0.475645	+	0.548923i	−0.466328	+	0.884612i	$0.654423\pi$
$332$		0			0
$333$	−0.820674	+	5.70791i	−0.0449727	+	0.312792i
$334$		0			0
$335$	−13.4796	−	8.66283i	−0.736471	−	0.473301i
$336$		0			0
$337$	−0.171381	−	0.375272i	−0.00933572	−	0.0204424i	0.904907	−	0.425610i	$-0.139940\pi$
$337$	−0.171381	−	0.375272i	−0.00933572	−	0.0204424i	−0.914242	+	0.405168i	$0.867213\pi$
$338$		0			0
$339$	13.1762	+	3.86888i	0.715632	+	0.210129i
$340$		0			0
$341$	−10.7394	+	3.15336i	−0.581569	+	0.170764i
$342$		0			0
$343$	3.16609	+	22.0207i	0.170953	+	1.18900i
$344$		0			0
$345$	−14.8405	+	9.16219i	−0.798985	+	0.493276i
$346$		0			0
$347$	−2.33726	−	16.2560i	−0.125470	−	0.872666i	−0.951195	−	0.308592i	$-0.900142\pi$
$347$	−2.33726	−	16.2560i	−0.125470	−	0.872666i	0.825724	−	0.564074i	$-0.190767\pi$
$348$		0			0
$349$	−19.4599	+	5.71394i	−1.04166	+	0.305860i	−0.757445	−	0.652899i	$-0.773552\pi$
$349$	−19.4599	+	5.71394i	−1.04166	+	0.305860i	−0.284219	+	0.958759i	$0.591734\pi$
$350$		0			0
$351$	5.90046	+	1.73253i	0.314943	+	0.0924757i
$352$		0			0
$353$	−1.33471	−	2.92262i	−0.0710397	−	0.155555i	0.870781	−	0.491671i	$-0.163614\pi$
$353$	−1.33471	−	2.92262i	−0.0710397	−	0.155555i	−0.941821	+	0.336116i	$0.890887\pi$
$354$		0			0
$355$	−31.2933	−	20.1110i	−1.66088	−	1.06738i
$356$		0			0
$357$	−0.818024	+	5.68948i	−0.0432944	+	0.301119i
$358$		0			0
$359$	15.1188	+	17.4481i	0.797941	+	0.920873i	0.998266	−	0.0588565i	$-0.0187454\pi$
$359$	15.1188	+	17.4481i	0.797941	+	0.920873i	−0.200326	+	0.979729i	$0.564200\pi$
$360$		0			0
$361$	8.42096	−	5.41182i	0.443209	−	0.284833i
$362$		0			0
$363$	2.30240	−	2.65712i	0.120845	−	0.139462i
$364$		0			0
$365$	−9.81368	+	21.4890i	−0.513672	+	1.12478i
$366$		0			0
$367$	−28.8899			−1.50804			−0.754019	−	0.656852i	$-0.771888\pi$
$367$	−28.8899			−1.50804			−0.754019	+	0.656852i	$0.771888\pi$
$368$		0			0
$369$	7.77719			0.404864
$370$		0			0
$371$	−7.41212	+	16.2303i	−0.384818	+	0.842634i
$372$		0			0
$373$	8.27775	−	9.55304i	0.428606	−	0.494637i	−0.499834	−	0.866121i	$-0.666605\pi$
$373$	8.27775	−	9.55304i	0.428606	−	0.494637i	0.928439	+	0.371484i	$0.121151\pi$
$374$		0			0
$375$	9.86792	−	6.34173i	0.509577	−	0.327486i
$376$		0			0
$377$	−26.3194	−	30.3742i	−1.35552	−	1.56435i
$378$		0			0
$379$	0.618344	−	4.30067i	0.0317622	−	0.220911i	−0.967758	−	0.251881i	$-0.918951\pi$
$379$	0.618344	−	4.30067i	0.0317622	−	0.220911i	0.999520	+	0.0309706i	$0.00985981\pi$
$380$		0			0
$381$	8.23677	+	5.29345i	0.421983	+	0.271192i
$382$		0			0
$383$	3.68558	+	8.07030i	0.188325	+	0.412373i	0.980118	−	0.198416i	$-0.0635796\pi$
$383$	3.68558	+	8.07030i	0.188325	+	0.412373i	−0.791793	+	0.610789i	$0.790852\pi$
$384$		0			0
$385$	41.7099	+	12.2471i	2.12573	+	0.624171i
$386$		0			0
$387$	9.03099	−	2.65174i	0.459071	−	0.134795i
$388$		0			0
$389$	0.965816	+	6.71740i	0.0489688	+	0.340586i	0.999547	+	0.0301000i	$0.00958258\pi$
$389$	0.965816	+	6.71740i	0.0489688	+	0.340586i	−0.950578	+	0.310486i	$0.899508\pi$
$390$		0			0
$391$	−1.01073	+	6.22749i	−0.0511149	+	0.314938i
$392$		0			0
$393$	−0.702823	−	4.88824i	−0.0354527	−	0.246579i
$394$		0			0
$395$	11.7901	−	3.46188i	0.593223	−	0.174186i
$396$		0			0
$397$	−25.4063	−	7.45996i	−1.27511	−	0.374405i	−0.427009	−	0.904247i	$-0.640433\pi$
$397$	−25.4063	−	7.45996i	−1.27511	−	0.374405i	−0.848096	+	0.529843i	$0.822251\pi$
$398$		0			0
$399$	9.77636	+	21.4072i	0.489430	+	1.07170i
$400$		0			0
$401$	27.9191	+	17.9425i	1.39421	+	0.896005i	0.999738	−	0.0229020i	$-0.00729058\pi$
$401$	27.9191	+	17.9425i	1.39421	+	0.896005i	0.394474	+	0.918907i	$0.370927\pi$
$402$		0			0
$403$	3.58063	−	24.9039i	0.178364	−	1.24055i
$404$		0			0
$405$	−2.38152	−	2.74842i	−0.118339	−	0.136570i
$406$		0			0
$407$	13.2714	−	8.52904i	0.657841	−	0.422769i
$408$		0			0
$409$	−18.9775	+	21.9012i	−0.938379	+	1.08295i	0.0580335	+	0.998315i	$0.481517\pi$
$409$	−18.9775	+	21.9012i	−0.938379	+	1.08295i	−0.996412	+	0.0846322i	$0.973028\pi$
$410$		0			0
$411$	−8.73753	+	19.1325i	−0.430991	+	0.943738i
$412$		0			0
$413$	15.0969			0.742869
$414$		0			0
$415$	−26.1631			−1.28429
$416$		0			0
$417$	−3.54053	+	7.75269i	−0.173381	+	0.379651i
$418$		0			0
$419$	−1.66642	+	1.92315i	−0.0814099	+	0.0939520i	−0.794993	−	0.606618i	$-0.792526\pi$
$419$	−1.66642	+	1.92315i	−0.0814099	+	0.0939520i	0.713583	+	0.700570i	$0.247071\pi$
$420$		0			0
$421$	6.57139	−	4.22317i	0.320270	−	0.205825i	−0.370621	−	0.928784i	$-0.620855\pi$
$421$	6.57139	−	4.22317i	0.320270	−	0.205825i	0.690890	+	0.722959i	$0.257219\pi$
$422$		0			0
$423$	3.32356	+	3.83559i	0.161597	+	0.186493i
$424$		0			0
$425$	1.53995	−	10.7106i	0.0746985	−	0.519539i
$426$		0			0
$427$	9.75770	+	6.27090i	0.472208	+	0.303470i
$428$		0			0
$429$	−6.98871	−	15.3031i	−0.337418	−	0.738843i
$430$		0			0
$431$	2.78212	+	0.816903i	0.134010	+	0.0393488i	0.348050	−	0.937476i	$-0.386844\pi$
$431$	2.78212	+	0.816903i	0.134010	+	0.0393488i	−0.214040	+	0.976825i	$0.568662\pi$
$432$		0			0
$433$	6.39277	−	1.87709i	0.307217	−	0.0902071i	−0.124490	−	0.992221i	$-0.539730\pi$
$433$	6.39277	−	1.87709i	0.307217	−	0.0902071i	0.431707	+	0.902014i	$0.357911\pi$
$434$		0			0
$435$	3.38251	+	23.5259i	0.162179	+	1.12798i
$436$		0			0
$437$	10.3035	+	23.6869i	0.492883	+	1.13310i
$438$		0			0
$439$	0.604131	+	4.20183i	0.0288336	+	0.200542i	0.999146	−	0.0413116i	$-0.0131536\pi$
$439$	0.604131	+	4.20183i	0.0288336	+	0.200542i	−0.970313	+	0.241854i	$0.922245\pi$
$440$		0			0
$441$	−11.6018	+	3.40659i	−0.552466	+	0.162219i
$442$		0			0
$443$	5.27795	+	1.54975i	0.250763	+	0.0736307i	0.404698	−	0.914450i	$-0.367377\pi$
$443$	5.27795	+	1.54975i	0.250763	+	0.0736307i	−0.153935	+	0.988081i	$0.549195\pi$
$444$		0			0
$445$	−14.8203	−	32.4519i	−0.702548	−	1.53837i
$446$		0			0
$447$	−2.46287	−	1.58279i	−0.116490	−	0.0748635i
$448$		0			0
$449$	−2.33564	+	16.2447i	−0.110226	+	0.766637i	0.857473	+	0.514529i	$0.172033\pi$
$449$	−2.33564	+	16.2447i	−0.110226	+	0.766637i	−0.967699	+	0.252108i	$0.918876\pi$
$450$		0			0
$451$	−13.9329	−	16.0795i	−0.656076	−	0.757152i
$452$		0			0
$453$	14.9062	−	9.57967i	0.700357	−	0.450092i
$454$		0			0
$455$	−63.9911	+	73.8497i	−2.99995	+	3.46213i
$456$		0			0
$457$	11.5754	−	25.3465i	0.541472	−	1.18566i	−0.419179	−	0.907903i	$-0.637682\pi$
$457$	11.5754	−	25.3465i	0.541472	−	1.18566i	0.960652	−	0.277756i	$-0.0895906\pi$
$458$		0			0
$459$	−1.31551			−0.0614029
$460$		0			0
$461$	27.4201			1.27708			0.638541	−	0.769588i	$-0.279538\pi$
$461$	27.4201			1.27708			0.638541	+	0.769588i	$0.279538\pi$
$462$		0			0
$463$	13.8112	−	30.2424i	0.641863	−	1.40548i	−0.256636	−	0.966508i	$-0.582614\pi$
$463$	13.8112	−	30.2424i	0.641863	−	1.40548i	0.898499	−	0.438976i	$-0.144659\pi$
$464$		0			0
$465$	−9.74362	+	11.2447i	−0.451849	+	0.521462i
$466$		0			0
$467$	−28.7156	+	18.4544i	−1.32880	+	0.853967i	−0.996028	−	0.0890402i	$-0.971620\pi$
$467$	−28.7156	+	18.4544i	−1.32880	+	0.853967i	−0.332771	+	0.943008i	$0.607984\pi$
$468$		0			0
$469$	−12.6071	−	14.5494i	−0.582142	−	0.671828i
$470$		0			0
$471$	1.00974	−	7.02292i	0.0465265	−	0.323599i
$472$		0			0
$473$	−21.6616	−	13.9211i	−0.996003	−	0.640092i
$474$		0			0
$475$	−18.4042	−	40.2996i	−0.844443	−	1.84907i
$476$		0			0
$477$	−3.91815	−	1.15047i	−0.179400	−	0.0526766i
$478$		0			0
$479$	−27.4641	+	8.06418i	−1.25486	+	0.368462i	−0.840581	−	0.541686i	$-0.817786\pi$
$479$	−27.4641	+	8.06418i	−1.25486	+	0.368462i	−0.414284	+	0.910148i	$0.635968\pi$
$480$		0			0
$481$	5.04678	+	35.1012i	0.230114	+	1.60047i
$482$		0			0
$483$	−20.2096	+	5.53882i	−0.919568	+	0.252025i
$484$		0			0
$485$	−1.26790	−	8.81847i	−0.0575726	−	0.400426i
$486$		0			0
$487$	−34.1056	+	10.0143i	−1.54547	+	0.453791i	−0.939743	−	0.341881i	$-0.888936\pi$
$487$	−34.1056	+	10.0143i	−1.54547	+	0.453791i	−0.605727	+	0.795672i	$0.707118\pi$
$488$		0			0
$489$	−0.809527	−	0.237699i	−0.0366081	−	0.0107491i
$490$		0			0
$491$	9.11835	+	19.9664i	0.411505	+	0.901071i	0.995973	+	0.0896538i	$0.0285761\pi$
$491$	9.11835	+	19.9664i	0.411505	+	0.901071i	−0.584468	+	0.811417i	$0.698697\pi$
$492$		0			0
$493$	7.23278	+	4.64822i	0.325748	+	0.209345i
$494$		0			0
$495$	−1.41588	+	9.84766i	−0.0636391	+	0.442619i
$496$		0			0
$497$	−29.2677	−	33.7767i	−1.31284	−	1.51509i
$498$		0			0
$499$	−10.7906	+	6.93468i	−0.483052	+	0.310439i	−0.759406	−	0.650617i	$-0.774510\pi$
$499$	−10.7906	+	6.93468i	−0.483052	+	0.310439i	0.276354	+	0.961056i	$0.410874\pi$
$500$		0			0
$501$	12.4858	−	14.4094i	0.557825	−	0.643764i
$502$		0			0
$503$	0.517099	−	1.13229i	0.0230563	−	0.0504863i	−0.897754	−	0.440498i	$-0.854802\pi$
$503$	0.517099	−	1.13229i	0.0230563	−	0.0504863i	0.920810	+	0.390012i	$0.127529\pi$
$504$		0			0
$505$	59.8166			2.66180
$506$		0			0
$507$	24.8171			1.10217
$508$		0			0
$509$	0.237544	−	0.520148i	0.0105289	−	0.0230552i	−0.904294	−	0.426909i	$-0.859602\pi$
$509$	0.237544	−	0.520148i	0.0105289	−	0.0230552i	0.914823	+	0.403854i	$0.132330\pi$
$510$		0			0
$511$	−18.5872	+	21.4508i	−0.822249	+	0.948926i
$512$		0			0
$513$	−4.53107	+	2.91194i	−0.200052	+	0.128565i
$514$		0			0
$515$	12.2639	+	14.1533i	0.540413	+	0.623670i
$516$		0			0
$517$	1.97595	−	13.7430i	0.0869021	−	0.604417i
$518$		0			0
$519$	−12.9825	−	8.34333i	−0.569867	−	0.366231i
$520$		0			0
$521$	−8.53713	−	18.6937i	−0.374018	−	0.818986i	−0.999257	−	0.0385519i	$-0.987726\pi$
$521$	−8.53713	−	18.6937i	−0.374018	−	0.818986i	0.625238	−	0.780434i	$-0.285002\pi$
$522$		0			0
$523$	−14.8487	−	4.35996i	−0.649287	−	0.190648i	−0.0595271	−	0.998227i	$-0.518959\pi$
$523$	−14.8487	−	4.35996i	−0.649287	−	0.190648i	−0.589759	+	0.807579i	$0.700777\pi$
$524$		0			0
$525$	34.4845	−	10.1256i	1.50503	−	0.441915i
$526$		0			0
$527$	0.765969	+	5.32743i	0.0333661	+	0.232066i
$528$		0			0
$529$	−22.2884	+	5.67695i	−0.969060	+	0.246824i
$530$		0			0
$531$	0.491718	+	3.41998i	0.0213388	+	0.148414i
$532$		0			0
$533$	45.8890	−	13.4742i	1.98767	−	0.583634i
$534$		0			0
$535$	31.6978	+	9.30733i	1.37042	+	0.402391i
$536$		0			0
$537$	−5.04991	−	11.0578i	−0.217920	−	0.477178i
$538$		0			0
$539$	27.8279	+	17.8839i	1.19863	+	0.770315i
$540$		0			0
$541$	1.32894	−	9.24297i	0.0571355	−	0.397386i	−0.941106	−	0.338111i	$-0.890212\pi$
$541$	1.32894	−	9.24297i	0.0571355	−	0.397386i	0.998242	−	0.0592750i	$-0.0188789\pi$
$542$		0			0
$543$	4.87996	+	5.63178i	0.209419	+	0.241683i
$544$		0			0
$545$	−9.66071	+	6.20856i	−0.413819	+	0.265945i
$546$		0			0
$547$	3.42649	−	3.95438i	0.146506	−	0.169077i	−0.677753	−	0.735289i	$-0.737046\pi$
$547$	3.42649	−	3.95438i	0.146506	−	0.169077i	0.824259	+	0.566212i	$0.191592\pi$
$548$		0			0
$549$	−1.10276	+	2.41471i	−0.0470648	+	0.103057i
$550$		0			0
$551$	35.2012			1.49962
$552$		0			0
$553$	14.7635			0.627809
$554$		0			0
$555$	8.71181	−	19.0762i	0.369796	−	0.809739i
$556$		0			0
$557$	30.0671	−	34.6992i	1.27398	−	1.47025i	0.461646	−	0.887064i	$-0.347259\pi$
$557$	30.0671	−	34.6992i	1.27398	−	1.47025i	0.812336	−	0.583189i	$-0.198195\pi$
$558$		0			0
$559$	48.6928	−	31.2930i	2.05949	−	1.32355i
$560$		0			0
$561$	2.35676	+	2.71984i	0.0995023	+	0.114832i
$562$		0			0
$563$	−3.29462	+	22.9146i	−0.138852	+	0.965734i	0.794626	+	0.607099i	$0.207667\pi$
$563$	−3.29462	+	22.9146i	−0.138852	+	0.965734i	−0.933478	+	0.358635i	$0.883242\pi$
$564$		0			0
$565$	−42.0127	−	26.9999i	−1.76749	−	1.13590i
$566$		0			0
$567$	−1.81511	−	3.97454i	−0.0762275	−	0.166915i
$568$		0			0
$569$	−4.68564	−	1.37583i	−0.196432	−	0.0576777i	0.182037	−	0.983292i	$-0.441731\pi$
$569$	−4.68564	−	1.37583i	−0.196432	−	0.0576777i	−0.378469	+	0.925614i	$0.623549\pi$
$570$		0			0
$571$	18.0598	−	5.30285i	0.755781	−	0.221917i	0.118928	−	0.992903i	$-0.462054\pi$
$571$	18.0598	−	5.30285i	0.755781	−	0.221917i	0.636853	+	0.770986i	$0.280236\pi$
$572$		0			0
$573$	1.09822	+	7.63830i	0.0458789	+	0.319095i
$574$		0			0
$575$	38.0450	−	10.4269i	1.58659	−	0.434834i
$576$		0			0
$577$	3.49109	+	24.2811i	0.145336	+	1.01083i	0.923726	+	0.383053i	$0.125127\pi$
$577$	3.49109	+	24.2811i	0.145336	+	1.01083i	−0.778390	+	0.627780i	$0.783964\pi$
$578$		0			0
$579$	8.27400	−	2.42947i	0.343856	−	0.100965i
$580$		0			0
$581$	−30.1610	−	8.85606i	−1.25129	−	0.367411i
$582$		0			0
$583$	4.64079	+	10.1619i	0.192202	+	0.420864i
$584$		0			0
$585$	−18.8138	−	12.0909i	−0.777855	−	0.499897i
$586$		0			0
$587$	6.71629	−	46.7128i	0.277211	−	1.92804i	−0.0859115	−	0.996303i	$-0.527380\pi$
$587$	6.71629	−	46.7128i	0.277211	−	1.92804i	0.363122	−	0.931741i	$-0.381711\pi$
$588$		0			0
$589$	14.4307	+	16.6540i	0.594608	+	0.686215i
$590$		0			0
$591$	8.19376	−	5.26581i	0.337046	−	0.216606i
$592$		0			0
$593$	6.41916	−	7.40810i	0.263603	−	0.304214i	−0.608483	−	0.793567i	$-0.708222\pi$
$593$	6.41916	−	7.40810i	0.263603	−	0.304214i	0.872086	+	0.489353i	$0.162767\pi$
$594$		0			0
$595$	8.68368	−	19.0146i	0.355996	−	0.779523i
$596$		0			0
$597$	15.9329			0.652090
$598$		0			0
$599$	−20.6101			−0.842108			−0.421054	−	0.907036i	$-0.638340\pi$
$599$	−20.6101			−0.842108			−0.421054	+	0.907036i	$0.638340\pi$
$600$		0			0
$601$	7.93332	−	17.3716i	0.323607	−	0.708601i	−0.675992	−	0.736909i	$-0.736285\pi$
$601$	7.93332	−	17.3716i	0.323607	−	0.708601i	0.999599	+	0.0283082i	$0.00901198\pi$
$602$		0			0
$603$	2.88532	−	3.32984i	0.117499	−	0.135602i
$604$		0			0
$605$	−10.7564	+	6.91269i	−0.437308	+	0.281041i
$606$		0			0
$607$	−9.24220	−	10.6661i	−0.375129	−	0.432922i	0.536522	−	0.843886i	$-0.319738\pi$
$607$	−9.24220	−	10.6661i	−0.375129	−	0.432922i	−0.911652	+	0.410964i	$0.865192\pi$
$608$		0			0
$609$	−4.06401	+	28.2658i	−0.164682	+	1.14539i
$610$		0			0
$611$	26.2558	+	16.8736i	1.06220	+	0.682633i
$612$		0			0
$613$	19.5194	+	42.7415i	0.788381	+	1.72631i	0.681228	+	0.732071i	$0.261446\pi$
$613$	19.5194	+	42.7415i	0.788381	+	1.72631i	0.107153	+	0.994243i	$0.465827\pi$
$614$		0			0
$615$	−27.1375	−	7.96829i	−1.09429	−	0.321313i
$616$		0			0
$617$	20.8751	−	6.12948i	0.840400	−	0.246764i	0.166921	−	0.985970i	$-0.446617\pi$
$617$	20.8751	−	6.12948i	0.840400	−	0.246764i	0.673479	+	0.739207i	$0.264799\pi$
$618$		0			0
$619$	4.53897	+	31.5692i	0.182436	+	1.26887i	0.850979	+	0.525200i	$0.176009\pi$
$619$	4.53897	+	31.5692i	0.182436	+	1.26887i	−0.668542	+	0.743674i	$0.733082\pi$
$620$		0			0
$621$	−1.91298	−	4.39778i	−0.0767653	−	0.176477i
$622$		0			0
$623$	−6.10013	−	42.4274i	−0.244397	−	1.69982i
$624$		0			0
$625$	−1.46901	+	0.431342i	−0.0587606	+	0.0172537i
$626$		0			0
$627$	14.1380	+	4.15128i	0.564615	+	0.165786i
$628$		0			0
$629$	−3.15136	−	6.90051i	−0.125653	−	0.275141i
$630$		0			0
$631$	5.29849	+	3.40513i	0.210929	+	0.135556i	0.641840	−	0.766838i	$-0.278171\pi$
$631$	5.29849	+	3.40513i	0.210929	+	0.135556i	−0.430911	+	0.902395i	$0.641808\pi$
$632$		0			0
$633$	−0.736943	+	5.12555i	−0.0292909	+	0.203722i
$634$		0			0
$635$	−23.3176	−	26.9100i	−0.925332	−	1.06789i
$636$		0			0
$637$	−62.5539	+	40.2009i	−2.47847	+	1.59282i
$638$		0			0
$639$	6.69835	−	7.73031i	0.264983	−	0.305806i
$640$		0			0
$641$	−11.4982	+	25.1776i	−0.454153	+	0.994456i	0.534628	+	0.845087i	$0.320452\pi$
$641$	−11.4982	+	25.1776i	−0.454153	+	0.994456i	−0.988781	+	0.149369i	$0.952276\pi$
$642$		0			0
$643$	−27.5964			−1.08830			−0.544148	−	0.838990i	$-0.683147\pi$
$643$	−27.5964			−1.08830			−0.544148	+	0.838990i	$0.683147\pi$
$644$		0			0
$645$	−34.2294			−1.34778
$646$		0			0
$647$	−0.127769	+	0.279774i	−0.00502310	+	0.0109991i	−0.912127	−	0.409908i	$-0.865561\pi$
$647$	−0.127769	+	0.279774i	−0.00502310	+	0.0109991i	0.907104	+	0.420907i	$0.138288\pi$
$648$		0			0
$649$	6.18993	−	7.14356i	0.242976	−	0.280409i
$650$		0			0
$651$	−15.0388	+	9.66486i	−0.589418	+	0.378796i
$652$		0			0
$653$	−11.3264	−	13.0713i	−0.443235	−	0.511520i	0.489540	−	0.871981i	$-0.337165\pi$
$653$	−11.3264	−	13.0713i	−0.443235	−	0.511520i	−0.932774	+	0.360461i	$0.882619\pi$
$654$		0			0
$655$	−2.55594	+	17.7770i	−0.0998690	+	0.694604i
$656$		0			0
$657$	−5.46476	−	3.51199i	−0.213201	−	0.137016i
$658$		0			0
$659$	−6.75581	−	14.7932i	−0.263169	−	0.576259i	0.731208	−	0.682154i	$-0.238957\pi$
$659$	−6.75581	−	14.7932i	−0.263169	−	0.576259i	−0.994377	+	0.105895i	$0.966229\pi$
$660$		0			0
$661$	−9.84350	−	2.89031i	−0.382868	−	0.112420i	0.0846344	−	0.996412i	$-0.473028\pi$
$661$	−9.84350	−	2.89031i	−0.382868	−	0.112420i	−0.467502	+	0.883992i	$0.654846\pi$
$662$		0			0
$663$	−7.76213	+	2.27917i	−0.301456	+	0.0885155i
$664$		0			0
$665$	−12.1801	−	84.7144i	−0.472324	−	3.28508i
$666$		0			0
$667$	−5.02139	+	30.9386i	−0.194429	+	1.19795i
$668$		0			0
$669$	−1.84633	−	12.8415i	−0.0713834	−	0.496482i
$670$		0			0
$671$	6.96807	−	2.04601i	0.268999	−	0.0789853i
$672$		0			0
$673$	25.2947	+	7.42720i	0.975040	+	0.286298i	0.730175	−	0.683260i	$-0.239438\pi$
$673$	25.2947	+	7.42720i	0.975040	+	0.286298i	0.244865	+	0.969557i	$0.421257\pi$
$674$		0			0
$675$	3.41698	+	7.48215i	0.131520	+	0.287988i
$676$		0			0
$677$	5.65459	+	3.63398i	0.217324	+	0.139665i	0.644774	−	0.764374i	$-0.276952\pi$
$677$	5.65459	+	3.63398i	0.217324	+	0.139665i	−0.427450	+	0.904039i	$0.640588\pi$
$678$		0			0
$679$	1.52336	−	10.5952i	0.0584611	−	0.406606i
$680$		0			0
$681$	6.22485	+	7.18386i	0.238537	+	0.275286i
$682$		0			0
$683$	−23.4551	+	15.0737i	−0.897485	+	0.576779i	−0.906043	−	0.423185i	$-0.860912\pi$
$683$	−23.4551	+	15.0737i	−0.897485	+	0.576779i	0.00855822	+	0.999963i	$0.497276\pi$
$684$		0			0
$685$	50.0912	−	57.8083i	1.91388	−	2.20874i
$686$		0			0
$687$	6.85343	−	15.0069i	0.261475	−	0.572549i
$688$		0			0
$689$	−25.1121			−0.956696
$690$		0			0
$691$	28.7827			1.09495			0.547474	−	0.836823i	$-0.315590\pi$
$691$	28.7827			1.09495			0.547474	+	0.836823i	$0.315590\pi$
$692$		0			0
$693$	−4.96562	+	10.8732i	−0.188628	+	0.413039i
$694$		0			0
$695$	20.2974	−	23.4245i	0.769925	−	0.888541i
$696$		0			0
$697$	−8.60686	+	5.53129i	−0.326008	+	0.209513i
$698$		0			0
$699$	−1.09864	−	1.26790i	−0.0415545	−	0.0479564i
$700$		0			0
$701$	−6.65027	+	46.2537i	−0.251177	+	1.74698i	0.339991	+	0.940429i	$0.389576\pi$
$701$	−6.65027	+	46.2537i	−0.251177	+	1.74698i	−0.591168	+	0.806548i	$0.701333\pi$
$702$		0			0
$703$	−26.1289	−	16.7920i	−0.985471	−	0.633323i
$704$		0			0
$705$	−7.66730	−	16.7890i	−0.288767	−	0.632312i
$706$		0			0
$707$	68.9571	+	20.2476i	2.59340	+	0.761490i
$708$		0			0
$709$	17.0777	−	5.01448i	0.641368	−	0.188323i	0.0551526	−	0.998478i	$-0.482435\pi$
$709$	17.0777	−	5.01448i	0.641368	−	0.188323i	0.586215	+	0.810155i	$0.300617\pi$
$710$		0			0
$711$	0.480861	+	3.34446i	0.0180337	+	0.125427i
$712$		0			0
$713$	−16.6958	+	10.3076i	−0.625264	+	0.386024i
$714$		0			0
$715$	8.70704	+	60.5588i	0.325625	+	2.26477i
$716$		0			0
$717$	−0.424580	+	0.124668i	−0.0158562	+	0.00465581i
$718$		0			0
$719$	25.5241	+	7.49456i	0.951889	+	0.279500i	0.720573	−	0.693379i	$-0.243879\pi$
$719$	25.5241	+	7.49456i	0.951889	+	0.279500i	0.231316	+	0.972879i	$0.425697\pi$
$720$		0			0
$721$	9.34713	+	20.4674i	0.348105	+	0.762244i
$722$		0			0
$723$	−24.4631	−	15.7215i	−0.909794	−	0.584689i
$724$		0			0
$725$	7.65058	−	53.2109i	0.284135	−	1.97620i
$726$		0			0
$727$	−17.1268	−	19.7654i	−0.635197	−	0.733056i	0.343321	−	0.939218i	$-0.388448\pi$
$727$	−17.1268	−	19.7654i	−0.635197	−	0.733056i	−0.978518	+	0.206162i	$0.933903\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	−8.10845	+	9.35765i	−0.299902	+	0.346105i
$732$		0			0
$733$	6.45127	−	14.1263i	0.238283	−	0.521767i	−0.752277	−	0.658847i	$-0.771044\pi$
$733$	6.45127	−	14.1263i	0.238283	−	0.521767i	0.990560	+	0.137080i	$0.0437717\pi$
$734$		0			0
$735$	43.9733			1.62198
$736$		0			0
$737$	−12.0536			−0.443999
$738$		0			0
$739$	−14.6210	+	32.0155i	−0.537841	+	1.17771i	0.424391	+	0.905479i	$0.360488\pi$
$739$	−14.6210	+	32.0155i	−0.537841	+	1.17771i	−0.962233	+	0.272229i	$0.912239\pi$
$740$		0			0
$741$	−21.6904	+	25.0320i	−0.796816	+	0.919574i
$742$		0			0
$743$	−44.9800	+	28.9069i	−1.65016	+	1.06049i	−0.719567	+	0.694423i	$0.755660\pi$
$743$	−44.9800	+	28.9069i	−1.65016	+	1.06049i	−0.930589	+	0.366067i	$0.880704\pi$
$744$		0			0
$745$	6.97220	+	8.04635i	0.255442	+	0.294795i
$746$		0			0
$747$	1.02384	−	7.12098i	0.0374604	−	0.260543i
$748$		0			0
$749$	33.3911	+	21.4591i	1.22008	+	0.784100i
$750$		0			0
$751$	−13.7032	−	30.0058i	−0.500036	−	1.09493i	−0.976458	−	0.215709i	$-0.930794\pi$
$751$	−13.7032	−	30.0058i	−0.500036	−	1.09493i	0.476422	−	0.879217i	$-0.341933\pi$
$752$		0			0
$753$	−7.39453	−	2.17123i	−0.269472	−	0.0791240i
$754$		0			0
$755$	−61.8285	+	18.1545i	−2.25017	+	0.660710i
$756$		0			0
$757$	−4.16104	−	28.9407i	−0.151236	−	1.05187i	−0.914152	−	0.405371i	$-0.867143\pi$
$757$	−4.16104	−	28.9407i	−0.151236	−	1.05187i	0.762917	−	0.646497i	$-0.223767\pi$
$758$		0			0
$759$	−5.66535	+	11.8338i	−0.205639	+	0.429540i
$760$		0			0
$761$	−5.92298	−	41.1953i	−0.214708	−	1.49333i	−0.757154	−	0.653236i	$-0.773411\pi$
$761$	−5.92298	−	41.1953i	−0.214708	−	1.49333i	0.542446	−	0.840091i	$-0.317498\pi$
$762$		0			0
$763$	−13.2385	+	3.88718i	−0.479266	+	0.140725i
$764$		0			0
$765$	4.59031	+	1.34784i	0.165963	+	0.0487312i
$766$		0			0
$767$	8.82658	+	19.3275i	0.318709	+	0.697876i
$768$		0			0
$769$	32.5329	+	20.9076i	1.17317	+	0.753949i	0.974118	−	0.226040i	$-0.0725782\pi$
$769$	32.5329	+	20.9076i	1.17317	+	0.753949i	0.199050	+	0.979989i	$0.436215\pi$
$770$		0			0
$771$	−2.84792	+	19.8077i	−0.102565	+	0.713357i
$772$		0			0
$773$	32.7885	+	37.8399i	1.17932	+	1.36101i	0.918403	+	0.395645i	$0.129479\pi$
$773$	32.7885	+	37.8399i	1.17932	+	1.36101i	0.260916	+	0.965362i	$0.415975\pi$
$774$		0			0
$775$	28.3109	−	18.1943i	1.01696	−	0.653559i
$776$		0			0
$777$	16.5002	−	19.0423i	0.591943	−	0.683139i
$778$		0			0
$779$	−17.4012	+	38.1033i	−0.623462	+	1.36519i
$780$		0			0
$781$	−27.9827			−1.00130
$782$		0			0
$783$	−6.53557			−0.233562
$784$		0			0
$785$	−10.7189	+	23.4710i	−0.382572	+	0.837717i
$786$		0			0
$787$	−22.1767	+	25.5932i	−0.790513	+	0.912300i	−0.997821	−	0.0659755i	$-0.978984\pi$
$787$	−22.1767	+	25.5932i	−0.790513	+	0.912300i	0.207309	+	0.978276i	$0.433530\pi$
$788$		0			0
$789$	10.8503	−	6.97308i	0.386282	−	0.248248i
$790$		0			0
$791$	−39.2933	−	45.3468i	−1.39711	−	1.61235i
$792$		0			0
$793$	−2.32324	+	16.1585i	−0.0825007	+	0.573805i
$794$		0			0
$795$	12.4932	+	8.02886i	0.443086	+	0.284754i
$796$		0			0
$797$	21.5854	+	47.2654i	0.764593	+	1.67423i	0.738207	+	0.674574i	$0.235673\pi$
$797$	21.5854	+	47.2654i	0.764593	+	1.67423i	0.0263863	+	0.999652i	$0.491600\pi$
$798$		0			0
$799$	−6.40607	−	1.88099i	−0.226630	−	0.0665447i
$800$		0			0
$801$	9.41261	−	2.76379i	0.332578	−	0.0976538i
$802$		0			0
$803$	2.52909	+	17.5902i	0.0892498	+	0.620746i
$804$		0			0
$805$	76.1937	+	1.37918i	2.68548	+	0.0486098i
$806$		0			0
$807$	−2.18718	−	15.2121i	−0.0769922	−	0.535493i
$808$		0			0
$809$	29.3559	−	8.61968i	1.03210	−	0.303052i	0.278535	−	0.960426i	$-0.410151\pi$
$809$	29.3559	−	8.61968i	1.03210	−	0.303052i	0.753564	+	0.657374i	$0.228333\pi$
$810$		0			0
$811$	−11.8106	−	3.46792i	−0.414728	−	0.121775i	0.0677105	−	0.997705i	$-0.478431\pi$
$811$	−11.8106	−	3.46792i	−0.414728	−	0.121775i	−0.482438	+	0.875930i	$0.660249\pi$
$812$		0			0
$813$	−8.38945	−	18.3703i	−0.294231	−	0.644276i
$814$		0			0
$815$	2.58120	+	1.65884i	0.0904156	+	0.0581066i
$816$		0			0
$817$	−7.21469	+	50.1793i	−0.252410	+	1.75555i
$818$		0			0
$819$	−17.5960	−	20.3069i	−0.614854	−	0.709579i
$820$		0			0
$821$	−39.5695	+	25.4298i	−1.38098	+	0.887505i	−0.999323	−	0.0367970i	$-0.988285\pi$
$821$	−39.5695	+	25.4298i	−1.38098	+	0.887505i	−0.381662	+	0.924302i	$0.624648\pi$
$822$		0			0
$823$	28.4959	−	32.8860i	0.993305	−	1.14634i	0.00407150	−	0.999992i	$-0.498704\pi$
$823$	28.4959	−	32.8860i	0.993305	−	1.14634i	0.989234	−	0.146344i	$-0.0467505\pi$
$824$		0			0
$825$	9.34789	−	20.4690i	0.325452	−	0.712640i
$826$		0			0
$827$	−11.4035			−0.396539			−0.198270	−	0.980148i	$-0.563532\pi$
$827$	−11.4035			−0.396539			−0.198270	+	0.980148i	$0.563532\pi$
$828$		0			0
$829$	−30.0821			−1.04479			−0.522397	−	0.852702i	$-0.674962\pi$
$829$	−30.0821			−1.04479			−0.522397	+	0.852702i	$0.674962\pi$
$830$		0			0
$831$	9.47142	−	20.7395i	0.328560	−	0.719446i
$832$		0			0
$833$	10.4166	−	12.0214i	0.360915	−	0.416518i
$834$		0			0
$835$	−58.3311	+	37.4871i	−2.01863	+	1.29730i
$836$		0			0
$837$	−2.67926	−	3.09203i	−0.0926087	−	0.106876i
$838$		0			0
$839$	−0.486324	+	3.38246i	−0.0167898	+	0.116776i	−0.996493	−	0.0836793i	$-0.973333\pi$
$839$	−0.486324	+	3.38246i	−0.0167898	+	0.116776i	0.979703	+	0.200455i	$0.0642420\pi$
$840$		0			0
$841$	11.5366	+	7.41414i	0.397815	+	0.255660i
$842$		0			0
$843$	6.18763	+	13.5490i	0.213113	+	0.466653i
$844$		0			0
$845$	−86.5961	−	25.4269i	−2.97900	−	0.874713i
$846$		0			0
$847$	−14.7399	+	4.32803i	−0.506470	+	0.148713i
$848$		0			0
$849$	−0.0897223	−	0.624032i	−0.00307926	−	0.0214167i
$850$		0			0
$851$	18.4859	−	20.5696i	0.633689	−	0.705116i
$852$		0			0
$853$	7.54820	+	52.4989i	0.258446	+	1.79753i	0.543915	+	0.839141i	$0.316942\pi$
$853$	7.54820	+	52.4989i	0.258446	+	1.79753i	−0.285469	+	0.958388i	$0.592149\pi$
$854$		0			0
$855$	18.7941	−	5.51844i	0.642744	−	0.188727i
$856$		0			0
$857$	17.6208	+	5.17393i	0.601914	+	0.176738i	0.568472	−	0.822703i	$-0.307535\pi$
$857$	17.6208	+	5.17393i	0.601914	+	0.176738i	0.0334423	+	0.999441i	$0.489353\pi$
$858$		0			0
$859$	−5.63587	−	12.3408i	−0.192293	−	0.421064i	0.788786	−	0.614667i	$-0.210710\pi$
$859$	−5.63587	−	12.3408i	−0.192293	−	0.421064i	−0.981080	+	0.193603i	$0.937982\pi$
$860$		0			0
$861$	−28.5871	−	18.3718i	−0.974247	−	0.626110i
$862$		0			0
$863$	0.550499	−	3.82881i	0.0187392	−	0.130334i	−0.978304	−	0.207173i	$-0.933574\pi$
$863$	0.550499	−	3.82881i	0.0187392	−	0.130334i	0.997044	+	0.0768390i	$0.0244827\pi$
$864$		0			0
$865$	36.7523	+	42.4145i	1.24962	+	1.44213i
$866$		0			0
$867$	−12.8455	+	8.25528i	−0.436255	+	0.280364i
$868$		0			0
$869$	6.05326	−	6.98583i	0.205343	−	0.236978i
$870$		0			0
$871$	11.2557	−	24.6465i	0.381384	−	0.835115i
$872$		0			0
$873$	2.44980			0.0829132
$874$		0			0
$875$	−51.2531			−1.73267
$876$		0			0
$877$	−13.2105	+	28.9270i	−0.446087	+	0.976795i	0.544353	+	0.838856i	$0.316775\pi$
$877$	−13.2105	+	28.9270i	−0.446087	+	0.976795i	−0.990441	+	0.137939i	$0.955952\pi$
$878$		0			0
$879$	−8.51783	+	9.83010i	−0.287299	+	0.331561i
$880$		0			0
$881$	27.7363	−	17.8251i	0.934460	−	0.600541i	0.0176415	−	0.999844i	$-0.494384\pi$
$881$	27.7363	−	17.8251i	0.934460	−	0.600541i	0.916819	+	0.399303i	$0.130748\pi$
$882$		0			0
$883$	30.6124	+	35.3286i	1.03019	+	1.18890i	0.981769	+	0.190076i	$0.0608736\pi$
$883$	30.6124	+	35.3286i	1.03019	+	1.18890i	0.0484214	+	0.998827i	$0.484581\pi$
$884$		0			0
$885$	1.78822	−	12.4374i	0.0601105	−	0.418078i
$886$		0			0
$887$	34.6122	+	22.2439i	1.16217	+	0.746878i	0.972025	−	0.234878i	$-0.0754692\pi$
$887$	34.6122	+	22.2439i	1.16217	+	0.746878i	0.190141	+	0.981757i	$0.439106\pi$
$888$		0			0
$889$	−17.7719	−	38.9150i	−0.596050	−	1.30517i
$890$		0			0
$891$	−2.62490	−	0.770740i	−0.0879374	−	0.0258208i
$892$		0			0
$893$	−26.2283	+	7.70133i	−0.877697	+	0.257715i
$894$		0			0
$895$	6.29155	+	43.7587i	0.210303	+	1.46269i
$896$		0			0
$897$	−18.9068	−	22.6346i	−0.631279	−	0.755749i
$898$		0			0
$899$	3.80539	+	26.4671i	0.126917	+	0.882726i
$900$		0			0
$901$	5.15438	−	1.51346i	0.171717	−	0.0504207i
$902$		0			0
$903$	−39.4599	−	11.5865i	−1.31314	−	0.385574i
$904$		0			0
$905$	−11.2579	−	24.6513i	−0.374224	−	0.819435i
$906$		0			0
$907$	44.8993	+	28.8550i	1.49086	+	0.958116i	0.996020	+	0.0891297i	$0.0284086\pi$
$907$	44.8993	+	28.8550i	1.49086	+	0.958116i	0.494837	+	0.868986i	$0.335228\pi$
$908$		0			0
$909$	−2.34081	+	16.2807i	−0.0776398	+	0.539997i
$910$		0			0
$911$	−21.7032	−	25.0468i	−0.719059	−	0.829838i	0.272135	−	0.962259i	$-0.412270\pi$
$911$	−21.7032	−	25.0468i	−0.719059	−	0.829838i	−0.991194	+	0.132421i	$0.957725\pi$
$912$		0			0
$913$	−16.5570	+	10.6405i	−0.547955	+	0.352149i
$914$		0			0
$915$	6.32200	−	7.29597i	0.208999	−	0.241197i
$916$		0			0
$917$	−8.96394	+	19.6283i	−0.296015	+	0.648183i
$918$		0			0
$919$	−21.2533			−0.701080			−0.350540	−	0.936548i	$-0.614002\pi$
$919$	−21.2533			−0.701080			−0.350540	+	0.936548i	$0.614002\pi$
$920$		0			0
$921$	−10.4705			−0.345014
$922$		0			0
$923$	26.1303	−	57.2175i	0.860091	−	1.88334i
$924$		0			0
$925$	−31.0621	+	35.8475i	−1.02131	+	1.17866i
$926$		0			0
$927$	−4.33213	+	2.78409i	−0.142286	+	0.0914416i
$928$		0			0
$929$	7.03100	+	8.11420i	0.230680	+	0.266218i	0.859275	−	0.511514i	$-0.170915\pi$
$929$	7.03100	+	8.11420i	0.230680	+	0.266218i	−0.628595	+	0.777733i	$0.716370\pi$
$930$		0			0
$931$	9.26845	−	64.4635i	0.303761	−	2.11271i
$932$		0			0
$933$	5.52391	+	3.55000i	0.180845	+	0.116222i
$934$		0			0
$935$	−5.43693	−	11.9052i	−0.177807	−	0.389342i
$936$		0			0
$937$	36.5131	+	10.7212i	1.19283	+	0.350247i	0.817107	−	0.576485i	$-0.195576\pi$
$937$	36.5131	+	10.7212i	1.19283	+	0.350247i	0.375723	+	0.926732i	$0.377394\pi$
$938$		0			0
$939$	8.86983	−	2.60442i	0.289456	−	0.0849919i
$940$		0			0
$941$	−4.08777	−	28.4310i	−0.133257	−	0.926826i	−0.941269	−	0.337659i	$-0.890365\pi$
$941$	−4.08777	−	28.4310i	−0.133257	−	0.926826i	0.808011	−	0.589167i	$-0.200544\pi$
$942$		0			0
$943$	−31.0071	−	20.7294i	−1.00973	−	0.675043i
$944$		0			0
$945$	2.26140	+	15.7284i	0.0735632	+	0.511644i
$946$		0			0
$947$	20.4458	−	6.00342i	0.664398	−	0.195085i	0.0678910	−	0.997693i	$-0.478373\pi$
$947$	20.4458	−	6.00342i	0.664398	−	0.195085i	0.596507	+	0.802608i	$0.296555\pi$
$948$		0			0
$949$	−38.3292	−	11.2545i	−1.24422	−	0.365336i
$950$		0			0
$951$	10.9105	+	23.8906i	0.353797	+	0.774707i
$952$		0			0
$953$	39.3009	+	25.2571i	1.27308	+	0.818159i	0.990018	−	0.140943i	$-0.0450133\pi$
$953$	39.3009	+	25.2571i	1.27308	+	0.818159i	0.283062	+	0.959102i	$0.408650\pi$
$954$		0			0
$955$	3.99389	−	27.7781i	0.129239	−	0.898878i
$956$		0			0
$957$	11.7085	+	13.5124i	0.378483	+	0.436793i
$958$		0			0
$959$	77.3133	−	49.6863i	2.49658	−	1.60445i
$960$		0			0
$961$	9.33892	−	10.7777i	0.301256	−	0.347667i
$962$		0			0
$963$	−3.77368	+	8.26320i	−0.121605	+	0.266278i
$964$		0			0
$965$	−31.3603			−1.00952
$966$		0			0
$967$	−16.9438			−0.544875			−0.272438	−	0.962173i	$-0.587830\pi$
$967$	−16.9438			−0.544875			−0.272438	+	0.962173i	$0.587830\pi$
$968$		0			0
$969$	2.94341	−	6.44518i	0.0945561	−	0.207049i
$970$		0			0
$971$	−19.1199	+	22.0656i	−0.613587	+	0.708117i	−0.974476	−	0.224491i	$-0.927928\pi$
$971$	−19.1199	+	22.0656i	−0.613587	+	0.708117i	0.360889	+	0.932609i	$0.382473\pi$
$972$		0			0
$973$	31.3281	−	20.1334i	1.00433	−	0.645446i
$974$		0			0
$975$	33.1248	+	38.2281i	1.06084	+	1.22428i
$976$		0			0
$977$	−1.97603	+	13.7436i	−0.0632188	+	0.439697i	0.933488	+	0.358608i	$0.116749\pi$
$977$	−1.97603	+	13.7436i	−0.0632188	+	0.439697i	−0.996707	+	0.0810883i	$0.974160\pi$
$978$		0			0
$979$	−22.5770	−	14.5093i	−0.721563	−	0.463721i
$980$		0			0
$981$	−1.31177	−	2.87238i	−0.0418817	−	0.0917081i
$982$		0			0
$983$	−2.52062	−	0.740122i	−0.0803954	−	0.0236062i	0.241287	−	0.970454i	$-0.422430\pi$
$983$	−2.52062	−	0.740122i	−0.0803954	−	0.0236062i	−0.321683	+	0.946847i	$0.604249\pi$
$984$		0			0
$985$	−33.9863	+	9.97927i	−1.08289	+	0.317966i
$986$		0			0
$987$	−3.15592	−	21.9499i	−0.100454	−	0.698673i
$988$		0			0
$989$	−43.0739	−	13.4991i	−1.36967	−	0.429245i
$990$		0			0
$991$	3.85140	+	26.7871i	0.122344	+	0.850920i	0.954889	+	0.296963i	$0.0959737\pi$
$991$	3.85140	+	26.7871i	0.122344	+	0.850920i	−0.832545	+	0.553957i	$0.813117\pi$
$992$		0			0
$993$	12.6791	−	3.72293i	0.402360	−	0.118144i
$994$		0			0
$995$	−55.5958	−	16.3244i	−1.76250	−	0.517518i
$996$		0			0
$997$	18.1844	+	39.8182i	0.575905	+	1.26106i	0.943593	+	0.331106i	$0.107422\pi$
$997$	18.1844	+	39.8182i	0.575905	+	1.26106i	−0.367689	+	0.929949i	$0.619851\pi$
$998$		0			0
$999$	4.85118	+	3.11766i	0.153485	+	0.0986385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.49.1	✓	20
3.2	odd	2		828.2.q.c.325.2		20
23.8	even	11	inner	276.2.i.a.169.1	yes	20
23.10	odd	22		6348.2.a.t.1.1		10
23.13	even	11		6348.2.a.s.1.10		10
69.8	odd	22		828.2.q.c.721.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.49.1	✓	20	1.1	even	1	trivial
276.2.i.a.169.1	yes	20	23.8	even	11	inner
828.2.q.c.325.2		20	3.2	odd	2
828.2.q.c.721.2		20	69.8	odd	22
6348.2.a.s.1.10		10	23.13	even	11
6348.2.a.t.1.1		10	23.10	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(-2.38152 + 2.74842i) q^{5} +(-3.67577 + 2.36227i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(-2.38152 + 2.74842i) q^{5} +(-3.67577 + 2.36227i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.389333 + 2.70787i) q^{11} +(-5.17334 - 3.32470i) q^{13} +(1.51073 + 3.30804i) q^{15} +(1.26223 + 0.370623i) q^{17} +(5.16792 - 1.51744i) q^{19} +(0.621829 + 4.32492i) q^{21} +(0.596495 + 4.75859i) q^{23} +(-1.17061 - 8.14175i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(6.27083 + 1.84128i) q^{29} +(1.69960 + 3.72161i) q^{31} +(2.30143 + 1.47904i) q^{33} +(2.26140 - 15.7284i) q^{35} +(-3.77633 - 4.35811i) q^{37} +(-5.17334 + 3.32470i) q^{39} +(-5.09298 + 5.87761i) q^{41} +(-3.90999 + 8.56169i) q^{43} +3.63668 q^{45} -5.07522 q^{47} +(5.02302 - 10.9989i) q^{49} +(0.861478 - 0.994198i) q^{51} +(3.43531 - 2.20774i) q^{53} +(-6.51516 - 7.51890i) q^{55} +(0.766521 - 5.33127i) q^{57} +(-2.90665 - 1.86799i) q^{59} +(-1.10276 - 2.41471i) q^{61} +(4.19240 + 1.23100i) q^{63} +(21.4581 - 6.30067i) q^{65} +(0.627040 + 4.36116i) q^{67} +(4.57636 + 1.43420i) q^{69} +(1.45569 + 10.1245i) q^{71} +(6.23284 - 1.83013i) q^{73} +(-7.89228 - 2.31738i) q^{75} +(-4.96562 - 10.8732i) q^{77} +(-2.84247 - 1.82675i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(4.71120 + 5.43702i) q^{83} +(-4.02464 + 2.58648i) q^{85} +(4.27989 - 4.93925i) q^{87} +(-4.07521 + 8.92347i) q^{89} +26.8698 q^{91} +4.09134 q^{93} +(-8.13695 + 17.8174i) q^{95} +(-1.60428 + 1.85144i) q^{97} +(2.30143 - 1.47904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more