LMFDB - Embedded newform 304.2.u.e.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(17,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("304.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.2
Root			$2.75227 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	304.81
Dual form			304.2.u.e.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.467454 - 2.65106i) q^{3} +(-0.982226 - 0.824185i) q^{5} +(-1.67233 - 2.89656i) q^{7} +(-3.99055 - 1.45244i) q^{9} +O(q^{10})$	\(q+(0.467454 - 2.65106i) q^{3} +(-0.982226 - 0.824185i) q^{5} +(-1.67233 - 2.89656i) q^{7} +(-3.99055 - 1.45244i) q^{9} +(-2.82821 + 4.89860i) q^{11} +(-0.0767659 - 0.435361i) q^{13} +(-2.64411 + 2.21868i) q^{15} +(4.46552 - 1.62532i) q^{17} +(4.08093 + 1.53166i) q^{19} +(-8.46072 + 3.07945i) q^{21} +(2.81422 - 2.36141i) q^{23} +(-0.582755 - 3.30497i) q^{25} +(-1.67798 + 2.90634i) q^{27} +(-2.83623 - 1.03230i) q^{29} +(-5.39123 - 9.33788i) q^{31} +(11.6644 + 9.78763i) q^{33} +(-0.744698 + 4.22339i) q^{35} -1.81198 q^{37} -1.19006 q^{39} +(0.700766 - 3.97424i) q^{41} +(2.06286 + 1.73095i) q^{43} +(2.72254 + 4.71558i) q^{45} +(5.70150 + 2.07517i) q^{47} +(-2.09339 + 3.62586i) q^{49} +(-2.22139 - 12.5981i) q^{51} +(1.25029 - 1.04911i) q^{53} +(6.81529 - 2.48056i) q^{55} +(5.96819 - 10.1028i) q^{57} +(8.03671 - 2.92512i) q^{59} +(1.98835 - 1.66843i) q^{61} +(2.46644 + 13.9879i) q^{63} +(-0.283417 + 0.490892i) q^{65} +(-3.79002 - 1.37945i) q^{67} +(-4.94473 - 8.56453i) q^{69} +(8.49861 + 7.13118i) q^{71} +(-1.27886 + 7.25275i) q^{73} -9.03409 q^{75} +18.9188 q^{77} +(-1.76413 + 10.0049i) q^{79} +(-2.83887 - 2.38209i) q^{81} +(2.27842 + 3.94633i) q^{83} +(-5.72571 - 2.08399i) q^{85} +(-4.06252 + 7.03648i) q^{87} +(2.24994 + 12.7600i) q^{89} +(-1.13267 + 0.950426i) q^{91} +(-27.2755 + 9.92746i) q^{93} +(-2.74602 - 4.86788i) q^{95} +(11.1841 - 4.07067i) q^{97} +(18.4010 - 15.4403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{7} - 3 q^{9} - 3 q^{11} - 9 q^{13} + 15 q^{15} - 3 q^{17} + 12 q^{19} - 15 q^{21} + 12 q^{23} - 18 q^{25} + 9 q^{27} + 27 q^{29} - 6 q^{31} + 48 q^{33} - 33 q^{35} - 12 q^{37} - 60 q^{39} + 3 q^{41} - 27 q^{43} + 24 q^{45} + 15 q^{47} + 9 q^{49} + 33 q^{51} - 21 q^{53} + 27 q^{55} - 42 q^{57} + 48 q^{59} - 6 q^{61} + 9 q^{63} - 33 q^{65} - 24 q^{67} - 33 q^{69} + 30 q^{73} - 42 q^{75} + 24 q^{77} - 3 q^{79} + 3 q^{81} - 3 q^{83} - 42 q^{85} + 18 q^{87} - 18 q^{89} + 24 q^{91} - 78 q^{93} - 9 q^{95} + 12 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 - 3 * q^11 - 9 * q^13 + 15 * q^15 - 3 * q^17 + 12 * q^19 - 15 * q^21 + 12 * q^23 - 18 * q^25 + 9 * q^27 + 27 * q^29 - 6 * q^31 + 48 * q^33 - 33 * q^35 - 12 * q^37 - 60 * q^39 + 3 * q^41 - 27 * q^43 + 24 * q^45 + 15 * q^47 + 9 * q^49 + 33 * q^51 - 21 * q^53 + 27 * q^55 - 42 * q^57 + 48 * q^59 - 6 * q^61 + 9 * q^63 - 33 * q^65 - 24 * q^67 - 33 * q^69 + 30 * q^73 - 42 * q^75 + 24 * q^77 - 3 * q^79 + 3 * q^81 - 3 * q^83 - 42 * q^85 + 18 * q^87 - 18 * q^89 + 24 * q^91 - 78 * q^93 - 9 * q^95 + 12 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	0.467454	−	2.65106i	0.269885	−	1.53059i	−0.484870	−	0.874586i	$-0.661133\pi$
$3$	0.467454	−	2.65106i	0.269885	−	1.53059i	0.754755	−	0.656007i	$-0.227756\pi$
$4$		0			0
$5$	−0.982226	−	0.824185i	−0.439265	−	0.368587i	0.396169	−	0.918177i	$-0.370339\pi$
$5$	−0.982226	−	0.824185i	−0.439265	−	0.368587i	−0.835434	+	0.549591i	$0.814784\pi$
$6$		0			0
$7$	−1.67233	−	2.89656i	−0.632082	−	1.09480i	−0.987125	−	0.159949i	$-0.948867\pi$
$7$	−1.67233	−	2.89656i	−0.632082	−	1.09480i	0.355043	−	0.934850i	$-0.384466\pi$
$8$		0			0
$9$	−3.99055	−	1.45244i	−1.33018	−	0.484147i
$10$		0			0
$11$	−2.82821	+	4.89860i	−0.852736	+	1.47698i	0.0259929	+	0.999662i	$0.491725\pi$
$11$	−2.82821	+	4.89860i	−0.852736	+	1.47698i	−0.878729	+	0.477321i	$0.841608\pi$
$12$		0			0
$13$	−0.0767659	−	0.435361i	−0.0212910	−	0.120747i	0.972310	−	0.233695i	$-0.0750818\pi$
$13$	−0.0767659	−	0.435361i	−0.0212910	−	0.120747i	−0.993601	+	0.112948i	$0.963971\pi$
$14$		0			0
$15$	−2.64411	+	2.21868i	−0.682707	+	0.572859i
$16$		0			0
$17$	4.46552	−	1.62532i	1.08305	−	0.394197i	0.262007	−	0.965066i	$-0.415616\pi$
$17$	4.46552	−	1.62532i	1.08305	−	0.394197i	0.821041	+	0.570869i	$0.193394\pi$
$18$		0			0
$19$	4.08093	+	1.53166i	0.936230	+	0.351388i
$19$	4.08093	+	1.53166i	0.936230	+	0.351388i
$20$		0			0
$21$	−8.46072	+	3.07945i	−1.84628	+	0.671991i
$22$		0			0
$23$	2.81422	−	2.36141i	0.586806	−	0.492388i	−0.300369	−	0.953823i	$-0.597110\pi$
$23$	2.81422	−	2.36141i	0.586806	−	0.492388i	0.887174	+	0.461435i	$0.152665\pi$
$24$		0			0
$25$	−0.582755	−	3.30497i	−0.116551	−	0.660993i
$26$		0			0
$27$	−1.67798	+	2.90634i	−0.322927	+	0.559325i
$28$		0			0
$29$	−2.83623	−	1.03230i	−0.526675	−	0.191694i	0.0649778	−	0.997887i	$-0.479302\pi$
$29$	−2.83623	−	1.03230i	−0.526675	−	0.191694i	−0.591653	+	0.806193i	$0.701525\pi$
$30$		0			0
$31$	−5.39123	−	9.33788i	−0.968293	−	1.67713i	−0.700495	−	0.713658i	$-0.747037\pi$
$31$	−5.39123	−	9.33788i	−0.968293	−	1.67713i	−0.267798	−	0.963475i	$-0.586296\pi$
$32$		0			0
$33$	11.6644	+	9.78763i	2.03052	+	1.70381i
$34$		0			0
$35$	−0.744698	+	4.22339i	−0.125877	+	0.713884i
$36$		0			0
$37$	−1.81198			−0.297888			−0.148944	−	0.988846i	$-0.547587\pi$
$37$	−1.81198			−0.297888			−0.148944	+	0.988846i	$0.547587\pi$
$38$		0			0
$39$	−1.19006			−0.190561
$40$		0			0
$41$	0.700766	−	3.97424i	0.109441	−	0.620672i	−0.879912	−	0.475137i	$-0.842399\pi$
$41$	0.700766	−	3.97424i	0.109441	−	0.620672i	0.989353	−	0.145535i	$-0.0464903\pi$
$42$		0			0
$43$	2.06286	+	1.73095i	0.314584	+	0.263967i	0.786383	−	0.617739i	$-0.211951\pi$
$43$	2.06286	+	1.73095i	0.314584	+	0.263967i	−0.471800	+	0.881706i	$0.656396\pi$
$44$		0			0
$45$	2.72254	+	4.71558i	0.405853	+	0.702957i
$46$		0			0
$47$	5.70150	+	2.07517i	0.831649	+	0.302695i	0.722535	−	0.691334i	$-0.242977\pi$
$47$	5.70150	+	2.07517i	0.831649	+	0.302695i	0.109113	+	0.994029i	$0.465199\pi$
$48$		0			0
$49$	−2.09339	+	3.62586i	−0.299056	+	0.517980i
$50$		0			0
$51$	−2.22139	−	12.5981i	−0.311057	−	1.76409i
$52$		0			0
$53$	1.25029	−	1.04911i	0.171740	−	0.144107i	−0.552866	−	0.833270i	$-0.686466\pi$
$53$	1.25029	−	1.04911i	0.171740	−	0.144107i	0.724606	+	0.689163i	$0.242022\pi$
$54$		0			0
$55$	6.81529	−	2.48056i	0.918973	−	0.334479i
$56$		0			0
$57$	5.96819	−	10.1028i	0.790506	−	1.33815i
$58$		0			0
$59$	8.03671	−	2.92512i	1.04629	−	0.380819i	0.239029	−	0.971012i	$-0.423171\pi$
$59$	8.03671	−	2.92512i	1.04629	−	0.380819i	0.807262	+	0.590194i	$0.200949\pi$
$60$		0			0
$61$	1.98835	−	1.66843i	0.254582	−	0.213620i	−0.506560	−	0.862205i	$-0.669083\pi$
$61$	1.98835	−	1.66843i	0.254582	−	0.213620i	0.761143	+	0.648585i	$0.224639\pi$
$62$		0			0
$63$	2.46644	+	13.9879i	0.310742	+	1.76230i
$64$		0			0
$65$	−0.283417	+	0.490892i	−0.0351535	+	0.0608877i
$66$		0			0
$67$	−3.79002	−	1.37945i	−0.463024	−	0.168527i	0.0999655	−	0.994991i	$-0.468127\pi$
$67$	−3.79002	−	1.37945i	−0.463024	−	0.168527i	−0.562990	+	0.826464i	$0.690349\pi$
$68$		0			0
$69$	−4.94473	−	8.56453i	−0.595276	−	1.03105i
$70$		0			0
$71$	8.49861	+	7.13118i	1.00860	+	0.846315i	0.988152	−	0.153476i	$-0.0490468\pi$
$71$	8.49861	+	7.13118i	1.00860	+	0.846315i	0.0204465	+	0.999791i	$0.493491\pi$
$72$		0			0
$73$	−1.27886	+	7.25275i	−0.149679	+	0.848871i	0.813812	+	0.581129i	$0.197389\pi$
$73$	−1.27886	+	7.25275i	−0.149679	+	0.848871i	−0.963491	+	0.267742i	$0.913722\pi$
$74$		0			0
$75$	−9.03409			−1.04317
$76$		0			0
$77$	18.9188			2.15600
$78$		0			0
$79$	−1.76413	+	10.0049i	−0.198480	+	1.12564i	0.708894	+	0.705315i	$0.249194\pi$
$79$	−1.76413	+	10.0049i	−0.198480	+	1.12564i	−0.907374	+	0.420323i	$0.861917\pi$
$80$		0			0
$81$	−2.83887	−	2.38209i	−0.315430	−	0.264677i
$82$		0			0
$83$	2.27842	+	3.94633i	0.250089	+	0.433166i	0.963550	−	0.267528i	$-0.0862069\pi$
$83$	2.27842	+	3.94633i	0.250089	+	0.433166i	−0.713461	+	0.700695i	$0.752874\pi$
$84$		0			0
$85$	−5.72571	−	2.08399i	−0.621041	−	0.226040i
$86$		0			0
$87$	−4.06252	+	7.03648i	−0.435547	+	0.754390i
$88$		0			0
$89$	2.24994	+	12.7600i	0.238493	+	1.35256i	0.835131	+	0.550050i	$0.185392\pi$
$89$	2.24994	+	12.7600i	0.238493	+	1.35256i	−0.596638	+	0.802510i	$0.703497\pi$
$90$		0			0
$91$	−1.13267	+	0.950426i	−0.118736	+	0.0996317i
$92$		0			0
$93$	−27.2755	+	9.92746i	−2.82833	+	1.02943i
$94$		0			0
$95$	−2.74602	−	4.86788i	−0.281736	−	0.499434i
$96$		0			0
$97$	11.1841	−	4.07067i	1.13557	−	0.413314i	0.295258	−	0.955417i	$-0.404594\pi$
$97$	11.1841	−	4.07067i	1.13557	−	0.413314i	0.840311	+	0.542104i	$0.182372\pi$
$98$		0			0
$99$	18.4010	−	15.4403i	1.84937	−	1.55181i
$100$		0			0
$101$	1.77055	+	10.0413i	0.176176	+	0.999144i	0.936778	+	0.349925i	$0.113793\pi$
$101$	1.77055	+	10.0413i	0.176176	+	0.999144i	−0.760602	+	0.649219i	$0.775096\pi$
$102$		0			0
$103$	−2.26339	+	3.92030i	−0.223018	+	0.386279i	−0.955723	−	0.294268i	$-0.904924\pi$
$103$	−2.26339	+	3.92030i	−0.223018	+	0.386279i	0.732705	+	0.680547i	$0.238258\pi$
$104$		0			0
$105$	10.8484	+	3.94849i	1.05869	+	0.385333i
$106$		0			0
$107$	0.639415	+	1.10750i	0.0618146	+	0.107066i	0.895277	−	0.445511i	$-0.146978\pi$
$107$	0.639415	+	1.10750i	0.0618146	+	0.107066i	−0.833462	+	0.552577i	$0.813645\pi$
$108$		0			0
$109$	4.92058	+	4.12885i	0.471306	+	0.395472i	0.847271	−	0.531161i	$-0.178244\pi$
$109$	4.92058	+	4.12885i	0.471306	+	0.395472i	−0.375965	+	0.926634i	$0.622689\pi$
$110$		0			0
$111$	−0.847018	+	4.80368i	−0.0803953	+	0.455945i
$112$		0			0
$113$	−1.77037			−0.166542			−0.0832710	−	0.996527i	$-0.526537\pi$
$113$	−1.77037			−0.166542			−0.0832710	+	0.996527i	$0.526537\pi$
$114$		0			0
$115$	−4.71044			−0.439251
$116$		0			0
$117$	−0.325998	+	1.84883i	−0.0301386	+	0.170924i
$118$		0			0
$119$	−12.1757	−	10.2166i	−1.11614	−	0.936554i
$120$		0			0
$121$	−10.4975	−	18.1822i	−0.954319	−	1.65293i
$122$		0			0
$123$	−10.2084	−	3.71555i	−0.920459	−	0.335020i
$124$		0			0
$125$	−5.35702	+	9.27863i	−0.479146	+	0.829906i
$126$		0			0
$127$	−2.34112	−	13.2771i	−0.207740	−	1.17815i	−0.893069	−	0.449920i	$-0.851452\pi$
$127$	−2.34112	−	13.2771i	−0.207740	−	1.17815i	0.685328	−	0.728234i	$-0.259659\pi$
$128$		0			0
$129$	5.55315	−	4.65964i	0.488927	−	0.410259i
$130$		0			0
$131$	−9.52163	+	3.46559i	−0.831908	+	0.302790i	−0.722642	−	0.691223i	$-0.757072\pi$
$131$	−9.52163	+	3.46559i	−0.831908	+	0.302790i	−0.109267	+	0.994012i	$0.534850\pi$
$132$		0			0
$133$	−2.38811	−	14.3821i	−0.207076	−	1.24709i
$134$		0			0
$135$	4.04351	−	1.47172i	0.348010	−	0.126665i
$136$		0			0
$137$	−2.67862	+	2.24763i	−0.228850	+	0.192028i	−0.750001	−	0.661436i	$-0.769947\pi$
$137$	−2.67862	+	2.24763i	−0.228850	+	0.192028i	0.521151	+	0.853464i	$0.325503\pi$
$138$		0			0
$139$	−1.85061	−	10.4953i	−0.156966	−	0.890201i	−0.956966	−	0.290200i	$-0.906278\pi$
$139$	−1.85061	−	10.4953i	−0.156966	−	0.890201i	0.800000	−	0.600000i	$-0.204833\pi$
$140$		0			0
$141$	8.16661	−	14.1450i	0.687753	−	1.19122i
$142$		0			0
$143$	2.34977	+	0.855246i	0.196498	+	0.0715193i
$144$		0			0
$145$	1.93501	+	3.35154i	0.160694	+	0.278330i
$146$		0			0
$147$	8.63383	+	7.24464i	0.712106	+	0.597528i
$148$		0			0
$149$	−1.46233	+	8.29331i	−0.119799	+	0.679415i	0.864463	+	0.502697i	$0.167659\pi$
$149$	−1.46233	+	8.29331i	−0.119799	+	0.679415i	−0.984262	+	0.176717i	$0.943452\pi$
$150$		0			0
$151$	11.3794			0.926039			0.463020	−	0.886348i	$-0.346766\pi$
$151$	11.3794			0.926039			0.463020	+	0.886348i	$0.346766\pi$
$152$		0			0
$153$	−20.1806			−1.63150
$154$		0			0
$155$	−2.40074	+	13.6153i	−0.192832	+	1.09361i
$156$		0			0
$157$	−3.58204	−	3.00569i	−0.285878	−	0.239880i	0.488560	−	0.872531i	$-0.337522\pi$
$157$	−3.58204	−	3.00569i	−0.285878	−	0.239880i	−0.774437	+	0.632651i	$0.781967\pi$
$158$		0			0
$159$	−2.19682	−	3.80500i	−0.174219	−	0.301756i
$160$		0			0
$161$	−11.5463	−	4.20251i	−0.909975	−	0.331204i
$162$		0			0
$163$	−0.914990	+	1.58481i	−0.0716676	+	0.124132i	−0.899632	−	0.436648i	$-0.856165\pi$
$163$	−0.914990	+	1.58481i	−0.0716676	+	0.124132i	0.827965	+	0.560780i	$0.189499\pi$
$164$		0			0
$165$	−3.39030	−	19.2273i	−0.263934	−	1.49684i
$166$		0			0
$167$	15.3013	−	12.8393i	1.18405	−	0.993534i	0.184104	−	0.982907i	$-0.441062\pi$
$167$	15.3013	−	12.8393i	1.18405	−	0.993534i	0.999944	−	0.0106275i	$-0.00338291\pi$
$168$		0			0
$169$	12.0324	−	4.37942i	0.925566	−	0.336878i
$170$		0			0
$171$	−14.0605	−	12.0395i	−1.07523	−	0.920683i
$172$		0			0
$173$	4.39155	−	1.59839i	0.333883	−	0.121524i	−0.169638	−	0.985506i	$-0.554260\pi$
$173$	4.39155	−	1.59839i	0.333883	−	0.121524i	0.503521	+	0.863983i	$0.332038\pi$
$174$		0			0
$175$	−8.59849	+	7.21499i	−0.649985	+	0.545402i
$176$		0			0
$177$	−3.99790	−	22.6732i	−0.300500	−	1.70422i
$178$		0			0
$179$	3.82125	−	6.61860i	0.285613	−	0.494697i	−0.687144	−	0.726521i	$-0.741136\pi$
$179$	3.82125	−	6.61860i	0.285613	−	0.494697i	0.972758	+	0.231824i	$0.0744693\pi$
$180$		0			0
$181$	−5.72692	−	2.08443i	−0.425678	−	0.154934i	0.120292	−	0.992739i	$-0.461617\pi$
$181$	−5.72692	−	2.08443i	−0.425678	−	0.154934i	−0.545971	+	0.837804i	$0.683839\pi$
$182$		0			0
$183$	−3.49364	−	6.05116i	−0.258257	−	0.447315i
$184$		0			0
$185$	1.77977	+	1.49341i	0.130852	+	0.109797i
$186$		0			0
$187$	−4.66764	+	26.4715i	−0.341332	+	1.93579i
$188$		0			0
$189$	11.2245			0.816465
$190$		0			0
$191$	−7.93272			−0.573992			−0.286996	−	0.957932i	$-0.592657\pi$
$191$	−7.93272			−0.573992			−0.286996	+	0.957932i	$0.592657\pi$
$192$		0			0
$193$	−1.18939	+	6.74535i	−0.0856140	+	0.485541i	0.911608	+	0.411060i	$0.134841\pi$
$193$	−1.18939	+	6.74535i	−0.0856140	+	0.485541i	−0.997222	+	0.0744815i	$0.976270\pi$
$194$		0			0
$195$	1.16890	+	0.980826i	0.0837069	+	0.0702384i
$196$		0			0
$197$	12.7754	+	22.1277i	0.910213	+	1.57653i	0.813763	+	0.581197i	$0.197415\pi$
$197$	12.7754	+	22.1277i	0.910213	+	1.57653i	0.0964500	+	0.995338i	$0.469251\pi$
$198$		0			0
$199$	−7.16718	−	2.60864i	−0.508068	−	0.184922i	0.0752513	−	0.997165i	$-0.476024\pi$
$199$	−7.16718	−	2.60864i	−0.508068	−	0.184922i	−0.583319	+	0.812243i	$0.698246\pi$
$200$		0			0
$201$	−5.42868	+	9.40275i	−0.382910	+	0.663219i
$202$		0			0
$203$	1.75299	+	9.94169i	0.123036	+	0.697770i
$204$		0			0
$205$	−3.96382	+	3.32604i	−0.276845	+	0.232301i
$206$		0			0
$207$	−14.6601	+	5.33584i	−1.01895	+	0.370867i
$208$		0			0
$209$	−19.0447	+	15.6590i	−1.31735	+	1.08315i
$210$		0			0
$211$	10.7791	−	3.92328i	0.742066	−	0.270090i	0.0568025	−	0.998385i	$-0.481909\pi$
$211$	10.7791	−	3.92328i	0.742066	−	0.270090i	0.685263	+	0.728296i	$0.259687\pi$
$212$		0			0
$213$	22.8779	−	19.1969i	1.56757	−	1.31535i
$214$		0			0
$215$	−0.599575	−	3.40036i	−0.0408907	−	0.231903i
$216$		0			0
$217$	−18.0318	+	31.2321i	−1.22408	+	2.12017i
$218$		0			0
$219$	18.6297	+	6.78066i	1.25888	+	0.458195i
$220$		0			0
$221$	−1.05040	−	1.81935i	−0.0706575	−	0.122382i
$222$		0			0
$223$	2.14399	+	1.79902i	0.143572	+	0.120471i	0.711745	−	0.702438i	$-0.247905\pi$
$223$	2.14399	+	1.79902i	0.143572	+	0.120471i	−0.568173	+	0.822909i	$0.692350\pi$
$224$		0			0
$225$	−2.47476	+	14.0351i	−0.164984	+	0.935670i
$226$		0			0
$227$	6.05837			0.402108			0.201054	−	0.979580i	$-0.435563\pi$
$227$	6.05837			0.402108			0.201054	+	0.979580i	$0.435563\pi$
$228$		0			0
$229$	−8.97380			−0.593005			−0.296503	−	0.955032i	$-0.595820\pi$
$229$	−8.97380			−0.593005			−0.296503	+	0.955032i	$0.595820\pi$
$230$		0			0
$231$	8.84368	−	50.1550i	0.581871	−	3.29996i
$232$		0			0
$233$	−5.62321	−	4.71843i	−0.368389	−	0.309115i	0.439735	−	0.898127i	$-0.355072\pi$
$233$	−5.62321	−	4.71843i	−0.368389	−	0.309115i	−0.808124	+	0.589013i	$0.799517\pi$
$234$		0			0
$235$	−3.88983	−	6.73738i	−0.253744	−	0.439498i
$236$		0			0
$237$	25.6990	+	9.35366i	1.66933	+	0.607585i
$238$		0			0
$239$	−9.58552	+	16.6026i	−0.620036	+	1.07393i	0.369443	+	0.929253i	$0.379549\pi$
$239$	−9.58552	+	16.6026i	−0.620036	+	1.07393i	−0.989479	+	0.144680i	$0.953785\pi$
$240$		0			0
$241$	−2.10589	−	11.9431i	−0.135652	−	0.769323i	−0.974403	−	0.224808i	$-0.927825\pi$
$241$	−2.10589	−	11.9431i	−0.135652	−	0.769323i	0.838751	−	0.544515i	$-0.183286\pi$
$242$		0			0
$243$	−15.3545	+	12.8840i	−0.984995	+	0.826509i
$244$		0			0
$245$	5.04457	−	1.83607i	0.322286	−	0.117302i
$246$		0			0
$247$	0.353550	−	1.89426i	0.0224959	−	0.120529i
$248$		0			0
$249$	11.5270	−	4.19550i	0.730496	−	0.265879i
$250$		0			0
$251$	−11.1944	+	9.39320i	−0.706583	+	0.592893i	−0.923638	−	0.383266i	$-0.874799\pi$
$251$	−11.1944	+	9.39320i	−0.706583	+	0.592893i	0.217055	+	0.976159i	$0.430355\pi$
$252$		0			0
$253$	3.60841	+	20.4643i	0.226859	+	1.28658i
$254$		0			0
$255$	−8.20130	+	14.2051i	−0.513585	+	0.889556i
$256$		0			0
$257$	−2.43492	−	0.886240i	−0.151886	−	0.0552821i	0.264958	−	0.964260i	$-0.414642\pi$
$257$	−2.43492	−	0.886240i	−0.151886	−	0.0552821i	−0.416845	+	0.908978i	$0.636864\pi$
$258$		0			0
$259$	3.03023	+	5.24852i	0.188289	+	0.326127i
$260$		0			0
$261$	9.81878	+	8.23893i	0.607767	+	0.509977i
$262$		0			0
$263$	3.99672	−	22.6665i	0.246448	−	1.39768i	−0.570657	−	0.821189i	$-0.693311\pi$
$263$	3.99672	−	22.6665i	0.246448	−	1.39768i	0.817105	−	0.576489i	$-0.195578\pi$
$264$		0			0
$265$	−2.09273			−0.128555
$266$		0			0
$267$	34.8794			2.13459
$268$		0			0
$269$	4.54659	−	25.7850i	0.277210	−	1.57214i	−0.454642	−	0.890674i	$-0.650233\pi$
$269$	4.54659	−	25.7850i	0.277210	−	1.57214i	0.731852	−	0.681464i	$-0.238656\pi$
$270$		0			0
$271$	11.3192	+	9.49794i	0.687592	+	0.576959i	0.918214	−	0.396085i	$-0.129631\pi$
$271$	11.3192	+	9.49794i	0.687592	+	0.576959i	−0.230621	+	0.973044i	$0.574076\pi$
$272$		0			0
$273$	1.99017	+	3.44707i	0.120450	+	0.208626i
$274$		0			0
$275$	17.8379	+	6.49245i	1.07566	+	0.391509i
$276$		0			0
$277$	7.37349	−	12.7713i	0.443030	−	0.767351i	−0.554882	−	0.831929i	$-0.687237\pi$
$277$	7.37349	−	12.7713i	0.443030	−	0.767351i	0.997913	+	0.0645778i	$0.0205701\pi$
$278$		0			0
$279$	7.95124	+	45.0937i	0.476028	+	2.69969i
$280$		0			0
$281$	10.6791	−	8.96081i	0.637061	−	0.534557i	−0.266053	−	0.963958i	$-0.585720\pi$
$281$	10.6791	−	8.96081i	0.637061	−	0.534557i	0.903114	+	0.429401i	$0.141275\pi$
$282$		0			0
$283$	−17.1859	+	6.25516i	−1.02160	+	0.371831i	−0.797876	−	0.602822i	$-0.794043\pi$
$283$	−17.1859	+	6.25516i	−1.02160	+	0.371831i	−0.223722	+	0.974653i	$0.571821\pi$
$284$		0			0
$285$	−14.1887	+	5.00437i	−0.840467	+	0.296433i
$286$		0			0
$287$	−12.6836	+	4.61644i	−0.748687	+	0.272500i
$288$		0			0
$289$	4.27647	−	3.58838i	0.251557	−	0.211081i
$290$		0			0
$291$	−5.56356	−	31.5525i	−0.326142	−	1.84964i
$292$		0			0
$293$	−12.3737	+	21.4319i	−0.722882	+	1.25207i	0.236958	+	0.971520i	$0.423850\pi$
$293$	−12.3737	+	21.4319i	−0.722882	+	1.25207i	−0.959840	+	0.280548i	$0.909484\pi$
$294$		0			0
$295$	−10.3047	−	3.75061i	−0.599964	−	0.218369i
$296$		0			0
$297$	−9.49132	−	16.4395i	−0.550742	−	0.953914i
$298$		0			0
$299$	−1.24410	−	1.04393i	−0.0719483	−	0.0603718i
$300$		0			0
$301$	1.56401	−	8.86993i	0.0901480	−	0.511254i
$302$		0			0
$303$	27.4477			1.57683
$304$		0			0
$305$	−3.32810			−0.190567
$306$		0			0
$307$	3.98228	−	22.5846i	0.227281	−	1.28897i	−0.630996	−	0.775786i	$-0.717354\pi$
$307$	3.98228	−	22.5846i	0.227281	−	1.28897i	0.858277	−	0.513187i	$-0.171535\pi$
$308$		0			0
$309$	9.33494	+	7.83295i	0.531046	+	0.445601i
$310$		0			0
$311$	14.8333	+	25.6920i	0.841119	+	1.45686i	0.888949	+	0.458005i	$0.151436\pi$
$311$	14.8333	+	25.6920i	0.841119	+	1.45686i	−0.0478305	+	0.998855i	$0.515231\pi$
$312$		0			0
$313$	19.4749	+	7.08829i	1.10079	+	0.400654i	0.827606	−	0.561309i	$-0.189702\pi$
$313$	19.4749	+	7.08829i	1.10079	+	0.400654i	0.273181	+	0.961963i	$0.411924\pi$
$314$		0			0
$315$	9.10599	−	15.7720i	0.513064	−	0.888654i
$316$		0			0
$317$	−5.62856	−	31.9211i	−0.316131	−	1.79287i	−0.565804	−	0.824540i	$-0.691434\pi$
$317$	−5.62856	−	31.9211i	−0.316131	−	1.79287i	0.249672	−	0.968330i	$-0.419677\pi$
$318$		0			0
$319$	13.0783	−	10.9740i	0.732244	−	0.614426i
$320$		0			0
$321$	3.23495	−	1.17743i	0.180557	−	0.0657175i
$322$		0			0
$323$	20.7129	+	0.206866i	1.15250	+	0.0115103i
$324$		0			0
$325$	−1.39412	+	0.507418i	−0.0773318	+	0.0281465i
$326$		0			0
$327$	13.2460	−	11.1147i	0.732506	−	0.614645i
$328$		0			0
$329$	−3.52392	−	19.9851i	−0.194280	−	1.10182i
$330$		0			0
$331$	−10.6194	+	18.3933i	−0.583694	+	1.01099i	0.411343	+	0.911481i	$0.365060\pi$
$331$	−10.6194	+	18.3933i	−0.583694	+	1.01099i	−0.995037	+	0.0995068i	$0.968273\pi$
$332$		0			0
$333$	7.23080	+	2.63180i	0.396245	+	0.144222i
$334$		0			0
$335$	2.58573	+	4.47861i	0.141273	+	0.244693i
$336$		0			0
$337$	−9.01391	−	7.56357i	−0.491019	−	0.412014i	0.363372	−	0.931644i	$-0.381625\pi$
$337$	−9.01391	−	7.56357i	−0.491019	−	0.412014i	−0.854391	+	0.519630i	$0.826070\pi$
$338$		0			0
$339$	−0.827565	+	4.69335i	−0.0449471	+	0.254908i
$340$		0			0
$341$	60.9900			3.30279
$342$		0			0
$343$	−9.40926			−0.508052
$344$		0			0
$345$	−2.20192	+	12.4877i	−0.118547	+	0.672314i
$346$		0			0
$347$	−19.7226	−	16.5492i	−1.05876	−	0.888408i	−0.0647756	−	0.997900i	$-0.520633\pi$
$347$	−19.7226	−	16.5492i	−1.05876	−	0.888408i	−0.993988	+	0.109492i	$0.965078\pi$
$348$		0			0
$349$	−5.07687	−	8.79340i	−0.271759	−	0.470700i	0.697554	−	0.716533i	$-0.254272\pi$
$349$	−5.07687	−	8.79340i	−0.271759	−	0.470700i	−0.969312	+	0.245833i	$0.920939\pi$
$350$		0			0
$351$	1.39412	+	0.507418i	0.0744125	+	0.0270839i
$352$		0			0
$353$	−7.62054	+	13.1992i	−0.405600	+	0.702521i	−0.994391	−	0.105765i	$-0.966271\pi$
$353$	−7.62054	+	13.1992i	−0.405600	+	0.702521i	0.588791	+	0.808286i	$0.299604\pi$
$354$		0			0
$355$	−2.47014	−	14.0089i	−0.131101	−	0.743513i
$356$		0			0
$357$	−32.7764	+	27.5027i	−1.73471	+	1.45560i
$358$		0			0
$359$	−17.6336	+	6.41811i	−0.930666	+	0.338735i	−0.762473	−	0.647020i	$-0.776015\pi$
$359$	−17.6336	+	6.41811i	−0.930666	+	0.338735i	−0.168192	+	0.985754i	$0.553793\pi$
$360$		0			0
$361$	14.3080	+	12.5012i	0.753054	+	0.657959i
$362$		0			0
$363$	−53.1093	+	19.3302i	−2.78752	+	1.01457i
$364$		0			0
$365$	7.23374	−	6.06983i	0.378631	−	0.317709i
$366$		0			0
$367$	−2.10282	−	11.9257i	−0.109766	−	0.622516i	−0.989209	−	0.146511i	$-0.953196\pi$
$367$	−2.10282	−	11.9257i	−0.109766	−	0.622516i	0.879443	−	0.476005i	$-0.157916\pi$
$368$		0			0
$369$	−8.56879	+	14.8416i	−0.446074	+	0.772622i
$370$		0			0
$371$	−5.12972	−	1.86707i	−0.266322	−	0.0969332i
$372$		0			0
$373$	16.5778	+	28.7136i	0.858366	+	1.48673i	0.873487	+	0.486847i	$0.161853\pi$
$373$	16.5778	+	28.7136i	0.858366	+	1.48673i	−0.0151214	+	0.999886i	$0.504813\pi$
$374$		0			0
$375$	22.0941	+	18.5391i	1.14093	+	0.957357i
$376$		0			0
$377$	−0.231699	+	1.31403i	−0.0119331	+	0.0676761i
$378$		0			0
$379$	19.5956			1.00656			0.503280	−	0.864123i	$-0.332126\pi$
$379$	19.5956			1.00656			0.503280	+	0.864123i	$0.332126\pi$
$380$		0			0
$381$	−36.2929			−1.85934
$382$		0			0
$383$	−4.34973	+	24.6685i	−0.222261	+	1.26050i	0.645592	+	0.763682i	$0.276611\pi$
$383$	−4.34973	+	24.6685i	−0.222261	+	1.26050i	−0.867853	+	0.496821i	$0.834501\pi$
$384$		0			0
$385$	−18.5825	−	15.5926i	−0.947054	−	0.794673i
$386$		0			0
$387$	−5.71786	−	9.90362i	−0.290655	−	0.503429i
$388$		0			0
$389$	15.5821	+	5.67141i	0.790042	+	0.287552i	0.705353	−	0.708856i	$-0.250788\pi$
$389$	15.5821	+	5.67141i	0.790042	+	0.287552i	0.0846883	+	0.996407i	$0.473011\pi$
$390$		0			0
$391$	8.72892	−	15.1189i	0.441440	−	0.764597i
$392$		0			0
$393$	4.73658	+	26.8625i	0.238929	+	1.35503i
$394$		0			0
$395$	9.97866	−	8.37309i	0.502081	−	0.421296i
$396$		0			0
$397$	−28.0884	+	10.2234i	−1.40972	+	0.513095i	−0.931047	−	0.364899i	$-0.881103\pi$
$397$	−28.0884	+	10.2234i	−1.40972	+	0.513095i	−0.478671	+	0.877994i	$0.658881\pi$
$398$		0			0
$399$	−39.2443	−	0.391944i	−1.96467	−	0.0196218i
$400$		0			0
$401$	−18.9709	+	6.90486i	−0.947364	+	0.344812i	−0.769070	−	0.639165i	$-0.779280\pi$
$401$	−18.9709	+	6.90486i	−0.947364	+	0.344812i	−0.178294	+	0.983977i	$0.557058\pi$
$402$		0			0
$403$	−3.65149	+	3.06396i	−0.181894	+	0.152627i
$404$		0			0
$405$	0.825123	+	4.67951i	0.0410007	+	0.232527i
$406$		0			0
$407$	5.12465	−	8.87616i	0.254020	−	0.439975i
$408$		0			0
$409$	11.1841	+	4.07067i	0.553016	+	0.201282i	0.603386	−	0.797449i	$-0.293818\pi$
$409$	11.1841	+	4.07067i	0.553016	+	0.201282i	−0.0503698	+	0.998731i	$0.516040\pi$
$410$		0			0
$411$	4.70647	+	8.15185i	0.232153	+	0.402101i
$412$		0			0
$413$	−21.9129	−	18.3871i	−1.07826	−	0.904769i
$414$		0			0
$415$	1.01459	−	5.75403i	0.0498043	−	0.282454i
$416$		0			0
$417$	−28.6888			−1.40490
$418$		0			0
$419$	−17.0337			−0.832151			−0.416076	−	0.909330i	$-0.636595\pi$
$419$	−17.0337			−0.832151			−0.416076	+	0.909330i	$0.636595\pi$
$420$		0			0
$421$	0.951328	−	5.39525i	0.0463649	−	0.262948i	−0.952810	−	0.303568i	$-0.901822\pi$
$421$	0.951328	−	5.39525i	0.0463649	−	0.262948i	0.999175	+	0.0406196i	$0.0129332\pi$
$422$		0			0
$423$	−19.7380	−	16.5622i	−0.959697	−	0.805281i
$424$		0			0
$425$	−7.97392	−	13.8112i	−0.386792	−	0.669943i
$426$		0			0
$427$	−8.15789	−	2.96923i	−0.394788	−	0.143691i
$428$		0			0
$429$	3.36572	−	5.82960i	0.162499	−	0.281456i
$430$		0			0
$431$	−0.0509718	−	0.289075i	−0.00245522	−	0.0139243i	0.983556	−	0.180606i	$-0.0578059\pi$
$431$	−0.0509718	−	0.289075i	−0.00245522	−	0.0139243i	−0.986011	+	0.166682i	$0.946695\pi$
$432$		0			0
$433$	16.6768	−	13.9935i	0.801437	−	0.672486i	−0.147111	−	0.989120i	$-0.546997\pi$
$433$	16.6768	−	13.9935i	0.801437	−	0.672486i	0.948548	+	0.316634i	$0.102553\pi$
$434$		0			0
$435$	9.78968	−	3.56315i	0.469379	−	0.170840i
$436$		0			0
$437$	15.1015	−	5.32632i	0.722404	−	0.254793i
$438$		0			0
$439$	−12.8607	+	4.68090i	−0.613806	+	0.223407i	−0.630168	−	0.776459i	$-0.717014\pi$
$439$	−12.8607	+	4.68090i	−0.613806	+	0.223407i	0.0163616	+	0.999866i	$0.494792\pi$
$440$		0			0
$441$	13.6201	−	11.4287i	0.648578	−	0.544222i
$442$		0			0
$443$	1.64994	+	9.35726i	0.0783909	+	0.444577i	0.998588	+	0.0531217i	$0.0169171\pi$
$443$	1.64994	+	9.35726i	0.0783909	+	0.444577i	−0.920197	+	0.391455i	$0.871972\pi$
$444$		0			0
$445$	8.30668	−	14.3876i	0.393775	−	0.682038i
$446$		0			0
$447$	21.3025	+	7.75349i	1.00758	+	0.366727i
$448$		0			0
$449$	−19.2411	−	33.3265i	−0.908043	−	1.57278i	−0.816779	−	0.576950i	$-0.804243\pi$
$449$	−19.2411	−	33.3265i	−0.908043	−	1.57278i	−0.0912636	−	0.995827i	$-0.529091\pi$
$450$		0			0
$451$	17.4863	+	14.6727i	0.823397	+	0.690912i
$452$		0			0
$453$	5.31933	−	30.1674i	0.249924	−	1.41739i
$454$		0			0
$455$	1.89587			0.0888797
$456$		0			0
$457$	12.3537			0.577880			0.288940	−	0.957347i	$-0.406697\pi$
$457$	12.3537			0.577880			0.288940	+	0.957347i	$0.406697\pi$
$458$		0			0
$459$	−2.76931	+	15.7056i	−0.129260	+	0.733073i
$460$		0			0
$461$	2.53645	+	2.12833i	0.118134	+	0.0991263i	0.699941	−	0.714201i	$-0.253210\pi$
$461$	2.53645	+	2.12833i	0.118134	+	0.0991263i	−0.581807	+	0.813327i	$0.697654\pi$
$462$		0			0
$463$	−2.08220	−	3.60648i	−0.0967682	−	0.167607i	0.813577	−	0.581457i	$-0.197517\pi$
$463$	−2.08220	−	3.60648i	−0.0967682	−	0.167607i	−0.910345	+	0.413850i	$0.864184\pi$
$464$		0			0
$465$	34.9727	+	12.7290i	1.62182	+	0.590295i
$466$		0			0
$467$	19.6094	−	33.9644i	0.907413	−	1.57168i	0.0897670	−	0.995963i	$-0.471388\pi$
$467$	19.6094	−	33.9644i	0.907413	−	1.57168i	0.817646	−	0.575722i	$-0.195279\pi$
$468$		0			0
$469$	2.34249	+	13.2849i	0.108166	+	0.613441i
$470$		0			0
$471$	−9.64271	+	8.09119i	−0.444312	+	0.372822i
$472$		0			0
$473$	−14.3134	+	5.20966i	−0.658131	+	0.239540i
$474$		0			0
$475$	2.68391	−	14.3799i	0.123146	−	0.659796i
$476$		0			0
$477$	−6.51311	+	2.37058i	−0.298215	+	0.108541i
$478$		0			0
$479$	5.68484	−	4.77014i	0.259747	−	0.217953i	−0.503609	−	0.863932i	$-0.667995\pi$
$479$	5.68484	−	4.77014i	0.259747	−	0.217953i	0.763356	+	0.645978i	$0.223550\pi$
$480$		0			0
$481$	0.139098	+	0.788866i	0.00634234	+	0.0359692i
$482$		0			0
$483$	−16.5385	+	28.6455i	−0.752527	+	1.30341i
$484$		0			0
$485$	−14.3403	−	5.21943i	−0.651158	−	0.237002i
$486$		0			0
$487$	16.3070	+	28.2445i	0.738940	+	1.27988i	0.952973	+	0.303055i	$0.0980067\pi$
$487$	16.3070	+	28.2445i	0.738940	+	1.27988i	−0.214033	+	0.976826i	$0.568660\pi$
$488$		0			0
$489$	3.77372	+	3.16652i	0.170653	+	0.143195i
$490$		0			0
$491$	4.18965	−	23.7607i	0.189076	−	1.07230i	−0.731529	−	0.681810i	$-0.761193\pi$
$491$	4.18965	−	23.7607i	0.189076	−	1.07230i	0.920605	−	0.390494i	$-0.127696\pi$
$492$		0			0
$493$	−14.3431			−0.645980
$494$		0			0
$495$	−30.7996			−1.38434
$496$		0			0
$497$	6.44342	−	36.5425i	0.289027	−	1.63915i
$498$		0			0
$499$	−13.1168	−	11.0063i	−0.587189	−	0.492710i	0.300110	−	0.953905i	$-0.402977\pi$
$499$	−13.1168	−	11.0063i	−0.587189	−	0.492710i	−0.887299	+	0.461195i	$0.847421\pi$
$500$		0			0
$501$	−26.8851	−	46.5664i	−1.20114	−	2.08044i
$502$		0			0
$503$	23.5533	+	8.57270i	1.05019	+	0.382238i	0.808734	−	0.588174i	$-0.200153\pi$
$503$	23.5533	+	8.57270i	1.05019	+	0.382238i	0.241455	+	0.970412i	$0.422375\pi$
$504$		0			0
$505$	6.53679	−	11.3221i	0.290883	−	0.503825i
$506$		0			0
$507$	−5.98555	−	33.9457i	−0.265828	−	1.50758i
$508$		0			0
$509$	−10.0036	+	8.39405i	−0.443403	+	0.372060i	−0.836981	−	0.547232i	$-0.815682\pi$
$509$	−10.0036	+	8.39405i	−0.443403	+	0.372060i	0.393578	+	0.919291i	$0.371237\pi$
$510$		0			0
$511$	23.1467	−	8.42473i	1.02395	−	0.372688i
$512$		0			0
$513$	−11.2992	+	9.29048i	−0.498873	+	0.410185i
$514$		0			0
$515$	5.45421	−	1.98517i	0.240341	−	0.0874771i
$516$		0			0
$517$	−26.2905	+	22.0603i	−1.15625	+	0.970211i
$518$		0			0
$519$	−2.18459	−	12.3894i	−0.0958930	−	0.543836i
$520$		0			0
$521$	−9.59896	+	16.6259i	−0.420538	+	0.728393i	−0.995992	−	0.0894407i	$-0.971492\pi$
$521$	−9.59896	+	16.6259i	−0.420538	+	0.728393i	0.575454	+	0.817834i	$0.304825\pi$
$522$		0			0
$523$	39.6821	+	14.4431i	1.73518	+	0.631553i	0.998977	−	0.0452101i	$-0.0143957\pi$
$523$	39.6821	+	14.4431i	1.73518	+	0.631553i	0.736201	+	0.676763i	$0.236618\pi$
$524$		0			0
$525$	15.1080	+	26.1678i	0.659367	+	1.14206i
$526$		0			0
$527$	−39.2516	−	32.9360i	−1.70983	−	1.43472i
$528$		0			0
$529$	−1.65033	+	9.35951i	−0.0717537	+	0.406935i
$530$		0			0
$531$	−36.3195			−1.57613
$532$		0			0
$533$	−1.78402			−0.0772747
$534$		0			0
$535$	0.284735	−	1.61481i	0.0123102	−	0.0698144i
$536$		0			0
$537$	−15.7601	−	13.2243i	−0.680097	−	0.570669i
$538$		0			0
$539$	−11.8411	−	20.5094i	−0.510032	−	0.883401i
$540$		0			0
$541$	−0.853270	−	0.310565i	−0.0366850	−	0.0133522i	0.323613	−	0.946190i	$-0.395103\pi$
$541$	−0.853270	−	0.310565i	−0.0366850	−	0.0133522i	−0.360297	+	0.932837i	$0.617325\pi$
$542$		0			0
$543$	−8.20302	+	14.2081i	−0.352025	+	0.609726i
$544$		0			0
$545$	−1.43018	−	8.11093i	−0.0612620	−	0.347434i
$546$		0			0
$547$	−26.5119	+	22.2462i	−1.13357	+	0.951177i	−0.999209	−	0.0397554i	$-0.987342\pi$
$547$	−26.5119	+	22.2462i	−1.13357	+	0.951177i	−0.134359	+	0.990933i	$0.542898\pi$
$548$		0			0
$549$	−10.3579	+	3.76997i	−0.442065	+	0.160898i
$550$		0			0
$551$	−9.99334	−	8.55692i	−0.425730	−	0.364537i
$552$		0			0
$553$	31.9300	−	11.6216i	1.35780	−	0.494200i
$554$		0			0
$555$	4.79108	−	4.02019i	0.203370	−	0.170648i
$556$		0			0
$557$	1.26237	+	7.15924i	0.0534882	+	0.303347i	0.999802	−	0.0199029i	$-0.00633570\pi$
$557$	1.26237	+	7.15924i	0.0534882	+	0.303347i	−0.946314	+	0.323250i	$0.895225\pi$
$558$		0			0
$559$	0.595230	−	1.03097i	0.0251755	−	0.0436053i
$560$		0			0
$561$	67.9958	+	24.7484i	2.87078	+	1.04488i
$562$		0			0
$563$	−1.22659	−	2.12451i	−0.0516944	−	0.0895373i	0.839020	−	0.544100i	$-0.183129\pi$
$563$	−1.22659	−	2.12451i	−0.0516944	−	0.0895373i	−0.890715	+	0.454563i	$0.849796\pi$
$564$		0			0
$565$	1.73890	+	1.45911i	0.0731560	+	0.0613852i
$566$		0			0
$567$	−2.15236	+	12.2066i	−0.0903904	+	0.512630i
$568$		0			0
$569$	18.1326			0.760159			0.380080	−	0.924954i	$-0.375897\pi$
$569$	18.1326			0.760159			0.380080	+	0.924954i	$0.375897\pi$
$570$		0			0
$571$	25.1171			1.05112			0.525560	−	0.850757i	$-0.323856\pi$
$571$	25.1171			1.05112			0.525560	+	0.850757i	$0.323856\pi$
$572$		0			0
$573$	−3.70819	+	21.0302i	−0.154912	+	0.878548i
$574$		0			0
$575$	−9.44439	−	7.92478i	−0.393858	−	0.330486i
$576$		0			0
$577$	10.3376	+	17.9053i	0.430361	+	0.745407i	0.996904	−	0.0786248i	$-0.0250529\pi$
$577$	10.3376	+	17.9053i	0.430361	+	0.745407i	−0.566543	+	0.824032i	$0.691720\pi$
$578$		0			0
$579$	17.3264	+	6.30629i	0.720060	+	0.262080i
$580$		0			0
$581$	7.62054	−	13.1992i	0.316153	−	0.547594i
$582$		0			0
$583$	1.60312	+	9.09176i	0.0663946	+	0.376542i
$584$		0			0
$585$	1.84398	−	1.54728i	0.0762393	−	0.0639723i
$586$		0			0
$587$	−23.5067	+	8.55575i	−0.970226	+	0.353133i	−0.778033	−	0.628224i	$-0.783782\pi$
$587$	−23.5067	+	8.55575i	−0.970226	+	0.353133i	−0.192193	+	0.981357i	$0.561560\pi$
$588$		0			0
$589$	−7.69875	−	46.3648i	−0.317221	−	1.91043i
$590$		0			0
$591$	64.6340	−	23.5248i	2.65869	−	0.967682i
$592$		0			0
$593$	−28.6911	+	24.0747i	−1.17820	+	0.988628i	−0.178212	+	0.983992i	$0.557031\pi$
$593$	−28.6911	+	24.0747i	−1.17820	+	0.988628i	−0.999989	+	0.00463610i	$0.998524\pi$
$594$		0			0
$595$	3.53889	+	20.0700i	0.145080	+	0.822791i
$596$		0			0
$597$	−10.2660	+	17.7812i	−0.420159	+	0.727737i
$598$		0			0
$599$	−39.3889	−	14.3364i	−1.60939	−	0.585768i	−0.628067	−	0.778159i	$-0.716154\pi$
$599$	−39.3889	−	14.3364i	−1.60939	−	0.585768i	−0.981318	+	0.192391i	$0.938376\pi$
$600$		0			0
$601$	12.1567	+	21.0559i	0.495880	+	0.858890i	0.999989	−	0.00475065i	$-0.00151218\pi$
$601$	12.1567	+	21.0559i	0.495880	+	0.858890i	−0.504109	+	0.863640i	$0.668179\pi$
$602$		0			0
$603$	13.1207	+	11.0096i	0.534316	+	0.448344i
$604$		0			0
$605$	−4.67459	+	26.5109i	−0.190049	+	1.07782i
$606$		0			0
$607$	19.2612			0.781790			0.390895	−	0.920435i	$-0.372166\pi$
$607$	19.2612			0.781790			0.390895	+	0.920435i	$0.372166\pi$
$608$		0			0
$609$	27.1755			1.10121
$610$		0			0
$611$	0.465770	−	2.64151i	0.0188430	−	0.106864i
$612$		0			0
$613$	12.3302	+	10.3463i	0.498012	+	0.417881i	0.856887	−	0.515504i	$-0.172395\pi$
$613$	12.3302	+	10.3463i	0.498012	+	0.417881i	−0.358875	+	0.933385i	$0.616840\pi$
$614$		0			0
$615$	6.96464	+	12.0631i	0.280841	+	0.486432i
$616$		0			0
$617$	−21.6306	−	7.87288i	−0.870813	−	0.316950i	−0.132317	−	0.991207i	$-0.542242\pi$
$617$	−21.6306	−	7.87288i	−0.870813	−	0.316950i	−0.738496	+	0.674257i	$0.764464\pi$
$618$		0			0
$619$	1.64450	−	2.84835i	0.0660979	−	0.114485i	−0.831083	−	0.556149i	$-0.812278\pi$
$619$	1.64450	−	2.84835i	0.0660979	−	0.114485i	0.897180	+	0.441664i	$0.145612\pi$
$620$		0			0
$621$	2.14087	+	12.1415i	0.0859101	+	0.487220i
$622$		0			0
$623$	33.1976	−	27.8561i	1.33003	−	1.11603i
$624$		0			0
$625$	−2.85870	+	1.04048i	−0.114348	+	0.0416192i
$626$		0			0
$627$	32.6104	+	57.8086i	1.30234	+	2.30865i
$628$		0			0
$629$	−8.09143	+	2.94504i	−0.322627	+	0.117426i
$630$		0			0
$631$	−32.2054	+	27.0235i	−1.28208	+	1.07579i	−0.289122	+	0.957292i	$0.593363\pi$
$631$	−32.2054	+	27.0235i	−1.28208	+	1.07579i	−0.992954	+	0.118497i	$0.962192\pi$
$632$		0			0
$633$	−5.36212	−	30.4101i	−0.213125	−	1.20869i
$634$		0			0
$635$	−8.64331	+	14.9707i	−0.342999	+	0.594092i
$636$		0			0
$637$	1.73926	+	0.633039i	0.0689120	+	0.0250819i
$638$		0			0
$639$	−23.5565	−	40.8011i	−0.931881	−	1.61407i
$640$		0			0
$641$	14.4111	+	12.0923i	0.569204	+	0.477618i	0.881382	−	0.472405i	$-0.156614\pi$
$641$	14.4111	+	12.0923i	0.569204	+	0.477618i	−0.312178	+	0.950024i	$0.601059\pi$
$642$		0			0
$643$	−2.74773	+	15.5832i	−0.108360	+	0.614540i	0.881465	+	0.472250i	$0.156558\pi$
$643$	−2.74773	+	15.5832i	−0.108360	+	0.614540i	−0.989825	+	0.142291i	$0.954553\pi$
$644$		0			0
$645$	−9.29485			−0.365984
$646$		0			0
$647$	8.04659			0.316344			0.158172	−	0.987412i	$-0.449440\pi$
$647$	8.04659			0.316344			0.158172	+	0.987412i	$0.449440\pi$
$648$		0			0
$649$	−8.40048	+	47.6415i	−0.329748	+	1.87009i
$650$		0			0
$651$	74.3692	+	62.4032i	2.91476	+	2.44577i
$652$		0			0
$653$	20.6792	+	35.8174i	0.809238	+	1.40164i	0.913392	+	0.407080i	$0.133453\pi$
$653$	20.6792	+	35.8174i	0.809238	+	1.40164i	−0.104154	+	0.994561i	$0.533214\pi$
$654$		0			0
$655$	12.2087	+	4.44359i	0.477032	+	0.173626i
$656$		0			0
$657$	15.6375	−	27.0850i	0.610079	−	1.05669i
$658$		0			0
$659$	−0.291051	−	1.65063i	−0.0113377	−	0.0642995i	0.978614	−	0.205705i	$-0.0659489\pi$
$659$	−0.291051	−	1.65063i	−0.0113377	−	0.0642995i	−0.989952	+	0.141406i	$0.954838\pi$
$660$		0			0
$661$	8.51230	−	7.14267i	0.331090	−	0.277818i	−0.462054	−	0.886852i	$-0.652887\pi$
$661$	8.51230	−	7.14267i	0.331090	−	0.277818i	0.793144	+	0.609034i	$0.208443\pi$
$662$		0			0
$663$	−5.31422	+	1.93422i	−0.206387	+	0.0751187i
$664$		0			0
$665$	−9.50788	+	16.0948i	−0.368700	+	0.624128i
$666$		0			0
$667$	−10.4195	+	3.79238i	−0.403444	+	0.146842i
$668$		0			0
$669$	5.77154	−	4.84290i	0.223141	−	0.187237i
$670$		0			0
$671$	2.54947	+	14.4588i	0.0984214	+	0.558175i
$672$		0			0
$673$	25.0800	−	43.4399i	0.966764	−	1.67448i	0.261966	−	0.965077i	$-0.415629\pi$
$673$	25.0800	−	43.4399i	0.966764	−	1.67448i	0.704798	−	0.709408i	$-0.251037\pi$
$674$		0			0
$675$	10.5832	+	3.85197i	0.407348	+	0.148262i
$676$		0			0
$677$	−12.2969	−	21.2989i	−0.472609	−	0.818583i	0.526900	−	0.849928i	$-0.323354\pi$
$677$	−12.2969	−	21.2989i	−0.472609	−	0.818583i	−0.999509	+	0.0313446i	$0.990021\pi$
$678$		0			0
$679$	−30.4944	−	25.5879i	−1.17027	−	0.981972i
$680$		0			0
$681$	2.83201	−	16.0611i	0.108523	−	0.615464i
$682$		0			0
$683$	−40.1865			−1.53769			−0.768846	−	0.639434i	$-0.779169\pi$
$683$	−40.1865			−1.53769			−0.768846	+	0.639434i	$0.779169\pi$
$684$		0			0
$685$	4.48347			0.171305
$686$		0			0
$687$	−4.19484	+	23.7901i	−0.160043	+	0.907649i
$688$		0			0
$689$	−0.552723	−	0.463790i	−0.0210571	−	0.0176690i
$690$		0			0
$691$	−4.69050	−	8.12419i	−0.178435	−	0.309059i	0.762910	−	0.646505i	$-0.223770\pi$
$691$	−4.69050	−	8.12419i	−0.178435	−	0.309059i	−0.941345	+	0.337447i	$0.890437\pi$
$692$		0			0
$693$	−75.4965	−	27.4785i	−2.86787	−	1.04382i
$694$		0			0
$695$	−6.83237	+	11.8340i	−0.259166	+	0.448889i
$696$		0			0
$697$	−3.33011	−	18.8860i	−0.126137	−	0.715359i
$698$		0			0
$699$	−15.1375	+	12.7018i	−0.572551	+	0.480428i
$700$		0			0
$701$	34.9329	−	12.7145i	1.31940	−	0.480221i	0.416132	−	0.909304i	$-0.363386\pi$
$701$	34.9329	−	12.7145i	1.31940	−	0.480221i	0.903265	+	0.429083i	$0.141163\pi$
$702$		0			0
$703$	−7.39457	−	2.77534i	−0.278891	−	0.104674i
$704$		0			0
$705$	−19.6795	+	7.16277i	−0.741175	+	0.269765i
$706$		0			0
$707$	26.1243	−	21.9209i	0.982504	−	0.824419i
$708$		0			0
$709$	−5.43054	−	30.7981i	−0.203948	−	1.15665i	−0.899086	−	0.437772i	$-0.855768\pi$
$709$	−5.43054	−	30.7981i	−0.203948	−	1.15665i	0.695138	−	0.718876i	$-0.255343\pi$
$710$		0			0
$711$	21.5714	−	37.3627i	0.808990	−	1.40121i
$712$		0			0
$713$	−37.2227	−	13.5479i	−1.39400	−	0.507375i
$714$		0			0
$715$	−1.60312	−	2.77669i	−0.0599534	−	0.103842i
$716$		0			0
$717$	39.5338	+	33.1728i	1.47642	+	1.23886i
$718$		0			0
$719$	−4.52330	+	25.6529i	−0.168691	+	0.956692i	0.776487	+	0.630134i	$0.217000\pi$
$719$	−4.52330	+	25.6529i	−0.168691	+	0.956692i	−0.945177	+	0.326558i	$0.894111\pi$
$720$		0			0
$721$	15.1405			0.563863
$722$		0			0
$723$	−32.6463			−1.21413
$724$		0			0
$725$	−1.75890	+	9.97524i	−0.0653241	+	0.370471i
$726$		0			0
$727$	1.59316	+	1.33682i	0.0590871	+	0.0495800i	0.671853	−	0.740685i	$-0.265499\pi$
$727$	1.59316	+	1.33682i	0.0590871	+	0.0495800i	−0.612766	+	0.790265i	$0.709943\pi$
$728$		0			0
$729$	21.4199	+	37.1004i	0.793331	+	1.37409i
$730$		0			0
$731$	12.0251	+	4.37677i	0.444764	+	0.161881i
$732$		0			0
$733$	3.46413	−	6.00006i	0.127951	−	0.221617i	−0.794932	−	0.606699i	$-0.792493\pi$
$733$	3.46413	−	6.00006i	0.127951	−	0.221617i	0.922882	+	0.385082i	$0.125827\pi$
$734$		0			0
$735$	−2.50944	−	14.2317i	−0.0925621	−	0.524946i
$736$		0			0
$737$	17.4763	−	14.6644i	0.643749	−	0.540170i
$738$		0			0
$739$	16.2765	−	5.92414i	0.598739	−	0.217923i	−0.0248298	−	0.999692i	$-0.507904\pi$
$739$	16.2765	−	5.92414i	0.598739	−	0.217923i	0.623569	+	0.781769i	$0.285682\pi$
$740$		0			0
$741$	−4.85653	−	1.82276i	−0.178409	−	0.0669609i
$742$		0			0
$743$	49.0096	−	17.8381i	1.79799	−	0.654415i	0.799430	−	0.600759i	$-0.205135\pi$
$743$	49.0096	−	17.8381i	1.79799	−	0.654415i	0.998560	−	0.0536553i	$-0.0170872\pi$
$744$		0			0
$745$	8.27157	−	6.94067i	0.303047	−	0.254286i
$746$		0			0
$747$	−3.36032	−	19.0573i	−0.122948	−	0.697271i
$748$		0			0
$749$	2.13863	−	3.70422i	0.0781439	−	0.135349i
$750$		0			0
$751$	10.9191	+	3.97421i	0.398442	+	0.145021i	0.533466	−	0.845821i	$-0.320889\pi$
$751$	10.9191	+	3.97421i	0.398442	+	0.145021i	−0.135025	+	0.990842i	$0.543111\pi$
$752$		0			0
$753$	19.6691	+	34.0679i	0.716783	+	1.24150i
$754$		0			0
$755$	−11.1771	−	9.37870i	−0.406776	−	0.341326i
$756$		0			0
$757$	−4.73400	+	26.8479i	−0.172060	+	0.975802i	0.769422	+	0.638741i	$0.220544\pi$
$757$	−4.73400	+	26.8479i	−0.172060	+	0.975802i	−0.941483	+	0.337062i	$0.890567\pi$
$758$		0			0
$759$	55.9389			2.03045
$760$		0			0
$761$	32.8211			1.18976			0.594882	−	0.803813i	$-0.297199\pi$
$761$	32.8211			1.18976			0.594882	+	0.803813i	$0.297199\pi$
$762$		0			0
$763$	3.73065	−	21.1576i	0.135059	−	0.765956i
$764$		0			0
$765$	19.8219	+	16.6325i	0.716661	+	0.601350i
$766$		0			0
$767$	−1.89043	−	3.27432i	−0.0682595	−	0.118229i
$768$		0			0
$769$	−2.30440	−	0.838733i	−0.0830988	−	0.0302455i	0.300136	−	0.953896i	$-0.402968\pi$
$769$	−2.30440	−	0.838733i	−0.0830988	−	0.0302455i	−0.383235	+	0.923651i	$0.625190\pi$
$770$		0			0
$771$	−3.48770	+	6.04087i	−0.125606	+	0.217556i
$772$		0			0
$773$	1.68579	+	9.56061i	0.0606338	+	0.343871i	1.00000		0.000954466i	$0.000303816\pi$
$773$	1.68579	+	9.56061i	0.0606338	+	0.343871i	−0.939366	+	0.342917i	$0.888585\pi$
$774$		0			0
$775$	−27.7196	+	23.2595i	−0.995718	+	0.835507i
$776$		0			0
$777$	15.3307	−	5.57990i	0.549984	−	0.200178i
$778$		0			0
$779$	8.94697	−	15.1453i	0.320559	−	0.542635i
$780$		0			0
$781$	−58.9686	+	21.4628i	−2.11006	+	0.768000i
$782$		0			0
$783$	7.75936	−	6.51088i	0.277297	−	0.232680i
$784$		0			0
$785$	1.04113	+	5.90453i	0.0371594	+	0.210742i
$786$		0			0
$787$	16.2014	−	28.0616i	0.577517	−	1.00029i	−0.418246	−	0.908334i	$-0.637355\pi$
$787$	16.2014	−	28.0616i	0.577517	−	1.00029i	0.995763	−	0.0919553i	$-0.0293117\pi$
$788$		0			0
$789$	−58.2221	−	21.1911i	−2.07276	−	0.754424i
$790$		0			0
$791$	2.96064	+	5.12798i	0.105268	+	0.182330i
$792$		0			0
$793$	−0.879005	−	0.737573i	−0.0312144	−	0.0261920i
$794$		0			0
$795$	−0.978254	+	5.54796i	−0.0346951	+	0.196766i
$796$		0			0
$797$	−14.1556			−0.501417			−0.250708	−	0.968063i	$-0.580664\pi$
$797$	−14.1556			−0.501417			−0.250708	+	0.968063i	$0.580664\pi$
$798$		0			0
$799$	28.8330			1.02004
$800$		0			0
$801$	9.55471	−	54.1875i	0.337599	−	1.91462i
$802$		0			0
$803$	−31.9115	−	26.7769i	−1.12613	−	0.944936i
$804$		0			0
$805$	7.87742	+	13.6441i	0.277643	+	0.480891i
$806$		0			0
$807$	−66.2323	−	24.1066i	−2.33149	−	0.848592i
$808$		0			0
$809$	2.09894	−	3.63547i	0.0737947	−	0.127816i	−0.826767	−	0.562545i	$-0.809822\pi$
$809$	2.09894	−	3.63547i	0.0737947	−	0.127816i	0.900562	+	0.434729i	$0.143156\pi$
$810$		0			0
$811$	−7.92815	−	44.9628i	−0.278395	−	1.57886i	−0.727967	−	0.685613i	$-0.759534\pi$
$811$	−7.92815	−	44.9628i	−0.278395	−	1.57886i	0.449571	−	0.893244i	$-0.351577\pi$
$812$		0			0
$813$	30.4709	−	25.5681i	1.06866	−	0.896712i
$814$		0			0
$815$	2.20490	−	0.802520i	0.0772344	−	0.0281110i
$816$		0			0
$817$	5.76717	+	10.2235i	0.201768	+	0.357675i
$818$		0			0
$819$	5.90043	−	2.14758i	0.206178	−	0.0750426i
$820$		0			0
$821$	3.18439	−	2.67202i	0.111136	−	0.0932540i	−0.585526	−	0.810653i	$-0.699112\pi$
$821$	3.18439	−	2.67202i	0.111136	−	0.0932540i	0.696662	+	0.717399i	$0.254668\pi$
$822$		0			0
$823$	8.05066	+	45.6576i	0.280628	+	1.59152i	0.720495	+	0.693460i	$0.243915\pi$
$823$	8.05066	+	45.6576i	0.280628	+	1.59152i	−0.439867	+	0.898063i	$0.644974\pi$
$824$		0			0
$825$	25.5503	−	44.2544i	0.889546	−	1.54074i
$826$		0			0
$827$	−28.6682	−	10.4344i	−0.996890	−	0.362838i	−0.208505	−	0.978021i	$-0.566860\pi$
$827$	−28.6682	−	10.4344i	−0.996890	−	0.362838i	−0.788384	+	0.615183i	$0.789082\pi$
$828$		0			0
$829$	−3.64171	−	6.30763i	−0.126482	−	0.219073i	0.795829	−	0.605521i	$-0.207035\pi$
$829$	−3.64171	−	6.30763i	−0.126482	−	0.219073i	−0.922311	+	0.386448i	$0.873702\pi$
$830$		0			0
$831$	−30.4107	−	25.5176i	−1.05493	−	0.885195i
$832$		0			0
$833$	−3.45491	+	19.5938i	−0.119706	+	0.678884i
$834$		0			0
$835$	−25.6113			−0.886314
$836$		0			0
$837$	36.1854			1.25075
$838$		0			0
$839$	2.30941	−	13.0973i	0.0797296	−	0.452169i	−0.918640	−	0.395095i	$-0.870712\pi$
$839$	2.30941	−	13.0973i	0.0797296	−	0.452169i	0.998370	−	0.0570742i	$-0.0181772\pi$
$840$		0			0
$841$	−15.2367	−	12.7851i	−0.525404	−	0.440866i
$842$		0			0
$843$	−18.7637	−	32.4997i	−0.646257	−	1.11935i
$844$		0			0
$845$	−15.4279	−	5.61531i	−0.530737	−	0.193173i
$846$		0			0
$847$	−35.1106	+	60.8134i	−1.20642	+	2.08957i
$848$		0			0
$849$	8.54921	+	48.4850i	0.293408	+	1.66400i
$850$		0			0
$851$	−5.09931	+	4.27883i	−0.174802	+	0.146676i
$852$		0			0
$853$	−15.3780	+	5.59712i	−0.526531	+	0.191642i	−0.591589	−	0.806240i	$-0.701499\pi$
$853$	−15.3780	+	5.59712i	−0.526531	+	0.191642i	0.0650576	+	0.997882i	$0.479277\pi$
$854$		0			0
$855$	3.88783	+	23.4140i	0.132961	+	0.800741i
$856$		0			0
$857$	−26.8834	+	9.78476i	−0.918320	+	0.334241i	−0.757570	−	0.652754i	$-0.773613\pi$
$857$	−26.8834	+	9.78476i	−0.918320	+	0.334241i	−0.160750	+	0.986995i	$0.551391\pi$
$858$		0			0
$859$	4.14252	−	3.47599i	0.141341	−	0.118599i	−0.569376	−	0.822077i	$-0.692815\pi$
$859$	4.14252	−	3.47599i	0.141341	−	0.118599i	0.710717	+	0.703478i	$0.248371\pi$
$860$		0			0
$861$	6.30949	+	35.7829i	0.215027	+	1.21948i
$862$		0			0
$863$	−21.0307	+	36.4262i	−0.715892	+	1.23996i	0.246723	+	0.969086i	$0.420646\pi$
$863$	−21.0307	+	36.4262i	−0.715892	+	1.23996i	−0.962615	+	0.270875i	$0.912687\pi$
$864$		0			0
$865$	−5.63086	−	2.04947i	−0.191455	−	0.0696839i
$866$		0			0
$867$	−7.51398	−	13.0146i	−0.255188	−	0.441999i
$868$		0			0
$869$	−44.0206	−	36.9377i	−1.49330	−	1.25302i
$870$		0			0
$871$	−0.309616	+	1.75592i	−0.0104909	+	0.0594971i
$872$		0			0
$873$	−50.5430			−1.71062
$874$		0			0
$875$	35.8349			1.21144
$876$		0			0
$877$	2.03774	−	11.5566i	0.0688096	−	0.390239i	−0.930880	−	0.365325i	$-0.880958\pi$
$877$	2.03774	−	11.5566i	0.0688096	−	0.390239i	0.999690	−	0.0249136i	$-0.00793107\pi$
$878$		0			0
$879$	51.0333	+	42.8220i	1.72131	+	1.44435i
$880$		0			0
$881$	−11.7659	−	20.3791i	−0.396403	−	0.686590i	0.596876	−	0.802333i	$-0.296408\pi$
$881$	−11.7659	−	20.3791i	−0.396403	−	0.686590i	−0.993279	+	0.115743i	$0.963075\pi$
$882$		0			0
$883$	−3.34723	−	1.21829i	−0.112643	−	0.0409987i	0.285084	−	0.958503i	$-0.407979\pi$
$883$	−3.34723	−	1.21829i	−0.112643	−	0.0409987i	−0.397727	+	0.917504i	$0.630201\pi$
$884$		0			0
$885$	−14.7601	+	25.5652i	−0.496155	+	0.859366i
$886$		0			0
$887$	4.27032	+	24.2182i	0.143383	+	0.813167i	0.968651	+	0.248425i	$0.0799130\pi$
$887$	4.27032	+	24.2182i	0.143383	+	0.813167i	−0.825268	+	0.564742i	$0.808976\pi$
$888$		0			0
$889$	−34.5429	+	28.9850i	−1.15853	+	0.972125i
$890$		0			0
$891$	19.6978	−	7.16942i	0.659902	−	0.240185i
$892$		0			0
$893$	20.0890	+	17.2014i	0.672251	+	0.575624i
$894$		0			0
$895$	−9.20828	+	3.35154i	−0.307799	+	0.112030i
$896$		0			0
$897$	−3.34908	+	2.81021i	−0.111822	+	0.0938302i
$898$		0			0
$899$	5.65125	+	32.0498i	0.188480	+	1.06892i
$900$		0			0
$901$	3.87803	−	6.71695i	0.129196	−	0.223774i
$902$		0			0
$903$	−22.7837	−	8.29257i	−0.758193	−	0.275960i
$904$		0			0
$905$	3.90717	+	6.76742i	0.129879	+	0.224957i
$906$		0			0
$907$	−2.27034	−	1.90505i	−0.0753855	−	0.0632560i	0.604316	−	0.796745i	$-0.293446\pi$
$907$	−2.27034	−	1.90505i	−0.0753855	−	0.0632560i	−0.679702	+	0.733489i	$0.737891\pi$
$908$		0			0
$909$	7.51891	−	42.6418i	0.249386	−	1.41434i
$910$		0			0
$911$	−31.6411			−1.04832			−0.524158	−	0.851621i	$-0.675620\pi$
$911$	−31.6411			−1.04832			−0.524158	+	0.851621i	$0.675620\pi$
$912$		0			0
$913$	−25.7753			−0.853039
$914$		0			0
$915$	−1.55574	+	8.82301i	−0.0514310	+	0.291680i
$916$		0			0
$917$	25.9616	+	21.7844i	0.857329	+	0.719384i
$918$		0			0
$919$	19.9033	+	34.4735i	0.656549	+	1.13718i	0.981503	+	0.191446i	$0.0613176\pi$
$919$	19.9033	+	34.4735i	0.656549	+	1.13718i	−0.324955	+	0.945730i	$0.605349\pi$
$920$		0			0
$921$	−58.0118	−	21.1146i	−1.91155	−	0.695749i
$922$		0			0
$923$	2.45223	−	4.24739i	0.0807163	−	0.139805i
$924$		0			0
$925$	1.05594	+	5.98853i	0.0347191	+	0.196902i
$926$		0			0
$927$	14.7262	−	12.3567i	0.483671	−	0.405848i
$928$		0			0
$929$	2.27410	−	0.827705i	0.0746108	−	0.0271561i	−0.304445	−	0.952530i	$-0.598471\pi$
$929$	2.27410	−	0.827705i	0.0746108	−	0.0271561i	0.379056	+	0.925374i	$0.376249\pi$
$930$		0			0
$931$	−14.0966	+	11.5905i	−0.461997	+	0.379864i
$932$		0			0
$933$	75.0451	−	27.3142i	2.45687	−	0.894226i
$934$		0			0
$935$	26.4021	−	22.1540i	0.863442	−	0.724514i
$936$		0			0
$937$	2.57266	+	14.5903i	0.0840453	+	0.476644i	0.997559	+	0.0698355i	$0.0222474\pi$
$937$	2.57266	+	14.5903i	0.0840453	+	0.476644i	−0.913513	+	0.406809i	$0.866641\pi$
$938$		0			0
$939$	27.8951	−	48.3158i	0.910323	−	1.57673i
$940$		0			0
$941$	−13.8828	−	5.05292i	−0.452566	−	0.164720i	0.105673	−	0.994401i	$-0.466300\pi$
$941$	−13.8828	−	5.05292i	−0.452566	−	0.164720i	−0.558239	+	0.829681i	$0.688523\pi$
$942$		0			0
$943$	−7.41271	−	12.8392i	−0.241391	−	0.418101i
$944$		0			0
$945$	−11.0250	−	9.25109i	−0.358644	−	0.300938i
$946$		0			0
$947$	−8.69019	+	49.2845i	−0.282393	+	1.60153i	0.432057	+	0.901846i	$0.357788\pi$
$947$	−8.69019	+	49.2845i	−0.282393	+	1.60153i	−0.714450	+	0.699686i	$0.753323\pi$
$948$		0			0
$949$	3.25574			0.105686
$950$		0			0
$951$	−87.2561			−2.82947
$952$		0			0
$953$	1.00531	−	5.70141i	0.0325653	−	0.184687i	−0.964186	−	0.265227i	$-0.914553\pi$
$953$	1.00531	−	5.70141i	0.0325653	−	0.184687i	0.996751	+	0.0805396i	$0.0256644\pi$
$954$		0			0
$955$	7.79173	+	6.53804i	0.252134	+	0.211566i
$956$		0			0
$957$	−22.9793	−	39.8013i	−0.742814	−	1.28659i
$958$		0			0
$959$	10.9899	+	4.00001i	0.354884	+	0.129167i
$960$		0			0
$961$	−42.6307	+	73.8385i	−1.37518	+	2.38189i
$962$		0			0
$963$	−0.943041	−	5.34825i	−0.0303891	−	0.172345i
$964$		0			0
$965$	6.72767	−	5.64519i	0.216571	−	0.181725i
$966$		0			0
$967$	29.8145	−	10.8516i	0.958770	−	0.348964i	0.185218	−	0.982697i	$-0.440701\pi$
$967$	29.8145	−	10.8516i	0.958770	−	0.348964i	0.773551	+	0.633734i	$0.218478\pi$
$968$		0			0
$969$	10.2308	−	54.8146i	0.328659	−	1.76090i
$970$		0			0
$971$	−8.47296	+	3.08391i	−0.271910	+	0.0989672i	−0.474377	−	0.880322i	$-0.657327\pi$
$971$	−8.47296	+	3.08391i	−0.271910	+	0.0989672i	0.202466	+	0.979289i	$0.435104\pi$
$972$		0			0
$973$	−27.3055	+	22.9120i	−0.875375	+	0.734527i
$974$		0			0
$975$	0.693510	+	3.93309i	0.0222101	+	0.125960i
$976$		0			0
$977$	21.2050	−	36.7281i	0.678407	−	1.17504i	−0.297053	−	0.954861i	$-0.596004\pi$
$977$	21.2050	−	36.7281i	0.678407	−	1.17504i	0.975460	−	0.220175i	$-0.0706628\pi$
$978$		0			0
$979$	−68.8695	−	25.0665i	−2.20108	−	0.801128i
$980$		0			0
$981$	−13.6389	−	23.6233i	−0.435456	−	0.754233i
$982$		0			0
$983$	38.8785	+	32.6230i	1.24003	+	1.04051i	0.997522	+	0.0703618i	$0.0224154\pi$
$983$	38.8785	+	32.6230i	1.24003	+	1.04051i	0.242511	+	0.970149i	$0.422029\pi$
$984$		0			0
$985$	5.68897	−	32.2638i	0.181266	−	1.02801i
$986$		0			0
$987$	−54.6292			−1.73887
$988$		0			0
$989$	9.89283			0.314574
$990$		0			0
$991$	1.74857	−	9.91662i	0.0555451	−	0.315012i	−0.944358	−	0.328919i	$-0.893316\pi$
$991$	1.74857	−	9.91662i	0.0555451	−	0.315012i	0.999903	+	0.0139069i	$0.00442685\pi$
$992$		0			0
$993$	43.7978	+	36.7507i	1.38988	+	1.16625i
$994$		0			0
$995$	4.88979	+	8.46936i	0.155017	+	0.268497i
$996$		0			0
$997$	30.7664	+	11.1981i	0.974382	+	0.354646i	0.779653	−	0.626211i	$-0.215395\pi$
$997$	30.7664	+	11.1981i	0.974382	+	0.354646i	0.194728	+	0.980857i	$0.437617\pi$
$998$		0			0
$999$	3.04046	−	5.26623i	0.0961958	−	0.166616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.e.81.2		12
4.3	odd	2		76.2.i.a.5.1	✓	12
12.11	even	2		684.2.bo.c.613.2		12
19.2	odd	18		5776.2.a.by.1.1		6
19.4	even	9	inner	304.2.u.e.289.2		12
19.17	even	9		5776.2.a.bw.1.6		6
76.3	even	18		1444.2.e.h.653.1		12
76.23	odd	18		76.2.i.a.61.1	yes	12
76.35	odd	18		1444.2.e.g.653.6		12
76.43	odd	18		1444.2.e.g.429.6		12
76.55	odd	18		1444.2.a.h.1.1		6
76.59	even	18		1444.2.a.g.1.6		6
76.71	even	18		1444.2.e.h.429.1		12
228.23	even	18		684.2.bo.c.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.5.1	✓	12	4.3	odd	2
76.2.i.a.61.1	yes	12	76.23	odd	18
304.2.u.e.81.2		12	1.1	even	1	trivial
304.2.u.e.289.2		12	19.4	even	9	inner
684.2.bo.c.289.2		12	228.23	even	18
684.2.bo.c.613.2		12	12.11	even	2
1444.2.a.g.1.6		6	76.59	even	18
1444.2.a.h.1.1		6	76.55	odd	18
1444.2.e.g.429.6		12	76.43	odd	18
1444.2.e.g.653.6		12	76.35	odd	18
1444.2.e.h.429.1		12	76.71	even	18
1444.2.e.h.653.1		12	76.3	even	18
5776.2.a.bw.1.6		6	19.17	even	9
5776.2.a.by.1.1		6	19.2	odd	18

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.467454 - 2.65106i) q^{3} +(-0.982226 - 0.824185i) q^{5} +(-1.67233 - 2.89656i) q^{7} +(-3.99055 - 1.45244i) q^{9} +O(q^{10})\)	\(q+(0.467454 - 2.65106i) q^{3} +(-0.982226 - 0.824185i) q^{5} +(-1.67233 - 2.89656i) q^{7} +(-3.99055 - 1.45244i) q^{9} +(-2.82821 + 4.89860i) q^{11} +(-0.0767659 - 0.435361i) q^{13} +(-2.64411 + 2.21868i) q^{15} +(4.46552 - 1.62532i) q^{17} +(4.08093 + 1.53166i) q^{19} +(-8.46072 + 3.07945i) q^{21} +(2.81422 - 2.36141i) q^{23} +(-0.582755 - 3.30497i) q^{25} +(-1.67798 + 2.90634i) q^{27} +(-2.83623 - 1.03230i) q^{29} +(-5.39123 - 9.33788i) q^{31} +(11.6644 + 9.78763i) q^{33} +(-0.744698 + 4.22339i) q^{35} -1.81198 q^{37} -1.19006 q^{39} +(0.700766 - 3.97424i) q^{41} +(2.06286 + 1.73095i) q^{43} +(2.72254 + 4.71558i) q^{45} +(5.70150 + 2.07517i) q^{47} +(-2.09339 + 3.62586i) q^{49} +(-2.22139 - 12.5981i) q^{51} +(1.25029 - 1.04911i) q^{53} +(6.81529 - 2.48056i) q^{55} +(5.96819 - 10.1028i) q^{57} +(8.03671 - 2.92512i) q^{59} +(1.98835 - 1.66843i) q^{61} +(2.46644 + 13.9879i) q^{63} +(-0.283417 + 0.490892i) q^{65} +(-3.79002 - 1.37945i) q^{67} +(-4.94473 - 8.56453i) q^{69} +(8.49861 + 7.13118i) q^{71} +(-1.27886 + 7.25275i) q^{73} -9.03409 q^{75} +18.9188 q^{77} +(-1.76413 + 10.0049i) q^{79} +(-2.83887 - 2.38209i) q^{81} +(2.27842 + 3.94633i) q^{83} +(-5.72571 - 2.08399i) q^{85} +(-4.06252 + 7.03648i) q^{87} +(2.24994 + 12.7600i) q^{89} +(-1.13267 + 0.950426i) q^{91} +(-27.2755 + 9.92746i) q^{93} +(-2.74602 - 4.86788i) q^{95} +(11.1841 - 4.07067i) q^{97} +(18.4010 - 15.4403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{7} - 3 q^{9} - 3 q^{11} - 9 q^{13} + 15 q^{15} - 3 q^{17} + 12 q^{19} - 15 q^{21} + 12 q^{23} - 18 q^{25} + 9 q^{27} + 27 q^{29} - 6 q^{31} + 48 q^{33} - 33 q^{35} - 12 q^{37} - 60 q^{39} + 3 q^{41} - 27 q^{43} + 24 q^{45} + 15 q^{47} + 9 q^{49} + 33 q^{51} - 21 q^{53} + 27 q^{55} - 42 q^{57} + 48 q^{59} - 6 q^{61} + 9 q^{63} - 33 q^{65} - 24 q^{67} - 33 q^{69} + 30 q^{73} - 42 q^{75} + 24 q^{77} - 3 q^{79} + 3 q^{81} - 3 q^{83} - 42 q^{85} + 18 q^{87} - 18 q^{89} + 24 q^{91} - 78 q^{93} - 9 q^{95} + 12 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 - 3 * q^11 - 9 * q^13 + 15 * q^15 - 3 * q^17 + 12 * q^19 - 15 * q^21 + 12 * q^23 - 18 * q^25 + 9 * q^27 + 27 * q^29 - 6 * q^31 + 48 * q^33 - 33 * q^35 - 12 * q^37 - 60 * q^39 + 3 * q^41 - 27 * q^43 + 24 * q^45 + 15 * q^47 + 9 * q^49 + 33 * q^51 - 21 * q^53 + 27 * q^55 - 42 * q^57 + 48 * q^59 - 6 * q^61 + 9 * q^63 - 33 * q^65 - 24 * q^67 - 33 * q^69 + 30 * q^73 - 42 * q^75 + 24 * q^77 - 3 * q^79 + 3 * q^81 - 3 * q^83 - 42 * q^85 + 18 * q^87 - 18 * q^89 + 24 * q^91 - 78 * q^93 - 9 * q^95 + 12 * q^97 + 6 * q^99

Introduction

L-functions

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Varieties

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