LMFDB - Embedded newform 304.2.u.f.177.2

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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.2
Root			$0.0744612 + 0.128971i$ of defining polynomial
Character	$\chi$	$=$	304.177
Dual form			304.2.u.f.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139941 + 0.0509345i) q^{3} +(-0.594280 - 3.37033i) q^{5} +(-0.960111 + 1.66296i) q^{7} +(-2.28114 - 1.91411i) q^{9} +O(q^{10})$	\(q+(0.139941 + 0.0509345i) q^{3} +(-0.594280 - 3.37033i) q^{5} +(-0.960111 + 1.66296i) q^{7} +(-2.28114 - 1.91411i) q^{9} +(-2.64301 - 4.57782i) q^{11} +(4.42242 - 1.60963i) q^{13} +(0.0885016 - 0.501917i) q^{15} +(-2.08794 + 1.75199i) q^{17} +(0.673054 + 4.30662i) q^{19} +(-0.219061 + 0.183814i) q^{21} +(1.16559 - 6.61040i) q^{23} +(-6.30748 + 2.29573i) q^{25} +(-0.445116 - 0.770963i) q^{27} +(0.769414 + 0.645615i) q^{29} +(1.92392 - 3.33233i) q^{31} +(-0.136697 - 0.775246i) q^{33} +(6.17530 + 2.24763i) q^{35} +10.3903 q^{37} +0.700865 q^{39} +(-1.64870 - 0.600077i) q^{41} +(-0.812201 - 4.60622i) q^{43} +(-5.09553 + 8.82572i) q^{45} +(2.83824 + 2.38156i) q^{47} +(1.65637 + 2.86892i) q^{49} +(-0.381426 + 0.138828i) q^{51} +(-1.09076 + 6.18603i) q^{53} +(-13.8581 + 11.6283i) q^{55} +(-0.125167 + 0.636956i) q^{57} +(-4.44430 + 3.72921i) q^{59} +(0.261694 - 1.48414i) q^{61} +(5.37324 - 1.95570i) q^{63} +(-8.05314 - 13.9484i) q^{65} +(3.63565 + 3.05067i) q^{67} +(0.499811 - 0.865699i) q^{69} +(2.19935 + 12.4731i) q^{71} +(-1.74925 - 0.636675i) q^{73} -0.999609 q^{75} +10.1503 q^{77} +(-5.54303 - 2.01750i) q^{79} +(1.52826 + 8.66719i) q^{81} +(1.29945 - 2.25071i) q^{83} +(7.14561 + 5.99588i) q^{85} +(0.0747887 + 0.129538i) q^{87} +(10.9425 - 3.98275i) q^{89} +(-1.56926 + 8.89974i) q^{91} +(0.438966 - 0.368337i) q^{93} +(14.1147 - 4.82775i) q^{95} +(-5.00808 + 4.20228i) q^{97} +(-2.73336 + 15.5017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{7} - 6 q^{9}+O(q^{10}) $ 18 * q + 9 * q^7 - 6 * q^9	$ 18 q + 9 q^{7} - 6 q^{9} + 3 q^{11} + 3 q^{13} - 33 q^{15} + 9 q^{17} + 24 q^{19} - 15 q^{21} - 6 q^{23} + 6 q^{25} + 12 q^{27} - 3 q^{29} + 6 q^{31} - 45 q^{33} + 15 q^{35} + 48 q^{37} - 12 q^{39} - 18 q^{41} + 39 q^{43} - 42 q^{45} + 27 q^{47} - 18 q^{49} - 48 q^{51} + 39 q^{53} + 27 q^{55} - 6 q^{57} - 9 q^{59} - 24 q^{61} - 3 q^{63} + 27 q^{65} - 39 q^{67} - 3 q^{69} + 12 q^{73} - 90 q^{75} + 60 q^{77} - 63 q^{79} - 6 q^{81} + 27 q^{83} - 30 q^{85} - 18 q^{87} + 66 q^{89} - 108 q^{91} + 60 q^{93} + 75 q^{95} - 81 q^{97} - 15 q^{99}+O(q^{100}) $ 18 * q + 9 * q^7 - 6 * q^9 + 3 * q^11 + 3 * q^13 - 33 * q^15 + 9 * q^17 + 24 * q^19 - 15 * q^21 - 6 * q^23 + 6 * q^25 + 12 * q^27 - 3 * q^29 + 6 * q^31 - 45 * q^33 + 15 * q^35 + 48 * q^37 - 12 * q^39 - 18 * q^41 + 39 * q^43 - 42 * q^45 + 27 * q^47 - 18 * q^49 - 48 * q^51 + 39 * q^53 + 27 * q^55 - 6 * q^57 - 9 * q^59 - 24 * q^61 - 3 * q^63 + 27 * q^65 - 39 * q^67 - 3 * q^69 + 12 * q^73 - 90 * q^75 + 60 * q^77 - 63 * q^79 - 6 * q^81 + 27 * q^83 - 30 * q^85 - 18 * q^87 + 66 * q^89 - 108 * q^91 + 60 * q^93 + 75 * q^95 - 81 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	0.139941	+	0.0509345i	0.0807952	+	0.0294070i	0.382102	−	0.924120i	$-0.375200\pi$
$3$	0.139941	+	0.0509345i	0.0807952	+	0.0294070i	−0.301306	+	0.953527i	$0.597423\pi$
$4$		0			0
$5$	−0.594280	−	3.37033i	−0.265770	−	1.50726i	−0.766834	−	0.641846i	$-0.778169\pi$
$5$	−0.594280	−	3.37033i	−0.265770	−	1.50726i	0.501064	−	0.865410i	$-0.332942\pi$
$6$		0			0
$7$	−0.960111	+	1.66296i	−0.362888	+	0.628540i	−0.988435	−	0.151646i	$-0.951543\pi$
$7$	−0.960111	+	1.66296i	−0.362888	+	0.628540i	0.625547	+	0.780187i	$0.284876\pi$
$8$		0			0
$9$	−2.28114	−	1.91411i	−0.760381	−	0.638036i
$10$		0			0
$11$	−2.64301	−	4.57782i	−0.796896	−	1.38026i	−0.921628	−	0.388074i	$-0.873140\pi$
$11$	−2.64301	−	4.57782i	−0.796896	−	1.38026i	0.124732	−	0.992191i	$-0.460193\pi$
$12$		0			0
$13$	4.42242	−	1.60963i	1.22656	−	0.446431i	0.354141	−	0.935192i	$-0.384773\pi$
$13$	4.42242	−	1.60963i	1.22656	−	0.446431i	0.872418	+	0.488761i	$0.162551\pi$
$14$		0			0
$15$	0.0885016	−	0.501917i	0.0228510	−	0.129595i
$16$		0			0
$17$	−2.08794	+	1.75199i	−0.506401	+	0.424920i	−0.859860	−	0.510529i	$-0.829450\pi$
$17$	−2.08794	+	1.75199i	−0.506401	+	0.424920i	0.353460	+	0.935450i	$0.385005\pi$
$18$		0			0
$19$	0.673054	+	4.30662i	0.154409	+	0.988007i
$19$	0.673054	+	4.30662i	0.154409	+	0.988007i
$20$		0			0
$21$	−0.219061	+	0.183814i	−0.0478031	+	0.0401116i
$22$		0			0
$23$	1.16559	−	6.61040i	0.243043	−	1.37836i	−0.581952	−	0.813223i	$-0.697711\pi$
$23$	1.16559	−	6.61040i	0.243043	−	1.37836i	0.824995	−	0.565140i	$-0.191178\pi$
$24$		0			0
$25$	−6.30748	+	2.29573i	−1.26150	+	0.459147i
$26$		0			0
$27$	−0.445116	−	0.770963i	−0.0856626	−	0.148372i
$28$		0			0
$29$	0.769414	+	0.645615i	0.142877	+	0.119888i	0.711425	−	0.702762i	$-0.248050\pi$
$29$	0.769414	+	0.645615i	0.142877	+	0.119888i	−0.568548	+	0.822650i	$0.692495\pi$
$30$		0			0
$31$	1.92392	−	3.33233i	0.345546	−	0.598504i	−0.639907	−	0.768453i	$-0.721027\pi$
$31$	1.92392	−	3.33233i	0.345546	−	0.598504i	0.985453	+	0.169949i	$0.0543603\pi$
$32$		0			0
$33$	−0.136697	−	0.775246i	−0.0237959	−	0.134953i
$34$		0			0
$35$	6.17530	+	2.24763i	1.04382	+	0.379918i
$36$		0			0
$37$	10.3903			1.70815			0.854076	−	0.520148i	$-0.174123\pi$
$37$	10.3903			1.70815			0.854076	+	0.520148i	$0.174123\pi$
$38$		0			0
$39$	0.700865			0.112228
$40$		0			0
$41$	−1.64870	−	0.600077i	−0.257483	−	0.0937162i	0.210053	−	0.977690i	$-0.432636\pi$
$41$	−1.64870	−	0.600077i	−0.257483	−	0.0937162i	−0.467537	+	0.883974i	$0.654858\pi$
$42$		0			0
$43$	−0.812201	−	4.60622i	−0.123859	−	0.702442i	−0.981979	−	0.188992i	$-0.939478\pi$
$43$	−0.812201	−	4.60622i	−0.123859	−	0.702442i	0.858119	−	0.513450i	$-0.171633\pi$
$44$		0			0
$45$	−5.09553	+	8.82572i	−0.759597	+	1.31566i
$46$		0			0
$47$	2.83824	+	2.38156i	0.413999	+	0.347387i	0.825875	−	0.563853i	$-0.190682\pi$
$47$	2.83824	+	2.38156i	0.413999	+	0.347387i	−0.411876	+	0.911240i	$0.635126\pi$
$48$		0			0
$49$	1.65637	+	2.86892i	0.236625	+	0.409846i
$50$		0			0
$51$	−0.381426	+	0.138828i	−0.0534104	+	0.0194398i
$52$		0			0
$53$	−1.09076	+	6.18603i	−0.149828	+	0.849716i	0.813535	+	0.581516i	$0.197540\pi$
$53$	−1.09076	+	6.18603i	−0.149828	+	0.849716i	−0.963363	+	0.268201i	$0.913571\pi$
$54$		0			0
$55$	−13.8581	+	11.6283i	−1.86862	+	1.56796i
$56$		0			0
$57$	−0.125167	+	0.636956i	−0.0165788	+	0.0843669i
$58$		0			0
$59$	−4.44430	+	3.72921i	−0.578599	+	0.485502i	−0.884487	−	0.466565i	$-0.845491\pi$
$59$	−4.44430	+	3.72921i	−0.578599	+	0.485502i	0.305888	+	0.952068i	$0.401047\pi$
$60$		0			0
$61$	0.261694	−	1.48414i	0.0335065	−	0.190025i	−0.963460	−	0.267850i	$-0.913687\pi$
$61$	0.261694	−	1.48414i	0.0335065	−	0.190025i	0.996967	+	0.0778258i	$0.0247978\pi$
$62$		0			0
$63$	5.37324	−	1.95570i	0.676965	−	0.246395i
$64$		0			0
$65$	−8.05314	−	13.9484i	−0.998869	−	1.73009i
$66$		0			0
$67$	3.63565	+	3.05067i	0.444165	+	0.372699i	0.837265	−	0.546797i	$-0.184153\pi$
$67$	3.63565	+	3.05067i	0.444165	+	0.372699i	−0.393100	+	0.919496i	$0.628597\pi$
$68$		0			0
$69$	0.499811	−	0.865699i	0.0601702	−	0.104218i
$70$		0			0
$71$	2.19935	+	12.4731i	0.261015	+	1.48029i	0.780148	+	0.625595i	$0.215144\pi$
$71$	2.19935	+	12.4731i	0.261015	+	1.48029i	−0.519133	+	0.854693i	$0.673745\pi$
$72$		0			0
$73$	−1.74925	−	0.636675i	−0.204734	−	0.0745172i	0.237618	−	0.971359i	$-0.423634\pi$
$73$	−1.74925	−	0.636675i	−0.204734	−	0.0745172i	−0.442352	+	0.896842i	$0.645856\pi$
$74$		0			0
$75$	−0.999609			−0.115425
$76$		0			0
$77$	10.1503			1.15674
$78$		0			0
$79$	−5.54303	−	2.01750i	−0.623640	−	0.226986i	0.0108208	−	0.999941i	$-0.496556\pi$
$79$	−5.54303	−	2.01750i	−0.623640	−	0.226986i	−0.634461	+	0.772955i	$0.718778\pi$
$80$		0			0
$81$	1.52826	+	8.66719i	0.169807	+	0.963021i
$82$		0			0
$83$	1.29945	−	2.25071i	0.142633	−	0.247048i	−0.785854	−	0.618412i	$-0.787776\pi$
$83$	1.29945	−	2.25071i	0.142633	−	0.247048i	0.928487	+	0.371364i	$0.121110\pi$
$84$		0			0
$85$	7.14561	+	5.99588i	0.775050	+	0.650344i
$86$		0			0
$87$	0.0747887	+	0.129538i	0.00801819	+	0.0138879i
$88$		0			0
$89$	10.9425	−	3.98275i	1.15990	−	0.422171i	0.310841	−	0.950462i	$-0.399389\pi$
$89$	10.9425	−	3.98275i	1.15990	−	0.422171i	0.849063	+	0.528291i	$0.177167\pi$
$90$		0			0
$91$	−1.56926	+	8.89974i	−0.164504	+	0.932947i
$92$		0			0
$93$	0.438966	−	0.368337i	0.0455187	−	0.0381947i
$94$		0			0
$95$	14.1147	−	4.82775i	1.44814	−	0.495317i
$96$		0			0
$97$	−5.00808	+	4.20228i	−0.508494	+	0.426677i	−0.860599	−	0.509284i	$-0.829910\pi$
$97$	−5.00808	+	4.20228i	−0.508494	+	0.426677i	0.352105	+	0.935960i	$0.385466\pi$
$98$		0			0
$99$	−2.73336	+	15.5017i	−0.274713	+	1.55798i
$100$		0			0
$101$	11.1993	−	4.07623i	1.11438	−	0.405600i	0.281779	−	0.959479i	$-0.409075\pi$
$101$	11.1993	−	4.07623i	1.11438	−	0.405600i	0.832597	+	0.553880i	$0.186853\pi$
$102$		0			0
$103$	−1.46675	−	2.54048i	−0.144523	−	0.250321i	0.784672	−	0.619911i	$-0.212831\pi$
$103$	−1.46675	−	2.54048i	−0.144523	−	0.250321i	−0.929195	+	0.369590i	$0.879498\pi$
$104$		0			0
$105$	0.749698	+	0.629071i	0.0731630	+	0.0613911i
$106$		0			0
$107$	10.0815	−	17.4617i	0.974620	−	1.68809i	0.293435	−	0.955979i	$-0.405201\pi$
$107$	10.0815	−	17.4617i	0.974620	−	1.68809i	0.681184	−	0.732112i	$-0.261465\pi$
$108$		0			0
$109$	−3.19963	−	18.1460i	−0.306469	−	1.73807i	−0.616509	−	0.787348i	$-0.711454\pi$
$109$	−3.19963	−	18.1460i	−0.306469	−	1.73807i	0.310040	−	0.950723i	$-0.399657\pi$
$110$		0			0
$111$	1.45403	+	0.529223i	0.138010	+	0.0502317i
$112$		0			0
$113$	−11.4430			−1.07647			−0.538234	−	0.842795i	$-0.680908\pi$
$113$	−11.4430			−1.07647			−0.538234	+	0.842795i	$0.680908\pi$
$114$		0			0
$115$	−22.9719			−2.14214
$116$		0			0
$117$	−13.1692	−	4.79319i	−1.21749	−	0.443131i
$118$		0			0
$119$	−0.908838	−	5.15428i	−0.0833130	−	0.472492i
$120$		0			0
$121$	−8.47096	+	14.6721i	−0.770088	+	1.33383i
$122$		0			0
$123$	−0.200156	−	0.167951i	−0.0180475	−	0.0151436i
$124$		0			0
$125$	2.92998	+	5.07488i	0.262066	+	0.453911i
$126$		0			0
$127$	−3.19899	+	1.16434i	−0.283865	+	0.103318i	−0.480029	−	0.877253i	$-0.659374\pi$
$127$	−3.19899	+	1.16434i	−0.283865	+	0.103318i	0.196164	+	0.980571i	$0.437152\pi$
$128$		0			0
$129$	0.120955	−	0.685969i	0.0106495	−	0.0603962i
$130$		0			0
$131$	13.6421	−	11.4470i	1.19191	−	1.00013i	0.192088	−	0.981378i	$-0.438474\pi$
$131$	13.6421	−	11.4470i	1.19191	−	1.00013i	0.999824	−	0.0187556i	$-0.00597044\pi$
$132$		0			0
$133$	−7.80796	−	3.01557i	−0.677036	−	0.261483i
$134$		0			0
$135$	−2.33388	+	1.95835i	−0.200868	+	0.168548i
$136$		0			0
$137$	−1.27972	+	7.25766i	−0.109334	+	0.620064i	0.880066	+	0.474851i	$0.157498\pi$
$137$	−1.27972	+	7.25766i	−0.109334	+	0.620064i	−0.989400	+	0.145213i	$0.953613\pi$
$138$		0			0
$139$	11.6202	−	4.22940i	0.985611	−	0.358733i	0.201592	−	0.979470i	$-0.435388\pi$
$139$	11.6202	−	4.22940i	0.985611	−	0.358733i	0.784019	+	0.620736i	$0.213166\pi$
$140$		0			0
$141$	0.275883	+	0.477843i	0.0232335	+	0.0402417i
$142$		0			0
$143$	−19.0571	−	15.9908i	−1.59363	−	1.33722i
$144$		0			0
$145$	1.71869	−	2.97685i	0.142729	−	0.247214i
$146$		0			0
$147$	0.0856679	+	0.485847i	0.00706577	+	0.0400720i
$148$		0			0
$149$	−8.94127	−	3.25436i	−0.732498	−	0.266607i	−0.0512759	−	0.998685i	$-0.516329\pi$
$149$	−8.94127	−	3.25436i	−0.732498	−	0.266607i	−0.681222	+	0.732077i	$0.738551\pi$
$150$		0			0
$151$	14.2798			1.16207			0.581037	−	0.813877i	$-0.302647\pi$
$151$	14.2798			1.16207			0.581037	+	0.813877i	$0.302647\pi$
$152$		0			0
$153$	8.11640			0.656172
$154$		0			0
$155$	−12.3744	−	4.50391i	−0.993935	−	0.361763i
$156$		0			0
$157$	−1.15475	−	6.54889i	−0.0921588	−	0.522659i	−0.995581	−	0.0939066i	$-0.970065\pi$
$157$	−1.15475	−	6.54889i	−0.0921588	−	0.522659i	0.903422	−	0.428752i	$-0.141047\pi$
$158$		0			0
$159$	−0.467725	+	0.810123i	−0.0370930	+	0.0642470i
$160$		0			0
$161$	9.87374	+	8.28505i	0.778160	+	0.652954i
$162$		0			0
$163$	−6.57069	−	11.3808i	−0.514656	−	0.891410i	−0.999855	−	0.0170068i	$-0.994586\pi$
$163$	−6.57069	−	11.3808i	−0.514656	−	0.891410i	0.485199	−	0.874404i	$-0.338747\pi$
$164$		0			0
$165$	−2.53160	+	0.921426i	−0.197085	+	0.0717330i
$166$		0			0
$167$	0.513285	−	2.91098i	0.0397192	−	0.225259i	−0.958486	−	0.285138i	$-0.907961\pi$
$167$	0.513285	−	2.91098i	0.0397192	−	0.225259i	0.998206	+	0.0598794i	$0.0190716\pi$
$168$		0			0
$169$	7.00833	−	5.88069i	0.539102	−	0.452361i
$170$		0			0
$171$	6.70800	−	11.1123i	0.512974	−	0.849781i
$172$		0			0
$173$	−2.04456	+	1.71559i	−0.155445	+	0.130434i	−0.717193	−	0.696874i	$-0.754573\pi$
$173$	−2.04456	+	1.71559i	−0.155445	+	0.130434i	0.561748	+	0.827308i	$0.310129\pi$
$174$		0			0
$175$	2.23816	−	12.6933i	0.169189	−	0.959520i
$176$		0			0
$177$	−0.811887	+	0.295503i	−0.0610252	+	0.0222113i
$178$		0			0
$179$	10.4360	+	18.0757i	0.780024	+	1.35104i	0.931927	+	0.362646i	$0.118127\pi$
$179$	10.4360	+	18.0757i	0.780024	+	1.35104i	−0.151903	+	0.988395i	$0.548540\pi$
$180$		0			0
$181$	3.27371	+	2.74697i	0.243333	+	0.204181i	0.756295	−	0.654231i	$-0.227007\pi$
$181$	3.27371	+	2.74697i	0.243333	+	0.204181i	−0.512962	+	0.858411i	$0.671452\pi$
$182$		0			0
$183$	0.112216	−	0.194363i	0.00829522	−	0.0143677i
$184$		0			0
$185$	−6.17473	−	35.0187i	−0.453975	−	2.57462i
$186$		0			0
$187$	13.5388	+	4.92770i	0.990052	+	0.360349i
$188$		0			0
$189$	1.70944			0.124344
$190$		0			0
$191$	1.26562			0.0915769			0.0457884	−	0.998951i	$-0.485420\pi$
$191$	1.26562			0.0915769			0.0457884	+	0.998951i	$0.485420\pi$
$192$		0			0
$193$	−4.09076	−	1.48892i	−0.294460	−	0.107175i	0.190566	−	0.981674i	$-0.438968\pi$
$193$	−4.09076	−	1.48892i	−0.294460	−	0.107175i	−0.485026	+	0.874500i	$0.661190\pi$
$194$		0			0
$195$	−0.416510	−	2.36215i	−0.0298269	−	0.169157i
$196$		0			0
$197$	−2.20777	+	3.82397i	−0.157297	+	0.272447i	−0.933893	−	0.357552i	$-0.883611\pi$
$197$	−2.20777	+	3.82397i	−0.157297	+	0.272447i	0.776596	+	0.629999i	$0.216945\pi$
$198$		0			0
$199$	16.1097	+	13.5177i	1.14199	+	0.958241i	0.999502	−	0.0315561i	$-0.0100463\pi$
$199$	16.1097	+	13.5177i	1.14199	+	0.958241i	0.142485	+	0.989797i	$0.454491\pi$
$200$		0			0
$201$	0.353393	+	0.612095i	0.0249264	+	0.0431738i
$202$		0			0
$203$	−1.81236	+	0.659643i	−0.127202	+	0.0462979i
$204$		0			0
$205$	−1.04267	+	5.91326i	−0.0728231	+	0.413000i
$206$		0			0
$207$	−15.3119	+	12.8482i	−1.06425	+	0.893012i
$208$		0			0
$209$	17.9361	−	14.4636i	1.24066	−	1.00046i
$210$		0			0
$211$	−17.0515	+	14.3079i	−1.17387	+	0.984995i	−0.173872	+	0.984768i	$0.555628\pi$
$211$	−17.0515	+	14.3079i	−1.17387	+	0.984995i	−1.00000		0.000226777i	$0.999928\pi$
$212$		0			0
$213$	−0.327532	+	1.85753i	−0.0224422	+	0.127276i
$214$		0			0
$215$	−15.0418	+	5.47477i	−1.02584	+	0.373376i
$216$		0			0
$217$	3.69436	+	6.39881i	0.250789	+	0.434380i
$218$		0			0
$219$	−0.212364	−	0.178194i	−0.0143502	−	0.0120413i
$220$		0			0
$221$	−6.41371	+	11.1089i	−0.431433	+	0.747263i
$222$		0			0
$223$	−2.98456	−	16.9263i	−0.199861	−	1.13347i	−0.905324	−	0.424722i	$-0.860372\pi$
$223$	−2.98456	−	16.9263i	−0.199861	−	1.13347i	0.705463	−	0.708747i	$-0.250739\pi$
$224$		0			0
$225$	18.7826	+	6.83629i	1.25217	+	0.455753i
$226$		0			0
$227$	−27.7795			−1.84379			−0.921893	−	0.387443i	$-0.873358\pi$
$227$	−27.7795			−1.84379			−0.921893	+	0.387443i	$0.873358\pi$
$228$		0			0
$229$	−21.5703			−1.42540			−0.712702	−	0.701467i	$-0.752529\pi$
$229$	−21.5703			−1.42540			−0.712702	+	0.701467i	$0.752529\pi$
$230$		0			0
$231$	1.42045	+	0.517001i	0.0934587	+	0.0340162i
$232$		0			0
$233$	−1.59481	−	9.04464i	−0.104480	−	0.592534i	−0.991427	−	0.130663i	$-0.958289\pi$
$233$	−1.59481	−	9.04464i	−0.104480	−	0.592534i	0.886947	−	0.461871i	$-0.152822\pi$
$234$		0			0
$235$	6.33994	−	10.9811i	0.413572	−	0.716328i
$236$		0			0
$237$	−0.672939	−	0.564663i	−0.0437121	−	0.0366788i
$238$		0			0
$239$	2.45842	+	4.25810i	0.159022	+	0.275434i	0.934516	−	0.355921i	$-0.115833\pi$
$239$	2.45842	+	4.25810i	0.159022	+	0.275434i	−0.775494	+	0.631354i	$0.782499\pi$
$240$		0			0
$241$	11.3055	−	4.11487i	0.728252	−	0.265062i	0.0488271	−	0.998807i	$-0.484452\pi$
$241$	11.3055	−	4.11487i	0.728252	−	0.265062i	0.679425	+	0.733745i	$0.262229\pi$
$242$		0			0
$243$	−0.691353	+	3.92086i	−0.0443503	+	0.251523i
$244$		0			0
$245$	8.68486	−	7.28746i	0.554855	−	0.465579i
$246$		0			0
$247$	9.90860	+	17.9623i	0.630469	+	1.14292i
$248$		0			0
$249$	0.296486	−	0.248781i	0.0187890	−	0.0157659i
$250$		0			0
$251$	−1.84548	+	10.4663i	−0.116486	+	0.660625i	0.869518	+	0.493902i	$0.164430\pi$
$251$	−1.84548	+	10.4663i	−0.116486	+	0.660625i	−0.986004	+	0.166723i	$0.946681\pi$
$252$		0			0
$253$	−33.3419	+	12.1355i	−2.09619	+	0.762949i
$254$		0			0
$255$	0.694569	+	1.20303i	0.0434956	+	0.0753366i
$256$		0			0
$257$	−5.72621	−	4.80486i	−0.357191	−	0.299719i	0.446479	−	0.894794i	$-0.352678\pi$
$257$	−5.72621	−	4.80486i	−0.357191	−	0.299719i	−0.803670	+	0.595075i	$0.797122\pi$
$258$		0			0
$259$	−9.97583	+	17.2786i	−0.619868	+	1.07364i
$260$		0			0
$261$	−0.519368	−	2.94548i	−0.0321481	−	0.182321i
$262$		0			0
$263$	16.3871	+	5.96441i	1.01047	+	0.367781i	0.793614	−	0.608422i	$-0.208197\pi$
$263$	16.3871	+	5.96441i	1.01047	+	0.367781i	0.216857	+	0.976203i	$0.430419\pi$
$264$		0			0
$265$	21.4972			1.32056
$266$		0			0
$267$	1.73417			0.106129
$268$		0			0
$269$	8.33134	+	3.03236i	0.507971	+	0.184886i	0.583276	−	0.812274i	$-0.301771\pi$
$269$	8.33134	+	3.03236i	0.507971	+	0.184886i	−0.0753048	+	0.997161i	$0.523993\pi$
$270$		0			0
$271$	−3.30522	−	18.7448i	−0.200778	−	1.13867i	−0.903947	−	0.427645i	$-0.859343\pi$
$271$	−3.30522	−	18.7448i	−0.200778	−	1.13867i	0.703169	−	0.711023i	$-0.251768\pi$
$272$		0			0
$273$	−0.672909	+	1.16551i	−0.0407263	+	0.0705400i
$274$		0			0
$275$	27.1802	+	22.8069i	1.63903	+	1.37531i
$276$		0			0
$277$	0.924871	+	1.60192i	0.0555701	+	0.0962503i	0.892472	−	0.451102i	$-0.148969\pi$
$277$	0.924871	+	1.60192i	0.0555701	+	0.0962503i	−0.836902	+	0.547353i	$0.815636\pi$
$278$		0			0
$279$	−10.7672	+	3.91893i	−0.644614	+	0.234620i
$280$		0			0
$281$	−3.25100	+	18.4373i	−0.193939	+	1.09988i	0.719984	+	0.693991i	$0.244149\pi$
$281$	−3.25100	+	18.4373i	−0.193939	+	1.09988i	−0.913922	+	0.405889i	$0.866962\pi$
$282$		0			0
$283$	12.7514	−	10.6997i	0.757991	−	0.636030i	−0.179612	−	0.983737i	$-0.557484\pi$
$283$	12.7514	−	10.6997i	0.757991	−	0.636030i	0.937603	+	0.347708i	$0.113040\pi$
$284$		0			0
$285$	2.22114	+	0.0433253i	0.131569	+	0.00256637i
$286$		0			0
$287$	2.58084	−	2.16558i	0.152342	−	0.127830i
$288$		0			0
$289$	−1.66199	+	9.42561i	−0.0977641	+	0.554448i
$290$		0			0
$291$	−0.914878	+	0.332988i	−0.0536311	+	0.0195201i
$292$		0			0
$293$	5.65710	+	9.79839i	0.330491	+	0.572428i	0.982608	−	0.185691i	$-0.0594522\pi$
$293$	5.65710	+	9.79839i	0.330491	+	0.572428i	−0.652117	+	0.758118i	$0.726119\pi$
$294$		0			0
$295$	15.2098	+	12.7626i	0.885551	+	0.743065i
$296$		0			0
$297$	−2.35289	+	4.07532i	−0.136528	+	0.236474i
$298$		0			0
$299$	−5.48556	−	31.1101i	−0.317238	−	1.79915i
$300$		0			0
$301$	8.43977	+	3.07183i	0.486460	+	0.177057i
$302$		0			0
$303$	1.77487			0.101964
$304$		0			0
$305$	−5.15756			−0.295321
$306$		0			0
$307$	7.42304	+	2.70177i	0.423655	+	0.154198i	0.545045	−	0.838407i	$-0.316513\pi$
$307$	7.42304	+	2.70177i	0.423655	+	0.154198i	−0.121389	+	0.992605i	$0.538735\pi$
$308$		0			0
$309$	−0.0758605	−	0.430226i	−0.00431555	−	0.0244747i
$310$		0			0
$311$	−11.2790	+	19.5358i	−0.639573	+	1.10777i	0.345954	+	0.938252i	$0.387555\pi$
$311$	−11.2790	+	19.5358i	−0.639573	+	1.10777i	−0.985527	+	0.169521i	$0.945778\pi$
$312$		0			0
$313$	19.9184	+	16.7135i	1.12585	+	0.944704i	0.998885	−	0.0472024i	$-0.0150306\pi$
$313$	19.9184	+	16.7135i	1.12585	+	0.944704i	0.126969	+	0.991907i	$0.459475\pi$
$314$		0			0
$315$	−9.78455	−	16.9473i	−0.551297	−	0.954875i
$316$		0			0
$317$	20.6792	−	7.52662i	1.16146	−	0.422737i	0.311842	−	0.950134i	$-0.399054\pi$
$317$	20.6792	−	7.52662i	1.16146	−	0.422737i	0.849619	+	0.527397i	$0.176832\pi$
$318$		0			0
$319$	0.921944	−	5.22860i	0.0516189	−	0.292746i
$320$		0			0
$321$	2.30023	−	1.93012i	0.128386	−	0.107729i
$322$		0			0
$323$	−8.95047	−	7.81280i	−0.498017	−	0.434716i
$324$		0			0
$325$	−24.1990	+	20.3054i	−1.34232	+	1.12634i
$326$		0			0
$327$	0.476496	−	2.70235i	0.0263503	−	0.149440i
$328$		0			0
$329$	−6.68547	+	2.43331i	−0.368582	+	0.134153i
$330$		0			0
$331$	7.15397	+	12.3910i	0.393218	+	0.681073i	0.992872	−	0.119186i	$-0.0380286\pi$
$331$	7.15397	+	12.3910i	0.393218	+	0.681073i	−0.599654	+	0.800259i	$0.704695\pi$
$332$		0			0
$333$	−23.7017	−	19.8881i	−1.29885	−	1.08986i
$334$		0			0
$335$	8.12117	−	14.0663i	0.443707	−	0.768523i
$336$		0			0
$337$	5.50436	+	31.2168i	0.299841	+	1.70048i	0.646845	+	0.762621i	$0.276088\pi$
$337$	5.50436	+	31.2168i	0.299841	+	1.70048i	−0.347004	+	0.937864i	$0.612801\pi$
$338$		0			0
$339$	−1.60135	−	0.582844i	−0.0869734	−	0.0316557i
$340$		0			0
$341$	−20.3397			−1.10146
$342$		0			0
$343$	−19.8028			−1.06925
$344$		0			0
$345$	−3.21472	−	1.17006i	−0.173075	−	0.0629940i
$346$		0			0
$347$	2.69884	+	15.3059i	0.144881	+	0.821662i	0.967462	+	0.253015i	$0.0814220\pi$
$347$	2.69884	+	15.3059i	0.144881	+	0.821662i	−0.822581	+	0.568648i	$0.807467\pi$
$348$		0			0
$349$	1.69048	−	2.92800i	0.0904894	−	0.156732i	−0.817228	−	0.576315i	$-0.804490\pi$
$349$	1.69048	−	2.92800i	0.0904894	−	0.156732i	0.907717	+	0.419583i	$0.137824\pi$
$350$		0			0
$351$	−3.20946	−	2.69305i	−0.171308	−	0.143745i
$352$		0			0
$353$	1.55506	+	2.69344i	0.0827673	+	0.143357i	0.904438	−	0.426606i	$-0.140291\pi$
$353$	1.55506	+	2.69344i	0.0827673	+	0.143357i	−0.821670	+	0.569963i	$0.806958\pi$
$354$		0			0
$355$	40.7315	−	14.8251i	2.16180	−	0.786832i
$356$		0			0
$357$	0.135346	−	0.767587i	0.00716329	−	0.0406250i
$358$		0			0
$359$	−5.99411	+	5.02965i	−0.316357	+	0.265455i	−0.787114	−	0.616808i	$-0.788425\pi$
$359$	−5.99411	+	5.02965i	−0.316357	+	0.265455i	0.470757	+	0.882263i	$0.343981\pi$
$360$		0			0
$361$	−18.0940	+	5.79718i	−0.952316	+	0.305115i
$362$		0			0
$363$	−1.93276	+	1.62177i	−0.101443	+	0.0851211i
$364$		0			0
$365$	−1.10626	+	6.27391i	−0.0579043	+	0.328391i
$366$		0			0
$367$	16.7026	−	6.07924i	0.871868	−	0.317334i	0.132945	−	0.991123i	$-0.457557\pi$
$367$	16.7026	−	6.07924i	0.871868	−	0.317334i	0.738923	+	0.673790i	$0.235335\pi$
$368$		0			0
$369$	2.61230	+	4.52464i	0.135991	+	0.235544i
$370$		0			0
$371$	−9.23987	−	7.75317i	−0.479710	−	0.402525i
$372$		0			0
$373$	16.1752	−	28.0163i	0.837521	−	1.45063i	−0.0544409	−	0.998517i	$-0.517338\pi$
$373$	16.1752	−	28.0163i	0.837521	−	1.45063i	0.891962	−	0.452111i	$-0.149329\pi$
$374$		0			0
$375$	0.151539	+	0.859423i	0.00782546	+	0.0443804i
$376$		0			0
$377$	4.44187	+	1.61671i	0.228768	+	0.0832648i
$378$		0			0
$379$	−16.9160			−0.868918			−0.434459	−	0.900692i	$-0.643060\pi$
$379$	−16.9160			−0.868918			−0.434459	+	0.900692i	$0.643060\pi$
$380$		0			0
$381$	−0.506976			−0.0259732
$382$		0			0
$383$	0.344675	+	0.125452i	0.0176121	+	0.00641028i	0.350811	−	0.936446i	$-0.385906\pi$
$383$	0.344675	+	0.125452i	0.0176121	+	0.00641028i	−0.333199	+	0.942856i	$0.608128\pi$
$384$		0			0
$385$	−6.03213	−	34.2099i	−0.307426	−	1.74350i
$386$		0			0
$387$	−6.96405	+	12.0621i	−0.354003	+	0.613151i
$388$		0			0
$389$	2.81140	+	2.35905i	0.142544	+	0.119608i	0.711271	−	0.702918i	$-0.248120\pi$
$389$	2.81140	+	2.35905i	0.142544	+	0.119608i	−0.568728	+	0.822526i	$0.692564\pi$
$390$		0			0
$391$	9.14767	+	15.8442i	0.462618	+	0.801278i
$392$		0			0
$393$	2.49214	−	0.907064i	0.125712	−	0.0457553i
$394$		0			0
$395$	−3.50552	+	19.8808i	−0.176382	+	1.00031i
$396$		0			0
$397$	−18.9382	+	15.8910i	−0.950479	+	0.797546i	−0.979378	−	0.202036i	$-0.935244\pi$
$397$	−18.9382	+	15.8910i	−0.950479	+	0.797546i	0.0288992	+	0.999582i	$0.490800\pi$
$398$		0			0
$399$	−0.939059	−	0.819697i	−0.0470117	−	0.0410362i
$400$		0			0
$401$	−8.66844	+	7.27368i	−0.432881	+	0.363230i	−0.833038	−	0.553217i	$-0.813400\pi$
$401$	−8.66844	+	7.27368i	−0.432881	+	0.363230i	0.400156	+	0.916447i	$0.368956\pi$
$402$		0			0
$403$	3.14457	−	17.8338i	0.156642	−	0.888363i
$404$		0			0
$405$	28.3030	−	10.3015i	1.40639	−	0.511884i
$406$		0			0
$407$	−27.4616	−	47.5648i	−1.36122	−	2.35770i
$408$		0			0
$409$	3.68740	+	3.09409i	0.182330	+	0.152993i	0.729385	−	0.684104i	$-0.239807\pi$
$409$	3.68740	+	3.09409i	0.182330	+	0.152993i	−0.547054	+	0.837097i	$0.684251\pi$
$410$		0			0
$411$	−0.548751	+	0.950464i	−0.0270679	+	0.0468830i
$412$		0			0
$413$	−1.93451	−	10.9712i	−0.0951911	−	0.539856i
$414$		0			0
$415$	−8.35788	−	3.04202i	−0.410272	−	0.149327i
$416$		0			0
$417$	1.84157			0.0901819
$418$		0			0
$419$	−4.83946			−0.236423			−0.118212	−	0.992988i	$-0.537716\pi$
$419$	−4.83946			−0.236423			−0.118212	+	0.992988i	$0.537716\pi$
$420$		0			0
$421$	−7.29147	−	2.65388i	−0.355364	−	0.129342i	0.158168	−	0.987412i	$-0.449441\pi$
$421$	−7.29147	−	2.65388i	−0.355364	−	0.129342i	−0.513533	+	0.858070i	$0.671663\pi$
$422$		0			0
$423$	−1.91586	−	10.8654i	−0.0931523	−	0.528293i
$424$		0			0
$425$	9.14755	−	15.8440i	0.443721	−	0.768548i
$426$		0			0
$427$	2.21681	+	1.86013i	0.107279	+	0.0900178i
$428$		0			0
$429$	−1.85239	−	3.20844i	−0.0894343	−	0.154905i
$430$		0			0
$431$	2.20314	−	0.801879i	0.106122	−	0.0386251i	−0.288414	−	0.957506i	$-0.593128\pi$
$431$	2.20314	−	0.801879i	0.106122	−	0.0386251i	0.394535	+	0.918881i	$0.370906\pi$
$432$		0			0
$433$	5.79390	−	32.8588i	0.278437	−	1.57910i	−0.449391	−	0.893335i	$-0.648359\pi$
$433$	5.79390	−	32.8588i	0.278437	−	1.57910i	0.727828	−	0.685760i	$-0.240530\pi$
$434$		0			0
$435$	0.392140	−	0.329044i	0.0188017	−	0.0157765i
$436$		0			0
$437$	29.2530	+	0.570607i	1.39936	+	0.0272958i
$438$		0			0
$439$	−1.61685	+	1.35670i	−0.0771680	+	0.0647517i	−0.680556	−	0.732696i	$-0.738262\pi$
$439$	−1.61685	+	1.35670i	−0.0771680	+	0.0647517i	0.603388	+	0.797448i	$0.293817\pi$
$440$		0			0
$441$	1.71300	−	9.71490i	0.0815713	−	0.462614i
$442$		0			0
$443$	−12.7891	+	4.65484i	−0.607627	+	0.221158i	−0.627465	−	0.778645i	$-0.715907\pi$
$443$	−12.7891	+	4.65484i	−0.607627	+	0.221158i	0.0198374	+	0.999803i	$0.493685\pi$
$444$		0			0
$445$	−19.9261	−	34.5130i	−0.944587	−	1.63607i
$446$		0			0
$447$	−1.08549	−	0.910838i	−0.0513421	−	0.0430812i
$448$		0			0
$449$	−2.47490	+	4.28665i	−0.116798	+	0.202299i	−0.918497	−	0.395428i	$-0.870596\pi$
$449$	−2.47490	+	4.28665i	−0.116798	+	0.202299i	0.801699	+	0.597728i	$0.203930\pi$
$450$		0			0
$451$	1.61047	+	9.13345i	0.0758342	+	0.430077i
$452$		0			0
$453$	1.99834	+	0.727334i	0.0938900	+	0.0341732i
$454$		0			0
$455$	30.9276			1.44991
$456$		0			0
$457$	−3.02248			−0.141386			−0.0706929	−	0.997498i	$-0.522521\pi$
$457$	−3.02248			−0.141386			−0.0706929	+	0.997498i	$0.522521\pi$
$458$		0			0
$459$	2.28010	+	0.829888i	0.106426	+	0.0387358i
$460$		0			0
$461$	2.46730	+	13.9928i	0.114914	+	0.651709i	0.986793	+	0.161987i	$0.0517904\pi$
$461$	2.46730	+	13.9928i	0.114914	+	0.651709i	−0.871879	+	0.489721i	$0.837099\pi$
$462$		0			0
$463$	−13.9938	+	24.2380i	−0.650348	+	1.12644i	0.332691	+	0.943036i	$0.392044\pi$
$463$	−13.9938	+	24.2380i	−0.650348	+	1.12644i	−0.983038	+	0.183400i	$0.941290\pi$
$464$		0			0
$465$	−1.50228	−	1.26057i	−0.0696667	−	0.0584573i
$466$		0			0
$467$	13.3865	+	23.1860i	0.619452	+	1.07292i	0.989586	+	0.143943i	$0.0459783\pi$
$467$	13.3865	+	23.1860i	0.619452	+	1.07292i	−0.370134	+	0.928978i	$0.620688\pi$
$468$		0			0
$469$	−8.56377	+	3.11696i	−0.395438	+	0.143928i
$470$		0			0
$471$	0.171968	−	0.975277i	0.00792385	−	0.0449384i
$472$		0			0
$473$	−18.9398	+	15.8924i	−0.870853	+	0.730732i
$474$		0			0
$475$	−14.1321	−	25.6188i	−0.648427	−	1.17547i
$476$		0			0
$477$	14.3289	−	12.0234i	0.656076	−	0.550513i
$478$		0			0
$479$	−4.46870	+	25.3433i	−0.204180	+	1.15796i	0.694544	+	0.719450i	$0.255606\pi$
$479$	−4.46870	+	25.3433i	−0.204180	+	1.15796i	−0.898725	+	0.438513i	$0.855505\pi$
$480$		0			0
$481$	45.9502	−	16.7245i	2.09515	−	0.762572i
$482$		0			0
$483$	0.959749	+	1.66233i	0.0436701	+	0.0756388i
$484$		0			0
$485$	17.1393	+	14.3815i	0.778254	+	0.653032i
$486$		0			0
$487$	−1.04070	+	1.80255i	−0.0471587	+	0.0816812i	−0.888641	−	0.458603i	$-0.848350\pi$
$487$	−1.04070	+	1.80255i	−0.0471587	+	0.0816812i	0.841483	+	0.540284i	$0.181683\pi$
$488$		0			0
$489$	−0.339837	−	1.92731i	−0.0153680	−	0.0871561i
$490$		0			0
$491$	−7.27075	−	2.64634i	−0.328124	−	0.119427i	0.172705	−	0.984974i	$-0.444749\pi$
$491$	−7.27075	−	2.64634i	−0.328124	−	0.119427i	−0.500829	+	0.865546i	$0.666972\pi$
$492$		0			0
$493$	−2.73760			−0.123295
$494$		0			0
$495$	53.8701			2.42128
$496$		0			0
$497$	−22.8540	−	8.31816i	−1.02514	−	0.373120i
$498$		0			0
$499$	−4.98110	−	28.2492i	−0.222985	−	1.26461i	−0.866501	−	0.499176i	$-0.833636\pi$
$499$	−4.98110	−	28.2492i	−0.222985	−	1.26461i	0.643516	−	0.765433i	$-0.277475\pi$
$500$		0			0
$501$	0.220099	−	0.381223i	0.00983331	−	0.0170318i
$502$		0			0
$503$	−16.7560	−	14.0600i	−0.747115	−	0.626904i	0.187623	−	0.982241i	$-0.439922\pi$
$503$	−16.7560	−	14.0600i	−0.747115	−	0.626904i	−0.934738	+	0.355337i	$0.884366\pi$
$504$		0			0
$505$	−20.3938	−	35.3230i	−0.907510	−	1.57185i
$506$		0			0
$507$	1.28028	−	0.465985i	0.0568594	−	0.0206951i
$508$		0			0
$509$	−0.939552	+	5.32846i	−0.0416449	+	0.236180i	−0.998524	−	0.0543052i	$-0.982706\pi$
$509$	−0.939552	+	5.32846i	−0.0416449	+	0.236180i	0.956879	+	0.290485i	$0.0938167\pi$
$510$		0			0
$511$	2.73824	−	2.29766i	0.121133	−	0.101642i
$512$		0			0
$513$	3.02066	−	2.43585i	0.133365	−	0.107545i
$514$		0			0
$515$	−7.69059	+	6.45317i	−0.338888	+	0.284361i
$516$		0			0
$517$	3.40089	−	19.2874i	0.149571	−	0.848260i
$518$		0			0
$519$	−0.373501	+	0.135943i	−0.0163949	+	0.00596725i
$520$		0			0
$521$	7.26867	+	12.5897i	0.318446	+	0.551565i	0.980164	−	0.198188i	$-0.0635057\pi$
$521$	7.26867	+	12.5897i	0.318446	+	0.551565i	−0.661718	+	0.749753i	$0.730172\pi$
$522$		0			0
$523$	−15.6026	−	13.0921i	−0.682254	−	0.572479i	0.234410	−	0.972138i	$-0.424684\pi$
$523$	−15.6026	−	13.0921i	−0.682254	−	0.572479i	−0.916664	+	0.399659i	$0.869129\pi$
$524$		0			0
$525$	0.959736	−	1.66231i	0.0418863	−	0.0725492i
$526$		0			0
$527$	1.82118	+	10.3284i	0.0793317	+	0.449912i
$528$		0			0
$529$	−20.7258	−	7.54358i	−0.901122	−	0.327982i
$530$		0			0
$531$	17.2762			0.749724
$532$		0			0
$533$	−8.25714			−0.357656
$534$		0			0
$535$	−64.8431	−	23.6009i	−2.80341	−	1.02036i
$536$		0			0
$537$	0.539753	+	3.06109i	0.0232921	+	0.132096i
$538$		0			0
$539$	8.75560	−	15.1652i	0.377131	−	0.653209i
$540$		0			0
$541$	22.7777	+	19.1128i	0.979291	+	0.821722i	0.983982	−	0.178267i	$-0.0570490\pi$
$541$	22.7777	+	19.1128i	0.979291	+	0.821722i	−0.00469166	+	0.999989i	$0.501493\pi$
$542$		0			0
$543$	0.318212	+	0.551159i	0.0136558	+	0.0236525i
$544$		0			0
$545$	−59.2565	+	21.5676i	−2.53827	+	0.923854i
$546$		0			0
$547$	1.65629	−	9.39330i	0.0708179	−	0.401629i	−0.928707	−	0.370814i	$-0.879079\pi$
$547$	1.65629	−	9.39330i	0.0708179	−	0.401629i	0.999525	−	0.0308146i	$-0.00981014\pi$
$548$		0			0
$549$	−3.43776	+	2.88463i	−0.146720	+	0.123113i
$550$		0			0
$551$	−2.26256	+	3.74811i	−0.0963884	+	0.159675i
$552$		0			0
$553$	8.67695	−	7.28083i	0.368982	−	0.309612i
$554$		0			0
$555$	0.919556	−	5.21506i	0.0390330	−	0.221367i
$556$		0			0
$557$	0.263095	−	0.0957586i	0.0111477	−	0.00405742i	−0.336440	−	0.941705i	$-0.609223\pi$
$557$	0.263095	−	0.0957586i	0.0111477	−	0.00405742i	0.347588	+	0.937647i	$0.387001\pi$
$558$		0			0
$559$	−11.0062	−	19.0633i	−0.465513	−	0.806292i
$560$		0			0
$561$	1.64364	+	1.37918i	0.0693946	+	0.0582290i
$562$		0			0
$563$	0.540112	−	0.935502i	0.0227630	−	0.0394267i	−0.854419	−	0.519584i	$-0.826087\pi$
$563$	0.540112	−	0.935502i	0.0227630	−	0.0394267i	0.877183	+	0.480157i	$0.159420\pi$
$564$		0			0
$565$	6.80035	+	38.5667i	0.286093	+	1.62251i
$566$		0			0
$567$	−15.8805	−	5.78003i	−0.666918	−	0.242738i
$568$		0			0
$569$	−10.6265			−0.445487			−0.222743	−	0.974877i	$-0.571501\pi$
$569$	−10.6265			−0.445487			−0.222743	+	0.974877i	$0.571501\pi$
$570$		0			0
$571$	18.3294			0.767062			0.383531	−	0.923528i	$-0.374708\pi$
$571$	18.3294			0.767062			0.383531	+	0.923528i	$0.374708\pi$
$572$		0			0
$573$	0.177112	+	0.0644636i	0.00739897	+	0.00269300i
$574$		0			0
$575$	7.82377	+	44.3708i	0.326274	+	1.85039i
$576$		0			0
$577$	−20.3428	+	35.2347i	−0.846881	+	1.46684i	0.0370960	+	0.999312i	$0.488189\pi$
$577$	−20.3428	+	35.2347i	−0.846881	+	1.46684i	−0.883977	+	0.467530i	$0.845144\pi$
$578$		0			0
$579$	−0.496630	−	0.416722i	−0.0206392	−	0.0173184i
$580$		0			0
$581$	2.49523	+	4.32187i	0.103520	+	0.179302i
$582$		0			0
$583$	31.2014	−	11.3564i	1.29223	−	0.470334i
$584$		0			0
$585$	−8.32845	+	47.2330i	−0.344339	+	1.95284i
$586$		0			0
$587$	−4.96988	+	4.17023i	−0.205129	+	0.172124i	−0.739565	−	0.673085i	$-0.764969\pi$
$587$	−4.96988	+	4.17023i	−0.205129	+	0.172124i	0.534436	+	0.845209i	$0.320524\pi$
$588$		0			0
$589$	15.6460	+	6.04276i	0.644682	+	0.248988i
$590$		0			0
$591$	−0.503730	+	0.422680i	−0.0207207	+	0.0173867i
$592$		0			0
$593$	5.19141	−	29.4419i	0.213186	−	1.20904i	−0.670842	−	0.741601i	$-0.734067\pi$
$593$	5.19141	−	29.4419i	0.213186	−	1.20904i	0.884027	−	0.467435i	$-0.154822\pi$
$594$		0			0
$595$	−16.8315	+	6.12616i	−0.690024	+	0.251148i
$596$		0			0
$597$	1.56590	+	2.71222i	0.0640880	+	0.111004i
$598$		0			0
$599$	25.3688	+	21.2869i	1.03654	+	0.869761i	0.991615	−	0.129229i	$-0.0412503\pi$
$599$	25.3688	+	21.2869i	1.03654	+	0.869761i	0.0449261	+	0.998990i	$0.485695\pi$
$600$		0			0
$601$	16.9150	−	29.2976i	0.689976	−	1.19507i	−0.281869	−	0.959453i	$-0.590954\pi$
$601$	16.9150	−	29.2976i	0.689976	−	1.19507i	0.971845	−	0.235620i	$-0.0757122\pi$
$602$		0			0
$603$	−2.45413	−	13.9180i	−0.0999397	−	0.566786i
$604$		0			0
$605$	54.4840	+	19.8306i	2.21509	+	0.806227i
$606$		0			0
$607$	39.0360			1.58442			0.792210	−	0.610248i	$-0.208930\pi$
$607$	39.0360			1.58442			0.792210	+	0.610248i	$0.208930\pi$
$608$		0			0
$609$	−0.287222			−0.0116388
$610$		0			0
$611$	16.3853	+	5.96377i	0.662879	+	0.241268i
$612$		0			0
$613$	0.959829	+	5.44346i	0.0387671	+	0.219859i	0.998037	−	0.0626333i	$-0.0199499\pi$
$613$	0.959829	+	5.44346i	0.0387671	+	0.219859i	−0.959269	+	0.282493i	$0.908839\pi$
$614$		0			0
$615$	−0.447101	+	0.774402i	−0.0180289	+	0.0312269i
$616$		0			0
$617$	−34.4249	−	28.8859i	−1.38589	−	1.16290i	−0.966972	−	0.254882i	$-0.917963\pi$
$617$	−34.4249	−	28.8859i	−1.38589	−	1.16290i	−0.418923	−	0.908022i	$-0.637592\pi$
$618$		0			0
$619$	20.9191	+	36.2329i	0.840809	+	1.45632i	0.889212	+	0.457496i	$0.151254\pi$
$619$	20.9191	+	36.2329i	0.840809	+	1.45632i	−0.0484028	+	0.998828i	$0.515413\pi$
$620$		0			0
$621$	−5.61520	+	2.04376i	−0.225330	+	0.0820134i
$622$		0			0
$623$	−3.88287	+	22.0209i	−0.155564	+	0.882247i
$624$		0			0
$625$	−10.3467	+	8.68194i	−0.413870	+	0.347278i
$626$		0			0
$627$	3.24669	−	1.11048i	0.129660	−	0.0443485i
$628$		0			0
$629$	−21.6943	+	18.2037i	−0.865009	+	0.725829i
$630$		0			0
$631$	−1.68361	+	9.54825i	−0.0670236	+	0.380110i	0.932783	+	0.360439i	$0.117373\pi$
$631$	−1.68361	+	9.54825i	−0.0670236	+	0.380110i	−0.999807	+	0.0196712i	$0.993738\pi$
$632$		0			0
$633$	−3.11497	+	1.13376i	−0.123809	+	0.0450628i
$634$		0			0
$635$	5.82530	+	10.0897i	0.231170	+	0.400398i
$636$		0			0
$637$	11.9431	+	10.0214i	0.473202	+	0.397064i
$638$		0			0
$639$	18.8579	−	32.6628i	0.746006	−	1.29212i
$640$		0			0
$641$	5.06457	+	28.7226i	0.200039	+	1.13448i	0.905058	+	0.425288i	$0.139827\pi$
$641$	5.06457	+	28.7226i	0.200039	+	1.13448i	−0.705020	+	0.709188i	$0.749062\pi$
$642$		0			0
$643$	−2.44615	−	0.890325i	−0.0964667	−	0.0351110i	0.293336	−	0.956009i	$-0.405235\pi$
$643$	−2.44615	−	0.890325i	−0.0964667	−	0.0351110i	−0.389803	+	0.920898i	$0.627457\pi$
$644$		0			0
$645$	−2.38382			−0.0938629
$646$		0			0
$647$	27.7163			1.08964			0.544820	−	0.838553i	$-0.316598\pi$
$647$	27.7163			1.08964			0.544820	+	0.838553i	$0.316598\pi$
$648$		0			0
$649$	28.8180	+	10.4889i	1.13121	+	0.411725i
$650$		0			0
$651$	0.191073	+	1.08363i	0.00748874	+	0.0424707i
$652$		0			0
$653$	2.47062	−	4.27925i	0.0966830	−	0.167460i	−0.813627	−	0.581388i	$-0.802510\pi$
$653$	2.47062	−	4.27925i	0.0966830	−	0.167460i	0.910310	+	0.413928i	$0.135843\pi$
$654$		0			0
$655$	−46.6875	−	39.1755i	−1.82423	−	1.53071i
$656$		0			0
$657$	2.77163	+	4.80060i	0.108131	+	0.187289i
$658$		0			0
$659$	−2.12073	+	0.771882i	−0.0826119	+	0.0300683i	−0.382996	−	0.923750i	$-0.625108\pi$
$659$	−2.12073	+	0.771882i	−0.0826119	+	0.0300683i	0.300384	+	0.953818i	$0.402885\pi$
$660$		0			0
$661$	4.17047	−	23.6519i	0.162212	−	0.919953i	−0.789680	−	0.613519i	$-0.789753\pi$
$661$	4.17047	−	23.6519i	0.162212	−	0.919953i	0.951892	−	0.306433i	$-0.0991356\pi$
$662$		0			0
$663$	−1.46337	+	1.22791i	−0.0568324	+	0.0476881i
$664$		0			0
$665$	−5.52336	+	28.1075i	−0.214187	+	1.08996i
$666$		0			0
$667$	5.16459	−	4.33361i	0.199974	−	0.167798i
$668$		0			0
$669$	0.444469	−	2.52071i	0.0171841	−	0.0974561i
$670$		0			0
$671$	−7.48579	+	2.72460i	−0.288986	+	0.105182i
$672$		0			0
$673$	9.23291	+	15.9919i	0.355902	+	0.616441i	0.987272	−	0.159041i	$-0.0508402\pi$
$673$	9.23291	+	15.9919i	0.355902	+	0.616441i	−0.631370	+	0.775482i	$0.717507\pi$
$674$		0			0
$675$	4.57749	+	3.84097i	0.176188	+	0.147839i
$676$		0			0
$677$	18.1902	−	31.5064i	0.699107	−	1.21089i	−0.269670	−	0.962953i	$-0.586914\pi$
$677$	18.1902	−	31.5064i	0.699107	−	1.21089i	0.968776	−	0.247936i	$-0.0797522\pi$
$678$		0			0
$679$	−2.17991	−	12.3629i	−0.0836574	−	0.474445i
$680$		0			0
$681$	−3.88749	−	1.41493i	−0.148969	−	0.0542203i
$682$		0			0
$683$	−12.8068			−0.490038			−0.245019	−	0.969518i	$-0.578794\pi$
$683$	−12.8068			−0.490038			−0.245019	+	0.969518i	$0.578794\pi$
$684$		0			0
$685$	25.2212			0.963653
$686$		0			0
$687$	−3.01857	−	1.09867i	−0.115166	−	0.0419169i
$688$		0			0
$689$	5.13340	+	29.1130i	0.195567	+	1.10912i
$690$		0			0
$691$	−13.1834	+	22.8343i	−0.501520	+	0.868659i	0.498478	+	0.866902i	$0.333892\pi$
$691$	−13.1834	+	22.8343i	−0.501520	+	0.868659i	−0.999998	+	0.00175656i	$0.999441\pi$
$692$		0			0
$693$	−23.1543	−	19.4288i	−0.879561	−	0.738039i
$694$		0			0
$695$	−21.1601	−	36.6504i	−0.802649	−	1.39023i
$696$		0			0
$697$	4.49371	−	1.63558i	0.170212	−	0.0619519i
$698$		0			0
$699$	0.237504	−	1.34695i	0.00898321	−	0.0509463i
$700$		0			0
$701$	−15.2095	+	12.7623i	−0.574455	+	0.482025i	−0.883121	−	0.469146i	$-0.844562\pi$
$701$	−15.2095	+	12.7623i	−0.574455	+	0.482025i	0.308666	+	0.951170i	$0.400117\pi$
$702$		0			0
$703$	6.99322	+	44.7470i	0.263754	+	1.68767i
$704$		0			0
$705$	1.44654	−	1.21379i	0.0544797	−	0.0457139i
$706$		0			0
$707$	−3.97401	+	22.5377i	−0.149458	+	0.847618i
$708$		0			0
$709$	−5.41220	+	1.96988i	−0.203259	+	0.0739804i	−0.441644	−	0.897191i	$-0.645604\pi$
$709$	−5.41220	+	1.96988i	−0.203259	+	0.0739804i	0.238384	+	0.971171i	$0.423382\pi$
$710$		0			0
$711$	8.78275	+	15.2122i	0.329379	+	0.570501i
$712$		0			0
$713$	−19.7855	−	16.6020i	−0.740973	−	0.621750i
$714$		0			0
$715$	−42.5690	+	73.7316i	−1.59199	+	2.75741i
$716$		0			0
$717$	0.127150	+	0.721102i	0.00474850	+	0.0269301i
$718$		0			0
$719$	−34.0837	−	12.4055i	−1.27111	−	0.462646i	−0.383627	−	0.923488i	$-0.625325\pi$
$719$	−34.0837	−	12.4055i	−1.27111	−	0.462646i	−0.887482	+	0.460842i	$0.847547\pi$
$720$		0			0
$721$	5.63296			0.209782
$722$		0			0
$723$	1.79170			0.0666339
$724$		0			0
$725$	−6.33522	−	2.30583i	−0.235284	−	0.0856364i
$726$		0			0
$727$	3.03113	+	17.1904i	0.112418	+	0.637556i	0.987996	+	0.154479i	$0.0493699\pi$
$727$	3.03113	+	17.1904i	0.112418	+	0.637556i	−0.875578	+	0.483077i	$0.839519\pi$
$728$		0			0
$729$	12.9049	−	22.3519i	0.477959	−	0.827848i
$730$		0			0
$731$	9.76589	+	8.19455i	0.361205	+	0.303087i
$732$		0			0
$733$	−20.6015	−	35.6829i	−0.760935	−	1.31798i	−0.942369	−	0.334575i	$-0.891407\pi$
$733$	−20.6015	−	35.6829i	−0.760935	−	1.31798i	0.181434	−	0.983403i	$-0.441926\pi$
$734$		0			0
$735$	1.58655	−	0.577458i	0.0585209	−	0.0212999i
$736$		0			0
$737$	4.35638	−	24.7063i	0.160469	−	0.910068i
$738$		0			0
$739$	22.6208	−	18.9811i	0.832119	−	0.698231i	−0.123657	−	0.992325i	$-0.539462\pi$
$739$	22.6208	−	18.9811i	0.832119	−	0.698231i	0.955776	+	0.294094i	$0.0950179\pi$
$740$		0			0
$741$	0.471720	+	3.01836i	0.0173291	+	0.110882i
$742$		0			0
$743$	8.49724	−	7.13003i	0.311734	−	0.261575i	−0.473475	−	0.880808i	$-0.657000\pi$
$743$	8.49724	−	7.13003i	0.311734	−	0.261575i	0.785208	+	0.619232i	$0.212556\pi$
$744$		0			0
$745$	−5.65463	+	32.0690i	−0.207170	+	1.17492i
$746$		0			0
$747$	−7.27234	+	2.64692i	−0.266081	+	0.0968456i
$748$		0			0
$749$	19.3588	+	33.5304i	0.707356	+	1.22518i
$750$		0			0
$751$	26.3370	+	22.0993i	0.961050	+	0.806417i	0.981124	−	0.193382i	$-0.0619457\pi$
$751$	26.3370	+	22.0993i	0.961050	+	0.806417i	−0.0200737	+	0.999799i	$0.506390\pi$
$752$		0			0
$753$	−0.791353	+	1.37066i	−0.0288385	+	0.0499498i
$754$		0			0
$755$	−8.48620	−	48.1276i	−0.308844	−	1.75154i
$756$		0			0
$757$	−2.18310	−	0.794584i	−0.0793462	−	0.0288797i	0.302042	−	0.953295i	$-0.402332\pi$
$757$	−2.18310	−	0.794584i	−0.0793462	−	0.0288797i	−0.381388	+	0.924415i	$0.624554\pi$
$758$		0			0
$759$	−5.28402			−0.191798
$760$		0			0
$761$	−39.3613			−1.42685			−0.713423	−	0.700734i	$-0.752856\pi$
$761$	−39.3613			−1.42685			−0.713423	+	0.700734i	$0.752856\pi$
$762$		0			0
$763$	33.2481	+	12.1013i	1.20366	+	0.438097i
$764$		0			0
$765$	−4.82341	−	27.3549i	−0.174391	−	0.989019i
$766$		0			0
$767$	−13.6519	+	23.6458i	−0.492943	+	0.853802i
$768$		0			0
$769$	14.6219	+	12.2692i	0.527280	+	0.442440i	0.867161	−	0.498028i	$-0.165942\pi$
$769$	14.6219	+	12.2692i	0.527280	+	0.442440i	−0.339881	+	0.940468i	$0.610387\pi$
$770$		0			0
$771$	−0.556600	−	0.964060i	−0.0200455	−	0.0347198i
$772$		0			0
$773$	19.9726	−	7.26945i	0.718366	−	0.261464i	0.0431340	−	0.999069i	$-0.486266\pi$
$773$	19.9726	−	7.26945i	0.718366	−	0.261464i	0.675232	+	0.737605i	$0.264044\pi$
$774$		0			0
$775$	−4.48495	+	25.4354i	−0.161104	+	0.913667i
$776$		0			0
$777$	−2.27611	+	1.90988i	−0.0816549	+	0.0685166i
$778$		0			0
$779$	1.47464	−	7.50420i	0.0528345	−	0.268866i
$780$		0			0
$781$	51.2869	−	43.0348i	1.83519	−	1.53991i
$782$		0			0
$783$	0.155267	−	0.880563i	0.00554879	−	0.0314688i
$784$		0			0
$785$	−21.3857	+	7.78375i	−0.763288	+	0.277814i
$786$		0			0
$787$	−17.3495	−	30.0503i	−0.618445	−	1.07118i	−0.989770	−	0.142675i	$-0.954430\pi$
$787$	−17.3495	−	30.0503i	−0.618445	−	1.07118i	0.371325	−	0.928503i	$-0.378904\pi$
$788$		0			0
$789$	1.98944	+	1.66934i	0.0708258	+	0.0594299i
$790$		0			0
$791$	10.9866	−	19.0293i	0.390637	−	0.676604i
$792$		0			0
$793$	−1.23160	−	6.98472i	−0.0437352	−	0.248035i
$794$		0			0
$795$	3.00834	+	1.09495i	0.106695	+	0.0388338i
$796$		0			0
$797$	11.9418			0.422999			0.211499	−	0.977378i	$-0.432165\pi$
$797$	11.9418			0.422999			0.211499	+	0.977378i	$0.432165\pi$
$798$		0			0
$799$	−10.0986			−0.357261
$800$		0			0
$801$	−32.5849	−	11.8599i	−1.15133	−	0.419050i
$802$		0			0
$803$	1.70870	+	9.69049i	0.0602985	+	0.341970i
$804$		0			0
$805$	22.0556	−	38.2014i	0.777357	−	1.34642i
$806$		0			0
$807$	1.01145	+	0.848705i	0.0356046	+	0.0298758i
$808$		0			0
$809$	3.35132	+	5.80466i	0.117826	+	0.204081i	0.918906	−	0.394477i	$-0.129074\pi$
$809$	3.35132	+	5.80466i	0.117826	+	0.204081i	−0.801080	+	0.598558i	$0.795741\pi$
$810$		0			0
$811$	−29.9967	+	10.9179i	−1.05333	+	0.383380i	−0.809918	−	0.586544i	$-0.800488\pi$
$811$	−29.9967	+	10.9179i	−1.05333	+	0.383380i	−0.243410	+	0.969923i	$0.578266\pi$
$812$		0			0
$813$	0.492222	−	2.79153i	0.0172630	−	0.0979032i
$814$		0			0
$815$	−34.4521	+	28.9087i	−1.20680	+	1.01263i
$816$		0			0
$817$	19.2906	−	6.59808i	0.674893	−	0.230838i
$818$		0			0
$819$	20.6148	−	17.2979i	0.720339	−	0.604436i
$820$		0			0
$821$	−5.18947	+	29.4309i	−0.181114	+	1.02715i	0.749734	+	0.661739i	$0.230181\pi$
$821$	−5.18947	+	29.4309i	−0.181114	+	1.02715i	−0.930848	+	0.365408i	$0.880930\pi$
$822$		0			0
$823$	−3.63222	+	1.32202i	−0.126611	+	0.0460827i	−0.404549	−	0.914516i	$-0.632571\pi$
$823$	−3.63222	+	1.32202i	−0.126611	+	0.0460827i	0.277937	+	0.960599i	$0.410349\pi$
$824$		0			0
$825$	2.64197	+	4.57603i	0.0919817	+	0.159317i
$826$		0			0
$827$	−8.78239	−	7.36930i	−0.305394	−	0.256256i	0.477191	−	0.878799i	$-0.341655\pi$
$827$	−8.78239	−	7.36930i	−0.305394	−	0.256256i	−0.782585	+	0.622544i	$0.786099\pi$
$828$		0			0
$829$	−22.4952	+	38.9629i	−0.781292	+	1.35324i	0.149898	+	0.988702i	$0.452106\pi$
$829$	−22.4952	+	38.9629i	−0.781292	+	1.35324i	−0.931189	+	0.364536i	$0.881228\pi$
$830$		0			0
$831$	0.0478345	+	0.271283i	0.00165936	+	0.00941071i
$832$		0			0
$833$	−8.48474	−	3.08819i	−0.293979	−	0.107000i
$834$		0			0
$835$	−10.1160			−0.350079
$836$		0			0
$837$	−3.42547			−0.118402
$838$		0			0
$839$	48.3070	+	17.5823i	1.66774	+	0.607008i	0.991551	−	0.129719i	$-0.0414074\pi$
$839$	48.3070	+	17.5823i	1.66774	+	0.607008i	0.676191	+	0.736727i	$0.263630\pi$
$840$		0			0
$841$	−4.86062	−	27.5659i	−0.167608	−	0.950549i
$842$		0			0
$843$	−1.39405	+	2.41456i	−0.0480135	+	0.0831618i
$844$		0			0
$845$	−23.9848	−	20.1256i	−0.825101	−	0.692342i
$846$		0			0
$847$	−16.2661	−	28.1738i	−0.558911	−	0.968062i
$848$		0			0
$849$	2.32943	−	0.847842i	0.0799457	−	0.0290979i
$850$		0			0
$851$	12.1108	−	68.6839i	0.415154	−	2.35445i
$852$		0			0
$853$	23.4848	−	19.7061i	0.804105	−	0.674724i	−0.145088	−	0.989419i	$-0.546347\pi$
$853$	23.4848	−	19.7061i	0.804105	−	0.674724i	0.949193	+	0.314695i	$0.101902\pi$
$854$		0			0
$855$	−41.4386	−	16.0043i	−1.41717	−	0.547337i
$856$		0			0
$857$	−11.7529	+	9.86188i	−0.401473	+	0.336876i	−0.821063	−	0.570838i	$-0.806618\pi$
$857$	−11.7529	+	9.86188i	−0.401473	+	0.336876i	0.419590	+	0.907714i	$0.362174\pi$
$858$		0			0
$859$	6.46597	−	36.6703i	0.220616	−	1.25117i	−0.650275	−	0.759699i	$-0.725346\pi$
$859$	6.46597	−	36.6703i	0.220616	−	1.25117i	0.870891	−	0.491476i	$-0.163543\pi$
$860$		0			0
$861$	0.471468	−	0.171600i	0.0160676	−	0.00584813i
$862$		0			0
$863$	−3.11373	−	5.39314i	−0.105993	−	0.183585i	0.808151	−	0.588976i	$-0.200469\pi$
$863$	−3.11373	−	5.39314i	−0.105993	−	0.183585i	−0.914143	+	0.405391i	$0.867135\pi$
$864$		0			0
$865$	6.99714	+	5.87130i	0.237910	+	0.199630i
$866$		0			0
$867$	−0.712670	+	1.23438i	−0.0242035	+	0.0419217i
$868$		0			0
$869$	5.41452	+	30.7073i	0.183675	+	1.04167i
$870$		0			0
$871$	20.9888	+	7.63930i	0.711179	+	0.258848i
$872$		0			0
$873$	19.4678			0.658884
$874$		0			0
$875$	−11.2524			−0.380402
$876$		0			0
$877$	28.5556	+	10.3934i	0.964256	+	0.350960i	0.775700	−	0.631102i	$-0.217397\pi$
$877$	28.5556	+	10.3934i	0.964256	+	0.350960i	0.188556	+	0.982062i	$0.439619\pi$
$878$		0			0
$879$	0.292587	+	1.65934i	0.00986870	+	0.0559682i
$880$		0			0
$881$	25.8796	−	44.8247i	0.871905	−	1.51018i	0.0118806	−	0.999929i	$-0.496218\pi$
$881$	25.8796	−	44.8247i	0.871905	−	1.51018i	0.860024	−	0.510254i	$-0.170448\pi$
$882$		0			0
$883$	15.5595	+	13.0560i	0.523618	+	0.439368i	0.865891	−	0.500233i	$-0.166752\pi$
$883$	15.5595	+	13.0560i	0.523618	+	0.439368i	−0.342273	+	0.939601i	$0.611197\pi$
$884$		0			0
$885$	1.47843	+	2.56071i	0.0496969	+	0.0860775i
$886$		0			0
$887$	25.2921	−	9.20556i	0.849224	−	0.309092i	0.119500	−	0.992834i	$-0.461871\pi$
$887$	25.2921	−	9.20556i	0.849224	−	0.309092i	0.729724	+	0.683742i	$0.239649\pi$
$888$		0			0
$889$	1.13514	−	6.43769i	0.0380713	−	0.215913i
$890$		0			0
$891$	35.6376	−	29.9035i	1.19391	−	1.00181i
$892$		0			0
$893$	−8.34621	+	13.8261i	−0.279295	+	0.462674i
$894$		0			0
$895$	54.7191	−	45.9148i	1.82906	−	1.53476i
$896$		0			0
$897$	0.816922	−	4.63300i	0.0272762	−	0.154691i
$898$		0			0
$899$	3.63169	−	1.32183i	0.121124	−	0.0440854i
$900$		0			0
$901$	−8.56042	−	14.8271i	−0.285189	−	0.493962i
$902$		0			0
$903$	1.02461	+	0.859751i	0.0340969	+	0.0286107i
$904$		0			0
$905$	7.31269	−	12.6659i	0.243082	−	0.421030i
$906$		0			0
$907$	1.74751	+	9.91064i	0.0580252	+	0.329077i	0.999978	−	0.00666870i	$-0.00212273\pi$
$907$	1.74751	+	9.91064i	0.0580252	+	0.329077i	−0.941953	+	0.335746i	$0.891012\pi$
$908$		0			0
$909$	−33.3496	−	12.1383i	−1.10614	−	0.402601i
$910$		0			0
$911$	−34.5665			−1.14524			−0.572620	−	0.819821i	$-0.694073\pi$
$911$	−34.5665			−1.14524			−0.572620	+	0.819821i	$0.694073\pi$
$912$		0			0
$913$	−13.7378			−0.454656
$914$		0			0
$915$	−0.721755	−	0.262697i	−0.0238605	−	0.00868451i
$916$		0			0
$917$	5.93810	+	33.6767i	0.196093	+	1.11210i
$918$		0			0
$919$	12.7978	−	22.1665i	0.422161	−	0.731204i	−0.573990	−	0.818863i	$-0.694605\pi$
$919$	12.7978	−	22.1665i	0.422161	−	0.731204i	0.996151	+	0.0876584i	$0.0279384\pi$
$920$		0			0
$921$	0.901177	+	0.756177i	0.0296948	+	0.0249169i
$922$		0			0
$923$	29.8036	+	51.6213i	0.980997	+	1.69914i
$924$		0			0
$925$	−65.5365	+	23.8533i	−2.15483	+	0.784293i
$926$		0			0
$927$	−1.51689	+	8.60271i	−0.0498212	+	0.282550i
$928$		0			0
$929$	13.9711	−	11.7231i	0.458377	−	0.384624i	−0.384157	−	0.923268i	$-0.625508\pi$
$929$	13.9711	−	11.7231i	0.458377	−	0.384624i	0.842533	+	0.538644i	$0.181063\pi$
$930$		0			0
$931$	−11.2405	+	9.06431i	−0.368394	+	0.297071i
$932$		0			0
$933$	−2.57344	+	2.15937i	−0.0842507	+	0.0706947i
$934$		0			0
$935$	8.56217	−	48.5585i	0.280013	−	1.58803i
$936$		0			0
$937$	−42.0495	+	15.3048i	−1.37370	+	0.499985i	−0.920261	−	0.391304i	$-0.872024\pi$
$937$	−42.0495	+	15.3048i	−1.37370	+	0.499985i	−0.453436	+	0.891289i	$0.649802\pi$
$938$		0			0
$939$	1.93611	+	3.35345i	0.0631827	+	0.109436i
$940$		0			0
$941$	−46.2337	−	38.7947i	−1.50718	−	1.26467i	−0.869034	−	0.494752i	$-0.835259\pi$
$941$	−46.2337	−	38.7947i	−1.50718	−	1.26467i	−0.638142	−	0.769919i	$-0.720297\pi$
$942$		0			0
$943$	−5.88845	+	10.1991i	−0.191754	+	0.332128i
$944$		0			0
$945$	−1.01589	−	5.76138i	−0.0330468	−	0.187418i
$946$		0			0
$947$	−13.4252	−	4.88636i	−0.436259	−	0.158785i	0.114548	−	0.993418i	$-0.463458\pi$
$947$	−13.4252	−	4.88636i	−0.436259	−	0.158785i	−0.550807	+	0.834632i	$0.685680\pi$
$948$		0			0
$949$	−8.76073			−0.284385
$950$		0			0
$951$	3.27724			0.106272
$952$		0			0
$953$	46.6911	+	16.9942i	1.51247	+	0.550496i	0.959255	−	0.282540i	$-0.0911771\pi$
$953$	46.6911	+	16.9942i	1.51247	+	0.550496i	0.553219	+	0.833036i	$0.313399\pi$
$954$		0			0
$955$	−0.752131	−	4.26555i	−0.0243384	−	0.138030i
$956$		0			0
$957$	0.395334	−	0.684739i	0.0127793	−	0.0221345i
$958$		0			0
$959$	−10.8405	−	9.09629i	−0.350059	−	0.293734i
$960$		0			0
$961$	8.09706	+	14.0245i	0.261195	+	0.452404i
$962$		0			0
$963$	−56.4211	+	20.5356i	−1.81814	+	0.661751i
$964$		0			0
$965$	−2.58708	+	14.6720i	−0.0832810	+	0.472310i
$966$		0			0
$967$	12.8932	−	10.8187i	0.414619	−	0.347907i	−0.411493	−	0.911413i	$-0.634992\pi$
$967$	12.8932	−	10.8187i	0.414619	−	0.347907i	0.826112	+	0.563506i	$0.190548\pi$
$968$		0			0
$969$	−0.854599	−	1.54922i	−0.0274537	−	0.0497681i
$970$		0			0
$971$	−22.1231	+	18.5635i	−0.709964	+	0.595731i	−0.924589	−	0.380966i	$-0.875592\pi$
$971$	−22.1231	+	18.5635i	−0.709964	+	0.595731i	0.214625	+	0.976697i	$0.431147\pi$
$972$		0			0
$973$	−4.12334	+	23.3846i	−0.132188	+	0.749677i
$974$		0			0
$975$	−4.42069	+	1.60900i	−0.141575	+	0.0515293i
$976$		0			0
$977$	−29.7364	−	51.5050i	−0.951353	−	1.64779i	−0.742502	−	0.669844i	$-0.766361\pi$
$977$	−29.7364	−	51.5050i	−0.951353	−	1.64779i	−0.208851	−	0.977947i	$-0.566972\pi$
$978$		0			0
$979$	−47.1534	−	39.5664i	−1.50703	−	1.26455i
$980$		0			0
$981$	−27.4346	+	47.5181i	−0.875918	+	1.51713i
$982$		0			0
$983$	2.52074	+	14.2959i	0.0803993	+	0.455967i	0.998255	+	0.0590524i	$0.0188079\pi$
$983$	2.52074	+	14.2959i	0.0803993	+	0.455967i	−0.917856	+	0.396914i	$0.870081\pi$
$984$		0			0
$985$	14.2001	+	5.16840i	0.452452	+	0.164679i
$986$		0			0
$987$	−1.05951			−0.0337247
$988$		0			0
$989$	−31.3956			−0.998323
$990$		0			0
$991$	−52.9479	−	19.2715i	−1.68195	−	0.612178i	−0.688372	−	0.725358i	$-0.741674\pi$
$991$	−52.9479	−	19.2715i	−1.68195	−	0.612178i	−0.993575	+	0.113180i	$0.963896\pi$
$992$		0			0
$993$	0.370005	+	2.09840i	0.0117417	+	0.0665907i
$994$		0			0
$995$	35.9852	−	62.3283i	1.14081	−	1.97594i
$996$		0			0
$997$	4.00883	+	3.36381i	0.126961	+	0.106533i	0.704057	−	0.710143i	$-0.251370\pi$
$997$	4.00883	+	3.36381i	0.126961	+	0.106533i	−0.577096	+	0.816676i	$0.695814\pi$
$998$		0			0
$999$	−4.62488	−	8.01053i	−0.146325	−	0.253442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.f.177.2		18
4.3	odd	2		152.2.q.c.25.2	✓	18
19.4	even	9		5776.2.a.cd.1.5		9
19.15	odd	18		5776.2.a.ce.1.5		9
19.16	even	9	inner	304.2.u.f.225.2		18
76.15	even	18		2888.2.a.x.1.5		9
76.23	odd	18		2888.2.a.y.1.5		9
76.35	odd	18		152.2.q.c.73.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.25.2	✓	18	4.3	odd	2
152.2.q.c.73.2	yes	18	76.35	odd	18
304.2.u.f.177.2		18	1.1	even	1	trivial
304.2.u.f.225.2		18	19.16	even	9	inner
2888.2.a.x.1.5		9	76.15	even	18
2888.2.a.y.1.5		9	76.23	odd	18
5776.2.a.cd.1.5		9	19.4	even	9
5776.2.a.ce.1.5		9	19.15	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)

\(f(q)\)	\(=\)	\(q+(0.139941 + 0.0509345i) q^{3} +(-0.594280 - 3.37033i) q^{5} +(-0.960111 + 1.66296i) q^{7} +(-2.28114 - 1.91411i) q^{9} +O(q^{10})\)	\(q+(0.139941 + 0.0509345i) q^{3} +(-0.594280 - 3.37033i) q^{5} +(-0.960111 + 1.66296i) q^{7} +(-2.28114 - 1.91411i) q^{9} +(-2.64301 - 4.57782i) q^{11} +(4.42242 - 1.60963i) q^{13} +(0.0885016 - 0.501917i) q^{15} +(-2.08794 + 1.75199i) q^{17} +(0.673054 + 4.30662i) q^{19} +(-0.219061 + 0.183814i) q^{21} +(1.16559 - 6.61040i) q^{23} +(-6.30748 + 2.29573i) q^{25} +(-0.445116 - 0.770963i) q^{27} +(0.769414 + 0.645615i) q^{29} +(1.92392 - 3.33233i) q^{31} +(-0.136697 - 0.775246i) q^{33} +(6.17530 + 2.24763i) q^{35} +10.3903 q^{37} +0.700865 q^{39} +(-1.64870 - 0.600077i) q^{41} +(-0.812201 - 4.60622i) q^{43} +(-5.09553 + 8.82572i) q^{45} +(2.83824 + 2.38156i) q^{47} +(1.65637 + 2.86892i) q^{49} +(-0.381426 + 0.138828i) q^{51} +(-1.09076 + 6.18603i) q^{53} +(-13.8581 + 11.6283i) q^{55} +(-0.125167 + 0.636956i) q^{57} +(-4.44430 + 3.72921i) q^{59} +(0.261694 - 1.48414i) q^{61} +(5.37324 - 1.95570i) q^{63} +(-8.05314 - 13.9484i) q^{65} +(3.63565 + 3.05067i) q^{67} +(0.499811 - 0.865699i) q^{69} +(2.19935 + 12.4731i) q^{71} +(-1.74925 - 0.636675i) q^{73} -0.999609 q^{75} +10.1503 q^{77} +(-5.54303 - 2.01750i) q^{79} +(1.52826 + 8.66719i) q^{81} +(1.29945 - 2.25071i) q^{83} +(7.14561 + 5.99588i) q^{85} +(0.0747887 + 0.129538i) q^{87} +(10.9425 - 3.98275i) q^{89} +(-1.56926 + 8.89974i) q^{91} +(0.438966 - 0.368337i) q^{93} +(14.1147 - 4.82775i) q^{95} +(-5.00808 + 4.20228i) q^{97} +(-2.73336 + 15.5017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{7} - 6 q^{9}+O(q^{10}) \) 18 * q + 9 * q^7 - 6 * q^9	\( 18 q + 9 q^{7} - 6 q^{9} + 3 q^{11} + 3 q^{13} - 33 q^{15} + 9 q^{17} + 24 q^{19} - 15 q^{21} - 6 q^{23} + 6 q^{25} + 12 q^{27} - 3 q^{29} + 6 q^{31} - 45 q^{33} + 15 q^{35} + 48 q^{37} - 12 q^{39} - 18 q^{41} + 39 q^{43} - 42 q^{45} + 27 q^{47} - 18 q^{49} - 48 q^{51} + 39 q^{53} + 27 q^{55} - 6 q^{57} - 9 q^{59} - 24 q^{61} - 3 q^{63} + 27 q^{65} - 39 q^{67} - 3 q^{69} + 12 q^{73} - 90 q^{75} + 60 q^{77} - 63 q^{79} - 6 q^{81} + 27 q^{83} - 30 q^{85} - 18 q^{87} + 66 q^{89} - 108 q^{91} + 60 q^{93} + 75 q^{95} - 81 q^{97} - 15 q^{99}+O(q^{100}) \) 18 * q + 9 * q^7 - 6 * q^9 + 3 * q^11 + 3 * q^13 - 33 * q^15 + 9 * q^17 + 24 * q^19 - 15 * q^21 - 6 * q^23 + 6 * q^25 + 12 * q^27 - 3 * q^29 + 6 * q^31 - 45 * q^33 + 15 * q^35 + 48 * q^37 - 12 * q^39 - 18 * q^41 + 39 * q^43 - 42 * q^45 + 27 * q^47 - 18 * q^49 - 48 * q^51 + 39 * q^53 + 27 * q^55 - 6 * q^57 - 9 * q^59 - 24 * q^61 - 3 * q^63 + 27 * q^65 - 39 * q^67 - 3 * q^69 + 12 * q^73 - 90 * q^75 + 60 * q^77 - 63 * q^79 - 6 * q^81 + 27 * q^83 - 30 * q^85 - 18 * q^87 + 66 * q^89 - 108 * q^91 + 60 * q^93 + 75 * q^95 - 81 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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