LMFDB - Embedded newform 304.2.u.c.81.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	304.81
Dual form			304.2.u.c.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.326352 - 1.85083i) q^{3} +(1.53209 + 1.28558i) q^{5} +(2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.181985i) q^{9} +O(q^{10})$	\(q+(0.326352 - 1.85083i) q^{3} +(1.53209 + 1.28558i) q^{5} +(2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.181985i) q^{9} +(-0.705737 + 1.22237i) q^{11} +(-0.226682 - 1.28558i) q^{13} +(2.87939 - 2.41609i) q^{15} +(-2.24510 + 0.817150i) q^{17} +(-2.23396 - 3.74292i) q^{19} +(8.94356 - 3.25519i) q^{21} +(2.34730 - 1.96962i) q^{23} +(-0.173648 - 0.984808i) q^{25} +(2.31908 - 4.01676i) q^{27} +(-7.94356 - 2.89122i) q^{29} +(0.184793 + 0.320070i) q^{31} +(2.03209 + 1.70513i) q^{33} +(-1.75877 + 9.97448i) q^{35} +4.82295 q^{37} -2.45336 q^{39} +(-0.266044 + 1.50881i) q^{41} +(0.581252 + 0.487728i) q^{43} +(-0.532089 - 0.921605i) q^{45} +(-9.59627 - 3.49276i) q^{47} +(-9.32295 + 16.1478i) q^{49} +(0.779715 + 4.42198i) q^{51} +(1.28312 - 1.07666i) q^{53} +(-2.65270 + 0.965505i) q^{55} +(-7.65657 + 2.91317i) q^{57} +(0.673648 - 0.245188i) q^{59} +(7.47565 - 6.27282i) q^{61} +(-0.467911 - 2.65366i) q^{63} +(1.30541 - 2.26103i) q^{65} +(-1.31908 - 0.480105i) q^{67} +(-2.87939 - 4.98724i) q^{69} +(4.87939 + 4.09429i) q^{71} +(-0.791737 + 4.49016i) q^{73} -1.87939 q^{75} -7.14796 q^{77} +(0.389185 - 2.20718i) q^{79} +(-7.90033 - 6.62916i) q^{81} +(-1.99273 - 3.45150i) q^{83} +(-4.49020 - 1.63430i) q^{85} +(-7.94356 + 13.7587i) q^{87} +(-1.84864 - 10.4842i) q^{89} +(5.06418 - 4.24935i) q^{91} +(0.652704 - 0.237565i) q^{93} +(1.38919 - 8.60640i) q^{95} +(1.43969 - 0.524005i) q^{97} +(0.575322 - 0.482753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 6 q^{15} - 12 q^{17} - 18 q^{19} + 24 q^{21} + 12 q^{23} - 3 q^{27} - 18 q^{29} - 6 q^{31} + 3 q^{33} + 12 q^{35} - 12 q^{37} + 12 q^{39} + 3 q^{41} + 6 q^{43} + 6 q^{45} - 30 q^{47} - 15 q^{49} - 21 q^{51} + 24 q^{53} - 18 q^{55} - 24 q^{57} + 3 q^{59} + 6 q^{61} - 12 q^{63} + 12 q^{65} + 9 q^{67} - 6 q^{69} + 18 q^{71} - 30 q^{73} - 12 q^{77} - 6 q^{79} - 33 q^{81} + 6 q^{83} - 24 q^{85} - 18 q^{87} + 12 q^{91} + 6 q^{93} + 3 q^{97} - 21 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 6 * q^15 - 12 * q^17 - 18 * q^19 + 24 * q^21 + 12 * q^23 - 3 * q^27 - 18 * q^29 - 6 * q^31 + 3 * q^33 + 12 * q^35 - 12 * q^37 + 12 * q^39 + 3 * q^41 + 6 * q^43 + 6 * q^45 - 30 * q^47 - 15 * q^49 - 21 * q^51 + 24 * q^53 - 18 * q^55 - 24 * q^57 + 3 * q^59 + 6 * q^61 - 12 * q^63 + 12 * q^65 + 9 * q^67 - 6 * q^69 + 18 * q^71 - 30 * q^73 - 12 * q^77 - 6 * q^79 - 33 * q^81 + 6 * q^83 - 24 * q^85 - 18 * q^87 + 12 * q^91 + 6 * q^93 + 3 * q^97 - 21 * 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
$3$	0.326352	−	1.85083i	0.188419	−	1.06858i	−0.733064	−	0.680160i	$-0.761910\pi$
$3$	0.326352	−	1.85083i	0.188419	−	1.06858i	0.921483	−	0.388419i	$-0.126979\pi$
$4$		0			0
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	0.917512	−	0.397708i	$-0.130194\pi$
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	−0.232341	+	0.972634i	$0.574639\pi$
$6$		0			0
$7$	2.53209	+	4.38571i	0.957040	+	1.65764i	0.729630	+	0.683842i	$0.239692\pi$
$7$	2.53209	+	4.38571i	0.957040	+	1.65764i	0.227410	+	0.973799i	$0.426974\pi$
$8$		0			0
$9$	−0.500000	−	0.181985i	−0.166667	−	0.0606617i
$10$		0			0
$11$	−0.705737	+	1.22237i	−0.212788	+	0.368559i	−0.952586	−	0.304270i	$-0.901588\pi$
$11$	−0.705737	+	1.22237i	−0.212788	+	0.368559i	0.739798	+	0.672829i	$0.234921\pi$
$12$		0			0
$13$	−0.226682	−	1.28558i	−0.0628702	−	0.356554i	−0.999972	−	0.00749804i	$-0.997613\pi$
$13$	−0.226682	−	1.28558i	−0.0628702	−	0.356554i	0.937102	−	0.349056i	$-0.113498\pi$
$14$		0			0
$15$	2.87939	−	2.41609i	0.743454	−	0.623832i
$16$		0			0
$17$	−2.24510	+	0.817150i	−0.544517	+	0.198188i	−0.599609	−	0.800293i	$-0.704677\pi$
$17$	−2.24510	+	0.817150i	−0.544517	+	0.198188i	0.0550919	+	0.998481i	$0.482455\pi$
$18$		0			0
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$20$		0			0
$21$	8.94356	−	3.25519i	1.95165	−	0.710341i
$22$		0			0
$23$	2.34730	−	1.96962i	0.489445	−	0.410693i	−0.364382	−	0.931249i	$-0.618720\pi$
$23$	2.34730	−	1.96962i	0.489445	−	0.410693i	0.853827	+	0.520556i	$0.174275\pi$
$24$		0			0
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$		0			0
$27$	2.31908	−	4.01676i	0.446307	−	0.773026i
$28$		0			0
$29$	−7.94356	−	2.89122i	−1.47508	−	0.536886i	−0.525607	−	0.850727i	$-0.676162\pi$
$29$	−7.94356	−	2.89122i	−1.47508	−	0.536886i	−0.949475	+	0.313841i	$0.898384\pi$
$30$		0			0
$31$	0.184793	+	0.320070i	0.0331897	+	0.0574863i	0.882143	−	0.470981i	$-0.156100\pi$
$31$	0.184793	+	0.320070i	0.0331897	+	0.0574863i	−0.848953	+	0.528468i	$0.822767\pi$
$32$		0			0
$33$	2.03209	+	1.70513i	0.353741	+	0.296824i
$34$		0			0
$35$	−1.75877	+	9.97448i	−0.297286	+	1.68600i
$36$		0			0
$37$	4.82295			0.792888			0.396444	−	0.918059i	$-0.370244\pi$
$37$	4.82295			0.792888			0.396444	+	0.918059i	$0.370244\pi$
$38$		0			0
$39$	−2.45336			−0.392853
$40$		0			0
$41$	−0.266044	+	1.50881i	−0.0415492	+	0.235637i	−0.998509	−	0.0545825i	$-0.982617\pi$
$41$	−0.266044	+	1.50881i	−0.0415492	+	0.235637i	0.956960	+	0.290220i	$0.0937283\pi$
$42$		0			0
$43$	0.581252	+	0.487728i	0.0886401	+	0.0743779i	0.686031	−	0.727572i	$-0.259351\pi$
$43$	0.581252	+	0.487728i	0.0886401	+	0.0743779i	−0.597391	+	0.801950i	$0.703796\pi$
$44$		0			0
$45$	−0.532089	−	0.921605i	−0.0793191	−	0.137385i
$46$		0			0
$47$	−9.59627	−	3.49276i	−1.39976	−	0.509471i	−0.471652	−	0.881785i	$-0.656342\pi$
$47$	−9.59627	−	3.49276i	−1.39976	−	0.509471i	−0.928107	+	0.372314i	$0.878565\pi$
$48$		0			0
$49$	−9.32295	+	16.1478i	−1.33185	+	2.30683i
$50$		0			0
$51$	0.779715	+	4.42198i	0.109182	+	0.619202i
$52$		0			0
$53$	1.28312	−	1.07666i	0.176250	−	0.147891i	−0.550395	−	0.834904i	$-0.685523\pi$
$53$	1.28312	−	1.07666i	0.176250	−	0.147891i	0.726645	+	0.687013i	$0.241078\pi$
$54$		0			0
$55$	−2.65270	+	0.965505i	−0.357690	+	0.130189i
$56$		0			0
$57$	−7.65657	+	2.91317i	−1.01414	+	0.385859i
$58$		0			0
$59$	0.673648	−	0.245188i	0.0877015	−	0.0319207i	−0.297797	−	0.954629i	$-0.596252\pi$
$59$	0.673648	−	0.245188i	0.0877015	−	0.0319207i	0.385498	+	0.922709i	$0.374030\pi$
$60$		0			0
$61$	7.47565	−	6.27282i	0.957159	−	0.803152i	−0.0233295	−	0.999728i	$-0.507427\pi$
$61$	7.47565	−	6.27282i	0.957159	−	0.803152i	0.980489	+	0.196576i	$0.0629822\pi$
$62$		0			0
$63$	−0.467911	−	2.65366i	−0.0589513	−	0.334329i
$64$		0			0
$65$	1.30541	−	2.26103i	0.161916	−	0.280446i
$66$		0			0
$67$	−1.31908	−	0.480105i	−0.161151	−	0.0586542i	0.260185	−	0.965559i	$-0.416216\pi$
$67$	−1.31908	−	0.480105i	−0.161151	−	0.0586542i	−0.421336	+	0.906905i	$0.638439\pi$
$68$		0			0
$69$	−2.87939	−	4.98724i	−0.346637	−	0.600393i
$70$		0			0
$71$	4.87939	+	4.09429i	0.579076	+	0.485903i	0.884644	−	0.466268i	$-0.154402\pi$
$71$	4.87939	+	4.09429i	0.579076	+	0.485903i	−0.305567	+	0.952171i	$0.598846\pi$
$72$		0			0
$73$	−0.791737	+	4.49016i	−0.0926658	+	0.525534i	0.902772	+	0.430120i	$0.141529\pi$
$73$	−0.791737	+	4.49016i	−0.0926658	+	0.525534i	−0.995438	+	0.0954141i	$0.969582\pi$
$74$		0			0
$75$	−1.87939			−0.217013
$76$		0			0
$77$	−7.14796			−0.814585
$78$		0			0
$79$	0.389185	−	2.20718i	0.0437868	−	0.248327i	−0.955056	−	0.296426i	$-0.904205\pi$
$79$	0.389185	−	2.20718i	0.0437868	−	0.248327i	0.998843	+	0.0480989i	$0.0153163\pi$
$80$		0			0
$81$	−7.90033	−	6.62916i	−0.877814	−	0.736574i
$82$		0			0
$83$	−1.99273	−	3.45150i	−0.218730	−	0.378852i	0.735690	−	0.677319i	$-0.236858\pi$
$83$	−1.99273	−	3.45150i	−0.218730	−	0.378852i	−0.954420	+	0.298467i	$0.903525\pi$
$84$		0			0
$85$	−4.49020	−	1.63430i	−0.487031	−	0.177265i
$86$		0			0
$87$	−7.94356	+	13.7587i	−0.851639	+	1.47508i
$88$		0			0
$89$	−1.84864	−	10.4842i	−0.195956	−	1.11132i	−0.911051	−	0.412293i	$-0.864728\pi$
$89$	−1.84864	−	10.4842i	−0.195956	−	1.11132i	0.715096	−	0.699026i	$-0.246383\pi$
$90$		0			0
$91$	5.06418	−	4.24935i	0.530870	−	0.445453i
$92$		0			0
$93$	0.652704	−	0.237565i	0.0676822	−	0.0246343i
$94$		0			0
$95$	1.38919	−	8.60640i	0.142527	−	0.882998i
$96$		0			0
$97$	1.43969	−	0.524005i	0.146179	−	0.0532047i	−0.267895	−	0.963448i	$-0.586328\pi$
$97$	1.43969	−	0.524005i	0.146179	−	0.0532047i	0.414073	+	0.910244i	$0.364106\pi$
$98$		0			0
$99$	0.575322	−	0.482753i	0.0578220	−	0.0485185i
$100$		0			0
$101$	1.53209	+	8.68891i	0.152449	+	0.864579i	0.961081	+	0.276265i	$0.0890968\pi$
$101$	1.53209	+	8.68891i	0.152449	+	0.864579i	−0.808633	+	0.588314i	$0.799792\pi$
$102$		0			0
$103$	−3.57398	+	6.19031i	−0.352155	+	0.609950i	−0.986627	−	0.162996i	$-0.947884\pi$
$103$	−3.57398	+	6.19031i	−0.352155	+	0.609950i	0.634472	+	0.772946i	$0.281218\pi$
$104$		0			0
$105$	17.8871	+	6.51038i	1.74560	+	0.635348i
$106$		0			0
$107$	−4.68479	−	8.11430i	−0.452896	−	0.784439i	0.545669	−	0.838001i	$-0.316276\pi$
$107$	−4.68479	−	8.11430i	−0.452896	−	0.784439i	−0.998565	+	0.0535622i	$0.982942\pi$
$108$		0			0
$109$	8.47565	+	7.11192i	0.811820	+	0.681198i	0.951041	−	0.309063i	$-0.100015\pi$
$109$	8.47565	+	7.11192i	0.811820	+	0.681198i	−0.139221	+	0.990261i	$0.544460\pi$
$110$		0			0
$111$	1.57398	−	8.92647i	0.149395	−	0.847263i
$112$		0			0
$113$	−13.2986			−1.25103			−0.625514	−	0.780213i	$-0.715110\pi$
$113$	−13.2986			−1.25103			−0.625514	+	0.780213i	$0.715110\pi$
$114$		0			0
$115$	6.12836			0.571472
$116$		0			0
$117$	−0.120615	+	0.684040i	−0.0111508	+	0.0632395i
$118$		0			0
$119$	−9.26857	−	7.77725i	−0.849648	−	0.712940i
$120$		0			0
$121$	4.50387	+	7.80093i	0.409443	+	0.709176i
$122$		0			0
$123$	2.70574	+	0.984808i	0.243968	+	0.0887971i
$124$		0			0
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$		0			0
$127$	0.992259	+	5.62738i	0.0880488	+	0.499349i	0.996657	+	0.0816999i	$0.0260349\pi$
$127$	0.992259	+	5.62738i	0.0880488	+	0.499349i	−0.908608	+	0.417650i	$0.862854\pi$
$128$		0			0
$129$	1.09240	−	0.916629i	0.0961801	−	0.0807047i
$130$		0			0
$131$	−9.28359	+	3.37895i	−0.811111	+	0.295220i	−0.714083	−	0.700062i	$-0.753156\pi$
$131$	−9.28359	+	3.37895i	−0.811111	+	0.295220i	−0.0970281	+	0.995282i	$0.530934\pi$
$132$		0			0
$133$	10.7588	−	19.2749i	0.932904	−	1.67134i
$134$		0			0
$135$	8.71688	−	3.17269i	0.750230	−	0.273061i
$136$		0			0
$137$	4.13429	−	3.46908i	0.353216	−	0.296383i	−0.448864	−	0.893600i	$-0.648171\pi$
$137$	4.13429	−	3.46908i	0.353216	−	0.296383i	0.802080	+	0.597217i	$0.203727\pi$
$138$		0			0
$139$	0.406260	+	2.30401i	0.0344585	+	0.195424i	0.997178	−	0.0750794i	$-0.0239210\pi$
$139$	0.406260	+	2.30401i	0.0344585	+	0.195424i	−0.962719	+	0.270503i	$0.912810\pi$
$140$		0			0
$141$	−9.59627	+	16.6212i	−0.808151	+	1.39976i
$142$		0			0
$143$	1.73143	+	0.630189i	0.144789	+	0.0526990i
$144$		0			0
$145$	−8.45336	−	14.6417i	−0.702014	−	1.21592i
$146$		0			0
$147$	26.8444	+	22.5251i	2.21409	+	1.85784i
$148$		0			0
$149$	−2.49525	+	14.1513i	−0.204419	+	1.15932i	0.693932	+	0.720040i	$0.255877\pi$
$149$	−2.49525	+	14.1513i	−0.204419	+	1.15932i	−0.898351	+	0.439278i	$0.855234\pi$
$150$		0			0
$151$	20.8384			1.69581			0.847904	−	0.530150i	$-0.177865\pi$
$151$	20.8384			1.69581			0.847904	+	0.530150i	$0.177865\pi$
$152$		0			0
$153$	1.27126			0.102775
$154$		0			0
$155$	−0.128356	+	0.727940i	−0.0103098	+	0.0584696i
$156$		0			0
$157$	4.87939	+	4.09429i	0.389417	+	0.326760i	0.816386	−	0.577506i	$-0.195974\pi$
$157$	4.87939	+	4.09429i	0.389417	+	0.326760i	−0.426969	+	0.904266i	$0.640419\pi$
$158$		0			0
$159$	−1.57398	−	2.72621i	−0.124825	−	0.216202i
$160$		0			0
$161$	14.5817	+	5.30731i	1.14920	+	0.418275i
$162$		0			0
$163$	2.36571	−	4.09754i	0.185297	−	0.320944i	−0.758380	−	0.651813i	$-0.774009\pi$
$163$	2.36571	−	4.09754i	0.185297	−	0.320944i	0.943677	+	0.330869i	$0.107342\pi$
$164$		0			0
$165$	0.921274	+	5.22481i	0.0717211	+	0.406751i
$166$		0			0
$167$	−13.2344	+	11.1050i	−1.02411	+	0.859331i	−0.990138	−	0.140092i	$-0.955260\pi$
$167$	−13.2344	+	11.1050i	−1.02411	+	0.859331i	−0.0339719	+	0.999423i	$0.510816\pi$
$168$		0			0
$169$	10.6147	−	3.86343i	0.816514	−	0.297187i
$170$		0			0
$171$	0.435822	+	2.27801i	0.0333282	+	0.174203i
$172$		0			0
$173$	−17.6878	+	6.43783i	−1.34478	+	0.489459i	−0.911314	−	0.411712i	$-0.864931\pi$
$173$	−17.6878	+	6.43783i	−1.34478	+	0.489459i	−0.433463	+	0.901171i	$0.642709\pi$
$174$		0			0
$175$	3.87939	−	3.25519i	0.293254	−	0.246069i
$176$		0			0
$177$	−0.233956	−	1.32683i	−0.0175852	−	0.0997305i
$178$		0			0
$179$	−6.91400	+	11.9754i	−0.516777	+	0.895083i	0.483034	+	0.875602i	$0.339535\pi$
$179$	−6.91400	+	11.9754i	−0.516777	+	0.895083i	−0.999810	+	0.0194816i	$0.993798\pi$
$180$		0			0
$181$	−11.5175	−	4.19204i	−0.856092	−	0.311592i	−0.123570	−	0.992336i	$-0.539434\pi$
$181$	−11.5175	−	4.19204i	−0.856092	−	0.311592i	−0.732522	+	0.680744i	$0.761657\pi$
$182$		0			0
$183$	−9.17024	−	15.8833i	−0.677884	−	1.17413i
$184$		0			0
$185$	7.38919	+	6.20026i	0.543264	+	0.455852i
$186$		0			0
$187$	0.585589	−	3.32104i	0.0428225	−	0.242859i
$188$		0			0
$189$	23.4884			1.70853
$190$		0			0
$191$	20.0993			1.45433			0.727166	−	0.686462i	$-0.240837\pi$
$191$	20.0993			1.45433			0.727166	+	0.686462i	$0.240837\pi$
$192$		0			0
$193$	2.89734	−	16.4316i	0.208555	−	1.18277i	−0.683192	−	0.730239i	$-0.739409\pi$
$193$	2.89734	−	16.4316i	0.208555	−	1.18277i	0.891747	−	0.452535i	$-0.149480\pi$
$194$		0			0
$195$	−3.75877	−	3.15398i	−0.269171	−	0.225861i
$196$		0			0
$197$	−6.49525	−	11.2501i	−0.462768	−	0.801537i	0.536330	−	0.844008i	$-0.319810\pi$
$197$	−6.49525	−	11.2501i	−0.462768	−	0.801537i	−0.999098	+	0.0424714i	$0.986477\pi$
$198$		0			0
$199$	16.1557	+	5.88019i	1.14525	+	0.416836i	0.843806	−	0.536649i	$-0.180310\pi$
$199$	16.1557	+	5.88019i	1.14525	+	0.416836i	0.301441	+	0.953485i	$0.402532\pi$
$200$		0			0
$201$	−1.31908	+	2.28471i	−0.0930406	+	0.161151i
$202$		0			0
$203$	−7.43376	−	42.1590i	−0.521748	−	2.95898i
$204$		0			0
$205$	−2.34730	+	1.96962i	−0.163942	+	0.137564i
$206$		0			0
$207$	−1.53209	+	0.557635i	−0.106488	+	0.0387583i
$208$		0			0
$209$	6.15183	−	0.0892091i	0.425531	−	0.00617072i
$210$		0			0
$211$	−15.1373	+	5.50952i	−1.04209	+	0.379291i	−0.805673	−	0.592360i	$-0.798196\pi$
$211$	−15.1373	+	5.50952i	−1.04209	+	0.379291i	−0.236420	+	0.971651i	$0.575974\pi$
$212$		0			0
$213$	9.17024	−	7.69475i	0.628335	−	0.527236i
$214$		0			0
$215$	0.263518	+	1.49449i	0.0179718	+	0.101923i
$216$		0			0
$217$	−0.935822	+	1.62089i	−0.0635278	+	0.110033i
$218$		0			0
$219$	8.05216	+	2.93075i	0.544114	+	0.198041i
$220$		0			0
$221$	1.55943	+	2.70101i	0.104899	+	0.181690i
$222$		0			0
$223$	−3.12836	−	2.62500i	−0.209490	−	0.175783i	0.532005	−	0.846741i	$-0.321439\pi$
$223$	−3.12836	−	2.62500i	−0.209490	−	0.175783i	−0.741495	+	0.670958i	$0.765883\pi$
$224$		0			0
$225$	−0.0923963	+	0.524005i	−0.00615975	+	0.0349337i
$226$		0			0
$227$	−13.6604			−0.906676			−0.453338	−	0.891339i	$-0.649767\pi$
$227$	−13.6604			−0.906676			−0.453338	+	0.891339i	$0.649767\pi$
$228$		0			0
$229$	−5.22163			−0.345055			−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163			−0.345055			−0.172527	+	0.985005i	$0.555193\pi$
$230$		0			0
$231$	−2.33275	+	13.2297i	−0.153484	+	0.870449i
$232$		0			0
$233$	−20.7160	−	17.3828i	−1.35715	−	1.13878i	−0.976851	−	0.213921i	$-0.931376\pi$
$233$	−20.7160	−	17.3828i	−1.35715	−	1.13878i	−0.380300	−	0.924863i	$-0.624179\pi$
$234$		0			0
$235$	−10.2121	−	17.6879i	−0.666166	−	1.15383i
$236$		0			0
$237$	−3.95811	−	1.44063i	−0.257107	−	0.0935793i
$238$		0			0
$239$	−0.142903	+	0.247516i	−0.00924366	+	0.0160105i	−0.870610	−	0.491973i	$-0.836276\pi$
$239$	−0.142903	+	0.247516i	−0.00924366	+	0.0160105i	0.861367	+	0.507984i	$0.169609\pi$
$240$		0			0
$241$	0.538485	+	3.05390i	0.0346869	+	0.196719i	0.997227	−	0.0744203i	$-0.0237106\pi$
$241$	0.538485	+	3.05390i	0.0346869	+	0.196719i	−0.962540	+	0.271139i	$0.912600\pi$
$242$		0			0
$243$	−4.18866	+	3.51471i	−0.268703	+	0.225468i
$244$		0			0
$245$	−35.0428	+	12.7545i	−2.23880	+	0.814858i
$246$		0			0
$247$	−4.30541	+	3.72037i	−0.273947	+	0.236721i
$248$		0			0
$249$	−7.03849	+	2.56180i	−0.446046	+	0.162347i
$250$		0			0
$251$	9.69640	−	8.13625i	0.612032	−	0.513555i	−0.283256	−	0.959044i	$-0.591415\pi$
$251$	9.69640	−	8.13625i	0.612032	−	0.513555i	0.895287	+	0.445489i	$0.146970\pi$
$252$		0			0
$253$	0.751030	+	4.25930i	0.0472168	+	0.267780i
$254$		0			0
$255$	−4.49020	+	7.77725i	−0.281187	+	0.487031i
$256$		0			0
$257$	28.5599	+	10.3950i	1.78152	+	0.648419i	0.999689	+	0.0249253i	$0.00793478\pi$
$257$	28.5599	+	10.3950i	1.78152	+	0.648419i	0.781828	+	0.623494i	$0.214287\pi$
$258$		0			0
$259$	12.2121	+	21.1520i	0.758825	+	1.31432i
$260$		0			0
$261$	3.44562	+	2.89122i	0.213279	+	0.178962i
$262$		0			0
$263$	−3.80335	+	21.5699i	−0.234524	+	1.33005i	0.609088	+	0.793102i	$0.291535\pi$
$263$	−3.80335	+	21.5699i	−0.234524	+	1.33005i	−0.843613	+	0.536952i	$0.819576\pi$
$264$		0			0
$265$	3.34998			0.205788
$266$		0			0
$267$	−20.0077			−1.22445
$268$		0			0
$269$	−0.248970	+	1.41198i	−0.0151800	+	0.0860900i	−0.991457	−	0.130437i	$-0.958362\pi$
$269$	−0.248970	+	1.41198i	−0.0151800	+	0.0860900i	0.976277	+	0.216527i	$0.0694730\pi$
$270$		0			0
$271$	−12.3892	−	10.3958i	−0.752589	−	0.631498i	0.183597	−	0.983002i	$-0.441226\pi$
$271$	−12.3892	−	10.3958i	−0.752589	−	0.631498i	−0.936186	+	0.351504i	$0.885670\pi$
$272$		0			0
$273$	−6.21213	−	10.7597i	−0.375975	−	0.651209i
$274$		0			0
$275$	1.32635	+	0.482753i	0.0799820	+	0.0291111i
$276$		0			0
$277$	−5.55438	+	9.62046i	−0.333730	+	0.578038i	−0.983240	−	0.182315i	$-0.941641\pi$
$277$	−5.55438	+	9.62046i	−0.333730	+	0.578038i	0.649510	+	0.760353i	$0.274974\pi$
$278$		0			0
$279$	−0.0341483	−	0.193665i	−0.00204440	−	0.0115944i
$280$		0			0
$281$	3.25490	−	2.73119i	0.194171	−	0.162929i	−0.540519	−	0.841332i	$-0.681772\pi$
$281$	3.25490	−	2.73119i	0.194171	−	0.162929i	0.734690	+	0.678403i	$0.237328\pi$
$282$		0			0
$283$	−5.12701	+	1.86608i	−0.304769	+	0.110927i	−0.489878	−	0.871791i	$-0.662959\pi$
$283$	−5.12701	+	1.86608i	−0.304769	+	0.110927i	0.185108	+	0.982718i	$0.440736\pi$
$284$		0			0
$285$	−15.4757	−	5.37987i	−0.916699	−	0.318676i
$286$		0			0
$287$	−7.29086	+	2.65366i	−0.430366	+	0.156640i
$288$		0			0
$289$	−8.65002	+	7.25822i	−0.508824	+	0.426954i
$290$		0			0
$291$	−0.500000	−	2.83564i	−0.0293105	−	0.166228i
$292$		0			0
$293$	−8.90673	+	15.4269i	−0.520337	+	0.901249i	0.479384	+	0.877605i	$0.340860\pi$
$293$	−8.90673	+	15.4269i	−0.520337	+	0.901249i	−0.999720	+	0.0236440i	$0.992473\pi$
$294$		0			0
$295$	1.34730	+	0.490376i	0.0784426	+	0.0285508i
$296$		0			0
$297$	3.27332	+	5.66955i	0.189937	+	0.328981i
$298$		0			0
$299$	−3.06418	−	2.57115i	−0.177206	−	0.148693i
$300$		0			0
$301$	−0.667252	+	3.78417i	−0.0384597	+	0.218116i
$302$		0			0
$303$	16.5817			0.952595
$304$		0			0
$305$	19.5175			1.11757
$306$		0			0
$307$	4.97653	−	28.2233i	0.284026	−	1.61079i	−0.424720	−	0.905325i	$-0.639627\pi$
$307$	4.97653	−	28.2233i	0.284026	−	1.61079i	0.708746	−	0.705464i	$-0.249261\pi$
$308$		0			0
$309$	10.2909	+	8.63506i	0.585427	+	0.491231i
$310$		0			0
$311$	7.90673	+	13.6949i	0.448349	+	0.776564i	0.998279	−	0.0586473i	$-0.0186787\pi$
$311$	7.90673	+	13.6949i	0.448349	+	0.776564i	−0.549929	+	0.835211i	$0.685345\pi$
$312$		0			0
$313$	−12.3478	−	4.49422i	−0.697937	−	0.254028i	−0.0314071	−	0.999507i	$-0.509999\pi$
$313$	−12.3478	−	4.49422i	−0.697937	−	0.254028i	−0.666530	+	0.745478i	$0.732221\pi$
$314$		0			0
$315$	2.69459	−	4.66717i	0.151823	−	0.262965i
$316$		0			0
$317$	−3.71688	−	21.0795i	−0.208761	−	1.18394i	−0.891411	−	0.453196i	$-0.850284\pi$
$317$	−3.71688	−	21.0795i	−0.208761	−	1.18394i	0.682650	−	0.730746i	$-0.260827\pi$
$318$		0			0
$319$	9.14022	−	7.66955i	0.511754	−	0.429412i
$320$		0			0
$321$	−16.5471	+	6.02265i	−0.923569	+	0.336152i
$322$		0			0
$323$	8.07398	+	6.57775i	0.449248	+	0.365996i
$324$		0			0
$325$	−1.22668	+	0.446476i	−0.0680441	+	0.0247660i
$326$		0			0
$327$	15.9290	−	13.3660i	0.880877	−	0.739143i
$328$		0			0
$329$	−8.98040	−	50.9304i	−0.495105	−	2.80788i
$330$		0			0
$331$	−12.6989	+	21.9952i	−0.697996	+	1.20897i	0.271164	+	0.962533i	$0.412591\pi$
$331$	−12.6989	+	21.9952i	−0.697996	+	1.20897i	−0.969160	+	0.246432i	$0.920742\pi$
$332$		0			0
$333$	−2.41147	−	0.877705i	−0.132148	−	0.0480979i
$334$		0			0
$335$	−1.40373	−	2.43134i	−0.0766941	−	0.132838i
$336$		0			0
$337$	20.2062	+	16.9550i	1.10070	+	0.923599i	0.997472	−	0.0710588i	$-0.0226378\pi$
$337$	20.2062	+	16.9550i	1.10070	+	0.923599i	0.103230	+	0.994658i	$0.467082\pi$
$338$		0			0
$339$	−4.34002	+	24.6135i	−0.235718	+	1.33682i
$340$		0			0
$341$	−0.521660			−0.0282495
$342$		0			0
$343$	−58.9769			−3.18445
$344$		0			0
$345$	2.00000	−	11.3426i	0.107676	−	0.610663i
$346$		0			0
$347$	19.6348	+	16.4755i	1.05405	+	0.884452i	0.993514	−	0.113714i	$-0.0362748\pi$
$347$	19.6348	+	16.4755i	1.05405	+	0.884452i	0.0605352	+	0.998166i	$0.480719\pi$
$348$		0			0
$349$	2.92127	+	5.05980i	0.156372	+	0.270845i	0.933558	−	0.358427i	$-0.116687\pi$
$349$	2.92127	+	5.05980i	0.156372	+	0.270845i	−0.777186	+	0.629271i	$0.783353\pi$
$350$		0			0
$351$	−5.68954	−	2.07082i	−0.303685	−	0.110532i
$352$		0			0
$353$	11.2049	−	19.4074i	0.596375	−	1.03295i	−0.396977	−	0.917829i	$-0.629941\pi$
$353$	11.2049	−	19.4074i	0.596375	−	1.03295i	0.993351	−	0.115122i	$-0.0367260\pi$
$354$		0			0
$355$	2.21213	+	12.5456i	0.117408	+	0.665853i
$356$		0			0
$357$	−17.4192	+	14.6165i	−0.921923	+	0.773585i
$358$		0			0
$359$	9.03684	−	3.28914i	0.476946	−	0.173594i	−0.0923503	−	0.995727i	$-0.529438\pi$
$359$	9.03684	−	3.28914i	0.476946	−	0.173594i	0.569296	+	0.822132i	$0.307216\pi$
$360$		0			0
$361$	−9.01889	+	16.7230i	−0.474678	+	0.880159i
$362$		0			0
$363$	15.9081	−	5.79006i	0.834957	−	0.303900i
$364$		0			0
$365$	−6.98545	+	5.86149i	−0.365635	+	0.306804i
$366$		0			0
$367$	−4.05644	−	23.0052i	−0.211744	−	1.20086i	−0.886468	−	0.462791i	$-0.846848\pi$
$367$	−4.05644	−	23.0052i	−0.211744	−	1.20086i	0.674723	−	0.738071i	$-0.264263\pi$
$368$		0			0
$369$	0.407604	−	0.705990i	0.0212190	−	0.0367524i
$370$		0			0
$371$	7.97090	+	2.90117i	0.413829	+	0.150621i
$372$		0			0
$373$	12.9709	+	22.4663i	0.671608	+	1.16326i	0.977448	+	0.211176i	$0.0677294\pi$
$373$	12.9709	+	22.4663i	0.671608	+	1.16326i	−0.305840	+	0.952083i	$0.598937\pi$
$374$		0			0
$375$	−17.2763	−	14.4965i	−0.892145	−	0.748598i
$376$		0			0
$377$	−1.91622	+	10.8674i	−0.0986904	+	0.559701i
$378$		0			0
$379$	−9.47834			−0.486870			−0.243435	−	0.969917i	$-0.578274\pi$
$379$	−9.47834			−0.486870			−0.243435	+	0.969917i	$0.578274\pi$
$380$		0			0
$381$	10.7392			0.550184
$382$		0			0
$383$	2.34224	−	13.2835i	0.119683	−	0.678756i	−0.864641	−	0.502390i	$-0.832454\pi$
$383$	2.34224	−	13.2835i	0.119683	−	0.678756i	0.984324	−	0.176367i	$-0.0564345\pi$
$384$		0			0
$385$	−10.9513	−	9.18923i	−0.558130	−	0.468327i
$386$		0			0
$387$	−0.201867	−	0.349643i	−0.0102615	−	0.0177734i
$388$		0			0
$389$	23.6313	+	8.60111i	1.19816	+	0.436093i	0.862581	−	0.505920i	$-0.168847\pi$
$389$	23.6313	+	8.60111i	1.19816	+	0.436093i	0.335576	+	0.942013i	$0.391069\pi$
$390$		0			0
$391$	−3.66044	+	6.34008i	−0.185117	+	0.320631i
$392$		0			0
$393$	3.22416	+	18.2851i	0.162637	+	0.922361i
$394$		0			0
$395$	3.43376	−	2.88127i	0.172771	−	0.144972i
$396$		0			0
$397$	−6.17024	+	2.24579i	−0.309676	+	0.112713i	−0.492183	−	0.870492i	$-0.663801\pi$
$397$	−6.17024	+	2.24579i	−0.309676	+	0.112713i	0.182507	+	0.983205i	$0.441579\pi$
$398$		0			0
$399$	−32.1634	−	26.2031i	−1.61019	−	1.31179i
$400$		0			0
$401$	27.7310	−	10.0933i	1.38482	−	0.504034i	0.461185	−	0.887304i	$-0.347425\pi$
$401$	27.7310	−	10.0933i	1.38482	−	0.504034i	0.923636	+	0.383270i	$0.125202\pi$
$402$		0			0
$403$	0.369585	−	0.310119i	0.0184103	−	0.0154481i
$404$		0			0
$405$	−3.58172	−	20.3129i	−0.177977	−	1.00936i
$406$		0			0
$407$	−3.40373	+	5.89544i	−0.168717	+	0.292226i
$408$		0			0
$409$	−19.8567	−	7.22724i	−0.981850	−	0.357364i	−0.199291	−	0.979940i	$-0.563864\pi$
$409$	−19.8567	−	7.22724i	−0.981850	−	0.357364i	−0.782559	+	0.622576i	$0.786086\pi$
$410$		0			0
$411$	−5.07145	−	8.78401i	−0.250156	−	0.433283i
$412$		0			0
$413$	2.78106	+	2.33359i	0.136847	+	0.114828i
$414$		0			0
$415$	1.38413	−	7.84981i	0.0679444	−	0.385332i
$416$		0			0
$417$	4.39693			0.215318
$418$		0			0
$419$	27.8830			1.36217			0.681087	−	0.732202i	$-0.261508\pi$
$419$	27.8830			1.36217			0.681087	+	0.732202i	$0.261508\pi$
$420$		0			0
$421$	−0.00774079	+	0.0439002i	−0.000377263	+	0.00213956i	−0.984996	−	0.172578i	$-0.944790\pi$
$421$	−0.00774079	+	0.0439002i	−0.000377263	+	0.00213956i	0.984619	+	0.174718i	$0.0559013\pi$
$422$		0			0
$423$	4.16250	+	3.49276i	0.202388	+	0.169824i
$424$		0			0
$425$	1.19459	+	2.06910i	0.0579463	+	0.100366i
$426$		0			0
$427$	46.4397	+	16.9027i	2.24738	+	0.817978i
$428$		0			0
$429$	1.73143	−	2.99892i	0.0835942	−	0.144789i
$430$		0			0
$431$	2.04694	+	11.6088i	0.0985977	+	0.559175i	0.993585	+	0.113084i	$0.0360731\pi$
$431$	2.04694	+	11.6088i	0.0985977	+	0.559175i	−0.894988	+	0.446091i	$0.852816\pi$
$432$		0			0
$433$	21.1780	−	17.7704i	1.01775	−	0.853993i	0.0284060	−	0.999596i	$-0.490957\pi$
$433$	21.1780	−	17.7704i	1.01775	−	0.853993i	0.989343	+	0.145604i	$0.0465124\pi$
$434$		0			0
$435$	−29.8580	+	10.8674i	−1.43158	+	0.521054i
$436$		0			0
$437$	−12.6159	−	4.38571i	−0.603499	−	0.209797i
$438$		0			0
$439$	35.1908	−	12.8084i	1.67956	−	0.611311i	0.686314	−	0.727305i	$-0.259227\pi$
$439$	35.1908	−	12.8084i	1.67956	−	0.611311i	0.993250	+	0.115994i	$0.0370052\pi$
$440$		0			0
$441$	7.60014	−	6.37727i	0.361911	−	0.303680i
$442$		0			0
$443$	−3.64455	−	20.6693i	−0.173158	−	0.982027i	−0.940249	−	0.340489i	$-0.889408\pi$
$443$	−3.64455	−	20.6693i	−0.173158	−	0.982027i	0.767091	−	0.641539i	$-0.221704\pi$
$444$		0			0
$445$	10.6459	−	18.4392i	0.504664	−	0.874104i
$446$		0			0
$447$	25.3773	+	9.23659i	1.20031	+	0.436876i
$448$		0			0
$449$	10.9474	+	18.9615i	0.516641	+	0.894849i	0.999813	+	0.0193235i	$0.00615126\pi$
$449$	10.9474	+	18.9615i	0.516641	+	0.894849i	−0.483172	+	0.875525i	$0.660515\pi$
$450$		0			0
$451$	−1.65657	−	1.39003i	−0.0780050	−	0.0654540i
$452$		0			0
$453$	6.80066	−	38.5685i	0.319523	−	1.81210i
$454$		0			0
$455$	13.2216			0.619840
$456$		0			0
$457$	−13.0496			−0.610436			−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496			−0.610436			−0.305218	+	0.952283i	$0.598729\pi$
$458$		0			0
$459$	−1.92427	+	10.9131i	−0.0898171	+	0.509378i
$460$		0			0
$461$	3.37733	+	2.83391i	0.157298	+	0.131988i	0.718040	−	0.696002i	$-0.245040\pi$
$461$	3.37733	+	2.83391i	0.157298	+	0.131988i	−0.560742	+	0.827991i	$0.689484\pi$
$462$		0			0
$463$	13.3327	+	23.0930i	0.619625	+	1.07322i	0.989554	+	0.144162i	$0.0460488\pi$
$463$	13.3327	+	23.0930i	0.619625	+	1.07322i	−0.369929	+	0.929060i	$0.620618\pi$
$464$		0			0
$465$	1.30541	+	0.475129i	0.0605368	+	0.0220336i
$466$		0			0
$467$	15.0569	−	26.0793i	0.696750	−	1.20681i	−0.272837	−	0.962060i	$-0.587962\pi$
$467$	15.0569	−	26.0793i	0.696750	−	1.20681i	0.969587	−	0.244747i	$-0.0787048\pi$
$468$		0			0
$469$	−1.23442	−	7.00076i	−0.0570003	−	0.323265i
$470$		0			0
$471$	9.17024	−	7.69475i	0.422543	−	0.354555i
$472$		0			0
$473$	−1.00640	+	0.366298i	−0.0462742	+	0.0168424i
$474$		0			0
$475$	−3.29813	+	2.84997i	−0.151329	+	0.130765i
$476$		0			0
$477$	−0.837496	+	0.304824i	−0.0383463	+	0.0139569i
$478$		0			0
$479$	−6.25671	+	5.25000i	−0.285876	+	0.239879i	−0.774437	−	0.632651i	$-0.781967\pi$
$479$	−6.25671	+	5.25000i	−0.285876	+	0.239879i	0.488560	+	0.872530i	$0.337522\pi$
$480$		0			0
$481$	−1.09327	−	6.20026i	−0.0498490	−	0.282708i
$482$		0			0
$483$	14.5817	−	25.2563i	0.663491	−	1.14920i
$484$		0			0
$485$	2.87939	+	1.04801i	0.130746	+	0.0475877i
$486$		0			0
$487$	13.2935	+	23.0251i	0.602388	+	1.04337i	0.992458	+	0.122582i	$0.0391174\pi$
$487$	13.2935	+	23.0251i	0.602388	+	1.04337i	−0.390070	+	0.920785i	$0.627549\pi$
$488$		0			0
$489$	−6.81180	−	5.71578i	−0.308040	−	0.258477i
$490$		0			0
$491$	−6.74257	+	38.2390i	−0.304288	+	1.72570i	0.322549	+	0.946553i	$0.395460\pi$
$491$	−6.74257	+	38.2390i	−0.304288	+	1.72570i	−0.626837	+	0.779151i	$0.715651\pi$
$492$		0			0
$493$	20.1967			0.909611
$494$		0			0
$495$	1.50206			0.0675125
$496$		0			0
$497$	−5.60132	+	31.7667i	−0.251253	+	1.42493i
$498$		0			0
$499$	−15.8255	−	13.2791i	−0.708446	−	0.594456i	0.215717	−	0.976456i	$-0.430791\pi$
$499$	−15.8255	−	13.2791i	−0.708446	−	0.594456i	−0.924163	+	0.382000i	$0.875236\pi$
$500$		0			0
$501$	16.2344	+	28.1188i	0.725301	+	1.25626i
$502$		0			0
$503$	0.0692302	+	0.0251977i	0.00308682	+	0.00112351i	0.343563	−	0.939130i	$-0.388366\pi$
$503$	0.0692302	+	0.0251977i	0.00308682	+	0.00112351i	−0.340476	+	0.940253i	$0.610588\pi$
$504$		0			0
$505$	−8.82295	+	15.2818i	−0.392616	+	0.680031i
$506$		0			0
$507$	−3.68644	−	20.9068i	−0.163721	−	0.928506i
$508$		0			0
$509$	11.5057	−	9.65441i	0.509980	−	0.427924i	−0.351142	−	0.936322i	$-0.614207\pi$
$509$	11.5057	−	9.65441i	0.509980	−	0.427924i	0.861122	+	0.508398i	$0.169762\pi$
$510$		0			0
$511$	−21.6973	+	7.89716i	−0.959831	+	0.349350i
$512$		0			0
$513$	−20.2151	+	0.293144i	−0.892520	+	0.0129426i
$514$		0			0
$515$	−13.4338	+	4.88949i	−0.591962	+	0.215457i
$516$		0			0
$517$	11.0419	−	9.26525i	0.485622	−	0.407485i
$518$		0			0
$519$	6.14290	+	34.8381i	0.269644	+	1.52922i
$520$		0			0
$521$	−22.5856	+	39.1194i	−0.989493	+	1.71385i	−0.369533	+	0.929217i	$0.620482\pi$
$521$	−22.5856	+	39.1194i	−0.989493	+	1.71385i	−0.619959	+	0.784634i	$0.712851\pi$
$522$		0			0
$523$	0.157451	+	0.0573076i	0.00688487	+	0.00250589i	0.345460	−	0.938433i	$-0.387723\pi$
$523$	0.157451	+	0.0573076i	0.00688487	+	0.00250589i	−0.338575	+	0.940939i	$0.609945\pi$
$524$		0			0
$525$	−4.75877	−	8.24243i	−0.207690	−	0.359729i
$526$		0			0
$527$	−0.676423	−	0.567586i	−0.0294654	−	0.0247244i
$528$		0			0
$529$	−2.36349	+	13.4040i	−0.102761	+	0.582784i
$530$		0			0
$531$	−0.381445			−0.0165533
$532$		0			0
$533$	2.00000			0.0866296
$534$		0			0
$535$	3.25402	−	18.4545i	0.140684	−	0.797857i
$536$		0			0
$537$	19.9081	+	16.7049i	0.859097	+	0.720868i
$538$		0			0
$539$	−13.1591	−	22.7922i	−0.566803	−	0.981731i
$540$		0			0
$541$	0.921274	+	0.335316i	0.0396087	+	0.0144164i	0.361749	−	0.932276i	$-0.382180\pi$
$541$	0.921274	+	0.335316i	0.0396087	+	0.0144164i	−0.322140	+	0.946692i	$0.604402\pi$
$542$		0			0
$543$	−11.5175	+	19.9490i	−0.494265	+	0.856092i
$544$		0			0
$545$	3.84255	+	21.7922i	0.164597	+	0.933474i
$546$		0			0
$547$	−21.7592	+	18.2582i	−0.930358	+	0.780663i	−0.975882	−	0.218300i	$-0.929949\pi$
$547$	−21.7592	+	18.2582i	−0.930358	+	0.780663i	0.0455238	+	0.998963i	$0.485504\pi$
$548$		0			0
$549$	−4.87939	+	1.77595i	−0.208247	+	0.0757957i
$550$		0			0
$551$	6.92396	+	36.1910i	0.294971	+	1.54179i
$552$		0			0
$553$	10.6655	−	3.88192i	0.453543	−	0.165076i
$554$		0			0
$555$	13.8871	−	11.6527i	0.589476	−	0.494629i
$556$		0			0
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	0.776969	+	0.629539i	$0.216756\pi$
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	−0.514797	+	0.857312i	$0.672133\pi$
$558$		0			0
$559$	0.495252	−	0.857802i	0.0209469	−	0.0362812i
$560$		0			0
$561$	−5.95558	−	2.16766i	−0.251445	−	0.0915185i
$562$		0			0
$563$	4.31386	+	7.47183i	0.181808	+	0.314900i	0.942496	−	0.334217i	$-0.108472\pi$
$563$	4.31386	+	7.47183i	0.181808	+	0.314900i	−0.760688	+	0.649117i	$0.775139\pi$
$564$		0			0
$565$	−20.3746	−	17.0964i	−0.857167	−	0.719249i
$566$		0			0
$567$	9.06923	−	51.4342i	0.380872	−	2.16003i
$568$		0			0
$569$	22.3310			0.936164			0.468082	−	0.883685i	$-0.344945\pi$
$569$	22.3310			0.936164			0.468082	+	0.883685i	$0.344945\pi$
$570$		0			0
$571$	9.56448			0.400261			0.200131	−	0.979769i	$-0.435863\pi$
$571$	9.56448			0.400261			0.200131	+	0.979769i	$0.435863\pi$
$572$		0			0
$573$	6.55943	−	37.2004i	0.274024	−	1.55407i
$574$		0			0
$575$	−2.34730	−	1.96962i	−0.0978890	−	0.0821386i
$576$		0			0
$577$	−11.2378	−	19.4645i	−0.467837	−	0.810317i	0.531488	−	0.847066i	$-0.321633\pi$
$577$	−11.2378	−	19.4645i	−0.467837	−	0.810317i	−0.999325	+	0.0367489i	$0.988300\pi$
$578$		0			0
$579$	−29.4666	−	10.7250i	−1.22459	−	0.445715i
$580$		0			0
$581$	10.0915	−	17.4790i	0.418667	−	0.725152i
$582$		0			0
$583$	0.410540	+	2.32829i	0.0170028	+	0.0964279i
$584$		0			0
$585$	−1.06418	+	0.892951i	−0.0439983	+	0.0369190i
$586$		0			0
$587$	3.89780	−	1.41868i	0.160880	−	0.0585554i	−0.260325	−	0.965521i	$-0.583830\pi$
$587$	3.89780	−	1.41868i	0.160880	−	0.0585554i	0.421205	+	0.906966i	$0.361607\pi$
$588$		0			0
$589$	0.785178	−	1.40669i	0.0323527	−	0.0579615i
$590$		0			0
$591$	−22.9418	+	8.35014i	−0.943700	+	0.343479i
$592$		0			0
$593$	7.98024	−	6.69621i	0.327709	−	0.274981i	−0.464057	−	0.885806i	$-0.653607\pi$
$593$	7.98024	−	6.69621i	0.327709	−	0.274981i	0.791766	+	0.610825i	$0.209162\pi$
$594$		0			0
$595$	−4.20203	−	23.8309i	−0.172266	−	0.976971i
$596$		0			0
$597$	16.1557	−	27.9825i	0.661209	−	1.14525i
$598$		0			0
$599$	−37.2645	−	13.5632i	−1.52258	−	0.554175i	−0.560792	−	0.827957i	$-0.689503\pi$
$599$	−37.2645	−	13.5632i	−1.52258	−	0.554175i	−0.961792	+	0.273781i	$0.911726\pi$
$600$		0			0
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	0.513150	−	0.858299i	$-0.328478\pi$
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	−0.999884	+	0.0152517i	$0.995145\pi$
$602$		0			0
$603$	0.572167	+	0.480105i	0.0233004	+	0.0195514i
$604$		0			0
$605$	−3.12836	+	17.7418i	−0.127186	+	0.721306i
$606$		0			0
$607$	29.9317			1.21489			0.607445	−	0.794362i	$-0.292194\pi$
$607$	29.9317			1.21489			0.607445	+	0.794362i	$0.292194\pi$
$608$		0			0
$609$	−80.4552			−3.26021
$610$		0			0
$611$	−2.31490	+	13.1285i	−0.0936509	+	0.531121i
$612$		0			0
$613$	−27.2540	−	22.8688i	−1.10078	−	0.923664i	−0.103302	−	0.994650i	$-0.532941\pi$
$613$	−27.2540	−	22.8688i	−1.10078	−	0.923664i	−0.997477	+	0.0709862i	$0.977385\pi$
$614$		0			0
$615$	2.87939	+	4.98724i	0.116108	+	0.201105i
$616$		0			0
$617$	−11.3068	−	4.11532i	−0.455193	−	0.165677i	0.104240	−	0.994552i	$-0.466759\pi$
$617$	−11.3068	−	4.11532i	−0.455193	−	0.165677i	−0.559433	+	0.828876i	$0.688981\pi$
$618$		0			0
$619$	−8.55644	+	14.8202i	−0.343912	+	0.595673i	−0.985156	−	0.171664i	$-0.945086\pi$
$619$	−8.55644	+	14.8202i	−0.343912	+	0.595673i	0.641243	+	0.767338i	$0.278419\pi$
$620$		0			0
$621$	−2.46791	−	13.9962i	−0.0990339	−	0.561649i
$622$		0			0
$623$	41.2995	−	34.6544i	1.65463	−	1.38840i
$624$		0			0
$625$	17.8542	−	6.49838i	0.714166	−	0.259935i
$626$		0			0
$627$	1.84255	−	11.4151i	0.0735843	−	0.455876i
$628$		0			0
$629$	−10.8280	+	3.94107i	−0.431741	+	0.157141i
$630$		0			0
$631$	−14.0496	+	11.7890i	−0.559307	+	0.469314i	−0.878078	−	0.478517i	$-0.841174\pi$
$631$	−14.0496	+	11.7890i	−0.559307	+	0.469314i	0.318771	+	0.947832i	$0.396730\pi$
$632$		0			0
$633$	5.25712	+	29.8146i	0.208952	+	1.18502i
$634$		0			0
$635$	−5.71419	+	9.89727i	−0.226761	+	0.392761i
$636$		0			0
$637$	22.8726	+	8.32494i	0.906245	+	0.329846i
$638$		0			0
$639$	−1.69459	−	2.93512i	−0.0670371	−	0.116112i
$640$		0			0
$641$	−23.8837	−	20.0408i	−0.943350	−	0.791565i	0.0348149	−	0.999394i	$-0.488916\pi$
$641$	−23.8837	−	20.0408i	−0.943350	−	0.791565i	−0.978165	+	0.207829i	$0.933360\pi$
$642$		0			0
$643$	5.54798	−	31.4642i	0.218791	−	1.24083i	−0.655414	−	0.755269i	$-0.727506\pi$
$643$	5.54798	−	31.4642i	0.218791	−	1.24083i	0.874206	−	0.485556i	$-0.161383\pi$
$644$		0			0
$645$	2.85204			0.112299
$646$		0			0
$647$	−2.99588			−0.117780			−0.0588901	−	0.998264i	$-0.518756\pi$
$647$	−2.99588			−0.117780			−0.0588901	+	0.998264i	$0.518756\pi$
$648$		0			0
$649$	−0.175708	+	0.996487i	−0.00689713	+	0.0391155i
$650$		0			0
$651$	2.69459	+	2.26103i	0.105609	+	0.0886168i
$652$		0			0
$653$	−0.467911	−	0.810446i	−0.0183108	−	0.0317152i	0.856725	−	0.515774i	$-0.172495\pi$
$653$	−0.467911	−	0.810446i	−0.0183108	−	0.0317152i	−0.875036	+	0.484059i	$0.839162\pi$
$654$		0			0
$655$	−18.5672	−	6.75790i	−0.725479	−	0.264053i
$656$		0			0
$657$	1.21301	−	2.10100i	0.0473241	−	0.0819677i
$658$		0			0
$659$	2.12495	+	12.0512i	0.0827764	+	0.469448i	0.997814	+	0.0660804i	$0.0210494\pi$
$659$	2.12495	+	12.0512i	0.0827764	+	0.469448i	−0.915038	+	0.403368i	$0.867840\pi$
$660$		0			0
$661$	−9.15839	+	7.68480i	−0.356220	+	0.298904i	−0.803282	−	0.595599i	$-0.796915\pi$
$661$	−9.15839	+	7.68480i	−0.356220	+	0.298904i	0.447062	+	0.894503i	$0.352470\pi$
$662$		0			0
$663$	5.50805	−	2.00476i	0.213915	−	0.0778586i
$664$		0			0
$665$	41.2627	−	15.6996i	1.60010	−	0.608805i
$666$		0			0
$667$	−24.3405	+	8.85921i	−0.942468	+	0.343030i
$668$		0			0
$669$	−5.87939	+	4.93339i	−0.227310	+	0.190736i
$670$		0			0
$671$	2.39187	+	13.5650i	0.0923373	+	0.523671i
$672$		0			0
$673$	−22.4317	+	38.8529i	−0.864679	+	1.49767i	0.00268731	+	0.999996i	$0.499145\pi$
$673$	−22.4317	+	38.8529i	−0.864679	+	1.49767i	−0.867366	+	0.497671i	$0.834189\pi$
$674$		0			0
$675$	−4.35844	−	1.58634i	−0.167756	−	0.0610584i
$676$		0			0
$677$	−0.472964	−	0.819197i	−0.0181775	−	0.0314843i	0.856794	−	0.515660i	$-0.172453\pi$
$677$	−0.472964	−	0.819197i	−0.0181775	−	0.0314843i	−0.874971	+	0.484175i	$0.839120\pi$
$678$		0			0
$679$	5.94356	+	4.98724i	0.228093	+	0.191393i
$680$		0			0
$681$	−4.45811	+	25.2832i	−0.170835	+	0.968854i
$682$		0			0
$683$	5.92221			0.226607			0.113303	−	0.993560i	$-0.463857\pi$
$683$	5.92221			0.226607			0.113303	+	0.993560i	$0.463857\pi$
$684$		0			0
$685$	10.7939			0.412412
$686$		0			0
$687$	−1.70409	+	9.66436i	−0.0650150	+	0.368718i
$688$		0			0
$689$	−1.67499	−	1.40549i	−0.0638121	−	0.0535447i
$690$		0			0
$691$	0.103074	+	0.178529i	0.00392111	+	0.00679156i	0.867979	−	0.496600i	$-0.165419\pi$
$691$	0.103074	+	0.178529i	0.00392111	+	0.00679156i	−0.864058	+	0.503392i	$0.832085\pi$
$692$		0			0
$693$	3.57398	+	1.30082i	0.135764	+	0.0494141i
$694$		0			0
$695$	−2.33956	+	4.05223i	−0.0887444	+	0.153710i
$696$		0			0
$697$	−0.635630	−	3.60483i	−0.0240762	−	0.136543i
$698$		0			0
$699$	−38.9334	+	32.6690i	−1.47259	+	1.23565i
$700$		0			0
$701$	−4.10607	+	1.49449i	−0.155084	+	0.0564460i	−0.418396	−	0.908265i	$-0.637407\pi$
$701$	−4.10607	+	1.49449i	−0.155084	+	0.0564460i	0.263312	+	0.964711i	$0.415185\pi$
$702$		0			0
$703$	−10.7743	−	18.0519i	−0.406359	−	0.680840i
$704$		0			0
$705$	−36.0702	+	13.1285i	−1.35848	+	0.494447i
$706$		0			0
$707$	−34.2276	+	28.7204i	−1.28726	+	1.08014i
$708$		0			0
$709$	1.52023	+	8.62165i	0.0570934	+	0.323793i	0.999956	−	0.00938924i	$-0.00298873\pi$
$709$	1.52023	+	8.62165i	0.0570934	+	0.323793i	−0.942863	+	0.333182i	$0.891878\pi$
$710$		0			0
$711$	−0.596267	+	1.03276i	−0.0223617	+	0.0387317i
$712$		0			0
$713$	1.06418	+	0.387329i	0.0398538	+	0.0145056i
$714$		0			0
$715$	1.84255	+	3.19139i	0.0689074	+	0.119351i
$716$		0			0
$717$	0.411474	+	0.345268i	0.0153668	+	0.0128943i
$718$		0			0
$719$	4.79385	−	27.1873i	0.178781	−	1.01391i	−0.754909	−	0.655830i	$-0.772319\pi$
$719$	4.79385	−	27.1873i	0.178781	−	1.01391i	0.933689	−	0.358085i	$-0.116570\pi$
$720$		0			0
$721$	−36.1985			−1.34810
$722$		0			0
$723$	5.82800			0.216746
$724$		0			0
$725$	−1.46791	+	8.32494i	−0.0545169	+	0.309180i
$726$		0			0
$727$	−21.9368	−	18.4071i	−0.813589	−	0.682682i	0.137872	−	0.990450i	$-0.455974\pi$
$727$	−21.9368	−	18.4071i	−0.813589	−	0.682682i	−0.951462	+	0.307768i	$0.900418\pi$
$728$		0			0
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$		0			0
$731$	−1.70352	−	0.620029i	−0.0630068	−	0.0229326i
$732$		0			0
$733$	−18.4807	+	32.0095i	−0.682600	+	1.18230i	0.291584	+	0.956545i	$0.405818\pi$
$733$	−18.4807	+	32.0095i	−0.682600	+	1.18230i	−0.974184	+	0.225753i	$0.927516\pi$
$734$		0			0
$735$	12.1702	+	69.0209i	0.448906	+	2.54587i
$736$		0			0
$737$	1.51779	−	1.27358i	0.0559085	−	0.0469128i
$738$		0			0
$739$	43.2508	−	15.7420i	1.59101	−	0.579079i	0.613446	−	0.789737i	$-0.289783\pi$
$739$	43.2508	−	15.7420i	1.59101	−	0.579079i	0.977560	+	0.210658i	$0.0675607\pi$
$740$		0			0
$741$	5.48070	+	9.18274i	0.201339	+	0.337336i
$742$		0			0
$743$	24.8179	−	9.03298i	0.910480	−	0.331388i	0.156036	−	0.987751i	$-0.450129\pi$
$743$	24.8179	−	9.03298i	0.910480	−	0.331388i	0.754445	+	0.656364i	$0.227906\pi$
$744$		0			0
$745$	−22.0155	+	18.4732i	−0.806585	+	0.676805i
$746$		0			0
$747$	0.368241	+	2.08840i	0.0134732	+	0.0764105i
$748$		0			0
$749$	23.7246	−	41.0923i	0.866879	−	1.50148i
$750$		0			0
$751$	−25.5381	−	9.29510i	−0.931898	−	0.339183i	−0.168936	−	0.985627i	$-0.554033\pi$
$751$	−25.5381	−	9.29510i	−0.931898	−	0.339183i	−0.762961	+	0.646444i	$0.776255\pi$
$752$		0			0
$753$	−11.8944	−	20.6017i	−0.433456	−	0.750768i
$754$		0			0
$755$	31.9263	+	26.7894i	1.16192	+	0.974965i
$756$		0			0
$757$	3.36959	−	19.1099i	0.122470	−	0.694560i	−0.860309	−	0.509773i	$-0.829729\pi$
$757$	3.36959	−	19.1099i	0.122470	−	0.694560i	0.982779	−	0.184787i	$-0.0591595\pi$
$758$		0			0
$759$	8.12836			0.295041
$760$		0			0
$761$	40.2645			1.45959			0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645			1.45959			0.729793	+	0.683669i	$0.239617\pi$
$762$		0			0
$763$	−9.72967	+	55.1797i	−0.352238	+	1.99764i
$764$		0			0
$765$	1.94768	+	1.63430i	0.0704186	+	0.0590882i
$766$		0			0
$767$	−0.467911	−	0.810446i	−0.0168953	−	0.0292635i
$768$		0			0
$769$	36.5933	+	13.3189i	1.31959	+	0.480291i	0.903327	−	0.428953i	$-0.141117\pi$
$769$	36.5933	+	13.3189i	1.31959	+	0.480291i	0.416263	+	0.909244i	$0.363340\pi$
$770$		0			0
$771$	28.5599	−	49.4672i	1.02856	−	1.78152i
$772$		0			0
$773$	−1.17436	−	6.66015i	−0.0422389	−	0.239549i	0.956378	−	0.292133i	$-0.0943652\pi$
$773$	−1.17436	−	6.66015i	−0.0422389	−	0.239549i	−0.998616	+	0.0525847i	$0.983254\pi$
$774$		0			0
$775$	0.283119	−	0.237565i	0.0101699	−	0.00853358i
$776$		0			0
$777$	43.1343	−	15.6996i	1.54744	−	0.563221i
$778$		0			0
$779$	6.24170	−	2.37484i	0.223632	−	0.0850874i
$780$		0			0
$781$	−8.44831	+	3.07493i	−0.302304	+	0.110030i
$782$		0			0
$783$	−30.0351	+	25.2024i	−1.07337	+	0.900661i
$784$		0			0
$785$	2.21213	+	12.5456i	0.0789544	+	0.447773i
$786$		0			0
$787$	2.90239	−	5.02709i	0.103459	−	0.179196i	−0.809649	−	0.586915i	$-0.800342\pi$
$787$	2.90239	−	5.02709i	0.103459	−	0.179196i	0.913108	+	0.407719i	$0.133676\pi$
$788$		0			0
$789$	38.6810	+	14.0787i	1.37708	+	0.501216i
$790$		0			0
$791$	−33.6732	−	58.3238i	−1.19728	−	2.07375i
$792$		0			0
$793$	−9.75877	−	8.18858i	−0.346544	−	0.290785i
$794$		0			0
$795$	1.09327	−	6.20026i	0.0387744	−	0.219901i
$796$		0			0
$797$	−39.2181			−1.38918			−0.694589	−	0.719407i	$-0.744414\pi$
$797$	−39.2181			−1.38918			−0.694589	+	0.719407i	$0.744414\pi$
$798$		0			0
$799$	24.3987			0.863163
$800$		0			0
$801$	−0.983641	+	5.57851i	−0.0347552	+	0.197107i
$802$		0			0
$803$	−4.92989	−	4.13667i	−0.173972	−	0.145980i
$804$		0			0
$805$	15.5175	+	26.8772i	0.546921	+	0.947296i
$806$		0			0
$807$	2.53209	+	0.921605i	0.0891338	+	0.0324420i
$808$		0			0
$809$	−3.50134	+	6.06451i	−0.123101	+	0.213217i	−0.920989	−	0.389589i	$-0.872617\pi$
$809$	−3.50134	+	6.06451i	−0.123101	+	0.213217i	0.797888	+	0.602805i	$0.205950\pi$
$810$		0			0
$811$	−7.58584	−	43.0214i	−0.266375	−	1.51069i	−0.765092	−	0.643921i	$-0.777306\pi$
$811$	−7.58584	−	43.0214i	−0.266375	−	1.51069i	0.498717	−	0.866765i	$-0.333805\pi$
$812$		0			0
$813$	−23.2841	+	19.5376i	−0.816607	+	0.685215i
$814$		0			0
$815$	8.89218	−	3.23649i	0.311479	−	0.113369i
$816$		0			0
$817$	0.527036	−	3.26514i	0.0184387	−	0.114233i
$818$		0			0
$819$	−3.30541	+	1.20307i	−0.115500	+	0.0420387i
$820$		0			0
$821$	9.48751	−	7.96097i	0.331116	−	0.277840i	−0.462038	−	0.886860i	$-0.652882\pi$
$821$	9.48751	−	7.96097i	0.331116	−	0.277840i	0.793155	+	0.609020i	$0.208437\pi$
$822$		0			0
$823$	2.22762	+	12.6334i	0.0776498	+	0.440374i	0.998702	+	0.0509347i	$0.0162200\pi$
$823$	2.22762	+	12.6334i	0.0776498	+	0.440374i	−0.921052	+	0.389439i	$0.872669\pi$
$824$		0			0
$825$	1.32635	−	2.29731i	0.0461776	−	0.0799820i
$826$		0			0
$827$	23.5831	+	8.58353i	0.820063	+	0.298479i	0.717774	−	0.696276i	$-0.245161\pi$
$827$	23.5831	+	8.58353i	0.820063	+	0.298479i	0.102289	+	0.994755i	$0.467383\pi$
$828$		0			0
$829$	−14.1634	−	24.5318i	−0.491917	−	0.852024i	0.508040	−	0.861333i	$-0.330370\pi$
$829$	−14.1634	−	24.5318i	−0.491917	−	0.852024i	−0.999957	+	0.00930899i	$0.997037\pi$
$830$		0			0
$831$	15.9932	+	13.4199i	0.554798	+	0.465531i
$832$		0			0
$833$	7.73577	−	43.8717i	0.268028	−	1.52006i
$834$		0			0
$835$	−34.5526			−1.19574
$836$		0			0
$837$	1.71419			0.0592512
$838$		0			0
$839$	5.26682	−	29.8696i	0.181831	−	1.03121i	−0.748129	−	0.663553i	$-0.769048\pi$
$839$	5.26682	−	29.8696i	0.181831	−	1.03121i	0.929960	−	0.367660i	$-0.119841\pi$
$840$		0			0
$841$	32.5257	+	27.2923i	1.12158	+	0.941115i
$842$		0			0
$843$	−3.99273	−	6.91560i	−0.137517	−	0.238186i
$844$		0			0
$845$	21.2294	+	7.72686i	0.730313	+	0.265812i
$846$		0			0
$847$	−22.8084	+	39.5053i	−0.783706	+	1.35742i
$848$		0			0
$849$	1.78059	+	10.0982i	0.0611098	+	0.346571i
$850$		0			0
$851$	11.3209	−	9.49935i	0.388075	−	0.325634i
$852$		0			0
$853$	41.0009	−	14.9231i	1.40385	−	0.510958i	0.474528	−	0.880240i	$-0.342619\pi$
$853$	41.0009	−	14.9231i	1.40385	−	0.510958i	0.929317	+	0.369283i	$0.120397\pi$
$854$		0			0
$855$	−2.26083	+	4.05039i	−0.0773188	+	0.138520i
$856$		0			0
$857$	29.6095	−	10.7770i	1.01144	−	0.368135i	0.217456	−	0.976070i	$-0.430224\pi$
$857$	29.6095	−	10.7770i	1.01144	−	0.368135i	0.793987	+	0.607935i	$0.208002\pi$
$858$		0			0
$859$	14.3234	−	12.0188i	0.488709	−	0.410075i	−0.364855	−	0.931065i	$-0.618881\pi$
$859$	14.3234	−	12.0188i	0.488709	−	0.410075i	0.853563	+	0.520989i	$0.174437\pi$
$860$		0			0
$861$	2.53209	+	14.3602i	0.0862934	+	0.489394i
$862$		0			0
$863$	5.31315	−	9.20264i	0.180862	−	0.313262i	−0.761313	−	0.648385i	$-0.775445\pi$
$863$	5.31315	−	9.20264i	0.180862	−	0.313262i	0.942174	+	0.335123i	$0.108778\pi$
$864$		0			0
$865$	−35.3756	−	12.8757i	−1.20281	−	0.437785i
$866$		0			0
$867$	10.6108	+	18.3785i	0.360362	+	0.624166i
$868$		0			0
$869$	2.42333	+	2.03342i	0.0822060	+	0.0689790i
$870$		0			0
$871$	−0.318201	+	1.80460i	−0.0107818	+	0.0611467i
$872$		0			0
$873$	−0.815207			−0.0275906
$874$		0			0
$875$	60.7701			2.05441
$876$		0			0
$877$	7.79654	−	44.2164i	0.263270	−	1.49308i	−0.510645	−	0.859792i	$-0.670593\pi$
$877$	7.79654	−	44.2164i	0.263270	−	1.49308i	0.773915	−	0.633289i	$-0.218296\pi$
$878$		0			0
$879$	25.6459	+	21.5195i	0.865015	+	0.725833i
$880$		0			0
$881$	9.00821	+	15.6027i	0.303494	+	0.525667i	0.976925	−	0.213583i	$-0.0685134\pi$
$881$	9.00821	+	15.6027i	0.303494	+	0.525667i	−0.673431	+	0.739250i	$0.735180\pi$
$882$		0			0
$883$	−43.7879	−	15.9375i	−1.47358	−	0.536340i	−0.524511	−	0.851404i	$-0.675752\pi$
$883$	−43.7879	−	15.9375i	−1.47358	−	0.536340i	−0.949070	+	0.315064i	$0.897974\pi$
$884$		0			0
$885$	1.34730	−	2.33359i	0.0452889	−	0.0784426i
$886$		0			0
$887$	−1.22937	−	6.97210i	−0.0412782	−	0.234100i	0.957188	−	0.289467i	$-0.0934782\pi$
$887$	−1.22937	−	6.97210i	−0.0412782	−	0.234100i	−0.998466	+	0.0553671i	$0.982367\pi$
$888$		0			0
$889$	−22.1676	+	18.6008i	−0.743476	+	0.623850i
$890$		0			0
$891$	13.6789	−	4.97870i	0.458259	−	0.166793i
$892$		0			0
$893$	8.36453	+	43.7207i	0.279908	+	1.46306i
$894$		0			0
$895$	−25.9881	+	9.45891i	−0.868688	+	0.316176i
$896$		0			0
$897$	−5.75877	+	4.83218i	−0.192280	+	0.161342i
$898$		0			0
$899$	−0.542518	−	3.07677i	−0.0180940	−	0.102616i
$900$		0			0
$901$	−2.00093	+	3.46572i	−0.0666608	+	0.115460i
$902$		0			0
$903$	6.78611	+	2.46994i	0.225828	+	0.0821945i
$904$		0			0
$905$	−12.2567	−	21.2292i	−0.407427	−	0.705684i
$906$		0			0
$907$	−11.5792	−	9.71610i	−0.384481	−	0.322618i	0.429978	−	0.902840i	$-0.358521\pi$
$907$	−11.5792	−	9.71610i	−0.384481	−	0.322618i	−0.814458	+	0.580222i	$0.802966\pi$
$908$		0			0
$909$	0.815207	−	4.62327i	0.0270387	−	0.153344i
$910$		0			0
$911$	12.8366			0.425294			0.212647	−	0.977129i	$-0.431792\pi$
$911$	12.8366			0.425294			0.212647	+	0.977129i	$0.431792\pi$
$912$		0			0
$913$	5.62536			0.186172
$914$		0			0
$915$	6.36959	−	36.1237i	0.210572	−	1.19421i
$916$		0			0
$917$	−38.3259	−	32.1593i	−1.26563	−	1.06199i
$918$		0			0
$919$	−10.3396	−	17.9086i	−0.341070	−	0.590751i	0.643561	−	0.765395i	$-0.277456\pi$
$919$	−10.3396	−	17.9086i	−0.341070	−	0.590751i	−0.984632	+	0.174643i	$0.944123\pi$
$920$		0			0
$921$	−50.6125	−	18.4215i	−1.66774	−	0.607007i
$922$		0			0
$923$	4.15745	−	7.20092i	0.136844	−	0.237021i
$924$		0			0
$925$	−0.837496	−	4.74968i	−0.0275367	−	0.156168i
$926$		0			0
$927$	2.91353	−	2.44474i	0.0956930	−	0.0802960i
$928$		0			0
$929$	17.1493	−	6.24183i	0.562650	−	0.204788i	−0.0450079	−	0.998987i	$-0.514331\pi$
$929$	17.1493	−	6.24183i	0.562650	−	0.204788i	0.607658	+	0.794199i	$0.292109\pi$
$930$		0			0
$931$	81.2670	−	1.17847i	2.66342	−	0.0386229i
$932$		0			0
$933$	27.9273	−	10.1647i	0.914297	−	0.332777i
$934$		0			0
$935$	5.16662	−	4.33531i	0.168967	−	0.141780i
$936$		0			0
$937$	−0.824292	−	4.67479i	−0.0269285	−	0.152719i	0.968379	−	0.249485i	$-0.0802613\pi$
$937$	−0.824292	−	4.67479i	−0.0269285	−	0.152719i	−0.995307	+	0.0967660i	$0.969150\pi$
$938$		0			0
$939$	−12.3478	+	21.3870i	−0.402954	+	0.697937i
$940$		0			0
$941$	−44.1857	−	16.0823i	−1.44041	−	0.524268i	−0.500517	−	0.865727i	$-0.666857\pi$
$941$	−44.1857	−	16.0823i	−1.44041	−	0.524268i	−0.939897	+	0.341459i	$0.889079\pi$
$942$		0			0
$943$	2.34730	+	4.06564i	0.0764385	+	0.132395i
$944$		0			0
$945$	35.9864	+	30.1962i	1.17064	+	0.982281i
$946$		0			0
$947$	−6.42427	+	36.4338i	−0.208761	+	1.18394i	0.682651	+	0.730745i	$0.260827\pi$
$947$	−6.42427	+	36.4338i	−0.208761	+	1.18394i	−0.891411	+	0.453195i	$0.850284\pi$
$948$		0			0
$949$	5.95191			0.193207
$950$		0			0
$951$	−40.2276			−1.30447
$952$		0			0
$953$	−6.54814	+	37.1364i	−0.212115	+	1.20296i	0.673728	+	0.738980i	$0.264692\pi$
$953$	−6.54814	+	37.1364i	−0.212115	+	1.20296i	−0.885843	+	0.463985i	$0.846419\pi$
$954$		0			0
$955$	30.7939	+	25.8391i	0.996466	+	0.836134i
$956$		0			0
$957$	−11.2121	−	19.4200i	−0.362437	−	0.627759i
$958$		0			0
$959$	25.6827	+	9.34775i	0.829339	+	0.301855i
$960$		0			0
$961$	15.4317	−	26.7285i	0.497797	−	0.862209i
$962$		0			0
$963$	0.865715	+	4.90971i	0.0278973	+	0.158213i
$964$		0			0
$965$	25.5631	−	21.4499i	0.822904	−	0.690498i
$966$		0			0
$967$	38.0702	−	13.8564i	1.22425	−	0.445592i	0.352628	−	0.935764i	$-0.385288\pi$
$967$	38.0702	−	13.8564i	1.22425	−	0.445592i	0.871626	+	0.490172i	$0.163066\pi$
$968$		0			0
$969$	14.8093	−	12.7969i	0.475743	−	0.411096i
$970$		0			0
$971$	−13.2289	+	4.81493i	−0.424536	+	0.154518i	−0.545448	−	0.838145i	$-0.683640\pi$
$971$	−13.2289	+	4.81493i	−0.424536	+	0.154518i	0.120912	+	0.992663i	$0.461418\pi$
$972$		0			0
$973$	−9.07604	+	7.61570i	−0.290964	+	0.244148i
$974$		0			0
$975$	0.426022	+	2.41609i	0.0136436	+	0.0773768i
$976$		0			0
$977$	17.6028	−	30.4890i	0.563164	−	0.975429i	−0.434054	−	0.900887i	$-0.642917\pi$
$977$	17.6028	−	30.4890i	0.563164	−	0.975429i	0.997218	−	0.0745421i	$-0.0237495\pi$
$978$		0			0
$979$	14.1202	+	5.13933i	0.451284	+	0.164254i
$980$		0			0
$981$	−2.94356	−	5.09840i	−0.0939807	−	0.162779i
$982$		0			0
$983$	−17.1898	−	14.4240i	−0.548271	−	0.460054i	0.326084	−	0.945341i	$-0.394271\pi$
$983$	−17.1898	−	14.4240i	−0.548271	−	0.460054i	−0.874355	+	0.485287i	$0.838715\pi$
$984$		0			0
$985$	4.51155	−	25.5863i	0.143750	−	0.815247i
$986$		0			0
$987$	−97.1944			−3.09373
$988$		0			0
$989$	2.32501			0.0739309
$990$		0			0
$991$	−4.70645	+	26.6916i	−0.149505	+	0.847887i	0.814133	+	0.580678i	$0.197213\pi$
$991$	−4.70645	+	26.6916i	−0.149505	+	0.847887i	−0.963639	+	0.267209i	$0.913899\pi$
$992$		0			0
$993$	36.5651	+	30.6818i	1.16036	+	0.973657i
$994$		0			0
$995$	17.1925	+	29.7783i	0.545040	+	0.944037i
$996$		0			0
$997$	−26.2618	−	9.55850i	−0.831718	−	0.302721i	−0.109154	−	0.994025i	$-0.534814\pi$
$997$	−26.2618	−	9.55850i	−0.831718	−	0.302721i	−0.722564	+	0.691304i	$0.757037\pi$
$998$		0			0
$999$	11.1848	−	19.3726i	0.353871	−	0.612923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.c.81.1		6
4.3	odd	2		38.2.e.a.5.1	✓	6
12.11	even	2		342.2.u.c.271.1		6
19.2	odd	18		5776.2.a.bo.1.1		3
19.4	even	9	inner	304.2.u.c.289.1		6
19.17	even	9		5776.2.a.bn.1.3		3
20.3	even	4		950.2.u.b.499.2		12
20.7	even	4		950.2.u.b.499.1		12
20.19	odd	2		950.2.l.d.651.1		6
76.3	even	18		722.2.c.l.653.1		6
76.7	odd	6		722.2.e.b.245.1		6
76.11	odd	6		722.2.e.m.415.1		6
76.15	even	18		722.2.e.k.99.1		6
76.23	odd	18		38.2.e.a.23.1	yes	6
76.27	even	6		722.2.e.a.415.1		6
76.31	even	6		722.2.e.l.245.1		6
76.35	odd	18		722.2.c.k.653.3		6
76.43	odd	18		722.2.c.k.429.3		6
76.47	odd	18		722.2.e.m.595.1		6
76.51	even	18		722.2.e.l.389.1		6
76.55	odd	18		722.2.a.l.1.1		3
76.59	even	18		722.2.a.k.1.3		3
76.63	odd	18		722.2.e.b.389.1		6
76.67	even	18		722.2.e.a.595.1		6
76.71	even	18		722.2.c.l.429.1		6
76.75	even	2		722.2.e.k.423.1		6
228.23	even	18		342.2.u.c.289.1		6
228.59	odd	18		6498.2.a.bq.1.3		3
228.131	even	18		6498.2.a.bl.1.3		3
380.23	even	36		950.2.u.b.99.1		12
380.99	odd	18		950.2.l.d.251.1		6
380.327	even	36		950.2.u.b.99.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	4.3	odd	2
38.2.e.a.23.1	yes	6	76.23	odd	18
304.2.u.c.81.1		6	1.1	even	1	trivial
304.2.u.c.289.1		6	19.4	even	9	inner
342.2.u.c.271.1		6	12.11	even	2
342.2.u.c.289.1		6	228.23	even	18
722.2.a.k.1.3		3	76.59	even	18
722.2.a.l.1.1		3	76.55	odd	18
722.2.c.k.429.3		6	76.43	odd	18
722.2.c.k.653.3		6	76.35	odd	18
722.2.c.l.429.1		6	76.71	even	18
722.2.c.l.653.1		6	76.3	even	18
722.2.e.a.415.1		6	76.27	even	6
722.2.e.a.595.1		6	76.67	even	18
722.2.e.b.245.1		6	76.7	odd	6
722.2.e.b.389.1		6	76.63	odd	18
722.2.e.k.99.1		6	76.15	even	18
722.2.e.k.423.1		6	76.75	even	2
722.2.e.l.245.1		6	76.31	even	6
722.2.e.l.389.1		6	76.51	even	18
722.2.e.m.415.1		6	76.11	odd	6
722.2.e.m.595.1		6	76.47	odd	18
950.2.l.d.251.1		6	380.99	odd	18
950.2.l.d.651.1		6	20.19	odd	2
950.2.u.b.99.1		12	380.23	even	36
950.2.u.b.99.2		12	380.327	even	36
950.2.u.b.499.1		12	20.7	even	4
950.2.u.b.499.2		12	20.3	even	4
5776.2.a.bn.1.3		3	19.17	even	9
5776.2.a.bo.1.1		3	19.2	odd	18
6498.2.a.bl.1.3		3	228.131	even	18
6498.2.a.bq.1.3		3	228.59	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)

\(f(q)\)	\(=\)	\(q+(0.326352 - 1.85083i) q^{3} +(1.53209 + 1.28558i) q^{5} +(2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.181985i) q^{9} +O(q^{10})\)	\(q+(0.326352 - 1.85083i) q^{3} +(1.53209 + 1.28558i) q^{5} +(2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.181985i) q^{9} +(-0.705737 + 1.22237i) q^{11} +(-0.226682 - 1.28558i) q^{13} +(2.87939 - 2.41609i) q^{15} +(-2.24510 + 0.817150i) q^{17} +(-2.23396 - 3.74292i) q^{19} +(8.94356 - 3.25519i) q^{21} +(2.34730 - 1.96962i) q^{23} +(-0.173648 - 0.984808i) q^{25} +(2.31908 - 4.01676i) q^{27} +(-7.94356 - 2.89122i) q^{29} +(0.184793 + 0.320070i) q^{31} +(2.03209 + 1.70513i) q^{33} +(-1.75877 + 9.97448i) q^{35} +4.82295 q^{37} -2.45336 q^{39} +(-0.266044 + 1.50881i) q^{41} +(0.581252 + 0.487728i) q^{43} +(-0.532089 - 0.921605i) q^{45} +(-9.59627 - 3.49276i) q^{47} +(-9.32295 + 16.1478i) q^{49} +(0.779715 + 4.42198i) q^{51} +(1.28312 - 1.07666i) q^{53} +(-2.65270 + 0.965505i) q^{55} +(-7.65657 + 2.91317i) q^{57} +(0.673648 - 0.245188i) q^{59} +(7.47565 - 6.27282i) q^{61} +(-0.467911 - 2.65366i) q^{63} +(1.30541 - 2.26103i) q^{65} +(-1.31908 - 0.480105i) q^{67} +(-2.87939 - 4.98724i) q^{69} +(4.87939 + 4.09429i) q^{71} +(-0.791737 + 4.49016i) q^{73} -1.87939 q^{75} -7.14796 q^{77} +(0.389185 - 2.20718i) q^{79} +(-7.90033 - 6.62916i) q^{81} +(-1.99273 - 3.45150i) q^{83} +(-4.49020 - 1.63430i) q^{85} +(-7.94356 + 13.7587i) q^{87} +(-1.84864 - 10.4842i) q^{89} +(5.06418 - 4.24935i) q^{91} +(0.652704 - 0.237565i) q^{93} +(1.38919 - 8.60640i) q^{95} +(1.43969 - 0.524005i) q^{97} +(0.575322 - 0.482753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 6 q^{15} - 12 q^{17} - 18 q^{19} + 24 q^{21} + 12 q^{23} - 3 q^{27} - 18 q^{29} - 6 q^{31} + 3 q^{33} + 12 q^{35} - 12 q^{37} + 12 q^{39} + 3 q^{41} + 6 q^{43} + 6 q^{45} - 30 q^{47} - 15 q^{49} - 21 q^{51} + 24 q^{53} - 18 q^{55} - 24 q^{57} + 3 q^{59} + 6 q^{61} - 12 q^{63} + 12 q^{65} + 9 q^{67} - 6 q^{69} + 18 q^{71} - 30 q^{73} - 12 q^{77} - 6 q^{79} - 33 q^{81} + 6 q^{83} - 24 q^{85} - 18 q^{87} + 12 q^{91} + 6 q^{93} + 3 q^{97} - 21 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 6 * q^15 - 12 * q^17 - 18 * q^19 + 24 * q^21 + 12 * q^23 - 3 * q^27 - 18 * q^29 - 6 * q^31 + 3 * q^33 + 12 * q^35 - 12 * q^37 + 12 * q^39 + 3 * q^41 + 6 * q^43 + 6 * q^45 - 30 * q^47 - 15 * q^49 - 21 * q^51 + 24 * q^53 - 18 * q^55 - 24 * q^57 + 3 * q^59 + 6 * q^61 - 12 * q^63 + 12 * q^65 + 9 * q^67 - 6 * q^69 + 18 * q^71 - 30 * q^73 - 12 * q^77 - 6 * q^79 - 33 * q^81 + 6 * q^83 - 24 * q^85 - 18 * q^87 + 12 * q^91 + 6 * q^93 + 3 * q^97 - 21 * q^99

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