LMFDB - Embedded newform 308.3.r.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	308.29
Dual form			308.3.r.a.85.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.715503 - 2.20209i) q^{3} +(-3.95398 + 2.87274i) q^{5} +(-2.51626 + 0.817582i) q^{7} +(2.94389 + 2.13886i) q^{9} +O(q^{10})$	\(q+(0.715503 - 2.20209i) q^{3} +(-3.95398 + 2.87274i) q^{5} +(-2.51626 + 0.817582i) q^{7} +(2.94389 + 2.13886i) q^{9} +(4.63272 + 9.97687i) q^{11} +(2.57049 - 3.53797i) q^{13} +(3.49694 + 10.7625i) q^{15} +(9.82291 + 13.5201i) q^{17} +(22.2593 + 7.23249i) q^{19} +6.12601i q^{21} -9.76126 q^{23} +(-0.344069 + 1.05894i) q^{25} +(23.6752 - 17.2011i) q^{27} +(-17.2390 + 5.60130i) q^{29} +(41.0408 + 29.8179i) q^{31} +(25.2847 - 3.06319i) q^{33} +(7.60054 - 10.4612i) q^{35} +(-14.5854 - 44.8892i) q^{37} +(-5.95175 - 8.19188i) q^{39} +(-25.1491 - 8.17144i) q^{41} +36.1538i q^{43} -17.7845 q^{45} +(1.67194 - 5.14569i) q^{47} +(5.66312 - 4.11450i) q^{49} +(36.8008 - 11.9573i) q^{51} +(58.4439 + 42.4620i) q^{53} +(-46.9786 - 26.1398i) q^{55} +(31.8532 - 43.8422i) q^{57} +(29.9892 + 92.2972i) q^{59} +(-11.0620 - 15.2255i) q^{61} +(-9.15629 - 2.97506i) q^{63} +21.3734i q^{65} -108.348 q^{67} +(-6.98421 + 21.4952i) q^{69} +(-78.7555 + 57.2192i) q^{71} +(32.9984 - 10.7218i) q^{73} +(2.08569 + 1.51534i) q^{75} +(-19.8140 - 21.3168i) q^{77} +(8.07725 - 11.1174i) q^{79} +(-10.8184 - 33.2957i) q^{81} +(-11.1106 - 15.2924i) q^{83} +(-77.6792 - 25.2395i) q^{85} +41.9697i q^{87} -36.3723 q^{89} +(-3.57543 + 11.0040i) q^{91} +(95.0266 - 69.0408i) q^{93} +(-108.790 + 35.3480i) q^{95} +(-23.5818 - 17.1332i) q^{97} +(-7.70093 + 39.2796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.715503	−	2.20209i	0.238501	−	0.734030i	−0.758137	−	0.652096i	$-0.773890\pi$
$3$	0.715503	−	2.20209i	0.238501	−	0.734030i	0.996638	−	0.0819349i	$-0.0261099\pi$
$4$		0			0
$5$	−3.95398	+	2.87274i	−0.790796	+	0.574547i	−0.908200	−	0.418537i	$-0.862543\pi$
$5$	−3.95398	+	2.87274i	−0.790796	+	0.574547i	0.117403	+	0.993084i	$0.462543\pi$
$6$		0			0
$7$	−2.51626	+	0.817582i	−0.359466	+	0.116797i
$7$	−2.51626	+	0.817582i	−0.359466	+	0.116797i
$8$		0			0
$9$	2.94389	+	2.13886i	0.327099	+	0.237651i
$10$		0			0
$11$	4.63272	+	9.97687i	0.421156	+	0.906988i
$11$	4.63272	+	9.97687i	0.421156	+	0.906988i
$12$		0			0
$13$	2.57049	−	3.53797i	0.197730	−	0.272152i	−0.698626	−	0.715487i	$-0.746205\pi$
$13$	2.57049	−	3.53797i	0.197730	−	0.272152i	0.896356	+	0.443335i	$0.146205\pi$
$14$		0			0
$15$	3.49694	+	10.7625i	0.233129	+	0.717498i
$16$		0			0
$17$	9.82291	+	13.5201i	0.577818	+	0.795299i	0.993454	−	0.114232i	$-0.0364409\pi$
$17$	9.82291	+	13.5201i	0.577818	+	0.795299i	−0.415636	+	0.909531i	$0.636441\pi$
$18$		0			0
$19$	22.2593	+	7.23249i	1.17154	+	0.380657i	0.829219	−	0.558924i	$-0.188786\pi$
$19$	22.2593	+	7.23249i	1.17154	+	0.380657i	0.342324	+	0.939582i	$0.388786\pi$
$20$		0			0
$21$			6.12601i			0.291715i
$22$		0			0
$23$	−9.76126			−0.424403			−0.212201	−	0.977226i	$-0.568063\pi$
$23$	−9.76126			−0.424403			−0.212201	+	0.977226i	$0.568063\pi$
$24$		0			0
$25$	−0.344069	+	1.05894i	−0.0137628	+	0.0423574i
$26$		0			0
$27$	23.6752	−	17.2011i	0.876860	−	0.637076i
$28$		0			0
$29$	−17.2390	+	5.60130i	−0.594449	+	0.193148i	−0.590763	−	0.806845i	$-0.701173\pi$
$29$	−17.2390	+	5.60130i	−0.594449	+	0.193148i	−0.00368608	+	0.999993i	$0.501173\pi$
$30$		0			0
$31$	41.0408	+	29.8179i	1.32390	+	0.961868i	0.999875	+	0.0158181i	$0.00503528\pi$
$31$	41.0408	+	29.8179i	1.32390	+	0.961868i	0.324022	+	0.946049i	$0.394965\pi$
$32$		0			0
$33$	25.2847	−	3.06319i	0.766203	−	0.0928239i
$34$		0			0
$35$	7.60054	−	10.4612i	0.217158	−	0.298893i
$36$		0			0
$37$	−14.5854	−	44.8892i	−0.394200	−	1.21322i	−0.929583	−	0.368613i	$-0.879833\pi$
$37$	−14.5854	−	44.8892i	−0.394200	−	1.21322i	0.535383	−	0.844609i	$-0.320167\pi$
$38$		0			0
$39$	−5.95175	−	8.19188i	−0.152609	−	0.210048i
$40$		0			0
$41$	−25.1491	−	8.17144i	−0.613392	−	0.199303i	−0.0141880	−	0.999899i	$-0.504516\pi$
$41$	−25.1491	−	8.17144i	−0.613392	−	0.199303i	−0.599204	+	0.800596i	$0.704516\pi$
$42$		0			0
$43$			36.1538i			0.840785i	0.907342	+	0.420392i	$0.138108\pi$
$43$			36.1538i			0.840785i	−0.907342	+	0.420392i	$0.861892\pi$
$44$		0			0
$45$	−17.7845			−0.395210
$46$		0			0
$47$	1.67194	−	5.14569i	0.0355731	−	0.109483i	−0.931693	−	0.363246i	$-0.881668\pi$
$47$	1.67194	−	5.14569i	0.0355731	−	0.109483i	0.967266	+	0.253763i	$0.0816684\pi$
$48$		0			0
$49$	5.66312	−	4.11450i	0.115574	−	0.0839693i
$50$		0			0
$51$	36.8008	−	11.9573i	0.721584	−	0.234457i
$52$		0			0
$53$	58.4439	+	42.4620i	1.10272	+	0.801170i	0.981501	−	0.191457i	$-0.0613211\pi$
$53$	58.4439	+	42.4620i	1.10272	+	0.801170i	0.121214	+	0.992626i	$0.461321\pi$
$54$		0			0
$55$	−46.9786	−	26.1398i	−0.854156	−	0.475269i
$56$		0			0
$57$	31.8532	−	43.8422i	0.558828	−	0.769161i
$58$		0			0
$59$	29.9892	+	92.2972i	0.508291	+	1.56436i	0.795166	+	0.606392i	$0.207384\pi$
$59$	29.9892	+	92.2972i	0.508291	+	1.56436i	−0.286874	+	0.957968i	$0.592616\pi$
$60$		0			0
$61$	−11.0620	−	15.2255i	−0.181344	−	0.249598i	0.708662	−	0.705549i	$-0.249299\pi$
$61$	−11.0620	−	15.2255i	−0.181344	−	0.249598i	−0.890005	+	0.455951i	$0.849299\pi$
$62$		0			0
$63$	−9.15629	−	2.97506i	−0.145338	−	0.0472231i
$64$		0			0
$65$			21.3734i			0.328822i
$66$		0			0
$67$	−108.348			−1.61713			−0.808567	−	0.588405i	$-0.799756\pi$
$67$	−108.348			−1.61713			−0.808567	+	0.588405i	$0.799756\pi$
$68$		0			0
$69$	−6.98421	+	21.4952i	−0.101220	+	0.311524i
$70$		0			0
$71$	−78.7555	+	57.2192i	−1.10923	+	0.805904i	−0.982542	−	0.186038i	$-0.940435\pi$
$71$	−78.7555	+	57.2192i	−1.10923	+	0.805904i	−0.126689	+	0.991942i	$0.540435\pi$
$72$		0			0
$73$	32.9984	−	10.7218i	0.452034	−	0.146875i	−0.0741473	−	0.997247i	$-0.523624\pi$
$73$	32.9984	−	10.7218i	0.452034	−	0.146875i	0.526181	+	0.850373i	$0.323624\pi$
$74$		0			0
$75$	2.08569	+	1.51534i	0.0278092	+	0.0202046i
$76$		0			0
$77$	−19.8140	−	21.3168i	−0.257325	−	0.276841i
$78$		0			0
$79$	8.07725	−	11.1174i	0.102244	−	0.140726i	−0.754829	−	0.655921i	$-0.772280\pi$
$79$	8.07725	−	11.1174i	0.102244	−	0.140726i	0.857073	+	0.515195i	$0.172280\pi$
$80$		0			0
$81$	−10.8184	−	33.2957i	−0.133561	−	0.411058i
$82$		0			0
$83$	−11.1106	−	15.2924i	−0.133862	−	0.184245i	0.736824	−	0.676085i	$-0.236325\pi$
$83$	−11.1106	−	15.2924i	−0.133862	−	0.184245i	−0.870686	+	0.491839i	$0.836325\pi$
$84$		0			0
$85$	−77.6792	−	25.2395i	−0.913873	−	0.296935i
$86$		0			0
$87$			41.9697i			0.482410i
$88$		0			0
$89$	−36.3723			−0.408678			−0.204339	−	0.978900i	$-0.565504\pi$
$89$	−36.3723			−0.408678			−0.204339	+	0.978900i	$0.565504\pi$
$90$		0			0
$91$	−3.57543	+	11.0040i	−0.0392904	+	0.120924i
$92$		0			0
$93$	95.0266	−	69.0408i	1.02179	−	0.742375i
$94$		0			0
$95$	−108.790	+	35.3480i	−1.14516	+	0.372084i
$96$		0			0
$97$	−23.5818	−	17.1332i	−0.243111	−	0.176631i	0.459557	−	0.888148i	$-0.348008\pi$
$97$	−23.5818	−	17.1332i	−0.243111	−	0.176631i	−0.702668	+	0.711518i	$0.748008\pi$
$98$		0			0
$99$	−7.70093	+	39.2796i	−0.0777872	+	0.396763i
$100$		0			0
$101$	92.7844	−	127.707i	0.918657	−	1.26442i	−0.0454656	−	0.998966i	$-0.514477\pi$
$101$	92.7844	−	127.707i	0.918657	−	1.26442i	0.964123	−	0.265457i	$-0.0855229\pi$
$102$		0			0
$103$	−42.9596	−	132.216i	−0.417084	−	1.28365i	−0.910374	−	0.413787i	$-0.864206\pi$
$103$	−42.9596	−	132.216i	−0.417084	−	1.28365i	0.493290	−	0.869865i	$-0.335794\pi$
$104$		0			0
$105$	−17.5984	−	24.2221i	−0.167604	−	0.230687i
$106$		0			0
$107$	45.3314	+	14.7291i	0.423658	+	0.137655i	0.513084	−	0.858339i	$-0.328503\pi$
$107$	45.3314	+	14.7291i	0.423658	+	0.137655i	−0.0894254	+	0.995994i	$0.528503\pi$
$108$		0			0
$109$		−	195.809i		−	1.79641i	−0.439578	−	0.898204i	$-0.644872\pi$
$109$		−	195.809i		−	1.79641i	0.439578	−	0.898204i	$-0.355128\pi$
$110$		0			0
$111$	−109.286			−0.984559
$112$		0			0
$113$	4.77980	−	14.7107i	0.0422991	−	0.130183i	−0.927677	−	0.373384i	$-0.878197\pi$
$113$	4.77980	−	14.7107i	0.0422991	−	0.130183i	0.969976	+	0.243201i	$0.0781974\pi$
$114$		0			0
$115$	38.5958	−	28.0415i	0.335616	−	0.243839i
$116$		0			0
$117$	15.1345	−	4.91749i	0.129354	−	0.0420298i
$118$		0			0
$119$	−35.7708	−	25.9890i	−0.300595	−	0.218395i
$120$		0			0
$121$	−78.0759	+	92.4400i	−0.645255	+	0.763967i
$122$		0			0
$123$	−35.9885	+	49.5339i	−0.292589	+	0.402715i
$124$		0			0
$125$	−39.4388	−	121.380i	−0.315510	−	0.971040i
$126$		0			0
$127$	−76.5311	−	105.336i	−0.602607	−	0.829418i	0.393337	−	0.919394i	$-0.371321\pi$
$127$	−76.5311	−	105.336i	−0.602607	−	0.829418i	−0.995944	+	0.0899770i	$0.971321\pi$
$128$		0			0
$129$	79.6139	+	25.8681i	0.617162	+	0.200528i
$130$		0			0
$131$			144.053i			1.09964i	0.835284	+	0.549819i	$0.185303\pi$
$131$			144.053i			1.09964i	−0.835284	+	0.549819i	$0.814697\pi$
$132$		0			0
$133$	−61.9234			−0.465589
$134$		0			0
$135$	−44.1973	+	136.025i	−0.327387	+	1.00759i
$136$		0			0
$137$	46.6216	−	33.8726i	0.340303	−	0.247245i	−0.404486	−	0.914544i	$-0.632550\pi$
$137$	46.6216	−	33.8726i	0.340303	−	0.247245i	0.744790	+	0.667299i	$0.232550\pi$
$138$		0			0
$139$	203.544	−	66.1355i	1.46435	−	0.475795i	0.534952	−	0.844883i	$-0.320330\pi$
$139$	203.544	−	66.1355i	1.46435	−	0.475795i	0.929395	+	0.369088i	$0.120330\pi$
$140$		0			0
$141$	−10.1350	−	7.36352i	−0.0718795	−	0.0522235i
$142$		0			0
$143$	47.2062	+	9.25499i	0.330113	+	0.0647202i
$144$		0			0
$145$	52.0717	−	71.6706i	0.359116	−	0.494280i
$146$		0			0
$147$	−5.00852	−	15.4146i	−0.0340716	−	0.104861i
$148$		0			0
$149$	17.0237	+	23.4312i	0.114253	+	0.157256i	0.862314	−	0.506375i	$-0.169015\pi$
$149$	17.0237	+	23.4312i	0.114253	+	0.157256i	−0.748060	+	0.663631i	$0.769015\pi$
$150$		0			0
$151$	−54.2519	−	17.6275i	−0.359284	−	0.116738i	0.123812	−	0.992306i	$-0.460488\pi$
$151$	−54.2519	−	17.6275i	−0.359284	−	0.116738i	−0.483096	+	0.875567i	$0.660488\pi$
$152$		0			0
$153$			60.8115i			0.397461i
$154$		0			0
$155$	−247.933			−1.59957
$156$		0			0
$157$	−11.7402	+	36.1326i	−0.0747782	+	0.230144i	−0.981458	−	0.191675i	$-0.938608\pi$
$157$	−11.7402	+	36.1326i	−0.0747782	+	0.230144i	0.906680	+	0.421819i	$0.138608\pi$
$158$		0			0
$159$	135.322	−	98.3172i	0.851082	−	0.618347i
$160$		0			0
$161$	24.5619	−	7.98063i	0.152558	−	0.0495691i
$162$		0			0
$163$	121.516	+	88.2866i	0.745498	+	0.541636i	0.894428	−	0.447212i	$-0.147583\pi$
$163$	121.516	+	88.2866i	0.745498	+	0.541636i	−0.148930	+	0.988848i	$0.547583\pi$
$164$		0			0
$165$	−91.1755	+	84.7480i	−0.552579	+	0.513624i
$166$		0			0
$167$	−45.3883	+	62.4716i	−0.271786	+	0.374082i	−0.922992	−	0.384820i	$-0.874264\pi$
$167$	−45.3883	+	62.4716i	−0.271786	+	0.374082i	0.651206	+	0.758901i	$0.274264\pi$
$168$		0			0
$169$	46.3140	+	142.540i	0.274048	+	0.843432i
$170$		0			0
$171$	50.0597	+	68.9013i	0.292747	+	0.402931i
$172$		0			0
$173$	132.351	+	43.0035i	0.765035	+	0.248575i	0.665438	−	0.746453i	$-0.268245\pi$
$173$	132.351	+	43.0035i	0.765035	+	0.248575i	0.0995967	+	0.995028i	$0.468245\pi$
$174$		0			0
$175$		−	2.94586i		−	0.0168335i
$176$		0			0
$177$	224.704			1.26952
$178$		0			0
$179$	−9.64990	+	29.6993i	−0.0539100	+	0.165918i	−0.974386	−	0.224880i	$-0.927801\pi$
$179$	−9.64990	+	29.6993i	−0.0539100	+	0.165918i	0.920476	+	0.390798i	$0.127801\pi$
$180$		0			0
$181$	−103.642	+	75.3006i	−0.572610	+	0.416025i	−0.836052	−	0.548650i	$-0.815142\pi$
$181$	−103.642	+	75.3006i	−0.572610	+	0.416025i	0.263443	+	0.964675i	$0.415142\pi$
$182$		0			0
$183$	−41.4427	+	13.4656i	−0.226463	+	0.0735823i
$184$		0			0
$185$	186.625	+	135.591i	1.00878	+	0.732925i
$186$		0			0
$187$	−89.3813	+	160.637i	−0.477975	+	0.859019i
$188$		0			0
$189$	−45.5097	+	62.6388i	−0.240792	+	0.331422i
$190$		0			0
$191$	83.3694	+	256.585i	0.436489	+	1.34338i	0.891553	+	0.452917i	$0.149617\pi$
$191$	83.3694	+	256.585i	0.436489	+	1.34338i	−0.455064	+	0.890459i	$0.650383\pi$
$192$		0			0
$193$	−208.118	−	286.450i	−1.07833	−	1.48420i	−0.861344	−	0.508022i	$-0.830377\pi$
$193$	−208.118	−	286.450i	−1.07833	−	1.48420i	−0.216988	−	0.976174i	$-0.569623\pi$
$194$		0			0
$195$	47.0662	+	15.2927i	0.241365	+	0.0784243i
$196$		0			0
$197$		−	278.376i		−	1.41307i	−0.707676	−	0.706537i	$-0.750256\pi$
$197$		−	278.376i		−	1.41307i	0.707676	−	0.706537i	$-0.249744\pi$
$198$		0			0
$199$	72.3224			0.363429			0.181715	−	0.983351i	$-0.441835\pi$
$199$	72.3224			0.363429			0.181715	+	0.983351i	$0.441835\pi$
$200$		0			0
$201$	−77.5233	+	238.592i	−0.385688	+	1.18703i
$202$		0			0
$203$	38.7983	−	28.1887i	0.191125	−	0.138860i
$204$		0			0
$205$	122.913	−	39.9370i	0.599578	−	0.194815i
$206$		0			0
$207$	−28.7361	−	20.8780i	−0.138822	−	0.100860i
$208$		0			0
$209$	30.9635	+	255.584i	0.148151	+	1.22289i
$210$		0			0
$211$	199.520	−	274.615i	0.945590	−	1.30149i	−0.00786831	−	0.999969i	$-0.502505\pi$
$211$	199.520	−	274.615i	0.945590	−	1.30149i	0.953459	−	0.301524i	$-0.0974954\pi$
$212$		0			0
$213$	69.6521	+	214.367i	0.327005	+	1.00642i
$214$		0			0
$215$	−103.860	−	142.951i	−0.483070	−	0.664889i
$216$		0			0
$217$	−127.648	−	41.4753i	−0.588239	−	0.191130i
$218$		0			0
$219$		−	80.3371i		−	0.366836i
$220$		0			0
$221$	73.0833			0.330694
$222$		0			0
$223$	−34.6057	+	106.505i	−0.155182	+	0.477602i	−0.998179	−	0.0603161i	$-0.980789\pi$
$223$	−34.6057	+	106.505i	−0.155182	+	0.477602i	0.842997	+	0.537918i	$0.180789\pi$
$224$		0			0
$225$	−3.27782	+	2.38147i	−0.0145681	+	0.0105843i
$226$		0			0
$227$	411.339	−	133.652i	1.81207	−	0.588776i	0.812079	−	0.583548i	$-0.198336\pi$
$227$	411.339	−	133.652i	1.81207	−	0.588776i	0.999986	−	0.00522796i	$-0.00166412\pi$
$228$		0			0
$229$	107.115	+	77.8234i	0.467750	+	0.339840i	0.796564	−	0.604555i	$-0.206649\pi$
$229$	107.115	+	77.8234i	0.467750	+	0.339840i	−0.328814	+	0.944395i	$0.606649\pi$
$230$		0			0
$231$	−61.1185	+	28.3801i	−0.264582	+	0.122858i
$232$		0			0
$233$	15.2061	−	20.9293i	0.0652620	−	0.0898255i	−0.775138	−	0.631792i	$-0.782320\pi$
$233$	15.2061	−	20.9293i	0.0652620	−	0.0898255i	0.840400	+	0.541966i	$0.182320\pi$
$234$		0			0
$235$	8.17141	+	25.1490i	0.0347720	+	0.107017i
$236$		0			0
$237$	−18.7022	−	25.7414i	−0.0789122	−	0.108613i
$238$		0			0
$239$	86.0941	+	27.9737i	0.360226	+	0.117045i	0.483538	−	0.875323i	$-0.339352\pi$
$239$	86.0941	+	27.9737i	0.360226	+	0.117045i	−0.123312	+	0.992368i	$0.539352\pi$
$240$		0			0
$241$		−	200.560i		−	0.832201i	−0.909319	−	0.416100i	$-0.863396\pi$
$241$		−	200.560i		−	0.832201i	0.909319	−	0.416100i	$-0.136604\pi$
$242$		0			0
$243$	182.317			0.750276
$244$		0			0
$245$	−10.5720	+	32.5373i	−0.0431510	+	0.132805i
$246$		0			0
$247$	82.8056	−	60.1618i	0.335246	−	0.243570i
$248$		0			0
$249$	−41.6248	+	13.5247i	−0.167168	+	0.0543161i
$250$		0			0
$251$	−226.896	−	164.850i	−0.903970	−	0.656773i	0.0355127	−	0.999369i	$-0.488694\pi$
$251$	−226.896	−	164.850i	−0.903970	−	0.656773i	−0.939483	+	0.342597i	$0.888694\pi$
$252$		0			0
$253$	−45.2212	−	97.3868i	−0.178740	−	0.384928i
$254$		0			0
$255$	−111.159	+	152.998i	−0.435919	+	0.599991i
$256$		0			0
$257$	64.9081	+	199.767i	0.252561	+	0.777302i	0.994300	+	0.106614i	$0.0340010\pi$
$257$	64.9081	+	199.767i	0.252561	+	0.777302i	−0.741740	+	0.670688i	$0.765999\pi$
$258$		0			0
$259$	73.4013	+	101.028i	0.283403	+	0.390070i
$260$		0			0
$261$	−62.7302	−	20.3823i	−0.240346	−	0.0780931i
$262$		0			0
$263$			398.406i			1.51485i	0.652921	+	0.757426i	$0.273544\pi$
$263$			398.406i			1.51485i	−0.652921	+	0.757426i	$0.726456\pi$
$264$		0			0
$265$	−353.068			−1.33233
$266$		0			0
$267$	−26.0245	+	80.0952i	−0.0974700	+	0.299982i
$268$		0			0
$269$	234.308	−	170.235i	0.871033	−	0.632843i	−0.0598309	−	0.998209i	$-0.519056\pi$
$269$	234.308	−	170.235i	0.871033	−	0.632843i	0.930864	+	0.365366i	$0.119056\pi$
$270$		0			0
$271$	245.966	−	79.9193i	0.907624	−	0.294905i	0.182244	−	0.983253i	$-0.441664\pi$
$271$	245.966	−	79.9193i	0.907624	−	0.294905i	0.725380	+	0.688348i	$0.241664\pi$
$272$		0			0
$273$	21.6737	+	15.7468i	0.0793907	+	0.0576807i
$274$		0			0
$275$	−12.1588	+	1.47302i	−0.0442140	+	0.00535643i
$276$		0			0
$277$	91.9382	−	126.542i	0.331907	−	0.456831i	−0.610149	−	0.792287i	$-0.708890\pi$
$277$	91.9382	−	126.542i	0.331907	−	0.456831i	0.942056	+	0.335456i	$0.108890\pi$
$278$		0			0
$279$	57.0433	+	175.561i	0.204456	+	0.629252i
$280$		0			0
$281$	−217.523	−	299.395i	−0.774104	−	1.06546i	−0.995908	−	0.0903720i	$-0.971194\pi$
$281$	−217.523	−	299.395i	−0.774104	−	1.06546i	0.221804	−	0.975091i	$-0.428806\pi$
$282$		0			0
$283$	261.229	+	84.8786i	0.923072	+	0.299924i	0.731726	−	0.681598i	$-0.238715\pi$
$283$	261.229	+	84.8786i	0.923072	+	0.299924i	0.191346	+	0.981523i	$0.438715\pi$
$284$		0			0
$285$			264.857i			0.929323i
$286$		0			0
$287$	69.9625			0.243772
$288$		0			0
$289$	3.00298	−	9.24221i	0.0103909	−	0.0319800i
$290$		0			0
$291$	−54.6017	+	39.6704i	−0.187635	+	0.136325i
$292$		0			0
$293$	12.0565	−	3.91739i	0.0411485	−	0.0133699i	−0.288370	−	0.957519i	$-0.593113\pi$
$293$	12.0565	−	3.91739i	0.0411485	−	0.0133699i	0.329519	+	0.944149i	$0.393113\pi$
$294$		0			0
$295$	−383.722	−	278.791i	−1.30075	−	0.945053i
$296$		0			0
$297$	281.293	+	156.517i	0.947116	+	0.526993i
$298$		0			0
$299$	−25.0912	+	34.5351i	−0.0839170	+	0.115502i
$300$		0			0
$301$	−29.5587	−	90.9722i	−0.0982015	−	0.302233i
$302$		0			0
$303$	−214.834	−	295.694i	−0.709024	−	0.975888i
$304$		0			0
$305$	87.4775	+	28.4232i	0.286811	+	0.0931907i
$306$		0			0
$307$		−	387.219i		−	1.26130i	−0.776068	−	0.630650i	$-0.782788\pi$
$307$		−	387.219i		−	1.26130i	0.776068	−	0.630650i	$-0.217212\pi$
$308$		0			0
$309$	−321.890			−1.04171
$310$		0			0
$311$	−49.7698	+	153.176i	−0.160032	+	0.492527i	−0.998636	−	0.0522143i	$-0.983372\pi$
$311$	−49.7698	+	153.176i	−0.160032	+	0.492527i	0.838604	+	0.544741i	$0.183372\pi$
$312$		0			0
$313$	88.8855	−	64.5791i	0.283979	−	0.206323i	−0.436672	−	0.899621i	$-0.643843\pi$
$313$	88.8855	−	64.5791i	0.283979	−	0.206323i	0.720651	+	0.693298i	$0.243843\pi$
$314$		0			0
$315$	44.7503	−	14.5403i	0.142065	−	0.0461596i
$316$		0			0
$317$	86.9166	+	63.1486i	0.274185	+	0.199207i	0.716377	−	0.697713i	$-0.245799\pi$
$317$	86.9166	+	63.1486i	0.274185	+	0.199207i	−0.442192	+	0.896920i	$0.645799\pi$
$318$		0			0
$319$	−135.747	−	146.042i	−0.425539	−	0.457813i
$320$		0			0
$321$	64.8695	−	89.2853i	0.202086	−	0.278147i
$322$		0			0
$323$	120.867	+	371.992i	0.374203	+	1.15168i
$324$		0			0
$325$	2.86206	+	3.93929i	0.00880634	+	0.0121209i
$326$		0			0
$327$	−431.188	−	140.102i	−1.31862	−	0.428445i
$328$		0			0
$329$			14.3148i			0.0435102i
$330$		0			0
$331$	−257.781			−0.778793			−0.389397	−	0.921070i	$-0.627316\pi$
$331$	−257.781			−0.778793			−0.389397	+	0.921070i	$0.627316\pi$
$332$		0			0
$333$	53.0740	−	163.345i	0.159382	−	0.490526i
$334$		0			0
$335$	428.406	−	311.255i	1.27882	−	0.929119i
$336$		0			0
$337$	−346.895	+	112.713i	−1.02936	+	0.334460i	−0.774538	−	0.632527i	$-0.782018\pi$
$337$	−346.895	+	112.713i	−1.02936	+	0.334460i	−0.254825	+	0.966987i	$0.582018\pi$
$338$		0			0
$339$	−28.9744	−	21.0511i	−0.0854702	−	0.0620977i
$340$		0			0
$341$	−107.359	+	547.597i	−0.314835	+	1.60586i
$342$		0			0
$343$	−10.8859	+	14.9832i	−0.0317374	+	0.0436828i
$344$		0			0
$345$	−34.1345	−	105.055i	−0.0989407	−	0.304508i
$346$		0			0
$347$	−321.745	−	442.845i	−0.927220	−	1.27621i	−0.960934	−	0.276777i	$-0.910734\pi$
$347$	−321.745	−	442.845i	−0.927220	−	1.27621i	0.0337139	−	0.999432i	$-0.489266\pi$
$348$		0			0
$349$	−521.379	−	169.406i	−1.49392	−	0.485405i	−0.555684	−	0.831393i	$-0.687544\pi$
$349$	−521.379	−	169.406i	−1.49392	−	0.485405i	−0.938239	+	0.345988i	$0.887544\pi$
$350$		0			0
$351$		−	127.977i		−	0.364608i
$352$		0			0
$353$	−562.864			−1.59452			−0.797258	−	0.603639i	$-0.793717\pi$
$353$	−562.864			−1.59452			−0.797258	+	0.603639i	$0.793717\pi$
$354$		0			0
$355$	147.022	−	452.487i	0.414146	−	1.27461i
$356$		0			0
$357$	−82.8242	+	60.1753i	−0.232001	+	0.168558i
$358$		0			0
$359$	97.8514	−	31.7938i	0.272567	−	0.0885623i	−0.169545	−	0.985523i	$-0.554230\pi$
$359$	97.8514	−	31.7938i	0.272567	−	0.0885623i	0.442111	+	0.896960i	$0.354230\pi$
$360$		0			0
$361$	151.113	+	109.790i	0.418596	+	0.304128i
$362$		0			0
$363$	147.698	+	238.071i	0.406881	+	0.655844i
$364$		0			0
$365$	−99.6742	+	137.190i	−0.273080	+	0.375862i
$366$		0			0
$367$	29.4085	+	90.5101i	0.0801322	+	0.246621i	0.983095	−	0.183098i	$-0.0586125\pi$
$367$	29.4085	+	90.5101i	0.0801322	+	0.246621i	−0.902963	+	0.429719i	$0.858613\pi$
$368$		0			0
$369$	−56.5586	−	77.8462i	−0.153275	−	0.210965i
$370$		0			0
$371$	−181.776	−	59.0627i	−0.489963	−	0.159199i
$372$		0			0
$373$			67.8871i			0.182003i	0.995851	+	0.0910014i	$0.0290068\pi$
$373$			67.8871i			0.182003i	−0.995851	+	0.0910014i	$0.970993\pi$
$374$		0			0
$375$	−295.508			−0.788022
$376$		0			0
$377$	−24.4955	+	75.3893i	−0.0649747	+	0.199972i
$378$		0			0
$379$	411.112	−	298.690i	1.08473	−	0.788101i	0.106227	−	0.994342i	$-0.466123\pi$
$379$	411.112	−	298.690i	1.08473	−	0.788101i	0.978501	+	0.206241i	$0.0661231\pi$
$380$		0			0
$381$	−286.718	+	93.1603i	−0.752540	+	0.244515i
$382$		0			0
$383$	−282.455	−	205.215i	−0.737480	−	0.535810i	0.154441	−	0.988002i	$-0.450642\pi$
$383$	−282.455	−	205.215i	−0.737480	−	0.535810i	−0.891921	+	0.452192i	$0.850642\pi$
$384$		0			0
$385$	139.582	+	27.3656i	0.362550	+	0.0710795i
$386$		0			0
$387$	−77.3279	+	106.433i	−0.199814	+	0.275020i
$388$		0			0
$389$	111.963	+	344.586i	0.287822	+	0.885826i	0.985539	+	0.169452i	$0.0541996\pi$
$389$	111.963	+	344.586i	0.287822	+	0.885826i	−0.697716	+	0.716374i	$0.745800\pi$
$390$		0			0
$391$	−95.8840	−	131.973i	−0.245228	−	0.337527i
$392$		0			0
$393$	317.217	+	103.070i	0.807168	+	0.262265i
$394$		0			0
$395$			67.1617i			0.170030i
$396$		0			0
$397$	73.0795			0.184079			0.0920397	−	0.995755i	$-0.470661\pi$
$397$	73.0795			0.184079			0.0920397	+	0.995755i	$0.470661\pi$
$398$		0			0
$399$	−44.3063	+	136.361i	−0.111043	+	0.341757i
$400$		0			0
$401$	−204.105	+	148.291i	−0.508989	+	0.369802i	−0.812440	−	0.583045i	$-0.801861\pi$
$401$	−204.105	+	148.291i	−0.508989	+	0.369802i	0.303451	+	0.952847i	$0.401861\pi$
$402$		0			0
$403$	210.990	−	68.5547i	0.523548	−	0.170111i
$404$		0			0
$405$	138.425	+	100.572i	0.341791	+	0.248326i
$406$		0			0
$407$	380.284	−	353.476i	0.934359	−	0.868491i
$408$		0			0
$409$	271.504	−	373.694i	0.663825	−	0.913676i	−0.335776	−	0.941942i	$-0.608998\pi$
$409$	271.504	−	373.694i	0.663825	−	0.913676i	0.999600	+	0.0282658i	$0.00899847\pi$
$410$		0			0
$411$	−41.2326	−	126.901i	−0.100323	−	0.308761i
$412$		0			0
$413$	−150.921	−	207.725i	−0.365427	−	0.502966i
$414$		0			0
$415$	87.8618	+	28.5480i	0.211715	+	0.0687904i
$416$		0			0
$417$		−	495.543i		−	1.18835i
$418$		0			0
$419$	164.021			0.391458			0.195729	−	0.980658i	$-0.437293\pi$
$419$	164.021			0.391458			0.195729	+	0.980658i	$0.437293\pi$
$420$		0			0
$421$	−224.754	+	691.723i	−0.533858	+	1.64305i	0.212245	+	0.977216i	$0.431922\pi$
$421$	−224.754	+	691.723i	−0.533858	+	1.64305i	−0.746103	+	0.665830i	$0.768078\pi$
$422$		0			0
$423$	15.9279	−	11.5723i	0.0376547	−	0.0273577i
$424$		0			0
$425$	−17.6967	+	5.74999i	−0.0416392	+	0.0135294i
$426$		0			0
$427$	40.2828	+	29.2672i	0.0943391	+	0.0685414i
$428$		0			0
$429$	54.1565	−	97.3305i	0.126239	−	0.226878i
$430$		0			0
$431$	−459.776	+	632.827i	−1.06676	+	1.46828i	−0.193456	+	0.981109i	$0.561970\pi$
$431$	−459.776	+	632.827i	−1.06676	+	1.46828i	−0.873309	+	0.487167i	$0.838030\pi$
$432$		0			0
$433$	−97.5144	−	300.118i	−0.225206	−	0.693114i	−0.998271	−	0.0587863i	$-0.981277\pi$
$433$	−97.5144	−	300.118i	−0.225206	−	0.693114i	0.773064	−	0.634328i	$-0.218723\pi$
$434$		0			0
$435$	−120.568	−	165.947i	−0.277167	−	0.381488i
$436$		0			0
$437$	−217.279	−	70.5982i	−0.497206	−	0.161552i
$438$		0			0
$439$			15.0607i			0.0343068i	0.999853	+	0.0171534i	$0.00546037\pi$
$439$			15.0607i			0.0343068i	−0.999853	+	0.0171534i	$0.994540\pi$
$440$		0			0
$441$	25.4719			0.0577595
$442$		0			0
$443$	37.9660	−	116.847i	0.0857021	−	0.263764i	−0.899017	−	0.437913i	$-0.855718\pi$
$443$	37.9660	−	116.847i	0.0857021	−	0.263764i	0.984719	+	0.174150i	$0.0557176\pi$
$444$		0			0
$445$	143.815	−	104.488i	0.323181	−	0.234805i
$446$		0			0
$447$	63.7781	−	20.7227i	0.142680	−	0.0463596i
$448$		0			0
$449$	441.442	+	320.727i	0.983168	+	0.714313i	0.958414	−	0.285380i	$-0.0921200\pi$
$449$	441.442	+	320.727i	0.983168	+	0.714313i	0.0247533	+	0.999694i	$0.492120\pi$
$450$		0			0
$451$	−34.9833	−	288.765i	−0.0775683	−	0.640278i
$452$		0			0
$453$	−77.6347	+	106.855i	−0.171379	+	0.235883i
$454$		0			0
$455$	−17.4745	−	53.7810i	−0.0384055	−	0.118200i
$456$		0			0
$457$	−224.547	−	309.063i	−0.491351	−	0.676286i	0.489286	−	0.872123i	$-0.337257\pi$
$457$	−224.547	−	309.063i	−0.491351	−	0.676286i	−0.980636	+	0.195838i	$0.937257\pi$
$458$		0			0
$459$	465.119	+	151.126i	1.01333	+	0.329252i
$460$		0			0
$461$			593.433i			1.28727i	0.765331	+	0.643637i	$0.222575\pi$
$461$			593.433i			1.28727i	−0.765331	+	0.643637i	$0.777425\pi$
$462$		0			0
$463$	−272.273			−0.588062			−0.294031	−	0.955796i	$-0.594997\pi$
$463$	−272.273			−0.588062			−0.294031	+	0.955796i	$0.594997\pi$
$464$		0			0
$465$	−177.397	+	545.972i	−0.381499	+	1.17413i
$466$		0			0
$467$	656.056	−	476.653i	1.40483	−	1.02067i	0.410783	−	0.911733i	$-0.365255\pi$
$467$	656.056	−	476.653i	1.40483	−	1.02067i	0.994049	−	0.108937i	$-0.0347447\pi$
$468$		0			0
$469$	272.631	−	88.5833i	0.581304	−	0.188877i
$470$		0			0
$471$	71.1671	+	51.7059i	0.151098	+	0.109779i
$472$		0			0
$473$	−360.701	+	167.490i	−0.762582	+	0.354102i
$474$		0			0
$475$	−15.3175	+	21.0827i	−0.0322473	+	0.0443846i
$476$		0			0
$477$	81.2322	+	250.007i	0.170298	+	0.524124i
$478$		0			0
$479$	−321.646	−	442.707i	−0.671494	−	0.924232i	0.328299	−	0.944574i	$-0.393525\pi$
$479$	−321.646	−	442.707i	−0.671494	−	0.924232i	−0.999793	+	0.0203418i	$0.993525\pi$
$480$		0			0
$481$	−196.308	−	63.7845i	−0.408126	−	0.132608i
$482$		0			0
$483$		−	59.7976i		−	0.123805i
$484$		0			0
$485$	142.461			0.293734
$486$		0			0
$487$	184.377	−	567.453i	0.378597	−	1.16520i	−0.562423	−	0.826850i	$-0.690131\pi$
$487$	184.377	−	567.453i	0.378597	−	1.16520i	0.941020	−	0.338352i	$-0.109869\pi$
$488$		0			0
$489$	281.360	−	204.420i	0.575379	−	0.418037i
$490$		0			0
$491$	−69.8315	+	22.6896i	−0.142223	+	0.0462110i	−0.379263	−	0.925289i	$-0.623823\pi$
$491$	−69.8315	+	22.6896i	−0.142223	+	0.0462110i	0.237040	+	0.971500i	$0.423823\pi$
$492$		0			0
$493$	−245.068	−	178.052i	−0.497094	−	0.361160i
$494$		0			0
$495$	−82.3904	−	177.433i	−0.166445	−	0.358451i
$496$		0			0
$497$	151.388	−	208.367i	0.304603	−	0.419250i
$498$		0			0
$499$	4.95722	+	15.2568i	0.00993431	+	0.0305747i	0.955901	−	0.293690i	$-0.0948832\pi$
$499$	4.95722	+	15.2568i	0.00993431	+	0.0305747i	−0.945966	+	0.324264i	$0.894883\pi$
$500$		0			0
$501$	105.093	+	144.648i	0.209766	+	0.288718i
$502$		0			0
$503$	−484.982	−	157.580i	−0.964180	−	0.313281i	−0.215715	−	0.976456i	$-0.569208\pi$
$503$	−484.982	−	157.580i	−0.964180	−	0.313281i	−0.748464	+	0.663175i	$0.769208\pi$
$504$		0			0
$505$			771.495i			1.52771i
$506$		0			0
$507$	347.024			0.684465
$508$		0			0
$509$	225.344	−	693.537i	0.442719	−	1.36255i	−0.442247	−	0.896893i	$-0.645819\pi$
$509$	225.344	−	693.537i	0.442719	−	1.36255i	0.884966	−	0.465655i	$-0.154181\pi$
$510$		0			0
$511$	−74.2666	+	53.9579i	−0.145336	+	0.105593i
$512$		0			0
$513$	651.401	−	211.653i	1.26979	−	0.412579i
$514$		0			0
$515$	549.683	+	399.368i	1.06735	+	0.775472i
$516$		0			0
$517$	59.0835	−	7.15785i	0.114282	−	0.0138450i
$518$		0			0
$519$	189.395	−	260.680i	0.364923	−	0.502274i
$520$		0			0
$521$	40.2932	+	124.010i	0.0773381	+	0.238022i	0.982250	−	0.187577i	$-0.0600634\pi$
$521$	40.2932	+	124.010i	0.0773381	+	0.238022i	−0.904912	+	0.425599i	$0.860063\pi$
$522$		0			0
$523$	107.392	+	147.812i	0.205338	+	0.282623i	0.899249	−	0.437438i	$-0.144114\pi$
$523$	107.392	+	147.812i	0.205338	+	0.282623i	−0.693911	+	0.720061i	$0.744114\pi$
$524$		0			0
$525$	−6.48706	−	2.10777i	−0.0123563	−	0.00401480i
$526$		0			0
$527$			847.774i			1.60868i
$528$		0			0
$529$	−433.718			−0.819882
$530$		0			0
$531$	−109.126	+	335.856i	−0.205511	+	0.632497i
$532$		0			0
$533$	−93.5557	+	67.9722i	−0.175527	+	0.127528i
$534$		0			0
$535$	−221.552	+	71.9867i	−0.414117	+	0.134555i
$536$		0			0
$537$	58.4961	+	42.4999i	0.108931	+	0.0791432i
$538$		0			0
$539$	67.2854	+	37.4389i	0.124834	+	0.0694599i
$540$		0			0
$541$	−95.9268	+	132.032i	−0.177314	+	0.244051i	−0.888418	−	0.459035i	$-0.848195\pi$
$541$	−95.9268	+	132.032i	−0.177314	+	0.244051i	0.711104	+	0.703086i	$0.248195\pi$
$542$		0			0
$543$	91.6623	+	282.108i	0.168807	+	0.519535i
$544$		0			0
$545$	562.506	+	774.223i	1.03212	+	1.42059i
$546$		0			0
$547$	758.285	+	246.382i	1.38626	+	0.450424i	0.904723	−	0.426001i	$-0.140078\pi$
$547$	758.285	+	246.382i	1.38626	+	0.450424i	0.481539	+	0.876425i	$0.340078\pi$
$548$		0			0
$549$		−	68.4821i		−	0.124740i
$550$		0			0
$551$	−424.240			−0.769946
$552$		0			0
$553$	−11.2351	+	34.5780i	−0.0203166	+	0.0625281i
$554$		0			0
$555$	432.115	−	313.950i	0.778586	−	0.565676i
$556$		0			0
$557$	381.133	−	123.838i	0.684260	−	0.222330i	0.0538007	−	0.998552i	$-0.482866\pi$
$557$	381.133	−	123.838i	0.684260	−	0.222330i	0.630460	+	0.776222i	$0.282866\pi$
$558$		0			0
$559$	127.911	+	92.9328i	0.228821	+	0.166248i
$560$		0			0
$561$	289.784	+	311.762i	0.516549	+	0.555725i
$562$		0			0
$563$	−118.795	+	163.507i	−0.211004	+	0.290422i	−0.901380	−	0.433029i	$-0.857445\pi$
$563$	−118.795	+	163.507i	−0.211004	+	0.290422i	0.690376	+	0.723450i	$0.257445\pi$
$564$		0			0
$565$	23.3608	+	71.8970i	0.0413465	+	0.127251i
$566$		0			0
$567$	54.4439	+	74.9356i	0.0960210	+	0.132162i
$568$		0			0
$569$	−784.798	−	254.996i	−1.37926	−	0.448148i	−0.476832	−	0.878994i	$-0.658215\pi$
$569$	−784.798	−	254.996i	−1.37926	−	0.448148i	−0.902425	+	0.430846i	$0.858215\pi$
$570$		0			0
$571$			531.619i			0.931032i	0.885040	+	0.465516i	$0.154131\pi$
$571$			531.619i			0.931032i	−0.885040	+	0.465516i	$0.845869\pi$
$572$		0			0
$573$	624.674			1.09018
$574$		0			0
$575$	3.35855	−	10.3365i	0.00584095	−	0.0179766i
$576$		0			0
$577$	−516.351	+	375.151i	−0.894889	+	0.650175i	−0.937148	−	0.348932i	$-0.886545\pi$
$577$	−516.351	+	375.151i	−0.894889	+	0.650175i	0.0422590	+	0.999107i	$0.486545\pi$
$578$		0			0
$579$	−779.698	+	253.339i	−1.34663	+	0.437546i
$580$		0			0
$581$	40.4598	+	29.3958i	0.0696382	+	0.0505951i
$582$		0			0
$583$	−152.884	+	779.802i	−0.262236	+	1.33757i
$584$		0			0
$585$	−45.7148	+	62.9210i	−0.0781449	+	0.107557i
$586$		0			0
$587$	−6.98810	−	21.5072i	−0.0119048	−	0.0366391i	0.944928	−	0.327279i	$-0.106132\pi$
$587$	−6.98810	−	21.5072i	−0.0119048	−	0.0366391i	−0.956832	+	0.290640i	$0.906132\pi$
$588$		0			0
$589$	697.883	+	960.553i	1.18486	+	1.63082i
$590$		0			0
$591$	−613.009	−	199.179i	−1.03724	−	0.337020i
$592$		0			0
$593$			67.1719i			0.113275i	0.998395	+	0.0566374i	$0.0180379\pi$
$593$			67.1719i			0.113275i	−0.998395	+	0.0566374i	$0.981962\pi$
$594$		0			0
$595$	216.096			0.363187
$596$		0			0
$597$	51.7469	−	159.261i	0.0866782	−	0.266768i
$598$		0			0
$599$	−269.920	+	196.108i	−0.450617	+	0.327393i	−0.789839	−	0.613314i	$-0.789836\pi$
$599$	−269.920	+	196.108i	−0.450617	+	0.327393i	0.339222	+	0.940706i	$0.389836\pi$
$600$		0			0
$601$	299.557	−	97.3320i	0.498431	−	0.161950i	−0.0490035	−	0.998799i	$-0.515605\pi$
$601$	299.557	−	97.3320i	0.498431	−	0.161950i	0.547434	+	0.836849i	$0.315605\pi$
$602$		0			0
$603$	−318.964	−	231.741i	−0.528963	−	0.384314i
$604$		0			0
$605$	43.1547	−	589.797i	0.0713301	−	0.974872i
$606$		0			0
$607$	314.994	−	433.552i	0.518936	−	0.714254i	−0.466458	−	0.884543i	$-0.654470\pi$
$607$	314.994	−	433.552i	0.518936	−	0.714254i	0.985394	+	0.170289i	$0.0544701\pi$
$608$		0			0
$609$	−34.3137	−	105.607i	−0.0563443	−	0.173410i
$610$		0			0
$611$	−13.9076	−	19.1422i	−0.0227621	−	0.0313293i
$612$		0			0
$613$	929.858	+	302.129i	1.51690	+	0.492870i	0.944893	−	0.327380i	$-0.106166\pi$
$613$	929.858	+	302.129i	1.51690	+	0.492870i	0.572005	+	0.820250i	$0.306166\pi$
$614$		0			0
$615$		−	299.242i		−	0.486572i
$616$		0			0
$617$	75.3108			0.122060			0.0610298	−	0.998136i	$-0.480562\pi$
$617$	75.3108			0.122060			0.0610298	+	0.998136i	$0.480562\pi$
$618$		0			0
$619$	−238.140	+	732.920i	−0.384717	+	1.18404i	0.551968	+	0.833865i	$0.313877\pi$
$619$	−238.140	+	732.920i	−0.384717	+	1.18404i	−0.936685	+	0.350173i	$0.886123\pi$
$620$		0			0
$621$	−231.100	+	167.904i	−0.372142	+	0.270377i
$622$		0			0
$623$	91.5222	−	29.7374i	0.146906	−	0.0477325i
$624$		0			0
$625$	482.113	+	350.276i	0.771381	+	0.560441i
$626$		0			0
$627$	584.975	+	114.687i	0.932974	+	0.182914i
$628$		0			0
$629$	463.635	−	638.139i	0.737098	−	1.01453i
$630$		0			0
$631$	207.976	+	640.085i	0.329598	+	1.01440i	0.969322	+	0.245794i	$0.0790485\pi$
$631$	207.976	+	640.085i	0.329598	+	1.01440i	−0.639724	+	0.768604i	$0.720951\pi$
$632$		0			0
$633$	−461.971	−	635.848i	−0.729812	−	1.00450i
$634$		0			0
$635$	605.205	+	196.643i	0.953079	+	0.309674i
$636$		0			0
$637$		−	30.6122i		−	0.0480569i
$638$		0			0
$639$	−354.231			−0.554353
$640$		0			0
$641$	183.582	−	565.007i	0.286399	−	0.881447i	−0.699576	−	0.714558i	$-0.746628\pi$
$641$	183.582	−	565.007i	0.286399	−	0.881447i	0.985976	−	0.166889i	$-0.0533721\pi$
$642$		0			0
$643$	−50.0668	+	36.3757i	−0.0778644	+	0.0565718i	−0.626036	−	0.779794i	$-0.715324\pi$
$643$	−50.0668	+	36.3757i	−0.0778644	+	0.0565718i	0.548172	+	0.836366i	$0.315324\pi$
$644$		0			0
$645$	−389.104	+	126.428i	−0.603262	+	0.196012i
$646$		0			0
$647$	−124.697	−	90.5978i	−0.192731	−	0.140028i	0.487235	−	0.873271i	$-0.338006\pi$
$647$	−124.697	−	90.5978i	−0.192731	−	0.140028i	−0.679966	+	0.733243i	$0.738006\pi$
$648$		0			0
$649$	−781.906	+	726.785i	−1.20479	+	1.11985i
$650$		0			0
$651$	−182.665	+	251.417i	−0.280591	+	0.386201i
$652$		0			0
$653$	−333.054	−	1025.04i	−0.510037	−	1.56973i	−0.792134	−	0.610347i	$-0.791030\pi$
$653$	−333.054	−	1025.04i	−0.510037	−	1.56973i	0.282097	−	0.959386i	$-0.408970\pi$
$654$		0			0
$655$	−413.825	−	569.581i	−0.631794	−	0.869589i
$656$		0			0
$657$	120.076	+	39.0152i	0.182765	+	0.0593838i
$658$		0			0
$659$		−	861.714i		−	1.30761i	−0.756664	−	0.653804i	$-0.773172\pi$
$659$		−	861.714i		−	1.30761i	0.756664	−	0.653804i	$-0.226828\pi$
$660$		0			0
$661$	−972.434			−1.47116			−0.735578	−	0.677440i	$-0.763089\pi$
$661$	−972.434			−1.47116			−0.735578	+	0.677440i	$0.763089\pi$
$662$		0			0
$663$	52.2913	−	160.936i	0.0788708	−	0.242739i
$664$		0			0
$665$	244.844	−	177.889i	0.368186	−	0.267503i
$666$		0			0
$667$	168.275	−	54.6758i	0.252286	−	0.0819727i
$668$		0			0
$669$	209.774	+	152.410i	0.313564	+	0.227817i
$670$		0			0
$671$	100.656	−	180.899i	0.150008	−	0.269596i
$672$		0			0
$673$	584.230	−	804.123i	0.868098	−	1.19483i	−0.111480	−	0.993767i	$-0.535559\pi$
$673$	584.230	−	804.123i	0.868098	−	1.19483i	0.979577	−	0.201067i	$-0.0644410\pi$
$674$		0			0
$675$	10.0689	+	30.9889i	0.0149169	+	0.0459095i
$676$		0			0
$677$	473.932	+	652.311i	0.700047	+	0.963532i	0.999954	+	0.00956384i	$0.00304431\pi$
$677$	473.932	+	652.311i	0.700047	+	0.963532i	−0.299907	+	0.953968i	$0.596956\pi$
$678$		0			0
$679$	73.3457	+	23.8315i	0.108020	+	0.0350979i
$680$		0			0
$681$		−	1001.43i		−	1.47053i
$682$		0			0
$683$	994.372			1.45589			0.727945	−	0.685636i	$-0.240476\pi$
$683$	994.372			1.45589			0.727945	+	0.685636i	$0.240476\pi$
$684$		0			0
$685$	−87.0339	+	267.863i	−0.127057	+	0.391041i
$686$		0			0
$687$	248.015	−	180.194i	0.361012	−	0.262290i
$688$		0			0
$689$	300.459	−	97.6250i	0.436079	−	0.141691i
$690$		0			0
$691$	−742.752	−	539.641i	−1.07489	−	0.780957i	−0.0981092	−	0.995176i	$-0.531279\pi$
$691$	−742.752	−	539.641i	−1.07489	−	0.780957i	−0.976786	+	0.214219i	$0.931279\pi$
$692$		0			0
$693$	−12.7367	−	105.134i	−0.0183791	−	0.151708i
$694$		0			0
$695$	−614.820	+	846.227i	−0.884633	+	1.21759i
$696$		0			0
$697$	−136.559	−	420.285i	−0.195924	−	0.602991i
$698$		0			0
$699$	−35.2083	−	48.4601i	−0.0503696	−	0.0693278i
$700$		0			0
$701$	−509.889	−	165.673i	−0.727374	−	0.236338i	−0.0781569	−	0.996941i	$-0.524904\pi$
$701$	−509.889	−	165.673i	−0.727374	−	0.236338i	−0.649218	+	0.760603i	$0.724904\pi$
$702$		0			0
$703$		−	1104.69i		−	1.57140i
$704$		0			0
$705$	61.2271			0.0868469
$706$		0			0
$707$	−129.059	+	397.202i	−0.182544	+	0.561813i
$708$		0			0
$709$	−773.008	+	561.623i	−1.09028	+	0.792134i	−0.979446	−	0.201705i	$-0.935352\pi$
$709$	−773.008	+	561.623i	−1.09028	+	0.792134i	−0.110833	+	0.993839i	$0.535352\pi$
$710$		0			0
$711$	47.5571	−	15.4522i	0.0668876	−	0.0217331i
$712$		0			0
$713$	−400.610	−	291.060i	−0.561865	−	0.408219i
$714$		0			0
$715$	−213.240	+	99.0169i	−0.298237	+	0.138485i
$716$		0			0
$717$	123.201	−	169.572i	0.171829	−	0.236502i
$718$		0			0
$719$	−265.068	−	815.794i	−0.368662	−	1.13462i	−0.947656	−	0.319292i	$-0.896555\pi$
$719$	−265.068	−	815.794i	−0.368662	−	1.13462i	0.578995	−	0.815331i	$-0.303445\pi$
$720$		0			0
$721$	216.195	+	297.567i	0.299854	+	0.412714i
$722$		0			0
$723$	−441.652	−	143.502i	−0.610861	−	0.198481i
$724$		0			0
$725$		−	20.1823i		−	0.0278376i
$726$		0			0
$727$	96.9474			0.133353			0.0666764	−	0.997775i	$-0.478760\pi$
$727$	96.9474			0.133353			0.0666764	+	0.997775i	$0.478760\pi$
$728$		0			0
$729$	227.814	−	701.140i	0.312502	−	0.961783i
$730$		0			0
$731$	−488.802	+	355.135i	−0.668675	+	0.485821i
$732$		0			0
$733$	−444.336	+	144.374i	−0.606189	+	0.196963i	−0.595999	−	0.802985i	$-0.703244\pi$
$733$	−444.336	+	144.374i	−0.606189	+	0.196963i	−0.0101900	+	0.999948i	$0.503244\pi$
$734$		0			0
$735$	64.0858	+	46.5610i	0.0871915	+	0.0633483i
$736$		0			0
$737$	−501.945	−	1080.97i	−0.681066	−	1.46672i
$738$		0			0
$739$	−19.8893	+	27.3753i	−0.0269138	+	0.0370437i	−0.822262	−	0.569109i	$-0.807288\pi$
$739$	−19.8893	+	27.3753i	−0.0269138	+	0.0370437i	0.795348	+	0.606153i	$0.207288\pi$
$740$		0			0
$741$	−73.2342	−	225.392i	−0.0988315	−	0.304172i
$742$		0			0
$743$	383.745	+	528.179i	0.516480	+	0.710874i	0.984995	−	0.172582i	$-0.0552109\pi$
$743$	383.745	+	528.179i	0.516480	+	0.710874i	−0.468515	+	0.883455i	$0.655211\pi$
$744$		0			0
$745$	−134.623	−	43.7417i	−0.180702	−	0.0587136i
$746$		0			0
$747$		−	68.7830i		−	0.0920789i
$748$		0			0
$749$	−126.108			−0.168368
$750$		0			0
$751$	−45.9686	+	141.477i	−0.0612098	+	0.188385i	−0.976986	−	0.213305i	$-0.931577\pi$
$751$	−45.9686	+	141.477i	−0.0612098	+	0.188385i	0.915776	+	0.401690i	$0.131577\pi$
$752$		0			0
$753$	−525.360	+	381.696i	−0.697689	+	0.506901i
$754$		0			0
$755$	265.150	−	86.1524i	0.351192	−	0.114109i
$756$		0			0
$757$	157.188	+	114.204i	0.207646	+	0.150864i	0.686748	−	0.726895i	$-0.259038\pi$
$757$	157.188	+	114.204i	0.207646	+	0.150864i	−0.479102	+	0.877759i	$0.659038\pi$
$758$		0			0
$759$	−246.811	+	29.9006i	−0.325179	+	0.0393947i
$760$		0			0
$761$	−18.4869	+	25.4450i	−0.0242929	+	0.0334363i	−0.820991	−	0.570942i	$-0.806578\pi$
$761$	−18.4869	+	25.4450i	−0.0242929	+	0.0334363i	0.796698	+	0.604378i	$0.206578\pi$
$762$		0			0
$763$	160.090	+	492.705i	0.209816	+	0.645747i
$764$		0			0
$765$	−174.695	−	240.447i	−0.228360	−	0.314310i
$766$		0			0
$767$	403.632	+	131.148i	0.526248	+	0.170988i
$768$		0			0
$769$			600.383i			0.780732i	0.920660	+	0.390366i	$0.127651\pi$
$769$			600.383i			0.780732i	−0.920660	+	0.390366i	$0.872349\pi$
$770$		0			0
$771$	486.346			0.630799
$772$		0			0
$773$	193.809	−	596.483i	0.250723	−	0.771647i	−0.743919	−	0.668270i	$-0.767035\pi$
$773$	193.809	−	596.483i	0.250723	−	0.771647i	0.994642	−	0.103377i	$-0.0329649\pi$
$774$		0			0
$775$	−45.6961	+	33.2002i	−0.0589627	+	0.0428389i
$776$		0			0
$777$	274.992	−	89.3503i	0.353915	−	0.114994i
$778$		0			0
$779$	−500.702	−	363.781i	−0.642749	−	0.466985i
$780$		0			0
$781$	−935.720	−	520.653i	−1.19811	−	0.666649i
$782$		0			0
$783$	−311.790	+	429.142i	−0.398199	+	0.548074i
$784$		0			0
$785$	−57.3788	−	176.594i	−0.0730941	−	0.224960i
$786$		0			0
$787$	648.259	+	892.252i	0.823710	+	1.13374i	0.989061	+	0.147504i	$0.0471240\pi$
$787$	648.259	+	892.252i	0.823710	+	1.13374i	−0.165352	+	0.986235i	$0.552876\pi$
$788$		0			0
$789$	877.327	+	285.061i	1.11195	+	0.361294i
$790$		0			0
$791$			40.9239i			0.0517369i
$792$		0			0
$793$	−82.3019			−0.103786
$794$		0			0
$795$	−252.621	+	777.488i	−0.317763	+	0.977973i
$796$		0			0
$797$	−467.148	+	339.403i	−0.586133	+	0.425850i	−0.840930	−	0.541144i	$-0.817991\pi$
$797$	−467.148	+	339.403i	−0.586133	+	0.425850i	0.254797	+	0.966995i	$0.417991\pi$
$798$		0			0
$799$	85.9935	−	27.9410i	0.107626	−	0.0349699i
$800$		0			0
$801$	−107.076	−	77.7953i	−0.133678	−	0.0971228i
$802$		0			0
$803$	259.843	+	279.550i	0.323590	+	0.348132i
$804$		0			0
$805$	−74.1909	+	102.115i	−0.0921626	+	0.126851i
$806$		0			0
$807$	−207.224	−	637.771i	−0.256784	−	0.790298i
$808$		0			0
$809$	−506.291	−	696.850i	−0.625824	−	0.861372i	0.371937	−	0.928258i	$-0.378694\pi$
$809$	−506.291	−	696.850i	−0.625824	−	0.861372i	−0.997761	+	0.0668857i	$0.978694\pi$
$810$		0			0
$811$	−213.328	−	69.3146i	−0.263044	−	0.0854681i	0.174526	−	0.984653i	$-0.444161\pi$
$811$	−213.328	−	69.3146i	−0.263044	−	0.0854681i	−0.437570	+	0.899184i	$0.644161\pi$
$812$		0			0
$813$		−	598.823i		−	0.736559i
$814$		0			0
$815$	−734.096			−0.900732
$816$		0			0
$817$	−261.482	+	804.758i	−0.320051	+	0.985016i
$818$		0			0
$819$	−34.0618	+	24.7473i	−0.0415895	+	0.0302165i
$820$		0			0
$821$	−1310.83	+	425.916i	−1.59663	+	0.518777i	−0.966271	−	0.257527i	$-0.917093\pi$
$821$	−1310.83	+	425.916i	−1.59663	+	0.518777i	−0.630360	+	0.776303i	$0.717093\pi$
$822$		0			0
$823$	1072.57	+	779.268i	1.30324	+	0.946862i	0.999982	−	0.00604457i	$-0.00192406\pi$
$823$	1072.57	+	779.268i	1.30324	+	0.946862i	0.303263	+	0.952907i	$0.401924\pi$
$824$		0			0
$825$	−5.45596	+	27.8288i	−0.00661329	+	0.0337319i
$826$		0			0
$827$	239.766	−	330.009i	0.289922	−	0.399044i	−0.639067	−	0.769151i	$-0.720679\pi$
$827$	239.766	−	330.009i	0.289922	−	0.399044i	0.928989	+	0.370108i	$0.120679\pi$
$828$		0			0
$829$	−374.711	−	1153.24i	−0.452004	−	1.39113i	−0.874617	−	0.484815i	$-0.838887\pi$
$829$	−374.711	−	1153.24i	−0.452004	−	1.39113i	0.422613	−	0.906310i	$-0.361113\pi$
$830$		0			0
$831$	−212.875	−	292.998i	−0.256168	−	0.352584i
$832$		0			0
$833$	111.257	+	36.1495i	0.133561	+	0.0433967i
$834$		0			0
$835$		−	377.400i		−	0.451976i
$836$		0			0
$837$	1484.55			1.77366
$838$		0			0
$839$	−136.294	+	419.470i	−0.162448	+	0.499964i	−0.998839	−	0.0481690i	$-0.984661\pi$
$839$	−136.294	+	419.470i	−0.162448	+	0.499964i	0.836391	+	0.548133i	$0.184661\pi$
$840$		0			0
$841$	−414.574	+	301.205i	−0.492953	+	0.358151i
$842$		0			0
$843$	−814.934	+	264.788i	−0.966707	+	0.314102i
$844$		0			0
$845$	−592.604	−	430.552i	−0.701307	−	0.509529i
$846$		0			0
$847$	120.882	−	296.437i	0.142718	−	0.349984i
$848$		0			0
$849$	373.821	−	514.520i	0.440307	−	0.606031i
$850$		0			0
$851$	142.372	+	438.175i	0.167299	+	0.514895i
$852$		0			0
$853$	158.709	+	218.445i	0.186060	+	0.256090i	0.891850	−	0.452331i	$-0.149408\pi$
$853$	158.709	+	218.445i	0.186060	+	0.256090i	−0.705790	+	0.708422i	$0.749408\pi$
$854$		0			0
$855$	−395.870	−	128.626i	−0.463006	−	0.150440i
$856$		0			0
$857$		−	722.386i		−	0.842924i	−0.906846	−	0.421462i	$-0.861517\pi$
$857$		−	722.386i		−	0.842924i	0.906846	−	0.421462i	$-0.138483\pi$
$858$		0			0
$859$	1387.36			1.61509			0.807546	−	0.589805i	$-0.200795\pi$
$859$	1387.36			1.61509			0.807546	+	0.589805i	$0.200795\pi$
$860$		0			0
$861$	50.0583	−	154.064i	0.0581398	−	0.178936i
$862$		0			0
$863$	−369.086	+	268.157i	−0.427678	+	0.310726i	−0.780720	−	0.624881i	$-0.785147\pi$
$863$	−369.086	+	268.157i	−0.427678	+	0.310726i	0.353042	+	0.935608i	$0.385147\pi$
$864$		0			0
$865$	−646.851	+	210.175i	−0.747805	+	0.242976i
$866$		0			0
$867$	−18.2036	−	13.2257i	−0.0209960	−	0.0152545i
$868$		0			0
$869$	148.336	+	29.0820i	0.170698	+	0.0334660i
$870$		0			0
$871$	−278.507	+	383.332i	−0.319755	+	0.440106i
$872$		0			0
$873$	−32.7767	−	100.876i	−0.0375449	−	0.115551i
$874$		0			0
$875$	198.476	+	273.179i	0.226830	+	0.312205i
$876$		0			0
$877$	1245.80	+	404.785i	1.42053	+	0.461557i	0.915769	−	0.401705i	$-0.131582\pi$
$877$	1245.80	+	404.785i	1.42053	+	0.461557i	0.504757	+	0.863262i	$0.331582\pi$
$878$		0			0
$879$		−	29.3524i		−	0.0333930i
$880$		0			0
$881$	−651.039			−0.738977			−0.369488	−	0.929235i	$-0.620467\pi$
$881$	−651.039			−0.738977			−0.369488	+	0.929235i	$0.620467\pi$
$882$		0			0
$883$	218.622	−	672.850i	0.247590	−	0.762004i	−0.747609	−	0.664139i	$-0.768798\pi$
$883$	218.622	−	672.850i	0.247590	−	0.762004i	0.995200	−	0.0978657i	$-0.0312016\pi$
$884$		0			0
$885$	−888.477	+	645.516i	−1.00393	+	0.729397i
$886$		0			0
$887$	−1052.16	+	341.867i	−1.18620	+	0.385420i	−0.834667	−	0.550756i	$-0.814340\pi$
$887$	−1052.16	+	341.867i	−1.18620	+	0.385420i	−0.351533	+	0.936175i	$0.614340\pi$
$888$		0			0
$889$	278.693	+	202.482i	0.313490	+	0.227764i
$890$		0			0
$891$	282.068	−	262.183i	0.316574	−	0.294257i
$892$		0			0
$893$	74.4324	−	102.447i	0.0833509	−	0.114723i
$894$		0			0
$895$	−47.1628	−	145.152i	−0.0526959	−	0.162181i
$896$		0			0
$897$	58.0966	+	79.9630i	0.0647676	+	0.0891450i
$898$		0			0
$899$	−874.523	−	284.150i	−0.972773	−	0.316073i
$900$		0			0
$901$			1207.27i			1.33992i
$902$		0			0
$903$	−221.478			−0.245270
$904$		0			0
$905$	193.481	−	595.474i	0.213791	−	0.657982i
$906$		0			0
$907$	−750.952	+	545.598i	−0.827951	+	0.601542i	−0.918979	−	0.394307i	$-0.870985\pi$
$907$	−750.952	+	545.598i	−0.827951	+	0.601542i	0.0910277	+	0.995848i	$0.470985\pi$
$908$		0			0
$909$	546.294	−	177.502i	0.600984	−	0.195271i
$910$		0			0
$911$	−441.815	−	320.997i	−0.484978	−	0.352357i	0.318272	−	0.948000i	$-0.396898\pi$
$911$	−441.815	−	320.997i	−0.484978	−	0.352357i	−0.803250	+	0.595642i	$0.796898\pi$
$912$		0			0
$913$	101.098	−	181.694i	0.110731	−	0.199007i
$914$		0			0
$915$	125.181	−	172.297i	0.136810	−	0.188302i
$916$		0			0
$917$	−117.775	−	362.474i	−0.128435	−	0.395282i
$918$		0			0
$919$	278.797	+	383.731i	0.303370	+	0.417552i	0.933299	−	0.359100i	$-0.116916\pi$
$919$	278.797	+	383.731i	0.303370	+	0.417552i	−0.629930	+	0.776652i	$0.716916\pi$
$920$		0			0
$921$	−852.692	−	277.056i	−0.925832	−	0.300821i
$922$		0			0
$923$			425.716i			0.461231i
$924$		0			0
$925$	52.5532			0.0568142
$926$		0			0
$927$	156.324	−	481.114i	0.168634	−	0.519001i
$928$		0			0
$929$	739.043	−	536.946i	0.795525	−	0.577983i	−0.114073	−	0.993472i	$-0.536390\pi$
$929$	739.043	−	536.946i	0.795525	−	0.577983i	0.909598	+	0.415490i	$0.136390\pi$
$930$		0			0
$931$	155.815	−	50.6274i	0.167363	−	0.0543796i
$932$		0			0
$933$	301.697	+	219.196i	0.323362	+	0.234936i
$934$		0			0
$935$	−108.055	−	891.923i	−0.115566	−	0.953928i
$936$		0			0
$937$	672.291	−	925.329i	0.717493	−	0.987544i	−0.282110	−	0.959382i	$-0.591034\pi$
$937$	672.291	−	925.329i	0.717493	−	0.987544i	0.999603	−	0.0281624i	$-0.00896555\pi$
$938$		0			0
$939$	−78.6113	−	241.941i	−0.0837181	−	0.257658i
$940$		0			0
$941$	255.681	+	351.914i	0.271712	+	0.373979i	0.922967	−	0.384880i	$-0.125757\pi$
$941$	255.681	+	351.914i	0.271712	+	0.373979i	−0.651255	+	0.758859i	$0.725757\pi$
$942$		0			0
$943$	245.487	+	79.7635i	0.260325	+	0.0845848i
$944$		0			0
$945$		−	378.410i		−	0.400434i
$946$		0			0
$947$	453.839			0.479238			0.239619	−	0.970867i	$-0.422977\pi$
$947$	453.839			0.479238			0.239619	+	0.970867i	$0.422977\pi$
$948$		0			0
$949$	46.8885	−	144.308i	0.0494083	−	0.152063i
$950$		0			0
$951$	201.248	−	146.215i	0.211617	−	0.153749i
$952$		0			0
$953$	620.164	−	201.504i	0.650749	−	0.211441i	0.0350049	−	0.999387i	$-0.488855\pi$
$953$	620.164	−	201.504i	0.650749	−	0.211441i	0.615745	+	0.787946i	$0.288855\pi$
$954$		0			0
$955$	−1066.74	−	775.033i	−1.11701	−	0.811553i
$956$		0			0
$957$	−418.726	+	194.434i	−0.437540	+	0.203170i
$958$		0			0
$959$	−89.6184	+	123.349i	−0.0934498	+	0.128623i
$960$		0			0
$961$	498.276	+	1533.54i	0.518497	+	1.59577i
$962$		0			0
$963$	101.947	+	140.318i	0.105864	+	0.145710i
$964$		0			0
$965$	1645.79	+	534.749i	1.70548	+	0.554145i
$966$		0			0
$967$			302.918i			0.313255i	0.987658	+	0.156628i	$0.0500622\pi$
$967$			302.918i			0.313255i	−0.987658	+	0.156628i	$0.949938\pi$
$968$		0			0
$969$	905.641			0.934614
$970$		0			0
$971$	438.040	−	1348.15i	0.451123	−	1.38841i	−0.424505	−	0.905426i	$-0.639552\pi$
$971$	438.040	−	1348.15i	0.451123	−	1.38841i	0.875628	−	0.482987i	$-0.160448\pi$
$972$		0			0
$973$	−458.098	+	332.828i	−0.470810	+	0.342064i
$974$		0			0
$975$	10.7225	−	3.48395i	0.0109974	−	0.00357328i
$976$		0			0
$977$	1423.03	+	1033.89i	1.45653	+	1.05823i	0.984249	+	0.176786i	$0.0565700\pi$
$977$	1423.03	+	1033.89i	1.45653	+	1.05823i	0.472283	+	0.881447i	$0.343430\pi$
$978$		0			0
$979$	−168.503	−	362.882i	−0.172117	−	0.370666i
$980$		0			0
$981$	418.807	−	576.439i	0.426919	−	0.587603i
$982$		0			0
$983$	208.350	+	641.235i	0.211953	+	0.652324i	0.999356	+	0.0358855i	$0.0114251\pi$
$983$	208.350	+	641.235i	0.211953	+	0.652324i	−0.787403	+	0.616439i	$0.788575\pi$
$984$		0			0
$985$	799.700	+	1100.69i	0.811878	+	1.11745i
$986$		0			0
$987$	31.5226	+	10.2423i	0.0319378	+	0.0103772i
$988$		0			0
$989$		−	352.906i		−	0.356831i
$990$		0			0
$991$	1579.79			1.59414			0.797071	−	0.603886i	$-0.206382\pi$
$991$	1579.79			1.59414			0.797071	+	0.603886i	$0.206382\pi$
$992$		0			0
$993$	−184.443	+	567.656i	−0.185743	+	0.571658i
$994$		0			0
$995$	−285.961	+	207.763i	−0.287398	+	0.208807i
$996$		0			0
$997$	1731.01	−	562.439i	1.73622	−	0.564131i	0.741893	−	0.670519i	$-0.233928\pi$
$997$	1731.01	−	562.439i	1.73622	−	0.564131i	0.994325	+	0.106387i	$0.0339283\pi$
$998$		0			0
$999$	−1117.45	−	811.878i	−1.11857	−	0.812691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.29.9	✓	48
11.8	odd	10	inner	308.3.r.a.85.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.29.9	✓	48	1.1	even	1	trivial
308.3.r.a.85.9	yes	48	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.715503 - 2.20209i) q^{3} +(-3.95398 + 2.87274i) q^{5} +(-2.51626 + 0.817582i) q^{7} +(2.94389 + 2.13886i) q^{9} +O(q^{10})\)	\(q+(0.715503 - 2.20209i) q^{3} +(-3.95398 + 2.87274i) q^{5} +(-2.51626 + 0.817582i) q^{7} +(2.94389 + 2.13886i) q^{9} +(4.63272 + 9.97687i) q^{11} +(2.57049 - 3.53797i) q^{13} +(3.49694 + 10.7625i) q^{15} +(9.82291 + 13.5201i) q^{17} +(22.2593 + 7.23249i) q^{19} +6.12601i q^{21} -9.76126 q^{23} +(-0.344069 + 1.05894i) q^{25} +(23.6752 - 17.2011i) q^{27} +(-17.2390 + 5.60130i) q^{29} +(41.0408 + 29.8179i) q^{31} +(25.2847 - 3.06319i) q^{33} +(7.60054 - 10.4612i) q^{35} +(-14.5854 - 44.8892i) q^{37} +(-5.95175 - 8.19188i) q^{39} +(-25.1491 - 8.17144i) q^{41} +36.1538i q^{43} -17.7845 q^{45} +(1.67194 - 5.14569i) q^{47} +(5.66312 - 4.11450i) q^{49} +(36.8008 - 11.9573i) q^{51} +(58.4439 + 42.4620i) q^{53} +(-46.9786 - 26.1398i) q^{55} +(31.8532 - 43.8422i) q^{57} +(29.9892 + 92.2972i) q^{59} +(-11.0620 - 15.2255i) q^{61} +(-9.15629 - 2.97506i) q^{63} +21.3734i q^{65} -108.348 q^{67} +(-6.98421 + 21.4952i) q^{69} +(-78.7555 + 57.2192i) q^{71} +(32.9984 - 10.7218i) q^{73} +(2.08569 + 1.51534i) q^{75} +(-19.8140 - 21.3168i) q^{77} +(8.07725 - 11.1174i) q^{79} +(-10.8184 - 33.2957i) q^{81} +(-11.1106 - 15.2924i) q^{83} +(-77.6792 - 25.2395i) q^{85} +41.9697i q^{87} -36.3723 q^{89} +(-3.57543 + 11.0040i) q^{91} +(95.0266 - 69.0408i) q^{93} +(-108.790 + 35.3480i) q^{95} +(-23.5818 - 17.1332i) q^{97} +(-7.70093 + 39.2796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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