LMFDB - Embedded newform 409.3.p.a.21.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,3,Mod(21,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(408)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	409.p (of order $408$, degree $128$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.1444428123$
Analytic rank:	$0$
Dimension:	$8576$
Relative dimension:	$67$ over $\Q(\zeta_{408})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{408}]$

Embedding invariants

Embedding label			21.8
Character	$\chi$	$=$	409.21
Dual form			409.3.p.a.39.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.68542 - 1.96373i) q^{2} +(4.21566 + 3.28667i) q^{3} +(2.14260 + 6.73512i) q^{4} +(1.36686 + 0.255510i) q^{5} +(-4.86665 - 17.1045i) q^{6} +(0.936382 - 0.718511i) q^{7} +(3.24329 - 9.67665i) q^{8} +(4.77435 + 18.9828i) q^{9} +(-3.16882 - 3.37029i) q^{10} +(1.43166 + 12.3402i) q^{11} +(-13.1036 + 35.4349i) q^{12} +(-14.2247 + 11.2672i) q^{13} +(-3.92554 + 0.0906959i) q^{14} +(4.92242 + 5.56954i) q^{15} +(-4.63738 + 3.28273i) q^{16} +(6.14755 - 9.27758i) q^{17} +(24.4560 - 60.3521i) q^{18} +(0.687461 - 0.656412i) q^{19} +(1.20773 + 9.75339i) q^{20} +(6.30897 + 0.0485799i) q^{21} +(20.3883 - 35.9500i) q^{22} +(1.24175 + 6.11946i) q^{23} +(45.4765 - 30.1338i) q^{24} +(-21.5088 - 8.33255i) q^{25} +(60.3250 - 2.32365i) q^{26} +(-22.8307 + 51.7065i) q^{27} +(6.84554 + 4.76716i) q^{28} +(-10.0799 + 12.3308i) q^{29} +(-2.28164 - 24.6229i) q^{30} +(16.6044 + 6.87775i) q^{31} +(-21.9183 - 0.337568i) q^{32} +(-34.5228 + 56.7275i) q^{33} +(-34.7274 + 12.8420i) q^{34} +(1.46349 - 0.742847i) q^{35} +(-117.622 + 72.8282i) q^{36} +(-26.8633 - 24.8706i) q^{37} +(-3.13514 + 0.412749i) q^{38} +(-96.9979 + 0.746897i) q^{39} +(6.90559 - 12.3979i) q^{40} +(12.2115 - 12.9879i) q^{41} +(-16.8468 - 12.5196i) q^{42} +(27.3181 - 28.6103i) q^{43} +(-80.0453 + 36.0825i) q^{44} +(1.67558 + 27.1666i) q^{45} +(8.68238 - 18.8717i) q^{46} +(-14.4699 + 63.7199i) q^{47} +(-30.3388 - 1.40265i) q^{48} +(-12.3216 + 45.9848i) q^{49} +(41.3971 + 64.6139i) q^{50} +(56.4083 - 18.9061i) q^{51} +(-106.364 - 71.6638i) q^{52} +(-5.57063 + 9.64861i) q^{53} +(162.848 - 94.0202i) q^{54} +(-1.19617 + 17.2331i) q^{55} +(-3.91583 - 11.3914i) q^{56} +(5.05551 - 0.507752i) q^{57} +(51.2832 - 13.3189i) q^{58} +(-9.77256 + 27.0658i) q^{59} +(-26.9648 + 45.0864i) q^{60} +(94.1156 - 55.3083i) q^{61} +(-31.0835 - 51.0762i) q^{62} +(18.1099 + 14.3447i) q^{63} +(76.3332 + 57.6442i) q^{64} +(-22.3220 + 11.7661i) q^{65} +(204.106 - 84.5433i) q^{66} +(4.50024 - 1.78337i) q^{67} +(75.6573 + 21.5264i) q^{68} +(-14.8778 + 29.8787i) q^{69} +(-5.38882 - 0.879045i) q^{70} +(48.2126 + 56.2740i) q^{71} +(199.174 + 15.3668i) q^{72} +(-57.1959 - 82.1321i) q^{73} +(23.2999 + 119.540i) q^{74} +(-63.2874 - 105.819i) q^{75} +(5.89397 + 3.22371i) q^{76} +(10.2072 + 10.5265i) q^{77} +(261.947 + 188.472i) q^{78} +(7.05220 + 33.4311i) q^{79} +(-7.17740 + 3.30213i) q^{80} +(-110.984 + 59.5974i) q^{81} +(-58.2979 + 10.8978i) q^{82} +(53.9951 + 108.437i) q^{83} +(13.1904 + 42.5958i) q^{84} +(10.7733 - 11.1104i) q^{85} +(-129.543 + 23.1850i) q^{86} +(-83.0207 + 18.8529i) q^{87} +(124.055 + 26.1691i) q^{88} +(52.5565 - 47.9116i) q^{89} +(48.8483 - 76.2440i) q^{90} +(-5.22412 + 20.7710i) q^{91} +(-38.5547 + 21.4748i) q^{92} +(47.3934 + 83.5673i) q^{93} +(163.987 - 142.699i) q^{94} +(1.10738 - 0.721568i) q^{95} +(-91.2906 - 73.4612i) q^{96} +(89.0056 + 29.0713i) q^{97} +(123.390 - 99.2919i) q^{98} +(-227.416 + 86.0934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) $ 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{408}\right)$

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 $

$2$	−2.68542	−	1.96373i	−1.34271	−	0.981867i	−0.999085	−	0.0427593i	$-0.986385\pi$
$2$	−2.68542	−	1.96373i	−1.34271	−	0.981867i	−0.343623	−	0.939108i	$-0.611654\pi$
$3$	4.21566	+	3.28667i	1.40522	+	1.09556i	0.981863	+	0.189592i	$0.0607167\pi$
$3$	4.21566	+	3.28667i	1.40522	+	1.09556i	0.423356	+	0.905963i	$0.360852\pi$
$4$	2.14260	+	6.73512i	0.535649	+	1.68378i
$5$	1.36686	+	0.255510i	0.273371	+	0.0511019i	0.318650	−	0.947872i	$-0.396771\pi$
$5$	1.36686	+	0.255510i	0.273371	+	0.0511019i	−0.0452788	+	0.998974i	$0.514418\pi$
$6$	−4.86665	−	17.1045i	−0.811108	−	2.85075i
$7$	0.936382	−	0.718511i	0.133769	−	0.102644i	−0.539710	−	0.841851i	$-0.681466\pi$
$7$	0.936382	−	0.718511i	0.133769	−	0.102644i	0.673479	+	0.739207i	$0.264799\pi$
$8$	3.24329	−	9.67665i	0.405411	−	1.20958i
$9$	4.77435	+	18.9828i	0.530484	+	2.10919i
$10$	−3.16882	−	3.37029i	−0.316882	−	0.337029i
$11$	1.43166	+	12.3402i	0.130151	+	1.12184i	0.884886	+	0.465807i	$0.154236\pi$
$11$	1.43166	+	12.3402i	0.130151	+	1.12184i	−0.754735	+	0.656030i	$0.772235\pi$
$12$	−13.1036	+	35.4349i	−1.09197	+	2.95291i
$13$	−14.2247	+	11.2672i	−1.09421	+	0.866709i	−0.991770	−	0.128031i	$-0.959134\pi$
$13$	−14.2247	+	11.2672i	−1.09421	+	0.866709i	−0.102436	+	0.994740i	$0.532664\pi$
$14$	−3.92554	+	0.0906959i	−0.280396	+	0.00647828i
$15$	4.92242	+	5.56954i	0.328161	+	0.371303i
$16$	−4.63738	+	3.28273i	−0.289836	+	0.205171i
$17$	6.14755	−	9.27758i	0.361620	−	0.545740i	−0.606867	−	0.794804i	$-0.707574\pi$
$17$	6.14755	−	9.27758i	0.361620	−	0.545740i	0.968487	+	0.249064i	$0.0801229\pi$
$18$	24.4560	−	60.3521i	1.35866	−	3.35290i
$19$	0.687461	−	0.656412i	0.0361822	−	0.0345480i	−0.672278	−	0.740299i	$-0.734684\pi$
$19$	0.687461	−	0.656412i	0.0361822	−	0.0345480i	0.708460	+	0.705751i	$0.249390\pi$
$20$	1.20773	+	9.75339i	0.0603866	+	0.487670i
$21$	6.30897	+	0.0485799i	0.300427	+	0.00231333i
$22$	20.3883	−	35.9500i	0.926740	−	1.63409i
$23$	1.24175	+	6.11946i	0.0539890	+	0.266063i	0.997950	−	0.0639925i	$-0.0203834\pi$
$23$	1.24175	+	6.11946i	0.0539890	+	0.266063i	−0.943961	+	0.330056i	$0.892932\pi$
$24$	45.4765	−	30.1338i	1.89486	−	1.25558i
$25$	−21.5088	−	8.33255i	−0.860352	−	0.333302i
$26$	60.3250	−	2.32365i	2.32019	−	0.0893713i
$27$	−22.8307	+	51.7065i	−0.845580	+	1.91506i
$28$	6.84554	+	4.76716i	0.244484	+	0.170256i
$29$	−10.0799	+	12.3308i	−0.347584	+	0.425199i	−0.918261	−	0.395976i	$-0.870406\pi$
$29$	−10.0799	+	12.3308i	−0.347584	+	0.425199i	0.570677	+	0.821175i	$0.306681\pi$
$30$	−2.28164	−	24.6229i	−0.0760548	−	0.820762i
$31$	16.6044	+	6.87775i	0.535625	+	0.221863i	0.634065	−	0.773280i	$-0.281385\pi$
$31$	16.6044	+	6.87775i	0.535625	+	0.221863i	−0.0984400	+	0.995143i	$0.531385\pi$
$32$	−21.9183	−	0.337568i	−0.684947	−	0.0105490i
$33$	−34.5228	+	56.7275i	−1.04614	+	1.71901i
$34$	−34.7274	+	12.8420i	−1.02139	+	0.377706i
$35$	1.46349	−	0.742847i	0.0418139	−	0.0212242i
$36$	−117.622	+	72.8282i	−3.26727	+	2.02301i
$37$	−26.8633	−	24.8706i	−0.726035	−	0.672177i	0.227391	−	0.973803i	$-0.426980\pi$
$37$	−26.8633	−	24.8706i	−0.726035	−	0.672177i	−0.953426	+	0.301626i	$0.902471\pi$
$38$	−3.13514	+	0.412749i	−0.0825036	+	0.0108618i
$39$	−96.9979	+	0.746897i	−2.48713	+	0.0191512i
$40$	6.90559	−	12.3979i	0.172640	−	0.309948i
$41$	12.2115	−	12.9879i	0.297842	−	0.316778i	−0.562200	−	0.827001i	$-0.690045\pi$
$41$	12.2115	−	12.9879i	0.297842	−	0.316778i	0.860042	+	0.510223i	$0.170437\pi$
$42$	−16.8468	−	12.5196i	−0.401115	−	0.298086i
$43$	27.3181	−	28.6103i	0.635304	−	0.665355i	−0.324545	−	0.945870i	$-0.605211\pi$
$43$	27.3181	−	28.6103i	0.635304	−	0.665355i	0.959850	+	0.280515i	$0.0905053\pi$
$44$	−80.0453	+	36.0825i	−1.81921	+	0.820056i
$45$	1.67558	+	27.1666i	0.0372351	+	0.603702i
$46$	8.68238	−	18.8717i	0.188747	−	0.410255i
$47$	−14.4699	+	63.7199i	−0.307871	+	1.35574i	0.547100	+	0.837067i	$0.315732\pi$
$47$	−14.4699	+	63.7199i	−0.307871	+	1.35574i	−0.854971	+	0.518676i	$0.826425\pi$
$48$	−30.3388	−	1.40265i	−0.632059	−	0.0292219i
$49$	−12.3216	+	45.9848i	−0.251461	+	0.938465i
$50$	41.3971	+	64.6139i	0.827943	+	1.29228i
$51$	56.4083	−	18.9061i	1.10604	−	0.370709i
$52$	−106.364	−	71.6638i	−2.04546	−	1.37815i
$53$	−5.57063	+	9.64861i	−0.105106	+	0.182049i	−0.913782	−	0.406206i	$-0.866852\pi$
$53$	−5.57063	+	9.64861i	−0.105106	+	0.182049i	0.808675	+	0.588255i	$0.200185\pi$
$54$	162.848	−	94.0202i	3.01570	−	1.74111i
$55$	−1.19617	+	17.2331i	−0.0217485	+	0.313329i
$56$	−3.91583	−	11.3914i	−0.0699255	−	0.203418i
$57$	5.05551	−	0.507752i	0.0886931	−	0.00890793i
$58$	51.2832	−	13.3189i	0.884193	−	0.229636i
$59$	−9.77256	+	27.0658i	−0.165637	+	0.458743i	−0.994989	−	0.0999827i	$-0.968121\pi$
$59$	−9.77256	+	27.0658i	−0.165637	+	0.458743i	0.829353	+	0.558726i	$0.188709\pi$
$60$	−26.9648	+	45.0864i	−0.449413	+	0.751439i
$61$	94.1156	−	55.3083i	1.54288	−	0.906693i	0.545221	−	0.838293i	$-0.316446\pi$
$61$	94.1156	−	55.3083i	1.54288	−	0.906693i	0.997658	−	0.0684001i	$-0.0217894\pi$
$62$	−31.0835	−	51.0762i	−0.501348	−	0.823809i
$63$	18.1099	+	14.3447i	0.287459	+	0.227693i
$64$	76.3332	+	57.6442i	1.19271	+	0.900690i
$65$	−22.3220	+	11.7661i	−0.343415	+	0.181017i
$66$	204.106	−	84.5433i	3.09251	−	1.28096i
$67$	4.50024	−	1.78337i	0.0671678	−	0.0266175i	−0.334587	−	0.942365i	$-0.608597\pi$
$67$	4.50024	−	1.78337i	0.0671678	−	0.0266175i	0.401754	+	0.915747i	$0.368401\pi$
$68$	75.6573	+	21.5264i	1.11261	+	0.316564i
$69$	−14.8778	+	29.8787i	−0.215621	+	0.433025i
$70$	−5.38882	−	0.879045i	−0.0769832	−	0.0125578i
$71$	48.2126	+	56.2740i	0.679051	+	0.792592i	0.987326	−	0.158706i	$-0.0507320\pi$
$71$	48.2126	+	56.2740i	0.679051	+	0.792592i	−0.308275	+	0.951297i	$0.599752\pi$
$72$	199.174	+	15.3668i	2.76631	+	0.213427i
$73$	−57.1959	−	82.1321i	−0.783506	−	1.12510i	−0.989213	−	0.146484i	$-0.953204\pi$
$73$	−57.1959	−	82.1321i	−0.783506	−	1.12510i	0.205707	−	0.978614i	$-0.434051\pi$
$74$	23.2999	+	119.540i	0.314864	+	1.61541i
$75$	−63.2874	−	105.819i	−0.843832	−	1.41093i
$76$	5.89397	+	3.22371i	0.0775522	+	0.0424172i
$77$	10.2072	+	10.5265i	0.132560	+	0.136708i
$78$	261.947	+	188.472i	3.35829	+	2.41631i
$79$	7.05220	+	33.4311i	0.0892684	+	0.423178i	0.999949	+	0.0100678i	$0.00320474\pi$
$79$	7.05220	+	33.4311i	0.0892684	+	0.423178i	−0.910681	+	0.413110i	$0.864442\pi$
$80$	−7.17740	+	3.30213i	−0.0897175	+	0.0412766i
$81$	−110.984	+	59.5974i	−1.37018	+	0.735770i
$82$	−58.2979	+	10.8978i	−0.710949	+	0.132899i
$83$	53.9951	+	108.437i	0.650543	+	1.30647i	0.937320	+	0.348470i	$0.113299\pi$
$83$	53.9951	+	108.437i	0.650543	+	1.30647i	−0.286777	+	0.957997i	$0.592584\pi$
$84$	13.1904	+	42.5958i	0.157028	+	0.507092i
$85$	10.7733	−	11.1104i	0.126745	−	0.130710i
$86$	−129.543	+	23.1850i	−1.50632	+	0.269593i
$87$	−83.0207	+	18.8529i	−0.954261	+	0.216700i
$88$	124.055	+	26.1691i	1.40972	+	0.297377i
$89$	52.5565	−	47.9116i	0.590523	−	0.538332i	−0.322327	−	0.946628i	$-0.604465\pi$
$89$	52.5565	−	47.9116i	0.590523	−	0.538332i	0.912850	+	0.408296i	$0.133877\pi$
$90$	48.8483	−	76.2440i	0.542759	−	0.847155i
$91$	−5.22412	+	20.7710i	−0.0574079	+	0.228253i
$92$	−38.5547	+	21.4748i	−0.419073	+	0.233422i
$93$	47.3934	+	83.5673i	0.509607	+	0.898573i
$94$	163.987	−	142.699i	1.74454	−	1.51808i
$95$	1.10738	−	0.721568i	0.0116566	−	0.00759545i
$96$	−91.2906	−	73.4612i	−0.950943	−	0.765221i
$97$	89.0056	+	29.0713i	0.917583	+	0.299704i	0.730716	−	0.682681i	$-0.239186\pi$
$97$	89.0056	+	29.0713i	0.917583	+	0.299704i	0.186867	+	0.982385i	$0.440167\pi$
$98$	123.390	−	99.2919i	1.25909	−	1.01318i
$99$	−227.416	+	86.0934i	−2.29713	+	0.869630i
$100$	10.0361	−	162.718i	0.100361	−	1.62718i
$101$	34.7590	+	18.6652i	0.344148	+	0.184804i	0.636056	−	0.771643i	$-0.280565\pi$
$101$	34.7590	+	18.6652i	0.344148	+	0.184804i	−0.291908	+	0.956446i	$0.594290\pi$
$102$	−188.606	−	60.0000i	−1.84908	−	0.588235i
$103$	42.0211	−	28.7851i	0.407972	−	0.279467i	−0.343603	−	0.939115i	$-0.611648\pi$
$103$	42.0211	−	28.7851i	0.407972	−	0.279467i	0.751575	+	0.659648i	$0.229295\pi$
$104$	62.8942	+	174.190i	0.604752	+	1.67490i
$105$	8.61104	+	1.67841i	0.0820099	+	0.0159848i
$106$	33.9068	−	14.9713i	0.319875	−	0.141239i
$107$	40.9606	+	83.8724i	0.382810	+	0.783855i	0.999996	−	0.00296268i	$-0.000943050\pi$
$107$	40.9606	+	83.8724i	0.382810	+	0.783855i	−0.617186	+	0.786817i	$0.711727\pi$
$108$	−397.166	−	42.9811i	−3.67747	−	0.397973i
$109$	−128.478	−	113.550i	−1.17869	−	1.04174i	−0.998308	−	0.0581456i	$-0.981481\pi$
$109$	−128.478	−	113.550i	−1.17869	−	1.04174i	−0.180385	−	0.983596i	$-0.557734\pi$
$110$	37.0534	−	43.9291i	0.336849	−	0.399355i
$111$	−31.5052	−	193.136i	−0.283830	−	1.73997i
$112$	−1.98368	+	6.40590i	−0.0177114	+	0.0571955i
$113$	88.4657	+	161.744i	0.782882	+	1.43136i	0.898919	+	0.438114i	$0.144353\pi$
$113$	88.4657	+	161.744i	0.782882	+	1.43136i	−0.116037	+	0.993245i	$0.537019\pi$
$114$	−14.5732	−	8.56415i	−0.127835	−	0.0751241i
$115$	0.133708	+	8.68170i	0.00116268	+	0.0754930i
$116$	−104.646	−	41.4697i	−0.902124	−	0.357498i
$117$	−281.796	−	216.230i	−2.40852	−	1.84812i
$118$	79.3935	−	53.4923i	0.672826	−	0.453324i
$119$	−0.909592	−	13.1044i	−0.00764363	−	0.110121i
$120$	69.8594	−	29.5689i	0.582161	−	0.246408i
$121$	−32.4450	+	7.63100i	−0.268141	+	0.0630661i
$122$	−361.350	−	36.2924i	−2.96189	−	0.297478i
$123$	94.1666	−	14.6174i	0.765582	−	0.118840i
$124$	−10.7460	+	126.569i	−0.0866617	+	1.02071i
$125$	−56.8267	−	35.1856i	−0.454614	−	0.281485i
$126$	−20.4636	−	74.0845i	−0.162409	−	0.587972i
$127$	−2.25463	−	41.7895i	−0.0177530	−	0.329051i	−0.993777	−	0.111388i	$-0.964470\pi$
$127$	−2.25463	−	41.7895i	−0.0177530	−	0.329051i	0.976024	−	0.217663i	$-0.0698434\pi$
$128$	−66.4970	−	220.740i	−0.519507	−	1.72453i
$129$	209.196	−	30.8256i	1.62168	−	0.238958i
$130$	83.0493	+	12.2375i	0.638841	+	0.0941348i
$131$	−43.8799	−	13.2186i	−0.334961	−	0.100906i	0.116515	−	0.993189i	$-0.462828\pi$
$131$	−43.8799	−	13.2186i	−0.334961	−	0.100906i	−0.451476	+	0.892283i	$0.649102\pi$
$132$	−456.035	−	110.971i	−3.45481	−	0.840688i
$133$	0.172087	−	1.10860i	0.00129388	−	0.00833534i
$134$	−15.5871	−	4.04817i	−0.116322	−	0.0302102i
$135$	−44.4178	+	64.8419i	−0.329020	+	0.480311i
$136$	−69.8376	−	89.5775i	−0.513512	−	0.658658i
$137$	−40.5615	+	1.24969i	−0.296069	+	0.00912180i	−0.178490	−	0.983942i	$-0.557121\pi$
$137$	−40.5615	+	1.24969i	−0.296069	+	0.00912180i	−0.117579	+	0.993064i	$0.537513\pi$
$138$	98.6271	−	51.0207i	0.714689	−	0.369715i
$139$	63.8240	+	181.119i	0.459165	+	1.30302i	0.911548	+	0.411193i	$0.134888\pi$
$139$	63.8240	+	181.119i	0.459165	+	1.30302i	−0.452383	+	0.891824i	$0.649426\pi$
$140$	8.13882	+	8.26513i	0.0581344	+	0.0590366i
$141$	−270.426	+	221.063i	−1.91792	+	1.56783i
$142$	−18.9637	−	245.796i	−0.133547	−	1.73096i
$143$	−159.405	−	159.405i	−1.11472	−	1.11472i
$144$	−84.4558	−	72.3573i	−0.586498	−	0.502481i
$145$	−16.9285	+	14.2789i	−0.116748	+	0.0984749i
$146$	−7.69080	+	332.877i	−0.0526767	+	2.27998i
$147$	−203.080	+	153.359i	−1.38150	+	1.04326i
$148$	109.949	−	234.215i	0.742899	−	1.58253i
$149$	5.00980	−	5.08755i	0.0336228	−	0.0341446i	−0.695515	−	0.718512i	$-0.744824\pi$
$149$	5.00980	−	5.08755i	0.0336228	−	0.0341446i	0.729137	+	0.684367i	$0.239922\pi$
$150$	−37.8484	+	408.449i	−0.252322	+	2.72299i
$151$	98.3601	−	186.603i	0.651391	−	1.23578i	−0.307376	−	0.951588i	$-0.599451\pi$
$151$	98.3601	−	186.603i	0.651391	−	1.23578i	0.958767	−	0.284193i	$-0.0917255\pi$
$152$	−4.12224	−	8.78126i	−0.0271200	−	0.0577714i
$153$	205.464	+	72.4029i	1.34291	+	0.473222i
$154$	−6.73925	−	48.3121i	−0.0437614	−	0.313715i
$155$	20.9384	+	13.6435i	0.135087	+	0.0880224i
$156$	−212.858	−	651.692i	−1.36447	−	4.17752i
$157$	−35.8927	−	13.5880i	−0.228616	−	0.0865478i	0.237088	−	0.971488i	$-0.423807\pi$
$157$	−35.8927	−	13.5880i	−0.228616	−	0.0865478i	−0.465704	+	0.884940i	$0.654199\pi$
$158$	46.7117	−	103.625i	0.295643	−	0.655855i
$159$	−55.1956	+	22.3664i	−0.347142	+	0.140669i
$160$	−29.8729	−	6.06175i	−0.186706	−	0.0378859i
$161$	5.55965	+	4.83794i	0.0345320	+	0.0300493i
$162$	415.073	+	57.9002i	2.56218	+	0.357409i
$163$	118.436	−	228.947i	0.726603	−	1.40458i	−0.180458	−	0.983583i	$-0.557758\pi$
$163$	118.436	−	228.947i	0.726603	−	1.40458i	0.907061	−	0.420999i	$-0.138320\pi$
$164$	113.640	+	54.4182i	0.692924	+	0.331819i
$165$	−61.6821	+	68.7174i	−0.373831	+	0.416469i
$166$	67.9417	−	397.230i	0.409287	−	2.39295i
$167$	71.0977	−	167.975i	0.425735	−	1.00584i	−0.558585	−	0.829447i	$-0.688656\pi$
$167$	71.0977	−	167.975i	0.425735	−	1.00584i	0.984320	−	0.176391i	$-0.0564425\pi$
$168$	20.9319	−	60.8922i	0.124595	−	0.362453i
$169$	36.6988	−	156.034i	0.217153	−	0.923278i
$170$	−50.7486	+	8.67998i	−0.298521	+	0.0510587i
$171$	15.7427	+	9.91596i	0.0920625	+	0.0579881i
$172$	251.225	+	122.690i	1.46061	+	0.713316i
$173$	−0.0998876	+	2.59321i	−0.000577385	+	0.0149896i	−0.999520	−	0.0309945i	$-0.990133\pi$
$173$	−0.0998876	+	2.59321i	−0.000577385	+	0.0149896i	0.998942	+	0.0459841i	$0.0146424\pi$
$174$	259.967	+	112.403i	1.49406	+	0.645993i
$175$	−26.1275	+	7.65186i	−0.149300	+	0.0437249i
$176$	−47.1488	−	52.5264i	−0.267891	−	0.298446i
$177$	−130.154	+	81.9811i	−0.735334	+	0.463170i
$178$	−235.222	+	25.4555i	−1.32147	+	0.143009i
$179$	255.158	+	180.623i	1.42546	+	1.00907i	0.994280	+	0.106802i	$0.0340610\pi$
$179$	255.158	+	180.623i	1.42546	+	1.00907i	0.431184	+	0.902264i	$0.358096\pi$
$180$	−179.380	+	69.4922i	−0.996556	+	0.386068i
$181$	−193.282	+	83.5699i	−1.06786	+	0.461712i	−0.856740	−	0.515749i	$-0.827514\pi$
$181$	−193.282	+	83.5699i	−1.06786	+	0.461712i	−0.211116	+	0.977461i	$0.567710\pi$
$182$	54.8177	−	45.5200i	0.301196	−	0.250110i
$183$	578.539	+	76.1661i	3.16141	+	0.416208i
$184$	63.2432	+	7.83121i	0.343713	+	0.0425609i
$185$	−30.3636	−	40.8583i	−0.164127	−	0.220856i
$186$	36.8329	−	317.481i	0.198026	−	1.70689i
$187$	123.288	+	62.5796i	0.659296	+	0.334650i
$188$	−460.164	+	39.0693i	−2.44768	+	0.207815i
$189$	15.7735	+	64.8211i	0.0834576	+	0.342969i
$190$	−4.39074	−	0.236890i	−0.0231092	−	0.00124679i
$191$	−197.464	+	43.2453i	−1.03384	+	0.226415i	−0.698447	−	0.715662i	$-0.746125\pi$
$191$	−197.464	+	43.2453i	−1.03384	+	0.226415i	−0.335397	+	0.942077i	$0.608870\pi$
$192$	132.337	+	493.890i	0.689257	+	2.57234i
$193$	−216.578	+	237.574i	−1.12216	+	1.23096i	−0.152033	+	0.988375i	$0.548582\pi$
$193$	−216.578	+	237.574i	−1.12216	+	1.23096i	−0.970131	+	0.242580i	$0.922006\pi$
$194$	−181.929	−	252.852i	−0.937777	−	1.30336i
$195$	−132.773	−	23.7630i	−0.680888	−	0.121862i
$196$	−336.113	+	15.5394i	−1.71486	+	0.0792829i
$197$	74.3486	−	339.486i	0.377404	−	1.72328i	−0.271525	−	0.962431i	$-0.587528\pi$
$197$	74.3486	−	339.486i	0.377404	−	1.72328i	0.648929	−	0.760849i	$-0.275217\pi$
$198$	779.771	+	215.388i	3.93824	+	1.08782i
$199$	286.608	−	265.347i	1.44024	−	1.33340i	0.589556	−	0.807727i	$-0.299303\pi$
$199$	286.608	−	265.347i	1.44024	−	1.33340i	0.850685	−	0.525676i	$-0.176188\pi$
$200$	−150.390	+	181.108i	−0.751952	+	0.905542i
$201$	24.8328	+	7.27270i	0.123546	+	0.0361826i
$202$	−56.6888	−	118.381i	−0.280638	−	0.586045i
$203$	−0.578878	+	18.7888i	−0.00285162	+	0.0925559i
$204$	248.195	+	339.408i	1.21664	+	1.66376i
$205$	20.0099	−	14.6324i	0.0976095	−	0.0713778i
$206$	−169.370	−	5.21825i	−0.822186	−	0.0253313i
$207$	−110.236	+	52.7882i	−0.532539	+	0.255016i
$208$	28.9780	−	98.9461i	0.139317	−	0.475703i
$209$	9.08447	+	7.54365i	0.0434664	+	0.0360940i
$210$	−19.8283	−	21.4170i	−0.0944204	−	0.101986i
$211$	64.3453	−	232.950i	0.304954	−	1.10403i	−0.637708	−	0.770278i	$-0.720117\pi$
$211$	64.3453	−	232.950i	0.304954	−	1.10403i	0.942662	−	0.333750i	$-0.108314\pi$
$212$	−76.9201	−	16.8458i	−0.362831	−	0.0794612i
$213$	18.2939	+	395.691i	0.0858868	+	1.85770i
$214$	54.7069	−	305.668i	0.255640	−	1.42836i
$215$	44.6501	−	32.1261i	0.207675	−	0.149424i
$216$	426.300	+	388.624i	1.97361	+	1.79918i
$217$	20.4898	−	5.49022i	0.0944229	−	0.0253005i
$218$	122.034	+	557.224i	0.559789	+	2.55608i
$219$	28.8226	−	534.225i	0.131610	−	2.43938i
$220$	−118.630	+	28.8672i	−0.539226	+	0.131215i
$221$	17.0855	+	201.236i	0.0773102	+	0.910571i
$222$	−294.664	+	580.519i	−1.32732	+	2.61495i
$223$	−199.496	−	23.1447i	−0.894601	−	0.103788i	−0.344402	−	0.938822i	$-0.611918\pi$
$223$	−199.496	−	23.1447i	−0.894601	−	0.103788i	−0.550198	+	0.835034i	$0.685448\pi$
$224$	−20.7664	+	15.4324i	−0.0927073	+	0.0688949i
$225$	55.4842	−	448.079i	0.246596	−	1.99146i
$226$	80.0542	−	608.072i	0.354222	−	2.69058i
$227$	15.0609	+	18.1371i	0.0663475	+	0.0798992i	0.801470	−	0.598035i	$-0.204052\pi$
$227$	15.0609	+	18.1371i	0.0663475	+	0.0798992i	−0.735122	+	0.677935i	$0.762875\pi$
$228$	14.2517	+	32.9615i	0.0625074	+	0.144568i
$229$	−38.9197	−	100.463i	−0.169955	−	0.438704i	0.821328	−	0.570457i	$-0.193234\pi$
$229$	−38.9197	−	100.463i	−0.169955	−	0.438704i	−0.991283	+	0.131752i	$0.957940\pi$
$230$	16.6895	−	23.5765i	0.0725630	−	0.102507i
$231$	8.43283	+	77.9236i	0.0365058	+	0.337331i
$232$	86.6284	+	137.532i	0.373398	+	0.592812i
$233$	310.027	−	278.286i	1.33059	−	1.19436i	0.365994	−	0.930617i	$-0.380729\pi$
$233$	310.027	−	278.286i	1.33059	−	1.19436i	0.964593	−	0.263743i	$-0.0849571\pi$
$234$	332.122	+	1134.04i	1.41933	+	4.84633i
$235$	−36.0594	+	83.3988i	−0.153444	+	0.354888i
$236$	−203.230	−	7.82821i	−0.861145	−	0.0331704i
$237$	−80.1472	+	164.112i	−0.338174	+	0.692457i
$238$	−23.2910	+	36.9770i	−0.0978613	+	0.155366i
$239$	−44.6554	−	261.083i	−0.186843	−	1.09240i	−0.913935	−	0.405859i	$-0.866972\pi$
$239$	−44.6554	−	261.083i	−0.186843	−	1.09240i	0.727093	−	0.686539i	$-0.240871\pi$
$240$	−41.1104	−	9.66909i	−0.171294	−	0.0402879i
$241$	64.5155	+	22.1774i	0.267699	+	0.0920225i	0.455660	−	0.890154i	$-0.349403\pi$
$241$	64.5155	+	22.1774i	0.267699	+	0.0920225i	−0.187961	+	0.982177i	$0.560188\pi$
$242$	102.114	+	43.2210i	0.421957	+	0.178599i
$243$	−162.327	−	27.7643i	−0.668014	−	0.114256i
$244$	574.159	+	515.376i	2.35311	+	2.11220i
$245$	−28.5914	+	59.7063i	−0.116700	+	0.243699i
$246$	−281.581	−	145.664i	−1.14464	−	0.592132i
$247$	−2.38298	+	17.0830i	−0.00964769	+	0.0691620i
$248$	120.406	−	138.368i	0.485510	−	0.557936i
$249$	−128.771	+	634.596i	−0.517152	+	2.54858i
$250$	83.5082	+	206.081i	0.334033	+	0.824323i
$251$	−312.786	−	140.996i	−1.24616	−	0.561739i	−0.323089	−	0.946369i	$-0.604721\pi$
$251$	−312.786	−	140.996i	−1.24616	−	0.561739i	−0.923071	+	0.384630i	$0.874329\pi$
$252$	−57.8108	+	152.707i	−0.229408	+	0.605982i
$253$	−73.7376	+	24.0844i	−0.291453	+	0.0951953i
$254$	−76.0089	+	116.650i	−0.299248	+	0.459251i
$255$	81.9327	−	11.4291i	0.321305	−	0.0448201i
$256$	−127.739	+	362.496i	−0.498980	+	1.41600i
$257$	13.8920	−	6.52141i	0.0540545	−	0.0253751i	−0.397726	−	0.917504i	$-0.630201\pi$
$257$	13.8920	−	6.52141i	0.0540545	−	0.0253751i	0.451781	+	0.892129i	$0.350789\pi$
$258$	−622.312	−	328.026i	−2.41206	−	1.27142i
$259$	−43.0241	−	3.98677i	−0.166116	−	0.0153929i
$260$	−127.073	−	125.131i	−0.488743	−	0.481274i
$261$	−282.197	−	132.473i	−1.08121	−	0.507561i
$262$	91.8780	+	121.666i	0.350679	+	0.464374i
$263$	50.4546	+	1.16571i	0.191842	+	0.00443234i	0.118913	−	0.992905i	$-0.462059\pi$
$263$	50.4546	+	1.16571i	0.191842	+	0.00443234i	0.0729299	+	0.997337i	$0.476765\pi$
$264$	436.965	+	518.048i	1.65517	+	1.96230i
$265$	−10.0796	+	11.7649i	−0.0380361	+	0.0443959i
$266$	−2.63912	+	2.63912i	−0.00992151	+	0.00992151i
$267$	379.030	−	29.2430i	1.41959	−	0.109524i
$268$	21.6534	+	26.4886i	0.0807964	+	0.0988380i
$269$	263.093	−	259.072i	0.978040	−	0.963093i	−0.0212866	−	0.999773i	$-0.506776\pi$
$269$	263.093	−	259.072i	0.978040	−	0.963093i	0.999327	+	0.0366800i	$0.0116782\pi$
$270$	246.612	−	86.9029i	0.913380	−	0.321863i
$271$	54.1580	+	104.692i	0.199845	+	0.386317i	0.966858	−	0.255315i	$-0.0821793\pi$
$271$	54.1580	+	104.692i	0.199845	+	0.386317i	−0.767013	+	0.641632i	$0.778258\pi$
$272$	1.94731	+	63.2044i	0.00715921	+	0.232369i
$273$	−90.2905	+	70.3935i	−0.330734	+	0.257852i
$274$	111.379	+	76.2961i	0.406491	+	0.278453i
$275$	72.0321	−	277.352i	0.261935	−	1.00855i
$276$	−233.114	−	36.1860i	−0.844616	−	0.131109i
$277$	−21.4711	+	88.2353i	−0.0775129	+	0.318539i	−0.997260	−	0.0739716i	$-0.976433\pi$
$277$	−21.4711	+	88.2353i	−0.0775129	+	0.318539i	0.919747	+	0.392511i	$0.128393\pi$
$278$	184.276	−	611.714i	0.662864	−	2.20041i
$279$	−51.2836	+	348.033i	−0.183812	+	1.24743i
$280$	−2.44176	−	16.5709i	−0.00872059	−	0.0591818i
$281$	32.0938	−	9.66811i	0.114213	−	0.0344061i	−0.230822	−	0.972996i	$-0.574142\pi$
$281$	32.0938	−	9.66811i	0.114213	−	0.0344061i	0.345035	+	0.938590i	$0.387867\pi$
$282$	1160.32	−	62.6016i	4.11460	−	0.221991i
$283$	233.190	−	64.4117i	0.823995	−	0.227603i	0.171295	−	0.985220i	$-0.445205\pi$
$283$	233.190	−	64.4117i	0.823995	−	0.227603i	0.652700	+	0.757617i	$0.273636\pi$
$284$	−275.712	+	445.290i	−0.970817	+	1.56792i
$285$	7.03989	+	0.597707i	0.0247014	+	0.00209722i
$286$	115.039	+	741.096i	0.402236	+	2.59125i
$287$	2.10269	−	20.9358i	0.00732646	−	0.0729469i
$288$	−98.2378	−	417.681i	−0.341103	−	1.45028i
$289$	64.3670	+	152.073i	0.222723	+	0.526204i
$290$	73.4998	−	5.10170i	0.253448	−	0.0175921i
$291$	279.669	+	415.086i	0.961063	+	1.42641i
$292$	430.622	−	561.197i	1.47473	−	1.92191i
$293$	−32.3520	+	81.6384i	−0.110416	+	0.278629i	−0.974374	−	0.224936i	$-0.927783\pi$
$293$	−32.3520	+	81.6384i	−0.110416	+	0.278629i	0.863957	+	0.503565i	$0.167979\pi$
$294$	846.511	−	13.0373i	2.87929	−	0.0443445i
$295$	−20.2733	+	34.4981i	−0.0687229	+	0.116943i
$296$	−327.789	+	179.284i	−1.10740	+	0.605691i
$297$	−670.755	−	207.709i	−2.25843	−	0.699356i
$298$	−23.4440	+	3.82427i	−0.0786711	+	0.0128331i
$299$	−86.6127	−	73.0563i	−0.289674	−	0.244335i
$300$	577.107	−	652.976i	1.92369	−	2.17659i
$301$	5.02337	−	46.4185i	0.0166890	−	0.154214i
$302$	−630.576	+	307.953i	−2.08800	+	1.01971i
$303$	85.1856	+	192.927i	0.281141	+	0.636723i
$304$	−1.03319	+	5.30078i	−0.00339866	+	0.0174368i
$305$	142.774	−	51.5510i	0.468112	−	0.169020i
$306$	−409.578	−	597.910i	−1.33849	−	1.95395i
$307$	−10.3355	+	32.4890i	−0.0336661	+	0.105827i	−0.968305	−	0.249771i	$-0.919645\pi$
$307$	−10.3355	+	32.4890i	−0.0336661	+	0.105827i	0.934639	+	0.355599i	$0.115723\pi$
$308$	−49.0273	+	91.3004i	−0.159179	+	0.296430i
$309$	271.754	+	16.7612i	0.879461	+	0.0542433i
$310$	−29.4363	−	77.7559i	−0.0949557	−	0.250826i
$311$	178.751	+	222.135i	0.574763	+	0.714260i	0.979787	−	0.200046i	$-0.0641092\pi$
$311$	178.751	+	222.135i	0.574763	+	0.714260i	−0.405023	+	0.914306i	$0.632737\pi$
$312$	−307.365	+	941.038i	−0.985143	+	3.01615i
$313$	−215.585	+	267.908i	−0.688770	+	0.855937i	−0.995391	−	0.0958948i	$-0.969429\pi$
$313$	−215.585	+	267.908i	−0.688770	+	0.855937i	0.306622	+	0.951831i	$0.400801\pi$
$314$	69.7036	+	106.973i	0.221986	+	0.340679i
$315$	21.0885	+	24.2344i	0.0669475	+	0.0769345i
$316$	−210.052	+	119.127i	−0.664722	+	0.376983i
$317$	−282.020	−	506.323i	−0.889653	−	1.59723i	−0.798984	−	0.601353i	$-0.794629\pi$
$317$	−282.020	−	506.323i	−0.889653	−	1.59723i	−0.0906700	−	0.995881i	$-0.528901\pi$
$318$	192.145	+	48.3264i	0.604229	+	0.151970i
$319$	−166.595	−	106.735i	−0.522242	−	0.334592i
$320$	89.6079	+	98.2952i	0.280025	+	0.307172i
$321$	−102.985	+	488.201i	−0.320825	+	1.52088i
$322$	−5.42953	−	23.9095i	−0.0168619	−	0.0742532i
$323$	−1.86372	−	10.4133i	−0.00577002	−	0.0322393i
$324$	−639.190	−	619.800i	−1.97281	−	1.91296i
$325$	399.840	−	123.816i	1.23028	−	0.380973i
$326$	−767.642	+	382.240i	−2.35473	+	1.17252i
$327$	−168.417	−	900.950i	−0.515036	−	2.75520i
$328$	−86.0741	−	160.290i	−0.262421	−	0.488690i
$329$	32.2341	+	70.0630i	0.0979759	+	0.212957i
$330$	300.585	−	63.4076i	0.910863	−	0.192144i
$331$	292.722	−	406.837i	0.884358	−	1.22912i	−0.0881178	−	0.996110i	$-0.528085\pi$
$331$	292.722	−	406.837i	0.884358	−	1.22912i	0.972475	−	0.233005i	$-0.0748560\pi$
$332$	−614.645	+	596.000i	−1.85134	+	1.79518i
$333$	343.857	−	628.680i	1.03260	−	1.88793i
$334$	−520.785	+	311.466i	−1.55924	+	0.932532i
$335$	6.60685	−	1.28776i	0.0197219	−	0.00384406i
$336$	−29.4166	+	20.4854i	−0.0875493	+	0.0609684i
$337$	32.8640	−	425.962i	0.0975193	−	1.26398i	−0.722388	−	0.691488i	$-0.756956\pi$
$337$	32.8640	−	425.962i	0.0975193	−	1.26398i	0.819908	−	0.572496i	$-0.194025\pi$
$338$	−404.961	+	346.949i	−1.19811	+	1.02648i
$339$	−158.656	+	972.613i	−0.468013	+	2.86906i
$340$	97.9124	+	48.7546i	0.287978	+	0.143396i
$341$	−61.1010	+	214.748i	−0.179182	+	0.629759i
$342$	−22.8034	−	57.5429i	−0.0666765	−	0.168254i
$343$	43.6349	+	105.344i	0.127216	+	0.307125i
$344$	−188.251	−	357.139i	−0.547242	−	1.03819i
$345$	−27.9702	+	37.0385i	−0.0810730	+	0.107358i
$346$	5.36061	−	6.76768i	0.0154931	−	0.0195598i
$347$	−101.312	+	61.6558i	−0.291966	+	0.177683i	−0.658206	−	0.752838i	$-0.728684\pi$
$347$	−101.312	+	61.6558i	−0.291966	+	0.177683i	0.366239	+	0.930521i	$0.380645\pi$
$348$	−304.856	−	518.760i	−0.876023	−	1.49069i
$349$	295.099	+	176.490i	0.845555	+	0.505701i	0.869454	−	0.494014i	$-0.164471\pi$
$349$	295.099	+	176.490i	0.845555	+	0.505701i	−0.0238988	+	0.999714i	$0.507608\pi$
$350$	85.1893	+	30.7590i	0.243398	+	0.0878829i
$351$	−257.829	−	992.747i	−0.734557	−	2.82834i
$352$	−27.2140	−	270.960i	−0.0773124	−	0.769772i
$353$	10.8737	−	3.73788i	0.0308037	−	0.0105889i	−0.309638	−	0.950855i	$-0.600208\pi$
$353$	10.8737	−	3.73788i	0.0308037	−	0.0105889i	0.340441	+	0.940266i	$0.389423\pi$
$354$	510.507	+	35.4348i	1.44211	+	0.100098i
$355$	51.5212	+	89.2373i	0.145130	+	0.251373i
$356$	435.298	+	251.319i	1.22275	+	0.705953i
$357$	39.2354	−	58.2333i	0.109903	−	0.163119i
$358$	−330.511	−	986.110i	−0.923214	−	2.75450i
$359$	−107.722	+	69.0160i	−0.300062	+	0.192245i	−0.680861	−	0.732413i	$-0.738394\pi$
$359$	−107.722	+	69.0160i	−0.300062	+	0.192245i	0.380799	+	0.924658i	$0.375649\pi$
$360$	268.316	+	71.8951i	0.745322	+	0.199709i
$361$	−16.6305	+	359.712i	−0.0460679	+	0.996433i
$362$	683.151	+	155.134i	1.88716	+	0.428548i
$363$	−161.858	−	74.4663i	−0.445889	−	0.205141i
$364$	−151.088	+	9.31881i	−0.415078	+	0.0256011i
$365$	−57.1931	−	126.877i	−0.156693	−	0.347608i
$366$	−1404.05	−	1340.63i	−3.83620	−	3.66294i
$367$	33.4609	−	45.0262i	0.0911743	−	0.122687i	−0.754699	−	0.656071i	$-0.772217\pi$
$367$	33.4609	−	45.0262i	0.0911743	−	0.122687i	0.845873	+	0.533384i	$0.179080\pi$
$368$	−25.8470	−	24.3019i	−0.0702364	−	0.0660378i
$369$	304.849	+	169.800i	0.826148	+	0.460161i
$370$	1.30400	+	169.348i	0.00352432	+	0.457696i
$371$	1.71640	+	13.0373i	0.00462641	+	0.0351411i
$372$	−461.291	+	498.251i	−1.24003	+	1.33938i
$373$	−122.042	−	197.105i	−0.327190	−	0.528431i	0.644526	−	0.764583i	$-0.277055\pi$
$373$	−122.042	−	197.105i	−0.327190	−	0.528431i	−0.971716	+	0.236152i	$0.924114\pi$
$374$	−208.191	−	410.158i	−0.556660	−	1.09668i
$375$	−123.919	−	335.101i	−0.330450	−	0.893603i
$376$	569.665	+	346.683i	1.51507	+	0.922028i
$377$	4.45054	−	288.974i	0.0118051	−	0.766509i
$378$	84.9331	−	205.047i	0.224691	−	0.542451i
$379$	−607.259	+	56.2709i	−1.60227	+	0.148472i	−0.855929	−	0.517094i	$-0.827014\pi$
$379$	−607.259	+	56.2709i	−1.60227	+	0.148472i	−0.746339	+	0.665566i	$0.768190\pi$
$380$	7.23251	+	5.91231i	0.0190329	+	0.0155587i
$381$	127.843	−	183.580i	0.335547	−	0.481839i
$382$	615.196	+	271.635i	1.61046	+	0.711087i
$383$	−15.8945	−	412.641i	−0.0415000	−	1.07739i	−0.862370	−	0.506278i	$-0.831021\pi$
$383$	−15.8945	−	412.641i	−0.0415000	−	1.07739i	0.820870	−	0.571114i	$-0.193489\pi$
$384$	445.170	−	1149.12i	1.15930	−	2.99249i
$385$	11.2621	+	16.9962i	0.0292522	+	0.0441460i
$386$	1048.13	−	212.685i	2.71537	−	0.550997i
$387$	673.528	+	381.977i	1.74038	+	0.987021i
$388$	−5.09557	+	661.751i	−0.0131329	+	1.70554i
$389$	−220.747	+	27.3344i	−0.567474	+	0.0702685i	−0.401496	−	0.915861i	$-0.631510\pi$
$389$	−220.747	+	27.3344i	−0.567474	+	0.0702685i	−0.165978	+	0.986129i	$0.553078\pi$
$390$	309.887	+	324.545i	0.794581	+	0.832166i
$391$	64.4074	+	26.0992i	0.164725	+	0.0667500i
$392$	405.016	+	268.373i	1.03320	+	0.684626i
$393$	−141.537	−	199.944i	−0.360146	−	0.508763i
$394$	−866.318	+	765.661i	−2.19878	+	1.94330i
$395$	1.09738	+	47.4974i	0.00277818	+	0.120247i
$396$	−1067.11	−	1347.21i	−2.69472	−	3.40204i
$397$	−636.652	−	235.430i	−1.60366	−	0.593023i	−0.621888	−	0.783106i	$-0.713634\pi$
$397$	−636.652	−	235.430i	−1.60366	−	0.593023i	−0.981768	+	0.190083i	$0.939124\pi$
$398$	−1290.73	+	149.746i	−3.24305	+	0.376246i
$399$	4.36906	−	4.10789i	0.0109500	−	0.0102955i
$400$	127.098	−	31.9664i	0.317745	−	0.0799161i
$401$	708.800	+	237.566i	1.76758	+	0.592433i	0.998886	−	0.0471824i	$-0.0150242\pi$
$401$	708.800	+	237.566i	1.76758	+	0.592433i	0.768695	+	0.639616i	$0.220907\pi$
$402$	−52.4048	−	68.2953i	−0.130360	−	0.169889i
$403$	−313.685	+	89.2510i	−0.778374	+	0.221467i
$404$	−51.2377	+	274.098i	−0.126826	+	0.678459i
$405$	−166.928	+	53.1035i	−0.412167	+	0.131120i
$406$	38.4508	−	49.3191i	0.0947065	−	0.121476i
$407$	268.449	−	367.105i	0.659579	−	0.901977i
$408$		−	607.161i		−	1.48814i
$409$	−54.7323	+	405.321i	−0.133820	+	0.991006i
$409$	−54.7323	+	405.321i	−0.133820	+	0.991006i
$410$	−82.4693			−0.201145
$411$	−175.101	−	128.044i	−0.426036	−	0.311542i
$412$	283.905	+	221.342i	0.689091	+	0.537238i
$413$	10.2962	+	32.3656i	0.0249304	+	0.0783672i
$414$	399.690	+	74.7151i	0.965436	+	0.180471i
$415$	46.0969	+	162.014i	0.111077	+	0.390395i
$416$	315.584	−	242.156i	0.758616	−	0.582107i
$417$	−326.219	+	973.305i	−0.782299	+	2.33406i
$418$	−9.58186	−	38.0973i	−0.0229231	−	0.0911419i
$419$	541.959	+	576.416i	1.29346	+	1.37569i	0.886826	+	0.462103i	$0.152905\pi$
$419$	541.959	+	576.416i	1.29346	+	1.37569i	0.406633	+	0.913592i	$0.366703\pi$
$420$	7.14572	+	61.5925i	0.0170136	+	0.146649i
$421$	−179.432	+	485.220i	−0.426203	+	1.15254i	0.526908	+	0.849922i	$0.323351\pi$
$421$	−179.432	+	485.220i	−0.426203	+	1.15254i	−0.953112	+	0.302619i	$0.902139\pi$
$422$	−630.246	+	499.211i	−1.49347	+	1.18296i
$423$	−1278.66	+	29.5423i	−3.02285	+	0.0698400i
$424$	75.2991	+	85.1983i	0.177592	+	0.200939i
$425$	−209.532	+	148.325i	−0.493017	+	0.348999i
$426$	727.905	−	1098.52i	1.70870	−	2.57868i
$427$	48.3885	−	119.413i	0.113322	−	0.279655i
$428$	−477.129	+	455.579i	−1.11479	+	1.06444i
$429$	−148.085	−	1195.91i	−0.345187	−	2.78766i
$430$	−182.991	−	1.40906i	−0.425561	−	0.00327688i
$431$	−133.433	+	235.279i	−0.309590	+	0.545890i	−0.980712	−	0.195456i	$-0.937381\pi$
$431$	−133.433	+	235.279i	−0.309590	+	0.545890i	0.671122	+	0.741347i	$0.265813\pi$
$432$	−63.8643	−	314.730i	−0.147834	−	0.728541i
$433$	−235.668	+	156.159i	−0.544268	+	0.360645i	−0.794237	−	0.607609i	$-0.792129\pi$
$433$	−235.668	+	156.159i	−0.544268	+	0.360645i	0.249968	+	0.968254i	$0.419580\pi$
$434$	−65.8049	−	25.4929i	−0.151624	−	0.0587395i
$435$	−118.294	+	4.55658i	−0.271941	+	0.0104749i
$436$	489.496	−	1108.60i	1.12270	−	2.54267i
$437$	4.87054	+	3.39179i	0.0111454	+	0.00776154i
$438$	−1126.48	+	1378.02i	−2.57186	+	3.14616i
$439$	69.5308	+	750.357i	0.158385	+	1.70924i	0.590182	+	0.807270i	$0.299056\pi$
$439$	69.5308	+	750.357i	0.158385	+	1.70924i	−0.431797	+	0.901971i	$0.642120\pi$
$440$	162.879	+	67.4667i	0.370180	+	0.153334i
$441$	−931.745	−	14.3500i	−2.11280	−	0.0325396i
$442$	349.293	−	573.954i	0.790255	−	1.29854i
$443$	−36.5111	+	13.5016i	−0.0824178	+	0.0304776i	−0.387713	−	0.921780i	$-0.626735\pi$
$443$	−36.5111	+	13.5016i	−0.0824178	+	0.0304776i	0.305296	+	0.952258i	$0.401245\pi$
$444$	1233.29	−	626.004i	2.77769	−	1.40992i
$445$	84.0791	−	52.0596i	0.188942	−	0.116988i
$446$	490.279	+	453.910i	1.09928	+	1.01774i
$447$	37.8407	−	4.98182i	0.0846547	−	0.0111450i
$448$	112.895	−	0.869307i	0.251998	−	0.00194042i
$449$	51.4580	−	92.3848i	0.114606	−	0.205757i	−0.810241	−	0.586097i	$-0.800664\pi$
$449$	51.4580	−	92.3848i	0.114606	−	0.205757i	0.924847	+	0.380340i	$0.124193\pi$
$450$	−1028.91	+	1094.32i	−2.28646	+	2.43183i
$451$	177.756	+	132.098i	0.394138	+	0.292901i
$452$	−899.816	+	942.378i	−1.99074	+	2.08491i
$453$	1027.95	−	463.377i	2.26921	−	1.02291i
$454$	−4.82822	−	78.2813i	−0.0106349	−	0.172426i
$455$	−12.4478	+	27.0562i	−0.0273578	+	0.0594641i
$456$	11.4831	−	50.5672i	0.0251823	−	0.110893i
$457$	502.827	+	23.2471i	1.10028	+	0.0508689i	0.588687	−	0.808361i	$-0.299645\pi$
$457$	502.827	+	23.2471i	1.10028	+	0.0508689i	0.511590	+	0.859230i	$0.329057\pi$
$458$	−92.7677	+	346.214i	−0.202549	+	0.755925i
$459$	339.359	+	529.681i	0.739344	+	1.15399i
$460$	−58.1858	+	19.5019i	−0.126491	+	0.0423954i
$461$	561.707	+	378.457i	1.21845	+	0.820947i	0.988347	−	0.152219i	$-0.0486418\pi$
$461$	561.707	+	378.457i	1.21845	+	0.820947i	0.230106	+	0.973166i	$0.426093\pi$
$462$	130.375	−	225.817i	0.282198	−	0.488781i
$463$	481.443	−	277.962i	1.03983	−	0.600349i	0.120048	−	0.992768i	$-0.461695\pi$
$463$	481.443	−	277.962i	1.03983	−	0.600349i	0.919786	+	0.392419i	$0.128362\pi$
$464$	6.26588	−	90.2722i	0.0135041	−	0.194552i
$465$	43.4277	+	126.334i	0.0933930	+	0.271686i
$466$	−1379.03	+	138.504i	−2.95929	+	0.297218i
$467$	274.862	−	71.3853i	0.588570	−	0.152859i	0.0548120	−	0.998497i	$-0.482544\pi$
$467$	274.862	−	71.3853i	0.588570	−	0.152859i	0.533758	+	0.845637i	$0.320779\pi$
$468$	852.559	−	2361.22i	1.82171	−	5.04535i
$469$	2.93257	−	4.90339i	0.00625281	−	0.0104550i
$470$	260.607	−	153.149i	0.554484	−	0.325850i
$471$	−106.652	−	175.250i	−0.226438	−	0.372080i
$472$	230.211	+	182.348i	0.487736	+	0.386330i
$473$	392.167	+	296.151i	0.829105	+	0.626111i
$474$	537.501	−	283.322i	1.13397	−	0.597725i
$475$	−20.2560	+	8.39033i	−0.0426443	+	0.0176639i
$476$	86.3110	−	34.2037i	0.181326	−	0.0718565i
$477$	−209.753	−	59.6800i	−0.439734	−	0.125115i
$478$	−392.780	+	788.808i	−0.821715	+	1.65023i
$479$	−765.493	−	124.870i	−1.59811	−	0.260689i	−0.704555	−	0.709649i	$-0.748853\pi$
$479$	−765.493	−	124.870i	−1.59811	−	0.260689i	−0.893552	+	0.448960i	$0.851795\pi$
$480$	−106.011	−	123.737i	−0.220856	−	0.257785i
$481$	662.344	+	51.1014i	1.37701	+	0.106240i
$482$	−129.700	−	186.247i	−0.269088	−	0.386404i
$483$	7.53686	+	38.6678i	0.0156043	+	0.0800576i
$484$	−120.912	−	202.171i	−0.249819	−	0.417708i
$485$	114.230	+	62.4781i	0.235525	+	0.128821i
$486$	381.395	+	393.326i	0.784763	+	0.809314i
$487$	420.501	+	302.553i	0.863451	+	0.621259i	0.926310	−	0.376763i	$-0.122963\pi$
$487$	420.501	+	302.553i	0.863451	+	0.621259i	−0.0628586	+	0.998022i	$0.520022\pi$
$488$	−229.955	−	1090.10i	−0.471219	−	2.23382i
$489$	1251.76	−	575.901i	2.55983	−	1.17771i
$490$	194.027	−	104.190i	0.395973	−	0.212633i
$491$	505.960	−	94.5803i	1.03047	−	0.192628i	0.358750	−	0.933434i	$-0.383203\pi$
$491$	505.960	−	94.5803i	1.03047	−	0.192628i	0.671719	+	0.740806i	$0.265556\pi$
$492$	300.211	+	602.904i	0.610184	+	1.22541i
$493$	52.4328	+	169.321i	0.106354	+	0.343451i
$494$	39.9458	−	41.1955i	0.0808620	−	0.0833917i
$495$	−332.842	+	59.5703i	−0.672409	+	0.120344i
$496$	−99.5785	+	22.6129i	−0.200763	+	0.0455906i
$497$	85.5789	+	18.0527i	0.172191	+	0.0363233i
$498$	1591.98	−	1451.28i	3.19675	−	2.91422i
$499$	131.700	−	205.561i	0.263927	−	0.411945i	−0.684465	−	0.729046i	$-0.739964\pi$
$499$	131.700	−	205.561i	0.263927	−	0.411945i	0.948392	+	0.317101i	$0.102709\pi$
$500$	115.223	−	458.123i	0.230445	−	0.916247i
$501$	851.802	−	474.451i	1.70020	−	0.947007i
$502$	563.081	+	992.863i	1.12168	+	1.97781i
$503$	−444.554	+	386.846i	−0.883806	+	0.769078i	−0.973929	−	0.226853i	$-0.927156\pi$
$503$	−444.554	+	386.846i	−0.883806	+	0.769078i	0.0901230	+	0.995931i	$0.471274\pi$
$504$	197.544	−	128.720i	0.391953	−	0.255396i
$505$	42.7414	+	34.3938i	0.0846363	+	0.0681066i
$506$	245.311	+	80.1244i	0.484805	+	0.158349i
$507$	667.541	−	537.169i	1.31665	−	1.05950i
$508$	276.627	−	104.723i	0.544541	−	0.206148i
$509$	−4.39826	+	71.3102i	−0.00864099	+	0.140099i	0.991322	+	0.131458i	$0.0419660\pi$
$509$	−4.39826	+	71.3102i	−0.00864099	+	0.140099i	−0.999963	+	0.00864022i	$0.997250\pi$
$510$	−242.467	−	130.202i	−0.475426	−	0.255298i
$511$	−112.570	−	35.8111i	−0.220294	−	0.0700805i
$512$	294.104	−	201.466i	0.574422	−	0.393488i
$513$	18.2456	+	50.5326i	0.0355665	+	0.0985040i
$514$	−50.1121	−	9.76751i	−0.0974944	−	0.0190029i
$515$	64.7916	−	28.6083i	0.125809	−	0.0555501i
$516$	655.836	+	1342.91i	1.27100	+	2.60255i
$517$	−807.033	−	87.3365i	−1.56099	−	0.168929i
$518$	107.709	+	95.1940i	0.207932	+	0.183772i
$519$	−8.94410	+	10.6038i	−0.0172333	+	0.0204312i
$520$	41.4600	+	254.163i	0.0797308	+	0.488775i
$521$	−214.775	+	693.574i	−0.412236	+	1.33124i	0.479047	+	0.877789i	$0.340982\pi$
$521$	−214.775	+	693.574i	−0.412236	+	1.33124i	−0.891283	+	0.453447i	$0.850194\pi$
$522$	497.674	+	909.906i	0.953398	+	1.74312i
$523$	−415.220	−	244.010i	−0.793921	−	0.466558i	0.0527938	−	0.998605i	$-0.483187\pi$
$523$	−415.220	−	244.010i	−0.793921	−	0.466558i	−0.846714	+	0.532048i	$0.821423\pi$
$524$	−4.98781	−	323.859i	−0.00951872	−	0.618051i
$525$	−135.294	−	53.6147i	−0.257702	−	0.102123i
$526$	−133.202	−	102.210i	−0.253236	−	0.194315i
$527$	165.885	−	111.767i	0.314772	−	0.212082i
$528$	−26.1260	−	376.396i	−0.0494811	−	0.712871i
$529$	451.253	−	190.999i	0.853031	−	0.361057i
$530$	50.1710	−	11.8001i	0.0946622	−	0.0222643i
$531$	−560.441	−	56.2882i	−1.05545	−	0.106004i
$532$	7.83527	−	1.21626i	0.0147280	−	0.00228620i
$533$	−27.3675	+	322.339i	−0.0513462	+	0.604763i
$534$	−1075.28	−	665.784i	−2.01363	−	1.24679i
$535$	34.5571	+	125.107i	0.0645927	+	0.233846i
$536$	−2.66153	−	49.3313i	−0.00496553	−	0.0920359i
$537$	482.012	+	1600.06i	0.897602	+	2.97963i
$538$	−1215.26	+	179.072i	−2.25885	+	0.332847i
$539$	−585.102	−	86.2162i	−1.08553	−	0.159956i
$540$	−531.887	−	160.229i	−0.984977	−	0.296720i
$541$	−172.535	−	41.9844i	−0.318918	−	0.0776051i	0.0737744	−	0.997275i	$-0.476496\pi$
$541$	−172.535	−	41.9844i	−0.318918	−	0.0776051i	−0.392692	+	0.919670i	$0.628456\pi$
$542$	60.1501	−	387.493i	0.110978	−	0.714932i
$543$	−1089.48	−	282.952i	−2.00640	−	0.521089i
$544$	−137.876	+	201.274i	−0.253448	+	0.369988i
$545$	−146.597	−	188.034i	−0.268986	−	0.345016i
$546$	380.702	−	11.7293i	0.697256	−	0.0214822i
$547$	−365.325	+	188.986i	−0.667871	+	0.345496i	−0.759695	−	0.650279i	$-0.774652\pi$
$547$	−365.325	+	188.986i	−0.667871	+	0.345496i	0.0918240	+	0.995775i	$0.470730\pi$
$548$	−95.3236	−	270.509i	−0.173948	−	0.493629i
$549$	1499.24	+	1522.51i	2.73086	+	2.77325i
$550$	−738.082	+	603.355i	−1.34197	+	1.09701i
$551$	1.16450	+	15.0935i	0.00211343	+	0.0273929i
$552$	240.873	+	240.873i	0.436364	+	0.436364i
$553$	30.6242	+	26.2372i	0.0553782	+	0.0474452i
$554$	230.929	−	194.785i	0.416840	−	0.351598i
$555$	6.28522	−	272.040i	0.0113247	−	0.490161i
$556$	−1083.11	+	817.927i	−1.94804	+	1.47109i
$557$	62.3153	−	132.745i	0.111877	−	0.238321i	−0.841404	−	0.540406i	$-0.818271\pi$
$557$	62.3153	−	132.745i	0.111877	−	0.238321i	0.953281	+	0.302085i	$0.0976825\pi$
$558$	821.163	−	833.907i	1.47162	−	1.49446i
$559$	−66.2332	+	714.771i	−0.118485	+	1.27866i
$560$	−4.34817	+	8.24909i	−0.00776459	+	0.0147305i
$561$	314.063	+	669.022i	0.559827	+	1.19255i
$562$	−105.171	−	37.0607i	−0.187137	−	0.0659444i
$563$	18.9386	+	135.766i	0.0336387	+	0.241148i	0.999863	−	0.0165548i	$-0.00526980\pi$
$563$	18.9386	+	135.766i	0.0336387	+	0.241148i	−0.966224	+	0.257703i	$0.917035\pi$
$564$	−2068.30	−	1347.70i	−3.66720	−	2.38955i
$565$	79.5928	+	243.684i	0.140872	+	0.431299i
$566$	−752.701	−	284.952i	−1.32986	−	0.503449i
$567$	−61.1024	+	135.549i	−0.107764	+	0.239064i
$568$	700.912	−	284.024i	1.23400	−	0.500042i
$569$	613.248	+	124.439i	1.07776	+	0.218698i	0.704985	−	0.709222i	$-0.250954\pi$
$569$	613.248	+	124.439i	1.07776	+	0.218698i	0.372780	+	0.927920i	$0.378405\pi$
$570$	−17.7313	−	15.4296i	−0.0311075	−	0.0270694i
$571$	319.562	+	44.5770i	0.559653	+	0.0780683i	0.412354	−	0.911024i	$-0.364707\pi$
$571$	319.562	+	44.5770i	0.559653	+	0.0780683i	0.147299	+	0.989092i	$0.452942\pi$
$572$	732.069	−	1415.15i	1.27984	−	2.47404i
$573$	−974.574	−	466.691i	−1.70083	−	0.814470i
$574$	−46.7589	+	52.0921i	−0.0814615	+	0.0907528i
$575$	24.2822	−	141.969i	0.0422299	−	0.246903i
$576$	−729.803	+	1724.23i	−1.26702	+	2.99345i
$577$	194.078	−	564.586i	0.336358	−	0.978485i	−0.641119	−	0.767441i	$-0.721530\pi$
$577$	194.078	−	564.586i	0.336358	−	0.978485i	0.977477	−	0.211043i	$-0.0676862\pi$
$578$	125.779	−	534.779i	0.217611	−	0.925223i
$579$	−1693.85	+	289.713i	−2.92547	+	0.500368i
$580$	−132.441	−	83.4213i	−0.228346	−	0.143830i
$581$	128.473	+	62.7422i	0.221124	+	0.107990i
$582$	64.0907	−	1663.88i	0.110122	−	2.85889i
$583$	−127.041	−	54.9291i	−0.217909	−	0.0942181i
$584$	−980.267	+	287.087i	−1.67854	+	0.491588i
$585$	−329.926	−	367.557i	−0.563976	−	0.628302i
$586$	247.195	−	155.702i	0.421834	−	0.265703i
$587$	−869.546	+	94.1016i	−1.48134	+	0.160309i	−0.812441	−	0.583044i	$-0.801861\pi$
$587$	−869.546	+	94.1016i	−1.48134	+	0.160309i	−0.668899	+	0.743354i	$0.733234\pi$
$588$	−1468.01	−	1039.18i	−2.49662	−	1.76732i
$589$	15.9295	−	6.17112i	0.0270450	−	0.0104773i
$590$	122.187	−	52.8305i	0.207097	−	0.0895432i
$591$	1429.21	−	1186.80i	2.41829	−	2.00812i
$592$	206.219	+	27.1492i	0.348342	+	0.0458601i
$593$	435.333	+	53.9059i	0.734120	+	0.0909037i	0.481234	−	0.876592i	$-0.340189\pi$
$593$	435.333	+	53.9059i	0.734120	+	0.0909037i	0.252886	+	0.967496i	$0.418620\pi$
$594$	1393.37	+	1874.97i	2.34574	+	3.15651i
$595$	2.10503	−	18.1443i	0.00353786	−	0.0304946i
$596$	44.9992	+	22.8410i	0.0755020	+	0.0383239i
$597$	2080.35	−	176.628i	3.48467	−	0.295859i
$598$	89.1279	+	366.271i	0.149043	+	0.612493i
$599$	−812.233	−	43.8217i	−1.35598	−	0.0731581i	−0.638439	−	0.769672i	$-0.720420\pi$
$599$	−812.233	−	43.8217i	−1.35598	−	0.0731581i	−0.717543	+	0.696514i	$0.754733\pi$
$600$	−1229.24	+	269.207i	−2.04873	+	0.448679i
$601$	68.1602	+	254.377i	0.113411	+	0.423257i	0.999163	−	0.0409023i	$-0.0130232\pi$
$601$	68.1602	+	254.377i	0.113411	+	0.423257i	−0.885752	+	0.464159i	$0.846357\pi$
$602$	−104.643	+	114.788i	−0.173826	+	0.190678i
$603$	55.3391	+	76.9125i	0.0917729	+	0.127550i
$604$	1467.54	+	262.652i	2.42970	+	0.434855i
$605$	−46.2975	+	2.14046i	−0.0765247	+	0.00353795i
$606$	150.099	−	685.371i	0.247687	−	1.13098i
$607$	−279.724	−	77.2652i	−0.460830	−	0.127290i	0.0281149	−	0.999605i	$-0.491050\pi$
$607$	−279.724	−	77.2652i	−0.460830	−	0.127290i	−0.488945	+	0.872314i	$0.662618\pi$
$608$	−15.2896	+	14.1554i	−0.0251473	+	0.0232819i
$609$	−64.1931	+	77.3048i	−0.105407	+	0.126937i
$610$	−484.641	−	141.935i	−0.794493	−	0.232680i
$611$	−512.116	−	1069.43i	−0.838160	−	1.75030i
$612$	−47.4148	+	1538.96i	−0.0774751	+	2.51464i
$613$	−572.041	−	782.269i	−0.933183	−	1.27613i	−0.961009	−	0.276519i	$-0.910819\pi$
$613$	−572.041	−	782.269i	−0.933183	−	1.27613i	0.0278260	−	0.999613i	$-0.491142\pi$
$614$	91.5548	−	66.9502i	0.149112	−	0.109039i
$615$	132.447	+	4.08065i	0.215361	+	0.00663520i
$616$	134.966	−	64.6307i	0.219100	−	0.104920i
$617$	−142.229	+	485.644i	−0.230517	+	0.787105i	0.760025	+	0.649894i	$0.225187\pi$
$617$	−142.229	+	485.644i	−0.230517	+	0.787105i	−0.990542	+	0.137212i	$0.956186\pi$
$618$	−696.857	−	578.662i	−1.12760	−	0.936347i
$619$	−65.4218	−	70.6637i	−0.105689	−	0.114158i	0.678732	−	0.734386i	$-0.262530\pi$
$619$	−65.4218	−	70.6637i	−0.105689	−	0.114158i	−0.784421	+	0.620229i	$0.787040\pi$
$620$	−47.0278	+	170.255i	−0.0758513	+	0.274605i
$621$	−344.766	−	75.5049i	−0.555178	−	0.121586i
$622$	−43.8076	−	947.545i	−0.0704303	−	1.52338i
$623$	14.7880	−	82.6260i	0.0237367	−	0.132626i
$624$	447.364	−	321.882i	0.716930	−	0.515836i
$625$	357.474	+	325.880i	0.571958	+	0.521408i
$626$	1105.04	−	296.093i	1.76523	−	0.472993i
$627$	13.5035	+	61.6591i	0.0215368	+	0.0983399i
$628$	14.6132	−	270.855i	0.0232695	−	0.431298i
$629$	−395.882	+	96.3334i	−0.629383	+	0.153153i
$630$	−9.04144	−	106.492i	−0.0143515	−	0.169034i
$631$	−244.733	+	482.149i	−0.387849	+	0.764103i	−0.999638	−	0.0269179i	$-0.991431\pi$
$631$	−244.733	+	482.149i	−0.387849	+	0.764103i	0.611789	+	0.791021i	$0.290450\pi$
$632$	346.373	+	40.1849i	0.548059	+	0.0635837i
$633$	1036.89	−	770.556i	1.63805	−	1.21731i
$634$	−236.943	+	1913.50i	−0.373727	+	3.01814i
$635$	7.59587	−	57.6963i	0.0119620	−	0.0908604i
$636$	−268.902	−	323.827i	−0.422803	−	0.509162i
$637$	−342.849	−	792.948i	−0.538225	−	1.24482i
$638$	237.778	+	613.777i	0.372693	+	0.962032i
$639$	−838.052	+	1183.88i	−1.31150	+	1.85271i
$640$	−34.4906	−	318.710i	−0.0538916	−	0.497985i
$641$	217.258	+	344.921i	0.338935	+	0.538098i	0.971691	−	0.236253i	$-0.0759196\pi$
$641$	217.258	+	344.921i	0.338935	+	0.538098i	−0.632756	+	0.774351i	$0.718076\pi$
$642$	1235.26	−	1108.79i	1.92407	−	1.72709i
$643$	−354.915	−	1211.87i	−0.551967	−	1.88471i	−0.457574	−	0.889172i	$-0.651282\pi$
$643$	−354.915	−	1211.87i	−0.551967	−	1.88471i	−0.0943930	−	0.995535i	$-0.530091\pi$
$644$	−20.6720	+	47.8106i	−0.0320994	+	0.0742401i
$645$	293.817	+	11.3175i	0.455531	+	0.0175466i
$646$	−15.4441	+	31.6239i	−0.0239073	+	0.0489534i
$647$	511.985	−	812.833i	0.791321	−	1.25631i	−0.171236	−	0.985230i	$-0.554776\pi$
$647$	511.985	−	812.833i	0.791321	−	1.25631i	0.962557	−	0.271080i	$-0.0873810\pi$
$648$	216.749	+	1267.25i	0.334489	+	1.95563i
$649$	−347.989	−	81.8462i	−0.536192	−	0.126111i
$650$	−1316.88	−	452.682i	−2.02597	−	0.696434i
$651$	104.422	+	44.1982i	0.160403	+	0.0678928i
$652$	1795.75	+	307.142i	2.75421	+	0.471077i
$653$	16.3541	+	14.6798i	0.0250446	+	0.0224806i	0.680413	−	0.732829i	$-0.261800\pi$
$653$	16.3541	+	14.6798i	0.0250446	+	0.0224806i	−0.655368	+	0.755309i	$0.727487\pi$
$654$	−1316.96	+	2750.15i	−2.01370	+	4.20513i
$655$	−56.6001	−	29.2797i	−0.0864123	−	0.0447019i
$656$	−13.9936	+	100.317i	−0.0213318	+	0.152922i
$657$	1286.02	−	1477.86i	1.95741	−	2.24941i
$658$	51.0232	−	251.447i	0.0775428	−	0.382139i
$659$	28.2117	+	69.6204i	0.0428098	+	0.105646i	0.946697	−	0.322125i	$-0.104397\pi$
$659$	28.2117	+	69.6204i	0.0428098	+	0.105646i	−0.903887	+	0.427771i	$0.859299\pi$
$660$	−594.979	−	268.202i	−0.901484	−	0.406367i
$661$	−272.954	+	721.008i	−0.412941	+	1.09078i	0.553264	+	0.833006i	$0.313382\pi$
$661$	−272.954	+	721.008i	−0.412941	+	1.09078i	−0.966204	+	0.257777i	$0.917010\pi$
$662$	−1585.00	+	517.698i	−2.39426	+	0.782021i
$663$	−589.370	+	904.497i	−0.888944	+	1.36425i
$664$	1224.43	−	170.800i	1.84402	−	0.257229i
$665$	0.518476	−	1.47133i	0.000779663	−	0.00221252i
$666$	−2157.96	+	1013.02i	−3.24018	+	1.52106i
$667$	−87.9743	−	46.3720i	−0.131896	−	0.0695233i
$668$	1283.67	+	118.949i	1.92166	+	0.178068i
$669$	−764.937	−	753.247i	−1.14340	−	1.12593i
$670$	−20.2710	−	9.51592i	−0.0302552	−	0.0142029i
$671$	817.257	+	1082.22i	1.21797	+	1.61285i
$672$	−138.266	−	3.19449i	−0.205752	−	0.00475371i
$673$	−323.146	−	383.109i	−0.480157	−	0.569255i	0.469346	−	0.883015i	$-0.344490\pi$
$673$	−323.146	−	383.109i	−0.480157	−	0.569255i	−0.949502	+	0.313760i	$0.898411\pi$
$674$	−924.731	+	1079.35i	−1.37200	+	1.60141i
$675$	921.907	−	921.907i	1.36579	−	1.36579i
$676$	1129.54	−	87.1465i	1.67091	−	0.128915i
$677$	487.901	+	596.848i	0.720681	+	0.881608i	0.996834	−	0.0795060i	$-0.0253343\pi$
$677$	487.901	+	596.848i	0.720681	+	0.881608i	−0.276153	+	0.961114i	$0.589060\pi$
$678$	2336.01	−	2300.31i	3.44544	−	3.39279i
$679$	104.231	−	36.7297i	0.153507	−	0.0540938i
$680$	−72.5701	−	140.284i	−0.106721	−	0.206300i
$681$	3.88079	+	125.960i	0.00569866	+	0.184963i
$682$	585.790	−	456.701i	0.858929	−	0.669650i
$683$	−488.309	−	334.499i	−0.714947	−	0.489750i	0.151855	−	0.988403i	$-0.451475\pi$
$683$	−488.309	−	334.499i	−0.714947	−	0.489750i	−0.866802	+	0.498653i	$0.833828\pi$
$684$	−33.0549	+	127.275i	−0.0483259	+	0.186074i
$685$	−55.7610	−	8.65571i	−0.0814030	−	0.0126361i
$686$	89.6898	−	368.580i	0.130743	−	0.537289i
$687$	166.117	−	551.435i	0.241801	−	0.802671i
$688$	−32.7645	+	222.355i	−0.0476228	+	0.323190i
$689$	−29.4725	−	200.014i	−0.0427758	−	0.290296i
$690$	147.845	−	44.5378i	0.214269	−	0.0645475i
$691$	−514.951	+	27.7827i	−0.745225	+	0.0402065i	−0.422595	−	0.906319i	$-0.638881\pi$
$691$	−514.951	+	27.7827i	−0.745225	+	0.0402065i	−0.322630	+	0.946525i	$0.604567\pi$
$692$	−17.6796	+	4.88344i	−0.0255485	+	0.00705699i
$693$	−151.089	+	244.017i	−0.218022	+	0.352117i
$694$	393.141	+	33.3789i	0.566486	+	0.0480963i
$695$	40.9605	+	263.872i	0.0589359	+	0.379671i
$696$	−86.8272	+	864.508i	−0.124752	+	1.24211i
$697$	−45.4255	−	193.137i	−0.0651728	−	0.277098i
$698$	−445.884	−	1053.44i	−0.638803	−	1.50923i
$699$	2221.60	−	154.203i	3.17825	−	0.220606i
$700$	−107.517	−	159.577i	−0.153595	−	0.227967i
$701$	760.610	−	991.246i	1.08504	−	1.41405i	0.182617	−	0.983184i	$-0.441543\pi$
$701$	760.610	−	991.246i	1.08504	−	1.41405i	0.902418	−	0.430861i	$-0.141790\pi$
$702$	−1257.11	+	3172.25i	−1.79076	+	4.51887i
$703$	−34.7928	+	0.535850i	−0.0494919	+	0.000762234i
$704$	−602.057	+	1024.49i	−0.855195	+	1.45525i
$705$	−426.118	+	233.065i	−0.604423	+	0.330589i
$706$	−36.5407	−	11.3153i	−0.0517573	−	0.0160274i
$707$	45.9588	−	7.49697i	0.0650053	−	0.0106039i
$708$	−831.020	−	700.951i	−1.17376	−	0.990044i
$709$	78.4570	−	88.7713i	0.110659	−	0.125206i	−0.691347	−	0.722523i	$-0.742982\pi$
$709$	78.4570	−	88.7713i	0.110659	−	0.125206i	0.802005	+	0.597317i	$0.203767\pi$
$710$	36.8825	−	340.813i	0.0519472	−	0.480018i
$711$	−600.944	+	293.482i	−0.845210	+	0.412774i
$712$	−293.168	−	663.962i	−0.411753	−	0.932531i
$713$	−21.4697	+	110.150i	−0.0301118	+	0.154488i
$714$	−219.718	+	79.3328i	−0.307728	+	0.111110i
$715$	−177.154	−	258.613i	−0.247768	−	0.361696i
$716$	−669.815	+	2105.52i	−0.935495	+	2.94067i
$717$	669.842	−	1247.40i	0.934229	−	1.73976i
$718$	424.808	+	26.2013i	0.591655	+	0.0364920i
$719$	−308.758	−	815.585i	−0.429427	−	1.13433i	−0.958333	−	0.285652i	$-0.907790\pi$
$719$	−308.758	−	815.585i	−0.429427	−	1.13433i	0.528906	−	0.848680i	$-0.322602\pi$
$720$	−96.9509	−	120.481i	−0.134654	−	0.167335i
$721$	18.6654	−	57.1465i	0.0258882	−	0.0792600i
$722$	751.039	−	933.319i	1.04022	−	1.29269i
$723$	199.085	+	305.533i	0.275360	+	0.422591i
$724$	−976.978	−	1122.72i	−1.34942	−	1.55072i
$725$	319.554	−	181.228i	0.440764	−	0.249970i
$726$	288.423	+	517.818i	0.397277	+	0.713248i
$727$	−732.671	−	184.274i	−1.00780	−	0.253472i	−0.295497	−	0.955344i	$-0.595485\pi$
$727$	−732.671	−	184.274i	−1.00780	−	0.253472i	−0.712304	+	0.701871i	$0.752348\pi$
$728$	184.050	+	117.918i	0.252817	+	0.161976i
$729$	170.748	+	187.301i	0.234222	+	0.256929i
$730$	−95.5654	+	453.029i	−0.130912	+	0.620588i
$731$	−97.4947	−	429.329i	−0.133372	−	0.587317i
$732$	726.587	+	4059.72i	0.992605	+	5.54607i
$733$	−292.825	−	283.942i	−0.399489	−	0.387370i	0.468903	−	0.883250i	$-0.344650\pi$
$733$	−292.825	−	283.942i	−0.399489	−	0.387370i	−0.868391	+	0.495880i	$0.834846\pi$
$734$	−178.276	+	55.2057i	−0.242883	+	0.0752122i
$735$	−316.766	+	157.731i	−0.430974	+	0.214600i
$736$	−25.1512	−	134.547i	−0.0341729	−	0.182809i
$737$	28.4500	+	52.9807i	0.0386025	+	0.0718870i
$738$	−485.204	−	1054.62i	−0.657458	−	1.42903i
$739$	−1168.56	+	246.505i	−1.58127	+	0.333566i	−0.912237	−	0.409662i	$-0.865646\pi$
$739$	−1168.56	+	246.505i	−1.58127	+	0.333566i	−0.669038	+	0.743228i	$0.733294\pi$
$740$	210.129	−	292.045i	0.283958	−	0.394656i
$741$	−66.1920	+	64.1841i	−0.0893280	+	0.0866182i
$742$	20.9926	−	38.3812i	0.0282920	−	0.0517267i
$743$	−153.518	+	91.8144i	−0.206619	+	0.123573i	−0.612854	−	0.790196i	$-0.709979\pi$
$743$	−153.518	+	91.8144i	−0.206619	+	0.123573i	0.406235	+	0.913769i	$0.366841\pi$
$744$	962.362	−	187.577i	1.29350	−	0.252120i
$745$	8.14759	−	5.67389i	0.0109364	−	0.00761597i
$746$	−59.3275	+	768.966i	−0.0795275	+	1.03079i
$747$	−1800.64	+	1542.69i	−2.41049	+	2.06518i
$748$	−157.324	+	964.445i	−0.210326	+	1.28936i
$749$	98.6181	+	49.1060i	0.131666	+	0.0655620i
$750$	−325.277	+	1143.23i	−0.433702	+	1.52431i
$751$	−315.855	−	797.042i	−0.420580	−	1.06131i	−0.973624	−	0.228157i	$-0.926730\pi$
$751$	−315.855	−	797.042i	−0.420580	−	1.06131i	0.553045	−	0.833152i	$-0.313466\pi$
$752$	−142.073	−	342.994i	−0.188927	−	0.456109i
$753$	−855.190	−	1622.42i	−1.13571	−	2.15460i
$754$	−579.420	+	767.276i	−0.768461	+	1.01761i
$755$	182.123	−	229.927i	0.241222	−	0.304540i
$756$	−402.782	+	245.122i	−0.532780	+	0.324235i
$757$	392.273	+	667.513i	0.518194	+	0.881788i	0.999985	+	0.00550143i	$0.00175117\pi$
$757$	392.273	+	667.513i	0.518194	+	0.881788i	−0.481791	+	0.876286i	$0.660014\pi$
$758$	1741.25	+	1041.39i	2.29716	+	1.37386i
$759$	−390.010	−	140.819i	−0.513847	−	0.185533i
$760$	−3.39081	−	13.0560i	−0.00446160	−	0.0171789i
$761$	−11.5894	−	115.392i	−0.0152292	−	0.151632i	0.984487	−	0.175458i	$-0.0561406\pi$
$761$	−11.5894	−	115.392i	−0.0152292	−	0.151632i	−0.999716	+	0.0238264i	$0.992415\pi$
$762$	−703.816	+	241.939i	−0.923643	+	0.317506i
$763$	−201.891	−	14.0134i	−0.264601	−	0.0183662i
$764$	−714.348	−	1237.29i	−0.935010	−	1.61949i
$765$	262.341	+	151.463i	0.342929	+	0.197990i
$766$	−767.634	+	1139.33i	−1.00213	+	1.48737i
$767$	−165.945	−	495.112i	−0.216356	−	0.645518i
$768$	−1729.91	+	1108.33i	−2.25248	+	1.44313i
$769$	356.028	+	95.3974i	0.462975	+	0.124054i	0.482764	−	0.875750i	$-0.339633\pi$
$769$	356.028	+	95.3974i	0.462975	+	0.124054i	−0.0197891	+	0.999804i	$0.506299\pi$
$770$	3.13263	−	67.7577i	0.00406834	−	0.0879970i
$771$	79.9976	+	18.1664i	0.103758	+	0.0235621i
$772$	−2064.13	−	949.650i	−2.67374	−	1.23012i
$773$	−1048.56	+	64.6728i	−1.35648	+	0.0836647i	−0.723403	−	0.690426i	$-0.757423\pi$
$773$	−1048.56	+	64.6728i	−1.35648	+	0.0836647i	−0.633075	+	0.774091i	$0.718207\pi$
$774$	−1058.60	−	2348.40i	−1.36770	−	3.03410i
$775$	−299.831	−	286.289i	−0.386878	−	0.369405i
$776$	569.983	−	766.990i	0.734515	−	0.988389i
$777$	−168.272	−	158.213i	−0.216566	−	0.203620i
$778$	646.476	+	360.085i	0.830946	+	0.462834i
$779$	−0.130475	−	16.9445i	−0.000167490	−	0.0217516i
$780$	−124.432	−	945.157i	−0.159529	−	1.21174i
$781$	−625.409	+	675.519i	−0.800779	+	0.864941i
$782$	−121.709	−	196.566i	−0.155638	−	0.251364i
$783$	−407.449	−	802.718i	−0.520370	−	1.02518i
$784$	−93.8158	−	253.697i	−0.119663	−	0.323593i
$785$	−45.5883	−	27.7438i	−0.0580743	−	0.0353424i
$786$	−12.5500	+	814.875i	−0.0159670	+	1.03674i
$787$	288.411	−	696.286i	0.366469	−	0.884734i	−0.627854	−	0.778331i	$-0.716067\pi$
$787$	288.411	−	696.286i	0.366469	−	0.884734i	0.994323	−	0.106403i	$-0.0339334\pi$
$788$	2445.78	−	226.635i	3.10378	−	0.287608i
$789$	208.868	+	170.742i	0.264725	+	0.216403i
$790$	90.3253	−	129.705i	0.114336	−	0.164184i
$791$	199.052	+	87.8902i	0.251646	+	0.111113i
$792$	95.5212	+	2479.85i	0.120608	+	3.13112i
$793$	−715.595	+	1847.16i	−0.902389	+	2.32933i
$794$	1247.35	+	1882.44i	1.57097	+	2.37083i
$795$	−81.1593	+	16.4687i	−0.102087	+	0.0207153i
$796$	2401.23	+	1361.81i	3.01662	+	1.71081i
$797$	−5.91076	+	767.618i	−0.00741626	+	0.963134i	0.872667	+	0.488315i	$0.162388\pi$
$797$	−5.91076	+	767.618i	−0.00741626	+	0.963134i	−0.880083	+	0.474819i	$0.842514\pi$
$798$	−19.7995	+	2.45172i	−0.0248115	+	0.00307233i
$799$	502.212	+	525.967i	0.628551	+	0.658282i
$800$	468.623	+	189.896i	0.585779	+	0.237370i
$801$	1160.42	+	768.920i	1.44871	+	0.959950i
$802$	−1436.91	−	2029.86i	−1.79165	−	2.53099i
$803$	931.642	−	823.395i	1.16020	−	1.02540i
$804$	4.22422	+	182.834i	0.00525400	+	0.227406i
$805$	6.36310	+	8.03331i	0.00790447	+	0.00997927i
$806$	1017.64	+	376.318i	1.26258	+	0.466895i
$807$	1960.59	−	227.460i	2.42948	−	0.281859i
$808$	293.350	−	275.814i	0.363056	−	0.341354i
$809$	1176.17	−	295.818i	1.45385	−	0.365658i	0.565472	−	0.824768i	$-0.308694\pi$
$809$	1176.17	−	295.818i	1.45385	−	0.365658i	0.888380	+	0.459109i	$0.151831\pi$
$810$	552.551	+	185.196i	0.682162	+	0.228638i
$811$	214.545	+	279.600i	0.264543	+	0.344760i	0.906671	−	0.421838i	$-0.138615\pi$
$811$	214.545	+	279.600i	0.264543	+	0.344760i	−0.642128	+	0.766597i	$0.721948\pi$
$812$	−127.785	+	36.3581i	−0.157371	+	0.0447760i
$813$	−115.776	+	619.344i	−0.142405	+	0.761801i
$814$	−1441.79	+	458.667i	−1.77124	+	0.563473i
$815$	220.384	−	282.676i	0.270409	−	0.346841i
$816$	−199.523	+	272.848i	−0.244513	+	0.334373i
$817$		−	37.6004i		−	0.0460225i
$818$	942.922	−	980.977i	1.15272	−	1.19924i
$819$	−419.233			−0.511883
$820$	141.424	+	103.418i	0.172469	+	0.126119i
$821$	−510.368	−	397.900i	−0.621642	−	0.484653i	0.254264	−	0.967135i	$-0.418167\pi$
$821$	−510.368	−	397.900i	−0.621642	−	0.484653i	−0.875906	+	0.482482i	$0.839735\pi$
$822$	218.774	+	687.702i	0.266148	+	0.836621i
$823$	−147.459	−	27.5649i	−0.179173	−	0.0334932i	0.0933983	−	0.995629i	$-0.470227\pi$
$823$	−147.459	−	27.5649i	−0.179173	−	0.0334932i	−0.272571	+	0.962136i	$0.587874\pi$
$824$	−142.257	−	499.982i	−0.172642	−	0.606774i
$825$	1215.23	−	932.477i	1.47300	−	1.13027i
$826$	35.9078	−	107.134i	0.0434719	−	0.129703i
$827$	−14.7728	−	58.7365i	−0.0178632	−	0.0710236i	0.960215	−	0.279262i	$-0.0900898\pi$
$827$	−14.7728	−	58.7365i	−0.0178632	−	0.0710236i	−0.978078	+	0.208238i	$0.933227\pi$
$828$	−591.725	−	629.346i	−0.714644	−	0.760080i
$829$	−104.933	−	904.469i	−0.126578	−	1.09104i	−0.893427	−	0.449209i	$-0.851706\pi$
$829$	−104.933	−	904.469i	−0.126578	−	1.09104i	0.766849	−	0.641827i	$-0.221823\pi$
$830$	194.363	−	525.596i	0.234172	−	0.633249i
$831$	−380.515	+	301.402i	−0.457900	+	0.362697i
$832$	−1735.30	+	40.0926i	−2.08570	+	0.0481882i
$833$	350.880	+	397.008i	0.421224	+	0.476600i
$834$	2787.35	−	1973.12i	3.34214	−	2.36585i
$835$	140.100	−	211.432i	0.167784	−	0.253211i
$836$	−31.3430	+	77.3480i	−0.0374917	+	0.0925215i
$837$	−734.713	+	701.530i	−0.877794	+	0.838149i
$838$	−323.458	−	2612.18i	−0.385988	−	3.11716i
$839$	913.559	+	7.03453i	1.08887	+	0.00838442i	0.550892	−	0.834576i	$-0.314288\pi$
$839$	913.559	+	7.03453i	1.08887	+	0.00838442i	0.537975	+	0.842961i	$0.319190\pi$
$840$	44.1694	−	77.8825i	0.0525827	−	0.0927173i
$841$	116.803	+	575.616i	0.138886	+	0.684442i
$842$	1434.69	−	950.661i	1.70391	−	1.12905i
$843$	167.072	+	64.7241i	0.198188	+	0.0767783i
$844$	1706.81	−	65.7446i	2.02229	−	0.0778964i
$845$	90.0302	−	203.899i	0.106545	−	0.241301i
$846$	3491.76	+	2431.62i	4.12737	+	2.87426i
$847$	−24.8980	+	30.4576i	−0.0293955	+	0.0359594i
$848$	−5.84069	−	63.0311i	−0.00688761	−	0.0743292i
$849$	1194.75	+	494.882i	1.40724	+	0.582900i
$850$	853.951	+	13.1519i	1.00465	+	0.0154728i
$851$	118.837	−	195.272i	0.139644	−	0.229461i
$852$	−2625.83	+	971.017i	−3.08196	+	1.13969i
$853$	616.657	−	313.007i	0.722928	−	0.366949i	−0.0522995	−	0.998631i	$-0.516655\pi$
$853$	616.657	−	313.007i	0.722928	−	0.366949i	0.775227	+	0.631683i	$0.217635\pi$
$854$	−364.438	+	225.651i	−0.426743	+	0.264228i
$855$	18.9844	+	17.5761i	0.0222039	+	0.0205568i
$856$	944.452	−	124.339i	1.10333	−	0.145256i
$857$	−368.215	+	2.83531i	−0.429656	+	0.00330841i	−0.222348	−	0.974967i	$-0.571372\pi$
$857$	−368.215	+	2.83531i	−0.429656	+	0.00330841i	−0.207308	+	0.978276i	$0.566470\pi$
$858$	−1950.77	+	3502.30i	−2.27362	+	4.08194i
$859$	578.845	−	615.647i	0.673859	−	0.716702i	−0.297393	−	0.954755i	$-0.596117\pi$
$859$	578.845	−	615.647i	0.673859	−	0.716702i	0.971252	+	0.238053i	$0.0765092\pi$
$860$	312.040	+	231.891i	0.362837	+	0.269640i
$861$	77.6731	−	81.3472i	0.0902127	−	0.0944799i
$862$	820.349	−	369.793i	0.951681	−	0.428995i
$863$	3.13654	+	50.8536i	0.00363446	+	0.0589265i	0.999486	−	0.0320708i	$-0.0102102\pi$
$863$	3.13654	+	50.8536i	0.00363446	+	0.0589265i	−0.995851	+	0.0909973i	$0.970995\pi$
$864$	517.864	−	1125.61i	0.599380	−	1.30279i
$865$	−0.799121	+	3.51902i	−0.000923839	+	0.00406823i
$866$	939.523	+	43.4368i	1.08490	+	0.0501579i
$867$	−228.464	+	852.641i	−0.263511	+	0.983438i
$868$	80.8785	+	126.238i	0.0931780	+	0.145435i
$869$	−402.450	+	134.888i	−0.463119	+	0.155222i
$870$	326.618	+	220.062i	0.375423	+	0.252945i
$871$	−43.9208	+	76.0731i	−0.0504257	+	0.0873399i
$872$	−1515.47	+	874.958i	−1.73793	+	1.00339i
$873$	−126.909	+	1828.37i	−0.145371	+	2.09435i
$874$	−6.41885	−	18.6728i	−0.00734422	−	0.0213648i
$875$	−78.4928	+	7.88346i	−0.0897061	+	0.00900967i
$876$	3659.82	−	950.504i	4.17788	−	1.08505i
$877$	173.302	−	479.972i	0.197607	−	0.547288i	−0.801077	−	0.598561i	$-0.795740\pi$
$877$	173.302	−	479.972i	0.197607	−	0.547288i	0.998685	+	0.0512727i	$0.0163278\pi$
$878$	1286.78	−	2151.56i	1.46558	−	2.45052i
$879$	−404.703	+	237.829i	−0.460413	+	0.270568i
$880$	−51.0245	−	83.8431i	−0.0579824	−	0.0952762i
$881$	−746.473	−	591.273i	−0.847302	−	0.671138i	0.0987646	−	0.995111i	$-0.468511\pi$
$881$	−746.473	−	591.273i	−0.847302	−	0.671138i	−0.946067	+	0.323972i	$0.894982\pi$
$882$	2473.94	+	1868.24i	2.80492	+	2.11818i
$883$	1136.25	−	598.926i	1.28680	−	0.678285i	0.323379	−	0.946269i	$-0.395181\pi$
$883$	1136.25	−	598.926i	1.28680	−	0.678285i	0.963423	+	0.267984i	$0.0863575\pi$
$884$	−1318.74	+	546.241i	−1.49179	+	0.617920i
$885$	−198.849	+	78.8007i	−0.224688	+	0.0890403i
$886$	124.561	+	35.4407i	0.140588	+	0.0400007i
$887$	2.86797	−	5.75966i	0.00323333	−	0.00649341i	−0.893541	−	0.448982i	$-0.851787\pi$
$887$	2.86797	−	5.75966i	0.00323333	−	0.00649341i	0.896774	+	0.442489i	$0.145904\pi$
$888$	−1971.09	−	321.533i	−2.21970	−	0.362086i
$889$	−32.1374	−	37.5110i	−0.0361501	−	0.0421946i
$890$	−328.018	−	25.3074i	−0.368560	−	0.0284353i
$891$	−894.337	−	1284.25i	−1.00374	−	1.44136i
$892$	−271.557	−	1393.22i	−0.304436	−	1.56190i
$893$	31.8790	+	53.3032i	0.0356988	+	0.0596900i
$894$	−111.401	−	60.9308i	−0.124609	−	0.0681552i
$895$	302.614	+	312.081i	0.338116	+	0.348693i
$896$	−220.871	−	158.918i	−0.246507	−	0.177364i
$897$	−125.017	−	592.647i	−0.139373	−	0.660699i
$898$	−319.605	+	147.042i	−0.355908	+	0.163744i
$899$	−252.179	+	135.417i	−0.280510	+	0.150631i
$900$	3136.74	−	586.359i	3.48527	−	0.651510i
$901$	55.2700	+	110.997i	0.0613430	+	0.123193i
$902$	−217.943	−	703.806i	−0.241622	−	0.780272i
$903$	173.739	−	179.174i	0.192402	−	0.198421i
$904$	1852.06	−	331.471i	2.04873	−	0.366672i
$905$	−285.542	+	64.8426i	−0.315516	+	0.0716493i
$906$	−3670.43	−	774.269i	−4.05125	−	0.854601i
$907$	−979.669	+	893.086i	−1.08012	+	0.984660i	−0.999927	−	0.0121196i	$-0.996142\pi$
$907$	−979.669	+	893.086i	−1.08012	+	0.984660i	−0.0801937	+	0.996779i	$0.525554\pi$
$908$	−89.8863	+	140.297i	−0.0989937	+	0.154512i
$909$	−188.365	+	748.935i	−0.207222	+	0.823910i
$910$	86.5586	−	48.2128i	0.0951194	−	0.0529812i
$911$	493.283	+	869.790i	0.541474	+	0.954764i	0.997886	+	0.0649951i	$0.0207032\pi$
$911$	493.283	+	869.790i	0.541474	+	0.954764i	−0.456411	+	0.889769i	$0.650865\pi$
$912$	−21.7775	+	18.9505i	−0.0238788	+	0.0207791i
$913$	−1260.83	+	821.555i	−1.38097	+	0.899842i
$914$	−1304.65	−	1049.85i	−1.42740	−	1.14863i
$915$	771.318	+	251.930i	0.842971	+	0.275334i
$916$	593.243	−	477.381i	0.647645	−	0.521158i
$917$	−50.5861	+	19.1505i	−0.0551648	+	0.0208839i
$918$	128.834	−	2088.83i	0.140342	−	2.27541i
$919$	−216.331	−	116.167i	−0.235398	−	0.126406i	0.351154	−	0.936318i	$-0.385790\pi$
$919$	−216.331	−	116.167i	−0.235398	−	0.126406i	−0.586552	+	0.809912i	$0.699515\pi$
$920$	84.4434	+	26.8634i	0.0917863	+	0.0291993i
$921$	−150.351	+	102.993i	−0.163248	+	0.111827i
$922$	−765.228	−	2119.36i	−0.829965	−	2.29865i
$923$	−1319.86	−	257.258i	−1.42997	−	0.278719i
$924$	−506.756	+	223.755i	−0.548437	+	0.242159i
$925$	370.562	+	758.775i	0.400607	+	0.820298i
$926$	−1838.72	−	198.985i	−1.98566	−	0.214886i
$927$	747.044	+	660.245i	0.805873	+	0.712239i
$928$	225.098	−	266.867i	0.242562	−	0.287572i
$929$	277.063	+	1698.48i	0.298238	+	1.82829i	0.521167	+	0.853455i	$0.325497\pi$
$929$	277.063	+	1698.48i	0.298238	+	1.82829i	−0.222930	+	0.974835i	$0.571562\pi$
$930$	131.465	−	424.540i	0.141360	−	0.456494i
$931$	21.7144	+	39.7008i	0.0233237	+	0.0426432i
$932$	2538.55	+	1491.81i	2.72377	+	1.60066i
$933$	23.4705	+	1523.94i	0.0251559	+	1.63338i
$934$	−878.301	−	348.057i	−0.940365	−	0.372652i
$935$	152.528	+	117.039i	0.163131	+	0.125175i
$936$	−3006.33	+	2025.55i	−3.21189	+	2.16405i
$937$	72.0021	+	1037.33i	0.0768432	+	1.10708i	0.868362	+	0.495931i	$0.165173\pi$
$937$	72.0021	+	1037.33i	0.0768432	+	1.10708i	−0.791519	+	0.611145i	$0.790709\pi$
$938$	−17.5041	+	7.40886i	−0.0186611	+	0.00789857i
$939$	−1789.36	+	420.853i	−1.90560	+	0.448193i
$940$	−638.961	−	64.1743i	−0.679746	−	0.0682706i
$941$	277.994	−	43.1527i	0.295424	−	0.0458583i	−0.00395623	−	0.999992i	$-0.501259\pi$
$941$	277.994	−	43.1527i	0.295424	−	0.0458583i	0.299380	+	0.954134i	$0.403220\pi$
$942$	−57.7386	+	680.055i	−0.0612937	+	0.721927i
$943$	94.6426	+	58.6002i	0.100363	+	0.0621423i
$944$	−43.5308	−	157.595i	−0.0461132	−	0.166944i
$945$	4.99766	+	92.6315i	0.00528853	+	0.0980227i
$946$	−471.570	−	1565.40i	−0.498488	−	1.65476i
$947$	−1220.12	+	179.788i	−1.28841	+	0.189850i	−0.754841	−	0.655907i	$-0.772286\pi$
$947$	−1220.12	+	179.788i	−1.28841	+	0.189850i	−0.533567	+	0.845758i	$0.679149\pi$
$948$	−1277.04	−	188.175i	−1.34709	−	0.198497i
$949$	1738.99	+	523.865i	1.83245	+	0.552017i
$950$	70.8723	+	17.2460i	0.0746024	+	0.0181537i
$951$	475.216	−	3061.39i	0.499701	−	3.21913i
$952$	−129.757	−	33.6996i	−0.136300	−	0.0353988i
$953$	−886.646	+	1294.34i	−0.930374	+	1.35818i	0.00327705	+	0.999995i	$0.498957\pi$
$953$	−886.646	+	1294.34i	−0.930374	+	1.35818i	−0.933651	+	0.358184i	$0.883396\pi$
$954$	446.079	+	572.165i	0.467588	+	0.599754i
$955$	−280.955	+	8.65612i	−0.294193	+	0.00906400i
$956$	1662.75	−	860.155i	1.73928	−	0.899744i
$957$	−351.506	−	997.501i	−0.367300	−	1.04232i
$958$	1810.46	+	1838.55i	1.88983	+	1.91916i
$959$	−37.0831	+	30.3141i	−0.0386685	+	0.0316101i
$960$	54.6925	+	708.890i	0.0569714	+	0.738427i
$961$	−451.128	−	451.128i	−0.469436	−	0.469436i
$962$	−1678.32	−	1437.90i	−1.74461	−	1.49469i
$963$	−1396.57	+	1177.98i	−1.45023	+	1.22324i
$964$	−11.1370	+	482.037i	−0.0115529	+	0.500038i
$965$	−356.733	+	269.392i	−0.369672	+	0.279163i
$966$	55.6937	−	118.640i	0.0576539	−	0.122815i
$967$	591.972	−	601.160i	0.612174	−	0.621675i	−0.335068	−	0.942194i	$-0.608759\pi$
$967$	591.972	−	601.160i	0.612174	−	0.621675i	0.947242	+	0.320519i	$0.103857\pi$
$968$	−31.3860	+	338.709i	−0.0324235	+	0.349906i
$969$	26.3683	−	50.0243i	0.0272118	−	0.0516247i
$970$	−184.064	−	392.097i	−0.189757	−	0.404223i
$971$	−1703.41	−	600.258i	−1.75428	−	0.618186i	−0.754989	−	0.655738i	$-0.772358\pi$
$971$	−1703.41	−	600.258i	−1.75428	−	0.618186i	−0.999295	+	0.0375521i	$0.988044\pi$
$972$	−160.806	−	1152.78i	−0.165438	−	1.18599i
$973$	189.900	+	123.739i	0.195169	+	0.127172i
$974$	−535.085	−	1638.23i	−0.549368	−	1.68196i
$975$	2092.53	+	792.176i	2.14619	+	0.812488i
$976$	−254.887	+	565.442i	−0.261155	+	0.579346i
$977$	985.545	−	399.363i	1.00875	−	0.408765i	0.189299	−	0.981920i	$-0.439379\pi$
$977$	985.545	−	399.363i	1.00875	−	0.408765i	0.819447	+	0.573155i	$0.194281\pi$
$978$	−4492.41	−	911.590i	−4.59347	−	0.932096i
$979$	666.482	+	579.965i	0.680778	+	0.592405i
$980$	−463.389	−	64.6399i	−0.472845	−	0.0659591i
$981$	1542.09	−	2980.99i	1.57196	−	3.03872i
$982$	−1544.44	−	739.584i	−1.57275	−	0.753140i
$983$	−142.090	+	158.297i	−0.144548	+	0.161034i	−0.812080	−	0.583547i	$-0.801664\pi$
$983$	−142.090	+	158.297i	−0.144548	+	0.161034i	0.667532	+	0.744581i	$0.267351\pi$
$984$	163.962	−	958.626i	0.166628	−	0.974213i
$985$	188.366	−	445.032i	0.191234	−	0.451809i
$986$	191.698	−	557.662i	0.194420	−	0.565580i
$987$	−94.3859	+	401.304i	−0.0956291	+	0.406590i
$988$	−120.162	+	20.5524i	−0.121621	+	0.0208020i
$989$	209.001	+	131.645i	0.211326	+	0.133109i
$990$	1010.80	+	493.643i	1.02101	+	0.498629i
$991$	−31.1885	+	809.693i	−0.0314717	+	0.817046i	0.896200	+	0.443650i	$0.146317\pi$
$991$	−31.1885	+	809.693i	−0.0314717	+	0.817046i	−0.927672	+	0.373396i	$0.878193\pi$
$992$	−361.618	−	156.354i	−0.364534	−	0.157615i
$993$	2571.16	−	753.005i	2.58928	−	0.758313i
$994$	−194.364	−	216.533i	−0.195538	−	0.217840i
$995$	459.551	−	289.460i	0.461860	−	0.290915i
$996$	−4549.98	+	492.396i	−4.56826	+	0.494373i
$997$	−946.592	−	670.079i	−0.949440	−	0.672095i	−0.00472576	−	0.999989i	$-0.501504\pi$
$997$	−946.592	−	670.079i	−0.949440	−	0.672095i	−0.944715	+	0.327894i	$0.893661\pi$
$998$	−757.334	+	293.393i	−0.758852	+	0.293981i
$999$	1899.28	−	821.196i	1.90118	−	0.822018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.3.p.a.21.8	✓	8576
409.39	odd	408	inner	409.3.p.a.39.8	yes	8576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.3.p.a.21.8	✓	8576	1.1	even	1	trivial
409.3.p.a.39.8	yes	8576	409.39	odd	408	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	409.p (of order \(408\), degree \(128\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68542 - 1.96373i) q^{2} +(4.21566 + 3.28667i) q^{3} +(2.14260 + 6.73512i) q^{4} +(1.36686 + 0.255510i) q^{5} +(-4.86665 - 17.1045i) q^{6} +(0.936382 - 0.718511i) q^{7} +(3.24329 - 9.67665i) q^{8} +(4.77435 + 18.9828i) q^{9} +(-3.16882 - 3.37029i) q^{10} +(1.43166 + 12.3402i) q^{11} +(-13.1036 + 35.4349i) q^{12} +(-14.2247 + 11.2672i) q^{13} +(-3.92554 + 0.0906959i) q^{14} +(4.92242 + 5.56954i) q^{15} +(-4.63738 + 3.28273i) q^{16} +(6.14755 - 9.27758i) q^{17} +(24.4560 - 60.3521i) q^{18} +(0.687461 - 0.656412i) q^{19} +(1.20773 + 9.75339i) q^{20} +(6.30897 + 0.0485799i) q^{21} +(20.3883 - 35.9500i) q^{22} +(1.24175 + 6.11946i) q^{23} +(45.4765 - 30.1338i) q^{24} +(-21.5088 - 8.33255i) q^{25} +(60.3250 - 2.32365i) q^{26} +(-22.8307 + 51.7065i) q^{27} +(6.84554 + 4.76716i) q^{28} +(-10.0799 + 12.3308i) q^{29} +(-2.28164 - 24.6229i) q^{30} +(16.6044 + 6.87775i) q^{31} +(-21.9183 - 0.337568i) q^{32} +(-34.5228 + 56.7275i) q^{33} +(-34.7274 + 12.8420i) q^{34} +(1.46349 - 0.742847i) q^{35} +(-117.622 + 72.8282i) q^{36} +(-26.8633 - 24.8706i) q^{37} +(-3.13514 + 0.412749i) q^{38} +(-96.9979 + 0.746897i) q^{39} +(6.90559 - 12.3979i) q^{40} +(12.2115 - 12.9879i) q^{41} +(-16.8468 - 12.5196i) q^{42} +(27.3181 - 28.6103i) q^{43} +(-80.0453 + 36.0825i) q^{44} +(1.67558 + 27.1666i) q^{45} +(8.68238 - 18.8717i) q^{46} +(-14.4699 + 63.7199i) q^{47} +(-30.3388 - 1.40265i) q^{48} +(-12.3216 + 45.9848i) q^{49} +(41.3971 + 64.6139i) q^{50} +(56.4083 - 18.9061i) q^{51} +(-106.364 - 71.6638i) q^{52} +(-5.57063 + 9.64861i) q^{53} +(162.848 - 94.0202i) q^{54} +(-1.19617 + 17.2331i) q^{55} +(-3.91583 - 11.3914i) q^{56} +(5.05551 - 0.507752i) q^{57} +(51.2832 - 13.3189i) q^{58} +(-9.77256 + 27.0658i) q^{59} +(-26.9648 + 45.0864i) q^{60} +(94.1156 - 55.3083i) q^{61} +(-31.0835 - 51.0762i) q^{62} +(18.1099 + 14.3447i) q^{63} +(76.3332 + 57.6442i) q^{64} +(-22.3220 + 11.7661i) q^{65} +(204.106 - 84.5433i) q^{66} +(4.50024 - 1.78337i) q^{67} +(75.6573 + 21.5264i) q^{68} +(-14.8778 + 29.8787i) q^{69} +(-5.38882 - 0.879045i) q^{70} +(48.2126 + 56.2740i) q^{71} +(199.174 + 15.3668i) q^{72} +(-57.1959 - 82.1321i) q^{73} +(23.2999 + 119.540i) q^{74} +(-63.2874 - 105.819i) q^{75} +(5.89397 + 3.22371i) q^{76} +(10.2072 + 10.5265i) q^{77} +(261.947 + 188.472i) q^{78} +(7.05220 + 33.4311i) q^{79} +(-7.17740 + 3.30213i) q^{80} +(-110.984 + 59.5974i) q^{81} +(-58.2979 + 10.8978i) q^{82} +(53.9951 + 108.437i) q^{83} +(13.1904 + 42.5958i) q^{84} +(10.7733 - 11.1104i) q^{85} +(-129.543 + 23.1850i) q^{86} +(-83.0207 + 18.8529i) q^{87} +(124.055 + 26.1691i) q^{88} +(52.5565 - 47.9116i) q^{89} +(48.8483 - 76.2440i) q^{90} +(-5.22412 + 20.7710i) q^{91} +(-38.5547 + 21.4748i) q^{92} +(47.3934 + 83.5673i) q^{93} +(163.987 - 142.699i) q^{94} +(1.10738 - 0.721568i) q^{95} +(-91.2906 - 73.4612i) q^{96} +(89.0056 + 29.0713i) q^{97} +(123.390 - 99.2919i) q^{98} +(-227.416 + 86.0934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) \) 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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