LMFDB - Embedded newform 78.3.j.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(17,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("78.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2 x^{18} - 12 x^{17} - 51 x^{16} - 180 x^{15} + 1136 x^{14} + 144 x^{13} + 6481 x^{12} + \cdots + 3486784401 $ x^20 + 2x^18 - 12x^17 - 51x^16 - 180x^15 + 1136x^14 + 144x^13 + 6481x^12 - 16152x^11 - 55134x^10 - 145368x^9 + 524961x^8 + 104976x^7 + 7453296x^6 - 10628820x^5 - 27103491x^4 - 57395628x^3 + 86093442*x^2 + 3486784401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.9
Root			$-2.45009 - 1.73120i$ of defining polynomial
Character	$\chi$	$=$	78.17
Dual form			78.3.j.a.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(2.45009 + 1.73120i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.77863 q^{5} +(3.85276 - 1.77659i) q^{6} +(10.9882 - 6.34403i) q^{7} -2.82843 q^{8} +(3.00587 + 8.48320i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(2.45009 + 1.73120i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.77863 q^{5} +(3.85276 - 1.77659i) q^{6} +(10.9882 - 6.34403i) q^{7} -2.82843 q^{8} +(3.00587 + 8.48320i) q^{9} +(-1.25768 + 2.17836i) q^{10} +(-5.17440 + 8.96232i) q^{11} +(0.548442 - 5.97488i) q^{12} +(-11.8980 - 5.23798i) q^{13} -17.9436i q^{14} +(-4.35780 - 3.07916i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-10.1789 + 5.87678i) q^{17} +(12.5152 + 2.31710i) q^{18} +(-0.0496245 + 0.0286507i) q^{19} +(1.77863 + 3.08067i) q^{20} +(37.9048 + 3.47933i) q^{21} +(7.31771 + 12.6746i) q^{22} +(-27.0257 - 15.6033i) q^{23} +(-6.92990 - 4.89658i) q^{24} -21.8365 q^{25} +(-14.8284 + 10.8683i) q^{26} +(-7.32148 + 25.9884i) q^{27} +(-21.9764 - 12.6881i) q^{28} +(26.2034 + 15.1285i) q^{29} +(-6.85262 + 3.15989i) q^{30} +8.94565i q^{31} +(2.82843 + 4.89898i) q^{32} +(-28.1933 + 13.0006i) q^{33} +16.6220i q^{34} +(-19.5439 + 11.2837i) q^{35} +(11.6875 - 13.6895i) q^{36} +(45.2171 + 26.1061i) q^{37} +0.0810365i q^{38} +(-20.0833 - 33.4315i) q^{39} +5.03072 q^{40} +(26.8888 - 46.5727i) q^{41} +(31.0641 - 43.9635i) q^{42} +(3.38349 + 5.86037i) q^{43} +20.6976 q^{44} +(-5.34633 - 15.0885i) q^{45} +(-38.2201 + 22.0664i) q^{46} -7.62439 q^{47} +(-10.8972 + 5.02495i) q^{48} +(55.9934 - 96.9835i) q^{49} +(-15.4407 + 26.7441i) q^{50} +(-35.1131 - 3.22307i) q^{51} +(2.82559 + 25.8460i) q^{52} -83.0208i q^{53} +(26.6521 + 27.3435i) q^{54} +(9.20333 - 15.9406i) q^{55} +(-31.0793 + 17.9436i) q^{56} +(-0.171185 - 0.0157132i) q^{57} +(37.0572 - 21.3950i) q^{58} +(23.4685 + 40.6486i) q^{59} +(-0.975473 + 10.6271i) q^{60} +(4.75002 + 8.22727i) q^{61} +(10.9561 + 6.32553i) q^{62} +(86.8468 + 74.1456i) q^{63} +8.00000 q^{64} +(21.1622 + 9.31642i) q^{65} +(-4.01333 + 43.7224i) q^{66} +(-34.9298 - 20.1667i) q^{67} +(20.3578 + 11.7536i) q^{68} +(-39.2029 - 85.0165i) q^{69} +31.9150i q^{70} +(5.96936 + 10.3392i) q^{71} +(-8.50190 - 23.9941i) q^{72} +41.6722i q^{73} +(63.9466 - 36.9196i) q^{74} +(-53.5013 - 37.8034i) q^{75} +(0.0992490 + 0.0573014i) q^{76} +131.306i q^{77} +(-55.1460 + 0.957271i) q^{78} -52.4233 q^{79} +(3.55725 - 6.16135i) q^{80} +(-62.9294 + 50.9989i) q^{81} +(-38.0265 - 65.8638i) q^{82} +46.5802 q^{83} +(-31.8785 - 69.1324i) q^{84} +(18.1044 - 10.4526i) q^{85} +9.56995 q^{86} +(38.0101 + 82.4297i) q^{87} +(14.6354 - 25.3493i) q^{88} +(67.4139 - 116.764i) q^{89} +(-22.2599 - 4.12126i) q^{90} +(-163.968 + 17.9257i) q^{91} +62.4132i q^{92} +(-15.4867 + 21.9176i) q^{93} +(-5.39126 + 9.33793i) q^{94} +(0.0882635 - 0.0509589i) q^{95} +(-1.55123 + 16.8995i) q^{96} +(62.8647 - 36.2950i) q^{97} +(-79.1867 - 137.155i) q^{98} +(-91.5828 - 16.9559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$	2.45009	+	1.73120i	0.816696	+	0.577068i
$3$	2.45009	+	1.73120i	0.816696	+	0.577068i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−1.77863			−0.355725			−0.177863	−	0.984055i	$-0.556918\pi$
$5$	−1.77863			−0.355725			−0.177863	+	0.984055i	$0.556918\pi$
$6$	3.85276	−	1.77659i	0.642126	−	0.296098i
$7$	10.9882	−	6.34403i	1.56974	−	0.906290i	0.573542	−	0.819176i	$-0.305569\pi$
$7$	10.9882	−	6.34403i	1.56974	−	0.906290i	0.996198	−	0.0871139i	$-0.0277644\pi$
$8$	−2.82843			−0.353553
$9$	3.00587	+	8.48320i	0.333986	+	0.942578i
$10$	−1.25768	+	2.17836i	−0.125768	+	0.217836i
$11$	−5.17440	+	8.96232i	−0.470400	+	0.814757i	−0.999427	−	0.0338484i	$-0.989224\pi$
$11$	−5.17440	+	8.96232i	−0.470400	+	0.814757i	0.529027	+	0.848605i	$0.322557\pi$
$12$	0.548442	−	5.97488i	0.0457035	−	0.497907i
$13$	−11.8980	−	5.23798i	−0.915234	−	0.402922i
$13$	−11.8980	−	5.23798i	−0.915234	−	0.402922i
$14$		−	17.9436i		−	1.28169i
$15$	−4.35780	−	3.07916i	−0.290520	−	0.205278i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−10.1789	+	5.87678i	−0.598758	+	0.345693i	−0.768553	−	0.639786i	$-0.779023\pi$
$17$	−10.1789	+	5.87678i	−0.598758	+	0.345693i	0.169795	+	0.985479i	$0.445689\pi$
$18$	12.5152	+	2.31710i	0.695291	+	0.128728i
$19$	−0.0496245	+	0.0286507i	−0.00261182	+	0.00150793i	−0.501305	−	0.865270i	$-0.667147\pi$
$19$	−0.0496245	+	0.0286507i	−0.00261182	+	0.00150793i	0.498694	+	0.866778i	$0.333813\pi$
$20$	1.77863	+	3.08067i	0.0889314	+	0.154034i
$21$	37.9048	+	3.47933i	1.80499	+	0.165682i
$22$	7.31771	+	12.6746i	0.332623	+	0.576120i
$23$	−27.0257	−	15.6033i	−1.17503	−	0.678405i	−0.220171	−	0.975461i	$-0.570662\pi$
$23$	−27.0257	−	15.6033i	−1.17503	−	0.678405i	−0.954860	+	0.297057i	$0.903995\pi$
$24$	−6.92990	−	4.89658i	−0.288746	−	0.204024i
$25$	−21.8365			−0.873459
$26$	−14.8284	+	10.8683i	−0.570322	+	0.418010i
$27$	−7.32148	+	25.9884i	−0.271166	+	0.962533i
$28$	−21.9764	−	12.6881i	−0.784870	−	0.453145i
$29$	26.2034	+	15.1285i	0.903565	+	0.521674i	0.878355	−	0.478008i	$-0.158641\pi$
$29$	26.2034	+	15.1285i	0.903565	+	0.521674i	0.0252101	+	0.999682i	$0.491975\pi$
$30$	−6.85262	+	3.15989i	−0.228421	+	0.105330i
$31$			8.94565i			0.288569i	0.989536	+	0.144285i	$0.0460881\pi$
$31$			8.94565i			0.288569i	−0.989536	+	0.144285i	$0.953912\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	−28.1933	+	13.0006i	−0.854344	+	0.393956i
$34$			16.6220i			0.488884i
$35$	−19.5439	+	11.2837i	−0.558397	+	0.322390i
$36$	11.6875	−	13.6895i	0.324652	−	0.380265i
$37$	45.2171	+	26.1061i	1.22208	+	0.705570i	0.965362	−	0.260915i	$-0.0840243\pi$
$37$	45.2171	+	26.1061i	1.22208	+	0.705570i	0.256722	+	0.966485i	$0.417358\pi$
$38$			0.0810365i			0.00213254i
$39$	−20.0833	−	33.4315i	−0.514956	−	0.857217i
$40$	5.03072			0.125768
$41$	26.8888	−	46.5727i	0.655824	−	1.13592i	−0.325863	−	0.945417i	$-0.605655\pi$
$41$	26.8888	−	46.5727i	0.655824	−	1.13592i	0.981687	−	0.190503i	$-0.0610120\pi$
$42$	31.0641	−	43.9635i	0.739620	−	1.04675i
$43$	3.38349	+	5.86037i	0.0786858	+	0.136288i	0.902683	−	0.430306i	$-0.141594\pi$
$43$	3.38349	+	5.86037i	0.0786858	+	0.136288i	−0.823997	+	0.566594i	$0.808261\pi$
$44$	20.6976			0.470400
$45$	−5.34633	−	15.0885i	−0.118807	−	0.335299i
$46$	−38.2201	+	22.0664i	−0.830872	+	0.479704i
$47$	−7.62439			−0.162221			−0.0811105	−	0.996705i	$-0.525847\pi$
$47$	−7.62439			−0.162221			−0.0811105	+	0.996705i	$0.525847\pi$
$48$	−10.8972	+	5.02495i	−0.227026	+	0.104687i
$49$	55.9934	−	96.9835i	1.14272	−	1.97925i
$50$	−15.4407	+	26.7441i	−0.308815	+	0.534882i
$51$	−35.1131	−	3.22307i	−0.688492	−	0.0631975i
$52$	2.82559	+	25.8460i	0.0543384	+	0.497039i
$53$		−	83.0208i		−	1.56643i	−0.621751	−	0.783215i	$-0.713578\pi$
$53$		−	83.0208i		−	1.56643i	0.621751	−	0.783215i	$-0.286422\pi$
$54$	26.6521	+	27.3435i	0.493557	+	0.506361i
$55$	9.20333	−	15.9406i	0.167333	−	0.289830i
$56$	−31.0793	+	17.9436i	−0.554987	+	0.320422i
$57$	−0.171185	−	0.0157132i	−0.00300324	−	0.000275671i
$58$	37.0572	−	21.3950i	0.638917	−	0.368879i
$59$	23.4685	+	40.6486i	0.397771	+	0.688959i	0.993451	−	0.114263i	$-0.0364507\pi$
$59$	23.4685	+	40.6486i	0.397771	+	0.688959i	−0.595680	+	0.803222i	$0.703117\pi$
$60$	−0.975473	+	10.6271i	−0.0162579	+	0.177118i
$61$	4.75002	+	8.22727i	0.0778692	+	0.134873i	0.902330	−	0.431045i	$-0.141855\pi$
$61$	4.75002	+	8.22727i	0.0778692	+	0.134873i	−0.824461	+	0.565918i	$0.808522\pi$
$62$	10.9561	+	6.32553i	0.176712	+	0.102025i
$63$	86.8468	+	74.1456i	1.37852	+	1.17691i
$64$	8.00000			0.125000
$65$	21.1622	+	9.31642i	0.325572	+	0.143330i
$66$	−4.01333	+	43.7224i	−0.0608081	+	0.662461i
$67$	−34.9298	−	20.1667i	−0.521340	−	0.300996i	0.216143	−	0.976362i	$-0.430652\pi$
$67$	−34.9298	−	20.1667i	−0.521340	−	0.300996i	−0.737483	+	0.675366i	$0.763986\pi$
$68$	20.3578	+	11.7536i	0.299379	+	0.172847i
$69$	−39.2029	−	85.0165i	−0.568158	−	1.23212i
$70$			31.9150i			0.455929i
$71$	5.96936	+	10.3392i	0.0840755	+	0.145623i	0.904997	−	0.425418i	$-0.139873\pi$
$71$	5.96936	+	10.3392i	0.0840755	+	0.145623i	−0.820921	+	0.571041i	$0.806540\pi$
$72$	−8.50190	−	23.9941i	−0.118082	−	0.333252i
$73$			41.6722i			0.570852i	0.958401	+	0.285426i	$0.0921352\pi$
$73$			41.6722i			0.570852i	−0.958401	+	0.285426i	$0.907865\pi$
$74$	63.9466	−	36.9196i	0.864143	−	0.498913i
$75$	−53.5013	−	37.8034i	−0.713351	−	0.504045i
$76$	0.0992490	+	0.0573014i	0.00130591	+	0.000753966i
$77$			131.306i			1.70528i
$78$	−55.1460	+	0.957271i	−0.707000	+	0.0122727i
$79$	−52.4233			−0.663586			−0.331793	−	0.943352i	$-0.607653\pi$
$79$	−52.4233			−0.663586			−0.331793	+	0.943352i	$0.607653\pi$
$80$	3.55725	−	6.16135i	0.0444657	−	0.0770168i
$81$	−62.9294	+	50.9989i	−0.776907	+	0.629616i
$82$	−38.0265	−	65.8638i	−0.463738	−	0.803217i
$83$	46.5802			0.561208			0.280604	−	0.959824i	$-0.409465\pi$
$83$	46.5802			0.561208			0.280604	+	0.959824i	$0.409465\pi$
$84$	−31.8785	−	69.1324i	−0.379505	−	0.823005i
$85$	18.1044	−	10.4526i	0.212993	−	0.122972i
$86$	9.56995			0.111278
$87$	38.0101	+	82.4297i	0.436898	+	0.947467i
$88$	14.6354	−	25.3493i	0.166311	−	0.288060i
$89$	67.4139	−	116.764i	0.757459	−	1.31196i	−0.186683	−	0.982420i	$-0.559774\pi$
$89$	67.4139	−	116.764i	0.757459	−	1.31196i	0.944142	−	0.329538i	$-0.106893\pi$
$90$	−22.2599	−	4.12126i	−0.247333	−	0.0457917i
$91$	−163.968	+	17.9257i	−1.80184	+	0.196985i
$92$			62.4132i			0.678405i
$93$	−15.4867	+	21.9176i	−0.166524	+	0.235673i
$94$	−5.39126	+	9.33793i	−0.0573538	+	0.0993397i
$95$	0.0882635	−	0.0509589i	0.000929089	−	0.000536410i
$96$	−1.55123	+	16.8995i	−0.0161586	+	0.176037i
$97$	62.8647	−	36.2950i	0.648090	−	0.374175i	−0.139634	−	0.990203i	$-0.544593\pi$
$97$	62.8647	−	36.2950i	0.648090	−	0.374175i	0.787724	+	0.616028i	$0.211259\pi$
$98$	−79.1867	−	137.155i	−0.808027	−	1.39954i
$99$	−91.5828	−	16.9559i	−0.925079	−	0.171271i
$100$	21.8365	+	37.8219i	0.218365	+	0.378219i
$101$	124.581	+	71.9267i	1.23347	+	0.712145i	0.967752	−	0.251905i	$-0.0810571\pi$
$101$	124.581	+	71.9267i	1.23347	+	0.712145i	0.265720	+	0.964050i	$0.414390\pi$
$102$	−28.7761	+	40.7255i	−0.282119	+	0.399270i
$103$	−10.8666			−0.105501			−0.0527506	−	0.998608i	$-0.516799\pi$
$103$	−10.8666			−0.105501			−0.0527506	+	0.998608i	$0.516799\pi$
$104$	33.6528	+	14.8153i	0.323584	+	0.142454i
$105$	−67.4186	−	6.18843i	−0.642082	−	0.0589374i
$106$	−101.679	−	58.7046i	−0.959238	−	0.553817i
$107$	−136.156	−	78.6095i	−1.27248	−	0.734668i	−0.297028	−	0.954869i	$-0.595996\pi$
$107$	−136.156	−	78.6095i	−1.27248	−	0.734668i	−0.975455	+	0.220200i	$0.929329\pi$
$108$	52.3347	−	13.3072i	0.484580	−	0.123215i
$109$			166.439i			1.52697i	0.645828	+	0.763483i	$0.276512\pi$
$109$			166.439i			1.52697i	−0.645828	+	0.763483i	$0.723488\pi$
$110$	−13.0155	−	22.5435i	−0.118322	−	0.204941i
$111$	65.5909	+	142.242i	0.590909	+	1.28146i
$112$			50.7522i			0.453145i
$113$	−119.853	+	69.1970i	−1.06064	+	0.612363i	−0.925610	−	0.378478i	$-0.876448\pi$
$113$	−119.853	+	69.1970i	−1.06064	+	0.612363i	−0.135033	+	0.990841i	$0.543114\pi$
$114$	−0.140291	+	0.198547i	−0.00123062	+	0.00174164i
$115$	48.0687	+	27.7525i	0.417988	+	0.241326i
$116$		−	60.5141i		−	0.521674i
$117$	8.67082	−	116.678i	0.0741096	−	0.997250i
$118$	66.3788			0.562532
$119$	−74.5650	+	129.150i	−0.626596	+	1.08530i
$120$	12.3257	+	8.70919i	0.102714	+	0.0725766i
$121$	6.95118	+	12.0398i	0.0574478	+	0.0995025i
$122$	13.4351			0.110124
$123$	146.507	−	67.5574i	1.19111	−	0.549247i
$124$	15.4943	−	8.94565i	0.124954	−	0.0721423i
$125$	83.3046			0.666437
$126$	152.219	−	53.9363i	1.20809	−	0.428066i
$127$	102.040	−	176.738i	0.803464	−	1.39164i	−0.113859	−	0.993497i	$-0.536321\pi$
$127$	102.040	−	176.738i	0.803464	−	1.39164i	0.917323	−	0.398143i	$-0.130345\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	−1.85565	+	20.2159i	−0.0143849	+	0.156713i
$130$	26.3742	−	19.3306i	0.202878	−	0.148697i
$131$			29.6858i			0.226609i	0.993560	+	0.113305i	$0.0361436\pi$
$131$			29.6858i			0.226609i	−0.993560	+	0.113305i	$0.963856\pi$
$132$	50.7110	+	35.8317i	0.384174	+	0.271453i
$133$	−0.363522	+	0.629639i	−0.00273325	+	0.00473413i
$134$	−49.3981	+	28.5200i	−0.368643	+	0.212836i
$135$	13.0222	−	46.2236i	0.0964606	−	0.342397i
$136$	28.7902	−	16.6220i	0.211693	−	0.122221i
$137$	−55.5078	−	96.1423i	−0.405166	−	0.701768i	0.589175	−	0.808006i	$-0.299453\pi$
$137$	−55.5078	−	96.1423i	−0.405166	−	0.701768i	−0.994341	+	0.106237i	$0.966120\pi$
$138$	−131.844	−	12.1021i	−0.955392	−	0.0876966i
$139$	18.9759	+	32.8672i	0.136517	+	0.236455i	0.926176	−	0.377092i	$-0.123076\pi$
$139$	18.9759	+	32.8672i	0.136517	+	0.236455i	−0.789659	+	0.613546i	$0.789742\pi$
$140$	39.0878	+	22.5673i	0.279198	+	0.161195i
$141$	−18.6804	−	13.1994i	−0.132485	−	0.0936125i
$142$	16.8839			0.118901
$143$	108.510	−	79.5307i	0.758809	−	0.556159i
$144$	−35.3984	−	6.55375i	−0.245822	−	0.0455121i
$145$	−46.6061	−	26.9080i	−0.321421	−	0.185573i
$146$	51.0378	+	29.4667i	0.349574	+	0.201827i
$147$	305.087	−	140.682i	2.07542	−	0.957022i
$148$		−	104.424i		−	0.705570i
$149$	40.4096	+	69.9914i	0.271205	+	0.469741i	0.969171	−	0.246390i	$-0.0792445\pi$
$149$	40.4096	+	69.9914i	0.271205	+	0.469741i	−0.697966	+	0.716131i	$0.745911\pi$
$150$	−84.1307	+	38.7945i	−0.560871	+	0.258630i
$151$			104.995i			0.695332i	0.937618	+	0.347666i	$0.113026\pi$
$151$			104.995i			0.695332i	−0.937618	+	0.347666i	$0.886974\pi$
$152$	0.140359	−	0.0810365i	0.000923416	−	0.000533135i
$153$	−80.4504	−	68.6847i	−0.525819	−	0.448919i
$154$	160.817	+	92.8475i	1.04426	+	0.602906i
$155$		−	15.9110i		−	0.102651i
$156$	−37.8217	+	68.2167i	−0.242447	+	0.437287i
$157$	164.598			1.04839			0.524196	−	0.851597i	$-0.324366\pi$
$157$	164.598			1.04839			0.524196	+	0.851597i	$0.324366\pi$
$158$	−37.0688	+	64.2051i	−0.234613	+	0.406362i
$159$	143.726	−	203.408i	0.903936	−	1.27930i
$160$	−5.03072	−	8.71346i	−0.0314420	−	0.0544591i
$161$	−395.951			−2.45932
$162$	17.9628	+	113.134i	0.110881	+	0.698359i
$163$	−116.491	+	67.2561i	−0.714669	+	0.412614i	−0.812787	−	0.582561i	$-0.802051\pi$
$163$	−116.491	+	67.2561i	−0.714669	+	0.412614i	0.0981187	+	0.995175i	$0.468718\pi$
$164$	−107.555			−0.655824
$165$	50.1454	−	23.1231i	0.303912	−	0.140140i
$166$	32.9372	−	57.0489i	0.198417	−	0.343668i
$167$	108.230	−	187.461i	0.648086	−	1.12252i	−0.335493	−	0.942043i	$-0.608903\pi$
$167$	108.230	−	187.461i	0.648086	−	1.12252i	0.983579	−	0.180476i	$-0.0577637\pi$
$168$	−107.211	−	9.84103i	−0.638161	−	0.0585776i
$169$	114.127	+	124.644i	0.675308	+	0.737536i
$170$		−	29.5644i		−	0.173908i
$171$	−0.392215	−	0.334854i	−0.00229365	−	0.00195821i
$172$	6.76698	−	11.7207i	0.0393429	−	0.0681439i
$173$	−182.945	+	105.624i	−1.05749	+	0.610541i	−0.924736	−	0.380608i	$-0.875715\pi$
$173$	−182.945	+	105.624i	−1.05749	+	0.610541i	−0.132752	+	0.991149i	$0.542381\pi$
$174$	127.832	+	11.7339i	0.734669	+	0.0674362i
$175$	−239.943	+	138.531i	−1.37110	+	0.791608i
$176$	−20.6976	−	35.8493i	−0.117600	−	0.203689i
$177$	−12.8711	+	140.221i	−0.0727180	+	0.792211i
$178$	−95.3376	−	165.130i	−0.535604	−	0.927694i
$179$	−100.760	−	58.1739i	−0.562906	−	0.324994i	0.191405	−	0.981511i	$-0.438696\pi$
$179$	−100.760	−	58.1739i	−0.562906	−	0.324994i	−0.754311	+	0.656517i	$0.772029\pi$
$180$	−20.7876	+	24.3486i	−0.115487	+	0.135270i
$181$	−179.357			−0.990921			−0.495461	−	0.868630i	$-0.665001\pi$
$181$	−179.357			−0.990921			−0.495461	+	0.868630i	$0.665001\pi$
$182$	−93.9884	+	213.494i	−0.516420	+	1.17304i
$183$	−2.60511	+	28.3808i	−0.0142356	+	0.155086i
$184$	76.4403	+	44.1328i	0.415436	+	0.239852i
$185$	−80.4243	−	46.4330i	−0.434726	−	0.250989i
$186$	15.8927	+	34.4654i	0.0854448	+	0.185298i
$187$		−	121.635i		−	0.650456i
$188$	7.62439	+	13.2058i	0.0405553	+	0.0702438i
$189$	84.4213	+	332.013i	0.446674	+	1.75668i
$190$		−	0.144134i		−	0.000758598i
$191$	5.13696	−	2.96583i	0.0268951	−	0.0155279i	−0.486492	−	0.873685i	$-0.661724\pi$
$191$	5.13696	−	2.96583i	0.0268951	−	0.0155279i	0.513387	+	0.858157i	$0.328390\pi$
$192$	19.6007	+	13.8496i	0.102087	+	0.0721334i
$193$	−124.859	−	72.0872i	−0.646936	−	0.373509i	0.140345	−	0.990103i	$-0.455179\pi$
$193$	−124.859	−	72.0872i	−0.646936	−	0.373509i	−0.787281	+	0.616594i	$0.788512\pi$
$194$		−	102.658i		−	0.529163i
$195$	35.7206	+	59.4621i	0.183183	+	0.304934i
$196$	−223.974			−1.14272
$197$	120.954	−	209.498i	0.613978	−	1.06344i	−0.376585	−	0.926382i	$-0.622902\pi$
$197$	120.954	−	209.498i	0.613978	−	1.06344i	0.990563	−	0.137059i	$-0.0437649\pi$
$198$	−85.5254	+	100.176i	−0.431947	+	0.505939i
$199$	−44.3009	−	76.7314i	−0.222618	−	0.385585i	0.732984	−	0.680245i	$-0.238127\pi$
$199$	−44.3009	−	76.7314i	−0.222618	−	0.385585i	−0.955602	+	0.294660i	$0.904793\pi$
$200$	61.7629			0.308815
$201$	−50.6684	−	109.881i	−0.252081	−	0.546670i
$202$	176.184	−	101.720i	0.872196	−	0.503563i
$203$	383.904			1.89115
$204$	29.5305	+	64.0407i	0.144758	+	0.313925i
$205$	−47.8251	+	82.8355i	−0.233293	+	0.404076i
$206$	−7.68386	+	13.3088i	−0.0373003	+	0.0646060i
$207$	51.1301	−	276.166i	0.247005	−	1.33414i
$208$	41.9410	−	30.7401i	0.201639	−	0.147789i
$209$		−	0.593001i		−	0.00283733i
$210$	−55.2514	+	78.1947i	−0.263102	+	0.372355i
$211$	−55.5761	+	96.2607i	−0.263394	+	0.456212i	−0.967142	−	0.254238i	$-0.918175\pi$
$211$	−55.5761	+	96.2607i	−0.263394	+	0.456212i	0.703748	+	0.710450i	$0.251509\pi$
$212$	−143.796	+	83.0208i	−0.678284	+	0.391607i
$213$	−3.27384	+	35.6662i	−0.0153702	+	0.167447i
$214$	−192.553	+	111.171i	−0.899781	+	0.519489i
$215$	−6.01796	−	10.4234i	−0.0279905	−	0.0484810i
$216$	20.7083	−	73.5062i	0.0958716	−	0.340307i
$217$	56.7515	+	98.2964i	0.261527	+	0.452979i
$218$	203.846	+	117.690i	0.935071	+	0.539864i
$219$	−72.1431	+	102.101i	−0.329420	+	0.466213i
$220$	−36.8133			−0.167333
$221$	151.891	−	16.6054i	0.687291	−	0.0751376i
$222$	220.590	+	20.2482i	0.993650	+	0.0912083i
$223$	−47.3203	−	27.3204i	−0.212199	−	0.122513i	0.390134	−	0.920758i	$-0.372429\pi$
$223$	−47.3203	−	27.3204i	−0.212199	−	0.122513i	−0.602333	+	0.798245i	$0.705762\pi$
$224$	62.1585	+	35.8873i	0.277494	+	0.160211i
$225$	−65.6377	−	185.243i	−0.291723	−	0.823304i
$226$			195.719i			0.866012i
$227$	102.668	+	177.826i	0.452281	+	0.783374i	0.998527	−	0.0542505i	$-0.0172770\pi$
$227$	102.668	+	177.826i	0.452281	+	0.783374i	−0.546246	+	0.837625i	$0.683944\pi$
$228$	0.143969	+	0.312214i	0.000631441	+	0.00136936i
$229$		−	402.266i		−	1.75662i	−0.478092	−	0.878309i	$-0.658672\pi$
$229$		−	402.266i		−	1.75662i	0.478092	−	0.878309i	$-0.341328\pi$
$230$	67.9794	−	39.2479i	0.295562	−	0.170643i
$231$	−227.318	+	321.712i	−0.984059	+	1.39269i
$232$	−74.1144	−	42.7900i	−0.319459	−	0.184439i
$233$			95.4657i			0.409724i	0.978791	+	0.204862i	$0.0656745\pi$
$233$			95.4657i			0.409724i	−0.978791	+	0.204862i	$0.934325\pi$
$234$	−136.770	−	93.1235i	−0.584487	−	0.397964i
$235$	13.5609			0.0577062
$236$	46.9369	−	81.2971i	0.198885	−	0.344479i
$237$	−128.442	−	90.7553i	−0.541948	−	0.382934i
$238$	105.451	+	182.646i	0.443070	+	0.767421i
$239$	−338.040			−1.41439			−0.707197	−	0.707016i	$-0.750041\pi$
$239$	−338.040			−1.41439			−0.707197	+	0.707016i	$0.750041\pi$
$240$	19.3821	−	8.93752i	0.0807589	−	0.0372397i
$241$	192.597	−	111.196i	0.799158	−	0.461394i	−0.0440189	−	0.999031i	$-0.514016\pi$
$241$	192.597	−	111.196i	0.799158	−	0.461394i	0.843176	+	0.537637i	$0.180683\pi$
$242$	19.6609			0.0812434
$243$	−242.472	+	16.0082i	−0.997828	+	0.0658775i
$244$	9.50004	−	16.4545i	0.0389346	−	0.0674367i
$245$	−99.5914	+	172.497i	−0.406496	+	0.704071i
$246$	20.8553	−	227.204i	0.0847777	−	0.923592i
$247$	0.740507	−	0.0809553i	0.00299800	−	0.000327754i
$248$		−	25.3021i		−	0.102025i
$249$	114.126	+	80.6398i	0.458336	+	0.323855i
$250$	58.9053	−	102.027i	0.235621	−	0.408108i
$251$	−30.2508	+	17.4653i	−0.120521	+	0.0695829i	−0.559049	−	0.829135i	$-0.688834\pi$
$251$	−30.2508	+	17.4653i	−0.120521	+	0.0695829i	0.438528	+	0.898718i	$0.355500\pi$
$252$	41.5772	−	224.569i	0.164989	−	0.891146i
$253$	279.684	−	161.475i	1.10547	−	0.638243i
$254$	−144.306	−	249.946i	−0.568135	−	0.984038i
$255$	62.4531	+	5.73264i	0.244914	+	0.0224809i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−31.8021	−	18.3609i	−0.123743	−	0.0714433i	0.436851	−	0.899534i	$-0.356094\pi$
$257$	−31.8021	−	18.3609i	−0.123743	−	0.0714433i	−0.560594	+	0.828091i	$0.689427\pi$
$258$	23.4472	+	16.5675i	0.0908807	+	0.0642152i
$259$	662.471			2.55780
$260$	−5.02568	−	45.9704i	−0.0193295	−	0.176809i
$261$	−49.5743	+	267.763i	−0.189940	+	1.02591i
$262$	36.3576	+	20.9910i	0.138769	+	0.0801185i
$263$	405.858	+	234.322i	1.54319	+	0.890960i	0.998635	+	0.0522335i	$0.0166340\pi$
$263$	405.858	+	234.322i	1.54319	+	0.890960i	0.544553	+	0.838726i	$0.316699\pi$
$264$	79.7428	−	36.7711i	0.302056	−	0.139285i
$265$			147.663i			0.557219i
$266$	0.514098	+	0.890444i	0.00193270	+	0.00334753i
$267$	367.313	−	169.376i	1.37570	−	0.634366i
$268$			80.6668i			0.300996i
$269$	−23.9360	+	13.8194i	−0.0889813	+	0.0513734i	−0.543830	−	0.839195i	$-0.683027\pi$
$269$	−23.9360	+	13.8194i	−0.0889813	+	0.0513734i	0.454849	+	0.890569i	$0.349693\pi$
$270$	−47.4041	−	48.6339i	−0.175571	−	0.180126i
$271$	−364.944	−	210.701i	−1.34666	−	0.777493i	−0.358882	−	0.933383i	$-0.616842\pi$
$271$	−364.944	−	210.701i	−1.34666	−	0.777493i	−0.987774	+	0.155890i	$0.950175\pi$
$272$		−	47.0142i		−	0.172847i
$273$	−432.769	−	239.942i	−1.58523	−	0.878909i
$274$	−157.000			−0.572992
$275$	112.991	−	195.706i	0.410875	−	0.711657i
$276$	−108.050	+	152.918i	−0.391485	+	0.554051i
$277$	100.659	+	174.346i	0.363389	+	0.629409i	0.988516	−	0.151114i	$-0.0482861\pi$
$277$	100.659	+	174.346i	0.363389	+	0.629409i	−0.625127	+	0.780523i	$0.714953\pi$
$278$	53.6719			0.193064
$279$	−75.8877	+	26.8895i	−0.271999	+	0.0963781i
$280$	55.2784	−	31.9150i	0.197423	−	0.113982i
$281$	−165.639			−0.589463			−0.294731	−	0.955580i	$-0.595230\pi$
$281$	−165.639			−0.589463			−0.294731	+	0.955580i	$0.595230\pi$
$282$	−29.3749	+	13.5454i	−0.104166	+	0.0480334i
$283$	−190.037	+	329.153i	−0.671508	+	1.16309i	0.305969	+	0.952041i	$0.401020\pi$
$283$	−190.037	+	329.153i	−0.671508	+	1.16309i	−0.977477	+	0.211044i	$0.932314\pi$
$284$	11.9387	−	20.6785i	0.0420377	−	0.0728115i
$285$	0.304474	+	0.0279480i	0.00106833	+	9.80632e-5i
$286$	−20.6769	−	189.133i	−0.0722968	−	0.661306i
$287$		−	682.333i		−	2.37747i
$288$	−33.0571	+	38.7198i	−0.114782	+	0.134444i
$289$	−75.4269	+	130.643i	−0.260993	+	0.452053i
$290$	−65.9109	+	38.0537i	−0.227279	+	0.131220i
$291$	216.858	+	19.9057i	0.745217	+	0.0684044i
$292$	72.1784	−	41.6722i	0.247186	−	0.142713i
$293$	199.413	+	345.393i	0.680589	+	1.17882i	0.974801	+	0.223075i	$0.0716095\pi$
$293$	199.413	+	345.393i	0.680589	+	1.17882i	−0.294212	+	0.955740i	$0.595057\pi$
$294$	43.4293	−	473.131i	0.147719	−	1.60929i
$295$	−41.7416	−	72.2986i	−0.141497	−	0.245080i
$296$	−127.893	−	73.8392i	−0.432072	−	0.249457i
$297$	−195.032	−	200.092i	−0.656673	−	0.673710i
$298$	114.296			0.383542
$299$	239.823	+	327.209i	0.802085	+	1.09434i
$300$	−11.9760	+	130.470i	−0.0399201	+	0.434901i
$301$	74.3568	+	42.9299i	0.247032	+	0.142624i
$302$	128.592	+	74.2428i	0.425802	+	0.245837i
$303$	180.714	+	391.901i	0.596416	+	1.29340i
$304$		−	0.229206i		−	0.000753966i
$305$	−8.44851	−	14.6333i	−0.0277000	−	0.0479779i
$306$	−141.008	+	49.9638i	−0.460811	+	0.163280i
$307$		−	253.956i		−	0.827218i	−0.910455	−	0.413609i	$-0.864268\pi$
$307$		−	253.956i		−	0.827218i	0.910455	−	0.413609i	$-0.135732\pi$
$308$	227.429	−	131.306i	0.738406	−	0.426319i
$309$	−26.6242	−	18.8123i	−0.0861624	−	0.0608813i
$310$	−19.4869	−	11.2508i	−0.0628609	−	0.0362928i
$311$			466.376i			1.49960i	0.661664	+	0.749801i	$0.269851\pi$
$311$			466.376i			1.49960i	−0.661664	+	0.749801i	$0.730149\pi$
$312$	56.8041	+	94.5584i	0.182064	+	0.303072i
$313$	364.068			1.16316			0.581579	−	0.813490i	$-0.302435\pi$
$313$	364.068			1.16316			0.581579	+	0.813490i	$0.302435\pi$
$314$	116.388	−	201.590i	0.370663	−	0.642007i
$315$	−154.468	−	131.877i	−0.490375	−	0.418658i
$316$	52.4233	+	90.7998i	0.165896	+	0.287341i
$317$	352.362			1.11155			0.555776	−	0.831332i	$-0.312421\pi$
$317$	352.362			1.11155			0.555776	+	0.831332i	$0.312421\pi$
$318$	−147.494	−	319.859i	−0.463817	−	1.00585i
$319$	−271.174	+	156.562i	−0.850074	+	0.490791i
$320$	−14.2290			−0.0444657
$321$	−197.505	−	428.313i	−0.615279	−	1.33431i
$322$	−279.980	+	484.939i	−0.869503	+	1.50602i
$323$	0.336748	−	0.583265i	0.00104256	−	0.00180577i
$324$	151.262	+	57.9981i	0.466858	+	0.179006i
$325$	259.812	+	114.379i	0.799420	+	0.351936i
$326$			190.229i			0.583524i
$327$	−288.140	+	407.791i	−0.881162	+	1.24707i
$328$	−76.0530	+	131.728i	−0.231869	+	0.401608i
$329$	−83.7782	+	48.3694i	−0.254645	+	0.147019i
$330$	7.13823	−	77.7659i	0.0216310	−	0.235654i
$331$	−195.038	+	112.605i	−0.589240	+	0.340198i	−0.764797	−	0.644272i	$-0.777161\pi$
$331$	−195.038	+	112.605i	−0.589240	+	0.340198i	0.175557	+	0.984469i	$0.443827\pi$
$332$	−46.5802	−	80.6793i	−0.140302	−	0.243010i
$333$	−85.5464	+	462.057i	−0.256896	+	1.38756i
$334$	−153.061	−	265.109i	−0.458266	−	0.793740i
$335$	62.1270	+	35.8691i	0.185454	+	0.107072i
$336$	−87.8624	+	124.348i	−0.261495	+	0.370082i
$337$	−340.457			−1.01026			−0.505129	−	0.863044i	$-0.668555\pi$
$337$	−340.457			−1.01026			−0.505129	+	0.863044i	$0.668555\pi$
$338$	233.357	−	51.6403i	0.690404	−	0.152782i
$339$	−413.444	−	37.9505i	−1.21960	−	0.111948i
$340$	−36.2089	−	20.9052i	−0.106497	−	0.0614859i
$341$	−80.1738	−	46.2883i	−0.235114	−	0.135743i
$342$	−0.687449	+	0.243586i	−0.00201008	+	0.000712238i
$343$		−	799.181i		−	2.32997i
$344$	−9.56995	−	16.5756i	−0.0278196	−	0.0481850i
$345$	69.7274	+	151.213i	0.202108	+	0.438297i
$346$			298.749i			0.863436i
$347$	−453.908	+	262.064i	−1.30809	+	0.755228i	−0.981778	−	0.190033i	$-0.939141\pi$
$347$	−453.908	+	262.064i	−1.30809	+	0.755228i	−0.326316	+	0.945261i	$0.605807\pi$
$348$	104.762	−	148.265i	0.301041	−	0.426049i
$349$	−124.688	−	71.9888i	−0.357273	−	0.206272i	0.310611	−	0.950537i	$-0.399466\pi$
$349$	−124.688	−	71.9888i	−0.357273	−	0.206272i	−0.667884	+	0.744265i	$0.732800\pi$
$350$			391.826i			1.11950i
$351$	223.238	−	270.861i	0.636006	−	0.771684i
$352$	−58.5416			−0.166311
$353$	187.495	−	324.751i	0.531147	−	0.919973i	−0.468192	−	0.883627i	$-0.655095\pi$
$353$	187.495	−	324.751i	0.531147	−	0.919973i	0.999339	−	0.0363469i	$-0.0115721\pi$
$354$	162.634	+	114.915i	0.459418	+	0.324619i
$355$	−10.6173	−	18.3896i	−0.0299078	−	0.0518018i
$356$	−269.655			−0.757459
$357$	−406.276	+	187.343i	−1.13803	+	0.524769i
$358$	−142.496	+	82.2704i	−0.398035	+	0.229805i
$359$	−135.865			−0.378454			−0.189227	−	0.981933i	$-0.560598\pi$
$359$	−135.865			−0.378454			−0.189227	+	0.981933i	$0.560598\pi$
$360$	15.1217	+	42.6766i	0.0420047	+	0.118546i
$361$	−180.498	+	312.632i	−0.499995	+	0.866018i
$362$	−126.824	+	219.666i	−0.350344	+	0.606813i
$363$	−3.81232	+	41.5325i	−0.0105023	+	0.114415i
$364$	195.016	+	266.075i	0.535758	+	0.730975i
$365$		−	74.1194i		−	0.203067i
$366$	32.9172	+	23.2589i	0.0899376	+	0.0635488i
$367$	−0.369674	+	0.640295i	−0.00100729	+	0.00174467i	−0.866529	−	0.499127i	$-0.833654\pi$
$367$	−0.369674	+	0.640295i	−0.00100729	+	0.00174467i	0.865521	+	0.500872i	$0.166987\pi$
$368$	108.103	−	62.4132i	0.293758	−	0.169601i
$369$	475.910	+	88.1111i	1.28973	+	0.238784i
$370$	−113.737	+	65.6662i	−0.307398	+	0.177476i
$371$	−526.686	−	912.247i	−1.41964	−	2.45889i
$372$	53.4492	+	4.90617i	0.143681	+	0.0131886i
$373$	−221.425	−	383.519i	−0.593633	−	1.02820i	−0.993738	−	0.111733i	$-0.964360\pi$
$373$	−221.425	−	383.519i	−0.593633	−	1.02820i	0.400106	−	0.916469i	$-0.368973\pi$
$374$	−148.972	−	86.0091i	−0.398321	−	0.229971i
$375$	204.104	+	144.217i	0.544277	+	0.384579i
$376$	21.5650			0.0573538
$377$	−232.526	−	317.253i	−0.616780	−	0.841520i
$378$	466.326	+	131.374i	1.23367	+	0.347550i
$379$	555.740	+	320.857i	1.46633	+	0.846588i	0.999291	−	0.0376472i	$-0.0119863\pi$
$379$	555.740	+	320.857i	1.46633	+	0.846588i	0.467042	+	0.884235i	$0.345320\pi$
$380$	−0.176527	−	0.101918i	−0.000464545	−	0.000268205i
$381$	555.977	−	256.373i	1.45926	−	0.672895i
$382$		−	8.38863i		−	0.0219598i
$383$	28.5969	+	49.5312i	0.0746654	+	0.129324i	0.900941	−	0.433942i	$-0.142878\pi$
$383$	28.5969	+	49.5312i	0.0746654	+	0.129324i	−0.826275	+	0.563266i	$0.809544\pi$
$384$	30.8221	−	14.2127i	0.0802658	−	0.0370123i
$385$		−	233.545i		−	0.606610i
$386$	−176.577	+	101.947i	−0.457453	+	0.264111i
$387$	−39.5444	+	46.3184i	−0.102182	+	0.119686i
$388$	−125.729	−	72.5899i	−0.324045	−	0.187087i
$389$			41.5396i			0.106786i	0.998574	+	0.0533929i	$0.0170036\pi$
$389$			41.5396i			0.106786i	−0.998574	+	0.0533929i	$0.982996\pi$
$390$	98.0842	−	1.70263i	0.251498	−	0.00436571i
$391$	366.789			0.938079
$392$	−158.373	+	274.311i	−0.404014	+	0.699772i
$393$	−51.3922	+	72.7329i	−0.130769	+	0.185071i
$394$	−171.054	−	296.275i	−0.434148	−	0.751966i
$395$	93.2414			0.236054
$396$	62.2144	+	175.582i	0.157107	+	0.443389i
$397$	159.760	−	92.2373i	0.402417	−	0.232336i	−0.285109	−	0.958495i	$-0.592030\pi$
$397$	159.760	−	92.2373i	0.402417	−	0.232336i	0.687526	+	0.726159i	$0.258697\pi$
$398$	−125.302			−0.314829
$399$	−1.98069	+	0.913341i	−0.00496414	+	0.00228907i
$400$	43.6730	−	75.6438i	0.109182	−	0.189110i
$401$	170.890	−	295.989i	0.426159	−	0.738128i	−0.570369	−	0.821388i	$-0.693200\pi$
$401$	170.890	−	295.989i	0.426159	−	0.738128i	0.996528	+	0.0832601i	$0.0265332\pi$
$402$	−170.404	−	15.6416i	−0.423890	−	0.0389094i
$403$	46.8571	−	106.436i	0.116271	−	0.264109i
$404$		−	287.707i		−	0.712145i
$405$	111.928	−	90.7080i	0.276365	−	0.223970i
$406$	271.461	−	470.184i	0.668623	−	1.15809i
$407$	−467.942	+	270.167i	−1.14974	+	0.663800i
$408$	99.3148	+	9.11622i	0.243419	+	0.0223437i
$409$	−238.878	+	137.916i	−0.584053	+	0.337203i	−0.762742	−	0.646702i	$-0.776148\pi$
$409$	−238.878	+	137.916i	−0.584053	+	0.337203i	0.178690	+	0.983906i	$0.442814\pi$
$410$	67.6349	+	117.147i	0.164963	+	0.285725i
$411$	30.4428	−	331.652i	0.0740700	−	0.806940i
$412$	10.8666	+	18.8215i	0.0263753	+	0.0456833i
$413$	515.751	+	297.769i	1.24879	+	0.720991i
$414$	−302.079	−	257.900i	−0.729659	−	0.622947i
$415$	−82.8488			−0.199636
$416$	−7.99199	−	73.1035i	−0.0192115	−	0.175730i
$417$	−10.4072	+	113.379i	−0.0249572	+	0.271891i
$418$	−0.726275	−	0.419315i	−0.00173750	−	0.00100315i
$419$	−266.600	−	153.922i	−0.636277	−	0.367355i	0.146902	−	0.989151i	$-0.453070\pi$
$419$	−266.600	−	153.922i	−0.636277	−	0.367355i	−0.783179	+	0.621796i	$0.786403\pi$
$420$	56.6999	+	122.961i	0.135000	+	0.292764i
$421$		−	292.993i		−	0.695945i	−0.937505	−	0.347972i	$-0.886870\pi$
$421$		−	292.993i		−	0.695945i	0.937505	−	0.347972i	$-0.113130\pi$
$422$	78.5965	+	136.133i	0.186248	+	0.322590i
$423$	−22.9180	−	64.6792i	−0.0541796	−	0.152906i
$424$			234.818i			0.553817i
$425$	222.271	−	128.328i	0.522991	−	0.301949i
$426$	41.3671	+	29.2294i	0.0971058	+	0.0686137i
$427$	104.388	+	60.2685i	0.244469	+	0.141144i
$428$			314.438i			0.734668i
$429$	403.542	−	7.00502i	0.940658	−	0.0163287i
$430$	−17.0214			−0.0395846
$431$	−324.909	+	562.759i	−0.753850	+	1.30571i	0.192094	+	0.981376i	$0.438472\pi$
$431$	−324.909	+	562.759i	−0.753850	+	1.30571i	−0.945944	+	0.324330i	$0.894861\pi$
$432$	−75.3834	−	77.3391i	−0.174499	−	0.179026i
$433$	147.765	+	255.936i	0.341259	+	0.591077i	0.984667	−	0.174446i	$-0.0558135\pi$
$433$	147.765	+	255.936i	0.341259	+	0.591077i	−0.643408	+	0.765523i	$0.722480\pi$
$434$	160.517			0.369856
$435$	−67.6058	−	146.612i	−0.155416	−	0.337038i
$436$	288.281	−	166.439i	0.661195	−	0.381741i
$437$	1.78818			0.00409195
$438$	74.0344	+	160.553i	0.169028	+	0.366559i
$439$	144.472	−	250.233i	0.329093	−	0.570006i	−0.653239	−	0.757152i	$-0.726590\pi$
$439$	144.472	−	250.233i	0.329093	−	0.570006i	0.982332	+	0.187146i	$0.0599236\pi$
$440$	−26.0309	+	45.0869i	−0.0591612	+	0.102470i
$441$	991.040	+	183.483i	2.24726	+	0.416062i
$442$	87.0660	−	197.770i	0.196982	−	0.447443i
$443$			218.694i			0.493665i	0.969058	+	0.246832i	$0.0793897\pi$
$443$			218.694i			0.493665i	−0.969058	+	0.246832i	$0.920610\pi$
$444$	180.780	−	255.849i	0.407162	−	0.576237i
$445$	−119.904	+	207.680i	−0.269447	+	0.466697i
$446$	−66.9210	+	38.6369i	−0.150047	+	0.0866298i
$447$	−22.1623	+	241.442i	−0.0495801	+	0.540140i
$448$	87.9055	−	50.7522i	0.196218	−	0.113286i
$449$	32.1111	+	55.6180i	0.0715168	+	0.123871i	0.899566	−	0.436784i	$-0.143883\pi$
$449$	32.1111	+	55.6180i	0.0715168	+	0.123871i	−0.828049	+	0.560655i	$0.810549\pi$
$450$	−273.289	−	50.5973i	−0.607308	−	0.112438i
$451$	278.267	+	481.972i	0.616999	+	1.06867i
$452$	239.705	+	138.394i	0.530322	+	0.306181i
$453$	−181.768	+	257.248i	−0.401254	+	0.567875i
$454$	290.389			0.639622
$455$	291.638	−	31.8831i	0.640962	−	0.0700727i
$456$	0.484183	+	0.0444438i	0.00106181	+	9.74644e-5i
$457$	126.015	+	72.7549i	0.275744	+	0.159201i	0.631495	−	0.775380i	$-0.282442\pi$
$457$	126.015	+	72.7549i	0.275744	+	0.159201i	−0.355751	+	0.934581i	$0.615775\pi$
$458$	−492.673	−	284.445i	−1.07571	−	0.621059i
$459$	−78.2035	−	307.559i	−0.170378	−	0.670064i
$460$		−	111.010i		−	0.241326i
$461$	−332.342	−	575.634i	−0.720916	−	1.24866i	−0.960633	−	0.277821i	$-0.910388\pi$
$461$	−332.342	−	575.634i	−0.720916	−	1.24866i	0.239717	−	0.970843i	$-0.422945\pi$
$462$	233.277	+	505.891i	0.504929	+	1.09500i
$463$		−	297.851i		−	0.643308i	−0.946857	−	0.321654i	$-0.895761\pi$
$463$		−	297.851i		−	0.643308i	0.946857	−	0.321654i	$-0.104239\pi$
$464$	−104.814	+	60.5141i	−0.225891	+	0.130418i
$465$	27.5451	−	38.9833i	0.0592368	−	0.0838350i
$466$	116.921	+	67.5044i	0.250904	+	0.144859i
$467$		−	144.137i		−	0.308645i	−0.988021	−	0.154322i	$-0.950681\pi$
$467$		−	144.137i		−	0.308645i	0.988021	−	0.154322i	$-0.0493194\pi$
$468$	−210.764	+	101.660i	−0.450349	+	0.217222i
$469$	−511.753			−1.09116
$470$	9.58904	−	16.6087i	0.0204022	−	0.0353377i
$471$	403.279	+	284.952i	0.856219	+	0.604993i
$472$	−66.3788	−	114.972i	−0.140633	−	0.243584i
$473$	−70.0301			−0.148055
$474$	−201.974	+	93.1346i	−0.426106	+	0.196487i
$475$	1.08362	−	0.625631i	0.00228132	−	0.00131712i
$476$	298.260			0.626596
$477$	704.282	−	249.550i	1.47648	−	0.523166i
$478$	−239.031	+	414.013i	−0.500064	+	0.866136i
$479$	−7.63612	+	13.2262i	−0.0159418	+	0.0276120i	−0.873886	−	0.486130i	$-0.838408\pi$
$479$	−7.63612	+	13.2262i	−0.0159418	+	0.0276120i	0.857944	+	0.513742i	$0.171741\pi$
$480$	2.75905	−	30.0579i	0.00574803	−	0.0626207i
$481$	−401.252	−	547.458i	−0.834203	−	1.13817i
$482$		−	314.510i		−	0.652509i
$483$	−970.116	−	685.472i	−2.00852	−	1.41920i
$484$	13.9024	−	24.0796i	0.0287239	−	0.0497512i
$485$	−111.813	+	64.5552i	−0.230542	+	0.133104i
$486$	−151.848	+	308.286i	−0.312444	+	0.634333i
$487$	−80.1330	+	46.2648i	−0.164544	+	0.0949996i	−0.580011	−	0.814609i	$-0.696952\pi$
$487$	−80.1330	+	46.2648i	−0.164544	+	0.0949996i	0.415467	+	0.909608i	$0.363618\pi$
$488$	−13.4351	−	23.2702i	−0.0275309	−	0.0476849i
$489$	−401.847	−	36.8860i	−0.821773	−	0.0754316i
$490$	140.844	+	243.948i	0.287436	+	0.497854i
$491$	−462.776	−	267.184i	−0.942518	−	0.544163i	−0.0517689	−	0.998659i	$-0.516486\pi$
$491$	−462.776	−	267.184i	−0.942518	−	0.544163i	−0.890749	+	0.454496i	$0.849819\pi$
$492$	−263.520	−	186.200i	−0.535609	−	0.378455i
$493$	−355.628			−0.721356
$494$	0.424468	−	0.964176i	0.000859246	−	0.00195177i
$495$	162.892	+	30.1581i	0.329074	+	0.0609255i
$496$	−30.9886	−	17.8913i	−0.0624771	−	0.0360712i
$497$	131.185	+	75.7396i	0.263953	+	0.152394i
$498$	179.462	−	82.7539i	0.360366	−	0.166173i
$499$			752.202i			1.50742i	0.657208	+	0.753710i	$0.271737\pi$
$499$			752.202i			1.50742i	−0.657208	+	0.753710i	$0.728263\pi$
$500$	−83.3046	−	144.288i	−0.166609	−	0.288576i
$501$	589.706	−	271.926i	1.17706	−	0.542767i
$502$			49.3994i			0.0984051i
$503$	69.9522	−	40.3869i	0.139070	−	0.0802921i	−0.428851	−	0.903375i	$-0.641081\pi$
$503$	69.9522	−	40.3869i	0.139070	−	0.0802921i	0.567921	+	0.823083i	$0.307748\pi$
$504$	−245.640	−	209.715i	−0.487381	−	0.416102i
$505$	−221.583	−	127.931i	−0.438777	−	0.253328i
$506$		−	456.722i		−	0.902612i
$507$	63.8383	+	502.965i	0.125914	+	0.992041i
$508$	−408.160			−0.803464
$509$	160.865	−	278.627i	0.316042	−	0.547400i	−0.663617	−	0.748073i	$-0.730979\pi$
$509$	160.865	−	278.627i	0.316042	−	0.547400i	0.979658	+	0.200672i	$0.0643127\pi$
$510$	51.1820	−	72.4355i	0.100357	−	0.142030i
$511$	264.370	+	457.902i	0.517358	+	0.896090i
$512$	−22.6274			−0.0441942
$513$	−0.381261	−	1.49943i	−0.000743199	−	0.00292286i
$514$	−44.9749	+	25.9663i	−0.0874998	+	0.0505180i
$515$	19.3277			0.0375294
$516$	36.8707	−	17.0019i	0.0714548	−	0.0329494i
$517$	39.4516	−	68.3322i	0.0763088	−	0.132171i
$518$	468.438	−	811.358i	0.904320	−	1.56633i
$519$	−631.089	−	57.9284i	−1.21597	−	0.111615i
$520$	−59.8557	−	26.3508i	−0.115107	−	0.0506746i
$521$			996.087i			1.91187i	0.293570	+	0.955937i	$0.405157\pi$
$521$			996.087i			1.91187i	−0.293570	+	0.955937i	$0.594843\pi$
$522$	292.887	+	250.053i	0.561087	+	0.479029i
$523$	−192.204	+	332.906i	−0.367502	+	0.636532i	−0.989174	−	0.146745i	$-0.953120\pi$
$523$	−192.204	+	332.906i	−0.367502	+	0.636532i	0.621672	+	0.783277i	$0.286454\pi$
$524$	51.4173	−	29.6858i	0.0981247	−	0.0566523i
$525$	−827.708	−	75.9763i	−1.57659	−	0.144717i
$526$	573.970	−	331.382i	1.09120	−	0.630004i
$527$	−52.5716	−	91.0567i	−0.0997564	−	0.172783i
$528$	11.3514	−	123.666i	0.0214989	−	0.234215i
$529$	222.426	+	385.253i	0.420465	+	0.728267i
$530$	180.850	+	104.414i	0.341225	+	0.197007i
$531$	−274.287	+	321.272i	−0.516548	+	0.605032i
$532$	1.45409			0.00273325
$533$	−563.871	+	413.282i	−1.05792	+	0.775388i
$534$	52.2871	−	569.631i	0.0979159	−	1.06672i
$535$	242.170	+	139.817i	0.452655	+	0.261340i
$536$	98.7963	+	57.0401i	0.184321	+	0.106418i
$537$	−146.161	−	316.968i	−0.272180	−	0.590256i
$538$			39.0873i			0.0726530i
$539$	579.465	+	1003.66i	1.07507	+	1.86208i
$540$	−93.0839	+	23.6686i	−0.172378	+	0.0438307i
$541$			8.58993i			0.0158779i	0.999968	+	0.00793894i	$0.00252707\pi$
$541$			8.58993i			0.0158779i	−0.999968	+	0.00793894i	$0.997473\pi$
$542$	−516.109	+	297.976i	−0.952230	+	0.549770i
$543$	−439.440	−	310.503i	−0.809282	−	0.571829i
$544$	−57.5805	−	33.2441i	−0.105846	−	0.0611105i
$545$		−	296.033i		−	0.543180i
$546$	−599.882	+	360.367i	−1.09868	+	0.660012i
$547$	−259.444			−0.474303			−0.237152	−	0.971473i	$-0.576214\pi$
$547$	−259.444			−0.474303			−0.237152	+	0.971473i	$0.576214\pi$
$548$	−111.016	+	192.285i	−0.202583	+	0.350884i
$549$	−55.5157	+	65.0255i	−0.101121	+	0.118444i
$550$	−159.793	−	276.770i	−0.290533	−	0.503217i
$551$	−1.73377			−0.00314659
$552$	110.883	+	240.463i	0.200874	+	0.435621i
$553$	−576.036	+	332.575i	−1.04166	+	0.601401i
$554$	284.706			0.513910
$555$	−116.662	−	252.996i	−0.210202	−	0.455848i
$556$	37.9517	−	65.7344i	0.0682585	−	0.118227i
$557$	−0.789999	+	1.36832i	−0.00141831	+	0.00245659i	−0.866734	−	0.498771i	$-0.833785\pi$
$557$	−0.789999	+	1.36832i	−0.00141831	+	0.00245659i	0.865315	+	0.501228i	$0.167118\pi$
$558$	−20.7280	+	111.957i	−0.0371469	+	0.200640i
$559$	−9.56037	−	87.4497i	−0.0171026	−	0.156439i
$560$		−	90.2693i		−	0.161195i
$561$	210.575	−	298.017i	0.375357	−	0.531225i
$562$	−117.124	+	202.866i	−0.208407	+	0.360971i
$563$	203.781	−	117.653i	0.361956	−	0.208976i	−0.307982	−	0.951392i	$-0.599654\pi$
$563$	203.781	−	117.653i	0.361956	−	0.208976i	0.669939	+	0.742417i	$0.266320\pi$
$564$	−4.18153	+	45.5548i	−0.00741406	+	0.0807710i
$565$	213.173	−	123.076i	0.377298	−	0.217833i
$566$	268.752	+	465.493i	0.474828	+	0.822425i
$567$	−367.942	+	959.611i	−0.648927	+	1.69244i
$568$	−16.8839	−	29.2438i	−0.0297252	−	0.0514855i
$569$	737.200	+	425.623i	1.29561	+	0.748019i	0.979642	−	0.200752i	$-0.0643384\pi$
$569$	737.200	+	425.623i	1.29561	+	0.748019i	0.315965	+	0.948771i	$0.397672\pi$
$570$	0.249525	−	0.353140i	0.000437762	−	0.000619544i
$571$	−412.288			−0.722045			−0.361023	−	0.932557i	$-0.617572\pi$
$571$	−412.288			−0.722045			−0.361023	+	0.932557i	$0.617572\pi$
$572$	−246.261	−	108.414i	−0.430526	−	0.189534i
$573$	17.7205	+	1.62658i	0.0309258	+	0.00283871i
$574$	−835.684	−	482.482i	−1.45590	−	0.840561i
$575$	590.147	+	340.721i	1.02634	+	0.592559i
$576$	24.0470	+	67.8656i	0.0417483	+	0.117822i
$577$		−	77.0452i		−	0.133527i	−0.997769	−	0.0667636i	$-0.978733\pi$
$577$		−	77.0452i		−	0.133527i	0.997769	−	0.0667636i	$-0.0212673\pi$
$578$	106.670	+	184.757i	0.184550	+	0.319649i
$579$	−181.117	−	392.776i	−0.312811	−	0.678369i
$580$			107.632i			0.185573i
$581$	511.832	−	295.506i	0.880950	−	0.508617i
$582$	177.721	−	251.520i	0.305363	−	0.432166i
$583$	744.059	+	429.583i	1.27626	+	0.736848i
$584$		−	117.867i		−	0.201827i
$585$	−15.4222	+	207.527i	−0.0263627	+	0.354747i
$586$	564.024			0.962499
$587$	−202.022	+	349.912i	−0.344160	+	0.596102i	−0.985201	−	0.171405i	$-0.945169\pi$
$587$	−202.022	+	349.912i	−0.344160	+	0.596102i	0.641041	+	0.767507i	$0.278503\pi$
$588$	−548.756	−	387.744i	−0.933258	−	0.659428i
$589$	−0.256299	−	0.443923i	−0.000435143	−	0.000753690i
$590$	−118.063			−0.200107
$591$	659.030	−	303.893i	1.11511	−	0.514202i
$592$	−180.868	+	104.424i	−0.305521	+	0.176393i
$593$	702.567			1.18477			0.592384	−	0.805656i	$-0.298187\pi$
$593$	702.567			1.18477			0.592384	+	0.805656i	$0.298187\pi$
$594$	−382.970	+	97.3782i	−0.644730	+	0.163936i
$595$	132.623	−	229.710i	0.222896	−	0.386068i
$596$	80.8191	−	139.983i	0.135603	−	0.234871i
$597$	24.2965	−	264.693i	0.0406976	−	0.443371i
$598$	570.328	−	62.3507i	0.953726	−	0.104265i
$599$		−	320.691i		−	0.535378i	−0.963505	−	0.267689i	$-0.913740\pi$
$599$		−	320.691i		−	0.535378i	0.963505	−	0.267689i	$-0.0862600\pi$
$600$	151.325	+	106.924i	0.252208	+	0.178207i
$601$	419.106	−	725.912i	0.697347	−	1.20784i	−0.272036	−	0.962287i	$-0.587697\pi$
$601$	419.106	−	725.912i	0.697347	−	1.20784i	0.969383	−	0.245554i	$-0.0789698\pi$
$602$	105.156	−	60.7121i	0.174678	−	0.100851i
$603$	66.0838	−	356.935i	0.109592	−	0.591932i
$604$	181.857	−	104.995i	0.301088	−	0.173833i
$605$	−12.3636	−	21.4143i	−0.0204356	−	0.0353956i
$606$	607.763	+	55.7873i	1.00291	+	0.0920583i
$607$	−270.102	−	467.831i	−0.444979	−	0.770727i	0.553072	−	0.833134i	$-0.313456\pi$
$607$	−270.102	−	467.831i	−0.444979	−	0.770727i	−0.998051	+	0.0624071i	$0.980122\pi$
$608$	−0.280719	−	0.162073i	−0.000461708	−	0.000266567i
$609$	940.598	+	664.615i	1.54450	+	1.09132i
$610$	−23.8960			−0.0391738
$611$	90.7153	+	39.9364i	0.148470	+	0.0653624i
$612$	−38.5149	+	208.029i	−0.0629329	+	0.339916i
$613$	157.674	+	91.0332i	0.257217	+	0.148504i	0.623064	−	0.782170i	$-0.285887\pi$
$613$	157.674	+	91.0332i	0.257217	+	0.148504i	−0.365847	+	0.930675i	$0.619221\pi$
$614$	−311.031	−	179.574i	−0.506566	−	0.292466i
$615$	−260.581	+	120.159i	−0.423709	+	0.195381i
$616$		−	371.390i		−	0.602906i
$617$	−214.557	−	371.623i	−0.347742	−	0.602307i	0.638106	−	0.769949i	$-0.279718\pi$
$617$	−214.557	−	371.623i	−0.347742	−	0.602307i	−0.985848	+	0.167642i	$0.946385\pi$
$618$	−41.8664	+	19.3055i	−0.0677450	+	0.0312387i
$619$			15.6691i			0.0253136i	0.999920	+	0.0126568i	$0.00402889\pi$
$619$			15.6691i			0.0253136i	−0.999920	+	0.0126568i	$0.995971\pi$
$620$	−27.5586	+	15.9110i	−0.0444494	+	0.0256629i
$621$	603.373	−	588.115i	0.971615	−	0.947046i
$622$	571.192	+	329.778i	0.918315	+	0.530189i
$623$		−	1710.70i		−	2.74591i
$624$	155.977	−	2.70757i	0.249962	−	0.00433905i
$625$	397.744			0.636391
$626$	257.435	−	445.891i	0.411238	−	0.712286i
$627$	1.02660	−	1.45291i	0.00163733	−	0.00231723i
$628$	−164.598	−	285.092i	−0.262098	−	0.453967i
$629$	−613.679			−0.975643
$630$	−270.742	+	95.9326i	−0.429749	+	0.152274i
$631$	−257.936	+	148.919i	−0.408773	+	0.236005i	−0.690263	−	0.723559i	$-0.742505\pi$
$631$	−257.936	+	148.919i	−0.408773	+	0.236005i	0.281489	+	0.959564i	$0.409172\pi$
$632$	148.275			0.234613
$633$	−302.813	+	139.634i	−0.478378	+	0.220590i
$634$	249.158	−	431.553i	0.392993	−	0.680684i
$635$	−181.491	+	314.352i	−0.285813	+	0.495042i
$636$	−496.039	−	45.5321i	−0.779936	−	0.0715913i
$637$	−1174.21	+	860.621i	−1.84334	+	1.35105i
$638$			442.825i			0.694083i
$639$	−69.7667	+	81.7177i	−0.109181	+	0.127884i
$640$	−10.0614	+	17.4269i	−0.0157210	+	0.0272296i
$641$	−225.956	+	130.456i	−0.352506	+	0.203519i	−0.665788	−	0.746141i	$-0.731905\pi$
$641$	−225.956	+	130.456i	−0.352506	+	0.203519i	0.313283	+	0.949660i	$0.398571\pi$
$642$	−664.231	−	60.9706i	−1.03463	−	0.0949698i
$643$	532.596	−	307.494i	0.828298	−	0.478218i	−0.0249714	−	0.999688i	$-0.507949\pi$
$643$	532.596	−	307.494i	0.828298	−	0.478218i	0.853270	+	0.521470i	$0.174616\pi$
$644$	395.951	+	685.808i	0.614831	+	1.06492i
$645$	3.30050	−	35.9566i	0.00511706	−	0.0557467i
$646$	−0.476234	−	0.824861i	−0.000737204	−	0.00127687i
$647$	−134.166	−	77.4609i	−0.207367	−	0.119723i	0.392720	−	0.919658i	$-0.371534\pi$
$647$	−134.166	−	77.4609i	−0.207367	−	0.119723i	−0.600087	+	0.799935i	$0.704867\pi$
$648$	177.991	−	144.247i	0.274678	−	0.222603i
$649$	−485.741			−0.748445
$650$	323.800	−	237.325i	0.498153	−	0.365115i
$651$	−31.1249	+	339.083i	−0.0478108	+	0.520865i
$652$	232.982	+	134.512i	0.357334	+	0.206307i
$653$	−364.821	−	210.629i	−0.558684	−	0.322556i	0.193933	−	0.981015i	$-0.437876\pi$
$653$	−364.821	−	210.629i	−0.558684	−	0.322556i	−0.752617	+	0.658458i	$0.771209\pi$
$654$	295.694	+	641.250i	0.452132	+	0.980504i
$655$		−	52.8000i		−	0.0806107i
$656$	107.555	+	186.291i	0.163956	+	0.283980i
$657$	−353.514	+	125.262i	−0.538073	+	0.190657i
$658$			136.809i			0.207917i
$659$	374.976	−	216.492i	0.569007	−	0.328517i	−0.187745	−	0.982218i	$-0.560118\pi$
$659$	374.976	−	216.492i	0.569007	−	0.328517i	0.756753	+	0.653701i	$0.226785\pi$
$660$	−90.1959	−	63.7313i	−0.136660	−	0.0965626i
$661$	300.540	+	173.517i	0.454675	+	0.262507i	0.709802	−	0.704401i	$-0.248784\pi$
$661$	300.540	+	173.517i	0.454675	+	0.262507i	−0.255128	+	0.966907i	$0.582118\pi$
$662$			318.496i			0.481112i
$663$	400.895	+	222.270i	0.604668	+	0.335249i
$664$	−131.749			−0.198417
$665$	0.646570	−	1.11989i	0.000972286	−	0.00168405i
$666$	505.412	+	431.496i	0.758877	+	0.647892i
$667$	−472.110	−	817.719i	−0.707812	−	1.22597i
$668$	−432.922			−0.648086
$669$	−68.6419	−	148.858i	−0.102604	−	0.222509i
$670$	87.8609	−	50.7265i	0.131136	−	0.0757112i
$671$	−98.3140			−0.146519
$672$	90.1659	+	195.536i	0.134175	+	0.290976i
$673$	423.688	−	733.849i	0.629551	−	1.09041i	−0.358091	−	0.933687i	$-0.616572\pi$
$673$	423.688	−	733.849i	0.629551	−	1.09041i	0.987642	−	0.156728i	$-0.0500945\pi$
$674$	−240.740	+	416.973i	−0.357180	+	0.618655i
$675$	159.875	−	567.495i	0.236852	−	0.840733i
$676$	101.762	−	322.317i	0.150535	−	0.476801i
$677$		−	627.156i		−	0.926375i	−0.886260	−	0.463187i	$-0.846706\pi$
$677$		−	627.156i		−	0.926375i	0.886260	−	0.463187i	$-0.153294\pi$
$678$	−338.829	+	479.528i	−0.499747	+	0.707269i
$679$	460.513	−	797.631i	0.678222	−	1.17471i
$680$	−51.2071	+	29.5644i	−0.0753045	+	0.0434771i
$681$	−56.3073	+	613.428i	−0.0826833	+	0.900776i
$682$	−113.383	+	65.4616i	−0.166250	+	0.0959848i
$683$	−53.2065	−	92.1564i	−0.0779012	−	0.134929i	0.824443	−	0.565945i	$-0.191489\pi$
$683$	−53.2065	−	92.1564i	−0.0779012	−	0.134929i	−0.902344	+	0.431016i	$0.858155\pi$
$684$	−0.187770	+	1.01419i	−0.000274517	+	0.00148273i
$685$	98.7276	+	171.001i	0.144128	+	0.249637i
$686$	−978.793	−	565.106i	−1.42681	−	0.823770i
$687$	696.404	−	985.587i	1.01369	−	1.43462i
$688$	−27.0679			−0.0393429
$689$	−434.861	+	987.785i	−0.631149	+	1.43365i
$690$	234.502	+	21.5252i	0.339857	+	0.0311959i
$691$	424.347	+	244.997i	0.614105	+	0.354554i	0.774570	−	0.632488i	$-0.217966\pi$
$691$	424.347	+	244.997i	0.614105	+	0.354554i	−0.160465	+	0.987042i	$0.551299\pi$
$692$	365.891	+	211.247i	0.528744	+	0.305271i
$693$	−1113.90	+	394.690i	−1.60735	+	0.569538i
$694$			741.229i			1.06805i
$695$	−33.7510	−	58.4585i	−0.0485626	−	0.0841129i
$696$	−107.509	−	233.146i	−0.154467	−	0.334980i
$697$			632.078i			0.906855i
$698$	−176.336	+	101.808i	−0.252630	+	0.145856i
$699$	−165.270	+	233.899i	−0.236438	+	0.334620i
$700$	479.887	+	277.063i	0.685552	+	0.395804i
$701$			653.183i			0.931787i	0.884841	+	0.465894i	$0.154267\pi$
$701$			653.183i			0.931787i	−0.884841	+	0.465894i	$0.845733\pi$
$702$	−173.883	−	464.937i	−0.247696	−	0.662304i
$703$	−2.99183			−0.00425581
$704$	−41.3952	+	71.6986i	−0.0588000	+	0.101845i
$705$	33.2255	+	23.4767i	0.0471284	+	0.0333003i
$706$	−265.158	−	459.267i	−0.375578	−	0.650519i
$707$	1825.22			2.58164
$708$	255.741	−	117.928i	0.361217	−	0.166565i
$709$	−473.911	+	273.613i	−0.668422	+	0.385914i	−0.795479	−	0.605982i	$-0.792780\pi$
$709$	−473.911	+	273.613i	−0.668422	+	0.385914i	0.127056	+	0.991896i	$0.459447\pi$
$710$	−30.0302			−0.0422960
$711$	−157.578	−	444.717i	−0.221628	−	0.625481i
$712$	−190.675	+	330.259i	−0.267802	+	0.463847i
$713$	139.582	−	241.762i	0.195767	−	0.339078i
$714$	−57.8336	+	630.056i	−0.0809994	+	0.882431i
$715$	−192.998	+	141.456i	−0.269928	+	0.197840i
$716$			232.696i			0.324994i
$717$	−828.229	−	585.216i	−1.15513	−	0.816201i
$718$	−96.0711	+	166.400i	−0.133804	+	0.231755i
$719$	1062.26	−	613.296i	1.47741	−	0.852985i	0.477739	−	0.878502i	$-0.341456\pi$
$719$	1062.26	−	613.296i	1.47741	−	0.852985i	0.999674	+	0.0255165i	$0.00812302\pi$
$720$	62.9606	+	11.6567i	0.0874453	+	0.0161898i
$721$	−119.404	+	68.9382i	−0.165609	+	0.0956146i
$722$	255.263	+	442.129i	0.353550	+	0.612367i
$723$	664.382	+	60.9845i	0.918925	+	0.0843492i
$724$	179.357	+	310.655i	0.247730	+	0.429082i
$725$	−572.190	−	330.354i	−0.789228	−	0.455661i
$726$	48.1710	+	34.0370i	0.0663512	+	0.0468830i
$727$	−276.718			−0.380630			−0.190315	−	0.981723i	$-0.560951\pi$
$727$	−276.718			−0.380630			−0.190315	+	0.981723i	$0.560951\pi$
$728$	463.771	−	50.7014i	0.637048	−	0.0696448i
$729$	−621.792	−	380.547i	−0.852938	−	0.522012i
$730$	−90.7773	−	52.4103i	−0.124352	−	0.0717949i
$731$	−68.8803	−	39.7680i	−0.0942274	−	0.0544022i
$732$	51.7621	−	23.8686i	0.0707133	−	0.0326074i
$733$			513.969i			0.701186i	0.936528	+	0.350593i	$0.114020\pi$
$733$			513.969i			0.701186i	−0.936528	+	0.350593i	$0.885980\pi$
$734$	0.522799	+	0.905514i	0.000712260	+	0.00123367i
$735$	−542.636	+	250.221i	−0.738280	+	0.340437i
$736$		−	176.531i		−	0.239852i
$737$	361.481	−	208.701i	0.490476	−	0.283177i
$738$	444.433	−	520.565i	0.602213	−	0.705372i
$739$	−710.412	−	410.157i	−0.961315	−	0.555016i	−0.0647377	−	0.997902i	$-0.520621\pi$
$739$	−710.412	−	410.157i	−0.961315	−	0.555016i	−0.896578	+	0.442887i	$0.853954\pi$
$740$			185.732i			0.250989i
$741$	1.95446	+	1.08362i	0.00263759	+	0.00146237i
$742$	−1489.69			−2.00767
$743$	−596.502	+	1033.17i	−0.802829	+	1.39054i	0.114918	+	0.993375i	$0.463340\pi$
$743$	−596.502	+	1033.17i	−0.802829	+	1.39054i	−0.917747	+	0.397166i	$0.869994\pi$
$744$	43.8031	−	61.9924i	0.0588751	−	0.0833232i
$745$	−71.8736	−	124.489i	−0.0964746	−	0.167099i
$746$	−626.284			−0.839523
$747$	140.014	+	395.149i	0.187436	+	0.528982i
$748$	−210.678	+	121.635i	−0.281656	+	0.162614i
$749$	−1994.80			−2.66329
$750$	320.952	−	147.998i	0.427937	−	0.197331i
$751$	440.324	−	762.663i	0.586316	−	1.01553i	−0.408394	−	0.912806i	$-0.633911\pi$
$751$	440.324	−	762.663i	0.586316	−	1.01553i	0.994710	−	0.102724i	$-0.0327558\pi$
$752$	15.2488	−	26.4117i	0.0202776	−	0.0351219i
$753$	−104.353	−	9.57870i	−0.138583	−	0.0127207i
$754$	−552.975	+	60.4536i	−0.733388	+	0.0801771i
$755$		−	186.747i		−	0.247347i
$756$	490.642	−	478.235i	0.648997	−	0.632586i
$757$	−90.9618	+	157.550i	−0.120161	+	0.208125i	−0.919831	−	0.392315i	$-0.871674\pi$
$757$	−90.9618	+	157.550i	−0.120161	+	0.208125i	0.799670	+	0.600440i	$0.205008\pi$
$758$	785.935	−	453.760i	1.03685	−	0.598628i
$759$	964.797	+	88.5599i	1.27114	+	0.116680i
$760$	−0.249647	+	0.144134i	−0.000328483	+	0.000189650i
$761$	−96.8233	−	167.703i	−0.127232	−	0.220372i	0.795371	−	0.606122i	$-0.207276\pi$
$761$	−96.8233	−	167.703i	−0.127232	−	0.220372i	−0.922603	+	0.385751i	$0.873942\pi$
$762$	79.1435	−	862.213i	0.103863	−	1.13151i
$763$	1055.90	+	1828.86i	1.38387	+	2.39694i
$764$	−10.2739	−	5.93165i	−0.0134475	−	0.00776394i
$765$	143.091	+	122.164i	0.187047	+	0.159692i
$766$	80.8841			0.105593
$767$	−66.3124	−	606.566i	−0.0864568	−	0.790829i
$768$	4.38753	−	47.7991i	0.00571293	−	0.0622384i
$769$	−720.772	−	416.138i	−0.937284	−	0.541141i	−0.0481765	−	0.998839i	$-0.515341\pi$
$769$	−720.772	−	416.138i	−0.937284	−	0.541141i	−0.889108	+	0.457697i	$0.848674\pi$
$770$	−286.033	−	165.141i	−0.371471	−	0.214469i
$771$	−46.1314	−	100.042i	−0.0598332	−	0.129756i
$772$			288.349i			0.373509i
$773$	31.0358	+	53.7556i	0.0401498	+	0.0695415i	0.885402	−	0.464826i	$-0.153883\pi$
$773$	31.0358	+	53.7556i	0.0401498	+	0.0695415i	−0.845252	+	0.534368i	$0.820550\pi$
$774$	28.7661	+	81.1838i	0.0371655	+	0.104889i
$775$		−	195.341i		−	0.252054i
$776$	−177.808	+	102.658i	−0.229134	+	0.132291i
$777$	1623.11	+	1146.87i	2.08895	+	1.47603i
$778$	50.8755	+	29.3730i	0.0653926	+	0.0377544i
$779$			3.08153i			0.00395575i
$780$	67.2707	−	121.332i	0.0862445	−	0.155554i
$781$	−123.551			−0.158196
$782$	259.359	−	449.223i	0.331661	−	0.574454i
$783$	−585.014	+	570.221i	−0.747144	+	0.728251i
$784$	223.974	+	387.934i	0.285681	+	0.494814i
$785$	−292.758			−0.372940
$786$	52.7395	+	114.372i	0.0670986	+	0.145512i
$787$	702.433	−	405.550i	0.892545	−	0.515311i	0.0177709	−	0.999842i	$-0.494343\pi$
$787$	702.433	−	405.550i	0.892545	−	0.515311i	0.874774	+	0.484531i	$0.161010\pi$
$788$	−483.814			−0.613978
$789$	588.730	+	1276.73i	0.746172	+	1.61817i
$790$	65.9317	−	114.197i	0.0834578	−	0.144553i
$791$	−877.976	+	1520.70i	−1.10996	+	1.92250i
$792$	259.035	+	47.9584i	0.327065	+	0.0605535i
$793$	−13.4216	−	122.769i	−0.0169251	−	0.154816i
$794$		−	260.886i		−	0.328572i
$795$	−255.635	+	361.788i	−0.321553	+	0.455079i
$796$	−88.6018	+	153.463i	−0.111309	+	0.192792i
$797$	−477.494	+	275.681i	−0.599115	+	0.345899i	−0.768693	−	0.639618i	$-0.779093\pi$
$797$	−477.494	+	275.681i	−0.599115	+	0.345899i	0.169579	+	0.985517i	$0.445759\pi$
$798$	−0.281953	+	3.07167i	−0.000353324	+	0.00384922i
$799$	77.6078	−	44.8069i	0.0971311	−	0.0560787i
$800$	−61.7629	−	106.976i	−0.0772036	−	0.133721i
$801$	1193.17	+	220.907i	1.48960	+	0.275789i
$802$	−241.674	−	418.592i	−0.301340	−	0.521935i
$803$	−373.480	−	215.629i	−0.465106	−	0.268529i
$804$	−139.651	+	197.641i	−0.173695	+	0.245822i
$805$	704.250			0.874844
$806$	−97.2236	−	132.649i	−0.120625	−	0.164578i
$807$	−82.5695	−	7.57916i	−0.102317	−	0.00939177i
$808$	−352.367	−	203.439i	−0.436098	−	0.251781i
$809$	−194.092	−	112.059i	−0.239916	−	0.138516i	0.375222	−	0.926935i	$-0.377566\pi$
$809$	−194.092	−	112.059i	−0.239916	−	0.138516i	−0.615138	+	0.788419i	$0.710900\pi$
$810$	−31.9491	−	201.223i	−0.0394434	−	0.248424i
$811$			1153.00i			1.42170i	0.703343	+	0.710850i	$0.251690\pi$
$811$			1153.00i			1.42170i	−0.703343	+	0.710850i	$0.748310\pi$
$812$	−383.904	−	664.940i	−0.472788	−	0.818892i
$813$	−529.380	−	1148.03i	−0.651144	−	1.41209i
$814$			764.147i			0.938755i
$815$	207.194	−	119.624i	0.254226	−	0.146777i
$816$	81.3912	−	115.189i	0.0997441	−	0.141163i
$817$	−0.335808	−	0.193879i	−0.000411026	−	0.000237306i
$818$			390.086i			0.476877i
$819$	−644.934	−	1337.09i	−0.787465	−	1.63259i
$820$	191.300			0.233293
$821$	565.166	−	978.896i	0.688387	−	1.19232i	−0.283973	−	0.958832i	$-0.591652\pi$
$821$	565.166	−	978.896i	0.688387	−	1.19232i	0.972359	−	0.233489i	$-0.0750142\pi$
$822$	−384.663	−	271.798i	−0.467960	−	0.330655i
$823$	−712.429	−	1233.96i	−0.865649	−	1.49935i	−0.866401	−	0.499349i	$-0.833573\pi$
$823$	−712.429	−	1233.96i	−0.865649	−	1.49935i	0.000751960	−	1.00000i	$-0.499761\pi$
$824$	30.7354			0.0373003
$825$	615.643	−	283.886i	0.746234	−	0.344105i
$826$	729.383	−	421.109i	0.883030	−	0.509818i
$827$	−1124.96			−1.36029			−0.680144	−	0.733079i	$-0.738083\pi$
$827$	−1124.96			−1.36029			−0.680144	+	0.733079i	$0.738083\pi$
$828$	−529.464	+	187.606i	−0.639449	+	0.226578i
$829$	18.3800	−	31.8351i	0.0221713	−	0.0384018i	−0.854727	−	0.519078i	$-0.826275\pi$
$829$	18.3800	−	31.8351i	0.0221713	−	0.0384018i	0.876898	+	0.480676i	$0.159609\pi$
$830$	−58.5830	+	101.469i	−0.0705819	+	0.122251i
$831$	−55.2055	+	601.425i	−0.0664326	+	0.723736i
$832$	−95.1844	−	41.9039i	−0.114404	−	0.0503652i
$833$			1316.24i			1.58013i
$834$	131.501	+	92.9169i	0.157675	+	0.111411i
$835$	−192.502	+	333.422i	−0.230541	+	0.399308i
$836$	−1.02711	+	0.593001i	−0.00122860	+	0.000709331i
$837$	−232.483	−	65.4954i	−0.277757	−	0.0782501i
$838$	−377.029	+	217.678i	−0.449916	+	0.259759i
$839$	257.986	+	446.846i	0.307493	+	0.532593i	0.977813	−	0.209479i	$-0.0671767\pi$
$839$	257.986	+	446.846i	0.307493	+	0.532593i	−0.670320	+	0.742072i	$0.733843\pi$
$840$	190.688	+	17.5035i	0.227010	+	0.0208375i
$841$	37.2452	+	64.5107i	0.0442869	+	0.0767071i
$842$	−358.841	−	207.177i	−0.426177	−	0.246054i
$843$	−405.830	−	286.755i	−0.481412	−	0.340160i
$844$	222.304			0.263394
$845$	−202.990	−	221.694i	−0.240224	−	0.262360i
$846$	−95.4210	−	17.6665i	−0.112791	−	0.0208824i
$847$	152.762	+	88.1970i	0.180356	+	0.104129i
$848$	287.592	+	166.042i	0.339142	+	0.195804i
$849$	−1035.44	+	477.463i	−1.21960	+	0.562382i
$850$		−	362.967i		−	0.427020i
$851$	−814.683	−	1411.07i	−0.957324	−	1.65813i
$852$	65.0495	−	29.9957i	0.0763492	−	0.0352063i
$853$		−	426.040i		−	0.499461i	−0.968315	−	0.249730i	$-0.919658\pi$
$853$		−	426.040i		−	0.499461i	0.968315	−	0.249730i	$-0.0803420\pi$
$854$	147.627	−	85.2326i	0.172866	−	0.0998039i
$855$	0.697604	+	0.595581i	0.000815911	+	0.000696586i
$856$	385.106	+	222.341i	0.449891	+	0.259745i
$857$			1253.72i			1.46292i	0.681886	+	0.731459i	$0.261160\pi$
$857$			1253.72i			1.46292i	−0.681886	+	0.731459i	$0.738840\pi$
$858$	276.768	−	499.190i	0.322574	−	0.581806i
$859$	1300.92			1.51446			0.757228	−	0.653151i	$-0.226553\pi$
$859$	1300.92			1.51446			0.757228	+	0.653151i	$0.226553\pi$
$860$	−12.0359	+	20.8468i	−0.0139953	+	0.0242405i
$861$	1181.26	−	1671.78i	1.37196	−	1.94167i
$862$	459.491	+	795.862i	0.533052	+	0.923274i
$863$	906.497			1.05040			0.525201	−	0.850978i	$-0.323990\pi$
$863$	906.497			1.05040			0.525201	+	0.850978i	$0.323990\pi$
$864$	−148.025	+	37.6385i	−0.171325	+	0.0435630i
$865$	325.392	−	187.865i	0.376175	−	0.217185i
$866$	417.942			0.482612
$867$	−410.972	+	189.508i	−0.474017	+	0.218579i
$868$	113.503	−	196.593i	0.130764	−	0.226489i
$869$	271.259	−	469.834i	0.312151	−	0.540661i
$870$	−227.366	−	20.8702i	−0.261341	−	0.0239888i
$871$	309.963	+	422.906i	0.355870	+	0.485541i
$872$		−	470.761i		−	0.539864i
$873$	496.861	+	424.196i	0.569142	+	0.485906i
$874$	1.26444	−	2.19007i	0.00144672	−	0.00250580i
$875$	915.367	−	528.487i	1.04613	−	0.603985i
$876$	248.987	+	22.8548i	0.284231	+	0.0260899i
$877$	469.977	−	271.341i	0.535891	−	0.309397i	−0.207521	−	0.978231i	$-0.566540\pi$
$877$	469.977	−	271.341i	0.535891	−	0.309397i	0.743412	+	0.668834i	$0.233206\pi$
$878$	−204.314	−	353.883i	−0.232704	−	0.403055i
$879$	−109.366	+	1191.47i	−0.124421	+	1.35548i
$880$	36.8133	+	63.7625i	0.0418333	+	0.0724574i
$881$	711.546	+	410.811i	0.807657	+	0.466301i	0.846142	−	0.532958i	$-0.178920\pi$
$881$	711.546	+	410.811i	0.807657	+	0.466301i	−0.0384846	+	0.999259i	$0.512253\pi$
$882$	925.491	−	1084.03i	1.04931	−	1.22906i
$883$	−222.792			−0.252312			−0.126156	−	0.992010i	$-0.540264\pi$
$883$	−222.792			−0.252312			−0.126156	+	0.992010i	$0.540264\pi$
$884$	−180.653	−	246.478i	−0.204358	−	0.278821i
$885$	22.8929	−	249.401i	0.0258676	−	0.281809i
$886$	267.844	+	154.640i	0.302307	+	0.174537i
$887$	28.4702	+	16.4373i	0.0320971	+	0.0185313i	0.515963	−	0.856611i	$-0.327434\pi$
$887$	28.4702	+	16.4373i	0.0320971	+	0.0185313i	−0.483866	+	0.875142i	$0.660768\pi$
$888$	−185.519	−	402.322i	−0.208918	−	0.453065i
$889$		−	2589.38i		−	2.91269i
$890$	169.570	+	293.704i	0.190528	+	0.330004i
$891$	−131.446	−	827.882i	−0.147527	−	0.929161i
$892$			109.282i			0.122513i
$893$	0.378357	−	0.218444i	0.000423692	−	0.000244618i
$894$	280.034	+	197.869i	0.313237	+	0.221330i
$895$	179.215	+	103.470i	0.200240	+	0.115609i
$896$		−	143.549i		−	0.160211i
$897$	21.1235	+	1216.87i	0.0235491	+	1.35660i
$898$	90.8238			0.101140
$899$	−135.335	+	234.406i	−0.150539	+	0.260741i
$900$	−255.213	+	298.931i	−0.283570	+	0.332146i
$901$	487.895	+	845.059i	0.541504	+	0.937912i
$902$	787.057			0.872568
$903$	107.860	+	233.909i	0.119447	+	0.259035i
$904$	338.995	−	195.719i	0.374994	−	0.216503i
$905$	319.009			0.352496
$906$	186.533	+	404.521i	0.205887	+	0.446491i
$907$	292.951	−	507.405i	0.322988	−	0.559432i	−0.658115	−	0.752918i	$-0.728646\pi$
$907$	292.951	−	507.405i	0.322988	−	0.559432i	0.981103	+	0.193485i	$0.0619792\pi$
$908$	205.336	−	355.652i	0.226141	−	0.391687i
$909$	−235.695	+	1273.05i	−0.259290	+	1.40049i
$910$	167.170	−	379.726i	0.183704	−	0.417282i
$911$			995.482i			1.09274i	0.837545	+	0.546368i	$0.183990\pi$
$911$			995.482i			1.09274i	−0.837545	+	0.546368i	$0.816010\pi$
$912$	0.396802	−	0.561575i	0.000435089	−	0.000615762i
$913$	−241.025	+	417.467i	−0.263992	+	0.457248i
$914$	178.212	−	102.891i	0.194981	−	0.112572i
$915$	4.63352	−	50.4789i	0.00506395	−	0.0551682i
$916$	−696.745	+	402.266i	−0.760638	+	0.439155i
$917$	188.328	+	326.193i	0.205374	+	0.355718i
$918$	−431.980	−	121.698i	−0.470567	−	0.132569i
$919$	−649.646	−	1125.22i	−0.706905	−	1.22440i	−0.965999	−	0.258544i	$-0.916757\pi$
$919$	−649.646	−	1125.22i	−0.706905	−	1.22440i	0.259094	−	0.965852i	$-0.416576\pi$
$920$	−135.959	−	78.4958i	−0.147781	−	0.0853215i
$921$	439.649	−	622.215i	0.477361	−	0.675586i
$922$	−940.006			−1.01953
$923$	−16.8670	−	154.284i	−0.0182741	−	0.167155i
$924$	784.539	+	72.0138i	0.849068	+	0.0779370i
$925$	−987.382	−	570.065i	−1.06744	−	0.616287i
$926$	−364.792	−	210.613i	−0.393944	−	0.227444i
$927$	−32.6637	−	92.1837i	−0.0352359	−	0.0994431i
$928$			171.160i			0.184439i
$929$	−224.850	−	389.451i	−0.242034	−	0.419215i	0.719259	−	0.694742i	$-0.244481\pi$
$929$	−224.850	−	389.451i	−0.242034	−	0.419215i	−0.961294	+	0.275526i	$0.911148\pi$
$930$	−28.2673	−	61.3011i	−0.0303949	−	0.0659152i
$931$			6.41701i			0.00689260i
$932$	165.351	−	95.4657i	0.177416	−	0.102431i
$933$	−807.391	+	1142.66i	−0.865371	+	1.22472i
$934$	−176.531	−	101.920i	−0.189006	−	0.109122i
$935$			216.344i			0.231384i
$936$	−24.5248	+	330.016i	−0.0262017	+	0.352581i
$937$	478.872			0.511069			0.255535	−	0.966800i	$-0.417749\pi$
$937$	478.872			0.511069			0.255535	+	0.966800i	$0.417749\pi$
$938$	−361.864	+	626.767i	−0.385782	+	0.668195i
$939$	892.000	+	630.276i	0.949947	+	0.671221i
$940$	−13.5609	−	23.4882i	−0.0144265	−	0.0249875i
$941$	457.912			0.486623			0.243311	−	0.969948i	$-0.421766\pi$
$941$	457.912			0.486623			0.243311	+	0.969948i	$0.421766\pi$
$942$	634.155	−	292.422i	0.673200	−	0.310427i
$943$	−1453.38	+	839.108i	−1.54123	+	0.889828i
$944$	−187.748			−0.198885
$945$	−150.154	−	590.527i	−0.158893	−	0.624896i
$946$	−49.5187	+	85.7690i	−0.0523454	+	0.0906649i
$947$	−315.228	+	545.991i	−0.332870	+	0.576548i	−0.983073	−	0.183212i	$-0.941350\pi$
$947$	−315.228	+	545.991i	−0.332870	+	0.576548i	0.650203	+	0.759760i	$0.274684\pi$
$948$	−28.7511	+	313.223i	−0.0303282	+	0.330404i
$949$	218.278	−	495.818i	0.230009	−	0.522464i
$950$		−	1.76955i		−	0.00186269i
$951$	863.318	+	610.010i	0.907800	+	0.641440i
$952$	210.902	−	365.292i	0.221535	−	0.383710i
$953$	−26.2075	+	15.1309i	−0.0275000	+	0.0158771i	−0.513687	−	0.857978i	$-0.671721\pi$
$953$	−26.2075	+	15.1309i	−0.0275000	+	0.0158771i	0.486187	+	0.873855i	$0.338387\pi$
$954$	192.367	−	1039.02i	0.201643	−	1.08912i
$955$	−9.13674	+	5.27510i	−0.00956727	+	0.00552367i
$956$	338.040	+	585.503i	0.353599	+	0.612451i
$957$	−935.441	−	85.8652i	−0.977472	−	0.0897233i
$958$	10.7991	+	18.7046i	0.0112726	+	0.0195246i
$959$	−1219.86	−	704.286i	−1.27201	−	0.734396i
$960$	−34.8624	−	24.6333i	−0.0363150	−	0.0256597i
$961$	880.975			0.916728
$962$	−954.224	+	104.320i	−0.991917	+	0.108441i
$963$	257.593	−	1391.33i	0.267491	−	1.44478i
$964$	−385.194	−	222.392i	−0.399579	−	0.230697i
$965$	222.077	+	128.216i	0.230132	+	0.132867i
$966$	−1525.50	+	703.443i	−1.57920	+	0.728202i
$967$			895.338i			0.925892i	0.886386	+	0.462946i	$0.153208\pi$
$967$			895.338i			0.925892i	−0.886386	+	0.462946i	$0.846792\pi$
$968$	−19.6609	−	34.0537i	−0.0203109	−	0.0351794i
$969$	1.83481	−	0.846071i	0.00189351	−	0.000873139i
$970$			182.590i			0.188237i
$971$	−69.8882	+	40.3500i	−0.0719755	+	0.0415551i	−0.535556	−	0.844500i	$-0.679898\pi$
$971$	−69.8882	+	40.3500i	−0.0719755	+	0.0415551i	0.463580	+	0.886055i	$0.346565\pi$
$972$	270.199	+	403.966i	0.277983	+	0.415603i
$973$	417.021	+	240.767i	0.428593	+	0.247448i
$974$			130.857i			0.134350i
$975$	438.548	+	730.026i	0.449793	+	0.748744i
$976$	−38.0002			−0.0389346
$977$	39.4153	−	68.2694i	0.0403432	−	0.0698765i	−0.845149	−	0.534531i	$-0.820488\pi$
$977$	39.4153	−	68.2694i	0.0403432	−	0.0698765i	0.885492	+	0.464655i	$0.153822\pi$
$978$	−329.325	+	466.078i	−0.336733	+	0.476562i
$979$	697.652	+	1208.37i	0.712617	+	1.23429i
$980$	398.366			0.406496
$981$	−1411.94	+	500.295i	−1.43928	+	0.509985i
$982$	−654.464	+	377.855i	−0.666461	+	0.384781i
$983$	1383.84			1.40777			0.703886	−	0.710313i	$-0.251447\pi$
$983$	1383.84			1.40777			0.703886	+	0.710313i	$0.251447\pi$
$984$	−414.384	+	191.081i	−0.421122	+	0.194188i
$985$	−215.131	+	372.618i	−0.218407	+	0.378293i
$986$	−251.467	+	435.554i	−0.255038	+	0.441738i
$987$	−289.001	−	26.5278i	−0.292808	−	0.0268772i
$988$	−0.880725	−	1.20164i	−0.000891422	−	0.00121623i
$989$		−	211.174i		−	0.213523i
$990$	152.118	−	178.176i	0.153654	−	0.179975i
$991$	102.613	−	177.730i	0.103545	−	0.179344i	−0.809598	−	0.586985i	$-0.800315\pi$
$991$	102.613	−	177.730i	0.103545	−	0.179344i	0.913143	+	0.407640i	$0.133648\pi$
$992$	−43.8245	+	25.3021i	−0.0441780	+	0.0255062i
$993$	−672.804	−	61.7575i	−0.677547	−	0.0621929i
$994$	185.523	−	107.112i	0.186643	−	0.107758i
$995$	78.7948	+	136.477i	0.0791907	+	0.137162i
$996$	25.5465	−	278.311i	0.0256491	−	0.279429i
$997$	−803.839	−	1392.29i	−0.806258	−	1.39648i	−0.915439	−	0.402458i	$-0.868156\pi$
$997$	−803.839	−	1392.29i	−0.806258	−	1.39648i	0.109181	−	0.994022i	$-0.465177\pi$
$998$	921.256	+	531.887i	0.923102	+	0.532953i
$999$	−1009.51	+	983.983i	−1.01052	+	0.984968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.j.a.17.9	yes	20
3.2	odd	2	inner	78.3.j.a.17.1	✓	20
13.10	even	6	inner	78.3.j.a.23.1	yes	20
39.23	odd	6	inner	78.3.j.a.23.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.j.a.17.1	✓	20	3.2	odd	2	inner
78.3.j.a.17.9	yes	20	1.1	even	1	trivial
78.3.j.a.23.1	yes	20	13.10	even	6	inner
78.3.j.a.23.9	yes	20	39.23	odd	6	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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(2.45009 + 1.73120i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.77863 q^{5} +(3.85276 - 1.77659i) q^{6} +(10.9882 - 6.34403i) q^{7} -2.82843 q^{8} +(3.00587 + 8.48320i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(2.45009 + 1.73120i) q^{3} +(-1.00000 - 1.73205i) q^{4} -1.77863 q^{5} +(3.85276 - 1.77659i) q^{6} +(10.9882 - 6.34403i) q^{7} -2.82843 q^{8} +(3.00587 + 8.48320i) q^{9} +(-1.25768 + 2.17836i) q^{10} +(-5.17440 + 8.96232i) q^{11} +(0.548442 - 5.97488i) q^{12} +(-11.8980 - 5.23798i) q^{13} -17.9436i q^{14} +(-4.35780 - 3.07916i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-10.1789 + 5.87678i) q^{17} +(12.5152 + 2.31710i) q^{18} +(-0.0496245 + 0.0286507i) q^{19} +(1.77863 + 3.08067i) q^{20} +(37.9048 + 3.47933i) q^{21} +(7.31771 + 12.6746i) q^{22} +(-27.0257 - 15.6033i) q^{23} +(-6.92990 - 4.89658i) q^{24} -21.8365 q^{25} +(-14.8284 + 10.8683i) q^{26} +(-7.32148 + 25.9884i) q^{27} +(-21.9764 - 12.6881i) q^{28} +(26.2034 + 15.1285i) q^{29} +(-6.85262 + 3.15989i) q^{30} +8.94565i q^{31} +(2.82843 + 4.89898i) q^{32} +(-28.1933 + 13.0006i) q^{33} +16.6220i q^{34} +(-19.5439 + 11.2837i) q^{35} +(11.6875 - 13.6895i) q^{36} +(45.2171 + 26.1061i) q^{37} +0.0810365i q^{38} +(-20.0833 - 33.4315i) q^{39} +5.03072 q^{40} +(26.8888 - 46.5727i) q^{41} +(31.0641 - 43.9635i) q^{42} +(3.38349 + 5.86037i) q^{43} +20.6976 q^{44} +(-5.34633 - 15.0885i) q^{45} +(-38.2201 + 22.0664i) q^{46} -7.62439 q^{47} +(-10.8972 + 5.02495i) q^{48} +(55.9934 - 96.9835i) q^{49} +(-15.4407 + 26.7441i) q^{50} +(-35.1131 - 3.22307i) q^{51} +(2.82559 + 25.8460i) q^{52} -83.0208i q^{53} +(26.6521 + 27.3435i) q^{54} +(9.20333 - 15.9406i) q^{55} +(-31.0793 + 17.9436i) q^{56} +(-0.171185 - 0.0157132i) q^{57} +(37.0572 - 21.3950i) q^{58} +(23.4685 + 40.6486i) q^{59} +(-0.975473 + 10.6271i) q^{60} +(4.75002 + 8.22727i) q^{61} +(10.9561 + 6.32553i) q^{62} +(86.8468 + 74.1456i) q^{63} +8.00000 q^{64} +(21.1622 + 9.31642i) q^{65} +(-4.01333 + 43.7224i) q^{66} +(-34.9298 - 20.1667i) q^{67} +(20.3578 + 11.7536i) q^{68} +(-39.2029 - 85.0165i) q^{69} +31.9150i q^{70} +(5.96936 + 10.3392i) q^{71} +(-8.50190 - 23.9941i) q^{72} +41.6722i q^{73} +(63.9466 - 36.9196i) q^{74} +(-53.5013 - 37.8034i) q^{75} +(0.0992490 + 0.0573014i) q^{76} +131.306i q^{77} +(-55.1460 + 0.957271i) q^{78} -52.4233 q^{79} +(3.55725 - 6.16135i) q^{80} +(-62.9294 + 50.9989i) q^{81} +(-38.0265 - 65.8638i) q^{82} +46.5802 q^{83} +(-31.8785 - 69.1324i) q^{84} +(18.1044 - 10.4526i) q^{85} +9.56995 q^{86} +(38.0101 + 82.4297i) q^{87} +(14.6354 - 25.3493i) q^{88} +(67.4139 - 116.764i) q^{89} +(-22.2599 - 4.12126i) q^{90} +(-163.968 + 17.9257i) q^{91} +62.4132i q^{92} +(-15.4867 + 21.9176i) q^{93} +(-5.39126 + 9.33793i) q^{94} +(0.0882635 - 0.0509589i) q^{95} +(-1.55123 + 16.8995i) q^{96} +(62.8647 - 36.2950i) q^{97} +(-79.1867 - 137.155i) q^{98} +(-91.5828 - 16.9559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

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