LMFDB - Embedded newform 39.3.c.a.14.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(14,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("39.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	39.c (of order $2$, degree $1$, 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:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 169x^{4} + 416x^{2} + 351 $ x^8 + 26x^6 + 169x^4 + 416*x^2 + 351
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.5
Root			$4.21041i$ of defining polynomial
Character	$\chi$	$=$	39.14
Dual form			39.3.c.a.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.285887i q^{2} +(-1.75324 + 2.43437i) q^{3} +3.91827 q^{4} +3.55207i q^{5} +(-0.695955 - 0.501228i) q^{6} +1.19376 q^{7} +2.26373i q^{8} +(-2.85231 - 8.53606i) q^{9} -1.01549 q^{10} -19.9630i q^{11} +(-6.86966 + 9.53852i) q^{12} -3.60555 q^{13} +0.341280i q^{14} +(-8.64706 - 6.22763i) q^{15} +15.0259 q^{16} +10.8293i q^{17} +(2.44035 - 0.815439i) q^{18} -6.62543 q^{19} +13.9180i q^{20} +(-2.09294 + 2.90605i) q^{21} +5.70717 q^{22} -20.3363i q^{23} +(-5.51076 - 3.96886i) q^{24} +12.3828 q^{25} -1.03078i q^{26} +(25.7807 + 8.02216i) q^{27} +4.67747 q^{28} +37.4601i q^{29} +(1.78040 - 2.47208i) q^{30} -37.3064 q^{31} +13.3506i q^{32} +(48.5974 + 34.9999i) q^{33} -3.09597 q^{34} +4.24032i q^{35} +(-11.1761 - 33.4466i) q^{36} -33.8710 q^{37} -1.89413i q^{38} +(6.32139 - 8.77725i) q^{39} -8.04093 q^{40} -40.6456i q^{41} +(-0.830802 - 0.598345i) q^{42} -11.0533 q^{43} -78.2205i q^{44} +(30.3207 - 10.1316i) q^{45} +5.81389 q^{46} -28.9236i q^{47} +(-26.3440 + 36.5786i) q^{48} -47.5749 q^{49} +3.54008i q^{50} +(-26.3626 - 18.9864i) q^{51} -14.1275 q^{52} +89.3566i q^{53} +(-2.29343 + 7.37037i) q^{54} +70.9101 q^{55} +2.70235i q^{56} +(11.6160 - 16.1288i) q^{57} -10.7094 q^{58} +55.3576i q^{59} +(-33.8815 - 24.4015i) q^{60} +43.8365 q^{61} -10.6654i q^{62} +(-3.40497 - 10.1900i) q^{63} +56.2868 q^{64} -12.8072i q^{65} +(-10.0060 + 13.8934i) q^{66} -69.3286 q^{67} +42.4323i q^{68} +(49.5061 + 35.6544i) q^{69} -1.21225 q^{70} -53.3845i q^{71} +(19.3233 - 6.45687i) q^{72} +107.566 q^{73} -9.68328i q^{74} +(-21.7100 + 30.1443i) q^{75} -25.9602 q^{76} -23.8310i q^{77} +(2.50930 + 1.80720i) q^{78} +51.8333 q^{79} +53.3731i q^{80} +(-64.7286 + 48.6950i) q^{81} +11.6200 q^{82} +105.439i q^{83} +(-8.20071 + 11.3867i) q^{84} -38.4666 q^{85} -3.15999i q^{86} +(-91.1918 - 65.6765i) q^{87} +45.1909 q^{88} -75.1768i q^{89} +(2.89650 + 8.66829i) q^{90} -4.30416 q^{91} -79.6832i q^{92} +(65.4070 - 90.8175i) q^{93} +8.26887 q^{94} -23.5340i q^{95} +(-32.5004 - 23.4068i) q^{96} -70.9688 q^{97} -13.6011i q^{98} +(-170.405 + 56.9408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 20 q^{4} + 8 q^{7} - 6 q^{9} + 18 q^{12} + 52 q^{15} + 24 q^{16} - 52 q^{18} - 8 q^{19} - 80 q^{21} + 52 q^{22} - 60 q^{25} - 44 q^{27} - 176 q^{28} + 182 q^{30} + 80 q^{31} + 52 q^{33}+ \cdots - 468 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 20 * q^4 + 8 * q^7 - 6 * q^9 + 18 * q^12 + 52 * q^15 + 24 * q^16 - 52 * q^18 - 8 * q^19 - 80 * q^21 + 52 * q^22 - 60 * q^25 - 44 * q^27 - 176 * q^28 + 182 * q^30 + 80 * q^31 + 52 * q^33 + 208 * q^34 - 50 * q^36 - 32 * q^37 + 104 * q^40 - 78 * q^42 - 196 * q^43 + 104 * q^45 - 104 * q^46 - 266 * q^48 - 20 * q^49 + 26 * q^51 - 52 * q^52 + 312 * q^54 + 208 * q^55 - 24 * q^57 - 208 * q^58 - 468 * q^60 + 248 * q^61 + 20 * q^63 + 252 * q^64 - 176 * q^67 + 208 * q^69 - 104 * q^70 + 468 * q^72 + 440 * q^73 + 28 * q^75 - 240 * q^76 + 130 * q^78 - 88 * q^79 - 366 * q^81 - 468 * q^82 + 304 * q^84 - 416 * q^85 - 364 * q^87 + 156 * q^88 - 546 * q^90 - 52 * q^91 - 72 * q^93 + 520 * q^94 + 208 * q^96 - 320 * q^97 - 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			0.285887i			0.142943i	0.997443	+	0.0714717i	$0.0227696\pi$
$2$			0.285887i			0.142943i	−0.997443	+	0.0714717i	$0.977230\pi$
$3$	−1.75324	+	2.43437i	−0.584413	+	0.811457i
$3$	−1.75324	+	2.43437i	−0.584413	+	0.811457i
$4$	3.91827			0.979567
$5$			3.55207i			0.710415i	0.934788	+	0.355207i	$0.115590\pi$
$5$			3.55207i			0.710415i	−0.934788	+	0.355207i	$0.884410\pi$
$6$	−0.695955	−	0.501228i	−0.115992	−	0.0835380i
$7$	1.19376			0.170537			0.0852685	−	0.996358i	$-0.472825\pi$
$7$	1.19376			0.170537			0.0852685	+	0.996358i	$0.472825\pi$
$8$			2.26373i			0.282966i
$9$	−2.85231	−	8.53606i	−0.316924	−	0.948451i
$10$	−1.01549			−0.101549
$11$		−	19.9630i		−	1.81482i	−0.420247	−	0.907410i	$-0.638057\pi$
$11$		−	19.9630i		−	1.81482i	0.420247	−	0.907410i	$-0.361943\pi$
$12$	−6.86966	+	9.53852i	−0.572471	+	0.794876i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$			0.341280i			0.0243771i
$15$	−8.64706	−	6.22763i	−0.576471	−	0.415175i
$16$	15.0259			0.939119
$17$			10.8293i			0.637020i	0.947920	+	0.318510i	$0.103182\pi$
$17$			10.8293i			0.637020i	−0.947920	+	0.318510i	$0.896818\pi$
$18$	2.44035	−	0.815439i	0.135575	−	0.0453022i
$19$	−6.62543			−0.348707			−0.174354	−	0.984683i	$-0.555784\pi$
$19$	−6.62543			−0.348707			−0.174354	+	0.984683i	$0.555784\pi$
$20$			13.9180i			0.695899i
$21$	−2.09294	+	2.90605i	−0.0996639	+	0.138383i
$22$	5.70717			0.259417
$23$		−	20.3363i		−	0.884188i	−0.896969	−	0.442094i	$-0.854236\pi$
$23$		−	20.3363i		−	0.884188i	0.896969	−	0.442094i	$-0.145764\pi$
$24$	−5.51076	−	3.96886i	−0.229615	−	0.165369i
$25$	12.3828			0.495311
$26$		−	1.03078i		−	0.0396454i
$27$	25.7807	+	8.02216i	0.954841	+	0.297117i
$28$	4.67747			0.167052
$29$			37.4601i			1.29173i	0.763452	+	0.645864i	$0.223503\pi$
$29$			37.4601i			1.29173i	−0.763452	+	0.645864i	$0.776497\pi$
$30$	1.78040	−	2.47208i	0.0593466	−	0.0824027i
$31$	−37.3064			−1.20343			−0.601716	−	0.798710i	$-0.705516\pi$
$31$	−37.3064			−1.20343			−0.601716	+	0.798710i	$0.705516\pi$
$32$			13.3506i			0.417207i
$33$	48.5974	+	34.9999i	1.47265	+	1.06060i
$34$	−3.09597			−0.0910578
$35$			4.24032i			0.121152i
$36$	−11.1761	−	33.4466i	−0.310448	−	0.929071i
$37$	−33.8710			−0.915432			−0.457716	−	0.889098i	$-0.651332\pi$
$37$	−33.8710			−0.915432			−0.457716	+	0.889098i	$0.651332\pi$
$38$		−	1.89413i		−	0.0498454i
$39$	6.32139	−	8.77725i	0.162087	−	0.225058i
$40$	−8.04093			−0.201023
$41$		−	40.6456i		−	0.991356i	−0.868507	−	0.495678i	$-0.834920\pi$
$41$		−	40.6456i		−	0.991356i	0.868507	−	0.495678i	$-0.165080\pi$
$42$	−0.830802	−	0.598345i	−0.0197810	−	0.0142463i
$43$	−11.0533			−0.257053			−0.128527	−	0.991706i	$-0.541025\pi$
$43$	−11.0533			−0.257053			−0.128527	+	0.991706i	$0.541025\pi$
$44$		−	78.2205i		−	1.77774i
$45$	30.3207	−	10.1316i	0.673793	−	0.225147i
$46$	5.81389			0.126389
$47$		−	28.9236i		−	0.615395i	−0.951484	−	0.307698i	$-0.900441\pi$
$47$		−	28.9236i		−	0.615395i	0.951484	−	0.307698i	$-0.0995585\pi$
$48$	−26.3440	+	36.5786i	−0.548833	+	0.762054i
$49$	−47.5749			−0.970917
$50$			3.54008i			0.0708015i
$51$	−26.3626	−	18.9864i	−0.516914	−	0.372282i
$52$	−14.1275			−0.271683
$53$			89.3566i			1.68597i	0.537934	+	0.842987i	$0.319205\pi$
$53$			89.3566i			1.68597i	−0.537934	+	0.842987i	$0.680795\pi$
$54$	−2.29343	+	7.37037i	−0.0424709	+	0.136488i
$55$	70.9101			1.28927
$56$			2.70235i			0.0482562i
$57$	11.6160	−	16.1288i	0.203789	−	0.282961i
$58$	−10.7094			−0.184644
$59$			55.3576i			0.938265i	0.883128	+	0.469132i	$0.155433\pi$
$59$			55.3576i			0.938265i	−0.883128	+	0.469132i	$0.844567\pi$
$60$	−33.8815	−	24.4015i	−0.564692	−	0.406692i
$61$	43.8365			0.718632			0.359316	−	0.933216i	$-0.383010\pi$
$61$	43.8365			0.718632			0.359316	+	0.933216i	$0.383010\pi$
$62$		−	10.6654i		−	0.172023i
$63$	−3.40497	−	10.1900i	−0.0540472	−	0.161746i
$64$	56.2868			0.879482
$65$		−	12.8072i		−	0.197034i
$66$	−10.0060	+	13.8934i	−0.151606	+	0.210505i
$67$	−69.3286			−1.03475			−0.517377	−	0.855757i	$-0.673092\pi$
$67$	−69.3286			−1.03475			−0.517377	+	0.855757i	$0.673092\pi$
$68$			42.4323i			0.624004i
$69$	49.5061	+	35.6544i	0.717480	+	0.516731i
$70$	−1.21225			−0.0173179
$71$		−	53.3845i		−	0.751894i	−0.926641	−	0.375947i	$-0.877317\pi$
$71$		−	53.3845i		−	0.751894i	0.926641	−	0.375947i	$-0.122683\pi$
$72$	19.3233	−	6.45687i	0.268380	−	0.0896787i
$73$	107.566			1.47351			0.736757	−	0.676158i	$-0.236356\pi$
$73$	107.566			1.47351			0.736757	+	0.676158i	$0.236356\pi$
$74$		−	9.68328i		−	0.130855i
$75$	−21.7100	+	30.1443i	−0.289466	+	0.401924i
$76$	−25.9602			−0.341582
$77$		−	23.8310i		−	0.309494i
$78$	2.50930	+	1.80720i	0.0321705	+	0.0231693i
$79$	51.8333			0.656118			0.328059	−	0.944657i	$-0.393605\pi$
$79$	51.8333			0.656118			0.328059	+	0.944657i	$0.393605\pi$
$80$			53.3731i			0.667164i
$81$	−64.7286	+	48.6950i	−0.799119	+	0.601173i
$82$	11.6200			0.141708
$83$			105.439i			1.27035i	0.772367	+	0.635177i	$0.219073\pi$
$83$			105.439i			1.27035i	−0.772367	+	0.635177i	$0.780927\pi$
$84$	−8.20071	+	11.3867i	−0.0976275	+	0.135556i
$85$	−38.4666			−0.452548
$86$		−	3.15999i		−	0.0367441i
$87$	−91.1918	−	65.6765i	−1.04818	−	0.754903i
$88$	45.1909			0.513533
$89$		−	75.1768i		−	0.844683i	−0.906437	−	0.422342i	$-0.861208\pi$
$89$		−	75.1768i		−	0.844683i	0.906437	−	0.422342i	$-0.138792\pi$
$90$	2.89650	+	8.66829i	0.0321833	+	0.0963144i
$91$	−4.30416			−0.0472984
$92$		−	79.6832i		−	0.866121i
$93$	65.4070	−	90.8175i	0.703301	−	0.976533i
$94$	8.26887			0.0879667
$95$		−	23.5340i		−	0.247727i
$96$	−32.5004	−	23.4068i	−0.338546	−	0.243821i
$97$	−70.9688			−0.731637			−0.365819	−	0.930686i	$-0.619211\pi$
$97$	−70.9688			−0.731637			−0.365819	+	0.930686i	$0.619211\pi$
$98$		−	13.6011i		−	0.138786i
$99$	−170.405	+	56.9408i	−1.72127	+	0.575159i
$100$	48.5191			0.485191
$101$			14.4299i			0.142870i	0.997445	+	0.0714350i	$0.0227578\pi$
$101$			14.4299i			0.142870i	−0.997445	+	0.0714350i	$0.977242\pi$
$102$	5.42797	−	7.53673i	0.0532154	−	0.0738895i
$103$	−70.2696			−0.682230			−0.341115	−	0.940022i	$-0.610804\pi$
$103$	−70.2696			−0.682230			−0.341115	+	0.940022i	$0.610804\pi$
$104$		−	8.16199i		−	0.0784807i
$105$	−10.3225	−	7.43428i	−0.0983095	−	0.0708027i
$106$	−25.5459			−0.240999
$107$		−	145.717i		−	1.36184i	−0.732356	−	0.680922i	$-0.761579\pi$
$107$		−	145.717i		−	1.36184i	0.732356	−	0.680922i	$-0.238421\pi$
$108$	101.016	+	31.4330i	0.935331	+	0.291046i
$109$	126.641			1.16184			0.580922	−	0.813959i	$-0.302692\pi$
$109$	126.641			1.16184			0.580922	+	0.813959i	$0.302692\pi$
$110$			20.2723i			0.184293i
$111$	59.3839	−	82.4545i	0.534990	−	0.742834i
$112$	17.9373			0.160154
$113$		−	18.1098i		−	0.160264i	−0.996784	−	0.0801320i	$-0.974466\pi$
$113$		−	18.1098i		−	0.160264i	0.996784	−	0.0801320i	$-0.0255342\pi$
$114$	4.61100	+	3.32085i	0.0404474	+	0.0291303i
$115$	72.2361			0.628140
$116$			146.779i			1.26533i
$117$	10.2842	+	30.7772i	0.0878988	+	0.263053i
$118$	−15.8260			−0.134119
$119$			12.9276i			0.108635i
$120$	14.0977	−	19.5746i	0.117481	−	0.163122i
$121$	−277.522			−2.29357
$122$			12.5323i			0.102724i
$123$	98.9464	+	71.2614i	0.804442	+	0.579361i
$124$	−146.176			−1.17884
$125$			132.786i			1.06229i
$126$	2.91319	−	0.973438i	0.0231205	−	0.00772569i
$127$	75.4359			0.593983			0.296992	−	0.954880i	$-0.404017\pi$
$127$	75.4359			0.593983			0.296992	+	0.954880i	$0.404017\pi$
$128$			69.4942i			0.542923i
$129$	19.3790	−	26.9078i	0.150225	−	0.208588i
$130$	3.66141			0.0281647
$131$		−	118.658i		−	0.905788i	−0.891564	−	0.452894i	$-0.850392\pi$
$131$		−	118.658i		−	0.905788i	0.891564	−	0.452894i	$-0.149608\pi$
$132$	190.418	+	137.139i	1.44256	+	1.03893i
$133$	−7.90917			−0.0594674
$134$		−	19.8201i		−	0.147911i
$135$	−28.4953	+	91.5750i	−0.211076	+	0.678333i
$136$	−24.5147			−0.180255
$137$		−	42.5637i		−	0.310684i	−0.987861	−	0.155342i	$-0.950352\pi$
$137$		−	42.5637i		−	0.310684i	0.987861	−	0.155342i	$-0.0496479\pi$
$138$	−10.1931	+	14.1532i	−0.0738633	+	0.102559i
$139$	148.591			1.06900			0.534499	−	0.845169i	$-0.320500\pi$
$139$	148.591			1.06900			0.534499	+	0.845169i	$0.320500\pi$
$140$			16.6147i			0.118676i
$141$	70.4107	+	50.7099i	0.499367	+	0.359645i
$142$	15.2619			0.107478
$143$			71.9777i			0.503340i
$144$	−42.8586	−	128.262i	−0.297629	−	0.890708i
$145$	−133.061			−0.917663
$146$			30.7519i			0.210629i
$147$	83.4102	−	115.815i	0.567416	−	0.787857i
$148$	−132.716			−0.896728
$149$			86.3648i			0.579629i	0.957083	+	0.289815i	$0.0935937\pi$
$149$			86.3648i			0.579629i	−0.957083	+	0.289815i	$0.906406\pi$
$150$	−8.61785	−	6.20659i	−0.0574524	−	0.0413773i
$151$	240.297			1.59137			0.795685	−	0.605711i	$-0.207111\pi$
$151$	240.297			1.59137			0.795685	+	0.605711i	$0.207111\pi$
$152$		−	14.9982i		−	0.0986723i
$153$	92.4399	−	30.8887i	0.604182	−	0.201887i
$154$	6.81298			0.0442401
$155$		−	132.515i		−	0.854935i
$156$	24.7689	−	34.3916i	0.158775	−	0.220459i
$157$	−55.8907			−0.355992			−0.177996	−	0.984031i	$-0.556961\pi$
$157$	−55.8907			−0.355992			−0.177996	+	0.984031i	$0.556961\pi$
$158$			14.8185i			0.0937878i
$159$	−217.527	−	156.663i	−1.36809	−	0.985304i
$160$	−47.4224			−0.296390
$161$		−	24.2767i		−	0.150787i
$162$	−13.9213	−	18.5051i	−0.0859338	−	0.114229i
$163$	−129.230			−0.792823			−0.396411	−	0.918073i	$-0.629745\pi$
$163$	−129.230			−0.792823			−0.396411	+	0.918073i	$0.629745\pi$
$164$		−	159.260i		−	0.971099i
$165$	−124.322	+	172.621i	−0.753468	+	1.04619i
$166$	−30.1437			−0.181589
$167$			287.252i			1.72007i	0.510235	+	0.860035i	$0.329559\pi$
$167$			287.252i			1.72007i	−0.510235	+	0.860035i	$0.670441\pi$
$168$	−6.57851	−	4.73786i	−0.0391578	−	0.0282015i
$169$	13.0000			0.0769231
$170$		−	10.9971i		−	0.0646888i
$171$	18.8978	+	56.5551i	0.110514	+	0.330732i
$172$	−43.3098			−0.251801
$173$		−	186.138i		−	1.07594i	−0.842964	−	0.537970i	$-0.819191\pi$
$173$		−	186.138i		−	1.07594i	0.842964	−	0.537970i	$-0.180809\pi$
$174$	18.7761	−	26.0706i	0.107908	−	0.149831i
$175$	14.7820			0.0844689
$176$		−	299.962i		−	1.70433i
$177$	−134.761	−	97.0551i	−0.761361	−	0.548334i
$178$	21.4921			0.120742
$179$			232.784i			1.30047i	0.759732	+	0.650236i	$0.225330\pi$
$179$			232.784i			1.30047i	−0.759732	+	0.650236i	$0.774670\pi$
$180$	118.805	−	39.6984i	0.660026	−	0.220547i
$181$	−31.4877			−0.173965			−0.0869825	−	0.996210i	$-0.527722\pi$
$181$	−31.4877			−0.173965			−0.0869825	+	0.996210i	$0.527722\pi$
$182$		−	1.23050i		−	0.00676100i
$183$	−76.8559	+	106.714i	−0.419977	+	0.583138i
$184$	46.0359			0.250195
$185$		−	120.312i		−	0.650337i
$186$	25.9635	+	18.6990i	0.139589	+	0.100532i
$187$	216.186			1.15608
$188$		−	113.330i		−	0.602821i
$189$	30.7759	+	9.57652i	0.162836	+	0.0506694i
$190$	6.72807			0.0354109
$191$			110.232i			0.577132i	0.957460	+	0.288566i	$0.0931785\pi$
$191$			110.232i			0.577132i	−0.957460	+	0.288566i	$0.906822\pi$
$192$	−98.6842	+	137.023i	−0.513980	+	0.713661i
$193$	98.1434			0.508515			0.254258	−	0.967137i	$-0.418169\pi$
$193$	98.1434			0.508515			0.254258	+	0.967137i	$0.418169\pi$
$194$		−	20.2891i		−	0.104583i
$195$	31.1774	+	22.4540i	0.159884	+	0.115149i
$196$	−186.411			−0.951079
$197$		−	19.8017i		−	0.100516i	−0.998736	−	0.0502581i	$-0.983996\pi$
$197$		−	19.8017i		−	0.100516i	0.998736	−	0.0502581i	$-0.0160044\pi$
$198$	−16.2786	−	48.7167i	−0.0822153	−	0.246044i
$199$	52.3330			0.262980			0.131490	−	0.991317i	$-0.458024\pi$
$199$	52.3330			0.262980			0.131490	+	0.991317i	$0.458024\pi$
$200$			28.0313i			0.140156i
$201$	121.549	−	168.771i	0.604724	−	0.839659i
$202$	−4.12531			−0.0204223
$203$			44.7184i			0.220287i
$204$	−103.296	−	74.3938i	−0.506352	−	0.364676i
$205$	144.376			0.704273
$206$		−	20.0892i		−	0.0975203i
$207$	−173.592	+	58.0056i	−0.838609	+	0.280220i
$208$	−54.1767			−0.260465
$209$			132.264i			0.632840i
$210$	2.12537	−	2.95107i	0.0101208	−	0.0140527i
$211$	112.546			0.533394			0.266697	−	0.963780i	$-0.414068\pi$
$211$	112.546			0.533394			0.266697	+	0.963780i	$0.414068\pi$
$212$			350.123i			1.65152i
$213$	129.958	+	93.5957i	0.610129	+	0.439416i
$214$	41.6587			0.194667
$215$		−	39.2621i		−	0.182614i
$216$	−18.1600	+	58.3606i	−0.0840741	+	0.270188i
$217$	−44.5348			−0.205230
$218$			36.2050i			0.166078i
$219$	−188.590	+	261.857i	−0.861140	+	1.19569i
$220$	277.845			1.26293
$221$		−	39.0457i		−	0.176678i
$222$	23.5727	+	16.9771i	0.106183	+	0.0764734i
$223$	149.561			0.670675			0.335337	−	0.942098i	$-0.391150\pi$
$223$	149.561			0.670675			0.335337	+	0.942098i	$0.391150\pi$
$224$			15.9374i			0.0711492i
$225$	−35.3196	−	105.700i	−0.156976	−	0.469778i
$226$	5.17737			0.0229087
$227$			62.7111i			0.276260i	0.990414	+	0.138130i	$0.0441092\pi$
$227$			62.7111i			0.276260i	−0.990414	+	0.138130i	$0.955891\pi$
$228$	45.5145	−	63.1968i	0.199625	−	0.277179i
$229$	176.248			0.769642			0.384821	−	0.922991i	$-0.374263\pi$
$229$	176.248			0.769642			0.384821	+	0.922991i	$0.374263\pi$
$230$			20.6514i			0.0897885i
$231$	58.0135	+	41.7814i	0.251141	+	0.180872i
$232$	−84.7996			−0.365516
$233$		−	245.434i		−	1.05336i	−0.850062	−	0.526682i	$-0.823436\pi$
$233$		−	245.434i		−	1.05336i	0.850062	−	0.526682i	$-0.176564\pi$
$234$	−8.79880	+	2.94011i	−0.0376017	+	0.0125646i
$235$	102.739			0.437186
$236$			216.906i			0.919093i
$237$	−90.8762	+	126.182i	−0.383444	+	0.532411i
$238$	−3.69584			−0.0155287
$239$			113.417i			0.474549i	0.971443	+	0.237275i	$0.0762542\pi$
$239$			113.417i			0.474549i	−0.971443	+	0.237275i	$0.923746\pi$
$240$	−129.930	−	93.5757i	−0.541374	−	0.389899i
$241$	−269.199			−1.11701			−0.558504	−	0.829502i	$-0.688624\pi$
$241$	−269.199			−1.11701			−0.558504	+	0.829502i	$0.688624\pi$
$242$		−	79.3399i		−	0.327851i
$243$	−5.05705	−	242.947i	−0.0208109	−	0.999783i
$244$	171.763			0.703948
$245$		−	168.990i		−	0.689754i
$246$	−20.3727	+	28.2875i	−0.0828158	+	0.114990i
$247$	23.8883			0.0967139
$248$		−	84.4516i		−	0.340531i
$249$	−256.678	−	184.860i	−1.03084	−	0.742411i
$250$	−37.9619			−0.151848
$251$		−	37.8046i		−	0.150616i	−0.997160	−	0.0753080i	$-0.976006\pi$
$251$		−	37.8046i		−	0.150616i	0.997160	−	0.0753080i	$-0.0239940\pi$
$252$	−13.3416	−	39.9271i	−0.0529429	−	0.158441i
$253$	−405.974			−1.60464
$254$			21.5661i			0.0849061i
$255$	67.4411	−	93.6419i	0.264475	−	0.367223i
$256$	205.280			0.801875
$257$		−	297.555i		−	1.15780i	−0.815398	−	0.578901i	$-0.803482\pi$
$257$		−	297.555i		−	1.15780i	0.815398	−	0.578901i	$-0.196518\pi$
$258$	7.69259	+	5.54022i	0.0298162	+	0.0214737i
$259$	−40.4338			−0.156115
$260$		−	50.1820i		−	0.193008i
$261$	319.762	−	106.848i	1.22514	−	0.409379i
$262$	33.9229			0.129477
$263$		−	75.9929i		−	0.288946i	−0.989509	−	0.144473i	$-0.953851\pi$
$263$		−	75.9929i		−	0.288946i	0.989509	−	0.144473i	$-0.0461487\pi$
$264$	−79.2304	+	110.011i	−0.300115	+	0.416709i
$265$	−317.401			−1.19774
$266$		−	2.26113i		−	0.00850048i
$267$	183.008	+	131.803i	0.685424	+	0.493644i
$268$	−271.648			−1.01361
$269$			2.23997i			0.00832703i	0.999991	+	0.00416352i	$0.00132529\pi$
$269$			2.23997i			0.00832703i	−0.999991	+	0.00416352i	$0.998675\pi$
$270$	−26.1801	−	8.14643i	−0.0969633	−	0.0301720i
$271$	−137.914			−0.508909			−0.254455	−	0.967085i	$-0.581896\pi$
$271$	−137.914			−0.508909			−0.254455	+	0.967085i	$0.581896\pi$
$272$			162.721i			0.598237i
$273$	7.54621	−	10.4779i	0.0276418	−	0.0383806i
$274$	12.1684			0.0444102
$275$		−	247.198i		−	0.898900i
$276$	193.978	+	139.704i	0.702820	+	0.506172i
$277$	34.0578			0.122952			0.0614762	−	0.998109i	$-0.480419\pi$
$277$	34.0578			0.122952			0.0614762	+	0.998109i	$0.480419\pi$
$278$			42.4801i			0.152806i
$279$	106.409	+	318.449i	0.381396	+	1.14140i
$280$	−9.59893			−0.0342819
$281$			274.814i			0.977985i	0.872288	+	0.488993i	$0.162636\pi$
$281$			274.814i			0.977985i	−0.872288	+	0.488993i	$0.837364\pi$
$282$	−14.4973	+	20.1295i	−0.0514089	+	0.0713812i
$283$	−501.133			−1.77079			−0.885394	−	0.464842i	$-0.846111\pi$
$283$	−501.133			−1.77079			−0.885394	+	0.464842i	$0.846111\pi$
$284$		−	209.175i		−	0.736531i
$285$	57.2905	+	41.2607i	0.201019	+	0.144775i
$286$	−20.5775			−0.0719492
$287$		−	48.5210i		−	0.169063i
$288$	113.962	−	38.0802i	0.395701	−	0.132223i
$289$	171.725			0.594206
$290$		−	38.0404i		−	0.131174i
$291$	124.425	−	172.764i	0.427578	−	0.593692i
$292$	421.474			1.44341
$293$			376.343i			1.28445i	0.766517	+	0.642224i	$0.221988\pi$
$293$			376.343i			1.28445i	−0.766517	+	0.642224i	$0.778012\pi$
$294$	33.1100	+	23.8459i	0.112619	+	0.0811085i
$295$	−196.634			−0.666557
$296$		−	76.6748i		−	0.259036i
$297$	160.146	−	514.661i	0.539214	−	1.73286i
$298$	−24.6906			−0.0828542
$299$			73.3237i			0.245230i
$300$	−85.0655	+	118.113i	−0.283552	+	0.393711i
$301$	−13.1950			−0.0438371
$302$			68.6977i			0.227476i
$303$	−35.1276	−	25.2990i	−0.115933	−	0.0834950i
$304$	−99.5531			−0.327477
$305$			155.711i			0.510526i
$306$	8.83067	+	26.4274i	0.0288584	+	0.0863639i
$307$	−336.364			−1.09565			−0.547824	−	0.836594i	$-0.684544\pi$
$307$	−336.364			−1.09565			−0.547824	+	0.836594i	$0.684544\pi$
$308$		−	93.3763i		−	0.303170i
$309$	123.199	−	171.062i	0.398704	−	0.553600i
$310$	37.8843			0.122207
$311$			283.331i			0.911031i	0.890228	+	0.455515i	$0.150545\pi$
$311$			283.331i			0.911031i	−0.890228	+	0.455515i	$0.849455\pi$
$312$	19.8693	+	14.3099i	0.0636837	+	0.0458651i
$313$	−56.1896			−0.179520			−0.0897598	−	0.995963i	$-0.528610\pi$
$313$	−56.1896			−0.179520			−0.0897598	+	0.995963i	$0.528610\pi$
$314$		−	15.9784i		−	0.0508867i
$315$	36.1956	−	12.0947i	0.114907	−	0.0383959i
$316$	203.097			0.642712
$317$		−	340.321i		−	1.07357i	−0.843719	−	0.536784i	$-0.819639\pi$
$317$		−	340.321i		−	1.07357i	0.843719	−	0.536784i	$-0.180361\pi$
$318$	44.7880	−	62.1881i	0.140843	−	0.195560i
$319$	747.817			2.34425
$320$			199.935i			0.624797i
$321$	354.730	+	255.477i	1.10508	+	0.795879i
$322$	6.94038			0.0215540
$323$		−	71.7491i		−	0.222133i
$324$	−253.624	+	190.800i	−0.782790	+	0.588890i
$325$	−44.6467			−0.137375
$326$		−	36.9452i		−	0.113329i
$327$	−222.032	+	308.291i	−0.678996	+	0.942786i
$328$	92.0106			0.280520
$329$		−	34.5278i		−	0.104948i
$330$	−49.3502	−	35.5421i	−0.149546	−	0.107703i
$331$	−108.271			−0.327103			−0.163551	−	0.986535i	$-0.552295\pi$
$331$	−108.271			−0.327103			−0.163551	+	0.986535i	$0.552295\pi$
$332$			413.140i			1.24440i
$333$	96.6107	+	289.125i	0.290122	+	0.868243i
$334$	−82.1215			−0.245873
$335$		−	246.260i		−	0.735105i
$336$	−31.4484	+	43.6660i	−0.0935963	+	0.129958i
$337$	−60.7589			−0.180294			−0.0901468	−	0.995928i	$-0.528734\pi$
$337$	−60.7589			−0.180294			−0.0901468	+	0.995928i	$0.528734\pi$
$338$			3.71653i			0.0109957i
$339$	44.0860	+	31.7509i	0.130047	+	0.0936603i
$340$	−150.722			−0.443301
$341$			744.748i			2.18401i
$342$	−16.1684	+	5.40264i	−0.0472759	+	0.0157972i
$343$	−115.287			−0.336114
$344$		−	25.0217i		−	0.0727374i
$345$	−126.647	+	175.849i	−0.367093	+	0.509708i
$346$	53.2143			0.153799
$347$		−	291.298i		−	0.839475i	−0.907645	−	0.419738i	$-0.862122\pi$
$347$		−	291.298i		−	0.839475i	0.907645	−	0.419738i	$-0.137878\pi$
$348$	−357.314	−	257.338i	−1.02676	−	0.739478i
$349$	34.9377			0.100108			0.0500540	−	0.998747i	$-0.484061\pi$
$349$	34.9377			0.100108			0.0500540	+	0.998747i	$0.484061\pi$
$350$			4.22600i			0.0120743i
$351$	−92.9537	−	28.9243i	−0.264825	−	0.0824054i
$352$	266.519			0.757156
$353$		−	348.377i		−	0.986904i	−0.869773	−	0.493452i	$-0.835735\pi$
$353$		−	348.377i		−	0.986904i	0.869773	−	0.493452i	$-0.164265\pi$
$354$	27.7468	−	38.5264i	0.0783807	−	0.108832i
$355$	189.626			0.534156
$356$		−	294.563i		−	0.827424i
$357$	−31.4706	−	22.6652i	−0.0881529	−	0.0634879i
$358$	−66.5500			−0.185894
$359$		−	632.920i		−	1.76301i	−0.472177	−	0.881504i	$-0.656532\pi$
$359$		−	632.920i		−	1.76301i	0.472177	−	0.881504i	$-0.343468\pi$
$360$	22.9353	+	68.6379i	0.0637091	+	0.190661i
$361$	−317.104			−0.878403
$362$		−	9.00191i		−	0.0248672i
$363$	486.562	−	675.591i	1.34039	−	1.86113i
$364$	−16.8648			−0.0463320
$365$			382.084i			1.04681i
$366$	−30.5082	−	21.9721i	−0.0833559	−	0.0600330i
$367$	−205.429			−0.559752			−0.279876	−	0.960036i	$-0.590293\pi$
$367$	−205.429			−0.559752			−0.279876	+	0.960036i	$0.590293\pi$
$368$		−	305.572i		−	0.830358i
$369$	−346.953	+	115.934i	−0.940252	+	0.314184i
$370$	34.3957			0.0929614
$371$			106.670i			0.287521i
$372$	256.282	−	355.847i	0.688930	−	0.956579i
$373$	40.0941			0.107491			0.0537454	−	0.998555i	$-0.482884\pi$
$373$	40.0941			0.107491			0.0537454	+	0.998555i	$0.482884\pi$
$374$			61.8048i			0.165254i
$375$	−323.251	−	232.806i	−0.862003	−	0.620816i
$376$	65.4752			0.174136
$377$		−	135.064i		−	0.358261i
$378$	−2.73780	+	8.79844i	−0.00724286	+	0.0232763i
$379$	14.3180			0.0377784			0.0188892	−	0.999822i	$-0.493987\pi$
$379$	14.3180			0.0377784			0.0188892	+	0.999822i	$0.493987\pi$
$380$		−	92.2126i		−	0.242665i
$381$	−132.257	+	183.639i	−0.347131	+	0.481992i
$382$	−31.5140			−0.0824973
$383$		−	298.220i		−	0.778643i	−0.921102	−	0.389322i	$-0.872710\pi$
$383$		−	298.220i		−	0.778643i	0.921102	−	0.389322i	$-0.127290\pi$
$384$	−169.175	−	121.840i	−0.440559	−	0.317291i
$385$	84.6495			0.219869
$386$			28.0579i			0.0726889i
$387$	31.5274	+	94.3515i	0.0814663	+	0.243802i
$388$	−278.075			−0.716688
$389$			365.041i			0.938408i	0.883090	+	0.469204i	$0.155459\pi$
$389$			365.041i			0.938408i	−0.883090	+	0.469204i	$0.844541\pi$
$390$	−6.41932	+	8.91322i	−0.0164598	+	0.0228544i
$391$	220.229			0.563245
$392$		−	107.697i		−	0.274737i
$393$	288.858	+	208.036i	0.735008	+	0.529354i
$394$	5.66105			0.0143681
$395$			184.116i			0.466116i
$396$	−667.694	+	223.109i	−1.68610	+	0.563407i
$397$	314.111			0.791212			0.395606	−	0.918420i	$-0.370535\pi$
$397$	314.111			0.791212			0.395606	+	0.918420i	$0.370535\pi$
$398$			14.9613i			0.0375913i
$399$	13.8667	−	19.2538i	0.0347535	−	0.0482552i
$400$	186.062			0.465156
$401$			46.8041i			0.116719i	0.998296	+	0.0583593i	$0.0185869\pi$
$401$			46.8041i			0.116719i	−0.998296	+	0.0583593i	$0.981413\pi$
$402$	48.2495	+	34.7494i	0.120024	+	0.0864413i
$403$	134.510			0.333772
$404$			56.5401i			0.139951i
$405$	−172.968	−	229.921i	−0.427082	−	0.567706i
$406$	−12.7844			−0.0314887
$407$			676.167i			1.66134i
$408$	42.9801	−	59.6778i	0.105343	−	0.146269i
$409$	390.431			0.954598			0.477299	−	0.878741i	$-0.341616\pi$
$409$	390.431			0.954598			0.477299	+	0.878741i	$0.341616\pi$
$410$			41.2752i			0.100671i
$411$	103.616	+	74.6243i	0.252107	+	0.181568i
$412$	−275.335			−0.668290
$413$			66.0836i			0.160009i
$414$	−16.5830	−	49.6277i	−0.0400556	−	0.119874i
$415$	−374.528			−0.902478
$416$		−	48.1364i		−	0.115712i
$417$	−260.515	+	361.725i	−0.624736	+	0.867445i
$418$	−37.8125			−0.0904604
$419$		−	352.663i		−	0.841678i	−0.907135	−	0.420839i	$-0.861736\pi$
$419$		−	352.663i		−	0.841678i	0.907135	−	0.420839i	$-0.138264\pi$
$420$	−40.4463	−	29.1295i	−0.0963008	−	0.0693560i
$421$	635.299			1.50902			0.754512	−	0.656287i	$-0.227874\pi$
$421$	635.299			1.50902			0.754512	+	0.656287i	$0.227874\pi$
$422$			32.1755i			0.0762453i
$423$	−246.893	+	82.4991i	−0.583672	+	0.195033i
$424$	−202.279			−0.477074
$425$			134.097i			0.315523i
$426$	−26.7578	+	37.1532i	−0.0628117	+	0.0872140i
$427$	52.3302			0.122553
$428$		−	570.960i		−	1.33402i
$429$	−175.220	−	126.194i	−0.408439	−	0.294158i
$430$	11.2245			0.0261035
$431$			380.318i			0.882407i	0.897407	+	0.441204i	$0.145448\pi$
$431$			380.318i			0.882407i	−0.897407	+	0.441204i	$0.854552\pi$
$432$	387.378	+	120.540i	0.896709	+	0.279028i
$433$	242.797			0.560732			0.280366	−	0.959893i	$-0.409544\pi$
$433$	242.797			0.560732			0.280366	+	0.959893i	$0.409544\pi$
$434$		−	12.7319i		−	0.0293362i
$435$	233.288	−	323.920i	0.536294	−	0.744644i
$436$	496.213			1.13810
$437$			134.737i			0.308323i
$438$	−74.8614	−	53.9153i	−0.170916	−	0.123094i
$439$	349.561			0.796266			0.398133	−	0.917328i	$-0.369658\pi$
$439$	349.561			0.796266			0.398133	+	0.917328i	$0.369658\pi$
$440$			160.521i			0.364821i
$441$	135.699	+	406.103i	0.307707	+	0.920867i
$442$	11.1627			0.0252549
$443$			478.149i			1.07934i	0.841876	+	0.539672i	$0.181452\pi$
$443$			478.149i			1.07934i	−0.841876	+	0.539672i	$0.818548\pi$
$444$	232.682	−	323.079i	0.524059	−	0.727656i
$445$	267.034			0.600075
$446$			42.7574i			0.0958686i
$447$	−210.244	−	151.418i	−0.470344	−	0.338743i
$448$	67.1929			0.149984
$449$		−	375.077i		−	0.835361i	−0.908594	−	0.417681i	$-0.862843\pi$
$449$		−	375.077i		−	0.835361i	0.908594	−	0.417681i	$-0.137157\pi$
$450$	30.2183	−	10.0974i	0.0671518	−	0.0224387i
$451$	−811.408			−1.79913
$452$		−	70.9592i		−	0.156989i
$453$	−421.297	+	584.971i	−0.930016	+	1.29133i
$454$	−17.9283			−0.0394896
$455$		−	15.2887i		−	0.0336015i
$456$	36.5112	+	26.2954i	0.0800683	+	0.0576654i
$457$	452.368			0.989865			0.494933	−	0.868931i	$-0.335193\pi$
$457$	452.368			0.989865			0.494933	+	0.868931i	$0.335193\pi$
$458$			50.3870i			0.110015i
$459$	−86.8746	+	279.188i	−0.189269	+	0.608253i
$460$	283.040			0.615305
$461$		−	627.330i		−	1.36080i	−0.732839	−	0.680402i	$-0.761805\pi$
$461$		−	627.330i		−	1.36080i	0.732839	−	0.680402i	$-0.238195\pi$
$462$	−11.9448	+	16.5853i	−0.0258545	+	0.0358989i
$463$	−611.972			−1.32175			−0.660876	−	0.750495i	$-0.729815\pi$
$463$	−611.972			−1.32175			−0.660876	+	0.750495i	$0.729815\pi$
$464$			562.872i			1.21309i
$465$	322.590	+	232.330i	0.693743	+	0.499635i
$466$	70.1664			0.150572
$467$		−	291.201i		−	0.623557i	−0.950155	−	0.311779i	$-0.899075\pi$
$467$		−	291.201i		−	0.623557i	0.950155	−	0.311779i	$-0.100925\pi$
$468$	40.2961	+	120.593i	0.0861028	+	0.257678i
$469$	−82.7616			−0.176464
$470$			29.3716i			0.0624928i
$471$	97.9897	−	136.059i	0.208046	−	0.288872i
$472$	−125.315			−0.265497
$473$			220.657i			0.466505i
$474$	−36.0737	−	25.9803i	−0.0761048	−	0.0548108i
$475$	−82.0413			−0.172719
$476$			50.6539i			0.106416i
$477$	762.753	−	254.873i	1.59906	−	0.534325i
$478$	−32.4245			−0.0678338
$479$		−	257.836i		−	0.538280i	−0.963101	−	0.269140i	$-0.913260\pi$
$479$		−	257.836i		−	0.538280i	0.963101	−	0.269140i	$-0.0867395\pi$
$480$	83.1428	−	115.444i	0.173214	−	0.240508i
$481$	122.124			0.253895
$482$		−	76.9605i		−	0.159669i
$483$	59.0984	+	42.5628i	0.122357	+	0.0881217i
$484$	−1087.41			−2.24671
$485$		−	252.086i		−	0.519766i
$486$	69.4555	−	1.44574i	0.142913	−	0.00297478i
$487$	−76.9294			−0.157966			−0.0789829	−	0.996876i	$-0.525167\pi$
$487$	−76.9294			−0.157966			−0.0789829	+	0.996876i	$0.525167\pi$
$488$			99.2341i			0.203349i
$489$	226.571	−	314.594i	0.463336	−	0.643341i
$490$	48.3119			0.0985958
$491$			12.3407i			0.0251339i	0.999921	+	0.0125669i	$0.00400029\pi$
$491$			12.3407i			0.0251339i	−0.999921	+	0.0125669i	$0.996000\pi$
$492$	387.698	+	279.221i	0.788005	+	0.567523i
$493$	−405.668			−0.822857
$494$			6.82937i			0.0138246i
$495$	−202.258	−	605.293i	−0.408602	−	1.22281i
$496$	−560.562			−1.13017
$497$		−	63.7282i		−	0.128226i
$498$	52.8491	−	73.3810i	0.106123	−	0.147351i
$499$	−572.272			−1.14684			−0.573419	−	0.819262i	$-0.694383\pi$
$499$	−572.272			−1.14684			−0.573419	+	0.819262i	$0.694383\pi$
$500$			520.293i			1.04059i
$501$	−699.277	−	503.621i	−1.39576	−	1.00523i
$502$	10.8078			0.0215296
$503$		−	279.314i		−	0.555296i	−0.960683	−	0.277648i	$-0.910445\pi$
$503$		−	279.314i		−	0.555296i	0.960683	−	0.277648i	$-0.0895549\pi$
$504$	23.0674	−	7.70794i	0.0457686	−	0.0152935i
$505$	−51.2559			−0.101497
$506$		−	116.063i		−	0.229373i
$507$	−22.7921	+	31.6468i	−0.0449548	+	0.0624197i
$508$	295.578			0.581847
$509$			203.201i			0.399216i	0.979876	+	0.199608i	$0.0639668\pi$
$509$			203.201i			0.399216i	−0.979876	+	0.199608i	$0.936033\pi$
$510$	26.7710	+	19.2805i	0.0524922	+	0.0378050i
$511$	128.408			0.251289
$512$			336.664i			0.657546i
$513$	−170.808	−	53.1503i	−0.332960	−	0.103607i
$514$	85.0671			0.165500
$515$		−	249.603i		−	0.484666i
$516$	75.9323	−	105.432i	0.147156	−	0.204325i
$517$	−577.402			−1.11683
$518$		−	11.5595i		−	0.0223156i
$519$	453.128	+	326.344i	0.873079	+	0.628793i
$520$	28.9920			0.0557538
$521$		−	922.000i		−	1.76967i	−0.465902	−	0.884836i	$-0.654270\pi$
$521$		−	922.000i		−	1.76967i	0.465902	−	0.884836i	$-0.345730\pi$
$522$	30.5465	+	91.4158i	0.0585181	+	0.175126i
$523$	−180.519			−0.345161			−0.172580	−	0.984995i	$-0.555210\pi$
$523$	−180.519			−0.345161			−0.172580	+	0.984995i	$0.555210\pi$
$524$		−	464.935i		−	0.887281i
$525$	−25.9165	+	35.9850i	−0.0493647	+	0.0685428i
$526$	21.7254			0.0413030
$527$		−	404.003i		−	0.766610i
$528$	730.219	+	525.905i	1.38299	+	0.996033i
$529$	115.434			0.218212
$530$		−	90.7408i		−	0.171209i
$531$	472.536	−	157.897i	0.889898	−	0.297358i
$532$	−30.9903			−0.0582524
$533$			146.550i			0.274953i
$534$	−37.6807	+	52.3197i	−0.0705632	+	0.0979769i
$535$	517.599			0.967474
$536$		−	156.941i		−	0.292801i
$537$	−566.683	−	408.127i	−1.05528	−	0.760012i
$538$	−0.640379			−0.00119029
$539$			949.739i			1.76204i
$540$	−111.652	+	358.815i	−0.206763	+	0.664473i
$541$	325.540			0.601738			0.300869	−	0.953666i	$-0.402723\pi$
$541$	325.540			0.601738			0.300869	+	0.953666i	$0.402723\pi$
$542$		−	39.4279i		−	0.0727452i
$543$	55.2054	−	76.6526i	0.101667	−	0.141165i
$544$	−144.578			−0.265769
$545$			449.838i			0.825391i
$546$	2.99550	+	2.15736i	0.00548626	+	0.00395122i
$547$	−537.929			−0.983416			−0.491708	−	0.870760i	$-0.663627\pi$
$547$	−537.929			−0.983416			−0.491708	+	0.870760i	$0.663627\pi$
$548$		−	166.776i		−	0.304336i
$549$	−125.036	−	374.191i	−0.227751	−	0.681587i
$550$	70.6706			0.128492
$551$		−	248.190i		−	0.450435i
$552$	−80.7120	+	112.069i	−0.146217	+	0.203023i
$553$	61.8765			0.111892
$554$			9.73669i			0.0175753i
$555$	292.885	+	210.936i	0.527720	+	0.380065i
$556$	582.218			1.04716
$557$			59.6466i			0.107085i	0.998566	+	0.0535427i	$0.0170513\pi$
$557$			59.6466i			0.107085i	−0.998566	+	0.0535427i	$0.982949\pi$
$558$	−91.0406	+	30.4211i	−0.163155	+	0.0545181i
$559$	39.8532			0.0712937
$560$			63.7146i			0.113776i
$561$	−379.026	+	526.277i	−0.675625	+	0.938106i
$562$	−78.5657			−0.139797
$563$		−	42.4012i		−	0.0753130i	−0.999291	−	0.0376565i	$-0.988011\pi$
$563$		−	42.4012i		−	0.0753130i	0.999291	−	0.0376565i	$-0.0119893\pi$
$564$	275.888	+	198.695i	0.489163	+	0.352296i
$565$	64.3275			0.113854
$566$		−	143.267i		−	0.253123i
$567$	−77.2703	+	58.1301i	−0.136279	+	0.102522i
$568$	120.848			0.212761
$569$			1025.71i			1.80266i	0.433134	+	0.901330i	$0.357408\pi$
$569$			1025.71i			1.80266i	−0.433134	+	0.901330i	$0.642592\pi$
$570$	−11.7959	+	16.3786i	−0.0206946	+	0.0287344i
$571$	−206.107			−0.360958			−0.180479	−	0.983579i	$-0.557765\pi$
$571$	−206.107			−0.360958			−0.180479	+	0.983579i	$0.557765\pi$
$572$			282.028i			0.493056i
$573$	−268.346	−	193.263i	−0.468318	−	0.337283i
$574$	13.8715			0.0241664
$575$		−	251.820i		−	0.437948i
$576$	−160.548	−	480.468i	−0.278729	−	0.834146i
$577$	101.642			0.176157			0.0880783	−	0.996114i	$-0.471927\pi$
$577$	101.642			0.176157			0.0880783	+	0.996114i	$0.471927\pi$
$578$			49.0941i			0.0849378i
$579$	−172.069	+	238.917i	−0.297183	+	0.412638i
$580$	−521.369			−0.898912
$581$			125.869i			0.216642i
$582$	49.3911	+	35.5715i	0.0848644	+	0.0611195i
$583$	1783.83			3.05974
$584$			243.501i			0.416955i
$585$	−109.323	+	36.5301i	−0.186877	+	0.0624446i
$586$	−107.592			−0.183604
$587$			582.432i			0.992218i	0.868260	+	0.496109i	$0.165238\pi$
$587$			582.432i			0.992218i	−0.868260	+	0.496109i	$0.834762\pi$
$588$	326.824	−	453.794i	0.555822	−	0.771759i
$589$	247.171			0.419645
$590$		−	56.2152i		−	0.0952800i
$591$	48.2047	+	34.7171i	0.0815646	+	0.0587430i
$592$	−508.942			−0.859700
$593$			923.673i			1.55763i	0.627255	+	0.778814i	$0.284178\pi$
$593$			923.673i			1.55763i	−0.627255	+	0.778814i	$0.715822\pi$
$594$	147.135	+	45.7838i	0.247702	+	0.0770771i
$595$	−45.9198			−0.0771762
$596$			338.400i			0.567786i
$597$	−91.7522	+	127.398i	−0.153689	+	0.213397i
$598$	−20.9623			−0.0350540
$599$		−	586.848i		−	0.979714i	−0.871803	−	0.489857i	$-0.837049\pi$
$599$		−	586.848i		−	0.979714i	0.871803	−	0.489857i	$-0.162951\pi$
$600$	−68.2385	−	49.1455i	−0.113731	−	0.0819091i
$601$	−321.522			−0.534978			−0.267489	−	0.963561i	$-0.586194\pi$
$601$	−321.522			−0.534978			−0.267489	+	0.963561i	$0.586194\pi$
$602$		−	3.77227i		−	0.00626622i
$603$	197.747	+	591.793i	0.327938	+	0.981414i
$604$	941.547			1.55885
$605$		−	985.778i		−	1.62939i
$606$	7.23265	−	10.0425i	0.0119351	−	0.0165718i
$607$	−425.679			−0.701284			−0.350642	−	0.936510i	$-0.614037\pi$
$607$	−425.679			−0.701284			−0.350642	+	0.936510i	$0.614037\pi$
$608$		−	88.4537i		−	0.145483i
$609$	−108.861	−	78.4019i	−0.178754	−	0.128739i
$610$	−44.5156			−0.0729764
$611$			104.285i			0.170680i
$612$	362.204	−	121.030i	0.591837	−	0.197762i
$613$	1064.22			1.73608			0.868040	−	0.496494i	$-0.165379\pi$
$613$	1064.22			1.73608			0.868040	+	0.496494i	$0.165379\pi$
$614$		−	96.1621i		−	0.156616i
$615$	−253.126	+	351.465i	−0.411586	+	0.571487i
$616$	53.9470			0.0875763
$617$		−	523.170i		−	0.847925i	−0.905680	−	0.423962i	$-0.860639\pi$
$617$		−	523.170i		−	0.847925i	0.905680	−	0.423962i	$-0.139361\pi$
$618$	48.9045	+	35.2211i	0.0791335	+	0.0569921i
$619$	−766.616			−1.23847			−0.619237	−	0.785204i	$-0.712558\pi$
$619$	−766.616			−1.23847			−0.619237	+	0.785204i	$0.712558\pi$
$620$		−	519.229i		−	0.837467i
$621$	163.141	−	524.285i	0.262707	−	0.844259i
$622$	−81.0005			−0.130226
$623$		−	89.7430i		−	0.144050i
$624$	94.9846	−	131.886i	0.152219	−	0.211356i
$625$	−162.097			−0.259356
$626$		−	16.0639i		−	0.0256612i
$627$	−321.979	−	231.890i	−0.513523	−	0.369840i
$628$	−218.995			−0.348718
$629$		−	366.800i		−	0.583149i
$630$	3.45772	+	10.3479i	0.00548845	+	0.0164252i
$631$	−34.0495			−0.0539611			−0.0269806	−	0.999636i	$-0.508589\pi$
$631$	−34.0495			−0.0539611			−0.0269806	+	0.999636i	$0.508589\pi$
$632$			117.337i			0.185659i
$633$	−197.320	+	273.979i	−0.311722	+	0.432826i
$634$	97.2934			0.153460
$635$			267.954i			0.421974i
$636$	−852.329	−	613.849i	−1.34014	−	0.965172i
$637$	171.534			0.269284
$638$			213.791i			0.335096i
$639$	−455.693	+	152.269i	−0.713135	+	0.238293i
$640$	−246.848			−0.385701
$641$			43.3971i			0.0677022i	0.999427	+	0.0338511i	$0.0107772\pi$
$641$			43.3971i			0.0677022i	−0.999427	+	0.0338511i	$0.989223\pi$
$642$	−73.0376	+	101.413i	−0.113766	+	0.157964i
$643$	−693.737			−1.07891			−0.539453	−	0.842015i	$-0.681369\pi$
$643$	−693.737			−1.07891			−0.539453	+	0.842015i	$0.681369\pi$
$644$		−	95.1225i		−	0.147706i
$645$	95.5784	+	68.8358i	0.148184	+	0.106722i
$646$	20.5121			0.0317525
$647$			168.954i			0.261135i	0.991439	+	0.130567i	$0.0416799\pi$
$647$			168.954i			0.261135i	−0.991439	+	0.130567i	$0.958320\pi$
$648$	−110.232	−	146.528i	−0.170112	−	0.226124i
$649$	1105.11			1.70278
$650$		−	12.7639i		−	0.0196368i
$651$	78.0801	−	108.414i	0.119939	−	0.166535i
$652$	−506.358			−0.776623
$653$			370.914i			0.568016i	0.958822	+	0.284008i	$0.0916642\pi$
$653$			370.914i			0.568016i	−0.958822	+	0.284008i	$0.908336\pi$
$654$	−88.1364	−	63.4760i	−0.134765	−	0.0970581i
$655$	421.483			0.643485
$656$		−	610.737i		−	0.931001i
$657$	−306.813	−	918.194i	−0.466991	−	1.39756i
$658$	9.87104			0.0150016
$659$		−	282.693i		−	0.428972i	−0.976727	−	0.214486i	$-0.931192\pi$
$659$		−	282.693i		−	0.428972i	0.976727	−	0.214486i	$-0.0688077\pi$
$660$	−487.128	+	676.377i	−0.738073	+	1.02481i
$661$	−857.105			−1.29668			−0.648340	−	0.761351i	$-0.724536\pi$
$661$	−857.105			−1.29668			−0.648340	+	0.761351i	$0.724536\pi$
$662$		−	30.9533i		−	0.0467572i
$663$	95.0517	+	68.4565i	0.143366	+	0.103253i
$664$	−238.686			−0.359467
$665$		−	28.0939i		−	0.0422465i
$666$	−82.6570	+	27.6197i	−0.124110	+	0.0414711i
$667$	761.801			1.14213
$668$			1125.53i			1.68492i
$669$	−262.215	+	364.086i	−0.391951	+	0.544224i
$670$	70.4026			0.105078
$671$		−	875.109i		−	1.30419i
$672$	−38.7976	−	27.9421i	−0.0577345	−	0.0415805i
$673$	713.513			1.06020			0.530099	−	0.847936i	$-0.322155\pi$
$673$	713.513			1.06020			0.530099	+	0.847936i	$0.322155\pi$
$674$		−	17.3702i		−	0.0257718i
$675$	319.237	+	99.3366i	0.472943	+	0.147165i
$676$	50.9375			0.0753513
$677$		−	817.934i		−	1.20817i	−0.796918	−	0.604087i	$-0.793538\pi$
$677$		−	817.934i		−	1.20817i	0.796918	−	0.604087i	$-0.206462\pi$
$678$	−9.07716	+	12.6036i	−0.0133881	+	0.0185894i
$679$	−84.7196			−0.124771
$680$		−	87.0780i		−	0.128056i
$681$	−152.662	−	109.947i	−0.224173	−	0.161450i
$682$	−212.914			−0.312190
$683$			469.442i			0.687324i	0.939093	+	0.343662i	$0.111667\pi$
$683$			469.442i			0.687324i	−0.939093	+	0.343662i	$0.888333\pi$
$684$	74.0467	+	221.598i	0.108255	+	0.323974i
$685$	151.189			0.220714
$686$		−	32.9591i		−	0.0480453i
$687$	−309.005	+	429.053i	−0.449788	+	0.624531i
$688$	−166.086			−0.241404
$689$		−	322.180i		−	0.467605i
$690$	−50.2730	−	36.2067i	−0.0728595	−	0.0524735i
$691$	1296.36			1.87606			0.938032	−	0.346550i	$-0.112647\pi$
$691$	1296.36			1.87606			0.938032	+	0.346550i	$0.112647\pi$
$692$		−	729.337i		−	1.05396i
$693$	−203.423	+	67.9735i	−0.293540	+	0.0980859i
$694$	83.2783			0.119998
$695$			527.805i			0.759431i
$696$	148.674	−	206.434i	0.213612	−	0.296600i
$697$	440.165			0.631513
$698$			9.98823i			0.0143098i
$699$	597.477	+	430.304i	0.854759	+	0.615599i
$700$	57.9200			0.0827429
$701$		−	339.479i		−	0.484279i	−0.970241	−	0.242139i	$-0.922151\pi$
$701$		−	339.479i		−	0.484279i	0.970241	−	0.242139i	$-0.0778491\pi$
$702$	8.26908	−	26.5742i	0.0117793	−	0.0378550i
$703$	224.410			0.319218
$704$		−	1123.66i		−	1.59610i
$705$	−180.125	+	250.104i	−0.255497	+	0.354757i
$706$	99.5965			0.141071
$707$			17.2258i			0.0243646i
$708$	−528.030	−	380.288i	−0.745804	−	0.537130i
$709$	−1309.75			−1.84731			−0.923657	−	0.383220i	$-0.874815\pi$
$709$	−1309.75			−1.84731			−0.923657	+	0.383220i	$0.874815\pi$
$710$			54.2115i			0.0763542i
$711$	−147.845	−	442.452i	−0.207939	−	0.622296i
$712$	170.180			0.239017
$713$			758.675i			1.06406i
$714$	6.47968	−	8.99703i	0.00907518	−	0.0126009i
$715$	−255.670			−0.357580
$716$			912.112i			1.27390i
$717$	−276.100	−	198.848i	−0.385076	−	0.277333i
$718$	180.944			0.252010
$719$			662.694i			0.921688i	0.887481	+	0.460844i	$0.152453\pi$
$719$			662.694i			0.921688i	−0.887481	+	0.460844i	$0.847547\pi$
$720$	455.596	−	152.237i	0.632772	−	0.211440i
$721$	−83.8850			−0.116345
$722$		−	90.6558i		−	0.125562i
$723$	471.970	−	655.330i	0.652794	−	0.906404i
$724$	−123.377			−0.170410
$725$			463.861i			0.639808i
$726$	193.143	+	139.102i	0.266037	+	0.191600i
$727$	−186.379			−0.256368			−0.128184	−	0.991750i	$-0.540915\pi$
$727$	−186.379			−0.256368			−0.128184	+	0.991750i	$0.540915\pi$
$728$		−	9.74345i		−	0.0133839i
$729$	600.290	+	413.634i	0.823443	+	0.567399i
$730$	−109.233			−0.149634
$731$		−	119.700i		−	0.163748i
$732$	−301.142	+	418.135i	−0.411396	+	0.571223i
$733$	−543.979			−0.742127			−0.371064	−	0.928607i	$-0.621007\pi$
$733$	−543.979			−0.742127			−0.371064	+	0.928607i	$0.621007\pi$
$734$		−	58.7295i		−	0.0800130i
$735$	411.383	+	296.279i	0.559705	+	0.403101i
$736$	271.503			0.368890
$737$			1384.01i			1.87789i
$738$	−33.1440	−	99.1894i	−0.0449106	−	0.134403i
$739$	−430.576			−0.582647			−0.291323	−	0.956625i	$-0.594096\pi$
$739$	−430.576			−0.582647			−0.291323	+	0.956625i	$0.594096\pi$
$740$		−	471.416i		−	0.637048i
$741$	−41.8820	+	58.1531i	−0.0565209	+	0.0784792i
$742$	−30.4956			−0.0410992
$743$			1248.45i			1.68028i	0.542371	+	0.840139i	$0.317527\pi$
$743$			1248.45i			1.68028i	−0.542371	+	0.840139i	$0.682473\pi$
$744$	205.586	+	148.064i	0.276326	+	0.199010i
$745$	−306.774			−0.411777
$746$			11.4624i			0.0153651i
$747$	900.037	−	300.746i	1.20487	−	0.402605i
$748$	847.076			1.13245
$749$		−	173.951i		−	0.232245i
$750$	66.5562	−	92.4133i	0.0887416	−	0.123218i
$751$	−904.563			−1.20448			−0.602239	−	0.798316i	$-0.705725\pi$
$751$	−904.563			−1.20448			−0.602239	+	0.798316i	$0.705725\pi$
$752$		−	434.603i		−	0.577929i
$753$	92.0304	+	66.2804i	0.122218	+	0.0880218i
$754$	38.6132			0.0512111
$755$			853.551i			1.13053i
$756$	120.588	+	37.5234i	0.159508	+	0.0496341i
$757$	1261.75			1.66678			0.833388	−	0.552689i	$-0.186398\pi$
$757$	1261.75			1.66678			0.833388	+	0.552689i	$0.186398\pi$
$758$			4.09334i			0.00540018i
$759$	711.770	−	988.292i	0.937773	−	1.30210i
$760$	53.2747			0.0700983
$761$			347.930i			0.457201i	0.973520	+	0.228601i	$0.0734150\pi$
$761$			347.930i			0.457201i	−0.973520	+	0.228601i	$0.926585\pi$
$762$	−52.5000	−	37.8106i	−0.0688976	−	0.0496202i
$763$	151.179			0.198137
$764$			431.920i			0.565340i
$765$	109.719	+	328.353i	0.143423	+	0.429220i
$766$	85.2573			0.111302
$767$		−	199.595i		−	0.260228i
$768$	−359.904	+	499.727i	−0.468626	+	0.650686i
$769$	−1391.91			−1.81003			−0.905015	−	0.425379i	$-0.860141\pi$
$769$	−1391.91			−1.81003			−0.905015	+	0.425379i	$0.860141\pi$
$770$			24.2002i			0.0314288i
$771$	724.359	+	521.685i	0.939506	+	0.676634i
$772$	384.552			0.498125
$773$		−	1127.54i		−	1.45865i	−0.684167	−	0.729325i	$-0.739834\pi$
$773$		−	1127.54i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$774$	−26.9739	+	9.01328i	−0.0348500	+	0.0116451i
$775$	−461.957			−0.596073
$776$		−	160.654i		−	0.207029i
$777$	70.8901	−	98.4308i	0.0912356	−	0.126681i
$778$	−104.360			−0.134139
$779$			269.295i			0.345693i
$780$	122.161	+	87.9809i	0.156617	+	0.112796i
$781$	−1065.71			−1.36455
$782$			62.9606i			0.0805122i
$783$	−300.511	+	965.749i	−0.383794	+	1.23340i
$784$	−714.856			−0.911807
$785$		−	198.528i		−	0.252902i
$786$	−59.4748	+	82.5808i	−0.0756677	+	0.105065i
$787$	317.705			0.403692			0.201846	−	0.979417i	$-0.435306\pi$
$787$	317.705			0.403692			0.201846	+	0.979417i	$0.435306\pi$
$788$		−	77.5884i		−	0.0984624i
$789$	184.995	+	133.234i	0.234467	+	0.168864i
$790$	−52.6363			−0.0666282
$791$		−	21.6188i		−	0.0273309i
$792$	−128.899	−	385.752i	−0.162751	−	0.487061i
$793$	−158.055			−0.199313
$794$			89.8003i			0.113099i
$795$	556.480	−	772.672i	0.699974	−	0.971914i
$796$	205.055			0.257607
$797$		−	1348.29i		−	1.69171i	−0.533412	−	0.845855i	$-0.679091\pi$
$797$		−	1348.29i		−	1.69171i	0.533412	−	0.845855i	$-0.320909\pi$
$798$	5.50442	+	3.96430i	0.00689777	+	0.00496779i
$799$	313.223			0.392019
$800$			165.318i			0.206647i
$801$	−641.714	+	214.428i	−0.801141	+	0.267700i
$802$	−13.3807			−0.0166842
$803$		−	2147.35i		−	2.67416i
$804$	476.264	−	661.292i	0.592368	−	0.822502i
$805$	86.2325			0.107121
$806$			38.4547i			0.0477105i
$807$	−5.45292	−	3.92720i	−0.00675702	−	0.00486642i
$808$	−32.6653			−0.0404274
$809$		−	716.662i		−	0.885862i	−0.896556	−	0.442931i	$-0.853939\pi$
$809$		−	716.662i		−	0.885862i	0.896556	−	0.442931i	$-0.146061\pi$
$810$	65.7313	−	49.4494i	0.0811498	−	0.0610486i
$811$	−1100.87			−1.35743			−0.678714	−	0.734403i	$-0.737462\pi$
$811$	−1100.87			−1.35743			−0.678714	+	0.734403i	$0.737462\pi$
$812$			175.219i			0.215786i
$813$	241.797	−	335.735i	0.297413	−	0.412958i
$814$	−193.307			−0.237478
$815$		−	459.035i		−	0.563233i
$816$	−396.122	−	285.288i	−0.485444	−	0.349618i
$817$	73.2328			0.0896363
$818$			111.619i			0.136454i
$819$	12.2768	+	36.7405i	0.0149900	+	0.0448603i
$820$	565.704			0.689883
$821$			32.0188i			0.0389997i	0.999810	+	0.0194999i	$0.00620740\pi$
$821$			32.0188i			0.0389997i	−0.999810	+	0.0194999i	$0.993793\pi$
$822$	−21.3341	+	29.6224i	−0.0259539	+	0.0360370i
$823$	513.916			0.624442			0.312221	−	0.950010i	$-0.398927\pi$
$823$	513.916			0.624442			0.312221	+	0.950010i	$0.398927\pi$
$824$		−	159.071i		−	0.193048i
$825$	601.770	+	433.396i	0.729419	+	0.525329i
$826$	−18.8925			−0.0228722
$827$			95.0942i			0.114987i	0.998346	+	0.0574934i	$0.0183108\pi$
$827$			95.0942i			0.114987i	−0.998346	+	0.0574934i	$0.981689\pi$
$828$	−680.180	+	227.281i	−0.821474	+	0.274494i
$829$	−877.880			−1.05896			−0.529482	−	0.848321i	$-0.677614\pi$
$829$	−877.880			−1.05896			−0.529482	+	0.848321i	$0.677614\pi$
$830$		−	107.073i		−	0.129003i
$831$	−59.7115	+	82.9094i	−0.0718550	+	0.0997706i
$832$	−202.945			−0.243924
$833$		−	515.205i		−	0.618493i
$834$	−103.412	−	74.4778i	−0.123996	−	0.0893019i
$835$	−1020.34			−1.22196
$836$			518.245i			0.619910i
$837$	−961.785	−	299.278i	−1.14909	−	0.357560i
$838$	100.822			0.120312
$839$			1356.48i			1.61679i	0.588643	+	0.808393i	$0.299662\pi$
$839$			1356.48i			1.61679i	−0.588643	+	0.808393i	$0.700338\pi$
$840$	16.8292	−	23.3674i	0.0200348	−	0.0278183i
$841$	−562.261			−0.668563
$842$			181.624i			0.215705i
$843$	−668.999	−	481.814i	−0.793593	−	0.571547i
$844$	440.986			0.522496
$845$			46.1769i			0.0546473i
$846$	−23.5854	−	70.5836i	−0.0278787	−	0.0834321i
$847$	−331.294			−0.391138
$848$			1342.66i			1.58333i
$849$	878.605	−	1219.94i	1.03487	−	1.43692i
$850$	−38.3367			−0.0451020
$851$			688.812i			0.809414i
$852$	509.209	+	366.733i	0.597663	+	0.430438i
$853$	1384.33			1.62289			0.811447	−	0.584426i	$-0.198680\pi$
$853$	1384.33			1.62289			0.811447	+	0.584426i	$0.198680\pi$
$854$			14.9605i			0.0175182i
$855$	−200.888	+	67.1264i	−0.234957	+	0.0785104i
$856$	329.865			0.385356
$857$			724.446i			0.845328i	0.906287	+	0.422664i	$0.138905\pi$
$857$			724.446i			0.845328i	−0.906287	+	0.422664i	$0.861095\pi$
$858$	36.0772	−	50.0932i	0.0420480	−	0.0583837i
$859$	898.435			1.04591			0.522954	−	0.852361i	$-0.324830\pi$
$859$	898.435			1.04591			0.522954	+	0.852361i	$0.324830\pi$
$860$		−	153.839i		−	0.178883i
$861$	118.118	+	85.0689i	0.137187	+	0.0988024i
$862$	−108.728			−0.126134
$863$		−	1394.95i		−	1.61640i	−0.588910	−	0.808198i	$-0.700443\pi$
$863$		−	1394.95i		−	1.61640i	0.588910	−	0.808198i	$-0.299557\pi$
$864$	−107.101	+	344.189i	−0.123959	+	0.398367i
$865$	661.174			0.764363
$866$			69.4125i			0.0801530i
$867$	−301.076	+	418.043i	−0.347261	+	0.482172i
$868$	−174.499			−0.201036
$869$		−	1034.75i		−	1.19074i
$870$	92.6045	+	66.6939i	0.106442	+	0.0766597i
$871$	249.968			0.286989
$872$			286.681i			0.328763i
$873$	202.425	+	605.794i	0.231873	+	0.693922i
$874$	−38.5195			−0.0440727
$875$			158.515i			0.181160i
$876$	−738.945	+	1026.02i	−0.843544	+	1.17126i
$877$	−1266.54			−1.44417			−0.722086	−	0.691803i	$-0.756817\pi$
$877$	−1266.54			−1.44417			−0.722086	+	0.691803i	$0.756817\pi$
$878$			99.9348i			0.113821i
$879$	−916.159	−	659.819i	−1.04227	−	0.750648i
$880$	1065.49			1.21078
$881$		−	974.680i		−	1.10633i	−0.833071	−	0.553167i	$-0.813419\pi$
$881$		−	974.680i		−	1.10633i	0.833071	−	0.553167i	$-0.186581\pi$
$882$	−116.099	+	38.7945i	−0.131632	+	0.0439847i
$883$	−998.150			−1.13041			−0.565204	−	0.824951i	$-0.691203\pi$
$883$	−998.150			−1.13041			−0.565204	+	0.824951i	$0.691203\pi$
$884$		−	152.992i		−	0.173067i
$885$	344.747	−	478.681i	0.389544	−	0.540882i
$886$	−136.697			−0.154285
$887$			1501.39i			1.69266i	0.532657	+	0.846331i	$0.321194\pi$
$887$			1501.39i			1.69266i	−0.532657	+	0.846331i	$0.678806\pi$
$888$	186.655	+	134.429i	0.210197	+	0.151384i
$889$	90.0523			0.101296
$890$			76.3414i			0.0857769i
$891$	972.100	+	1292.18i	1.09102	+	1.45026i
$892$	586.018			0.656971
$893$			191.631i			0.214593i
$894$	43.2884	−	60.1060i	0.0484211	−	0.0672326i
$895$	−826.867			−0.923874
$896$			82.9593i			0.0925885i
$897$	−178.497	−	128.554i	−0.198993	−	0.143315i
$898$	107.230			0.119409
$899$		−	1397.50i		−	1.55451i
$900$	−138.392	−	414.162i	−0.153768	−	0.460180i
$901$	−967.673			−1.07400
$902$		−	231.971i		−	0.257174i
$903$	23.1339	−	32.1214i	0.0256189	−	0.0355719i
$904$	40.9958			0.0453493
$905$		−	111.846i		−	0.123587i
$906$	−167.236	−	120.443i	−0.184587	−	0.132940i
$907$	827.646			0.912509			0.456255	−	0.889849i	$-0.349191\pi$
$907$	827.646			0.912509			0.456255	+	0.889849i	$0.349191\pi$
$908$			245.719i			0.270616i
$909$	123.174	−	41.1585i	0.135505	−	0.0452789i
$910$	4.37083			0.00480311
$911$			225.732i			0.247785i	0.992296	+	0.123892i	$0.0395377\pi$
$911$			225.732i			0.247785i	−0.992296	+	0.123892i	$0.960462\pi$
$912$	174.540	−	242.349i	0.191382	−	0.265734i
$913$	2104.89			2.30546
$914$			129.326i			0.141495i
$915$	−379.057	−	272.998i	−0.414270	−	0.298358i
$916$	690.587			0.753916
$917$		−	141.649i		−	0.154470i
$918$	−79.8162	−	24.8363i	−0.0869458	−	0.0270548i
$919$	1451.93			1.57991			0.789953	−	0.613168i	$-0.210105\pi$
$919$	1451.93			1.57991			0.789953	+	0.613168i	$0.210105\pi$
$920$			163.523i			0.177742i
$921$	589.726	−	818.834i	0.640310	−	0.889071i
$922$	179.346			0.194518
$923$			192.480i			0.208538i
$924$	227.313	+	163.711i	0.246009	+	0.177176i
$925$	−419.417			−0.453424
$926$		−	174.955i		−	0.188936i
$927$	200.431	+	599.826i	0.216215	+	0.647061i
$928$	−500.116			−0.538918
$929$			1356.64i			1.46032i	0.683276	+	0.730160i	$0.260554\pi$
$929$			1356.64i			1.46032i	−0.683276	+	0.730160i	$0.739446\pi$
$930$	−66.4202	+	92.2244i	−0.0714196	+	0.0991660i
$931$	315.205			0.338566
$932$		−	961.676i		−	1.03184i
$933$	−689.731	−	496.746i	−0.739262	−	0.532418i
$934$	83.2506			0.0891335
$935$			767.909i			0.821293i
$936$	−69.6713	+	23.2806i	−0.0744351	+	0.0248724i
$937$	709.291			0.756981			0.378491	−	0.925605i	$-0.376443\pi$
$937$	709.291			0.756981			0.378491	+	0.925605i	$0.376443\pi$
$938$		−	23.6605i		−	0.0252244i
$939$	98.5138	−	136.786i	0.104914	−	0.145672i
$940$	402.558			0.428253
$941$			836.171i			0.888598i	0.895879	+	0.444299i	$0.146547\pi$
$941$			836.171i			0.888598i	−0.895879	+	0.444299i	$0.853453\pi$
$942$	38.8974	+	28.0140i	0.0412923	+	0.0297388i
$943$	−826.582			−0.876545
$944$			831.798i			0.881142i
$945$	−34.0165	+	109.318i	−0.0359963	+	0.115681i
$946$	−63.0830			−0.0666839
$947$		−	827.536i		−	0.873850i	−0.899498	−	0.436925i	$-0.856067\pi$
$947$		−	827.536i		−	0.873850i	0.899498	−	0.436925i	$-0.143933\pi$
$948$	−356.077	+	494.413i	−0.375609	+	0.521533i
$949$	−387.837			−0.408679
$950$		−	23.4545i		−	0.0246890i
$951$	828.468	+	596.664i	0.871154	+	0.627407i
$952$	−29.2646			−0.0307402
$953$			1446.75i			1.51810i	0.651031	+	0.759051i	$0.274337\pi$
$953$			1446.75i			1.51810i	−0.651031	+	0.759051i	$0.725663\pi$
$954$	72.8649	+	218.061i	0.0763783	+	0.228576i
$955$	−391.553			−0.410003
$956$			444.400i			0.464853i
$957$	−1311.10	+	1820.46i	−1.37001	+	1.90226i
$958$	73.7121			0.0769437
$959$		−	50.8108i		−	0.0529831i
$960$	−486.716	−	350.534i	−0.506995	−	0.365139i
$961$	430.766			0.448248
$962$			34.9136i			0.0362927i
$963$	−1243.85	+	415.632i	−1.29164	+	0.431601i
$964$	−1054.79			−1.09418
$965$			348.613i			0.361257i
$966$	−12.1681	+	16.8955i	−0.0125964	+	0.0174901i
$967$	1503.12			1.55442			0.777208	−	0.629243i	$-0.216635\pi$
$967$	1503.12			1.55442			0.777208	+	0.629243i	$0.216635\pi$
$968$		−	628.235i		−	0.649003i
$969$	174.664	+	125.793i	0.180252	+	0.129818i
$970$	72.0682			0.0742971
$971$		−	1137.67i		−	1.17165i	−0.810439	−	0.585823i	$-0.800771\pi$
$971$		−	1137.67i		−	1.17165i	0.810439	−	0.585823i	$-0.199229\pi$
$972$	−19.8149	−	951.933i	−0.0203857	−	0.979355i
$973$	177.381			0.182304
$974$		−	21.9931i		−	0.0225802i
$975$	78.2764	−	108.687i	0.0802835	−	0.111474i
$976$	658.684			0.674881
$977$		−	939.716i		−	0.961838i	−0.876765	−	0.480919i	$-0.840303\pi$
$977$		−	939.716i		−	0.961838i	0.876765	−	0.480919i	$-0.159697\pi$
$978$	89.9383	+	64.7737i	0.0919614	+	0.0662308i
$979$	−1500.76			−1.53295
$980$		−	662.147i		−	0.675660i
$981$	−361.220	−	1081.02i	−0.368216	−	1.10195i
$982$	−3.52806			−0.00359272
$983$		−	210.610i		−	0.214252i	−0.994245	−	0.107126i	$-0.965835\pi$
$983$		−	210.610i		−	0.214252i	0.994245	−	0.107126i	$-0.0341648\pi$
$984$	−161.316	+	223.988i	−0.163940	+	0.227630i
$985$	70.3371			0.0714082
$986$		−	115.975i		−	0.117622i
$987$	84.0534	+	60.5354i	0.0851604	+	0.0613327i
$988$	93.6010			0.0947378
$989$			224.783i			0.227283i
$990$	173.045	−	57.8229i	0.174793	−	0.0584069i
$991$	1102.36			1.11237			0.556185	−	0.831058i	$-0.312264\pi$
$991$	1102.36			1.11237			0.556185	+	0.831058i	$0.312264\pi$
$992$		−	498.064i		−	0.502080i
$993$	189.825	−	263.572i	0.191163	−	0.265430i
$994$	18.2191			0.0183290
$995$			185.891i			0.186825i
$996$	−1005.73	−	724.332i	−1.00977	−	0.727241i
$997$	−74.4115			−0.0746354			−0.0373177	−	0.999303i	$-0.511881\pi$
$997$	−74.4115			−0.0746354			−0.0373177	+	0.999303i	$0.511881\pi$
$998$		−	163.605i		−	0.163933i
$999$	−873.218	−	271.719i	−0.874093	−	0.271990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.c.a.14.5	yes	8
3.2	odd	2	inner	39.3.c.a.14.4	✓	8
4.3	odd	2		624.3.f.c.209.5		8
12.11	even	2		624.3.f.c.209.6		8
13.5	odd	4		507.3.d.e.506.10		16
13.8	odd	4		507.3.d.e.506.8		16
13.12	even	2		507.3.c.i.170.4		8
39.5	even	4		507.3.d.e.506.7		16
39.8	even	4		507.3.d.e.506.9		16
39.38	odd	2		507.3.c.i.170.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.c.a.14.4	✓	8	3.2	odd	2	inner
39.3.c.a.14.5	yes	8	1.1	even	1	trivial
507.3.c.i.170.4		8	13.12	even	2
507.3.c.i.170.5		8	39.38	odd	2
507.3.d.e.506.7		16	39.5	even	4
507.3.d.e.506.8		16	13.8	odd	4
507.3.d.e.506.9		16	39.8	even	4
507.3.d.e.506.10		16	13.5	odd	4
624.3.f.c.209.5		8	4.3	odd	2
624.3.f.c.209.6		8	12.11	even	2

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	39.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.285887i q^{2} +(-1.75324 + 2.43437i) q^{3} +3.91827 q^{4} +3.55207i q^{5} +(-0.695955 - 0.501228i) q^{6} +1.19376 q^{7} +2.26373i q^{8} +(-2.85231 - 8.53606i) q^{9} -1.01549 q^{10} -19.9630i q^{11} +(-6.86966 + 9.53852i) q^{12} -3.60555 q^{13} +0.341280i q^{14} +(-8.64706 - 6.22763i) q^{15} +15.0259 q^{16} +10.8293i q^{17} +(2.44035 - 0.815439i) q^{18} -6.62543 q^{19} +13.9180i q^{20} +(-2.09294 + 2.90605i) q^{21} +5.70717 q^{22} -20.3363i q^{23} +(-5.51076 - 3.96886i) q^{24} +12.3828 q^{25} -1.03078i q^{26} +(25.7807 + 8.02216i) q^{27} +4.67747 q^{28} +37.4601i q^{29} +(1.78040 - 2.47208i) q^{30} -37.3064 q^{31} +13.3506i q^{32} +(48.5974 + 34.9999i) q^{33} -3.09597 q^{34} +4.24032i q^{35} +(-11.1761 - 33.4466i) q^{36} -33.8710 q^{37} -1.89413i q^{38} +(6.32139 - 8.77725i) q^{39} -8.04093 q^{40} -40.6456i q^{41} +(-0.830802 - 0.598345i) q^{42} -11.0533 q^{43} -78.2205i q^{44} +(30.3207 - 10.1316i) q^{45} +5.81389 q^{46} -28.9236i q^{47} +(-26.3440 + 36.5786i) q^{48} -47.5749 q^{49} +3.54008i q^{50} +(-26.3626 - 18.9864i) q^{51} -14.1275 q^{52} +89.3566i q^{53} +(-2.29343 + 7.37037i) q^{54} +70.9101 q^{55} +2.70235i q^{56} +(11.6160 - 16.1288i) q^{57} -10.7094 q^{58} +55.3576i q^{59} +(-33.8815 - 24.4015i) q^{60} +43.8365 q^{61} -10.6654i q^{62} +(-3.40497 - 10.1900i) q^{63} +56.2868 q^{64} -12.8072i q^{65} +(-10.0060 + 13.8934i) q^{66} -69.3286 q^{67} +42.4323i q^{68} +(49.5061 + 35.6544i) q^{69} -1.21225 q^{70} -53.3845i q^{71} +(19.3233 - 6.45687i) q^{72} +107.566 q^{73} -9.68328i q^{74} +(-21.7100 + 30.1443i) q^{75} -25.9602 q^{76} -23.8310i q^{77} +(2.50930 + 1.80720i) q^{78} +51.8333 q^{79} +53.3731i q^{80} +(-64.7286 + 48.6950i) q^{81} +11.6200 q^{82} +105.439i q^{83} +(-8.20071 + 11.3867i) q^{84} -38.4666 q^{85} -3.15999i q^{86} +(-91.1918 - 65.6765i) q^{87} +45.1909 q^{88} -75.1768i q^{89} +(2.89650 + 8.66829i) q^{90} -4.30416 q^{91} -79.6832i q^{92} +(65.4070 - 90.8175i) q^{93} +8.26887 q^{94} -23.5340i q^{95} +(-32.5004 - 23.4068i) q^{96} -70.9688 q^{97} -13.6011i q^{98} +(-170.405 + 56.9408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 20 q^{4} + 8 q^{7} - 6 q^{9} + 18 q^{12} + 52 q^{15} + 24 q^{16} - 52 q^{18} - 8 q^{19} - 80 q^{21} + 52 q^{22} - 60 q^{25} - 44 q^{27} - 176 q^{28} + 182 q^{30} + 80 q^{31} + 52 q^{33}+ \cdots - 468 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 20 * q^4 + 8 * q^7 - 6 * q^9 + 18 * q^12 + 52 * q^15 + 24 * q^16 - 52 * q^18 - 8 * q^19 - 80 * q^21 + 52 * q^22 - 60 * q^25 - 44 * q^27 - 176 * q^28 + 182 * q^30 + 80 * q^31 + 52 * q^33 + 208 * q^34 - 50 * q^36 - 32 * q^37 + 104 * q^40 - 78 * q^42 - 196 * q^43 + 104 * q^45 - 104 * q^46 - 266 * q^48 - 20 * q^49 + 26 * q^51 - 52 * q^52 + 312 * q^54 + 208 * q^55 - 24 * q^57 - 208 * q^58 - 468 * q^60 + 248 * q^61 + 20 * q^63 + 252 * q^64 - 176 * q^67 + 208 * q^69 - 104 * q^70 + 468 * q^72 + 440 * q^73 + 28 * q^75 - 240 * q^76 + 130 * q^78 - 88 * q^79 - 366 * q^81 - 468 * q^82 + 304 * q^84 - 416 * q^85 - 364 * q^87 + 156 * q^88 - 546 * q^90 - 52 * q^91 - 72 * q^93 + 520 * q^94 + 208 * q^96 - 320 * q^97 - 468 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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