LMFDB - Embedded newform 985.2.b.a.789.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [985,2,Mod(789,985)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("985.789"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(985, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 985 = 5 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	985.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.86526459910$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			789.37
Character	$\chi$	$=$	985.789
Dual form			985.2.b.a.789.62

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.870537i q^{2} -1.92866i q^{3} +1.24217 q^{4} +(2.23259 - 0.124596i) q^{5} -1.67897 q^{6} +4.43166i q^{7} -2.82242i q^{8} -0.719722 q^{9} +(-0.108466 - 1.94356i) q^{10} +1.70316 q^{11} -2.39571i q^{12} +0.123746i q^{13} +3.85792 q^{14} +(-0.240304 - 4.30591i) q^{15} +0.0273066 q^{16} +1.14261i q^{17} +0.626545i q^{18} -8.45775 q^{19} +(2.77325 - 0.154769i) q^{20} +8.54715 q^{21} -1.48266i q^{22} -4.49103i q^{23} -5.44349 q^{24} +(4.96895 - 0.556347i) q^{25} +0.107725 q^{26} -4.39788i q^{27} +5.50485i q^{28} +3.89888 q^{29} +(-3.74845 + 0.209193i) q^{30} +10.9216 q^{31} -5.66862i q^{32} -3.28481i q^{33} +0.994687 q^{34} +(0.552169 + 9.89409i) q^{35} -0.894014 q^{36} +3.64436i q^{37} +7.36279i q^{38} +0.238663 q^{39} +(-0.351664 - 6.30133i) q^{40} +0.728472 q^{41} -7.44061i q^{42} -5.84768i q^{43} +2.11560 q^{44} +(-1.60685 + 0.0896748i) q^{45} -3.90961 q^{46} -11.6020i q^{47} -0.0526651i q^{48} -12.6396 q^{49} +(-0.484320 - 4.32566i) q^{50} +2.20371 q^{51} +0.153713i q^{52} +12.1066i q^{53} -3.82851 q^{54} +(3.80246 - 0.212207i) q^{55} +12.5080 q^{56} +16.3121i q^{57} -3.39412i q^{58} +7.96100 q^{59} +(-0.298497 - 5.34865i) q^{60} -12.8875 q^{61} -9.50769i q^{62} -3.18956i q^{63} -4.88013 q^{64} +(0.0154183 + 0.276274i) q^{65} -2.85955 q^{66} +12.2474i q^{67} +1.41932i q^{68} -8.66166 q^{69} +(8.61317 - 0.480683i) q^{70} -10.6231 q^{71} +2.03136i q^{72} +6.59861i q^{73} +3.17255 q^{74} +(-1.07300 - 9.58341i) q^{75} -10.5059 q^{76} +7.54781i q^{77} -0.207765i q^{78} -9.80240 q^{79} +(0.0609646 - 0.00340231i) q^{80} -10.6412 q^{81} -0.634162i q^{82} -2.94971i q^{83} +10.6170 q^{84} +(0.142366 + 2.55099i) q^{85} -5.09062 q^{86} -7.51960i q^{87} -4.80703i q^{88} -10.4622 q^{89} +(0.0780653 + 1.39882i) q^{90} -0.548398 q^{91} -5.57860i q^{92} -21.0641i q^{93} -10.0999 q^{94} +(-18.8827 + 1.05381i) q^{95} -10.9328 q^{96} +3.31388i q^{97} +11.0032i q^{98} -1.22580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) $ 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/985\mathbb{Z}\right)^\times$.

$n$	$396$	$592$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.870537i		−	0.615563i	−0.951457	−	0.307781i	$-0.900414\pi$
$2$		−	0.870537i		−	0.615563i	0.951457	−	0.307781i	$-0.0995865\pi$
$3$		−	1.92866i		−	1.11351i	−0.830676	−	0.556756i	$-0.812046\pi$
$3$		−	1.92866i		−	1.11351i	0.830676	−	0.556756i	$-0.187954\pi$
$4$	1.24217			0.621083
$5$	2.23259	−	0.124596i	0.998446	−	0.0557212i
$5$	2.23259	−	0.124596i	0.998446	−	0.0557212i
$6$	−1.67897			−0.685436
$7$			4.43166i			1.67501i	0.546430	+	0.837505i	$0.315986\pi$
$7$			4.43166i			1.67501i	−0.546430	+	0.837505i	$0.684014\pi$
$8$		−	2.82242i		−	0.997878i
$9$	−0.719722			−0.239907
$10$	−0.108466	−	1.94356i	−0.0342999	−	0.614606i
$11$	1.70316			0.513521			0.256761	−	0.966475i	$-0.417345\pi$
$11$	1.70316			0.513521			0.256761	+	0.966475i	$0.417345\pi$
$12$		−	2.39571i		−	0.691583i
$13$			0.123746i			0.0343209i	0.999853	+	0.0171604i	$0.00546261\pi$
$13$			0.123746i			0.0343209i	−0.999853	+	0.0171604i	$0.994537\pi$
$14$	3.85792			1.03107
$15$	−0.240304	−	4.30591i	−0.0620462	−	1.11178i
$16$	0.0273066			0.00682665
$17$			1.14261i			0.277124i	0.990354	+	0.138562i	$0.0442481\pi$
$17$			1.14261i			0.277124i	−0.990354	+	0.138562i	$0.955752\pi$
$18$			0.626545i			0.147678i
$19$	−8.45775			−1.94034			−0.970171	−	0.242422i	$-0.922058\pi$
$19$	−8.45775			−1.94034			−0.970171	+	0.242422i	$0.922058\pi$
$20$	2.77325	−	0.154769i	0.620118	−	0.0346075i
$21$	8.54715			1.86514
$22$		−	1.48266i		−	0.316104i
$23$		−	4.49103i		−	0.936445i	−0.883611	−	0.468222i	$-0.844895\pi$
$23$		−	4.49103i		−	0.936445i	0.883611	−	0.468222i	$-0.155105\pi$
$24$	−5.44349			−1.11115
$25$	4.96895	−	0.556347i	0.993790	−	0.111269i
$26$	0.107725			0.0211266
$27$		−	4.39788i		−	0.846372i
$28$			5.50485i			1.04032i
$29$	3.89888			0.724004			0.362002	−	0.932177i	$-0.382093\pi$
$29$	3.89888			0.724004			0.362002	+	0.932177i	$0.382093\pi$
$30$	−3.74845	+	0.209193i	−0.684371	+	0.0381933i
$31$	10.9216			1.96158			0.980792	−	0.195056i	$-0.0624888\pi$
$31$	10.9216			1.96158			0.980792	+	0.195056i	$0.0624888\pi$
$32$		−	5.66862i		−	1.00208i
$33$		−	3.28481i		−	0.571812i
$34$	0.994687			0.170587
$35$	0.552169	+	9.89409i	0.0933336	+	1.67241i
$36$	−0.894014			−0.149002
$37$			3.64436i			0.599128i	0.954076	+	0.299564i	$0.0968413\pi$
$37$			3.64436i			0.599128i	−0.954076	+	0.299564i	$0.903159\pi$
$38$			7.36279i			1.19440i
$39$	0.238663			0.0382167
$40$	−0.351664	−	6.30133i	−0.0556030	−	0.996327i
$41$	0.728472			0.113768			0.0568841	−	0.998381i	$-0.481883\pi$
$41$	0.728472			0.113768			0.0568841	+	0.998381i	$0.481883\pi$
$42$		−	7.44061i		−	1.14811i
$43$		−	5.84768i		−	0.891763i	−0.895092	−	0.445881i	$-0.852890\pi$
$43$		−	5.84768i		−	0.891763i	0.895092	−	0.445881i	$-0.147110\pi$
$44$	2.11560			0.318939
$45$	−1.60685	+	0.0896748i	−0.239535	+	0.0133679i
$46$	−3.90961			−0.576440
$47$		−	11.6020i		−	1.69232i	−0.532929	−	0.846160i	$-0.678909\pi$
$47$		−	11.6020i		−	1.69232i	0.532929	−	0.846160i	$-0.321091\pi$
$48$		−	0.0526651i		−	0.00760155i
$49$	−12.6396			−1.80566
$50$	−0.484320	−	4.32566i	−0.0684932	−	0.611740i
$51$	2.20371			0.308581
$52$			0.153713i			0.0213161i
$53$			12.1066i			1.66297i	0.555547	+	0.831485i	$0.312509\pi$
$53$			12.1066i			1.66297i	−0.555547	+	0.831485i	$0.687491\pi$
$54$	−3.82851			−0.520995
$55$	3.80246	−	0.212207i	0.512723	−	0.0286140i
$56$	12.5080			1.67145
$57$			16.3121i			2.16059i
$58$		−	3.39412i		−	0.445669i
$59$	7.96100			1.03643			0.518217	−	0.855249i	$-0.326596\pi$
$59$	7.96100			1.03643			0.518217	+	0.855249i	$0.326596\pi$
$60$	−0.298497	−	5.34865i	−0.0385358	−	0.690508i
$61$	−12.8875			−1.65008			−0.825038	−	0.565077i	$-0.808846\pi$
$61$	−12.8875			−1.65008			−0.825038	+	0.565077i	$0.808846\pi$
$62$		−	9.50769i		−	1.20748i
$63$		−	3.18956i		−	0.401847i
$64$	−4.88013			−0.610016
$65$	0.0154183	+	0.276274i	0.00191240	+	0.0342676i
$66$	−2.85955			−0.351986
$67$			12.2474i			1.49626i	0.663553	+	0.748129i	$0.269048\pi$
$67$			12.2474i			1.49626i	−0.663553	+	0.748129i	$0.730952\pi$
$68$			1.41932i			0.172117i
$69$	−8.66166			−1.04274
$70$	8.61317	−	0.480683i	1.02947	−	0.0574527i
$71$	−10.6231			−1.26073			−0.630367	−	0.776297i	$-0.717096\pi$
$71$	−10.6231			−1.26073			−0.630367	+	0.776297i	$0.717096\pi$
$72$			2.03136i			0.239398i
$73$			6.59861i			0.772309i	0.922434	+	0.386155i	$0.126197\pi$
$73$			6.59861i			0.772309i	−0.922434	+	0.386155i	$0.873803\pi$
$74$	3.17255			0.368801
$75$	−1.07300	−	9.58341i	−0.123900	−	1.10660i
$76$	−10.5059			−1.20511
$77$			7.54781i			0.860153i
$78$		−	0.207765i		−	0.0235248i
$79$	−9.80240			−1.10286			−0.551428	−	0.834222i	$-0.685917\pi$
$79$	−9.80240			−1.10286			−0.551428	+	0.834222i	$0.685917\pi$
$80$	0.0609646	−	0.00340231i	0.00681605	−	0.000380390i
$81$	−10.6412			−1.18235
$82$		−	0.634162i		−	0.0700315i
$83$		−	2.94971i		−	0.323773i	−0.986809	−	0.161887i	$-0.948242\pi$
$83$		−	2.94971i		−	0.323773i	0.986809	−	0.161887i	$-0.0517579\pi$
$84$	10.6170			1.15841
$85$	0.142366	+	2.55099i	0.0154417	+	0.276694i
$86$	−5.09062			−0.548936
$87$		−	7.51960i		−	0.806186i
$88$		−	4.80703i		−	0.512431i
$89$	−10.4622			−1.10899			−0.554496	−	0.832186i	$-0.687089\pi$
$89$	−10.4622			−1.10899			−0.554496	+	0.832186i	$0.687089\pi$
$90$	0.0780653	+	1.39882i	0.00822880	+	0.147449i
$91$	−0.548398			−0.0574878
$92$		−	5.57860i		−	0.581610i
$93$		−	21.0641i		−	2.18425i
$94$	−10.0999			−1.04173
$95$	−18.8827	+	1.05381i	−1.93733	+	0.108118i
$96$	−10.9328			−1.11583
$97$			3.31388i			0.336474i	0.985747	+	0.168237i	$0.0538074\pi$
$97$			3.31388i			0.336474i	−0.985747	+	0.168237i	$0.946193\pi$
$98$			11.0032i			1.11149i
$99$	−1.22580			−0.123198
$100$	6.17226	−	0.691075i	0.617226	−	0.0691075i
$101$	12.2480			1.21872			0.609362	−	0.792892i	$-0.291426\pi$
$101$	12.2480			1.21872			0.609362	+	0.792892i	$0.291426\pi$
$102$		−	1.91841i		−	0.189951i
$103$			1.25200i			0.123363i	0.998096	+	0.0616815i	$0.0196463\pi$
$103$			1.25200i			0.123363i	−0.998096	+	0.0616815i	$0.980354\pi$
$104$	0.349263			0.0342480
$105$	19.0823	−	1.06495i	1.86224	−	0.103928i
$106$	10.5392			1.02366
$107$			10.1858i			0.984702i	0.870397	+	0.492351i	$0.163862\pi$
$107$			10.1858i			0.984702i	−0.870397	+	0.492351i	$0.836138\pi$
$108$		−	5.46289i		−	0.525667i
$109$	0.528072			0.0505801			0.0252900	−	0.999680i	$-0.491949\pi$
$109$	0.528072			0.0505801			0.0252900	+	0.999680i	$0.491949\pi$
$110$	−0.184734	−	3.31018i	−0.0176137	−	0.315613i
$111$	7.02872			0.667136
$112$			0.121014i			0.0114347i
$113$			3.75605i			0.353339i	0.984270	+	0.176670i	$0.0565324\pi$
$113$			3.75605i			0.353339i	−0.984270	+	0.176670i	$0.943468\pi$
$114$	14.2003			1.32998
$115$	−0.559567	−	10.0266i	−0.0521799	−	0.934990i
$116$	4.84305			0.449666
$117$		−	0.0890625i		−	0.00823383i
$118$		−	6.93034i		−	0.637990i
$119$	−5.06367			−0.464186
$120$	−12.1531	+	0.678240i	−1.10942	+	0.0619145i
$121$	−8.09926			−0.736296
$122$			11.2190i			1.01573i
$123$		−	1.40497i		−	0.126682i
$124$	13.5665			1.21831
$125$	11.0243	−	1.86121i	0.986046	−	0.166472i
$126$	−2.77663			−0.247362
$127$		−	4.51202i		−	0.400377i	−0.979757	−	0.200188i	$-0.935845\pi$
$127$		−	4.51202i		−	0.400377i	0.979757	−	0.200188i	$-0.0641554\pi$
$128$		−	7.08891i		−	0.626577i
$129$	−11.2782			−0.992988
$130$	0.240507	−	0.0134222i	0.0210938	−	0.00117720i
$131$	−6.74933			−0.589692			−0.294846	−	0.955545i	$-0.595268\pi$
$131$	−6.74933			−0.589692			−0.294846	+	0.955545i	$0.595268\pi$
$132$		−	4.08028i		−	0.355142i
$133$		−	37.4819i		−	3.25009i
$134$	10.6618			0.921041
$135$	−0.547960	−	9.81867i	−0.0471609	−	0.845057i
$136$	3.22494			0.276536
$137$			14.4330i			1.23309i	0.787319	+	0.616546i	$0.211468\pi$
$137$			14.4330i			1.23309i	−0.787319	+	0.616546i	$0.788532\pi$
$138$			7.54030i			0.641873i
$139$	7.31604			0.620538			0.310269	−	0.950649i	$-0.399581\pi$
$139$	7.31604			0.620538			0.310269	+	0.950649i	$0.399581\pi$
$140$	0.685885	+	12.2901i	0.0579679	+	1.03870i
$141$	−22.3762			−1.88442
$142$			9.24784i			0.776061i
$143$			0.210758i			0.0176245i
$144$	−0.0196532			−0.00163776
$145$	8.70461	−	0.485787i	0.722879	−	0.0403424i
$146$	5.74434			0.475405
$147$			24.3774i			2.01062i
$148$			4.52689i			0.372108i
$149$	−4.10236			−0.336079			−0.168039	−	0.985780i	$-0.553744\pi$
$149$	−4.10236			−0.336079			−0.168039	+	0.985780i	$0.553744\pi$
$150$	−8.34271	+	0.934088i	−0.681179	+	0.0762680i
$151$	−13.3414			−1.08570			−0.542852	−	0.839828i	$-0.682656\pi$
$151$	−13.3414			−1.08570			−0.542852	+	0.839828i	$0.682656\pi$
$152$			23.8714i			1.93622i
$153$		−	0.822364i		−	0.0664842i
$154$	6.57065			0.529478
$155$	24.3836	−	1.36080i	1.95854	−	0.109302i
$156$	0.296459			0.0237357
$157$		−	15.6461i		−	1.24870i	−0.781145	−	0.624349i	$-0.785364\pi$
$157$		−	15.6461i		−	1.24870i	0.781145	−	0.624349i	$-0.214636\pi$
$158$			8.53335i			0.678877i
$159$	23.3495			1.85174
$160$	−0.706290	−	12.6557i	−0.0558371	−	1.00052i
$161$	19.9027			1.56855
$162$			9.26353i			0.727811i
$163$			10.1824i			0.797543i	0.917050	+	0.398772i	$0.130563\pi$
$163$			10.1824i			0.797543i	−0.917050	+	0.398772i	$0.869437\pi$
$164$	0.904883			0.0706595
$165$	−0.409275	−	7.33364i	−0.0318621	−	0.570923i
$166$	−2.56783			−0.199303
$167$			11.4059i			0.882619i	0.897355	+	0.441309i	$0.145486\pi$
$167$			11.4059i			0.882619i	−0.897355	+	0.441309i	$0.854514\pi$
$168$		−	24.1237i		−	1.86118i
$169$	12.9847			0.998822
$170$	2.22073	−	0.123934i	0.170322	−	0.00950534i
$171$	6.08723			0.465502
$172$		−	7.26378i		−	0.553858i
$173$			24.8344i			1.88812i	0.329771	+	0.944061i	$0.393028\pi$
$173$			24.8344i			1.88812i	−0.329771	+	0.944061i	$0.606972\pi$
$174$	−6.54609			−0.496258
$175$	2.46554	+	22.0207i	0.186377	+	1.66461i
$176$	0.0465075			0.00350563
$177$		−	15.3540i		−	1.15408i
$178$			9.10775i			0.682655i
$179$	−21.0550			−1.57372			−0.786861	−	0.617130i	$-0.788295\pi$
$179$	−21.0550			−1.57372			−0.786861	+	0.617130i	$0.788295\pi$
$180$	−1.99597	+	0.111391i	−0.148771	+	0.00830259i
$181$	−4.58253			−0.340617			−0.170308	−	0.985391i	$-0.554476\pi$
$181$	−4.58253			−0.340617			−0.170308	+	0.985391i	$0.554476\pi$
$182$			0.477401i			0.0353873i
$183$			24.8556i			1.83738i
$184$	−12.6756			−0.934457
$185$	0.454074	+	8.13637i	0.0333842	+	0.598198i
$186$	−18.3371			−1.34454
$187$			1.94605i			0.142309i
$188$		−	14.4116i		−	1.05107i
$189$	19.4899			1.41768
$190$	0.917377	+	16.4381i	0.0665535	+	1.19255i
$191$	−12.9687			−0.938385			−0.469193	−	0.883096i	$-0.655455\pi$
$191$	−12.9687			−0.938385			−0.469193	+	0.883096i	$0.655455\pi$
$192$			9.41210i			0.679260i
$193$			4.21268i			0.303235i	0.988439	+	0.151618i	$0.0484482\pi$
$193$			4.21268i			0.303235i	−0.988439	+	0.151618i	$0.951552\pi$
$194$	2.88486			0.207121
$195$	0.532838	−	0.0297366i	0.0381573	−	0.00212948i
$196$	−15.7005			−1.12146
$197$		−	1.00000i		−	0.0712470i
$197$		−	1.00000i		−	0.0712470i
$198$			1.06710i			0.0758358i
$199$	9.85404			0.698534			0.349267	−	0.937023i	$-0.386431\pi$
$199$	9.85404			0.698534			0.349267	+	0.937023i	$0.386431\pi$
$200$	−1.57025	−	14.0245i	−0.111033	−	0.991681i
$201$	23.6211			1.66610
$202$		−	10.6623i		−	0.750200i
$203$			17.2785i			1.21271i
$204$	2.73737			0.191654
$205$	1.62638	−	0.0907651i	0.113592	−	0.00633931i
$206$	1.08991			0.0759376
$207$			3.23229i			0.224660i
$208$			0.00337907i			0.000234297i
$209$	−14.4049			−0.996407
$210$	−0.927074	−	16.6119i	−0.0639742	−	1.14633i
$211$	−9.42984			−0.649177			−0.324588	−	0.945855i	$-0.605226\pi$
$211$	−9.42984			−0.649177			−0.324588	+	0.945855i	$0.605226\pi$
$212$			15.0384i			1.03284i
$213$			20.4884i			1.40384i
$214$	8.86714			0.606145
$215$	−0.728600	−	13.0555i	−0.0496901	−	0.890377i
$216$	−12.4127			−0.844576
$217$			48.4010i			3.28567i
$218$		−	0.459706i		−	0.0311352i
$219$	12.7265			0.859975
$220$	4.72328	−	0.263597i	0.318444	−	0.0177717i
$221$	−0.141393			−0.00951115
$222$		−	6.11876i		−	0.410664i
$223$		−	22.5192i		−	1.50800i	−0.656876	−	0.753999i	$-0.728123\pi$
$223$		−	22.5192i		−	1.50800i	0.656876	−	0.753999i	$-0.271877\pi$
$224$	25.1214			1.67849
$225$	−3.57626	+	0.400415i	−0.238418	+	0.0266943i
$226$	3.26978			0.217502
$227$		−	0.372248i		−	0.0247070i	−0.999924	−	0.0123535i	$-0.996068\pi$
$227$		−	0.372248i		−	0.0247070i	0.999924	−	0.0123535i	$-0.00393234\pi$
$228$			20.2624i			1.34191i
$229$	−16.0618			−1.06139			−0.530696	−	0.847562i	$-0.678070\pi$
$229$	−16.0618			−1.06139			−0.530696	+	0.847562i	$0.678070\pi$
$230$	−8.72857	+	0.487123i	−0.575545	+	0.0321200i
$231$	14.5571			0.957790
$232$		−	11.0043i		−	0.722467i
$233$			3.23653i			0.212032i	0.994364	+	0.106016i	$0.0338095\pi$
$233$			3.23653i			0.212032i	−0.994364	+	0.106016i	$0.966190\pi$
$234$	−0.0775322			−0.00506844
$235$	−1.44556	−	25.9025i	−0.0942981	−	1.68969i
$236$	9.88888			0.643711
$237$			18.9055i			1.22804i
$238$			4.40811i			0.285736i
$239$	23.8140			1.54040			0.770200	−	0.637802i	$-0.220156\pi$
$239$	23.8140			1.54040			0.770200	+	0.637802i	$0.220156\pi$
$240$	−0.00656189	−	0.117580i	−0.000423568	−	0.00758974i
$241$	22.1911			1.42945			0.714727	−	0.699403i	$-0.246551\pi$
$241$	22.1911			1.42945			0.714727	+	0.699403i	$0.246551\pi$
$242$			7.05070i			0.453236i
$243$			7.32954i			0.470190i
$244$	−16.0084			−1.02483
$245$	−28.2191	+	1.57485i	−1.80285	+	0.100613i
$246$	−1.22308			−0.0779808
$247$		−	1.04661i		−	0.0665942i
$248$		−	30.8255i		−	1.95742i
$249$	−5.68899			−0.360525
$250$	−1.62025	−	9.59709i	−0.102474	−	0.606973i
$251$	−2.15167			−0.135812			−0.0679062	−	0.997692i	$-0.521632\pi$
$251$	−2.15167			−0.135812			−0.0679062	+	0.997692i	$0.521632\pi$
$252$		−	3.96196i		−	0.249580i
$253$		−	7.64893i		−	0.480884i
$254$	−3.92788			−0.246457
$255$	4.91999	−	0.274575i	0.308102	−	0.0171945i
$256$	−15.9314			−0.995713
$257$		−	10.9521i		−	0.683176i	−0.939850	−	0.341588i	$-0.889035\pi$
$257$		−	10.9521i		−	0.683176i	0.939850	−	0.341588i	$-0.110965\pi$
$258$			9.81806i			0.611246i
$259$	−16.1505			−1.00355
$260$	0.0191520	+	0.343178i	0.00118776	+	0.0212830i
$261$	−2.80611			−0.173694
$262$			5.87554i			0.362992i
$263$		−	8.66154i		−	0.534093i	−0.963684	−	0.267047i	$-0.913952\pi$
$263$		−	8.66154i		−	0.534093i	0.963684	−	0.267047i	$-0.0860478\pi$
$264$	−9.27112			−0.570598
$265$	1.50844	+	27.0291i	0.0926627	+	1.66039i
$266$	−32.6294			−2.00063
$267$			20.1780i			1.23488i
$268$			15.2133i			0.929301i
$269$	−10.4447			−0.636824			−0.318412	−	0.947952i	$-0.603150\pi$
$269$	−10.4447			−0.636824			−0.318412	+	0.947952i	$0.603150\pi$
$270$	−8.54752	+	0.477019i	−0.520185	+	0.0290305i
$271$	4.55775			0.276864			0.138432	−	0.990372i	$-0.455794\pi$
$271$	4.55775			0.276864			0.138432	+	0.990372i	$0.455794\pi$
$272$			0.0312009i			0.00189183i
$273$			1.05767i			0.0640133i
$274$	12.5644			0.759045
$275$	8.46291	−	0.947546i	0.510332	−	0.0571392i
$276$	−10.7592			−0.647629
$277$			29.5789i			1.77722i	0.458660	+	0.888612i	$0.348329\pi$
$277$			29.5789i			1.77722i	−0.458660	+	0.888612i	$0.651671\pi$
$278$		−	6.36888i		−	0.381980i
$279$	−7.86055			−0.470599
$280$	27.9253	−	1.55846i	1.66886	−	0.0931355i
$281$	−5.02303			−0.299649			−0.149824	−	0.988713i	$-0.547871\pi$
$281$	−5.02303			−0.299649			−0.149824	+	0.988713i	$0.547871\pi$
$282$			19.4793i			1.15998i
$283$		−	7.53723i		−	0.448042i	−0.974584	−	0.224021i	$-0.928082\pi$
$283$		−	7.53723i		−	0.448042i	0.974584	−	0.224021i	$-0.0719184\pi$
$284$	−13.1957			−0.783021
$285$	2.03243	+	36.4183i	0.120391	+	2.15724i
$286$	0.183473			0.0108490
$287$			3.22834i			0.190563i
$288$			4.07983i			0.240406i
$289$	15.6944			0.923202
$290$	−0.422895	−	7.57769i	−0.0248333	−	0.444977i
$291$	6.39135			0.374668
$292$			8.19657i			0.479668i
$293$		−	5.84987i		−	0.341753i	−0.985292	−	0.170877i	$-0.945340\pi$
$293$		−	5.84987i		−	0.341753i	0.985292	−	0.170877i	$-0.0546599\pi$
$294$	21.2215			1.23766
$295$	17.7737	−	0.991912i	1.03482	−	0.0577514i
$296$	10.2859			0.597857
$297$		−	7.49028i		−	0.434630i
$298$			3.57126i			0.206877i
$299$	0.555746			0.0321396
$300$	−1.33285	−	11.9042i	−0.0769519	−	0.687288i
$301$	25.9149			1.49371
$302$			11.6141i			0.668319i
$303$		−	23.6222i		−	1.35706i
$304$	−0.230953			−0.0132460
$305$	−28.7726	+	1.60574i	−1.64751	+	0.0919443i
$306$	−0.715898			−0.0409252
$307$		−	22.8530i		−	1.30429i	−0.758094	−	0.652146i	$-0.773869\pi$
$307$		−	22.8530i		−	1.30429i	0.758094	−	0.652146i	$-0.226131\pi$
$308$			9.37563i			0.534226i
$309$	2.41467			0.137366
$310$	−1.18462	−	21.2268i	−0.0672822	−	1.20560i
$311$	0.848574			0.0481182			0.0240591	−	0.999711i	$-0.492341\pi$
$311$	0.848574			0.0481182			0.0240591	+	0.999711i	$0.492341\pi$
$312$		−	0.673609i		−	0.0381356i
$313$		−	24.2552i		−	1.37099i	−0.728078	−	0.685494i	$-0.759586\pi$
$313$		−	24.2552i		−	1.37099i	0.728078	−	0.685494i	$-0.240414\pi$
$314$	−13.6205			−0.768652
$315$	−0.397408	−	7.12100i	−0.0223914	−	0.401223i
$316$	−12.1762			−0.684965
$317$		−	9.50882i		−	0.534069i	−0.963687	−	0.267034i	$-0.913956\pi$
$317$		−	9.50882i		−	0.534069i	0.963687	−	0.267034i	$-0.0860437\pi$
$318$		−	20.3266i		−	1.13986i
$319$	6.64040			0.371791
$320$	−10.8953	+	0.608047i	−0.609068	+	0.0339909i
$321$	19.6450			1.09648
$322$		−	17.3260i		−	0.965543i
$323$		−	9.66394i		−	0.537716i
$324$	−13.2181			−0.734338
$325$	0.0688455	+	0.614886i	0.00381886	+	0.0341078i
$326$	8.86411			0.490938
$327$		−	1.01847i		−	0.0563215i
$328$		−	2.05606i		−	0.113527i
$329$	51.4159			2.83465
$330$	−6.38421	+	0.356289i	−0.351439	+	0.0196131i
$331$	2.55412			0.140387			0.0701936	−	0.997533i	$-0.477638\pi$
$331$	2.55412			0.140387			0.0701936	+	0.997533i	$0.477638\pi$
$332$		−	3.66403i		−	0.201090i
$333$		−	2.62292i		−	0.143735i
$334$	9.92930			0.543307
$335$	1.52598	+	27.3435i	0.0833734	+	1.49393i
$336$	0.233394			0.0127327
$337$			7.54624i			0.411070i	0.978650	+	0.205535i	$0.0658934\pi$
$337$			7.54624i			0.411070i	−0.978650	+	0.205535i	$0.934107\pi$
$338$		−	11.3036i		−	0.614837i
$339$	7.24413			0.393447
$340$	0.176842	+	3.16875i	0.00959058	+	0.171850i
$341$	18.6013			1.00732
$342$		−	5.29916i		−	0.286546i
$343$		−	24.9927i		−	1.34948i
$344$	−16.5046			−0.889870
$345$	−19.3380	+	1.07921i	−1.04112	+	0.0581029i
$346$	21.6192			1.16226
$347$			13.6684i			0.733756i	0.930269	+	0.366878i	$0.119573\pi$
$347$			13.6684i			0.733756i	−0.930269	+	0.366878i	$0.880427\pi$
$348$		−	9.34059i		−	0.500708i
$349$	−30.5829			−1.63706			−0.818531	−	0.574462i	$-0.805211\pi$
$349$	−30.5829			−1.63706			−0.818531	+	0.574462i	$0.805211\pi$
$350$	19.1698	−	2.14634i	1.02467	−	0.114727i
$351$	0.544218			0.0290482
$352$		−	9.65455i		−	0.514589i
$353$		−	8.32483i		−	0.443086i	−0.975151	−	0.221543i	$-0.928891\pi$
$353$		−	8.32483i		−	0.443086i	0.975151	−	0.221543i	$-0.0711093\pi$
$354$	−13.3663			−0.710409
$355$	−23.7172	+	1.32361i	−1.25878	+	0.0702497i
$356$	−12.9958			−0.688776
$357$			9.76609i			0.516876i
$358$			18.3291i			0.968725i
$359$	−12.4077			−0.654855			−0.327428	−	0.944876i	$-0.606182\pi$
$359$	−12.4077			−0.654855			−0.327428	+	0.944876i	$0.606182\pi$
$360$	0.253100	+	4.53521i	0.0133396	+	0.239026i
$361$	52.5336			2.76493
$362$			3.98926i			0.209671i
$363$			15.6207i			0.819874i
$364$	−0.681202			−0.0357047
$365$	0.822164	+	14.7320i	0.0430340	+	0.771109i
$366$	21.6377			1.13102
$367$		−	33.0594i		−	1.72569i	−0.505472	−	0.862843i	$-0.668682\pi$
$367$		−	33.0594i		−	1.72569i	0.505472	−	0.862843i	$-0.331318\pi$
$368$		−	0.122635i		−	0.00639278i
$369$	−0.524298			−0.0272938
$370$	7.08301	−	0.395288i	0.368228	−	0.0205500i
$371$	−53.6523			−2.78549
$372$		−	26.1651i		−	1.35660i
$373$		−	24.6346i		−	1.27553i	−0.770231	−	0.637765i	$-0.779859\pi$
$373$		−	24.6346i		−	1.27553i	0.770231	−	0.637765i	$-0.220141\pi$
$374$	1.69411			0.0876003
$375$	−3.58964	−	21.2622i	−0.185368	−	1.09797i
$376$	−32.7457			−1.68873
$377$			0.482469i			0.0248484i
$378$		−	16.9667i		−	0.872671i
$379$	−2.30362			−0.118329			−0.0591645	−	0.998248i	$-0.518844\pi$
$379$	−2.30362			−0.118329			−0.0591645	+	0.998248i	$0.518844\pi$
$380$	−23.4555	+	1.30900i	−1.20324	+	0.0671504i
$381$	−8.70214			−0.445824
$382$			11.2898i			0.577635i
$383$		−	22.6666i		−	1.15821i	−0.815253	−	0.579104i	$-0.803402\pi$
$383$		−	22.6666i		−	1.15821i	0.815253	−	0.579104i	$-0.196598\pi$
$384$	−13.6721			−0.697700
$385$	0.940430	+	16.8512i	0.0479288	+	0.858816i
$386$	3.66729			0.186660
$387$			4.20870i			0.213940i
$388$			4.11639i			0.208978i
$389$	10.8248			0.548840			0.274420	−	0.961610i	$-0.411514\pi$
$389$	10.8248			0.548840			0.274420	+	0.961610i	$0.411514\pi$
$390$	−0.0258868	−	0.463855i	−0.00131083	−	0.0234882i
$391$	5.13151			0.259512
$392$			35.6743i			1.80182i
$393$			13.0172i			0.656629i
$394$	−0.870537			−0.0438570
$395$	−21.8848	+	1.22134i	−1.10114	+	0.0614525i
$396$	−1.52265			−0.0765159
$397$			14.2272i			0.714040i	0.934097	+	0.357020i	$0.116207\pi$
$397$			14.2272i			0.714040i	−0.934097	+	0.357020i	$0.883793\pi$
$398$		−	8.57830i		−	0.429991i
$399$	−72.2897			−3.61901
$400$	0.135685	−	0.0151919i	0.00678426	−	0.000759597i
$401$	31.7277			1.58441			0.792203	−	0.610257i	$-0.208934\pi$
$401$	31.7277			1.58441			0.792203	+	0.610257i	$0.208934\pi$
$402$		−	20.5630i		−	1.02559i
$403$			1.35151i			0.0673233i
$404$	15.2141			0.756928
$405$	−23.7574	+	1.32585i	−1.18051	+	0.0658821i
$406$	15.0416			0.746500
$407$			6.20691i			0.307665i
$408$		−	6.21981i		−	0.307926i
$409$	−23.4878			−1.16140			−0.580698	−	0.814119i	$-0.697220\pi$
$409$	−23.4878			−1.16140			−0.580698	+	0.814119i	$0.697220\pi$
$410$	−0.0790144	−	1.41583i	−0.00390224	−	0.0699227i
$411$	27.8362			1.37306
$412$			1.55519i			0.0766186i
$413$			35.2804i			1.73604i
$414$	2.81383			0.138292
$415$	−0.367524	−	6.58551i	−0.0180410	−	0.323270i
$416$	0.701467			0.0343923
$417$		−	14.1101i		−	0.690976i
$418$			12.5400i			0.613351i
$419$	−18.4285			−0.900292			−0.450146	−	0.892955i	$-0.648628\pi$
$419$	−18.4285			−0.900292			−0.450146	+	0.892955i	$0.648628\pi$
$420$	23.7034	−	1.32284i	1.15661	−	0.0645479i
$421$	−12.9360			−0.630460			−0.315230	−	0.949015i	$-0.602082\pi$
$421$	−12.9360			−0.630460			−0.315230	+	0.949015i	$0.602082\pi$
$422$			8.20902i			0.399609i
$423$			8.35019i			0.406000i
$424$	34.1700			1.65944
$425$	0.635689	+	5.67759i	0.0308355	+	0.275404i
$426$	17.8359			0.864153
$427$		−	57.1130i		−	2.76389i
$428$			12.6525i			0.611581i
$429$	0.406481			0.0196251
$430$	−11.3653	+	0.634273i	−0.548083	+	0.0305874i
$431$	−17.2655			−0.831650			−0.415825	−	0.909445i	$-0.636507\pi$
$431$	−17.2655			−0.831650			−0.415825	+	0.909445i	$0.636507\pi$
$432$		−	0.120091i		−	0.00577789i
$433$			24.0953i			1.15795i	0.815347	+	0.578973i	$0.196546\pi$
$433$			24.0953i			1.15795i	−0.815347	+	0.578973i	$0.803454\pi$
$434$	42.1348			2.02254
$435$	−0.936916	−	16.7882i	−0.0449217	−	0.804934i
$436$	0.655953			0.0314144
$437$			37.9840i			1.81702i
$438$		−	11.0789i		−	0.529368i
$439$	−0.725758			−0.0346386			−0.0173193	−	0.999850i	$-0.505513\pi$
$439$	−0.725758			−0.0346386			−0.0173193	+	0.999850i	$0.505513\pi$
$440$	−0.598939	−	10.7322i	−0.0285533	−	0.511635i
$441$	9.09699			0.433190
$442$			0.123088i			0.00585471i
$443$		−	25.6666i		−	1.21945i	−0.792611	−	0.609727i	$-0.791279\pi$
$443$		−	25.6666i		−	1.21945i	0.792611	−	0.609727i	$-0.208721\pi$
$444$	8.73083			0.414347
$445$	−23.3579	+	1.30356i	−1.10727	+	0.0617945i
$446$	−19.6038			−0.928266
$447$			7.91205i			0.374227i
$448$		−	21.6271i		−	1.02178i
$449$	30.2263			1.42647			0.713235	−	0.700925i	$-0.247229\pi$
$449$	30.2263			1.42647			0.713235	+	0.700925i	$0.247229\pi$
$450$	0.348576	+	3.11327i	0.0164320	+	0.146761i
$451$	1.24070			0.0584224
$452$			4.66563i			0.219453i
$453$			25.7309i			1.20894i
$454$	−0.324056			−0.0152087
$455$	−1.22435	+	0.0683285i	−0.0573985	+	0.00320329i
$456$	46.0397			2.15601
$457$		−	6.05210i		−	0.283105i	−0.989931	−	0.141553i	$-0.954791\pi$
$457$		−	6.05210i		−	0.283105i	0.989931	−	0.141553i	$-0.0452095\pi$
$458$			13.9824i			0.653354i
$459$	5.02507			0.234550
$460$	−0.695074	−	12.4548i	−0.0324080	−	0.580706i
$461$	−6.19623			−0.288587			−0.144293	−	0.989535i	$-0.546091\pi$
$461$	−6.19623			−0.288587			−0.144293	+	0.989535i	$0.546091\pi$
$462$		−	12.6725i		−	0.589580i
$463$			17.4621i			0.811533i	0.913977	+	0.405767i	$0.132995\pi$
$463$			17.4621i			0.811533i	−0.913977	+	0.405767i	$0.867005\pi$
$464$	0.106465			0.00494252
$465$	−2.62451	−	47.0276i	−0.121709	−	2.18085i
$466$	2.81752			0.130519
$467$			26.8068i			1.24047i	0.784416	+	0.620236i	$0.212963\pi$
$467$			26.8068i			1.24047i	−0.784416	+	0.620236i	$0.787037\pi$
$468$		−	0.110630i		−	0.00511389i
$469$	−54.2763			−2.50625
$470$	−22.5490	+	1.25842i	−1.04011	+	0.0580464i
$471$	−30.1761			−1.39044
$472$		−	22.4693i		−	1.03423i
$473$		−	9.95952i		−	0.457939i
$474$	16.4579			0.755937
$475$	−42.0262	+	4.70544i	−1.92829	+	0.215901i
$476$	−6.28992			−0.288298
$477$		−	8.71339i		−	0.398959i
$478$		−	20.7310i		−	0.948213i
$479$	17.4704			0.798244			0.399122	−	0.916898i	$-0.369315\pi$
$479$	17.4704			0.798244			0.399122	+	0.916898i	$0.369315\pi$
$480$	−24.4086	+	1.36219i	−1.11409	+	0.0621753i
$481$	−0.450973			−0.0205626
$482$		−	19.3182i		−	0.879919i
$483$		−	38.3855i		−	1.74660i
$484$	−10.0606			−0.457301
$485$	0.412898	+	7.39856i	0.0187487	+	0.335951i
$486$	6.38064			0.289432
$487$			13.3952i			0.606996i	0.952832	+	0.303498i	$0.0981546\pi$
$487$			13.3952i			0.606996i	−0.952832	+	0.303498i	$0.901845\pi$
$488$			36.3740i			1.64657i
$489$	19.6383			0.888074
$490$	1.37096	+	24.5657i	0.0619338	+	1.10977i
$491$	2.76836			0.124934			0.0624672	−	0.998047i	$-0.480103\pi$
$491$	2.76836			0.124934			0.0624672	+	0.998047i	$0.480103\pi$
$492$		−	1.74521i		−	0.0786802i
$493$			4.45491i			0.200639i
$494$	−0.911113			−0.0409929
$495$	−2.73671	+	0.152730i	−0.123006	+	0.00686472i
$496$	0.298233			0.0133911
$497$		−	47.0781i		−	2.11174i
$498$			4.95247i			0.221926i
$499$	19.6857			0.881253			0.440627	−	0.897690i	$-0.354756\pi$
$499$	19.6857			0.881253			0.440627	+	0.897690i	$0.354756\pi$
$500$	13.6940	−	2.31193i	0.612416	−	0.103393i
$501$	21.9982			0.982806
$502$			1.87311i			0.0836010i
$503$		−	9.61308i		−	0.428626i	−0.976765	−	0.214313i	$-0.931249\pi$
$503$		−	9.61308i		−	0.428626i	0.976765	−	0.214313i	$-0.0687513\pi$
$504$	−9.00230			−0.400994
$505$	27.3448	−	1.52606i	1.21683	−	0.0679088i
$506$	−6.65868			−0.296014
$507$		−	25.0430i		−	1.11220i
$508$		−	5.60467i		−	0.248667i
$509$	27.0505			1.19899			0.599496	−	0.800377i	$-0.295368\pi$
$509$	27.0505			1.19899			0.599496	+	0.800377i	$0.295368\pi$
$510$	−0.239027	−	4.28303i	−0.0105843	−	0.189656i
$511$	−29.2428			−1.29363
$512$		−	0.308933i		−	0.0136530i
$513$			37.1962i			1.64225i
$514$	−9.53425			−0.420538
$515$	0.155994	+	2.79520i	0.00687394	+	0.123171i
$516$	−14.0094			−0.616728
$517$		−	19.7600i		−	0.869042i
$518$			14.0596i			0.617745i
$519$	47.8970			2.10244
$520$	0.779762	−	0.0435169i	0.0341948	−	0.00190834i
$521$	−22.9932			−1.00735			−0.503676	−	0.863893i	$-0.668019\pi$
$521$	−22.9932			−1.00735			−0.503676	+	0.863893i	$0.668019\pi$
$522$			2.44282i			0.106919i
$523$		−	15.6933i		−	0.686219i	−0.939295	−	0.343110i	$-0.888520\pi$
$523$		−	15.6933i		−	0.686219i	0.939295	−	0.343110i	$-0.111480\pi$
$524$	−8.38379			−0.366248
$525$	42.4704	−	4.75518i	1.85356	−	0.207533i
$526$	−7.54019			−0.328768
$527$			12.4792i			0.543603i
$528$		−	0.0896970i		−	0.00390356i
$529$	2.83064			0.123071
$530$	23.5299	−	1.31315i	1.02207	−	0.0570397i
$531$	−5.72971			−0.248648
$532$		−	46.5587i		−	2.01858i
$533$			0.0901453i			0.00390463i
$534$	17.5657			0.760143
$535$	1.26912	+	22.7408i	0.0548688	+	0.983172i
$536$	34.5674			1.49308
$537$			40.6079i			1.75236i
$538$			9.09249i			0.392005i
$539$	−21.5272			−0.927243
$540$	−0.680657	−	12.1964i	−0.0292908	−	0.524850i
$541$	27.6492			1.18873			0.594366	−	0.804194i	$-0.297403\pi$
$541$	27.6492			1.18873			0.594366	+	0.804194i	$0.297403\pi$
$542$		−	3.96769i		−	0.170427i
$543$			8.83814i			0.379281i
$544$	6.47704			0.277701
$545$	1.17897	−	0.0657959i	0.0505015	−	0.00281839i
$546$	0.920743			0.0394042
$547$			27.9155i			1.19358i	0.802397	+	0.596790i	$0.203558\pi$
$547$			27.9155i			1.19358i	−0.802397	+	0.596790i	$0.796442\pi$
$548$			17.9281i			0.765852i
$549$	9.27542			0.395865
$550$	−0.824874	−	7.36727i	−0.0351727	−	0.314142i
$551$	−32.9758			−1.40481
$552$			24.4469i			1.04053i
$553$		−	43.4409i		−	1.84729i
$554$	25.7495			1.09399
$555$	15.6923	−	0.875753i	0.666100	−	0.0371737i
$556$	9.08773			0.385406
$557$		−	9.60825i		−	0.407115i	−0.979063	−	0.203557i	$-0.934750\pi$
$557$		−	9.60825i		−	0.407115i	0.979063	−	0.203557i	$-0.0652503\pi$
$558$			6.84289i			0.289683i
$559$	0.723625			0.0306061
$560$	0.0150779	+	0.270174i	0.000637156	+	0.0114169i
$561$	3.75327			0.158463
$562$			4.37273i			0.184452i
$563$			22.1977i			0.935520i	0.883855	+	0.467760i	$0.154939\pi$
$563$			22.1977i			0.935520i	−0.883855	+	0.467760i	$0.845061\pi$
$564$	−27.7950			−1.17038
$565$	0.467990	+	8.38573i	0.0196885	+	0.352790i
$566$	−6.56144			−0.275798
$567$		−	47.1580i		−	1.98045i
$568$			29.9830i			1.25806i
$569$	12.3835			0.519145			0.259573	−	0.965724i	$-0.416418\pi$
$569$	12.3835			0.519145			0.259573	+	0.965724i	$0.416418\pi$
$570$	31.7035	−	1.76931i	1.32791	−	0.0741081i
$571$	−27.9621			−1.17018			−0.585090	−	0.810969i	$-0.698941\pi$
$571$	−27.9621			−1.17018			−0.585090	+	0.810969i	$0.698941\pi$
$572$			0.261797i			0.0109463i
$573$			25.0123i			1.04490i
$574$	2.81039			0.117303
$575$	−2.49857	−	22.3157i	−0.104198	−	0.930630i
$576$	3.51234			0.146347
$577$		−	34.3719i		−	1.43092i	−0.698654	−	0.715460i	$-0.746217\pi$
$577$		−	34.3719i		−	1.43092i	0.698654	−	0.715460i	$-0.253783\pi$
$578$		−	13.6626i		−	0.568289i
$579$	8.12481			0.337656
$580$	10.8126	−	0.603427i	0.448968	−	0.0250560i
$581$	13.0721			0.542323
$582$		−	5.56391i		−	0.230631i
$583$			20.6194i			0.853970i
$584$	18.6241			0.770670
$585$	−0.0110969	−	0.198840i	−0.000458799	−	0.00822104i
$586$	−5.09253			−0.210370
$587$		−	47.0526i		−	1.94207i	−0.238944	−	0.971033i	$-0.576801\pi$
$587$		−	47.0526i		−	1.94207i	0.238944	−	0.971033i	$-0.423199\pi$
$588$			30.2808i			1.24876i
$589$	−92.3725			−3.80614
$590$	−0.863496	−	15.4726i	−0.0355496	−	0.636999i
$591$	−1.92866			−0.0793344
$592$			0.0995150i			0.00409004i
$593$		−	10.0447i		−	0.412486i	−0.978501	−	0.206243i	$-0.933876\pi$
$593$		−	10.0447i		−	0.412486i	0.978501	−	0.206243i	$-0.0661238\pi$
$594$	−6.52056			−0.267542
$595$	−11.3051	+	0.630916i	−0.463465	+	0.0258650i
$596$	−5.09581			−0.208733
$597$		−	19.0051i		−	0.777826i
$598$		−	0.483797i		−	0.0197839i
$599$	29.0212			1.18577			0.592886	−	0.805286i	$-0.297988\pi$
$599$	29.0212			1.18577			0.592886	+	0.805286i	$0.297988\pi$
$600$	−27.0484	+	3.02847i	−1.10425	+	0.123637i
$601$	−0.756067			−0.0308406			−0.0154203	−	0.999881i	$-0.504909\pi$
$601$	−0.756067			−0.0308406			−0.0154203	+	0.999881i	$0.504909\pi$
$602$		−	22.5599i		−	0.919472i
$603$		−	8.81473i		−	0.358964i
$604$	−16.5722			−0.674313
$605$	−18.0823	+	1.00914i	−0.735152	+	0.0410273i
$606$	−20.5640			−0.835357
$607$			0.980632i			0.0398026i	0.999802	+	0.0199013i	$0.00633520\pi$
$607$			0.980632i			0.0398026i	−0.999802	+	0.0199013i	$0.993665\pi$
$608$			47.9438i			1.94438i
$609$	33.3243			1.35037
$610$	1.39785	+	25.0476i	0.0565975	+	1.01415i
$611$	1.43569			0.0580819
$612$		−	1.02151i		−	0.0412922i
$613$		−	32.3831i		−	1.30794i	−0.756520	−	0.653971i	$-0.773102\pi$
$613$		−	32.3831i		−	1.30794i	0.756520	−	0.653971i	$-0.226898\pi$
$614$	−19.8944			−0.802873
$615$	−0.175055	−	3.13674i	−0.00705889	−	0.126485i
$616$	21.3031			0.858327
$617$		−	4.27331i		−	0.172037i	−0.996294	−	0.0860185i	$-0.972586\pi$
$617$		−	4.27331i		−	0.172037i	0.996294	−	0.0860185i	$-0.0274144\pi$
$618$		−	2.10206i		−	0.0845574i
$619$	23.6528			0.950687			0.475343	−	0.879800i	$-0.342324\pi$
$619$	23.6528			0.950687			0.475343	+	0.879800i	$0.342324\pi$
$620$	30.2885	−	1.69034i	1.21641	−	0.0678855i
$621$	−19.7510			−0.792580
$622$		−	0.738715i		−	0.0296198i
$623$		−	46.3650i		−	1.85757i
$624$	0.00651708			0.000260892
$625$	24.3810	−	5.52892i	0.975238	−	0.221157i
$626$	−21.1151			−0.843929
$627$			27.7821i			1.10951i
$628$		−	19.4351i		−	0.775545i
$629$	−4.16409			−0.166033
$630$	−6.19909	+	0.345958i	−0.246978	+	0.0137833i
$631$	−2.75054			−0.109497			−0.0547487	−	0.998500i	$-0.517436\pi$
$631$	−2.75054			−0.109497			−0.0547487	+	0.998500i	$0.517436\pi$
$632$			27.6665i			1.10052i
$633$			18.1869i			0.722866i
$634$	−8.27778			−0.328753
$635$	−0.562182	−	10.0735i	−0.0223095	−	0.399755i
$636$	29.0039			1.15008
$637$		−	1.56409i		−	0.0619717i
$638$		−	5.78072i		−	0.228861i
$639$	7.64571			0.302460
$640$	−0.883253	−	15.8267i	−0.0349136	−	0.625603i
$641$	−11.3606			−0.448719			−0.224359	−	0.974506i	$-0.572029\pi$
$641$	−11.3606			−0.448719			−0.224359	+	0.974506i	$0.572029\pi$
$642$		−	17.1017i		−	0.674950i
$643$		−	33.8558i		−	1.33514i	−0.744545	−	0.667572i	$-0.767334\pi$
$643$		−	33.8558i		−	1.33514i	0.744545	−	0.667572i	$-0.232666\pi$
$644$	24.7225			0.974202
$645$	−25.1796	+	1.40522i	−0.991445	+	0.0553305i
$646$	−8.41282			−0.330998
$647$			37.0829i			1.45788i	0.684579	+	0.728939i	$0.259986\pi$
$647$			37.0829i			1.45788i	−0.684579	+	0.728939i	$0.740014\pi$
$648$			30.0339i			1.17984i
$649$	13.5588			0.532231
$650$	0.535281	−	0.0599325i	0.0209955	−	0.00235075i
$651$	93.3489			3.65863
$652$			12.6482i			0.495340i
$653$		−	28.2327i		−	1.10483i	−0.833569	−	0.552415i	$-0.813706\pi$
$653$		−	28.2327i		−	1.10483i	0.833569	−	0.552415i	$-0.186294\pi$
$654$	−0.886615			−0.0346694
$655$	−15.0685	+	0.840943i	−0.588776	+	0.0328584i
$656$	0.0198921			0.000776656
$657$		−	4.74917i		−	0.185283i
$658$		−	44.7594i		−	1.74490i
$659$	−32.3003			−1.25824			−0.629120	−	0.777308i	$-0.716585\pi$
$659$	−32.3003			−1.25824			−0.629120	+	0.777308i	$0.716585\pi$
$660$	−0.508388	−	9.10960i	−0.0197890	−	0.354591i
$661$	−11.4499			−0.445350			−0.222675	−	0.974893i	$-0.571479\pi$
$661$	−11.4499			−0.445350			−0.222675	+	0.974893i	$0.571479\pi$
$662$		−	2.22346i		−	0.0864171i
$663$			0.272700i			0.0105908i
$664$	−8.32534			−0.323086
$665$	−4.67011	−	83.6818i	−0.181099	−	3.24504i
$666$	−2.28335			−0.0884781
$667$		−	17.5100i		−	0.677989i
$668$			14.1681i			0.548179i
$669$	−43.4318			−1.67917
$670$	23.8035	−	1.32842i	0.919610	−	0.0513215i
$671$	−21.9495			−0.847349
$672$		−	48.4506i		−	1.86902i
$673$			15.0187i			0.578928i	0.957189	+	0.289464i	$0.0934771\pi$
$673$			15.0187i			0.578928i	−0.957189	+	0.289464i	$0.906523\pi$
$674$	6.56928			0.253039
$675$	−2.44674	−	21.8528i	−0.0941752	−	0.841116i
$676$	16.1291			0.620351
$677$			3.69635i			0.142062i	0.997474	+	0.0710312i	$0.0226290\pi$
$677$			3.69635i			0.142062i	−0.997474	+	0.0710312i	$0.977371\pi$
$678$		−	6.30628i		−	0.242191i
$679$	−14.6860			−0.563597
$680$	7.19998	−	0.401816i	0.276107	−	0.0154089i
$681$	−0.717939			−0.0275115
$682$		−	16.1931i		−	0.620065i
$683$			9.96233i			0.381198i	0.981668	+	0.190599i	$0.0610430\pi$
$683$			9.96233i			0.381198i	−0.981668	+	0.190599i	$0.938957\pi$
$684$	7.56135			0.289116
$685$	1.79830	+	32.2229i	0.0687094	+	1.23118i
$686$	−21.7571			−0.830690
$687$			30.9777i			1.18187i
$688$		−	0.159680i		−	0.00608775i
$689$	−1.49814			−0.0570746
$690$	0.939494	+	16.8344i	0.0357659	+	0.640876i
$691$	−24.9722			−0.949986			−0.474993	−	0.879990i	$-0.657549\pi$
$691$	−24.9722			−0.949986			−0.474993	+	0.879990i	$0.657549\pi$
$692$			30.8484i			1.17268i
$693$		−	5.43233i		−	0.206357i
$694$	11.8988			0.451673
$695$	16.3337	−	0.911552i	0.619574	−	0.0345772i
$696$	−21.2235			−0.804475
$697$			0.832362i			0.0315280i
$698$			26.6235i			1.00771i
$699$	6.24217			0.236100
$700$	3.06261	+	27.3533i	0.115756	+	1.03386i
$701$	26.1263			0.986777			0.493388	−	0.869809i	$-0.335758\pi$
$701$	26.1263			0.986777			0.493388	+	0.869809i	$0.335758\pi$
$702$		−	0.473762i		−	0.0178810i
$703$		−	30.8231i		−	1.16251i
$704$	−8.31163			−0.313256
$705$	−49.9570	+	2.78800i	−1.88149	+	0.105002i
$706$	−7.24707			−0.272747
$707$			54.2790i			2.04137i
$708$		−	19.0723i		−	0.716780i
$709$	−0.447942			−0.0168228			−0.00841142	−	0.999965i	$-0.502677\pi$
$709$	−0.447942			−0.0168228			−0.00841142	+	0.999965i	$0.502677\pi$
$710$	1.15225	+	20.6467i	0.0432431	+	0.774855i
$711$	7.05500			0.264583
$712$			29.5288i			1.10664i
$713$		−	49.0494i		−	1.83692i
$714$	8.50174			0.318170
$715$	0.0262597	+	0.470538i	0.000982059	+	0.0175971i
$716$	−26.1538			−0.977412
$717$		−	45.9291i		−	1.71525i
$718$			10.8014i			0.403104i
$719$	22.7145			0.847107			0.423553	−	0.905871i	$-0.360783\pi$
$719$	22.7145			0.847107			0.423553	+	0.905871i	$0.360783\pi$
$720$	−0.0438776	+	0.00244872i	−0.00163522	+	9.12583e-5i
$721$	−5.54842			−0.206634
$722$		−	45.7324i		−	1.70199i
$723$		−	42.7990i		−	1.59171i
$724$	−5.69226			−0.211551
$725$	19.3733	−	2.16913i	0.719508	−	0.0805594i
$726$	13.5984			0.504684
$727$			25.7370i			0.954534i	0.878758	+	0.477267i	$0.158373\pi$
$727$			25.7370i			0.954534i	−0.878758	+	0.477267i	$0.841627\pi$
$728$			1.54781i			0.0573658i
$729$	−17.7873			−0.658790
$730$	12.8248	−	0.715724i	0.474666	−	0.0264901i
$731$	6.68164			0.247129
$732$			30.8748i			1.14116i
$733$			11.8624i			0.438147i	0.975708	+	0.219074i	$0.0703035\pi$
$733$			11.8624i			0.438147i	−0.975708	+	0.219074i	$0.929696\pi$
$734$	−28.7794			−1.06227
$735$	3.03734	+	54.4249i	0.112034	+	2.00749i
$736$	−25.4580			−0.938393
$737$			20.8593i			0.768361i
$738$			0.456420i			0.0168011i
$739$	38.0649			1.40024			0.700120	−	0.714026i	$-0.253130\pi$
$739$	38.0649			1.40024			0.700120	+	0.714026i	$0.253130\pi$
$740$	0.564035	+	10.1067i	0.0207343	+	0.371530i
$741$	−2.01855			−0.0741534
$742$			46.7063i			1.71464i
$743$			8.55413i			0.313821i	0.987613	+	0.156910i	$0.0501534\pi$
$743$			8.55413i			0.313821i	−0.987613	+	0.156910i	$0.949847\pi$
$744$	−59.4519			−2.17961
$745$	−9.15891	+	0.511140i	−0.335556	+	0.0187267i
$746$	−21.4453			−0.785169
$747$			2.12297i			0.0776756i
$748$			2.41732i			0.0883859i
$749$	−45.1401			−1.64938
$750$	−18.5095	+	3.12491i	−0.675871	+	0.114106i
$751$	−29.4966			−1.07635			−0.538174	−	0.842834i	$-0.680886\pi$
$751$	−29.4966			−1.07635			−0.538174	+	0.842834i	$0.680886\pi$
$752$		−	0.316810i		−	0.0115529i
$753$			4.14984i			0.151229i
$754$	0.420007			0.0152958
$755$	−29.7858	+	1.66229i	−1.08402	+	0.0604968i
$756$	24.2097			0.880497
$757$		−	24.3569i		−	0.885265i	−0.896703	−	0.442633i	$-0.854045\pi$
$757$		−	24.3569i		−	0.885265i	0.896703	−	0.442633i	$-0.145955\pi$
$758$			2.00539i			0.0728389i
$759$	−14.7522			−0.535470
$760$	2.97429	+	53.2951i	0.107889	+	1.93322i
$761$	23.6562			0.857537			0.428768	−	0.903414i	$-0.358948\pi$
$761$	23.6562			0.857537			0.428768	+	0.903414i	$0.358948\pi$
$762$			7.57553i			0.274433i
$763$			2.34023i			0.0847221i
$764$	−16.1093			−0.582815
$765$	−0.102464	−	1.83601i	−0.00370458	−	0.0663809i
$766$	−19.7321			−0.712950
$767$			0.985139i			0.0355713i
$768$			30.7263i			1.10874i
$769$	−4.60006			−0.165883			−0.0829413	−	0.996554i	$-0.526431\pi$
$769$	−4.60006			−0.165883			−0.0829413	+	0.996554i	$0.526431\pi$
$770$	14.6696	−	0.818679i	0.528655	−	0.0295032i
$771$	−21.1229			−0.760724
$772$			5.23284i			0.188334i
$773$			9.80949i			0.352823i	0.984317	+	0.176411i	$0.0564489\pi$
$773$			9.80949i			0.352823i	−0.984317	+	0.176411i	$0.943551\pi$
$774$	3.66383			0.131694
$775$	54.2691	−	6.07622i	1.94940	−	0.218264i
$776$	9.35319			0.335760
$777$			31.1489i			1.11746i
$778$		−	9.42340i		−	0.337845i
$779$	−6.16124			−0.220749
$780$	0.661873	−	0.0369378i	0.0236988	−	0.00132258i
$781$	−18.0929			−0.647414
$782$		−	4.46717i		−	0.159746i
$783$		−	17.1468i		−	0.612776i
$784$	−0.345144			−0.0123266
$785$	−1.94945	−	34.9315i	−0.0695790	−	1.24676i
$786$	11.3319			0.404196
$787$			14.8242i			0.528426i	0.964464	+	0.264213i	$0.0851122\pi$
$787$			14.8242i			0.528426i	−0.964464	+	0.264213i	$0.914888\pi$
$788$		−	1.24217i		−	0.0442503i
$789$	−16.7051			−0.594719
$790$	1.06323	+	19.0515i	0.0378279	+	0.677822i
$791$	−16.6455			−0.591846
$792$			3.45973i			0.122936i
$793$		−	1.59477i		−	0.0566321i
$794$	12.3853			0.439536
$795$	52.1299	−	2.90926i	1.84886	−	0.103181i
$796$	12.2403			0.433848
$797$		−	8.53761i		−	0.302418i	−0.988502	−	0.151209i	$-0.951683\pi$
$797$		−	8.53761i		−	0.302418i	0.988502	−	0.151209i	$-0.0483166\pi$
$798$			62.9309i			2.22773i
$799$	13.2566			0.468983
$800$	−3.15372	−	28.1671i	−0.111501	−	0.995857i
$801$	7.52989			0.266056
$802$		−	27.6201i		−	0.975301i
$803$			11.2385i			0.396597i
$804$	29.3413			1.03479
$805$	44.4347	−	2.47981i	1.56612	−	0.0874017i
$806$	1.17654			0.0414417
$807$			20.1442i			0.709111i
$808$		−	34.5691i		−	1.21614i
$809$	−17.6854			−0.621786			−0.310893	−	0.950445i	$-0.600628\pi$
$809$	−17.6854			−0.621786			−0.310893	+	0.950445i	$0.600628\pi$
$810$	1.15420	+	20.6817i	0.0405546	+	0.726681i
$811$	−45.0258			−1.58107			−0.790534	−	0.612418i	$-0.790197\pi$
$811$	−45.0258			−1.58107			−0.790534	+	0.612418i	$0.790197\pi$
$812$			21.4628i			0.753195i
$813$		−	8.79035i		−	0.308291i
$814$	5.40334			0.189387
$815$	1.26869	+	22.7331i	0.0444401	+	0.796304i
$816$	0.0601759			0.00210658
$817$			49.4582i			1.73032i
$818$			20.4470i			0.714911i
$819$	0.394695			0.0137917
$820$	2.02024	−	0.112745i	0.0705497	−	0.00393724i
$821$	10.8106			0.377291			0.188646	−	0.982045i	$-0.439590\pi$
$821$	10.8106			0.377291			0.188646	+	0.982045i	$0.439590\pi$
$822$		−	24.2325i		−	0.845205i
$823$			16.3476i			0.569841i	0.958551	+	0.284921i	$0.0919672\pi$
$823$			16.3476i			0.569841i	−0.958551	+	0.284921i	$0.908033\pi$
$824$	3.53367			0.123101
$825$	−1.82749	−	16.3221i	−0.0636251	−	0.568261i
$826$	30.7129			1.06864
$827$		−	27.1543i		−	0.944248i	−0.881532	−	0.472124i	$-0.843487\pi$
$827$		−	27.1543i		−	0.944248i	0.881532	−	0.472124i	$-0.156513\pi$
$828$			4.01505i			0.139532i
$829$	−14.3838			−0.499572			−0.249786	−	0.968301i	$-0.580360\pi$
$829$	−14.3838			−0.499572			−0.249786	+	0.968301i	$0.580360\pi$
$830$	−5.73293	+	0.319943i	−0.198993	+	0.0111054i
$831$	57.0476			1.97896
$832$		−	0.603895i		−	0.0209363i
$833$		−	14.4422i		−	0.500391i
$834$	−12.2834			−0.425339
$835$	1.42114	+	25.4648i	0.0491806	+	0.881247i
$836$	−17.8933			−0.618851
$837$		−	48.0320i		−	1.66023i
$838$			16.0427i			0.554186i
$839$	49.7122			1.71626			0.858128	−	0.513435i	$-0.171627\pi$
$839$	49.7122			1.71626			0.858128	+	0.513435i	$0.171627\pi$
$840$	−3.00573	−	53.8584i	−0.103707	−	1.85829i
$841$	−13.7987			−0.475819
$842$			11.2612i			0.388088i
$843$			9.68770i			0.333662i
$844$	−11.7134			−0.403192
$845$	28.9895	−	1.61785i	0.997270	−	0.0556556i
$846$	7.26915			0.249918
$847$		−	35.8931i		−	1.23330i
$848$			0.330590i			0.0113525i
$849$	−14.5367			−0.498900
$850$	4.94255	−	0.553391i	0.169528	−	0.0189811i
$851$	16.3669			0.561051
$852$			25.4500i			0.871903i
$853$			0.189159i			0.00647668i	0.999995	+	0.00323834i	$0.00103080\pi$
$853$			0.189159i			0.00647668i	−0.999995	+	0.00323834i	$0.998969\pi$
$854$	−49.7190			−1.70135
$855$	13.5903	−	0.758448i	0.464779	−	0.0259384i
$856$	28.7487			0.982612
$857$			12.1359i			0.414554i	0.978282	+	0.207277i	$0.0664601\pi$
$857$			12.1359i			0.414554i	−0.978282	+	0.207277i	$0.933540\pi$
$858$		−	0.353857i		−	0.0120805i
$859$	8.97076			0.306078			0.153039	−	0.988220i	$-0.451094\pi$
$859$	8.97076			0.306078			0.153039	+	0.988220i	$0.451094\pi$
$860$	−0.905042	−	16.2171i	−0.0308617	−	0.552998i
$861$	6.22636			0.212194
$862$			15.0303i			0.511933i
$863$			48.5734i			1.65346i	0.562600	+	0.826729i	$0.309801\pi$
$863$			48.5734i			1.65346i	−0.562600	+	0.826729i	$0.690199\pi$
$864$	−24.9299			−0.848132
$865$	3.09427	+	55.4451i	0.105208	+	1.88519i
$866$	20.9758			0.712788
$867$		−	30.2692i		−	1.02800i
$868$			60.1220i			2.04067i
$869$	−16.6950			−0.566340
$870$	−14.6148	+	0.815620i	−0.495487	+	0.0276521i
$871$	−1.51556			−0.0513529
$872$		−	1.49044i		−	0.0504728i
$873$		−	2.38508i		−	0.0807226i
$874$	33.0665			1.11849
$875$	8.24825	+	48.8561i	0.278842	+	1.65164i
$876$	15.8084			0.534116
$877$		−	33.1053i		−	1.11789i	−0.829206	−	0.558944i	$-0.811207\pi$
$877$		−	33.1053i		−	1.11789i	0.829206	−	0.558944i	$-0.188793\pi$
$878$			0.631799i			0.0213222i
$879$	−11.2824			−0.380546
$880$	0.103832	−	0.00579466i	0.00350018	−	0.000195338i
$881$	34.8931			1.17558			0.587790	−	0.809014i	$-0.299998\pi$
$881$	34.8931			1.17558			0.587790	+	0.809014i	$0.299998\pi$
$882$		−	7.91927i		−	0.266656i
$883$			15.7765i			0.530921i	0.964122	+	0.265461i	$0.0855240\pi$
$883$			15.7765i			0.530921i	−0.964122	+	0.265461i	$0.914476\pi$
$884$	−0.175634			−0.00590721
$885$	−1.91306	−	34.2793i	−0.0643068	−	1.15229i
$886$	−22.3437			−0.750651
$887$		−	52.7863i		−	1.77239i	−0.463311	−	0.886196i	$-0.653339\pi$
$887$		−	52.7863i		−	1.77239i	0.463311	−	0.886196i	$-0.346661\pi$
$888$		−	19.8380i		−	0.665720i
$889$	19.9957			0.670635
$890$	1.13479	+	20.3339i	0.0380384	+	0.681594i
$891$	−18.1236			−0.607163
$892$		−	27.9726i		−	0.936591i
$893$			98.1265i			3.28368i
$894$	6.88773			0.230360
$895$	−47.0072	+	2.62338i	−1.57128	+	0.0876898i
$896$	31.4156			1.04952
$897$		−	1.07184i		−	0.0357878i
$898$		−	26.3131i		−	0.878081i
$899$	42.5821			1.42019
$900$	−4.44231	+	0.497382i	−0.148077	+	0.0165794i
$901$	−13.8332			−0.460850
$902$		−	1.08008i		−	0.0359627i
$903$		−	49.9810i		−	1.66326i
$904$	10.6012			0.352589
$905$	−10.2309	+	0.570967i	−0.340088	+	0.0189796i
$906$	22.3997			0.744181
$907$			26.3884i			0.876212i	0.898923	+	0.438106i	$0.144351\pi$
$907$			26.3884i			0.876212i	−0.898923	+	0.438106i	$0.855649\pi$
$908$		−	0.462394i		−	0.0153451i
$909$	−8.81517			−0.292381
$910$	0.0594825	+	1.06584i	0.00197183	+	0.0353323i
$911$	54.8309			1.81663			0.908314	−	0.418289i	$-0.137370\pi$
$911$	54.8309			1.81663			0.908314	+	0.418289i	$0.137370\pi$
$912$			0.445429i			0.0147496i
$913$		−	5.02383i		−	0.166264i
$914$	−5.26858			−0.174269
$915$	3.09692	+	55.4924i	0.102381	+	1.83452i
$916$	−19.9514			−0.659213
$917$		−	29.9107i		−	0.987740i
$918$		−	4.37451i		−	0.144380i
$919$	0.151198			0.00498757			0.00249378	−	0.999997i	$-0.499206\pi$
$919$	0.151198			0.00498757			0.00249378	+	0.999997i	$0.499206\pi$
$920$	−28.2995	+	1.57933i	−0.933006	+	0.0520691i
$921$	−44.0757			−1.45234
$922$			5.39404i			0.177643i
$923$		−	1.31457i		−	0.0432695i
$924$	18.0824			0.594867
$925$	2.02753	+	18.1086i	0.0666646	+	0.595408i
$926$	15.2014			0.499549
$927$		−	0.901090i		−	0.0295957i
$928$		−	22.1013i		−	0.725510i
$929$	53.5301			1.75627			0.878134	−	0.478416i	$-0.158789\pi$
$929$	53.5301			1.75627			0.878134	+	0.478416i	$0.158789\pi$
$930$	−40.9393	+	2.28474i	−1.34245	+	0.0749194i
$931$	106.903			3.50359
$932$			4.02031i			0.131690i
$933$		−	1.63661i		−	0.0535802i
$934$	23.3363			0.763587
$935$	0.242471	+	4.34474i	0.00792965	+	0.142088i
$936$	−0.251372			−0.00821636
$937$			35.9511i			1.17447i	0.809416	+	0.587236i	$0.199784\pi$
$937$			35.9511i			1.17447i	−0.809416	+	0.587236i	$0.800216\pi$
$938$			47.2495i			1.54275i
$939$	−46.7801			−1.52661
$940$	−1.79563	−	32.1751i	−0.0585670	−	1.04944i
$941$	11.7311			0.382423			0.191211	−	0.981549i	$-0.438758\pi$
$941$	11.7311			0.382423			0.191211	+	0.981549i	$0.438758\pi$
$942$			26.2694i			0.855903i
$943$		−	3.27159i		−	0.106538i
$944$	0.217388			0.00707537
$945$	43.5130	−	2.42837i	1.41548	−	0.0789949i
$946$	−8.67012			−0.281890
$947$			41.2862i			1.34162i	0.741629	+	0.670810i	$0.234053\pi$
$947$			41.2862i			1.34162i	−0.741629	+	0.670810i	$0.765947\pi$
$948$			23.4837i			0.762716i
$949$	−0.816550			−0.0265063
$950$	4.09626	+	36.5853i	0.132900	+	1.18698i
$951$	−18.3393			−0.594691
$952$			14.2918i			0.463201i
$953$			25.0112i			0.810192i	0.914274	+	0.405096i	$0.132762\pi$
$953$			25.0112i			0.810192i	−0.914274	+	0.405096i	$0.867238\pi$
$954$	−7.58533			−0.245584
$955$	−28.9539	+	1.61586i	−0.936927	+	0.0522880i
$956$	29.5809			0.956716
$957$		−	12.8071i		−	0.413994i
$958$		−	15.2086i		−	0.491369i
$959$	−63.9619			−2.06544
$960$	1.17271	+	21.0134i	0.0378492	+	0.678205i
$961$	88.2822			2.84781
$962$			0.392589i			0.0126576i
$963$		−	7.33097i		−	0.236237i
$964$	27.5650			0.887810
$965$	0.524885	+	9.40520i	0.0168966	+	0.302764i
$966$	−33.4160			−1.07514
$967$			9.45167i			0.303945i	0.988385	+	0.151973i	$0.0485625\pi$
$967$			9.45167i			0.303945i	−0.988385	+	0.151973i	$0.951437\pi$
$968$			22.8595i			0.734733i
$969$	−18.6384			−0.598753
$970$	6.44072	−	0.359443i	0.206799	−	0.0115410i
$971$	−19.0888			−0.612589			−0.306295	−	0.951937i	$-0.599089\pi$
$971$	−19.0888			−0.612589			−0.306295	+	0.951937i	$0.599089\pi$
$972$			9.10451i			0.292027i
$973$			32.4222i			1.03941i
$974$	11.6610			0.373644
$975$	1.18591	−	0.132779i	0.0379794	−	0.00425234i
$976$	−0.351914			−0.0112645
$977$			6.91399i			0.221198i	0.993865	+	0.110599i	$0.0352770\pi$
$977$			6.91399i			0.221198i	−0.993865	+	0.110599i	$0.964723\pi$
$978$		−	17.0958i		−	0.546665i
$979$	−17.8188			−0.569491
$980$	−35.0528	+	1.95622i	−1.11972	+	0.0624892i
$981$	−0.380065			−0.0121345
$982$		−	2.40996i		−	0.0769050i
$983$			37.4654i			1.19496i	0.801883	+	0.597481i	$0.203832\pi$
$983$			37.4654i			1.19496i	−0.801883	+	0.597481i	$0.796168\pi$
$984$	−3.96543			−0.126413
$985$	−0.124596	−	2.23259i	−0.00396997	−	0.0711364i
$986$	3.87816			0.123506
$987$		−	99.1637i		−	3.15642i
$988$		−	1.30006i		−	0.0413605i
$989$	−26.2621			−0.835086
$990$	0.132957	+	2.38241i	0.00422566	+	0.0757180i
$991$	−29.5473			−0.938601			−0.469300	−	0.883039i	$-0.655494\pi$
$991$	−29.5473			−0.938601			−0.469300	+	0.883039i	$0.655494\pi$
$992$		−	61.9106i		−	1.96566i
$993$		−	4.92603i		−	0.156323i
$994$	−40.9832			−1.29991
$995$	22.0001	−	1.22778i	0.697449	−	0.0389232i
$996$	−7.06667			−0.223916
$997$		−	10.9241i		−	0.345970i	−0.984924	−	0.172985i	$-0.944659\pi$
$997$		−	10.9241i		−	0.345970i	0.984924	−	0.172985i	$-0.0553411\pi$
$998$		−	17.1371i		−	0.542466i
$999$	16.0274			0.507085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	985.2.b.a.789.37	✓	98
5.2	odd	4		4925.2.a.r.1.32		49
5.3	odd	4		4925.2.a.s.1.18		49
5.4	even	2	inner	985.2.b.a.789.62	yes	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
985.2.b.a.789.37	✓	98	1.1	even	1	trivial
985.2.b.a.789.62	yes	98	5.4	even	2	inner
4925.2.a.r.1.32		49	5.2	odd	4
4925.2.a.s.1.18		49	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.870537i q^{2} -1.92866i q^{3} +1.24217 q^{4} +(2.23259 - 0.124596i) q^{5} -1.67897 q^{6} +4.43166i q^{7} -2.82242i q^{8} -0.719722 q^{9} +(-0.108466 - 1.94356i) q^{10} +1.70316 q^{11} -2.39571i q^{12} +0.123746i q^{13} +3.85792 q^{14} +(-0.240304 - 4.30591i) q^{15} +0.0273066 q^{16} +1.14261i q^{17} +0.626545i q^{18} -8.45775 q^{19} +(2.77325 - 0.154769i) q^{20} +8.54715 q^{21} -1.48266i q^{22} -4.49103i q^{23} -5.44349 q^{24} +(4.96895 - 0.556347i) q^{25} +0.107725 q^{26} -4.39788i q^{27} +5.50485i q^{28} +3.89888 q^{29} +(-3.74845 + 0.209193i) q^{30} +10.9216 q^{31} -5.66862i q^{32} -3.28481i q^{33} +0.994687 q^{34} +(0.552169 + 9.89409i) q^{35} -0.894014 q^{36} +3.64436i q^{37} +7.36279i q^{38} +0.238663 q^{39} +(-0.351664 - 6.30133i) q^{40} +0.728472 q^{41} -7.44061i q^{42} -5.84768i q^{43} +2.11560 q^{44} +(-1.60685 + 0.0896748i) q^{45} -3.90961 q^{46} -11.6020i q^{47} -0.0526651i q^{48} -12.6396 q^{49} +(-0.484320 - 4.32566i) q^{50} +2.20371 q^{51} +0.153713i q^{52} +12.1066i q^{53} -3.82851 q^{54} +(3.80246 - 0.212207i) q^{55} +12.5080 q^{56} +16.3121i q^{57} -3.39412i q^{58} +7.96100 q^{59} +(-0.298497 - 5.34865i) q^{60} -12.8875 q^{61} -9.50769i q^{62} -3.18956i q^{63} -4.88013 q^{64} +(0.0154183 + 0.276274i) q^{65} -2.85955 q^{66} +12.2474i q^{67} +1.41932i q^{68} -8.66166 q^{69} +(8.61317 - 0.480683i) q^{70} -10.6231 q^{71} +2.03136i q^{72} +6.59861i q^{73} +3.17255 q^{74} +(-1.07300 - 9.58341i) q^{75} -10.5059 q^{76} +7.54781i q^{77} -0.207765i q^{78} -9.80240 q^{79} +(0.0609646 - 0.00340231i) q^{80} -10.6412 q^{81} -0.634162i q^{82} -2.94971i q^{83} +10.6170 q^{84} +(0.142366 + 2.55099i) q^{85} -5.09062 q^{86} -7.51960i q^{87} -4.80703i q^{88} -10.4622 q^{89} +(0.0780653 + 1.39882i) q^{90} -0.548398 q^{91} -5.57860i q^{92} -21.0641i q^{93} -10.0999 q^{94} +(-18.8827 + 1.05381i) q^{95} -10.9328 q^{96} +3.31388i q^{97} +11.0032i q^{98} -1.22580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) \) 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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