LMFDB - Embedded newform 690.2.d.d.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(139,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.d (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.4
Root			$-1.75233 - 1.75233i$ of defining polynomial
Character	$\chi$	$=$	690.139
Dual form			690.2.d.d.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.75233 - 1.38900i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.75233 - 1.38900i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.38900 - 1.75233i) q^{10} +3.50466 q^{11} -1.00000i q^{12} +2.72666i q^{13} +2.00000 q^{14} +(1.38900 - 1.75233i) q^{15} +1.00000 q^{16} +0.726656i q^{17} -1.00000i q^{18} +7.78734 q^{19} +(1.75233 + 1.38900i) q^{20} +2.00000 q^{21} +3.50466i q^{22} +1.00000i q^{23} +1.00000 q^{24} +(1.14134 + 4.86799i) q^{25} -2.72666 q^{26} -1.00000i q^{27} +2.00000i q^{28} +2.00000 q^{29} +(1.75233 + 1.38900i) q^{30} +8.28267 q^{31} +1.00000i q^{32} +3.50466i q^{33} -0.726656 q^{34} +(-2.77801 + 3.50466i) q^{35} +1.00000 q^{36} -9.50466i q^{37} +7.78734i q^{38} -2.72666 q^{39} +(-1.38900 + 1.75233i) q^{40} +0.726656 q^{41} +2.00000i q^{42} +5.50466i q^{43} -3.50466 q^{44} +(1.75233 + 1.38900i) q^{45} -1.00000 q^{46} -2.72666i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.86799 + 1.14134i) q^{50} -0.726656 q^{51} -2.72666i q^{52} -0.231321i q^{53} +1.00000 q^{54} +(-6.14134 - 4.86799i) q^{55} -2.00000 q^{56} +7.78734i q^{57} +2.00000i q^{58} -9.29200 q^{59} +(-1.38900 + 1.75233i) q^{60} +4.05135 q^{61} +8.28267i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(3.78734 - 4.77801i) q^{65} -3.50466 q^{66} -4.05135i q^{67} -0.726656i q^{68} -1.00000 q^{69} +(-3.50466 - 2.77801i) q^{70} -11.7360 q^{71} +1.00000i q^{72} +3.71733i q^{73} +9.50466 q^{74} +(-4.86799 + 1.14134i) q^{75} -7.78734 q^{76} -7.00933i q^{77} -2.72666i q^{78} +9.73599 q^{79} +(-1.75233 - 1.38900i) q^{80} +1.00000 q^{81} +0.726656i q^{82} -13.5233i q^{83} -2.00000 q^{84} +(1.00933 - 1.27334i) q^{85} -5.50466 q^{86} +2.00000i q^{87} -3.50466i q^{88} +9.55602 q^{89} +(-1.38900 + 1.75233i) q^{90} +5.45331 q^{91} -1.00000i q^{92} +8.28267i q^{93} +2.72666 q^{94} +(-13.6460 - 10.8166i) q^{95} -1.00000 q^{96} -4.54669i q^{97} +3.00000i q^{98} -3.50466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{14} + 2 q^{15} + 6 q^{16} - 8 q^{19} + 12 q^{21} + 6 q^{24} - 10 q^{25} - 8 q^{26} + 12 q^{29} + 16 q^{31} + 4 q^{34} - 4 q^{35} + 6 q^{36} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 6 q^{46} + 18 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{54} - 20 q^{55} - 12 q^{56} + 20 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{64} - 32 q^{65} - 6 q^{69} - 20 q^{71} + 36 q^{74} - 4 q^{75} + 8 q^{76} + 8 q^{79} + 6 q^{81} - 12 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{89} - 2 q^{90} + 16 q^{91} + 8 q^{94} - 44 q^{95} - 6 q^{96}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^14 + 2 * q^15 + 6 * q^16 - 8 * q^19 + 12 * q^21 + 6 * q^24 - 10 * q^25 - 8 * q^26 + 12 * q^29 + 16 * q^31 + 4 * q^34 - 4 * q^35 + 6 * q^36 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 6 * q^46 + 18 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^54 - 20 * q^55 - 12 * q^56 + 20 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^64 - 32 * q^65 - 6 * q^69 - 20 * q^71 + 36 * q^74 - 4 * q^75 + 8 * q^76 + 8 * q^79 + 6 * q^81 - 12 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^89 - 2 * q^90 + 16 * q^91 + 8 * q^94 - 44 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$6$	−1.00000			−0.408248
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	1.38900	−	1.75233i	0.439242	−	0.554136i
$11$	3.50466			1.05670			0.528348	−	0.849028i	$-0.322812\pi$
$11$	3.50466			1.05670			0.528348	+	0.849028i	$0.322812\pi$
$12$		−	1.00000i		−	0.288675i
$13$			2.72666i			0.756238i	0.925757	+	0.378119i	$0.123429\pi$
$13$			2.72666i			0.756238i	−0.925757	+	0.378119i	$0.876571\pi$
$14$	2.00000			0.534522
$15$	1.38900	−	1.75233i	0.358639	−	0.452450i
$16$	1.00000			0.250000
$17$			0.726656i			0.176240i	0.996110	+	0.0881200i	$0.0280859\pi$
$17$			0.726656i			0.176240i	−0.996110	+	0.0881200i	$0.971914\pi$
$18$		−	1.00000i		−	0.235702i
$19$	7.78734			1.78654			0.893269	−	0.449523i	$-0.148406\pi$
$19$	7.78734			1.78654			0.893269	+	0.449523i	$0.148406\pi$
$20$	1.75233	+	1.38900i	0.391833	+	0.310591i
$21$	2.00000			0.436436
$22$			3.50466i			0.747197i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	1.00000			0.204124
$25$	1.14134	+	4.86799i	0.228267	+	0.973599i
$26$	−2.72666			−0.534741
$27$		−	1.00000i		−	0.192450i
$28$			2.00000i			0.377964i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	1.75233	+	1.38900i	0.319931	+	0.253596i
$31$	8.28267			1.48761			0.743806	−	0.668396i	$-0.233019\pi$
$31$	8.28267			1.48761			0.743806	+	0.668396i	$0.233019\pi$
$32$			1.00000i			0.176777i
$33$			3.50466i			0.610084i
$34$	−0.726656			−0.124621
$35$	−2.77801	+	3.50466i	−0.469569	+	0.592396i
$36$	1.00000			0.166667
$37$		−	9.50466i		−	1.56256i	−0.624182	−	0.781279i	$-0.714568\pi$
$37$		−	9.50466i		−	1.56256i	0.624182	−	0.781279i	$-0.285432\pi$
$38$			7.78734i			1.26327i
$39$	−2.72666			−0.436614
$40$	−1.38900	+	1.75233i	−0.219621	+	0.277068i
$41$	0.726656			0.113485			0.0567423	−	0.998389i	$-0.481929\pi$
$41$	0.726656			0.113485			0.0567423	+	0.998389i	$0.481929\pi$
$42$			2.00000i			0.308607i
$43$			5.50466i			0.839453i	0.907651	+	0.419727i	$0.137874\pi$
$43$			5.50466i			0.839453i	−0.907651	+	0.419727i	$0.862126\pi$
$44$	−3.50466			−0.528348
$45$	1.75233	+	1.38900i	0.261222	+	0.207060i
$46$	−1.00000			−0.147442
$47$		−	2.72666i		−	0.397724i	−0.980028	−	0.198862i	$-0.936275\pi$
$47$		−	2.72666i		−	0.397724i	0.980028	−	0.198862i	$-0.0637245\pi$
$48$			1.00000i			0.144338i
$49$	3.00000			0.428571
$50$	−4.86799	+	1.14134i	−0.688438	+	0.161409i
$51$	−0.726656			−0.101752
$52$		−	2.72666i		−	0.378119i
$53$		−	0.231321i		−	0.0317744i	−0.999874	−	0.0158872i	$-0.994943\pi$
$53$		−	0.231321i		−	0.0317744i	0.999874	−	0.0158872i	$-0.00505726\pi$
$54$	1.00000			0.136083
$55$	−6.14134	−	4.86799i	−0.828098	−	0.656400i
$56$	−2.00000			−0.267261
$57$			7.78734i			1.03146i
$58$			2.00000i			0.262613i
$59$	−9.29200			−1.20972			−0.604858	−	0.796334i	$-0.706770\pi$
$59$	−9.29200			−1.20972			−0.604858	+	0.796334i	$0.706770\pi$
$60$	−1.38900	+	1.75233i	−0.179320	+	0.226225i
$61$	4.05135			0.518722			0.259361	−	0.965780i	$-0.416488\pi$
$61$	4.05135			0.518722			0.259361	+	0.965780i	$0.416488\pi$
$62$			8.28267i			1.05190i
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$	3.78734	−	4.77801i	0.469761	−	0.592639i
$66$	−3.50466			−0.431394
$67$		−	4.05135i		−	0.494951i	−0.968894	−	0.247476i	$-0.920399\pi$
$67$		−	4.05135i		−	0.494951i	0.968894	−	0.247476i	$-0.0796010\pi$
$68$		−	0.726656i		−	0.0881200i
$69$	−1.00000			−0.120386
$70$	−3.50466	−	2.77801i	−0.418888	−	0.332035i
$71$	−11.7360			−1.39281			−0.696403	−	0.717651i	$-0.745217\pi$
$71$	−11.7360			−1.39281			−0.696403	+	0.717651i	$0.745217\pi$
$72$			1.00000i			0.117851i
$73$			3.71733i			0.435080i	0.976051	+	0.217540i	$0.0698033\pi$
$73$			3.71733i			0.435080i	−0.976051	+	0.217540i	$0.930197\pi$
$74$	9.50466			1.10489
$75$	−4.86799	+	1.14134i	−0.562107	+	0.131790i
$76$	−7.78734			−0.893269
$77$		−	7.00933i		−	0.798787i
$78$		−	2.72666i		−	0.308733i
$79$	9.73599			1.09538			0.547692	−	0.836680i	$-0.315507\pi$
$79$	9.73599			1.09538			0.547692	+	0.836680i	$0.315507\pi$
$80$	−1.75233	−	1.38900i	−0.195917	−	0.155295i
$81$	1.00000			0.111111
$82$			0.726656i			0.0802458i
$83$		−	13.5233i		−	1.48438i	−0.670191	−	0.742189i	$-0.733788\pi$
$83$		−	13.5233i		−	1.48438i	0.670191	−	0.742189i	$-0.266212\pi$
$84$	−2.00000			−0.218218
$85$	1.00933	−	1.27334i	0.109477	−	0.138113i
$86$	−5.50466			−0.593583
$87$			2.00000i			0.214423i
$88$		−	3.50466i		−	0.373598i
$89$	9.55602			1.01294			0.506468	−	0.862259i	$-0.330951\pi$
$89$	9.55602			1.01294			0.506468	+	0.862259i	$0.330951\pi$
$90$	−1.38900	+	1.75233i	−0.146414	+	0.184712i
$91$	5.45331			0.571663
$92$		−	1.00000i		−	0.104257i
$93$			8.28267i			0.858873i
$94$	2.72666			0.281233
$95$	−13.6460	−	10.8166i	−1.40005	−	1.10976i
$96$	−1.00000			−0.102062
$97$		−	4.54669i		−	0.461646i	−0.972996	−	0.230823i	$-0.925858\pi$
$97$		−	4.54669i		−	0.461646i	0.972996	−	0.230823i	$-0.0741419\pi$
$98$			3.00000i			0.303046i
$99$	−3.50466			−0.352232
$100$	−1.14134	−	4.86799i	−0.114134	−	0.486799i
$101$	3.45331			0.343617			0.171809	−	0.985130i	$-0.445039\pi$
$101$	3.45331			0.343617			0.171809	+	0.985130i	$0.445039\pi$
$102$		−	0.726656i		−	0.0719497i
$103$			14.4626i			1.42505i	0.701649	+	0.712523i	$0.252448\pi$
$103$			14.4626i			1.42505i	−0.701649	+	0.712523i	$0.747552\pi$
$104$	2.72666			0.267371
$105$	−3.50466	−	2.77801i	−0.342020	−	0.271106i
$106$	0.231321			0.0224679
$107$			13.0607i			1.26262i	0.775529	+	0.631312i	$0.217483\pi$
$107$			13.0607i			1.26262i	−0.775529	+	0.631312i	$0.782517\pi$
$108$			1.00000i			0.0962250i
$109$	10.9580			1.04958			0.524792	−	0.851231i	$-0.324143\pi$
$109$	10.9580			1.04958			0.524792	+	0.851231i	$0.324143\pi$
$110$	4.86799	−	6.14134i	0.464145	−	0.585553i
$111$	9.50466			0.902143
$112$		−	2.00000i		−	0.188982i
$113$			11.7360i			1.10403i	0.833835	+	0.552014i	$0.186141\pi$
$113$			11.7360i			1.10403i	−0.833835	+	0.552014i	$0.813859\pi$
$114$	−7.78734			−0.729351
$115$	1.38900	−	1.75233i	0.129525	−	0.163406i
$116$	−2.00000			−0.185695
$117$		−	2.72666i		−	0.252079i
$118$		−	9.29200i		−	0.855398i
$119$	1.45331			0.133225
$120$	−1.75233	−	1.38900i	−0.159965	−	0.126798i
$121$	1.28267			0.116607
$122$			4.05135i			0.366792i
$123$			0.726656i			0.0655204i
$124$	−8.28267			−0.743806
$125$	4.76166	−	10.1157i	0.425896	−	0.904772i
$126$	−2.00000			−0.178174
$127$		−	12.2827i		−	1.08991i	−0.838465	−	0.544955i	$-0.816547\pi$
$127$		−	12.2827i		−	1.08991i	0.838465	−	0.544955i	$-0.183453\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.50466			−0.484659
$130$	4.77801	+	3.78734i	0.419059	+	0.332171i
$131$	−14.8480			−1.29728			−0.648639	−	0.761097i	$-0.724661\pi$
$131$	−14.8480			−1.29728			−0.648639	+	0.761097i	$0.724661\pi$
$132$		−	3.50466i		−	0.305042i
$133$		−	15.5747i		−	1.35050i
$134$	4.05135			0.349983
$135$	−1.38900	+	1.75233i	−0.119546	+	0.150817i
$136$	0.726656			0.0623103
$137$		−	3.27334i		−	0.279661i	−0.990175	−	0.139830i	$-0.955344\pi$
$137$		−	3.27334i		−	0.279661i	0.990175	−	0.139830i	$-0.0446557\pi$
$138$		−	1.00000i		−	0.0851257i
$139$	−14.0187			−1.18905			−0.594524	−	0.804078i	$-0.702659\pi$
$139$	−14.0187			−1.18905			−0.594524	+	0.804078i	$0.702659\pi$
$140$	2.77801	−	3.50466i	0.234785	−	0.296198i
$141$	2.72666			0.229626
$142$		−	11.7360i		−	0.984862i
$143$			9.55602i			0.799114i
$144$	−1.00000			−0.0833333
$145$	−3.50466	−	2.77801i	−0.291047	−	0.230701i
$146$	−3.71733			−0.307648
$147$			3.00000i			0.247436i
$148$			9.50466i			0.781279i
$149$	4.49534			0.368272			0.184136	−	0.982901i	$-0.441051\pi$
$149$	4.49534			0.368272			0.184136	+	0.982901i	$0.441051\pi$
$150$	−1.14134	−	4.86799i	−0.0931897	−	0.397470i
$151$	22.3013			1.81486			0.907428	−	0.420207i	$-0.138043\pi$
$151$	22.3013			1.81486			0.907428	+	0.420207i	$0.138043\pi$
$152$		−	7.78734i		−	0.631636i
$153$		−	0.726656i		−	0.0587467i
$154$	7.00933			0.564828
$155$	−14.5140	−	11.5047i	−1.16579	−	0.924077i
$156$	2.72666			0.218307
$157$		−	9.60737i		−	0.766751i	−0.923592	−	0.383376i	$-0.874761\pi$
$157$		−	9.60737i		−	0.766751i	0.923592	−	0.383376i	$-0.125239\pi$
$158$			9.73599i			0.774553i
$159$	0.231321			0.0183449
$160$	1.38900	−	1.75233i	0.109810	−	0.138534i
$161$	2.00000			0.157622
$162$			1.00000i			0.0785674i
$163$			14.1214i			1.10607i	0.833158	+	0.553035i	$0.186530\pi$
$163$			14.1214i			1.10607i	−0.833158	+	0.553035i	$0.813470\pi$
$164$	−0.726656			−0.0567423
$165$	4.86799	−	6.14134i	0.378973	−	0.478102i
$166$	13.5233			1.04961
$167$		−	8.74531i		−	0.676733i	−0.941014	−	0.338366i	$-0.890126\pi$
$167$		−	8.74531i		−	0.676733i	0.941014	−	0.338366i	$-0.109874\pi$
$168$		−	2.00000i		−	0.154303i
$169$	5.56534			0.428103
$170$	1.27334	+	1.00933i	0.0976610	+	0.0774120i
$171$	−7.78734			−0.595513
$172$		−	5.50466i		−	0.419727i
$173$			5.89730i			0.448363i	0.974547	+	0.224182i	$0.0719709\pi$
$173$			5.89730i			0.448363i	−0.974547	+	0.224182i	$0.928029\pi$
$174$	−2.00000			−0.151620
$175$	9.73599	−	2.28267i	0.735971	−	0.172554i
$176$	3.50466			0.264174
$177$		−	9.29200i		−	0.698430i
$178$			9.55602i			0.716254i
$179$	0.623954			0.0466365			0.0233182	−	0.999728i	$-0.492577\pi$
$179$	0.623954			0.0466365			0.0233182	+	0.999728i	$0.492577\pi$
$180$	−1.75233	−	1.38900i	−0.130611	−	0.103530i
$181$	−14.0700			−1.04582			−0.522908	−	0.852389i	$-0.675153\pi$
$181$	−14.0700			−1.04582			−0.522908	+	0.852389i	$0.675153\pi$
$182$			5.45331i			0.404226i
$183$			4.05135i			0.299485i
$184$	1.00000			0.0737210
$185$	−13.2020	+	16.6553i	−0.970632	+	1.22452i
$186$	−8.28267			−0.607315
$187$			2.54669i			0.186232i
$188$			2.72666i			0.198862i
$189$	−2.00000			−0.145479
$190$	10.8166	−	13.6460i	0.784722	−	0.989985i
$191$	−19.5747			−1.41637			−0.708187	−	0.706025i	$-0.750487\pi$
$191$	−19.5747			−1.41637			−0.708187	+	0.706025i	$0.750487\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	10.0187i		−	0.721159i	−0.932729	−	0.360579i	$-0.882579\pi$
$193$		−	10.0187i		−	0.721159i	0.932729	−	0.360579i	$-0.117421\pi$
$194$	4.54669			0.326433
$195$	4.77801	+	3.78734i	0.342160	+	0.271217i
$196$	−3.00000			−0.214286
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	3.50466i		−	0.249066i
$199$	−23.1893			−1.64385			−0.821923	−	0.569599i	$-0.807099\pi$
$199$	−23.1893			−1.64385			−0.821923	+	0.569599i	$0.807099\pi$
$200$	4.86799	−	1.14134i	0.344219	−	0.0807047i
$201$	4.05135			0.285760
$202$			3.45331i			0.242974i
$203$		−	4.00000i		−	0.280745i
$204$	0.726656			0.0508761
$205$	−1.27334	−	1.00933i	−0.0889342	−	0.0704946i
$206$	−14.4626			−1.00766
$207$		−	1.00000i		−	0.0695048i
$208$			2.72666i			0.189060i
$209$	27.2920			1.88783
$210$	2.77801	−	3.50466i	0.191701	−	0.241845i
$211$	−7.57467			−0.521462			−0.260731	−	0.965411i	$-0.583964\pi$
$211$	−7.57467			−0.521462			−0.260731	+	0.965411i	$0.583964\pi$
$212$			0.231321i			0.0158872i
$213$		−	11.7360i		−	0.804136i
$214$	−13.0607			−0.892810
$215$	7.64600	−	9.64600i	0.521453	−	0.657852i
$216$	−1.00000			−0.0680414
$217$		−	16.5653i		−	1.12453i
$218$			10.9580i			0.742168i
$219$	−3.71733			−0.251194
$220$	6.14134	+	4.86799i	0.414049	+	0.328200i
$221$	−1.98134			−0.133280
$222$			9.50466i			0.637911i
$223$		−	26.5840i		−	1.78020i	−0.455769	−	0.890098i	$-0.650636\pi$
$223$		−	26.5840i		−	1.78020i	0.455769	−	0.890098i	$-0.349364\pi$
$224$	2.00000			0.133631
$225$	−1.14134	−	4.86799i	−0.0760891	−	0.324533i
$226$	−11.7360			−0.780666
$227$			11.9673i			0.794298i	0.917754	+	0.397149i	$0.130000\pi$
$227$			11.9673i			0.794298i	−0.917754	+	0.397149i	$0.870000\pi$
$228$		−	7.78734i		−	0.515729i
$229$	−26.5327			−1.75333			−0.876663	−	0.481104i	$-0.840236\pi$
$229$	−26.5327			−1.75333			−0.876663	+	0.481104i	$0.840236\pi$
$230$	1.75233	+	1.38900i	0.115545	+	0.0915882i
$231$	7.00933			0.461180
$232$		−	2.00000i		−	0.131306i
$233$			24.4040i			1.59876i	0.600825	+	0.799381i	$0.294839\pi$
$233$			24.4040i			1.59876i	−0.600825	+	0.799381i	$0.705161\pi$
$234$	2.72666			0.178247
$235$	−3.78734	+	4.77801i	−0.247059	+	0.311683i
$236$	9.29200			0.604858
$237$			9.73599i			0.632420i
$238$			1.45331i			0.0942043i
$239$	3.55602			0.230020			0.115010	−	0.993364i	$-0.463310\pi$
$239$	3.55602			0.230020			0.115010	+	0.993364i	$0.463310\pi$
$240$	1.38900	−	1.75233i	0.0896598	−	0.113113i
$241$	3.55602			0.229063			0.114532	−	0.993420i	$-0.463463\pi$
$241$	3.55602			0.229063			0.114532	+	0.993420i	$0.463463\pi$
$242$			1.28267i			0.0824533i
$243$			1.00000i			0.0641500i
$244$	−4.05135			−0.259361
$245$	−5.25700	−	4.16701i	−0.335857	−	0.266221i
$246$	−0.726656			−0.0463299
$247$			21.2334i			1.35105i
$248$		−	8.28267i		−	0.525950i
$249$	13.5233			0.857006
$250$	10.1157	+	4.76166i	0.639771	+	0.301154i
$251$	6.05135			0.381958			0.190979	−	0.981594i	$-0.438834\pi$
$251$	6.05135			0.381958			0.190979	+	0.981594i	$0.438834\pi$
$252$		−	2.00000i		−	0.125988i
$253$			3.50466i			0.220336i
$254$	12.2827			0.770683
$255$	1.27334	+	1.00933i	0.0797399	+	0.0632066i
$256$	1.00000			0.0625000
$257$		−	16.9066i		−	1.05461i	−0.849677	−	0.527303i	$-0.823203\pi$
$257$		−	16.9066i		−	1.05461i	0.849677	−	0.527303i	$-0.176797\pi$
$258$		−	5.50466i		−	0.342705i
$259$	−19.0093			−1.18118
$260$	−3.78734	+	4.77801i	−0.234881	+	0.296319i
$261$	−2.00000			−0.123797
$262$		−	14.8480i		−	0.917314i
$263$			0.887968i			0.0547545i	0.999625	+	0.0273772i	$0.00871554\pi$
$263$			0.887968i			0.0547545i	−0.999625	+	0.0273772i	$0.991284\pi$
$264$	3.50466			0.215697
$265$	−0.321306	+	0.405351i	−0.0197376	+	0.0249005i
$266$	15.5747			0.954944
$267$			9.55602i			0.584819i
$268$			4.05135i			0.247476i
$269$	−20.1214			−1.22682			−0.613410	−	0.789764i	$-0.710203\pi$
$269$	−20.1214			−1.22682			−0.613410	+	0.789764i	$0.710203\pi$
$270$	−1.75233	−	1.38900i	−0.106644	−	0.0845321i
$271$	−30.5840			−1.85785			−0.928923	−	0.370273i	$-0.879264\pi$
$271$	−30.5840			−1.85785			−0.928923	+	0.370273i	$0.879264\pi$
$272$			0.726656i			0.0440600i
$273$			5.45331i			0.330050i
$274$	3.27334			0.197750
$275$	4.00000	+	17.0607i	0.241209	+	1.02880i
$276$	1.00000			0.0601929
$277$			4.38538i			0.263492i	0.991284	+	0.131746i	$0.0420583\pi$
$277$			4.38538i			0.263492i	−0.991284	+	0.131746i	$0.957942\pi$
$278$		−	14.0187i		−	0.840783i
$279$	−8.28267			−0.495871
$280$	3.50466	+	2.77801i	0.209444	+	0.166018i
$281$	10.1214			0.603790			0.301895	−	0.953341i	$-0.402381\pi$
$281$	10.1214			0.603790			0.301895	+	0.953341i	$0.402381\pi$
$282$			2.72666i			0.162370i
$283$			25.1820i			1.49692i	0.663182	+	0.748458i	$0.269206\pi$
$283$			25.1820i			1.49692i	−0.663182	+	0.748458i	$0.730794\pi$
$284$	11.7360			0.696403
$285$	10.8166	−	13.6460i	0.640723	−	0.808319i
$286$	−9.55602			−0.565059
$287$		−	1.45331i		−	0.0857864i
$288$		−	1.00000i		−	0.0589256i
$289$	16.4720			0.968939
$290$	2.77801	−	3.50466i	0.163130	−	0.205801i
$291$	4.54669			0.266532
$292$		−	3.71733i		−	0.217540i
$293$			0.759350i			0.0443617i	0.999754	+	0.0221809i	$0.00706097\pi$
$293$			0.759350i			0.0443617i	−0.999754	+	0.0221809i	$0.992939\pi$
$294$	−3.00000			−0.174964
$295$	16.2827	+	12.9066i	0.948014	+	0.751453i
$296$	−9.50466			−0.552447
$297$		−	3.50466i		−	0.203361i
$298$			4.49534i			0.260408i
$299$	−2.72666			−0.157687
$300$	4.86799	−	1.14134i	0.281054	−	0.0658951i
$301$	11.0093			0.634567
$302$			22.3013i			1.28330i
$303$			3.45331i			0.198388i
$304$	7.78734			0.446634
$305$	−7.09931	−	5.62734i	−0.406506	−	0.322221i
$306$	0.726656			0.0415402
$307$			27.5747i			1.57377i	0.617100	+	0.786885i	$0.288307\pi$
$307$			27.5747i			1.57377i	−0.617100	+	0.786885i	$0.711693\pi$
$308$			7.00933i			0.399394i
$309$	−14.4626			−0.822751
$310$	11.5047	−	14.5140i	0.653421	−	0.824339i
$311$	24.1214			1.36780			0.683898	−	0.729577i	$-0.260283\pi$
$311$	24.1214			1.36780			0.683898	+	0.729577i	$0.260283\pi$
$312$			2.72666i			0.154367i
$313$			8.58400i			0.485196i	0.970127	+	0.242598i	$0.0779997\pi$
$313$			8.58400i			0.485196i	−0.970127	+	0.242598i	$0.922000\pi$
$314$	9.60737			0.542175
$315$	2.77801	−	3.50466i	0.156523	−	0.197465i
$316$	−9.73599			−0.547692
$317$		−	24.1214i		−	1.35479i	−0.735619	−	0.677395i	$-0.763109\pi$
$317$		−	24.1214i		−	1.35479i	0.735619	−	0.677395i	$-0.236891\pi$
$318$			0.231321i			0.0129718i
$319$	7.00933			0.392447
$320$	1.75233	+	1.38900i	0.0979583	+	0.0776477i
$321$	−13.0607			−0.728976
$322$			2.00000i			0.111456i
$323$			5.65872i			0.314860i
$324$	−1.00000			−0.0555556
$325$	−13.2733	+	3.11203i	−0.736273	+	0.172624i
$326$	−14.1214			−0.782110
$327$			10.9580i			0.605978i
$328$		−	0.726656i		−	0.0401229i
$329$	−5.45331			−0.300651
$330$	6.14134	+	4.86799i	0.338069	+	0.267974i
$331$	8.10270			0.445365			0.222682	−	0.974891i	$-0.428519\pi$
$331$	8.10270			0.445365			0.222682	+	0.974891i	$0.428519\pi$
$332$			13.5233i			0.742189i
$333$			9.50466i			0.520852i
$334$	8.74531			0.478522
$335$	−5.62734	+	7.09931i	−0.307455	+	0.387877i
$336$	2.00000			0.109109
$337$			24.1214i			1.31397i	0.753902	+	0.656987i	$0.228169\pi$
$337$			24.1214i			1.31397i	−0.753902	+	0.656987i	$0.771831\pi$
$338$			5.56534i			0.302715i
$339$	−11.7360			−0.637411
$340$	−1.00933	+	1.27334i	−0.0547385	+	0.0690567i
$341$	29.0280			1.57195
$342$		−	7.78734i		−	0.421091i
$343$		−	20.0000i		−	1.07990i
$344$	5.50466			0.296792
$345$	1.75233	+	1.38900i	0.0943424	+	0.0747815i
$346$	−5.89730			−0.317041
$347$			21.9160i			1.17651i	0.808675	+	0.588255i	$0.200185\pi$
$347$			21.9160i			1.17651i	−0.808675	+	0.588255i	$0.799815\pi$
$348$		−	2.00000i		−	0.107211i
$349$	−26.5653			−1.42201			−0.711005	−	0.703187i	$-0.751760\pi$
$349$	−26.5653			−1.42201			−0.711005	+	0.703187i	$0.751760\pi$
$350$	2.28267	+	9.73599i	0.122014	+	0.520410i
$351$	2.72666			0.145538
$352$			3.50466i			0.186799i
$353$		−	22.9507i		−	1.22154i	−0.791807	−	0.610772i	$-0.790859\pi$
$353$		−	22.9507i		−	1.22154i	0.791807	−	0.610772i	$-0.209141\pi$
$354$	9.29200			0.493864
$355$	20.5653	+	16.3013i	1.09150	+	0.865185i
$356$	−9.55602			−0.506468
$357$			1.45331i			0.0769175i
$358$			0.623954i			0.0329770i
$359$	−5.02799			−0.265367			−0.132683	−	0.991158i	$-0.542359\pi$
$359$	−5.02799			−0.265367			−0.132683	+	0.991158i	$0.542359\pi$
$360$	1.38900	−	1.75233i	0.0732069	−	0.0923560i
$361$	41.6426			2.19172
$362$		−	14.0700i		−	0.739503i
$363$			1.28267i			0.0673228i
$364$	−5.45331			−0.285831
$365$	5.16338	−	6.51399i	0.270264	−	0.340958i
$366$	−4.05135			−0.211768
$367$		−	7.45331i		−	0.389060i	−0.980897	−	0.194530i	$-0.937682\pi$
$367$		−	7.45331i		−	0.389060i	0.980897	−	0.194530i	$-0.0623181\pi$
$368$			1.00000i			0.0521286i
$369$	−0.726656			−0.0378282
$370$	−16.6553	−	13.2020i	−0.865869	−	0.686340i
$371$	−0.462642			−0.0240192
$372$		−	8.28267i		−	0.429437i
$373$			14.4953i			0.750540i	0.926916	+	0.375270i	$0.122450\pi$
$373$			14.4953i			0.750540i	−0.926916	+	0.375270i	$0.877550\pi$
$374$	−2.54669			−0.131686
$375$	10.1157	+	4.76166i	0.522370	+	0.245891i
$376$	−2.72666			−0.140617
$377$			5.45331i			0.280860i
$378$		−	2.00000i		−	0.102869i
$379$	−17.1379			−0.880317			−0.440159	−	0.897920i	$-0.645078\pi$
$379$	−17.1379			−0.880317			−0.440159	+	0.897920i	$0.645078\pi$
$380$	13.6460	+	10.8166i	0.700025	+	0.554882i
$381$	12.2827			0.629260
$382$		−	19.5747i		−	1.00153i
$383$			0.565344i			0.0288878i	0.999896	+	0.0144439i	$0.00459779\pi$
$383$			0.565344i			0.0288878i	−0.999896	+	0.0144439i	$0.995402\pi$
$384$	1.00000			0.0510310
$385$	−9.73599	+	12.2827i	−0.496192	+	0.625983i
$386$	10.0187			0.509936
$387$		−	5.50466i		−	0.279818i
$388$			4.54669i			0.230823i
$389$	29.5233			1.49689			0.748446	−	0.663196i	$-0.230800\pi$
$389$	29.5233			1.49689			0.748446	+	0.663196i	$0.230800\pi$
$390$	−3.78734	+	4.77801i	−0.191779	+	0.241944i
$391$	−0.726656			−0.0367486
$392$		−	3.00000i		−	0.151523i
$393$		−	14.8480i		−	0.748983i
$394$	2.00000			0.100759
$395$	−17.0607	−	13.5233i	−0.858416	−	0.680432i
$396$	3.50466			0.176116
$397$			37.7360i			1.89391i	0.321359	+	0.946957i	$0.395860\pi$
$397$			37.7360i			1.89391i	−0.321359	+	0.946957i	$0.604140\pi$
$398$		−	23.1893i		−	1.16237i
$399$	15.5747			0.779709
$400$	1.14134	+	4.86799i	0.0570668	+	0.243400i
$401$	−6.90663			−0.344900			−0.172450	−	0.985018i	$-0.555168\pi$
$401$	−6.90663			−0.344900			−0.172450	+	0.985018i	$0.555168\pi$
$402$			4.05135i			0.202063i
$403$			22.5840i			1.12499i
$404$	−3.45331			−0.171809
$405$	−1.75233	−	1.38900i	−0.0870741	−	0.0690202i
$406$	4.00000			0.198517
$407$		−	33.3107i		−	1.65115i
$408$			0.726656i			0.0359749i
$409$	−2.00000			−0.0988936			−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000			−0.0988936			−0.0494468	+	0.998777i	$0.515746\pi$
$410$	1.00933	−	1.27334i	0.0498472	−	0.0628860i
$411$	3.27334			0.161462
$412$		−	14.4626i		−	0.712523i
$413$			18.5840i			0.914459i
$414$	1.00000			0.0491473
$415$	−18.7839	+	23.6974i	−0.922068	+	1.16326i
$416$	−2.72666			−0.133685
$417$		−	14.0187i		−	0.686497i
$418$			27.2920i			1.33490i
$419$	−27.9673			−1.36629			−0.683146	−	0.730282i	$-0.739389\pi$
$419$	−27.9673			−1.36629			−0.683146	+	0.730282i	$0.739389\pi$
$420$	3.50466	+	2.77801i	0.171010	+	0.135553i
$421$	2.59804			0.126621			0.0633103	−	0.997994i	$-0.479834\pi$
$421$	2.59804			0.126621			0.0633103	+	0.997994i	$0.479834\pi$
$422$		−	7.57467i		−	0.368729i
$423$			2.72666i			0.132575i
$424$	−0.231321			−0.0112339
$425$	−3.53736	+	0.829359i	−0.171587	+	0.0402298i
$426$	11.7360			0.568610
$427$		−	8.10270i		−	0.392117i
$428$		−	13.0607i		−	0.631312i
$429$	−9.55602			−0.461369
$430$	9.64600	+	7.64600i	0.465171	+	0.368723i
$431$	−15.2147			−0.732868			−0.366434	−	0.930444i	$-0.619421\pi$
$431$	−15.2147			−0.732868			−0.366434	+	0.930444i	$0.619421\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	27.1307i		−	1.30382i	−0.758297	−	0.651909i	$-0.773968\pi$
$433$		−	27.1307i		−	1.30382i	0.758297	−	0.651909i	$-0.226032\pi$
$434$	16.5653			0.795162
$435$	2.77801	−	3.50466i	0.133195	−	0.168036i
$436$	−10.9580			−0.524792
$437$			7.78734i			0.372519i
$438$		−	3.71733i		−	0.177621i
$439$	1.65872			0.0791663			0.0395832	−	0.999216i	$-0.487397\pi$
$439$	1.65872			0.0791663			0.0395832	+	0.999216i	$0.487397\pi$
$440$	−4.86799	+	6.14134i	−0.232072	+	0.292777i
$441$	−3.00000			−0.142857
$442$		−	1.98134i		−	0.0942429i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	−9.50466			−0.451071
$445$	−16.7453	−	13.2733i	−0.793804	−	0.629217i
$446$	26.5840			1.25879
$447$			4.49534i			0.212622i
$448$			2.00000i			0.0944911i
$449$	14.9507			0.705568			0.352784	−	0.935705i	$-0.385235\pi$
$449$	14.9507			0.705568			0.352784	+	0.935705i	$0.385235\pi$
$450$	4.86799	−	1.14134i	0.229479	−	0.0538031i
$451$	2.54669			0.119919
$452$		−	11.7360i		−	0.552014i
$453$			22.3013i			1.04781i
$454$	−11.9673			−0.561654
$455$	−9.55602	−	7.57467i	−0.447993	−	0.355106i
$456$	7.78734			0.364675
$457$		−	1.43466i		−	0.0671104i	−0.999437	−	0.0335552i	$-0.989317\pi$
$457$		−	1.43466i		−	0.0671104i	0.999437	−	0.0335552i	$-0.0106830\pi$
$458$		−	26.5327i		−	1.23979i
$459$	0.726656			0.0339174
$460$	−1.38900	+	1.75233i	−0.0647626	+	0.0817029i
$461$	−13.5747			−0.632236			−0.316118	−	0.948720i	$-0.602379\pi$
$461$	−13.5747			−0.632236			−0.316118	+	0.948720i	$0.602379\pi$
$462$			7.00933i			0.326103i
$463$			1.73599i			0.0806781i	0.999186	+	0.0403390i	$0.0128438\pi$
$463$			1.73599i			0.0806781i	−0.999186	+	0.0403390i	$0.987156\pi$
$464$	2.00000			0.0928477
$465$	11.5047	−	14.5140i	0.533516	−	0.673070i
$466$	−24.4040			−1.13049
$467$			28.1727i			1.30368i	0.758358	+	0.651839i	$0.226002\pi$
$467$			28.1727i			1.30368i	−0.758358	+	0.651839i	$0.773998\pi$
$468$			2.72666i			0.126040i
$469$	−8.10270			−0.374148
$470$	−4.77801	−	3.78734i	−0.220393	−	0.174697i
$471$	9.60737			0.442684
$472$			9.29200i			0.427699i
$473$			19.2920i			0.887047i
$474$	−9.73599			−0.447189
$475$	8.88797	+	37.9087i	0.407808	+	1.73937i
$476$	−1.45331			−0.0666125
$477$			0.231321i			0.0105915i
$478$			3.55602i			0.162648i
$479$	26.3786			1.20527			0.602634	−	0.798017i	$-0.294118\pi$
$479$	26.3786			1.20527			0.602634	+	0.798017i	$0.294118\pi$
$480$	1.75233	+	1.38900i	0.0799827	+	0.0633991i
$481$	25.9160			1.18167
$482$			3.55602i			0.161972i
$483$			2.00000i			0.0910032i
$484$	−1.28267			−0.0583033
$485$	−6.31537	+	7.96731i	−0.286766	+	0.361777i
$486$	−1.00000			−0.0453609
$487$		−	20.2827i		−	0.919096i	−0.888153	−	0.459548i	$-0.848011\pi$
$487$		−	20.2827i		−	0.919096i	0.888153	−	0.459548i	$-0.151989\pi$
$488$		−	4.05135i		−	0.183396i
$489$	−14.1214			−0.638590
$490$	4.16701	−	5.25700i	0.188246	−	0.237487i
$491$	18.6426			0.841329			0.420665	−	0.907216i	$-0.361797\pi$
$491$	18.6426			0.841329			0.420665	+	0.907216i	$0.361797\pi$
$492$		−	0.726656i		−	0.0327602i
$493$			1.45331i			0.0654539i
$494$	−21.2334			−0.955335
$495$	6.14134	+	4.86799i	0.276033	+	0.218800i
$496$	8.28267			0.371903
$497$			23.4720i			1.05286i
$498$			13.5233i			0.605995i
$499$	−20.9907			−0.939671			−0.469836	−	0.882754i	$-0.655687\pi$
$499$	−20.9907			−0.939671			−0.469836	+	0.882754i	$0.655687\pi$
$500$	−4.76166	+	10.1157i	−0.212948	+	0.452386i
$501$	8.74531			0.390712
$502$			6.05135i			0.270085i
$503$		−	13.5560i		−	0.604433i	−0.953239	−	0.302216i	$-0.902273\pi$
$503$		−	13.5560i		−	0.604433i	0.953239	−	0.302216i	$-0.0977265\pi$
$504$	2.00000			0.0890871
$505$	−6.05135	−	4.79667i	−0.269282	−	0.213449i
$506$	−3.50466			−0.155801
$507$			5.56534i			0.247166i
$508$			12.2827i			0.544955i
$509$	26.0000			1.15243			0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000			1.15243			0.576215	+	0.817298i	$0.304529\pi$
$510$	−1.00933	+	1.27334i	−0.0446938	+	0.0563846i
$511$	7.43466			0.328890
$512$			1.00000i			0.0441942i
$513$		−	7.78734i		−	0.343819i
$514$	16.9066			0.745719
$515$	20.0887	−	25.3434i	0.885212	−	1.11676i
$516$	5.50466			0.242329
$517$		−	9.55602i		−	0.420273i
$518$		−	19.0093i		−	0.835222i
$519$	−5.89730			−0.258863
$520$	−4.77801	−	3.78734i	−0.209530	−	0.166086i
$521$	−44.6027			−1.95408			−0.977039	−	0.213061i	$-0.931657\pi$
$521$	−44.6027			−1.95408			−0.977039	+	0.213061i	$0.931657\pi$
$522$		−	2.00000i		−	0.0875376i
$523$			19.7287i			0.862677i	0.902190	+	0.431339i	$0.141959\pi$
$523$			19.7287i			0.862677i	−0.902190	+	0.431339i	$0.858041\pi$
$524$	14.8480			0.648639
$525$	2.28267	+	9.73599i	0.0996240	+	0.424913i
$526$	−0.887968			−0.0387173
$527$			6.01866i			0.262177i
$528$			3.50466i			0.152521i
$529$	−1.00000			−0.0434783
$530$	−0.405351	−	0.321306i	−0.0176073	−	0.0139566i
$531$	9.29200			0.403238
$532$			15.5747i			0.675248i
$533$			1.98134i			0.0858215i
$534$	−9.55602			−0.413529
$535$	18.1413	−	22.8867i	0.784318	−	0.989476i
$536$	−4.05135			−0.174992
$537$			0.623954i			0.0269256i
$538$		−	20.1214i		−	0.867493i
$539$	10.5140			0.452870
$540$	1.38900	−	1.75233i	0.0597732	−	0.0754084i
$541$	−13.4720			−0.579205			−0.289603	−	0.957147i	$-0.593523\pi$
$541$	−13.4720			−0.579205			−0.289603	+	0.957147i	$0.593523\pi$
$542$		−	30.5840i		−	1.31370i
$543$		−	14.0700i		−	0.603802i
$544$	−0.726656			−0.0311551
$545$	−19.2020	−	15.2207i	−0.822524	−	0.651982i
$546$	−5.45331			−0.233380
$547$		−	23.0466i		−	0.985403i	−0.870198	−	0.492702i	$-0.836009\pi$
$547$		−	23.0466i		−	0.985403i	0.870198	−	0.492702i	$-0.163991\pi$
$548$			3.27334i			0.139830i
$549$	−4.05135			−0.172907
$550$	−17.0607	+	4.00000i	−0.727470	+	0.170561i
$551$	15.5747			0.663503
$552$			1.00000i			0.0425628i
$553$		−	19.4720i		−	0.828032i
$554$	−4.38538			−0.186317
$555$	−16.6553	−	13.2020i	−0.706979	−	0.560394i
$556$	14.0187			0.594524
$557$		−	37.2593i		−	1.57873i	−0.613926	−	0.789364i	$-0.710411\pi$
$557$		−	37.2593i		−	1.57873i	0.613926	−	0.789364i	$-0.289589\pi$
$558$		−	8.28267i		−	0.350633i
$559$	−15.0093			−0.634827
$560$	−2.77801	+	3.50466i	−0.117392	+	0.148099i
$561$	−2.54669			−0.107521
$562$			10.1214i			0.426944i
$563$		−	46.5513i		−	1.96190i	−0.194251	−	0.980952i	$-0.562228\pi$
$563$		−	46.5513i		−	1.96190i	0.194251	−	0.980952i	$-0.437772\pi$
$564$	−2.72666			−0.114813
$565$	16.3013	−	20.5653i	0.685802	−	0.865191i
$566$	−25.1820			−1.05848
$567$		−	2.00000i		−	0.0839921i
$568$			11.7360i			0.492431i
$569$	20.0000			0.838444			0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000			0.838444			0.419222	+	0.907884i	$0.362303\pi$
$570$	13.6460	+	10.8166i	0.571568	+	0.453059i
$571$	−13.6660			−0.571903			−0.285952	−	0.958244i	$-0.592310\pi$
$571$	−13.6660			−0.571903			−0.285952	+	0.958244i	$0.592310\pi$
$572$		−	9.55602i		−	0.399557i
$573$		−	19.5747i		−	0.817744i
$574$	1.45331			0.0606601
$575$	−4.86799	+	1.14134i	−0.203009	+	0.0475970i
$576$	1.00000			0.0416667
$577$		−	6.30133i		−	0.262328i	−0.991361	−	0.131164i	$-0.958129\pi$
$577$		−	6.30133i		−	0.262328i	0.991361	−	0.131164i	$-0.0418714\pi$
$578$			16.4720i			0.685144i
$579$	10.0187			0.416361
$580$	3.50466	+	2.77801i	0.145523	+	0.115350i
$581$	−27.0466			−1.12208
$582$			4.54669i			0.188466i
$583$		−	0.810702i		−	0.0335758i
$584$	3.71733			0.153824
$585$	−3.78734	+	4.77801i	−0.156587	+	0.197546i
$586$	−0.759350			−0.0313685
$587$		−	35.5747i		−	1.46832i	−0.678974	−	0.734162i	$-0.737575\pi$
$587$		−	35.5747i		−	1.46832i	0.678974	−	0.734162i	$-0.262425\pi$
$588$		−	3.00000i		−	0.123718i
$589$	64.5000			2.65767
$590$	−12.9066	+	16.2827i	−0.531357	+	0.670347i
$591$	2.00000			0.0822690
$592$		−	9.50466i		−	0.390639i
$593$		−	4.54669i		−	0.186710i	−0.995633	−	0.0933550i	$-0.970241\pi$
$593$		−	4.54669i		−	0.186710i	0.995633	−	0.0933550i	$-0.0297592\pi$
$594$	3.50466			0.143798
$595$	−2.54669	−	2.01866i	−0.104404	−	0.0827569i
$596$	−4.49534			−0.184136
$597$		−	23.1893i		−	0.949075i
$598$		−	2.72666i		−	0.111501i
$599$	−16.1214			−0.658701			−0.329350	−	0.944208i	$-0.606830\pi$
$599$	−16.1214			−0.658701			−0.329350	+	0.944208i	$0.606830\pi$
$600$	1.14134	+	4.86799i	0.0465949	+	0.198735i
$601$	−9.39470			−0.383218			−0.191609	−	0.981471i	$-0.561371\pi$
$601$	−9.39470			−0.383218			−0.191609	+	0.981471i	$0.561371\pi$
$602$			11.0093i			0.448707i
$603$			4.05135i			0.164984i
$604$	−22.3013			−0.907428
$605$	−2.24767	−	1.78164i	−0.0913807	−	0.0724338i
$606$	−3.45331			−0.140281
$607$			10.9066i			0.442686i	0.975196	+	0.221343i	$0.0710441\pi$
$607$			10.9066i			0.442686i	−0.975196	+	0.221343i	$0.928956\pi$
$608$			7.78734i			0.315818i
$609$	4.00000			0.162088
$610$	5.62734	−	7.09931i	0.227844	−	0.287443i
$611$	7.43466			0.300774
$612$			0.726656i			0.0293733i
$613$		−	43.4206i		−	1.75374i	−0.480725	−	0.876871i	$-0.659627\pi$
$613$		−	43.4206i		−	1.75374i	0.480725	−	0.876871i	$-0.340373\pi$
$614$	−27.5747			−1.11282
$615$	1.00933	−	1.27334i	0.0407001	−	0.0513462i
$616$	−7.00933			−0.282414
$617$			20.0959i			0.809031i	0.914531	+	0.404516i	$0.132560\pi$
$617$			20.0959i			0.809031i	−0.914531	+	0.404516i	$0.867440\pi$
$618$		−	14.4626i		−	0.581773i
$619$	−27.3247			−1.09827			−0.549136	−	0.835733i	$-0.685043\pi$
$619$	−27.3247			−1.09827			−0.549136	+	0.835733i	$0.685043\pi$
$620$	14.5140	+	11.5047i	0.582896	+	0.462038i
$621$	1.00000			0.0401286
$622$			24.1214i			0.967178i
$623$		−	19.1120i		−	0.765707i
$624$	−2.72666			−0.109154
$625$	−22.3947	+	11.1120i	−0.895788	+	0.444481i
$626$	−8.58400			−0.343086
$627$			27.2920i			1.08994i
$628$			9.60737i			0.383376i
$629$	6.90663			0.275385
$630$	3.50466	+	2.77801i	0.139629	+	0.110678i
$631$	39.8947			1.58818			0.794091	−	0.607799i	$-0.207947\pi$
$631$	39.8947			1.58818			0.794091	+	0.607799i	$0.207947\pi$
$632$		−	9.73599i		−	0.387277i
$633$		−	7.57467i		−	0.301066i
$634$	24.1214			0.957982
$635$	−17.0607	+	21.5233i	−0.677032	+	0.854127i
$636$	−0.231321			−0.00917247
$637$			8.17997i			0.324102i
$638$			7.00933i			0.277502i
$639$	11.7360			0.464268
$640$	−1.38900	+	1.75233i	−0.0549052	+	0.0692670i
$641$	49.1680			1.94202			0.971010	−	0.239040i	$-0.0768327\pi$
$641$	49.1680			1.94202			0.971010	+	0.239040i	$0.0768327\pi$
$642$		−	13.0607i		−	0.515464i
$643$		−	20.9766i		−	0.827238i	−0.910450	−	0.413619i	$-0.864265\pi$
$643$		−	20.9766i		−	0.827238i	0.910450	−	0.413619i	$-0.135735\pi$
$644$	−2.00000			−0.0788110
$645$	9.64600	+	7.64600i	0.379811	+	0.301061i
$646$	−5.65872			−0.222639
$647$			25.9813i			1.02143i	0.859749	+	0.510716i	$0.170620\pi$
$647$			25.9813i			1.02143i	−0.859749	+	0.510716i	$0.829380\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−32.5653			−1.27830
$650$	−3.11203	−	13.2733i	−0.122064	−	0.520623i
$651$	16.5653			0.649247
$652$		−	14.1214i		−	0.553035i
$653$		−	0.0840454i		−	0.00328895i	−0.999999	−	0.00164448i	$-0.999477\pi$
$653$		−	0.0840454i		−	0.00328895i	0.999999	−	0.00164448i	$-0.000523453\pi$
$654$	−10.9580			−0.428491
$655$	26.0187	+	20.6240i	1.01663	+	0.805845i
$656$	0.726656			0.0283712
$657$		−	3.71733i		−	0.145027i
$658$		−	5.45331i		−	0.212592i
$659$	−10.6167			−0.413568			−0.206784	−	0.978387i	$-0.566300\pi$
$659$	−10.6167			−0.413568			−0.206784	+	0.978387i	$0.566300\pi$
$660$	−4.86799	+	6.14134i	−0.189486	+	0.239051i
$661$	−39.9860			−1.55527			−0.777637	−	0.628714i	$-0.783582\pi$
$661$	−39.9860			−1.55527			−0.777637	+	0.628714i	$0.783582\pi$
$662$			8.10270i			0.314920i
$663$		−	1.98134i		−	0.0769490i
$664$	−13.5233			−0.524807
$665$	−21.6333	+	27.2920i	−0.838903	+	1.05834i
$666$	−9.50466			−0.368298
$667$			2.00000i			0.0774403i
$668$			8.74531i			0.338366i
$669$	26.5840			1.02780
$670$	−7.09931	−	5.62734i	−0.274270	−	0.217403i
$671$	14.1986			0.548132
$672$			2.00000i			0.0771517i
$673$			2.86667i			0.110502i	0.998472	+	0.0552511i	$0.0175959\pi$
$673$			2.86667i			0.110502i	−0.998472	+	0.0552511i	$0.982404\pi$
$674$	−24.1214			−0.929120
$675$	4.86799	−	1.14134i	0.187369	−	0.0439300i
$676$	−5.56534			−0.214052
$677$			3.76868i			0.144842i	0.997374	+	0.0724211i	$0.0230725\pi$
$677$			3.76868i			0.144842i	−0.997374	+	0.0724211i	$0.976927\pi$
$678$		−	11.7360i		−	0.450718i
$679$	−9.09337			−0.348972
$680$	−1.27334	−	1.00933i	−0.0488305	−	0.0387060i
$681$	−11.9673			−0.458588
$682$			29.0280i			1.11154i
$683$		−	39.6120i		−	1.51571i	−0.652423	−	0.757855i	$-0.726247\pi$
$683$		−	39.6120i		−	1.51571i	0.652423	−	0.757855i	$-0.273753\pi$
$684$	7.78734			0.297756
$685$	−4.54669	+	5.73599i	−0.173720	+	0.219161i
$686$	20.0000			0.763604
$687$		−	26.5327i		−	1.01228i
$688$			5.50466i			0.209863i
$689$	0.630732			0.0240290
$690$	−1.38900	+	1.75233i	−0.0528785	+	0.0667101i
$691$	−49.0653			−1.86653			−0.933266	−	0.359186i	$-0.883054\pi$
$691$	−49.0653			−1.86653			−0.933266	+	0.359186i	$0.883054\pi$
$692$		−	5.89730i		−	0.224182i
$693$			7.00933i			0.266262i
$694$	−21.9160			−0.831918
$695$	24.5653	+	19.4720i	0.931817	+	0.738614i
$696$	2.00000			0.0758098
$697$			0.528030i			0.0200005i
$698$		−	26.5653i		−	1.00551i
$699$	−24.4040			−0.923045
$700$	−9.73599	+	2.28267i	−0.367986	+	0.0862769i
$701$	−10.5140			−0.397108			−0.198554	−	0.980090i	$-0.563625\pi$
$701$	−10.5140			−0.397108			−0.198554	+	0.980090i	$0.563625\pi$
$702$			2.72666i			0.102911i
$703$		−	74.0160i		−	2.79157i
$704$	−3.50466			−0.132087
$705$	−4.77801	−	3.78734i	−0.179950	−	0.142639i
$706$	22.9507			0.863762
$707$		−	6.90663i		−	0.259750i
$708$			9.29200i			0.349215i
$709$	17.1447			0.643884			0.321942	−	0.946759i	$-0.395664\pi$
$709$	17.1447			0.643884			0.321942	+	0.946759i	$0.395664\pi$
$710$	−16.3013	+	20.5653i	−0.611778	+	0.771804i
$711$	−9.73599			−0.365128
$712$		−	9.55602i		−	0.358127i
$713$			8.28267i			0.310189i
$714$	−1.45331			−0.0543889
$715$	13.2733	−	16.7453i	0.496395	−	0.626239i
$716$	−0.623954			−0.0233182
$717$			3.55602i			0.132802i
$718$		−	5.02799i		−	0.187643i
$719$	−29.0093			−1.08187			−0.540933	−	0.841066i	$-0.681929\pi$
$719$	−29.0093			−1.08187			−0.540933	+	0.841066i	$0.681929\pi$
$720$	1.75233	+	1.38900i	0.0653056	+	0.0517651i
$721$	28.9253			1.07723
$722$			41.6426i			1.54978i
$723$			3.55602i			0.132250i
$724$	14.0700			0.522908
$725$	2.28267	+	9.73599i	0.0847763	+	0.361585i
$726$	−1.28267			−0.0476044
$727$			38.9253i			1.44366i	0.692071	+	0.721829i	$0.256698\pi$
$727$			38.9253i			1.44366i	−0.692071	+	0.721829i	$0.743302\pi$
$728$		−	5.45331i		−	0.202113i
$729$	−1.00000			−0.0370370
$730$	6.51399	+	5.16338i	0.241094	+	0.191105i
$731$	−4.00000			−0.147945
$732$		−	4.05135i		−	0.149742i
$733$		−	5.50466i		−	0.203319i	−0.994819	−	0.101660i	$-0.967585\pi$
$733$		−	5.50466i		−	0.203319i	0.994819	−	0.101660i	$-0.0324153\pi$
$734$	7.45331			0.275107
$735$	4.16701	−	5.25700i	0.153703	−	0.193907i
$736$	−1.00000			−0.0368605
$737$		−	14.1986i		−	0.523013i
$738$		−	0.726656i		−	0.0267486i
$739$	−28.6027			−1.05217			−0.526083	−	0.850433i	$-0.676340\pi$
$739$	−28.6027			−1.05217			−0.526083	+	0.850433i	$0.676340\pi$
$740$	13.2020	−	16.6553i	0.485316	−	0.612262i
$741$	−21.2334			−0.780028
$742$		−	0.462642i		−	0.0169841i
$743$		−	9.98134i		−	0.366180i	−0.983096	−	0.183090i	$-0.941390\pi$
$743$		−	9.98134i		−	0.366180i	0.983096	−	0.183090i	$-0.0586100\pi$
$744$	8.28267			0.303657
$745$	−7.87732	−	6.24404i	−0.288603	−	0.228764i
$746$	−14.4953			−0.530712
$747$			13.5233i			0.494792i
$748$		−	2.54669i		−	0.0931161i
$749$	26.1214			0.954454
$750$	−4.76166	+	10.1157i	−0.173871	+	0.369372i
$751$	−21.8387			−0.796905			−0.398453	−	0.917189i	$-0.630453\pi$
$751$	−21.8387			−0.796905			−0.398453	+	0.917189i	$0.630453\pi$
$752$		−	2.72666i		−	0.0994309i
$753$			6.05135i			0.220524i
$754$	−5.45331			−0.198598
$755$	−39.0793	−	30.9766i	−1.42224	−	1.12736i
$756$	2.00000			0.0727393
$757$		−	16.5513i		−	0.601568i	−0.953692	−	0.300784i	$-0.902752\pi$
$757$		−	16.5513i		−	0.601568i	0.953692	−	0.300784i	$-0.0972482\pi$
$758$		−	17.1379i		−	0.622478i
$759$	−3.50466			−0.127211
$760$	−10.8166	+	13.6460i	−0.392361	+	0.494992i
$761$	20.5840			0.746169			0.373085	−	0.927797i	$-0.378300\pi$
$761$	20.5840			0.746169			0.373085	+	0.927797i	$0.378300\pi$
$762$			12.2827i			0.444954i
$763$		−	21.9160i		−	0.793411i
$764$	19.5747			0.708187
$765$	−1.00933	+	1.27334i	−0.0364924	+	0.0460378i
$766$	−0.565344			−0.0204267
$767$		−	25.3361i		−	0.914833i
$768$			1.00000i			0.0360844i
$769$	−7.76142			−0.279884			−0.139942	−	0.990160i	$-0.544692\pi$
$769$	−7.76142			−0.279884			−0.139942	+	0.990160i	$0.544692\pi$
$770$	−12.2827	−	9.73599i	−0.442637	−	0.350861i
$771$	16.9066			0.608877
$772$			10.0187i			0.360579i
$773$			21.8247i			0.784978i	0.919757	+	0.392489i	$0.128386\pi$
$773$			21.8247i			0.784978i	−0.919757	+	0.392489i	$0.871614\pi$
$774$	5.50466			0.197861
$775$	9.45331	+	40.3200i	0.339573	+	1.44834i
$776$	−4.54669			−0.163217
$777$		−	19.0093i		−	0.681956i
$778$			29.5233i			1.05846i
$779$	5.65872			0.202745
$780$	−4.77801	−	3.78734i	−0.171080	−	0.135608i
$781$	−41.1307			−1.47177
$782$		−	0.726656i		−	0.0259852i
$783$		−	2.00000i		−	0.0714742i
$784$	3.00000			0.107143
$785$	−13.3447	+	16.8353i	−0.476292	+	0.600878i
$786$	14.8480			0.529611
$787$		−	46.4299i		−	1.65505i	−0.561430	−	0.827524i	$-0.689748\pi$
$787$		−	46.4299i		−	1.65505i	0.561430	−	0.827524i	$-0.310252\pi$
$788$			2.00000i			0.0712470i
$789$	−0.887968			−0.0316125
$790$	13.5233	−	17.0607i	0.481138	−	0.606992i
$791$	23.4720			0.834567
$792$			3.50466i			0.124533i
$793$			11.0466i			0.392278i
$794$	−37.7360			−1.33920
$795$	−0.405351	−	0.321306i	−0.0143763	−	0.0113955i
$796$	23.1893			0.821923
$797$			44.3340i			1.57039i	0.619248	+	0.785196i	$0.287438\pi$
$797$			44.3340i			1.57039i	−0.619248	+	0.785196i	$0.712562\pi$
$798$			15.5747i			0.551337i
$799$	1.98134			0.0700949
$800$	−4.86799	+	1.14134i	−0.172110	+	0.0403523i
$801$	−9.55602			−0.337645
$802$		−	6.90663i		−	0.243881i
$803$			13.0280i			0.459748i
$804$	−4.05135			−0.142880
$805$	−3.50466	−	2.77801i	−0.123523	−	0.0979119i
$806$	−22.5840			−0.795488
$807$		−	20.1214i		−	0.708305i
$808$		−	3.45331i		−	0.121487i
$809$	1.96269			0.0690043			0.0345022	−	0.999405i	$-0.489015\pi$
$809$	1.96269			0.0690043			0.0345022	+	0.999405i	$0.489015\pi$
$810$	1.38900	−	1.75233i	0.0488046	−	0.0615707i
$811$	31.8973			1.12007			0.560033	−	0.828470i	$-0.310789\pi$
$811$	31.8973			1.12007			0.560033	+	0.828470i	$0.310789\pi$
$812$			4.00000i			0.140372i
$813$		−	30.5840i		−	1.07263i
$814$	33.3107			1.16754
$815$	19.6146	−	24.7453i	0.687070	−	0.866791i
$816$	−0.726656			−0.0254381
$817$			42.8667i			1.49972i
$818$		−	2.00000i		−	0.0699284i
$819$	−5.45331			−0.190554
$820$	1.27334	+	1.00933i	0.0444671	+	0.0352473i
$821$	11.4906			0.401026			0.200513	−	0.979691i	$-0.435739\pi$
$821$	11.4906			0.401026			0.200513	+	0.979691i	$0.435739\pi$
$822$			3.27334i			0.114171i
$823$		−	37.1307i		−	1.29429i	−0.762365	−	0.647147i	$-0.775962\pi$
$823$		−	37.1307i		−	1.29429i	0.762365	−	0.647147i	$-0.224038\pi$
$824$	14.4626			0.503830
$825$	−17.0607	+	4.00000i	−0.593977	+	0.139262i
$826$	−18.5840			−0.646620
$827$			40.2100i			1.39824i	0.715005	+	0.699120i	$0.246425\pi$
$827$			40.2100i			1.39824i	−0.715005	+	0.699120i	$0.753575\pi$
$828$			1.00000i			0.0347524i
$829$	6.88797			0.239229			0.119615	−	0.992820i	$-0.461834\pi$
$829$	6.88797			0.239229			0.119615	+	0.992820i	$0.461834\pi$
$830$	−23.6974	−	18.7839i	−0.822547	−	0.652000i
$831$	−4.38538			−0.152127
$832$		−	2.72666i		−	0.0945298i
$833$			2.17997i			0.0755315i
$834$	14.0187			0.485426
$835$	−12.1473	+	15.3247i	−0.420374	+	0.530333i
$836$	−27.2920			−0.943914
$837$		−	8.28267i		−	0.286291i
$838$		−	27.9673i		−	0.966115i
$839$	26.3786			0.910690			0.455345	−	0.890315i	$-0.349516\pi$
$839$	26.3786			0.910690			0.455345	+	0.890315i	$0.349516\pi$
$840$	−2.77801	+	3.50466i	−0.0958504	+	0.120922i
$841$	−25.0000			−0.862069
$842$			2.59804i			0.0895343i
$843$			10.1214i			0.348598i
$844$	7.57467			0.260731
$845$	−9.75233	−	7.73029i	−0.335490	−	0.265930i
$846$	−2.72666			−0.0937444
$847$		−	2.56534i		−	0.0881463i
$848$		−	0.231321i		−	0.00794359i
$849$	−25.1820			−0.864245
$850$	−0.829359	−	3.53736i	−0.0284468	−	0.121330i
$851$	9.50466			0.325816
$852$			11.7360i			0.402068i
$853$			11.7546i			0.402471i	0.979543	+	0.201236i	$0.0644957\pi$
$853$			11.7546i			0.402471i	−0.979543	+	0.201236i	$0.935504\pi$
$854$	8.10270			0.277269
$855$	13.6460	+	10.8166i	0.466683	+	0.369921i
$856$	13.0607			0.446405
$857$			53.5347i			1.82871i	0.404912	+	0.914356i	$0.367302\pi$
$857$			53.5347i			1.82871i	−0.404912	+	0.914356i	$0.632698\pi$
$858$		−	9.55602i		−	0.326237i
$859$	7.11203			0.242659			0.121330	−	0.992612i	$-0.461284\pi$
$859$	7.11203			0.242659			0.121330	+	0.992612i	$0.461284\pi$
$860$	−7.64600	+	9.64600i	−0.260726	+	0.328926i
$861$	1.45331			0.0495288
$862$		−	15.2147i		−	0.518216i
$863$			28.0373i			0.954401i	0.878794	+	0.477201i	$0.158349\pi$
$863$			28.0373i			0.954401i	−0.878794	+	0.477201i	$0.841651\pi$
$864$	1.00000			0.0340207
$865$	8.19137	−	10.3340i	0.278515	−	0.351367i
$866$	27.1307			0.921938
$867$			16.4720i			0.559417i
$868$			16.5653i			0.562264i
$869$	34.1214			1.15749
$870$	3.50466	+	2.77801i	0.118819	+	0.0941833i
$871$	11.0466			0.374301
$872$		−	10.9580i		−	0.371084i
$873$			4.54669i			0.153882i
$874$	−7.78734			−0.263411
$875$	−20.2313	−	9.52332i	−0.683943	−	0.321947i
$876$	3.71733			0.125597
$877$			46.4040i			1.56695i	0.621422	+	0.783476i	$0.286555\pi$
$877$			46.4040i			1.56695i	−0.621422	+	0.783476i	$0.713445\pi$
$878$			1.65872i			0.0559790i
$879$	−0.759350			−0.0256123
$880$	−6.14134	−	4.86799i	−0.207024	−	0.164100i
$881$	14.6494			0.493550			0.246775	−	0.969073i	$-0.420629\pi$
$881$	14.6494			0.493550			0.246775	+	0.969073i	$0.420629\pi$
$882$		−	3.00000i		−	0.101015i
$883$		−	13.7614i		−	0.463109i	−0.972822	−	0.231554i	$-0.925619\pi$
$883$		−	13.7614i		−	0.463109i	0.972822	−	0.231554i	$-0.0743811\pi$
$884$	1.98134			0.0666398
$885$	−12.9066	+	16.2827i	−0.433851	+	0.547336i
$886$	−4.00000			−0.134383
$887$		−	35.8573i		−	1.20397i	−0.798507	−	0.601986i	$-0.794376\pi$
$887$		−	35.8573i		−	1.20397i	0.798507	−	0.601986i	$-0.205624\pi$
$888$		−	9.50466i		−	0.318956i
$889$	−24.5653			−0.823895
$890$	13.2733	−	16.7453i	0.444923	−	0.561304i
$891$	3.50466			0.117411
$892$			26.5840i			0.890098i
$893$		−	21.2334i		−	0.710548i
$894$	−4.49534			−0.150347
$895$	−1.09337	−	0.866674i	−0.0365475	−	0.0289697i
$896$	−2.00000			−0.0668153
$897$		−	2.72666i		−	0.0910404i
$898$			14.9507i			0.498912i
$899$	16.5653			0.552485
$900$	1.14134	+	4.86799i	0.0380445	+	0.162266i
$901$	0.168091			0.00559992
$902$			2.54669i			0.0847954i
$903$			11.0093i			0.366368i
$904$	11.7360			0.390333
$905$	24.6553	+	19.5433i	0.819571	+	0.649641i
$906$	−22.3013			−0.740912
$907$		−	1.60737i		−	0.0533718i	−0.999644	−	0.0266859i	$-0.991505\pi$
$907$		−	1.60737i		−	0.0533718i	0.999644	−	0.0266859i	$-0.00849539\pi$
$908$		−	11.9673i		−	0.397149i
$909$	−3.45331			−0.114539
$910$	7.57467	−	9.55602i	0.251098	−	0.316779i
$911$	−15.8973			−0.526701			−0.263350	−	0.964700i	$-0.584828\pi$
$911$	−15.8973			−0.526701			−0.263350	+	0.964700i	$0.584828\pi$
$912$			7.78734i			0.257864i
$913$		−	47.3947i		−	1.56854i
$914$	1.43466			0.0474542
$915$	5.62734	−	7.09931i	0.186034	−	0.234696i
$916$	26.5327			0.876663
$917$			29.6960i			0.980649i
$918$			0.726656i			0.0239832i
$919$	42.3013			1.39539			0.697696	−	0.716394i	$-0.254209\pi$
$919$	42.3013			1.39539			0.697696	+	0.716394i	$0.254209\pi$
$920$	−1.75233	−	1.38900i	−0.0577727	−	0.0457941i
$921$	−27.5747			−0.908616
$922$		−	13.5747i		−	0.447058i
$923$		−	32.0000i		−	1.05329i
$924$	−7.00933			−0.230590
$925$	46.2686	−	10.8480i	1.52130	−	0.356681i
$926$	−1.73599			−0.0570480
$927$		−	14.4626i		−	0.475015i
$928$			2.00000i			0.0656532i
$929$	42.0628			1.38003			0.690017	−	0.723793i	$-0.257603\pi$
$929$	42.0628			1.38003			0.690017	+	0.723793i	$0.257603\pi$
$930$	14.5140	+	11.5047i	0.475933	+	0.377253i
$931$	23.3620			0.765659
$932$		−	24.4040i		−	0.799381i
$933$			24.1214i			0.789698i
$934$	−28.1727			−0.921839
$935$	3.53736	−	4.46264i	0.115684	−	0.145944i
$936$	−2.72666			−0.0891236
$937$		−	8.44398i		−	0.275853i	−0.990442	−	0.137926i	$-0.955956\pi$
$937$		−	8.44398i		−	0.275853i	0.990442	−	0.137926i	$-0.0440438\pi$
$938$		−	8.10270i		−	0.264563i
$939$	−8.58400			−0.280128
$940$	3.78734	−	4.77801i	0.123529	−	0.155841i
$941$	−19.2993			−0.629138			−0.314569	−	0.949235i	$-0.601860\pi$
$941$	−19.2993			−0.629138			−0.314569	+	0.949235i	$0.601860\pi$
$942$			9.60737i			0.313025i
$943$			0.726656i			0.0236632i
$944$	−9.29200			−0.302429
$945$	3.50466	+	2.77801i	0.114007	+	0.0903686i
$946$	−19.2920			−0.627237
$947$			3.36927i			0.109486i	0.998500	+	0.0547432i	$0.0174340\pi$
$947$			3.36927i			0.109486i	−0.998500	+	0.0547432i	$0.982566\pi$
$948$		−	9.73599i		−	0.316210i
$949$	−10.1359			−0.329024
$950$	−37.9087	+	8.88797i	−1.22992	+	0.288364i
$951$	24.1214			0.782189
$952$		−	1.45331i		−	0.0471021i
$953$			24.0441i			0.778865i	0.921055	+	0.389432i	$0.127329\pi$
$953$			24.0441i			0.778865i	−0.921055	+	0.389432i	$0.872671\pi$
$954$	−0.231321			−0.00748929
$955$	34.3013	+	27.1893i	1.10996	+	0.879825i
$956$	−3.55602			−0.115010
$957$			7.00933i			0.226579i
$958$			26.3786i			0.852254i
$959$	−6.54669			−0.211404
$960$	−1.38900	+	1.75233i	−0.0448299	+	0.0565563i
$961$	37.6027			1.21299
$962$			25.9160i			0.835564i
$963$		−	13.0607i		−	0.420875i
$964$	−3.55602			−0.114532
$965$	−13.9160	+	17.5560i	−0.447970	+	0.565148i
$966$	−2.00000			−0.0643489
$967$			26.9439i			0.866459i	0.901284	+	0.433229i	$0.142626\pi$
$967$			26.9439i			0.866459i	−0.901284	+	0.433229i	$0.857374\pi$
$968$		−	1.28267i		−	0.0412266i
$969$	−5.65872			−0.181784
$970$	−7.96731	−	6.31537i	−0.255815	−	0.202774i
$971$	−5.84595			−0.187605			−0.0938027	−	0.995591i	$-0.529902\pi$
$971$	−5.84595			−0.187605			−0.0938027	+	0.995591i	$0.529902\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			28.0373i			0.898835i
$974$	20.2827			0.649899
$975$	−3.11203	−	13.2733i	−0.0996648	−	0.425087i
$976$	4.05135			0.129681
$977$		−	23.8387i		−	0.762667i	−0.924437	−	0.381334i	$-0.875465\pi$
$977$		−	23.8387i		−	0.762667i	0.924437	−	0.381334i	$-0.124535\pi$
$978$		−	14.1214i		−	0.451551i
$979$	33.4906			1.07037
$980$	5.25700	+	4.16701i	0.167929	+	0.133110i
$981$	−10.9580			−0.349861
$982$			18.6426i			0.594910i
$983$			44.6680i			1.42469i	0.701830	+	0.712345i	$0.252367\pi$
$983$			44.6680i			1.42469i	−0.701830	+	0.712345i	$0.747633\pi$
$984$	0.726656			0.0231650
$985$	−2.77801	+	3.50466i	−0.0885147	+	0.111668i
$986$	−1.45331			−0.0462829
$987$		−	5.45331i		−	0.173581i
$988$		−	21.2334i		−	0.675524i
$989$	−5.50466			−0.175038
$990$	−4.86799	+	6.14134i	−0.154715	+	0.195184i
$991$	−10.0586			−0.319522			−0.159761	−	0.987156i	$-0.551072\pi$
$991$	−10.0586			−0.319522			−0.159761	+	0.987156i	$0.551072\pi$
$992$			8.28267i			0.262975i
$993$			8.10270i			0.257132i
$994$	−23.4720			−0.744486
$995$	40.6354	+	32.2100i	1.28823	+	1.02113i
$996$	−13.5233			−0.428503
$997$			38.2640i			1.21183i	0.795528	+	0.605917i	$0.207194\pi$
$997$			38.2640i			1.21183i	−0.795528	+	0.605917i	$0.792806\pi$
$998$		−	20.9907i		−	0.664448i
$999$	−9.50466			−0.300714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.d.d.139.4	yes	6
3.2	odd	2		2070.2.d.d.829.3		6
5.2	odd	4		3450.2.a.bq.1.3		3
5.3	odd	4		3450.2.a.br.1.3		3
5.4	even	2	inner	690.2.d.d.139.1	✓	6
15.14	odd	2		2070.2.d.d.829.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.d.139.1	✓	6	5.4	even	2	inner
690.2.d.d.139.4	yes	6	1.1	even	1	trivial
2070.2.d.d.829.3		6	3.2	odd	2
2070.2.d.d.829.6		6	15.14	odd	2
3450.2.a.bq.1.3		3	5.2	odd	4
3450.2.a.br.1.3		3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.75233 - 1.38900i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.75233 - 1.38900i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.38900 - 1.75233i) q^{10} +3.50466 q^{11} -1.00000i q^{12} +2.72666i q^{13} +2.00000 q^{14} +(1.38900 - 1.75233i) q^{15} +1.00000 q^{16} +0.726656i q^{17} -1.00000i q^{18} +7.78734 q^{19} +(1.75233 + 1.38900i) q^{20} +2.00000 q^{21} +3.50466i q^{22} +1.00000i q^{23} +1.00000 q^{24} +(1.14134 + 4.86799i) q^{25} -2.72666 q^{26} -1.00000i q^{27} +2.00000i q^{28} +2.00000 q^{29} +(1.75233 + 1.38900i) q^{30} +8.28267 q^{31} +1.00000i q^{32} +3.50466i q^{33} -0.726656 q^{34} +(-2.77801 + 3.50466i) q^{35} +1.00000 q^{36} -9.50466i q^{37} +7.78734i q^{38} -2.72666 q^{39} +(-1.38900 + 1.75233i) q^{40} +0.726656 q^{41} +2.00000i q^{42} +5.50466i q^{43} -3.50466 q^{44} +(1.75233 + 1.38900i) q^{45} -1.00000 q^{46} -2.72666i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.86799 + 1.14134i) q^{50} -0.726656 q^{51} -2.72666i q^{52} -0.231321i q^{53} +1.00000 q^{54} +(-6.14134 - 4.86799i) q^{55} -2.00000 q^{56} +7.78734i q^{57} +2.00000i q^{58} -9.29200 q^{59} +(-1.38900 + 1.75233i) q^{60} +4.05135 q^{61} +8.28267i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(3.78734 - 4.77801i) q^{65} -3.50466 q^{66} -4.05135i q^{67} -0.726656i q^{68} -1.00000 q^{69} +(-3.50466 - 2.77801i) q^{70} -11.7360 q^{71} +1.00000i q^{72} +3.71733i q^{73} +9.50466 q^{74} +(-4.86799 + 1.14134i) q^{75} -7.78734 q^{76} -7.00933i q^{77} -2.72666i q^{78} +9.73599 q^{79} +(-1.75233 - 1.38900i) q^{80} +1.00000 q^{81} +0.726656i q^{82} -13.5233i q^{83} -2.00000 q^{84} +(1.00933 - 1.27334i) q^{85} -5.50466 q^{86} +2.00000i q^{87} -3.50466i q^{88} +9.55602 q^{89} +(-1.38900 + 1.75233i) q^{90} +5.45331 q^{91} -1.00000i q^{92} +8.28267i q^{93} +2.72666 q^{94} +(-13.6460 - 10.8166i) q^{95} -1.00000 q^{96} -4.54669i q^{97} +3.00000i q^{98} -3.50466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{14} + 2 q^{15} + 6 q^{16} - 8 q^{19} + 12 q^{21} + 6 q^{24} - 10 q^{25} - 8 q^{26} + 12 q^{29} + 16 q^{31} + 4 q^{34} - 4 q^{35} + 6 q^{36} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 6 q^{46} + 18 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{54} - 20 q^{55} - 12 q^{56} + 20 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{64} - 32 q^{65} - 6 q^{69} - 20 q^{71} + 36 q^{74} - 4 q^{75} + 8 q^{76} + 8 q^{79} + 6 q^{81} - 12 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{89} - 2 q^{90} + 16 q^{91} + 8 q^{94} - 44 q^{95} - 6 q^{96}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^14 + 2 * q^15 + 6 * q^16 - 8 * q^19 + 12 * q^21 + 6 * q^24 - 10 * q^25 - 8 * q^26 + 12 * q^29 + 16 * q^31 + 4 * q^34 - 4 * q^35 + 6 * q^36 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 6 * q^46 + 18 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^54 - 20 * q^55 - 12 * q^56 + 20 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^64 - 32 * q^65 - 6 * q^69 - 20 * q^71 + 36 * q^74 - 4 * q^75 + 8 * q^76 + 8 * q^79 + 6 * q^81 - 12 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^89 - 2 * q^90 + 16 * q^91 + 8 * q^94 - 44 * q^95 - 6 * q^96

Introduction

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