LMFDB - Embedded newform 187.2.d.a.67.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(67,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("187.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 172x^{12} + 700x^{10} + 1492x^{8} + 1620x^{6} + 840x^{4} + 196x^{2} + 16 $ x^16 + 21x^14 + 172x^12 + 700x^10 + 1492x^8 + 1620x^6 + 840x^4 + 196*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.14
Root			$-1.89309i$ of defining polynomial
Character	$\chi$	$=$	187.67
Dual form			187.2.d.a.67.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89309 q^{2} +1.04073i q^{3} +1.58380 q^{4} +1.83662i q^{5} +1.97021i q^{6} -1.61788i q^{7} -0.787912 q^{8} +1.91687 q^{9} +O(q^{10})$	\(q+1.89309 q^{2} +1.04073i q^{3} +1.58380 q^{4} +1.83662i q^{5} +1.97021i q^{6} -1.61788i q^{7} -0.787912 q^{8} +1.91687 q^{9} +3.47689i q^{10} -1.00000i q^{11} +1.64831i q^{12} +1.28326 q^{13} -3.06279i q^{14} -1.91143 q^{15} -4.65918 q^{16} +(-2.42711 - 3.33304i) q^{17} +3.62882 q^{18} -3.44044 q^{19} +2.90883i q^{20} +1.68378 q^{21} -1.89309i q^{22} -4.87213i q^{23} -0.820007i q^{24} +1.62683 q^{25} +2.42933 q^{26} +5.11716i q^{27} -2.56239i q^{28} -5.71335i q^{29} -3.61852 q^{30} +3.11322i q^{31} -7.24444 q^{32} +1.04073 q^{33} +(-4.59474 - 6.30975i) q^{34} +2.97142 q^{35} +3.03594 q^{36} +6.82692i q^{37} -6.51307 q^{38} +1.33553i q^{39} -1.44709i q^{40} +4.07841i q^{41} +3.18755 q^{42} -8.87325 q^{43} -1.58380i q^{44} +3.52056i q^{45} -9.22340i q^{46} +5.88243 q^{47} -4.84897i q^{48} +4.38248 q^{49} +3.07974 q^{50} +(3.46881 - 2.52597i) q^{51} +2.03242 q^{52} -3.22736 q^{53} +9.68725i q^{54} +1.83662 q^{55} +1.27474i q^{56} -3.58058i q^{57} -10.8159i q^{58} -2.40670 q^{59} -3.02732 q^{60} +13.3232i q^{61} +5.89361i q^{62} -3.10126i q^{63} -4.39602 q^{64} +2.35686i q^{65} +1.97021 q^{66} +5.72734 q^{67} +(-3.84404 - 5.27886i) q^{68} +5.07060 q^{69} +5.62517 q^{70} +6.48669i q^{71} -1.51033 q^{72} +4.32713i q^{73} +12.9240i q^{74} +1.69310i q^{75} -5.44895 q^{76} -1.61788 q^{77} +2.52828i q^{78} -15.1696i q^{79} -8.55714i q^{80} +0.425016 q^{81} +7.72080i q^{82} -8.83664 q^{83} +2.66676 q^{84} +(6.12152 - 4.45767i) q^{85} -16.7979 q^{86} +5.94608 q^{87} +0.787912i q^{88} -0.224416 q^{89} +6.66475i q^{90} -2.07615i q^{91} -7.71647i q^{92} -3.24004 q^{93} +11.1360 q^{94} -6.31877i q^{95} -7.53953i q^{96} -3.00802i q^{97} +8.29644 q^{98} -1.91687i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.89309			1.33862			0.669309	−	0.742984i	$-0.266590\pi$
$2$	1.89309			1.33862			0.669309	+	0.742984i	$0.266590\pi$
$3$			1.04073i			0.600868i	0.953803	+	0.300434i	$0.0971315\pi$
$3$			1.04073i			0.600868i	−0.953803	+	0.300434i	$0.902868\pi$
$4$	1.58380			0.791898
$5$			1.83662i			0.821361i	0.911779	+	0.410680i	$0.134709\pi$
$5$			1.83662i			0.821361i	−0.911779	+	0.410680i	$0.865291\pi$
$6$			1.97021i			0.804333i
$7$		−	1.61788i		−	0.611499i	−0.952112	−	0.305750i	$-0.901093\pi$
$7$		−	1.61788i		−	0.611499i	0.952112	−	0.305750i	$-0.0989071\pi$
$8$	−0.787912			−0.278569
$9$	1.91687			0.638957
$10$			3.47689i			1.09949i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$			1.64831i			0.475826i
$13$	1.28326			0.355912			0.177956	−	0.984038i	$-0.443052\pi$
$13$	1.28326			0.355912			0.177956	+	0.984038i	$0.443052\pi$
$14$		−	3.06279i		−	0.818564i
$15$	−1.91143			−0.493530
$16$	−4.65918			−1.16480
$17$	−2.42711	−	3.33304i	−0.588660	−	0.808381i
$17$	−2.42711	−	3.33304i	−0.588660	−	0.808381i
$18$	3.62882			0.855320
$19$	−3.44044			−0.789291			−0.394645	−	0.918834i	$-0.629133\pi$
$19$	−3.44044			−0.789291			−0.394645	+	0.918834i	$0.629133\pi$
$20$			2.90883i			0.650434i
$21$	1.68378			0.367431
$22$		−	1.89309i		−	0.403609i
$23$		−	4.87213i		−	1.01591i	−0.861384	−	0.507955i	$-0.830402\pi$
$23$		−	4.87213i		−	1.01591i	0.861384	−	0.507955i	$-0.169598\pi$
$24$		−	0.820007i		−	0.167383i
$25$	1.62683			0.325366
$26$	2.42933			0.476430
$27$			5.11716i			0.984797i
$28$		−	2.56239i		−	0.484245i
$29$		−	5.71335i		−	1.06094i	−0.847703	−	0.530472i	$-0.822015\pi$
$29$		−	5.71335i		−	1.06094i	0.847703	−	0.530472i	$-0.177985\pi$
$30$	−3.61852			−0.660648
$31$			3.11322i			0.559151i	0.960124	+	0.279576i	$0.0901938\pi$
$31$			3.11322i			0.559151i	−0.960124	+	0.279576i	$0.909806\pi$
$32$	−7.24444			−1.28065
$33$	1.04073			0.181169
$34$	−4.59474	−	6.30975i	−0.787991	−	1.08211i
$35$	2.97142			0.502262
$36$	3.03594			0.505989
$37$			6.82692i			1.12234i	0.827701	+	0.561169i	$0.189648\pi$
$37$			6.82692i			1.12234i	−0.827701	+	0.561169i	$0.810352\pi$
$38$	−6.51307			−1.05656
$39$			1.33553i			0.213856i
$40$		−	1.44709i		−	0.228806i
$41$			4.07841i			0.636940i	0.947933	+	0.318470i	$0.103169\pi$
$41$			4.07841i			0.636940i	−0.947933	+	0.318470i	$0.896831\pi$
$42$	3.18755			0.491849
$43$	−8.87325			−1.35316			−0.676579	−	0.736370i	$-0.736538\pi$
$43$	−8.87325			−1.35316			−0.676579	+	0.736370i	$0.736538\pi$
$44$		−	1.58380i		−	0.238766i
$45$			3.52056i			0.524815i
$46$		−	9.22340i		−	1.35992i
$47$	5.88243			0.858041			0.429021	−	0.903295i	$-0.358859\pi$
$47$	5.88243			0.858041			0.429021	+	0.903295i	$0.358859\pi$
$48$		−	4.84897i		−	0.699889i
$49$	4.38248			0.626068
$50$	3.07974			0.435541
$51$	3.46881	−	2.52597i	0.485730	−	0.353707i
$52$	2.03242			0.281846
$53$	−3.22736			−0.443312			−0.221656	−	0.975125i	$-0.571146\pi$
$53$	−3.22736			−0.443312			−0.221656	+	0.975125i	$0.571146\pi$
$54$			9.68725i			1.31827i
$55$	1.83662			0.247650
$56$			1.27474i			0.170345i
$57$		−	3.58058i		−	0.474260i
$58$		−	10.8159i		−	1.42020i
$59$	−2.40670			−0.313326			−0.156663	−	0.987652i	$-0.550074\pi$
$59$	−2.40670			−0.313326			−0.156663	+	0.987652i	$0.550074\pi$
$60$	−3.02732			−0.390825
$61$			13.3232i			1.70587i	0.522020	+	0.852933i	$0.325179\pi$
$61$			13.3232i			1.70587i	−0.522020	+	0.852933i	$0.674821\pi$
$62$			5.89361i			0.748490i
$63$		−	3.10126i		−	0.390722i
$64$	−4.39602			−0.549502
$65$			2.35686i			0.292332i
$66$	1.97021			0.242516
$67$	5.72734			0.699706			0.349853	−	0.936805i	$-0.386232\pi$
$67$	5.72734			0.699706			0.349853	+	0.936805i	$0.386232\pi$
$68$	−3.84404	−	5.27886i	−0.466159	−	0.640155i
$69$	5.07060			0.610428
$70$	5.62517			0.672337
$71$			6.48669i			0.769828i	0.922952	+	0.384914i	$0.125769\pi$
$71$			6.48669i			0.769828i	−0.922952	+	0.384914i	$0.874231\pi$
$72$	−1.51033			−0.177994
$73$			4.32713i			0.506453i	0.967407	+	0.253226i	$0.0814917\pi$
$73$			4.32713i			0.506453i	−0.967407	+	0.253226i	$0.918508\pi$
$74$			12.9240i			1.50238i
$75$			1.69310i			0.195502i
$76$	−5.44895			−0.625038
$77$	−1.61788			−0.184374
$78$			2.52828i			0.286272i
$79$		−	15.1696i		−	1.70671i	−0.521330	−	0.853355i	$-0.674564\pi$
$79$		−	15.1696i		−	1.70671i	0.521330	−	0.853355i	$-0.325436\pi$
$80$		−	8.55714i		−	0.956717i
$81$	0.425016			0.0472240
$82$			7.72080i			0.852620i
$83$	−8.83664			−0.969947			−0.484974	−	0.874529i	$-0.661171\pi$
$83$	−8.83664			−0.969947			−0.484974	+	0.874529i	$0.661171\pi$
$84$	2.66676			0.290968
$85$	6.12152	−	4.45767i	0.663972	−	0.483502i
$86$	−16.7979			−1.81136
$87$	5.94608			0.637487
$88$			0.787912i			0.0839917i
$89$	−0.224416			−0.0237881			−0.0118940	−	0.999929i	$-0.503786\pi$
$89$	−0.224416			−0.0237881			−0.0118940	+	0.999929i	$0.503786\pi$
$90$			6.66475i			0.702526i
$91$		−	2.07615i		−	0.217640i
$92$		−	7.71647i		−	0.804498i
$93$	−3.24004			−0.335976
$94$	11.1360			1.14859
$95$		−	6.31877i		−	0.648293i
$96$		−	7.53953i		−	0.769500i
$97$		−	3.00802i		−	0.305418i	−0.988271	−	0.152709i	$-0.951200\pi$
$97$		−	3.00802i		−	0.305418i	0.988271	−	0.152709i	$-0.0487998\pi$
$98$	8.29644			0.838067
$99$		−	1.91687i		−	0.192653i
$100$	2.57657			0.257657
$101$	10.9859			1.09314			0.546570	−	0.837413i	$-0.315933\pi$
$101$	10.9859			1.09314			0.546570	+	0.837413i	$0.315933\pi$
$102$	6.56677	−	4.78190i	0.650207	−	0.473479i
$103$	−2.28423			−0.225071			−0.112536	−	0.993648i	$-0.535897\pi$
$103$	−2.28423			−0.225071			−0.112536	+	0.993648i	$0.535897\pi$
$104$	−1.01109			−0.0991459
$105$			3.09246i			0.301793i
$106$	−6.10968			−0.593425
$107$		−	0.820377i		−	0.0793088i	−0.999213	−	0.0396544i	$-0.987374\pi$
$107$		−	0.820377i		−	0.0793088i	0.999213	−	0.0396544i	$-0.0126257\pi$
$108$			8.10454i			0.779859i
$109$			14.9626i			1.43316i	0.697504	+	0.716581i	$0.254294\pi$
$109$			14.9626i			1.43316i	−0.697504	+	0.716581i	$0.745706\pi$
$110$	3.47689			0.331508
$111$	−7.10501			−0.674377
$112$			7.53798i			0.712272i
$113$		−	7.81788i		−	0.735444i	−0.929936	−	0.367722i	$-0.880138\pi$
$113$		−	7.81788i		−	0.735444i	0.929936	−	0.367722i	$-0.119862\pi$
$114$		−	6.77837i		−	0.634853i
$115$	8.94825			0.834429
$116$		−	9.04879i		−	0.840159i
$117$	2.45984			0.227412
$118$	−4.55611			−0.419423
$119$	−5.39244	+	3.92676i	−0.494324	+	0.359965i
$120$	1.50604			0.137482
$121$	−1.00000			−0.0909091
$122$			25.2221i			2.28350i
$123$	−4.24454			−0.382717
$124$			4.93071i			0.442791i
$125$			12.1710i			1.08860i
$126$		−	5.87097i		−	0.523028i
$127$	1.46313			0.129832			0.0649159	−	0.997891i	$-0.479322\pi$
$127$	1.46313			0.129832			0.0649159	+	0.997891i	$0.479322\pi$
$128$	6.16681			0.545074
$129$		−	9.23470i		−	0.813070i
$130$			4.46175i			0.391321i
$131$		−	19.7300i		−	1.72382i	−0.507061	−	0.861910i	$-0.669268\pi$
$131$		−	19.7300i		−	1.72382i	0.507061	−	0.861910i	$-0.330732\pi$
$132$	1.64831			0.143467
$133$			5.56620i			0.482651i
$134$	10.8424			0.936639
$135$	−9.39827			−0.808874
$136$	1.91235	+	2.62614i	0.163982	+	0.225190i
$137$	−4.14244			−0.353913			−0.176956	−	0.984219i	$-0.556625\pi$
$137$	−4.14244			−0.353913			−0.176956	+	0.984219i	$0.556625\pi$
$138$	9.59911			0.817130
$139$			12.5213i			1.06204i	0.847359	+	0.531020i	$0.178191\pi$
$139$			12.5213i			1.06204i	−0.847359	+	0.531020i	$0.821809\pi$
$140$	4.70613			0.397740
$141$			6.12205i			0.515570i
$142$			12.2799i			1.03051i
$143$		−	1.28326i		−	0.107311i
$144$	−8.93106			−0.744255
$145$	10.4933			0.871417
$146$			8.19166i			0.677946i
$147$			4.56100i			0.376185i
$148$			10.8124i			0.888778i
$149$	−10.1258			−0.829538			−0.414769	−	0.909927i	$-0.636138\pi$
$149$	−10.1258			−0.829538			−0.414769	+	0.909927i	$0.636138\pi$
$150$			3.20519i			0.261703i
$151$	12.6399			1.02862			0.514310	−	0.857604i	$-0.328048\pi$
$151$	12.6399			1.02862			0.514310	+	0.857604i	$0.328048\pi$
$152$	2.71076			0.219872
$153$	−4.65245	−	6.38901i	−0.376129	−	0.516521i
$154$	−3.06279			−0.246806
$155$	−5.71780			−0.459265
$156$			2.11521i			0.169352i
$157$	19.0978			1.52417			0.762084	−	0.647478i	$-0.224176\pi$
$157$	19.0978			1.52417			0.762084	+	0.647478i	$0.224176\pi$
$158$		−	28.7174i		−	2.28463i
$159$		−	3.35882i		−	0.266372i
$160$		−	13.3053i		−	1.05187i
$161$	−7.88251			−0.621229
$162$	0.804594			0.0632149
$163$		−	14.6835i		−	1.15010i	−0.818119	−	0.575049i	$-0.804983\pi$
$163$		−	14.6835i		−	1.15010i	0.818119	−	0.575049i	$-0.195017\pi$
$164$			6.45937i			0.504392i
$165$			1.91143i			0.148805i
$166$	−16.7286			−1.29839
$167$		−	14.4124i		−	1.11526i	−0.830089	−	0.557631i	$-0.811710\pi$
$167$		−	14.4124i		−	1.11526i	0.830089	−	0.557631i	$-0.188290\pi$
$168$	−1.32667			−0.102355
$169$	−11.3532			−0.873327
$170$	11.5886	−	8.43878i	0.888805	−	0.647225i
$171$	−6.59488			−0.504323
$172$	−14.0534			−1.07156
$173$		−	2.54891i		−	0.193790i	−0.995295	−	0.0968949i	$-0.969109\pi$
$173$		−	2.54891i		−	0.193790i	0.995295	−	0.0968949i	$-0.0308911\pi$
$174$	11.2565			0.853352
$175$		−	2.63201i		−	0.198961i
$176$			4.65918i			0.351199i
$177$		−	2.50474i		−	0.188267i
$178$	−0.424840			−0.0318431
$179$	−22.0524			−1.64828			−0.824138	−	0.566389i	$-0.808340\pi$
$179$	−22.0524			−1.64828			−0.824138	+	0.566389i	$0.808340\pi$
$180$			5.57586i			0.415600i
$181$		−	8.84565i		−	0.657492i	−0.944418	−	0.328746i	$-0.893374\pi$
$181$		−	8.84565i		−	0.657492i	0.944418	−	0.328746i	$-0.106626\pi$
$182$		−	3.93035i		−	0.291337i
$183$	−13.8660			−1.02500
$184$			3.83881i			0.283001i
$185$	−12.5384			−0.921845
$186$	−6.13369			−0.449744
$187$	−3.33304	+	2.42711i	−0.243736	+	0.177488i
$188$	9.31658			0.679481
$189$	8.27892			0.602203
$190$		−	11.9620i		−	0.867816i
$191$	−19.2858			−1.39547			−0.697735	−	0.716356i	$-0.745809\pi$
$191$	−19.2858			−1.39547			−0.697735	+	0.716356i	$0.745809\pi$
$192$		−	4.57509i		−	0.330178i
$193$		−	4.08551i		−	0.294081i	−0.989130	−	0.147041i	$-0.953025\pi$
$193$		−	4.08551i		−	0.294081i	0.989130	−	0.147041i	$-0.0469748\pi$
$194$		−	5.69446i		−	0.408838i
$195$	−2.45286			−0.175653
$196$	6.94095			0.495782
$197$		−	23.2199i		−	1.65435i	−0.561944	−	0.827175i	$-0.689946\pi$
$197$		−	23.2199i		−	1.65435i	0.561944	−	0.827175i	$-0.310054\pi$
$198$		−	3.62882i		−	0.257889i
$199$			11.8668i			0.841218i	0.907242	+	0.420609i	$0.138184\pi$
$199$			11.8668i			0.841218i	−0.907242	+	0.420609i	$0.861816\pi$
$200$	−1.28180			−0.0906369
$201$			5.96064i			0.420431i
$202$	20.7974			1.46330
$203$	−9.24350			−0.648766
$204$	5.49389	−	4.00063i	0.384649	−	0.280100i
$205$	−7.49048			−0.523158
$206$	−4.32425			−0.301285
$207$		−	9.33926i		−	0.649123i
$208$	−5.97893			−0.414564
$209$			3.44044i			0.237980i
$210$			5.85431i			0.403986i
$211$			2.35501i			0.162126i	0.996709	+	0.0810629i	$0.0258315\pi$
$211$			2.35501i			0.162126i	−0.996709	+	0.0810629i	$0.974169\pi$
$212$	−5.11148			−0.351058
$213$	−6.75092			−0.462565
$214$		−	1.55305i		−	0.106164i
$215$		−	16.2968i		−	1.11143i
$216$		−	4.03187i		−	0.274334i
$217$	5.03681			0.341921
$218$			28.3257i			1.91846i
$219$	−4.50339			−0.304311
$220$	2.90883			0.196113
$221$	−3.11460	−	4.27715i	−0.209511	−	0.287712i
$222$	−13.4504			−0.902734
$223$	−17.4889			−1.17115			−0.585573	−	0.810619i	$-0.699131\pi$
$223$	−17.4889			−1.17115			−0.585573	+	0.810619i	$0.699131\pi$
$224$			11.7206i			0.783115i
$225$	3.11843			0.207895
$226$		−	14.8000i		−	0.984479i
$227$			18.8429i			1.25064i	0.780366	+	0.625322i	$0.215033\pi$
$227$			18.8429i			1.25064i	−0.780366	+	0.625322i	$0.784967\pi$
$228$		−	5.67091i		−	0.375565i
$229$	28.7799			1.90183			0.950913	−	0.309457i	$-0.100147\pi$
$229$	28.7799			1.90183			0.950913	+	0.309457i	$0.100147\pi$
$230$	16.9399			1.11698
$231$		−	1.68378i		−	0.110784i
$232$			4.50162i			0.295546i
$233$		−	11.3102i		−	0.740957i	−0.928841	−	0.370479i	$-0.879194\pi$
$233$		−	11.3102i		−	0.740957i	0.928841	−	0.370479i	$-0.120806\pi$
$234$	4.65671			0.304418
$235$			10.8038i			0.704761i
$236$	−3.81172			−0.248122
$237$	15.7875			1.02551
$238$	−10.2084	+	7.43371i	−0.661712	+	0.481856i
$239$	12.5722			0.813226			0.406613	−	0.913601i	$-0.366710\pi$
$239$	12.5722			0.813226			0.406613	+	0.913601i	$0.366710\pi$
$240$	8.90571			0.574861
$241$			8.91176i			0.574057i	0.957922	+	0.287029i	$0.0926675\pi$
$241$			8.91176i			0.574057i	−0.957922	+	0.287029i	$0.907333\pi$
$242$	−1.89309			−0.121693
$243$			15.7938i			1.01317i
$244$			21.1013i			1.35087i
$245$			8.04894i			0.514228i
$246$	−8.03530			−0.512312
$247$	−4.41497			−0.280918
$248$		−	2.45294i		−	0.155762i
$249$		−	9.19660i		−	0.582811i
$250$			23.0407i			1.45722i
$251$	−11.2312			−0.708905			−0.354453	−	0.935074i	$-0.615333\pi$
$251$	−11.2312			−0.708905			−0.354453	+	0.935074i	$0.615333\pi$
$252$		−	4.91176i		−	0.309412i
$253$	−4.87213			−0.306308
$254$	2.76984			0.173795
$255$	4.63925	+	6.37088i	0.290521	+	0.398960i
$256$	20.4664			1.27915
$257$	−9.26127			−0.577702			−0.288851	−	0.957374i	$-0.593273\pi$
$257$	−9.26127			−0.577702			−0.288851	+	0.957374i	$0.593273\pi$
$258$		−	17.4821i		−	1.08839i
$259$	11.0451			0.686309
$260$			3.73278i			0.231497i
$261$		−	10.9518i		−	0.677898i
$262$		−	37.3507i		−	2.30754i
$263$	23.0851			1.42349			0.711743	−	0.702440i	$-0.247906\pi$
$263$	23.0851			1.42349			0.711743	+	0.702440i	$0.247906\pi$
$264$	−0.820007			−0.0504679
$265$		−	5.92743i		−	0.364119i
$266$			10.5373i			0.646085i
$267$		−	0.233558i		−	0.0142935i
$268$	9.07094			0.554096
$269$			11.3134i			0.689789i	0.938641	+	0.344895i	$0.112085\pi$
$269$			11.3134i			0.689789i	−0.938641	+	0.344895i	$0.887915\pi$
$270$	−17.7918			−1.08277
$271$	25.3568			1.54032			0.770159	−	0.637852i	$-0.220177\pi$
$271$	25.3568			1.54032			0.770159	+	0.637852i	$0.220177\pi$
$272$	11.3083	+	15.5292i	0.685668	+	0.941598i
$273$	2.16072			0.130773
$274$	−7.84202			−0.473754
$275$		−	1.62683i		−	0.0981016i
$276$	8.03079			0.483397
$277$			11.6243i			0.698434i	0.937042	+	0.349217i	$0.113552\pi$
$277$			11.6243i			0.698434i	−0.937042	+	0.349217i	$0.886448\pi$
$278$			23.7039i			1.42167i
$279$			5.96765i			0.357274i
$280$	−2.34122			−0.139914
$281$	28.2677			1.68631			0.843156	−	0.537669i	$-0.180695\pi$
$281$	28.2677			1.68631			0.843156	+	0.537669i	$0.180695\pi$
$282$			11.5896i			0.690151i
$283$		−	21.0144i		−	1.24917i	−0.780955	−	0.624587i	$-0.785267\pi$
$283$		−	21.0144i		−	1.24917i	0.780955	−	0.624587i	$-0.214733\pi$
$284$			10.2736i			0.609625i
$285$	6.57616			0.389538
$286$		−	2.42933i		−	0.143649i
$287$	6.59835			0.389489
$288$	−13.8867			−0.818279
$289$	−5.21830	+	16.1793i	−0.306959	+	0.951723i
$290$	19.8647			1.16649
$291$	3.13055			0.183516
$292$			6.85330i			0.401059i
$293$	−8.19871			−0.478974			−0.239487	−	0.970900i	$-0.576979\pi$
$293$	−8.19871			−0.478974			−0.239487	+	0.970900i	$0.576979\pi$
$294$			8.63438i			0.503568i
$295$		−	4.42019i		−	0.257354i
$296$		−	5.37901i		−	0.312649i
$297$	5.11716			0.296928
$298$	−19.1691			−1.11043
$299$		−	6.25221i		−	0.361574i
$300$			2.68152i			0.154818i
$301$			14.3558i			0.827455i
$302$	23.9285			1.37693
$303$			11.4334i			0.656834i
$304$	16.0296			0.919362
$305$	−24.4697			−1.40113
$306$	−8.80752	−	12.0950i	−0.503493	−	0.691424i
$307$	2.90161			0.165604			0.0828020	−	0.996566i	$-0.473613\pi$
$307$	2.90161			0.165604			0.0828020	+	0.996566i	$0.473613\pi$
$308$	−2.56239			−0.146005
$309$		−	2.37727i		−	0.135238i
$310$	−10.8243			−0.614780
$311$			14.2764i			0.809541i	0.914418	+	0.404770i	$0.132649\pi$
$311$			14.2764i			0.809541i	−0.914418	+	0.404770i	$0.867351\pi$
$312$		−	1.05228i		−	0.0595736i
$313$		−	23.8601i		−	1.34866i	−0.738432	−	0.674328i	$-0.764434\pi$
$313$		−	23.8601i		−	1.34866i	0.738432	−	0.674328i	$-0.235566\pi$
$314$	36.1538			2.04028
$315$	5.69583			0.320924
$316$		−	24.0255i		−	1.35154i
$317$			5.67962i			0.318999i	0.987198	+	0.159499i	$0.0509880\pi$
$317$			5.67962i			0.318999i	−0.987198	+	0.159499i	$0.949012\pi$
$318$		−	6.35856i		−	0.356570i
$319$	−5.71335			−0.319886
$320$		−	8.07381i		−	0.451340i
$321$	0.853794			0.0476541
$322$	−14.9223			−0.831588
$323$	8.35031	+	11.4671i	0.464624	+	0.638047i
$324$	0.673139			0.0373966
$325$	2.08764			0.115802
$326$		−	27.7971i		−	1.53954i
$327$	−15.5721			−0.861141
$328$		−	3.21342i		−	0.177432i
$329$		−	9.51704i		−	0.524692i
$330$			3.61852i			0.199193i
$331$	12.1892			0.669976			0.334988	−	0.942222i	$-0.391268\pi$
$331$	12.1892			0.669976			0.334988	+	0.942222i	$0.391268\pi$
$332$	−13.9954			−0.768100
$333$			13.0863i			0.717126i
$334$		−	27.2839i		−	1.49291i
$335$			10.5189i			0.574711i
$336$	−7.84503			−0.427981
$337$			17.3002i			0.942403i	0.882026	+	0.471201i	$0.156180\pi$
$337$			17.3002i			0.942403i	−0.882026	+	0.471201i	$0.843820\pi$
$338$	−21.4927			−1.16905
$339$	8.13634			0.441905
$340$	9.69525	−	7.06004i	0.525799	−	0.382885i
$341$	3.11322			0.168590
$342$	−12.4847			−0.675096
$343$		−	18.4154i		−	0.994340i
$344$	6.99134			0.376948
$345$			9.31276i			0.501382i
$346$		−	4.82531i		−	0.259410i
$347$			16.5351i			0.887652i	0.896113	+	0.443826i	$0.146379\pi$
$347$			16.5351i			0.887652i	−0.896113	+	0.443826i	$0.853621\pi$
$348$	9.41739			0.504825
$349$	18.3064			0.979917			0.489958	−	0.871746i	$-0.337012\pi$
$349$	18.3064			0.979917			0.489958	+	0.871746i	$0.337012\pi$
$350$		−	4.98264i		−	0.266333i
$351$			6.56663i			0.350501i
$352$			7.24444i			0.386130i
$353$	20.1864			1.07442			0.537208	−	0.843450i	$-0.319479\pi$
$353$	20.1864			1.07442			0.537208	+	0.843450i	$0.319479\pi$
$354$		−	4.74169i		−	0.252018i
$355$	−11.9136			−0.632307
$356$	−0.355429			−0.0188377
$357$	−4.08671	−	5.61210i	−0.216292	−	0.297024i
$358$	−41.7473			−2.20641
$359$	2.91364			0.153776			0.0768880	−	0.997040i	$-0.475502\pi$
$359$	2.91364			0.153776			0.0768880	+	0.997040i	$0.475502\pi$
$360$		−	2.77389i		−	0.146197i
$361$	−7.16338			−0.377020
$362$		−	16.7456i		−	0.880131i
$363$		−	1.04073i		−	0.0546244i
$364$		−	3.28820i		−	0.172349i
$365$	−7.94729			−0.415980
$366$	−26.2495			−1.37208
$367$		−	4.13761i		−	0.215982i	−0.994152	−	0.107991i	$-0.965558\pi$
$367$		−	4.13761i		−	0.215982i	0.994152	−	0.107991i	$-0.0344417\pi$
$368$			22.7002i			1.18333i
$369$			7.81779i			0.406978i
$370$	−23.7364			−1.23400
$371$			5.22146i			0.271085i
$372$	−5.13156			−0.266059
$373$	−21.3727			−1.10664			−0.553319	−	0.832969i	$-0.686639\pi$
$373$	−21.3727			−1.10664			−0.553319	+	0.832969i	$0.686639\pi$
$374$	−6.30975	+	4.59474i	−0.326269	+	0.237588i
$375$	−12.6667			−0.654108
$376$	−4.63484			−0.239024
$377$		−	7.33171i		−	0.377602i
$378$	15.6728			0.806120
$379$			23.5046i			1.20735i	0.797231	+	0.603675i	$0.206297\pi$
$379$			23.5046i			1.20735i	−0.797231	+	0.603675i	$0.793703\pi$
$380$		−	10.0077i		−	0.513382i
$381$			1.52273i			0.0780118i
$382$	−36.5098			−1.86800
$383$	2.05353			0.104930			0.0524651	−	0.998623i	$-0.483292\pi$
$383$	2.05353			0.104930			0.0524651	+	0.998623i	$0.483292\pi$
$384$			6.41801i			0.327518i
$385$		−	2.97142i		−	0.151438i
$386$		−	7.73424i		−	0.393663i
$387$	−17.0089			−0.864610
$388$		−	4.76409i		−	0.241860i
$389$	19.2367			0.975338			0.487669	−	0.873029i	$-0.337847\pi$
$389$	19.2367			0.975338			0.487669	+	0.873029i	$0.337847\pi$
$390$	−4.64349			−0.235132
$391$	−16.2390	+	11.8252i	−0.821242	+	0.598026i
$392$	−3.45301			−0.174403
$393$	20.5337			1.03579
$394$		−	43.9574i		−	2.21454i
$395$	27.8607			1.40183
$396$		−	3.03594i		−	0.152561i
$397$		−	32.8511i		−	1.64875i	−0.566044	−	0.824375i	$-0.691527\pi$
$397$		−	32.8511i		−	1.64875i	0.566044	−	0.824375i	$-0.308473\pi$
$398$			22.4650i			1.12607i
$399$	−5.79294			−0.290010
$400$	−7.57970			−0.378985
$401$		−	34.5217i		−	1.72393i	−0.506965	−	0.861966i	$-0.669233\pi$
$401$		−	34.5217i		−	1.72393i	0.506965	−	0.861966i	$-0.330767\pi$
$402$			11.2840i			0.562797i
$403$			3.99507i			0.199009i
$404$	17.3995			0.865656
$405$			0.780592i			0.0387879i
$406$	−17.4988			−0.868450
$407$	6.82692			0.338398
$408$	−2.73311	+	1.99024i	−0.135309	+	0.0985318i
$409$	−4.94755			−0.244641			−0.122320	−	0.992491i	$-0.539034\pi$
$409$	−4.94755			−0.244641			−0.122320	+	0.992491i	$0.539034\pi$
$410$	−14.1802			−0.700308
$411$		−	4.31118i		−	0.212655i
$412$	−3.61775			−0.178234
$413$			3.89374i			0.191599i
$414$		−	17.6801i		−	0.868928i
$415$		−	16.2295i		−	0.796677i
$416$	−9.29648			−0.455798
$417$	−13.0313			−0.638146
$418$			6.51307i			0.318564i
$419$		−	35.9029i		−	1.75397i	−0.480517	−	0.876985i	$-0.659551\pi$
$419$		−	35.9029i		−	1.75397i	0.480517	−	0.876985i	$-0.340449\pi$
$420$			4.89783i			0.238989i
$421$	36.4835			1.77810			0.889048	−	0.457815i	$-0.151368\pi$
$421$	36.4835			1.77810			0.889048	+	0.457815i	$0.151368\pi$
$422$			4.45825i			0.217024i
$423$	11.2759			0.548252
$424$	2.54287			0.123493
$425$	−3.94849	−	5.42229i	−0.191530	−	0.263020i
$426$	−12.7801			−0.619198
$427$	21.5553			1.04314
$428$		−	1.29931i		−	0.0628045i
$429$	1.33553			0.0644800
$430$		−	30.8513i		−	1.48778i
$431$			16.8667i			0.812438i	0.913776	+	0.406219i	$0.133153\pi$
$431$			16.8667i			0.812438i	−0.913776	+	0.406219i	$0.866847\pi$
$432$		−	23.8418i		−	1.14709i
$433$	−37.6635			−1.80999			−0.904996	−	0.425419i	$-0.860127\pi$
$433$	−37.6635			−1.80999			−0.904996	+	0.425419i	$0.860127\pi$
$434$	9.53513			0.457701
$435$			10.9207i			0.523607i
$436$			23.6978i			1.13492i
$437$			16.7623i			0.801849i
$438$	−8.52534			−0.407356
$439$			6.36970i			0.304009i	0.988380	+	0.152005i	$0.0485729\pi$
$439$			6.36970i			0.304009i	−0.988380	+	0.152005i	$0.951427\pi$
$440$	−1.44709			−0.0689875
$441$	8.40065			0.400031
$442$	−5.89623	−	8.09704i	−0.280455	−	0.385137i
$443$	32.7843			1.55763			0.778814	−	0.627254i	$-0.215821\pi$
$443$	32.7843			1.55763			0.778814	+	0.627254i	$0.215821\pi$
$444$	−11.2529			−0.534038
$445$		−	0.412167i		−	0.0195386i
$446$	−33.1082			−1.56772
$447$		−	10.5383i		−	0.498443i
$448$			7.11221i			0.336020i
$449$			26.9500i			1.27185i	0.771751	+	0.635925i	$0.219381\pi$
$449$			26.9500i			1.27185i	−0.771751	+	0.635925i	$0.780619\pi$
$450$	5.90347			0.278292
$451$	4.07841			0.192045
$452$		−	12.3819i		−	0.582397i
$453$			13.1548i			0.618065i
$454$			35.6713i			1.67414i
$455$	3.81310			0.178761
$456$			2.82118i			0.132114i
$457$	−38.4562			−1.79890			−0.899451	−	0.437021i	$-0.856034\pi$
$457$	−38.4562			−1.79890			−0.899451	+	0.437021i	$0.856034\pi$
$458$	54.4829			2.54582
$459$	17.0557	−	12.4199i	0.796091	−	0.579711i
$460$	14.1722			0.660783
$461$	9.17232			0.427197			0.213599	−	0.976921i	$-0.431482\pi$
$461$	9.17232			0.427197			0.213599	+	0.976921i	$0.431482\pi$
$462$		−	3.18755i		−	0.148298i
$463$	17.3391			0.805816			0.402908	−	0.915241i	$-0.368000\pi$
$463$	17.3391			0.805816			0.402908	+	0.915241i	$0.368000\pi$
$464$			26.6196i			1.23578i
$465$		−	5.95071i		−	0.275958i
$466$		−	21.4113i		−	0.991859i
$467$	−14.5702			−0.674228			−0.337114	−	0.941464i	$-0.609451\pi$
$467$	−14.5702			−0.674228			−0.337114	+	0.941464i	$0.609451\pi$
$468$	3.89589			0.180088
$469$		−	9.26612i		−	0.427870i
$470$			20.4526i			0.943406i
$471$			19.8757i			0.915824i
$472$	1.89627			0.0872828
$473$			8.87325i			0.407992i
$474$	29.8872			1.37276
$475$	−5.59701			−0.256809
$476$	−8.54053	+	6.21918i	−0.391455	+	0.285056i
$477$	−6.18643			−0.283257
$478$	23.8003			1.08860
$479$			17.1903i			0.785447i	0.919657	+	0.392723i	$0.128467\pi$
$479$			17.1903i			0.785447i	−0.919657	+	0.392723i	$0.871533\pi$
$480$	13.8472			0.632037
$481$			8.76070i			0.399453i
$482$			16.8708i			0.768443i
$483$		−	8.20359i		−	0.373276i
$484$	−1.58380			−0.0719907
$485$	5.52459			0.250859
$486$			29.8991i			1.35625i
$487$		−	14.8971i		−	0.675052i	−0.941316	−	0.337526i	$-0.890410\pi$
$487$		−	14.8971i		−	0.675052i	0.941316	−	0.337526i	$-0.109590\pi$
$488$		−	10.4975i		−	0.475201i
$489$	15.2816			0.691057
$490$			15.2374i			0.688355i
$491$	26.9549			1.21646			0.608230	−	0.793761i	$-0.291880\pi$
$491$	26.9549			1.21646			0.608230	+	0.793761i	$0.291880\pi$
$492$	−6.72248			−0.303073
$493$	−19.0428	+	13.8669i	−0.857646	+	0.624535i
$494$	−8.35794			−0.376042
$495$	3.52056			0.158238
$496$		−	14.5051i		−	0.651297i
$497$	10.4947			0.470749
$498$		−	17.4100i		−	0.780161i
$499$		−	35.3431i		−	1.58218i	−0.611703	−	0.791088i	$-0.709515\pi$
$499$		−	35.3431i		−	1.58218i	0.611703	−	0.791088i	$-0.290485\pi$
$500$			19.2763i			0.862064i
$501$	14.9994			0.670125
$502$	−21.2616			−0.948953
$503$			14.1091i			0.629092i	0.949242	+	0.314546i	$0.101852\pi$
$503$			14.1091i			0.629092i	−0.949242	+	0.314546i	$0.898148\pi$
$504$			2.44352i			0.108843i
$505$			20.1770i			0.897863i
$506$	−9.22340			−0.410030
$507$		−	11.8157i		−	0.524754i
$508$	2.31730			0.102814
$509$	−34.9202			−1.54781			−0.773905	−	0.633302i	$-0.781699\pi$
$509$	−34.9202			−1.54781			−0.773905	+	0.633302i	$0.781699\pi$
$510$	8.78253	+	12.0607i	0.388897	+	0.534055i
$511$	7.00076			0.309695
$512$	26.4111			1.16722
$513$		−	17.6053i		−	0.777291i
$514$	−17.5324			−0.773322
$515$		−	4.19525i		−	0.184865i
$516$		−	14.6259i		−	0.643868i
$517$		−	5.88243i		−	0.258709i
$518$	20.9094			0.918706
$519$	2.65273			0.116442
$520$		−	1.85699i		−	0.0814346i
$521$			16.3331i			0.715566i	0.933805	+	0.357783i	$0.116467\pi$
$521$			16.3331i			0.715566i	−0.933805	+	0.357783i	$0.883533\pi$
$522$		−	20.7327i		−	0.907446i
$523$	−38.9674			−1.70393			−0.851963	−	0.523602i	$-0.824588\pi$
$523$	−38.9674			−1.70393			−0.851963	+	0.523602i	$0.824588\pi$
$524$		−	31.2483i		−	1.36509i
$525$	2.73922			0.119549
$526$	43.7022			1.90550
$527$	10.3765	−	7.55612i	0.452007	−	0.329150i
$528$	−4.84897			−0.211024
$529$	−0.737696			−0.0320738
$530$		−	11.2212i		−	0.487416i
$531$	−4.61334			−0.200202
$532$			8.81573i			0.382210i
$533$			5.23365i			0.226695i
$534$		−	0.442146i		−	0.0191335i
$535$	1.50672			0.0651412
$536$	−4.51264			−0.194916
$537$		−	22.9507i		−	0.990396i
$538$			21.4173i			0.923364i
$539$		−	4.38248i		−	0.188767i
$540$	−14.8849			−0.640546
$541$		−	2.74107i		−	0.117848i	−0.998262	−	0.0589240i	$-0.981233\pi$
$541$		−	2.74107i		−	0.117848i	0.998262	−	0.0589240i	$-0.0187670\pi$
$542$	48.0028			2.06190
$543$	9.20598			0.395066
$544$	17.5830	+	24.1460i	0.753866	+	1.03525i
$545$	−27.4807			−1.17714
$546$	4.09045			0.175055
$547$		−	15.7423i		−	0.673090i	−0.941667	−	0.336545i	$-0.890742\pi$
$547$		−	15.7423i		−	0.673090i	0.941667	−	0.336545i	$-0.109258\pi$
$548$	−6.56079			−0.280263
$549$			25.5390i			1.08998i
$550$		−	3.07974i		−	0.131321i
$551$			19.6564i			0.837393i
$552$	−3.99518			−0.170046
$553$	−24.5425			−1.04365
$554$			22.0058i			0.934936i
$555$		−	13.0492i		−	0.553907i
$556$			19.8311i			0.841027i
$557$	−35.4962			−1.50402			−0.752011	−	0.659151i	$-0.770916\pi$
$557$	−35.4962			−1.50402			−0.752011	+	0.659151i	$0.770916\pi$
$558$			11.2973i			0.478253i
$559$	−11.3867			−0.481605
$560$	−13.8444			−0.585032
$561$	−2.52597	−	3.46881i	−0.106647	−	0.146453i
$562$	53.5134			2.25733
$563$	−9.71344			−0.409373			−0.204686	−	0.978828i	$-0.565617\pi$
$563$	−9.71344			−0.409373			−0.204686	+	0.978828i	$0.565617\pi$
$564$			9.69608i			0.408279i
$565$	14.3585			0.604065
$566$		−	39.7821i		−	1.67217i
$567$		−	0.687623i		−	0.0288774i
$568$		−	5.11094i		−	0.214450i
$569$	−40.5109			−1.69831			−0.849153	−	0.528146i	$-0.822887\pi$
$569$	−40.5109			−1.69831			−0.849153	+	0.528146i	$0.822887\pi$
$570$	12.4493			0.521443
$571$			11.6285i			0.486639i	0.969946	+	0.243319i	$0.0782363\pi$
$571$			11.6285i			0.486639i	−0.969946	+	0.243319i	$0.921764\pi$
$572$		−	2.03242i		−	0.0849797i
$573$		−	20.0714i		−	0.838494i
$574$	12.4913			0.521376
$575$		−	7.92614i		−	0.330543i
$576$	−8.42660			−0.351108
$577$	−39.1972			−1.63180			−0.815901	−	0.578191i	$-0.803759\pi$
$577$	−39.1972			−1.63180			−0.815901	+	0.578191i	$0.803759\pi$
$578$	−9.87873	+	30.6289i	−0.410901	+	1.27399i
$579$	4.25193			0.176704
$580$	16.6192			0.690074
$581$			14.2966i			0.593122i
$582$	5.92642			0.245658
$583$			3.22736i			0.133663i
$584$		−	3.40940i		−	0.141082i
$585$			4.51779i			0.186788i
$586$	−15.5209			−0.641163
$587$	−1.65131			−0.0681570			−0.0340785	−	0.999419i	$-0.510850\pi$
$587$	−1.65131			−0.0681570			−0.0340785	+	0.999419i	$0.510850\pi$
$588$			7.22369i			0.297900i
$589$		−	10.7108i		−	0.441333i
$590$		−	8.36783i		−	0.344498i
$591$	24.1658			0.994047
$592$		−	31.8079i		−	1.30729i
$593$	−16.1778			−0.664344			−0.332172	−	0.943219i	$-0.607781\pi$
$593$	−16.1778			−0.664344			−0.332172	+	0.943219i	$0.607781\pi$
$594$	9.68725			0.397473
$595$	−7.21196	−	9.90386i	−0.295661	−	0.406019i
$596$	−16.0372			−0.656910
$597$	−12.3502			−0.505461
$598$		−	11.8360i		−	0.484010i
$599$	−24.6091			−1.00550			−0.502751	−	0.864431i	$-0.667679\pi$
$599$	−24.6091			−1.00550			−0.502751	+	0.864431i	$0.667679\pi$
$600$		−	1.33401i		−	0.0544608i
$601$			21.8034i			0.889379i	0.895685	+	0.444690i	$0.146686\pi$
$601$			21.8034i			0.889379i	−0.895685	+	0.444690i	$0.853314\pi$
$602$			27.1769i			1.10765i
$603$	10.9786			0.447082
$604$	20.0190			0.814562
$605$		−	1.83662i		−	0.0746692i
$606$			21.6445i			0.879249i
$607$			23.6599i			0.960326i	0.877179	+	0.480163i	$0.159422\pi$
$607$			23.6599i			0.960326i	−0.877179	+	0.480163i	$0.840578\pi$
$608$	24.9240			1.01080
$609$		−	9.62002i		−	0.389823i
$610$	−46.3234			−1.87558
$611$	7.54868			0.305387
$612$	−7.36854	−	10.1189i	−0.297856	−	0.409032i
$613$	9.35899			0.378006			0.189003	−	0.981977i	$-0.439474\pi$
$613$	9.35899			0.378006			0.189003	+	0.981977i	$0.439474\pi$
$614$	5.49302			0.221680
$615$		−	7.79560i		−	0.314349i
$616$	1.27474			0.0513609
$617$		−	44.6480i		−	1.79746i	−0.438501	−	0.898731i	$-0.644490\pi$
$617$		−	44.6480i		−	1.79746i	0.438501	−	0.898731i	$-0.355510\pi$
$618$		−	4.50039i		−	0.181032i
$619$			48.1191i			1.93407i	0.254646	+	0.967034i	$0.418041\pi$
$619$			48.1191i			1.93407i	−0.254646	+	0.967034i	$0.581959\pi$
$620$	−9.05583			−0.363691
$621$	24.9315			1.00047
$622$			27.0265i			1.08367i
$623$			0.363077i			0.0145464i
$624$		−	6.22248i		−	0.249099i
$625$	−14.2193			−0.568771
$626$		−	45.1694i		−	1.80533i
$627$	−3.58058			−0.142995
$628$	30.2470			1.20699
$629$	22.7544	−	16.5697i	0.907277	−	0.660676i
$630$	10.7827			0.429594
$631$	0.800363			0.0318620			0.0159310	−	0.999873i	$-0.494929\pi$
$631$	0.800363			0.0318620			0.0159310	+	0.999873i	$0.494929\pi$
$632$			11.9523i			0.475436i
$633$	−2.45094			−0.0974162
$634$			10.7520i			0.427018i
$635$			2.68721i			0.106639i
$636$		−	5.31969i		−	0.210939i
$637$	5.62385			0.222825
$638$	−10.8159			−0.428206
$639$			12.4342i			0.491887i
$640$			11.3261i			0.447702i
$641$		−	31.4348i		−	1.24160i	−0.783970	−	0.620799i	$-0.786808\pi$
$641$		−	31.4348i		−	1.24160i	0.783970	−	0.620799i	$-0.213192\pi$
$642$	1.61631			0.0637907
$643$		−	17.2003i		−	0.678313i	−0.940730	−	0.339156i	$-0.889858\pi$
$643$		−	17.2003i		−	0.678313i	0.940730	−	0.339156i	$-0.110142\pi$
$644$	−12.4843			−0.491950
$645$	16.9606			0.667824
$646$	15.8079	+	21.7083i	0.621954	+	0.854102i
$647$	−30.8508			−1.21287			−0.606434	−	0.795134i	$-0.707401\pi$
$647$	−30.8508			−1.21287			−0.606434	+	0.795134i	$0.707401\pi$
$648$	−0.334875			−0.0131551
$649$			2.40670i			0.0944713i
$650$	3.95210			0.155014
$651$			5.24198i			0.205449i
$652$		−	23.2556i		−	0.910760i
$653$			27.8033i			1.08803i	0.839076	+	0.544014i	$0.183096\pi$
$653$			27.8033i			1.08803i	−0.839076	+	0.544014i	$0.816904\pi$
$654$	−29.4795			−1.15274
$655$	36.2365			1.41588
$656$		−	19.0020i		−	0.741905i
$657$			8.29456i			0.323602i
$658$		−	18.0166i		−	0.702362i
$659$	26.7714			1.04286			0.521432	−	0.853293i	$-0.325398\pi$
$659$	26.7714			1.04286			0.521432	+	0.853293i	$0.325398\pi$
$660$			3.02732i			0.117838i
$661$	29.0467			1.12979			0.564893	−	0.825164i	$-0.308917\pi$
$661$	29.0467			1.12979			0.564893	+	0.825164i	$0.308917\pi$
$662$	23.0752			0.896842
$663$	4.45138	−	3.24148i	0.172877	−	0.125888i
$664$	6.96249			0.270197
$665$	−10.2230			−0.396431
$666$			24.7736i			0.959958i
$667$	−27.8362			−1.07782
$668$		−	22.8262i		−	0.883174i
$669$		−	18.2013i		−	0.703705i
$670$			19.9133i			0.769319i
$671$	13.3232			0.514338
$672$	−12.1980			−0.470549
$673$		−	11.2184i		−	0.432436i	−0.976345	−	0.216218i	$-0.930628\pi$
$673$		−	11.2184i		−	0.432436i	0.976345	−	0.216218i	$-0.0693722\pi$
$674$			32.7509i			1.26152i
$675$			8.32475i			0.320420i
$676$	−17.9812			−0.691586
$677$		−	38.4702i		−	1.47853i	−0.673415	−	0.739265i	$-0.735173\pi$
$677$		−	38.4702i		−	1.47853i	0.673415	−	0.739265i	$-0.264827\pi$
$678$	15.4028			0.591542
$679$	−4.86660			−0.186763
$680$	−4.82322	+	3.51225i	−0.184962	+	0.134689i
$681$	−19.6104			−0.751473
$682$	5.89361			0.225678
$683$			1.93556i			0.0740620i	0.999314	+	0.0370310i	$0.0117900\pi$
$683$			1.93556i			0.0740620i	−0.999314	+	0.0370310i	$0.988210\pi$
$684$	−10.4449			−0.399373
$685$		−	7.60809i		−	0.290690i
$686$		−	34.8621i		−	1.33104i
$687$			29.9522i			1.14275i
$688$	41.3421			1.57615
$689$	−4.14153			−0.157780
$690$			17.6299i			0.671159i
$691$			15.0187i			0.571336i	0.958329	+	0.285668i	$0.0922155\pi$
$691$			15.0187i			0.571336i	−0.958329	+	0.285668i	$0.907784\pi$
$692$		−	4.03695i		−	0.153462i
$693$	−3.10126			−0.117807
$694$			31.3025i			1.18823i
$695$	−22.9968			−0.872318
$696$	−4.68499			−0.177584
$697$	13.5935	−	9.89873i	0.514890	−	0.374941i
$698$	34.6556			1.31173
$699$	11.7709			0.445218
$700$		−	4.16857i		−	0.157557i
$701$	12.0090			0.453573			0.226787	−	0.973944i	$-0.427178\pi$
$701$	12.0090			0.453573			0.226787	+	0.973944i	$0.427178\pi$
$702$			12.4312i			0.469187i
$703$		−	23.4876i		−	0.885851i
$704$			4.39602i			0.165681i
$705$	−11.2439			−0.423469
$706$	38.2148			1.43823
$707$		−	17.7739i		−	0.668455i
$708$		−	3.96699i		−	0.149089i
$709$			5.86949i			0.220433i	0.993908	+	0.110217i	$0.0351545\pi$
$709$			5.86949i			0.220433i	−0.993908	+	0.110217i	$0.964846\pi$
$710$	−22.5535			−0.846417
$711$		−	29.0781i		−	1.09052i
$712$	0.176820			0.00662661
$713$	15.1680			0.568047
$714$	−7.73652	−	10.6242i	−0.289532	−	0.397601i
$715$	2.35686			0.0881414
$716$	−34.9266			−1.30527
$717$			13.0843i			0.488641i
$718$	5.51579			0.205847
$719$		−	16.3726i		−	0.610596i	−0.952257	−	0.305298i	$-0.901244\pi$
$719$		−	16.3726i		−	0.610596i	0.952257	−	0.305298i	$-0.0987561\pi$
$720$		−	16.4029i		−	0.611302i
$721$			3.69559i			0.137631i
$722$	−13.5609			−0.504686
$723$	−9.27478			−0.344933
$724$		−	14.0097i		−	0.520667i
$725$		−	9.29466i		−	0.345195i
$726$		−	1.97021i		−	0.0731212i
$727$	2.82341			0.104714			0.0523572	−	0.998628i	$-0.483327\pi$
$727$	2.82341			0.104714			0.0523572	+	0.998628i	$0.483327\pi$
$728$			1.63582i			0.0606277i
$729$	−15.1621			−0.561559
$730$	−15.0450			−0.556839
$731$	21.5363	+	29.5749i	0.796550	+	1.09387i
$732$	−21.9608			−0.811696
$733$	−12.8741			−0.475515			−0.237757	−	0.971325i	$-0.576412\pi$
$733$	−12.8741			−0.475515			−0.237757	+	0.971325i	$0.576412\pi$
$734$		−	7.83288i		−	0.289117i
$735$	−8.37681			−0.308983
$736$			35.2959i			1.30102i
$737$		−	5.72734i		−	0.210969i
$738$			14.7998i			0.544788i
$739$	−3.30278			−0.121495			−0.0607473	−	0.998153i	$-0.519348\pi$
$739$	−3.30278			−0.121495			−0.0607473	+	0.998153i	$0.519348\pi$
$740$	−19.8583			−0.730007
$741$		−	4.59481i		−	0.168795i
$742$			9.88471i			0.362879i
$743$		−	32.6094i		−	1.19632i	−0.801376	−	0.598161i	$-0.795898\pi$
$743$		−	32.6094i		−	1.19632i	0.801376	−	0.598161i	$-0.204102\pi$
$744$	2.55286			0.0935925
$745$		−	18.5972i		−	0.681350i
$746$	−40.4606			−1.48137
$747$	−16.9387			−0.619755
$748$	−5.27886	+	3.84404i	−0.193014	+	0.140552i
$749$	−1.32727			−0.0484973
$750$	−23.9793			−0.875600
$751$			8.35109i			0.304736i	0.988324	+	0.152368i	$0.0486898\pi$
$751$			8.35109i			0.304736i	−0.988324	+	0.152368i	$0.951310\pi$
$752$	−27.4073			−0.999442
$753$		−	11.6887i		−	0.425959i
$754$		−	13.8796i		−	0.505465i
$755$			23.2147i			0.844868i
$756$	13.1121			0.476883
$757$	24.5010			0.890504			0.445252	−	0.895405i	$-0.353114\pi$
$757$	24.5010			0.890504			0.445252	+	0.895405i	$0.353114\pi$
$758$			44.4963i			1.61618i
$759$		−	5.07060i		−	0.184051i
$760$			4.97864i			0.180594i
$761$	−45.1252			−1.63579			−0.817893	−	0.575370i	$-0.804858\pi$
$761$	−45.1252			−1.63579			−0.817893	+	0.575370i	$0.804858\pi$
$762$			2.88267i			0.104428i
$763$	24.2077			0.876377
$764$	−30.5447			−1.10507
$765$	11.7342	−	8.54478i	0.424250	−	0.308937i
$766$	3.88751			0.140462
$767$	−3.08842			−0.111516
$768$			21.3000i			0.768599i
$769$	−44.8524			−1.61742			−0.808709	−	0.588208i	$-0.799834\pi$
$769$	−44.8524			−1.61742			−0.808709	+	0.588208i	$0.799834\pi$
$770$		−	5.62517i		−	0.202717i
$771$		−	9.63852i		−	0.347123i
$772$		−	6.47061i		−	0.232882i
$773$	−31.7881			−1.14334			−0.571670	−	0.820484i	$-0.693704\pi$
$773$	−31.7881			−1.14334			−0.571670	+	0.820484i	$0.693704\pi$
$774$	−32.1994			−1.15738
$775$			5.06469i			0.181929i
$776$			2.37006i			0.0850800i
$777$			11.4950i			0.412381i
$778$	36.4168			1.30560
$779$		−	14.0315i		−	0.502731i
$780$	−3.88483			−0.139099
$781$	6.48669			0.232112
$782$	−30.7419	+	22.3862i	−1.09933	+	0.800528i
$783$	29.2361			1.04481
$784$	−20.4188			−0.729242
$785$			35.0753i			1.25189i
$786$	38.8722			1.38653
$787$			5.53260i			0.197216i	0.995126	+	0.0986079i	$0.0314389\pi$
$787$			5.53260i			0.197216i	−0.995126	+	0.0986079i	$0.968561\pi$
$788$		−	36.7756i		−	1.31008i
$789$			24.0254i			0.855328i
$790$	52.7429			1.87651
$791$	−12.6484			−0.449724
$792$			1.51033i			0.0536671i
$793$			17.0972i			0.607138i
$794$		−	62.1902i		−	2.20705i
$795$	6.16888			0.218787
$796$			18.7947i			0.666159i
$797$	13.0130			0.460943			0.230471	−	0.973079i	$-0.425973\pi$
$797$	13.0130			0.460943			0.230471	+	0.973079i	$0.425973\pi$
$798$	−10.9666			−0.388212
$799$	−14.2773	−	19.6064i	−0.505094	−	0.693624i
$800$	−11.7855			−0.416679
$801$	−0.430177			−0.0151996
$802$		−	65.3528i		−	2.30769i
$803$	4.32713			0.152701
$804$			9.44044i			0.332939i
$805$		−	14.4772i		−	0.510253i
$806$			7.56303i			0.266396i
$807$	−11.7742			−0.414472
$808$	−8.65594			−0.304515
$809$		−	53.2764i		−	1.87310i	−0.350537	−	0.936549i	$-0.614001\pi$
$809$		−	53.2764i		−	1.87310i	0.350537	−	0.936549i	$-0.385999\pi$
$810$			1.47773i			0.0519222i
$811$		−	7.78374i		−	0.273324i	−0.990618	−	0.136662i	$-0.956363\pi$
$811$		−	7.78374i		−	0.273324i	0.990618	−	0.136662i	$-0.0436374\pi$
$812$	−14.6398			−0.513757
$813$			26.3897i			0.925528i
$814$	12.9240			0.452985
$815$	26.9679			0.944645
$816$	−16.1618	+	11.7690i	−0.565776	+	0.411996i
$817$	30.5279			1.06803
$818$	−9.36617			−0.327480
$819$		−	3.97972i		−	0.139063i
$820$	−11.8634			−0.414288
$821$		−	6.90266i		−	0.240904i	−0.992719	−	0.120452i	$-0.961566\pi$
$821$		−	6.90266i		−	0.240904i	0.992719	−	0.120452i	$-0.0384345\pi$
$822$		−	8.16146i		−	0.284664i
$823$			14.9280i			0.520359i	0.965560	+	0.260179i	$0.0837817\pi$
$823$			14.9280i			0.520359i	−0.965560	+	0.260179i	$0.916218\pi$
$824$	1.79977			0.0626979
$825$	1.69310			0.0589461
$826$			7.37121i			0.256477i
$827$			37.7846i			1.31390i	0.753935	+	0.656949i	$0.228153\pi$
$827$			37.7846i			1.31390i	−0.753935	+	0.656949i	$0.771847\pi$
$828$		−	14.7915i		−	0.514040i
$829$	21.2552			0.738225			0.369112	−	0.929385i	$-0.379662\pi$
$829$	21.2552			0.738225			0.369112	+	0.929385i	$0.379662\pi$
$830$		−	30.7240i		−	1.06645i
$831$	−12.0978			−0.419667
$832$	−5.64123			−0.195574
$833$	−10.6367	−	14.6070i	−0.368541	−	0.506102i
$834$	−24.6695			−0.854233
$835$	26.4700			0.916032
$836$			5.44895i			0.188456i
$837$	−15.9308			−0.550651
$838$		−	67.9675i		−	2.34790i
$839$			45.0109i			1.55395i	0.629533	+	0.776974i	$0.283246\pi$
$839$			45.0109i			1.55395i	−0.629533	+	0.776974i	$0.716754\pi$
$840$		−	2.43658i		−	0.0840702i
$841$	−3.64242			−0.125601
$842$	69.0666			2.38019
$843$			29.4192i			1.01325i
$844$			3.72986i			0.128387i
$845$		−	20.8516i		−	0.717317i
$846$	21.3463			0.733900
$847$			1.61788i			0.0555909i
$848$	15.0368			0.516367
$849$	21.8704			0.750589
$850$	−7.47486	−	10.2649i	−0.256386	−	0.352083i
$851$	33.2617			1.14020
$852$	−10.6921			−0.366305
$853$		−	22.2427i		−	0.761575i	−0.924663	−	0.380787i	$-0.875653\pi$
$853$		−	22.2427i		−	0.761575i	0.924663	−	0.380787i	$-0.124347\pi$
$854$	40.8062			1.39636
$855$		−	12.1123i		−	0.414231i
$856$			0.646384i			0.0220930i
$857$		−	16.2076i		−	0.553643i	−0.960921	−	0.276821i	$-0.910719\pi$
$857$		−	16.2076i		−	0.553643i	0.960921	−	0.276821i	$-0.0892810\pi$
$858$	2.52828			0.0863141
$859$	−49.0231			−1.67265			−0.836324	−	0.548236i	$-0.815300\pi$
$859$	−49.0231			−1.67265			−0.836324	+	0.548236i	$0.815300\pi$
$860$		−	25.8108i		−	0.880140i
$861$			6.86713i			0.234031i
$862$			31.9301i			1.08754i
$863$	38.6478			1.31559			0.657793	−	0.753199i	$-0.271490\pi$
$863$	38.6478			1.31559			0.657793	+	0.753199i	$0.271490\pi$
$864$		−	37.0709i		−	1.26118i
$865$	4.68137			0.159171
$866$	−71.3005			−2.42289
$867$	−16.8383	−	5.43087i	−0.571860	−	0.184442i
$868$	7.97727			0.270766
$869$	−15.1696			−0.514593
$870$			20.6739i			0.700910i
$871$	7.34966			0.249034
$872$		−	11.7892i		−	0.399234i
$873$		−	5.76599i		−	0.195149i
$874$			31.7325i			1.07337i
$875$	19.6911			0.665681
$876$	−7.13246			−0.240983
$877$			20.9561i			0.707636i	0.935314	+	0.353818i	$0.115117\pi$
$877$			20.9561i			0.707636i	−0.935314	+	0.353818i	$0.884883\pi$
$878$			12.0584i			0.406952i
$879$		−	8.53267i		−	0.287800i
$880$	−8.55714			−0.288461
$881$		−	12.6670i		−	0.426763i	−0.976969	−	0.213381i	$-0.931552\pi$
$881$		−	12.6670i		−	0.426763i	0.976969	−	0.213381i	$-0.0684477\pi$
$882$	15.9032			0.535489
$883$	−18.7345			−0.630466			−0.315233	−	0.949014i	$-0.602083\pi$
$883$	−18.7345			−0.630466			−0.315233	+	0.949014i	$0.602083\pi$
$884$	−4.93290	−	6.77414i	−0.165911	−	0.227839i
$885$	4.60025			0.154636
$886$	62.0637			2.08507
$887$			53.7375i			1.80433i	0.431392	+	0.902165i	$0.358023\pi$
$887$			53.7375i			1.80433i	−0.431392	+	0.902165i	$0.641977\pi$
$888$	5.59812			0.187861
$889$		−	2.36716i		−	0.0793921i
$890$		−	0.780270i		−	0.0261547i
$891$		−	0.425016i		−	0.0142386i
$892$	−27.6989			−0.927429
$893$	−20.2381			−0.677244
$894$		−	19.9499i		−	0.667225i
$895$		−	40.5019i		−	1.35383i
$896$		−	9.97713i		−	0.333312i
$897$	6.50689			0.217259
$898$			51.0189i			1.70252i
$899$	17.7869			0.593228
$900$	4.93895			0.164632
$901$	7.83314	+	10.7569i	0.260960	+	0.358365i
$902$	7.72080			0.257074
$903$	−14.9406			−0.497192
$904$			6.15980i			0.204872i
$905$	16.2461			0.540039
$906$			24.9032i			0.827353i
$907$			46.0800i			1.53006i	0.643994	+	0.765031i	$0.277276\pi$
$907$			46.0800i			1.53006i	−0.643994	+	0.765031i	$0.722724\pi$
$908$			29.8433i			0.990383i
$909$	21.0586			0.698470
$910$	7.21855			0.239293
$911$			48.5919i			1.60992i	0.593329	+	0.804960i	$0.297814\pi$
$911$			48.5919i			1.60992i	−0.593329	+	0.804960i	$0.702186\pi$
$912$			16.6826i			0.552415i
$913$			8.83664i			0.292450i
$914$	−72.8010			−2.40804
$915$		−	25.4665i		−	0.841896i
$916$	45.5814			1.50605
$917$	−31.9207			−1.05411
$918$	32.2880	−	23.5120i	1.06566	−	0.776011i
$919$	−39.7916			−1.31260			−0.656301	−	0.754499i	$-0.727880\pi$
$919$	−39.7916			−1.31260			−0.656301	+	0.754499i	$0.727880\pi$
$920$	−7.05043			−0.232446
$921$			3.01981i			0.0995061i
$922$	17.3640			0.571854
$923$			8.32409i			0.273991i
$924$		−	2.66676i		−	0.0877300i
$925$			11.1062i			0.365171i
$926$	32.8245			1.07868
$927$	−4.37857			−0.143811
$928$			41.3900i			1.35869i
$929$		−	25.1461i		−	0.825015i	−0.910954	−	0.412508i	$-0.864653\pi$
$929$		−	25.1461i		−	0.825015i	0.910954	−	0.412508i	$-0.135347\pi$
$930$		−	11.2652i		−	0.369402i
$931$	−15.0776			−0.494150
$932$		−	17.9131i		−	0.586763i
$933$	−14.8579			−0.486427
$934$	−27.5827			−0.902534
$935$	−4.45767	−	6.12152i	−0.145781	−	0.200195i
$936$	−1.93814			−0.0633500
$937$	17.0306			0.556365			0.278182	−	0.960528i	$-0.410268\pi$
$937$	17.0306			0.556365			0.278182	+	0.960528i	$0.410268\pi$
$938$		−	17.5416i		−	0.572754i
$939$	24.8321			0.810364
$940$			17.1110i			0.558099i
$941$		−	6.00656i		−	0.195808i	−0.995196	−	0.0979041i	$-0.968786\pi$
$941$		−	6.00656i		−	0.195808i	0.995196	−	0.0979041i	$-0.0312139\pi$
$942$			37.6265i			1.22594i
$943$	19.8705			0.647074
$944$	11.2133			0.364960
$945$			15.2052i			0.494626i
$946$			16.7979i			0.546146i
$947$			11.9775i			0.389217i	0.980881	+	0.194609i	$0.0623437\pi$
$947$			11.9775i			0.389217i	−0.980881	+	0.194609i	$0.937656\pi$
$948$	25.0042			0.812098
$949$			5.55283i			0.180252i
$950$	−10.5957			−0.343768
$951$	−5.91097			−0.191676
$952$	4.24877	−	3.09394i	0.137703	−	0.100275i
$953$	−8.71556			−0.282325			−0.141162	−	0.989986i	$-0.545084\pi$
$953$	−8.71556			−0.282325			−0.141162	+	0.989986i	$0.545084\pi$
$954$	−11.7115			−0.379173
$955$		−	35.4206i		−	1.14618i
$956$	19.9117			0.643992
$957$		−	5.94608i		−	0.192210i
$958$			32.5429i			1.05141i
$959$			6.70196i			0.216417i
$960$	8.40269			0.271196
$961$	21.3078			0.687350
$962$			16.5848i			0.534716i
$963$		−	1.57256i		−	0.0506749i
$964$			14.1144i			0.454595i
$965$	7.50352			0.241547
$966$		−	15.5302i		−	0.499675i
$967$	16.1880			0.520571			0.260286	−	0.965532i	$-0.416183\pi$
$967$	16.1880			0.520571			0.260286	+	0.965532i	$0.416183\pi$
$968$	0.787912			0.0253244
$969$	−11.9342	+	8.69046i	−0.383382	+	0.279178i
$970$	10.4586			0.335804
$971$	6.82159			0.218915			0.109458	−	0.993991i	$-0.465089\pi$
$971$	6.82159			0.218915			0.109458	+	0.993991i	$0.465089\pi$
$972$			25.0142i			0.802330i
$973$	20.2578			0.649436
$974$		−	28.2016i		−	0.903637i
$975$			2.17268i			0.0695815i
$976$		−	62.0754i		−	1.98699i
$977$	49.6393			1.58810			0.794050	−	0.607852i	$-0.207969\pi$
$977$	49.6393			1.58810			0.794050	+	0.607852i	$0.207969\pi$
$978$	28.9294			0.925062
$979$			0.224416i			0.00717237i
$980$			12.7479i			0.407216i
$981$			28.6815i			0.915729i
$982$	51.0282			1.62837
$983$		−	39.8844i		−	1.27212i	−0.771641	−	0.636058i	$-0.780564\pi$
$983$		−	39.8844i		−	1.27212i	0.771641	−	0.636058i	$-0.219436\pi$
$984$	3.34432			0.106613
$985$	42.6461			1.35882
$986$	−36.0498	+	26.2514i	−1.14806	+	0.836013i
$987$	9.90471			0.315271
$988$	−6.99241			−0.222458
$989$			43.2317i			1.37469i
$990$	6.66475			0.211820
$991$			51.9941i			1.65165i	0.563928	+	0.825824i	$0.309289\pi$
$991$			51.9941i			1.65165i	−0.563928	+	0.825824i	$0.690711\pi$
$992$		−	22.5535i		−	0.716075i
$993$			12.6857i			0.402568i
$994$	19.8673			0.630154
$995$	−21.7949			−0.690944
$996$		−	14.5655i		−	0.461527i
$997$			37.2080i			1.17839i	0.807991	+	0.589195i	$0.200555\pi$
$997$			37.2080i			1.17839i	−0.807991	+	0.589195i	$0.799445\pi$
$998$		−	66.9078i		−	2.11793i
$999$	−34.9344			−1.10528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.d.a.67.14	yes	16
3.2	odd	2		1683.2.g.b.1189.3		16
4.3	odd	2		2992.2.b.g.1937.6		16
17.4	even	4		3179.2.a.bc.1.2		8
17.13	even	4		3179.2.a.bb.1.2		8
17.16	even	2	inner	187.2.d.a.67.13	✓	16
51.50	odd	2		1683.2.g.b.1189.4		16
68.67	odd	2		2992.2.b.g.1937.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.13	✓	16	17.16	even	2	inner
187.2.d.a.67.14	yes	16	1.1	even	1	trivial
1683.2.g.b.1189.3		16	3.2	odd	2
1683.2.g.b.1189.4		16	51.50	odd	2
2992.2.b.g.1937.6		16	4.3	odd	2
2992.2.b.g.1937.11		16	68.67	odd	2
3179.2.a.bb.1.2		8	17.13	even	4
3179.2.a.bc.1.2		8	17.4	even	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.89309 q^{2} +1.04073i q^{3} +1.58380 q^{4} +1.83662i q^{5} +1.97021i q^{6} -1.61788i q^{7} -0.787912 q^{8} +1.91687 q^{9} +O(q^{10})\)	\(q+1.89309 q^{2} +1.04073i q^{3} +1.58380 q^{4} +1.83662i q^{5} +1.97021i q^{6} -1.61788i q^{7} -0.787912 q^{8} +1.91687 q^{9} +3.47689i q^{10} -1.00000i q^{11} +1.64831i q^{12} +1.28326 q^{13} -3.06279i q^{14} -1.91143 q^{15} -4.65918 q^{16} +(-2.42711 - 3.33304i) q^{17} +3.62882 q^{18} -3.44044 q^{19} +2.90883i q^{20} +1.68378 q^{21} -1.89309i q^{22} -4.87213i q^{23} -0.820007i q^{24} +1.62683 q^{25} +2.42933 q^{26} +5.11716i q^{27} -2.56239i q^{28} -5.71335i q^{29} -3.61852 q^{30} +3.11322i q^{31} -7.24444 q^{32} +1.04073 q^{33} +(-4.59474 - 6.30975i) q^{34} +2.97142 q^{35} +3.03594 q^{36} +6.82692i q^{37} -6.51307 q^{38} +1.33553i q^{39} -1.44709i q^{40} +4.07841i q^{41} +3.18755 q^{42} -8.87325 q^{43} -1.58380i q^{44} +3.52056i q^{45} -9.22340i q^{46} +5.88243 q^{47} -4.84897i q^{48} +4.38248 q^{49} +3.07974 q^{50} +(3.46881 - 2.52597i) q^{51} +2.03242 q^{52} -3.22736 q^{53} +9.68725i q^{54} +1.83662 q^{55} +1.27474i q^{56} -3.58058i q^{57} -10.8159i q^{58} -2.40670 q^{59} -3.02732 q^{60} +13.3232i q^{61} +5.89361i q^{62} -3.10126i q^{63} -4.39602 q^{64} +2.35686i q^{65} +1.97021 q^{66} +5.72734 q^{67} +(-3.84404 - 5.27886i) q^{68} +5.07060 q^{69} +5.62517 q^{70} +6.48669i q^{71} -1.51033 q^{72} +4.32713i q^{73} +12.9240i q^{74} +1.69310i q^{75} -5.44895 q^{76} -1.61788 q^{77} +2.52828i q^{78} -15.1696i q^{79} -8.55714i q^{80} +0.425016 q^{81} +7.72080i q^{82} -8.83664 q^{83} +2.66676 q^{84} +(6.12152 - 4.45767i) q^{85} -16.7979 q^{86} +5.94608 q^{87} +0.787912i q^{88} -0.224416 q^{89} +6.66475i q^{90} -2.07615i q^{91} -7.71647i q^{92} -3.24004 q^{93} +11.1360 q^{94} -6.31877i q^{95} -7.53953i q^{96} -3.00802i q^{97} +8.29644 q^{98} -1.91687i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

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