LMFDB - Embedded newform 138.3.c.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,3,Mod(47,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("138.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	138.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.76022764817$
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} - 4 x^{15} + 10 x^{14} + 8 x^{13} - 119 x^{12} + 416 x^{11} - 774 x^{10} - 1284 x^{9} + \cdots + 43046721 $ x^16 - 4x^15 + 10x^14 + 8x^13 - 119x^12 + 416x^11 - 774x^10 - 1284x^9 + 7956x^8 - 11556x^7 - 62694x^6 + 303264x^5 - 780759x^4 + 472392x^3 + 5314410x^2 - 19131876*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.10
Root			$-2.52762 + 1.61590i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-2.52762 + 1.61590i) q^{3} -2.00000 q^{4} +7.30416i q^{5} +(-2.28522 - 3.57460i) q^{6} -0.709880 q^{7} -2.82843i q^{8} +(3.77777 - 8.16875i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-2.52762 + 1.61590i) q^{3} -2.00000 q^{4} +7.30416i q^{5} +(-2.28522 - 3.57460i) q^{6} -0.709880 q^{7} -2.82843i q^{8} +(3.77777 - 8.16875i) q^{9} -10.3296 q^{10} -9.86845i q^{11} +(5.05525 - 3.23179i) q^{12} -21.4745 q^{13} -1.00392i q^{14} +(-11.8028 - 18.4622i) q^{15} +4.00000 q^{16} +17.8501i q^{17} +(11.5524 + 5.34257i) q^{18} -8.45342 q^{19} -14.6083i q^{20} +(1.79431 - 1.14709i) q^{21} +13.9561 q^{22} +4.79583i q^{23} +(4.57044 + 7.14920i) q^{24} -28.3507 q^{25} -30.3695i q^{26} +(3.65107 + 26.7520i) q^{27} +1.41976 q^{28} +4.47621i q^{29} +(26.1094 - 16.6916i) q^{30} +55.2374 q^{31} +5.65685i q^{32} +(15.9464 + 24.9437i) q^{33} -25.2439 q^{34} -5.18507i q^{35} +(-7.55553 + 16.3375i) q^{36} -19.3291 q^{37} -11.9549i q^{38} +(54.2794 - 34.7005i) q^{39} +20.6593 q^{40} +75.6542i q^{41} +(1.62223 + 2.53754i) q^{42} -66.6055 q^{43} +19.7369i q^{44} +(59.6658 + 27.5934i) q^{45} -6.78233 q^{46} +30.7589i q^{47} +(-10.1105 + 6.46358i) q^{48} -48.4961 q^{49} -40.0939i q^{50} +(-28.8439 - 45.1184i) q^{51} +42.9489 q^{52} +39.2428i q^{53} +(-37.8330 + 5.16339i) q^{54} +72.0807 q^{55} +2.00784i q^{56} +(21.3671 - 13.6598i) q^{57} -6.33031 q^{58} -1.11395i q^{59} +(23.6055 + 36.9243i) q^{60} -46.9023 q^{61} +78.1174i q^{62} +(-2.68176 + 5.79883i) q^{63} -8.00000 q^{64} -156.853i q^{65} +(-35.2758 + 22.5516i) q^{66} +12.3457 q^{67} -35.7003i q^{68} +(-7.74956 - 12.1221i) q^{69} +7.33280 q^{70} -5.12755i q^{71} +(-23.1047 - 10.6851i) q^{72} +67.8005 q^{73} -27.3355i q^{74} +(71.6599 - 45.8118i) q^{75} +16.9068 q^{76} +7.00542i q^{77} +(49.0739 + 76.7626i) q^{78} +137.452 q^{79} +29.2166i q^{80} +(-52.4570 - 61.7193i) q^{81} -106.991 q^{82} -26.8265i q^{83} +(-3.58862 + 2.29418i) q^{84} -130.380 q^{85} -94.1944i q^{86} +(-7.23308 - 11.3142i) q^{87} -27.9122 q^{88} +88.0712i q^{89} +(-39.0230 + 84.3802i) q^{90} +15.2443 q^{91} -9.59166i q^{92} +(-139.619 + 89.2578i) q^{93} -43.4997 q^{94} -61.7451i q^{95} +(-9.14088 - 14.2984i) q^{96} +0.0454437 q^{97} -68.5838i q^{98} +(-80.6129 - 37.2807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−2.52762	+	1.61590i	−0.842541	+	0.538632i
$3$	−2.52762	+	1.61590i	−0.842541	+	0.538632i
$4$	−2.00000			−0.500000
$5$			7.30416i			1.46083i	0.683003	+	0.730416i	$0.260674\pi$
$5$			7.30416i			1.46083i	−0.683003	+	0.730416i	$0.739326\pi$
$6$	−2.28522	−	3.57460i	−0.380870	−	0.595767i
$7$	−0.709880			−0.101411			−0.0507057	−	0.998714i	$-0.516147\pi$
$7$	−0.709880			−0.101411			−0.0507057	+	0.998714i	$0.516147\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.77777	−	8.16875i	0.419752	−	0.907639i
$10$	−10.3296			−1.03296
$11$		−	9.86845i		−	0.897132i	−0.893750	−	0.448566i	$-0.851935\pi$
$11$		−	9.86845i		−	0.897132i	0.893750	−	0.448566i	$-0.148065\pi$
$12$	5.05525	−	3.23179i	0.421271	−	0.269316i
$13$	−21.4745			−1.65188			−0.825941	−	0.563757i	$-0.809356\pi$
$13$	−21.4745			−1.65188			−0.825941	+	0.563757i	$0.809356\pi$
$14$		−	1.00392i		−	0.0717087i
$15$	−11.8028	−	18.4622i	−0.786850	−	1.23081i
$16$	4.00000			0.250000
$17$			17.8501i			1.05001i	0.851100	+	0.525004i	$0.175936\pi$
$17$			17.8501i			1.05001i	−0.851100	+	0.525004i	$0.824064\pi$
$18$	11.5524	+	5.34257i	0.641798	+	0.296809i
$19$	−8.45342			−0.444917			−0.222458	−	0.974942i	$-0.571408\pi$
$19$	−8.45342			−0.444917			−0.222458	+	0.974942i	$0.571408\pi$
$20$		−	14.6083i		−	0.730416i
$21$	1.79431	−	1.14709i	0.0854433	−	0.0546234i
$22$	13.9561			0.634368
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	4.57044	+	7.14920i	0.190435	+	0.297883i
$25$	−28.3507			−1.13403
$26$		−	30.3695i		−	1.16806i
$27$	3.65107	+	26.7520i	0.135225	+	0.990815i
$28$	1.41976			0.0507057
$29$			4.47621i			0.154352i	0.997017	+	0.0771760i	$0.0245903\pi$
$29$			4.47621i			0.154352i	−0.997017	+	0.0771760i	$0.975410\pi$
$30$	26.1094	−	16.6916i	0.870315	−	0.556387i
$31$	55.2374			1.78185			0.890925	−	0.454150i	$-0.150057\pi$
$31$	55.2374			1.78185			0.890925	+	0.454150i	$0.150057\pi$
$32$			5.65685i			0.176777i
$33$	15.9464	+	24.9437i	0.483224	+	0.755871i
$34$	−25.2439			−0.742468
$35$		−	5.18507i		−	0.148145i
$36$	−7.55553	+	16.3375i	−0.209876	+	0.453819i
$37$	−19.3291			−0.522408			−0.261204	−	0.965284i	$-0.584120\pi$
$37$	−19.3291			−0.522408			−0.261204	+	0.965284i	$0.584120\pi$
$38$		−	11.9549i		−	0.314604i
$39$	54.2794	−	34.7005i	1.39178	−	0.889756i
$40$	20.6593			0.516482
$41$			75.6542i			1.84523i	0.385728	+	0.922613i	$0.373950\pi$
$41$			75.6542i			1.84523i	−0.385728	+	0.922613i	$0.626050\pi$
$42$	1.62223	+	2.53754i	0.0386246	+	0.0604175i
$43$	−66.6055			−1.54896			−0.774482	−	0.632596i	$-0.781990\pi$
$43$	−66.6055			−1.54896			−0.774482	+	0.632596i	$0.781990\pi$
$44$			19.7369i			0.448566i
$45$	59.6658	+	27.5934i	1.32591	+	0.613187i
$46$	−6.78233			−0.147442
$47$			30.7589i			0.654445i	0.944947	+	0.327222i	$0.106113\pi$
$47$			30.7589i			0.654445i	−0.944947	+	0.327222i	$0.893887\pi$
$48$	−10.1105	+	6.46358i	−0.210635	+	0.134658i
$49$	−48.4961			−0.989716
$50$		−	40.0939i		−	0.801879i
$51$	−28.8439	−	45.1184i	−0.565567	−	0.884675i
$52$	42.9489			0.825941
$53$			39.2428i			0.740430i	0.928946	+	0.370215i	$0.120716\pi$
$53$			39.2428i			0.740430i	−0.928946	+	0.370215i	$0.879284\pi$
$54$	−37.8330	+	5.16339i	−0.700612	+	0.0956184i
$55$	72.0807			1.31056
$56$			2.00784i			0.0358543i
$57$	21.3671	−	13.6598i	0.374861	−	0.239646i
$58$	−6.33031			−0.109143
$59$		−	1.11395i		−	0.0188805i	−0.999955	−	0.00944026i	$-0.996995\pi$
$59$		−	1.11395i		−	0.0188805i	0.999955	−	0.00944026i	$-0.00300497\pi$
$60$	23.6055	+	36.9243i	0.393425	+	0.615405i
$61$	−46.9023			−0.768890			−0.384445	−	0.923148i	$-0.625607\pi$
$61$	−46.9023			−0.768890			−0.384445	+	0.923148i	$0.625607\pi$
$62$			78.1174i			1.25996i
$63$	−2.68176	+	5.79883i	−0.0425676	+	0.0920449i
$64$	−8.00000			−0.125000
$65$		−	156.853i		−	2.41312i
$66$	−35.2758	+	22.5516i	−0.534481	+	0.341691i
$67$	12.3457			0.184265			0.0921324	−	0.995747i	$-0.470632\pi$
$67$	12.3457			0.184265			0.0921324	+	0.995747i	$0.470632\pi$
$68$		−	35.7003i		−	0.525004i
$69$	−7.74956	−	12.1221i	−0.112312	−	0.175682i
$70$	7.33280			0.104754
$71$		−	5.12755i		−	0.0722191i	−0.999348	−	0.0361095i	$-0.988503\pi$
$71$		−	5.12755i		−	0.0722191i	0.999348	−	0.0361095i	$-0.0114965\pi$
$72$	−23.1047	−	10.6851i	−0.320899	−	0.148405i
$73$	67.8005			0.928774			0.464387	−	0.885632i	$-0.346275\pi$
$73$	67.8005			0.928774			0.464387	+	0.885632i	$0.346275\pi$
$74$		−	27.3355i		−	0.369398i
$75$	71.6599	−	45.8118i	0.955466	−	0.610823i
$76$	16.9068			0.222458
$77$			7.00542i			0.0909794i
$78$	49.0739	+	76.7626i	0.629152	+	0.984136i
$79$	137.452			1.73990			0.869951	−	0.493137i	$-0.164150\pi$
$79$	137.452			1.73990			0.869951	+	0.493137i	$0.164150\pi$
$80$			29.2166i			0.365208i
$81$	−52.4570	−	61.7193i	−0.647617	−	0.761966i
$82$	−106.991			−1.30477
$83$		−	26.8265i		−	0.323210i	−0.986856	−	0.161605i	$-0.948333\pi$
$83$		−	26.8265i		−	0.323210i	0.986856	−	0.161605i	$-0.0516671\pi$
$84$	−3.58862	+	2.29418i	−0.0427217	+	0.0273117i
$85$	−130.380			−1.53388
$86$		−	94.1944i		−	1.09528i
$87$	−7.23308	−	11.3142i	−0.0831388	−	0.130048i
$88$	−27.9122			−0.317184
$89$			88.0712i			0.989564i	0.869017	+	0.494782i	$0.164752\pi$
$89$			88.0712i			0.989564i	−0.869017	+	0.494782i	$0.835248\pi$
$90$	−39.0230	+	84.3802i	−0.433588	+	0.937558i
$91$	15.2443			0.167520
$92$		−	9.59166i		−	0.104257i
$93$	−139.619	+	89.2578i	−1.50128	+	0.959761i
$94$	−43.4997			−0.462762
$95$		−	61.7451i		−	0.649948i
$96$	−9.14088	−	14.2984i	−0.0952175	−	0.148942i
$97$	0.0454437			0.000468492			0.000234246	−	1.00000i	$-0.499925\pi$
$97$	0.0454437			0.000468492			0.000234246		1.00000i	$0.499925\pi$
$98$		−	68.5838i		−	0.699835i
$99$	−80.6129	−	37.2807i	−0.814272	−	0.376573i
$100$	56.7014			0.567014
$101$		−	103.598i		−	1.02572i	−0.858472	−	0.512861i	$-0.828586\pi$
$101$		−	103.598i		−	1.02572i	0.858472	−	0.512861i	$-0.171414\pi$
$102$	63.8071	−	40.7915i	0.625560	−	0.399917i
$103$	−108.174			−1.05023			−0.525117	−	0.851030i	$-0.675978\pi$
$103$	−108.174			−1.05023			−0.525117	+	0.851030i	$0.675978\pi$
$104$			60.7390i			0.584028i
$105$	8.37853	+	13.1059i	0.0797956	+	0.124818i
$106$	−55.4977			−0.523563
$107$			0.217685i			0.00203444i	0.999999	+	0.00101722i	$0.000323792\pi$
$107$			0.217685i			0.00203444i	−0.999999	+	0.00101722i	$0.999676\pi$
$108$	−7.30214	−	53.5040i	−0.0676124	−	0.495407i
$109$	133.129			1.22137			0.610684	−	0.791874i	$-0.290894\pi$
$109$	133.129			1.22137			0.610684	+	0.791874i	$0.290894\pi$
$110$			101.938i			0.926705i
$111$	48.8567	−	31.2338i	0.440150	−	0.281385i
$112$	−2.83952			−0.0253529
$113$		−	19.4826i		−	0.172413i	−0.996277	−	0.0862064i	$-0.972526\pi$
$113$		−	19.4826i		−	0.172413i	0.996277	−	0.0862064i	$-0.0274745\pi$
$114$	19.3179	+	30.2176i	0.169456	+	0.265067i
$115$	−35.0295			−0.304604
$116$		−	8.95241i		−	0.0771760i
$117$	−81.1255	+	175.420i	−0.693380	+	1.49931i
$118$	1.57536			0.0133505
$119$		−	12.6714i		−	0.106483i
$120$	−52.2189	+	33.3832i	−0.435157	+	0.278193i
$121$	23.6136			0.195154
$122$		−	66.3299i		−	0.543687i
$123$	−122.249	−	191.225i	−0.993897	−	1.55468i
$124$	−110.475			−0.890925
$125$		−	24.4741i		−	0.195792i
$126$	−8.20079	−	3.79258i	−0.0650856	−	0.0300999i
$127$	210.414			1.65681			0.828403	−	0.560132i	$-0.189250\pi$
$127$	210.414			1.65681			0.828403	+	0.560132i	$0.189250\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	168.354	−	107.627i	1.30507	−	0.834321i
$130$	221.823			1.70633
$131$		−	65.4708i		−	0.499777i	−0.968275	−	0.249889i	$-0.919606\pi$
$131$		−	65.4708i		−	0.499777i	0.968275	−	0.249889i	$-0.0803940\pi$
$132$	−31.8928	−	49.8875i	−0.241612	−	0.377935i
$133$	6.00091			0.0451196
$134$			17.4595i			0.130295i
$135$	−195.401	+	26.6680i	−1.44741	+	0.197541i
$136$	50.4878			0.371234
$137$			240.233i			1.75353i	0.480922	+	0.876763i	$0.340302\pi$
$137$			240.233i			1.75353i	−0.480922	+	0.876763i	$0.659698\pi$
$138$	17.1432	−	10.9595i	0.124226	−	0.0794169i
$139$	−104.089			−0.748838			−0.374419	−	0.927260i	$-0.622158\pi$
$139$	−104.089			−0.748838			−0.374419	+	0.927260i	$0.622158\pi$
$140$			10.3701i			0.0740725i
$141$	−49.7032	−	77.7470i	−0.352505	−	0.551397i
$142$	7.25146			0.0510666
$143$			211.920i			1.48196i
$144$	15.1111	−	32.6750i	0.104938	−	0.226910i
$145$	−32.6949			−0.225482
$146$			95.8844i			0.656742i
$147$	122.580	−	78.3646i	0.833876	−	0.533092i
$148$	38.6582			0.261204
$149$			88.0087i			0.590662i	0.955395	+	0.295331i	$0.0954300\pi$
$149$			88.0087i			0.590662i	−0.955395	+	0.295331i	$0.904570\pi$
$150$	64.7876	+	101.342i	0.431917	+	0.675616i
$151$	−210.235			−1.39229			−0.696144	−	0.717902i	$-0.745102\pi$
$151$	−210.235			−1.39229			−0.696144	+	0.717902i	$0.745102\pi$
$152$			23.9099i			0.157302i
$153$	145.813	+	67.4336i	0.953028	+	0.440743i
$154$	−9.90716			−0.0643322
$155$			403.462i			2.60298i
$156$	−108.559	+	69.4010i	−0.695889	+	0.444878i
$157$	309.742			1.97288			0.986441	−	0.164118i	$-0.0524777\pi$
$157$	309.742			1.97288			0.986441	+	0.164118i	$0.0524777\pi$
$158$			194.387i			1.23030i
$159$	−63.4122	−	99.1910i	−0.398819	−	0.623843i
$160$	−41.3185			−0.258241
$161$		−	3.40446i		−	0.0211457i
$162$	87.2842	−	74.1853i	0.538791	−	0.457934i
$163$	155.712			0.955290			0.477645	−	0.878553i	$-0.341490\pi$
$163$	155.712			0.955290			0.477645	+	0.878553i	$0.341490\pi$
$164$		−	151.308i		−	0.922613i
$165$	−182.193	+	116.475i	−1.10420	+	0.705908i
$166$	37.9383			0.228544
$167$		−	105.718i		−	0.633045i	−0.948585	−	0.316522i	$-0.897485\pi$
$167$		−	105.718i		−	0.633045i	0.948585	−	0.316522i	$-0.102515\pi$
$168$	−3.24446	−	5.07507i	−0.0193123	−	0.0302088i
$169$	292.153			1.72871
$170$		−	184.385i		−	1.08462i
$171$	−31.9350	+	69.0539i	−0.186755	+	0.403824i
$172$	133.211			0.774482
$173$		−	109.519i		−	0.633057i	−0.948583	−	0.316529i	$-0.897483\pi$
$173$		−	109.519i		−	0.633057i	0.948583	−	0.316529i	$-0.102517\pi$
$174$	16.0006	−	10.2291i	0.0919577	−	0.0587880i
$175$	20.1256			0.115003
$176$		−	39.4738i		−	0.224283i
$177$	1.80003	+	2.81565i	0.0101696	+	0.0159076i
$178$	−124.552			−0.699728
$179$		−	138.686i		−	0.774784i	−0.921915	−	0.387392i	$-0.873376\pi$
$179$		−	138.686i		−	0.774784i	0.921915	−	0.387392i	$-0.126624\pi$
$180$	−119.332	−	55.1868i	−0.662954	−	0.306593i
$181$	128.749			0.711322			0.355661	−	0.934615i	$-0.384256\pi$
$181$	128.749			0.711322			0.355661	+	0.934615i	$0.384256\pi$
$182$			21.5587i			0.118454i
$183$	118.551	−	75.7892i	0.647822	−	0.414149i
$184$	13.5647			0.0737210
$185$		−	141.183i		−	0.763150i
$186$	−126.230	−	197.451i	−0.678653	−	1.06157i
$187$	176.153			0.941996
$188$		−	61.5178i		−	0.327222i
$189$	−2.59182	−	18.9907i	−0.0137133	−	0.100480i
$190$	87.3207			0.459583
$191$		−	220.556i		−	1.15474i	−0.816482	−	0.577371i	$-0.804079\pi$
$191$		−	220.556i		−	1.15474i	0.816482	−	0.577371i	$-0.195921\pi$
$192$	20.2210	−	12.9272i	0.105318	−	0.0673290i
$193$	−149.434			−0.774269			−0.387135	−	0.922023i	$-0.626535\pi$
$193$	−149.434			−0.774269			−0.387135	+	0.922023i	$0.626535\pi$
$194$			0.0642671i			0.000331274i
$195$	253.458	+	396.465i	1.29978	+	2.03315i
$196$	96.9921			0.494858
$197$			376.111i			1.90919i	0.297902	+	0.954596i	$0.403713\pi$
$197$			376.111i			1.90919i	−0.297902	+	0.954596i	$0.596287\pi$
$198$	52.7229	−	114.004i	0.266277	−	0.575777i
$199$	68.6304			0.344876			0.172438	−	0.985020i	$-0.444836\pi$
$199$	68.6304			0.344876			0.172438	+	0.985020i	$0.444836\pi$
$200$			80.1879i			0.400939i
$201$	−31.2054	+	19.9494i	−0.155251	+	0.0992508i
$202$	146.510			0.725295
$203$		−	3.17757i		−	0.0156530i
$204$	57.6879	+	90.2369i	0.282784	+	0.442338i
$205$	−552.590			−2.69556
$206$		−	152.981i		−	0.742627i
$207$	39.1759	+	18.1175i	0.189256	+	0.0875243i
$208$	−85.8979			−0.412970
$209$			83.4222i			0.399149i
$210$	−18.5346	+	11.8490i	−0.0882598	+	0.0564240i
$211$	−299.755			−1.42064			−0.710321	−	0.703878i	$-0.751450\pi$
$211$	−299.755			−1.42064			−0.710321	+	0.703878i	$0.751450\pi$
$212$		−	78.4856i		−	0.370215i
$213$	8.28559	+	12.9605i	0.0388995	+	0.0608476i
$214$	−0.307853			−0.00143857
$215$		−	486.497i		−	2.26278i
$216$	75.6661	−	10.3268i	0.350306	−	0.0478092i
$217$	−39.2119			−0.180700
$218$			188.273i			0.863638i
$219$	−171.374	+	109.559i	−0.782531	+	0.500267i
$220$	−144.161			−0.655279
$221$		−	383.322i		−	1.73449i
$222$	44.1712	+	69.0938i	0.198970	+	0.311233i
$223$	−234.306			−1.05070			−0.525350	−	0.850886i	$-0.676066\pi$
$223$	−234.306			−1.05070			−0.525350	+	0.850886i	$0.676066\pi$
$224$		−	4.01569i		−	0.0179272i
$225$	−107.102	+	231.590i	−0.476010	+	1.02929i
$226$	27.5526			0.121914
$227$			326.611i			1.43881i	0.694589	+	0.719407i	$0.255586\pi$
$227$			326.611i			1.43881i	−0.694589	+	0.719407i	$0.744414\pi$
$228$	−42.7341	+	27.3197i	−0.187430	+	0.119823i
$229$	−81.3640			−0.355301			−0.177651	−	0.984094i	$-0.556850\pi$
$229$	−81.3640			−0.355301			−0.177651	+	0.984094i	$0.556850\pi$
$230$		−	49.5392i		−	0.215388i
$231$	−11.3200	−	17.7071i	−0.0490044	−	0.0766539i
$232$	12.6606			0.0545717
$233$			76.1470i			0.326811i	0.986559	+	0.163406i	$0.0522479\pi$
$233$			76.1470i			0.326811i	−0.986559	+	0.163406i	$0.947752\pi$
$234$	−248.081	−	114.729i	−1.06017	−	0.490294i
$235$	−224.668			−0.956034
$236$			2.22790i			0.00944026i
$237$	−347.428	+	222.109i	−1.46594	+	0.937167i
$238$	17.9201			0.0752947
$239$		−	49.6435i		−	0.207713i	−0.994592	−	0.103857i	$-0.966882\pi$
$239$		−	49.6435i		−	0.207713i	0.994592	−	0.103857i	$-0.0331183\pi$
$240$	−47.2110	−	73.8486i	−0.196713	−	0.307703i
$241$	−274.475			−1.13890			−0.569450	−	0.822026i	$-0.692844\pi$
$241$	−274.475			−1.13890			−0.569450	+	0.822026i	$0.692844\pi$
$242$			33.3947i			0.137995i
$243$	232.323	+	71.2381i	0.956063	+	0.293161i
$244$	93.8046			0.384445
$245$		−	354.223i		−	1.44581i
$246$	270.434	−	172.887i	1.09932	−	0.702791i
$247$	181.533			0.734950
$248$		−	156.235i		−	0.629979i
$249$	43.3487	+	67.8072i	0.174091	+	0.272318i
$250$	34.6115			0.138446
$251$			481.432i			1.91806i	0.283311	+	0.959028i	$0.408567\pi$
$251$			481.432i			1.91806i	−0.283311	+	0.959028i	$0.591433\pi$
$252$	5.36352	−	11.5977i	0.0212838	−	0.0460225i
$253$	47.3274			0.187065
$254$			297.571i			1.17154i
$255$	329.552	−	210.681i	1.29236	−	0.826199i
$256$	16.0000			0.0625000
$257$		−	495.574i		−	1.92830i	−0.265353	−	0.964151i	$-0.585489\pi$
$257$		−	495.574i		−	1.92830i	0.265353	−	0.964151i	$-0.414511\pi$
$258$	152.208	+	238.088i	0.589954	+	0.922822i
$259$	13.7213			0.0529781
$260$			313.706i			1.20656i
$261$	36.5650	+	16.9101i	0.140096	+	0.0647895i
$262$	92.5897			0.353396
$263$			122.589i			0.466119i	0.972463	+	0.233059i	$0.0748736\pi$
$263$			122.589i			0.466119i	−0.972463	+	0.233059i	$0.925126\pi$
$264$	70.5516	−	45.1032i	0.267241	−	0.170845i
$265$	−286.636			−1.08164
$266$			8.48657i			0.0319044i
$267$	−142.314	−	222.611i	−0.533011	−	0.833749i
$268$	−24.6915			−0.0921324
$269$		−	110.985i		−	0.412584i	−0.978490	−	0.206292i	$-0.933860\pi$
$269$		−	110.985i		−	0.412584i	0.978490	−	0.206292i	$-0.0661397\pi$
$270$	−37.7142	−	276.338i	−0.139682	−	1.02348i
$271$	−42.3479			−0.156265			−0.0781326	−	0.996943i	$-0.524896\pi$
$271$	−42.3479			−0.156265			−0.0781326	+	0.996943i	$0.524896\pi$
$272$			71.4005i			0.262502i
$273$	−38.5318	+	24.6332i	−0.141142	+	0.0902314i
$274$	−339.741			−1.23993
$275$			279.778i			1.01737i
$276$	15.4991	+	24.2441i	0.0561562	+	0.0878410i
$277$	195.474			0.705681			0.352840	−	0.935683i	$-0.385216\pi$
$277$	195.474			0.705681			0.352840	+	0.935683i	$0.385216\pi$
$278$		−	147.203i		−	0.529509i
$279$	208.674	−	451.220i	0.747935	−	1.61728i
$280$	−14.6656			−0.0523772
$281$		−	362.056i		−	1.28845i	−0.764834	−	0.644227i	$-0.777179\pi$
$281$		−	362.056i		−	1.28845i	0.764834	−	0.644227i	$-0.222821\pi$
$282$	109.951	−	70.2909i	0.389896	−	0.249258i
$283$	−140.512			−0.496508			−0.248254	−	0.968695i	$-0.579857\pi$
$283$	−140.512			−0.496508			−0.248254	+	0.968695i	$0.579857\pi$
$284$			10.2551i			0.0361095i
$285$	99.7736	+	156.068i	0.350083	+	0.547608i
$286$	−299.700			−1.04790
$287$		−	53.7054i		−	0.187127i
$288$	46.2094	+	21.3703i	0.160449	+	0.0742023i
$289$	−29.6273			−0.102516
$290$		−	46.2376i		−	0.159440i
$291$	−0.114865	+	0.0734323i	−0.000394724	+	0.000252345i
$292$	−135.601			−0.464387
$293$			138.522i			0.472770i	0.971660	+	0.236385i	$0.0759626\pi$
$293$			138.522i			0.472770i	−0.971660	+	0.236385i	$0.924037\pi$
$294$	110.824	+	173.354i	0.376953	+	0.589640i
$295$	8.13647			0.0275812
$296$			54.6709i			0.184699i
$297$	264.001	−	36.0304i	0.888892	−	0.121315i
$298$	−124.463			−0.417661
$299$		−	102.988i		−	0.344441i
$300$	−143.320	+	91.6235i	−0.477733	+	0.305412i
$301$	47.2819			0.157083
$302$		−	297.318i		−	0.984496i
$303$	167.403	+	261.857i	0.552487	+	0.864214i
$304$	−33.8137			−0.111229
$305$		−	342.582i		−	1.12322i
$306$	−95.3656	+	206.211i	−0.311652	+	0.673893i
$307$	231.248			0.753251			0.376626	−	0.926366i	$-0.377084\pi$
$307$	231.248			0.753251			0.376626	+	0.926366i	$0.377084\pi$
$308$		−	14.0108i		−	0.0454897i
$309$	273.423	−	174.798i	0.884865	−	0.565689i
$310$	−570.582			−1.84059
$311$			455.660i			1.46515i	0.680688	+	0.732573i	$0.261681\pi$
$311$			455.660i			1.46515i	−0.680688	+	0.732573i	$0.738319\pi$
$312$	−98.1478	−	153.525i	−0.314576	−	0.492068i
$313$	356.557			1.13916			0.569580	−	0.821936i	$-0.307106\pi$
$313$	356.557			1.13916			0.569580	+	0.821936i	$0.307106\pi$
$314$			438.042i			1.39504i
$315$	−42.3556	−	19.5880i	−0.134462	−	0.0621841i
$316$	−274.905			−0.869951
$317$		−	349.849i		−	1.10363i	−0.833968	−	0.551813i	$-0.813936\pi$
$317$		−	349.849i		−	1.10363i	0.833968	−	0.551813i	$-0.186064\pi$
$318$	140.277	−	89.6785i	0.441124	−	0.282008i
$319$	44.1732			0.138474
$320$		−	58.4333i		−	0.182604i
$321$	−0.351757	−	0.550227i	−0.00109581	−	0.00171410i
$322$	4.81464			0.0149523
$323$		−	150.895i		−	0.467166i
$324$	104.914	+	123.439i	0.323808	+	0.380983i
$325$	608.816			1.87328
$326$			220.210i			0.675492i
$327$	−336.501	+	215.123i	−1.02905	+	0.657868i
$328$	213.982			0.652386
$329$		−	21.8351i		−	0.0663682i
$330$	−164.720	−	257.660i	−0.499153	−	0.780787i
$331$	13.1374			0.0396901			0.0198451	−	0.999803i	$-0.493683\pi$
$331$	13.1374			0.0396901			0.0198451	+	0.999803i	$0.493683\pi$
$332$			53.6529i			0.161605i
$333$	−73.0208	+	157.895i	−0.219282	+	0.474158i
$334$	149.509			0.447630
$335$			90.1752i			0.269180i
$336$	7.17724	−	4.58837i	0.0213608	−	0.0136558i
$337$	−393.903			−1.16885			−0.584426	−	0.811447i	$-0.698680\pi$
$337$	−393.903			−1.16885			−0.584426	+	0.811447i	$0.698680\pi$
$338$			413.166i			1.22238i
$339$	31.4819	+	49.2448i	0.0928670	+	0.145265i
$340$	260.760			0.766942
$341$		−	545.107i		−	1.59856i
$342$	−97.6569	−	45.1630i	−0.285547	−	0.132055i
$343$	69.2105			0.201780
$344$			188.389i			0.547642i
$345$	88.5414	−	56.6040i	0.256642	−	0.164070i
$346$	154.883			0.447639
$347$		−	54.2364i		−	0.156301i	−0.996942	−	0.0781505i	$-0.975099\pi$
$347$		−	54.2364i		−	0.156301i	0.996942	−	0.0781505i	$-0.0249015\pi$
$348$	14.4662	+	22.6283i	0.0415694	+	0.0650239i
$349$	601.542			1.72362			0.861808	−	0.507235i	$-0.169333\pi$
$349$	601.542			1.72362			0.861808	+	0.507235i	$0.169333\pi$
$350$			28.4619i			0.0813197i
$351$	−78.4048	−	574.485i	−0.223375	−	1.63671i
$352$	55.8244			0.158592
$353$			245.437i			0.695288i	0.937627	+	0.347644i	$0.113018\pi$
$353$			245.437i			0.695288i	−0.937627	+	0.347644i	$0.886982\pi$
$354$	−3.98193	+	2.54562i	−0.0112484	+	0.00719102i
$355$	37.4525			0.105500
$356$		−	176.142i		−	0.494782i
$357$	20.4757	+	32.0287i	0.0573550	+	0.0897161i
$358$	196.132			0.547855
$359$			187.322i			0.521788i	0.965367	+	0.260894i	$0.0840174\pi$
$359$			187.322i			0.521788i	−0.965367	+	0.260894i	$0.915983\pi$
$360$	78.0459	−	168.760i	0.216794	−	0.468779i
$361$	−289.540			−0.802049
$362$			182.079i			0.502980i
$363$	−59.6863	+	38.1571i	−0.164425	+	0.105116i
$364$	−30.4886			−0.0837598
$365$			495.226i			1.35678i
$366$	107.182	+	167.657i	0.292847	+	0.458079i
$367$	−346.893			−0.945212			−0.472606	−	0.881274i	$-0.656687\pi$
$367$	−346.893			−0.945212			−0.472606	+	0.881274i	$0.656687\pi$
$368$			19.1833i			0.0521286i
$369$	618.001	+	285.804i	1.67480	+	0.774537i
$370$	199.663			0.539628
$371$		−	27.8577i		−	0.0750881i
$372$	279.239	−	178.516i	0.750641	−	0.479880i
$373$	381.472			1.02271			0.511357	−	0.859369i	$-0.329143\pi$
$373$	381.472			1.02271			0.511357	+	0.859369i	$0.329143\pi$
$374$			249.118i			0.666092i
$375$	39.5475	+	61.8612i	0.105460	+	0.164963i
$376$	86.9993			0.231381
$377$		−	96.1241i		−	0.254971i
$378$	26.8569	−	3.66539i	0.0710500	−	0.00969679i
$379$	199.581			0.526600			0.263300	−	0.964714i	$-0.415189\pi$
$379$	199.581			0.526600			0.263300	+	0.964714i	$0.415189\pi$
$380$			123.490i			0.324974i
$381$	−531.849	+	340.008i	−1.39593	+	0.892409i
$382$	311.913			0.816526
$383$		−	674.404i		−	1.76085i	−0.474190	−	0.880423i	$-0.657259\pi$
$383$		−	674.404i		−	1.76085i	0.474190	−	0.880423i	$-0.342741\pi$
$384$	18.2818	+	28.5968i	0.0476088	+	0.0744708i
$385$	−51.1687			−0.132906
$386$		−	211.332i		−	0.547491i
$387$	−251.620	+	544.084i	−0.650181	+	1.40590i
$388$	−0.0908874			−0.000234246
$389$			256.820i			0.660205i	0.943945	+	0.330102i	$0.107083\pi$
$389$			256.820i			0.660205i	−0.943945	+	0.330102i	$0.892917\pi$
$390$	−560.686	+	358.443i	−1.43766	+	0.919086i
$391$	−85.6062			−0.218942
$392$			137.168i			0.349917i
$393$	105.794	+	165.486i	0.269196	+	0.421083i
$394$	−531.901			−1.35000
$395$			1003.97i			2.54170i
$396$	161.226	+	74.5614i	0.407136	+	0.188286i
$397$	79.2116			0.199525			0.0997627	−	0.995011i	$-0.468192\pi$
$397$	79.2116			0.199525			0.0997627	+	0.995011i	$0.468192\pi$
$398$			97.0580i			0.243864i
$399$	−15.1680	+	9.69684i	−0.0380152	+	0.0243029i
$400$	−113.403			−0.283507
$401$			150.928i			0.376380i	0.982133	+	0.188190i	$0.0602621\pi$
$401$			150.928i			0.376380i	−0.982133	+	0.188190i	$0.939738\pi$
$402$	−28.2127	−	44.1311i	−0.0701809	−	0.109779i
$403$	−1186.19			−2.94341
$404$			207.196i			0.512861i
$405$	450.807	−	383.154i	1.11310	−	0.946059i
$406$	4.49376			0.0110684
$407$			190.748i			0.468669i
$408$	−127.614	+	81.5830i	−0.312780	+	0.199958i
$409$	87.7350			0.214511			0.107256	−	0.994231i	$-0.465794\pi$
$409$	87.7350			0.214511			0.107256	+	0.994231i	$0.465794\pi$
$410$		−	781.481i		−	1.90605i
$411$	−388.192	−	607.219i	−0.944505	−	1.47742i
$412$	216.348			0.525117
$413$			0.790771i			0.00191470i
$414$	−25.6221	+	55.4032i	−0.0618890	+	0.133824i
$415$	195.945			0.472156
$416$		−	121.478i		−	0.292014i
$417$	263.097	−	168.196i	0.630927	−	0.403348i
$418$	−117.977			−0.282241
$419$			596.652i			1.42399i	0.702184	+	0.711995i	$0.252208\pi$
$419$			596.652i			1.42399i	−0.702184	+	0.711995i	$0.747792\pi$
$420$	−16.7571	−	26.2118i	−0.0398978	−	0.0624091i
$421$	32.5966			0.0774266			0.0387133	−	0.999250i	$-0.487674\pi$
$421$	32.5966			0.0774266			0.0387133	+	0.999250i	$0.487674\pi$
$422$		−	423.918i		−	1.00455i
$423$	251.262	+	116.200i	0.594000	+	0.274704i
$424$	110.995			0.261782
$425$		−	506.064i		−	1.19074i
$426$	−18.3290	+	11.7176i	−0.0430257	+	0.0275061i
$427$	33.2950			0.0779742
$428$		−	0.435371i		−	0.00101722i
$429$	−342.440	−	535.653i	−0.798229	−	1.24861i
$430$	688.010			1.60002
$431$		−	265.885i		−	0.616904i	−0.951240	−	0.308452i	$-0.900189\pi$
$431$		−	265.885i		−	0.616904i	0.951240	−	0.308452i	$-0.0998109\pi$
$432$	14.6043	+	107.008i	0.0338062	+	0.247704i
$433$	−130.151			−0.300581			−0.150290	−	0.988642i	$-0.548021\pi$
$433$	−130.151			−0.300581			−0.150290	+	0.988642i	$0.548021\pi$
$434$		−	55.4540i		−	0.127774i
$435$	82.6404	−	52.8315i	0.189978	−	0.121452i
$436$	−266.258			−0.610684
$437$		−	40.5412i		−	0.0927716i
$438$	−154.939	−	242.360i	−0.353742	−	0.553333i
$439$	−549.031			−1.25064			−0.625320	−	0.780369i	$-0.715031\pi$
$439$	−549.031			−1.25064			−0.625320	+	0.780369i	$0.715031\pi$
$440$		−	203.875i		−	0.463353i
$441$	−183.207	+	396.152i	−0.415435	+	0.898305i
$442$	542.099			1.22647
$443$		−	407.076i		−	0.918908i	−0.888201	−	0.459454i	$-0.848045\pi$
$443$		−	407.076i		−	0.918908i	0.888201	−	0.459454i	$-0.151955\pi$
$444$	−97.7134	+	62.4676i	−0.220075	+	0.140693i
$445$	−643.286			−1.44559
$446$		−	331.359i		−	0.742957i
$447$	−142.213	−	222.453i	−0.318149	−	0.497657i
$448$	5.67904			0.0126764
$449$		−	338.318i		−	0.753492i	−0.926317	−	0.376746i	$-0.877043\pi$
$449$		−	338.318i		−	0.753492i	0.926317	−	0.376746i	$-0.122957\pi$
$450$	−327.517	−	151.466i	−0.727817	−	0.336590i
$451$	746.590			1.65541
$452$			38.9653i			0.0862064i
$453$	531.396	−	339.718i	1.17306	−	0.749930i
$454$	−461.897			−1.01740
$455$			111.347i			0.244718i
$456$	−38.6359	−	60.4352i	−0.0847278	−	0.132533i
$457$	−356.266			−0.779576			−0.389788	−	0.920905i	$-0.627452\pi$
$457$	−356.266			−0.779576			−0.389788	+	0.920905i	$0.627452\pi$
$458$		−	115.066i		−	0.251236i
$459$	−477.527	+	65.1721i	−1.04036	+	0.141987i
$460$	70.0590			0.152302
$461$		−	469.576i		−	1.01860i	−0.860588	−	0.509301i	$-0.829904\pi$
$461$		−	469.576i		−	1.01860i	0.860588	−	0.509301i	$-0.170096\pi$
$462$	25.0416	−	16.0089i	0.0542025	−	0.0346513i
$463$	494.228			1.06745			0.533723	−	0.845659i	$-0.320792\pi$
$463$	494.228			1.06745			0.533723	+	0.845659i	$0.320792\pi$
$464$			17.9048i			0.0385880i
$465$	−651.953	−	1019.80i	−1.40205	−	2.19312i
$466$	−107.688			−0.231090
$467$			494.716i			1.05935i	0.848201	+	0.529674i	$0.177686\pi$
$467$			494.716i			1.05935i	−0.848201	+	0.529674i	$0.822314\pi$
$468$	162.251	−	350.839i	0.346690	−	0.749656i
$469$	−8.76399			−0.0186865
$470$		−	317.728i		−	0.676018i
$471$	−782.912	+	500.511i	−1.66223	+	1.06266i
$472$	−3.15073			−0.00667527
$473$			657.293i			1.38963i
$474$	−314.109	−	491.337i	−0.662677	−	1.03658i
$475$	239.660			0.504548
$476$			25.3429i			0.0532414i
$477$	320.565	+	148.250i	0.672043	+	0.310797i
$478$	70.2065			0.146876
$479$		−	98.8610i		−	0.206390i	−0.994661	−	0.103195i	$-0.967093\pi$
$479$		−	98.8610i		−	0.206390i	0.994661	−	0.103195i	$-0.0329066\pi$
$480$	104.438	−	66.7664i	0.217579	−	0.139097i
$481$	415.082			0.862956
$482$		−	388.166i		−	0.805323i
$483$	5.50126	+	8.60521i	0.0113898	+	0.0178162i
$484$	−47.2272			−0.0975769
$485$			0.331928i			0.000684387i
$486$	−100.746	+	328.555i	−0.207296	+	0.676039i
$487$	93.1375			0.191247			0.0956237	−	0.995418i	$-0.469515\pi$
$487$	93.1375			0.191247			0.0956237	+	0.995418i	$0.469515\pi$
$488$			132.660i			0.271844i
$489$	−393.582	+	251.615i	−0.804872	+	0.514550i
$490$	500.947			1.02234
$491$			472.709i			0.962747i	0.876516	+	0.481373i	$0.159862\pi$
$491$			472.709i			0.962747i	−0.876516	+	0.481373i	$0.840138\pi$
$492$	244.499	+	382.451i	0.496948	+	0.777339i
$493$	−79.9009			−0.162071
$494$			256.726i			0.519688i
$495$	272.304	−	588.810i	0.550109	−	1.18951i
$496$	220.949			0.445463
$497$			3.63995i			0.00732384i
$498$	−95.8938	+	61.3044i	−0.192558	+	0.123101i
$499$	−41.2580			−0.0826814			−0.0413407	−	0.999145i	$-0.513163\pi$
$499$	−41.2580			−0.0826814			−0.0413407	+	0.999145i	$0.513163\pi$
$500$			48.9481i			0.0978962i
$501$	170.830	+	267.217i	0.340978	+	0.533366i
$502$	−680.848			−1.35627
$503$		−	320.442i		−	0.637061i	−0.947913	−	0.318531i	$-0.896811\pi$
$503$		−	320.442i		−	0.637061i	0.947913	−	0.318531i	$-0.103189\pi$
$504$	16.4016	+	7.58516i	0.0325428	+	0.0150499i
$505$	756.696			1.49841
$506$			66.9311i			0.132275i
$507$	−738.452	+	472.088i	−1.45651	+	0.931140i
$508$	−420.829			−0.828403
$509$		−	40.8657i		−	0.0802862i	−0.999194	−	0.0401431i	$-0.987219\pi$
$509$		−	40.8657i		−	0.0802862i	0.999194	−	0.0401431i	$-0.0127814\pi$
$510$	297.947	+	466.057i	0.584211	+	0.913837i
$511$	−48.1302			−0.0941883
$512$			22.6274i			0.0441942i
$513$	−30.8640	−	226.146i	−0.0601638	−	0.440830i
$514$	700.847			1.36352
$515$		−	790.120i		−	1.53421i
$516$	−336.707	+	215.255i	−0.652533	+	0.417161i
$517$	303.543			0.587124
$518$			19.4049i			0.0374612i
$519$	176.971	+	276.823i	0.340985	+	0.533377i
$520$	−443.647			−0.853167
$521$			619.361i			1.18879i	0.804172	+	0.594397i	$0.202609\pi$
$521$			619.361i			1.18879i	−0.804172	+	0.594397i	$0.797391\pi$
$522$	−23.9144	+	51.7107i	−0.0458131	+	0.0990627i
$523$	−572.405			−1.09447			−0.547233	−	0.836980i	$-0.684319\pi$
$523$	−572.405			−1.09447			−0.547233	+	0.836980i	$0.684319\pi$
$524$			130.942i			0.249889i
$525$	−50.8699	+	32.5208i	−0.0968951	+	0.0619445i
$526$	−173.367			−0.329596
$527$			985.994i			1.87096i
$528$	63.7855	+	99.7750i	0.120806	+	0.188968i
$529$	−23.0000			−0.0434783
$530$		−	405.364i		−	0.764838i
$531$	−9.09958	−	4.20824i	−0.0171367	−	0.00792513i
$532$	−12.0018			−0.0225598
$533$		−	1624.63i		−	3.04809i
$534$	314.819	−	201.262i	0.589550	−	0.376896i
$535$	−1.59001			−0.00297198
$536$		−	34.9190i		−	0.0651474i
$537$	224.103	+	350.547i	0.417323	+	0.652788i
$538$	156.957			0.291741
$539$			478.581i			0.887906i
$540$	390.802	−	53.3360i	0.723707	−	0.0987703i
$541$	−656.684			−1.21383			−0.606917	−	0.794765i	$-0.707594\pi$
$541$	−656.684			−1.21383			−0.606917	+	0.794765i	$0.707594\pi$
$542$		−	59.8889i		−	0.110496i
$543$	−325.430	+	208.045i	−0.599318	+	0.383140i
$544$	−100.976			−0.185617
$545$			972.397i			1.78421i
$546$	−34.8366	−	54.4922i	−0.0638032	−	0.0998026i
$547$	−803.323			−1.46860			−0.734298	−	0.678827i	$-0.762489\pi$
$547$	−803.323			−1.46860			−0.734298	+	0.678827i	$0.762489\pi$
$548$		−	480.466i		−	0.876763i
$549$	−177.186	+	383.133i	−0.322743	+	0.697875i
$550$	−395.665			−0.719391
$551$		−	37.8392i		−	0.0686738i
$552$	−34.2864	+	21.9191i	−0.0621130	+	0.0397085i
$553$	−97.5746			−0.176446
$554$			276.441i			0.498992i
$555$	228.136	+	356.857i	0.411057	+	0.642985i
$556$	208.177			0.374419
$557$			212.745i			0.381948i	0.981595	+	0.190974i	$0.0611647\pi$
$557$			212.745i			0.381948i	−0.981595	+	0.190974i	$0.938835\pi$
$558$	638.122	+	295.109i	1.14359	+	0.528870i
$559$	1430.32			2.55871
$560$		−	20.7403i		−	0.0370362i
$561$	−445.249	+	284.645i	−0.793670	+	0.507389i
$562$	512.024			0.911075
$563$		−	585.167i		−	1.03937i	−0.854357	−	0.519686i	$-0.826049\pi$
$563$		−	585.167i		−	1.03937i	0.854357	−	0.519686i	$-0.173951\pi$
$564$	99.4063	+	155.494i	0.176252	+	0.275698i
$565$	142.304			0.251866
$566$		−	198.713i		−	0.351084i
$567$	37.2381	+	43.8133i	0.0656757	+	0.0772721i
$568$	−14.5029			−0.0255333
$569$			265.413i			0.466455i	0.972422	+	0.233228i	$0.0749287\pi$
$569$			265.413i			0.466455i	−0.972422	+	0.233228i	$0.925071\pi$
$570$	−220.714	+	141.101i	−0.387218	+	0.247546i
$571$	1092.93			1.91407			0.957035	−	0.289971i	$-0.0936458\pi$
$571$	1092.93			1.91407			0.957035	+	0.289971i	$0.0936458\pi$
$572$		−	423.840i		−	0.740978i
$573$	356.395	+	557.482i	0.621981	+	0.972918i
$574$	75.9509			0.132319
$575$		−	135.965i		−	0.236461i
$576$	−30.2221	+	65.3500i	−0.0524690	+	0.113455i
$577$	472.593			0.819052			0.409526	−	0.912299i	$-0.365694\pi$
$577$	472.593			0.819052			0.409526	+	0.912299i	$0.365694\pi$
$578$		−	41.8993i		−	0.0724901i
$579$	377.713	−	241.470i	0.652354	−	0.417046i
$580$	65.3898			0.112741
$581$			19.0436i			0.0327772i
$582$	−0.103849	−	0.162443i	−0.000178435	−	0.000279112i
$583$	387.266			0.664264
$584$		−	191.769i		−	0.328371i
$585$	−1281.29	−	592.553i	−2.19024	−	1.01291i
$586$	−195.899			−0.334299
$587$		−	133.774i		−	0.227895i	−0.993487	−	0.113947i	$-0.963650\pi$
$587$		−	133.774i		−	0.227895i	0.993487	−	0.113947i	$-0.0363495\pi$
$588$	−245.160	+	156.729i	−0.416938	+	0.266546i
$589$	−466.944			−0.792775
$590$			11.5067i			0.0195029i
$591$	−607.756	−	950.667i	−1.02835	−	1.60857i
$592$	−77.3164			−0.130602
$593$			76.3913i			0.128822i	0.997923	+	0.0644109i	$0.0205168\pi$
$593$			76.3913i			0.128822i	−0.997923	+	0.0644109i	$0.979483\pi$
$594$	50.9547	+	373.354i	0.0857823	+	0.628542i
$595$	92.5543			0.155553
$596$		−	176.017i		−	0.295331i
$597$	−173.472	+	110.899i	−0.290573	+	0.185761i
$598$	145.647			0.243557
$599$		−	456.246i		−	0.761679i	−0.924641	−	0.380839i	$-0.875635\pi$
$599$		−	456.246i		−	0.761679i	0.924641	−	0.380839i	$-0.124365\pi$
$600$	−129.575	−	202.685i	−0.215959	−	0.337808i
$601$	134.636			0.224020			0.112010	−	0.993707i	$-0.464271\pi$
$601$	134.636			0.224020			0.112010	+	0.993707i	$0.464271\pi$
$602$			66.8667i			0.111074i
$603$	46.6393	−	100.849i	0.0773455	−	0.167246i
$604$	420.471			0.696144
$605$			172.478i			0.285087i
$606$	−370.321	+	236.744i	−0.611091	+	0.390667i
$607$	313.294			0.516135			0.258067	−	0.966127i	$-0.416914\pi$
$607$	313.294			0.516135			0.258067	+	0.966127i	$0.416914\pi$
$608$		−	47.8198i		−	0.0786509i
$609$	5.13462	+	8.03170i	0.00843123	+	0.0131883i
$610$	484.484			0.794236
$611$		−	660.531i		−	1.08107i
$612$	−291.627	−	134.867i	−0.476514	−	0.220371i
$613$	−1173.93			−1.91505			−0.957527	−	0.288345i	$-0.906895\pi$
$613$	−1173.93			−1.91505			−0.957527	+	0.288345i	$0.906895\pi$
$614$			327.034i			0.532629i
$615$	1396.74	−	892.928i	2.27112	−	1.45192i
$616$	19.8143			0.0321661
$617$			957.462i			1.55180i	0.630854	+	0.775902i	$0.282705\pi$
$617$			957.462i			1.55180i	−0.630854	+	0.775902i	$0.717295\pi$
$618$	247.201	+	386.679i	0.400002	+	0.625694i
$619$	−411.891			−0.665413			−0.332706	−	0.943030i	$-0.607962\pi$
$619$	−411.891			−0.665413			−0.332706	+	0.943030i	$0.607962\pi$
$620$		−	806.925i		−	1.30149i
$621$	−128.298	+	17.5099i	−0.206599	+	0.0281963i
$622$	−644.401			−1.03601
$623$		−	62.5200i		−	0.100353i
$624$	217.117	−	138.802i	0.347945	−	0.222439i
$625$	−530.005			−0.848008
$626$			504.248i			0.805508i
$627$	−134.801	−	210.860i	−0.214994	−	0.336300i
$628$	−619.485			−0.986441
$629$		−	345.027i		−	0.548532i
$630$	27.7016	−	59.8998i	0.0439708	−	0.0950791i
$631$	156.033			0.247279			0.123639	−	0.992327i	$-0.460543\pi$
$631$	156.033			0.247279			0.123639	+	0.992327i	$0.460543\pi$
$632$		−	388.774i		−	0.615149i
$633$	757.669	−	484.373i	1.19695	−	0.765203i
$634$	494.762			0.780381
$635$			1536.90i			2.42032i
$636$	126.824	+	198.382i	0.199410	+	0.311922i
$637$	1041.43			1.63489
$638$			62.4704i			0.0979160i
$639$	−41.8857	−	19.3707i	−0.0655488	−	0.0303141i
$640$	82.6371			0.129120
$641$			757.728i			1.18210i	0.806634	+	0.591052i	$0.201287\pi$
$641$			757.728i			1.18210i	−0.806634	+	0.591052i	$0.798713\pi$
$642$	0.778138	−	0.497459i	0.00121205	−	0.000774858i
$643$	743.881			1.15689			0.578446	−	0.815721i	$-0.303660\pi$
$643$	743.881			1.15689			0.578446	+	0.815721i	$0.303660\pi$
$644$			6.80893i			0.0105729i
$645$	786.128	+	1229.68i	1.21880	+	1.90648i
$646$	213.397			0.330336
$647$			457.375i			0.706916i	0.935450	+	0.353458i	$0.114994\pi$
$647$			457.375i			0.706916i	−0.935450	+	0.353458i	$0.885006\pi$
$648$	−174.568	+	148.371i	−0.269396	+	0.228967i
$649$	−10.9930			−0.0169383
$650$			860.996i			1.32461i
$651$	99.1129	−	63.3623i	0.152247	−	0.0973307i
$652$	−311.425			−0.477645
$653$		−	136.673i		−	0.209300i	−0.994509	−	0.104650i	$-0.966628\pi$
$653$		−	136.673i		−	0.209300i	0.994509	−	0.104650i	$-0.0333722\pi$
$654$	−304.230	−	475.884i	−0.465183	−	0.727651i
$655$	478.209			0.730090
$656$			302.617i			0.461306i
$657$	256.134	−	553.845i	0.389855	−	0.842992i
$658$	30.8795			0.0469294
$659$			941.245i			1.42829i	0.699996	+	0.714146i	$0.253185\pi$
$659$			941.245i			1.42829i	−0.699996	+	0.714146i	$0.746815\pi$
$660$	364.386	−	232.950i	0.552100	−	0.352954i
$661$	323.358			0.489195			0.244598	−	0.969625i	$-0.421344\pi$
$661$	323.358			0.489195			0.244598	+	0.969625i	$0.421344\pi$
$662$			18.5791i			0.0280652i
$663$	619.408	+	968.894i	0.934251	+	1.46138i
$664$	−75.8767			−0.114272
$665$			43.8316i			0.0659122i
$666$	−223.297	−	103.267i	−0.335280	−	0.155056i
$667$	−21.4671			−0.0321846
$668$			211.437i			0.316522i
$669$	592.238	−	378.614i	0.885258	−	0.565940i
$670$	−127.527			−0.190339
$671$			462.853i			0.689796i
$672$	6.48893	+	10.1501i	0.00965614	+	0.0151044i
$673$	−363.661			−0.540358			−0.270179	−	0.962810i	$-0.587083\pi$
$673$	−363.661			−0.540358			−0.270179	+	0.962810i	$0.587083\pi$
$674$		−	557.063i		−	0.826503i
$675$	−103.510	−	758.438i	−0.153349	−	1.12361i
$676$	−584.305			−0.864357
$677$		−	914.192i		−	1.35036i	−0.737654	−	0.675179i	$-0.764066\pi$
$677$		−	914.192i		−	1.35036i	0.737654	−	0.675179i	$-0.235934\pi$
$678$	−69.6427	+	44.5222i	−0.102718	+	0.0656669i
$679$	−0.0322596			−4.75104e−5
$680$			368.771i			0.542310i
$681$	−527.769	−	825.549i	−0.774991	−	1.21226i
$682$	770.898			1.13035
$683$		−	385.781i		−	0.564832i	−0.959292	−	0.282416i	$-0.908864\pi$
$683$		−	385.781i		−	0.564832i	0.959292	−	0.282416i	$-0.0911359\pi$
$684$	63.8701	−	138.108i	0.0933773	−	0.201912i
$685$	−1754.70			−2.56161
$686$			97.8784i			0.142680i
$687$	205.657	−	131.476i	0.299356	−	0.191376i
$688$	−266.422			−0.387241
$689$		−	842.718i		−	1.22310i
$690$	80.0501	+	125.216i	0.116015	+	0.181473i
$691$	−38.6872			−0.0559873			−0.0279936	−	0.999608i	$-0.508912\pi$
$691$	−38.6872			−0.0559873			−0.0279936	+	0.999608i	$0.508912\pi$
$692$			219.038i			0.316529i
$693$	57.2255	+	26.4648i	0.0825765	+	0.0381888i
$694$	76.7019			0.110521
$695$		−	760.279i		−	1.09393i
$696$	−32.0013	+	20.4582i	−0.0459789	+	0.0293940i
$697$	−1350.44			−1.93750
$698$			850.708i			1.21878i
$699$	−123.046	−	192.471i	−0.176031	−	0.275352i
$700$	−40.2512			−0.0575017
$701$			1145.56i			1.63419i	0.576506	+	0.817093i	$0.304416\pi$
$701$			1145.56i			1.63419i	−0.576506	+	0.817093i	$0.695584\pi$
$702$	812.444	−	110.881i	1.15733	−	0.157950i
$703$	163.397			0.232428
$704$			78.9476i			0.112142i
$705$	567.876	−	363.040i	0.805498	−	0.514950i
$706$	−347.100			−0.491643
$707$			73.5421i			0.104020i
$708$	−3.60005	−	5.63130i	−0.00508482	−	0.00795381i
$709$	856.240			1.20767			0.603837	−	0.797108i	$-0.293638\pi$
$709$	856.240			1.20767			0.603837	+	0.797108i	$0.293638\pi$
$710$			52.9658i			0.0745997i
$711$	519.263	−	1122.81i	0.730327	−	1.57920i
$712$	249.103			0.349864
$713$			264.909i			0.371541i
$714$	−45.2954	+	28.9571i	−0.0634389	+	0.0405561i
$715$	−1547.90			−2.16489
$716$			277.373i			0.387392i
$717$	80.2187	+	125.480i	0.111881	+	0.175007i
$718$	−264.913			−0.368960
$719$		−	1093.74i		−	1.52119i	−0.649225	−	0.760597i	$-0.724907\pi$
$719$		−	1093.74i		−	1.52119i	0.649225	−	0.760597i	$-0.275093\pi$
$720$	238.663	+	110.374i	0.331477	+	0.153297i
$721$	76.7905			0.106506
$722$		−	409.471i		−	0.567134i
$723$	693.769	−	443.522i	0.959570	−	0.613447i
$724$	−257.498			−0.355661
$725$		−	126.904i		−	0.175039i
$726$	−53.9623	−	84.4092i	−0.0743283	−	0.116266i
$727$	−832.454			−1.14505			−0.572527	−	0.819886i	$-0.694037\pi$
$727$	−832.454			−1.14505			−0.572527	+	0.819886i	$0.694037\pi$
$728$		−	43.1174i		−	0.0592271i
$729$	−702.339	+	195.347i	−0.963429	+	0.267966i
$730$	−700.355			−0.959390
$731$		−	1188.92i		−	1.62643i
$732$	−237.103	+	151.578i	−0.323911	+	0.207074i
$733$	860.998			1.17462			0.587311	−	0.809361i	$-0.300186\pi$
$733$	860.998			1.17462			0.587311	+	0.809361i	$0.300186\pi$
$734$		−	490.581i		−	0.668366i
$735$	572.387	+	895.342i	0.778758	+	1.21815i
$736$	−27.1293			−0.0368605
$737$		−	121.833i		−	0.165310i
$738$	−404.188	+	873.985i	−0.547680	+	1.18426i
$739$	−847.334			−1.14660			−0.573298	−	0.819347i	$-0.694336\pi$
$739$	−847.334			−1.14660			−0.573298	+	0.819347i	$0.694336\pi$
$740$			282.365i			0.381575i
$741$	−458.846	+	293.338i	−0.619226	+	0.395867i
$742$	39.3967			0.0530953
$743$		−	941.108i		−	1.26663i	−0.773893	−	0.633316i	$-0.781693\pi$
$743$		−	941.108i		−	1.26663i	0.773893	−	0.633316i	$-0.218307\pi$
$744$	252.459	+	394.903i	0.339327	+	0.530783i
$745$	−642.829			−0.862858
$746$			539.483i			0.723167i
$747$	−219.139	−	101.344i	−0.293358	−	0.135668i
$748$	−352.306			−0.470998
$749$		−	0.154530i		−	0.000206316i
$750$	−87.4850	+	55.9286i	−0.116647	+	0.0745715i
$751$	766.059			1.02005			0.510026	−	0.860159i	$-0.329636\pi$
$751$	766.059			1.02005			0.510026	+	0.860159i	$0.329636\pi$
$752$			123.036i			0.163611i
$753$	−777.944	−	1216.88i	−1.03313	−	1.61604i
$754$	135.940			0.180292
$755$		−	1535.59i		−	2.03390i
$756$	5.18364	+	37.9814i	0.00685667	+	0.0502400i
$757$	244.584			0.323096			0.161548	−	0.986865i	$-0.448351\pi$
$757$	244.584			0.323096			0.161548	+	0.986865i	$0.448351\pi$
$758$			282.251i			0.372362i
$759$	−119.626	+	76.4762i	−0.157610	+	0.100759i
$760$	−174.641			−0.229791
$761$			164.972i			0.216783i	0.994108	+	0.108392i	$0.0345701\pi$
$761$			164.972i			0.216783i	−0.994108	+	0.108392i	$0.965430\pi$
$762$	−480.844	−	752.148i	−0.631028	−	0.987070i
$763$	−94.5057			−0.123861
$764$			441.112i			0.577371i
$765$	−492.546	+	1065.04i	−0.643851	+	1.39221i
$766$	953.751			1.24511
$767$			23.9215i			0.0311884i
$768$	−40.4420	+	25.8543i	−0.0526588	+	0.0336645i
$769$	509.199			0.662157			0.331079	−	0.943603i	$-0.392587\pi$
$769$	509.199			0.662157			0.331079	+	0.943603i	$0.392587\pi$
$770$		−	72.3634i		−	0.0939785i
$771$	800.795	+	1252.62i	1.03864	+	1.62467i
$772$	298.868			0.387135
$773$			1169.64i			1.51312i	0.653922	+	0.756562i	$0.273122\pi$
$773$			1169.64i			1.51312i	−0.653922	+	0.756562i	$0.726878\pi$
$774$	−769.450	−	355.844i	−0.994122	−	0.459747i
$775$	−1566.02			−2.02067
$776$		−	0.128534i		−	0.000165637i
$777$	−34.6824	+	22.1722i	−0.0446363	+	0.0285357i
$778$	−363.198			−0.466835
$779$		−	639.537i		−	0.820972i
$780$	−506.915	−	792.930i	−0.649892	−	1.01658i
$781$	−50.6010			−0.0647901
$782$		−	121.065i		−	0.154815i
$783$	−119.747	+	16.3429i	−0.152934	+	0.0208722i
$784$	−193.984			−0.247429
$785$			2262.41i			2.88205i
$786$	−234.032	+	149.615i	−0.297751	+	0.190350i
$787$	−756.432			−0.961159			−0.480579	−	0.876951i	$-0.659574\pi$
$787$	−756.432			−0.961159			−0.480579	+	0.876951i	$0.659574\pi$
$788$		−	752.222i		−	0.954596i
$789$	−198.091	−	309.859i	−0.251066	−	0.392724i
$790$	−1419.83			−1.79726
$791$			13.8303i			0.0174846i
$792$	−105.446	+	228.008i	−0.133139	+	0.287889i
$793$	1007.20			1.27012
$794$			112.022i			0.141086i
$795$	724.507	−	463.173i	0.911329	−	0.582608i
$796$	−137.261			−0.172438
$797$		−	416.653i		−	0.522777i	−0.965234	−	0.261388i	$-0.915820\pi$
$797$		−	416.653i		−	0.522777i	0.965234	−	0.261388i	$-0.0841803\pi$
$798$	−13.7134	−	21.4509i	−0.0171847	−	0.0268808i
$799$	−549.051			−0.687172
$800$		−	160.376i		−	0.200470i
$801$	719.432	+	332.713i	0.898167	+	0.415372i
$802$	−213.445			−0.266141
$803$		−	669.086i		−	0.833233i
$804$	62.4108	−	39.8988i	0.0776253	−	0.0496254i
$805$	24.8667			0.0308904
$806$		−	1677.53i		−	2.08130i
$807$	179.340	+	280.529i	0.222231	+	0.347619i
$808$	−293.019			−0.362648
$809$		−	706.178i		−	0.872902i	−0.899728	−	0.436451i	$-0.856235\pi$
$809$		−	706.178i		−	0.872902i	0.899728	−	0.436451i	$-0.143765\pi$
$810$	541.861	+	637.538i	0.668965	+	0.787083i
$811$	−554.264			−0.683432			−0.341716	−	0.939803i	$-0.611008\pi$
$811$	−554.264			−0.683432			−0.341716	+	0.939803i	$0.611008\pi$
$812$			6.35514i			0.00782652i
$813$	107.040	−	68.4297i	0.131660	−	0.0841694i
$814$	−269.759			−0.331399
$815$			1137.35i			1.39552i
$816$	−115.376	−	180.474i	−0.141392	−	0.221169i
$817$	563.044			0.689160
$818$			124.076i			0.151682i
$819$	57.5894	−	124.527i	0.0703167	−	0.152047i
$820$	1105.18			1.34778
$821$			25.6399i			0.0312301i	0.999878	+	0.0156150i	$0.00497063\pi$
$821$			25.6399i			0.0312301i	−0.999878	+	0.0156150i	$0.995029\pi$
$822$	858.737	−	548.986i	1.04469	−	0.667866i
$823$	48.2433			0.0586188			0.0293094	−	0.999570i	$-0.490669\pi$
$823$	48.2433			0.0586188			0.0293094	+	0.999570i	$0.490669\pi$
$824$			305.962i			0.371313i
$825$	−452.091	−	707.173i	−0.547989	−	0.857179i
$826$	−1.11832			−0.00135390
$827$		−	246.742i		−	0.298358i	−0.988810	−	0.149179i	$-0.952337\pi$
$827$		−	246.742i		−	0.298358i	0.988810	−	0.149179i	$-0.0476631\pi$
$828$	−78.3519	−	36.2351i	−0.0946279	−	0.0437622i
$829$	−621.530			−0.749735			−0.374867	−	0.927078i	$-0.622312\pi$
$829$	−621.530			−0.749735			−0.374867	+	0.927078i	$0.622312\pi$
$830$			277.108i			0.333864i
$831$	−494.084	+	315.865i	−0.594565	+	0.380102i
$832$	171.796			0.206485
$833$		−	865.661i		−	1.03921i
$834$	237.865	+	372.075i	0.285210	+	0.446133i
$835$	772.184			0.924772
$836$		−	166.844i		−	0.199575i
$837$	201.675	+	1477.71i	0.240950	+	1.76548i
$838$	−843.793			−1.00691
$839$		−	553.677i		−	0.659924i	−0.943994	−	0.329962i	$-0.892964\pi$
$839$		−	553.677i		−	0.659924i	0.943994	−	0.329962i	$-0.107036\pi$
$840$	37.0691	−	23.6981i	0.0441299	−	0.0282120i
$841$	820.964			0.976175
$842$			46.0985i			0.0547488i
$843$	585.044	+	915.141i	0.694002	+	1.08558i
$844$	599.511			0.710321
$845$			2133.93i			2.52536i
$846$	−164.332	+	355.338i	−0.194245	+	0.420021i
$847$	−16.7628			−0.0197908
$848$			156.971i			0.185108i
$849$	355.161	−	227.052i	0.418328	−	0.267435i
$850$	715.682			0.841979
$851$		−	92.6991i		−	0.108930i
$852$	−16.5712	−	25.9211i	−0.0194497	−	0.0304238i
$853$	−843.957			−0.989399			−0.494700	−	0.869064i	$-0.664722\pi$
$853$	−843.957			−0.989399			−0.494700	+	0.869064i	$0.664722\pi$
$854$			47.0862i			0.0551361i
$855$	−504.380	−	233.259i	−0.589918	−	0.272817i
$856$	0.615707			0.000719284
$857$			855.482i			0.998229i	0.866536	+	0.499114i	$0.166341\pi$
$857$			855.482i			0.998229i	−0.866536	+	0.499114i	$0.833659\pi$
$858$	757.528	−	484.283i	0.882900	−	0.564433i
$859$	−367.458			−0.427774			−0.213887	−	0.976858i	$-0.568612\pi$
$859$	−367.458			−0.427774			−0.213887	+	0.976858i	$0.568612\pi$
$860$			972.994i			1.13139i
$861$	86.7823	+	135.747i	0.100792	+	0.157662i
$862$	376.019			0.436217
$863$		−	887.668i		−	1.02858i	−0.857615	−	0.514292i	$-0.828055\pi$
$863$		−	887.668i		−	1.02858i	0.857615	−	0.514292i	$-0.171945\pi$
$864$	−151.332	+	20.6536i	−0.175153	+	0.0239046i
$865$	799.943			0.924790
$866$		−	184.062i		−	0.212543i
$867$	74.8866	−	47.8745i	0.0863744	−	0.0552186i
$868$	78.4238			0.0903500
$869$		−	1356.44i		−	1.56092i
$870$	74.7151	+	116.871i	0.0858794	+	0.134335i
$871$	−265.118			−0.304384
$872$		−	376.546i		−	0.431819i
$873$	0.171676	−	0.371218i	0.000196650	−	0.000425221i
$874$	57.3339			0.0655994
$875$			17.3736i			0.0198556i
$876$	342.748	−	219.117i	0.391265	−	0.250134i
$877$	−45.4585			−0.0518341			−0.0259170	−	0.999664i	$-0.508251\pi$
$877$	−45.4585			−0.0518341			−0.0259170	+	0.999664i	$0.508251\pi$
$878$		−	776.447i		−	0.884336i
$879$	−223.836	−	350.130i	−0.254649	−	0.398328i
$880$	288.323			0.327640
$881$		−	232.268i		−	0.263642i	−0.991274	−	0.131821i	$-0.957918\pi$
$881$		−	232.268i		−	0.263642i	0.991274	−	0.131821i	$-0.0420824\pi$
$882$	−560.244	−	259.094i	−0.635197	−	0.293757i
$883$	481.122			0.544872			0.272436	−	0.962174i	$-0.412171\pi$
$883$	481.122			0.544872			0.272436	+	0.962174i	$0.412171\pi$
$884$			766.644i			0.867244i
$885$	−20.5659	+	13.1477i	−0.0232383	+	0.0148561i
$886$	575.693			0.649766
$887$		−	367.753i		−	0.414604i	−0.978277	−	0.207302i	$-0.933532\pi$
$887$		−	367.753i		−	0.414604i	0.978277	−	0.207302i	$-0.0664682\pi$
$888$	−88.3425	−	138.188i	−0.0994848	−	0.155617i
$889$	−149.369			−0.168019
$890$		−	909.744i		−	1.02218i
$891$	−609.074	+	517.669i	−0.683584	+	0.580998i
$892$	468.612			0.525350
$893$		−	260.018i		−	0.291174i
$894$	314.596	−	201.119i	0.351897	−	0.224966i
$895$	1012.99			1.13183
$896$			8.03137i			0.00896359i
$897$	166.418	+	260.315i	0.185527	+	0.290206i
$898$	478.454			0.532799
$899$			247.254i			0.275032i
$900$	214.205	−	463.180i	0.238005	−	0.514644i
$901$	−700.489			−0.777458
$902$			1055.84i			1.17055i
$903$	−119.511	+	76.4026i	−0.132349	+	0.0846097i
$904$	−55.1053			−0.0609571
$905$			940.404i			1.03912i
$906$	480.434	+	751.508i	0.530281	+	0.829479i
$907$	1115.89			1.23030			0.615152	−	0.788408i	$-0.289095\pi$
$907$	1115.89			1.23030			0.615152	+	0.788408i	$0.289095\pi$
$908$		−	653.222i		−	0.719407i
$909$	−846.266	−	391.369i	−0.930986	−	0.430549i
$910$	−157.468			−0.173042
$911$			737.850i			0.809934i	0.914331	+	0.404967i	$0.132717\pi$
$911$			737.850i			0.809934i	−0.914331	+	0.404967i	$0.867283\pi$
$912$	85.4683	−	54.6393i	0.0937152	−	0.0599116i
$913$	−264.736			−0.289962
$914$		−	503.837i		−	0.551244i
$915$	553.576	+	865.918i	0.605001	+	0.946358i
$916$	162.728			0.177651
$917$			46.4764i			0.0506831i
$918$	−92.1672	−	675.325i	−0.100400	−	0.735648i
$919$	−390.440			−0.424853			−0.212427	−	0.977177i	$-0.568137\pi$
$919$	−390.440			−0.424853			−0.212427	+	0.977177i	$0.568137\pi$
$920$			99.0784i			0.107694i
$921$	−584.508	+	373.673i	−0.634645	+	0.405725i
$922$	664.080			0.720261
$923$			110.111i			0.119297i
$924$	22.6400	+	35.4141i	0.0245022	+	0.0383270i
$925$	547.993			0.592425
$926$			698.944i			0.754799i
$927$	−408.656	+	883.646i	−0.440837	+	0.953232i
$928$	−25.3212			−0.0272858
$929$		−	50.6757i		−	0.0545486i	−0.999628	−	0.0272743i	$-0.991317\pi$
$929$		−	50.6757i		−	0.0545486i	0.999628	−	0.0272743i	$-0.00868276\pi$
$930$	1442.22	−	922.000i	1.55077	−	0.991398i
$931$	409.958			0.440341
$932$		−	152.294i		−	0.163406i
$933$	−736.299	−	1151.74i	−0.789174	−	1.23445i
$934$	−699.633			−0.749072
$935$			1286.65i			1.37610i
$936$	496.161	+	229.458i	0.530087	+	0.245147i
$937$	1374.26			1.46666			0.733332	−	0.679871i	$-0.237964\pi$
$937$	1374.26			1.46666			0.733332	+	0.679871i	$0.237964\pi$
$938$		−	12.3942i		−	0.0132134i
$939$	−901.242	+	576.159i	−0.959790	+	0.613588i
$940$	449.336			0.478017
$941$		−	936.470i		−	0.995186i	−0.867411	−	0.497593i	$-0.834217\pi$
$941$		−	936.470i		−	0.995186i	0.867411	−	0.497593i	$-0.165783\pi$
$942$	−707.830	−	1107.21i	−0.751412	−	1.17538i
$943$	−362.825			−0.384756
$944$		−	4.45580i		−	0.00472013i
$945$	138.711	−	18.9311i	0.146784	−	0.0200329i
$946$	−929.553			−0.982614
$947$		−	126.262i		−	0.133328i	−0.997775	−	0.0666640i	$-0.978764\pi$
$947$		−	126.262i		−	0.133328i	0.997775	−	0.0666640i	$-0.0212356\pi$
$948$	694.856	−	444.217i	0.732970	−	0.468583i
$949$	−1455.98			−1.53423
$950$			338.931i			0.356769i
$951$	565.320	+	884.287i	0.594448	+	0.929850i
$952$	−35.8403			−0.0376473
$953$			1547.70i			1.62403i	0.583635	+	0.812016i	$0.301630\pi$
$953$			1547.70i			1.62403i	−0.583635	+	0.812016i	$0.698370\pi$
$954$	−209.657	+	453.347i	−0.219767	+	0.475206i
$955$	1610.97			1.68688
$956$			99.2870i			0.103857i
$957$	−111.653	+	71.3793i	−0.116670	+	0.0745865i
$958$	139.811			0.145940
$959$		−	170.537i		−	0.177828i
$960$	94.4220	+	147.697i	0.0983563	+	0.153851i
$961$	2090.17			2.17499
$962$			587.014i			0.610202i
$963$	1.77822	+	0.822364i	0.00184654	+	0.000853961i
$964$	548.949			0.569450
$965$		−	1091.49i		−	1.13108i
$966$	−12.1696	+	7.77995i	−0.0125979	+	0.00805378i
$967$	−455.275			−0.470812			−0.235406	−	0.971897i	$-0.575642\pi$
$967$	−455.275			−0.470812			−0.235406	+	0.971897i	$0.575642\pi$
$968$		−	66.7894i		−	0.0689973i
$969$	243.830	+	381.405i	0.251630	+	0.393607i
$970$	−0.469417			−0.000483935
$971$		−	460.089i		−	0.473830i	−0.971530	−	0.236915i	$-0.923864\pi$
$971$		−	460.089i		−	0.473830i	0.971530	−	0.236915i	$-0.0761363\pi$
$972$	−464.647	−	142.476i	−0.478032	−	0.146581i
$973$	73.8904			0.0759408
$974$			131.716i			0.135232i
$975$	−1538.86	+	983.783i	−1.57832	+	1.00901i
$976$	−187.609			−0.192223
$977$		−	1009.93i		−	1.03371i	−0.856074	−	0.516854i	$-0.827103\pi$
$977$		−	1009.93i		−	1.03371i	0.856074	−	0.516854i	$-0.172897\pi$
$978$	−355.837	−	556.609i	−0.363842	−	0.569130i
$979$	869.127			0.887770
$980$			708.446i			0.722904i
$981$	502.931	−	1087.50i	0.512672	−	1.10856i
$982$	−668.511			−0.680765
$983$			33.2649i			0.0338401i	0.999857	+	0.0169201i	$0.00538608\pi$
$983$			33.2649i			0.0338401i	−0.999857	+	0.0169201i	$0.994614\pi$
$984$	−540.867	+	345.773i	−0.549662	+	0.351396i
$985$	−2747.17			−2.78901
$986$		−	112.997i		−	0.114601i
$987$	35.2833	+	55.1910i	0.0357480	+	0.0559179i
$988$	−363.065			−0.367475
$989$		−	319.429i		−	0.322981i
$990$	832.702	+	385.096i	0.841114	+	0.388986i
$991$	683.518			0.689725			0.344863	−	0.938653i	$-0.387926\pi$
$991$	683.518			0.689725			0.344863	+	0.938653i	$0.387926\pi$
$992$			312.470i			0.314990i
$993$	−33.2065	+	21.2287i	−0.0334406	+	0.0213784i
$994$	−5.14766			−0.00517874
$995$			501.287i			0.503806i
$996$	−86.6975	−	135.614i	−0.0870456	−	0.136159i
$997$	94.3287			0.0946126			0.0473063	−	0.998880i	$-0.484936\pi$
$997$	94.3287			0.0946126			0.0473063	+	0.998880i	$0.484936\pi$
$998$		−	58.3476i		−	0.0584646i
$999$	−70.5719	−	517.092i	−0.0706425	−	0.517610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.10	yes	16
3.2	odd	2	inner	138.3.c.a.47.2	✓	16
4.3	odd	2		1104.3.g.c.737.13		16
12.11	even	2		1104.3.g.c.737.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.2	✓	16	3.2	odd	2	inner
138.3.c.a.47.10	yes	16	1.1	even	1	trivial
1104.3.g.c.737.13		16	4.3	odd	2
1104.3.g.c.737.14		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	138.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-2.52762 + 1.61590i) q^{3} -2.00000 q^{4} +7.30416i q^{5} +(-2.28522 - 3.57460i) q^{6} -0.709880 q^{7} -2.82843i q^{8} +(3.77777 - 8.16875i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-2.52762 + 1.61590i) q^{3} -2.00000 q^{4} +7.30416i q^{5} +(-2.28522 - 3.57460i) q^{6} -0.709880 q^{7} -2.82843i q^{8} +(3.77777 - 8.16875i) q^{9} -10.3296 q^{10} -9.86845i q^{11} +(5.05525 - 3.23179i) q^{12} -21.4745 q^{13} -1.00392i q^{14} +(-11.8028 - 18.4622i) q^{15} +4.00000 q^{16} +17.8501i q^{17} +(11.5524 + 5.34257i) q^{18} -8.45342 q^{19} -14.6083i q^{20} +(1.79431 - 1.14709i) q^{21} +13.9561 q^{22} +4.79583i q^{23} +(4.57044 + 7.14920i) q^{24} -28.3507 q^{25} -30.3695i q^{26} +(3.65107 + 26.7520i) q^{27} +1.41976 q^{28} +4.47621i q^{29} +(26.1094 - 16.6916i) q^{30} +55.2374 q^{31} +5.65685i q^{32} +(15.9464 + 24.9437i) q^{33} -25.2439 q^{34} -5.18507i q^{35} +(-7.55553 + 16.3375i) q^{36} -19.3291 q^{37} -11.9549i q^{38} +(54.2794 - 34.7005i) q^{39} +20.6593 q^{40} +75.6542i q^{41} +(1.62223 + 2.53754i) q^{42} -66.6055 q^{43} +19.7369i q^{44} +(59.6658 + 27.5934i) q^{45} -6.78233 q^{46} +30.7589i q^{47} +(-10.1105 + 6.46358i) q^{48} -48.4961 q^{49} -40.0939i q^{50} +(-28.8439 - 45.1184i) q^{51} +42.9489 q^{52} +39.2428i q^{53} +(-37.8330 + 5.16339i) q^{54} +72.0807 q^{55} +2.00784i q^{56} +(21.3671 - 13.6598i) q^{57} -6.33031 q^{58} -1.11395i q^{59} +(23.6055 + 36.9243i) q^{60} -46.9023 q^{61} +78.1174i q^{62} +(-2.68176 + 5.79883i) q^{63} -8.00000 q^{64} -156.853i q^{65} +(-35.2758 + 22.5516i) q^{66} +12.3457 q^{67} -35.7003i q^{68} +(-7.74956 - 12.1221i) q^{69} +7.33280 q^{70} -5.12755i q^{71} +(-23.1047 - 10.6851i) q^{72} +67.8005 q^{73} -27.3355i q^{74} +(71.6599 - 45.8118i) q^{75} +16.9068 q^{76} +7.00542i q^{77} +(49.0739 + 76.7626i) q^{78} +137.452 q^{79} +29.2166i q^{80} +(-52.4570 - 61.7193i) q^{81} -106.991 q^{82} -26.8265i q^{83} +(-3.58862 + 2.29418i) q^{84} -130.380 q^{85} -94.1944i q^{86} +(-7.23308 - 11.3142i) q^{87} -27.9122 q^{88} +88.0712i q^{89} +(-39.0230 + 84.3802i) q^{90} +15.2443 q^{91} -9.59166i q^{92} +(-139.619 + 89.2578i) q^{93} -43.4997 q^{94} -61.7451i q^{95} +(-9.14088 - 14.2984i) q^{96} +0.0454437 q^{97} -68.5838i q^{98} +(-80.6129 - 37.2807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

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