LMFDB - Embedded newform 138.3.c.a.47.4

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			47.4
Root			$-0.0515370 + 2.99956i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.0515370 + 2.99956i) q^{3} -2.00000 q^{4} +2.42657i q^{5} +(4.24201 + 0.0728843i) q^{6} -2.87957 q^{7} +2.82843i q^{8} +(-8.99469 - 0.309176i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.0515370 + 2.99956i) q^{3} -2.00000 q^{4} +2.42657i q^{5} +(4.24201 + 0.0728843i) q^{6} -2.87957 q^{7} +2.82843i q^{8} +(-8.99469 - 0.309176i) q^{9} +3.43169 q^{10} +19.9504i q^{11} +(0.103074 - 5.99911i) q^{12} -4.20991 q^{13} +4.07233i q^{14} +(-7.27863 - 0.125058i) q^{15} +4.00000 q^{16} +13.3259i q^{17} +(-0.437241 + 12.7204i) q^{18} -0.0578122 q^{19} -4.85314i q^{20} +(0.148405 - 8.63745i) q^{21} +28.2141 q^{22} +4.79583i q^{23} +(-8.48403 - 0.145769i) q^{24} +19.1118 q^{25} +5.95372i q^{26} +(1.39095 - 26.9641i) q^{27} +5.75915 q^{28} -38.4686i q^{29} +(-0.176859 + 10.2935i) q^{30} +30.7346 q^{31} -5.65685i q^{32} +(-59.8423 - 1.02818i) q^{33} +18.8456 q^{34} -6.98748i q^{35} +(17.9894 + 0.618353i) q^{36} -28.1184 q^{37} +0.0817588i q^{38} +(0.216966 - 12.6279i) q^{39} -6.86337 q^{40} +38.6706i q^{41} +(-12.2152 - 0.209876i) q^{42} +35.5114 q^{43} -39.9008i q^{44} +(0.750237 - 21.8262i) q^{45} +6.78233 q^{46} +23.2785i q^{47} +(-0.206148 + 11.9982i) q^{48} -40.7081 q^{49} -27.0281i q^{50} +(-39.9717 - 0.686775i) q^{51} +8.41983 q^{52} -74.5485i q^{53} +(-38.1331 - 1.96710i) q^{54} -48.4110 q^{55} -8.14466i q^{56} +(0.00297947 - 0.173411i) q^{57} -54.4028 q^{58} -42.4883i q^{59} +(14.5573 + 0.250116i) q^{60} +39.0181 q^{61} -43.4652i q^{62} +(25.9009 + 0.890296i) q^{63} -8.00000 q^{64} -10.2156i q^{65} +(-1.45407 + 84.6298i) q^{66} +118.385 q^{67} -26.6517i q^{68} +(-14.3854 - 0.247163i) q^{69} -9.88179 q^{70} +108.860i q^{71} +(0.874483 - 25.4408i) q^{72} -24.5455 q^{73} +39.7654i q^{74} +(-0.984963 + 57.3268i) q^{75} +0.115624 q^{76} -57.4486i q^{77} +(-17.8585 - 0.306837i) q^{78} +49.3033 q^{79} +9.70627i q^{80} +(80.8088 + 5.56189i) q^{81} +54.6885 q^{82} +69.9817i q^{83} +(-0.296809 + 17.2749i) q^{84} -32.3361 q^{85} -50.2208i q^{86} +(115.389 + 1.98255i) q^{87} -56.4282 q^{88} +142.393i q^{89} +(-30.8669 - 1.06100i) q^{90} +12.1228 q^{91} -9.59166i q^{92} +(-1.58397 + 92.1901i) q^{93} +32.9208 q^{94} -0.140285i q^{95} +(16.9681 + 0.291537i) q^{96} +42.6941 q^{97} +57.5699i q^{98} +(6.16819 - 179.447i) 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
$3$	−0.0515370	+	2.99956i	−0.0171790	+	0.999852i
$3$	−0.0515370	+	2.99956i	−0.0171790	+	0.999852i
$4$	−2.00000			−0.500000
$5$			2.42657i			0.485314i	0.970112	+	0.242657i	$0.0780189\pi$
$5$			2.42657i			0.485314i	−0.970112	+	0.242657i	$0.921981\pi$
$6$	4.24201	+	0.0728843i	0.707002	+	0.0121474i
$7$	−2.87957			−0.411368			−0.205684	−	0.978618i	$-0.565942\pi$
$7$	−2.87957			−0.411368			−0.205684	+	0.978618i	$0.565942\pi$
$8$			2.82843i			0.353553i
$9$	−8.99469	−	0.309176i	−0.999410	−	0.0343529i
$10$	3.43169			0.343169
$11$			19.9504i			1.81367i	0.421484	+	0.906836i	$0.361509\pi$
$11$			19.9504i			1.81367i	−0.421484	+	0.906836i	$0.638491\pi$
$12$	0.103074	−	5.99911i	0.00858950	−	0.499926i
$13$	−4.20991			−0.323840			−0.161920	−	0.986804i	$-0.551769\pi$
$13$	−4.20991			−0.323840			−0.161920	+	0.986804i	$0.551769\pi$
$14$			4.07233i			0.290881i
$15$	−7.27863	−	0.125058i	−0.485242	−	0.00833720i
$16$	4.00000			0.250000
$17$			13.3259i			0.783874i	0.919992	+	0.391937i	$0.128195\pi$
$17$			13.3259i			0.783874i	−0.919992	+	0.391937i	$0.871805\pi$
$18$	−0.437241	+	12.7204i	−0.0242912	+	0.706689i
$19$	−0.0578122			−0.00304275			−0.00152137	−	0.999999i	$-0.500484\pi$
$19$	−0.0578122			−0.00304275			−0.00152137	+	0.999999i	$0.500484\pi$
$20$		−	4.85314i		−	0.242657i
$21$	0.148405	−	8.63745i	0.00706688	−	0.411307i
$22$	28.2141			1.28246
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−8.48403	−	0.145769i	−0.353501	−	0.00607369i
$25$	19.1118			0.764471
$26$			5.95372i			0.228989i
$27$	1.39095	−	26.9641i	0.0515167	−	0.998672i
$28$	5.75915			0.205684
$29$		−	38.4686i		−	1.32650i	−0.748397	−	0.663251i	$-0.769176\pi$
$29$		−	38.4686i		−	1.32650i	0.748397	−	0.663251i	$-0.230824\pi$
$30$	−0.176859	+	10.2935i	−0.00589529	+	0.343118i
$31$	30.7346			0.991437			0.495719	−	0.868483i	$-0.334905\pi$
$31$	30.7346			0.991437			0.495719	+	0.868483i	$0.334905\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−59.8423	−	1.02818i	−1.81340	−	0.0311571i
$34$	18.8456			0.554283
$35$		−	6.98748i		−	0.199642i
$36$	17.9894	+	0.618353i	0.499705	+	0.0171765i
$37$	−28.1184			−0.759957			−0.379978	−	0.924995i	$-0.624069\pi$
$37$	−28.1184			−0.759957			−0.379978	+	0.924995i	$0.624069\pi$
$38$			0.0817588i			0.00215155i
$39$	0.216966	−	12.6279i	0.00556324	−	0.323792i
$40$	−6.86337			−0.171584
$41$			38.6706i			0.943186i	0.881816	+	0.471593i	$0.156321\pi$
$41$			38.6706i			0.943186i	−0.881816	+	0.471593i	$0.843679\pi$
$42$	−12.2152	−	0.209876i	−0.290838	−	0.00499704i
$43$	35.5114			0.825847			0.412924	−	0.910766i	$-0.364508\pi$
$43$	35.5114			0.825847			0.412924	+	0.910766i	$0.364508\pi$
$44$		−	39.9008i		−	0.906836i
$45$	0.750237	−	21.8262i	0.0166719	−	0.485027i
$46$	6.78233			0.147442
$47$			23.2785i			0.495287i	0.968851	+	0.247644i	$0.0796562\pi$
$47$			23.2785i			0.495287i	−0.968851	+	0.247644i	$0.920344\pi$
$48$	−0.206148	+	11.9982i	−0.00429475	+	0.249963i
$49$	−40.7081			−0.830777
$50$		−	27.0281i		−	0.540562i
$51$	−39.9717	−	0.686775i	−0.783759	−	0.0134662i
$52$	8.41983			0.161920
$53$		−	74.5485i		−	1.40658i	−0.710905	−	0.703288i	$-0.751714\pi$
$53$		−	74.5485i		−	1.40658i	0.710905	−	0.703288i	$-0.248286\pi$
$54$	−38.1331	−	1.96710i	−0.706168	−	0.0364278i
$55$	−48.4110			−0.880199
$56$		−	8.14466i		−	0.145440i
$57$	0.00297947	−	0.173411i	5.22714e−5	−	0.00304230i
$58$	−54.4028			−0.937979
$59$		−	42.4883i		−	0.720141i	−0.932925	−	0.360071i	$-0.882753\pi$
$59$		−	42.4883i		−	0.720141i	0.932925	−	0.360071i	$-0.117247\pi$
$60$	14.5573	+	0.250116i	0.242621	+	0.00416860i
$61$	39.0181			0.639642			0.319821	−	0.947478i	$-0.396377\pi$
$61$	39.0181			0.639642			0.319821	+	0.947478i	$0.396377\pi$
$62$		−	43.4652i		−	0.701052i
$63$	25.9009	+	0.890296i	0.411125	+	0.0141317i
$64$	−8.00000			−0.125000
$65$		−	10.2156i		−	0.157164i
$66$	−1.45407	+	84.6298i	−0.0220314	+	1.28227i
$67$	118.385			1.76693			0.883467	−	0.468493i	$-0.155203\pi$
$67$	118.385			1.76693			0.883467	+	0.468493i	$0.155203\pi$
$68$		−	26.6517i		−	0.391937i
$69$	−14.3854	−	0.247163i	−0.208484	−	0.00358207i
$70$	−9.88179			−0.141168
$71$			108.860i			1.53324i	0.642100	+	0.766621i	$0.278064\pi$
$71$			108.860i			1.53324i	−0.642100	+	0.766621i	$0.721936\pi$
$72$	0.874483	−	25.4408i	0.0121456	−	0.353345i
$73$	−24.5455			−0.336240			−0.168120	−	0.985767i	$-0.553770\pi$
$73$	−24.5455			−0.336240			−0.168120	+	0.985767i	$0.553770\pi$
$74$			39.7654i			0.537371i
$75$	−0.984963	+	57.3268i	−0.0131328	+	0.764358i
$76$	0.115624			0.00152137
$77$		−	57.4486i		−	0.746086i
$78$	−17.8585	−	0.306837i	−0.228955	−	0.00393380i
$79$	49.3033			0.624093			0.312046	−	0.950067i	$-0.398986\pi$
$79$	49.3033			0.624093			0.312046	+	0.950067i	$0.398986\pi$
$80$			9.70627i			0.121328i
$81$	80.8088	+	5.56189i	0.997640	+	0.0686653i
$82$	54.6885			0.666933
$83$			69.9817i			0.843153i	0.906793	+	0.421577i	$0.138523\pi$
$83$			69.9817i			0.843153i	−0.906793	+	0.421577i	$0.861477\pi$
$84$	−0.296809	+	17.2749i	−0.00353344	+	0.205653i
$85$	−32.3361			−0.380425
$86$		−	50.2208i		−	0.583962i
$87$	115.389	+	1.98255i	1.32631	+	0.0227880i
$88$	−56.4282			−0.641230
$89$			142.393i			1.59992i	0.600050	+	0.799962i	$0.295147\pi$
$89$			142.393i			1.59992i	−0.600050	+	0.799962i	$0.704853\pi$
$90$	−30.8669	−	1.06100i	−0.342966	−	0.0117888i
$91$	12.1228			0.133217
$92$		−	9.59166i		−	0.104257i
$93$	−1.58397	+	92.1901i	−0.0170319	+	0.991291i
$94$	32.9208			0.350221
$95$		−	0.140285i		−	0.00147669i
$96$	16.9681	+	0.291537i	0.176751	+	0.00303685i
$97$	42.6941			0.440145			0.220073	−	0.975483i	$-0.429371\pi$
$97$	42.6941			0.440145			0.220073	+	0.975483i	$0.429371\pi$
$98$			57.5699i			0.587448i
$99$	6.16819	−	179.447i	0.0623049	−	1.81260i
$100$	−38.2235			−0.382235
$101$			73.1888i			0.724642i	0.932053	+	0.362321i	$0.118016\pi$
$101$			73.1888i			0.724642i	−0.932053	+	0.362321i	$0.881984\pi$
$102$	−0.971247	+	56.5285i	−0.00952203	+	0.554201i
$103$	63.5492			0.616983			0.308491	−	0.951227i	$-0.400176\pi$
$103$	63.5492			0.616983			0.308491	+	0.951227i	$0.400176\pi$
$104$		−	11.9074i		−	0.114495i
$105$	20.9593	+	0.360114i	0.199613	+	0.00342966i
$106$	−105.428			−0.994600
$107$			24.1708i			0.225896i	0.993601	+	0.112948i	$0.0360293\pi$
$107$			24.1708i			0.225896i	−0.993601	+	0.112948i	$0.963971\pi$
$108$	−2.78190	+	53.9283i	−0.0257584	+	0.499336i
$109$	−130.129			−1.19384			−0.596921	−	0.802300i	$-0.703609\pi$
$109$	−130.129			−1.19384			−0.596921	+	0.802300i	$0.703609\pi$
$110$			68.4634i			0.622395i
$111$	1.44914	−	84.3428i	0.0130553	−	0.759845i
$112$	−11.5183			−0.102842
$113$		−	93.0833i		−	0.823746i	−0.911241	−	0.411873i	$-0.864875\pi$
$113$		−	93.0833i		−	0.823746i	0.911241	−	0.411873i	$-0.135125\pi$
$114$	−0.245240	−	0.00421360i	−0.00215123	−	3.69614e-5i
$115$	−11.6374			−0.101195
$116$			76.9372i			0.663251i
$117$	37.8669	+	1.30161i	0.323648	+	0.0111248i
$118$	−60.0876			−0.509217
$119$		−	38.3728i		−	0.322461i
$120$	0.353717	−	20.5871i	0.00294765	−	0.171559i
$121$	−277.018			−2.28940
$122$		−	55.1800i		−	0.452295i
$123$	−115.995	−	1.99297i	−0.943047	−	0.0162030i
$124$	−61.4691			−0.495719
$125$			107.040i			0.856322i
$126$	1.25907	−	36.6294i	0.00999261	−	0.290709i
$127$	−25.5886			−0.201485			−0.100743	−	0.994913i	$-0.532122\pi$
$127$	−25.5886			−0.201485			−0.100743	+	0.994913i	$0.532122\pi$
$128$			11.3137i			0.0883883i
$129$	−1.83015	+	106.519i	−0.0141872	+	0.825726i
$130$	−14.4471			−0.111132
$131$		−	98.7994i		−	0.754194i	−0.926174	−	0.377097i	$-0.876922\pi$
$131$		−	98.7994i		−	0.754194i	0.926174	−	0.377097i	$-0.123078\pi$
$132$	119.685	+	2.05637i	0.906702	+	0.0155785i
$133$	0.166475			0.00125169
$134$		−	167.421i		−	1.24941i
$135$	65.4303	+	3.37524i	0.484669	+	0.0250018i
$136$	−37.6912			−0.277141
$137$			31.2779i			0.228306i	0.993463	+	0.114153i	$0.0364154\pi$
$137$			31.2779i			0.228306i	−0.993463	+	0.114153i	$0.963585\pi$
$138$	−0.349541	+	20.3440i	−0.00253291	+	0.147420i
$139$	121.623			0.874982			0.437491	−	0.899223i	$-0.355867\pi$
$139$	121.623			0.874982			0.437491	+	0.899223i	$0.355867\pi$
$140$			13.9750i			0.0998212i
$141$	−69.8252	−	1.19970i	−0.495214	−	0.00850854i
$142$	153.952			1.08417
$143$		−	83.9894i		−	0.587338i
$144$	−35.9788	−	1.23671i	−0.249852	−	0.00858823i
$145$	93.3466			0.643770
$146$			34.7126i			0.237757i
$147$	2.09797	−	122.106i	0.0142719	−	0.830654i
$148$	56.2368			0.379978
$149$			99.3256i			0.666615i	0.942818	+	0.333307i	$0.108165\pi$
$149$			99.3256i			0.666615i	−0.942818	+	0.333307i	$0.891835\pi$
$150$	81.0724	+	1.39295i	0.540483	+	0.00928632i
$151$	274.989			1.82112			0.910560	−	0.413378i	$-0.135651\pi$
$151$	274.989			1.82112			0.910560	+	0.413378i	$0.135651\pi$
$152$		−	0.163518i		−	0.00107577i
$153$	4.12004	−	119.862i	0.0269284	−	0.783412i
$154$	−81.2446			−0.527562
$155$			74.5795i			0.481158i
$156$	−0.433933	+	25.2558i	−0.00278162	+	0.161896i
$157$	−161.569			−1.02910			−0.514552	−	0.857459i	$-0.672042\pi$
$157$	−161.569			−1.02910			−0.514552	+	0.857459i	$0.672042\pi$
$158$		−	69.7254i		−	0.441300i
$159$	223.613	+	3.84201i	1.40637	+	0.0241636i
$160$	13.7267			0.0857921
$161$		−	13.8100i		−	0.0857761i
$162$	7.86570	−	114.281i	0.0485537	−	0.705438i
$163$	−301.953			−1.85248			−0.926238	−	0.376940i	$-0.876976\pi$
$163$	−301.953			−1.85248			−0.926238	+	0.376940i	$0.876976\pi$
$164$		−	77.3413i		−	0.471593i
$165$	2.49496	−	145.211i	0.0151209	−	0.880069i
$166$	98.9691			0.596199
$167$		−	173.276i		−	1.03758i	−0.854902	−	0.518789i	$-0.826383\pi$
$167$		−	173.276i		−	1.03758i	0.854902	−	0.518789i	$-0.173617\pi$
$168$	24.4304	+	0.419752i	0.145419	+	0.00249852i
$169$	−151.277			−0.895128
$170$			45.7302i			0.269001i
$171$	0.520003	+	0.0178742i	0.00304095	+	0.000104527i
$172$	−71.0229			−0.412924
$173$		−	244.246i		−	1.41183i	−0.708297	−	0.705914i	$-0.750536\pi$
$173$		−	244.246i		−	1.41183i	0.708297	−	0.705914i	$-0.249464\pi$
$174$	2.80376	−	163.184i	0.0161135	−	0.937841i
$175$	−55.0337			−0.314479
$176$			79.8015i			0.453418i
$177$	127.446	+	2.18972i	0.720035	+	0.0123713i
$178$	201.375			1.13132
$179$			273.327i			1.52697i	0.645826	+	0.763484i	$0.276513\pi$
$179$			273.327i			1.52697i	−0.645826	+	0.763484i	$0.723487\pi$
$180$	−1.50047	+	43.6524i	−0.00833597	+	0.242514i
$181$	312.364			1.72577			0.862884	−	0.505401i	$-0.168656\pi$
$181$	312.364			1.72577			0.862884	+	0.505401i	$0.168656\pi$
$182$		−	17.1442i		−	0.0941987i
$183$	−2.01088	+	117.037i	−0.0109884	+	0.639547i
$184$	−13.5647			−0.0737210
$185$		−	68.2312i		−	0.368817i
$186$	130.376	+	2.24007i	0.700949	+	0.0120434i
$187$	−265.856			−1.42169
$188$		−	46.5570i		−	0.247644i
$189$	−4.00535	+	77.6453i	−0.0211923	+	0.410821i
$190$	−0.198393			−0.00104418
$191$			54.6549i			0.286151i	0.989712	+	0.143076i	$0.0456992\pi$
$191$			54.6549i			0.286151i	−0.989712	+	0.143076i	$0.954301\pi$
$192$	0.412296	−	23.9965i	0.00214737	−	0.124982i
$193$	−8.17662			−0.0423659			−0.0211830	−	0.999776i	$-0.506743\pi$
$193$	−8.17662			−0.0423659			−0.0211830	+	0.999776i	$0.506743\pi$
$194$		−	60.3786i		−	0.311230i
$195$	30.6424	+	0.526484i	0.157141	+	0.00269992i
$196$	81.4161			0.415388
$197$		−	297.633i		−	1.51083i	−0.655247	−	0.755414i	$-0.727436\pi$
$197$		−	297.633i		−	1.51083i	0.655247	−	0.755414i	$-0.272564\pi$
$198$	−253.777	−	8.72313i	−1.28170	−	0.0440562i
$199$	−269.701			−1.35528			−0.677641	−	0.735393i	$-0.736998\pi$
$199$	−269.701			−1.35528			−0.677641	+	0.735393i	$0.736998\pi$
$200$			54.0562i			0.270281i
$201$	−6.10119	+	355.101i	−0.0303542	+	1.76667i
$202$	103.505			0.512399
$203$			110.773i			0.545680i
$204$	79.9434	+	1.37355i	0.391879	+	0.00673309i
$205$	−93.8369			−0.457741
$206$		−	89.8721i		−	0.436273i
$207$	1.48276	−	43.1370i	0.00716308	−	0.208391i
$208$	−16.8397			−0.0809599
$209$		−	1.15338i		−	0.00551855i
$210$	0.509278	−	29.6410i	0.00242513	−	0.141148i
$211$	−218.290			−1.03455			−0.517274	−	0.855820i	$-0.673053\pi$
$211$	−218.290			−1.03455			−0.517274	+	0.855820i	$0.673053\pi$
$212$			149.097i			0.703288i
$213$	−326.532	−	5.61033i	−1.53302	−	0.0263396i
$214$	34.1827			0.159732
$215$			86.1709i			0.400795i
$216$	76.2661	+	3.93420i	0.353084	+	0.0182139i
$217$	−88.5024			−0.407845
$218$			184.030i			0.844174i
$219$	1.26500	−	73.6256i	0.00577626	−	0.336190i
$220$	96.8219			0.440100
$221$		−	56.1007i		−	0.253850i
$222$	−119.279	−	2.04939i	−0.537291	−	0.00923149i
$223$	136.835			0.613611			0.306806	−	0.951772i	$-0.400740\pi$
$223$	136.835			0.613611			0.306806	+	0.951772i	$0.400740\pi$
$224$			16.2893i			0.0727202i
$225$	−171.904	−	5.90891i	−0.764020	−	0.0262618i
$226$	−131.640			−0.582476
$227$		−	300.256i		−	1.32271i	−0.750072	−	0.661356i	$-0.769981\pi$
$227$		−	300.256i		−	1.32271i	0.750072	−	0.661356i	$-0.230019\pi$
$228$	−0.00595894	+	0.346822i	−2.61357e−5	+	0.00152115i
$229$	330.005			1.44107			0.720534	−	0.693420i	$-0.243897\pi$
$229$	330.005			1.44107			0.720534	+	0.693420i	$0.243897\pi$
$230$			16.4578i			0.0715556i
$231$	172.320	+	2.96073i	0.745976	+	0.0128170i
$232$	108.806			0.468990
$233$		−	12.1703i		−	0.0522329i	−0.999659	−	0.0261164i	$-0.991686\pi$
$233$		−	12.1703i		−	0.0522329i	0.999659	−	0.0261164i	$-0.00831406\pi$
$234$	1.84075	−	53.5518i	0.00786645	−	0.228854i
$235$	−56.4868			−0.240370
$236$			84.9767i			0.360071i
$237$	−2.54094	+	147.888i	−0.0107213	+	0.624000i
$238$	−54.2673			−0.228014
$239$			144.178i			0.603254i	0.953426	+	0.301627i	$0.0975298\pi$
$239$			144.178i			0.603254i	−0.953426	+	0.301627i	$0.902470\pi$
$240$	−29.1145	−	0.500232i	−0.121310	−	0.00208430i
$241$	470.046			1.95040			0.975199	−	0.221328i	$-0.0710391\pi$
$241$	470.046			1.95040			0.975199	+	0.221328i	$0.0710391\pi$
$242$			391.762i			1.61885i
$243$	−20.8479	+	242.104i	−0.0857936	+	0.996313i
$244$	−78.0363			−0.319821
$245$		−	98.7809i		−	0.403187i
$246$	−2.81848	+	164.041i	−0.0114572	+	0.666835i
$247$	0.243384			0.000985362
$248$			86.9305i			0.350526i
$249$	−209.914	−	3.60665i	−0.843029	−	0.0144845i
$250$	151.378			0.605511
$251$			70.5461i			0.281060i	0.990076	+	0.140530i	$0.0448807\pi$
$251$			70.5461i			0.281060i	−0.990076	+	0.140530i	$0.955119\pi$
$252$	−51.8017	−	1.78059i	−0.205562	−	0.00706584i
$253$	−95.6787			−0.378177
$254$			36.1878i			0.142472i
$255$	1.66651	−	96.9940i	0.00653532	−	0.380369i
$256$	16.0000			0.0625000
$257$			232.613i			0.905107i	0.891737	+	0.452554i	$0.149487\pi$
$257$			232.613i			0.905107i	−0.891737	+	0.452554i	$0.850513\pi$
$258$	150.640	+	2.58823i	0.583876	+	0.0100319i
$259$	80.9690			0.312622
$260$			20.4313i			0.0785819i
$261$	−11.8936	+	346.013i	−0.0455693	+	1.32572i
$262$	−139.723			−0.533296
$263$			160.774i			0.611307i	0.952143	+	0.305653i	$0.0988749\pi$
$263$			160.774i			0.611307i	−0.952143	+	0.305653i	$0.901125\pi$
$264$	2.90814	−	169.260i	0.0110157	−	0.641135i
$265$	180.897			0.682630
$266$		−	0.235431i		−	0.000885077i
$267$	−427.117	−	7.33852i	−1.59969	−	0.0274851i
$268$	−236.769			−0.883467
$269$		−	355.115i		−	1.32013i	−0.751208	−	0.660065i	$-0.770529\pi$
$269$		−	355.115i		−	1.32013i	0.751208	−	0.660065i	$-0.229471\pi$
$270$	4.77331	−	92.5325i	0.0176789	−	0.342713i
$271$	156.478			0.577409			0.288705	−	0.957418i	$-0.406775\pi$
$271$	156.478			0.577409			0.288705	+	0.957418i	$0.406775\pi$
$272$			53.3035i			0.195969i
$273$	−0.624771	+	36.3629i	−0.00228854	+	0.133197i
$274$	44.2337			0.161437
$275$			381.287i			1.38650i
$276$	28.7707	+	0.494326i	0.104242	+	0.00179103i
$277$	144.584			0.521965			0.260983	−	0.965344i	$-0.415953\pi$
$277$	144.584			0.521965			0.260983	+	0.965344i	$0.415953\pi$
$278$		−	172.000i		−	0.618706i
$279$	−276.448	−	9.50240i	−0.990852	−	0.0340588i
$280$	19.7636			0.0705842
$281$		−	253.655i		−	0.902686i	−0.892350	−	0.451343i	$-0.850945\pi$
$281$		−	253.655i		−	0.902686i	0.892350	−	0.451343i	$-0.149055\pi$
$282$	−1.69664	+	98.7477i	−0.00601644	+	0.350169i
$283$	466.396			1.64804			0.824022	−	0.566558i	$-0.191725\pi$
$283$	466.396			1.64804			0.824022	+	0.566558i	$0.191725\pi$
$284$		−	217.720i		−	0.766621i
$285$	0.420794	+	0.00722988i	0.00147647	+	2.53680e-5i
$286$	−118.779			−0.415311
$287$		−	111.355i		−	0.387996i
$288$	−1.74897	+	50.8816i	−0.00607280	+	0.176672i
$289$	111.421			0.385541
$290$		−	132.012i		−	0.455214i
$291$	−2.20033	+	128.063i	−0.00756126	+	0.440080i
$292$	49.0910			0.168120
$293$		−	338.279i		−	1.15453i	−0.816555	−	0.577267i	$-0.804119\pi$
$293$		−	338.279i		−	1.15453i	0.816555	−	0.577267i	$-0.195881\pi$
$294$	−172.684	−	2.96698i	−0.587361	−	0.0100918i
$295$	103.101			0.349494
$296$		−	79.5309i		−	0.268685i
$297$	537.945	+	27.7500i	1.81126	+	0.0934344i
$298$	140.468			0.471368
$299$		−	20.1900i		−	0.0675252i
$300$	1.96993	−	114.654i	0.00656642	−	0.382179i
$301$	−102.258			−0.339727
$302$		−	388.893i		−	1.28773i
$303$	−219.534	−	3.77193i	−0.724535	−	0.0124486i
$304$	−0.231249			−0.000760687
$305$			94.6802i			0.310427i
$306$	−169.510	−	5.82662i	−0.553956	−	0.0190412i
$307$	−360.282			−1.17356			−0.586779	−	0.809747i	$-0.699604\pi$
$307$	−360.282			−1.17356			−0.586779	+	0.809747i	$0.699604\pi$
$308$			114.897i			0.373043i
$309$	−3.27514	+	190.619i	−0.0105991	+	0.616892i
$310$	105.471			0.340230
$311$			200.546i			0.644844i	0.946596	+	0.322422i	$0.104497\pi$
$311$			200.546i			0.644844i	−0.946596	+	0.322422i	$0.895503\pi$
$312$	35.7170	+	0.613673i	0.114478	+	0.00196690i
$313$	−54.7909			−0.175051			−0.0875253	−	0.996162i	$-0.527896\pi$
$313$	−54.7909			−0.175051			−0.0875253	+	0.996162i	$0.527896\pi$
$314$			228.494i			0.727687i
$315$	−2.16036	+	62.8502i	−0.00685830	+	0.199524i
$316$	−98.6066			−0.312046
$317$		−	459.941i		−	1.45092i	−0.688265	−	0.725460i	$-0.741627\pi$
$317$		−	459.941i		−	1.45092i	0.688265	−	0.725460i	$-0.258373\pi$
$318$	5.43342	−	316.236i	0.0170862	−	0.994453i
$319$	767.463			2.40584
$320$		−	19.4125i		−	0.0606642i
$321$	−72.5018	−	1.24569i	−0.225862	−	0.00388066i
$322$	−19.5302			−0.0606529
$323$		−	0.770398i		−	0.00238513i
$324$	−161.618	−	11.1238i	−0.498820	−	0.0343327i
$325$	−80.4589			−0.247566
$326$			427.027i			1.30990i
$327$	6.70645	−	390.329i	0.0205090	−	1.19367i
$328$	−109.377			−0.333467
$329$		−	67.0321i		−	0.203745i
$330$	−205.360	−	3.52840i	−0.622303	−	0.0106921i
$331$	−571.172			−1.72560			−0.862798	−	0.505549i	$-0.831290\pi$
$331$	−571.172			−1.72560			−0.862798	+	0.505549i	$0.831290\pi$
$332$		−	139.963i		−	0.421577i
$333$	252.916	+	8.69355i	0.759508	+	0.0261067i
$334$	−245.049			−0.733679
$335$			287.268i			0.857517i
$336$	0.593618	−	34.5498i	0.00176672	−	0.102827i
$337$	−31.8440			−0.0944925			−0.0472463	−	0.998883i	$-0.515045\pi$
$337$	−31.8440			−0.0944925			−0.0472463	+	0.998883i	$0.515045\pi$
$338$			213.937i			0.632951i
$339$	279.209	+	4.79723i	0.823624	+	0.0141511i
$340$	64.6722			0.190212
$341$			613.166i			1.79814i
$342$	0.0252779	−	0.735395i	7.39120e−5	−	0.00215028i
$343$	258.321			0.753122
$344$			100.442i			0.291981i
$345$	0.599757	−	34.9071i	0.00173843	−	0.101180i
$346$	−345.416			−0.998313
$347$		−	228.358i		−	0.658092i	−0.944314	−	0.329046i	$-0.893273\pi$
$347$		−	228.358i		−	0.658092i	0.944314	−	0.329046i	$-0.106727\pi$
$348$	−230.777	−	3.96511i	−0.663153	−	0.0113940i
$349$	578.854			1.65861			0.829303	−	0.558798i	$-0.188737\pi$
$349$	578.854			1.65861			0.829303	+	0.558798i	$0.188737\pi$
$350$			77.8295i			0.222370i
$351$	−5.85579	+	113.517i	−0.0166832	+	0.323410i
$352$	112.856			0.320615
$353$		−	477.785i		−	1.35350i	−0.736213	−	0.676750i	$-0.763388\pi$
$353$		−	477.785i		−	1.35350i	0.736213	−	0.676750i	$-0.236612\pi$
$354$	3.09673	−	180.236i	0.00874784	−	0.509142i
$355$	−264.157			−0.744103
$356$		−	284.787i		−	0.799962i
$357$	115.101	+	1.97762i	0.322413	+	0.00553955i
$358$	386.543			1.07973
$359$		−	409.276i		−	1.14004i	−0.821630	−	0.570022i	$-0.806935\pi$
$359$		−	409.276i		−	1.14004i	0.821630	−	0.570022i	$-0.193065\pi$
$360$	61.7339	+	2.12199i	0.171483	+	0.00589442i
$361$	−360.997			−0.999991
$362$		−	441.750i		−	1.22030i
$363$	14.2767	−	830.931i	0.0393297	−	2.28907i
$364$	−24.2455			−0.0666086
$365$		−	59.5613i		−	0.163182i
$366$	165.516	+	2.84381i	0.452228	+	0.00776997i
$367$	−178.094			−0.485270			−0.242635	−	0.970118i	$-0.578012\pi$
$367$	−178.094			−0.485270			−0.242635	+	0.970118i	$0.578012\pi$
$368$			19.1833i			0.0521286i
$369$	11.9560	−	347.830i	0.0324012	−	0.942629i
$370$	−96.4935			−0.260793
$371$			214.668i			0.578620i
$372$	3.16793	−	184.380i	0.00851595	−	0.495646i
$373$	480.186			1.28736			0.643681	−	0.765294i	$-0.277406\pi$
$373$	480.186			1.28736			0.643681	+	0.765294i	$0.277406\pi$
$374$			375.977i			1.00529i
$375$	−321.073	−	5.51653i	−0.856195	−	0.0147107i
$376$	−65.8415			−0.175110
$377$			161.949i			0.429574i
$378$	109.807	+	5.66442i	0.290495	+	0.0149852i
$379$	−102.317			−0.269966			−0.134983	−	0.990848i	$-0.543098\pi$
$379$	−102.317			−0.269966			−0.134983	+	0.990848i	$0.543098\pi$
$380$			0.280571i			0.000738344i
$381$	1.31876	−	76.7546i	0.00346132	−	0.201456i
$382$	77.2937			0.202339
$383$		−	77.4169i		−	0.202133i	−0.994880	−	0.101066i	$-0.967775\pi$
$383$		−	77.4169i		−	0.202133i	0.994880	−	0.101066i	$-0.0322255\pi$
$384$	−33.9361	−	0.583075i	−0.0883753	−	0.00151842i
$385$	139.403			0.362086
$386$			11.5635i			0.0299572i
$387$	−319.414	−	10.9793i	−0.825360	−	0.0283703i
$388$	−85.3882			−0.220073
$389$			253.265i			0.651068i	0.945530	+	0.325534i	$0.105544\pi$
$389$			253.265i			0.651068i	−0.945530	+	0.325534i	$0.894456\pi$
$390$	0.744560	−	43.3349i	0.00190913	−	0.111115i
$391$	−63.9086			−0.163449
$392$		−	115.140i		−	0.293724i
$393$	296.354	+	5.09182i	0.754082	+	0.0129563i
$394$	−420.917			−1.06832
$395$			119.638i			0.302881i
$396$	−12.3364	+	358.895i	−0.0311525	+	0.906300i
$397$	−523.236			−1.31797			−0.658987	−	0.752154i	$-0.729015\pi$
$397$	−523.236			−1.31797			−0.658987	+	0.752154i	$0.729015\pi$
$398$			381.415i			0.958330i
$399$	−0.00857960	+	0.499350i	−2.15028e−5	+	0.00125150i
$400$	76.4471			0.191118
$401$		−	249.566i		−	0.622359i	−0.950351	−	0.311180i	$-0.899276\pi$
$401$		−	249.566i		−	0.622359i	0.950351	−	0.311180i	$-0.100724\pi$
$402$	502.189	+	8.62838i	1.24923	+	0.0214636i
$403$	−129.390			−0.321067
$404$		−	146.378i		−	0.362321i
$405$	−13.4963	+	196.088i	−0.0333242	+	0.484168i
$406$	156.657			0.385854
$407$		−	560.973i		−	1.37831i
$408$	1.94249	−	113.057i	0.00476101	−	0.277101i
$409$	200.782			0.490908			0.245454	−	0.969408i	$-0.421063\pi$
$409$	200.782			0.490908			0.245454	+	0.969408i	$0.421063\pi$
$410$			132.705i			0.323672i
$411$	−93.8199	−	1.61197i	−0.228272	−	0.00392207i
$412$	−127.098			−0.308491
$413$			122.348i			0.296243i
$414$	−61.0049	−	2.09694i	−0.147355	−	0.00506506i
$415$	−169.815			−0.409194
$416$			23.8149i			0.0572473i
$417$	−6.26806	+	364.814i	−0.0150313	+	0.874853i
$418$	−1.63112			−0.00390220
$419$		−	211.854i		−	0.505618i	−0.967516	−	0.252809i	$-0.918646\pi$
$419$		−	211.854i		−	0.505618i	0.967516	−	0.252809i	$-0.0813544\pi$
$420$	−41.9187	−	0.720228i	−0.0998064	−	0.00171483i
$421$	281.184			0.667896			0.333948	−	0.942592i	$-0.391619\pi$
$421$	281.184			0.667896			0.333948	+	0.942592i	$0.391619\pi$
$422$			308.708i			0.731536i
$423$	7.19716	−	209.383i	0.0170146	−	0.494995i
$424$	210.855			0.497300
$425$			254.681i			0.599249i
$426$	−7.93420	+	461.787i	−0.0186249	+	1.08401i
$427$	−112.356			−0.263128
$428$		−	48.3417i		−	0.112948i
$429$	251.931	+	4.32856i	0.587252	+	0.0100899i
$430$	121.864			0.283405
$431$			599.951i			1.39200i	0.718043	+	0.695998i	$0.245038\pi$
$431$			599.951i			1.39200i	−0.718043	+	0.695998i	$0.754962\pi$
$432$	5.56381	−	107.857i	0.0128792	−	0.249668i
$433$	−68.9980			−0.159349			−0.0796743	−	0.996821i	$-0.525388\pi$
$433$	−68.9980			−0.159349			−0.0796743	+	0.996821i	$0.525388\pi$
$434$			125.161i			0.288390i
$435$	−4.81080	+	279.999i	−0.0110593	+	0.643675i
$436$	260.258			0.596921
$437$		−	0.277258i		−	0.000634457i
$438$	−104.122	−	1.78898i	−0.237722	−	0.00408443i
$439$	215.544			0.490989			0.245494	−	0.969398i	$-0.421050\pi$
$439$	215.544			0.490989			0.245494	+	0.969398i	$0.421050\pi$
$440$		−	136.927i		−	0.311197i
$441$	366.156	+	12.5860i	0.830286	+	0.0285396i
$442$	−79.3384			−0.179499
$443$		−	454.824i		−	1.02669i	−0.858182	−	0.513345i	$-0.828406\pi$
$443$		−	454.824i		−	1.02669i	0.858182	−	0.513345i	$-0.171594\pi$
$444$	−2.89828	+	168.686i	−0.00652765	+	0.379922i
$445$	−345.527			−0.776465
$446$		−	193.514i		−	0.433889i
$447$	−297.933	−	5.11894i	−0.666516	−	0.0114518i
$448$	23.0366			0.0514210
$449$		−	165.195i		−	0.367918i	−0.982934	−	0.183959i	$-0.941109\pi$
$449$		−	165.195i		−	0.367918i	0.982934	−	0.183959i	$-0.0588914\pi$
$450$	−8.35646	+	243.110i	−0.0185699	+	0.540243i
$451$	−771.494			−1.71063
$452$			186.167i			0.411873i
$453$	−14.1721	+	824.845i	−0.0312850	+	1.82085i
$454$	−424.625			−0.935298
$455$			29.4167i			0.0646521i
$456$	0.490481	+	0.00842721i	0.00107562	+	1.84807e-5i
$457$	−112.400			−0.245953			−0.122976	−	0.992410i	$-0.539244\pi$
$457$	−112.400			−0.245953			−0.122976	+	0.992410i	$0.539244\pi$
$458$		−	466.697i		−	1.01899i
$459$	359.321	+	18.5356i	0.782833	+	0.0403826i
$460$	23.2748			0.0505974
$461$			439.849i			0.954119i	0.878871	+	0.477060i	$0.158297\pi$
$461$			439.849i			0.954119i	−0.878871	+	0.477060i	$0.841703\pi$
$462$	4.18710	−	243.698i	0.00906299	−	0.527484i
$463$	89.2007			0.192658			0.0963290	−	0.995350i	$-0.469290\pi$
$463$	89.2007			0.192658			0.0963290	+	0.995350i	$0.469290\pi$
$464$		−	153.874i		−	0.331626i
$465$	−223.705	−	3.84360i	−0.481087	−	0.00826581i
$466$	−17.2113			−0.0369342
$467$			568.904i			1.21821i	0.793090	+	0.609104i	$0.208471\pi$
$467$			568.904i			1.21821i	−0.793090	+	0.609104i	$0.791529\pi$
$468$	−75.7337	−	2.60321i	−0.161824	−	0.00556242i
$469$	−340.897			−0.726860
$470$			79.8845i			0.169967i
$471$	8.32680	−	484.637i	0.0176790	−	1.02895i
$472$	120.175			0.254608
$473$			708.467i			1.49782i
$474$	209.145	+	3.59344i	0.441235	+	0.00758109i
$475$	−1.10489			−0.00232609
$476$			76.7456i			0.161230i
$477$	−23.0486	+	670.541i	−0.0483200	+	1.40575i
$478$	203.898			0.426565
$479$			663.293i			1.38475i	0.721540	+	0.692373i	$0.243435\pi$
$479$			663.293i			1.38475i	−0.721540	+	0.692373i	$0.756565\pi$
$480$	−0.707435	+	41.1741i	−0.00147382	+	0.0857795i
$481$	118.376			0.246104
$482$		−	664.746i		−	1.37914i
$483$	41.4237	+	0.711723i	0.0857634	+	0.00147355i
$484$	554.036			1.14470
$485$			103.600i			0.213609i
$486$	342.387	+	29.4833i	0.704500	+	0.0606653i
$487$	−372.902			−0.765712			−0.382856	−	0.923808i	$-0.625059\pi$
$487$	−372.902			−0.765712			−0.382856	+	0.923808i	$0.625059\pi$
$488$			110.360i			0.226147i
$489$	15.5618	−	905.727i	0.0318237	−	1.85220i
$490$	−139.697			−0.285096
$491$			461.147i			0.939199i	0.882880	+	0.469599i	$0.155602\pi$
$491$			461.147i			0.939199i	−0.882880	+	0.469599i	$0.844398\pi$
$492$	231.990	+	3.98594i	0.471523	+	0.00810150i
$493$	512.627			1.03981
$494$		−	0.344198i		−	0.000696756i
$495$	435.441	+	14.9675i	0.879680	+	0.0302374i
$496$	122.938			0.247859
$497$		−	313.471i		−	0.630726i
$498$	−5.10057	+	296.863i	−0.0102421	+	0.596111i
$499$	−406.587			−0.814804			−0.407402	−	0.913249i	$-0.633565\pi$
$499$	−406.587			−0.814804			−0.407402	+	0.913249i	$0.633565\pi$
$500$		−	214.080i		−	0.428161i
$501$	519.750	+	8.93010i	1.03743	+	0.0178246i
$502$	99.7673			0.198740
$503$		−	894.483i		−	1.77830i	−0.457620	−	0.889148i	$-0.651298\pi$
$503$		−	894.483i		−	1.77830i	0.457620	−	0.889148i	$-0.348702\pi$
$504$	−2.51814	+	73.2587i	−0.00499630	+	0.145355i
$505$	−177.598			−0.351679
$506$			135.310i			0.267411i
$507$	7.79634	−	453.763i	0.0153774	−	0.894996i
$508$	51.1773			0.100743
$509$			803.761i			1.57910i	0.613687	+	0.789549i	$0.289686\pi$
$509$			803.761i			1.57910i	−0.613687	+	0.789549i	$0.710314\pi$
$510$	−137.170	−	2.35680i	−0.268961	−	0.00462117i
$511$	70.6805			0.138318
$512$		−	22.6274i		−	0.0441942i
$513$	−0.0804140	+	1.55886i	−0.000156752	+	0.00303871i
$514$	328.964			0.640007
$515$			154.206i			0.299430i
$516$	3.66031	−	213.037i	0.00709362	−	0.412863i
$517$	−464.415			−0.898288
$518$		−	114.508i		−	0.221057i
$519$	732.631	+	12.5877i	1.41162	+	0.0242538i
$520$	28.8942			0.0555658
$521$		−	631.562i		−	1.21221i	−0.795384	−	0.606105i	$-0.792731\pi$
$521$		−	631.562i		−	1.21221i	0.795384	−	0.606105i	$-0.207269\pi$
$522$	489.336	+	16.8201i	0.937425	+	0.0322223i
$523$	209.011			0.399638			0.199819	−	0.979833i	$-0.435965\pi$
$523$	209.011			0.399638			0.199819	+	0.979833i	$0.435965\pi$
$524$			197.599i			0.377097i
$525$	2.83627	−	165.077i	0.00540243	−	0.314432i
$526$	227.368			0.432259
$527$			409.565i			0.777162i
$528$	−239.369	−	4.11273i	−0.453351	−	0.00778926i
$529$	−23.0000			−0.0434783
$530$		−	255.827i		−	0.482693i
$531$	−13.1364	+	382.169i	−0.0247390	+	0.719716i
$532$	−0.332949			−0.000625844
$533$		−	162.800i		−	0.305441i
$534$	−10.3782	+	604.034i	−0.0194349	+	1.13115i
$535$	−58.6522			−0.109630
$536$			334.842i			0.624706i
$537$	−819.861	−	14.0865i	−1.52674	−	0.0262318i
$538$	−502.208			−0.933473
$539$		−	812.141i		−	1.50676i
$540$	−130.861	−	6.75048i	−0.242335	−	0.0125009i
$541$	−481.904			−0.890766			−0.445383	−	0.895340i	$-0.646932\pi$
$541$	−481.904			−0.890766			−0.445383	+	0.895340i	$0.646932\pi$
$542$		−	221.293i		−	0.408290i
$543$	−16.0983	+	936.954i	−0.0296470	+	1.72551i
$544$	75.3825			0.138571
$545$		−	315.766i		−	0.579388i
$546$	51.4249	+	0.883559i	0.0941848	+	0.00161824i
$547$	−594.330			−1.08653			−0.543264	−	0.839562i	$-0.682812\pi$
$547$	−594.330			−1.08653			−0.543264	+	0.839562i	$0.682812\pi$
$548$		−	62.5559i		−	0.114153i
$549$	−350.956	−	12.0635i	−0.639264	−	0.0219736i
$550$	539.221			0.980403
$551$			2.22395i			0.00403621i
$552$	0.699082	−	40.6880i	0.00126645	−	0.0737101i
$553$	−141.973			−0.256731
$554$		−	204.473i		−	0.369085i
$555$	204.663	+	3.51643i	0.368763	+	0.00633591i
$556$	−243.245			−0.437491
$557$		−	297.145i		−	0.533474i	−0.963769	−	0.266737i	$-0.914055\pi$
$557$		−	297.145i		−	0.533474i	0.963769	−	0.266737i	$-0.0859454\pi$
$558$	−13.4384	+	390.956i	−0.0240832	+	0.700638i
$559$	−149.500			−0.267442
$560$		−	27.9499i		−	0.0499106i
$561$	13.7014	−	797.451i	0.0244232	−	1.42148i
$562$	−358.722			−0.638296
$563$			932.755i			1.65676i	0.560168	+	0.828379i	$0.310736\pi$
$563$			932.755i			1.65676i	−0.560168	+	0.828379i	$0.689264\pi$
$564$	139.650	+	2.39941i	0.247607	+	0.00425427i
$565$	225.873			0.399775
$566$		−	659.584i		−	1.16534i
$567$	−232.695	−	16.0159i	−0.410397	−	0.0282467i
$568$	−307.903			−0.542083
$569$		−	281.514i		−	0.494753i	−0.968919	−	0.247376i	$-0.920432\pi$
$569$		−	281.514i		−	0.494753i	0.968919	−	0.247376i	$-0.0795684\pi$
$570$	0.0102246	−	0.595092i	1.79379e−5	−	0.00104402i
$571$	−543.682			−0.952157			−0.476078	−	0.879403i	$-0.657942\pi$
$571$	−543.682			−0.952157			−0.476078	+	0.879403i	$0.657942\pi$
$572$			167.979i			0.293669i
$573$	−163.940	−	2.81675i	−0.286109	−	0.00491579i
$574$	−157.480			−0.274355
$575$			91.6568i			0.159403i
$576$	71.9575	+	2.47341i	0.124926	+	0.00429412i
$577$	−118.581			−0.205513			−0.102756	−	0.994707i	$-0.532766\pi$
$577$	−118.581			−0.205513			−0.102756	+	0.994707i	$0.532766\pi$
$578$		−	157.574i		−	0.272619i
$579$	0.421399	−	24.5262i	0.000727804	−	0.0423597i
$580$	−186.693			−0.321885
$581$		−	201.518i		−	0.346846i
$582$	181.109	+	3.11173i	0.311184	+	0.00534662i
$583$	1487.27			2.55107
$584$		−	69.4251i		−	0.118879i
$585$	−3.15843	+	91.8865i	−0.00539903	+	0.157071i
$586$	−478.398			−0.816379
$587$		−	573.659i		−	0.977273i	−0.872487	−	0.488637i	$-0.837494\pi$
$587$		−	573.659i		−	0.977273i	0.872487	−	0.488637i	$-0.162506\pi$
$588$	−4.19594	+	244.212i	−0.00713596	+	0.415327i
$589$	−1.77683			−0.00301669
$590$		−	145.807i		−	0.247130i
$591$	892.768	+	15.3391i	1.51061	+	0.0259545i
$592$	−112.474			−0.189989
$593$			265.533i			0.447778i	0.974615	+	0.223889i	$0.0718754\pi$
$593$			265.533i			0.447778i	−0.974615	+	0.223889i	$0.928125\pi$
$594$	39.2444	−	760.769i	0.0660681	−	1.28076i
$595$	93.1142			0.156494
$596$		−	198.651i		−	0.333307i
$597$	13.8996	−	808.984i	0.0232824	−	1.35508i
$598$	−28.5530			−0.0477475
$599$			297.358i			0.496424i	0.968706	+	0.248212i	$0.0798430\pi$
$599$			297.358i			0.496424i	−0.968706	+	0.248212i	$0.920157\pi$
$600$	−162.145	−	2.78590i	−0.270241	−	0.00464316i
$601$	−756.049			−1.25798			−0.628992	−	0.777412i	$-0.716532\pi$
$601$	−756.049			−1.25798			−0.628992	+	0.777412i	$0.716532\pi$
$602$			144.614i			0.240223i
$603$	−1064.83	−	36.6017i	−1.76589	−	0.0606994i
$604$	−549.978			−0.910560
$605$		−	672.203i		−	1.11108i
$606$	−5.33432	+	310.468i	−0.00880250	+	0.512324i
$607$	786.212			1.29524			0.647621	−	0.761962i	$-0.275764\pi$
$607$	786.212			1.29524			0.647621	+	0.761962i	$0.275764\pi$
$608$			0.327035i			0.000537887i
$609$	−332.270	−	5.70891i	−0.545600	−	0.00937424i
$610$	133.898			0.219505
$611$		−	98.0005i		−	0.160394i
$612$	−8.24008	+	239.724i	−0.0134642	+	0.391706i
$613$	71.8089			0.117143			0.0585717	−	0.998283i	$-0.481345\pi$
$613$	71.8089			0.117143			0.0585717	+	0.998283i	$0.481345\pi$
$614$			509.516i			0.829831i
$615$	4.83607	−	281.469i	0.00786353	−	0.457673i
$616$	162.489			0.263781
$617$			158.466i			0.256834i	0.991720	+	0.128417i	$0.0409895\pi$
$617$			158.466i			0.256834i	−0.991720	+	0.128417i	$0.959010\pi$
$618$	269.577	+	4.63174i	0.436208	+	0.00749473i
$619$	−1204.94			−1.94658			−0.973292	−	0.229570i	$-0.926268\pi$
$619$	−1204.94			−1.94658			−0.973292	+	0.229570i	$0.926268\pi$
$620$		−	149.159i		−	0.240579i
$621$	129.316	+	6.67077i	0.208238	+	0.0107420i
$622$	283.615			0.455973
$623$		−	410.032i		−	0.658157i
$624$	0.867865	−	50.5115i	0.00139081	−	0.0809479i
$625$	218.054			0.348886
$626$			77.4860i			0.123780i
$627$	3.45962	+	0.0594415i	0.00551773	+	9.48031e-5i
$628$	323.139			0.514552
$629$		−	374.702i		−	0.595711i
$630$	88.8836	+	3.05522i	0.141085	+	0.00484955i
$631$	87.4901			0.138653			0.0693265	−	0.997594i	$-0.477915\pi$
$631$	87.4901			0.138653			0.0693265	+	0.997594i	$0.477915\pi$
$632$			139.451i			0.220650i
$633$	11.2500	−	654.772i	0.0177725	−	1.03440i
$634$	−650.455			−1.02595
$635$		−	62.0926i		−	0.0977836i
$636$	−447.225	−	7.68402i	−0.703184	−	0.0120818i
$637$	171.377			0.269038
$638$		−	1085.36i		−	1.70119i
$639$	33.6570	−	979.164i	0.0526714	−	1.53234i
$640$	−27.4535			−0.0428961
$641$			522.066i			0.814456i	0.913327	+	0.407228i	$0.133505\pi$
$641$			522.066i			0.814456i	−0.913327	+	0.407228i	$0.866495\pi$
$642$	−1.76168	+	102.533i	−0.00274404	+	0.159709i
$643$	1226.65			1.90769			0.953846	−	0.300295i	$-0.0970852\pi$
$643$	1226.65			1.90769			0.953846	+	0.300295i	$0.0970852\pi$
$644$			27.6199i			0.0428880i
$645$	−258.475	−	4.44099i	−0.400736	−	0.00688526i
$646$	−1.08951			−0.00168654
$647$			417.196i			0.644816i	0.946601	+	0.322408i	$0.104492\pi$
$647$			417.196i			0.644816i	−0.946601	+	0.322408i	$0.895508\pi$
$648$	−15.7314	+	228.562i	−0.0242769	+	0.352719i
$649$	847.659			1.30610
$650$			113.786i			0.175055i
$651$	4.56115	−	265.468i	0.00700637	−	0.407785i
$652$	603.907			0.926238
$653$			747.390i			1.14455i	0.820062	+	0.572274i	$0.193939\pi$
$653$			747.390i			1.14455i	−0.820062	+	0.572274i	$0.806061\pi$
$654$	−552.008	−	9.48435i	−0.844049	−	0.0145021i
$655$	239.743			0.366020
$656$			154.683i			0.235797i
$657$	220.779	+	7.58888i	0.336041	+	0.0115508i
$658$	−94.7978			−0.144070
$659$		−	574.151i		−	0.871246i	−0.900129	−	0.435623i	$-0.856528\pi$
$659$		−	574.151i		−	0.871246i	0.900129	−	0.435623i	$-0.143472\pi$
$660$	−4.98991	+	290.423i	−0.00756047	+	0.440035i
$661$	125.477			0.189829			0.0949144	−	0.995485i	$-0.469742\pi$
$661$	125.477			0.189829			0.0949144	+	0.995485i	$0.469742\pi$
$662$			807.759i			1.22018i
$663$	168.277	+	2.89126i	0.253812	+	0.00436088i
$664$	−197.938			−0.298100
$665$			0.403962i			0.000607461i
$666$	12.2945	−	357.678i	0.0184603	−	0.537054i
$667$	184.489			0.276595
$668$			346.551i			0.518789i
$669$	−7.05208	+	410.445i	−0.0105412	+	0.613521i
$670$	406.259			0.606356
$671$			778.427i			1.16010i
$672$	−48.8608	−	0.839503i	−0.0727095	−	0.00124926i
$673$	688.620			1.02321			0.511604	−	0.859221i	$-0.329051\pi$
$673$	688.620			1.02321			0.511604	+	0.859221i	$0.329051\pi$
$674$			45.0342i			0.0668163i
$675$	26.5835	−	515.333i	0.0393830	−	0.763456i
$676$	302.553			0.447564
$677$		−	613.784i		−	0.906624i	−0.891352	−	0.453312i	$-0.850242\pi$
$677$		−	613.784i		−	0.906624i	0.891352	−	0.453312i	$-0.149758\pi$
$678$	6.78431	−	394.861i	0.0100064	−	0.582390i
$679$	−122.941			−0.181062
$680$		−	91.4603i		−	0.134501i
$681$	900.634	+	15.4743i	1.32252	+	0.0227229i
$682$	867.148			1.27148
$683$		−	222.659i		−	0.326001i	−0.986626	−	0.163001i	$-0.947883\pi$
$683$		−	222.659i		−	0.326001i	0.986626	−	0.163001i	$-0.0521173\pi$
$684$	−1.04001	−	0.0357483i	−0.00152048	−	5.22637e-5i
$685$	−75.8980			−0.110800
$686$		−	365.321i		−	0.532538i
$687$	−17.0074	+	989.867i	−0.0247561	+	1.44086i
$688$	142.046			0.206462
$689$			313.843i			0.455505i
$690$	−49.3661	−	0.848185i	−0.0715450	−	0.00122925i
$691$	994.928			1.43984			0.719919	−	0.694058i	$-0.244179\pi$
$691$	994.928			1.43984			0.719919	+	0.694058i	$0.244179\pi$
$692$			488.493i			0.705914i
$693$	−17.7617	+	516.732i	−0.0256302	+	0.745645i
$694$	−322.947			−0.465341
$695$			295.125i			0.424641i
$696$	−5.60751	+	326.369i	−0.00805677	+	0.468920i
$697$	−515.320			−0.739339
$698$		−	818.623i		−	1.17281i
$699$	36.5054	+	0.627219i	0.0522252	+	0.000897308i
$700$	110.067			0.157239
$701$		−	768.537i		−	1.09634i	−0.836366	−	0.548172i	$-0.815324\pi$
$701$		−	768.537i		−	1.09634i	0.836366	−	0.548172i	$-0.184676\pi$
$702$	160.537	+	8.28133i	0.228685	+	0.0117968i
$703$	1.62559			0.00231236
$704$		−	159.603i		−	0.226709i
$705$	2.91116	−	169.436i	0.00412931	−	0.240334i
$706$	−675.690			−0.957069
$707$		−	210.753i		−	0.298094i
$708$	−254.892	−	4.37944i	−0.360018	−	0.00618565i
$709$	661.519			0.933031			0.466516	−	0.884513i	$-0.345509\pi$
$709$	661.519			0.933031			0.466516	+	0.884513i	$0.345509\pi$
$710$			373.574i			0.526161i
$711$	−443.468	−	15.2434i	−0.623724	−	0.0214394i
$712$	−402.749			−0.565659
$713$			147.398i			0.206729i
$714$	2.79678	−	162.778i	0.00391705	−	0.227980i
$715$	203.806			0.285043
$716$		−	546.655i		−	0.763484i
$717$	−432.469	−	7.43049i	−0.603165	−	0.0103633i
$718$	−578.803			−0.806133
$719$			165.579i			0.230291i	0.993349	+	0.115146i	$0.0367335\pi$
$719$			165.579i			0.230291i	−0.993349	+	0.115146i	$0.963267\pi$
$720$	3.00095	−	87.3049i	0.00416799	−	0.121257i
$721$	−182.995			−0.253807
$722$			510.526i			0.707100i
$723$	−24.2248	+	1409.93i	−0.0335059	+	1.95011i
$724$	−624.728			−0.862884
$725$		−	735.203i		−	1.01407i
$726$	−1175.11	−	20.1903i	−1.61861	−	0.0278103i
$727$	483.378			0.664894			0.332447	−	0.943122i	$-0.392126\pi$
$727$	483.378			0.664894			0.332447	+	0.943122i	$0.392126\pi$
$728$			34.2883i			0.0470994i
$729$	−725.131	−	75.0116i	−0.994692	−	0.102897i
$730$	−84.2324			−0.115387
$731$			473.221i			0.647361i
$732$	4.02176	−	234.074i	0.00549420	−	0.319774i
$733$	−592.862			−0.808816			−0.404408	−	0.914579i	$-0.632522\pi$
$733$	−592.862			−0.808816			−0.404408	+	0.914579i	$0.632522\pi$
$734$			251.863i			0.343138i
$735$	296.299	+	5.09087i	0.403128	+	0.00692635i
$736$	27.1293			0.0368605
$737$			2361.82i			3.20464i
$738$	−491.906	−	16.9084i	−0.666540	−	0.0229111i
$739$	1013.89			1.37198			0.685991	−	0.727610i	$-0.259369\pi$
$739$	1013.89			1.37198			0.685991	+	0.727610i	$0.259369\pi$
$740$			136.462i			0.184409i
$741$	−0.0125433	+	0.730046i	−1.69275e−5	+	0.000985217i
$742$	303.586			0.409146
$743$		−	211.292i		−	0.284377i	−0.989840	−	0.142189i	$-0.954586\pi$
$743$		−	211.292i		−	0.284377i	0.989840	−	0.142189i	$-0.0454140\pi$
$744$	−260.753	−	4.48013i	−0.350474	−	0.00602169i
$745$	−241.020			−0.323517
$746$		−	679.085i		−	0.910302i
$747$	21.6367	−	629.464i	0.0289648	−	0.842656i
$748$	531.712			0.710845
$749$		−	69.6017i		−	0.0929262i
$750$	−7.80155	+	454.066i	−0.0104021	+	0.605421i
$751$	−1199.08			−1.59664			−0.798320	−	0.602234i	$-0.794277\pi$
$751$	−1199.08			−1.59664			−0.798320	+	0.602234i	$0.794277\pi$
$752$			93.1140i			0.123822i
$753$	−211.607	−	3.63574i	−0.281019	−	0.00482833i
$754$	229.031			0.303755
$755$			667.279i			0.883814i
$756$	8.01069	−	155.291i	0.0105962	−	0.205411i
$757$	44.3910			0.0586407			0.0293203	−	0.999570i	$-0.490666\pi$
$757$	44.3910			0.0586407			0.0293203	+	0.999570i	$0.490666\pi$
$758$			144.698i			0.190895i
$759$	4.93099	−	286.994i	0.00649670	−	0.378121i
$760$	0.396787			0.000522088
$761$			1431.08i			1.88053i	0.340447	+	0.940264i	$0.389421\pi$
$761$			1431.08i			1.88053i	−0.340447	+	0.940264i	$0.610579\pi$
$762$	−108.547	−	1.86501i	−0.142451	−	0.00244752i
$763$	374.715			0.491108
$764$		−	109.310i		−	0.143076i
$765$	290.853	+	9.99756i	0.380200	+	0.0130687i
$766$	−109.484			−0.142930
$767$			178.872i			0.233210i
$768$	−0.824592	+	47.9929i	−0.00107369	+	0.0624908i
$769$	1123.91			1.46153			0.730763	−	0.682631i	$-0.239164\pi$
$769$	1123.91			1.46153			0.730763	+	0.682631i	$0.239164\pi$
$770$		−	197.146i		−	0.256033i
$771$	−697.735	−	11.9882i	−0.904974	−	0.0155488i
$772$	16.3532			0.0211830
$773$			1028.97i			1.33114i	0.746337	+	0.665568i	$0.231811\pi$
$773$			1028.97i			1.33114i	−0.746337	+	0.665568i	$0.768189\pi$
$774$	−15.5271	+	451.720i	−0.0200608	+	0.583618i
$775$	587.392			0.757925
$776$			120.757i			0.155615i
$777$	−4.17290	+	242.871i	−0.00537053	+	0.312576i
$778$	358.171			0.460375
$779$		−	2.23564i		−	0.00286988i
$780$	−61.2848	−	1.05297i	−0.0785703	−	0.00134996i
$781$	−2171.80			−2.78080
$782$			90.3804i			0.115576i
$783$	−1037.27	−	53.5079i	−1.32474	−	0.0683371i
$784$	−162.832			−0.207694
$785$		−	392.059i		−	0.499438i
$786$	7.20093	−	419.108i	0.00916148	−	0.533217i
$787$	215.778			0.274178			0.137089	−	0.990559i	$-0.456225\pi$
$787$	215.778			0.274178			0.137089	+	0.990559i	$0.456225\pi$
$788$			595.267i			0.755414i
$789$	−482.250	−	8.28580i	−0.611217	−	0.0105016i
$790$	169.193			0.214169
$791$			268.040i			0.338862i
$792$	507.554	+	17.4463i	0.640851	+	0.0220281i
$793$	−164.263			−0.207141
$794$			739.967i			0.931948i
$795$	−9.32289	+	542.611i	−0.0117269	+	0.682530i
$796$	539.402			0.677641
$797$		−	327.256i		−	0.410610i	−0.978698	−	0.205305i	$-0.934181\pi$
$797$		−	327.256i		−	0.410610i	0.978698	−	0.205305i	$-0.0658187\pi$
$798$	0.706187	+	0.0121334i	0.000884947	+	1.52047e-5i
$799$	−310.206			−0.388243
$800$		−	108.112i		−	0.135141i
$801$	44.0246	−	1280.78i	0.0549621	−	1.59898i
$802$	−352.940			−0.440074
$803$		−	489.692i		−	0.609828i
$804$	12.2024	−	710.203i	0.0151771	−	0.883337i
$805$	33.5108			0.0416283
$806$			182.985i			0.227028i
$807$	1065.19	+	18.3016i	1.31994	+	0.0226785i
$808$	−207.009			−0.256200
$809$			358.846i			0.443567i	0.975096	+	0.221784i	$0.0711878\pi$
$809$			358.846i			0.443567i	−0.975096	+	0.221784i	$0.928812\pi$
$810$	277.310	+	19.0867i	0.342359	+	0.0235638i
$811$	1322.05			1.63015			0.815075	−	0.579355i	$-0.196696\pi$
$811$	1322.05			1.63015			0.815075	+	0.579355i	$0.196696\pi$
$812$		−	221.546i		−	0.272840i
$813$	−8.06440	+	469.364i	−0.00991931	+	0.577324i
$814$	−793.336			−0.974614
$815$		−	732.711i		−	0.899031i
$816$	−159.887	−	2.74710i	−0.195940	−	0.00336654i
$817$	−2.05299			−0.00251285
$818$		−	283.948i		−	0.347125i
$819$	−109.040	−	3.74807i	−0.133138	−	0.00457640i
$820$	187.674			0.228871
$821$		−	1317.22i		−	1.60441i	−0.597051	−	0.802204i	$-0.703661\pi$
$821$		−	1317.22i		−	1.60441i	0.597051	−	0.802204i	$-0.296339\pi$
$822$	−2.27967	+	132.681i	−0.00277332	+	0.161413i
$823$	−611.565			−0.743093			−0.371546	−	0.928414i	$-0.621172\pi$
$823$	−611.565			−0.743093			−0.371546	+	0.928414i	$0.621172\pi$
$824$			179.744i			0.218136i
$825$	−1143.69	−	19.6504i	−1.38629	−	0.0238187i
$826$	173.027			0.209475
$827$			482.446i			0.583369i	0.956515	+	0.291684i	$0.0942157\pi$
$827$			482.446i			0.583369i	−0.956515	+	0.291684i	$0.905784\pi$
$828$	−2.96552	+	86.2740i	−0.00358154	+	0.104196i
$829$	−1171.97			−1.41371			−0.706856	−	0.707357i	$-0.749887\pi$
$829$	−1171.97			−1.41371			−0.706856	+	0.707357i	$0.749887\pi$
$830$			240.155i			0.289344i
$831$	−7.45144	+	433.689i	−0.00896684	+	0.521888i
$832$	33.6793			0.0404799
$833$		−	542.470i		−	0.651225i
$834$	515.925	+	8.86437i	0.618615	+	0.0106287i
$835$	420.465			0.503551
$836$			2.30675i			0.00275927i
$837$	42.7503	−	828.731i	0.0510756	−	0.990121i
$838$	−299.607			−0.357526
$839$			628.263i			0.748823i	0.927263	+	0.374412i	$0.122155\pi$
$839$			628.263i			0.748823i	−0.927263	+	0.374412i	$0.877845\pi$
$840$	−1.01856	+	59.2820i	−0.00121257	+	0.0705738i
$841$	−638.831			−0.759609
$842$		−	397.654i		−	0.472274i
$843$	760.852	+	13.0726i	0.902553	+	0.0155072i
$844$	436.579			0.517274
$845$		−	367.083i		−	0.434418i
$846$	−296.112	−	10.1783i	−0.350014	−	0.0120311i
$847$	797.693			0.941787
$848$		−	298.194i		−	0.351644i
$849$	−24.0367	+	1398.98i	−0.0283117	+	1.64780i
$850$	360.173			0.423733
$851$		−	134.851i		−	0.158462i
$852$	653.065	+	11.2207i	0.766508	+	0.0131698i
$853$	−330.792			−0.387799			−0.193899	−	0.981021i	$-0.562114\pi$
$853$	−330.792			−0.387799			−0.193899	+	0.981021i	$0.562114\pi$
$854$			158.895i			0.186060i
$855$	−0.0433729	+	1.26182i	−5.07285e−5	+	0.00147582i
$856$	−68.3655			−0.0798662
$857$		−	596.526i		−	0.696064i	−0.937483	−	0.348032i	$-0.886850\pi$
$857$		−	596.526i		−	0.696064i	0.937483	−	0.348032i	$-0.113150\pi$
$858$	6.12151	−	356.284i	0.00713463	−	0.415250i
$859$	238.452			0.277592			0.138796	−	0.990321i	$-0.455677\pi$
$859$	238.452			0.277592			0.138796	+	0.990321i	$0.455677\pi$
$860$		−	172.342i		−	0.200397i
$861$	334.016	+	5.73890i	0.387939	+	0.00666539i
$862$	848.458			0.984290
$863$		−	895.953i		−	1.03818i	−0.854718	−	0.519092i	$-0.826270\pi$
$863$		−	895.953i		−	1.03818i	0.854718	−	0.519092i	$-0.173730\pi$
$864$	−152.532	−	7.86841i	−0.176542	−	0.00910696i
$865$	592.680			0.685179
$866$			97.5779i			0.112677i
$867$	−5.74232	+	334.215i	−0.00662321	+	0.385484i
$868$	177.005			0.203923
$869$			983.620i			1.13190i
$870$	395.978	+	6.80350i	0.455147	+	0.00782012i
$871$	−498.389			−0.572203
$872$		−	368.060i		−	0.422087i
$873$	−384.020	−	13.2000i	−0.439886	−	0.0151203i
$874$	−0.392102			−0.000448629
$875$		−	308.230i		−	0.352263i
$876$	−2.53000	+	147.251i	−0.00288813	+	0.168095i
$877$	1456.94			1.66128			0.830638	−	0.556814i	$-0.187976\pi$
$877$	1456.94			1.66128			0.830638	+	0.556814i	$0.187976\pi$
$878$		−	304.825i		−	0.347181i
$879$	1014.69	+	17.4339i	1.15436	+	0.0198337i
$880$	−193.644			−0.220050
$881$		−	727.493i		−	0.825759i	−0.910786	−	0.412879i	$-0.864523\pi$
$881$		−	727.493i		−	0.825759i	0.910786	−	0.412879i	$-0.135477\pi$
$882$	17.7992	−	517.823i	0.0201806	−	0.587101i
$883$	1323.75			1.49915			0.749574	−	0.661920i	$-0.230258\pi$
$883$	1323.75			1.49915			0.749574	+	0.661920i	$0.230258\pi$
$884$			112.201i			0.126925i
$885$	−5.31351	+	309.257i	−0.00600396	+	0.349443i
$886$	−643.218			−0.725980
$887$		−	1309.33i		−	1.47613i	−0.674731	−	0.738064i	$-0.735740\pi$
$887$		−	1309.33i		−	1.47613i	0.674731	−	0.738064i	$-0.264260\pi$
$888$	238.557	+	4.09878i	0.268646	+	0.00461575i
$889$	73.6844			0.0828846
$890$			488.649i			0.549044i
$891$	−110.962	+	1612.17i	−0.124536	+	1.80939i
$892$	−273.671			−0.306806
$893$		−	1.34578i		−	0.00150703i
$894$	−7.23928	+	421.340i	−0.00809762	+	0.471298i
$895$	−663.247			−0.741059
$896$		−	32.5787i		−	0.0363601i
$897$	60.5612	+	1.04053i	0.0675152	+	0.00116002i
$898$	−233.622			−0.260158
$899$		−	1182.31i		−	1.31514i
$900$	343.809	+	11.8178i	0.382010	+	0.0131309i
$901$	993.424			1.10258
$902$			1091.06i			1.20960i
$903$	5.27006	−	306.728i	0.00583617	−	0.339677i
$904$	263.279			0.291238
$905$			757.973i			0.837539i
$906$	1166.51	+	20.0424i	1.28754	+	0.0221218i
$907$	−1197.57			−1.32037			−0.660184	−	0.751104i	$-0.729522\pi$
$907$	−1197.57			−1.32037			−0.660184	+	0.751104i	$0.729522\pi$
$908$			600.511i			0.661356i
$909$	22.6283	−	658.311i	0.0248936	−	0.724214i
$910$	41.6015			0.0457159
$911$		−	1714.48i		−	1.88198i	−0.338433	−	0.940991i	$-0.609897\pi$
$911$		−	1714.48i		−	1.88198i	0.338433	−	0.940991i	$-0.390103\pi$
$912$	0.0119179	−	0.693644i	1.30678e−5	−	0.000760575i
$913$	−1396.16			−1.52920
$914$			158.958i			0.173915i
$915$	−283.999	−	4.87953i	−0.310381	−	0.00533282i
$916$	−660.009			−0.720534
$917$			284.500i			0.310251i
$918$	26.2133	−	508.156i	0.0285548	−	0.553547i
$919$	−212.587			−0.231324			−0.115662	−	0.993289i	$-0.536899\pi$
$919$	−212.587			−0.231324			−0.115662	+	0.993289i	$0.536899\pi$
$920$		−	32.9156i		−	0.0357778i
$921$	18.5679	−	1080.69i	0.0201606	−	1.17339i
$922$	622.040			0.674664
$923$		−	458.292i		−	0.496525i
$924$	−344.641	−	5.92146i	−0.372988	−	0.00640850i
$925$	−537.393			−0.580965
$926$		−	126.149i		−	0.136230i
$927$	−571.605	−	19.6479i	−0.616618	−	0.0211952i
$928$	−217.611			−0.234495
$929$		−	134.445i		−	0.144720i	−0.997379	−	0.0723599i	$-0.976947\pi$
$929$		−	134.445i		−	0.144720i	0.997379	−	0.0723599i	$-0.0230530\pi$
$930$	−5.43568	+	316.367i	−0.00584481	+	0.340180i
$931$	2.35342			0.00252784
$932$			24.3405i			0.0261164i
$933$	−601.550	−	10.3356i	−0.644748	−	0.0110778i
$934$	804.551			0.861404
$935$		−	645.118i		−	0.689966i
$936$	−3.68150	+	107.104i	−0.00393322	+	0.114427i
$937$	181.730			0.193949			0.0969743	−	0.995287i	$-0.469084\pi$
$937$	181.730			0.193949			0.0969743	+	0.995287i	$0.469084\pi$
$938$			482.101i			0.513967i
$939$	2.82376	−	164.348i	0.00300720	−	0.175025i
$940$	112.974			0.120185
$941$		−	1641.28i		−	1.74419i	−0.489335	−	0.872096i	$-0.662761\pi$
$941$		−	1641.28i		−	1.74419i	0.489335	−	0.872096i	$-0.337239\pi$
$942$	−685.380	−	11.7759i	−0.727579	−	0.0125009i
$943$	−185.458			−0.196668
$944$		−	169.953i		−	0.180035i
$945$	−188.411	−	9.71925i	−0.199377	−	0.0102849i
$946$	1001.92			1.05912
$947$		−	943.256i		−	0.996046i	−0.867164	−	0.498023i	$-0.834060\pi$
$947$		−	943.256i		−	0.996046i	0.867164	−	0.498023i	$-0.165940\pi$
$948$	5.08189	−	295.776i	0.00536064	−	0.312000i
$949$	103.334			0.108888
$950$			1.56256i			0.00164480i
$951$	1379.62	+	23.7040i	1.45071	+	0.0249253i
$952$	108.535			0.114007
$953$			674.538i			0.707804i	0.935282	+	0.353902i	$0.115145\pi$
$953$			674.538i			0.707804i	−0.935282	+	0.353902i	$0.884855\pi$
$954$	948.288	+	32.5957i	0.994013	+	0.0341674i
$955$	−132.624			−0.138873
$956$		−	288.355i		−	0.301627i
$957$	−39.5527	+	2302.05i	−0.0413299	+	2.40548i
$958$	938.039			0.979163
$959$		−	90.0671i		−	0.0939177i
$960$	58.2290	+	1.00046i	0.0606552	+	0.00104215i
$961$	−16.3870			−0.0170521
$962$		−	167.409i		−	0.174022i
$963$	7.47305	−	217.409i	0.00776018	−	0.225762i
$964$	−940.092			−0.975199
$965$		−	19.8411i		−	0.0205608i
$966$	1.00653	−	58.5820i	0.00104196	−	0.0606439i
$967$	−1677.18			−1.73442			−0.867210	−	0.497943i	$-0.834089\pi$
$967$	−1677.18			−1.73442			−0.867210	+	0.497943i	$0.834089\pi$
$968$		−	783.525i		−	0.809426i
$969$	2.31085	+	0.0397040i	0.00238478	+	4.09742e-5i
$970$	146.513			0.151044
$971$		−	877.700i		−	0.903913i	−0.892040	−	0.451957i	$-0.850726\pi$
$971$		−	877.700i		−	0.903913i	0.892040	−	0.451957i	$-0.149274\pi$
$972$	41.6957	−	484.208i	0.0428968	−	0.498156i
$973$	−350.221			−0.359939
$974$			527.363i			0.541440i
$975$	4.14661	−	241.341i	0.00425293	−	0.247529i
$976$	156.073			0.159910
$977$			1451.52i			1.48569i	0.669464	+	0.742844i	$0.266524\pi$
$977$			1451.52i			1.48569i	−0.669464	+	0.742844i	$0.733476\pi$
$978$	−1280.89	−	22.0077i	−1.30970	−	0.0225027i
$979$	−2840.80			−2.90174
$980$			197.562i			0.201594i
$981$	1170.47	+	40.2327i	1.19314	+	0.0410120i
$982$	652.160			0.664114
$983$			283.956i			0.288867i	0.989515	+	0.144433i	$0.0461359\pi$
$983$			283.956i			0.288867i	−0.989515	+	0.144433i	$0.953864\pi$
$984$	5.63697	−	328.083i	0.00572862	−	0.333417i
$985$	722.227			0.733226
$986$		−	724.964i		−	0.735258i
$987$	201.067	+	3.45464i	0.203715	+	0.00350014i
$988$	−0.486769			−0.000492681
$989$			170.307i			0.172201i
$990$	21.1673	−	615.807i	0.0213811	−	0.622028i
$991$	−292.124			−0.294777			−0.147389	−	0.989079i	$-0.547087\pi$
$991$	−292.124			−0.294777			−0.147389	+	0.989079i	$0.547087\pi$
$992$		−	173.861i		−	0.175263i
$993$	29.4365	−	1713.26i	0.0296440	−	1.72534i
$994$	−443.315			−0.445991
$995$		−	654.448i		−	0.657737i
$996$	419.828	+	7.21330i	0.421514	+	0.00724226i
$997$	−692.311			−0.694394			−0.347197	−	0.937792i	$-0.612867\pi$
$997$	−692.311			−0.694394			−0.347197	+	0.937792i	$0.612867\pi$
$998$			575.001i			0.576153i
$999$	−39.1113	+	758.189i	−0.0391505	+	0.758948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.4	✓	16
3.2	odd	2	inner	138.3.c.a.47.12	yes	16
4.3	odd	2		1104.3.g.c.737.9		16
12.11	even	2		1104.3.g.c.737.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.4	✓	16	1.1	even	1	trivial
138.3.c.a.47.12	yes	16	3.2	odd	2	inner
1104.3.g.c.737.9		16	4.3	odd	2
1104.3.g.c.737.10		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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.0515370 + 2.99956i) q^{3} -2.00000 q^{4} +2.42657i q^{5} +(4.24201 + 0.0728843i) q^{6} -2.87957 q^{7} +2.82843i q^{8} +(-8.99469 - 0.309176i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.0515370 + 2.99956i) q^{3} -2.00000 q^{4} +2.42657i q^{5} +(4.24201 + 0.0728843i) q^{6} -2.87957 q^{7} +2.82843i q^{8} +(-8.99469 - 0.309176i) q^{9} +3.43169 q^{10} +19.9504i q^{11} +(0.103074 - 5.99911i) q^{12} -4.20991 q^{13} +4.07233i q^{14} +(-7.27863 - 0.125058i) q^{15} +4.00000 q^{16} +13.3259i q^{17} +(-0.437241 + 12.7204i) q^{18} -0.0578122 q^{19} -4.85314i q^{20} +(0.148405 - 8.63745i) q^{21} +28.2141 q^{22} +4.79583i q^{23} +(-8.48403 - 0.145769i) q^{24} +19.1118 q^{25} +5.95372i q^{26} +(1.39095 - 26.9641i) q^{27} +5.75915 q^{28} -38.4686i q^{29} +(-0.176859 + 10.2935i) q^{30} +30.7346 q^{31} -5.65685i q^{32} +(-59.8423 - 1.02818i) q^{33} +18.8456 q^{34} -6.98748i q^{35} +(17.9894 + 0.618353i) q^{36} -28.1184 q^{37} +0.0817588i q^{38} +(0.216966 - 12.6279i) q^{39} -6.86337 q^{40} +38.6706i q^{41} +(-12.2152 - 0.209876i) q^{42} +35.5114 q^{43} -39.9008i q^{44} +(0.750237 - 21.8262i) q^{45} +6.78233 q^{46} +23.2785i q^{47} +(-0.206148 + 11.9982i) q^{48} -40.7081 q^{49} -27.0281i q^{50} +(-39.9717 - 0.686775i) q^{51} +8.41983 q^{52} -74.5485i q^{53} +(-38.1331 - 1.96710i) q^{54} -48.4110 q^{55} -8.14466i q^{56} +(0.00297947 - 0.173411i) q^{57} -54.4028 q^{58} -42.4883i q^{59} +(14.5573 + 0.250116i) q^{60} +39.0181 q^{61} -43.4652i q^{62} +(25.9009 + 0.890296i) q^{63} -8.00000 q^{64} -10.2156i q^{65} +(-1.45407 + 84.6298i) q^{66} +118.385 q^{67} -26.6517i q^{68} +(-14.3854 - 0.247163i) q^{69} -9.88179 q^{70} +108.860i q^{71} +(0.874483 - 25.4408i) q^{72} -24.5455 q^{73} +39.7654i q^{74} +(-0.984963 + 57.3268i) q^{75} +0.115624 q^{76} -57.4486i q^{77} +(-17.8585 - 0.306837i) q^{78} +49.3033 q^{79} +9.70627i q^{80} +(80.8088 + 5.56189i) q^{81} +54.6885 q^{82} +69.9817i q^{83} +(-0.296809 + 17.2749i) q^{84} -32.3361 q^{85} -50.2208i q^{86} +(115.389 + 1.98255i) q^{87} -56.4282 q^{88} +142.393i q^{89} +(-30.8669 - 1.06100i) q^{90} +12.1228 q^{91} -9.59166i q^{92} +(-1.58397 + 92.1901i) q^{93} +32.9208 q^{94} -0.140285i q^{95} +(16.9681 + 0.291537i) q^{96} +42.6941 q^{97} +57.5699i q^{98} +(6.16819 - 179.447i) 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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