LMFDB - Embedded newform 392.3.g.i.99.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(99,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("392.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.g (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.15582448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 $ x^6 - 3x^5 + 13x^4 - 21x^3 + 20x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Root			$0.500000 + 0.148124i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.i.99.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67727 - 1.08938i) q^{2} +3.98103 q^{3} +(1.62649 - 3.65439i) q^{4} -1.88252i q^{5} +(6.67727 - 4.33687i) q^{6} +(-1.25297 - 7.90127i) q^{8} +6.84860 q^{9} +O(q^{10})$	\(q+(1.67727 - 1.08938i) q^{2} +3.98103 q^{3} +(1.62649 - 3.65439i) q^{4} -1.88252i q^{5} +(6.67727 - 4.33687i) q^{6} +(-1.25297 - 7.90127i) q^{8} +6.84860 q^{9} +(-2.05079 - 3.15750i) q^{10} -7.87946 q^{11} +(6.47509 - 14.5482i) q^{12} -11.4863i q^{13} -7.49437i q^{15} +(-10.7091 - 11.8876i) q^{16} +2.89843 q^{17} +(11.4870 - 7.46076i) q^{18} +30.0447 q^{19} +(-6.87946 - 3.06189i) q^{20} +(-13.2160 + 8.58375i) q^{22} +38.5483i q^{23} +(-4.98812 - 31.4552i) q^{24} +21.4561 q^{25} +(-12.5130 - 19.2657i) q^{26} -8.56478 q^{27} +27.8701i q^{29} +(-8.16424 - 12.5701i) q^{30} -22.4831i q^{31} +(-30.9122 - 8.27246i) q^{32} -31.3684 q^{33} +(4.86145 - 3.15750i) q^{34} +(11.1392 - 25.0274i) q^{36} +45.5552i q^{37} +(50.3931 - 32.7302i) q^{38} -45.7274i q^{39} +(-14.8743 + 2.35874i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(-12.8158 + 28.7946i) q^{44} -12.8926i q^{45} +(41.9939 + 64.6560i) q^{46} +82.5809i q^{47} +(-42.6332 - 47.3250i) q^{48} +(35.9878 - 23.3739i) q^{50} +11.5387 q^{51} +(-41.9755 - 18.6824i) q^{52} -26.8841i q^{53} +(-14.3655 + 9.33033i) q^{54} +14.8332i q^{55} +119.609 q^{57} +(30.3613 + 46.7458i) q^{58} +10.4111 q^{59} +(-27.3873 - 12.1895i) q^{60} -22.1624i q^{61} +(-24.4927 - 37.7103i) q^{62} +(-60.8601 + 19.8001i) q^{64} -21.6233 q^{65} +(-52.6133 + 34.1722i) q^{66} -59.3099 q^{67} +(4.71425 - 10.5920i) q^{68} +153.462i q^{69} -38.2541i q^{71} +(-8.58110 - 54.1127i) q^{72} -13.9778 q^{73} +(49.6271 + 76.4085i) q^{74} +85.4175 q^{75} +(48.8672 - 109.795i) q^{76} +(-49.8147 - 76.6974i) q^{78} -51.1895i q^{79} +(-22.3787 + 20.1601i) q^{80} -95.7341 q^{81} +(68.1497 - 44.2631i) q^{82} +89.4458 q^{83} -5.45635i q^{85} +(-79.3024 + 51.5067i) q^{86} +110.952i q^{87} +(9.87273 + 62.2577i) q^{88} -105.258 q^{89} +(-14.0450 - 21.6245i) q^{90} +(140.870 + 62.6982i) q^{92} -89.5059i q^{93} +(89.9623 + 138.511i) q^{94} -56.5597i q^{95} +(-123.063 - 32.9329i) q^{96} -55.3301 q^{97} -53.9633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9} - 6 q^{10} - 30 q^{11} + 32 q^{12} - 16 q^{16} + 30 q^{17} + 16 q^{18} + 78 q^{19} - 24 q^{20} + 12 q^{22} - 76 q^{24} + 92 q^{25} - 128 q^{26} - 78 q^{27} + 16 q^{30} - 112 q^{32} - 78 q^{33} - 38 q^{34} - 124 q^{36} + 80 q^{38} + 44 q^{40} + 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} - 88 q^{48} + 24 q^{50} - 10 q^{51} + 132 q^{52} - 36 q^{54} + 166 q^{57} - 4 q^{58} - 110 q^{59} - 84 q^{60} + 48 q^{62} - 80 q^{64} + 32 q^{65} - 138 q^{66} - 434 q^{67} + 96 q^{68} + 328 q^{72} + 102 q^{73} + 34 q^{74} - 60 q^{75} + 84 q^{76} + 360 q^{78} - 256 q^{80} + 82 q^{81} - 24 q^{82} + 268 q^{83} - 240 q^{86} + 204 q^{88} + 214 q^{89} - 220 q^{90} + 80 q^{92} - 16 q^{94} + 48 q^{96} + 76 q^{97} + 252 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9 - 6 * q^10 - 30 * q^11 + 32 * q^12 - 16 * q^16 + 30 * q^17 + 16 * q^18 + 78 * q^19 - 24 * q^20 + 12 * q^22 - 76 * q^24 + 92 * q^25 - 128 * q^26 - 78 * q^27 + 16 * q^30 - 112 * q^32 - 78 * q^33 - 38 * q^34 - 124 * q^36 + 80 * q^38 + 44 * q^40 + 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 - 88 * q^48 + 24 * q^50 - 10 * q^51 + 132 * q^52 - 36 * q^54 + 166 * q^57 - 4 * q^58 - 110 * q^59 - 84 * q^60 + 48 * q^62 - 80 * q^64 + 32 * q^65 - 138 * q^66 - 434 * q^67 + 96 * q^68 + 328 * q^72 + 102 * q^73 + 34 * q^74 - 60 * q^75 + 84 * q^76 + 360 * q^78 - 256 * q^80 + 82 * q^81 - 24 * q^82 + 268 * q^83 - 240 * q^86 + 204 * q^88 + 214 * q^89 - 220 * q^90 + 80 * q^92 - 16 * q^94 + 48 * q^96 + 76 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.67727	−	1.08938i	0.838636	−	0.544692i
$2$	1.67727	−	1.08938i	0.838636	−	0.544692i
$3$	3.98103			1.32701			0.663505	−	0.748172i	$-0.269068\pi$
$3$	3.98103			1.32701			0.663505	+	0.748172i	$0.269068\pi$
$4$	1.62649	−	3.65439i	0.406621	−	0.913597i
$5$		−	1.88252i		−	0.376504i	−0.982121	−	0.188252i	$-0.939718\pi$
$5$		−	1.88252i		−	0.376504i	0.982121	−	0.188252i	$-0.0602822\pi$
$6$	6.67727	−	4.33687i	1.11288	−	0.722812i
$7$		0			0
$7$		0			0
$8$	−1.25297	−	7.90127i	−0.156621	−	0.987659i
$9$	6.84860			0.760956
$10$	−2.05079	−	3.15750i	−0.205079	−	0.315750i
$11$	−7.87946			−0.716314			−0.358157	−	0.933661i	$-0.616595\pi$
$11$	−7.87946			−0.716314			−0.358157	+	0.933661i	$0.616595\pi$
$12$	6.47509	−	14.5482i	0.539591	−	1.21235i
$13$		−	11.4863i		−	0.883564i	−0.897122	−	0.441782i	$-0.854346\pi$
$13$		−	11.4863i		−	0.883564i	0.897122	−	0.441782i	$-0.145654\pi$
$14$		0			0
$15$		−	7.49437i		−	0.499625i
$16$	−10.7091	−	11.8876i	−0.669318	−	0.742976i
$17$	2.89843			0.170496			0.0852478	−	0.996360i	$-0.472832\pi$
$17$	2.89843			0.170496			0.0852478	+	0.996360i	$0.472832\pi$
$18$	11.4870	−	7.46076i	0.638165	−	0.414487i
$19$	30.0447			1.58130			0.790649	−	0.612270i	$-0.209743\pi$
$19$	30.0447			1.58130			0.790649	+	0.612270i	$0.209743\pi$
$20$	−6.87946	−	3.06189i	−0.343973	−	0.153095i
$21$		0			0
$22$	−13.2160	+	8.58375i	−0.600727	+	0.390171i
$23$			38.5483i			1.67601i	0.545661	+	0.838006i	$0.316279\pi$
$23$			38.5483i			1.67601i	−0.545661	+	0.838006i	$0.683721\pi$
$24$	−4.98812	−	31.4552i	−0.207838	−	1.31063i
$25$	21.4561			0.858245
$26$	−12.5130	−	19.2657i	−0.481270	−	0.740989i
$27$	−8.56478			−0.317214
$28$		0			0
$29$			27.8701i			0.961039i	0.876984	+	0.480519i	$0.159552\pi$
$29$			27.8701i			0.961039i	−0.876984	+	0.480519i	$0.840448\pi$
$30$	−8.16424	−	12.5701i	−0.272141	−	0.419003i
$31$		−	22.4831i		−	0.725262i	−0.931933	−	0.362631i	$-0.881879\pi$
$31$		−	22.4831i		−	0.725262i	0.931933	−	0.362631i	$-0.118121\pi$
$32$	−30.9122	−	8.27246i	−0.966007	−	0.258514i
$33$	−31.3684			−0.950556
$34$	4.86145	−	3.15750i	0.142984	−	0.0928676i
$35$		0			0
$36$	11.1392	−	25.0274i	0.309421	−	0.695207i
$37$			45.5552i			1.23122i	0.788050	+	0.615611i	$0.211091\pi$
$37$			45.5552i			1.23122i	−0.788050	+	0.615611i	$0.788909\pi$
$38$	50.3931	−	32.7302i	1.32613	−	0.861320i
$39$		−	45.7274i		−	1.17250i
$40$	−14.8743	+	2.35874i	−0.371857	+	0.0589686i
$41$	40.6313			0.991007			0.495503	−	0.868606i	$-0.334984\pi$
$41$	40.6313			0.991007			0.495503	+	0.868606i	$0.334984\pi$
$42$		0			0
$43$	−47.2806			−1.09955			−0.549774	−	0.835313i	$-0.685286\pi$
$43$	−47.2806			−1.09955			−0.549774	+	0.835313i	$0.685286\pi$
$44$	−12.8158	+	28.7946i	−0.291269	+	0.654422i
$45$		−	12.8926i		−	0.286503i
$46$	41.9939	+	64.6560i	0.912910	+	1.40556i
$47$			82.5809i			1.75704i	0.477705	+	0.878520i	$0.341469\pi$
$47$			82.5809i			1.75704i	−0.477705	+	0.878520i	$0.658531\pi$
$48$	−42.6332	−	47.3250i	−0.888192	−	0.985937i
$49$		0			0
$50$	35.9878	−	23.3739i	0.719755	−	0.467479i
$51$	11.5387			0.226249
$52$	−41.9755	−	18.6824i	−0.807221	−	0.359276i
$53$		−	26.8841i		−	0.507247i	−0.967303	−	0.253623i	$-0.918378\pi$
$53$		−	26.8841i		−	0.507247i	0.967303	−	0.253623i	$-0.0816224\pi$
$54$	−14.3655	+	9.33033i	−0.266027	+	0.172784i
$55$			14.8332i			0.269695i
$56$		0			0
$57$	119.609			2.09840
$58$	30.3613	+	46.7458i	0.523470	+	0.805962i
$59$	10.4111			0.176459			0.0882296	−	0.996100i	$-0.471879\pi$
$59$	10.4111			0.176459			0.0882296	+	0.996100i	$0.471879\pi$
$60$	−27.3873	−	12.1895i	−0.456455	−	0.203158i
$61$		−	22.1624i		−	0.363318i	−0.983362	−	0.181659i	$-0.941853\pi$
$61$		−	22.1624i		−	0.363318i	0.983362	−	0.181659i	$-0.0581467\pi$
$62$	−24.4927	−	37.7103i	−0.395044	−	0.608231i
$63$		0			0
$64$	−60.8601	+	19.8001i	−0.950939	+	0.309377i
$65$	−21.6233			−0.332665
$66$	−52.6133	+	34.1722i	−0.797171	+	0.517760i
$67$	−59.3099			−0.885222			−0.442611	−	0.896714i	$-0.645948\pi$
$67$	−59.3099			−0.885222			−0.442611	+	0.896714i	$0.645948\pi$
$68$	4.71425	−	10.5920i	0.0693272	−	0.155764i
$69$			153.462i			2.22409i
$70$		0			0
$71$		−	38.2541i		−	0.538791i	−0.963030	−	0.269395i	$-0.913176\pi$
$71$		−	38.2541i		−	0.538791i	0.963030	−	0.269395i	$-0.0868238\pi$
$72$	−8.58110	−	54.1127i	−0.119182	−	0.751565i
$73$	−13.9778			−0.191477			−0.0957383	−	0.995407i	$-0.530521\pi$
$73$	−13.9778			−0.191477			−0.0957383	+	0.995407i	$0.530521\pi$
$74$	49.6271	+	76.4085i	0.670636	+	1.03255i
$75$	85.4175			1.13890
$76$	48.8672	−	109.795i	0.642990	−	1.44467i
$77$		0			0
$78$	−49.8147	−	76.6974i	−0.638651	−	0.983300i
$79$		−	51.1895i		−	0.647969i	−0.946062	−	0.323984i	$-0.894978\pi$
$79$		−	51.1895i		−	0.647969i	0.946062	−	0.323984i	$-0.105022\pi$
$80$	−22.3787	+	20.1601i	−0.279733	+	0.252001i
$81$	−95.7341			−1.18190
$82$	68.1497	−	44.2631i	0.831094	−	0.539793i
$83$	89.4458			1.07766			0.538830	−	0.842414i	$-0.318866\pi$
$83$	89.4458			1.07766			0.538830	+	0.842414i	$0.318866\pi$
$84$		0			0
$85$		−	5.45635i		−	0.0641923i
$86$	−79.3024	+	51.5067i	−0.922121	+	0.598915i
$87$			110.952i			1.27531i
$88$	9.87273	+	62.2577i	0.112190	+	0.707474i
$89$	−105.258			−1.18267			−0.591335	−	0.806426i	$-0.701399\pi$
$89$	−105.258			−1.18267			−0.591335	+	0.806426i	$0.701399\pi$
$90$	−14.0450	−	21.6245i	−0.156056	−	0.240272i
$91$		0			0
$92$	140.870	+	62.6982i	1.53120	+	0.681502i
$93$		−	89.5059i		−	0.962429i
$94$	89.9623	+	138.511i	0.957046	+	1.47352i
$95$		−	56.5597i		−	0.595365i
$96$	−123.063	−	32.9329i	−1.28190	−	0.343051i
$97$	−55.3301			−0.570413			−0.285206	−	0.958466i	$-0.592062\pi$
$97$	−55.3301			−0.570413			−0.285206	+	0.958466i	$0.592062\pi$
$98$		0			0
$99$	−53.9633			−0.545084
$100$	34.8981	−	78.4090i	0.348981	−	0.784090i
$101$		−	31.4328i		−	0.311216i	−0.987819	−	0.155608i	$-0.950266\pi$
$101$		−	31.4328i		−	0.311216i	0.987819	−	0.155608i	$-0.0497337\pi$
$102$	19.3536	−	12.5701i	0.189741	−	0.123236i
$103$			79.9862i			0.776565i	0.921540	+	0.388283i	$0.126932\pi$
$103$			79.9862i			0.776565i	−0.921540	+	0.388283i	$0.873068\pi$
$104$	−90.7566	+	14.3920i	−0.872660	+	0.138385i
$105$		0			0
$106$	−29.2871	−	45.0919i	−0.276293	−	0.425395i
$107$	48.7634			0.455732			0.227866	−	0.973692i	$-0.426825\pi$
$107$	48.7634			0.455732			0.227866	+	0.973692i	$0.426825\pi$
$108$	−13.9305	+	31.2990i	−0.128986	+	0.289806i
$109$		−	115.069i		−	1.05568i	−0.849344	−	0.527840i	$-0.823002\pi$
$109$		−	115.069i		−	1.05568i	0.849344	−	0.527840i	$-0.176998\pi$
$110$	16.1591	+	24.8794i	0.146901	+	0.226176i
$111$			181.357i			1.63384i
$112$		0			0
$113$	−55.7570			−0.493425			−0.246712	−	0.969089i	$-0.579350\pi$
$113$	−55.7570			−0.493425			−0.246712	+	0.969089i	$0.579350\pi$
$114$	200.616	−	130.300i	1.75979	−	1.14298i
$115$	72.5679			0.631025
$116$	101.848	+	45.3304i	0.878002	+	0.390779i
$117$		−	78.6653i		−	0.672353i
$118$	17.4622	−	11.3417i	0.147985	−	0.0961159i
$119$		0			0
$120$	−59.2150	+	9.39023i	−0.493459	+	0.0782519i
$121$	−58.9142			−0.486894
$122$	−24.1433	−	37.1724i	−0.197896	−	0.304691i
$123$	161.754			1.31508
$124$	−82.1620	−	36.5684i	−0.662597	−	0.294907i
$125$		−	87.4546i		−	0.699637i
$126$		0			0
$127$			35.6964i			0.281074i	0.990075	+	0.140537i	$0.0448828\pi$
$127$			35.6964i			0.281074i	−0.990075	+	0.140537i	$0.955117\pi$
$128$	−80.5091	+	99.5102i	−0.628977	+	0.777424i
$129$	−188.225			−1.45911
$130$	−36.2681	+	23.5560i	−0.278985	+	0.181200i
$131$	121.292			0.925896			0.462948	−	0.886385i	$-0.346792\pi$
$131$	121.292			0.925896			0.462948	+	0.886385i	$0.346792\pi$
$132$	−51.0202	+	114.632i	−0.386516	+	0.868425i
$133$		0			0
$134$	−99.4788	+	64.6112i	−0.742379	+	0.482173i
$135$			16.1234i			0.119432i
$136$	−3.63164	−	22.9012i	−0.0267033	−	0.168392i
$137$	−8.49670			−0.0620197			−0.0310099	−	0.999519i	$-0.509872\pi$
$137$	−8.49670			−0.0620197			−0.0310099	+	0.999519i	$0.509872\pi$
$138$	167.179	+	257.397i	1.21144	+	1.86520i
$139$	3.05942			0.0220102			0.0110051	−	0.999939i	$-0.496497\pi$
$139$	3.05942			0.0220102			0.0110051	+	0.999939i	$0.496497\pi$
$140$		0			0
$141$			328.757i			2.33161i
$142$	−41.6734	−	64.1626i	−0.293475	−	0.451849i
$143$			90.5061i			0.632910i
$144$	−73.3423	−	81.4136i	−0.509322	−	0.565372i
$145$	52.4661			0.361835
$146$	−23.4446	+	15.2272i	−0.160579	+	0.104296i
$147$		0			0
$148$	166.476	+	74.0949i	1.12484	+	0.500641i
$149$		−	31.7242i		−	0.212914i	−0.994317	−	0.106457i	$-0.966049\pi$
$149$		−	31.7242i		−	0.212914i	0.994317	−	0.106457i	$-0.0339507\pi$
$150$	143.268	−	93.0524i	0.955122	−	0.620349i
$151$			253.596i			1.67945i	0.543016	+	0.839723i	$0.317282\pi$
$151$			253.596i			1.67945i	−0.543016	+	0.839723i	$0.682718\pi$
$152$	−37.6451	−	237.391i	−0.247665	−	1.56178i
$153$	19.8502			0.129740
$154$		0			0
$155$	−42.3249			−0.273064
$156$	−167.106	−	74.3750i	−1.07119	−	0.476763i
$157$			49.3273i			0.314186i	0.987584	+	0.157093i	$0.0502123\pi$
$157$			49.3273i			0.314186i	−0.987584	+	0.157093i	$0.949788\pi$
$158$	−55.7650	−	85.8588i	−0.352943	−	0.543410i
$159$		−	107.026i		−	0.673121i
$160$	−15.5731	+	58.1929i	−0.0973317	+	0.363706i
$161$		0			0
$162$	−160.572	+	104.291i	−0.991186	+	0.643773i
$163$	115.719			0.709934			0.354967	−	0.934879i	$-0.384492\pi$
$163$	115.719			0.709934			0.354967	+	0.934879i	$0.384492\pi$
$164$	66.0862	−	148.482i	0.402965	−	0.905381i
$165$			59.0516i			0.357888i
$166$	150.025	−	97.4408i	0.903765	−	0.586993i
$167$		−	32.3859i		−	0.193928i	−0.995288	−	0.0969639i	$-0.969087\pi$
$167$		−	32.3859i		−	0.193928i	0.995288	−	0.0969639i	$-0.0309131\pi$
$168$		0			0
$169$	37.0641			0.219314
$170$	−5.94405	−	9.15178i	−0.0349650	−	0.0538340i
$171$	205.764			1.20330
$172$	−76.9012	+	172.782i	−0.447100	+	1.00454i
$173$			207.245i			1.19795i	0.800769	+	0.598973i	$0.204424\pi$
$173$			207.245i			1.19795i	−0.800769	+	0.598973i	$0.795576\pi$
$174$	120.869	+	186.096i	0.694650	+	1.06952i
$175$		0			0
$176$	84.3818	+	93.6679i	0.479442	+	0.532204i
$177$	41.4469			0.234163
$178$	−176.546	+	114.666i	−0.991830	+	0.644191i
$179$	174.167			0.973002			0.486501	−	0.873680i	$-0.338273\pi$
$179$	174.167			0.973002			0.486501	+	0.873680i	$0.338273\pi$
$180$	−47.1147	−	20.9697i	−0.261748	−	0.116498i
$181$		−	204.244i		−	1.12842i	−0.825632	−	0.564209i	$-0.809181\pi$
$181$		−	204.244i		−	1.12842i	0.825632	−	0.564209i	$-0.190819\pi$
$182$		0			0
$183$		−	88.2291i		−	0.482126i
$184$	304.580	−	48.2999i	1.65533	−	0.262499i
$185$	85.7586			0.463560
$186$	−97.5063	−	150.126i	−0.524228	−	0.807128i
$187$	−22.8380			−0.122128
$188$	301.783	+	134.317i	1.60523	+	0.714450i
$189$		0			0
$190$	−61.6152	−	94.8660i	−0.324291	−	0.499295i
$191$			298.511i			1.56288i	0.623978	+	0.781442i	$0.285515\pi$
$191$			298.511i			1.56288i	−0.623978	+	0.781442i	$0.714485\pi$
$192$	−242.286	+	78.8249i	−1.26191	+	0.410546i
$193$	−330.762			−1.71379			−0.856896	−	0.515490i	$-0.827610\pi$
$193$	−330.762			−1.71379			−0.856896	+	0.515490i	$0.827610\pi$
$194$	−92.8036	+	60.2757i	−0.478369	+	0.310699i
$195$	−86.0828			−0.441450
$196$		0			0
$197$		−	327.309i		−	1.66146i	−0.556672	−	0.830732i	$-0.687922\pi$
$197$		−	327.309i		−	1.66146i	0.556672	−	0.830732i	$-0.312078\pi$
$198$	−90.5111	+	58.7867i	−0.457127	+	0.296903i
$199$		−	12.7358i		−	0.0639989i	−0.999488	−	0.0319994i	$-0.989813\pi$
$199$		−	12.7358i		−	0.0639989i	0.999488	−	0.0319994i	$-0.0101875\pi$
$200$	−26.8839	−	169.531i	−0.134419	−	0.847653i
$201$	−236.114			−1.17470
$202$	−34.2424	−	52.7214i	−0.169517	−	0.260997i
$203$		0			0
$204$	18.7676	−	42.1670i	0.0919979	−	0.206701i
$205$		−	76.4892i		−	0.373118i
$206$	87.1357	+	134.159i	0.422989	+	0.651256i
$207$			264.002i			1.27537i
$208$	−136.545	+	123.008i	−0.656467	+	0.591386i
$209$	−236.736			−1.13271
$210$		0			0
$211$	120.455			0.570875			0.285437	−	0.958397i	$-0.407861\pi$
$211$	120.455			0.570875			0.285437	+	0.958397i	$0.407861\pi$
$212$	−98.2448	−	43.7266i	−0.463419	−	0.206257i
$213$		−	152.291i		−	0.714981i
$214$	81.7894	−	53.1220i	0.382194	−	0.248234i
$215$			89.0067i			0.413984i
$216$	10.7314	+	67.6726i	0.0496825	+	0.313299i
$217$		0			0
$218$	−125.354	−	193.002i	−0.575020	−	0.885331i
$219$	−55.6460			−0.254092
$220$	54.2064	+	24.1260i	0.246393	+	0.109664i
$221$		−	33.2923i		−	0.150644i
$222$	197.567	+	304.184i	0.889941	+	1.37020i
$223$		−	372.958i		−	1.67246i	−0.548382	−	0.836228i	$-0.684756\pi$
$223$		−	372.958i		−	1.67246i	0.548382	−	0.836228i	$-0.315244\pi$
$224$		0			0
$225$	146.944			0.653086
$226$	−93.5197	+	60.7408i	−0.413804	+	0.268764i
$227$	−73.4256			−0.323461			−0.161730	−	0.986835i	$-0.551708\pi$
$227$	−73.4256			−0.323461			−0.161730	+	0.986835i	$0.551708\pi$
$228$	194.542	−	437.097i	0.853254	−	1.91709i
$229$		−	424.453i		−	1.85350i	−0.375673	−	0.926752i	$-0.622588\pi$
$229$		−	424.453i		−	1.85350i	0.375673	−	0.926752i	$-0.377412\pi$
$230$	121.716	−	79.0543i	0.529201	−	0.343714i
$231$		0			0
$232$	220.209	−	34.9205i	0.949179	−	0.150519i
$233$	−83.4140			−0.358000			−0.179000	−	0.983849i	$-0.557286\pi$
$233$	−83.4140			−0.358000			−0.179000	+	0.983849i	$0.557286\pi$
$234$	−85.6968	−	131.943i	−0.366225	−	0.563860i
$235$	155.460			0.661533
$236$	16.9335	−	38.0462i	0.0717521	−	0.161213i
$237$		−	203.787i		−	0.859861i
$238$		0			0
$239$		−	112.561i		−	0.470967i	−0.971878	−	0.235484i	$-0.924333\pi$
$239$		−	112.561i		−	0.470967i	0.971878	−	0.235484i	$-0.0756674\pi$
$240$	−89.0902	+	80.2579i	−0.371209	+	0.334408i
$241$	−280.432			−1.16362			−0.581809	−	0.813325i	$-0.697655\pi$
$241$	−280.432			−1.16362			−0.581809	+	0.813325i	$0.697655\pi$
$242$	−98.8151	+	64.1801i	−0.408327	+	0.265207i
$243$	−304.037			−1.25118
$244$	−80.9899	−	36.0468i	−0.331926	−	0.147733i
$245$		0			0
$246$	271.306	−	176.213i	1.10287	−	0.716311i
$247$		−	345.103i		−	1.39718i
$248$	−177.645	+	28.1707i	−0.716311	+	0.113591i
$249$	356.086			1.43007
$250$	−95.2716	−	146.685i	−0.381086	−	0.586741i
$251$	32.9560			0.131299			0.0656493	−	0.997843i	$-0.479088\pi$
$251$	32.9560			0.131299			0.0656493	+	0.997843i	$0.479088\pi$
$252$		0			0
$253$		−	303.740i		−	1.20055i
$254$	38.8870	+	59.8725i	0.153099	+	0.235719i
$255$		−	21.7219i		−	0.0851838i
$256$	−26.6308	+	254.611i	−0.104027	+	0.994575i
$257$	224.219			0.872446			0.436223	−	0.899839i	$-0.356316\pi$
$257$	224.219			0.872446			0.436223	+	0.899839i	$0.356316\pi$
$258$	−315.705	+	205.050i	−1.22366	+	0.794767i
$259$		0			0
$260$	−35.1699	+	79.0197i	−0.135269	+	0.303922i
$261$			190.871i			0.731308i
$262$	203.440	−	132.134i	0.776490	−	0.504328i
$263$		−	169.961i		−	0.646239i	−0.946358	−	0.323119i	$-0.895268\pi$
$263$		−	169.961i		−	0.646239i	0.946358	−	0.323119i	$-0.104732\pi$
$264$	39.3036	+	247.850i	0.148877	+	0.938825i
$265$	−50.6098			−0.190980
$266$		0			0
$267$	−419.034			−1.56942
$268$	−96.4667	+	216.741i	−0.359950	+	0.808736i
$269$		−	108.526i		−	0.403442i	−0.979443	−	0.201721i	$-0.935347\pi$
$269$		−	108.526i		−	0.403442i	0.979443	−	0.201721i	$-0.0646535\pi$
$270$	17.5645	+	27.0433i	0.0650538	+	0.100160i
$271$			19.3631i			0.0714507i	0.999362	+	0.0357253i	$0.0113741\pi$
$271$			19.3631i			0.0714507i	−0.999362	+	0.0357253i	$0.988626\pi$
$272$	−31.0395	−	34.4554i	−0.114116	−	0.126674i
$273$		0			0
$274$	−14.2513	+	9.25617i	−0.0520120	+	0.0337817i
$275$	−169.063			−0.614773
$276$	560.809	+	249.604i	2.03192	+	0.904361i
$277$			129.446i			0.467315i	0.972319	+	0.233658i	$0.0750695\pi$
$277$			129.446i			0.467315i	−0.972319	+	0.233658i	$0.924931\pi$
$278$	5.13148	−	3.33288i	0.0184586	−	0.0119888i
$279$		−	153.978i		−	0.551892i
$280$		0			0
$281$	83.3608			0.296658			0.148329	−	0.988938i	$-0.452611\pi$
$281$	83.3608			0.296658			0.148329	+	0.988938i	$0.452611\pi$
$282$	358.143	+	551.415i	1.27001	+	1.95537i
$283$	−28.9293			−0.102224			−0.0511118	−	0.998693i	$-0.516276\pi$
$283$	−28.9293			−0.102224			−0.0511118	+	0.998693i	$0.516276\pi$
$284$	−139.795	−	62.2198i	−0.492237	−	0.219084i
$285$		−	225.166i		−	0.790055i
$286$	98.5959	+	151.803i	0.344741	+	0.530781i
$287$		0			0
$288$	−211.706	−	56.6548i	−0.735089	−	0.196718i
$289$	−280.599			−0.970931
$290$	87.9999	−	57.1557i	0.303448	−	0.197089i
$291$	−220.271			−0.756944
$292$	−22.7347	+	51.0803i	−0.0778585	+	0.174932i
$293$			214.613i			0.732468i	0.930523	+	0.366234i	$0.119353\pi$
$293$			214.613i			0.732468i	−0.930523	+	0.366234i	$0.880647\pi$
$294$		0			0
$295$		−	19.5991i		−	0.0664376i
$296$	359.944	−	57.0793i	1.21603	−	0.192836i
$297$	67.4858			0.227225
$298$	−34.5598	−	53.2101i	−0.115973	−	0.178557i
$299$	442.778			1.48086
$300$	138.930	−	312.148i	0.463101	−	1.04049i
$301$		0			0
$302$	276.264	+	425.350i	0.914780	+	1.40844i
$303$		−	125.135i		−	0.412987i
$304$	−321.751	−	357.159i	−1.05839	−	1.17487i
$305$	−41.7211			−0.136791
$306$	33.2941	−	21.6245i	0.108804	−	0.0706682i
$307$	120.542			0.392644			0.196322	−	0.980539i	$-0.437100\pi$
$307$	120.542			0.392644			0.196322	+	0.980539i	$0.437100\pi$
$308$		0			0
$309$			318.427i			1.03051i
$310$	−70.9904	+	46.1081i	−0.229001	+	0.148736i
$311$		−	325.361i		−	1.04618i	−0.852278	−	0.523089i	$-0.824780\pi$
$311$		−	325.361i		−	1.04618i	0.852278	−	0.523089i	$-0.175220\pi$
$312$	−361.305	+	57.2952i	−1.15803	+	0.183638i
$313$	−456.756			−1.45928			−0.729642	−	0.683829i	$-0.760313\pi$
$313$	−456.756			−1.45928			−0.729642	+	0.683829i	$0.760313\pi$
$314$	53.7363	+	82.7353i	0.171135	+	0.263488i
$315$		0			0
$316$	−187.066	−	83.2590i	−0.591982	−	0.263478i
$317$		−	121.220i		−	0.382399i	−0.981551	−	0.191199i	$-0.938762\pi$
$317$		−	121.220i		−	0.382399i	0.981551	−	0.191199i	$-0.0612377\pi$
$318$	−116.593	−	179.512i	−0.366644	−	0.564504i
$319$		−	219.601i		−	0.688406i
$320$	37.2741	+	114.570i	0.116482	+	0.358033i
$321$	194.128			0.604761
$322$		0			0
$323$	87.0822			0.269604
$324$	−155.710	+	349.849i	−0.480587	+	1.07978i
$325$		−	246.452i		−	0.758314i
$326$	194.093	−	126.063i	0.595377	−	0.386696i
$327$		−	458.094i		−	1.40090i
$328$	−50.9098	−	321.039i	−0.155213	−	0.978777i
$329$		0			0
$330$	64.3298	+	99.0455i	0.194939	+	0.300138i
$331$	121.168			0.366068			0.183034	−	0.983107i	$-0.441408\pi$
$331$	121.168			0.366068			0.183034	+	0.983107i	$0.441408\pi$
$332$	145.482	−	326.870i	0.438200	−	0.984547i
$333$			311.989i			0.936905i
$334$	−35.2807	−	54.3201i	−0.105631	−	0.162635i
$335$			111.652i			0.333290i
$336$		0			0
$337$	−464.021			−1.37692			−0.688459	−	0.725275i	$-0.741713\pi$
$337$	−464.021			−1.37692			−0.688459	+	0.725275i	$0.741713\pi$
$338$	62.1666	−	40.3771i	0.183925	−	0.119459i
$339$	−221.970			−0.654780
$340$	−19.9396	−	8.87467i	−0.0586459	−	0.0261020i
$341$			177.155i			0.519515i
$342$	345.122	−	224.156i	1.00913	−	0.655427i
$343$		0			0
$344$	59.2412	+	373.577i	0.172213	+	1.08598i
$345$	288.895			0.837377
$346$	225.769	+	347.606i	0.652512	+	1.00464i
$347$	−371.186			−1.06970			−0.534851	−	0.844947i	$-0.679632\pi$
$347$	−371.186			−1.06970			−0.534851	+	0.844947i	$0.679632\pi$
$348$	405.461	+	180.462i	1.16512	+	0.518568i
$349$		−	207.871i		−	0.595619i	−0.954625	−	0.297809i	$-0.903744\pi$
$349$		−	207.871i		−	0.595619i	0.954625	−	0.297809i	$-0.0962560\pi$
$350$		0			0
$351$			98.3779i			0.280279i
$352$	243.572	+	65.1825i	0.691965	+	0.185178i
$353$	614.014			1.73942			0.869708	−	0.493567i	$-0.164307\pi$
$353$	614.014			1.73942			0.869708	+	0.493567i	$0.164307\pi$
$354$	69.5177	−	45.1516i	0.196378	−	0.127547i
$355$	−72.0142			−0.202857
$356$	−171.200	+	384.652i	−0.480899	+	1.08048i
$357$		0			0
$358$	292.126	−	189.735i	0.815995	−	0.529986i
$359$			108.072i			0.301036i	0.988607	+	0.150518i	$0.0480941\pi$
$359$			108.072i			0.301036i	−0.988607	+	0.150518i	$0.951906\pi$
$360$	−101.868	+	16.1541i	−0.282967	+	0.0448725i
$361$	541.682			1.50050
$362$	−222.500	−	342.573i	−0.614641	−	0.946333i
$363$	−234.539			−0.646113
$364$		0			0
$365$			26.3135i			0.0720917i
$366$	−96.1154	−	147.984i	−0.262610	−	0.404329i
$367$		−	454.815i		−	1.23928i	−0.784887	−	0.619639i	$-0.787279\pi$
$367$		−	454.815i		−	1.23928i	0.784887	−	0.619639i	$-0.212721\pi$
$368$	458.247	−	412.817i	1.24524	−	1.12179i
$369$	278.268			0.754113
$370$	143.840	−	93.4240i	0.388758	−	0.252497i
$371$		0			0
$372$	−327.089	−	145.580i	−0.879272	−	0.391344i
$373$		−	271.752i		−	0.728557i	−0.931290	−	0.364279i	$-0.881316\pi$
$373$		−	271.752i		−	0.728557i	0.931290	−	0.364279i	$-0.118684\pi$
$374$	−38.3056	+	24.8794i	−0.102421	+	0.0665224i
$375$		−	348.159i		−	0.928425i
$376$	652.494	−	103.471i	1.73536	−	0.275190i
$377$	320.126			0.849140
$378$		0			0
$379$	268.351			0.708051			0.354026	−	0.935236i	$-0.384813\pi$
$379$	268.351			0.708051			0.354026	+	0.935236i	$0.384813\pi$
$380$	−206.691	−	91.9935i	−0.543924	−	0.242088i
$381$			142.108i			0.372988i
$382$	325.193	+	500.684i	0.851290	+	1.31069i
$383$			327.610i			0.855377i	0.903926	+	0.427689i	$0.140672\pi$
$383$			327.610i			0.855377i	−0.903926	+	0.427689i	$0.859328\pi$
$384$	−320.509	+	396.153i	−0.834659	+	1.03165i
$385$		0			0
$386$	−554.778	+	360.327i	−1.43725	+	0.933489i
$387$	−323.806			−0.836708
$388$	−89.9935	+	202.197i	−0.231942	+	0.521127i
$389$		−	126.301i		−	0.324682i	−0.986735	−	0.162341i	$-0.948096\pi$
$389$		−	126.301i		−	0.324682i	0.986735	−	0.162341i	$-0.0519044\pi$
$390$	−144.384	+	93.7772i	−0.370216	+	0.240454i
$391$			111.729i			0.285753i
$392$		0			0
$393$	482.869			1.22867
$394$	−356.565	−	548.986i	−0.904986	−	1.39336i
$395$	−96.3653			−0.243963
$396$	−87.7705	+	197.203i	−0.221643	+	0.497987i
$397$		−	127.144i		−	0.320262i	−0.987096	−	0.160131i	$-0.948808\pi$
$397$		−	127.144i		−	0.320262i	0.987096	−	0.160131i	$-0.0511917\pi$
$398$	−13.8741	−	21.3614i	−0.0348597	−	0.0536718i
$399$		0			0
$400$	−229.775	−	255.062i	−0.574439	−	0.637655i
$401$	60.1502			0.150001			0.0750003	−	0.997184i	$-0.476104\pi$
$401$	60.1502			0.150001			0.0750003	+	0.997184i	$0.476104\pi$
$402$	−396.028	+	257.219i	−0.985145	+	0.639849i
$403$	−258.248			−0.640815
$404$	−114.868	−	51.1250i	−0.284326	−	0.126547i
$405$			180.221i			0.444991i
$406$		0			0
$407$		−	358.950i		−	0.881941i
$408$	−14.4577	−	91.1706i	−0.0354355	−	0.223457i
$409$	69.7747			0.170598			0.0852991	−	0.996355i	$-0.472815\pi$
$409$	69.7747			0.170598			0.0852991	+	0.996355i	$0.472815\pi$
$410$	−83.3261	−	128.293i	−0.203234	−	0.312910i
$411$	−33.8256			−0.0823008
$412$	292.301	+	130.096i	0.709467	+	0.315768i
$413$		0			0
$414$	287.599	+	442.803i	0.694685	+	1.06957i
$415$		−	168.384i		−	0.405743i
$416$	−95.0202	+	355.068i	−0.228414	+	0.853530i
$417$	12.1796			0.0292078
$418$	−397.070	+	257.896i	−0.949929	+	0.616976i
$419$	−714.794			−1.70595			−0.852976	−	0.521950i	$-0.825205\pi$
$419$	−714.794			−1.70595			−0.852976	+	0.521950i	$0.825205\pi$
$420$		0			0
$421$			303.440i			0.720759i	0.932806	+	0.360380i	$0.117353\pi$
$421$			303.440i			0.720759i	−0.932806	+	0.360380i	$0.882647\pi$
$422$	202.035	−	131.221i	0.478756	−	0.310951i
$423$			565.564i			1.33703i
$424$	−212.418	+	33.6850i	−0.500987	+	0.0794457i
$425$	62.1890			0.146327
$426$	−165.903	−	255.433i	−0.389444	−	0.599609i
$427$		0			0
$428$	79.3129	−	178.200i	0.185310	−	0.416356i
$429$			360.307i			0.839877i
$430$	96.9624	+	149.288i	0.225494	+	0.347182i
$431$			431.495i			1.00115i	0.865694	+	0.500574i	$0.166878\pi$
$431$			431.495i			1.00115i	−0.865694	+	0.500574i	$0.833122\pi$
$432$	91.7210	+	101.815i	0.212317	+	0.235682i
$433$	−194.875			−0.450057			−0.225029	−	0.974352i	$-0.572248\pi$
$433$	−194.875			−0.450057			−0.225029	+	0.974352i	$0.572248\pi$
$434$		0			0
$435$	208.869			0.480159
$436$	−420.507	−	187.158i	−0.964466	−	0.429262i
$437$			1158.17i			2.65028i
$438$	−93.3336	+	60.6199i	−0.213090	+	0.138402i
$439$		−	305.970i		−	0.696969i	−0.937314	−	0.348485i	$-0.886696\pi$
$439$		−	305.970i		−	0.696969i	0.937314	−	0.348485i	$-0.113304\pi$
$440$	117.201	−	18.5856i	0.266367	−	0.0422400i
$441$		0			0
$442$	−36.2681	−	55.8402i	−0.0820545	−	0.126335i
$443$	250.197			0.564779			0.282390	−	0.959300i	$-0.408873\pi$
$443$	250.197			0.564779			0.282390	+	0.959300i	$0.408873\pi$
$444$	662.747	+	294.974i	1.49267	+	0.664356i
$445$			198.150i			0.445280i
$446$	−406.294	−	625.552i	−0.910973	−	1.40258i
$447$		−	126.295i		−	0.282539i
$448$		0			0
$449$	−688.681			−1.53381			−0.766905	−	0.641761i	$-0.778204\pi$
$449$	−688.681			−1.53381			−0.766905	+	0.641761i	$0.778204\pi$
$450$	246.466	−	160.079i	0.547702	−	0.355731i
$451$	−320.152			−0.709872
$452$	−90.6879	+	203.758i	−0.200637	+	0.450791i
$453$			1009.57i			2.22864i
$454$	−123.155	+	79.9887i	−0.271266	+	0.176187i
$455$		0			0
$456$	−149.866	−	945.061i	−0.328654	−	2.07250i
$457$	804.518			1.76043			0.880217	−	0.474572i	$-0.157397\pi$
$457$	804.518			1.76043			0.880217	+	0.474572i	$0.157397\pi$
$458$	−462.392	−	711.923i	−1.00959	−	1.55442i
$459$	−24.8244			−0.0540836
$460$	118.031	−	265.191i	0.256588	−	0.576503i
$461$			693.657i			1.50468i	0.658776	+	0.752339i	$0.271074\pi$
$461$			693.657i			1.50468i	−0.658776	+	0.752339i	$0.728926\pi$
$462$		0			0
$463$			321.194i			0.693724i	0.937916	+	0.346862i	$0.112753\pi$
$463$			321.194i			0.693724i	−0.937916	+	0.346862i	$0.887247\pi$
$464$	331.309	−	298.464i	0.714029	−	0.643241i
$465$	−168.497			−0.362359
$466$	−139.908	+	90.8698i	−0.300232	+	0.195000i
$467$	−751.875			−1.61001			−0.805005	−	0.593268i	$-0.797837\pi$
$467$	−751.875			−1.61001			−0.805005	+	0.593268i	$0.797837\pi$
$468$	−287.474	−	127.948i	−0.614260	−	0.273393i
$469$		0			0
$470$	260.749	−	169.356i	0.554785	−	0.360332i
$471$			196.373i			0.416929i
$472$	−13.0448	−	82.2609i	−0.0276373	−	0.174281i
$473$	372.545			0.787622
$474$	−222.002	−	341.806i	−0.468359	−	0.721110i
$475$	644.642			1.35714
$476$		0			0
$477$		−	184.118i		−	0.385992i
$478$	−122.622	−	188.796i	−0.256532	−	0.394970i
$479$			722.140i			1.50760i	0.657104	+	0.753800i	$0.271781\pi$
$479$			722.140i			1.50760i	−0.657104	+	0.753800i	$0.728219\pi$
$480$	−61.9969	+	231.668i	−0.129160	+	0.482641i
$481$	523.262			1.08786
$482$	−470.361	+	305.498i	−0.975853	+	0.633814i
$483$		0			0
$484$	−95.8230	+	215.295i	−0.197981	+	0.444825i
$485$			104.160i			0.214763i
$486$	−509.953	+	331.213i	−1.04929	+	0.681509i
$487$		−	47.8290i		−	0.0982114i	−0.998794	−	0.0491057i	$-0.984363\pi$
$487$		−	47.8290i		−	0.0982114i	0.998794	−	0.0491057i	$-0.0156371\pi$
$488$	−175.111	+	27.7688i	−0.358834	+	0.0569033i
$489$	460.682			0.942090
$490$		0			0
$491$	44.4724			0.0905752			0.0452876	−	0.998974i	$-0.485580\pi$
$491$	44.4724			0.0905752			0.0452876	+	0.998974i	$0.485580\pi$
$492$	263.091	−	591.113i	0.534738	−	1.20145i
$493$			80.7795i			0.163853i
$494$	−375.950	−	578.832i	−0.761032	−	1.17172i
$495$			101.587i			0.205226i
$496$	−267.271	+	240.774i	−0.538852	+	0.485431i
$497$		0			0
$498$	597.254	−	387.915i	1.19931	−	0.778945i
$499$	−501.572			−1.00515			−0.502577	−	0.864532i	$-0.667615\pi$
$499$	−501.572			−1.00515			−0.502577	+	0.864532i	$0.667615\pi$
$500$	−319.593	−	142.244i	−0.639186	−	0.284487i
$501$		−	128.929i		−	0.257344i
$502$	55.2761	−	35.9017i	0.110112	−	0.0715173i
$503$			462.733i			0.919946i	0.887933	+	0.459973i	$0.152141\pi$
$503$			462.733i			0.919946i	−0.887933	+	0.459973i	$0.847859\pi$
$504$		0			0
$505$	−59.1729			−0.117174
$506$	−330.889	−	509.454i	−0.653931	−	1.00683i
$507$	147.553			0.291032
$508$	130.448	+	58.0596i	0.256788	+	0.114291i
$509$			471.985i			0.927278i	0.886024	+	0.463639i	$0.153457\pi$
$509$			471.985i			0.927278i	−0.886024	+	0.463639i	$0.846543\pi$
$510$	−23.6635	−	36.4335i	−0.0463989	−	0.0714382i
$511$		0			0
$512$	232.702	+	456.063i	0.454496	+	0.890749i
$513$	−257.326			−0.501610
$514$	376.076	−	244.260i	0.731665	−	0.475214i
$515$	150.576			0.292380
$516$	−306.146	+	687.849i	−0.593306	+	1.33304i
$517$		−	650.693i		−	1.25859i
$518$		0			0
$519$			825.047i			1.58969i
$520$	27.0933	+	170.851i	0.0521025	+	0.328560i
$521$	90.7419			0.174169			0.0870843	−	0.996201i	$-0.472245\pi$
$521$	90.7419			0.174169			0.0870843	+	0.996201i	$0.472245\pi$
$522$	207.932	+	320.143i	0.398338	+	0.613302i
$523$	360.512			0.689316			0.344658	−	0.938728i	$-0.387995\pi$
$523$	360.512			0.689316			0.344658	+	0.938728i	$0.387995\pi$
$524$	197.280	−	443.249i	0.376489	−	0.845896i
$525$		0			0
$526$	−185.152	−	285.070i	−0.352001	−	0.541959i
$527$		−	65.1656i		−	0.123654i
$528$	335.927	+	372.895i	0.636224	+	0.706240i
$529$	−956.970			−1.80902
$530$	−84.8864	+	55.1335i	−0.160163	+	0.104025i
$531$	71.3014			0.134278
$532$		0			0
$533$		−	466.705i		−	0.875618i
$534$	−702.834	+	456.489i	−1.31617	+	0.854848i
$535$		−	91.7980i		−	0.171585i
$536$	74.3136	+	468.623i	0.138645	+	0.874297i
$537$	693.366			1.29118
$538$	−118.226	−	182.028i	−0.219752	−	0.338341i
$539$		0			0
$540$	58.9210	+	26.2244i	0.109113	+	0.0485637i
$541$			561.148i			1.03724i	0.855004	+	0.518621i	$0.173555\pi$
$541$			561.148i			1.03724i	−0.855004	+	0.518621i	$0.826445\pi$
$542$	21.0939	+	32.4772i	0.0389186	+	0.0599211i
$543$		−	813.101i		−	1.49742i
$544$	−89.5968	−	23.9771i	−0.164700	−	0.0440756i
$545$	−216.620			−0.397468
$546$		0			0
$547$	1043.62			1.90790			0.953952	−	0.299960i	$-0.0969733\pi$
$547$	1043.62			1.90790			0.953952	+	0.299960i	$0.0969733\pi$
$548$	−13.8198	+	31.0502i	−0.0252186	+	0.0566610i
$549$		−	151.781i		−	0.276469i
$550$	−283.564	+	184.174i	−0.515571	+	0.334862i
$551$			837.349i			1.51969i
$552$	1212.54	−	192.283i	2.19664	−	0.348339i
$553$		0			0
$554$	141.017	+	217.117i	0.254543	+	0.391907i
$555$	341.407			0.615148
$556$	4.97610	−	11.1803i	0.00894983	−	0.0201085i
$557$			48.6444i			0.0873328i	0.999046	+	0.0436664i	$0.0139039\pi$
$557$			48.6444i			0.0873328i	−0.999046	+	0.0436664i	$0.986096\pi$
$558$	−167.741	−	258.263i	−0.300611	−	0.462837i
$559$			543.081i			0.971522i
$560$		0			0
$561$	−90.9189			−0.162066
$562$	139.819	−	90.8119i	0.248788	−	0.161587i
$563$	−726.031			−1.28957			−0.644787	−	0.764362i	$-0.723054\pi$
$563$	−726.031			−1.28957			−0.644787	+	0.764362i	$0.723054\pi$
$564$	1201.41	+	534.719i	2.13015	+	0.948083i
$565$			104.964i			0.185776i
$566$	−48.5223	+	31.5151i	−0.0857284	+	0.0556804i
$567$		0			0
$568$	−302.256	+	47.9313i	−0.532141	+	0.0843861i
$569$	−481.392			−0.846032			−0.423016	−	0.906122i	$-0.639029\pi$
$569$	−481.392			−0.846032			−0.423016	+	0.906122i	$0.639029\pi$
$570$	−245.292	−	377.664i	−0.430337	−	0.662569i
$571$	110.127			0.192866			0.0964331	−	0.995339i	$-0.469257\pi$
$571$	110.127			0.192866			0.0964331	+	0.995339i	$0.469257\pi$
$572$	330.744	+	147.207i	0.578224	+	0.257355i
$573$			1188.38i			2.07396i
$574$		0			0
$575$			827.097i			1.43843i
$576$	−416.807	+	135.603i	−0.723623	+	0.235422i
$577$	202.336			0.350669			0.175335	−	0.984509i	$-0.443899\pi$
$577$	202.336			0.350669			0.175335	+	0.984509i	$0.443899\pi$
$578$	−470.641	+	305.680i	−0.814258	+	0.528858i
$579$	−1316.77			−2.27422
$580$	85.3353	−	191.731i	0.147130	−	0.330571i
$581$		0			0
$582$	−369.454	+	239.959i	−0.634800	+	0.412301i
$583$			211.832i			0.363348i
$584$	17.5138	+	110.442i	0.0299893	+	0.189114i
$585$	−148.089			−0.253144
$586$	233.796	+	359.965i	0.398970	+	0.614274i
$587$	568.689			0.968805			0.484403	−	0.874845i	$-0.339037\pi$
$587$	568.689			0.968805			0.484403	+	0.874845i	$0.339037\pi$
$588$		0			0
$589$		−	675.497i		−	1.14685i
$590$	−21.3509	−	32.8730i	−0.0361880	−	0.0557170i
$591$		−	1303.03i		−	2.20478i
$592$	541.543	−	487.855i	0.914768	−	0.824079i
$593$	685.373			1.15577			0.577886	−	0.816117i	$-0.303878\pi$
$593$	685.373			1.15577			0.577886	+	0.816117i	$0.303878\pi$
$594$	113.192	−	73.5179i	0.190559	−	0.123768i
$595$		0			0
$596$	−115.932	−	51.5989i	−0.194518	−	0.0865754i
$597$		−	50.7015i		−	0.0849271i
$598$	742.660	−	482.356i	1.24191	−	0.806615i
$599$			367.283i			0.613161i	0.951845	+	0.306580i	$0.0991848\pi$
$599$			367.283i			0.613161i	−0.951845	+	0.306580i	$0.900815\pi$
$600$	−107.026	−	674.906i	−0.178376	−	1.12484i
$601$	−412.344			−0.686097			−0.343049	−	0.939318i	$-0.611460\pi$
$601$	−412.344			−0.686097			−0.343049	+	0.939318i	$0.611460\pi$
$602$		0			0
$603$	−406.190			−0.673615
$604$	926.739	+	412.471i	1.53434	+	0.682898i
$605$			110.907i			0.183318i
$606$	−136.320	−	209.886i	−0.224951	−	0.346346i
$607$		−	1166.78i		−	1.92220i	−0.276195	−	0.961102i	$-0.589074\pi$
$607$		−	1166.78i		−	1.92220i	0.276195	−	0.961102i	$-0.410926\pi$
$608$	−928.748	−	248.543i	−1.52755	−	0.408788i
$609$		0			0
$610$	−69.9777	+	45.4503i	−0.114718	+	0.0745087i
$611$	948.552			1.55246
$612$	32.2860	−	72.5402i	0.0527549	−	0.118530i
$613$		−	431.743i		−	0.704311i	−0.935942	−	0.352155i	$-0.885449\pi$
$613$		−	431.743i		−	0.704311i	0.935942	−	0.352155i	$-0.114551\pi$
$614$	202.181	−	131.316i	0.329286	−	0.213870i
$615$		−	304.506i		−	0.495131i
$616$		0			0
$617$	−333.751			−0.540926			−0.270463	−	0.962730i	$-0.587177\pi$
$617$	−333.751			−0.540926			−0.270463	+	0.962730i	$0.587177\pi$
$618$	346.890	+	534.090i	0.561310	+	0.864223i
$619$	976.316			1.57725			0.788624	−	0.614876i	$-0.210794\pi$
$619$	976.316			1.57725			0.788624	+	0.614876i	$0.210794\pi$
$620$	−68.8408	+	154.672i	−0.111034	+	0.249470i
$621$		−	330.157i		−	0.531655i
$622$	−354.443	−	545.719i	−0.569844	−	0.877362i
$623$		0			0
$624$	−543.590	+	489.699i	−0.871138	+	0.784775i
$625$	371.768			0.594829
$626$	−766.104	+	497.583i	−1.22381	+	0.794860i
$627$	−942.452			−1.50311
$628$	180.261	+	80.2301i	0.287040	+	0.127755i
$629$			132.038i			0.209918i
$630$		0			0
$631$			639.885i			1.01408i	0.861922	+	0.507040i	$0.169261\pi$
$631$			639.885i			1.01408i	−0.861922	+	0.507040i	$0.830739\pi$
$632$	−404.462	+	64.1390i	−0.639972	+	0.101486i
$633$	479.533			0.757556
$634$	−132.055	−	203.320i	−0.208289	−	0.320693i
$635$	67.1991			0.105825
$636$	−391.116	−	174.077i	−0.614962	−	0.273706i
$637$		0			0
$638$	−239.230	−	368.332i	−0.374969	−	0.577322i
$639$		−	261.987i		−	0.409996i
$640$	187.330	+	151.560i	0.292703	+	0.236812i
$641$	20.8591			0.0325415			0.0162707	−	0.999868i	$-0.494821\pi$
$641$	20.8591			0.0325415			0.0162707	+	0.999868i	$0.494821\pi$
$642$	325.606	−	211.480i	0.507175	−	0.329409i
$643$	69.1348			0.107519			0.0537596	−	0.998554i	$-0.482880\pi$
$643$	69.1348			0.107519			0.0537596	+	0.998554i	$0.482880\pi$
$644$		0			0
$645$			354.338i			0.549362i
$646$	146.061	−	94.8660i	0.226100	−	0.146851i
$647$		−	358.959i		−	0.554806i	−0.960754	−	0.277403i	$-0.910526\pi$
$647$		−	358.959i		−	0.554806i	0.960754	−	0.277403i	$-0.0894737\pi$
$648$	119.952	+	756.421i	0.185111	+	1.16732i
$649$	−82.0338			−0.126400
$650$	−268.481	−	413.367i	−0.413048	−	0.635950i
$651$		0			0
$652$	188.216	−	422.883i	0.288675	−	0.648594i
$653$		−	37.0921i		−	0.0568026i	−0.999597	−	0.0284013i	$-0.990958\pi$
$653$		−	37.0921i		−	0.0568026i	0.999597	−	0.0284013i	$-0.00904163\pi$
$654$	−499.040	−	768.348i	−0.763058	−	1.17484i
$655$		−	228.335i		−	0.348604i
$656$	−435.124	−	483.009i	−0.663299	−	0.736294i
$657$	−95.7284			−0.145705
$658$		0			0
$659$	197.302			0.299396			0.149698	−	0.988732i	$-0.452170\pi$
$659$	197.302			0.299396			0.149698	+	0.988732i	$0.452170\pi$
$660$	215.797	+	96.0465i	0.326966	+	0.145525i
$661$		−	1083.83i		−	1.63969i	−0.572589	−	0.819843i	$-0.694061\pi$
$661$		−	1083.83i		−	1.63969i	0.572589	−	0.819843i	$-0.305939\pi$
$662$	203.232	−	131.999i	0.306998	−	0.199394i
$663$		−	132.538i		−	0.199906i
$664$	−112.073	−	706.735i	−0.168785	−	1.06436i
$665$		0			0
$666$	339.876	+	523.291i	0.510325	+	0.785723i
$667$	−1074.35			−1.61071
$668$	−118.351	−	52.6753i	−0.177172	−	0.0788552i
$669$		−	1484.76i		−	2.21937i
$670$	121.632	+	187.271i	0.181540	+	0.279509i
$671$			174.628i			0.260250i
$672$		0			0
$673$	−286.066			−0.425061			−0.212530	−	0.977154i	$-0.568170\pi$
$673$	−286.066			−0.425061			−0.212530	+	0.977154i	$0.568170\pi$
$674$	−778.290	+	505.497i	−1.15473	+	0.749996i
$675$	−183.767			−0.272247
$676$	60.2843	−	135.447i	0.0891779	−	0.200365i
$677$			500.360i			0.739083i	0.929214	+	0.369542i	$0.120485\pi$
$677$			500.360i			0.739083i	−0.929214	+	0.369542i	$0.879515\pi$
$678$	−372.305	+	241.811i	−0.549122	+	0.356653i
$679$		0			0
$680$	−43.1121	+	6.83664i	−0.0634001	+	0.0100539i
$681$	−292.310			−0.429236
$682$	192.989	+	297.137i	0.282976	+	0.435684i
$683$	946.450			1.38572			0.692862	−	0.721070i	$-0.256349\pi$
$683$	946.450			1.38572			0.692862	+	0.721070i	$0.256349\pi$
$684$	334.672	−	751.941i	0.489287	−	1.09933i
$685$			15.9952i			0.0233507i
$686$		0			0
$687$		−	1689.76i		−	2.45962i
$688$	506.332	+	562.054i	0.735948	+	0.816938i
$689$	−308.799			−0.448185
$690$	484.556	−	314.718i	0.702255	−	0.456112i
$691$	−303.264			−0.438877			−0.219439	−	0.975626i	$-0.570423\pi$
$691$	−303.264			−0.438877			−0.219439	+	0.975626i	$0.570423\pi$
$692$	757.352	+	337.080i	1.09444	+	0.487111i
$693$		0			0
$694$	−622.580	+	404.364i	−0.897090	+	0.582658i
$695$		−	5.75942i		−	0.00828694i
$696$	876.660	−	139.019i	1.25957	−	0.199741i
$697$	117.767			0.168962
$698$	−226.451	−	348.656i	−0.324429	−	0.499508i
$699$	−332.074			−0.475069
$700$		0			0
$701$		−	390.864i		−	0.557580i	−0.960352	−	0.278790i	$-0.910067\pi$
$701$		−	390.864i		−	0.557580i	0.960352	−	0.278790i	$-0.0899333\pi$
$702$	107.171	+	165.007i	0.152666	+	0.235052i
$703$			1368.69i			1.94693i
$704$	479.545	−	156.014i	0.681171	−	0.221611i
$705$	618.892			0.877861
$706$	1029.87	−	668.897i	1.45874	−	0.947446i
$707$		0			0
$708$	67.4128	−	151.463i	0.0952158	−	0.213931i
$709$		−	961.165i		−	1.35566i	−0.735217	−	0.677831i	$-0.762920\pi$
$709$		−	961.165i		−	1.35566i	0.735217	−	0.677831i	$-0.237080\pi$
$710$	−120.787	+	78.4511i	−0.170123	+	0.110494i
$711$		−	350.577i		−	0.493075i
$712$	131.885	+	831.669i	0.185231	+	1.16807i
$713$	866.685			1.21555
$714$		0			0
$715$	170.379			0.238293
$716$	283.281	−	636.475i	0.395643	−	0.888931i
$717$		−	448.109i		−	0.624978i
$718$	117.732	+	181.266i	0.163972	+	0.252460i
$719$		−	525.126i		−	0.730356i	−0.930938	−	0.365178i	$-0.881008\pi$
$719$		−	525.126i		−	0.730356i	0.930938	−	0.365178i	$-0.118992\pi$
$720$	−153.263	+	138.068i	−0.212865	+	0.191762i
$721$		0			0
$722$	908.548	−	590.100i	1.25838	−	0.817312i
$723$	−1116.41			−1.54413
$724$	−746.386	−	332.200i	−1.03092	−	0.458839i
$725$			597.985i			0.824807i
$726$	−393.386	+	255.503i	−0.541854	+	0.351933i
$727$			108.633i			0.149426i	0.997205	+	0.0747131i	$0.0238041\pi$
$727$			108.633i			0.149426i	−0.997205	+	0.0747131i	$0.976196\pi$
$728$		0			0
$729$	−348.775			−0.478429
$730$	28.6655	+	44.1349i	0.0392678	+	0.0604587i
$731$	−137.039			−0.187468
$732$	−322.423	−	143.503i	−0.440469	−	0.196043i
$733$			40.2540i			0.0549167i	0.999623	+	0.0274584i	$0.00874137\pi$
$733$			40.2540i			0.0549167i	−0.999623	+	0.0274584i	$0.991259\pi$
$734$	−495.468	−	762.849i	−0.675025	−	1.03930i
$735$		0			0
$736$	318.889	−	1191.61i	0.433273	−	1.61904i
$737$	467.330			0.634097
$738$	466.730	−	303.140i	0.632426	−	0.410759i
$739$	997.203			1.34940			0.674698	−	0.738094i	$-0.264274\pi$
$739$	997.203			1.34940			0.674698	+	0.738094i	$0.264274\pi$
$740$	139.485	−	313.395i	0.188493	−	0.423507i
$741$		−	1373.87i		−	1.85407i
$742$		0			0
$743$		−	476.575i		−	0.641420i	−0.947177	−	0.320710i	$-0.896078\pi$
$743$		−	476.575i		−	0.641420i	0.947177	−	0.320710i	$-0.103922\pi$
$744$	−707.211	+	112.148i	−0.950552	+	0.150737i
$745$	−59.7214			−0.0801630
$746$	−296.042	−	455.802i	−0.396839	−	0.610994i
$747$	612.579			0.820052
$748$	−37.1457	+	83.4590i	−0.0496600	+	0.111576i
$749$		0			0
$750$	−379.279	−	583.958i	−0.505706	−	0.778611i
$751$			528.496i			0.703723i	0.936052	+	0.351862i	$0.114451\pi$
$751$			528.496i			0.703723i	−0.936052	+	0.351862i	$0.885549\pi$
$752$	981.690	−	884.366i	1.30544	−	1.17602i
$753$	131.199			0.174235
$754$	536.938	−	348.740i	0.712119	−	0.462520i
$755$	477.400			0.632318
$756$		0			0
$757$			455.964i			0.602331i	0.953572	+	0.301165i	$0.0973756\pi$
$757$			455.964i			0.602331i	−0.953572	+	0.301165i	$0.902624\pi$
$758$	450.098	−	292.338i	0.593797	−	0.385670i
$759$		−	1209.20i		−	1.59314i
$760$	−446.893	+	70.8676i	−0.588017	+	0.0932469i
$761$	−476.650			−0.626347			−0.313174	−	0.949696i	$-0.601392\pi$
$761$	−476.650			−0.626347			−0.313174	+	0.949696i	$0.601392\pi$
$762$	154.810	+	238.354i	0.203163	+	0.312801i
$763$		0			0
$764$	1090.87	+	485.523i	1.42784	+	0.635502i
$765$		−	37.3683i		−	0.0488475i
$766$	356.893	+	549.490i	0.465917	+	0.717350i
$767$		−	119.585i		−	0.155913i
$768$	−106.018	+	1013.61i	−0.138044	+	1.31981i
$769$	568.246			0.738941			0.369471	−	0.929242i	$-0.379539\pi$
$769$	568.246			0.738941			0.369471	+	0.929242i	$0.379539\pi$
$770$		0			0
$771$	892.621			1.15774
$772$	−537.979	+	1208.73i	−0.696864	+	1.56571i
$773$			1197.03i			1.54855i	0.632849	+	0.774275i	$0.281885\pi$
$773$			1197.03i			1.54855i	−0.632849	+	0.774275i	$0.718115\pi$
$774$	−543.111	+	352.749i	−0.701694	+	0.455748i
$775$		−	482.400i		−	0.622452i
$776$	69.3270	+	437.178i	0.0893389	+	0.563373i
$777$		0			0
$778$	−137.590	−	211.842i	−0.176852	−	0.272290i
$779$	1220.75			1.56708
$780$	−140.012	+	314.580i	−0.179503	+	0.403308i
$781$			301.422i			0.385943i
$782$	121.716	+	187.401i	0.155647	+	0.239643i
$783$		−	238.701i		−	0.304855i
$784$		0			0
$785$	92.8596			0.118292
$786$	809.902	−	526.029i	1.03041	−	0.669248i
$787$	−452.269			−0.574674			−0.287337	−	0.957830i	$-0.592770\pi$
$787$	−452.269			−0.574674			−0.287337	+	0.957830i	$0.592770\pi$
$788$	−1196.11	−	532.363i	−1.51791	−	0.675587i
$789$		−	676.619i		−	0.857565i
$790$	−161.631	+	104.979i	−0.204596	+	0.132885i
$791$		0			0
$792$	67.6144	+	426.378i	0.0853717	+	0.538356i
$793$	−254.565			−0.321015
$794$	−138.509	−	213.255i	−0.174444	−	0.268583i
$795$	−201.479			−0.253433
$796$	−46.5414	−	20.7145i	−0.0584691	−	0.0260233i
$797$		−	1047.47i		−	1.31426i	−0.753777	−	0.657130i	$-0.771770\pi$
$797$		−	1047.47i		−	1.31426i	0.753777	−	0.657130i	$-0.228230\pi$
$798$		0			0
$799$			239.355i			0.299568i
$800$	−663.257	−	177.495i	−0.829071	−	0.221869i
$801$	−720.868			−0.899960
$802$	100.888	−	65.5267i	0.125796	−	0.0817041i
$803$	110.137			0.137157
$804$	−384.037	+	862.854i	−0.477658	+	1.07320i
$805$		0			0
$806$	−433.153	+	281.332i	−0.537411	+	0.349047i
$807$		−	432.045i		−	0.535372i
$808$	−248.359	+	39.3844i	−0.307375	+	0.0487431i
$809$	−298.665			−0.369178			−0.184589	−	0.982816i	$-0.559095\pi$
$809$	−298.665			−0.369178			−0.184589	+	0.982816i	$0.559095\pi$
$810$	196.330	+	302.280i	0.242383	+	0.373185i
$811$	−633.054			−0.780584			−0.390292	−	0.920691i	$-0.627626\pi$
$811$	−633.054			−0.780584			−0.390292	+	0.920691i	$0.627626\pi$
$812$		0			0
$813$			77.0852i			0.0948158i
$814$	−391.034	−	602.057i	−0.480386	−	0.739628i
$815$		−	217.844i		−	0.267293i
$816$	−123.569	−	137.168i	−0.151433	−	0.168098i
$817$	−1420.53			−1.73871
$818$	117.031	−	76.0114i	0.143070	−	0.0929235i
$819$		0			0
$820$	−279.521	−	124.409i	−0.340879	−	0.151718i
$821$			1251.50i			1.52436i	0.647367	+	0.762178i	$0.275870\pi$
$821$			1251.50i			1.52436i	−0.647367	+	0.762178i	$0.724130\pi$
$822$	−56.7348	+	36.8491i	−0.0690205	+	0.0448286i
$823$			1226.82i			1.49066i	0.666693	+	0.745332i	$0.267709\pi$
$823$			1226.82i			1.49066i	−0.666693	+	0.745332i	$0.732291\pi$
$824$	631.993	−	100.220i	0.766981	−	0.121627i
$825$	−673.043			−0.815810
$826$		0			0
$827$	−1438.26			−1.73913			−0.869566	−	0.493816i	$-0.835602\pi$
$827$	−1438.26			−1.73913			−0.869566	+	0.493816i	$0.835602\pi$
$828$	964.765	+	429.395i	1.16518	+	0.518593i
$829$		−	626.488i		−	0.755715i	−0.925864	−	0.377858i	$-0.876661\pi$
$829$		−	626.488i		−	0.755715i	0.925864	−	0.377858i	$-0.123339\pi$
$830$	−183.434	−	282.425i	−0.221005	−	0.340271i
$831$			515.330i			0.620132i
$832$	227.431	+	699.060i	0.273354	+	0.840216i
$833$		0			0
$834$	20.4286	−	13.2683i	0.0244947	−	0.0159092i
$835$	−60.9672			−0.0730146
$836$	−385.047	+	865.124i	−0.460583	+	1.03484i
$837$			192.563i			0.230063i
$838$	−1198.90	+	778.685i	−1.43067	+	0.929219i
$839$		−	1062.37i		−	1.26624i	−0.774055	−	0.633118i	$-0.781775\pi$
$839$		−	1062.37i		−	1.26624i	0.774055	−	0.633118i	$-0.218225\pi$
$840$		0			0
$841$	64.2558			0.0764041
$842$	330.562	+	508.951i	0.392592	+	0.604455i
$843$	331.862			0.393668
$844$	195.918	−	440.188i	0.232130	−	0.521549i
$845$		−	69.7739i		−	0.0825727i
$846$	616.116	+	948.605i	0.728270	+	1.12128i
$847$		0			0
$848$	−319.588	+	287.904i	−0.376872	+	0.339509i
$849$	−115.168			−0.135652
$850$	104.308	−	67.7477i	0.122715	−	0.0797031i
$851$	−1756.07			−2.06354
$852$	−556.530	−	247.699i	−0.653204	−	0.290726i
$853$			698.388i			0.818743i	0.912368	+	0.409372i	$0.134252\pi$
$853$			698.388i			0.818743i	−0.912368	+	0.409372i	$0.865748\pi$
$854$		0			0
$855$		−	387.355i		−	0.453047i
$856$	−61.0991	−	385.292i	−0.0713774	−	0.450108i
$857$	730.324			0.852187			0.426094	−	0.904679i	$-0.359889\pi$
$857$	730.324			0.852187			0.426094	+	0.904679i	$0.359889\pi$
$858$	392.513	+	604.334i	0.457474	+	0.704352i
$859$	966.259			1.12487			0.562433	−	0.826843i	$-0.309866\pi$
$859$	966.259			1.12487			0.562433	+	0.826843i	$0.309866\pi$
$860$	325.265	+	144.768i	0.378215	+	0.168335i
$861$		0			0
$862$	470.063	+	723.734i	0.545317	+	0.839598i
$863$			294.475i			0.341222i	0.985338	+	0.170611i	$0.0545742\pi$
$863$			294.475i			0.341222i	−0.985338	+	0.170611i	$0.945426\pi$
$864$	264.756	+	70.8518i	0.306431	+	0.0820044i
$865$	390.142			0.451032
$866$	−326.858	+	212.294i	−0.377434	+	0.245143i
$867$	−1117.07			−1.28844
$868$		0			0
$869$			403.346i			0.464149i
$870$	350.330	−	227.539i	0.402678	−	0.261539i
$871$			681.253i			0.782151i
$872$	−909.192	+	144.178i	−1.04265	+	0.165342i
$873$	−378.934			−0.434059
$874$	1261.69	+	1942.57i	1.44358	+	2.22262i
$875$		0			0
$876$	−90.5075	+	203.352i	−0.103319	+	0.232137i
$877$			944.891i			1.07741i	0.842494	+	0.538706i	$0.181087\pi$
$877$			944.891i			1.07741i	−0.842494	+	0.538706i	$0.818913\pi$
$878$	−333.318	−	513.194i	−0.379634	−	0.584504i
$879$			854.382i			0.971993i
$880$	176.332	−	158.850i	0.200377	−	0.180512i
$881$	−744.098			−0.844606			−0.422303	−	0.906455i	$-0.638778\pi$
$881$	−744.098			−0.844606			−0.422303	+	0.906455i	$0.638778\pi$
$882$		0			0
$883$	23.9032			0.0270704			0.0135352	−	0.999908i	$-0.495691\pi$
$883$	23.9032			0.0270704			0.0135352	+	0.999908i	$0.495691\pi$
$884$	−121.663	−	54.1494i	−0.137628	−	0.0612550i
$885$		−	78.0246i		−	0.0881634i
$886$	419.649	−	272.561i	0.473644	−	0.307631i
$887$			947.312i			1.06800i	0.845486	+	0.533998i	$0.179311\pi$
$887$			947.312i			1.06800i	−0.845486	+	0.533998i	$0.820689\pi$
$888$	1432.95	−	227.235i	1.61368	−	0.255895i
$889$		0			0
$890$	215.861	+	332.351i	0.242541	+	0.373428i
$891$	754.332			0.846613
$892$	−1362.93	−	606.610i	−1.52795	−	0.680057i
$893$			2481.12i			2.77840i
$894$	−137.584	−	211.831i	−0.153897	−	0.236948i
$895$		−	327.874i		−	0.366339i
$896$		0			0
$897$	1762.71			1.96512
$898$	−1155.11	+	750.238i	−1.28631	+	0.835454i
$899$	626.607			0.697005
$900$	239.003	−	536.992i	0.265559	−	0.596658i
$901$		−	77.9215i		−	0.0864834i
$902$	−536.983	+	348.769i	−0.595325	+	0.386662i
$903$		0			0
$904$	69.8619	+	440.551i	0.0772809	+	0.487335i
$905$	−384.493			−0.424854
$906$	1099.81	+	1693.33i	1.21392	+	1.86902i
$907$	551.023			0.607523			0.303761	−	0.952748i	$-0.401757\pi$
$907$	551.023			0.607523			0.303761	+	0.952748i	$0.401757\pi$
$908$	−119.426	+	268.326i	−0.131526	+	0.295513i
$909$		−	215.271i		−	0.236822i
$910$		0			0
$911$		−	827.652i		−	0.908509i	−0.890872	−	0.454254i	$-0.849906\pi$
$911$		−	827.652i		−	0.908509i	0.890872	−	0.454254i	$-0.150094\pi$
$912$	−1280.90	−	1421.86i	−1.40450	−	1.55906i
$913$	−704.784			−0.771943
$914$	1349.40	−	876.429i	1.47636	−	0.958894i
$915$	−166.093			−0.181523
$916$	−1551.11	−	690.366i	−1.69336	−	0.753675i
$917$		0			0
$918$	−41.6372	+	27.0433i	−0.0453565	+	0.0294589i
$919$			356.993i			0.388458i	0.980956	+	0.194229i	$0.0622205\pi$
$919$			356.993i			0.388458i	−0.980956	+	0.194229i	$0.937779\pi$
$920$	−90.9255	−	573.379i	−0.0988321	−	0.623238i
$921$	479.880			0.521043
$922$	755.658	+	1163.45i	0.819586	+	1.26188i
$923$	−439.400			−0.476056
$924$		0			0
$925$			977.438i			1.05669i
$926$	349.904	+	538.730i	0.377866	+	0.581782i
$927$			547.794i			0.590932i
$928$	230.555	−	861.528i	0.248442	−	0.928371i
$929$	−969.745			−1.04386			−0.521930	−	0.852988i	$-0.674788\pi$
$929$	−969.745			−1.04386			−0.521930	+	0.852988i	$0.674788\pi$
$930$	−282.615	+	183.558i	−0.303887	+	0.197374i
$931$		0			0
$932$	−135.672	+	304.827i	−0.145570	+	0.327068i
$933$		−	1295.27i		−	1.38829i
$934$	−1261.10	+	819.080i	−1.35021	+	0.876959i
$935$			42.9930i			0.0459819i
$936$	−621.556	+	98.5654i	−0.664056	+	0.105305i
$937$	−1287.55			−1.37412			−0.687061	−	0.726600i	$-0.741099\pi$
$937$	−1287.55			−1.37412			−0.687061	+	0.726600i	$0.741099\pi$
$938$		0			0
$939$	−1818.36			−1.93649
$940$	252.854	−	568.112i	0.268993	−	0.604374i
$941$			456.796i			0.485436i	0.970097	+	0.242718i	$0.0780390\pi$
$941$			456.796i			0.485436i	−0.970097	+	0.242718i	$0.921961\pi$
$942$	213.926	+	329.372i	0.227098	+	0.349651i
$943$			1566.27i			1.66094i
$944$	−111.493	−	123.763i	−0.118107	−	0.131105i
$945$		0			0
$946$	624.860	−	405.845i	0.660529	−	0.429012i
$947$	−1147.85			−1.21209			−0.606045	−	0.795430i	$-0.707245\pi$
$947$	−1147.85			−1.21209			−0.606045	+	0.795430i	$0.707245\pi$
$948$	−744.717	−	331.457i	−0.785566	−	0.349638i
$949$			160.554i			0.169182i
$950$	1081.24	−	702.262i	1.13815	−	0.739224i
$951$		−	482.582i		−	0.507447i
$952$		0			0
$953$	873.170			0.916232			0.458116	−	0.888892i	$-0.348524\pi$
$953$	873.170			0.916232			0.458116	+	0.888892i	$0.348524\pi$
$954$	−200.576	−	308.817i	−0.210247	−	0.323707i
$955$	561.952			0.588432
$956$	−411.342	−	183.079i	−0.430274	−	0.191505i
$957$		−	874.240i		−	0.913522i
$958$	786.688	+	1211.23i	0.821177	+	1.26433i
$959$		0			0
$960$	148.389	+	456.108i	0.154572	+	0.475113i
$961$	455.510			0.473996
$962$	877.653	−	570.033i	0.912321	−	0.592550i
$963$	333.961			0.346792
$964$	−456.119	+	1024.81i	−0.473152	+	1.06308i
$965$			622.666i			0.645249i
$966$		0			0
$967$			449.047i			0.464372i	0.972671	+	0.232186i	$0.0745878\pi$
$967$			449.047i			0.464372i	−0.972671	+	0.232186i	$0.925412\pi$
$968$	73.8177	+	465.497i	0.0762580	+	0.480885i
$969$	346.677			0.357768
$970$	113.470	+	174.705i	0.116980	+	0.180108i
$971$	1237.86			1.27483			0.637414	−	0.770521i	$-0.280004\pi$
$971$	1237.86			1.27483			0.637414	+	0.770521i	$0.280004\pi$
$972$	−494.512	+	1111.07i	−0.508757	+	1.14308i
$973$		0			0
$974$	−52.1041	−	80.2222i	−0.0534950	−	0.0823636i
$975$		−	981.134i		−	1.00629i
$976$	−263.458	+	237.339i	−0.269936	+	0.243175i
$977$	1706.89			1.74707			0.873536	−	0.486760i	$-0.161821\pi$
$977$	1706.89			1.74707			0.873536	+	0.486760i	$0.161821\pi$
$978$	772.689	−	501.860i	0.790071	−	0.513149i
$979$	829.373			0.847164
$980$		0			0
$981$		−	788.063i		−	0.803326i
$982$	74.5924	−	48.4475i	0.0759596	−	0.0493356i
$983$			1152.15i			1.17208i	0.810283	+	0.586039i	$0.199313\pi$
$983$			1152.15i			1.17208i	−0.810283	+	0.586039i	$0.800687\pi$
$984$	−202.674	−	1278.06i	−0.205969	−	1.29885i
$985$	−616.165			−0.625548
$986$	87.9999	+	135.489i	0.0892494	+	0.137413i
$987$		0			0
$988$	−1261.14	−	561.305i	−1.27646	−	0.568123i
$989$		−	1822.59i		−	1.84286i
$990$	110.667	+	170.389i	0.111785	+	0.172110i
$991$		−	412.818i		−	0.416567i	−0.978068	−	0.208283i	$-0.933212\pi$
$991$		−	412.818i		−	0.416567i	0.978068	−	0.208283i	$-0.0667877\pi$
$992$	−185.991	+	695.003i	−0.187491	+	0.700608i
$993$	482.375			0.485776
$994$		0			0
$995$	−23.9753			−0.0240958
$996$	579.169	−	1301.28i	0.581495	−	1.30650i
$997$		−	301.152i		−	0.302058i	−0.988529	−	0.151029i	$-0.951741\pi$
$997$		−	301.152i		−	0.302058i	0.988529	−	0.151029i	$-0.0482587\pi$
$998$	−841.273	+	546.405i	−0.842959	+	0.547500i
$999$		−	390.170i		−	0.390561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.i.99.5		6
4.3	odd	2		1568.3.g.l.687.1		6
7.2	even	3		392.3.k.l.67.1		12
7.3	odd	6		56.3.k.d.51.3	yes	12
7.4	even	3		392.3.k.l.275.3		12
7.5	odd	6		56.3.k.d.11.1	✓	12
7.6	odd	2		392.3.g.j.99.5		6
8.3	odd	2	inner	392.3.g.i.99.6		6
8.5	even	2		1568.3.g.l.687.2		6
28.3	even	6		224.3.o.d.79.1		12
28.19	even	6		224.3.o.d.207.2		12
28.27	even	2		1568.3.g.j.687.6		6
56.3	even	6		56.3.k.d.51.1	yes	12
56.5	odd	6		224.3.o.d.207.1		12
56.11	odd	6		392.3.k.l.275.1		12
56.13	odd	2		1568.3.g.j.687.5		6
56.19	even	6		56.3.k.d.11.3	yes	12
56.27	even	2		392.3.g.j.99.6		6
56.45	odd	6		224.3.o.d.79.2		12
56.51	odd	6		392.3.k.l.67.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.1	✓	12	7.5	odd	6
56.3.k.d.11.3	yes	12	56.19	even	6
56.3.k.d.51.1	yes	12	56.3	even	6
56.3.k.d.51.3	yes	12	7.3	odd	6
224.3.o.d.79.1		12	28.3	even	6
224.3.o.d.79.2		12	56.45	odd	6
224.3.o.d.207.1		12	56.5	odd	6
224.3.o.d.207.2		12	28.19	even	6
392.3.g.i.99.5		6	1.1	even	1	trivial
392.3.g.i.99.6		6	8.3	odd	2	inner
392.3.g.j.99.5		6	7.6	odd	2
392.3.g.j.99.6		6	56.27	even	2
392.3.k.l.67.1		12	7.2	even	3
392.3.k.l.67.3		12	56.51	odd	6
392.3.k.l.275.1		12	56.11	odd	6
392.3.k.l.275.3		12	7.4	even	3
1568.3.g.j.687.5		6	56.13	odd	2
1568.3.g.j.687.6		6	28.27	even	2
1568.3.g.l.687.1		6	4.3	odd	2
1568.3.g.l.687.2		6	8.5	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67727 - 1.08938i) q^{2} +3.98103 q^{3} +(1.62649 - 3.65439i) q^{4} -1.88252i q^{5} +(6.67727 - 4.33687i) q^{6} +(-1.25297 - 7.90127i) q^{8} +6.84860 q^{9} +O(q^{10})\)	\(q+(1.67727 - 1.08938i) q^{2} +3.98103 q^{3} +(1.62649 - 3.65439i) q^{4} -1.88252i q^{5} +(6.67727 - 4.33687i) q^{6} +(-1.25297 - 7.90127i) q^{8} +6.84860 q^{9} +(-2.05079 - 3.15750i) q^{10} -7.87946 q^{11} +(6.47509 - 14.5482i) q^{12} -11.4863i q^{13} -7.49437i q^{15} +(-10.7091 - 11.8876i) q^{16} +2.89843 q^{17} +(11.4870 - 7.46076i) q^{18} +30.0447 q^{19} +(-6.87946 - 3.06189i) q^{20} +(-13.2160 + 8.58375i) q^{22} +38.5483i q^{23} +(-4.98812 - 31.4552i) q^{24} +21.4561 q^{25} +(-12.5130 - 19.2657i) q^{26} -8.56478 q^{27} +27.8701i q^{29} +(-8.16424 - 12.5701i) q^{30} -22.4831i q^{31} +(-30.9122 - 8.27246i) q^{32} -31.3684 q^{33} +(4.86145 - 3.15750i) q^{34} +(11.1392 - 25.0274i) q^{36} +45.5552i q^{37} +(50.3931 - 32.7302i) q^{38} -45.7274i q^{39} +(-14.8743 + 2.35874i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(-12.8158 + 28.7946i) q^{44} -12.8926i q^{45} +(41.9939 + 64.6560i) q^{46} +82.5809i q^{47} +(-42.6332 - 47.3250i) q^{48} +(35.9878 - 23.3739i) q^{50} +11.5387 q^{51} +(-41.9755 - 18.6824i) q^{52} -26.8841i q^{53} +(-14.3655 + 9.33033i) q^{54} +14.8332i q^{55} +119.609 q^{57} +(30.3613 + 46.7458i) q^{58} +10.4111 q^{59} +(-27.3873 - 12.1895i) q^{60} -22.1624i q^{61} +(-24.4927 - 37.7103i) q^{62} +(-60.8601 + 19.8001i) q^{64} -21.6233 q^{65} +(-52.6133 + 34.1722i) q^{66} -59.3099 q^{67} +(4.71425 - 10.5920i) q^{68} +153.462i q^{69} -38.2541i q^{71} +(-8.58110 - 54.1127i) q^{72} -13.9778 q^{73} +(49.6271 + 76.4085i) q^{74} +85.4175 q^{75} +(48.8672 - 109.795i) q^{76} +(-49.8147 - 76.6974i) q^{78} -51.1895i q^{79} +(-22.3787 + 20.1601i) q^{80} -95.7341 q^{81} +(68.1497 - 44.2631i) q^{82} +89.4458 q^{83} -5.45635i q^{85} +(-79.3024 + 51.5067i) q^{86} +110.952i q^{87} +(9.87273 + 62.2577i) q^{88} -105.258 q^{89} +(-14.0450 - 21.6245i) q^{90} +(140.870 + 62.6982i) q^{92} -89.5059i q^{93} +(89.9623 + 138.511i) q^{94} -56.5597i q^{95} +(-123.063 - 32.9329i) q^{96} -55.3301 q^{97} -53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9} - 6 q^{10} - 30 q^{11} + 32 q^{12} - 16 q^{16} + 30 q^{17} + 16 q^{18} + 78 q^{19} - 24 q^{20} + 12 q^{22} - 76 q^{24} + 92 q^{25} - 128 q^{26} - 78 q^{27} + 16 q^{30} - 112 q^{32} - 78 q^{33} - 38 q^{34} - 124 q^{36} + 80 q^{38} + 44 q^{40} + 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} - 88 q^{48} + 24 q^{50} - 10 q^{51} + 132 q^{52} - 36 q^{54} + 166 q^{57} - 4 q^{58} - 110 q^{59} - 84 q^{60} + 48 q^{62} - 80 q^{64} + 32 q^{65} - 138 q^{66} - 434 q^{67} + 96 q^{68} + 328 q^{72} + 102 q^{73} + 34 q^{74} - 60 q^{75} + 84 q^{76} + 360 q^{78} - 256 q^{80} + 82 q^{81} - 24 q^{82} + 268 q^{83} - 240 q^{86} + 204 q^{88} + 214 q^{89} - 220 q^{90} + 80 q^{92} - 16 q^{94} + 48 q^{96} + 76 q^{97} + 252 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9 - 6 * q^10 - 30 * q^11 + 32 * q^12 - 16 * q^16 + 30 * q^17 + 16 * q^18 + 78 * q^19 - 24 * q^20 + 12 * q^22 - 76 * q^24 + 92 * q^25 - 128 * q^26 - 78 * q^27 + 16 * q^30 - 112 * q^32 - 78 * q^33 - 38 * q^34 - 124 * q^36 + 80 * q^38 + 44 * q^40 + 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 - 88 * q^48 + 24 * q^50 - 10 * q^51 + 132 * q^52 - 36 * q^54 + 166 * q^57 - 4 * q^58 - 110 * q^59 - 84 * q^60 + 48 * q^62 - 80 * q^64 + 32 * q^65 - 138 * q^66 - 434 * q^67 + 96 * q^68 + 328 * q^72 + 102 * q^73 + 34 * q^74 - 60 * q^75 + 84 * q^76 + 360 * q^78 - 256 * q^80 + 82 * q^81 - 24 * q^82 + 268 * q^83 - 240 * q^86 + 204 * q^88 + 214 * q^89 - 220 * q^90 + 80 * q^92 - 16 * q^94 + 48 * q^96 + 76 * q^97 + 252 * q^99

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