LMFDB - Embedded newform 392.3.g.m.99.7

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:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.7
Root			$1.85837 + 0.739226i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.m.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85837 - 0.739226i) q^{2} -0.0974366 q^{3} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} +(-0.181073 + 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} -8.99051 q^{9} +O(q^{10})$	\(q+(1.85837 - 0.739226i) q^{2} -0.0974366 q^{3} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} +(-0.181073 + 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} -8.99051 q^{9} +(-2.56177 - 6.44013i) q^{10} -2.92866 q^{11} +(-0.283257 + 0.267708i) q^{12} -19.1586i q^{13} +0.337664i q^{15} +(0.902343 - 15.9745i) q^{16} +14.3897 q^{17} +(-16.7077 + 6.64602i) q^{18} -8.09744 q^{19} +(-9.52143 - 10.0744i) q^{20} +(-5.44254 + 2.16494i) q^{22} -16.7598i q^{23} +(-0.328500 + 0.706892i) q^{24} +12.9905 q^{25} +(-14.1625 - 35.6038i) q^{26} +1.75293 q^{27} +27.1649i q^{29} +(0.249610 + 0.627505i) q^{30} +44.8923i q^{31} +(-10.1319 - 30.3537i) q^{32} +0.285359 q^{33} +(26.7415 - 10.6373i) q^{34} +(-26.1362 + 24.7015i) q^{36} -39.5687i q^{37} +(-15.0480 + 5.98584i) q^{38} +1.86675i q^{39} +(-25.1416 - 11.6836i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(-8.51388 + 8.04653i) q^{44} +31.1563i q^{45} +(-12.3893 - 31.1459i) q^{46} -46.2793i q^{47} +(-0.0879212 + 1.55650i) q^{48} +(24.1412 - 9.60292i) q^{50} -1.40209 q^{51} +(-52.6385 - 55.6957i) q^{52} -9.69424i q^{53} +(3.25760 - 1.29581i) q^{54} +10.1492i q^{55} +0.788986 q^{57} +(20.0810 + 50.4825i) q^{58} +114.554 q^{59} +(0.927735 + 0.981619i) q^{60} -7.48032i q^{61} +(33.1855 + 83.4265i) q^{62} +(-41.2671 - 48.9186i) q^{64} -66.3935 q^{65} +(0.530302 - 0.210944i) q^{66} -12.0590 q^{67} +(41.8323 - 39.5360i) q^{68} +1.63302i q^{69} +129.187i q^{71} +(-30.3108 + 65.2252i) q^{72} +18.2854 q^{73} +(-29.2502 - 73.5334i) q^{74} -1.26575 q^{75} +(-23.5400 + 22.2478i) q^{76} +(1.37995 + 3.46911i) q^{78} +42.6168i q^{79} +(-55.3593 - 3.12704i) q^{80} +80.7438 q^{81} +(-85.2558 + 33.9132i) q^{82} +109.670 q^{83} -49.8673i q^{85} +(113.423 - 45.1174i) q^{86} -2.64685i q^{87} +(-9.87374 + 21.2471i) q^{88} +80.9162 q^{89} +(23.0316 + 57.9001i) q^{90} +(-46.0478 - 48.7223i) q^{92} -4.37415i q^{93} +(-34.2109 - 86.0041i) q^{94} +28.0614i q^{95} +(0.987218 + 2.95756i) q^{96} -162.086 q^{97} +26.3301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9} - 16 q^{10} - 32 q^{11} - 30 q^{12} - 71 q^{16} + 80 q^{17} - 29 q^{18} - 56 q^{19} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 q^{64} - 72 q^{65} + 276 q^{66} + 304 q^{67} + 190 q^{68} - 209 q^{72} + 112 q^{73} + 8 q^{74} - 72 q^{75} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9 - 16 * q^10 - 32 * q^11 - 30 * q^12 - 71 * q^16 + 80 * q^17 - 29 * q^18 - 56 * q^19 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * q^64 - 72 * q^65 + 276 * q^66 + 304 * q^67 + 190 * q^68 - 209 * q^72 + 112 * q^73 + 8 * q^74 - 72 * q^75 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * 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 $

$2$	1.85837	−	0.739226i	0.929186	−	0.369613i
$2$	1.85837	−	0.739226i	0.929186	−	0.369613i
$3$	−0.0974366			−0.0324789			−0.0162394	−	0.999868i	$-0.505169\pi$
$3$	−0.0974366			−0.0324789			−0.0162394	+	0.999868i	$0.505169\pi$
$4$	2.90709	−	2.74751i	0.726772	−	0.686878i
$5$		−	3.46547i		−	0.693094i	−0.938033	−	0.346547i	$-0.887354\pi$
$5$		−	3.46547i		−	0.693094i	0.938033	−	0.346547i	$-0.112646\pi$
$6$	−0.181073	+	0.0720276i	−0.0301789	+	0.0120046i
$7$		0			0
$7$		0			0
$8$	3.37142	−	7.25490i	0.421428	−	0.906862i
$9$	−8.99051			−0.998945
$10$	−2.56177	−	6.44013i	−0.256177	−	0.644013i
$11$	−2.92866			−0.266242			−0.133121	−	0.991100i	$-0.542500\pi$
$11$	−2.92866			−0.266242			−0.133121	+	0.991100i	$0.542500\pi$
$12$	−0.283257	+	0.267708i	−0.0236047	+	0.0223090i
$13$		−	19.1586i		−	1.47374i	−0.676036	−	0.736869i	$-0.736304\pi$
$13$		−	19.1586i		−	1.47374i	0.676036	−	0.736869i	$-0.263696\pi$
$14$		0			0
$15$			0.337664i			0.0225109i
$16$	0.902343	−	15.9745i	0.0563964	−	0.998408i
$17$	14.3897			0.846456			0.423228	−	0.906023i	$-0.360897\pi$
$17$	14.3897			0.846456			0.423228	+	0.906023i	$0.360897\pi$
$18$	−16.7077	+	6.64602i	−0.928206	+	0.369223i
$19$	−8.09744			−0.426181			−0.213090	−	0.977032i	$-0.568353\pi$
$19$	−8.09744			−0.426181			−0.213090	+	0.977032i	$0.568353\pi$
$20$	−9.52143	−	10.0744i	−0.476071	−	0.503722i
$21$		0			0
$22$	−5.44254	+	2.16494i	−0.247388	+	0.0984064i
$23$		−	16.7598i		−	0.728687i	−0.931265	−	0.364344i	$-0.881293\pi$
$23$		−	16.7598i		−	0.728687i	0.931265	−	0.364344i	$-0.118707\pi$
$24$	−0.328500	+	0.706892i	−0.0136875	+	0.0294538i
$25$	12.9905			0.519620
$26$	−14.1625	−	35.6038i	−0.544713	−	1.36938i
$27$	1.75293			0.0649234
$28$		0			0
$29$			27.1649i			0.936720i	0.883538	+	0.468360i	$0.155155\pi$
$29$			27.1649i			0.936720i	−0.883538	+	0.468360i	$0.844845\pi$
$30$	0.249610	+	0.627505i	0.00832032	+	0.0209168i
$31$			44.8923i			1.44814i	0.689728	+	0.724069i	$0.257730\pi$
$31$			44.8923i			1.44814i	−0.689728	+	0.724069i	$0.742270\pi$
$32$	−10.1319	−	30.3537i	−0.316622	−	0.948552i
$33$	0.285359			0.00864723
$34$	26.7415	−	10.6373i	0.786515	−	0.312861i
$35$		0			0
$36$	−26.1362	+	24.7015i	−0.726006	+	0.686154i
$37$		−	39.5687i		−	1.06943i	−0.845034	−	0.534713i	$-0.820420\pi$
$37$		−	39.5687i		−	1.06943i	0.845034	−	0.534713i	$-0.179580\pi$
$38$	−15.0480	+	5.98584i	−0.396001	+	0.157522i
$39$			1.86675i			0.0478653i
$40$	−25.1416	−	11.6836i	−0.628541	−	0.292089i
$41$	−45.8766			−1.11894			−0.559471	−	0.828850i	$-0.688996\pi$
$41$	−45.8766			−1.11894			−0.559471	+	0.828850i	$0.688996\pi$
$42$		0			0
$43$	61.0334			1.41938			0.709690	−	0.704514i	$-0.248835\pi$
$43$	61.0334			1.41938			0.709690	+	0.704514i	$0.248835\pi$
$44$	−8.51388	+	8.04653i	−0.193497	+	0.182876i
$45$			31.1563i			0.692363i
$46$	−12.3893	−	31.1459i	−0.269332	−	0.677086i
$47$		−	46.2793i		−	0.984666i	−0.870407	−	0.492333i	$-0.836144\pi$
$47$		−	46.2793i		−	0.984666i	0.870407	−	0.492333i	$-0.163856\pi$
$48$	−0.0879212	+	1.55650i	−0.00183169	+	0.0324272i
$49$		0			0
$50$	24.1412	−	9.60292i	0.482824	−	0.192058i
$51$	−1.40209			−0.0274919
$52$	−52.6385	−	55.6957i	−1.01228	−	1.07107i
$53$		−	9.69424i		−	0.182910i	−0.995809	−	0.0914551i	$-0.970848\pi$
$53$		−	9.69424i		−	0.182910i	0.995809	−	0.0914551i	$-0.0291518\pi$
$54$	3.25760	−	1.29581i	0.0603259	−	0.0239965i
$55$			10.1492i			0.184531i
$56$		0			0
$57$	0.788986			0.0138419
$58$	20.0810	+	50.4825i	0.346224	+	0.870387i
$59$	114.554			1.94159			0.970796	−	0.239907i	$-0.0771170\pi$
$59$	114.554			1.94159			0.970796	+	0.239907i	$0.0771170\pi$
$60$	0.927735	+	0.981619i	0.0154623	+	0.0163603i
$61$		−	7.48032i		−	0.122628i	−0.998119	−	0.0613141i	$-0.980471\pi$
$61$		−	7.48032i		−	0.122628i	0.998119	−	0.0613141i	$-0.0195291\pi$
$62$	33.1855	+	83.4265i	0.535251	+	1.34559i
$63$		0			0
$64$	−41.2671	−	48.9186i	−0.644798	−	0.764353i
$65$	−66.3935			−1.02144
$66$	0.530302	−	0.210944i	0.00803488	−	0.00319613i
$67$	−12.0590			−0.179985			−0.0899925	−	0.995942i	$-0.528684\pi$
$67$	−12.0590			−0.179985			−0.0899925	+	0.995942i	$0.528684\pi$
$68$	41.8323	−	39.5360i	0.615181	−	0.581412i
$69$			1.63302i			0.0236669i
$70$		0			0
$71$			129.187i			1.81953i	0.415124	+	0.909765i	$0.363738\pi$
$71$			129.187i			1.81953i	−0.415124	+	0.909765i	$0.636262\pi$
$72$	−30.3108	+	65.2252i	−0.420983	+	0.905905i
$73$	18.2854			0.250484			0.125242	−	0.992126i	$-0.460029\pi$
$73$	18.2854			0.250484			0.125242	+	0.992126i	$0.460029\pi$
$74$	−29.2502	−	73.5334i	−0.395273	−	0.993695i
$75$	−1.26575			−0.0168767
$76$	−23.5400	+	22.2478i	−0.309737	+	0.292734i
$77$		0			0
$78$	1.37995	+	3.46911i	0.0176916	+	0.0444758i
$79$			42.6168i			0.539454i	0.962937	+	0.269727i	$0.0869334\pi$
$79$			42.6168i			0.539454i	−0.962937	+	0.269727i	$0.913067\pi$
$80$	−55.3593	−	3.12704i	−0.691991	−	0.0390880i
$81$	80.7438			0.996836
$82$	−85.2558	+	33.9132i	−1.03971	+	0.413576i
$83$	109.670			1.32133			0.660663	−	0.750683i	$-0.270275\pi$
$83$	109.670			1.32133			0.660663	+	0.750683i	$0.270275\pi$
$84$		0			0
$85$		−	49.8673i		−	0.586674i
$86$	113.423	−	45.1174i	1.31887	−	0.524622i
$87$		−	2.64685i		−	0.0304236i
$88$	−9.87374	+	21.2471i	−0.112202	+	0.241445i
$89$	80.9162			0.909170			0.454585	−	0.890703i	$-0.349788\pi$
$89$	80.9162			0.909170			0.454585	+	0.890703i	$0.349788\pi$
$90$	23.0316	+	57.9001i	0.255906	+	0.643334i
$91$		0			0
$92$	−46.0478	−	48.7223i	−0.500519	−	0.529590i
$93$		−	4.37415i		−	0.0470339i
$94$	−34.2109	−	86.0041i	−0.363945	−	0.914937i
$95$			28.0614i			0.295384i
$96$	0.987218	+	2.95756i	0.0102835	+	0.0308079i
$97$	−162.086			−1.67099			−0.835495	−	0.549498i	$-0.814819\pi$
$97$	−162.086			−1.67099			−0.835495	+	0.549498i	$0.814819\pi$
$98$		0			0
$99$	26.3301			0.265961
$100$	37.7646	−	35.6916i	0.377646	−	0.356916i
$101$			106.827i			1.05769i	0.848717	+	0.528847i	$0.177375\pi$
$101$			106.827i			1.05769i	−0.848717	+	0.528847i	$0.822625\pi$
$102$	−2.60560	+	1.03646i	−0.0255451	+	0.0101614i
$103$			126.626i			1.22938i	0.788768	+	0.614691i	$0.210719\pi$
$103$			126.626i			1.22938i	−0.788768	+	0.614691i	$0.789281\pi$
$104$	−138.994	−	64.5916i	−1.33648	−	0.621074i
$105$		0			0
$106$	−7.16623	−	18.0155i	−0.0676060	−	0.169958i
$107$	87.0191			0.813263			0.406632	−	0.913592i	$-0.366703\pi$
$107$	87.0191			0.813263			0.406632	+	0.913592i	$0.366703\pi$
$108$	5.09593	−	4.81621i	0.0471846	−	0.0445945i
$109$			189.921i			1.74240i	0.490930	+	0.871199i	$0.336657\pi$
$109$			189.921i			1.74240i	−0.490930	+	0.871199i	$0.663343\pi$
$110$	7.50254	+	18.8610i	0.0682050	+	0.171463i
$111$			3.85544i			0.0347337i
$112$		0			0
$113$	−40.1848			−0.355617			−0.177809	−	0.984065i	$-0.556901\pi$
$113$	−40.1848			−0.355617			−0.177809	+	0.984065i	$0.556901\pi$
$114$	1.46623	−	0.583239i	0.0128617	−	0.00511613i
$115$	−58.0806			−0.505049
$116$	74.6359	+	78.9708i	0.643413	+	0.680783i
$117$			172.245i			1.47218i
$118$	212.884	−	84.6812i	1.80410	−	0.717638i
$119$		0			0
$120$	2.44971	+	1.13841i	0.0204143	+	0.00948672i
$121$	−112.423			−0.929115
$122$	−5.52964	−	13.9012i	−0.0453249	−	0.113944i
$123$	4.47006			0.0363420
$124$	123.342	+	130.506i	0.994695	+	1.05247i
$125$		−	131.655i		−	1.05324i
$126$		0			0
$127$		−	153.657i		−	1.20989i	−0.796266	−	0.604947i	$-0.793194\pi$
$127$		−	153.657i		−	1.20989i	0.796266	−	0.604947i	$-0.206806\pi$
$128$	−112.851	−	60.4033i	−0.881652	−	0.471901i
$129$	−5.94688			−0.0460999
$130$	−123.384	+	49.0798i	−0.949107	+	0.377537i
$131$	−61.8649			−0.472251			−0.236126	−	0.971723i	$-0.575878\pi$
$131$	−61.8649			−0.472251			−0.236126	+	0.971723i	$0.575878\pi$
$132$	0.829563	−	0.784026i	0.00628457	−	0.00593959i
$133$		0			0
$134$	−22.4101	+	8.91433i	−0.167240	+	0.0665248i
$135$		−	6.07474i		−	0.0449981i
$136$	48.5139	−	104.396i	0.356720	−	0.767619i
$137$	105.943			0.773307			0.386653	−	0.922225i	$-0.373631\pi$
$137$	105.943			0.773307			0.386653	+	0.922225i	$0.373631\pi$
$138$	1.20717	+	3.03475i	0.00874760	+	0.0219910i
$139$	185.384			1.33370			0.666848	−	0.745194i	$-0.267643\pi$
$139$	185.384			1.33370			0.666848	+	0.745194i	$0.267643\pi$
$140$		0			0
$141$			4.50930i			0.0319808i
$142$	95.4981	+	240.077i	0.672522	+	1.69068i
$143$			56.1090i			0.392371i
$144$	−8.11252	+	143.619i	−0.0563369	+	0.997355i
$145$	94.1392			0.649236
$146$	33.9810	−	13.5170i	0.232747	−	0.0925823i
$147$		0			0
$148$	−108.716	−	115.030i	−0.734565	−	0.777229i
$149$		−	47.4096i		−	0.318185i	−0.987264	−	0.159093i	$-0.949143\pi$
$149$		−	47.4096i		−	0.318185i	0.987264	−	0.159093i	$-0.0508568\pi$
$150$	−2.35223	+	0.935675i	−0.0156816	+	0.00623784i
$151$		−	114.576i		−	0.758780i	−0.925237	−	0.379390i	$-0.876134\pi$
$151$		−	114.576i		−	0.758780i	0.925237	−	0.379390i	$-0.123866\pi$
$152$	−27.2999	+	58.7461i	−0.179604	+	0.386487i
$153$	−129.371			−0.845563
$154$		0			0
$155$	155.573			1.00370
$156$	5.12891	+	5.42680i	0.0328776	+	0.0347872i
$157$		−	294.095i		−	1.87322i	−0.350378	−	0.936608i	$-0.613947\pi$
$157$		−	294.095i		−	1.87322i	0.350378	−	0.936608i	$-0.386053\pi$
$158$	31.5035	+	79.1979i	0.199389	+	0.501253i
$159$			0.944573i			0.00594071i
$160$	−105.190	+	35.1118i	−0.657436	+	0.219449i
$161$		0			0
$162$	150.052	−	59.6879i	0.926246	−	0.368444i
$163$	171.021			1.04921			0.524603	−	0.851347i	$-0.324214\pi$
$163$	171.021			1.04921			0.524603	+	0.851347i	$0.324214\pi$
$164$	−133.367	+	126.047i	−0.813216	+	0.768577i
$165$		−	0.988902i		−	0.00599335i
$166$	203.808	−	81.0709i	1.22776	−	0.488379i
$167$			120.657i			0.722499i	0.932469	+	0.361249i	$0.117650\pi$
$167$			120.657i			0.722499i	−0.932469	+	0.361249i	$0.882350\pi$
$168$		0			0
$169$	−198.052			−1.17190
$170$	−36.8632	−	92.6719i	−0.216842	−	0.545129i
$171$	72.8001			0.425731
$172$	177.429	−	167.690i	1.03157	−	0.974942i
$173$		−	108.339i		−	0.626236i	−0.949714	−	0.313118i	$-0.898626\pi$
$173$		−	108.339i		−	0.626236i	0.949714	−	0.313118i	$-0.101374\pi$
$174$	−1.95662	−	4.91884i	−0.0112450	−	0.0282692i
$175$		0			0
$176$	−2.64266	+	46.7840i	−0.0150151	+	0.265818i
$177$	−11.1617			−0.0630607
$178$	150.372	−	59.8153i	0.844788	−	0.336041i
$179$	−161.438			−0.901886			−0.450943	−	0.892553i	$-0.648912\pi$
$179$	−161.438			−0.901886			−0.450943	+	0.892553i	$0.648912\pi$
$180$	85.6025	+	90.5743i	0.475569	+	0.503191i
$181$		−	7.14696i		−	0.0394860i	−0.999805	−	0.0197430i	$-0.993715\pi$
$181$		−	7.14696i		−	0.0394860i	0.999805	−	0.0197430i	$-0.00628479\pi$
$182$		0			0
$183$			0.728856i			0.00398282i
$184$	−121.591	−	56.5043i	−0.660819	−	0.307089i
$185$	−137.124			−0.741212
$186$	−3.23348	−	8.12879i	−0.0173843	−	0.0437032i
$187$	−42.1427			−0.225362
$188$	−127.153	−	134.538i	−0.676346	−	0.715628i
$189$		0			0
$190$	20.7437	+	52.1486i	0.109178	+	0.274466i
$191$			73.2983i			0.383761i	0.981418	+	0.191880i	$0.0614586\pi$
$191$			73.2983i			0.383761i	−0.981418	+	0.191880i	$0.938541\pi$
$192$	4.02092	+	4.76646i	0.0209423	+	0.0248253i
$193$	−85.0705			−0.440780			−0.220390	−	0.975412i	$-0.570733\pi$
$193$	−85.0705			−0.440780			−0.220390	+	0.975412i	$0.570733\pi$
$194$	−301.216	+	119.818i	−1.55266	+	0.617620i
$195$	6.46916			0.0331752
$196$		0			0
$197$		−	140.460i		−	0.712996i	−0.934296	−	0.356498i	$-0.883971\pi$
$197$		−	140.460i		−	0.712996i	0.934296	−	0.356498i	$-0.116029\pi$
$198$	48.9312	−	19.4639i	0.247127	−	0.0983026i
$199$		−	143.082i		−	0.719006i	−0.933144	−	0.359503i	$-0.882946\pi$
$199$		−	143.082i		−	0.719006i	0.933144	−	0.359503i	$-0.117054\pi$
$200$	43.7965	−	94.2448i	0.218982	−	0.471224i
$201$	1.17499			0.00584571
$202$	78.9694	+	198.524i	0.390937	+	0.982794i
$203$		0			0
$204$	−4.07599	+	3.85225i	−0.0199804	+	0.0188836i
$205$			158.984i			0.775532i
$206$	93.6055	+	235.319i	0.454396	+	1.14232i
$207$			150.679i			0.727919i
$208$	−306.050	−	17.2876i	−1.47139	−	0.0831135i
$209$	23.7146			0.113467
$210$		0			0
$211$	−111.955			−0.530591			−0.265295	−	0.964167i	$-0.585469\pi$
$211$	−111.955			−0.530591			−0.265295	+	0.964167i	$0.585469\pi$
$212$	−26.6350	−	28.1820i	−0.125637	−	0.132934i
$213$		−	12.5875i		−	0.0590962i
$214$	161.714	−	64.3268i	0.755672	−	0.300593i
$215$		−	211.509i		−	0.983765i
$216$	5.90987	−	12.7173i	0.0273605	−	0.0588766i
$217$		0			0
$218$	140.395	+	352.944i	0.644013	+	1.61901i
$219$	−1.78166			−0.00813545
$220$	27.8850	+	29.5046i	0.126750	+	0.134112i
$221$		−	275.687i		−	1.24745i
$222$	2.85004	+	7.16484i	0.0128380	+	0.0322741i
$223$			311.438i			1.39658i	0.715814	+	0.698291i	$0.246056\pi$
$223$			311.438i			1.39658i	−0.715814	+	0.698291i	$0.753944\pi$
$224$		0			0
$225$	−116.791			−0.519072
$226$	−74.6782	+	29.7056i	−0.330435	+	0.131441i
$227$	−74.3581			−0.327569			−0.163784	−	0.986496i	$-0.552370\pi$
$227$	−74.3581			−0.327569			−0.163784	+	0.986496i	$0.552370\pi$
$228$	2.29365	−	2.16775i	0.0100599	−	0.00950768i
$229$		−	78.2710i		−	0.341795i	−0.985289	−	0.170897i	$-0.945333\pi$
$229$		−	78.2710i		−	0.341795i	0.985289	−	0.170897i	$-0.0546667\pi$
$230$	−107.935	+	42.9347i	−0.469284	+	0.186673i
$231$		0			0
$232$	197.078	+	91.5842i	0.849476	+	0.394760i
$233$	93.0573			0.399388			0.199694	−	0.979858i	$-0.436005\pi$
$233$	93.0573			0.399388			0.199694	+	0.979858i	$0.436005\pi$
$234$	127.328	+	320.096i	0.544138	+	1.36793i
$235$	−160.380			−0.682466
$236$	333.019	−	314.738i	1.41110	−	1.33364i
$237$		−	4.15244i		−	0.0175208i
$238$		0			0
$239$			291.605i			1.22011i	0.792361	+	0.610053i	$0.208852\pi$
$239$			291.605i			1.22011i	−0.792361	+	0.610053i	$0.791148\pi$
$240$	5.39402	+	0.304688i	0.0224751	+	0.00126953i
$241$	−223.748			−0.928413			−0.464207	−	0.885727i	$-0.653660\pi$
$241$	−223.748			−0.928413			−0.464207	+	0.885727i	$0.653660\pi$
$242$	−208.924	+	83.1060i	−0.863321	+	0.343413i
$243$	−23.6438			−0.0972996
$244$	−20.5523	−	21.7459i	−0.0842306	−	0.0891227i
$245$		0			0
$246$	8.30703	−	3.30438i	0.0337684	−	0.0134325i
$247$			155.135i			0.628079i
$248$	325.689	+	151.351i	1.31326	+	0.610285i
$249$	−10.6859			−0.0429151
$250$	−97.3228	−	244.664i	−0.389291	−	0.978656i
$251$	310.605			1.23747			0.618734	−	0.785600i	$-0.287646\pi$
$251$	310.605			1.23747			0.618734	+	0.785600i	$0.287646\pi$
$252$		0			0
$253$			49.0838i			0.194007i
$254$	−113.587	−	285.551i	−0.447193	−	1.12422i
$255$			4.85889i			0.0190545i
$256$	−254.372	−	28.8290i	−0.993639	−	0.112613i
$257$	−175.472			−0.682769			−0.341385	−	0.939924i	$-0.610896\pi$
$257$	−175.472			−0.682769			−0.341385	+	0.939924i	$0.610896\pi$
$258$	−11.0515	+	4.39609i	−0.0428353	+	0.0170391i
$259$		0			0
$260$	−193.012	+	182.417i	−0.742354	+	0.701604i
$261$		−	244.226i		−	0.935732i
$262$	−114.968	+	45.7321i	−0.438809	+	0.174550i
$263$		−	312.127i		−	1.18680i	−0.804910	−	0.593398i	$-0.797786\pi$
$263$		−	312.127i		−	1.18680i	0.804910	−	0.593398i	$-0.202214\pi$
$264$	0.962064	−	2.07025i	0.00364418	−	0.00784185i
$265$	−33.5951			−0.126774
$266$		0			0
$267$	−7.88419			−0.0295288
$268$	−35.0566	+	33.1323i	−0.130808	+	0.123628i
$269$			142.817i			0.530918i	0.964122	+	0.265459i	$0.0855234\pi$
$269$			142.817i			0.530918i	−0.964122	+	0.265459i	$0.914477\pi$
$270$	−4.49061	−	11.2891i	−0.0166319	−	0.0418116i
$271$		−	266.117i		−	0.981982i	−0.871165	−	0.490991i	$-0.836635\pi$
$271$		−	266.117i		−	0.981982i	0.871165	−	0.490991i	$-0.163365\pi$
$272$	12.9845	−	229.870i	0.0477371	−	0.845108i
$273$		0			0
$274$	196.882	−	78.3158i	0.718546	−	0.285824i
$275$	−38.0448			−0.138345
$276$	4.48674	+	4.74733i	0.0162563	+	0.0172005i
$277$		−	366.740i		−	1.32397i	−0.749516	−	0.661986i	$-0.769714\pi$
$277$		−	366.740i		−	1.32397i	0.749516	−	0.661986i	$-0.230286\pi$
$278$	344.512	−	137.040i	1.23925	−	0.492951i
$279$		−	403.604i		−	1.44661i
$280$		0			0
$281$	147.977			0.526607			0.263303	−	0.964713i	$-0.415188\pi$
$281$	147.977			0.526607			0.263303	+	0.964713i	$0.415188\pi$
$282$	3.33339	+	8.37995i	0.0118205	+	0.0297161i
$283$	−327.739			−1.15809			−0.579043	−	0.815297i	$-0.696574\pi$
$283$	−327.739			−1.15809			−0.579043	+	0.815297i	$0.696574\pi$
$284$	354.942	+	375.557i	1.24980	+	1.32238i
$285$		−	2.73421i		−	0.00959372i
$286$	41.4772	+	104.271i	0.145025	+	0.364585i
$287$		0			0
$288$	91.0909	+	272.895i	0.316288	+	0.947551i
$289$	−81.9352			−0.283513
$290$	174.946	−	69.5901i	0.603260	−	0.239966i
$291$	15.7931			0.0542718
$292$	53.1572	−	50.2393i	0.182045	−	0.172052i
$293$			259.881i			0.886966i	0.896283	+	0.443483i	$0.146257\pi$
$293$			259.881i			0.886966i	−0.896283	+	0.443483i	$0.853743\pi$
$294$		0			0
$295$		−	396.983i		−	1.34571i
$296$	−287.067	−	133.403i	−0.969821	−	0.450685i
$297$	−5.13375			−0.0172853
$298$	−35.0464	−	88.1046i	−0.117605	−	0.295653i
$299$	−321.094			−1.07389
$300$	−3.67965	+	3.47767i	−0.0122655	+	0.0115922i
$301$		0			0
$302$	−84.6974	−	212.924i	−0.280455	−	0.705047i
$303$		−	10.4089i		−	0.0343527i
$304$	−7.30666	+	129.353i	−0.0240351	+	0.425503i
$305$	−25.9228			−0.0849929
$306$	−240.420	+	95.6345i	−0.785685	+	0.312531i
$307$	−290.462			−0.946131			−0.473065	−	0.881027i	$-0.656853\pi$
$307$	−290.462			−0.946131			−0.473065	+	0.881027i	$0.656853\pi$
$308$		0			0
$309$		−	12.3380i		−	0.0399289i
$310$	289.112	−	115.004i	0.932620	−	0.370979i
$311$		−	74.9081i		−	0.240862i	−0.992722	−	0.120431i	$-0.961572\pi$
$311$		−	74.9081i		−	0.240862i	0.992722	−	0.120431i	$-0.0384276\pi$
$312$	13.5431	+	6.29359i	0.0434072	+	0.0201718i
$313$	−284.507			−0.908969			−0.454485	−	0.890755i	$-0.650177\pi$
$313$	−284.507			−0.908969			−0.454485	+	0.890755i	$0.650177\pi$
$314$	−217.403	−	546.538i	−0.692365	−	1.74057i
$315$		0			0
$316$	117.090	+	123.891i	0.370539	+	0.392060i
$317$		−	12.2631i		−	0.0386850i	−0.999813	−	0.0193425i	$-0.993843\pi$
$317$		−	12.2631i		−	0.0386850i	0.999813	−	0.0193425i	$-0.00615729\pi$
$318$	0.698253	+	1.75537i	0.00219576	+	0.00552003i
$319$		−	79.5567i		−	0.249394i
$320$	−169.526	+	143.010i	−0.529769	+	0.446906i
$321$	−8.47885			−0.0264139
$322$		0			0
$323$	−116.520			−0.360743
$324$	234.729	−	221.845i	0.724473	−	0.684705i
$325$		−	248.880i		−	0.765784i
$326$	317.820	−	126.423i	0.974908	−	0.387800i
$327$		−	18.5053i		−	0.0565911i
$328$	−154.669	+	332.830i	−0.471553	+	1.01473i
$329$		0			0
$330$	−0.731022	−	1.83775i	−0.00221522	−	0.00556893i
$331$	194.466			0.587510			0.293755	−	0.955881i	$-0.405095\pi$
$331$	194.466			0.587510			0.293755	+	0.955881i	$0.405095\pi$
$332$	318.821	−	301.320i	0.960303	−	0.907590i
$333$			355.743i			1.06830i
$334$	89.1930	+	224.226i	0.267045	+	0.671336i
$335$			41.7901i			0.124747i
$336$		0			0
$337$	0.596077			0.00176877			0.000884387	−	1.00000i	$-0.499718\pi$
$337$	0.596077			0.00176877			0.000884387		1.00000i	$0.499718\pi$
$338$	−368.053	+	146.405i	−1.08892	+	0.433150i
$339$	3.91547			0.0115500
$340$	−137.011	−	144.969i	−0.402973	−	0.426378i
$341$		−	131.474i		−	0.385555i
$342$	135.290	−	53.8157i	0.395583	−	0.157356i
$343$		0			0
$344$	205.769	−	442.791i	0.598166	−	1.28718i
$345$	5.65918			0.0164034
$346$	−80.0869	−	201.334i	−0.231465	−	0.581890i
$347$	−204.867			−0.590394			−0.295197	−	0.955436i	$-0.595385\pi$
$347$	−204.867			−0.590394			−0.295197	+	0.955436i	$0.595385\pi$
$348$	−7.27226	−	7.69464i	−0.0208973	−	0.0221110i
$349$		−	128.396i		−	0.367898i	−0.982936	−	0.183949i	$-0.941112\pi$
$349$		−	128.396i		−	0.367898i	0.982936	−	0.183949i	$-0.0588882\pi$
$350$		0			0
$351$		−	33.5837i		−	0.0956801i
$352$	29.6729	+	88.8956i	0.0842980	+	0.252544i
$353$	190.841			0.540627			0.270314	−	0.962772i	$-0.412873\pi$
$353$	190.841			0.540627			0.270314	+	0.962772i	$0.412873\pi$
$354$	−20.7427	+	8.25105i	−0.0585951	+	0.0233080i
$355$	447.692			1.26111
$356$	235.231	−	222.318i	0.660760	−	0.624489i
$357$		0			0
$358$	−300.011	+	119.339i	−0.838020	+	0.333349i
$359$		−	215.704i		−	0.600847i	−0.953806	−	0.300424i	$-0.902872\pi$
$359$		−	215.704i		−	0.600847i	0.953806	−	0.300424i	$-0.0971281\pi$
$360$	226.036	+	105.041i	0.627878	+	0.291781i
$361$	−295.432			−0.818370
$362$	−5.28322	−	13.2817i	−0.0145945	−	0.0366898i
$363$	10.9541			0.0301766
$364$		0			0
$365$		−	63.3674i		−	0.173609i
$366$	0.538789	+	1.35449i	0.00147210	+	0.00370078i
$367$		−	454.789i		−	1.23921i	−0.784915	−	0.619604i	$-0.787293\pi$
$367$		−	454.789i		−	1.23921i	0.784915	−	0.619604i	$-0.212707\pi$
$368$	−267.730	−	15.1231i	−0.727527	−	0.0410954i
$369$	412.454			1.11776
$370$	−254.828	+	101.366i	−0.688724	+	0.273962i
$371$		0			0
$372$	−12.0180	−	12.7160i	−0.0323065	−	0.0341829i
$373$			360.748i			0.967153i	0.875302	+	0.483576i	$0.160662\pi$
$373$			360.748i			0.967153i	−0.875302	+	0.483576i	$0.839338\pi$
$374$	−78.3168	+	31.1530i	−0.209403	+	0.0832967i
$375$			12.8280i			0.0342080i
$376$	−335.751	−	156.027i	−0.892956	−	0.414965i
$377$	520.441			1.38048
$378$		0			0
$379$	−268.427			−0.708250			−0.354125	−	0.935198i	$-0.615221\pi$
$379$	−268.427			−0.708250			−0.354125	+	0.935198i	$0.615221\pi$
$380$	77.0992	+	81.5771i	0.202893	+	0.214677i
$381$			14.9718i			0.0392960i
$382$	54.1840	+	136.215i	0.141843	+	0.356585i
$383$			581.532i			1.51836i	0.650881	+	0.759180i	$0.274400\pi$
$383$			581.532i			1.51836i	−0.650881	+	0.759180i	$0.725600\pi$
$384$	10.9959	+	5.88549i	0.0286350	+	0.0153268i
$385$		0			0
$386$	−158.093	+	62.8863i	−0.409566	+	0.162918i
$387$	−548.721			−1.41788
$388$	−471.199	+	445.334i	−1.21443	+	1.14777i
$389$			512.278i			1.31691i	0.752620	+	0.658455i	$0.228790\pi$
$389$			512.278i			1.31691i	−0.752620	+	0.658455i	$0.771210\pi$
$390$	12.0221	−	4.78217i	0.0308259	−	0.0122620i
$391$		−	241.169i		−	0.616801i
$392$		0			0
$393$	6.02790			0.0153382
$394$	−103.832	−	261.027i	−0.263532	−	0.662505i
$395$	147.687			0.373892
$396$	76.5441	−	72.3424i	0.193293	−	0.182683i
$397$		−	81.3250i		−	0.204849i	−0.994741	−	0.102424i	$-0.967340\pi$
$397$		−	81.3250i		−	0.204849i	0.994741	−	0.102424i	$-0.0326600\pi$
$398$	−105.770	−	265.900i	−0.265754	−	0.668090i
$399$		0			0
$400$	11.7219	−	207.517i	0.0293047	−	0.518793i
$401$	527.441			1.31531			0.657657	−	0.753318i	$-0.271548\pi$
$401$	527.441			1.31531			0.657657	+	0.753318i	$0.271548\pi$
$402$	2.18356	−	0.868581i	0.00543175	−	0.00216065i
$403$	860.073			2.13418
$404$	293.509	+	310.556i	0.726507	+	0.768703i
$405$		−	279.815i		−	0.690902i
$406$		0			0
$407$			115.883i			0.284726i
$408$	−4.72703	+	10.1720i	−0.0115858	+	0.0249314i
$409$	58.6727			0.143454			0.0717270	−	0.997424i	$-0.477149\pi$
$409$	58.6727			0.143454			0.0717270	+	0.997424i	$0.477149\pi$
$410$	117.525	+	295.452i	0.286647	+	0.720614i
$411$	−10.3227			−0.0251161
$412$	347.908	+	368.114i	0.844436	+	0.893481i
$413$		0			0
$414$	111.386	+	280.018i	0.269048	+	0.676372i
$415$		−	380.058i		−	0.915803i
$416$	−581.533	+	194.113i	−1.39792	+	0.466618i
$417$	−18.0632			−0.0433169
$418$	44.0706	−	17.5305i	0.105432	−	0.0419389i
$419$	−760.704			−1.81552			−0.907761	−	0.419487i	$-0.862210\pi$
$419$	−760.704			−1.81552			−0.907761	+	0.419487i	$0.862210\pi$
$420$		0			0
$421$			46.2918i			0.109957i	0.998488	+	0.0549784i	$0.0175090\pi$
$421$			46.2918i			0.109957i	−0.998488	+	0.0549784i	$0.982491\pi$
$422$	−208.053	+	82.7598i	−0.493017	+	0.196113i
$423$			416.074i			0.983627i
$424$	−70.3307	−	32.6834i	−0.165874	−	0.0770834i
$425$	186.930			0.439835
$426$	−9.30501	−	23.3922i	−0.0218427	−	0.0549114i
$427$		0			0
$428$	252.972	−	239.086i	0.591057	−	0.558613i
$429$		−	5.46707i		−	0.0127437i
$430$	−156.353	−	393.063i	−0.363612	−	0.914100i
$431$			336.176i			0.779991i	0.920817	+	0.389996i	$0.127523\pi$
$431$			336.176i			0.779991i	−0.920817	+	0.389996i	$0.872477\pi$
$432$	1.58175	−	28.0023i	0.00366145	−	0.0648201i
$433$	372.694			0.860725			0.430363	−	0.902656i	$-0.358386\pi$
$433$	372.694			0.860725			0.430363	+	0.902656i	$0.358386\pi$
$434$		0			0
$435$	−9.17260			−0.0210864
$436$	521.811	+	552.118i	1.19682	+	1.26633i
$437$			135.711i			0.310553i
$438$	−3.31099	+	1.31705i	−0.00755934	+	0.00300697i
$439$			397.478i			0.905418i	0.891658	+	0.452709i	$0.149542\pi$
$439$			397.478i			0.905418i	−0.891658	+	0.452709i	$0.850458\pi$
$440$	73.6313	+	34.2172i	0.167344	+	0.0777663i
$441$		0			0
$442$	−203.795	−	512.329i	−0.461075	−	1.15912i
$443$	273.530			0.617450			0.308725	−	0.951151i	$-0.400098\pi$
$443$	273.530			0.617450			0.308725	+	0.951151i	$0.400098\pi$
$444$	10.5929	+	11.2081i	0.0238578	+	0.0252435i
$445$		−	280.413i		−	0.630141i
$446$	230.223	+	578.767i	0.516195	+	1.29768i
$447$			4.61943i			0.0103343i
$448$		0			0
$449$	428.702			0.954792			0.477396	−	0.878688i	$-0.341581\pi$
$449$	428.702			0.954792			0.477396	+	0.878688i	$0.341581\pi$
$450$	−217.041	+	86.3351i	−0.482314	+	0.191856i
$451$	134.357			0.297909
$452$	−116.821	+	110.408i	−0.258453	+	0.244266i
$453$			11.1639i			0.0246443i
$454$	−138.185	+	54.9674i	−0.304372	+	0.121074i
$455$		0			0
$456$	2.66000	−	5.72401i	0.00583334	−	0.0125527i
$457$	10.0500			0.0219913			0.0109956	−	0.999940i	$-0.496500\pi$
$457$	10.0500			0.0219913			0.0109956	+	0.999940i	$0.496500\pi$
$458$	−57.8600	−	145.457i	−0.126332	−	0.317591i
$459$	25.2243			0.0549548
$460$	−168.846	+	159.577i	−0.367056	+	0.346907i
$461$			825.802i			1.79133i	0.444732	+	0.895664i	$0.353299\pi$
$461$			825.802i			1.79133i	−0.444732	+	0.895664i	$0.646701\pi$
$462$		0			0
$463$		−	114.707i		−	0.247748i	−0.992298	−	0.123874i	$-0.960468\pi$
$463$		−	114.707i		−	0.247748i	0.992298	−	0.123874i	$-0.0395318\pi$
$464$	433.946	+	24.5120i	0.935229	+	0.0528277i
$465$	−15.1585			−0.0325989
$466$	172.935	−	68.7904i	0.371105	−	0.147619i
$467$	201.727			0.431964			0.215982	−	0.976397i	$-0.430705\pi$
$467$	201.727			0.431964			0.215982	+	0.976397i	$0.430705\pi$
$468$	473.247	+	500.733i	1.01121	+	1.06994i
$469$		0			0
$470$	−298.045	+	118.557i	−0.634138	+	0.252248i
$471$			28.6556i			0.0608399i
$472$	386.209	−	831.077i	0.818240	−	1.76076i
$473$	−178.746			−0.377899
$474$	−3.06959	−	7.71677i	−0.00647593	−	0.0162801i
$475$	−105.190			−0.221452
$476$		0			0
$477$			87.1561i			0.182717i
$478$	215.562	+	541.911i	0.450967	+	1.13371i
$479$			597.538i			1.24747i	0.781636	+	0.623735i	$0.214385\pi$
$479$			597.538i			1.24747i	−0.781636	+	0.623735i	$0.785615\pi$
$480$	10.2493	−	3.42118i	0.0213528	−	0.00712745i
$481$	−758.081			−1.57605
$482$	−415.806	+	165.400i	−0.862668	+	0.343154i
$483$		0			0
$484$	−326.824	+	308.884i	−0.675255	+	0.638189i
$485$			561.705i			1.15815i
$486$	−43.9389	+	17.4781i	−0.0904094	+	0.0359632i
$487$			345.125i			0.708675i	0.935118	+	0.354337i	$0.115294\pi$
$487$			345.125i			0.708675i	−0.935118	+	0.354337i	$0.884706\pi$
$488$	−54.2689	−	25.2193i	−0.111207	−	0.0516789i
$489$	−16.6637			−0.0340770
$490$		0			0
$491$	373.498			0.760689			0.380344	−	0.924845i	$-0.375805\pi$
$491$	373.498			0.760689			0.380344	+	0.924845i	$0.375805\pi$
$492$	12.9949	−	12.2816i	0.0264123	−	0.0249625i
$493$			390.896i			0.792892i
$494$	114.680	+	288.299i	0.232146	+	0.583602i
$495$		−	91.2464i		−	0.184336i
$496$	717.133	+	40.5082i	1.44583	+	0.0816698i
$497$		0			0
$498$	−19.8583	+	7.89927i	−0.0398761	+	0.0158620i
$499$	−850.317			−1.70404			−0.852021	−	0.523508i	$-0.824623\pi$
$499$	−850.317			−1.70404			−0.852021	+	0.523508i	$0.824623\pi$
$500$	−361.724	−	382.733i	−0.723448	−	0.765466i
$501$		−	11.7564i		−	0.0234659i
$502$	577.219	−	229.607i	1.14984	−	0.457384i
$503$			459.256i			0.913033i	0.889715	+	0.456517i	$0.150903\pi$
$503$			459.256i			0.913033i	−0.889715	+	0.456517i	$0.849097\pi$
$504$		0			0
$505$	370.206			0.733082
$506$	36.2840	+	91.2159i	0.0717075	+	0.180269i
$507$	19.2975			0.0380620
$508$	−422.174	−	446.694i	−0.831050	−	0.879318i
$509$			673.910i			1.32399i	0.749509	+	0.661994i	$0.230290\pi$
$509$			673.910i			1.32399i	−0.749509	+	0.661994i	$0.769710\pi$
$510$	3.59182	+	9.02963i	0.00704279	+	0.0177052i
$511$		0			0
$512$	−494.028	+	134.463i	−0.964898	+	0.262623i
$513$	−14.1943			−0.0276691
$514$	−326.092	+	129.713i	−0.634419	+	0.252360i
$515$	438.820			0.852078
$516$	−17.2881	+	16.3391i	−0.0335041	+	0.0316650i
$517$			135.536i			0.262159i
$518$		0			0
$519$			10.5562i			0.0203394i
$520$	−223.841	+	481.678i	−0.430463	+	0.926304i
$521$	486.473			0.933729			0.466864	−	0.884329i	$-0.345384\pi$
$521$	486.473			0.933729			0.466864	+	0.884329i	$0.345384\pi$
$522$	−180.538	−	453.863i	−0.345859	−	0.869469i
$523$	680.087			1.30036			0.650179	−	0.759781i	$-0.274694\pi$
$523$	680.087			1.30036			0.650179	+	0.759781i	$0.274694\pi$
$524$	−179.847	+	169.975i	−0.343219	+	0.324379i
$525$		0			0
$526$	−230.732	−	580.048i	−0.438655	−	1.10275i
$527$			645.988i			1.22578i
$528$	0.257491	−	4.55847i	0.000487673	−	0.00863347i
$529$	248.109			0.469015
$530$	−62.4322	+	24.8344i	−0.117797	+	0.0468573i
$531$	−1029.90			−1.93954
$532$		0			0
$533$			878.931i			1.64903i
$534$	−14.6518	+	5.82820i	−0.0274378	+	0.0109142i
$535$		−	301.562i		−	0.563668i
$536$	−40.6559	+	87.4868i	−0.0758507	+	0.163222i
$537$	15.7299			0.0292922
$538$	105.574	+	265.407i	0.196234	+	0.493321i
$539$		0			0
$540$	−16.6904	−	17.6598i	−0.0309082	−	0.0327034i
$541$		−	794.999i		−	1.46950i	−0.678339	−	0.734749i	$-0.737300\pi$
$541$		−	794.999i		−	1.46950i	0.678339	−	0.734749i	$-0.262700\pi$
$542$	−196.721	−	494.544i	−0.362953	−	0.912444i
$543$			0.696375i			0.00128246i
$544$	−145.796	−	436.781i	−0.268006	−	0.802907i
$545$	658.167			1.20765
$546$		0			0
$547$	−736.752			−1.34690			−0.673448	−	0.739235i	$-0.735187\pi$
$547$	−736.752			−1.34690			−0.673448	+	0.739235i	$0.735187\pi$
$548$	307.986	−	291.080i	0.562018	−	0.531168i
$549$			67.2518i			0.122499i
$550$	−70.7013	+	28.1237i	−0.128548	+	0.0511340i
$551$		−	219.966i		−	0.399212i
$552$	11.8474	+	5.50559i	0.0214626	+	0.00997389i
$553$		0			0
$554$	−271.104	−	681.540i	−0.489357	−	1.23022i
$555$	13.3609			0.0240737
$556$	538.927	−	509.344i	0.969294	−	0.916087i
$557$		−	415.758i		−	0.746423i	−0.927746	−	0.373212i	$-0.878257\pi$
$557$		−	415.758i		−	0.746423i	0.927746	−	0.373212i	$-0.121743\pi$
$558$	−298.355	−	750.047i	−0.534686	−	1.34417i
$559$		−	1169.31i		−	2.09179i
$560$		0			0
$561$	4.10624			0.00731950
$562$	274.995	−	109.388i	0.489316	−	0.194641i
$563$	96.4996			0.171402			0.0857012	−	0.996321i	$-0.472687\pi$
$563$	96.4996			0.171402			0.0857012	+	0.996321i	$0.472687\pi$
$564$	12.3893	+	13.1089i	0.0219669	+	0.0232428i
$565$			139.259i			0.246476i
$566$	−609.060	+	242.273i	−1.07608	+	0.428044i
$567$		0			0
$568$	937.235	+	435.542i	1.65006	+	0.766800i
$569$	347.953			0.611517			0.305759	−	0.952109i	$-0.401090\pi$
$569$	347.953			0.611517			0.305759	+	0.952109i	$0.401090\pi$
$570$	−2.02120	−	5.08118i	−0.00354596	−	0.00891435i
$571$	−13.7251			−0.0240370			−0.0120185	−	0.999928i	$-0.503826\pi$
$571$	−13.7251			−0.0240370			−0.0120185	+	0.999928i	$0.503826\pi$
$572$	154.160	+	163.114i	0.269511	+	0.285164i
$573$		−	7.14193i		−	0.0124641i
$574$		0			0
$575$		−	217.718i		−	0.378641i
$576$	371.012	+	439.803i	0.644118	+	0.763547i
$577$	827.320			1.43383			0.716915	−	0.697161i	$-0.245554\pi$
$577$	827.320			1.43383			0.716915	+	0.697161i	$0.245554\pi$
$578$	−152.266	+	60.5686i	−0.263436	+	0.104790i
$579$	8.28898			0.0143160
$580$	273.671	−	258.649i	0.471847	−	0.445946i
$581$		0			0
$582$	29.3495	−	11.6747i	0.0504286	−	0.0200596i
$583$			28.3911i			0.0486983i
$584$	61.6476	−	132.658i	0.105561	−	0.227155i
$585$	596.912			1.02036
$586$	192.111	+	482.955i	0.327834	+	0.824156i
$587$	675.987			1.15160			0.575798	−	0.817592i	$-0.304692\pi$
$587$	675.987			1.15160			0.575798	+	0.817592i	$0.304692\pi$
$588$		0			0
$589$		−	363.512i		−	0.617169i
$590$	−293.460	−	737.743i	−0.497391	−	1.25041i
$591$			13.6860i			0.0231573i
$592$	−632.092	−	35.7046i	−1.06772	−	0.0603118i
$593$	414.116			0.698341			0.349171	−	0.937059i	$-0.386463\pi$
$593$	414.116			0.698341			0.349171	+	0.937059i	$0.386463\pi$
$594$	−9.54041	+	3.79500i	−0.0160613	+	0.00638889i
$595$		0			0
$596$	−130.258	−	137.824i	−0.218554	−	0.231248i
$597$			13.9414i			0.0233525i
$598$	−596.712	+	237.361i	−0.997847	+	0.396925i
$599$			723.303i			1.20752i	0.797167	+	0.603759i	$0.206331\pi$
$599$			723.303i			1.20752i	−0.797167	+	0.603759i	$0.793669\pi$
$600$	−4.26738	+	9.18289i	−0.00711229	+	0.0153048i
$601$	−68.7503			−0.114393			−0.0571966	−	0.998363i	$-0.518216\pi$
$601$	−68.7503			−0.114393			−0.0571966	+	0.998363i	$0.518216\pi$
$602$		0			0
$603$	108.416			0.179795
$604$	−314.798	−	333.082i	−0.521189	−	0.551460i
$605$			389.599i			0.643965i
$606$	−7.69450	−	19.3435i	−0.0126972	−	0.0319200i
$607$		−	141.263i		−	0.232724i	−0.993207	−	0.116362i	$-0.962877\pi$
$607$		−	141.263i		−	0.232724i	0.993207	−	0.116362i	$-0.0371232\pi$
$608$	82.0424	+	245.787i	0.134938	+	0.404255i
$609$		0			0
$610$	−48.1742	+	19.1628i	−0.0789742	+	0.0314145i
$611$	−886.646			−1.45114
$612$	−376.093	+	355.449i	−0.614532	+	0.580799i
$613$			96.7370i			0.157809i	0.996882	+	0.0789046i	$0.0251422\pi$
$613$			96.7370i			0.157809i	−0.996882	+	0.0789046i	$0.974858\pi$
$614$	−539.787	+	214.717i	−0.879131	+	0.349702i
$615$		−	15.4909i		−	0.0251884i
$616$		0			0
$617$	580.418			0.940709			0.470355	−	0.882478i	$-0.344126\pi$
$617$	580.418			0.940709			0.470355	+	0.882478i	$0.344126\pi$
$618$	−9.12060	−	22.9287i	−0.0147582	−	0.0371014i
$619$	−157.945			−0.255161			−0.127581	−	0.991828i	$-0.540721\pi$
$619$	−157.945			−0.255161			−0.127581	+	0.991828i	$0.540721\pi$
$620$	452.264	−	427.439i	0.729459	−	0.689417i
$621$		−	29.3788i		−	0.0473089i
$622$	−55.3740	−	139.207i	−0.0890257	−	0.223806i
$623$		0			0
$624$	29.8204	+	1.68445i	0.0477891	+	0.00269943i
$625$	−131.484			−0.210375
$626$	−528.720	+	210.315i	−0.844601	+	0.335967i
$627$	−2.31067			−0.00368528
$628$	−808.030	−	854.961i	−1.28667	−	1.36140i
$629$		−	569.384i		−	0.905221i
$630$		0			0
$631$			771.793i			1.22313i	0.791195	+	0.611564i	$0.209459\pi$
$631$			771.793i			1.22313i	−0.791195	+	0.611564i	$0.790541\pi$
$632$	309.181	+	143.679i	0.489210	+	0.227341i
$633$	10.9085			0.0172330
$634$	−9.06523	−	22.7895i	−0.0142985	−	0.0359455i
$635$	−532.493			−0.838571
$636$	2.59523	+	2.74596i	0.00408055	+	0.00431755i
$637$		0			0
$638$	−58.8104	−	147.846i	−0.0921793	−	0.231733i
$639$		−	1161.45i		−	1.81761i
$640$	−209.326	+	391.083i	−0.327072	+	0.611068i
$641$	−586.903			−0.915605			−0.457802	−	0.889054i	$-0.651363\pi$
$641$	−586.903			−0.915605			−0.457802	+	0.889054i	$0.651363\pi$
$642$	−15.7568	+	6.26778i	−0.0245434	+	0.00976290i
$643$	−865.328			−1.34577			−0.672883	−	0.739749i	$-0.734944\pi$
$643$	−865.328			−1.34577			−0.672883	+	0.739749i	$0.734944\pi$
$644$		0			0
$645$			20.6087i			0.0319515i
$646$	−216.538	+	86.1347i	−0.335197	+	0.133335i
$647$			132.883i			0.205383i	0.994713	+	0.102691i	$0.0327454\pi$
$647$			132.883i			0.205383i	−0.994713	+	0.102691i	$0.967255\pi$
$648$	272.221	−	585.788i	0.420094	−	0.903993i
$649$	−335.489			−0.516933
$650$	−183.978	−	462.511i	−0.283044	−	0.711555i
$651$		0			0
$652$	497.173	−	469.882i	0.762535	−	0.720677i
$653$			364.309i			0.557900i	0.960306	+	0.278950i	$0.0899865\pi$
$653$			364.309i			0.557900i	−0.960306	+	0.278950i	$0.910014\pi$
$654$	−13.6796	−	34.3897i	−0.0209168	−	0.0525836i
$655$			214.391i			0.327315i
$656$	−41.3964	+	732.858i	−0.0631043	+	1.11716i
$657$	−164.395			−0.250220
$658$		0			0
$659$	−18.8972			−0.0286756			−0.0143378	−	0.999897i	$-0.504564\pi$
$659$	−18.8972			−0.0286756			−0.0143378	+	0.999897i	$0.504564\pi$
$660$	−2.71702	−	2.87483i	−0.00411670	−	0.00435580i
$661$			339.106i			0.513019i	0.966542	+	0.256510i	$0.0825725\pi$
$661$			339.106i			0.513019i	−0.966542	+	0.256510i	$0.917427\pi$
$662$	361.390	−	143.754i	0.545906	−	0.217151i
$663$			26.8620i			0.0405159i
$664$	369.744	−	795.645i	0.556843	−	1.19826i
$665$		0			0
$666$	262.974	+	661.102i	0.394856	+	0.992646i
$667$	455.278			0.682576
$668$	331.508	+	350.762i	0.496269	+	0.525092i
$669$		−	30.3454i		−	0.0453594i
$670$	30.8923	+	77.6616i	0.0461080	+	0.115913i
$671$			21.9073i			0.0326487i
$672$		0			0
$673$	674.869			1.00278			0.501389	−	0.865222i	$-0.332823\pi$
$673$	674.869			1.00278			0.501389	+	0.865222i	$0.332823\pi$
$674$	1.10773	−	0.440635i	0.00164352	−	0.000653762i
$675$	22.7715			0.0337355
$676$	−575.754	+	544.149i	−0.851706	+	0.804954i
$677$		−	988.747i		−	1.46048i	−0.683189	−	0.730242i	$-0.739407\pi$
$677$		−	988.747i		−	1.46048i	0.683189	−	0.730242i	$-0.260593\pi$
$678$	7.27639	−	2.89441i	0.0107321	−	0.00426905i
$679$		0			0
$680$	−361.782	−	168.123i	−0.532032	−	0.247240i
$681$	7.24520			0.0106391
$682$	−97.1892	−	244.328i	−0.142506	−	0.358252i
$683$	−518.125			−0.758602			−0.379301	−	0.925273i	$-0.623835\pi$
$683$	−518.125			−0.758602			−0.379301	+	0.925273i	$0.623835\pi$
$684$	211.636	−	200.019i	0.309410	−	0.292426i
$685$		−	367.143i		−	0.535975i
$686$		0			0
$687$			7.62646i			0.0111011i
$688$	55.0730	−	974.980i	0.0800480	−	1.41712i
$689$	−185.728			−0.269562
$690$	10.5169	−	4.18341i	0.0152418	−	0.00606291i
$691$	617.021			0.892940			0.446470	−	0.894799i	$-0.352681\pi$
$691$	617.021			0.892940			0.446470	+	0.894799i	$0.352681\pi$
$692$	−297.662	−	314.951i	−0.430148	−	0.455131i
$693$		0			0
$694$	−380.718	+	151.443i	−0.548585	+	0.218217i
$695$		−	642.442i		−	0.924377i
$696$	−19.2026	−	8.92365i	−0.0275900	−	0.0128213i
$697$	−660.153			−0.947135
$698$	−94.9140	−	238.608i	−0.135980	−	0.341846i
$699$	−9.06718			−0.0129717
$700$		0			0
$701$			97.6954i			0.139366i	0.997569	+	0.0696829i	$0.0221987\pi$
$701$			97.6954i			0.139366i	−0.997569	+	0.0696829i	$0.977801\pi$
$702$	−24.8260	−	62.4110i	−0.0353646	−	0.0889046i
$703$			320.405i			0.455768i
$704$	120.857	+	143.266i	0.171672	+	0.203503i
$705$	15.6268			0.0221657
$706$	354.654	−	141.075i	0.502343	−	0.199823i
$707$		0			0
$708$	−32.4482	+	30.6670i	−0.0458308	+	0.0433150i
$709$		−	1249.74i		−	1.76269i	−0.472476	−	0.881343i	$-0.656640\pi$
$709$		−	1249.74i		−	1.76269i	0.472476	−	0.881343i	$-0.343360\pi$
$710$	831.979	−	330.946i	1.17180	−	0.466121i
$711$		−	383.147i		−	0.538885i
$712$	272.802	−	587.038i	0.383149	−	0.824492i
$713$	752.386			1.05524
$714$		0			0
$715$	194.444			0.271950
$716$	−469.314	+	443.552i	−0.655466	+	0.619486i
$717$		−	28.4130i		−	0.0396277i
$718$	−159.454	−	400.859i	−0.222081	−	0.558299i
$719$		−	424.744i		−	0.590743i	−0.955382	−	0.295372i	$-0.904557\pi$
$719$		−	424.744i		−	0.590743i	0.955382	−	0.295372i	$-0.0954435\pi$
$720$	497.708	+	28.1137i	0.691261	+	0.0390468i
$721$		0			0
$722$	−549.022	+	218.391i	−0.760418	+	0.302480i
$723$	21.8012			0.0301538
$724$	−19.6364	−	20.7768i	−0.0271220	−	0.0286973i
$725$			352.886i			0.486739i
$726$	20.3568	−	8.09756i	0.0280397	−	0.0111537i
$727$		−	79.1445i		−	0.108865i	−0.998517	−	0.0544323i	$-0.982665\pi$
$727$		−	79.1445i		−	0.108865i	0.998517	−	0.0544323i	$-0.0173349\pi$
$728$		0			0
$729$	−724.390			−0.993676
$730$	−46.8428	−	117.760i	−0.0641683	−	0.161315i
$731$	878.255			1.20144
$732$	2.00254	+	2.11885i	0.00273571	+	0.00289460i
$733$		−	663.766i		−	0.905548i	−0.891625	−	0.452774i	$-0.850434\pi$
$733$		−	663.766i		−	0.905548i	0.891625	−	0.452774i	$-0.149566\pi$
$734$	−336.192	−	845.167i	−0.458027	−	1.15145i
$735$		0			0
$736$	−508.721	+	169.809i	−0.691198	+	0.230718i
$737$	35.3167			0.0479196
$738$	766.493	−	304.897i	1.03861	−	0.413139i
$739$	832.112			1.12600			0.562998	−	0.826458i	$-0.309648\pi$
$739$	832.112			1.12600			0.562998	+	0.826458i	$0.309648\pi$
$740$	−398.633	+	376.751i	−0.538693	+	0.509123i
$741$		−	15.1159i		−	0.0203993i
$742$		0			0
$743$		−	283.217i		−	0.381180i	−0.981670	−	0.190590i	$-0.938960\pi$
$743$		−	283.217i		−	0.381180i	0.981670	−	0.190590i	$-0.0610401\pi$
$744$	−31.7340	−	14.7471i	−0.0426532	−	0.0198214i
$745$	−164.297			−0.220532
$746$	266.674	+	670.404i	0.357472	+	0.898665i
$747$	−985.989			−1.31993
$748$	−122.513	+	115.788i	−0.163787	+	0.154796i
$749$		0			0
$750$	9.48280	+	23.8392i	0.0126437	+	0.0317856i
$751$			374.981i			0.499309i	0.968335	+	0.249654i	$0.0803170\pi$
$751$			374.981i			0.499309i	−0.968335	+	0.249654i	$0.919683\pi$
$752$	−739.290	−	41.7598i	−0.983099	−	0.0555316i
$753$	−30.2642			−0.0401916
$754$	967.173	−	384.723i	1.28272	−	0.510243i
$755$	−397.059			−0.525906
$756$		0			0
$757$			63.0951i			0.0833488i	0.999131	+	0.0416744i	$0.0132692\pi$
$757$			63.0951i			0.0833488i	−0.999131	+	0.0416744i	$0.986731\pi$
$758$	−498.837	+	198.428i	−0.658096	+	0.261779i
$759$		−	4.78255i		−	0.00630113i
$760$	203.583	+	94.6069i	0.267872	+	0.124483i
$761$	−467.505			−0.614330			−0.307165	−	0.951656i	$-0.599380\pi$
$761$	−467.505			−0.614330			−0.307165	+	0.951656i	$0.599380\pi$
$762$	11.0675	+	27.8231i	0.0145243	+	0.0365133i
$763$		0			0
$764$	201.388	+	213.085i	0.263597	+	0.278907i
$765$			448.332i			0.586055i
$766$	429.884	+	1080.70i	0.561206	+	1.41084i
$767$		−	2194.69i		−	2.86140i
$768$	24.7851	+	2.80900i	0.0322723	+	0.00365755i
$769$	−900.573			−1.17110			−0.585548	−	0.810638i	$-0.699121\pi$
$769$	−900.573			−1.17110			−0.585548	+	0.810638i	$0.699121\pi$
$770$		0			0
$771$	17.0974			0.0221756
$772$	−247.308	+	233.732i	−0.320347	+	0.302762i
$773$		−	1222.76i		−	1.58184i	−0.611920	−	0.790919i	$-0.709603\pi$
$773$		−	1222.76i		−	1.58184i	0.611920	−	0.790919i	$-0.290397\pi$
$774$	−1019.73	+	405.629i	−1.31748	+	0.524068i
$775$			583.173i			0.752482i
$776$	−546.460	+	1175.92i	−0.704201	+	1.51536i
$777$		0			0
$778$	378.689	+	952.003i	0.486747	+	1.22365i
$779$	371.483			0.476872
$780$	18.8064	−	17.7741i	0.0241108	−	0.0227873i
$781$		−	378.344i		−	0.484435i
$782$	−178.279	−	448.182i	−0.227978	−	0.573123i
$783$			47.6182i			0.0608151i
$784$		0			0
$785$	−1019.18			−1.29832
$786$	11.2021	−	4.45598i	0.0142520	−	0.00566919i
$787$	−862.942			−1.09650			−0.548248	−	0.836316i	$-0.684705\pi$
$787$	−862.942			−1.09650			−0.548248	+	0.836316i	$0.684705\pi$
$788$	−385.916	−	408.330i	−0.489741	−	0.518186i
$789$			30.4126i			0.0385457i
$790$	274.458	−	109.174i	0.347415	−	0.138195i
$791$		0			0
$792$	88.7700	−	191.022i	0.112083	−	0.241190i
$793$	−143.312			−0.180722
$794$	−60.1175	−	151.132i	−0.0757148	−	0.190343i
$795$	3.27339			0.00411747
$796$	−393.120	−	415.953i	−0.493869	−	0.522554i
$797$			1078.34i			1.35300i	0.736442	+	0.676500i	$0.236504\pi$
$797$			1078.34i			1.35300i	−0.736442	+	0.676500i	$0.763496\pi$
$798$		0			0
$799$		−	665.947i		−	0.833476i
$800$	−131.619	−	394.309i	−0.164523	−	0.492887i
$801$	−727.477			−0.908211
$802$	980.180	−	389.898i	1.22217	−	0.486157i
$803$	−53.5516			−0.0666894
$804$	3.41579	−	3.22829i	0.00424850	−	0.00401529i
$805$		0			0
$806$	1598.33	−	635.788i	1.98305	−	0.788819i
$807$		−	13.9156i		−	0.0172436i
$808$	775.020	+	360.159i	0.959183	+	0.445741i
$809$	333.388			0.412099			0.206050	−	0.978542i	$-0.433939\pi$
$809$	333.388			0.412099			0.206050	+	0.978542i	$0.433939\pi$
$810$	−206.847	−	520.001i	−0.255366	−	0.641976i
$811$	1246.04			1.53642			0.768211	−	0.640197i	$-0.221147\pi$
$811$	1246.04			1.53642			0.768211	+	0.640197i	$0.221147\pi$
$812$		0			0
$813$			25.9295i			0.0318936i
$814$	85.6640	+	215.354i	0.105238	+	0.264563i
$815$		−	592.667i		−	0.727199i
$816$	−1.26516	+	22.3977i	−0.00155045	+	0.0274482i
$817$	−494.214			−0.604913
$818$	109.036	−	43.3724i	0.133295	−	0.0530224i
$819$		0			0
$820$	436.811	+	462.181i	0.532696	+	0.563636i
$821$			1458.68i			1.77671i	0.459162	+	0.888353i	$0.348150\pi$
$821$			1458.68i			1.77671i	−0.459162	+	0.888353i	$0.651850\pi$
$822$	−19.1835	+	7.63083i	−0.0233375	+	0.00928324i
$823$			464.047i			0.563848i	0.959437	+	0.281924i	$0.0909725\pi$
$823$			464.047i			0.563848i	−0.959437	+	0.281924i	$0.909027\pi$
$824$	918.661	+	426.911i	1.11488	+	0.518095i
$825$	3.70695			0.00449328
$826$		0			0
$827$	1077.41			1.30279			0.651394	−	0.758739i	$-0.274184\pi$
$827$	1077.41			1.30279			0.651394	+	0.758739i	$0.274184\pi$
$828$	413.993	+	438.038i	0.499991	+	0.529031i
$829$			35.9354i			0.0433479i	0.999765	+	0.0216740i	$0.00689958\pi$
$829$			35.9354i			0.0433479i	−0.999765	+	0.0216740i	$0.993100\pi$
$830$	−280.949	−	706.290i	−0.338493	−	0.850951i
$831$			35.7339i			0.0430011i
$832$	−937.211	+	790.619i	−1.12646	+	0.950263i
$833$		0			0
$834$	−33.5681	+	13.3528i	−0.0402495	+	0.0160105i
$835$	418.134			0.500760
$836$	68.9406	−	65.1563i	0.0824648	−	0.0779381i
$837$			78.6932i			0.0940181i
$838$	−1413.67	+	562.332i	−1.68696	+	0.671041i
$839$			734.676i			0.875656i	0.899059	+	0.437828i	$0.144252\pi$
$839$			734.676i			0.875656i	−0.899059	+	0.437828i	$0.855748\pi$
$840$		0			0
$841$	103.069			0.122555
$842$	34.2201	+	86.0274i	0.0406415	+	0.102170i
$843$	−14.4183			−0.0171036
$844$	−325.462	+	307.597i	−0.385619	+	0.364451i
$845$			686.342i			0.812239i
$846$	307.573	+	773.221i	0.363561	+	0.913972i
$847$		0			0
$848$	−154.861	−	8.74753i	−0.182619	−	0.0103155i
$849$	31.9337			0.0376133
$850$	347.386	−	138.184i	0.408689	−	0.162569i
$851$	−663.164			−0.779276
$852$	−34.5843	−	36.5930i	−0.0405919	−	0.0429495i
$853$			402.566i			0.471942i	0.971760	+	0.235971i	$0.0758270\pi$
$853$			402.566i			0.471942i	−0.971760	+	0.235971i	$0.924173\pi$
$854$		0			0
$855$		−	252.287i		−	0.295072i
$856$	293.378	−	631.315i	0.342731	−	0.737517i
$857$	−552.003			−0.644110			−0.322055	−	0.946721i	$-0.604374\pi$
$857$	−552.003			−0.644110			−0.322055	+	0.946721i	$0.604374\pi$
$858$	−4.04140	−	10.1598i	−0.00471025	−	0.0118413i
$859$	330.117			0.384303			0.192152	−	0.981365i	$-0.438453\pi$
$859$	330.117			0.384303			0.192152	+	0.981365i	$0.438453\pi$
$860$	−581.125	−	614.877i	−0.675727	−	0.714973i
$861$		0			0
$862$	248.510	+	624.740i	0.288295	+	0.724757i
$863$			1116.67i			1.29394i	0.762516	+	0.646969i	$0.223964\pi$
$863$			1116.67i			1.29394i	−0.762516	+	0.646969i	$0.776036\pi$
$864$	−17.7605	−	53.2079i	−0.0205562	−	0.0615833i
$865$	−375.445			−0.434041
$866$	692.604	−	275.505i	0.799774	−	0.318135i
$867$	7.98348			0.00920817
$868$		0			0
$869$		−	124.810i		−	0.143625i
$870$	−17.0461	+	6.78062i	−0.0195932	+	0.00779382i
$871$			231.033i			0.265251i
$872$	1377.86	+	640.305i	1.58011	+	0.734294i
$873$	1457.24			1.66923
$874$	100.321	+	252.202i	0.114784	+	0.288561i
$875$		0			0
$876$	−5.17945	+	4.89514i	−0.00591262	+	0.00558806i
$877$		−	0.747441i		−	0.000852270i	−1.00000		0.000426135i	$-0.999864\pi$
$877$		−	0.747441i		−	0.000852270i	1.00000		0.000426135i	$-0.000135643\pi$
$878$	293.826	+	738.662i	0.334654	+	0.841301i
$879$		−	25.3219i		−	0.0288076i
$880$	162.129	+	9.15805i	0.184237	+	0.0104069i
$881$	247.826			0.281301			0.140650	−	0.990059i	$-0.455081\pi$
$881$	247.826			0.281301			0.140650	+	0.990059i	$0.455081\pi$
$882$		0			0
$883$	−1613.74			−1.82757			−0.913784	−	0.406200i	$-0.866854\pi$
$883$	−1613.74			−1.82757			−0.913784	+	0.406200i	$0.866854\pi$
$884$	−757.454	−	801.448i	−0.856849	−	0.906615i
$885$			38.6807i			0.0437070i
$886$	508.321	−	202.201i	0.573726	−	0.228217i
$887$		−	1110.59i		−	1.25207i	−0.779795	−	0.626034i	$-0.784677\pi$
$887$		−	1110.59i		−	1.25207i	0.779795	−	0.626034i	$-0.215323\pi$
$888$	27.9708	+	12.9983i	0.0314987	+	0.0146377i
$889$		0			0
$890$	−207.288	−	521.111i	−0.232908	−	0.585518i
$891$	−236.471			−0.265400
$892$	855.680	+	905.378i	0.959282	+	1.01500i
$893$			374.744i			0.419646i
$894$	3.41480	+	8.58461i	0.00381969	+	0.00960247i
$895$			559.458i			0.625092i
$896$		0			0
$897$	31.2863			0.0348788
$898$	796.687	−	316.907i	0.887179	−	0.352904i
$899$	−1219.49			−1.35650
$900$	−339.523	+	320.885i	−0.377247	+	0.356539i
$901$		−	139.498i		−	0.154825i
$902$	249.685	−	99.3202i	0.276813	−	0.110111i
$903$		0			0
$904$	−135.480	+	291.536i	−0.149867	+	0.322496i
$905$	−24.7676			−0.0273675
$906$	8.25262	+	20.7466i	0.00910885	+	0.0228991i
$907$	−518.009			−0.571123			−0.285562	−	0.958360i	$-0.592180\pi$
$907$	−518.009			−0.571123			−0.285562	+	0.958360i	$0.592180\pi$
$908$	−216.166	+	204.300i	−0.238068	+	0.225000i
$909$		−	960.430i		−	1.05658i
$910$		0			0
$911$			1065.61i			1.16972i	0.811135	+	0.584860i	$0.198850\pi$
$911$			1065.61i			1.16972i	−0.811135	+	0.584860i	$0.801150\pi$
$912$	0.711936	−	12.6037i	0.000780632	−	0.0138198i
$913$	−321.186			−0.351792
$914$	18.6767	−	7.42923i	0.0204340	−	0.00812826i
$915$	2.52583			0.00276047
$916$	−215.051	−	227.541i	−0.234772	−	0.248407i
$917$		0			0
$918$	46.8761	−	18.6464i	0.0510632	−	0.0203120i
$919$			1183.66i			1.28799i	0.765030	+	0.643994i	$0.222724\pi$
$919$			1183.66i			1.28799i	−0.765030	+	0.643994i	$0.777276\pi$
$920$	−195.814	+	421.369i	−0.212842	+	0.458010i
$921$	28.3016			0.0307292
$922$	610.454	+	1534.65i	0.662098	+	1.66448i
$923$	2475.03			2.68151
$924$		0			0
$925$		−	514.018i		−	0.555695i
$926$	−84.7946	−	213.169i	−0.0915708	−	0.230204i
$927$		−	1138.43i		−	1.22809i
$928$	824.554	−	275.232i	0.888528	−	0.296586i
$929$	379.019			0.407986			0.203993	−	0.978972i	$-0.434608\pi$
$929$	379.019			0.407986			0.203993	+	0.978972i	$0.434608\pi$
$930$	−28.1701	+	11.2055i	−0.0302904	+	0.0120490i
$931$		0			0
$932$	270.526	−	255.676i	0.290264	−	0.274331i
$933$			7.29878i			0.00782292i
$934$	374.884	−	149.122i	0.401375	−	0.159660i
$935$			146.044i			0.156197i
$936$	1249.62	+	580.712i	1.33507	+	0.620418i
$937$	−1316.09			−1.40458			−0.702289	−	0.711892i	$-0.747839\pi$
$937$	−1316.09			−1.40458			−0.702289	+	0.711892i	$0.747839\pi$
$938$		0			0
$939$	27.7214			0.0295223
$940$	−466.238	+	440.645i	−0.495998	+	0.468771i
$941$		−	497.031i		−	0.528194i	−0.964496	−	0.264097i	$-0.914926\pi$
$941$		−	497.031i		−	0.528194i	0.964496	−	0.264097i	$-0.0850739\pi$
$942$	21.1830	+	53.2528i	0.0224872	+	0.0565316i
$943$			768.883i			0.815359i
$944$	103.367	−	1829.95i	0.109499	−	1.93850i
$945$		0			0
$946$	−332.176	+	132.134i	−0.351138	+	0.139676i
$947$	808.487			0.853735			0.426867	−	0.904314i	$-0.359617\pi$
$947$	808.487			0.853735			0.426867	+	0.904314i	$0.359617\pi$
$948$	−11.4089	−	12.0715i	−0.0120347	−	0.0127337i
$949$		−	350.322i		−	0.369148i
$950$	−195.482	+	77.7590i	−0.205770	+	0.0818516i
$951$			1.19488i			0.00125644i
$952$		0			0
$953$	−1345.58			−1.41194			−0.705969	−	0.708243i	$-0.749488\pi$
$953$	−1345.58			−1.41194			−0.705969	+	0.708243i	$0.749488\pi$
$954$	64.4281	+	161.968i	0.0675347	+	0.169778i
$955$	254.013			0.265982
$956$	801.190	+	847.723i	0.838064	+	0.886740i
$957$			7.75173i			0.00810004i
$958$	441.715	+	1110.45i	0.461081	+	1.15913i
$959$		0			0
$960$	16.5180	−	13.9344i	0.0172063	−	0.0145150i
$961$	−1054.32			−1.09710
$962$	−1408.80	+	560.393i	−1.46444	+	0.582529i
$963$	−782.346			−0.812405
$964$	−650.454	+	614.749i	−0.674745	+	0.637707i
$965$			294.809i			0.305502i
$966$		0			0
$967$			140.279i			0.145066i	0.997366	+	0.0725330i	$0.0231083\pi$
$967$			140.279i			0.145066i	−0.997366	+	0.0725330i	$0.976892\pi$
$968$	−379.025	+	815.617i	−0.391555	+	0.842579i
$969$	11.3533			0.0117165
$970$	415.227	+	1043.86i	0.428069	+	1.07614i
$971$	−1438.67			−1.48164			−0.740820	−	0.671704i	$-0.765563\pi$
$971$	−1438.67			−1.48164			−0.740820	+	0.671704i	$0.765563\pi$
$972$	−68.7346	+	64.9616i	−0.0707146	+	0.0668330i
$973$		0			0
$974$	255.125	+	641.370i	0.261935	+	0.658491i
$975$			24.2500i			0.0248718i
$976$	−119.495	−	6.74981i	−0.122433	−	0.00691579i
$977$	902.190			0.923428			0.461714	−	0.887029i	$-0.347235\pi$
$977$	902.190			0.923428			0.461714	+	0.887029i	$0.347235\pi$
$978$	−30.9673	+	12.3182i	−0.0316639	+	0.0125953i
$979$	−236.976			−0.242059
$980$		0			0
$981$		−	1707.49i		−	1.74056i
$982$	694.098	−	276.100i	0.706821	−	0.281160i
$983$		−	503.193i		−	0.511896i	−0.966691	−	0.255948i	$-0.917612\pi$
$983$		−	503.193i		−	0.511896i	0.966691	−	0.255948i	$-0.0823875\pi$
$984$	15.0705	−	32.4298i	0.0153155	−	0.0329571i
$985$	−486.761			−0.494173
$986$	288.960	+	726.430i	0.293063	+	0.736744i
$987$		0			0
$988$	426.237	+	450.993i	0.431414	+	0.456470i
$989$		−	1022.91i		−	1.03428i
$990$	−67.4517	−	169.570i	−0.0681330	−	0.171282i
$991$			906.322i			0.914553i	0.889325	+	0.457277i	$0.151175\pi$
$991$			906.322i			0.914553i	−0.889325	+	0.457277i	$0.848825\pi$
$992$	1362.64	−	454.844i	1.37363	−	0.458512i
$993$	−18.9481			−0.0190816
$994$		0			0
$995$	−495.847			−0.498339
$996$	−31.0648	+	29.3596i	−0.0311895	+	0.0294775i
$997$			608.625i			0.610457i	0.952279	+	0.305228i	$0.0987328\pi$
$997$			608.625i			0.610457i	−0.952279	+	0.305228i	$0.901267\pi$
$998$	−1580.20	+	628.576i	−1.58337	+	0.629836i
$999$		−	69.3613i		−	0.0694308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.m.99.7		8
4.3	odd	2		1568.3.g.m.687.5		8
7.2	even	3		392.3.k.n.67.2		16
7.3	odd	6		392.3.k.o.275.4		16
7.4	even	3		392.3.k.n.275.4		16
7.5	odd	6		392.3.k.o.67.2		16
7.6	odd	2		56.3.g.b.43.7	✓	8
8.3	odd	2	inner	392.3.g.m.99.8		8
8.5	even	2		1568.3.g.m.687.6		8
21.20	even	2		504.3.g.b.379.2		8
28.27	even	2		224.3.g.b.15.4		8
56.3	even	6		392.3.k.o.275.2		16
56.11	odd	6		392.3.k.n.275.2		16
56.13	odd	2		224.3.g.b.15.3		8
56.19	even	6		392.3.k.o.67.4		16
56.27	even	2		56.3.g.b.43.8	yes	8
56.51	odd	6		392.3.k.n.67.4		16
84.83	odd	2		2016.3.g.b.1135.4		8
112.13	odd	4		1792.3.d.j.1023.10		16
112.27	even	4		1792.3.d.j.1023.9		16
112.69	odd	4		1792.3.d.j.1023.7		16
112.83	even	4		1792.3.d.j.1023.8		16
168.83	odd	2		504.3.g.b.379.1		8
168.125	even	2		2016.3.g.b.1135.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.7	✓	8	7.6	odd	2
56.3.g.b.43.8	yes	8	56.27	even	2
224.3.g.b.15.3		8	56.13	odd	2
224.3.g.b.15.4		8	28.27	even	2
392.3.g.m.99.7		8	1.1	even	1	trivial
392.3.g.m.99.8		8	8.3	odd	2	inner
392.3.k.n.67.2		16	7.2	even	3
392.3.k.n.67.4		16	56.51	odd	6
392.3.k.n.275.2		16	56.11	odd	6
392.3.k.n.275.4		16	7.4	even	3
392.3.k.o.67.2		16	7.5	odd	6
392.3.k.o.67.4		16	56.19	even	6
392.3.k.o.275.2		16	56.3	even	6
392.3.k.o.275.4		16	7.3	odd	6
504.3.g.b.379.1		8	168.83	odd	2
504.3.g.b.379.2		8	21.20	even	2
1568.3.g.m.687.5		8	4.3	odd	2
1568.3.g.m.687.6		8	8.5	even	2
1792.3.d.j.1023.7		16	112.69	odd	4
1792.3.d.j.1023.8		16	112.83	even	4
1792.3.d.j.1023.9		16	112.27	even	4
1792.3.d.j.1023.10		16	112.13	odd	4
2016.3.g.b.1135.4		8	84.83	odd	2
2016.3.g.b.1135.5		8	168.125	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)

\(f(q)\)	\(=\)	\(q+(1.85837 - 0.739226i) q^{2} -0.0974366 q^{3} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} +(-0.181073 + 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} -8.99051 q^{9} +O(q^{10})\)	\(q+(1.85837 - 0.739226i) q^{2} -0.0974366 q^{3} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} +(-0.181073 + 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} -8.99051 q^{9} +(-2.56177 - 6.44013i) q^{10} -2.92866 q^{11} +(-0.283257 + 0.267708i) q^{12} -19.1586i q^{13} +0.337664i q^{15} +(0.902343 - 15.9745i) q^{16} +14.3897 q^{17} +(-16.7077 + 6.64602i) q^{18} -8.09744 q^{19} +(-9.52143 - 10.0744i) q^{20} +(-5.44254 + 2.16494i) q^{22} -16.7598i q^{23} +(-0.328500 + 0.706892i) q^{24} +12.9905 q^{25} +(-14.1625 - 35.6038i) q^{26} +1.75293 q^{27} +27.1649i q^{29} +(0.249610 + 0.627505i) q^{30} +44.8923i q^{31} +(-10.1319 - 30.3537i) q^{32} +0.285359 q^{33} +(26.7415 - 10.6373i) q^{34} +(-26.1362 + 24.7015i) q^{36} -39.5687i q^{37} +(-15.0480 + 5.98584i) q^{38} +1.86675i q^{39} +(-25.1416 - 11.6836i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(-8.51388 + 8.04653i) q^{44} +31.1563i q^{45} +(-12.3893 - 31.1459i) q^{46} -46.2793i q^{47} +(-0.0879212 + 1.55650i) q^{48} +(24.1412 - 9.60292i) q^{50} -1.40209 q^{51} +(-52.6385 - 55.6957i) q^{52} -9.69424i q^{53} +(3.25760 - 1.29581i) q^{54} +10.1492i q^{55} +0.788986 q^{57} +(20.0810 + 50.4825i) q^{58} +114.554 q^{59} +(0.927735 + 0.981619i) q^{60} -7.48032i q^{61} +(33.1855 + 83.4265i) q^{62} +(-41.2671 - 48.9186i) q^{64} -66.3935 q^{65} +(0.530302 - 0.210944i) q^{66} -12.0590 q^{67} +(41.8323 - 39.5360i) q^{68} +1.63302i q^{69} +129.187i q^{71} +(-30.3108 + 65.2252i) q^{72} +18.2854 q^{73} +(-29.2502 - 73.5334i) q^{74} -1.26575 q^{75} +(-23.5400 + 22.2478i) q^{76} +(1.37995 + 3.46911i) q^{78} +42.6168i q^{79} +(-55.3593 - 3.12704i) q^{80} +80.7438 q^{81} +(-85.2558 + 33.9132i) q^{82} +109.670 q^{83} -49.8673i q^{85} +(113.423 - 45.1174i) q^{86} -2.64685i q^{87} +(-9.87374 + 21.2471i) q^{88} +80.9162 q^{89} +(23.0316 + 57.9001i) q^{90} +(-46.0478 - 48.7223i) q^{92} -4.37415i q^{93} +(-34.2109 - 86.0041i) q^{94} +28.0614i q^{95} +(0.987218 + 2.95756i) q^{96} -162.086 q^{97} +26.3301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9} - 16 q^{10} - 32 q^{11} - 30 q^{12} - 71 q^{16} + 80 q^{17} - 29 q^{18} - 56 q^{19} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 q^{64} - 72 q^{65} + 276 q^{66} + 304 q^{67} + 190 q^{68} - 209 q^{72} + 112 q^{73} + 8 q^{74} - 72 q^{75} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9 - 16 * q^10 - 32 * q^11 - 30 * q^12 - 71 * q^16 + 80 * q^17 - 29 * q^18 - 56 * q^19 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * q^64 - 72 * q^65 + 276 * q^66 + 304 * q^67 + 190 * q^68 - 209 * q^72 + 112 * q^73 + 8 * q^74 - 72 * q^75 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * q^99

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