LMFDB - Embedded newform 232.3.b.c.115.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,3,Mod(115,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("232.115");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	232.b (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:	$6.32154213316$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			115.11
Character	$\chi$	$=$	232.115
Dual form			232.3.b.c.115.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64262 - 1.14096i) q^{2} +1.23647i q^{3} +(1.39641 + 3.74834i) q^{4} +6.52788i q^{5} +(1.41077 - 2.03106i) q^{6} -8.84035i q^{7} +(1.98293 - 7.75035i) q^{8} +7.47113 q^{9} +O(q^{10})$	\(q+(-1.64262 - 1.14096i) q^{2} +1.23647i q^{3} +(1.39641 + 3.74834i) q^{4} +6.52788i q^{5} +(1.41077 - 2.03106i) q^{6} -8.84035i q^{7} +(1.98293 - 7.75035i) q^{8} +7.47113 q^{9} +(7.44806 - 10.7228i) q^{10} -8.03032i q^{11} +(-4.63472 + 1.72663i) q^{12} +23.9693i q^{13} +(-10.0865 + 14.5213i) q^{14} -8.07155 q^{15} +(-12.1001 + 10.4685i) q^{16} +3.61156i q^{17} +(-12.2722 - 8.52427i) q^{18} +25.4722i q^{19} +(-24.4687 + 9.11562i) q^{20} +10.9309 q^{21} +(-9.16228 + 13.1908i) q^{22} +12.7195i q^{23} +(9.58312 + 2.45184i) q^{24} -17.6132 q^{25} +(27.3481 - 39.3725i) q^{26} +20.3661i q^{27} +(33.1366 - 12.3448i) q^{28} +(-28.6905 - 4.22540i) q^{29} +(13.2585 + 9.20933i) q^{30} +31.7948 q^{31} +(31.8199 - 3.39001i) q^{32} +9.92928 q^{33} +(4.12065 - 5.93242i) q^{34} +57.7087 q^{35} +(10.4328 + 28.0043i) q^{36} -28.0952 q^{37} +(29.0628 - 41.8412i) q^{38} -29.6374 q^{39} +(50.5934 + 12.9443i) q^{40} +58.3896i q^{41} +(-17.9553 - 12.4717i) q^{42} +20.5039i q^{43} +(30.1003 - 11.2136i) q^{44} +48.7706i q^{45} +(14.5125 - 20.8934i) q^{46} -53.0390 q^{47} +(-12.9440 - 14.9614i) q^{48} -29.1517 q^{49} +(28.9318 + 20.0960i) q^{50} -4.46560 q^{51} +(-89.8451 + 33.4711i) q^{52} -77.4712i q^{53} +(23.2370 - 33.4539i) q^{54} +52.4209 q^{55} +(-68.5158 - 17.5298i) q^{56} -31.4958 q^{57} +(42.3067 + 39.6755i) q^{58} +36.8773 q^{59} +(-11.2712 - 30.2549i) q^{60} +114.321 q^{61} +(-52.2269 - 36.2767i) q^{62} -66.0474i q^{63} +(-56.1360 - 30.7368i) q^{64} -156.469 q^{65} +(-16.3101 - 11.3289i) q^{66} +21.5732 q^{67} +(-13.5373 + 5.04323i) q^{68} -15.7274 q^{69} +(-94.7936 - 65.8434i) q^{70} -18.8089i q^{71} +(14.8147 - 57.9039i) q^{72} +105.400i q^{73} +(46.1498 + 32.0555i) q^{74} -21.7783i q^{75} +(-95.4785 + 35.5698i) q^{76} -70.9908 q^{77} +(48.6831 + 33.8152i) q^{78} +17.8244 q^{79} +(-68.3368 - 78.9877i) q^{80} +42.0580 q^{81} +(66.6203 - 95.9120i) q^{82} -0.565354 q^{83} +(15.2640 + 40.9726i) q^{84} -23.5758 q^{85} +(23.3942 - 33.6802i) q^{86} +(5.22460 - 35.4751i) q^{87} +(-62.2378 - 15.9236i) q^{88} -91.6468i q^{89} +(55.6454 - 80.1117i) q^{90} +211.897 q^{91} +(-47.6771 + 17.7617i) q^{92} +39.3135i q^{93} +(87.1231 + 60.5155i) q^{94} -166.280 q^{95} +(4.19166 + 39.3445i) q^{96} -86.0400i q^{97} +(47.8853 + 33.2610i) q^{98} -59.9955i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{4} - 184 q^{9}+O(q^{10}) $ 56 * q - 4 * q^4 - 184 * q^9	$ 56 q - 4 q^{4} - 184 q^{9} - 44 q^{16} - 12 q^{20} - 68 q^{22} - 72 q^{24} - 280 q^{25} + 116 q^{28} + 8 q^{30} + 32 q^{33} - 116 q^{34} + 96 q^{35} - 112 q^{36} - 176 q^{38} + 156 q^{42} - 424 q^{49} + 32 q^{51} - 56 q^{52} + 160 q^{54} + 32 q^{57} + 296 q^{58} + 512 q^{59} + 640 q^{62} - 304 q^{64} + 192 q^{65} + 352 q^{67} + 472 q^{74} + 44 q^{78} + 424 q^{80} + 280 q^{81} - 76 q^{82} + 128 q^{83} + 412 q^{86} - 84 q^{88} + 96 q^{91} - 92 q^{92} + 276 q^{94} + 300 q^{96}+O(q^{100}) $ 56 * q - 4 * q^4 - 184 * q^9 - 44 * q^16 - 12 * q^20 - 68 * q^22 - 72 * q^24 - 280 * q^25 + 116 * q^28 + 8 * q^30 + 32 * q^33 - 116 * q^34 + 96 * q^35 - 112 * q^36 - 176 * q^38 + 156 * q^42 - 424 * q^49 + 32 * q^51 - 56 * q^52 + 160 * q^54 + 32 * q^57 + 296 * q^58 + 512 * q^59 + 640 * q^62 - 304 * q^64 + 192 * q^65 + 352 * q^67 + 472 * q^74 + 44 * q^78 + 424 * q^80 + 280 * q^81 - 76 * q^82 + 128 * q^83 + 412 * q^86 - 84 * q^88 + 96 * q^91 - 92 * q^92 + 276 * q^94 + 300 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.64262	−	1.14096i	−0.821311	−	0.570481i
$2$	−1.64262	−	1.14096i	−0.821311	−	0.570481i
$3$			1.23647i			0.412158i	0.978535	+	0.206079i	$0.0660704\pi$
$3$			1.23647i			0.412158i	−0.978535	+	0.206079i	$0.933930\pi$
$4$	1.39641	+	3.74834i	0.349103	+	0.937084i
$5$			6.52788i			1.30558i	0.757541	+	0.652788i	$0.226401\pi$
$5$			6.52788i			1.30558i	−0.757541	+	0.652788i	$0.773599\pi$
$6$	1.41077	−	2.03106i	0.235128	−	0.338510i
$7$		−	8.84035i		−	1.26291i	−0.775414	−	0.631453i	$-0.782459\pi$
$7$		−	8.84035i		−	1.26291i	0.775414	−	0.631453i	$-0.217541\pi$
$8$	1.98293	−	7.75035i	0.247866	−	0.968794i
$9$	7.47113			0.830126
$10$	7.44806	−	10.7228i	0.744806	−	1.07228i
$11$		−	8.03032i		−	0.730029i	−0.931002	−	0.365014i	$-0.881064\pi$
$11$		−	8.03032i		−	0.730029i	0.931002	−	0.365014i	$-0.118936\pi$
$12$	−4.63472	+	1.72663i	−0.386227	+	0.143886i
$13$			23.9693i			1.84379i	0.387436	+	0.921897i	$0.373361\pi$
$13$			23.9693i			1.84379i	−0.387436	+	0.921897i	$0.626639\pi$
$14$	−10.0865	+	14.5213i	−0.720464	+	1.03724i
$15$	−8.07155			−0.538104
$16$	−12.1001	+	10.4685i	−0.756254	+	0.654278i
$17$			3.61156i			0.212445i	0.994342	+	0.106222i	$0.0338755\pi$
$17$			3.61156i			0.212445i	−0.994342	+	0.106222i	$0.966124\pi$
$18$	−12.2722	−	8.52427i	−0.681791	−	0.473571i
$19$			25.4722i			1.34064i	0.742070	+	0.670322i	$0.233844\pi$
$19$			25.4722i			1.34064i	−0.742070	+	0.670322i	$0.766156\pi$
$20$	−24.4687	+	9.11562i	−1.22343	+	0.455781i
$21$	10.9309			0.520517
$22$	−9.16228	+	13.1908i	−0.416467	+	0.599581i
$23$			12.7195i			0.553023i	0.961011	+	0.276511i	$0.0891784\pi$
$23$			12.7195i			0.553023i	−0.961011	+	0.276511i	$0.910822\pi$
$24$	9.58312	+	2.45184i	0.399297	+	0.102160i
$25$	−17.6132			−0.704527
$26$	27.3481	−	39.3725i	1.05185	−	1.51433i
$27$			20.3661i			0.754301i
$28$	33.1366	−	12.3448i	1.18345	−	0.440885i
$29$	−28.6905	−	4.22540i	−0.989328	−	0.145703i
$29$	−28.6905	−	4.22540i	−0.989328	−	0.145703i
$30$	13.2585	+	9.20933i	0.441950	+	0.306978i
$31$	31.7948			1.02564			0.512820	−	0.858496i	$-0.328601\pi$
$31$	31.7948			1.02564			0.512820	+	0.858496i	$0.328601\pi$
$32$	31.8199	−	3.39001i	0.994373	−	0.105938i
$33$	9.92928			0.300887
$34$	4.12065	−	5.93242i	0.121196	−	0.174483i
$35$	57.7087			1.64882
$36$	10.4328	+	28.0043i	0.289800	+	0.777898i
$37$	−28.0952			−0.759330			−0.379665	−	0.925124i	$-0.623961\pi$
$37$	−28.0952			−0.759330			−0.379665	+	0.925124i	$0.623961\pi$
$38$	29.0628	−	41.8412i	0.764812	−	1.10109i
$39$	−29.6374			−0.759935
$40$	50.5934	+	12.9443i	1.26483	+	0.323608i
$41$			58.3896i			1.42414i	0.702110	+	0.712068i	$0.252241\pi$
$41$			58.3896i			1.42414i	−0.702110	+	0.712068i	$0.747759\pi$
$42$	−17.9553	−	12.4717i	−0.427507	−	0.296945i
$43$			20.5039i			0.476836i	0.971163	+	0.238418i	$0.0766288\pi$
$43$			20.5039i			0.476836i	−0.971163	+	0.238418i	$0.923371\pi$
$44$	30.1003	−	11.2136i	0.684099	−	0.254856i
$45$			48.7706i			1.08379i
$46$	14.5125	−	20.8934i	0.315489	−	0.454204i
$47$	−53.0390			−1.12849			−0.564245	−	0.825607i	$-0.690833\pi$
$47$	−53.0390			−1.12849			−0.564245	+	0.825607i	$0.690833\pi$
$48$	−12.9440	−	14.9614i	−0.269666	−	0.311696i
$49$	−29.1517			−0.594933
$50$	28.9318	+	20.0960i	0.578636	+	0.401919i
$51$	−4.46560			−0.0875608
$52$	−89.8451	+	33.4711i	−1.72779	+	0.643674i
$53$		−	77.4712i		−	1.46172i	−0.682527	−	0.730861i	$-0.739119\pi$
$53$		−	77.4712i		−	1.46172i	0.682527	−	0.730861i	$-0.260881\pi$
$54$	23.2370	−	33.4539i	0.430314	−	0.619516i
$55$	52.4209			0.953108
$56$	−68.5158	−	17.5298i	−1.22350	−	0.313032i
$57$	−31.4958			−0.552557
$58$	42.3067	+	39.6755i	0.729425	+	0.684061i
$59$	36.8773			0.625040			0.312520	−	0.949911i	$-0.398827\pi$
$59$	36.8773			0.625040			0.312520	+	0.949911i	$0.398827\pi$
$60$	−11.2712	−	30.2549i	−0.187854	−	0.504248i
$61$	114.321			1.87411			0.937057	−	0.349177i	$-0.113539\pi$
$61$	114.321			1.87411			0.937057	+	0.349177i	$0.113539\pi$
$62$	−52.2269	−	36.2767i	−0.842369	−	0.585107i
$63$		−	66.0474i		−	1.04837i
$64$	−56.1360	−	30.7368i	−0.877125	−	0.480263i
$65$	−156.469			−2.40721
$66$	−16.3101	−	11.3289i	−0.247122	−	0.171650i
$67$	21.5732			0.321987			0.160994	−	0.986955i	$-0.448530\pi$
$67$	21.5732			0.321987			0.160994	+	0.986955i	$0.448530\pi$
$68$	−13.5373	+	5.04323i	−0.199078	+	0.0741651i
$69$	−15.7274			−0.227933
$70$	−94.7936	−	65.8434i	−1.35419	−	0.940620i
$71$		−	18.8089i		−	0.264915i	−0.991189	−	0.132457i	$-0.957713\pi$
$71$		−	18.8089i		−	0.264915i	0.991189	−	0.132457i	$-0.0422867\pi$
$72$	14.8147	−	57.9039i	0.205760	−	0.804221i
$73$			105.400i			1.44383i	0.691981	+	0.721915i	$0.256738\pi$
$73$			105.400i			1.44383i	−0.691981	+	0.721915i	$0.743262\pi$
$74$	46.1498	+	32.0555i	0.623646	+	0.433183i
$75$		−	21.7783i		−	0.290377i
$76$	−95.4785	+	35.5698i	−1.25630	+	0.468023i
$77$	−70.9908			−0.921958
$78$	48.6831	+	33.8152i	0.624143	+	0.433528i
$79$	17.8244			0.225625			0.112813	−	0.993616i	$-0.464014\pi$
$79$	17.8244			0.225625			0.112813	+	0.993616i	$0.464014\pi$
$80$	−68.3368	−	78.9877i	−0.854210	−	0.987346i
$81$	42.0580			0.519234
$82$	66.6203	−	95.9120i	0.812443	−	1.16966i
$83$	−0.565354			−0.00681149			−0.00340575	−	0.999994i	$-0.501084\pi$
$83$	−0.565354			−0.00681149			−0.00340575	+	0.999994i	$0.501084\pi$
$84$	15.2640	+	40.9726i	0.181714	+	0.487769i
$85$	−23.5758			−0.277362
$86$	23.3942	−	33.6802i	0.272026	−	0.391630i
$87$	5.22460	−	35.4751i	0.0600529	−	0.407760i
$88$	−62.2378	−	15.9236i	−0.707248	−	0.180949i
$89$		−	91.6468i		−	1.02974i	−0.857268	−	0.514870i	$-0.827840\pi$
$89$		−	91.6468i		−	1.02974i	0.857268	−	0.514870i	$-0.172160\pi$
$90$	55.6454	−	80.1117i	0.618282	−	0.890130i
$91$	211.897			2.32854
$92$	−47.6771	+	17.7617i	−0.518229	+	0.193062i
$93$			39.3135i			0.422726i
$94$	87.1231	+	60.5155i	0.926841	+	0.643782i
$95$	−166.280			−1.75031
$96$	4.19166	+	39.3445i	0.0436632	+	0.409839i
$97$		−	86.0400i		−	0.887010i	−0.896272	−	0.443505i	$-0.853735\pi$
$97$		−	86.0400i		−	0.887010i	0.896272	−	0.443505i	$-0.146265\pi$
$98$	47.8853	+	33.2610i	0.488625	+	0.339398i
$99$		−	59.9955i		−	0.606016i
$100$	−24.5953	−	66.0201i	−0.245953	−	0.660201i
$101$	−13.3964			−0.132637			−0.0663187	−	0.997798i	$-0.521125\pi$
$101$	−13.3964			−0.132637			−0.0663187	+	0.997798i	$0.521125\pi$
$102$	7.33529	+	5.09508i	0.0719146	+	0.0499517i
$103$		−	123.281i		−	1.19690i	−0.801160	−	0.598450i	$-0.795783\pi$
$103$		−	123.281i		−	1.19690i	0.801160	−	0.598450i	$-0.204217\pi$
$104$	185.771	+	47.5294i	1.78626	+	0.457014i
$105$			71.3553i			0.679575i
$106$	−88.3917	+	127.256i	−0.833884	+	1.20053i
$107$	−121.653			−1.13695			−0.568473	−	0.822702i	$-0.692466\pi$
$107$	−121.653			−1.13695			−0.568473	+	0.822702i	$0.692466\pi$
$108$	−76.3391	+	28.4395i	−0.706844	+	0.263329i
$109$			60.4520i			0.554606i	0.960783	+	0.277303i	$0.0894405\pi$
$109$			60.4520i			0.554606i	−0.960783	+	0.277303i	$0.910559\pi$
$110$	−86.1078	−	59.8103i	−0.782798	−	0.543730i
$111$		−	34.7390i		−	0.312964i
$112$	92.5448	+	106.969i	0.826293	+	0.955078i
$113$		−	52.0761i		−	0.460851i	−0.973090	−	0.230425i	$-0.925988\pi$
$113$		−	52.0761i		−	0.460851i	0.973090	−	0.230425i	$-0.0740118\pi$
$114$	51.7356	+	35.9355i	0.453821	+	0.315223i
$115$	−83.0315			−0.722013
$116$	−24.2256	−	113.442i	−0.208841	−	0.977950i
$117$			179.078i			1.53058i
$118$	−60.5755	−	42.0756i	−0.513352	−	0.356573i
$119$	31.9274			0.268298
$120$	−16.0053	+	62.5574i	−0.133378	+	0.521312i
$121$	56.5140			0.467058
$122$	−187.786	−	130.436i	−1.53923	−	1.06915i
$123$	−72.1973			−0.586970
$124$	44.3987	+	119.178i	0.358054	+	0.961110i
$125$			48.2202i			0.385762i
$126$	−75.3575	+	108.491i	−0.598076	+	0.861039i
$127$	97.8761			0.770678			0.385339	−	0.922775i	$-0.374085\pi$
$127$	97.8761			0.770678			0.385339	+	0.922775i	$0.374085\pi$
$128$	57.1407	+	114.538i	0.446412	+	0.894828i
$129$	−25.3526			−0.196532
$130$	257.019	+	178.525i	1.97707	+	1.37327i
$131$		−	229.929i		−	1.75518i	−0.479408	−	0.877592i	$-0.659149\pi$
$131$		−	229.929i		−	1.75518i	0.479408	−	0.877592i	$-0.340851\pi$
$132$	13.8654	+	37.2183i	0.105041	+	0.281957i
$133$	225.183			1.69311
$134$	−35.4365	−	24.6141i	−0.264452	−	0.183688i
$135$	−132.948			−0.984797
$136$	27.9908	+	7.16146i	0.205815	+	0.0526578i
$137$			81.0099i			0.591313i	0.955294	+	0.295656i	$0.0955384\pi$
$137$			81.0099i			0.591313i	−0.955294	+	0.295656i	$0.904462\pi$
$138$	25.8341	+	17.9443i	0.187204	+	0.130031i
$139$	122.442			0.880878			0.440439	−	0.897782i	$-0.354823\pi$
$139$	122.442			0.880878			0.440439	+	0.897782i	$0.354823\pi$
$140$	80.5852	+	216.312i	0.575609	+	1.54508i
$141$		−	65.5814i		−	0.465116i
$142$	−21.4603	+	30.8960i	−0.151129	+	0.217577i
$143$	192.481			1.34602
$144$	−90.4011	+	78.2112i	−0.627786	+	0.543133i
$145$	27.5829	−	187.288i	0.190227	−	1.29164i
$146$	120.257	−	173.132i	0.823678	−	1.18583i
$147$		−	36.0454i		−	0.245207i
$148$	−39.2325	−	105.310i	−0.265085	−	0.711556i
$149$		−	1.76709i		−	0.0118597i	−0.999982	−	0.00592983i	$-0.998112\pi$
$149$		−	1.76709i		−	0.0118597i	0.999982	−	0.00592983i	$-0.00188753\pi$
$150$	−24.8481	+	35.7734i	−0.165654	+	0.238490i
$151$			180.821i			1.19749i	0.800939	+	0.598747i	$0.204334\pi$
$151$			180.821i			1.19749i	−0.800939	+	0.598747i	$0.795666\pi$
$152$	197.419	+	50.5096i	1.29881	+	0.332300i
$153$			26.9824i			0.176356i
$154$	116.611	+	80.9978i	0.757214	+	0.525960i
$155$			207.553i			1.33905i
$156$	−41.3861	−	111.091i	−0.265296	−	0.712123i
$157$	53.7550			0.342388			0.171194	−	0.985237i	$-0.445237\pi$
$157$	53.7550			0.342388			0.171194	+	0.985237i	$0.445237\pi$
$158$	−29.2788	−	20.3370i	−0.185309	−	0.128715i
$159$	95.7912			0.602460
$160$	22.1296	+	207.717i	0.138310	+	1.29823i
$161$	112.445			0.698416
$162$	−69.0853	−	47.9865i	−0.426453	−	0.296213i
$163$		−	234.231i		−	1.43700i	−0.695528	−	0.718499i	$-0.744829\pi$
$163$		−	234.231i		−	1.43700i	0.695528	−	0.718499i	$-0.255171\pi$
$164$	−218.864	+	81.5360i	−1.33454	+	0.497171i
$165$			64.8171i			0.392831i
$166$	0.928663	+	0.645047i	0.00559435	+	0.00388583i
$167$		−	223.946i		−	1.34099i	−0.741913	−	0.670496i	$-0.766081\pi$
$167$		−	223.946i		−	1.34099i	0.741913	−	0.670496i	$-0.233919\pi$
$168$	21.6751	−	84.7181i	0.129019	−	0.504274i
$169$	−405.528			−2.39957
$170$	38.7261	+	26.8991i	0.227801	+	0.158230i
$171$			190.306i			1.11290i
$172$	−76.8556	+	28.6320i	−0.446835	+	0.166465i
$173$		−	79.6404i		−	0.460349i	−0.973149	−	0.230175i	$-0.926070\pi$
$173$		−	79.6404i		−	0.460349i	0.973149	−	0.230175i	$-0.0739298\pi$
$174$	−49.0578	+	52.3111i	−0.281941	+	0.300639i
$175$			155.707i			0.889752i
$176$	84.0650	+	97.1673i	0.477642	+	0.552087i
$177$			45.5979i			0.257615i
$178$	−104.566	+	150.541i	−0.587447	+	0.845737i
$179$	218.155			1.21874			0.609371	−	0.792885i	$-0.291422\pi$
$179$	218.155			1.21874			0.609371	+	0.792885i	$0.291422\pi$
$180$	−182.809	+	68.1040i	−1.01560	+	0.378355i
$181$		−	86.7152i		−	0.479090i	−0.970885	−	0.239545i	$-0.923002\pi$
$181$		−	86.7152i		−	0.479090i	0.970885	−	0.239545i	$-0.0769982\pi$
$182$	−348.067	−	241.766i	−1.91245	−	1.32839i
$183$			141.355i			0.772431i
$184$	98.5808	+	25.2219i	0.535765	+	0.137076i
$185$		−	183.402i		−	0.991362i
$186$	44.8552	−	64.5772i	0.241157	−	0.347189i
$187$	29.0020			0.155091
$188$	−74.0644	−	198.808i	−0.393960	−	1.05749i
$189$	180.044			0.952612
$190$	273.135	+	189.719i	1.43755	+	0.998519i
$191$	119.023			0.623156			0.311578	−	0.950221i	$-0.399142\pi$
$191$	119.023			0.623156			0.311578	+	0.950221i	$0.399142\pi$
$192$	38.0053	−	69.4107i	0.197944	−	0.361514i
$193$			28.0803i			0.145494i	0.997350	+	0.0727468i	$0.0231765\pi$
$193$			28.0803i			0.145494i	−0.997350	+	0.0727468i	$0.976823\pi$
$194$	−98.1683	+	141.331i	−0.506022	+	0.728511i
$195$		−	193.470i		−	0.992152i
$196$	−40.7079	−	109.271i	−0.207693	−	0.557503i
$197$		−	70.7646i		−	0.359211i	−0.983739	−	0.179606i	$-0.942518\pi$
$197$		−	70.7646i		−	0.359211i	0.983739	−	0.179606i	$-0.0574821\pi$
$198$	−68.4526	+	98.5500i	−0.345720	+	0.497727i
$199$			281.244i			1.41329i	0.707569	+	0.706644i	$0.249792\pi$
$199$			281.244i			1.41329i	−0.707569	+	0.706644i	$0.750208\pi$
$200$	−34.9257	+	136.508i	−0.174628	+	0.682542i
$201$			26.6747i			0.132710i
$202$	22.0052	+	15.2848i	0.108937	+	0.0756671i
$203$	−37.3540	+	253.634i	−0.184010	+	1.24943i
$204$	−6.23582	−	16.7386i	−0.0305678	−	0.0820518i
$205$	−381.160			−1.85932
$206$	−140.659	+	202.504i	−0.682809	+	0.983027i
$207$			95.0292i			0.459078i
$208$	−250.922	−	290.030i	−1.20635	−	1.39438i
$209$	204.550			0.978709
$210$	81.4137	−	117.210i	0.387684	−	0.558142i
$211$		−	251.923i		−	1.19395i	−0.802260	−	0.596975i	$-0.796369\pi$
$211$		−	251.923i		−	1.19395i	0.802260	−	0.596975i	$-0.203631\pi$
$212$	290.388	−	108.182i	1.36976	−	0.510292i
$213$	23.2568			0.109187
$214$	199.830	+	138.802i	0.933786	+	0.648606i
$215$	−133.847			−0.622545
$216$	157.845	+	40.3846i	0.730763	+	0.186966i
$217$		−	281.077i		−	1.29529i
$218$	68.9734	−	99.2998i	0.316392	−	0.455504i
$219$	−130.324			−0.595087
$220$	73.2013	+	196.491i	0.332733	+	0.893142i
$221$	−86.5665			−0.391704
$222$	−39.6359	+	57.0630i	−0.178540	+	0.257041i
$223$		−	219.801i		−	0.985653i	−0.870128	−	0.492826i	$-0.835964\pi$
$223$		−	219.801i		−	0.985653i	0.870128	−	0.492826i	$-0.164036\pi$
$224$	−29.9689	−	281.299i	−0.133790	−	1.25580i
$225$	−131.590			−0.584846
$226$	−59.4169	+	85.5414i	−0.262907	+	0.378502i
$227$	−450.034			−1.98253			−0.991264	−	0.131892i	$-0.957895\pi$
$227$	−450.034			−1.98253			−0.991264	+	0.131892i	$0.957895\pi$
$228$	−43.9811	−	118.057i	−0.192900	−	0.517793i
$229$	−354.060			−1.54611			−0.773057	−	0.634336i	$-0.781274\pi$
$229$	−354.060			−1.54611			−0.773057	+	0.634336i	$0.781274\pi$
$230$	136.389	+	94.7357i	0.592997	+	0.411895i
$231$		−	87.7783i		−	0.379993i
$232$	−89.6396	+	213.983i	−0.386378	+	0.922341i
$233$	382.640			1.64223			0.821116	−	0.570761i	$-0.193352\pi$
$233$	382.640			1.64223			0.821116	+	0.570761i	$0.193352\pi$
$234$	204.321	−	294.157i	0.873166	−	1.25708i
$235$		−	346.232i		−	1.47333i
$236$	51.4960	+	138.229i	0.218203	+	0.585715i
$237$			22.0394i			0.0929933i
$238$	−52.4447	−	36.4280i	−0.220356	−	0.153059i
$239$		−	83.7394i		−	0.350374i	−0.984535	−	0.175187i	$-0.943947\pi$
$239$		−	83.7394i		−	0.350374i	0.984535	−	0.175187i	$-0.0560530\pi$
$240$	97.6663	−	84.4967i	0.406943	−	0.352070i
$241$	−243.346			−1.00973			−0.504867	−	0.863197i	$-0.668459\pi$
$241$	−243.346			−1.00973			−0.504867	+	0.863197i	$0.668459\pi$
$242$	−92.8311	−	64.4803i	−0.383600	−	0.266448i
$243$			235.299i			0.968308i
$244$	159.639	+	428.513i	0.654259	+	1.75620i
$245$		−	190.299i		−	0.776730i
$246$	118.593	+	82.3743i	0.482085	+	0.334855i
$247$	−610.552			−2.47187
$248$	63.0469	−	246.421i	0.254221	−	0.993633i
$249$		−	0.699046i		−	0.00280741i
$250$	55.0174	−	79.2076i	0.220070	−	0.316831i
$251$			313.357i			1.24844i	0.781250	+	0.624218i	$0.214582\pi$
$251$			313.357i			1.24844i	−0.781250	+	0.624218i	$0.785418\pi$
$252$	247.568	−	92.2295i	0.982412	−	0.365990i
$253$	102.142			0.403723
$254$	−160.773	−	111.673i	−0.632966	−	0.439657i
$255$		−	29.1509i		−	0.114317i
$256$	36.8229	−	253.338i	0.143839	−	0.989601i
$257$	102.651			0.399419			0.199710	−	0.979855i	$-0.436000\pi$
$257$	102.651			0.399419			0.199710	+	0.979855i	$0.436000\pi$
$258$	41.6447	+	28.9263i	0.161414	+	0.112118i
$259$			248.371i			0.958963i
$260$	−218.495	−	586.498i	−0.840366	−	2.25576i
$261$	−214.351	−	31.5685i	−0.821267	−	0.120952i
$262$	−262.340	+	377.687i	−1.00130	+	1.44155i
$263$	46.1457			0.175459			0.0877294	−	0.996144i	$-0.472039\pi$
$263$	46.1457			0.175459			0.0877294	+	0.996144i	$0.472039\pi$
$264$	19.6891	−	76.9555i	0.0745798	−	0.291498i
$265$	505.723			1.90839
$266$	−369.891	−	256.926i	−1.39057	−	0.965886i
$267$	113.319			0.424416
$268$	30.1250	+	80.8635i	0.112407	+	0.301729i
$269$	404.551			1.50391			0.751953	−	0.659217i	$-0.229112\pi$
$269$	404.551			1.50391			0.751953	+	0.659217i	$0.229112\pi$
$270$	218.383	+	151.688i	0.808825	+	0.561808i
$271$	277.241			1.02303			0.511516	−	0.859274i	$-0.329084\pi$
$271$	277.241			1.02303			0.511516	+	0.859274i	$0.329084\pi$
$272$	−37.8074	−	43.7001i	−0.138998	−	0.160662i
$273$			262.005i			0.959726i
$274$	92.4292	−	133.069i	0.337333	−	0.485652i
$275$			141.439i			0.514325i
$276$	−21.9619	−	58.9515i	−0.0795721	−	0.213592i
$277$		−	225.726i		−	0.814894i	−0.913229	−	0.407447i	$-0.866419\pi$
$277$		−	225.726i		−	0.814894i	0.913229	−	0.407447i	$-0.133581\pi$
$278$	−201.126	−	139.702i	−0.723475	−	0.502524i
$279$	237.543			0.851409
$280$	114.432	−	447.263i	0.408687	−	1.59737i
$281$	−65.4123			−0.232784			−0.116392	−	0.993203i	$-0.537133\pi$
$281$	−65.4123			−0.232784			−0.116392	+	0.993203i	$0.537133\pi$
$282$	−74.8259	+	107.725i	−0.265340	+	0.382005i
$283$	−515.470			−1.82145			−0.910724	−	0.413015i	$-0.864476\pi$
$283$	−515.470			−1.82145			−0.910724	+	0.413015i	$0.864476\pi$
$284$	70.5022	−	26.2651i	0.248247	−	0.0924826i
$285$		−	205.601i		−	0.721405i
$286$	−316.174	−	219.614i	−1.10550	−	0.767880i
$287$	516.184			1.79855
$288$	237.731	−	25.3272i	0.825454	−	0.0879417i
$289$	275.957			0.954867
$290$	−258.997	+	276.173i	−0.893093	+	0.952320i
$291$	106.386			0.365589
$292$	−395.073	+	147.181i	−1.35299	+	0.504046i
$293$	170.234			0.581005			0.290502	−	0.956874i	$-0.406178\pi$
$293$	170.234			0.581005			0.290502	+	0.956874i	$0.406178\pi$
$294$	−41.1264	+	59.2089i	−0.139886	+	0.201391i
$295$			240.731i			0.816037i
$296$	−55.7108	+	217.748i	−0.188212	+	0.735634i
$297$	163.547			0.550662
$298$	−2.01618	+	2.90266i	−0.00676570	+	0.00974046i
$299$	−304.878			−1.01966
$300$	81.6322	−	30.4114i	0.272107	−	0.101371i
$301$	181.262			0.602199
$302$	206.310	−	297.021i	0.683147	−	0.983514i
$303$		−	16.5643i		−	0.0546676i
$304$	−266.655	−	308.216i	−0.877154	−	1.01387i
$305$			746.273i			2.44680i
$306$	30.7859	−	44.3219i	0.100608	−	0.144843i
$307$			506.327i			1.64927i	0.565663	+	0.824637i	$0.308620\pi$
$307$			506.327i			1.64927i	−0.565663	+	0.824637i	$0.691380\pi$
$308$	−99.1325	−	266.097i	−0.321859	−	0.863953i
$309$	152.433			0.493312
$310$	236.810	−	340.931i	0.763902	−	1.09978i
$311$	−391.438			−1.25864			−0.629321	−	0.777145i	$-0.716667\pi$
$311$	−391.438			−1.25864			−0.629321	+	0.777145i	$0.716667\pi$
$312$	−58.7690	+	229.701i	−0.188362	+	0.736220i
$313$	−156.982			−0.501540			−0.250770	−	0.968047i	$-0.580684\pi$
$313$	−156.982			−0.501540			−0.250770	+	0.968047i	$0.580684\pi$
$314$	−88.2991	−	61.3324i	−0.281207	−	0.195326i
$315$	431.149			1.36873
$316$	24.8902	+	66.8119i	0.0787666	+	0.211430i
$317$	−145.018			−0.457471			−0.228736	−	0.973489i	$-0.573459\pi$
$317$	−145.018			−0.457471			−0.228736	+	0.973489i	$0.573459\pi$
$318$	−157.349	−	109.294i	−0.494807	−	0.343692i
$319$	−33.9313	+	230.394i	−0.106368	+	0.722238i
$320$	200.646	−	366.449i	0.627019	−	1.14515i
$321$		−	150.421i		−	0.468602i
$322$	−184.705	−	128.295i	−0.573617	−	0.398433i
$323$	−91.9944			−0.284812
$324$	58.7303	+	157.647i	0.181266	+	0.486566i
$325$		−	422.176i		−	1.29900i
$326$	−267.248	+	384.753i	−0.819780	+	1.18022i
$327$	−74.7474			−0.228585
$328$	452.540	+	115.782i	1.37970	+	0.352995i
$329$			468.883i			1.42518i
$330$	73.9539	−	106.470i	0.224103	−	0.322637i
$331$		−	386.070i		−	1.16637i	−0.812338	−	0.583187i	$-0.801805\pi$
$331$		−	386.070i		−	1.16637i	0.812338	−	0.583187i	$-0.198195\pi$
$332$	−0.789468	−	2.11914i	−0.00237791	−	0.00638294i
$333$	−209.903			−0.630339
$334$	−255.513	+	367.858i	−0.765010	+	1.10137i
$335$			140.827i			0.420379i
$336$	−132.264	+	114.429i	−0.393643	+	0.340563i
$337$		−	150.855i		−	0.447641i	−0.974630	−	0.223820i	$-0.928147\pi$
$337$		−	150.855i		−	0.447641i	0.974630	−	0.223820i	$-0.0718529\pi$
$338$	666.129	+	462.692i	1.97080	+	1.36891i
$339$	64.3908			0.189943
$340$	−32.9216	−	88.3701i	−0.0968281	−	0.259912i
$341$		−	255.322i		−	0.748746i
$342$	217.132	−	312.601i	0.634890	−	0.914039i
$343$		−	175.466i		−	0.511561i
$344$	158.913	+	40.6578i	0.461956	+	0.118191i
$345$		−	102.666i		−	0.297584i
$346$	−90.8667	+	130.819i	−0.262620	+	0.378090i
$347$	−32.6034			−0.0939579			−0.0469790	−	0.998896i	$-0.514959\pi$
$347$	−32.6034			−0.0939579			−0.0469790	+	0.998896i	$0.514959\pi$
$348$	140.268	−	29.9543i	0.403070	−	0.0860757i
$349$			470.346i			1.34770i	0.738869	+	0.673849i	$0.235360\pi$
$349$			470.346i			1.34770i	−0.738869	+	0.673849i	$0.764640\pi$
$350$	177.655	−	255.767i	0.507587	−	0.730763i
$351$	−488.162			−1.39078
$352$	−27.2229	−	255.524i	−0.0773377	−	0.725921i
$353$	300.585			0.851515			0.425758	−	0.904837i	$-0.360008\pi$
$353$	300.585			0.851515			0.425758	+	0.904837i	$0.360008\pi$
$354$	52.0255	−	74.9001i	0.146965	−	0.211582i
$355$	122.782			0.345866
$356$	343.523	−	127.977i	0.964953	−	0.359486i
$357$			39.4774i			0.110581i
$358$	−358.346	−	248.906i	−1.00097	−	0.695269i
$359$	−304.011			−0.846827			−0.423413	−	0.905937i	$-0.639168\pi$
$359$	−304.011			−0.846827			−0.423413	+	0.905937i	$0.639168\pi$
$360$	377.990	+	96.7087i	1.04997	+	0.268635i
$361$	−287.835			−0.797326
$362$	−98.9387	+	142.440i	−0.273311	+	0.393482i
$363$			69.8781i			0.192502i
$364$	295.896	+	794.262i	0.812901	+	2.18204i
$365$	−688.036			−1.88503
$366$	161.281	−	232.193i	0.440657	−	0.634406i
$367$	577.287			1.57299			0.786495	−	0.617597i	$-0.211894\pi$
$367$	577.287			1.57299			0.786495	+	0.617597i	$0.211894\pi$
$368$	−133.154	−	153.907i	−0.361831	−	0.418226i
$369$			436.236i			1.18221i
$370$	−209.255	+	301.260i	−0.565553	+	0.814217i
$371$	−684.872			−1.84602
$372$	−147.360	+	54.8979i	−0.396130	+	0.147575i
$373$			443.642i			1.18939i	0.803952	+	0.594694i	$0.202727\pi$
$373$			443.642i			1.18939i	−0.803952	+	0.594694i	$0.797273\pi$
$374$	−47.6392	−	33.0901i	−0.127378	−	0.0884762i
$375$	−59.6231			−0.158995
$376$	−105.173	+	411.071i	−0.279714	+	1.09327i
$377$	101.280	−	687.692i	0.268647	−	1.82412i
$378$	−295.744	−	205.423i	−0.782391	−	0.543447i
$379$		−	293.481i		−	0.774357i	−0.922005	−	0.387179i	$-0.873450\pi$
$379$		−	293.481i		−	0.774357i	0.922005	−	0.387179i	$-0.126550\pi$
$380$	−232.195	−	623.272i	−0.611040	−	1.64019i
$381$			121.021i			0.317641i
$382$	−195.509	−	135.800i	−0.511805	−	0.355498i
$383$		−	202.204i		−	0.527949i	−0.964530	−	0.263974i	$-0.914967\pi$
$383$		−	202.204i		−	0.527949i	0.964530	−	0.263974i	$-0.0850334\pi$
$384$	−141.623	+	70.6530i	−0.368811	+	0.183992i
$385$		−	463.419i		−	1.20369i
$386$	32.0385	−	46.1253i	0.0830013	−	0.119496i
$387$			153.188i			0.395833i
$388$	322.507	−	120.147i	0.831204	−	0.309658i
$389$	127.641			0.328126			0.164063	−	0.986450i	$-0.447540\pi$
$389$	127.641			0.328126			0.164063	+	0.986450i	$0.447540\pi$
$390$	−220.741	+	317.797i	−0.566004	+	0.814865i
$391$	−45.9373			−0.117487
$392$	−57.8058	+	225.936i	−0.147464	+	0.576368i
$393$	284.302			0.723414
$394$	−80.7397	+	116.239i	−0.204923	+	0.295024i
$395$			116.356i			0.294571i
$396$	224.884	−	83.7786i	0.567888	−	0.211562i
$397$			29.5557i			0.0744477i	0.999307	+	0.0372239i	$0.0118515\pi$
$397$			29.5557i			0.0744477i	−0.999307	+	0.0372239i	$0.988149\pi$
$398$	320.889	−	461.978i	0.806254	−	1.16075i
$399$			278.434i			0.697828i
$400$	213.121	−	184.383i	0.532801	−	0.460957i
$401$	273.221			0.681350			0.340675	−	0.940181i	$-0.389344\pi$
$401$	273.221			0.681350			0.340675	+	0.940181i	$0.389344\pi$
$402$	30.4348	−	43.8164i	0.0757084	−	0.108996i
$403$			762.100i			1.89107i
$404$	−18.7069	−	50.2141i	−0.0463042	−	0.124292i
$405$			274.549i			0.677899i
$406$	350.745	−	374.006i	0.863905	−	0.921196i
$407$			225.613i			0.554333i
$408$	−8.85497	+	34.6100i	−0.0217033	+	0.0848284i
$409$			116.481i			0.284795i	0.989810	+	0.142398i	$0.0454812\pi$
$409$			116.481i			0.284795i	−0.989810	+	0.142398i	$0.954519\pi$
$410$	626.102	+	434.889i	1.52708	+	1.06071i
$411$	−100.167			−0.243714
$412$	462.098	−	172.151i	1.12160	−	0.417842i
$413$		−	326.009i		−	0.789367i
$414$	108.425	−	156.097i	0.261895	−	0.377046i
$415$		−	3.69056i		−	0.00889292i
$416$	81.2563	+	762.702i	0.195328	+	1.83342i
$417$			151.397i			0.363061i
$418$	−335.999	−	233.384i	−0.803824	−	0.558335i
$419$	−341.609			−0.815296			−0.407648	−	0.913139i	$-0.633651\pi$
$419$	−341.609			−0.815296			−0.407648	+	0.913139i	$0.633651\pi$
$420$	−267.464	+	99.6416i	−0.636819	+	0.237242i
$421$	98.8121			0.234708			0.117354	−	0.993090i	$-0.462559\pi$
$421$	98.8121			0.234708			0.117354	+	0.993090i	$0.462559\pi$
$422$	−287.435	+	413.815i	−0.681126	+	0.980604i
$423$	−396.262			−0.936789
$424$	−600.429	−	153.620i	−1.41611	−	0.362311i
$425$		−	63.6110i		−	0.149673i
$426$	−38.2021	−	26.5351i	−0.0896763	−	0.0622889i
$427$		−	1010.64i		−	2.36683i
$428$	−169.878	−	455.997i	−0.396912	−	1.06541i
$429$			237.998i			0.554774i
$430$	219.860	+	152.714i	0.511303	+	0.355150i
$431$			256.201i			0.594434i	0.954810	+	0.297217i	$0.0960584\pi$
$431$			256.201i			0.594434i	−0.954810	+	0.297217i	$0.903942\pi$
$432$	−213.202	−	246.431i	−0.493523	−	0.570443i
$433$			258.832i			0.597764i	0.954290	+	0.298882i	$0.0966138\pi$
$433$			258.832i			0.597764i	−0.954290	+	0.298882i	$0.903386\pi$
$434$	−320.698	+	461.704i	−0.738936	+	1.06383i
$435$	231.577	+	34.1056i	0.532361	+	0.0784036i
$436$	−226.594	+	84.4160i	−0.519712	+	0.193615i
$437$	−323.995			−0.741407
$438$	214.073	+	148.695i	0.488751	+	0.339486i
$439$		−	435.711i		−	0.992508i	−0.868177	−	0.496254i	$-0.834708\pi$
$439$		−	435.711i		−	0.992508i	0.868177	−	0.496254i	$-0.165292\pi$
$440$	103.947	−	406.281i	0.236243	−	0.923365i
$441$	−217.796			−0.493869
$442$	142.196	+	98.7691i	0.321711	+	0.223460i
$443$		−	108.453i		−	0.244815i	−0.992480	−	0.122408i	$-0.960938\pi$
$443$		−	108.453i		−	0.244815i	0.992480	−	0.122408i	$-0.0390615\pi$
$444$	130.213	−	48.5100i	0.293274	−	0.109257i
$445$	598.259			1.34440
$446$	−250.784	+	361.049i	−0.562296	+	0.809527i
$447$	2.18496			0.00488805
$448$	−271.724	+	496.262i	−0.606527	+	1.10773i
$449$			233.260i			0.519509i	0.965675	+	0.259755i	$0.0836417\pi$
$449$			233.260i			0.519509i	−0.965675	+	0.259755i	$0.916358\pi$
$450$	216.153	+	150.140i	0.480341	+	0.333643i
$451$	468.887			1.03966
$452$	195.199	−	72.7198i	0.431856	−	0.160885i
$453$	−223.581			−0.493557
$454$	739.236	+	513.471i	1.62827	+	1.13099i
$455$			1383.24i			3.04008i
$456$	−62.4539	+	244.103i	−0.136960	+	0.535314i
$457$	−248.835			−0.544497			−0.272249	−	0.962227i	$-0.587767\pi$
$457$	−248.835			−0.544497			−0.272249	+	0.962227i	$0.587767\pi$
$458$	581.587	+	403.969i	1.26984	+	0.882029i
$459$	−73.5535			−0.160247
$460$	−115.946	−	311.230i	−0.252057	−	0.676587i
$461$	378.704			0.821484			0.410742	−	0.911752i	$-0.365270\pi$
$461$	378.704			0.821484			0.410742	+	0.911752i	$0.365270\pi$
$462$	−100.152	+	144.187i	−0.216779	+	0.312092i
$463$		−	768.303i		−	1.65940i	−0.558208	−	0.829701i	$-0.688511\pi$
$463$		−	768.303i		−	1.65940i	0.558208	−	0.829701i	$-0.311489\pi$
$464$	391.390	−	249.218i	0.843514	−	0.537107i
$465$	−256.634			−0.551900
$466$	−628.533	−	436.578i	−1.34878	−	0.936862i
$467$			38.3026i			0.0820184i	0.999159	+	0.0410092i	$0.0130573\pi$
$467$			38.3026i			0.0820184i	−0.999159	+	0.0410092i	$0.986943\pi$
$468$	−671.244	+	250.067i	−1.43428	+	0.534331i
$469$		−	190.714i		−	0.406640i
$470$	−395.038	+	568.729i	−0.840506	+	1.21006i
$471$			66.4667i			0.141118i
$472$	73.1252	−	285.813i	0.154926	−	0.605535i
$473$	164.653			0.348104
$474$	25.1461	−	36.2024i	0.0530509	−	0.0763764i
$475$		−	448.647i		−	0.944520i
$476$	44.5839	+	119.675i	0.0936636	+	0.251417i
$477$		−	578.798i		−	1.21341i
$478$	−95.5435	+	137.552i	−0.199882	+	0.287766i
$479$	660.995			1.37995			0.689973	−	0.723835i	$-0.257622\pi$
$479$	660.995			1.37995			0.689973	+	0.723835i	$0.257622\pi$
$480$	−256.836	+	27.3627i	−0.535076	+	0.0570056i
$481$		−	673.423i		−	1.40005i
$482$	399.726	+	277.648i	0.829306	+	0.576034i
$483$			139.035i			0.287858i
$484$	78.9169	+	211.834i	0.163051	+	0.437673i
$485$	561.659			1.15806
$486$	268.467	−	386.507i	0.552401	−	0.795282i
$487$			137.898i			0.283158i	0.989927	+	0.141579i	$0.0452180\pi$
$487$			137.898i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$488$	226.690	−	886.028i	0.464529	−	1.81563i
$489$	289.620			0.592271
$490$	−217.124	+	312.589i	−0.443110	+	0.637937i
$491$			186.714i			0.380274i	0.981758	+	0.190137i	$0.0608931\pi$
$491$			186.714i			0.380274i	−0.981758	+	0.190137i	$0.939107\pi$
$492$	−100.817	−	270.620i	−0.204913	−	0.550040i
$493$	15.2603	−	103.617i	0.0309539	−	0.210177i
$494$	1002.91	+	696.616i	2.03017	+	1.41015i
$495$	391.644			0.791199
$496$	−384.719	+	332.843i	−0.775643	+	0.671054i
$497$	−166.278			−0.334562
$498$	−0.797584	+	1.14827i	−0.00160157	+	0.00230576i
$499$	342.947			0.687268			0.343634	−	0.939104i	$-0.388342\pi$
$499$	342.947			0.687268			0.343634	+	0.939104i	$0.388342\pi$
$500$	−180.746	+	67.3354i	−0.361491	+	0.134671i
$501$	276.903			0.552701
$502$	357.529	−	514.728i	0.712209	−	1.02535i
$503$	−363.632			−0.722926			−0.361463	−	0.932386i	$-0.617723\pi$
$503$	−363.632			−0.722926			−0.361463	+	0.932386i	$0.617723\pi$
$504$	−511.891	−	130.967i	−1.01566	−	0.259856i
$505$		−	87.4499i		−	0.173168i
$506$	−167.780	−	116.540i	−0.331582	−	0.230316i
$507$		−	501.425i		−	0.989004i
$508$	136.675	+	366.873i	0.269046	+	0.722190i
$509$			37.9726i			0.0746023i	0.999304	+	0.0373012i	$0.0118761\pi$
$509$			37.9726i			0.0746023i	−0.999304	+	0.0373012i	$0.988124\pi$
$510$	−33.2600	+	47.8839i	−0.0652158	+	0.0938900i
$511$	931.769			1.82342
$512$	−349.535	+	374.125i	−0.682685	+	0.730713i
$513$	−518.771			−1.01125
$514$	−168.616	−	117.121i	−0.328047	−	0.227861i
$515$	804.761			1.56264
$516$	−35.4027	−	95.0301i	−0.0686099	−	0.184167i
$517$			425.920i			0.823830i
$518$	283.382	−	407.980i	0.547070	−	0.787607i
$519$	98.4734			0.189737
$520$	−310.266	+	1212.69i	−0.596666	+	2.33209i
$521$	−406.563			−0.780351			−0.390175	−	0.920741i	$-0.627586\pi$
$521$	−406.563			−0.780351			−0.390175	+	0.920741i	$0.627586\pi$
$522$	316.079	+	296.421i	0.605514	+	0.567856i
$523$	−153.421			−0.293348			−0.146674	−	0.989185i	$-0.546857\pi$
$523$	−153.421			−0.293348			−0.146674	+	0.989185i	$0.546857\pi$
$524$	861.852	−	321.076i	1.64476	−	0.612741i
$525$	−192.527			−0.366719
$526$	−75.7999	−	52.6505i	−0.144106	−	0.100096i
$527$			114.829i			0.217891i
$528$	−120.145	+	103.944i	−0.227547	+	0.196864i
$529$	367.214			0.694166
$530$	−830.711	−	577.010i	−1.56738	−	1.08870i
$531$	275.515			0.518862
$532$	314.449	+	844.063i	0.591070	+	1.58659i
$533$	−1399.56			−2.62581
$534$	−186.140	−	129.293i	−0.348577	−	0.242121i
$535$		−	794.137i		−	1.48437i
$536$	42.7780	−	167.200i	0.0798098	−	0.311940i
$537$			269.743i			0.502315i
$538$	−664.524	−	461.577i	−1.23517	−	0.857949i
$539$			234.098i			0.434319i
$540$	−185.650	−	498.333i	−0.343796	−	0.922838i
$541$	−58.5232			−0.108176			−0.0540880	−	0.998536i	$-0.517225\pi$
$541$	−58.5232			−0.108176			−0.0540880	+	0.998536i	$0.517225\pi$
$542$	−455.403	−	316.322i	−0.840227	−	0.583620i
$543$	107.221			0.197461
$544$	12.2432	+	114.919i	0.0225059	+	0.211249i
$545$	−394.623			−0.724079
$546$	298.938	−	430.376i	0.547505	−	0.788234i
$547$	−97.3827			−0.178031			−0.0890153	−	0.996030i	$-0.528372\pi$
$547$	−97.3827			−0.178031			−0.0890153	+	0.996030i	$0.528372\pi$
$548$	−303.652	+	113.123i	−0.554110	+	0.206429i
$549$	854.107			1.55575
$550$	161.377	−	232.332i	0.293413	−	0.422421i
$551$	107.630	−	730.812i	0.195336	−	1.32634i
$552$	−31.1863	+	121.893i	−0.0564968	+	0.220820i
$553$		−	157.574i		−	0.284944i
$554$	−257.544	+	370.782i	−0.464881	+	0.669281i
$555$	226.772			0.408598
$556$	170.980	+	458.954i	0.307518	+	0.825457i
$557$		−	363.577i		−	0.652741i	−0.945242	−	0.326371i	$-0.894174\pi$
$557$		−	363.577i		−	0.652741i	0.945242	−	0.326371i	$-0.105826\pi$
$558$	−390.194	−	271.028i	−0.699272	−	0.485713i
$559$	−491.465			−0.879186
$560$	−698.279	+	604.121i	−1.24693	+	1.07879i
$561$			35.8602i			0.0639219i
$562$	107.448	+	74.6329i	0.191188	+	0.132799i
$563$			247.139i			0.438968i	0.975616	+	0.219484i	$0.0704374\pi$
$563$			247.139i			0.438968i	−0.975616	+	0.219484i	$0.929563\pi$
$564$	245.821	−	91.5788i	0.435853	−	0.162374i
$565$	339.947			0.601676
$566$	846.722	+	588.131i	1.49598	+	1.03910i
$567$		−	371.807i		−	0.655744i
$568$	−145.776	−	37.2968i	−0.256648	−	0.0656634i
$569$		−	1066.94i		−	1.87511i	−0.347834	−	0.937556i	$-0.613083\pi$
$569$		−	1066.94i		−	1.87511i	0.347834	−	0.937556i	$-0.386917\pi$
$570$	−234.582	+	337.724i	−0.411548	+	0.592498i
$571$	11.3272			0.0198375			0.00991874	−	0.999951i	$-0.496843\pi$
$571$	11.3272			0.0198375			0.00991874	+	0.999951i	$0.496843\pi$
$572$	268.783	+	721.484i	0.469901	+	1.26134i
$573$			147.169i			0.256839i
$574$	−847.896	−	588.946i	−1.47717	−	1.02604i
$575$		−	224.031i		−	0.389620i
$576$	−419.399	−	229.639i	−0.728124	−	0.398678i
$577$		−	754.505i		−	1.30763i	−0.756652	−	0.653817i	$-0.773166\pi$
$577$		−	754.505i		−	1.30763i	0.756652	−	0.653817i	$-0.226834\pi$
$578$	−453.292	−	314.856i	−0.784243	−	0.544733i
$579$	−34.7205			−0.0599664
$580$	740.536	−	158.142i	1.27679	−	0.272658i
$581$			4.99792i			0.00860228i
$582$	−174.752	−	121.383i	−0.300262	−	0.208561i
$583$	−622.118			−1.06710
$584$	816.885	+	209.000i	1.39877	+	0.357877i
$585$	−1169.00			−1.99829
$586$	−279.631	−	194.231i	−0.477185	−	0.331452i
$587$	56.5736			0.0963775			0.0481887	−	0.998838i	$-0.484655\pi$
$587$	56.5736			0.0963775			0.0481887	+	0.998838i	$0.484655\pi$
$588$	135.110	−	50.3343i	0.229779	−	0.0856025i
$589$			809.885i			1.37502i
$590$	274.665	−	395.430i	0.465533	−	0.670220i
$591$	87.4986			0.148052
$592$	339.954	−	294.113i	0.574246	−	0.496813i
$593$	218.323			0.368167			0.184083	−	0.982911i	$-0.441068\pi$
$593$	218.323			0.368167			0.184083	+	0.982911i	$0.441068\pi$
$594$	−268.645	−	186.600i	−0.452264	−	0.314142i
$595$			208.418i			0.350283i
$596$	6.62364	−	2.46759i	0.0111135	−	0.00414024i
$597$	−347.752			−0.582498
$598$	500.800	+	347.854i	0.837458	+	0.581696i
$599$	44.2277			0.0738358			0.0369179	−	0.999318i	$-0.488246\pi$
$599$	44.2277			0.0738358			0.0369179	+	0.999318i	$0.488246\pi$
$600$	−168.789	−	43.1847i	−0.281315	−	0.0719746i
$601$			717.250i			1.19343i	0.802454	+	0.596714i	$0.203527\pi$
$601$			717.250i			1.19343i	−0.802454	+	0.596714i	$0.796473\pi$
$602$	−297.745	−	206.813i	−0.494593	−	0.343543i
$603$	161.176			0.267290
$604$	−677.780	+	252.501i	−1.12215	+	0.418049i
$605$			368.916i			0.609779i
$606$	−18.8992	+	27.2089i	−0.0311868	+	0.0448991i
$607$	−233.407			−0.384526			−0.192263	−	0.981343i	$-0.561583\pi$
$607$	−233.407			−0.384526			−0.192263	+	0.981343i	$0.561583\pi$
$608$	86.3512	+	810.525i	0.142025	+	1.33310i
$609$	−313.612	−	46.1873i	−0.514963	−	0.0758412i
$610$	851.469	−	1225.84i	1.39585	−	2.00958i
$611$		−	1271.31i		−	2.08070i
$612$	−101.139	+	37.6786i	−0.165260	+	0.0615664i
$613$			186.431i			0.304130i	0.988371	+	0.152065i	$0.0485922\pi$
$613$			186.431i			0.304130i	−0.988371	+	0.152065i	$0.951408\pi$
$614$	577.699	−	831.704i	0.940879	−	1.35457i
$615$		−	471.295i		−	0.766333i
$616$	−140.770	+	550.204i	−0.228522	+	0.893188i
$617$		−	51.9925i		−	0.0842665i	−0.999112	−	0.0421333i	$-0.986585\pi$
$617$		−	51.9925i		−	0.0842665i	0.999112	−	0.0421333i	$-0.0134154\pi$
$618$	−250.391	−	173.921i	−0.405163	−	0.281425i
$619$		−	582.738i		−	0.941419i	−0.882288	−	0.470709i	$-0.843998\pi$
$619$		−	582.738i		−	0.941419i	0.882288	−	0.470709i	$-0.156002\pi$
$620$	−777.977	+	289.829i	−1.25480	+	0.467467i
$621$	−259.048			−0.417146
$622$	642.985	+	446.616i	1.03374	+	0.718032i
$623$	−810.190			−1.30047
$624$	358.615	−	310.258i	0.574703	−	0.497209i
$625$	−755.105			−1.20817
$626$	257.862	+	179.111i	0.411920	+	0.286119i
$627$			252.921i			0.403383i
$628$	75.0642	+	201.492i	0.119529	+	0.320847i
$629$		−	101.467i		−	0.161315i
$630$	−708.215	−	491.925i	−1.12415	−	0.780833i
$631$		−	925.171i		−	1.46620i	−0.680122	−	0.733099i	$-0.738073\pi$
$631$		−	925.171i		−	1.46620i	0.680122	−	0.733099i	$-0.261927\pi$
$632$	35.3445	−	138.145i	0.0559249	−	0.218585i
$633$	311.497			0.492096
$634$	238.210	+	165.460i	0.375726	+	0.260979i
$635$			638.923i			1.00618i
$636$	133.764	+	359.058i	0.210321	+	0.564556i
$637$		−	698.747i		−	1.09693i
$638$	318.607	−	339.736i	0.499384	−	0.532501i
$639$		−	140.524i		−	0.219912i
$640$	−747.690	+	373.007i	−1.16827	+	0.582824i
$641$		−	1030.85i		−	1.60819i	−0.594498	−	0.804097i	$-0.702649\pi$
$641$		−	1030.85i		−	1.60819i	0.594498	−	0.804097i	$-0.297351\pi$
$642$	−171.625	+	247.085i	−0.267328	+	0.384868i
$643$	−1173.19			−1.82456			−0.912278	−	0.409572i	$-0.865678\pi$
$643$	−1173.19			−1.82456			−0.912278	+	0.409572i	$0.865678\pi$
$644$	157.020	+	421.482i	0.243819	+	0.654475i
$645$		−	165.499i		−	0.256587i
$646$	151.112	+	104.962i	0.233920	+	0.162480i
$647$			976.029i			1.50855i	0.656561	+	0.754273i	$0.272010\pi$
$647$			976.029i			1.50855i	−0.656561	+	0.754273i	$0.727990\pi$
$648$	83.3980	−	325.964i	0.128701	−	0.503031i
$649$		−	296.137i		−	0.456297i
$650$	−481.686	+	693.475i	−0.741056	+	1.06689i
$651$	347.545			0.533863
$652$	877.976	−	327.083i	1.34659	−	0.501661i
$653$	528.389			0.809171			0.404586	−	0.914500i	$-0.367416\pi$
$653$	528.389			0.809171			0.404586	+	0.914500i	$0.367416\pi$
$654$	122.782	+	85.2839i	0.187740	+	0.130403i
$655$	1500.95			2.29153
$656$	−611.249	−	706.518i	−0.931782	−	1.07701i
$657$			787.454i			1.19856i
$658$	534.978	−	770.198i	0.813037	−	1.17051i
$659$		−	835.795i		−	1.26828i	−0.773219	−	0.634139i	$-0.781355\pi$
$659$		−	835.795i		−	1.26828i	0.773219	−	0.634139i	$-0.218645\pi$
$660$	−242.956	+	90.5115i	−0.368116	+	0.137139i
$661$			691.575i			1.04626i	0.852254	+	0.523128i	$0.175235\pi$
$661$			691.575i			1.04626i	−0.852254	+	0.523128i	$0.824765\pi$
$662$	−440.491	+	634.167i	−0.665394	+	0.957956i
$663$		−	107.037i		−	0.161444i
$664$	−1.12106	+	4.38169i	−0.00168834	+	0.00659894i
$665$			1469.97i			2.21048i
$666$	344.791	+	239.491i	0.517704	+	0.359596i
$667$	53.7451	−	364.930i	0.0805773	−	0.547121i
$668$	839.423	−	312.721i	1.25662	−	0.468145i
$669$	271.778			0.406245
$670$	160.678	−	231.325i	0.239818	−	0.345262i
$671$		−	918.033i		−	1.36816i
$672$	347.819	−	37.0558i	0.517588	−	0.0551425i
$673$	−556.526			−0.826933			−0.413466	−	0.910519i	$-0.635682\pi$
$673$	−556.526			−0.826933			−0.413466	+	0.910519i	$0.635682\pi$
$674$	−172.120	+	247.798i	−0.255370	+	0.367652i
$675$		−	358.712i		−	0.531426i
$676$	−566.285	−	1520.06i	−0.837699	−	2.24860i
$677$	157.217			0.232225			0.116113	−	0.993236i	$-0.462957\pi$
$677$	157.217			0.232225			0.116113	+	0.993236i	$0.462957\pi$
$678$	−105.770	−	73.4675i	−0.156003	−	0.108359i
$679$	−760.624			−1.12021
$680$	−46.7491	+	182.721i	−0.0687487	+	0.268707i
$681$		−	556.456i		−	0.817115i
$682$	−291.313	+	419.398i	−0.427145	+	0.614953i
$683$	1109.74			1.62480			0.812401	−	0.583099i	$-0.198160\pi$
$683$	1109.74			1.62480			0.812401	+	0.583099i	$0.198160\pi$
$684$	−713.332	+	265.746i	−1.04288	+	0.388518i
$685$	−528.823			−0.772004
$686$	−200.199	+	288.224i	−0.291836	+	0.420151i
$687$		−	437.787i		−	0.637244i
$688$	−214.645	−	248.099i	−0.311983	−	0.360609i
$689$	1856.93			2.69511
$690$	−117.138	+	168.642i	−0.169766	+	0.244409i
$691$	749.369			1.08447			0.542235	−	0.840227i	$-0.317578\pi$
$691$	749.369			1.08447			0.542235	+	0.840227i	$0.317578\pi$
$692$	298.519	−	111.211i	0.431386	−	0.160710i
$693$	−530.381			−0.765341
$694$	53.5551	+	37.1992i	0.0771687	+	0.0536012i
$695$			799.287i			1.15005i
$696$	−264.585	−	110.837i	−0.380150	−	0.159249i
$697$	−210.877			−0.302550
$698$	536.647	−	772.601i	0.768836	−	1.10688i
$699$			473.125i			0.676859i
$700$	−583.641	+	217.431i	−0.833773	+	0.310615i
$701$			684.233i			0.976081i	0.872821	+	0.488041i	$0.162288\pi$
$701$			684.233i			0.976081i	−0.872821	+	0.488041i	$0.837712\pi$
$702$	801.866	+	556.974i	1.14226	+	0.793411i
$703$		−	715.648i		−	1.01799i
$704$	−246.826	+	450.790i	−0.350606	+	0.640326i
$705$	428.107			0.607245
$706$	−493.747	−	342.956i	−0.699359	−	0.485773i
$707$			118.429i			0.167509i
$708$	−170.916	+	63.6735i	−0.241407	+	0.0899344i
$709$			173.047i			0.244073i	0.992526	+	0.122036i	$0.0389424\pi$
$709$			173.047i			0.244073i	−0.992526	+	0.122036i	$0.961058\pi$
$710$	−201.685	−	140.090i	−0.284064	−	0.197310i
$711$	133.168			0.187297
$712$	−710.295	−	181.729i	−0.997606	−	0.255238i
$713$			404.415i			0.567202i
$714$	45.0422	−	64.8465i	0.0630844	−	0.0908215i
$715$			1256.49i			1.75733i
$716$	304.634	+	817.718i	0.425467	+	1.14206i
$717$	103.542			0.144410
$718$	499.375	+	346.865i	0.695508	+	0.483098i
$719$			947.226i			1.31742i	0.752396	+	0.658711i	$0.228898\pi$
$719$			947.226i			1.31742i	−0.752396	+	0.658711i	$0.771102\pi$
$720$	−510.553	−	590.127i	−0.709102	−	0.819621i
$721$	−1089.84			−1.51157
$722$	472.804	+	328.408i	0.654853	+	0.454859i
$723$		−	300.891i		−	0.416170i
$724$	325.038	−	121.090i	0.448947	−	0.167252i
$725$	505.331	+	74.4228i	0.697009	+	0.102652i
$726$	79.7283	−	114.783i	0.109819	−	0.158104i
$727$	−754.844			−1.03830			−0.519150	−	0.854683i	$-0.673751\pi$
$727$	−754.844			−1.03830			−0.519150	+	0.854683i	$0.673751\pi$
$728$	420.177	−	1642.28i	0.577166	−	2.25588i
$729$	87.5806			0.120138
$730$	1130.18	+	785.023i	1.54820	+	1.07537i
$731$	−74.0511			−0.101301
$732$	−529.846	+	197.390i	−0.723833	+	0.269658i
$733$	−295.912			−0.403700			−0.201850	−	0.979416i	$-0.564695\pi$
$733$	−295.912			−0.403700			−0.201850	+	0.979416i	$0.564695\pi$
$734$	−948.265	−	658.663i	−1.29191	−	0.897361i
$735$	235.300			0.320136
$736$	43.1193	+	404.734i	0.0585861	+	0.549911i
$737$		−	173.239i		−	0.235060i
$738$	497.729	−	716.571i	0.674429	−	0.970964i
$739$			568.516i			0.769304i	0.923062	+	0.384652i	$0.125679\pi$
$739$			568.516i			0.769304i	−0.923062	+	0.384652i	$0.874321\pi$
$740$	687.453	−	256.105i	0.928990	−	0.346088i
$741$		−	754.932i		−	1.01880i
$742$	1124.99	+	781.413i	1.51615	+	1.05312i
$743$	−210.064			−0.282724			−0.141362	−	0.989958i	$-0.545148\pi$
$743$	−210.064			−0.282724			−0.141362	+	0.989958i	$0.545148\pi$
$744$	304.693	+	77.9559i	0.409534	+	0.104779i
$745$	11.5353			0.0154837
$746$	506.178	−	728.736i	0.678523	−	0.976858i
$747$	−4.22383			−0.00565439
$748$	40.4987	+	108.709i	0.0541427	+	0.145333i
$749$			1075.46i			1.43586i
$750$	97.9382	+	68.0277i	0.130584	+	0.0907036i
$751$	319.921			0.425993			0.212997	−	0.977053i	$-0.431678\pi$
$751$	319.921			0.425993			0.212997	+	0.977053i	$0.431678\pi$
$752$	641.775	−	555.237i	0.853425	−	0.738347i
$753$	−387.459			−0.514553
$754$	−950.995	+	1014.06i	−1.26127	+	1.34491i
$755$	−1180.38			−1.56342
$756$	251.415	+	674.864i	0.332560	+	0.892678i
$757$	1121.45			1.48144			0.740718	−	0.671816i	$-0.234485\pi$
$757$	1121.45			1.48144			0.740718	+	0.671816i	$0.234485\pi$
$758$	−334.851	+	482.079i	−0.441756	+	0.635988i
$759$			126.296i			0.166398i
$760$	−329.721	+	1288.73i	−0.433843	+	1.69569i
$761$	−239.760			−0.315059			−0.157529	−	0.987514i	$-0.550353\pi$
$761$	−239.760			−0.315059			−0.157529	+	0.987514i	$0.550353\pi$
$762$	138.081	−	198.792i	0.181208	−	0.260882i
$763$	534.417			0.700415
$764$	166.205	+	446.137i	0.217546	+	0.583950i
$765$	−176.138			−0.230246
$766$	−230.707	+	332.145i	−0.301185	+	0.433610i
$767$			883.925i			1.15244i
$768$	313.246	+	45.5305i	0.407872	+	0.0592846i
$769$			337.494i			0.438874i	0.975627	+	0.219437i	$0.0704221\pi$
$769$			337.494i			0.438874i	−0.975627	+	0.219437i	$0.929578\pi$
$770$	−528.743	+	761.222i	−0.686680	+	0.988601i
$771$			126.925i			0.164624i
$772$	−105.254	+	39.2117i	−0.136340	+	0.0507923i
$773$	−411.788			−0.532714			−0.266357	−	0.963874i	$-0.585820\pi$
$773$	−411.788			−0.532714			−0.266357	+	0.963874i	$0.585820\pi$
$774$	174.781	−	251.629i	0.225815	−	0.325102i
$775$	−560.008			−0.722591
$776$	−666.841	−	170.611i	−0.859331	−	0.219860i
$777$	−307.105			−0.395244
$778$	−209.666	−	145.634i	−0.269494	−	0.187190i
$779$	−1487.31			−1.90926
$780$	725.189	−	270.164i	0.929730	−	0.346364i
$781$	−151.042			−0.193395
$782$	75.4576	+	52.4127i	0.0964931	+	0.0670239i
$783$	86.0551	−	584.315i	0.109904	−	0.746252i
$784$	352.738	−	305.174i	0.449921	−	0.389252i
$785$			350.906i			0.447014i
$786$	−467.000	−	324.377i	−0.594148	−	0.412694i
$787$	−33.0333			−0.0419737			−0.0209869	−	0.999780i	$-0.506681\pi$
$787$	−33.0333			−0.0419737			−0.0209869	+	0.999780i	$0.506681\pi$
$788$	265.250	−	98.8166i	0.336611	−	0.125402i
$789$			57.0580i			0.0723168i
$790$	132.757	−	191.128i	0.168047	−	0.241934i
$791$	−460.371			−0.582012
$792$	−464.987	−	118.967i	−0.587104	−	0.150211i
$793$			2740.19i			3.45548i
$794$	33.7220	−	48.5489i	0.0424710	−	0.0611447i
$795$			625.313i			0.786557i
$796$	−1054.20	+	392.733i	−1.32437	+	0.493384i
$797$	358.483			0.449791			0.224895	−	0.974383i	$-0.427796\pi$
$797$	358.483			0.449791			0.224895	+	0.974383i	$0.427796\pi$
$798$	317.682	−	457.361i	0.398098	−	0.573134i
$799$		−	191.554i		−	0.239742i
$800$	−560.450	+	59.7089i	−0.700563	+	0.0746361i
$801$		−	684.706i		−	0.854813i
$802$	−448.800	−	311.735i	−0.559600	−	0.388697i
$803$	846.393			1.05404
$804$	−99.9856	+	37.2489i	−0.124360	+	0.0463294i
$805$			734.027i			0.911835i
$806$	869.527	−	1251.84i	1.07882	−	1.55315i
$807$			500.217i			0.619847i
$808$	−26.5641	+	103.827i	−0.0328763	+	0.128498i
$809$			556.938i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$809$			556.938i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$810$	313.250	−	450.981i	0.386729	−	0.556766i
$811$	295.938			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$811$	295.938			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$812$	−1002.87	+	214.163i	−1.23506	+	0.263747i
$813$			342.802i			0.421651i
$814$	257.416	−	370.597i	0.316236	−	0.455279i
$815$	1529.03			1.87611
$816$	54.0340	−	46.7479i	0.0662182	−	0.0572891i
$817$	−522.281			−0.639267
$818$	132.901	−	191.335i	0.162470	−	0.233905i
$819$	1583.11			1.93298
$820$	−532.257	−	1428.72i	−0.649094	−	1.74234i
$821$			739.559i			0.900803i	0.892826	+	0.450402i	$0.148719\pi$
$821$			739.559i			0.900803i	−0.892826	+	0.450402i	$0.851281\pi$
$822$	164.536	+	114.286i	0.200165	+	0.139034i
$823$	653.161			0.793634			0.396817	−	0.917898i	$-0.370115\pi$
$823$	653.161			0.793634			0.396817	+	0.917898i	$0.370115\pi$
$824$	−955.469	−	244.457i	−1.15955	−	0.296671i
$825$	−174.886			−0.211983
$826$	−371.963	+	535.509i	−0.450319	+	0.648316i
$827$			897.006i			1.08465i	0.840169	+	0.542325i	$0.182456\pi$
$827$			897.006i			1.08465i	−0.840169	+	0.542325i	$0.817544\pi$
$828$	−356.202	+	132.700i	−0.430195	+	0.160266i
$829$	−349.807			−0.421962			−0.210981	−	0.977490i	$-0.567666\pi$
$829$	−349.807			−0.421962			−0.210981	+	0.977490i	$0.567666\pi$
$830$	−4.21079	+	6.06220i	−0.00507324	+	0.00730385i
$831$	279.104			0.335865
$832$	736.740	−	1345.54i	0.885505	−	1.61724i
$833$		−	105.283i		−	0.126390i
$834$	172.738	−	248.687i	0.207119	−	0.298186i
$835$	1461.89			1.75077
$836$	285.637	+	766.723i	0.341670	+	0.917133i
$837$			647.538i			0.773641i
$838$	561.135	+	389.763i	0.669612	+	0.465111i
$839$	−426.644			−0.508515			−0.254258	−	0.967137i	$-0.581831\pi$
$839$	−426.644			−0.508515			−0.254258	+	0.967137i	$0.581831\pi$
$840$	553.029	+	141.493i	0.658368	+	0.168444i
$841$	805.292	+	242.458i	0.957541	+	0.288297i
$842$	−162.311	−	112.741i	−0.192768	−	0.133896i
$843$		−	80.8806i		−	0.0959438i
$844$	944.294	−	351.789i	1.11883	−	0.416812i
$845$		−	2647.24i		−	3.13282i
$846$	650.908	+	452.119i	0.769395	+	0.534420i
$847$		−	499.603i		−	0.589851i
$848$	811.004	+	937.406i	0.956373	+	1.10543i
$849$		−	637.365i		−	0.750725i
$850$	−72.5777	+	104.489i	−0.0853856	+	0.122928i
$851$		−	357.358i		−	0.419927i
$852$	32.4761	+	87.1742i	0.0381175	+	0.102317i
$853$	785.349			0.920690			0.460345	−	0.887740i	$-0.347726\pi$
$853$	785.349			0.920690			0.460345	+	0.887740i	$0.347726\pi$
$854$	−1153.10	+	1660.09i	−1.35023	+	1.94390i
$855$	−1242.30			−1.45298
$856$	−241.230	+	942.856i	−0.281810	+	1.10147i
$857$	1087.79			1.26930			0.634652	−	0.772798i	$-0.281144\pi$
$857$	1087.79			1.26930			0.634652	+	0.772798i	$0.281144\pi$
$858$	271.547	−	390.941i	0.316488	−	0.455642i
$859$		−	559.776i		−	0.651660i	−0.945428	−	0.325830i	$-0.894356\pi$
$859$		−	559.776i		−	0.651660i	0.945428	−	0.325830i	$-0.105644\pi$
$860$	−186.906	−	501.704i	−0.217333	−	0.583377i
$861$			638.249i			0.741288i
$862$	292.315	−	420.841i	0.339113	−	0.488215i
$863$			1011.37i			1.17193i	0.810337	+	0.585964i	$0.199284\pi$
$863$			1011.37i			1.17193i	−0.810337	+	0.585964i	$0.800716\pi$
$864$	69.0414	+	648.049i	0.0799091	+	0.750057i
$865$	519.883			0.601021
$866$	295.317	−	425.163i	0.341013	−	0.490950i
$867$			341.213i			0.393556i
$868$	1053.57	−	392.500i	1.21379	−	0.452189i
$869$		−	143.136i		−	0.164713i
$870$	−341.481	−	320.243i	−0.392506	−	0.368096i
$871$			517.094i			0.593678i
$872$	468.524	+	119.872i	0.537299	+	0.137468i
$873$		−	642.816i		−	0.736330i
$874$	532.201	+	369.665i	0.608925	+	0.422958i
$875$	426.284			0.487181
$876$	−181.986	−	488.498i	−0.207747	−	0.557646i
$877$		−	816.846i		−	0.931409i	−0.884940	−	0.465704i	$-0.845801\pi$
$877$		−	816.846i		−	0.931409i	0.884940	−	0.465704i	$-0.154199\pi$
$878$	−497.130	+	715.709i	−0.566207	+	0.815158i
$879$			210.490i			0.239466i
$880$	−634.296	+	548.766i	−0.720791	+	0.623598i
$881$			916.922i			1.04077i	0.853931	+	0.520387i	$0.174212\pi$
$881$			916.922i			1.04077i	−0.853931	+	0.520387i	$0.825788\pi$
$882$	357.757	+	248.497i	0.405620	+	0.281743i
$883$	166.543			0.188611			0.0943054	−	0.995543i	$-0.469937\pi$
$883$	166.543			0.188611			0.0943054	+	0.995543i	$0.469937\pi$
$884$	−120.883	−	324.481i	−0.136745	−	0.367059i
$885$	−297.658			−0.336336
$886$	−123.741	+	178.148i	−0.139662	+	0.201070i
$887$	557.936			0.629014			0.314507	−	0.949255i	$-0.398161\pi$
$887$	557.936			0.629014			0.314507	+	0.949255i	$0.398161\pi$
$888$	−269.240	−	68.8850i	−0.303198	−	0.0775732i
$889$		−	865.259i		−	0.973294i
$890$	−982.714	−	682.591i	−1.10417	−	0.766956i
$891$		−	337.739i		−	0.379056i
$892$	823.886	−	306.932i	0.923640	−	0.344095i
$893$		−	1351.02i		−	1.51290i
$894$	−3.58906	−	2.49296i	−0.00401461	−	0.00278854i
$895$			1424.09i			1.59116i
$896$	1012.56	−	505.143i	1.13008	−	0.563776i
$897$		−	376.974i		−	0.420261i
$898$	266.140	−	383.158i	0.296370	−	0.426679i
$899$	−912.210	−	134.346i	−1.01469	−	0.149439i
$900$	−183.755	−	493.245i	−0.204172	−	0.548050i
$901$	279.792			0.310535
$902$	−770.204	−	534.982i	−0.853885	−	0.593107i
$903$			224.126i			0.248201i
$904$	−403.609	−	103.263i	−0.446470	−	0.114229i
$905$	566.066			0.625488
$906$	367.259	+	255.097i	0.405363	+	0.281565i
$907$			136.822i			0.150851i	0.997151	+	0.0754257i	$0.0240316\pi$
$907$			136.822i			0.150851i	−0.997151	+	0.0754257i	$0.975968\pi$
$908$	−628.433	−	1686.88i	−0.692107	−	1.85780i
$909$	−100.086			−0.110106
$910$	1578.22	−	2272.14i	1.73431	−	2.49685i
$911$	−1231.76			−1.35210			−0.676048	−	0.736858i	$-0.736309\pi$
$911$	−1231.76			−1.35210			−0.676048	+	0.736858i	$0.736309\pi$
$912$	381.101	−	329.712i	0.417874	−	0.361526i
$913$			4.53997i			0.00497259i
$914$	408.742	+	283.911i	0.447201	+	0.310625i
$915$	−922.748			−1.00847
$916$	−494.414	−	1327.14i	−0.539754	−	1.44884i
$917$	−2032.65			−2.21663
$918$	120.821	+	83.9217i	0.131613	+	0.0914180i
$919$			977.438i			1.06359i	0.846873	+	0.531794i	$0.178482\pi$
$919$			977.438i			1.06359i	−0.846873	+	0.531794i	$0.821518\pi$
$920$	−164.646	+	643.523i	−0.178963	+	0.699482i
$921$	−626.060			−0.679761
$922$	−622.068	−	432.087i	−0.674694	−	0.468641i
$923$	450.837			0.488448
$924$	329.023	−	122.575i	0.356085	−	0.132657i
$925$	494.846			0.534969
$926$	−876.604	+	1262.03i	−0.946657	+	1.36289i
$927$		−	921.046i		−	0.993578i
$928$	−927.254	−	37.1907i	−0.999197	−	0.0400762i
$929$	−1547.17			−1.66542			−0.832708	−	0.553713i	$-0.813211\pi$
$929$	−1547.17			−1.66542			−0.832708	+	0.553713i	$0.813211\pi$
$930$	421.552	+	292.809i	0.453282	+	0.314848i
$931$		−	742.560i		−	0.797594i
$932$	534.324	+	1434.26i	0.573309	+	1.53891i
$933$		−	484.003i		−	0.518760i
$934$	43.7018	−	62.9167i	0.0467899	−	0.0673626i
$935$			189.321i			0.202483i
$936$	1387.92	+	355.099i	1.48282	+	0.379379i
$937$	73.0644			0.0779770			0.0389885	−	0.999240i	$-0.487586\pi$
$937$	73.0644			0.0779770			0.0389885	+	0.999240i	$0.487586\pi$
$938$	−217.598	+	313.271i	−0.231980	+	0.333978i
$939$		−	194.104i		−	0.206714i
$940$	1297.80	−	483.483i	1.38063	−	0.514344i
$941$			189.365i			0.201238i	0.994925	+	0.100619i	$0.0320823\pi$
$941$			189.365i			0.201238i	−0.994925	+	0.100619i	$0.967918\pi$
$942$	75.8359	−	109.180i	0.0805052	−	0.115902i
$943$	−742.688			−0.787580
$944$	−446.218	+	386.049i	−0.472689	+	0.408950i
$945$			1175.30i			1.24371i
$946$	−270.463	−	187.863i	−0.285901	−	0.198587i
$947$			548.657i			0.579364i	0.957123	+	0.289682i	$0.0935495\pi$
$947$			548.657i			0.579364i	−0.957123	+	0.289682i	$0.906451\pi$
$948$	−82.6112	+	30.7761i	−0.0871426	+	0.0324643i
$949$	−2526.36			−2.66213
$950$	−511.889	+	736.958i	−0.538831	+	0.775745i
$951$		−	179.312i		−	0.188551i
$952$	63.3098	−	247.449i	0.0665019	−	0.259925i
$953$	−661.587			−0.694215			−0.347107	−	0.937825i	$-0.612836\pi$
$953$	−661.587			−0.694215			−0.347107	+	0.937825i	$0.612836\pi$
$954$	−660.386	+	950.746i	−0.692228	+	0.996589i
$955$			776.966i			0.813577i
$956$	313.884	−	116.935i	0.328330	−	0.122317i
$957$	−284.876	−	41.9552i	−0.297676	−	0.0438403i
$958$	−1085.76	−	754.169i	−1.13337	−	0.787233i
$959$	716.155			0.746773
$960$	453.105	+	248.094i	0.471984	+	0.258431i
$961$	49.9103			0.0519358
$962$	−768.349	+	1106.18i	−0.798700	+	1.14987i
$963$	−908.887			−0.943808
$964$	−339.812	−	912.143i	−0.352502	−	0.946206i
$965$	−183.305			−0.189953
$966$	158.634	−	228.383i	0.164217	−	0.236421i
$967$	−45.5659			−0.0471209			−0.0235605	−	0.999722i	$-0.507500\pi$
$967$	−45.5659			−0.0471209			−0.0235605	+	0.999722i	$0.507500\pi$
$968$	112.063	−	438.004i	0.115768	−	0.452483i
$969$		−	113.749i		−	0.117388i
$970$	−922.593	−	640.831i	−0.951127	−	0.660650i
$971$			279.275i			0.287616i	0.989606	+	0.143808i	$0.0459348\pi$
$971$			279.275i			0.287616i	−0.989606	+	0.143808i	$0.954065\pi$
$972$	−881.979	+	328.574i	−0.907386	+	0.338040i
$973$		−	1082.43i		−	1.11247i
$974$	157.336	−	226.515i	0.161536	−	0.232561i
$975$	522.010			0.535395
$976$	−1383.29	+	1196.76i	−1.41731	+	1.22619i
$977$	1194.22			1.22234			0.611168	−	0.791501i	$-0.290700\pi$
$977$	1194.22			1.22234			0.611168	+	0.791501i	$0.290700\pi$
$978$	−475.737	−	330.446i	−0.486439	−	0.337879i
$979$	−735.953			−0.751740
$980$	713.305	−	265.736i	0.727862	−	0.271159i
$981$			451.645i			0.460392i
$982$	213.034	−	306.701i	0.216939	−	0.312323i
$983$	−1876.04			−1.90849			−0.954244	−	0.299030i	$-0.903337\pi$
$983$	−1876.04			−1.90849			−0.954244	+	0.299030i	$0.903337\pi$
$984$	−143.162	+	559.554i	−0.145490	+	0.568653i
$985$	461.943			0.468977
$986$	−143.290	+	152.793i	−0.145325	+	0.154962i
$987$	−579.763			−0.587399
$988$	−852.583	−	2288.55i	−0.862938	−	2.31635i
$989$	−260.800			−0.263701
$990$	−643.322	−	446.850i	−0.649821	−	0.451364i
$991$		−	1206.19i		−	1.21715i	−0.793497	−	0.608574i	$-0.791742\pi$
$991$		−	1206.19i		−	1.21715i	0.793497	−	0.608574i	$-0.208258\pi$
$992$	1011.71	−	107.785i	1.01987	−	0.108654i
$993$	477.366			0.480731
$994$	273.131	+	189.716i	0.274780	+	0.190861i
$995$	−1835.93			−1.84515
$996$	2.62026	−	0.976157i	0.00263078	−	0.000980077i
$997$	1603.13			1.60795			0.803977	−	0.594660i	$-0.202713\pi$
$997$	1603.13			1.60795			0.803977	+	0.594660i	$0.202713\pi$
$998$	−563.332	−	391.289i	−0.564461	−	0.392073i
$999$		−	572.191i		−	0.572763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.3.b.c.115.11	✓	56
4.3	odd	2		928.3.b.c.463.24		56
8.3	odd	2	inner	232.3.b.c.115.45	yes	56
8.5	even	2		928.3.b.c.463.23		56
29.28	even	2	inner	232.3.b.c.115.46	yes	56
116.115	odd	2		928.3.b.c.463.34		56
232.115	odd	2	inner	232.3.b.c.115.12	yes	56
232.173	even	2		928.3.b.c.463.33		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.3.b.c.115.11	✓	56	1.1	even	1	trivial
232.3.b.c.115.12	yes	56	232.115	odd	2	inner
232.3.b.c.115.45	yes	56	8.3	odd	2	inner
232.3.b.c.115.46	yes	56	29.28	even	2	inner
928.3.b.c.463.23		56	8.5	even	2
928.3.b.c.463.24		56	4.3	odd	2
928.3.b.c.463.33		56	232.173	even	2
928.3.b.c.463.34		56	116.115	odd	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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	232.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64262 - 1.14096i) q^{2} +1.23647i q^{3} +(1.39641 + 3.74834i) q^{4} +6.52788i q^{5} +(1.41077 - 2.03106i) q^{6} -8.84035i q^{7} +(1.98293 - 7.75035i) q^{8} +7.47113 q^{9} +O(q^{10})\)	\(q+(-1.64262 - 1.14096i) q^{2} +1.23647i q^{3} +(1.39641 + 3.74834i) q^{4} +6.52788i q^{5} +(1.41077 - 2.03106i) q^{6} -8.84035i q^{7} +(1.98293 - 7.75035i) q^{8} +7.47113 q^{9} +(7.44806 - 10.7228i) q^{10} -8.03032i q^{11} +(-4.63472 + 1.72663i) q^{12} +23.9693i q^{13} +(-10.0865 + 14.5213i) q^{14} -8.07155 q^{15} +(-12.1001 + 10.4685i) q^{16} +3.61156i q^{17} +(-12.2722 - 8.52427i) q^{18} +25.4722i q^{19} +(-24.4687 + 9.11562i) q^{20} +10.9309 q^{21} +(-9.16228 + 13.1908i) q^{22} +12.7195i q^{23} +(9.58312 + 2.45184i) q^{24} -17.6132 q^{25} +(27.3481 - 39.3725i) q^{26} +20.3661i q^{27} +(33.1366 - 12.3448i) q^{28} +(-28.6905 - 4.22540i) q^{29} +(13.2585 + 9.20933i) q^{30} +31.7948 q^{31} +(31.8199 - 3.39001i) q^{32} +9.92928 q^{33} +(4.12065 - 5.93242i) q^{34} +57.7087 q^{35} +(10.4328 + 28.0043i) q^{36} -28.0952 q^{37} +(29.0628 - 41.8412i) q^{38} -29.6374 q^{39} +(50.5934 + 12.9443i) q^{40} +58.3896i q^{41} +(-17.9553 - 12.4717i) q^{42} +20.5039i q^{43} +(30.1003 - 11.2136i) q^{44} +48.7706i q^{45} +(14.5125 - 20.8934i) q^{46} -53.0390 q^{47} +(-12.9440 - 14.9614i) q^{48} -29.1517 q^{49} +(28.9318 + 20.0960i) q^{50} -4.46560 q^{51} +(-89.8451 + 33.4711i) q^{52} -77.4712i q^{53} +(23.2370 - 33.4539i) q^{54} +52.4209 q^{55} +(-68.5158 - 17.5298i) q^{56} -31.4958 q^{57} +(42.3067 + 39.6755i) q^{58} +36.8773 q^{59} +(-11.2712 - 30.2549i) q^{60} +114.321 q^{61} +(-52.2269 - 36.2767i) q^{62} -66.0474i q^{63} +(-56.1360 - 30.7368i) q^{64} -156.469 q^{65} +(-16.3101 - 11.3289i) q^{66} +21.5732 q^{67} +(-13.5373 + 5.04323i) q^{68} -15.7274 q^{69} +(-94.7936 - 65.8434i) q^{70} -18.8089i q^{71} +(14.8147 - 57.9039i) q^{72} +105.400i q^{73} +(46.1498 + 32.0555i) q^{74} -21.7783i q^{75} +(-95.4785 + 35.5698i) q^{76} -70.9908 q^{77} +(48.6831 + 33.8152i) q^{78} +17.8244 q^{79} +(-68.3368 - 78.9877i) q^{80} +42.0580 q^{81} +(66.6203 - 95.9120i) q^{82} -0.565354 q^{83} +(15.2640 + 40.9726i) q^{84} -23.5758 q^{85} +(23.3942 - 33.6802i) q^{86} +(5.22460 - 35.4751i) q^{87} +(-62.2378 - 15.9236i) q^{88} -91.6468i q^{89} +(55.6454 - 80.1117i) q^{90} +211.897 q^{91} +(-47.6771 + 17.7617i) q^{92} +39.3135i q^{93} +(87.1231 + 60.5155i) q^{94} -166.280 q^{95} +(4.19166 + 39.3445i) q^{96} -86.0400i q^{97} +(47.8853 + 33.2610i) q^{98} -59.9955i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{4} - 184 q^{9}+O(q^{10}) \) 56 * q - 4 * q^4 - 184 * q^9	\( 56 q - 4 q^{4} - 184 q^{9} - 44 q^{16} - 12 q^{20} - 68 q^{22} - 72 q^{24} - 280 q^{25} + 116 q^{28} + 8 q^{30} + 32 q^{33} - 116 q^{34} + 96 q^{35} - 112 q^{36} - 176 q^{38} + 156 q^{42} - 424 q^{49} + 32 q^{51} - 56 q^{52} + 160 q^{54} + 32 q^{57} + 296 q^{58} + 512 q^{59} + 640 q^{62} - 304 q^{64} + 192 q^{65} + 352 q^{67} + 472 q^{74} + 44 q^{78} + 424 q^{80} + 280 q^{81} - 76 q^{82} + 128 q^{83} + 412 q^{86} - 84 q^{88} + 96 q^{91} - 92 q^{92} + 276 q^{94} + 300 q^{96}+O(q^{100}) \) 56 * q - 4 * q^4 - 184 * q^9 - 44 * q^16 - 12 * q^20 - 68 * q^22 - 72 * q^24 - 280 * q^25 + 116 * q^28 + 8 * q^30 + 32 * q^33 - 116 * q^34 + 96 * q^35 - 112 * q^36 - 176 * q^38 + 156 * q^42 - 424 * q^49 + 32 * q^51 - 56 * q^52 + 160 * q^54 + 32 * q^57 + 296 * q^58 + 512 * q^59 + 640 * q^62 - 304 * q^64 + 192 * q^65 + 352 * q^67 + 472 * q^74 + 44 * q^78 + 424 * q^80 + 280 * q^81 - 76 * q^82 + 128 * q^83 + 412 * q^86 - 84 * q^88 + 96 * q^91 - 92 * q^92 + 276 * q^94 + 300 * q^96

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