LMFDB - Embedded newform 1148.2.ba.a.113.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.19
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +O(q^{10})$	\(q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +(-4.77283 - 1.55079i) q^{11} +(0.248079 - 0.341451i) q^{13} +(6.49774 - 2.11124i) q^{15} +(5.89651 + 1.91589i) q^{17} +(0.733357 + 1.00938i) q^{19} +(2.35093 - 1.70805i) q^{21} +(-2.51563 - 1.82771i) q^{23} +(-0.426963 + 0.310207i) q^{25} -7.10286i q^{27} +(7.39618 - 2.40316i) q^{29} +(1.65461 - 5.09237i) q^{31} +(4.50644 - 13.8694i) q^{33} +(-1.38195 + 1.90209i) q^{35} +(-3.61986 - 11.1408i) q^{37} +(0.992224 + 0.720893i) q^{39} +(3.63509 - 5.27126i) q^{41} +(3.80506 + 2.76454i) q^{43} +(3.95546 + 12.1737i) q^{45} +(4.46898 - 6.15102i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-5.56740 + 17.1347i) q^{51} +(8.91995 - 2.89827i) q^{53} +11.7990i q^{55} +(-2.93316 + 2.13107i) q^{57} +(-9.13002 - 6.63335i) q^{59} +(-4.00070 + 2.90668i) q^{61} +(3.20007 + 4.40452i) q^{63} +(-0.943738 - 0.306639i) q^{65} +(-8.17082 + 2.65486i) q^{67} +(5.31116 - 7.31018i) q^{69} +(-3.69294 - 1.19991i) q^{71} +0.525670 q^{73} +(-0.901431 - 1.24071i) q^{75} +(1.55079 + 4.77283i) q^{77} +12.5264i q^{79} +4.30737 q^{81} +1.32207 q^{83} -14.5768i q^{85} +(6.98337 + 21.4926i) q^{87} +(-5.80911 - 7.99555i) q^{89} -0.422057 q^{91} +(14.7980 + 4.80815i) q^{93} +(1.72421 - 2.37317i) q^{95} +(-7.11564 + 2.31201i) q^{97} +(25.9847 + 8.44293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$		0			0
$2$		0			0
$3$			2.90590i			1.67772i	0.544343	+	0.838862i	$0.316779\pi$
$3$			2.90590i			1.67772i	−0.544343	+	0.838862i	$0.683221\pi$
$4$		0			0
$5$	−0.726535	−	2.23605i	−0.324916	−	0.999990i	−0.971478	−	0.237129i	$-0.923794\pi$
$5$	−0.726535	−	2.23605i	−0.324916	−	0.999990i	0.646562	−	0.762862i	$-0.276206\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	−5.44428			−1.81476
$10$		0			0
$11$	−4.77283	−	1.55079i	−1.43906	−	0.467580i	−0.517458	−	0.855708i	$-0.673122\pi$
$11$	−4.77283	−	1.55079i	−1.43906	−	0.467580i	−0.921605	+	0.388128i	$0.873122\pi$
$12$		0			0
$13$	0.248079	−	0.341451i	0.0688046	−	0.0947014i	−0.773228	−	0.634128i	$-0.781359\pi$
$13$	0.248079	−	0.341451i	0.0688046	−	0.0947014i	0.842032	+	0.539427i	$0.181359\pi$
$14$		0			0
$15$	6.49774	−	2.11124i	1.67771	−	0.545121i
$16$		0			0
$17$	5.89651	+	1.91589i	1.43011	+	0.464672i	0.918801	−	0.394722i	$-0.129159\pi$
$17$	5.89651	+	1.91589i	1.43011	+	0.464672i	0.511314	+	0.859394i	$0.329159\pi$
$18$		0			0
$19$	0.733357	+	1.00938i	0.168244	+	0.231567i	0.884811	−	0.465951i	$-0.154288\pi$
$19$	0.733357	+	1.00938i	0.168244	+	0.231567i	−0.716567	+	0.697518i	$0.754288\pi$
$20$		0			0
$21$	2.35093	−	1.70805i	0.513014	−	0.372727i
$22$		0			0
$23$	−2.51563	−	1.82771i	−0.524545	−	0.381104i	0.293768	−	0.955877i	$-0.405091\pi$
$23$	−2.51563	−	1.82771i	−0.524545	−	0.381104i	−0.818313	+	0.574772i	$0.805091\pi$
$24$		0			0
$25$	−0.426963	+	0.310207i	−0.0853925	+	0.0620413i
$26$		0			0
$27$		−	7.10286i		−	1.36695i
$28$		0			0
$29$	7.39618	−	2.40316i	1.37344	−	0.446256i	0.472930	−	0.881100i	$-0.343196\pi$
$29$	7.39618	−	2.40316i	1.37344	−	0.446256i	0.900506	+	0.434844i	$0.143196\pi$
$30$		0			0
$31$	1.65461	−	5.09237i	0.297177	−	0.914617i	−0.685304	−	0.728257i	$-0.740331\pi$
$31$	1.65461	−	5.09237i	0.297177	−	0.914617i	0.982481	−	0.186360i	$-0.0596692\pi$
$32$		0			0
$33$	4.50644	−	13.8694i	0.784471	−	2.41435i
$34$		0			0
$35$	−1.38195	+	1.90209i	−0.233593	+	0.321513i
$36$		0			0
$37$	−3.61986	−	11.1408i	−0.595102	−	1.83154i	−0.554218	−	0.832372i	$-0.686982\pi$
$37$	−3.61986	−	11.1408i	−0.595102	−	1.83154i	−0.0408844	−	0.999164i	$-0.513018\pi$
$38$		0			0
$39$	0.992224	+	0.720893i	0.158883	+	0.115435i
$40$		0			0
$41$	3.63509	−	5.27126i	0.567705	−	0.823232i
$41$	3.63509	−	5.27126i	0.567705	−	0.823232i
$42$		0			0
$43$	3.80506	+	2.76454i	0.580266	+	0.421588i	0.838820	−	0.544409i	$-0.183246\pi$
$43$	3.80506	+	2.76454i	0.580266	+	0.421588i	−0.258554	+	0.965997i	$0.583246\pi$
$44$		0			0
$45$	3.95546	+	12.1737i	0.589646	+	1.81474i
$46$		0			0
$47$	4.46898	−	6.15102i	0.651868	−	0.897219i	−0.347310	−	0.937750i	$-0.612905\pi$
$47$	4.46898	−	6.15102i	0.651868	−	0.897219i	0.999178	+	0.0405311i	$0.0129050\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−5.56740	+	17.1347i	−0.779592	+	2.39934i
$52$		0			0
$53$	8.91995	−	2.89827i	1.22525	−	0.398108i	0.376259	−	0.926515i	$-0.377210\pi$
$53$	8.91995	−	2.89827i	1.22525	−	0.398108i	0.848991	+	0.528407i	$0.177210\pi$
$54$		0			0
$55$			11.7990i			1.59097i
$56$		0			0
$57$	−2.93316	+	2.13107i	−0.388507	+	0.282267i
$58$		0			0
$59$	−9.13002	−	6.63335i	−1.18863	−	0.863589i	−0.195509	−	0.980702i	$-0.562636\pi$
$59$	−9.13002	−	6.63335i	−1.18863	−	0.863589i	−0.993119	+	0.117113i	$0.962636\pi$
$60$		0			0
$61$	−4.00070	+	2.90668i	−0.512237	+	0.372162i	−0.813672	−	0.581325i	$-0.802535\pi$
$61$	−4.00070	+	2.90668i	−0.512237	+	0.372162i	0.301434	+	0.953487i	$0.402535\pi$
$62$		0			0
$63$	3.20007	+	4.40452i	0.403171	+	0.554917i
$64$		0			0
$65$	−0.943738	−	0.306639i	−0.117056	−	0.0380339i
$66$		0			0
$67$	−8.17082	+	2.65486i	−0.998224	+	0.324343i	−0.762156	−	0.647394i	$-0.775859\pi$
$67$	−8.17082	+	2.65486i	−0.998224	+	0.324343i	−0.236068	+	0.971736i	$0.575859\pi$
$68$		0			0
$69$	5.31116	−	7.31018i	0.639388	−	0.880043i
$70$		0			0
$71$	−3.69294	−	1.19991i	−0.438271	−	0.142403i	0.0815668	−	0.996668i	$-0.474008\pi$
$71$	−3.69294	−	1.19991i	−0.438271	−	0.142403i	−0.519838	+	0.854265i	$0.674008\pi$
$72$		0			0
$73$	0.525670			0.0615250			0.0307625	−	0.999527i	$-0.490206\pi$
$73$	0.525670			0.0615250			0.0307625	+	0.999527i	$0.490206\pi$
$74$		0			0
$75$	−0.901431	−	1.24071i	−0.104088	−	0.143265i
$76$		0			0
$77$	1.55079	+	4.77283i	0.176729	+	0.543915i
$78$		0			0
$79$			12.5264i			1.40933i	0.709542	+	0.704663i	$0.248902\pi$
$79$			12.5264i			1.40933i	−0.709542	+	0.704663i	$0.751098\pi$
$80$		0			0
$81$	4.30737			0.478597
$82$		0			0
$83$	1.32207			0.145116			0.0725579	−	0.997364i	$-0.476884\pi$
$83$	1.32207			0.145116			0.0725579	+	0.997364i	$0.476884\pi$
$84$		0			0
$85$		−	14.5768i		−	1.58108i
$86$		0			0
$87$	6.98337	+	21.4926i	0.748695	+	2.30425i
$88$		0			0
$89$	−5.80911	−	7.99555i	−0.615764	−	0.847527i	0.381272	−	0.924463i	$-0.375486\pi$
$89$	−5.80911	−	7.99555i	−0.615764	−	0.847527i	−0.997036	+	0.0769361i	$0.975486\pi$
$90$		0			0
$91$	−0.422057			−0.0442435
$92$		0			0
$93$	14.7980	+	4.80815i	1.53448	+	0.498582i
$94$		0			0
$95$	1.72421	−	2.37317i	0.176900	−	0.243482i
$96$		0			0
$97$	−7.11564	+	2.31201i	−0.722484	+	0.234749i	−0.647100	−	0.762405i	$-0.724018\pi$
$97$	−7.11564	+	2.31201i	−0.722484	+	0.234749i	−0.0753842	+	0.997155i	$0.524018\pi$
$98$		0			0
$99$	25.9847	+	8.44293i	2.61156	+	0.848546i
$100$		0			0
$101$	0.102287	+	0.140786i	0.0101779	+	0.0140087i	0.814076	−	0.580759i	$-0.197244\pi$
$101$	0.102287	+	0.140786i	0.0101779	+	0.0140087i	−0.803898	+	0.594768i	$0.797244\pi$
$102$		0			0
$103$	6.73237	−	4.89135i	0.663360	−	0.481959i	−0.204436	−	0.978880i	$-0.565536\pi$
$103$	6.73237	−	4.89135i	0.663360	−	0.481959i	0.867796	+	0.496921i	$0.165536\pi$
$104$		0			0
$105$	−5.52731	−	4.01582i	−0.539410	−	0.391904i
$106$		0			0
$107$	−2.43783	+	1.77119i	−0.235674	+	0.171227i	−0.699354	−	0.714776i	$-0.746529\pi$
$107$	−2.43783	+	1.77119i	−0.235674	+	0.171227i	0.463680	+	0.886003i	$0.346529\pi$
$108$		0			0
$109$			6.16999i			0.590978i	0.955346	+	0.295489i	$0.0954825\pi$
$109$			6.16999i			0.590978i	−0.955346	+	0.295489i	$0.904517\pi$
$110$		0			0
$111$	32.3741	−	10.5190i	3.07281	−	0.998418i
$112$		0			0
$113$	5.59020	−	17.2049i	0.525881	−	1.61850i	−0.236685	−	0.971587i	$-0.576061\pi$
$113$	5.59020	−	17.2049i	0.525881	−	1.61850i	0.762566	−	0.646910i	$-0.223939\pi$
$114$		0			0
$115$	−2.25915	+	6.95296i	−0.210667	+	0.648367i
$116$		0			0
$117$	−1.35061	+	1.85896i	−0.124864	+	0.171860i
$118$		0			0
$119$	−1.91589	−	5.89651i	−0.175630	−	0.540532i
$120$		0			0
$121$	11.4758	+	8.33767i	1.04326	+	0.757970i
$122$		0			0
$123$	15.3178	+	10.5632i	1.38116	+	0.952453i
$124$		0			0
$125$	−8.50663	−	6.18043i	−0.760856	−	0.552794i
$126$		0			0
$127$	−5.82882	−	17.9393i	−0.517224	−	1.59185i	−0.779198	−	0.626777i	$-0.784373\pi$
$127$	−5.82882	−	17.9393i	−0.517224	−	1.59185i	0.261974	−	0.965075i	$-0.415627\pi$
$128$		0			0
$129$	−8.03348	+	11.0571i	−0.707308	+	0.973526i
$130$		0			0
$131$	1.79703	−	5.53070i	0.157008	−	0.483220i	−0.841351	−	0.540489i	$-0.818239\pi$
$131$	1.79703	−	5.53070i	0.157008	−	0.483220i	0.998359	+	0.0572692i	$0.0182393\pi$
$132$		0			0
$133$	0.385549	−	1.18660i	0.0334313	−	0.102891i
$134$		0			0
$135$	−15.8823	+	5.16048i	−1.36693	+	0.444143i
$136$		0			0
$137$			15.8668i			1.35560i	0.735248	+	0.677798i	$0.237066\pi$
$137$			15.8668i			1.35560i	−0.735248	+	0.677798i	$0.762934\pi$
$138$		0			0
$139$	−14.3953	+	10.4588i	−1.22099	+	0.887101i	−0.996182	−	0.0873019i	$-0.972176\pi$
$139$	−14.3953	+	10.4588i	−1.22099	+	0.887101i	−0.224808	+	0.974403i	$0.572176\pi$
$140$		0			0
$141$	17.8743	+	12.9864i	1.50529	+	1.09365i
$142$		0			0
$143$	−1.71356	+	1.24497i	−0.143295	+	0.104110i
$144$		0			0
$145$	−10.7472	−	14.7922i	−0.892504	−	1.22843i
$146$		0			0
$147$	−2.76368	−	0.897974i	−0.227944	−	0.0740636i
$148$		0			0
$149$	2.08749	−	0.678266i	0.171014	−	0.0555657i	−0.222259	−	0.974988i	$-0.571343\pi$
$149$	2.08749	−	0.678266i	0.171014	−	0.0555657i	0.393272	+	0.919422i	$0.371343\pi$
$150$		0			0
$151$	−4.56570	+	6.28414i	−0.371551	+	0.511396i	−0.953322	−	0.301957i	$-0.902360\pi$
$151$	−4.56570	+	6.28414i	−0.371551	+	0.511396i	0.581771	+	0.813353i	$0.302360\pi$
$152$		0			0
$153$	−32.1023	−	10.4307i	−2.59532	−	0.843269i
$154$		0			0
$155$	−12.5889			−1.01117
$156$		0			0
$157$	−8.58928	−	11.8221i	−0.685499	−	0.943509i	0.314484	−	0.949263i	$-0.398168\pi$
$157$	−8.58928	−	11.8221i	−0.685499	−	0.943509i	−0.999983	+	0.00575395i	$0.998168\pi$
$158$		0			0
$159$	8.42209	+	25.9205i	0.667915	+	2.05563i
$160$		0			0
$161$			3.10949i			0.245062i
$162$		0			0
$163$	−10.3868			−0.813556			−0.406778	−	0.913527i	$-0.633348\pi$
$163$	−10.3868			−0.813556			−0.406778	+	0.913527i	$0.633348\pi$
$164$		0			0
$165$	−34.2867			−2.66922
$166$		0			0
$167$		−	0.923298i		−	0.0714470i	−0.999362	−	0.0357235i	$-0.988626\pi$
$167$		−	0.923298i		−	0.0714470i	0.999362	−	0.0357235i	$-0.0113736\pi$
$168$		0			0
$169$	3.96218	+	12.1943i	0.304783	+	0.938025i
$170$		0			0
$171$	−3.99260	−	5.49535i	−0.305322	−	0.420240i
$172$		0			0
$173$	−0.214787			−0.0163299			−0.00816496	−	0.999967i	$-0.502599\pi$
$173$	−0.214787			−0.0163299			−0.00816496	+	0.999967i	$0.502599\pi$
$174$		0			0
$175$	0.501925	+	0.163085i	0.0379419	+	0.0123281i
$176$		0			0
$177$	19.2759	−	26.5310i	1.44886	−	1.99419i
$178$		0			0
$179$	22.9289	−	7.45005i	1.71379	−	0.556843i	0.722830	−	0.691026i	$-0.242841\pi$
$179$	22.9289	−	7.45005i	1.71379	−	0.556843i	0.990957	+	0.134183i	$0.0428409\pi$
$180$		0			0
$181$	1.62666	+	0.528533i	0.120908	+	0.0392855i	0.368846	−	0.929490i	$-0.379753\pi$
$181$	1.62666	+	0.528533i	0.120908	+	0.0392855i	−0.247938	+	0.968776i	$0.579753\pi$
$182$		0			0
$183$	−8.44653	−	11.6257i	−0.624385	−	0.859393i
$184$		0			0
$185$	−22.2814	+	16.1884i	−1.63816	+	1.19019i
$186$		0			0
$187$	−25.1719	−	18.2885i	−1.84075	−	1.33739i
$188$		0			0
$189$	−5.74633	+	4.17495i	−0.417984	+	0.303683i
$190$		0			0
$191$			6.33542i			0.458415i	0.973378	+	0.229208i	$0.0736135\pi$
$191$			6.33542i			0.458415i	−0.973378	+	0.229208i	$0.926387\pi$
$192$		0			0
$193$	2.00704	−	0.652128i	0.144470	−	0.0469412i	−0.235889	−	0.971780i	$-0.575800\pi$
$193$	2.00704	−	0.652128i	0.144470	−	0.0469412i	0.380359	+	0.924839i	$0.375800\pi$
$194$		0			0
$195$	0.891064	−	2.74241i	0.0638104	−	0.196388i
$196$		0			0
$197$	−2.43110	+	7.48217i	−0.173209	+	0.533083i	−0.999547	−	0.0300917i	$-0.990420\pi$
$197$	−2.43110	+	7.48217i	−0.173209	+	0.533083i	0.826338	+	0.563174i	$0.190420\pi$
$198$		0			0
$199$	13.2737	−	18.2697i	0.940947	−	1.29510i	−0.0144862	−	0.999895i	$-0.504611\pi$
$199$	13.2737	−	18.2697i	0.940947	−	1.29510i	0.955433	−	0.295207i	$-0.0953888\pi$
$200$		0			0
$201$	−7.71477	−	23.7436i	−0.544158	−	1.67475i
$202$		0			0
$203$	−6.29156	−	4.57109i	−0.441581	−	0.320828i
$204$		0			0
$205$	−14.4278	−	4.29846i	−1.00768	−	0.300218i
$206$		0			0
$207$	13.6958	+	9.95058i	0.951924	+	0.691613i
$208$		0			0
$209$	−1.93486	−	5.95488i	−0.133837	−	0.411908i
$210$		0			0
$211$	−4.66055	+	6.41469i	−0.320845	+	0.441606i	−0.938725	−	0.344667i	$-0.887992\pi$
$211$	−4.66055	+	6.41469i	−0.320845	+	0.441606i	0.617880	+	0.786273i	$0.287992\pi$
$212$		0			0
$213$	3.48682	−	10.7313i	0.238913	−	0.735298i
$214$		0			0
$215$	3.41712	−	10.5168i	0.233046	−	0.717241i
$216$		0			0
$217$	−5.09237	+	1.65461i	−0.345693	+	0.112322i
$218$		0			0
$219$			1.52755i			0.103222i
$220$		0			0
$221$	2.11698	−	1.53808i	0.142404	−	0.103462i
$222$		0			0
$223$	6.66151	+	4.83987i	0.446088	+	0.324102i	0.788049	−	0.615612i	$-0.211091\pi$
$223$	6.66151	+	4.83987i	0.446088	+	0.324102i	−0.341961	+	0.939714i	$0.611091\pi$
$224$		0			0
$225$	2.32451	−	1.68885i	0.154967	−	0.112590i
$226$		0			0
$227$	−15.2206	−	20.9494i	−1.01023	−	1.39046i	−0.918834	−	0.394643i	$-0.870868\pi$
$227$	−15.2206	−	20.9494i	−1.01023	−	1.39046i	−0.0913924	−	0.995815i	$-0.529132\pi$
$228$		0			0
$229$	12.7491	+	4.14245i	0.842487	+	0.273741i	0.698296	−	0.715809i	$-0.253942\pi$
$229$	12.7491	+	4.14245i	0.842487	+	0.273741i	0.144191	+	0.989550i	$0.453942\pi$
$230$		0			0
$231$	−13.8694	+	4.50644i	−0.912540	+	0.296502i
$232$		0			0
$233$	−0.887101	+	1.22099i	−0.0581159	+	0.0799897i	−0.837086	−	0.547072i	$-0.815742\pi$
$233$	−0.887101	+	1.22099i	−0.0581159	+	0.0799897i	0.778970	+	0.627061i	$0.215742\pi$
$234$		0			0
$235$	−17.0008	−	5.52391i	−1.10901	−	0.360340i
$236$		0			0
$237$	−36.4004			−2.36446
$238$		0			0
$239$	17.7379	+	24.4141i	1.14737	+	1.57922i	0.749825	+	0.661637i	$0.230138\pi$
$239$	17.7379	+	24.4141i	1.14737	+	1.57922i	0.397545	+	0.917583i	$0.369862\pi$
$240$		0			0
$241$	4.87693	+	15.0097i	0.314151	+	0.966857i	0.976103	+	0.217311i	$0.0697284\pi$
$241$	4.87693	+	15.0097i	0.314151	+	0.966857i	−0.661952	+	0.749547i	$0.730272\pi$
$242$		0			0
$243$		−	8.79175i		−	0.563991i
$244$		0			0
$245$	2.35112			0.150207
$246$		0			0
$247$	0.526584			0.0335057
$248$		0			0
$249$			3.84181i			0.243465i
$250$		0			0
$251$	−4.17207	−	12.8403i	−0.263339	−	0.810473i	−0.992072	−	0.125675i	$-0.959890\pi$
$251$	−4.17207	−	12.8403i	−0.263339	−	0.810473i	0.728733	−	0.684798i	$-0.240110\pi$
$252$		0			0
$253$	9.17229	+	12.6246i	0.576657	+	0.793700i
$254$		0			0
$255$	42.3589			2.65262
$256$		0			0
$257$	−3.00094	−	0.975064i	−0.187193	−	0.0608228i	0.213920	−	0.976851i	$-0.431377\pi$
$257$	−3.00094	−	0.975064i	−0.187193	−	0.0608228i	−0.401114	+	0.916028i	$0.631377\pi$
$258$		0			0
$259$	−6.88539	+	9.47693i	−0.427837	+	0.588868i
$260$		0			0
$261$	−40.2669	+	13.0835i	−2.49246	+	0.809849i
$262$		0			0
$263$	9.81843	+	3.19020i	0.605430	+	0.196716i	0.595661	−	0.803236i	$-0.296890\pi$
$263$	9.81843	+	3.19020i	0.605430	+	0.196716i	0.00976941	+	0.999952i	$0.496890\pi$
$264$		0			0
$265$	−12.9613	−	17.8397i	−0.796208	−	1.09589i
$266$		0			0
$267$	23.2343	−	16.8807i	1.42192	−	1.03308i
$268$		0			0
$269$	−17.1783	−	12.4808i	−1.04738	−	0.760966i	−0.0756673	−	0.997133i	$-0.524109\pi$
$269$	−17.1783	−	12.4808i	−1.04738	−	0.760966i	−0.971712	+	0.236167i	$0.924109\pi$
$270$		0			0
$271$	13.1341	−	9.54251i	0.797842	−	0.579666i	−0.112438	−	0.993659i	$-0.535866\pi$
$271$	13.1341	−	9.54251i	0.797842	−	0.579666i	0.910280	+	0.413993i	$0.135866\pi$
$272$		0			0
$273$		−	1.22646i		−	0.0742285i
$274$		0			0
$275$	2.51889	−	0.818436i	0.151895	−	0.0493535i
$276$		0			0
$277$	−7.48606	+	23.0397i	−0.449794	+	1.38432i	0.427346	+	0.904088i	$0.359449\pi$
$277$	−7.48606	+	23.0397i	−0.449794	+	1.38432i	−0.877140	+	0.480235i	$0.840551\pi$
$278$		0			0
$279$	−9.00818	+	27.7243i	−0.539306	+	1.65981i
$280$		0			0
$281$	6.39227	−	8.79820i	0.381331	−	0.524857i	−0.574606	−	0.818430i	$-0.694845\pi$
$281$	6.39227	−	8.79820i	0.381331	−	0.524857i	0.955936	+	0.293574i	$0.0948446\pi$
$282$		0			0
$283$	3.74286	+	11.5193i	0.222490	+	0.684754i	0.998537	+	0.0540784i	$0.0172221\pi$
$283$	3.74286	+	11.5193i	0.222490	+	0.684754i	−0.776047	+	0.630676i	$0.782778\pi$
$284$		0			0
$285$	6.89621	+	5.01039i	0.408496	+	0.296790i
$286$		0			0
$287$	−6.40119	+	0.157521i	−0.377850	+	0.00929815i
$288$		0			0
$289$	17.3449	+	12.6018i	1.02029	+	0.741284i
$290$		0			0
$291$	−6.71849	−	20.6774i	−0.393845	−	1.21213i
$292$		0			0
$293$	3.35516	−	4.61798i	0.196010	−	0.269785i	−0.699687	−	0.714450i	$-0.746677\pi$
$293$	3.35516	−	4.61798i	0.196010	−	0.269785i	0.895697	+	0.444665i	$0.146677\pi$
$294$		0			0
$295$	−8.19919	+	25.2345i	−0.477375	+	1.46921i
$296$		0			0
$297$	−11.0150	+	33.9008i	−0.639156	+	1.96712i
$298$		0			0
$299$	−1.24815	+	0.405548i	−0.0721823	+	0.0234534i
$300$		0			0
$301$		−	4.70331i		−	0.271094i
$302$		0			0
$303$	−0.409110	+	0.297236i	−0.0235028	+	0.0170757i
$304$		0			0
$305$	9.40612	+	6.83394i	0.538593	+	0.391310i
$306$		0			0
$307$	18.5160	−	13.4527i	1.05676	−	0.767784i	0.0832770	−	0.996526i	$-0.473461\pi$
$307$	18.5160	−	13.4527i	1.05676	−	0.767784i	0.973487	+	0.228742i	$0.0734614\pi$
$308$		0			0
$309$	14.2138	+	19.5636i	0.808595	+	1.11294i
$310$		0			0
$311$	−8.82919	−	2.86878i	−0.500658	−	0.162674i	0.0477917	−	0.998857i	$-0.484782\pi$
$311$	−8.82919	−	2.86878i	−0.500658	−	0.162674i	−0.548449	+	0.836184i	$0.684782\pi$
$312$		0			0
$313$	0.217363	−	0.0706255i	0.0122861	−	0.00399199i	−0.302868	−	0.953033i	$-0.597944\pi$
$313$	0.217363	−	0.0706255i	0.0122861	−	0.00399199i	0.315154	+	0.949041i	$0.397944\pi$
$314$		0			0
$315$	7.52374	−	10.3555i	0.423915	−	0.583469i
$316$		0			0
$317$	−28.2440	−	9.17702i	−1.58634	−	0.515433i	−0.622659	−	0.782493i	$-0.713948\pi$
$317$	−28.2440	−	9.17702i	−1.58634	−	0.515433i	−0.963680	+	0.267061i	$0.913948\pi$
$318$		0			0
$319$	−39.0275			−2.18512
$320$		0			0
$321$	−5.14691	−	7.08411i	−0.287272	−	0.395397i
$322$		0			0
$323$	2.39039	+	7.35685i	0.133005	+	0.409346i
$324$		0			0
$325$			0.222742i			0.0123555i
$326$		0			0
$327$	−17.9294			−0.991498
$328$		0			0
$329$	−7.60308			−0.419172
$330$		0			0
$331$		−	17.3341i		−	0.952766i	−0.879238	−	0.476383i	$-0.841948\pi$
$331$		−	17.3341i		−	0.952766i	0.879238	−	0.476383i	$-0.158052\pi$
$332$		0			0
$333$	19.7076	+	60.6537i	1.07997	+	3.32380i
$334$		0			0
$335$	11.8728	+	16.3415i	0.648679	+	0.892830i
$336$		0			0
$337$	−13.4045			−0.730192			−0.365096	−	0.930970i	$-0.618964\pi$
$337$	−13.4045			−0.730192			−0.365096	+	0.930970i	$0.618964\pi$
$338$		0			0
$339$	49.9957	+	16.2446i	2.71539	+	0.882284i
$340$		0			0
$341$	−15.7944	+	21.7391i	−0.855314	+	1.17724i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	−20.2046	−	6.56489i	−1.08778	−	0.353442i
$346$		0			0
$347$	15.4823	+	21.3096i	0.831135	+	1.14396i	0.987711	+	0.156293i	$0.0499543\pi$
$347$	15.4823	+	21.3096i	0.831135	+	1.14396i	−0.156576	+	0.987666i	$0.550046\pi$
$348$		0			0
$349$	−19.3479	+	14.0571i	−1.03567	+	0.752458i	−0.969436	−	0.245346i	$-0.921099\pi$
$349$	−19.3479	+	14.0571i	−1.03567	+	0.752458i	−0.0662344	+	0.997804i	$0.521099\pi$
$350$		0			0
$351$	−2.42528	−	1.76207i	−0.129452	−	0.0940521i
$352$		0			0
$353$	26.7863	−	19.4614i	1.42569	−	1.03583i	0.434892	−	0.900482i	$-0.356786\pi$
$353$	26.7863	−	19.4614i	1.42569	−	1.03583i	0.990799	−	0.135343i	$-0.0432136\pi$
$354$		0			0
$355$			9.12935i			0.484536i
$356$		0			0
$357$	17.1347	−	5.56740i	0.906865	−	0.294658i
$358$		0			0
$359$	2.82170	−	8.68431i	0.148924	−	0.458340i	−0.848571	−	0.529082i	$-0.822537\pi$
$359$	2.82170	−	8.68431i	0.148924	−	0.458340i	0.997495	+	0.0707414i	$0.0225365\pi$
$360$		0			0
$361$	5.39029	−	16.5896i	0.283699	−	0.873137i
$362$		0			0
$363$	−24.2285	+	33.3476i	−1.27167	+	1.75030i
$364$		0			0
$365$	−0.381918	−	1.17542i	−0.0199905	−	0.0615244i
$366$		0			0
$367$	2.83816	+	2.06204i	0.148151	+	0.107638i	0.659392	−	0.751800i	$-0.270814\pi$
$367$	2.83816	+	2.06204i	0.148151	+	0.107638i	−0.511241	+	0.859437i	$0.670814\pi$
$368$		0			0
$369$	−19.7904	+	28.6982i	−1.03025	+	1.49397i
$370$		0			0
$371$	−7.58777	−	5.51283i	−0.393937	−	0.286212i
$372$		0			0
$373$	−0.127453	−	0.392260i	−0.00659926	−	0.0203104i	0.947703	−	0.319155i	$-0.103399\pi$
$373$	−0.127453	−	0.392260i	−0.00659926	−	0.0203104i	−0.954302	+	0.298844i	$0.903399\pi$
$374$		0			0
$375$	17.9597	−	24.7195i	0.927437	−	1.27651i
$376$		0			0
$377$	1.01427	−	3.12160i	0.0522376	−	0.160771i
$378$		0			0
$379$	−3.73524	+	11.4959i	−0.191866	+	0.590504i	0.808132	+	0.589001i	$0.200479\pi$
$379$	−3.73524	+	11.4959i	−0.191866	+	0.590504i	−0.999999	+	0.00150332i	$0.999521\pi$
$380$		0			0
$381$	52.1298	−	16.9380i	2.67069	−	0.867760i
$382$		0			0
$383$			30.3337i			1.54998i	0.631973	+	0.774990i	$0.282245\pi$
$383$			30.3337i			1.54998i	−0.631973	+	0.774990i	$0.717755\pi$
$384$		0			0
$385$	9.54557	−	6.93527i	0.486488	−	0.353454i
$386$		0			0
$387$	−20.7158	−	15.0509i	−1.05304	−	0.765081i
$388$		0			0
$389$	13.3750	−	9.71751i	0.678140	−	0.492697i	−0.194600	−	0.980883i	$-0.562341\pi$
$389$	13.3750	−	9.71751i	0.678140	−	0.492697i	0.872740	+	0.488185i	$0.162341\pi$
$390$		0			0
$391$	−11.3317	−	15.5968i	−0.573071	−	0.788764i
$392$		0			0
$393$	16.0717	+	5.22201i	0.810709	+	0.263415i
$394$		0			0
$395$	28.0095	−	9.10085i	1.40931	−	0.457913i
$396$		0			0
$397$	−6.67368	+	9.18553i	−0.334942	+	0.461008i	−0.942956	−	0.332918i	$-0.891967\pi$
$397$	−6.67368	+	9.18553i	−0.334942	+	0.461008i	0.608013	+	0.793927i	$0.291967\pi$
$398$		0			0
$399$	3.44814	+	1.12037i	0.172623	+	0.0560885i
$400$		0			0
$401$	39.6870			1.98187			0.990937	−	0.134331i	$-0.0428885\pi$
$401$	39.6870			1.98187			0.990937	+	0.134331i	$0.0428885\pi$
$402$		0			0
$403$	−1.32832	−	1.82828i	−0.0661684	−	0.0910730i
$404$		0			0
$405$	−3.12946	−	9.63148i	−0.155504	−	0.478592i
$406$		0			0
$407$			58.7868i			2.91395i
$408$		0			0
$409$	−4.81376			−0.238025			−0.119012	−	0.992893i	$-0.537973\pi$
$409$	−4.81376			−0.238025			−0.119012	+	0.992893i	$0.537973\pi$
$410$		0			0
$411$	−46.1075			−2.27432
$412$		0			0
$413$			11.2853i			0.555315i
$414$		0			0
$415$	−0.960529	−	2.95621i	−0.0471505	−	0.145114i
$416$		0			0
$417$	−30.3922	−	41.8313i	−1.48831	−	2.04849i
$418$		0			0
$419$	2.06373			0.100820			0.0504099	−	0.998729i	$-0.483947\pi$
$419$	2.06373			0.100820			0.0504099	+	0.998729i	$0.483947\pi$
$420$		0			0
$421$	15.8001	+	5.13376i	0.770049	+	0.250204i	0.667586	−	0.744533i	$-0.267328\pi$
$421$	15.8001	+	5.13376i	0.770049	+	0.250204i	0.102463	+	0.994737i	$0.467328\pi$
$422$		0			0
$423$	−24.3304	+	33.4879i	−1.18298	+	1.62824i
$424$		0			0
$425$	−3.11191	+	1.01112i	−0.150950	+	0.0490466i
$426$		0			0
$427$	4.70310	+	1.52813i	0.227599	+	0.0739514i
$428$		0			0
$429$	−3.61777	−	4.97943i	−0.174667	−	0.240409i
$430$		0			0
$431$	30.3663	−	22.0624i	1.46269	−	1.06271i	0.480042	−	0.877245i	$-0.340621\pi$
$431$	30.3663	−	22.0624i	1.46269	−	1.06271i	0.982651	−	0.185464i	$-0.0593787\pi$
$432$		0			0
$433$	1.70515	+	1.23887i	0.0819444	+	0.0595361i	0.628003	−	0.778211i	$-0.283872\pi$
$433$	1.70515	+	1.23887i	0.0819444	+	0.0595361i	−0.546059	+	0.837747i	$0.683872\pi$
$434$		0			0
$435$	42.9848	−	31.2302i	2.06096	−	1.49738i
$436$		0			0
$437$		−	3.87959i		−	0.185586i
$438$		0			0
$439$	4.09799	−	1.33152i	0.195587	−	0.0635499i	−0.209586	−	0.977790i	$-0.567212\pi$
$439$	4.09799	−	1.33152i	0.195587	−	0.0635499i	0.405172	+	0.914240i	$0.367212\pi$
$440$		0			0
$441$	1.68238	−	5.17782i	0.0801131	−	0.246563i
$442$		0			0
$443$	−6.99947	+	21.5422i	−0.332555	+	1.02350i	0.635359	+	0.772217i	$0.280852\pi$
$443$	−6.99947	+	21.5422i	−0.332555	+	1.02350i	−0.967914	+	0.251282i	$0.919148\pi$
$444$		0			0
$445$	−13.6579	+	18.7985i	−0.647447	+	0.891134i
$446$		0			0
$447$	1.97098	+	6.06604i	0.0932240	+	0.286914i
$448$		0			0
$449$	8.57166	+	6.22767i	0.404521	+	0.293902i	0.771380	−	0.636375i	$-0.219567\pi$
$449$	8.57166	+	6.22767i	0.404521	+	0.293902i	−0.366859	+	0.930277i	$0.619567\pi$
$450$		0			0
$451$	−25.5243	+	19.5216i	−1.20189	+	0.919236i
$452$		0			0
$453$	−18.2611	−	13.2675i	−0.857982	−	0.623360i
$454$		0			0
$455$	0.306639	+	0.943738i	0.0143755	+	0.0442431i
$456$		0			0
$457$	−0.120284	+	0.165557i	−0.00562667	+	0.00774445i	−0.811821	−	0.583906i	$-0.801524\pi$
$457$	−0.120284	+	0.165557i	−0.00562667	+	0.00774445i	0.806194	+	0.591651i	$0.201524\pi$
$458$		0			0
$459$	13.6083	−	41.8821i	0.635182	−	1.95489i
$460$		0			0
$461$	−7.45306	+	22.9382i	−0.347124	+	1.06834i	0.613313	+	0.789840i	$0.289836\pi$
$461$	−7.45306	+	22.9382i	−0.347124	+	1.06834i	−0.960437	+	0.278497i	$0.910164\pi$
$462$		0			0
$463$	−10.7040	+	3.47793i	−0.497455	+	0.161633i	−0.546990	−	0.837139i	$-0.684226\pi$
$463$	−10.7040	+	3.47793i	−0.497455	+	0.161633i	0.0495342	+	0.998772i	$0.484226\pi$
$464$		0			0
$465$		−	36.5822i		−	1.69646i
$466$		0			0
$467$	26.9050	−	19.5476i	1.24501	−	0.904556i	0.247093	−	0.968992i	$-0.420525\pi$
$467$	26.9050	−	19.5476i	1.24501	−	0.904556i	0.997922	+	0.0644357i	$0.0205247\pi$
$468$		0			0
$469$	6.95051	+	5.04984i	0.320945	+	0.233180i
$470$		0			0
$471$	34.3540	−	24.9596i	1.58295	−	1.15008i
$472$		0			0
$473$	−13.8737	−	19.0955i	−0.637913	−	0.878012i
$474$		0			0
$475$	−0.626232	−	0.203475i	−0.0287335	−	0.00933608i
$476$		0			0
$477$	−48.5628	+	15.7790i	−2.22354	+	0.722471i
$478$		0			0
$479$	25.1855	−	34.6649i	1.15076	−	1.58388i	0.410030	−	0.912072i	$-0.365518\pi$
$479$	25.1855	−	34.6649i	1.15076	−	1.58388i	0.740726	−	0.671808i	$-0.234482\pi$
$480$		0			0
$481$	−4.70205	−	1.52779i	−0.214395	−	0.0696611i
$482$		0			0
$483$	−9.03588			−0.411147
$484$		0			0
$485$	10.3395	+	14.2311i	0.469494	+	0.646203i
$486$		0			0
$487$	3.17612	+	9.77511i	0.143924	+	0.442952i	0.996871	−	0.0790450i	$-0.0251871\pi$
$487$	3.17612	+	9.77511i	0.143924	+	0.442952i	−0.852947	+	0.521997i	$0.825187\pi$
$488$		0			0
$489$		−	30.1830i		−	1.36492i
$490$		0			0
$491$	−21.5980			−0.974703			−0.487352	−	0.873206i	$-0.662037\pi$
$491$	−21.5980			−0.974703			−0.487352	+	0.873206i	$0.662037\pi$
$492$		0			0
$493$	48.2159			2.17153
$494$		0			0
$495$		−	64.2370i		−	2.88724i
$496$		0			0
$497$	1.19991	+	3.69294i	0.0538232	+	0.165651i
$498$		0			0
$499$	−18.7697	−	25.8342i	−0.840246	−	1.15650i	−0.985928	−	0.167168i	$-0.946538\pi$
$499$	−18.7697	−	25.8342i	−0.840246	−	1.15650i	0.145682	−	0.989331i	$-0.453462\pi$
$500$		0			0
$501$	2.68302			0.119868
$502$		0			0
$503$	31.6161	+	10.2727i	1.40969	+	0.458036i	0.912311	−	0.409497i	$-0.134296\pi$
$503$	31.6161	+	10.2727i	1.40969	+	0.458036i	0.497379	+	0.867533i	$0.334296\pi$
$504$		0			0
$505$	0.240488	−	0.331004i	0.0107016	−	0.0147295i
$506$		0			0
$507$	−35.4355	+	11.5137i	−1.57375	+	0.511342i
$508$		0			0
$509$	−8.14726	−	2.64721i	−0.361121	−	0.117335i	0.122836	−	0.992427i	$-0.460801\pi$
$509$	−8.14726	−	2.64721i	−0.361121	−	0.117335i	−0.483957	+	0.875092i	$0.660801\pi$
$510$		0			0
$511$	−0.308981	−	0.425276i	−0.0136685	−	0.0188131i
$512$		0			0
$513$	7.16948	−	5.20893i	0.316540	−	0.229980i
$514$		0			0
$515$	−15.8286	−	11.5001i	−0.697491	−	0.506757i
$516$		0			0
$517$	−30.8686	+	22.4274i	−1.35760	+	0.986355i
$518$		0			0
$519$		−	0.624150i		−	0.0273971i
$520$		0			0
$521$	7.98370	−	2.59406i	0.349772	−	0.113648i	−0.128861	−	0.991663i	$-0.541132\pi$
$521$	7.98370	−	2.59406i	0.349772	−	0.113648i	0.478634	+	0.878015i	$0.341132\pi$
$522$		0			0
$523$	−0.969993	+	2.98533i	−0.0424149	+	0.130539i	−0.970022	−	0.243019i	$-0.921862\pi$
$523$	−0.969993	+	2.98533i	−0.0424149	+	0.130539i	0.927607	+	0.373558i	$0.121862\pi$
$524$		0			0
$525$	−0.473910	+	1.45855i	−0.0206831	+	0.0636561i
$526$		0			0
$527$	19.5129	−	26.8572i	0.849995	−	1.16992i
$528$		0			0
$529$	−4.11953	−	12.6786i	−0.179110	−	0.551244i
$530$		0			0
$531$	49.7064	+	36.1138i	2.15708	+	1.56721i
$532$		0			0
$533$	−0.898088	−	2.54889i	−0.0389005	−	0.110405i
$534$		0			0
$535$	5.73163	+	4.16428i	0.247800	+	0.180037i
$536$		0			0
$537$	21.6491	+	66.6292i	0.934230	+	2.87526i
$538$		0			0
$539$	2.94977	−	4.06002i	0.127056	−	0.174877i
$540$		0			0
$541$	12.6485	−	38.9280i	0.543800	−	1.67364i	−0.180027	−	0.983662i	$-0.557619\pi$
$541$	12.6485	−	38.9280i	0.543800	−	1.67364i	0.723827	−	0.689982i	$-0.242381\pi$
$542$		0			0
$543$	−1.53587	+	4.72691i	−0.0659103	+	0.202851i
$544$		0			0
$545$	13.7964	−	4.48271i	0.590972	−	0.192018i
$546$		0			0
$547$			12.1156i			0.518024i	0.965874	+	0.259012i	$0.0833970\pi$
$547$			12.1156i			0.518024i	−0.965874	+	0.259012i	$0.916603\pi$
$548$		0			0
$549$	21.7809	−	15.8248i	0.929588	−	0.675385i
$550$		0			0
$551$	7.84974	+	5.70317i	0.334410	+	0.242963i
$552$		0			0
$553$	10.1340	−	7.36282i	0.430943	−	0.313099i
$554$		0			0
$555$	−47.0419	−	64.7476i	−1.99682	−	2.74838i
$556$		0			0
$557$	−37.6203	−	12.2236i	−1.59402	−	0.517930i	−0.628405	−	0.777887i	$-0.716292\pi$
$557$	−37.6203	−	12.2236i	−1.59402	−	0.517930i	−0.965620	+	0.259957i	$0.916292\pi$
$558$		0			0
$559$	1.88791	−	0.613418i	0.0798499	−	0.0259448i
$560$		0			0
$561$	53.1446	−	73.1472i	2.24377	−	3.08828i
$562$		0			0
$563$	14.0115	+	4.55261i	0.590514	+	0.191869i	0.589005	−	0.808129i	$-0.299520\pi$
$563$	14.0115	+	4.55261i	0.590514	+	0.191869i	0.00150854	+	0.999999i	$0.499520\pi$
$564$		0			0
$565$	−42.5323			−1.78935
$566$		0			0
$567$	−2.53181	−	3.48474i	−0.106326	−	0.146345i
$568$		0			0
$569$	11.1768	+	34.3988i	0.468557	+	1.44207i	0.854453	+	0.519528i	$0.173892\pi$
$569$	11.1768	+	34.3988i	0.468557	+	1.44207i	−0.385896	+	0.922542i	$0.626108\pi$
$570$		0			0
$571$			5.78334i			0.242025i	0.992651	+	0.121013i	$0.0386142\pi$
$571$			5.78334i			0.242025i	−0.992651	+	0.121013i	$0.961386\pi$
$572$		0			0
$573$	−18.4101			−0.769095
$574$		0			0
$575$	1.64105			0.0684365
$576$		0			0
$577$		−	46.0210i		−	1.91588i	−0.286968	−	0.957940i	$-0.592647\pi$
$577$		−	46.0210i		−	1.91588i	0.286968	−	0.957940i	$-0.407353\pi$
$578$		0			0
$579$	1.89502	+	5.83227i	0.0787544	+	0.242381i
$580$		0			0
$581$	−0.777092	−	1.06958i	−0.0322392	−	0.0443735i
$582$		0			0
$583$	−47.0681			−1.94936
$584$		0			0
$585$	5.13798	+	1.66943i	0.212429	+	0.0690224i
$586$		0			0
$587$	−9.85118	+	13.5590i	−0.406602	+	0.559639i	−0.962386	−	0.271687i	$-0.912418\pi$
$587$	−9.85118	+	13.5590i	−0.406602	+	0.559639i	0.555784	+	0.831327i	$0.312418\pi$
$588$		0			0
$589$	6.35356	−	2.06440i	0.261794	−	0.0850620i
$590$		0			0
$591$	−21.7425	−	7.06456i	−0.894366	−	0.290597i
$592$		0			0
$593$	−11.4632	−	15.7777i	−0.470737	−	0.647914i	0.505955	−	0.862560i	$-0.331140\pi$
$593$	−11.4632	−	15.7777i	−0.470737	−	0.647914i	−0.976692	+	0.214646i	$0.931140\pi$
$594$		0			0
$595$	−11.7929	+	8.56805i	−0.483462	+	0.351256i
$596$		0			0
$597$	53.0899	+	38.5721i	2.17283	+	1.57865i
$598$		0			0
$599$	4.56803	−	3.31887i	0.186645	−	0.135605i	−0.490539	−	0.871419i	$-0.663200\pi$
$599$	4.56803	−	3.31887i	0.186645	−	0.135605i	0.677184	+	0.735814i	$0.263200\pi$
$600$		0			0
$601$		−	14.2231i		−	0.580172i	−0.957001	−	0.290086i	$-0.906316\pi$
$601$		−	14.2231i		−	0.580172i	0.957001	−	0.290086i	$-0.0936839\pi$
$602$		0			0
$603$	44.4842	−	14.4538i	1.81154	−	0.588604i
$604$		0			0
$605$	10.3058	−	31.7181i	0.418991	−	1.28952i
$606$		0			0
$607$	−3.11043	+	9.57292i	−0.126248	+	0.388553i	−0.994126	−	0.108225i	$-0.965483\pi$
$607$	−3.11043	+	9.57292i	−0.126248	+	0.388553i	0.867878	+	0.496777i	$0.165483\pi$
$608$		0			0
$609$	13.2831	−	18.2827i	0.538260	−	0.740852i
$610$		0			0
$611$	−0.991614	−	3.05187i	−0.0401164	−	0.123466i
$612$		0			0
$613$	33.8404	+	24.5865i	1.36680	+	0.993038i	0.997979	+	0.0635371i	$0.0202381\pi$
$613$	33.8404	+	24.5865i	1.36680	+	0.993038i	0.368820	+	0.929501i	$0.379762\pi$
$614$		0			0
$615$	12.4909	−	41.9258i	0.503683	−	1.69061i
$616$		0			0
$617$	−18.3094	−	13.3025i	−0.737107	−	0.535540i	0.154697	−	0.987962i	$-0.450560\pi$
$617$	−18.3094	−	13.3025i	−0.737107	−	0.535540i	−0.891804	+	0.452422i	$0.850560\pi$
$618$		0			0
$619$	10.8023	+	33.2459i	0.434180	+	1.33627i	0.893925	+	0.448217i	$0.147941\pi$
$619$	10.8023	+	33.2459i	0.434180	+	1.33627i	−0.459745	+	0.888051i	$0.652059\pi$
$620$		0			0
$621$	−12.9820	+	17.8682i	−0.520949	+	0.717025i
$622$		0			0
$623$	−3.05403	+	9.39934i	−0.122357	+	0.376576i
$624$		0			0
$625$	−8.45478	+	26.0211i	−0.338191	+	1.04085i
$626$		0			0
$627$	17.3043	−	5.62251i	0.691068	−	0.224542i
$628$		0			0
$629$		−	72.6271i		−	2.89583i
$630$		0			0
$631$	−40.2156	+	29.2183i	−1.60096	+	1.16316i	−0.715306	+	0.698812i	$0.753713\pi$
$631$	−40.2156	+	29.2183i	−1.60096	+	1.16316i	−0.885651	+	0.464351i	$0.846287\pi$
$632$		0			0
$633$	−18.6405	−	13.5431i	−0.740893	−	0.538290i
$634$		0			0
$635$	−35.8782	+	26.0670i	−1.42378	+	1.03444i
$636$		0			0
$637$	0.248079	+	0.341451i	0.00982923	+	0.0135288i
$638$		0			0
$639$	20.1054	+	6.53264i	0.795357	+	0.258427i
$640$		0			0
$641$	−14.2980	+	4.64570i	−0.564737	+	0.183494i	−0.577451	−	0.816425i	$-0.695953\pi$
$641$	−14.2980	+	4.64570i	−0.564737	+	0.183494i	0.0127146	+	0.999919i	$0.495953\pi$
$642$		0			0
$643$	−20.4655	+	28.1684i	−0.807081	+	1.11085i	0.184686	+	0.982798i	$0.440873\pi$
$643$	−20.4655	+	28.1684i	−0.807081	+	1.11085i	−0.991767	+	0.128055i	$0.959127\pi$
$644$		0			0
$645$	30.5609	+	9.92983i	1.20333	+	0.390987i
$646$		0			0
$647$	−25.3856			−0.998012			−0.499006	−	0.866599i	$-0.666301\pi$
$647$	−25.3856			−0.998012			−0.499006	+	0.866599i	$0.666301\pi$
$648$		0			0
$649$	33.2892	+	45.8186i	1.30671	+	1.79854i
$650$		0			0
$651$	−4.80815	−	14.7980i	−0.188446	−	0.579978i
$652$		0			0
$653$		−	12.1027i		−	0.473615i	−0.971557	−	0.236808i	$-0.923899\pi$
$653$		−	12.1027i		−	0.473615i	0.971557	−	0.236808i	$-0.0761011\pi$
$654$		0			0
$655$	−13.6725			−0.534229
$656$		0			0
$657$	−2.86189			−0.111653
$658$		0			0
$659$			4.99529i			0.194589i	0.995256	+	0.0972945i	$0.0310189\pi$
$659$			4.99529i			0.194589i	−0.995256	+	0.0972945i	$0.968981\pi$
$660$		0			0
$661$	−7.93165	−	24.4111i	−0.308505	−	0.949482i	−0.978346	−	0.206977i	$-0.933637\pi$
$661$	−7.93165	−	24.4111i	−0.308505	−	0.949482i	0.669840	−	0.742505i	$-0.266363\pi$
$662$		0			0
$663$	4.46951	+	6.15175i	0.173581	+	0.238914i
$664$		0			0
$665$	−2.93340			−0.113752
$666$		0			0
$667$	−22.9983	−	7.47261i	−0.890499	−	0.289341i
$668$		0			0
$669$	−14.0642	+	19.3577i	−0.543754	+	0.748413i
$670$		0			0
$671$	23.6023	−	7.66886i	0.911157	−	0.296053i
$672$		0			0
$673$	−19.8851	−	6.46106i	−0.766514	−	0.249056i	−0.100442	−	0.994943i	$-0.532026\pi$
$673$	−19.8851	−	6.46106i	−0.766514	−	0.249056i	−0.666072	+	0.745887i	$0.732026\pi$
$674$		0			0
$675$	2.20335	+	3.03265i	0.0848071	+	0.116727i
$676$		0			0
$677$	−10.9123	+	7.92828i	−0.419395	+	0.304708i	−0.777394	−	0.629013i	$-0.783459\pi$
$677$	−10.9123	+	7.92828i	−0.419395	+	0.304708i	0.357999	+	0.933722i	$0.383459\pi$
$678$		0			0
$679$	6.05293	+	4.39771i	0.232290	+	0.168769i
$680$		0			0
$681$	60.8769	−	44.2296i	2.33281	−	1.69488i
$682$		0			0
$683$		−	19.4682i		−	0.744930i	−0.928046	−	0.372465i	$-0.878513\pi$
$683$		−	19.4682i		−	0.744930i	0.928046	−	0.372465i	$-0.121487\pi$
$684$		0			0
$685$	35.4790	−	11.5278i	1.35558	−	0.440455i
$686$		0			0
$687$	−12.0376	+	37.0478i	−0.459261	+	1.41346i
$688$		0			0
$689$	1.22323	−	3.76472i	0.0466015	−	0.143425i
$690$		0			0
$691$	−14.8862	+	20.4891i	−0.566297	+	0.779441i	−0.992110	−	0.125370i	$-0.959988\pi$
$691$	−14.8862	+	20.4891i	−0.566297	+	0.779441i	0.425813	+	0.904811i	$0.359988\pi$
$692$		0			0
$693$	−8.44293	−	25.9847i	−0.320720	−	0.987076i
$694$		0			0
$695$	33.8450	+	24.5898i	1.28381	+	0.932744i
$696$		0			0
$697$	31.5335	−	24.1176i	1.19442	−	0.913519i
$698$		0			0
$699$	−3.54808	−	2.57783i	−0.134201	−	0.0975025i
$700$		0			0
$701$	5.50977	+	16.9573i	0.208101	+	0.640469i	0.999572	+	0.0292620i	$0.00931570\pi$
$701$	5.50977	+	16.9573i	0.208101	+	0.640469i	−0.791471	+	0.611207i	$0.790684\pi$
$702$		0			0
$703$	8.59064	−	11.8240i	0.324002	−	0.445951i
$704$		0			0
$705$	16.0520	−	49.4028i	0.604552	−	1.86062i
$706$		0			0
$707$	0.0537754	−	0.165504i	0.00202243	−	0.00622440i
$708$		0			0
$709$	−19.5175	+	6.34162i	−0.732995	+	0.238164i	−0.651648	−	0.758521i	$-0.725922\pi$
$709$	−19.5175	+	6.34162i	−0.732995	+	0.238164i	−0.0813467	+	0.996686i	$0.525922\pi$
$710$		0			0
$711$		−	68.1971i		−	2.55759i
$712$		0			0
$713$	−13.4698	+	9.78637i	−0.504448	+	0.366503i
$714$		0			0
$715$	4.02877	+	2.92707i	0.150668	+	0.109466i
$716$		0			0
$717$	−70.9452	+	51.5447i	−2.64950	+	1.92497i
$718$		0			0
$719$	5.18710	+	7.13943i	0.193446	+	0.266256i	0.894711	−	0.446645i	$-0.147381\pi$
$719$	5.18710	+	7.13943i	0.193446	+	0.266256i	−0.701265	+	0.712900i	$0.747381\pi$
$720$		0			0
$721$	−7.91437	−	2.57153i	−0.294747	−	0.0957690i
$722$		0			0
$723$	−43.6166	+	14.1719i	−1.62212	+	0.527059i
$724$		0			0
$725$	−2.41241	+	3.32040i	−0.0895948	+	0.123317i
$726$		0			0
$727$	7.79091	+	2.53142i	0.288949	+	0.0938852i	0.449905	−	0.893076i	$-0.351458\pi$
$727$	7.79091	+	2.53142i	0.288949	+	0.0938852i	−0.160956	+	0.986962i	$0.551458\pi$
$728$		0			0
$729$	38.4701			1.42482
$730$		0			0
$731$	17.1400	+	23.5912i	0.633946	+	0.872552i
$732$		0			0
$733$	5.73236	+	17.6424i	0.211729	+	0.651636i	0.999370	+	0.0355008i	$0.0113026\pi$
$733$	5.73236	+	17.6424i	0.211729	+	0.651636i	−0.787640	+	0.616135i	$0.788697\pi$
$734$		0			0
$735$			6.83212i			0.252007i
$736$		0			0
$737$	43.1151			1.58816
$738$		0			0
$739$	38.1266			1.40251			0.701256	−	0.712910i	$-0.252623\pi$
$739$	38.1266			1.40251			0.701256	+	0.712910i	$0.252623\pi$
$740$		0			0
$741$			1.53020i			0.0562134i
$742$		0			0
$743$	8.54675	+	26.3042i	0.313550	+	0.965007i	0.976347	+	0.216209i	$0.0693691\pi$
$743$	8.54675	+	26.3042i	0.313550	+	0.965007i	−0.662797	+	0.748799i	$0.730631\pi$
$744$		0			0
$745$	−3.03327	−	4.17493i	−0.111130	−	0.152958i
$746$		0			0
$747$	−7.19772			−0.263351
$748$		0			0
$749$	2.86585	+	0.931170i	0.104716	+	0.0340242i
$750$		0			0
$751$	13.6308	−	18.7612i	0.497395	−	0.684606i	−0.484335	−	0.874883i	$-0.660938\pi$
$751$	13.6308	−	18.7612i	0.497395	−	0.684606i	0.981731	+	0.190276i	$0.0609384\pi$
$752$		0			0
$753$	37.3127	−	12.1236i	1.35975	−	0.441810i
$754$		0			0
$755$	17.3688	+	5.64345i	0.632114	+	0.205386i
$756$		0			0
$757$	8.00729	+	11.0211i	0.291030	+	0.400568i	0.929348	−	0.369204i	$-0.120370\pi$
$757$	8.00729	+	11.0211i	0.291030	+	0.400568i	−0.638318	+	0.769772i	$0.720370\pi$
$758$		0			0
$759$	−36.6858	+	26.6538i	−1.33161	+	0.967472i
$760$		0			0
$761$	22.5410	+	16.3770i	0.817111	+	0.593666i	0.915884	−	0.401444i	$-0.131492\pi$
$761$	22.5410	+	16.3770i	0.817111	+	0.593666i	−0.0987723	+	0.995110i	$0.531492\pi$
$762$		0			0
$763$	4.99163	−	3.62663i	0.180709	−	0.131293i
$764$		0			0
$765$			79.3604i			2.86928i
$766$		0			0
$767$	−4.52993	+	1.47186i	−0.163566	+	0.0531459i
$768$		0			0
$769$	−8.18457	+	25.1895i	−0.295143	+	0.908357i	0.688030	+	0.725682i	$0.258476\pi$
$769$	−8.18457	+	25.1895i	−0.295143	+	0.908357i	−0.983173	+	0.182675i	$0.941524\pi$
$770$		0			0
$771$	2.83344	−	8.72044i	0.102044	−	0.314059i
$772$		0			0
$773$	5.59401	−	7.69950i	0.201203	−	0.276932i	−0.696478	−	0.717578i	$-0.745251\pi$
$773$	5.59401	−	7.69950i	0.201203	−	0.276932i	0.897681	+	0.440646i	$0.145251\pi$
$774$		0			0
$775$	0.873230	+	2.68753i	0.0313673	+	0.0965388i
$776$		0			0
$777$	−27.5391	−	20.0083i	−0.987958	−	0.717793i
$778$		0			0
$779$	7.98651	−	0.196532i	0.286147	−	0.00704150i
$780$		0			0
$781$	15.7650	+	11.4539i	0.564115	+	0.409854i
$782$		0			0
$783$	−17.0693	−	52.5340i	−0.610008	−	1.87741i
$784$		0			0
$785$	−20.1944	+	27.7952i	−0.720769	+	0.992054i
$786$		0			0
$787$	−8.83279	+	27.1845i	−0.314855	+	0.969024i	0.660959	+	0.750422i	$0.270150\pi$
$787$	−8.83279	+	27.1845i	−0.314855	+	0.969024i	−0.975814	+	0.218602i	$0.929850\pi$
$788$		0			0
$789$	−9.27042	+	28.5314i	−0.330036	+	1.01575i
$790$		0			0
$791$	−17.2049	+	5.59020i	−0.611734	+	0.198765i
$792$		0			0
$793$			2.08713i			0.0741161i
$794$		0			0
$795$	51.8406	−	37.6644i	1.83860	−	1.33582i
$796$		0			0
$797$	30.7194	+	22.3190i	1.08814	+	0.790579i	0.979084	−	0.203457i	$-0.0652177\pi$
$797$	30.7194	+	22.3190i	1.08814	+	0.790579i	0.109054	+	0.994036i	$0.465218\pi$
$798$		0			0
$799$	38.1361	−	27.7075i	1.34916	−	0.980221i
$800$		0			0
$801$	31.6264	+	43.5301i	1.11747	+	1.53806i
$802$		0			0
$803$	−2.50893	−	0.815202i	−0.0885384	−	0.0287679i
$804$		0			0
$805$	6.95296	−	2.25915i	0.245060	−	0.0796247i
$806$		0			0
$807$	36.2679	−	49.9185i	1.27669	−	1.75722i
$808$		0			0
$809$	25.3720	+	8.24386i	0.892031	+	0.289839i	0.718944	−	0.695068i	$-0.244626\pi$
$809$	25.3720	+	8.24386i	0.892031	+	0.289839i	0.173087	+	0.984906i	$0.444626\pi$
$810$		0			0
$811$	−38.0874			−1.33743			−0.668715	−	0.743518i	$-0.733156\pi$
$811$	−38.0874			−1.33743			−0.668715	+	0.743518i	$0.733156\pi$
$812$		0			0
$813$	27.7296	+	38.1666i	0.972520	+	1.33856i
$814$		0			0
$815$	7.54637	+	23.2253i	0.264338	+	0.813548i
$816$		0			0
$817$			5.86814i			0.205300i
$818$		0			0
$819$	2.29780			0.0802915
$820$		0			0
$821$	−35.5541			−1.24085			−0.620423	−	0.784267i	$-0.713039\pi$
$821$	−35.5541			−1.24085			−0.620423	+	0.784267i	$0.713039\pi$
$822$		0			0
$823$		−	15.9971i		−	0.557623i	−0.960346	−	0.278812i	$-0.910059\pi$
$823$		−	15.9971i		−	0.557623i	0.960346	−	0.278812i	$-0.0899405\pi$
$824$		0			0
$825$	2.37830	+	7.31965i	0.0828017	+	0.254837i
$826$		0			0
$827$	12.6402	+	17.3978i	0.439544	+	0.604981i	0.970111	−	0.242663i	$-0.0780208\pi$
$827$	12.6402	+	17.3978i	0.439544	+	0.604981i	−0.530567	+	0.847643i	$0.678021\pi$
$828$		0			0
$829$	−1.11213			−0.0386258			−0.0193129	−	0.999813i	$-0.506148\pi$
$829$	−1.11213			−0.0386258			−0.0193129	+	0.999813i	$0.506148\pi$
$830$		0			0
$831$	−66.9512	−	21.7538i	−2.32251	−	0.754630i
$832$		0			0
$833$	−3.64424	+	5.01587i	−0.126266	+	0.173790i
$834$		0			0
$835$	−2.06454	+	0.670809i	−0.0714463	+	0.0232143i
$836$		0			0
$837$	−36.1704	−	11.7525i	−1.25023	−	0.406225i
$838$		0			0
$839$	−25.2982	−	34.8200i	−0.873392	−	1.20212i	−0.978208	−	0.207629i	$-0.933425\pi$
$839$	−25.2982	−	34.8200i	−0.873392	−	1.20212i	0.104816	−	0.994492i	$-0.466575\pi$
$840$		0			0
$841$	25.4667	−	18.5027i	0.878164	−	0.638023i
$842$		0			0
$843$	25.5667	+	18.5753i	0.880565	+	0.639768i
$844$		0			0
$845$	24.3884	−	17.7192i	0.838987	−	0.609559i
$846$		0			0
$847$		−	14.1849i		−	0.487399i
$848$		0			0
$849$	−33.4741	+	10.8764i	−1.14883	+	0.373277i
$850$		0			0
$851$	−11.2559	+	34.6422i	−0.385848	+	1.18752i
$852$		0			0
$853$	−12.0190	+	36.9908i	−0.411524	+	1.26654i	0.503800	+	0.863820i	$0.331935\pi$
$853$	−12.0190	+	36.9908i	−0.411524	+	1.26654i	−0.915324	+	0.402719i	$0.868065\pi$
$854$		0			0
$855$	−9.38708	+	12.9202i	−0.321031	+	0.441862i
$856$		0			0
$857$	1.47298	+	4.53337i	0.0503161	+	0.154857i	0.973057	−	0.230563i	$-0.0740567\pi$
$857$	1.47298	+	4.53337i	0.0503161	+	0.154857i	−0.922741	+	0.385420i	$0.874057\pi$
$858$		0			0
$859$	10.9500	+	7.95567i	0.373610	+	0.271444i	0.758706	−	0.651433i	$-0.225832\pi$
$859$	10.9500	+	7.95567i	0.373610	+	0.271444i	−0.385096	+	0.922876i	$0.625832\pi$
$860$		0			0
$861$	−0.457740	−	18.6012i	−0.0155997	−	0.633929i
$862$		0			0
$863$	−16.0360	−	11.6508i	−0.545872	−	0.396599i	0.280389	−	0.959886i	$-0.409536\pi$
$863$	−16.0360	−	11.6508i	−0.545872	−	0.396599i	−0.826261	+	0.563287i	$0.809536\pi$
$864$		0			0
$865$	0.156050	+	0.480273i	0.00530586	+	0.0163298i
$866$		0			0
$867$	−36.6197	+	50.4027i	−1.24367	+	1.71177i
$868$		0			0
$869$	19.4257	−	59.7863i	0.658973	−	2.02811i
$870$		0			0
$871$	−1.12050	+	3.44855i	−0.0379667	+	0.116850i
$872$		0			0
$873$	38.7396	−	12.5873i	1.31114	−	0.426014i
$874$		0			0
$875$			10.5148i			0.355464i
$876$		0			0
$877$	10.2499	−	7.44696i	0.346113	−	0.251466i	−0.401123	−	0.916024i	$-0.631380\pi$
$877$	10.2499	−	7.44696i	0.346113	−	0.251466i	0.747237	+	0.664558i	$0.231380\pi$
$878$		0			0
$879$	13.4194	+	9.74976i	0.452625	+	0.328851i
$880$		0			0
$881$	−38.1736	+	27.7348i	−1.28610	+	0.934408i	−0.999719	−	0.0237066i	$-0.992453\pi$
$881$	−38.1736	+	27.7348i	−1.28610	+	0.934408i	−0.286384	+	0.958115i	$0.592453\pi$
$882$		0			0
$883$	−23.2691	−	32.0272i	−0.783069	−	1.07780i	−0.994937	−	0.100503i	$-0.967955\pi$
$883$	−23.2691	−	32.0272i	−0.783069	−	1.07780i	0.211868	−	0.977298i	$-0.432045\pi$
$884$		0			0
$885$	−73.3291	−	23.8261i	−2.46493	−	0.800905i
$886$		0			0
$887$	24.0475	−	7.81351i	0.807437	−	0.262352i	0.123925	−	0.992292i	$-0.460452\pi$
$887$	24.0475	−	7.81351i	0.807437	−	0.262352i	0.683512	+	0.729939i	$0.260452\pi$
$888$		0			0
$889$	−11.0871	+	15.2601i	−0.371849	+	0.511806i
$890$		0			0
$891$	−20.5584	−	6.67982i	−0.688731	−	0.223782i
$892$		0			0
$893$	9.48607			0.317439
$894$		0			0
$895$	−33.3173	−	45.8574i	−1.11368	−	1.53284i
$896$		0			0
$897$	−1.17848	−	3.62700i	−0.0393484	−	0.121102i
$898$		0			0
$899$		−	41.6404i		−	1.38879i
$900$		0			0
$901$	58.1494			1.93724
$902$		0			0
$903$	13.6674			0.454822
$904$		0			0
$905$		−	4.02128i		−	0.133672i
$906$		0			0
$907$	11.2576	+	34.6473i	0.373802	+	1.15044i	0.944283	+	0.329133i	$0.106757\pi$
$907$	11.2576	+	34.6473i	0.373802	+	1.15044i	−0.570482	+	0.821310i	$0.693243\pi$
$908$		0			0
$909$	−0.556878	−	0.766477i	−0.0184705	−	0.0254225i
$910$		0			0
$911$	−38.5202			−1.27623			−0.638116	−	0.769940i	$-0.720286\pi$
$911$	−38.5202			−1.27623			−0.638116	+	0.769940i	$0.720286\pi$
$912$		0			0
$913$	−6.31001	−	2.05025i	−0.208831	−	0.0678533i
$914$		0			0
$915$	−19.8588	+	27.3333i	−0.656511	+	0.903610i
$916$		0			0
$917$	−5.53070	+	1.79703i	−0.182640	+	0.0593433i
$918$		0			0
$919$	−11.8337	−	3.84500i	−0.390357	−	0.126835i	0.107261	−	0.994231i	$-0.465792\pi$
$919$	−11.8337	−	3.84500i	−0.390357	−	0.126835i	−0.497618	+	0.867396i	$0.665792\pi$
$920$		0			0
$921$	39.0922	+	53.8057i	1.28813	+	1.77296i
$922$		0			0
$923$	−1.32585	+	0.963285i	−0.0436408	+	0.0317069i
$924$		0			0
$925$	5.00150	+	3.63380i	0.164448	+	0.119479i
$926$		0			0
$927$	−36.6529	+	26.6299i	−1.20384	+	0.874641i
$928$		0			0
$929$		−	3.97735i		−	0.130493i	−0.997869	−	0.0652463i	$-0.979217\pi$
$929$		−	3.97735i		−	0.130493i	0.997869	−	0.0652463i	$-0.0207833\pi$
$930$		0			0
$931$	−1.18660	+	0.385549i	−0.0388891	+	0.0126358i
$932$		0			0
$933$	8.33640	−	25.6568i	0.272921	−	0.839966i
$934$		0			0
$935$	−22.6056	+	69.5728i	−0.739282	+	2.27527i
$936$		0			0
$937$	−20.9362	+	28.8162i	−0.683956	+	0.941385i	−0.999973	−	0.00736901i	$-0.997654\pi$
$937$	−20.9362	+	28.8162i	−0.683956	+	0.941385i	0.316017	+	0.948754i	$0.397654\pi$
$938$		0			0
$939$	0.205231	+	0.631636i	0.00669746	+	0.0206127i
$940$		0			0
$941$	22.4388	+	16.3027i	0.731484	+	0.531454i	0.890033	−	0.455897i	$-0.150681\pi$
$941$	22.4388	+	16.3027i	0.731484	+	0.531454i	−0.158548	+	0.987351i	$0.550681\pi$
$942$		0			0
$943$	−18.7789	+	6.61664i	−0.611524	+	0.215468i
$944$		0			0
$945$	13.5103	+	9.81581i	0.439490	+	0.319308i
$946$		0			0
$947$	12.6811	+	39.0285i	0.412081	+	1.26826i	0.914836	+	0.403826i	$0.132320\pi$
$947$	12.6811	+	39.0285i	0.412081	+	1.26826i	−0.502755	+	0.864429i	$0.667680\pi$
$948$		0			0
$949$	0.130407	−	0.179490i	0.00423320	−	0.00582650i
$950$		0			0
$951$	26.6675	−	82.0742i	0.864754	−	2.66144i
$952$		0			0
$953$	−11.2387	+	34.5891i	−0.364056	+	1.12045i	0.586513	+	0.809939i	$0.300500\pi$
$953$	−11.2387	+	34.5891i	−0.364056	+	1.12045i	−0.950570	+	0.310511i	$0.899500\pi$
$954$		0			0
$955$	14.1663	−	4.60291i	0.458411	−	0.148947i
$956$		0			0
$957$		−	113.410i		−	3.66603i
$958$		0			0
$959$	12.8365	−	9.32630i	0.414514	−	0.301162i
$960$		0			0
$961$	1.88500	+	1.36953i	0.0608064	+	0.0441784i
$962$		0			0
$963$	13.2723	−	9.64286i	0.427693	−	0.310737i
$964$		0			0
$965$	−2.91637	−	4.01405i	−0.0938814	−	0.129217i
$966$		0			0
$967$	−17.3418	−	5.63471i	−0.557676	−	0.181200i	0.0165991	−	0.999862i	$-0.494716\pi$
$967$	−17.3418	−	5.63471i	−0.557676	−	0.181200i	−0.574275	+	0.818662i	$0.694716\pi$
$968$		0			0
$969$	−21.3783	+	6.94623i	−0.686770	+	0.223145i
$970$		0			0
$971$	4.88857	−	6.72854i	0.156882	−	0.215929i	−0.723340	−	0.690492i	$-0.757394\pi$
$971$	4.88857	−	6.72854i	0.156882	−	0.215929i	0.880222	+	0.474563i	$0.157394\pi$
$972$		0			0
$973$	16.9226	+	5.49850i	0.542515	+	0.176274i
$974$		0			0
$975$	−0.647268			−0.0207292
$976$		0			0
$977$	16.1268	+	22.1966i	0.515941	+	0.710132i	0.984907	−	0.173084i	$-0.0553733\pi$
$977$	16.1268	+	22.1966i	0.515941	+	0.710132i	−0.468966	+	0.883216i	$0.655373\pi$
$978$		0			0
$979$	15.3265	+	47.1701i	0.489837	+	1.50756i
$980$		0			0
$981$		−	33.5912i		−	1.07248i
$982$		0			0
$983$	−45.3735			−1.44719			−0.723594	−	0.690226i	$-0.757511\pi$
$983$	−45.3735			−1.44719			−0.723594	+	0.690226i	$0.757511\pi$
$984$		0			0
$985$	18.4968			0.589356
$986$		0			0
$987$		−	22.0938i		−	0.703255i
$988$		0			0
$989$	−4.51934	−	13.9091i	−0.143707	−	0.442284i
$990$		0			0
$991$	21.2903	+	29.3036i	0.676310	+	0.930861i	0.999882	−	0.0153429i	$-0.00488398\pi$
$991$	21.2903	+	29.3036i	0.676310	+	0.930861i	−0.323573	+	0.946203i	$0.604884\pi$
$992$		0			0
$993$	50.3711			1.59848
$994$		0			0
$995$	−50.4956	−	16.4070i	−1.60082	−	0.520138i
$996$		0			0
$997$	27.2454	−	37.5001i	0.862871	−	1.18764i	−0.118006	−	0.993013i	$-0.537650\pi$
$997$	27.2454	−	37.5001i	0.862871	−	1.18764i	0.980877	−	0.194627i	$-0.0623497\pi$
$998$		0			0
$999$	−79.1315	+	25.7114i	−2.50361	+	0.813472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.19	✓	80
41.4	even	10	inner	1148.2.ba.a.701.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.19	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.2	yes	80	41.4	even	10	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +O(q^{10})\)	\(q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +(-4.77283 - 1.55079i) q^{11} +(0.248079 - 0.341451i) q^{13} +(6.49774 - 2.11124i) q^{15} +(5.89651 + 1.91589i) q^{17} +(0.733357 + 1.00938i) q^{19} +(2.35093 - 1.70805i) q^{21} +(-2.51563 - 1.82771i) q^{23} +(-0.426963 + 0.310207i) q^{25} -7.10286i q^{27} +(7.39618 - 2.40316i) q^{29} +(1.65461 - 5.09237i) q^{31} +(4.50644 - 13.8694i) q^{33} +(-1.38195 + 1.90209i) q^{35} +(-3.61986 - 11.1408i) q^{37} +(0.992224 + 0.720893i) q^{39} +(3.63509 - 5.27126i) q^{41} +(3.80506 + 2.76454i) q^{43} +(3.95546 + 12.1737i) q^{45} +(4.46898 - 6.15102i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-5.56740 + 17.1347i) q^{51} +(8.91995 - 2.89827i) q^{53} +11.7990i q^{55} +(-2.93316 + 2.13107i) q^{57} +(-9.13002 - 6.63335i) q^{59} +(-4.00070 + 2.90668i) q^{61} +(3.20007 + 4.40452i) q^{63} +(-0.943738 - 0.306639i) q^{65} +(-8.17082 + 2.65486i) q^{67} +(5.31116 - 7.31018i) q^{69} +(-3.69294 - 1.19991i) q^{71} +0.525670 q^{73} +(-0.901431 - 1.24071i) q^{75} +(1.55079 + 4.77283i) q^{77} +12.5264i q^{79} +4.30737 q^{81} +1.32207 q^{83} -14.5768i q^{85} +(6.98337 + 21.4926i) q^{87} +(-5.80911 - 7.99555i) q^{89} -0.422057 q^{91} +(14.7980 + 4.80815i) q^{93} +(1.72421 - 2.37317i) q^{95} +(-7.11564 + 2.31201i) q^{97} +(25.9847 + 8.44293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more