LMFDB - Embedded newform 1197.2.j.m.172.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(172,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1197.172");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, 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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} - 2 x^{13} + 118 x^{12} - 16 x^{11} + 534 x^{10} - 21 x^{9} + 1743 x^{8} - 101 x^{7} + \cdots + 256 $ x^16 + 13x^14 - 2x^13 + 118x^12 - 16x^11 + 534x^10 - 21x^9 + 1743x^8 - 101x^7 + 2902x^6 - 401x^5 + 3427x^4 - 294x^3 + 1076x^2 + 96x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.7
Root			$1.14143 + 1.97701i$ of defining polynomial
Character	$\chi$	$=$	1197.172
Dual form			1197.2.j.m.856.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14143 + 1.97701i) q^{2} +(-1.60570 + 2.78116i) q^{4} +(-1.27263 - 2.20425i) q^{5} +(-2.54832 + 0.711380i) q^{7} -2.76546 q^{8} +O(q^{10})$	\(q+(1.14143 + 1.97701i) q^{2} +(-1.60570 + 2.78116i) q^{4} +(-1.27263 - 2.20425i) q^{5} +(-2.54832 + 0.711380i) q^{7} -2.76546 q^{8} +(2.90522 - 5.03198i) q^{10} +(1.64814 - 2.85466i) q^{11} -4.96243 q^{13} +(-4.31512 - 4.22606i) q^{14} +(0.0548414 + 0.0949880i) q^{16} +(2.79818 - 4.84659i) q^{17} +(0.500000 + 0.866025i) q^{19} +8.17384 q^{20} +7.52492 q^{22} +(-2.90990 - 5.04010i) q^{23} +(-0.739156 + 1.28026i) q^{25} +(-5.66425 - 9.81077i) q^{26} +(2.11339 - 8.22955i) q^{28} +9.32850 q^{29} +(3.21154 - 5.56255i) q^{31} +(-2.89065 + 5.00676i) q^{32} +12.7757 q^{34} +(4.81112 + 4.71182i) q^{35} +(-3.85024 - 6.66882i) q^{37} +(-1.14143 + 1.97701i) q^{38} +(3.51940 + 6.09577i) q^{40} -6.13136 q^{41} -4.62835 q^{43} +(5.29285 + 9.16748i) q^{44} +(6.64288 - 11.5058i) q^{46} +(-3.15720 - 5.46842i) q^{47} +(5.98788 - 3.62565i) q^{49} -3.37477 q^{50} +(7.96820 - 13.8013i) q^{52} +(-4.58210 + 7.93643i) q^{53} -8.38987 q^{55} +(7.04728 - 1.96729i) q^{56} +(10.6478 + 18.4425i) q^{58} +(4.90555 - 8.49667i) q^{59} +(0.907947 + 1.57261i) q^{61} +14.6629 q^{62} -12.9785 q^{64} +(6.31533 + 10.9385i) q^{65} +(-1.68164 + 2.91269i) q^{67} +(8.98609 + 15.5644i) q^{68} +(-3.82377 + 14.8898i) q^{70} -2.01667 q^{71} +(2.36284 - 4.09256i) q^{73} +(8.78953 - 15.2239i) q^{74} -3.21141 q^{76} +(-2.16924 + 8.44705i) q^{77} +(6.44927 + 11.1705i) q^{79} +(0.139585 - 0.241769i) q^{80} +(-6.99849 - 12.1217i) q^{82} +0.743338 q^{83} -14.2442 q^{85} +(-5.28291 - 9.15027i) q^{86} +(-4.55787 + 7.89445i) q^{88} +(-5.70242 - 9.87688i) q^{89} +(12.6459 - 3.53018i) q^{91} +18.6898 q^{92} +(7.20741 - 12.4836i) q^{94} +(1.27263 - 2.20425i) q^{95} -16.9210 q^{97} +(14.0026 + 7.69967i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.14143	+	1.97701i	0.807110	+	1.39795i	0.914858	+	0.403776i	$0.132303\pi$
$2$	1.14143	+	1.97701i	0.807110	+	1.39795i	−0.107748	+	0.994178i	$0.534364\pi$
$3$		0			0
$3$		0			0
$4$	−1.60570	+	2.78116i	−0.802852	+	1.39058i
$5$	−1.27263	−	2.20425i	−0.569136	−	0.985772i	−0.996652	−	0.0817643i	$-0.973945\pi$
$5$	−1.27263	−	2.20425i	−0.569136	−	0.985772i	0.427516	−	0.904008i	$-0.359389\pi$
$6$		0			0
$7$	−2.54832	+	0.711380i	−0.963175	+	0.268876i
$7$	−2.54832	+	0.711380i	−0.963175	+	0.268876i
$8$	−2.76546			−0.977737
$9$		0			0
$10$	2.90522	−	5.03198i	0.918710	−	1.59125i
$11$	1.64814	−	2.85466i	0.496933	−	0.860713i	−0.503061	−	0.864251i	$-0.667793\pi$
$11$	1.64814	−	2.85466i	0.496933	−	0.860713i	0.999994	+	0.00353776i	$0.00112611\pi$
$12$		0			0
$13$	−4.96243			−1.37633			−0.688166	−	0.725553i	$-0.741584\pi$
$13$	−4.96243			−1.37633			−0.688166	+	0.725553i	$0.741584\pi$
$14$	−4.31512	−	4.22606i	−1.15326	−	1.12946i
$15$		0			0
$16$	0.0548414	+	0.0949880i	0.0137103	+	0.0237470i
$17$	2.79818	−	4.84659i	0.678658	−	1.17547i	−0.296727	−	0.954962i	$-0.595895\pi$
$17$	2.79818	−	4.84659i	0.678658	−	1.17547i	0.975385	−	0.220508i	$-0.0707717\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$	8.17384			1.82773
$21$		0			0
$22$	7.52492			1.60432
$23$	−2.90990	−	5.04010i	−0.606757	−	1.05093i	−0.991771	−	0.128023i	$-0.959137\pi$
$23$	−2.90990	−	5.04010i	−0.606757	−	1.05093i	0.385014	−	0.922911i	$-0.374197\pi$
$24$		0			0
$25$	−0.739156	+	1.28026i	−0.147831	+	0.256051i
$26$	−5.66425	−	9.81077i	−1.11085	−	1.92405i
$27$		0			0
$28$	2.11339	−	8.22955i	0.399392	−	1.55524i
$29$	9.32850			1.73226			0.866129	−	0.499820i	$-0.166601\pi$
$29$	9.32850			1.73226			0.866129	+	0.499820i	$0.166601\pi$
$30$		0			0
$31$	3.21154	−	5.56255i	0.576809	−	0.999063i	−0.419033	−	0.907971i	$-0.637631\pi$
$31$	3.21154	−	5.56255i	0.576809	−	0.999063i	0.995842	−	0.0910919i	$-0.0290357\pi$
$32$	−2.89065	+	5.00676i	−0.511000	+	0.885078i
$33$		0			0
$34$	12.7757			2.19101
$35$	4.81112	+	4.71182i	0.813228	+	0.796444i
$36$		0			0
$37$	−3.85024	−	6.66882i	−0.632976	−	1.09635i	−0.986940	−	0.161088i	$-0.948500\pi$
$37$	−3.85024	−	6.66882i	−0.632976	−	1.09635i	0.353964	−	0.935259i	$-0.384833\pi$
$38$	−1.14143	+	1.97701i	−0.185164	+	0.320713i
$39$		0			0
$40$	3.51940	+	6.09577i	0.556465	+	0.963826i
$41$	−6.13136			−0.957558			−0.478779	−	0.877936i	$-0.658920\pi$
$41$	−6.13136			−0.957558			−0.478779	+	0.877936i	$0.658920\pi$
$42$		0			0
$43$	−4.62835			−0.705816			−0.352908	−	0.935658i	$-0.614807\pi$
$43$	−4.62835			−0.705816			−0.352908	+	0.935658i	$0.614807\pi$
$44$	5.29285	+	9.16748i	0.797927	+	1.38205i
$45$		0			0
$46$	6.64288	−	11.5058i	0.979439	−	1.69644i
$47$	−3.15720	−	5.46842i	−0.460524	−	0.797652i	0.538463	−	0.842649i	$-0.319005\pi$
$47$	−3.15720	−	5.46842i	−0.460524	−	0.797652i	−0.998987	+	0.0449977i	$0.985672\pi$
$48$		0			0
$49$	5.98788	−	3.62565i	0.855411	−	0.517950i
$50$	−3.37477			−0.477264
$51$		0			0
$52$	7.96820	−	13.8013i	1.10499	−	1.91390i
$53$	−4.58210	+	7.93643i	−0.629400	+	1.09015i	0.358273	+	0.933617i	$0.383366\pi$
$53$	−4.58210	+	7.93643i	−0.629400	+	1.09015i	−0.987672	+	0.156535i	$0.949967\pi$
$54$		0			0
$55$	−8.38987			−1.13129
$56$	7.04728	−	1.96729i	0.941732	−	0.262890i
$57$		0			0
$58$	10.6478	+	18.4425i	1.39812	+	2.42162i
$59$	4.90555	−	8.49667i	0.638649	−	1.10617i	−0.347081	−	0.937835i	$-0.612827\pi$
$59$	4.90555	−	8.49667i	0.638649	−	1.10617i	0.985730	−	0.168337i	$-0.0538395\pi$
$60$		0			0
$61$	0.907947	+	1.57261i	0.116251	+	0.201352i	0.918279	−	0.395934i	$-0.129579\pi$
$61$	0.907947	+	1.57261i	0.116251	+	0.201352i	−0.802028	+	0.597286i	$0.796246\pi$
$62$	14.6629			1.86219
$63$		0			0
$64$	−12.9785			−1.62231
$65$	6.31533	+	10.9385i	0.783320	+	1.35675i
$66$		0			0
$67$	−1.68164	+	2.91269i	−0.205445	+	0.355842i	−0.950275	−	0.311413i	$-0.899198\pi$
$67$	−1.68164	+	2.91269i	−0.205445	+	0.355842i	0.744829	+	0.667255i	$0.232531\pi$
$68$	8.98609	+	15.5644i	1.08972	+	1.88746i
$69$		0			0
$70$	−3.82377	+	14.8898i	−0.457028	+	1.77967i
$71$	−2.01667			−0.239335			−0.119667	−	0.992814i	$-0.538183\pi$
$71$	−2.01667			−0.239335			−0.119667	+	0.992814i	$0.538183\pi$
$72$		0			0
$73$	2.36284	−	4.09256i	0.276550	−	0.478998i	−0.693975	−	0.719999i	$-0.744142\pi$
$73$	2.36284	−	4.09256i	0.276550	−	0.478998i	0.970525	+	0.241001i	$0.0774757\pi$
$74$	8.78953	−	15.2239i	1.02176	−	1.76974i
$75$		0			0
$76$	−3.21141			−0.368374
$77$	−2.16924	+	8.44705i	−0.247208	+	0.962631i
$78$		0			0
$79$	6.44927	+	11.1705i	0.725599	+	1.25677i	0.958727	+	0.284329i	$0.0917707\pi$
$79$	6.44927	+	11.1705i	0.725599	+	1.25677i	−0.233128	+	0.972446i	$0.574896\pi$
$80$	0.139585	−	0.241769i	0.0156061	−	0.0270305i
$81$		0			0
$82$	−6.99849	−	12.1217i	−0.772854	−	1.33862i
$83$	0.743338			0.0815919			0.0407960	−	0.999167i	$-0.487011\pi$
$83$	0.743338			0.0815919			0.0407960	+	0.999167i	$0.487011\pi$
$84$		0			0
$85$	−14.2442			−1.54500
$86$	−5.28291	−	9.15027i	−0.569671	−	0.986699i
$87$		0			0
$88$	−4.55787	+	7.89445i	−0.485870	+	0.841552i
$89$	−5.70242	−	9.87688i	−0.604455	−	1.04695i	−0.992137	−	0.125154i	$-0.960058\pi$
$89$	−5.70242	−	9.87688i	−0.604455	−	1.04695i	0.387682	−	0.921793i	$-0.373276\pi$
$90$		0			0
$91$	12.6459	−	3.53018i	1.32565	−	0.370063i
$92$	18.6898			1.94854
$93$		0			0
$94$	7.20741	−	12.4836i	0.743387	−	1.28758i
$95$	1.27263	−	2.20425i	0.130569	−	0.226152i
$96$		0			0
$97$	−16.9210			−1.71807			−0.859035	−	0.511918i	$-0.828935\pi$
$97$	−16.9210			−1.71807			−0.859035	+	0.511918i	$0.828935\pi$
$98$	14.0026	+	7.69967i	1.41448	+	0.777784i
$99$		0			0
$100$	−2.37373	−	4.11142i	−0.237373	−	0.411142i
$101$	−5.42936	+	9.40393i	−0.540242	+	0.935726i	0.458648	+	0.888618i	$0.348334\pi$
$101$	−5.42936	+	9.40393i	−0.540242	+	0.935726i	−0.998890	+	0.0471079i	$0.985000\pi$
$102$		0			0
$103$	−2.08791	−	3.61637i	−0.205728	−	0.356331i	0.744637	−	0.667470i	$-0.232623\pi$
$103$	−2.08791	−	3.61637i	−0.205728	−	0.356331i	−0.950364	+	0.311139i	$0.899290\pi$
$104$	13.7234			1.34569
$105$		0			0
$106$	−20.9205			−2.03198
$107$	−1.82373	−	3.15880i	−0.176307	−	0.305373i	0.764306	−	0.644854i	$-0.223082\pi$
$107$	−1.82373	−	3.15880i	−0.176307	−	0.305373i	−0.940613	+	0.339481i	$0.889748\pi$
$108$		0			0
$109$	−7.08585	+	12.2731i	−0.678701	+	1.17555i	0.296671	+	0.954980i	$0.404124\pi$
$109$	−7.08585	+	12.2731i	−0.678701	+	1.17555i	−0.975372	+	0.220566i	$0.929210\pi$
$110$	−9.57641	−	16.5868i	−0.913075	−	1.58149i
$111$		0			0
$112$	−0.207326	−	0.203047i	−0.0195905	−	0.0191861i
$113$	9.20761			0.866179			0.433089	−	0.901351i	$-0.357423\pi$
$113$	9.20761			0.866179			0.433089	+	0.901351i	$0.357423\pi$
$114$		0			0
$115$	−7.40644	+	12.8283i	−0.690654	+	1.19625i
$116$	−14.9788	+	25.9440i	−1.39075	+	2.40884i
$117$		0			0
$118$	22.3973			2.06184
$119$	−3.68290	+	14.3412i	−0.337610	+	1.31466i
$120$		0			0
$121$	0.0672653	+	0.116507i	0.00611502	+	0.0105915i
$122$	−2.07271	+	3.59004i	−0.187654	+	0.325027i
$123$		0			0
$124$	10.3136	+	17.8636i	0.926184	+	1.60420i
$125$	−8.96359			−0.801728
$126$		0			0
$127$	−5.26815			−0.467472			−0.233736	−	0.972300i	$-0.575095\pi$
$127$	−5.26815			−0.467472			−0.233736	+	0.972300i	$0.575095\pi$
$128$	−9.03267	−	15.6451i	−0.798383	−	1.38284i
$129$		0			0
$130$	−14.4169	+	24.9709i	−1.26445	+	2.19009i
$131$	−3.96817	−	6.87308i	−0.346701	−	0.600503i	0.638960	−	0.769240i	$-0.279365\pi$
$131$	−3.96817	−	6.87308i	−0.346701	−	0.600503i	−0.985661	+	0.168736i	$0.946031\pi$
$132$		0			0
$133$	−1.89023	−	1.85122i	−0.163904	−	0.160521i
$134$	−7.67788			−0.663268
$135$		0			0
$136$	−7.73825	+	13.4030i	−0.663550	+	1.14930i
$137$	4.09826	−	7.09839i	0.350138	−	0.606456i	−0.636136	−	0.771577i	$-0.719468\pi$
$137$	4.09826	−	7.09839i	0.350138	−	0.606456i	0.986273	+	0.165121i	$0.0528015\pi$
$138$		0			0
$139$	9.20860			0.781063			0.390531	−	0.920590i	$-0.372291\pi$
$139$	9.20860			0.781063			0.390531	+	0.920590i	$0.372291\pi$
$140$	−20.8296	+	5.81470i	−1.76042	+	0.491432i
$141$		0			0
$142$	−2.30188	−	3.98697i	−0.193169	−	0.334579i
$143$	−8.17879	+	14.1661i	−0.683945	+	1.18463i
$144$		0			0
$145$	−11.8717	−	20.5624i	−0.985890	−	1.70761i
$146$	10.7880			0.892823
$147$		0			0
$148$	24.7294			2.03274
$149$	2.39764	+	4.15284i	0.196423	+	0.340214i	0.947366	−	0.320153i	$-0.103734\pi$
$149$	2.39764	+	4.15284i	0.196423	+	0.340214i	−0.750943	+	0.660367i	$0.770401\pi$
$150$		0			0
$151$	−3.83040	+	6.63446i	−0.311714	+	0.539904i	−0.978734	−	0.205136i	$-0.934236\pi$
$151$	−3.83040	+	6.63446i	−0.311714	+	0.539904i	0.667020	+	0.745040i	$0.267570\pi$
$152$	−1.38273	−	2.39496i	−0.112154	−	0.194257i
$153$		0			0
$154$	−19.1759	+	5.35307i	−1.54524	+	0.431363i
$155$	−16.3483			−1.31313
$156$		0			0
$157$	2.46803	−	4.27475i	0.196970	−	0.341162i	−0.750574	−	0.660786i	$-0.770223\pi$
$157$	2.46803	−	4.27475i	0.196970	−	0.341162i	0.947545	+	0.319624i	$0.103556\pi$
$158$	−14.7227	+	25.5005i	−1.17128	+	2.02871i
$159$		0			0
$160$	14.7149			1.16331
$161$	11.0008	+	10.7737i	0.866984	+	0.849090i
$162$		0			0
$163$	−1.27555	−	2.20932i	−0.0999090	−	0.173047i	0.811738	−	0.584022i	$-0.198522\pi$
$163$	−1.27555	−	2.20932i	−0.0999090	−	0.173047i	−0.911647	+	0.410975i	$0.865189\pi$
$164$	9.84515	−	17.0523i	0.768777	−	1.33156i
$165$		0			0
$166$	0.848465	+	1.46958i	0.0658536	+	0.114062i
$167$	1.94706			0.150668			0.0753340	−	0.997158i	$-0.475998\pi$
$167$	1.94706			0.150668			0.0753340	+	0.997158i	$0.475998\pi$
$168$		0			0
$169$	11.6258			0.894289
$170$	−16.2586	−	28.1608i	−1.24698	−	2.15983i
$171$		0			0
$172$	7.43175	−	12.8722i	0.566665	−	0.981493i
$173$	7.53471	+	13.0505i	0.572853	+	0.992211i	0.996271	+	0.0862768i	$0.0274969\pi$
$173$	7.53471	+	13.0505i	0.572853	+	0.992211i	−0.423418	+	0.905935i	$0.639170\pi$
$174$		0			0
$175$	0.972859	−	3.78832i	0.0735412	−	0.286370i
$176$	0.361545			0.0272525
$177$		0			0
$178$	13.0178	−	22.5474i	0.975723	−	1.69000i
$179$	11.6786	−	20.2280i	0.872901	−	1.51191i	0.0139195	−	0.999903i	$-0.495569\pi$
$179$	11.6786	−	20.2280i	0.872901	−	1.51191i	0.858982	−	0.512006i	$-0.171098\pi$
$180$		0			0
$181$	21.8279			1.62246			0.811228	−	0.584730i	$-0.198800\pi$
$181$	21.8279			1.62246			0.811228	+	0.584730i	$0.198800\pi$
$182$	21.4135	+	20.9715i	1.58727	+	1.55451i
$183$		0			0
$184$	8.04722	+	13.9382i	0.593249	+	1.02754i
$185$	−9.79984	+	16.9738i	−0.720499	+	1.24794i
$186$		0			0
$187$	−9.22359	−	15.9757i	−0.674496	−	1.16826i
$188$	20.2781			1.47893
$189$		0			0
$190$	5.81043			0.421533
$191$	−5.36754	−	9.29685i	−0.388381	−	0.672696i	0.603851	−	0.797097i	$-0.293632\pi$
$191$	−5.36754	−	9.29685i	−0.388381	−	0.672696i	−0.992232	+	0.124401i	$0.960299\pi$
$192$		0			0
$193$	−9.01029	+	15.6063i	−0.648575	+	1.12336i	0.334889	+	0.942258i	$0.391301\pi$
$193$	−9.01029	+	15.6063i	−0.648575	+	1.12336i	−0.983463	+	0.181107i	$0.942032\pi$
$194$	−19.3141	−	33.4530i	−1.38667	−	2.40178i
$195$		0			0
$196$	0.468750	+	22.4750i	0.0334821	+	1.60535i
$197$	3.39251			0.241706			0.120853	−	0.992670i	$-0.461437\pi$
$197$	3.39251			0.241706			0.120853	+	0.992670i	$0.461437\pi$
$198$		0			0
$199$	−0.0554566	+	0.0960536i	−0.00393121	+	0.00680906i	−0.867984	−	0.496592i	$-0.834585\pi$
$199$	−0.0554566	+	0.0960536i	−0.00393121	+	0.00680906i	0.864053	+	0.503401i	$0.167918\pi$
$200$	2.04411	−	3.54049i	0.144540	−	0.250351i
$201$		0			0
$202$	−24.7888			−1.74414
$203$	−23.7720	+	6.63610i	−1.66847	+	0.465763i
$204$		0			0
$205$	7.80293	+	13.5151i	0.544980	+	0.943934i
$206$	4.76639	−	8.25562i	0.332090	−	0.575197i
$207$		0			0
$208$	−0.272147	−	0.471372i	−0.0188700	−	0.0326838i
$209$	3.29628			0.228009
$210$		0			0
$211$	11.6596			0.802681			0.401340	−	0.915929i	$-0.368544\pi$
$211$	11.6596			0.802681			0.401340	+	0.915929i	$0.368544\pi$
$212$	−14.7150	−	25.4871i	−1.01063	−	1.75046i
$213$		0			0
$214$	4.16331	−	7.21106i	0.284598	−	0.492938i
$215$	5.89015	+	10.2020i	0.401705	+	0.695774i
$216$		0			0
$217$	−4.22695	+	16.4598i	−0.286944	+	1.11736i
$218$	−32.3519			−2.19115
$219$		0			0
$220$	13.4716	−	23.3336i	0.908258	−	1.57315i
$221$	−13.8858	+	24.0509i	−0.934059	+	1.61784i
$222$		0			0
$223$	13.8313			0.926214			0.463107	−	0.886302i	$-0.346735\pi$
$223$	13.8313			0.926214			0.463107	+	0.886302i	$0.346735\pi$
$224$	3.80461	−	14.8152i	0.254206	−	0.989881i
$225$		0			0
$226$	10.5098	+	18.2035i	0.699101	+	1.21088i
$227$	6.89519	−	11.9428i	0.457650	−	0.792673i	−0.541187	−	0.840903i	$-0.682025\pi$
$227$	6.89519	−	11.9428i	0.457650	−	0.792673i	0.998836	+	0.0482300i	$0.0153580\pi$
$228$		0			0
$229$	−6.98222	−	12.0936i	−0.461398	−	0.799165i	0.537633	−	0.843179i	$-0.319319\pi$
$229$	−6.98222	−	12.0936i	−0.461398	−	0.799165i	−0.999031	+	0.0440139i	$0.985985\pi$
$230$	−33.8156			−2.22973
$231$		0			0
$232$	−25.7976			−1.69369
$233$	−8.49188	−	14.7084i	−0.556322	−	0.963578i	−0.997799	−	0.0663053i	$-0.978879\pi$
$233$	−8.49188	−	14.7084i	−0.556322	−	0.963578i	0.441478	−	0.897272i	$-0.354454\pi$
$234$		0			0
$235$	−8.03586	+	13.9185i	−0.524202	+	0.907944i
$236$	15.7537	+	27.2862i	1.02548	+	1.77618i
$237$		0			0
$238$	−32.5565	+	9.08834i	−2.11032	+	0.589110i
$239$	−2.74352			−0.177463			−0.0887317	−	0.996056i	$-0.528281\pi$
$239$	−2.74352			−0.177463			−0.0887317	+	0.996056i	$0.528281\pi$
$240$		0			0
$241$	−4.96607	+	8.60149i	−0.319893	+	0.554071i	−0.980465	−	0.196692i	$-0.936980\pi$
$241$	−4.96607	+	8.60149i	−0.319893	+	0.554071i	0.660573	+	0.750762i	$0.270314\pi$
$242$	−0.153557	+	0.265968i	−0.00987099	+	0.0170971i
$243$		0			0
$244$	−5.83157			−0.373328
$245$	−15.6122	−	8.58471i	−0.997425	−	0.548457i
$246$		0			0
$247$	−2.48122	−	4.29759i	−0.157876	−	0.273449i
$248$	−8.88138	+	15.3830i	−0.563968	+	0.976821i
$249$		0			0
$250$	−10.2313	−	17.7211i	−0.647082	−	1.12078i
$251$	−0.0936224			−0.00590940			−0.00295470	−	0.999996i	$-0.500941\pi$
$251$	−0.0936224			−0.00590940			−0.00295470	+	0.999996i	$0.500941\pi$
$252$		0			0
$253$	−19.1837			−1.20607
$254$	−6.01319	−	10.4152i	−0.377301	−	0.653505i
$255$		0			0
$256$	7.64175	−	13.2359i	0.477609	−	0.827244i
$257$	5.33246	+	9.23609i	0.332630	+	0.576132i	0.983027	−	0.183463i	$-0.0587307\pi$
$257$	5.33246	+	9.23609i	0.332630	+	0.576132i	−0.650397	+	0.759595i	$0.725397\pi$
$258$		0			0
$259$	14.5557	+	14.2553i	0.904448	+	0.885781i
$260$	−40.5621			−2.51556
$261$		0			0
$262$	9.05874	−	15.6902i	0.559651	−	0.969344i
$263$	1.35596	−	2.34860i	0.0836124	−	0.144821i	−0.821187	−	0.570660i	$-0.806688\pi$
$263$	1.35596	−	2.34860i	0.0836124	−	0.144821i	0.904799	+	0.425839i	$0.140021\pi$
$264$		0			0
$265$	23.3252			1.43286
$266$	1.50232	−	5.85003i	0.0921129	−	0.358689i
$267$		0			0
$268$	−5.40044	−	9.35383i	−0.329884	−	0.571376i
$269$	−0.382993	+	0.663364i	−0.0233515	+	0.0404460i	−0.877465	−	0.479641i	$-0.840767\pi$
$269$	−0.382993	+	0.663364i	−0.0233515	+	0.0404460i	0.854113	+	0.520087i	$0.174100\pi$
$270$		0			0
$271$	−2.80999	−	4.86704i	−0.170695	−	0.295652i	0.767968	−	0.640488i	$-0.221268\pi$
$271$	−2.80999	−	4.86704i	−0.170695	−	0.295652i	−0.938663	+	0.344836i	$0.887934\pi$
$272$	0.613824			0.0372186
$273$		0			0
$274$	18.7114			1.13040
$275$	2.43647	+	4.22008i	0.146924	+	0.254481i
$276$		0			0
$277$	14.1778	−	24.5567i	0.851863	−	1.47547i	−0.0276623	−	0.999617i	$-0.508806\pi$
$277$	14.1778	−	24.5567i	0.851863	−	1.47547i	0.879525	−	0.475852i	$-0.157860\pi$
$278$	10.5109	+	18.2055i	0.630403	+	1.09189i
$279$		0			0
$280$	−13.3050	−	13.0304i	−0.795123	−	0.778713i
$281$	30.7742			1.83583			0.917916	−	0.396774i	$-0.129870\pi$
$281$	30.7742			1.83583			0.917916	+	0.396774i	$0.129870\pi$
$282$		0			0
$283$	7.70015	−	13.3370i	0.457726	−	0.792805i	−0.541114	−	0.840949i	$-0.681997\pi$
$283$	7.70015	−	13.3370i	0.457726	−	0.792805i	0.998840	+	0.0481441i	$0.0153307\pi$
$284$	3.23818	−	5.60869i	0.192150	−	0.332814i
$285$		0			0
$286$	−37.3419			−2.20807
$287$	15.6247	−	4.36173i	0.922295	−	0.257465i
$288$		0			0
$289$	−7.15963	−	12.4008i	−0.421155	−	0.729461i
$290$	27.1013	−	46.9408i	1.59144	−	2.75646i
$291$		0			0
$292$	7.58804	+	13.1429i	0.444056	+	0.769128i
$293$	3.63257			0.212217			0.106109	−	0.994355i	$-0.466161\pi$
$293$	3.63257			0.212217			0.106109	+	0.994355i	$0.466161\pi$
$294$		0			0
$295$	−24.9717			−1.45391
$296$	10.6477	+	18.4423i	0.618884	+	1.07194i
$297$		0			0
$298$	−5.47346	+	9.48031i	−0.317069	+	0.549180i
$299$	14.4402	+	25.0112i	0.835099	+	1.44643i
$300$		0			0
$301$	11.7945	−	3.29251i	0.679824	−	0.189777i
$302$	−17.4885			−1.00635
$303$		0			0
$304$	−0.0548414	+	0.0949880i	−0.00314537	+	0.00544794i
$305$	2.31096	−	4.00269i	0.132325	−	0.229193i
$306$		0			0
$307$	20.4805			1.16888			0.584442	−	0.811436i	$-0.301314\pi$
$307$	20.4805			1.16888			0.584442	+	0.811436i	$0.301314\pi$
$308$	−20.0094	−	19.5965i	−1.14014	−	1.11661i
$309$		0			0
$310$	−18.6604	−	32.3208i	−1.05984	−	1.83570i
$311$	−11.4343	+	19.8048i	−0.648382	+	1.12303i	0.335128	+	0.942173i	$0.391221\pi$
$311$	−11.4343	+	19.8048i	−0.648382	+	1.12303i	−0.983509	+	0.180857i	$0.942113\pi$
$312$		0			0
$313$	10.7262	+	18.5783i	0.606279	+	1.05011i	0.991848	+	0.127427i	$0.0406720\pi$
$313$	10.7262	+	18.5783i	0.606279	+	1.05011i	−0.385569	+	0.922679i	$0.625995\pi$
$314$	11.2683			0.635906
$315$		0			0
$316$	−41.4224			−2.33019
$317$	11.3236	+	19.6130i	0.635996	+	1.10158i	0.986303	+	0.164942i	$0.0527439\pi$
$317$	11.3236	+	19.6130i	0.635996	+	1.10158i	−0.350307	+	0.936635i	$0.613923\pi$
$318$		0			0
$319$	15.3747	−	26.6297i	0.860816	−	1.49098i
$320$	16.5168	+	28.6079i	0.923316	+	1.59923i
$321$		0			0
$322$	−8.74319	+	34.0461i	−0.487239	+	1.89731i
$323$	5.59636			0.311390
$324$		0			0
$325$	3.66801	−	6.35319i	0.203465	−	0.352411i
$326$	2.91190	−	5.04355i	0.161275	−	0.279337i
$327$		0			0
$328$	16.9560			0.936240
$329$	11.9357	+	11.6893i	0.658035	+	0.644454i
$330$		0			0
$331$	−14.3534	−	24.8609i	−0.788937	−	1.36648i	−0.926619	−	0.376002i	$-0.877299\pi$
$331$	−14.3534	−	24.8609i	−0.788937	−	1.36648i	0.137682	−	0.990476i	$-0.456035\pi$
$332$	−1.19358	+	2.06734i	−0.0655062	+	0.113460i
$333$		0			0
$334$	2.22242	+	3.84935i	0.121606	+	0.210627i
$335$	8.56041			0.467705
$336$		0			0
$337$	27.9822			1.52428			0.762142	−	0.647409i	$-0.224148\pi$
$337$	27.9822			1.52428			0.762142	+	0.647409i	$0.224148\pi$
$338$	13.2699	+	22.9842i	0.721789	+	1.25018i
$339$		0			0
$340$	22.8719	−	39.6153i	1.24040	−	2.14844i
$341$	−10.5861	−	18.3357i	−0.573271	−	0.992935i
$342$		0			0
$343$	−12.6798	+	13.4990i	−0.684646	+	0.728876i
$344$	12.7995			0.690103
$345$		0			0
$346$	−17.2006	+	29.7923i	−0.924711	+	1.60165i
$347$	9.05812	−	15.6891i	0.486265	−	0.842236i	−0.513610	−	0.858024i	$-0.671692\pi$
$347$	9.05812	−	15.6891i	0.486265	−	0.842236i	0.999875	+	0.0157875i	$0.00502552\pi$
$348$		0			0
$349$	−16.1254			−0.863170			−0.431585	−	0.902072i	$-0.642046\pi$
$349$	−16.1254			−0.863170			−0.431585	+	0.902072i	$0.642046\pi$
$350$	8.59998	−	2.40074i	0.459688	−	0.128325i
$351$		0			0
$352$	9.52841	+	16.5037i	0.507866	+	0.879649i
$353$	−9.51891	+	16.4872i	−0.506641	+	0.877527i	0.493330	+	0.869842i	$0.335780\pi$
$353$	−9.51891	+	16.4872i	−0.506641	+	0.877527i	−0.999970	+	0.00768495i	$0.997554\pi$
$354$		0			0
$355$	2.56647	+	4.44526i	0.136214	+	0.235930i
$356$	36.6256			1.94115
$357$		0			0
$358$	53.3211			2.81811
$359$	−2.58582	−	4.47877i	−0.136474	−	0.236380i	0.789685	−	0.613512i	$-0.210244\pi$
$359$	−2.58582	−	4.47877i	−0.136474	−	0.236380i	−0.926160	+	0.377132i	$0.876910\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	24.9149	+	43.1539i	1.30950	+	2.26812i
$363$		0			0
$364$	−10.4875	+	40.8386i	−0.549696	+	2.14052i
$365$	−12.0281			−0.629577
$366$		0			0
$367$	−2.81392	+	4.87386i	−0.146886	+	0.254413i	−0.930075	−	0.367370i	$-0.880258\pi$
$367$	−2.81392	+	4.87386i	−0.146886	+	0.254413i	0.783189	+	0.621783i	$0.213592\pi$
$368$	0.319166	−	0.552812i	0.0166377	−	0.0288173i
$369$		0			0
$370$	−44.7431			−2.32609
$371$	6.03085	−	23.4842i	0.313106	−	1.21924i
$372$		0			0
$373$	−1.79728	−	3.11298i	−0.0930596	−	0.161184i	0.815738	−	0.578422i	$-0.196331\pi$
$373$	−1.79728	−	3.11298i	−0.0930596	−	0.161184i	−0.908797	+	0.417238i	$0.862998\pi$
$374$	21.0561	−	36.4702i	1.08878	−	1.88583i
$375$		0			0
$376$	8.73110	+	15.1227i	0.450272	+	0.779894i
$377$	−46.2920			−2.38416
$378$		0			0
$379$	8.82165			0.453138			0.226569	−	0.973995i	$-0.427249\pi$
$379$	8.82165			0.453138			0.226569	+	0.973995i	$0.427249\pi$
$380$	4.08692	+	7.07875i	0.209655	+	0.363132i
$381$		0			0
$382$	12.2533	−	21.2233i	0.626933	−	1.08588i
$383$	−15.6624	−	27.1281i	−0.800311	−	1.38618i	−0.919412	−	0.393297i	$-0.871335\pi$
$383$	−15.6624	−	27.1281i	−0.800311	−	1.38618i	0.119101	−	0.992882i	$-0.461999\pi$
$384$		0			0
$385$	21.3801	−	5.96838i	1.08963	−	0.304177i
$386$	−41.1383			−2.09388
$387$		0			0
$388$	27.1701	−	47.0600i	1.37935	−	2.38911i
$389$	−0.122913	+	0.212891i	−0.00623193	+	0.0107940i	−0.869125	−	0.494593i	$-0.835317\pi$
$389$	−0.122913	+	0.212891i	−0.00623193	+	0.0107940i	0.862893	+	0.505387i	$0.168650\pi$
$390$		0			0
$391$	−32.5697			−1.64712
$392$	−16.5592	+	10.0266i	−0.836367	+	0.506419i
$393$		0			0
$394$	3.87229	+	6.70701i	0.195083	+	0.337894i
$395$	16.4150	−	28.4316i	0.825929	−	1.43055i
$396$		0			0
$397$	0.897652	+	1.55478i	0.0450519	+	0.0780321i	0.887672	−	0.460476i	$-0.152321\pi$
$397$	0.897652	+	1.55478i	0.0450519	+	0.0780321i	−0.842620	+	0.538508i	$0.818988\pi$
$398$	−0.253198			−0.0126917
$399$		0			0
$400$	−0.162145			−0.00810726
$401$	−12.2512	−	21.2196i	−0.611793	−	1.05966i	−0.990938	−	0.134320i	$-0.957115\pi$
$401$	−12.2512	−	21.2196i	−0.611793	−	1.05966i	0.379145	−	0.925337i	$-0.376218\pi$
$402$		0			0
$403$	−15.9370	+	27.6038i	−0.793881	+	1.37504i
$404$	−17.4359	−	30.1998i	−0.867467	−	1.50250i
$405$		0			0
$406$	−40.2536	−	39.4228i	−1.99775	−	1.95652i
$407$	−25.3830			−1.25819
$408$		0			0
$409$	−13.5524	+	23.4735i	−0.670125	+	1.16069i	0.307743	+	0.951470i	$0.400426\pi$
$409$	−13.5524	+	23.4735i	−0.670125	+	1.16069i	−0.977868	+	0.209222i	$0.932907\pi$
$410$	−17.8129	+	30.8529i	−0.879718	+	1.52372i
$411$		0			0
$412$	13.4103			0.660676
$413$	−6.45657	+	25.1419i	−0.317707	+	1.23715i
$414$		0			0
$415$	−0.945992	−	1.63851i	−0.0464369	−	0.0804311i
$416$	14.3447	−	24.8457i	0.703306	−	1.21816i
$417$		0			0
$418$	3.76246	+	6.51677i	0.184028	+	0.318746i
$419$	24.5949			1.20154			0.600771	−	0.799421i	$-0.294860\pi$
$419$	24.5949			1.20154			0.600771	+	0.799421i	$0.294860\pi$
$420$		0			0
$421$	17.1191			0.834334			0.417167	−	0.908830i	$-0.363023\pi$
$421$	17.1191			0.834334			0.417167	+	0.908830i	$0.363023\pi$
$422$	13.3086	+	23.0511i	0.647851	+	1.12211i
$423$		0			0
$424$	12.6716	−	21.9479i	0.615388	−	1.06588i
$425$	4.13658	+	7.16477i	0.200654	+	0.347543i
$426$		0			0
$427$	−3.43246	−	3.36162i	−0.166109	−	0.162680i
$428$	11.7135			0.566193
$429$		0			0
$430$	−13.4463	+	23.2897i	−0.648440	+	1.12313i
$431$	−9.81420	+	16.9987i	−0.472733	+	0.818798i	−0.999513	−	0.0312037i	$-0.990066\pi$
$431$	−9.81420	+	16.9987i	−0.472733	+	0.818798i	0.526780	+	0.850002i	$0.323399\pi$
$432$		0			0
$433$	30.0095			1.44216			0.721082	−	0.692850i	$-0.243645\pi$
$433$	30.0095			1.44216			0.721082	+	0.692850i	$0.243645\pi$
$434$	−37.3658	+	10.4309i	−1.79362	+	0.500699i
$435$		0			0
$436$	−22.7555	−	39.4138i	−1.08979	−	1.88758i
$437$	2.90990	−	5.04010i	0.139200	−	0.241101i
$438$		0			0
$439$	5.82201	+	10.0840i	0.277869	+	0.481284i	0.970855	−	0.239667i	$-0.0770384\pi$
$439$	5.82201	+	10.0840i	0.277869	+	0.481284i	−0.692986	+	0.720951i	$0.743705\pi$
$440$	23.2018			1.10610
$441$		0			0
$442$	−63.3984			−3.01555
$443$	−9.66895	−	16.7471i	−0.459386	−	0.795679i	0.539543	−	0.841958i	$-0.318597\pi$
$443$	−9.66895	−	16.7471i	−0.459386	−	0.795679i	−0.998929	+	0.0462788i	$0.985264\pi$
$444$		0			0
$445$	−14.5141	+	25.1391i	−0.688034	+	1.19171i
$446$	15.7874	+	27.3446i	0.747556	+	1.29481i
$447$		0			0
$448$	33.0734	−	9.23264i	1.56257	−	0.436201i
$449$	34.8975			1.64692			0.823458	−	0.567377i	$-0.192042\pi$
$449$	34.8975			1.64692			0.823458	+	0.567377i	$0.192042\pi$
$450$		0			0
$451$	−10.1053	+	17.5030i	−0.475842	+	0.824183i
$452$	−14.7847	+	25.6078i	−0.695413	+	1.20449i
$453$		0			0
$454$	31.4814			1.47749
$455$	−23.8749	−	23.3821i	−1.11927	−	1.09617i
$456$		0			0
$457$	1.55603	+	2.69512i	0.0727878	+	0.126072i	0.900122	−	0.435638i	$-0.143477\pi$
$457$	1.55603	+	2.69512i	0.0727878	+	0.126072i	−0.827334	+	0.561710i	$0.810144\pi$
$458$	15.9394	−	27.6078i	0.744798	−	1.29003i
$459$		0			0
$460$	−23.7851	−	41.1970i	−1.10899	−	1.92082i
$461$	−21.6573			−1.00868			−0.504341	−	0.863505i	$-0.668264\pi$
$461$	−21.6573			−1.00868			−0.504341	+	0.863505i	$0.668264\pi$
$462$		0			0
$463$	−27.4240			−1.27450			−0.637252	−	0.770656i	$-0.719929\pi$
$463$	−27.4240			−1.27450			−0.637252	+	0.770656i	$0.719929\pi$
$464$	0.511587	+	0.886095i	0.0237498	+	0.0411359i
$465$		0			0
$466$	19.3857	−	33.5770i	0.898025	−	1.55543i
$467$	−13.6273	−	23.6031i	−0.630595	−	1.09222i	−0.987430	−	0.158056i	$-0.949477\pi$
$467$	−13.6273	−	23.6031i	−0.630595	−	1.09222i	0.356835	−	0.934167i	$-0.383856\pi$
$468$		0			0
$469$	2.21334	−	8.61876i	0.102202	−	0.397977i
$470$	−36.6893			−1.69235
$471$		0			0
$472$	−13.5661	+	23.4972i	−0.624431	+	1.08155i
$473$	−7.62816	+	13.2124i	−0.350743	+	0.607505i
$474$		0			0
$475$	−1.47831			−0.0678296
$476$	−33.9716	−	33.2705i	−1.55709	−	1.52495i
$477$		0			0
$478$	−3.13152	−	5.42395i	−0.143232	−	0.248086i
$479$	−17.7994	+	30.8295i	−0.813277	+	1.40864i	0.0972820	+	0.995257i	$0.468985\pi$
$479$	−17.7994	+	30.8295i	−0.813277	+	1.40864i	−0.910559	+	0.413380i	$0.864348\pi$
$480$		0			0
$481$	19.1066	+	33.0936i	0.871185	+	1.50894i
$482$	−22.6736			−1.03275
$483$		0			0
$484$	−0.432032			−0.0196378
$485$	21.5341	+	37.2982i	0.977815	+	1.69362i
$486$		0			0
$487$	−10.7802	+	18.6719i	−0.488498	+	0.846104i	−0.999912	−	0.0132307i	$-0.995788\pi$
$487$	−10.7802	+	18.6719i	−0.488498	+	0.846104i	0.511414	+	0.859334i	$0.329122\pi$
$488$	−2.51089	−	4.34899i	−0.113663	−	0.196870i
$489$		0			0
$490$	−0.848114	−	40.6642i	−0.0383139	−	1.83702i
$491$	−4.06065			−0.183255			−0.0916273	−	0.995793i	$-0.529207\pi$
$491$	−4.06065			−0.183255			−0.0916273	+	0.995793i	$0.529207\pi$
$492$		0			0
$493$	26.1028	−	45.2114i	1.17561	−	2.03622i
$494$	5.66425	−	9.81077i	0.254847	−	0.441407i
$495$		0			0
$496$	0.704500			0.0316330
$497$	5.13913	−	1.43462i	0.230521	−	0.0643515i
$498$		0			0
$499$	6.84108	+	11.8491i	0.306249	+	0.530439i	0.977539	−	0.210756i	$-0.0675926\pi$
$499$	6.84108	+	11.8491i	0.306249	+	0.530439i	−0.671290	+	0.741195i	$0.734259\pi$
$500$	14.3929	−	24.9292i	0.643668	−	1.11487i
$501$		0			0
$502$	−0.106863	−	0.185092i	−0.00476953	−	0.00826107i
$503$	−16.8353			−0.750650			−0.375325	−	0.926893i	$-0.622469\pi$
$503$	−16.8353			−0.750650			−0.375325	+	0.926893i	$0.622469\pi$
$504$		0			0
$505$	27.6382			1.22988
$506$	−21.8968	−	37.9263i	−0.973431	−	1.68603i
$507$		0			0
$508$	8.45908	−	14.6516i	0.375311	−	0.650057i
$509$	2.09067	+	3.62115i	0.0926673	+	0.160504i	0.908633	−	0.417596i	$-0.137127\pi$
$509$	2.09067	+	3.62115i	0.0926673	+	0.160504i	−0.815965	+	0.578101i	$0.803794\pi$
$510$		0			0
$511$	−3.10991	+	12.1100i	−0.137574	+	0.535716i
$512$	−1.24076			−0.0548342
$513$		0			0
$514$	−12.1732	+	21.0846i	−0.536937	+	0.930003i
$515$	−5.31426	+	9.20457i	−0.234174	+	0.405602i
$516$		0			0
$517$	−20.8140			−0.915399
$518$	−11.5686	+	45.0481i	−0.508293	+	1.97930i
$519$		0			0
$520$	−17.4648	−	30.2499i	−0.765881	−	1.32654i
$521$	−6.38585	+	11.0606i	−0.279769	+	0.484575i	−0.971327	−	0.237746i	$-0.923591\pi$
$521$	−6.38585	+	11.0606i	−0.279769	+	0.484575i	0.691558	+	0.722321i	$0.256925\pi$
$522$		0			0
$523$	12.9659	+	22.4575i	0.566957	+	0.981999i	0.996865	+	0.0791260i	$0.0252129\pi$
$523$	12.9659	+	22.4575i	0.566957	+	0.981999i	−0.429907	+	0.902873i	$0.641454\pi$
$524$	25.4868			1.11340
$525$		0			0
$526$	6.19093			0.269937
$527$	−17.9729	−	31.1300i	−0.782913	−	1.35604i
$528$		0			0
$529$	−5.43508	+	9.41384i	−0.236308	+	0.409298i
$530$	26.6240	+	46.1141i	1.15647	+	2.00307i
$531$		0			0
$532$	8.18369	−	2.28453i	0.354808	−	0.0990469i
$533$	30.4265			1.31792
$534$		0			0
$535$	−4.64186	+	8.03994i	−0.200685	+	0.347597i
$536$	4.65051	−	8.05493i	0.200872	−	0.347920i
$537$		0			0
$538$	−1.74863			−0.0753889
$539$	−0.481138	−	23.0690i	−0.0207241	−	0.993650i
$540$		0			0
$541$	11.4156	+	19.7724i	0.490795	+	0.850082i	0.999944	−	0.0105967i	$-0.00337311\pi$
$541$	11.4156	+	19.7724i	0.490795	+	0.850082i	−0.509149	+	0.860678i	$0.670040\pi$
$542$	6.41478	−	11.1107i	0.275538	−	0.477247i
$543$		0			0
$544$	16.1771	+	28.0196i	0.693589	+	1.20133i
$545$	36.0706			1.54509
$546$		0			0
$547$	−21.0599			−0.900455			−0.450227	−	0.892914i	$-0.648657\pi$
$547$	−21.0599			−0.900455			−0.450227	+	0.892914i	$0.648657\pi$
$548$	13.1612	+	22.7958i	0.562217	+	0.973788i
$549$		0			0
$550$	−5.56209	+	9.63382i	−0.237168	+	0.410787i
$551$	4.66425	+	8.07871i	0.198704	+	0.344165i
$552$		0			0
$553$	−24.3812	−	23.8780i	−1.03680	−	1.01540i
$554$	64.7317			2.75019
$555$		0			0
$556$	−14.7863	+	25.6106i	−0.627078	+	1.08613i
$557$	21.7768	−	37.7185i	0.922713	−	1.59819i	0.127514	−	0.991837i	$-0.459300\pi$
$557$	21.7768	−	37.7185i	0.922713	−	1.59819i	0.795199	−	0.606348i	$-0.207366\pi$
$558$		0			0
$559$	22.9679			0.971437
$560$	−0.183718	+	0.715402i	−0.00776352	+	0.0302312i
$561$		0			0
$562$	35.1264	+	60.8407i	1.48172	+	2.56641i
$563$	−10.7691	+	18.6526i	−0.453862	+	0.786112i	−0.998622	−	0.0524800i	$-0.983287\pi$
$563$	−10.7691	+	18.6526i	−0.453862	+	0.786112i	0.544760	+	0.838592i	$0.316621\pi$
$564$		0			0
$565$	−11.7178	−	20.2959i	−0.492973	−	0.853855i
$566$	35.1566			1.47774
$567$		0			0
$568$	5.57702			0.234007
$569$	6.91119	+	11.9705i	0.289732	+	0.501831i	0.973746	−	0.227639i	$-0.0731005\pi$
$569$	6.91119	+	11.9705i	0.289732	+	0.501831i	−0.684014	+	0.729469i	$0.739767\pi$
$570$		0			0
$571$	3.18585	−	5.51805i	0.133324	−	0.230923i	−0.791632	−	0.610998i	$-0.790768\pi$
$571$	3.18585	−	5.51805i	0.133324	−	0.230923i	0.924956	+	0.380075i	$0.124102\pi$
$572$	−26.2654	−	45.4930i	−1.09821	−	1.90216i
$573$		0			0
$574$	26.4576	+	25.9115i	1.10432	+	1.08153i
$575$	8.60349			0.358790
$576$		0			0
$577$	−9.19733	+	15.9302i	−0.382890	+	0.663185i	−0.991474	−	0.130305i	$-0.958405\pi$
$577$	−9.19733	+	15.9302i	−0.382890	+	0.663185i	0.608584	+	0.793489i	$0.291738\pi$
$578$	16.3444	−	28.3093i	0.679836	−	1.17751i
$579$		0			0
$580$	76.2496			3.16609
$581$	−1.89426	+	0.528796i	−0.0785873	+	0.0219381i
$582$		0			0
$583$	15.1039	+	26.1607i	0.625539	+	1.08347i
$584$	−6.53434	+	11.3178i	−0.270393	+	0.468334i
$585$		0			0
$586$	4.14631	+	7.18162i	0.171282	+	0.296670i
$587$	28.7021			1.18466			0.592331	−	0.805695i	$-0.298208\pi$
$587$	28.7021			1.18466			0.592331	+	0.805695i	$0.298208\pi$
$588$		0			0
$589$	6.42307			0.264658
$590$	−28.5034	−	49.3693i	−1.17347	−	2.03250i
$591$		0			0
$592$	0.422305	−	0.731454i	0.0173566	−	0.0300626i
$593$	16.3272	+	28.2795i	0.670478	+	1.16130i	0.977769	+	0.209686i	$0.0672441\pi$
$593$	16.3272	+	28.2795i	0.670478	+	1.16130i	−0.307291	+	0.951616i	$0.599423\pi$
$594$		0			0
$595$	36.2987	−	10.1330i	1.48810	−	0.415413i
$596$	−15.3996			−0.630793
$597$		0			0
$598$	−32.9648	+	57.0968i	−1.34803	+	2.33486i
$599$	4.63577	−	8.02939i	0.189412	−	0.328072i	−0.755642	−	0.654985i	$-0.772675\pi$
$599$	4.63577	−	8.02939i	0.189412	−	0.328072i	0.945054	+	0.326913i	$0.106008\pi$
$600$		0			0
$601$	6.44868			0.263047			0.131524	−	0.991313i	$-0.458013\pi$
$601$	6.44868			0.263047			0.131524	+	0.991313i	$0.458013\pi$
$602$	19.9719	+	19.5597i	0.813992	+	0.797192i
$603$		0			0
$604$	−12.3010	−	21.3059i	−0.500520	−	0.866926i
$605$	0.171207	−	0.296539i	0.00696056	−	0.0120560i
$606$		0			0
$607$	4.88593	+	8.46267i	0.198314	+	0.343489i	0.947982	−	0.318325i	$-0.103120\pi$
$607$	4.88593	+	8.46267i	0.198314	+	0.343489i	−0.749668	+	0.661814i	$0.769787\pi$
$608$	−5.78131			−0.234463
$609$		0			0
$610$	10.5511			0.427203
$611$	15.6674	+	27.1367i	0.633834	+	1.09783i
$612$		0			0
$613$	22.3319	−	38.6801i	0.901979	−	1.56227i	0.0770563	−	0.997027i	$-0.475448\pi$
$613$	22.3319	−	38.6801i	0.901979	−	1.56227i	0.824922	−	0.565246i	$-0.191219\pi$
$614$	23.3770	+	40.4901i	0.943417	+	1.63405i
$615$		0			0
$616$	5.99895	−	23.3600i	0.241705	−	0.941200i
$617$	25.1695			1.01329			0.506643	−	0.862156i	$-0.330886\pi$
$617$	25.1695			1.01329			0.506643	+	0.862156i	$0.330886\pi$
$618$		0			0
$619$	19.7418	−	34.1938i	0.793490	−	1.37436i	−0.130304	−	0.991474i	$-0.541595\pi$
$619$	19.7418	−	34.1938i	0.793490	−	1.37436i	0.923794	−	0.382891i	$-0.125071\pi$
$620$	26.2506	−	45.4674i	1.05425	−	1.82601i
$621$		0			0
$622$	−52.2058			−2.09326
$623$	21.5578	+	21.1129i	0.863695	+	0.845869i
$624$		0			0
$625$	15.1031	+	26.1593i	0.604123	+	1.04637i
$626$	−24.4863	+	42.4114i	−0.978668	+	1.69510i
$627$		0			0
$628$	7.92584	+	13.7280i	0.316276	+	0.547805i
$629$	−43.0947			−1.71830
$630$		0			0
$631$	5.92164			0.235737			0.117868	−	0.993029i	$-0.462394\pi$
$631$	5.92164			0.235737			0.117868	+	0.993029i	$0.462394\pi$
$632$	−17.8352	−	30.8914i	−0.709446	−	1.22880i
$633$		0			0
$634$	−25.8501	+	44.7736i	−1.02664	+	1.77819i
$635$	6.70438	+	11.6123i	0.266055	+	0.460821i
$636$		0			0
$637$	−29.7145	+	17.9920i	−1.17733	+	0.712871i
$638$	70.1962			2.77909
$639$		0			0
$640$	−22.9904	+	39.8206i	−0.908777	+	1.57405i
$641$	−7.56670	+	13.1059i	−0.298867	+	0.517652i	−0.975877	−	0.218321i	$-0.929942\pi$
$641$	−7.56670	+	13.1059i	−0.298867	+	0.517652i	0.677010	+	0.735973i	$0.263275\pi$
$642$		0			0
$643$	14.5709			0.574619			0.287310	−	0.957838i	$-0.407239\pi$
$643$	14.5709			0.574619			0.287310	+	0.957838i	$0.407239\pi$
$644$	−47.6275	+	13.2955i	−1.87679	+	0.523917i
$645$		0			0
$646$	6.38783	+	11.0640i	0.251326	+	0.435309i
$647$	−1.45937	+	2.52771i	−0.0573739	+	0.0993745i	−0.893286	−	0.449489i	$-0.851606\pi$
$647$	−1.45937	+	2.52771i	−0.0573739	+	0.0993745i	0.835912	+	0.548864i	$0.184939\pi$
$648$		0			0
$649$	−16.1701	−	28.0074i	−0.634731	−	1.09939i
$650$	16.7471			0.656873
$651$		0			0
$652$	8.19264			0.320848
$653$	−13.8699	−	24.0233i	−0.542770	−	0.940106i	−0.998744	−	0.0501122i	$-0.984042\pi$
$653$	−13.8699	−	24.0233i	−0.542770	−	0.940106i	0.455973	−	0.889993i	$-0.349291\pi$
$654$		0			0
$655$	−10.1000	+	17.4937i	−0.394640	+	0.683536i
$656$	−0.336252	−	0.582406i	−0.0131284	−	0.0227391i
$657$		0			0
$658$	−9.48621	+	36.9394i	−0.369811	+	1.44005i
$659$	−14.7834			−0.575880			−0.287940	−	0.957648i	$-0.592970\pi$
$659$	−14.7834			−0.575880			−0.287940	+	0.957648i	$0.592970\pi$
$660$		0			0
$661$	−17.6266	+	30.5302i	−0.685596	+	1.18749i	0.287654	+	0.957735i	$0.407125\pi$
$661$	−17.6266	+	30.5302i	−0.685596	+	1.18749i	−0.973249	+	0.229752i	$0.926208\pi$
$662$	32.7668	−	56.7537i	1.27352	−	2.20580i
$663$		0			0
$664$	−2.05567			−0.0797755
$665$	−1.67500	+	6.52247i	−0.0649537	+	0.252930i
$666$		0			0
$667$	−27.1450	−	47.0166i	−1.05106	−	1.82049i
$668$	−3.12640	+	5.41508i	−0.120964	+	0.209516i
$669$		0			0
$670$	9.77107	+	16.9240i	0.377489	+	0.653831i
$671$	5.98570			0.231075
$672$		0			0
$673$	−22.4607			−0.865796			−0.432898	−	0.901443i	$-0.642509\pi$
$673$	−22.4607			−0.865796			−0.432898	+	0.901443i	$0.642509\pi$
$674$	31.9395	+	55.3209i	1.23026	+	2.13088i
$675$		0			0
$676$	−18.6675	+	32.3331i	−0.717981	+	1.24358i
$677$	−4.64321	−	8.04228i	−0.178453	−	0.309090i	0.762898	−	0.646519i	$-0.223776\pi$
$677$	−4.64321	−	8.04228i	−0.178453	−	0.309090i	−0.941351	+	0.337429i	$0.890443\pi$
$678$		0			0
$679$	43.1202	−	12.0373i	1.65480	−	0.461948i
$680$	39.3916			1.51060
$681$		0			0
$682$	24.1666	−	41.8577i	0.925385	−	1.60281i
$683$	9.61953	−	16.6615i	0.368081	−	0.637535i	−0.621184	−	0.783664i	$-0.713348\pi$
$683$	9.61953	−	16.6615i	0.368081	−	0.637535i	0.989266	+	0.146129i	$0.0466815\pi$
$684$		0			0
$685$	−20.8622			−0.797103
$686$	−41.1606	−	9.66003i	−1.57152	−	0.368822i
$687$		0			0
$688$	−0.253825	−	0.439637i	−0.00967698	−	0.0167610i
$689$	22.7384	−	39.3840i	0.866263	−	1.50041i
$690$		0			0
$691$	−11.5353	−	19.9797i	−0.438823	−	0.760064i	0.558776	−	0.829319i	$-0.311271\pi$
$691$	−11.5353	−	19.9797i	−0.438823	−	0.760064i	−0.997599	+	0.0692547i	$0.977938\pi$
$692$	−48.3940			−1.83967
$693$		0			0
$694$	41.3567			1.56988
$695$	−11.7191	−	20.2981i	−0.444531	−	0.769950i
$696$		0			0
$697$	−17.1567	+	29.7162i	−0.649855	+	1.12558i
$698$	−18.4059	−	31.8799i	−0.696673	−	1.20667i
$699$		0			0
$700$	8.97381	+	8.78860i	0.339178	+	0.332178i
$701$	18.6485			0.704344			0.352172	−	0.935935i	$-0.385443\pi$
$701$	18.6485			0.704344			0.352172	+	0.935935i	$0.385443\pi$
$702$		0			0
$703$	3.85024	−	6.66882i	0.145215	−	0.251519i
$704$	−21.3904	+	37.0492i	−0.806180	+	1.39635i
$705$		0			0
$706$	−43.4605			−1.63566
$707$	7.14599	−	27.8266i	0.268753	−	1.04653i
$708$		0			0
$709$	−22.2557	−	38.5481i	−0.835832	−	1.44770i	−0.893351	−	0.449359i	$-0.851653\pi$
$709$	−22.2557	−	38.5481i	−0.835832	−	1.44770i	0.0575196	−	0.998344i	$-0.481681\pi$
$710$	−5.85887	+	10.1479i	−0.219879	+	0.380842i
$711$		0			0
$712$	15.7698	+	27.3141i	0.590998	+	1.02364i
$713$	−37.3811			−1.39993
$714$		0			0
$715$	41.6342			1.55703
$716$	37.5048	+	64.9602i	1.40162	+	2.42768i
$717$		0			0
$718$	5.90304	−	10.2244i	0.220299	−	0.381570i
$719$	11.8983	+	20.6085i	0.443733	+	0.768567i	0.997963	−	0.0637960i	$-0.0203207\pi$
$719$	11.8983	+	20.6085i	0.443733	+	0.768567i	−0.554230	+	0.832363i	$0.686987\pi$
$720$		0			0
$721$	7.89327	+	7.73036i	0.293961	+	0.287894i
$722$	−2.28285			−0.0849589
$723$		0			0
$724$	−35.0491	+	60.7069i	−1.30259	+	2.25615i
$725$	−6.89521	+	11.9429i	−0.256082	+	0.443547i
$726$		0			0
$727$	−28.5209			−1.05778			−0.528891	−	0.848689i	$-0.677392\pi$
$727$	−28.5209			−1.05778			−0.528891	+	0.848689i	$0.677392\pi$
$728$	−34.9717	+	9.76256i	−1.29614	+	0.361824i
$729$		0			0
$730$	−13.7291	−	23.7795i	−0.508138	−	0.880120i
$731$	−12.9509	+	22.4317i	−0.479008	+	0.829666i
$732$		0			0
$733$	8.13938	+	14.0978i	0.300635	+	0.520715i	0.976280	−	0.216512i	$-0.0694681\pi$
$733$	8.13938	+	14.0978i	0.300635	+	0.520715i	−0.675645	+	0.737227i	$0.736135\pi$
$734$	−12.8475			−0.474211
$735$		0			0
$736$	33.6461			1.24021
$737$	5.54317	+	9.60105i	0.204185	+	0.353659i
$738$		0			0
$739$	−26.2459	+	45.4592i	−0.965470	+	1.67224i	−0.257121	+	0.966379i	$0.582774\pi$
$739$	−26.2459	+	45.4592i	−0.965470	+	1.67224i	−0.708348	+	0.705863i	$0.750559\pi$
$740$	−31.4713	−	54.5098i	−1.15691	−	2.00382i
$741$		0			0
$742$	53.3121	−	14.8824i	1.95715	−	0.546351i
$743$	31.9433			1.17189			0.585944	−	0.810352i	$-0.300724\pi$
$743$	31.9433			1.17189			0.585944	+	0.810352i	$0.300724\pi$
$744$		0			0
$745$	6.10261	−	10.5700i	0.223582	−	0.387256i
$746$	4.10292	−	7.10647i	0.150219	−	0.260186i
$747$		0			0
$748$	59.2414			2.16608
$749$	6.89456	+	6.75226i	0.251922	+	0.246722i
$750$		0			0
$751$	3.40492	+	5.89749i	0.124247	+	0.215202i	0.921438	−	0.388524i	$-0.127015\pi$
$751$	3.40492	+	5.89749i	0.124247	+	0.215202i	−0.797191	+	0.603727i	$0.793682\pi$
$752$	0.346290	−	0.599792i	0.0126279	−	0.0218721i
$753$		0			0
$754$	−52.8389	−	91.5197i	−1.92428	−	3.33295i
$755$	19.4987			0.709630
$756$		0			0
$757$	9.00239			0.327198			0.163599	−	0.986527i	$-0.447690\pi$
$757$	9.00239			0.327198			0.163599	+	0.986527i	$0.447690\pi$
$758$	10.0693	+	17.4405i	0.365732	+	0.633466i
$759$		0			0
$760$	−3.51940	+	6.09577i	−0.127662	+	0.221117i
$761$	2.58982	+	4.48569i	0.0938808	+	0.162606i	0.909141	−	0.416489i	$-0.136739\pi$
$761$	2.58982	+	4.48569i	0.0938808	+	0.162606i	−0.815260	+	0.579095i	$0.803406\pi$
$762$		0			0
$763$	9.32622	−	36.3164i	0.337632	−	1.31474i
$764$	34.4747			1.24725
$765$		0			0
$766$	35.7549	−	61.9293i	1.29188	−	2.23760i
$767$	−24.3435	+	42.1641i	−0.878992	+	1.52246i
$768$		0			0
$769$	41.5253			1.49744			0.748720	−	0.662886i	$-0.230669\pi$
$769$	41.5253			1.49744			0.748720	+	0.662886i	$0.230669\pi$
$770$	36.2033	+	35.4561i	1.30468	+	1.27775i
$771$		0			0
$772$	−28.9357	−	50.1181i	−1.04142	−	1.80379i
$773$	−1.41901	+	2.45780i	−0.0510382	+	0.0884008i	−0.890416	−	0.455148i	$-0.849586\pi$
$773$	−1.41901	+	2.45780i	−0.0510382	+	0.0884008i	0.839378	+	0.543549i	$0.182920\pi$
$774$		0			0
$775$	4.74765	+	8.22318i	0.170541	+	0.295385i
$776$	46.7944			1.67982
$777$		0			0
$778$	−0.561183			−0.0201194
$779$	−3.06568	−	5.30991i	−0.109839	−	0.190247i
$780$		0			0
$781$	−3.32376	+	5.75692i	−0.118933	+	0.205999i
$782$	−37.1759	−	64.3906i	−1.32941	−	2.30260i
$783$		0			0
$784$	0.672776	+	0.369941i	0.0240277	+	0.0132122i
$785$	−12.5635			−0.448411
$786$		0			0
$787$	20.7488	−	35.9379i	0.739614	−	1.28105i	−0.213056	−	0.977040i	$-0.568342\pi$
$787$	20.7488	−	35.9379i	0.739614	−	1.28105i	0.952669	−	0.304009i	$-0.0983251\pi$
$788$	−5.44736	+	9.43510i	−0.194054	+	0.336111i
$789$		0			0
$790$	74.9461			2.66646
$791$	−23.4639	+	6.55011i	−0.834282	+	0.232895i
$792$		0			0
$793$	−4.50563	−	7.80398i	−0.160000	−	0.277127i
$794$	−2.04921	+	3.54933i	−0.0727236	+	0.125961i
$795$		0			0
$796$	−0.178094	−	0.308467i	−0.00631236	−	0.0109333i
$797$	34.7178			1.22977			0.614884	−	0.788618i	$-0.289203\pi$
$797$	34.7178			1.22977			0.614884	+	0.788618i	$0.289203\pi$
$798$		0			0
$799$	−35.3376			−1.25016
$800$	−4.27329	−	7.40155i	−0.151084	−	0.261684i
$801$		0			0
$802$	27.9676	−	48.4412i	0.987569	−	1.71052i
$803$	−7.78859	−	13.4902i	−0.274853	−	0.476060i
$804$		0			0
$805$	9.74817	−	37.9595i	0.343578	−	1.33790i
$806$	−72.7638			−2.56299
$807$		0			0
$808$	15.0147	−	26.0062i	0.528214	−	0.914894i
$809$	−18.4335	+	31.9278i	−0.648087	+	1.12252i	0.335492	+	0.942043i	$0.391098\pi$
$809$	−18.4335	+	31.9278i	−0.648087	+	1.12252i	−0.983579	+	0.180477i	$0.942236\pi$
$810$		0			0
$811$	−45.4803			−1.59703			−0.798515	−	0.601974i	$-0.794381\pi$
$811$	−45.4803			−1.59703			−0.798515	+	0.601974i	$0.794381\pi$
$812$	19.7147	−	76.7693i	0.691851	−	2.69408i
$813$		0			0
$814$	−28.9728	−	50.1823i	−1.01549	−	1.75889i
$815$	−3.24660	+	5.62328i	−0.113724	+	0.196975i
$816$		0			0
$817$	−2.31417	−	4.00826i	−0.0809626	−	0.140231i
$818$	−61.8764			−2.16346
$819$		0			0
$820$	−50.1168			−1.75015
$821$	12.7761	+	22.1288i	0.445888	+	0.772301i	0.998114	−	0.0613939i	$-0.0195546\pi$
$821$	12.7761	+	22.1288i	0.445888	+	0.772301i	−0.552226	+	0.833695i	$0.686221\pi$
$822$		0			0
$823$	−3.77591	+	6.54008i	−0.131620	+	0.227973i	−0.924301	−	0.381664i	$-0.875351\pi$
$823$	−3.77591	+	6.54008i	−0.131620	+	0.227973i	0.792681	+	0.609636i	$0.208685\pi$
$824$	5.77403	+	10.0009i	0.201148	+	0.348398i
$825$		0			0
$826$	−57.0755	+	15.9330i	−1.98591	+	0.554379i
$827$	30.8901			1.07415			0.537077	−	0.843533i	$-0.319528\pi$
$827$	30.8901			1.07415			0.537077	+	0.843533i	$0.319528\pi$
$828$		0			0
$829$	−13.1893	+	22.8446i	−0.458084	+	0.793424i	−0.998860	−	0.0477425i	$-0.984797\pi$
$829$	−13.1893	+	22.8446i	−0.458084	+	0.793424i	0.540776	+	0.841167i	$0.318131\pi$
$830$	2.15956	−	3.74046i	0.0749593	−	0.129833i
$831$		0			0
$832$	64.4049			2.23284
$833$	−0.816867	−	39.1660i	−0.0283028	−	1.35702i
$834$		0			0
$835$	−2.47788	−	4.29181i	−0.0857506	−	0.148524i
$836$	−5.29285	+	9.16748i	−0.183057	+	0.317064i
$837$		0			0
$838$	28.0733	+	48.6244i	0.969776	+	1.67970i
$839$	2.55457			0.0881935			0.0440968	−	0.999027i	$-0.485959\pi$
$839$	2.55457			0.0881935			0.0440968	+	0.999027i	$0.485959\pi$
$840$		0			0
$841$	58.0208			2.00072
$842$	19.5402	+	33.8446i	0.673399	+	1.16636i
$843$		0			0
$844$	−18.7219	+	32.4272i	−0.644433	+	1.11619i
$845$	−14.7952	−	25.6261i	−0.508972	−	0.881565i
$846$		0			0
$847$	−0.254294	−	0.249046i	−0.00873765	−	0.00855731i
$848$	−1.00515			−0.0345171
$849$		0			0
$850$	−9.44320	+	16.3561i	−0.323899	+	0.561010i
$851$	−22.4077	+	38.8112i	−0.768125	+	1.33043i
$852$		0			0
$853$	−52.1083			−1.78416			−0.892078	−	0.451882i	$-0.850753\pi$
$853$	−52.1083			−1.78416			−0.892078	+	0.451882i	$0.850753\pi$
$854$	2.72805	−	10.6230i	0.0933518	−	0.363513i
$855$		0			0
$856$	5.04346	+	8.73553i	0.172382	+	0.298574i
$857$	−3.72754	+	6.45628i	−0.127330	+	0.220542i	−0.922641	−	0.385659i	$-0.873974\pi$
$857$	−3.72754	+	6.45628i	−0.127330	+	0.220542i	0.795311	+	0.606201i	$0.207307\pi$
$858$		0			0
$859$	14.9701	+	25.9289i	0.510772	+	0.884684i	0.999922	+	0.0124838i	$0.00397382\pi$
$859$	14.9701	+	25.9289i	0.510772	+	0.884684i	−0.489150	+	0.872200i	$0.662693\pi$
$860$	−37.8314			−1.29004
$861$		0			0
$862$	−44.8087			−1.52619
$863$	−7.19480	−	12.4618i	−0.244914	−	0.424204i	0.717193	−	0.696874i	$-0.245426\pi$
$863$	−7.19480	−	12.4618i	−0.244914	−	0.424204i	−0.962107	+	0.272671i	$0.912093\pi$
$864$		0			0
$865$	19.1777	−	33.2168i	0.652063	−	1.12941i
$866$	34.2536	+	59.3289i	1.16398	+	2.01608i
$867$		0			0
$868$	−38.9900	−	38.1853i	−1.32341	−	1.29609i
$869$	42.5172			1.44230
$870$		0			0
$871$	8.34504	−	14.4540i	0.282761	−	0.489756i
$872$	19.5956	−	33.9406i	0.663592	−	1.14937i
$873$		0			0
$874$	13.2858			0.449397
$875$	22.8421	−	6.37651i	0.772204	−	0.215566i
$876$		0			0
$877$	−27.3998	−	47.4579i	−0.925226	−	1.60254i	−0.791197	−	0.611561i	$-0.790542\pi$
$877$	−27.3998	−	47.4579i	−0.925226	−	1.60254i	−0.134029	−	0.990977i	$-0.542792\pi$
$878$	−13.2908	+	23.0203i	−0.448542	+	0.776898i
$879$		0			0
$880$	−0.460112	−	0.796937i	−0.0155104	−	0.0268647i
$881$	20.3805			0.686638			0.343319	−	0.939219i	$-0.388449\pi$
$881$	20.3805			0.686638			0.343319	+	0.939219i	$0.388449\pi$
$882$		0			0
$883$	−20.1615			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$883$	−20.1615			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$884$	−44.5929	−	77.2372i	−1.49982	−	2.59777i
$885$		0			0
$886$	22.0728	−	38.2312i	0.741549	−	1.28440i
$887$	−22.5022	−	38.9749i	−0.755549	−	1.30865i	−0.945101	−	0.326778i	$-0.894037\pi$
$887$	−22.5022	−	38.9749i	−0.755549	−	1.30865i	0.189552	−	0.981871i	$-0.439296\pi$
$888$		0			0
$889$	13.4249	−	3.74765i	0.450258	−	0.125692i
$890$	−66.2670			−2.22128
$891$		0			0
$892$	−22.2090	+	38.4671i	−0.743613	+	1.28797i
$893$	3.15720	−	5.46842i	0.105652	−	0.182994i
$894$		0			0
$895$	−59.4501			−1.98720
$896$	34.1477	+	33.4429i	1.14080	+	1.11725i
$897$		0			0
$898$	39.8329	+	68.9927i	1.32924	+	2.30231i
$899$	29.9588	−	51.8902i	0.999182	−	1.73063i
$900$		0			0
$901$	25.6431	+	44.4151i	0.854295	+	1.47968i
$902$	−46.1380			−1.53623
$903$		0			0
$904$	−25.4633			−0.846895
$905$	−27.7788	−	48.1142i	−0.923398	−	1.59937i
$906$		0			0
$907$	12.9338	−	22.4020i	0.429459	−	0.743846i	−0.567366	−	0.823466i	$-0.692037\pi$
$907$	12.9338	−	22.4020i	0.429459	−	0.743846i	0.996825	+	0.0796203i	$0.0253708\pi$
$908$	22.1433	+	38.3532i	0.734850	+	1.27280i
$909$		0			0
$910$	18.9752	−	73.8897i	0.629022	−	2.44942i
$911$	8.50711			0.281853			0.140927	−	0.990020i	$-0.454992\pi$
$911$	8.50711			0.281853			0.140927	+	0.990020i	$0.454992\pi$
$912$		0			0
$913$	1.22513	−	2.12198i	0.0405457	−	0.0702273i
$914$	−3.55218	+	6.15255i	−0.117496	+	0.203508i
$915$		0			0
$916$	44.8455			1.48174
$917$	15.0015	+	14.6919i	0.495395	+	0.485170i
$918$		0			0
$919$	−13.8584	−	24.0034i	−0.457146	−	0.791800i	0.541663	−	0.840596i	$-0.317795\pi$
$919$	−13.8584	−	24.0034i	−0.457146	−	0.791800i	−0.998809	+	0.0487956i	$0.984462\pi$
$920$	20.4822	−	35.4762i	0.675279	−	1.16962i
$921$		0			0
$922$	−24.7202	−	42.8166i	−0.814116	−	1.41009i
$923$	10.0076			0.329404
$924$		0			0
$925$	11.3837			0.374294
$926$	−31.3025	−	54.2175i	−1.02866	−	1.78170i
$927$		0			0
$928$	−26.9655	+	46.7055i	−0.885184	+	1.53318i
$929$	−9.84267	−	17.0480i	−0.322928	−	0.559327i	0.658163	−	0.752875i	$-0.271334\pi$
$929$	−9.84267	−	17.0480i	−0.322928	−	0.559327i	−0.981091	+	0.193548i	$0.938000\pi$
$930$		0			0
$931$	6.13384	+	3.37283i	0.201029	+	0.110540i
$932$	54.5418			1.78658
$933$		0			0
$934$	31.1090	−	53.8824i	1.01792	−	1.76309i
$935$	−23.4764	+	40.6623i	−0.767759	+	1.32980i
$936$		0			0
$937$	39.0825			1.27677			0.638385	−	0.769717i	$-0.279603\pi$
$937$	39.0825			1.27677			0.638385	+	0.769717i	$0.279603\pi$
$938$	19.5657	−	5.46189i	0.638843	−	0.178337i
$939$		0			0
$940$	−25.8064	−	44.6980i	−0.841713	−	1.45789i
$941$	23.0669	−	39.9530i	0.751958	−	1.30243i	−0.194914	−	0.980820i	$-0.562443\pi$
$941$	23.0669	−	39.9530i	0.751958	−	1.30243i	0.946872	−	0.321610i	$-0.104224\pi$
$942$		0			0
$943$	17.8417	+	30.9027i	0.581005	+	1.00633i
$944$	1.07611			0.0350244
$945$		0			0
$946$	−34.8279			−1.13235
$947$	4.92484	+	8.53007i	0.160036	+	0.277190i	0.934881	−	0.354961i	$-0.115506\pi$
$947$	4.92484	+	8.53007i	0.160036	+	0.277190i	−0.774846	+	0.632151i	$0.782172\pi$
$948$		0			0
$949$	−11.7254	+	20.3091i	−0.380624	+	0.659260i
$950$	−1.68738	−	2.92263i	−0.0547459	−	0.0948227i
$951$		0			0
$952$	10.1849	−	39.6601i	0.330094	−	1.28539i
$953$	−23.5275			−0.762131			−0.381066	−	0.924548i	$-0.624443\pi$
$953$	−23.5275			−0.762131			−0.381066	+	0.924548i	$0.624443\pi$
$954$		0			0
$955$	−13.6617	+	23.6628i	−0.442083	+	0.765711i
$956$	4.40528	−	7.63016i	0.142477	−	0.246777i
$957$		0			0
$958$	−81.2669			−2.62561
$959$	−5.39402	+	21.0044i	−0.174182	+	0.678267i
$960$		0			0
$961$	−5.12794	−	8.88186i	−0.165418	−	0.286512i
$962$	−43.6175	+	75.5476i	−1.40628	+	2.43575i
$963$		0			0
$964$	−15.9481	−	27.6229i	−0.513653	−	0.889673i
$965$	45.8669			1.47651
$966$		0			0
$967$	19.3664			0.622783			0.311391	−	0.950282i	$-0.399205\pi$
$967$	19.3664			0.622783			0.311391	+	0.950282i	$0.399205\pi$
$968$	−0.186019	−	0.322195i	−0.00597889	−	0.0103557i
$969$		0			0
$970$	−49.1592	+	85.1462i	−1.57841	+	2.73388i
$971$	−19.5531	−	33.8669i	−0.627488	−	1.08684i	−0.988054	−	0.154108i	$-0.950750\pi$
$971$	−19.5531	−	33.8669i	−0.627488	−	1.08684i	0.360566	−	0.932734i	$-0.382584\pi$
$972$		0			0
$973$	−23.4665	+	6.55081i	−0.752300	+	0.210009i
$974$	−49.2192			−1.57709
$975$		0			0
$976$	−0.0995861	+	0.172488i	−0.00318767	+	0.00552121i
$977$	21.6273	−	37.4595i	0.691917	−	1.19844i	−0.279291	−	0.960206i	$-0.590100\pi$
$977$	21.6273	−	37.4595i	0.691917	−	1.19844i	0.971209	−	0.238230i	$-0.0765671\pi$
$978$		0			0
$979$	−37.5935			−1.20149
$980$	48.9440	−	29.6355i	1.56346	−	0.946670i
$981$		0			0
$982$	−4.63493	−	8.02793i	−0.147907	−	0.256182i
$983$	−0.0719590	+	0.124637i	−0.00229513	+	0.00397529i	−0.867171	−	0.498011i	$-0.834064\pi$
$983$	−0.0719590	+	0.124637i	−0.00229513	+	0.00397529i	0.864876	+	0.501986i	$0.167397\pi$
$984$		0			0
$985$	−4.31739	−	7.47794i	−0.137564	−	0.238267i
$986$	119.178			3.79539
$987$		0			0
$988$	15.9364			0.507004
$989$	13.4680	+	23.3273i	0.428259	+	0.741766i
$990$		0			0
$991$	−6.34137	+	10.9836i	−0.201440	+	0.348905i	−0.948993	−	0.315298i	$-0.897896\pi$
$991$	−6.34137	+	10.9836i	−0.201440	+	0.348905i	0.747552	+	0.664203i	$0.231229\pi$
$992$	18.5669	+	32.1588i	0.589499	+	1.02104i
$993$		0			0
$994$	8.70218	+	8.52258i	0.276016	+	0.270320i
$995$	0.282302			0.00894958
$996$		0			0
$997$	11.1801	−	19.3645i	0.354078	−	0.613281i	−0.632882	−	0.774248i	$-0.718128\pi$
$997$	11.1801	−	19.3645i	0.354078	−	0.613281i	0.986960	+	0.160967i	$0.0514614\pi$
$998$	−15.6172	+	27.0497i	−0.494353	+	0.856245i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.m.172.7		16
3.2	odd	2		399.2.j.g.172.2	yes	16
7.2	even	3	inner	1197.2.j.m.856.7		16
7.3	odd	6		8379.2.a.cq.1.2		8
7.4	even	3		8379.2.a.cr.1.2		8
21.2	odd	6		399.2.j.g.58.2	✓	16
21.11	odd	6		2793.2.a.bm.1.7		8
21.17	even	6		2793.2.a.bn.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.2	✓	16	21.2	odd	6
399.2.j.g.172.2	yes	16	3.2	odd	2
1197.2.j.m.172.7		16	1.1	even	1	trivial
1197.2.j.m.856.7		16	7.2	even	3	inner
2793.2.a.bm.1.7		8	21.11	odd	6
2793.2.a.bn.1.7		8	21.17	even	6
8379.2.a.cq.1.2		8	7.3	odd	6
8379.2.a.cr.1.2		8	7.4	even	3

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14143 + 1.97701i) q^{2} +(-1.60570 + 2.78116i) q^{4} +(-1.27263 - 2.20425i) q^{5} +(-2.54832 + 0.711380i) q^{7} -2.76546 q^{8} +O(q^{10})\)	\(q+(1.14143 + 1.97701i) q^{2} +(-1.60570 + 2.78116i) q^{4} +(-1.27263 - 2.20425i) q^{5} +(-2.54832 + 0.711380i) q^{7} -2.76546 q^{8} +(2.90522 - 5.03198i) q^{10} +(1.64814 - 2.85466i) q^{11} -4.96243 q^{13} +(-4.31512 - 4.22606i) q^{14} +(0.0548414 + 0.0949880i) q^{16} +(2.79818 - 4.84659i) q^{17} +(0.500000 + 0.866025i) q^{19} +8.17384 q^{20} +7.52492 q^{22} +(-2.90990 - 5.04010i) q^{23} +(-0.739156 + 1.28026i) q^{25} +(-5.66425 - 9.81077i) q^{26} +(2.11339 - 8.22955i) q^{28} +9.32850 q^{29} +(3.21154 - 5.56255i) q^{31} +(-2.89065 + 5.00676i) q^{32} +12.7757 q^{34} +(4.81112 + 4.71182i) q^{35} +(-3.85024 - 6.66882i) q^{37} +(-1.14143 + 1.97701i) q^{38} +(3.51940 + 6.09577i) q^{40} -6.13136 q^{41} -4.62835 q^{43} +(5.29285 + 9.16748i) q^{44} +(6.64288 - 11.5058i) q^{46} +(-3.15720 - 5.46842i) q^{47} +(5.98788 - 3.62565i) q^{49} -3.37477 q^{50} +(7.96820 - 13.8013i) q^{52} +(-4.58210 + 7.93643i) q^{53} -8.38987 q^{55} +(7.04728 - 1.96729i) q^{56} +(10.6478 + 18.4425i) q^{58} +(4.90555 - 8.49667i) q^{59} +(0.907947 + 1.57261i) q^{61} +14.6629 q^{62} -12.9785 q^{64} +(6.31533 + 10.9385i) q^{65} +(-1.68164 + 2.91269i) q^{67} +(8.98609 + 15.5644i) q^{68} +(-3.82377 + 14.8898i) q^{70} -2.01667 q^{71} +(2.36284 - 4.09256i) q^{73} +(8.78953 - 15.2239i) q^{74} -3.21141 q^{76} +(-2.16924 + 8.44705i) q^{77} +(6.44927 + 11.1705i) q^{79} +(0.139585 - 0.241769i) q^{80} +(-6.99849 - 12.1217i) q^{82} +0.743338 q^{83} -14.2442 q^{85} +(-5.28291 - 9.15027i) q^{86} +(-4.55787 + 7.89445i) q^{88} +(-5.70242 - 9.87688i) q^{89} +(12.6459 - 3.53018i) q^{91} +18.6898 q^{92} +(7.20741 - 12.4836i) q^{94} +(1.27263 - 2.20425i) q^{95} -16.9210 q^{97} +(14.0026 + 7.69967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

Introduction

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