LMFDB - Embedded newform 184.2.i.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,2,Mod(9,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("184.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.i (of order $11$, degree $10$, 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:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	184.9
Dual form			184.2.i.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63153 - 1.88288i) q^{3} +(-0.385137 - 2.67869i) q^{5} +(-1.44647 + 3.16732i) q^{7} +(-0.456422 + 3.17448i) q^{9} +O(q^{10})$	\(q+(-1.63153 - 1.88288i) q^{3} +(-0.385137 - 2.67869i) q^{5} +(-1.44647 + 3.16732i) q^{7} +(-0.456422 + 3.17448i) q^{9} +(-4.75524 - 1.39626i) q^{11} +(-0.641271 - 1.40419i) q^{13} +(-4.41529 + 5.09552i) q^{15} +(-1.64693 - 1.05842i) q^{17} +(3.90366 - 2.50873i) q^{19} +(8.32364 - 2.44404i) q^{21} +(1.16577 - 4.65199i) q^{23} +(-2.22957 + 0.654662i) q^{25} +(0.434117 - 0.278990i) q^{27} +(0.0668418 + 0.0429566i) q^{29} +(4.56621 - 5.26969i) q^{31} +(5.12930 + 11.2316i) q^{33} +(9.04135 + 2.65478i) q^{35} +(-1.64030 + 11.4085i) q^{37} +(-1.59767 + 3.49841i) q^{39} +(-1.27547 - 8.87110i) q^{41} +(-6.41438 - 7.40258i) q^{43} +8.67923 q^{45} +7.58145 q^{47} +(-3.35562 - 3.87260i) q^{49} +(0.694133 + 4.82780i) q^{51} +(3.78454 - 8.28699i) q^{53} +(-1.90874 + 13.2756i) q^{55} +(-11.0926 - 3.25707i) q^{57} +(3.40314 + 7.45184i) q^{59} +(5.31982 - 6.13940i) q^{61} +(-9.39440 - 6.03742i) q^{63} +(-3.51440 + 2.25857i) q^{65} +(-3.11750 + 0.915379i) q^{67} +(-10.6611 + 5.39483i) q^{69} +(4.21244 - 1.23688i) q^{71} +(-12.5238 + 8.04857i) q^{73} +(4.87026 + 3.12992i) q^{75} +(11.3007 - 13.0417i) q^{77} +(-2.37381 - 5.19793i) q^{79} +(7.99807 + 2.34844i) q^{81} +(-0.0660414 + 0.459328i) q^{83} +(-2.20087 + 4.81924i) q^{85} +(-0.0281720 - 0.195940i) q^{87} +(1.26661 + 1.46175i) q^{89} +5.37509 q^{91} -17.3721 q^{93} +(-8.22354 - 9.49048i) q^{95} +(0.241080 + 1.67675i) q^{97} +(6.60281 - 14.4581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9	$ 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9} + 2 q^{11} - 2 q^{15} - 22 q^{17} + 3 q^{19} + 2 q^{21} + q^{23} + 13 q^{25} - 31 q^{27} + 7 q^{29} + 18 q^{31} - 8 q^{33} + 41 q^{35} - 62 q^{37} + 6 q^{39} - 15 q^{41} - 47 q^{43} + 8 q^{45} - 72 q^{47} - 16 q^{49} - 7 q^{51} - 43 q^{53} - 9 q^{55} - 42 q^{57} - 11 q^{59} + 57 q^{61} - 62 q^{63} + 14 q^{65} - 27 q^{67} - 22 q^{69} + 48 q^{71} - 12 q^{73} + 87 q^{75} - 3 q^{77} + 8 q^{79} + 123 q^{81} - 18 q^{83} + 54 q^{85} + 137 q^{87} - 23 q^{89} + 142 q^{91} - 110 q^{93} + 119 q^{95} + 47 q^{97} - 17 q^{99}+O(q^{100}) $ 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9 + 2 * q^11 - 2 * q^15 - 22 * q^17 + 3 * q^19 + 2 * q^21 + q^23 + 13 * q^25 - 31 * q^27 + 7 * q^29 + 18 * q^31 - 8 * q^33 + 41 * q^35 - 62 * q^37 + 6 * q^39 - 15 * q^41 - 47 * q^43 + 8 * q^45 - 72 * q^47 - 16 * q^49 - 7 * q^51 - 43 * q^53 - 9 * q^55 - 42 * q^57 - 11 * q^59 + 57 * q^61 - 62 * q^63 + 14 * q^65 - 27 * q^67 - 22 * q^69 + 48 * q^71 - 12 * q^73 + 87 * q^75 - 3 * q^77 + 8 * q^79 + 123 * q^81 - 18 * q^83 + 54 * q^85 + 137 * q^87 - 23 * q^89 + 142 * q^91 - 110 * q^93 + 119 * q^95 + 47 * q^97 - 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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
$3$	−1.63153	−	1.88288i	−0.941962	−	1.08708i	−0.996072	−	0.0885476i	$-0.971777\pi$
$3$	−1.63153	−	1.88288i	−0.941962	−	1.08708i	0.0541095	−	0.998535i	$-0.482768\pi$
$4$		0			0
$5$	−0.385137	−	2.67869i	−0.172239	−	1.19795i	−0.874141	−	0.485672i	$-0.838575\pi$
$5$	−0.385137	−	2.67869i	−0.172239	−	1.19795i	0.701902	−	0.712273i	$-0.252334\pi$
$6$		0			0
$7$	−1.44647	+	3.16732i	−0.546713	+	1.19713i	0.411587	+	0.911370i	$0.364975\pi$
$7$	−1.44647	+	3.16732i	−0.546713	+	1.19713i	−0.958300	+	0.285764i	$0.907753\pi$
$8$		0			0
$9$	−0.456422	+	3.17448i	−0.152141	+	1.05816i
$10$		0			0
$11$	−4.75524	−	1.39626i	−1.43376	−	0.420990i	−0.529622	−	0.848234i	$-0.677666\pi$
$11$	−4.75524	−	1.39626i	−1.43376	−	0.420990i	−0.904136	+	0.427244i	$0.859484\pi$
$12$		0			0
$13$	−0.641271	−	1.40419i	−0.177857	−	0.389452i	0.799617	−	0.600511i	$-0.205036\pi$
$13$	−0.641271	−	1.40419i	−0.177857	−	0.389452i	−0.977473	+	0.211059i	$0.932309\pi$
$14$		0			0
$15$	−4.41529	+	5.09552i	−1.14002	+	1.31566i
$16$		0			0
$17$	−1.64693	−	1.05842i	−0.399438	−	0.256704i	0.325465	−	0.945554i	$-0.394479\pi$
$17$	−1.64693	−	1.05842i	−0.399438	−	0.256704i	−0.724903	+	0.688851i	$0.758116\pi$
$18$		0			0
$19$	3.90366	−	2.50873i	0.895561	−	0.575542i	−0.00990999	−	0.999951i	$-0.503154\pi$
$19$	3.90366	−	2.50873i	0.895561	−	0.575542i	0.905471	+	0.424409i	$0.139518\pi$
$20$		0			0
$21$	8.32364	−	2.44404i	1.81637	−	0.533334i
$22$		0			0
$23$	1.16577	−	4.65199i	0.243080	−	0.970006i
$23$	1.16577	−	4.65199i	0.243080	−	0.970006i
$24$		0			0
$25$	−2.22957	+	0.654662i	−0.445914	+	0.130932i
$26$		0			0
$27$	0.434117	−	0.278990i	0.0835458	−	0.0536916i
$28$		0			0
$29$	0.0668418	+	0.0429566i	0.0124122	+	0.00797685i	0.546832	−	0.837242i	$-0.315834\pi$
$29$	0.0668418	+	0.0429566i	0.0124122	+	0.00797685i	−0.534420	+	0.845219i	$0.679470\pi$
$30$		0			0
$31$	4.56621	−	5.26969i	0.820116	−	0.946464i	−0.179186	−	0.983815i	$-0.557347\pi$
$31$	4.56621	−	5.26969i	0.820116	−	0.946464i	0.999302	+	0.0373511i	$0.0118920\pi$
$32$		0			0
$33$	5.12930	+	11.2316i	0.892896	+	1.95517i
$34$		0			0
$35$	9.04135	+	2.65478i	1.52827	+	0.448740i
$36$		0			0
$37$	−1.64030	+	11.4085i	−0.269664	+	1.87555i	0.181904	+	0.983316i	$0.441774\pi$
$37$	−1.64030	+	11.4085i	−0.269664	+	1.87555i	−0.451568	+	0.892237i	$0.649135\pi$
$38$		0			0
$39$	−1.59767	+	3.49841i	−0.255832	+	0.560193i
$40$		0			0
$41$	−1.27547	−	8.87110i	−0.199195	−	1.38543i	−0.806627	−	0.591061i	$-0.798709\pi$
$41$	−1.27547	−	8.87110i	−0.199195	−	1.38543i	0.607432	−	0.794372i	$-0.292200\pi$
$42$		0			0
$43$	−6.41438	−	7.40258i	−0.978183	−	1.12888i	−0.991648	−	0.128974i	$-0.958832\pi$
$43$	−6.41438	−	7.40258i	−0.978183	−	1.12888i	0.0134648	−	0.999909i	$-0.495714\pi$
$44$		0			0
$45$	8.67923			1.29382
$46$		0			0
$47$	7.58145			1.10587			0.552934	−	0.833225i	$-0.313508\pi$
$47$	7.58145			1.10587			0.552934	+	0.833225i	$0.313508\pi$
$48$		0			0
$49$	−3.35562	−	3.87260i	−0.479375	−	0.553228i
$50$		0			0
$51$	0.694133	+	4.82780i	0.0971981	+	0.676028i
$52$		0			0
$53$	3.78454	−	8.28699i	0.519846	−	1.13830i	−0.449651	−	0.893204i	$-0.648452\pi$
$53$	3.78454	−	8.28699i	0.519846	−	1.13830i	0.969498	−	0.245101i	$-0.0788210\pi$
$54$		0			0
$55$	−1.90874	+	13.2756i	−0.257374	+	1.79008i
$56$		0			0
$57$	−11.0926	−	3.25707i	−1.46925	−	0.431410i
$58$		0			0
$59$	3.40314	+	7.45184i	0.443051	+	0.970147i	0.991028	+	0.133653i	$0.0426709\pi$
$59$	3.40314	+	7.45184i	0.443051	+	0.970147i	−0.547977	+	0.836493i	$0.684602\pi$
$60$		0			0
$61$	5.31982	−	6.13940i	0.681133	−	0.786070i	−0.304942	−	0.952371i	$-0.598637\pi$
$61$	5.31982	−	6.13940i	0.681133	−	0.786070i	0.986075	+	0.166301i	$0.0531825\pi$
$62$		0			0
$63$	−9.39440	−	6.03742i	−1.18358	−	0.760643i
$64$		0			0
$65$	−3.51440	+	2.25857i	−0.435908	+	0.280141i
$66$		0			0
$67$	−3.11750	+	0.915379i	−0.380863	+	0.111831i	−0.466559	−	0.884490i	$-0.654507\pi$
$67$	−3.11750	+	0.915379i	−0.380863	+	0.111831i	0.0856967	+	0.996321i	$0.472688\pi$
$68$		0			0
$69$	−10.6611	+	5.39483i	−1.28345	+	0.649461i
$70$		0			0
$71$	4.21244	−	1.23688i	0.499924	−	0.146791i	−0.0220421	−	0.999757i	$-0.507017\pi$
$71$	4.21244	−	1.23688i	0.499924	−	0.146791i	0.521966	+	0.852966i	$0.325199\pi$
$72$		0			0
$73$	−12.5238	+	8.04857i	−1.46580	+	0.942013i	−0.467486	+	0.884001i	$0.654840\pi$
$73$	−12.5238	+	8.04857i	−1.46580	+	0.942013i	−0.998316	+	0.0580126i	$0.981524\pi$
$74$		0			0
$75$	4.87026	+	3.12992i	0.562369	+	0.361413i
$76$		0			0
$77$	11.3007	−	13.0417i	1.28784	−	1.48624i
$78$		0			0
$79$	−2.37381	−	5.19793i	−0.267075	−	0.584812i	0.727816	−	0.685773i	$-0.240536\pi$
$79$	−2.37381	−	5.19793i	−0.267075	−	0.584812i	−0.994890	+	0.100961i	$0.967808\pi$
$80$		0			0
$81$	7.99807	+	2.34844i	0.888674	+	0.260938i
$82$		0			0
$83$	−0.0660414	+	0.459328i	−0.00724899	+	0.0504178i	−0.993125	−	0.117060i	$-0.962653\pi$
$83$	−0.0660414	+	0.459328i	−0.00724899	+	0.0504178i	0.985876	+	0.167478i	$0.0535622\pi$
$84$		0			0
$85$	−2.20087	+	4.81924i	−0.238718	+	0.522720i
$86$		0			0
$87$	−0.0281720	−	0.195940i	−0.00302035	−	0.0210070i
$88$		0			0
$89$	1.26661	+	1.46175i	0.134261	+	0.154945i	0.818899	−	0.573938i	$-0.194585\pi$
$89$	1.26661	+	1.46175i	0.134261	+	0.154945i	−0.684638	+	0.728883i	$0.740040\pi$
$90$		0			0
$91$	5.37509			0.563462
$92$		0			0
$93$	−17.3721			−1.80140
$94$		0			0
$95$	−8.22354	−	9.49048i	−0.843718	−	0.973702i
$96$		0			0
$97$	0.241080	+	1.67675i	0.0244779	+	0.170248i	0.998393	−	0.0566637i	$-0.0180463\pi$
$97$	0.241080	+	1.67675i	0.0244779	+	0.170248i	−0.973915	+	0.226911i	$0.927137\pi$
$98$		0			0
$99$	6.60281	−	14.4581i	0.663607	−	1.45310i
$100$		0			0
$101$	−0.556037	+	3.86733i	−0.0553278	+	0.384813i	0.943277	+	0.332007i	$0.107726\pi$
$101$	−0.556037	+	3.86733i	−0.0553278	+	0.384813i	−0.998605	+	0.0528064i	$0.983183\pi$
$102$		0			0
$103$	4.72149	+	1.38635i	0.465222	+	0.136602i	0.505939	−	0.862569i	$-0.331146\pi$
$103$	4.72149	+	1.38635i	0.465222	+	0.136602i	−0.0407169	+	0.999171i	$0.512964\pi$
$104$		0			0
$105$	−9.75257	−	21.3551i	−0.951753	−	2.08405i
$106$		0			0
$107$	−7.64209	+	8.81945i	−0.738789	+	0.852608i	−0.993432	−	0.114427i	$-0.963497\pi$
$107$	−7.64209	+	8.81945i	−0.738789	+	0.852608i	0.254643	+	0.967035i	$0.418042\pi$
$108$		0			0
$109$	−0.770219	−	0.494990i	−0.0737736	−	0.0474114i	0.503234	−	0.864150i	$-0.332143\pi$
$109$	−0.770219	−	0.494990i	−0.0737736	−	0.0474114i	−0.577008	+	0.816739i	$0.695780\pi$
$110$		0			0
$111$	24.1571	−	15.5249i	2.29289	−	1.47355i
$112$		0			0
$113$	−16.1649	+	4.74646i	−1.52067	+	0.446509i	−0.932180	−	0.361996i	$-0.882096\pi$
$113$	−16.1649	+	4.74646i	−1.52067	+	0.446509i	−0.588490	+	0.808504i	$0.700277\pi$
$114$		0			0
$115$	−12.9102	−	1.33109i	−1.20388	−	0.124125i
$116$		0			0
$117$	4.75026	−	1.39480i	0.439161	−	0.128949i
$118$		0			0
$119$	5.73457	−	3.68538i	0.525687	−	0.337838i
$120$		0			0
$121$	11.4090	+	7.33209i	1.03718	+	0.666554i
$122$		0			0
$123$	−14.6223	+	16.8750i	−1.31845	+	1.52157i
$124$		0			0
$125$	−3.00872	−	6.58819i	−0.269109	−	0.589265i
$126$		0			0
$127$	0.927036	+	0.272202i	0.0822611	+	0.0241540i	0.322604	−	0.946534i	$-0.395442\pi$
$127$	0.927036	+	0.272202i	0.0822611	+	0.0241540i	−0.240343	+	0.970688i	$0.577260\pi$
$128$		0			0
$129$	−3.47297	+	24.1550i	−0.305778	+	2.12673i
$130$		0			0
$131$	0.361581	−	0.791752i	0.0315915	−	0.0691757i	−0.893178	−	0.449702i	$-0.851530\pi$
$131$	0.361581	−	0.791752i	0.0315915	−	0.0691757i	0.924770	+	0.380527i	$0.124257\pi$
$132$		0			0
$133$	2.29944	+	15.9929i	0.199386	+	1.38676i
$134$		0			0
$135$	−0.914521	−	1.05541i	−0.0787094	−	0.0908355i
$136$		0			0
$137$	−3.08371			−0.263459			−0.131730	−	0.991286i	$-0.542053\pi$
$137$	−3.08371			−0.263459			−0.131730	+	0.991286i	$0.542053\pi$
$138$		0			0
$139$	4.17897			0.354456			0.177228	−	0.984170i	$-0.443287\pi$
$139$	4.17897			0.354456			0.177228	+	0.984170i	$0.443287\pi$
$140$		0			0
$141$	−12.3693	−	14.2750i	−1.04169	−	1.20217i
$142$		0			0
$143$	1.08878	+	7.57263i	0.0910484	+	0.633255i
$144$		0			0
$145$	0.0893242	−	0.195593i	0.00741797	−	0.0162431i
$146$		0			0
$147$	−1.81685	+	12.6365i	−0.149852	+	1.04224i
$148$		0			0
$149$	10.6800	+	3.13592i	0.874936	+	0.256904i	0.688213	−	0.725508i	$-0.258395\pi$
$149$	10.6800	+	3.13592i	0.874936	+	0.256904i	0.186723	+	0.982413i	$0.440213\pi$
$150$		0			0
$151$	0.475271	+	1.04070i	0.0386770	+	0.0846909i	0.927984	−	0.372619i	$-0.121540\pi$
$151$	0.475271	+	1.04070i	0.0386770	+	0.0846909i	−0.889307	+	0.457310i	$0.848813\pi$
$152$		0			0
$153$	4.11161	−	4.74506i	0.332404	−	0.383615i
$154$		0			0
$155$	−15.8745	−	10.2019i	−1.27507	−	0.819436i
$156$		0			0
$157$	−0.797016	+	0.512211i	−0.0636088	+	0.0408789i	−0.572059	−	0.820213i	$-0.693855\pi$
$157$	−0.797016	+	0.512211i	−0.0636088	+	0.0408789i	0.508450	+	0.861092i	$0.330219\pi$
$158$		0			0
$159$	−21.7780	+	6.39460i	−1.72711	+	0.507125i
$160$		0			0
$161$	13.0481	+	10.4213i	1.02833	+	0.821315i
$162$		0			0
$163$	21.9850	−	6.45537i	1.72200	−	0.505624i	0.736662	−	0.676261i	$-0.236401\pi$
$163$	21.9850	−	6.45537i	1.72200	−	0.505624i	0.985334	+	0.170637i	$0.0545826\pi$
$164$		0			0
$165$	28.1105	−	18.0655i	2.18840	−	1.40640i
$166$		0			0
$167$	7.44900	+	4.78718i	0.576421	+	0.370443i	0.796133	−	0.605121i	$-0.206875\pi$
$167$	7.44900	+	4.78718i	0.576421	+	0.370443i	−0.219712	+	0.975565i	$0.570512\pi$
$168$		0			0
$169$	6.95268	−	8.02382i	0.534821	−	0.617217i
$170$		0			0
$171$	6.18220	+	13.5371i	0.472765	+	1.03521i
$172$		0			0
$173$	14.5861	+	4.28287i	1.10896	+	0.325620i	0.784407	−	0.620247i	$-0.212967\pi$
$173$	14.5861	+	4.28287i	1.10896	+	0.325620i	0.324555	+	0.945867i	$0.394786\pi$
$174$		0			0
$175$	1.15148	−	8.00872i	0.0870437	−	0.605402i
$176$		0			0
$177$	8.47862	−	18.5656i	0.637292	−	1.39548i
$178$		0			0
$179$	−3.17654	−	22.0934i	−0.237426	−	1.65133i	−0.664625	−	0.747177i	$-0.731409\pi$
$179$	−3.17654	−	22.0934i	−0.237426	−	1.65133i	0.427199	−	0.904158i	$-0.359500\pi$
$180$		0			0
$181$	8.73880	+	10.0851i	0.649550	+	0.749620i	0.981033	−	0.193841i	$-0.0620945\pi$
$181$	8.73880	+	10.0851i	0.649550	+	0.749620i	−0.331483	+	0.943461i	$0.607549\pi$
$182$		0			0
$183$	−20.2392			−1.49612
$184$		0			0
$185$	31.1917			2.29326
$186$		0			0
$187$	6.35370	+	7.33256i	0.464629	+	0.536210i
$188$		0			0
$189$	0.255715	+	1.77854i	0.0186005	+	0.129369i
$190$		0			0
$191$	−4.80508	+	10.5217i	−0.347683	+	0.761320i	0.652311	+	0.757951i	$0.273800\pi$
$191$	−4.80508	+	10.5217i	−0.347683	+	0.761320i	−0.999994	+	0.00336891i	$0.998928\pi$
$192$		0			0
$193$	2.03482	−	14.1524i	0.146469	−	1.01872i	−0.775471	−	0.631383i	$-0.782488\pi$
$193$	2.03482	−	14.1524i	0.146469	−	1.01872i	0.921940	−	0.387332i	$-0.126603\pi$
$194$		0			0
$195$	9.98646	+	2.93229i	0.715145	+	0.209986i
$196$		0			0
$197$	−5.89808	−	12.9150i	−0.420221	−	0.920155i	−0.994814	−	0.101716i	$-0.967567\pi$
$197$	−5.89808	−	12.9150i	−0.420221	−	0.920155i	0.574593	−	0.818439i	$-0.305160\pi$
$198$		0			0
$199$	4.35808	−	5.02949i	0.308936	−	0.356531i	−0.579956	−	0.814648i	$-0.696930\pi$
$199$	4.35808	−	5.02949i	0.308936	−	0.356531i	0.888892	+	0.458117i	$0.151476\pi$
$200$		0			0
$201$	6.80983	+	4.37641i	0.480328	+	0.308688i
$202$		0			0
$203$	−0.232742	+	0.149574i	−0.0163353	+	0.0104980i
$204$		0			0
$205$	−23.2717	+	6.83318i	−1.62536	+	0.477250i
$206$		0			0
$207$	14.2356	+	5.82399i	0.989440	+	0.404795i
$208$		0			0
$209$	−22.0657	+	6.47907i	−1.52631	+	0.448166i
$210$		0			0
$211$	−13.9118	+	8.94059i	−0.957730	+	0.615496i	−0.923369	−	0.383914i	$-0.874576\pi$
$211$	−13.9118	+	8.94059i	−0.957730	+	0.615496i	−0.0343612	+	0.999409i	$0.510940\pi$
$212$		0			0
$213$	−9.20161	−	5.91352i	−0.630484	−	0.405188i
$214$		0			0
$215$	−17.3588	+	20.0331i	−1.18386	+	1.36625i
$216$		0			0
$217$	10.0859	+	22.0851i	0.684677	+	1.49923i
$218$		0			0
$219$	35.5874	+	10.4494i	2.40478	+	0.706106i
$220$		0			0
$221$	−0.430088	+	2.99133i	−0.0289308	+	0.201218i
$222$		0			0
$223$	1.66966	−	3.65605i	0.111809	−	0.244827i	−0.845453	−	0.534050i	$-0.820669\pi$
$223$	1.66966	−	3.65605i	0.111809	−	0.244827i	0.957262	+	0.289222i	$0.0933967\pi$
$224$		0			0
$225$	−1.06059	−	7.37654i	−0.0707057	−	0.491769i
$226$		0			0
$227$	−8.93394	−	10.3103i	−0.592967	−	0.684320i	0.377374	−	0.926061i	$-0.376827\pi$
$227$	−8.93394	−	10.3103i	−0.592967	−	0.684320i	−0.970341	+	0.241741i	$0.922282\pi$
$228$		0			0
$229$	2.39057			0.157973			0.0789867	−	0.996876i	$-0.474832\pi$
$229$	2.39057			0.157973			0.0789867	+	0.996876i	$0.474832\pi$
$230$		0			0
$231$	−42.9934			−2.82876
$232$		0			0
$233$	−1.13018	−	1.30429i	−0.0740403	−	0.0854471i	0.717521	−	0.696537i	$-0.245277\pi$
$233$	−1.13018	−	1.30429i	−0.0740403	−	0.0854471i	−0.791561	+	0.611090i	$0.790731\pi$
$234$		0			0
$235$	−2.91990	−	20.3083i	−0.190473	−	1.32477i
$236$		0			0
$237$	−5.91414	+	12.9502i	−0.384165	+	0.841204i
$238$		0			0
$239$	1.45779	−	10.1392i	0.0942969	−	0.655849i	−0.886774	−	0.462203i	$-0.847059\pi$
$239$	1.45779	−	10.1392i	0.0942969	−	0.655849i	0.981071	−	0.193647i	$-0.0620316\pi$
$240$		0			0
$241$	5.49033	+	1.61211i	0.353663	+	0.103845i	0.453738	−	0.891135i	$-0.350090\pi$
$241$	5.49033	+	1.61211i	0.353663	+	0.103845i	−0.100075	+	0.994980i	$0.531908\pi$
$242$		0			0
$243$	−9.27032	−	20.2992i	−0.594691	−	1.30219i
$244$		0			0
$245$	−9.08110	+	10.4802i	−0.580170	+	0.669552i
$246$		0			0
$247$	−6.02603	−	3.87269i	−0.383427	−	0.246414i
$248$		0			0
$249$	0.972609	−	0.625058i	0.0616366	−	0.0396114i
$250$		0			0
$251$	−5.45679	+	1.60226i	−0.344429	+	0.101134i	−0.449372	−	0.893345i	$-0.648352\pi$
$251$	−5.45679	+	1.60226i	−0.344429	+	0.101134i	0.104943	+	0.994478i	$0.466534\pi$
$252$		0			0
$253$	−12.0389	+	20.4936i	−0.756881	+	1.28842i
$254$		0			0
$255$	12.6648	−	3.71873i	0.793103	−	0.232876i
$256$		0			0
$257$	15.2431	−	9.79612i	0.950836	−	0.611065i	0.0293888	−	0.999568i	$-0.490644\pi$
$257$	15.2431	−	9.79612i	0.950836	−	0.611065i	0.921448	+	0.388503i	$0.127008\pi$
$258$		0			0
$259$	−33.7619	−	21.6974i	−2.09786	−	1.34821i
$260$		0			0
$261$	−0.166873	+	0.192582i	−0.0103292	+	0.0119205i
$262$		0			0
$263$	10.5375	+	23.0739i	0.649771	+	1.42280i	0.891755	+	0.452519i	$0.149475\pi$
$263$	10.5375	+	23.0739i	0.649771	+	1.42280i	−0.241984	+	0.970280i	$0.577798\pi$
$264$		0			0
$265$	−23.6558	−	6.94597i	−1.45317	−	0.426688i
$266$		0			0
$267$	0.685789	−	4.76976i	0.0419696	−	0.291905i
$268$		0			0
$269$	1.09780	−	2.40385i	0.0669343	−	0.146566i	−0.873208	−	0.487348i	$-0.837964\pi$
$269$	1.09780	−	2.40385i	0.0669343	−	0.146566i	0.940142	+	0.340782i	$0.110692\pi$
$270$		0			0
$271$	−1.20466	−	8.37859i	−0.0731778	−	0.508963i	−0.993138	−	0.116951i	$-0.962688\pi$
$271$	−1.20466	−	8.37859i	−0.0731778	−	0.508963i	0.919960	−	0.392012i	$-0.128221\pi$
$272$		0			0
$273$	−8.76960	−	10.1207i	−0.530760	−	0.612530i
$274$		0			0
$275$	11.5162			0.694455
$276$		0			0
$277$	−14.2482			−0.856089			−0.428044	−	0.903758i	$-0.640797\pi$
$277$	−14.2482			−0.856089			−0.428044	+	0.903758i	$0.640797\pi$
$278$		0			0
$279$	14.6444	+	16.9006i	0.876738	+	1.01181i
$280$		0			0
$281$	−0.533022	−	3.70725i	−0.0317974	−	0.221156i	0.967727	−	0.252002i	$-0.0810889\pi$
$281$	−0.533022	−	3.70725i	−0.0317974	−	0.221156i	−0.999524	+	0.0308461i	$0.990180\pi$
$282$		0			0
$283$	−4.21621	+	9.23221i	−0.250628	+	0.548798i	−0.992571	−	0.121664i	$-0.961177\pi$
$283$	−4.21621	+	9.23221i	−0.250628	+	0.548798i	0.741944	+	0.670462i	$0.233904\pi$
$284$		0			0
$285$	−4.45252	+	30.9679i	−0.263744	+	1.83438i
$286$		0			0
$287$	29.9425	+	8.79192i	1.76745	+	0.518971i
$288$		0			0
$289$	−5.46993	−	11.9775i	−0.321761	−	0.704557i
$290$		0			0
$291$	2.76379	−	3.18958i	0.162016	−	0.186977i
$292$		0			0
$293$	−20.8377	−	13.3916i	−1.21735	−	0.782343i	−0.235476	−	0.971880i	$-0.575665\pi$
$293$	−20.8377	−	13.3916i	−1.21735	−	0.782343i	−0.981874	+	0.189537i	$0.939301\pi$
$294$		0			0
$295$	18.6505	−	11.9859i	1.08587	−	0.697848i
$296$		0			0
$297$	−2.45387	+	0.720522i	−0.142388	+	0.0418089i
$298$		0			0
$299$	−7.27984	+	1.34622i	−0.421004	+	0.0778539i
$300$		0			0
$301$	32.7245	−	9.60879i	1.88621	−	0.553841i
$302$		0			0
$303$	8.18891	−	5.26269i	0.470440	−	0.302334i
$304$		0			0
$305$	−18.4944	−	11.8856i	−1.05899	−	0.680569i
$306$		0			0
$307$	19.8413	−	22.8981i	1.13240	−	1.30686i	0.186486	−	0.982458i	$-0.440290\pi$
$307$	19.8413	−	22.8981i	1.13240	−	1.30686i	0.945918	−	0.324406i	$-0.105164\pi$
$308$		0			0
$309$	−5.09290	−	11.1519i	−0.289725	−	0.634409i
$310$		0			0
$311$	−18.3595	−	5.39082i	−1.04107	−	0.305685i	−0.283865	−	0.958864i	$-0.591617\pi$
$311$	−18.3595	−	5.39082i	−1.04107	−	0.305685i	−0.757204	+	0.653179i	$0.773435\pi$
$312$		0			0
$313$	4.78780	−	33.2999i	0.270622	−	1.88222i	−0.171380	−	0.985205i	$-0.554823\pi$
$313$	4.78780	−	33.2999i	0.270622	−	1.88222i	0.442002	−	0.897014i	$-0.354268\pi$
$314$		0			0
$315$	−12.5542	+	27.4899i	−0.707350	+	1.54888i
$316$		0			0
$317$	−0.191278	−	1.33037i	−0.0107433	−	0.0747211i	0.983744	−	0.179574i	$-0.0574719\pi$
$317$	−0.191278	−	1.33037i	−0.0107433	−	0.0747211i	−0.994488	+	0.104853i	$0.966563\pi$
$318$		0			0
$319$	−0.257870	−	0.297598i	−0.0144380	−	0.0166623i
$320$		0			0
$321$	29.0743			1.62277
$322$		0			0
$323$	−9.08432			−0.505465
$324$		0			0
$325$	2.34903	+	2.71092i	0.130301	+	0.150375i
$326$		0			0
$327$	0.324626	+	2.25782i	0.0179518	+	0.124858i
$328$		0			0
$329$	−10.9663	+	24.0129i	−0.604592	+	1.32387i
$330$		0			0
$331$	−0.000467111		0.00324883i	−2.56747e−5		0.000178572i	−0.989834	−	0.142226i	$-0.954574\pi$
$331$	−0.000467111		0.00324883i	−2.56747e−5		0.000178572i	0.989809	+	0.142404i	$0.0454833\pi$
$332$		0			0
$333$	−35.4675	−	10.4142i	−1.94361	−	0.570695i
$334$		0			0
$335$	3.65268	+	7.99825i	0.199567	+	0.436991i
$336$		0			0
$337$	4.63404	−	5.34797i	0.252433	−	0.291323i	−0.615363	−	0.788244i	$-0.710991\pi$
$337$	4.63404	−	5.34797i	0.252433	−	0.291323i	0.867796	+	0.496921i	$0.165536\pi$
$338$		0			0
$339$	35.3106	+	22.6927i	1.91781	+	1.23250i
$340$		0			0
$341$	−29.0713	+	18.6830i	−1.57430	+	1.01174i
$342$		0			0
$343$	−6.26699	+	1.84015i	−0.338386	+	0.0993590i
$344$		0			0
$345$	18.5571	+	26.4801i	0.999078	+	1.42564i
$346$		0			0
$347$	−17.3307	+	5.08874i	−0.930358	+	0.273178i	−0.711587	−	0.702598i	$-0.752023\pi$
$347$	−17.3307	+	5.08874i	−0.930358	+	0.273178i	−0.218772	+	0.975776i	$0.570205\pi$
$348$		0			0
$349$	11.8147	−	7.59285i	0.632427	−	0.406436i	−0.184780	−	0.982780i	$-0.559157\pi$
$349$	11.8147	−	7.59285i	0.632427	−	0.406436i	0.817207	+	0.576344i	$0.195521\pi$
$350$		0			0
$351$	−0.670140	−	0.430673i	−0.0357694	−	0.0229876i
$352$		0			0
$353$	4.86032	−	5.60910i	0.258689	−	0.298542i	−0.611517	−	0.791231i	$-0.709440\pi$
$353$	4.86032	−	5.60910i	0.258689	−	0.298542i	0.870206	+	0.492689i	$0.163986\pi$
$354$		0			0
$355$	−4.93559	−	10.8074i	−0.261954	−	0.573599i
$356$		0			0
$357$	−16.2952	−	4.78471i	−0.862435	−	0.253234i
$358$		0			0
$359$	−0.963614	+	6.70208i	−0.0508576	+	0.353722i	0.948464	+	0.316886i	$0.102637\pi$
$359$	−0.963614	+	6.70208i	−0.0508576	+	0.353722i	−0.999321	+	0.0368366i	$0.988272\pi$
$360$		0			0
$361$	1.05194	−	2.30343i	0.0553653	−	0.121233i
$362$		0			0
$363$	−4.80855	−	33.4442i	−0.252384	−	1.75537i
$364$		0			0
$365$	26.3830	+	30.4476i	1.38095	+	1.59370i
$366$		0			0
$367$	2.23720			0.116781			0.0583905	−	0.998294i	$-0.481403\pi$
$367$	2.23720			0.116781			0.0583905	+	0.998294i	$0.481403\pi$
$368$		0			0
$369$	28.7433			1.49632
$370$		0			0
$371$	20.7733	+	23.9737i	1.07850	+	1.24465i
$372$		0			0
$373$	2.25200	+	15.6630i	0.116604	+	0.811001i	0.961251	+	0.275676i	$0.0889017\pi$
$373$	2.25200	+	15.6630i	0.116604	+	0.811001i	−0.844646	+	0.535325i	$0.820189\pi$
$374$		0			0
$375$	−7.49597	+	16.4139i	−0.387090	+	0.847609i
$376$		0			0
$377$	0.0174554	−	0.121405i	0.000899001	−	0.00625269i
$378$		0			0
$379$	9.41124	+	2.76339i	0.483423	+	0.141946i	0.514358	−	0.857576i	$-0.328030\pi$
$379$	9.41124	+	2.76339i	0.483423	+	0.141946i	−0.0309350	+	0.999521i	$0.509848\pi$
$380$		0			0
$381$	−0.999959	−	2.18960i	−0.0512294	−	0.112177i
$382$		0			0
$383$	−12.1479	+	14.0194i	−0.620727	+	0.716357i	−0.975845	−	0.218464i	$-0.929895\pi$
$383$	−12.1479	+	14.0194i	−0.620727	+	0.716357i	0.355118	+	0.934822i	$0.384441\pi$
$384$		0			0
$385$	−39.2870	−	25.2482i	−2.00225	−	1.28677i
$386$		0			0
$387$	26.4270	−	16.9836i	1.34336	−	0.863326i
$388$		0			0
$389$	−0.400785	+	0.117681i	−0.0203206	+	0.00596667i	−0.291877	−	0.956456i	$-0.594280\pi$
$389$	−0.400785	+	0.117681i	−0.0203206	+	0.00596667i	0.271556	+	0.962423i	$0.412462\pi$
$390$		0			0
$391$	−6.84368	+	6.42761i	−0.346100	+	0.325058i
$392$		0			0
$393$	−2.08071	+	0.610950i	−0.104958	+	0.0308184i
$394$		0			0
$395$	−13.0094	+	8.36062i	−0.654573	+	0.420668i
$396$		0			0
$397$	24.8286	+	15.9564i	1.24611	+	0.800828i	0.986321	−	0.164836i	$-0.0527095\pi$
$397$	24.8286	+	15.9564i	1.24611	+	0.800828i	0.259792	+	0.965665i	$0.416346\pi$
$398$		0			0
$399$	26.3612	−	30.4225i	1.31971	−	1.52303i
$400$		0			0
$401$	4.12832	+	9.03977i	0.206159	+	0.451424i	0.984263	−	0.176711i	$-0.0565457\pi$
$401$	4.12832	+	9.03977i	0.206159	+	0.451424i	−0.778104	+	0.628135i	$0.783818\pi$
$402$		0			0
$403$	−10.3278	−	3.03252i	−0.514465	−	0.151060i
$404$		0			0
$405$	3.21040	−	22.3288i	0.159526	−	1.10953i
$406$		0			0
$407$	23.7294	−	51.9601i	1.17622	−	2.57556i
$408$		0			0
$409$	3.43956	+	23.9227i	0.170075	+	1.18290i	0.878721	+	0.477335i	$0.158397\pi$
$409$	3.43956	+	23.9227i	0.170075	+	1.18290i	−0.708646	+	0.705564i	$0.750694\pi$
$410$		0			0
$411$	5.03116	+	5.80627i	0.248169	+	0.286402i
$412$		0			0
$413$	−28.5249			−1.40362
$414$		0			0
$415$	1.25583			0.0616463
$416$		0			0
$417$	−6.81810	−	7.86851i	−0.333884	−	0.385323i
$418$		0			0
$419$	2.06235	+	14.3439i	0.100752	+	0.700747i	0.976111	+	0.217273i	$0.0697161\pi$
$419$	2.06235	+	14.3439i	0.100752	+	0.700747i	−0.875359	+	0.483474i	$0.839375\pi$
$420$		0			0
$421$	−2.28602	+	5.00569i	−0.111414	+	0.243962i	−0.957123	−	0.289682i	$-0.906451\pi$
$421$	−2.28602	+	5.00569i	−0.111414	+	0.243962i	0.845709	+	0.533644i	$0.179178\pi$
$422$		0			0
$423$	−3.46034	+	24.0672i	−0.168247	+	1.17019i
$424$		0			0
$425$	4.36485	+	1.28163i	0.211726	+	0.0621684i
$426$		0			0
$427$	11.7505	+	25.7300i	0.568647	+	1.24516i
$428$		0			0
$429$	12.4820	−	14.4050i	0.602637	−	0.695480i
$430$		0			0
$431$	−7.79649	−	5.01050i	−0.375543	−	0.241347i	0.339230	−	0.940704i	$-0.389834\pi$
$431$	−7.79649	−	5.01050i	−0.375543	−	0.241347i	−0.714773	+	0.699356i	$0.753470\pi$
$432$		0			0
$433$	25.8704	−	16.6259i	1.24325	−	0.798991i	0.257352	−	0.966318i	$-0.417150\pi$
$433$	25.8704	−	16.6259i	1.24325	−	0.798991i	0.985901	+	0.167327i	$0.0535136\pi$
$434$		0			0
$435$	−0.514013	+	0.150928i	−0.0246450	+	0.00723643i
$436$		0			0
$437$	−7.11979	−	21.0844i	−0.340586	−	1.00860i
$438$		0			0
$439$	−10.7180	+	3.14709i	−0.511542	+	0.150202i	−0.527309	−	0.849673i	$-0.676799\pi$
$439$	−10.7180	+	3.14709i	−0.511542	+	0.150202i	0.0157674	+	0.999876i	$0.494981\pi$
$440$		0			0
$441$	13.8251	−	8.88483i	0.658337	−	0.423087i
$442$		0			0
$443$	26.2741	+	16.8853i	1.24832	+	0.802246i	0.986641	−	0.162910i	$-0.0520879\pi$
$443$	26.2741	+	16.8853i	1.24832	+	0.802246i	0.261678	+	0.965155i	$0.415724\pi$
$444$		0			0
$445$	3.42775	−	3.95583i	0.162491	−	0.187524i
$446$		0			0
$447$	−11.5201	−	25.2254i	−0.544881	−	1.19312i
$448$		0			0
$449$	12.4765	+	3.66342i	0.588801	+	0.172888i	0.562544	−	0.826768i	$-0.309823\pi$
$449$	12.4765	+	3.66342i	0.588801	+	0.172888i	0.0262576	+	0.999655i	$0.491641\pi$
$450$		0			0
$451$	−6.32123	+	43.9651i	−0.297655	+	2.07024i
$452$		0			0
$453$	1.18410	−	2.59281i	0.0556337	−	0.121821i
$454$		0			0
$455$	−2.07015	−	14.3982i	−0.0970499	−	0.674997i
$456$		0			0
$457$	−7.94975	−	9.17450i	−0.371874	−	0.429165i	0.538709	−	0.842492i	$-0.318912\pi$
$457$	−7.94975	−	9.17450i	−0.371874	−	0.429165i	−0.910583	+	0.413327i	$0.864367\pi$
$458$		0			0
$459$	−1.01025			−0.0471542
$460$		0			0
$461$	−25.5360			−1.18933			−0.594664	−	0.803974i	$-0.702715\pi$
$461$	−25.5360			−1.18933			−0.594664	+	0.803974i	$0.702715\pi$
$462$		0			0
$463$	21.6178	+	24.9483i	1.00467	+	1.15945i	0.987182	+	0.159599i	$0.0510201\pi$
$463$	21.6178	+	24.9483i	1.00467	+	1.15945i	0.0174838	+	0.999847i	$0.494434\pi$
$464$		0			0
$465$	6.69064	+	46.5344i	0.310271	+	2.15798i
$466$		0			0
$467$	10.3131	−	22.5826i	0.477235	−	1.04500i	−0.505980	−	0.862545i	$-0.668869\pi$
$467$	10.3131	−	22.5826i	0.477235	−	1.04500i	0.983215	−	0.182453i	$-0.0584038\pi$
$468$		0			0
$469$	1.61005	−	11.1982i	0.0743454	−	0.517083i
$470$		0			0
$471$	2.26479	+	0.665001i	0.104356	+	0.0306416i
$472$		0			0
$473$	20.1659	+	44.1572i	0.927230	+	2.03035i
$474$		0			0
$475$	−7.06112	+	8.14897i	−0.323986	+	0.373900i
$476$		0			0
$477$	24.5795	+	15.7963i	1.12542	+	0.723263i
$478$		0			0
$479$	−8.38631	+	5.38956i	−0.383180	+	0.246255i	−0.718024	−	0.696019i	$-0.754953\pi$
$479$	−8.38631	+	5.38956i	−0.383180	+	0.246255i	0.334843	+	0.942274i	$0.391317\pi$
$480$		0			0
$481$	17.0716	−	5.01268i	0.778398	−	0.228558i
$482$		0			0
$483$	−1.66618	−	41.5707i	−0.0758137	−	1.89153i
$484$		0			0
$485$	4.39863	−	1.29155i	0.199732	−	0.0586465i
$486$		0			0
$487$	29.1310	−	18.7214i	1.32005	−	0.848345i	0.324809	−	0.945780i	$-0.394700\pi$
$487$	29.1310	−	18.7214i	1.32005	−	0.848345i	0.995242	+	0.0974341i	$0.0310635\pi$
$488$		0			0
$489$	−48.0238	−	30.8630i	−2.17171	−	1.39567i
$490$		0			0
$491$	−2.41646	+	2.78874i	−0.109053	+	0.125854i	−0.807652	−	0.589660i	$-0.799262\pi$
$491$	−2.41646	+	2.78874i	−0.109053	+	0.125854i	0.698599	+	0.715514i	$0.253807\pi$
$492$		0			0
$493$	−0.0646176	−	0.141493i	−0.00291023	−	0.00637252i
$494$		0			0
$495$	−41.2718	−	12.1185i	−1.85503	−	0.544686i
$496$		0			0
$497$	−2.17555	+	15.1312i	−0.0975865	+	0.678729i
$498$		0			0
$499$	−11.8799	+	26.0133i	−0.531817	+	1.16452i	0.432951	+	0.901417i	$0.357472\pi$
$499$	−11.8799	+	26.0133i	−0.531817	+	1.16452i	−0.964769	+	0.263100i	$0.915255\pi$
$500$		0			0
$501$	−3.13955	−	21.8360i	−0.140265	−	0.975561i
$502$		0			0
$503$	3.68949	+	4.25790i	0.164506	+	0.189850i	0.832018	−	0.554749i	$-0.187186\pi$
$503$	3.68949	+	4.25790i	0.164506	+	0.189850i	−0.667511	+	0.744600i	$0.732640\pi$
$504$		0			0
$505$	10.5735			0.470515
$506$		0			0
$507$	−26.4514			−1.17475
$508$		0			0
$509$	−14.2880	−	16.4892i	−0.633303	−	0.730871i	0.344873	−	0.938649i	$-0.387922\pi$
$509$	−14.2880	−	16.4892i	−0.633303	−	0.730871i	−0.978176	+	0.207779i	$0.933377\pi$
$510$		0			0
$511$	−7.37711	−	51.3089i	−0.326344	−	2.26977i
$512$		0			0
$513$	0.994733	−	2.17816i	0.0439185	−	0.0961682i
$514$		0			0
$515$	1.89519	−	13.1813i	0.0835120	−	0.580839i
$516$		0			0
$517$	−36.0516	−	10.5857i	−1.58555	−	0.465559i
$518$		0			0
$519$	−15.7335	−	34.4515i	−0.690624	−	1.51226i
$520$		0			0
$521$	15.1943	−	17.5351i	0.665673	−	0.768228i	−0.318020	−	0.948084i	$-0.603018\pi$
$521$	15.1943	−	17.5351i	0.665673	−	0.768228i	0.983693	+	0.179856i	$0.0575633\pi$
$522$		0			0
$523$	−0.326217	−	0.209647i	−0.0142645	−	0.00916722i	0.533489	−	0.845807i	$-0.320881\pi$
$523$	−0.326217	−	0.209647i	−0.0142645	−	0.00916722i	−0.547754	+	0.836640i	$0.684517\pi$
$524$		0			0
$525$	−16.9581	+	10.8983i	−0.740114	+	0.475642i
$526$		0			0
$527$	−13.0977	+	3.84584i	−0.570546	+	0.167528i
$528$		0			0
$529$	−20.2820	−	10.8463i	−0.881824	−	0.471579i
$530$		0			0
$531$	−25.2090	+	7.40203i	−1.09398	+	0.321221i
$532$		0			0
$533$	−11.6388	+	7.47978i	−0.504131	+	0.323985i
$534$		0			0
$535$	26.5678	+	17.0741i	1.14863	+	0.738177i
$536$		0			0
$537$	−36.4166	+	42.0270i	−1.57149	+	1.81360i
$538$		0			0
$539$	10.5496	+	23.1005i	0.454405	+	0.995008i
$540$		0			0
$541$	30.5687	+	8.97579i	1.31425	+	0.385899i	0.862416	−	0.506201i	$-0.168951\pi$
$541$	30.5687	+	8.97579i	1.31425	+	0.385899i	0.451837	+	0.892100i	$0.350769\pi$
$542$		0			0
$543$	4.73149	−	32.9083i	0.203048	−	1.41223i
$544$		0			0
$545$	−1.02928	+	2.25382i	−0.0440896	+	0.0965428i
$546$		0			0
$547$	3.23104	+	22.4724i	0.138149	+	0.960850i	0.934487	+	0.355998i	$0.115859\pi$
$547$	3.23104	+	22.4724i	0.138149	+	0.960850i	−0.796337	+	0.604853i	$0.793232\pi$
$548$		0			0
$549$	17.0613	+	19.6898i	0.728160	+	0.840341i
$550$		0			0
$551$	0.368694			0.0157069
$552$		0			0
$553$	19.8971			0.846112
$554$		0			0
$555$	−50.8900	−	58.7302i	−2.16016	−	2.49296i
$556$		0			0
$557$	3.24153	+	22.5453i	0.137348	+	0.955277i	0.935627	+	0.352989i	$0.114835\pi$
$557$	3.24153	+	22.5453i	0.137348	+	0.955277i	−0.798279	+	0.602287i	$0.794256\pi$
$558$		0			0
$559$	−6.28126	+	13.7540i	−0.265669	+	0.581734i
$560$		0			0
$561$	3.44012	−	23.9266i	0.145242	−	1.01018i
$562$		0			0
$563$	−13.3163	−	3.91002i	−0.561215	−	0.164787i	−0.0111922	−	0.999937i	$-0.503563\pi$
$563$	−13.3163	−	3.91002i	−0.561215	−	0.164787i	−0.550022	+	0.835150i	$0.685381\pi$
$564$		0			0
$565$	18.9400	+	41.4728i	0.796811	+	1.74477i
$566$		0			0
$567$	−19.0072	+	21.9355i	−0.798228	+	0.921204i
$568$		0			0
$569$	9.60079	+	6.17005i	0.402486	+	0.258662i	0.726187	−	0.687497i	$-0.241291\pi$
$569$	9.60079	+	6.17005i	0.402486	+	0.258662i	−0.323701	+	0.946160i	$0.604927\pi$
$570$		0			0
$571$	−28.0935	+	18.0546i	−1.17567	+	0.755560i	−0.974586	−	0.224013i	$-0.928084\pi$
$571$	−28.0935	+	18.0546i	−1.17567	+	0.755560i	−0.201089	+	0.979573i	$0.564448\pi$
$572$		0			0
$573$	27.6507	−	8.11897i	1.15512	−	0.339175i
$574$		0			0
$575$	0.446303	+	11.1351i	0.0186121	+	0.464367i
$576$		0			0
$577$	−17.7733	+	5.21872i	−0.739913	+	0.217258i	−0.629905	−	0.776672i	$-0.716906\pi$
$577$	−17.7733	+	5.21872i	−0.739913	+	0.217258i	−0.110009	+	0.993931i	$0.535088\pi$
$578$		0			0
$579$	−29.9673	+	19.2588i	−1.24540	+	0.800368i
$580$		0			0
$581$	−1.35931	−	0.873577i	−0.0563938	−	0.0362421i
$582$		0			0
$583$	−29.5672	+	34.1224i	−1.22455	+	1.41320i
$584$		0			0
$585$	−5.56574	−	12.1873i	−0.230115	−	0.503881i
$586$		0			0
$587$	10.4673	+	3.07347i	0.432031	+	0.126856i	0.490515	−	0.871433i	$-0.336809\pi$
$587$	10.4673	+	3.07347i	0.432031	+	0.126856i	−0.0584843	+	0.998288i	$0.518627\pi$
$588$		0			0
$589$	4.60471	−	32.0264i	0.189734	−	1.31963i
$590$		0			0
$591$	−14.6945	+	32.1765i	−0.604452	+	1.32357i
$592$		0			0
$593$	1.32504	+	9.21588i	0.0544130	+	0.378451i	0.998772	+	0.0495353i	$0.0157740\pi$
$593$	1.32504	+	9.21588i	0.0544130	+	0.378451i	−0.944359	+	0.328915i	$0.893317\pi$
$594$		0			0
$595$	−12.0806	−	13.9417i	−0.495256	−	0.571555i
$596$		0			0
$597$	−16.5803			−0.678585
$598$		0			0
$599$	−12.8667			−0.525718			−0.262859	−	0.964834i	$-0.584665\pi$
$599$	−12.8667			−0.525718			−0.262859	+	0.964834i	$0.584665\pi$
$600$		0			0
$601$	−26.7315	−	30.8498i	−1.09040	−	1.25839i	−0.963855	−	0.266429i	$-0.914156\pi$
$601$	−26.7315	−	30.8498i	−1.09040	−	1.25839i	−0.126546	−	0.991961i	$-0.540389\pi$
$602$		0			0
$603$	−1.48296	−	10.3142i	−0.0603909	−	0.420028i
$604$		0			0
$605$	15.2464	−	33.3849i	0.619853	−	1.35729i
$606$		0			0
$607$	4.99791	−	34.7612i	0.202859	−	1.41091i	−0.592889	−	0.805285i	$-0.702013\pi$
$607$	4.99791	−	34.7612i	0.202859	−	1.41091i	0.795747	−	0.605629i	$-0.207078\pi$
$608$		0			0
$609$	0.661355	+	0.194191i	0.0267995	+	0.00786903i
$610$		0			0
$611$	−4.86176	−	10.6458i	−0.196686	−	0.430682i
$612$		0			0
$613$	30.5049	−	35.2045i	1.23208	−	1.42190i	0.359703	−	0.933067i	$-0.382878\pi$
$613$	30.5049	−	35.2045i	1.23208	−	1.42190i	0.872379	−	0.488831i	$-0.162576\pi$
$614$		0			0
$615$	50.8344	+	32.6693i	2.04984	+	1.31735i
$616$		0			0
$617$	5.71131	−	3.67043i	0.229929	−	0.147766i	−0.420604	−	0.907244i	$-0.638182\pi$
$617$	5.71131	−	3.67043i	0.229929	−	0.147766i	0.650533	+	0.759478i	$0.274546\pi$
$618$		0			0
$619$	21.9488	−	6.44475i	0.882197	−	0.259036i	0.190902	−	0.981609i	$-0.438859\pi$
$619$	21.9488	−	6.44475i	0.882197	−	0.259036i	0.691295	+	0.722573i	$0.257040\pi$
$620$		0			0
$621$	−0.791776	−	2.34474i	−0.0317729	−	0.0940913i
$622$		0			0
$623$	−6.46194	+	1.89740i	−0.258892	+	0.0760176i
$624$		0			0
$625$	−26.2630	+	16.8782i	−1.05052	+	0.675129i
$626$		0			0
$627$	48.2001	+	30.9763i	1.92493	+	1.23707i
$628$		0			0
$629$	14.7764	−	17.0529i	0.589175	−	0.679944i
$630$		0			0
$631$	−0.523246	−	1.14575i	−0.0208301	−	0.0456116i	0.898931	−	0.438090i	$-0.144345\pi$
$631$	−0.523246	−	1.14575i	−0.0208301	−	0.0456116i	−0.919761	+	0.392479i	$0.871618\pi$
$632$		0			0
$633$	39.5316	+	11.6075i	1.57124	+	0.461358i
$634$		0			0
$635$	0.372109	−	2.58807i	0.0147667	−	0.102705i
$636$		0			0
$637$	−3.28599	+	7.19531i	−0.130196	+	0.285089i
$638$		0			0
$639$	2.00382	+	13.9368i	0.0792697	+	0.551333i
$640$		0			0
$641$	−6.69656	−	7.72824i	−0.264498	−	0.305247i	0.607929	−	0.793991i	$-0.292001\pi$
$641$	−6.69656	−	7.72824i	−0.264498	−	0.305247i	−0.872427	+	0.488744i	$0.837455\pi$
$642$		0			0
$643$	10.1651			0.400871			0.200435	−	0.979707i	$-0.435764\pi$
$643$	10.1651			0.400871			0.200435	+	0.979707i	$0.435764\pi$
$644$		0			0
$645$	66.0414			2.60038
$646$		0			0
$647$	3.98869	+	4.60319i	0.156812	+	0.180970i	0.828719	−	0.559665i	$-0.189070\pi$
$647$	3.98869	+	4.60319i	0.156812	+	0.180970i	−0.671907	+	0.740635i	$0.734525\pi$
$648$		0			0
$649$	−5.77801	−	40.1870i	−0.226807	−	1.57748i
$650$		0			0
$651$	25.1282	−	55.0230i	0.984850	−	2.15652i
$652$		0			0
$653$	−4.41125	+	30.6809i	−0.172626	+	1.20064i	0.700684	+	0.713472i	$0.252878\pi$
$653$	−4.41125	+	30.6809i	−0.172626	+	1.20064i	−0.873310	+	0.487165i	$0.838031\pi$
$654$		0			0
$655$	−2.26012	−	0.663630i	−0.0883100	−	0.0259302i
$656$		0			0
$657$	−19.8339	−	43.4302i	−0.773794	−	1.69437i
$658$		0			0
$659$	5.65437	−	6.52549i	0.220263	−	0.254197i	−0.634854	−	0.772632i	$-0.718940\pi$
$659$	5.65437	−	6.52549i	0.220263	−	0.254197i	0.855117	+	0.518435i	$0.173485\pi$
$660$		0			0
$661$	9.59343	+	6.16532i	0.373141	+	0.239803i	0.713748	−	0.700403i	$-0.246996\pi$
$661$	9.59343	+	6.16532i	0.373141	+	0.239803i	−0.340607	+	0.940206i	$0.610633\pi$
$662$		0			0
$663$	6.33401	−	4.07062i	0.245993	−	0.158090i
$664$		0			0
$665$	41.9545	−	12.3189i	1.62692	−	0.477708i
$666$		0			0
$667$	0.277756	−	0.260870i	0.0107548	−	0.0101009i
$668$		0			0
$669$	−9.60802	+	2.82117i	−0.371467	+	0.109073i
$670$		0			0
$671$	−33.8692	+	21.7664i	−1.30751	+	0.840284i
$672$		0			0
$673$	−17.3274	−	11.1357i	−0.667923	−	0.429248i	0.162253	−	0.986749i	$-0.448124\pi$
$673$	−17.3274	−	11.1357i	−0.667923	−	0.429248i	−0.830176	+	0.557501i	$0.811760\pi$
$674$		0			0
$675$	−0.785250	+	0.906227i	−0.0302243	+	0.0348807i
$676$		0			0
$677$	−10.6863	−	23.3997i	−0.410708	−	0.899325i	−0.996071	−	0.0885538i	$-0.971775\pi$
$677$	−10.6863	−	23.3997i	−0.410708	−	0.899325i	0.585364	−	0.810771i	$-0.300952\pi$
$678$		0			0
$679$	−5.65951	−	1.66178i	−0.217192	−	0.0637733i
$680$		0			0
$681$	−4.83715	+	33.6431i	−0.185360	+	1.28921i
$682$		0			0
$683$	12.0611	−	26.4100i	0.461504	−	1.01055i	−0.525639	−	0.850708i	$-0.676174\pi$
$683$	12.0611	−	26.4100i	0.461504	−	1.01055i	0.987142	−	0.159844i	$-0.0510992\pi$
$684$		0			0
$685$	1.18765	+	8.26030i	0.0453779	+	0.315610i
$686$		0			0
$687$	−3.90028	−	4.50117i	−0.148805	−	0.171730i
$688$		0			0
$689$	−14.0634			−0.535773
$690$		0			0
$691$	22.9857			0.874419			0.437210	−	0.899360i	$-0.355967\pi$
$691$	22.9857			0.874419			0.437210	+	0.899360i	$0.355967\pi$
$692$		0			0
$693$	36.2428	+	41.8264i	1.37675	+	1.58885i
$694$		0			0
$695$	−1.60948	−	11.1942i	−0.0610510	−	0.424619i
$696$		0			0
$697$	−7.28870	+	15.9600i	−0.276079	+	0.604529i
$698$		0			0
$699$	−0.611917	+	4.25598i	−0.0231448	+	0.160976i
$700$		0			0
$701$	47.4005	+	13.9180i	1.79029	+	0.525677i	0.996581	−	0.0826187i	$-0.0263283\pi$
$701$	47.4005	+	13.9180i	1.79029	+	0.525677i	0.793710	+	0.608296i	$0.208147\pi$
$702$		0			0
$703$	22.2178	+	48.6501i	0.837959	+	1.83487i
$704$		0			0
$705$	−33.4743	+	38.6314i	−1.26072	+	1.45494i
$706$		0			0
$707$	−11.4448	−	7.35510i	−0.430425	−	0.276617i
$708$		0			0
$709$	−35.5680	+	22.8582i	−1.33578	+	0.858456i	−0.996610	−	0.0822679i	$-0.973784\pi$
$709$	−35.5680	+	22.8582i	−1.33578	+	0.858456i	−0.339173	+	0.940724i	$0.610147\pi$
$710$		0			0
$711$	17.5842	−	5.16318i	0.659458	−	0.193634i
$712$		0			0
$713$	−19.1914	−	27.3852i	−0.718722	−	1.02558i
$714$		0			0
$715$	19.8654	−	5.83300i	0.742923	−	0.218142i
$716$		0			0
$717$	−21.4693	+	13.7975i	−0.801787	+	0.515277i
$718$		0			0
$719$	10.9383	+	7.02959i	0.407928	+	0.262159i	0.728474	−	0.685074i	$-0.240230\pi$
$719$	10.9383	+	7.02959i	0.407928	+	0.262159i	−0.320546	+	0.947233i	$0.603866\pi$
$720$		0			0
$721$	−11.2205	+	12.9492i	−0.417873	+	0.482252i
$722$		0			0
$723$	−5.92221	−	12.9678i	−0.220250	−	0.482279i
$724$		0			0
$725$	−0.177151	−	0.0520162i	−0.00657921	−	0.00193183i
$726$		0			0
$727$	−6.70284	+	46.6193i	−0.248595	+	1.72901i	0.357755	+	0.933815i	$0.383542\pi$
$727$	−6.70284	+	46.6193i	−0.248595	+	1.72901i	−0.606350	+	0.795198i	$0.707367\pi$
$728$		0			0
$729$	−12.7078	+	27.8263i	−0.470660	+	1.03060i
$730$		0			0
$731$	2.72900	+	18.9806i	0.100936	+	0.702023i
$732$		0			0
$733$	−10.8934	−	12.5716i	−0.402356	−	0.464344i	0.518026	−	0.855365i	$-0.326667\pi$
$733$	−10.8934	−	12.5716i	−0.402356	−	0.464344i	−0.920381	+	0.391022i	$0.872122\pi$
$734$		0			0
$735$	34.5490			1.27436
$736$		0			0
$737$	16.1025			0.593145
$738$		0			0
$739$	−3.35074	−	3.86696i	−0.123259	−	0.142248i	0.690766	−	0.723079i	$-0.257274\pi$
$739$	−3.35074	−	3.86696i	−0.123259	−	0.142248i	−0.814025	+	0.580830i	$0.802728\pi$
$740$		0			0
$741$	2.53980	+	17.6647i	0.0933019	+	0.648929i
$742$		0			0
$743$	−1.62848	+	3.56588i	−0.0597432	+	0.130819i	−0.937149	−	0.348930i	$-0.886545\pi$
$743$	−1.62848	+	3.56588i	−0.0597432	+	0.130819i	0.877406	+	0.479749i	$0.159272\pi$
$744$		0			0
$745$	4.28690	−	29.8160i	0.157060	−	1.09237i
$746$		0			0
$747$	−1.42799	−	0.419295i	−0.0522473	−	0.0153412i
$748$		0			0
$749$	−16.8800	−	36.9620i	−0.616781	−	1.35056i
$750$		0			0
$751$	4.44948	−	5.13497i	0.162364	−	0.187378i	−0.668738	−	0.743498i	$-0.733165\pi$
$751$	4.44948	−	5.13497i	0.162364	−	0.187378i	0.831102	+	0.556120i	$0.187711\pi$
$752$		0			0
$753$	11.9198	+	7.66036i	0.434380	+	0.279159i
$754$		0			0
$755$	2.60466	−	1.67392i	0.0947934	−	0.0609200i
$756$		0			0
$757$	−28.9916	+	8.51269i	−1.05372	+	0.309399i	−0.762318	−	0.647203i	$-0.775939\pi$
$757$	−28.9916	+	8.51269i	−1.05372	+	0.309399i	−0.291398	+	0.956602i	$0.594121\pi$
$758$		0			0
$759$	58.2288	−	10.7679i	2.11357	−	0.390852i
$760$		0			0
$761$	−11.0286	+	3.23829i	−0.399787	+	0.117388i	−0.475444	−	0.879746i	$-0.657713\pi$
$761$	−11.0286	+	3.23829i	−0.399787	+	0.117388i	0.0756572	+	0.997134i	$0.475895\pi$
$762$		0			0
$763$	2.68189	−	1.72354i	0.0970908	−	0.0623965i
$764$		0			0
$765$	−14.2941	−	9.18623i	−0.516803	−	0.332129i
$766$		0			0
$767$	8.28144	−	9.55730i	0.299026	−	0.345094i
$768$		0			0
$769$	21.5723	+	47.2367i	0.777916	+	1.70340i	0.708392	+	0.705819i	$0.249421\pi$
$769$	21.5723	+	47.2367i	0.777916	+	1.70340i	0.0695241	+	0.997580i	$0.477852\pi$
$770$		0			0
$771$	−43.3144	−	12.7183i	−1.55993	−	0.458037i
$772$		0			0
$773$	−0.758418	+	5.27491i	−0.0272784	+	0.189725i	−0.998904	−	0.0467970i	$-0.985099\pi$
$773$	−0.758418	+	5.27491i	−0.0272784	+	0.189725i	0.971626	+	0.236522i	$0.0760077\pi$
$774$		0			0
$775$	−6.73084	+	14.7385i	−0.241779	+	0.529422i
$776$		0			0
$777$	14.2297	+	98.9696i	0.510487	+	3.55051i
$778$		0			0
$779$	−27.2342	−	31.4299i	−0.975766	−	1.12609i
$780$		0			0
$781$	−21.7582			−0.778568
$782$		0			0
$783$	0.0410016			0.00146528
$784$		0			0
$785$	1.67901	+	1.93769i	0.0599266	+	0.0691589i
$786$		0			0
$787$	−5.66497	−	39.4007i	−0.201934	−	1.40448i	−0.798536	−	0.601947i	$-0.794392\pi$
$787$	−5.66497	−	39.4007i	−0.201934	−	1.40448i	0.596602	−	0.802538i	$-0.296517\pi$
$788$		0			0
$789$	26.2533	−	57.4866i	0.934641	−	2.04658i
$790$		0			0
$791$	8.34851	−	58.0651i	0.296839	−	2.06456i
$792$		0			0
$793$	−12.0323	−	3.53301i	−0.427280	−	0.125461i
$794$		0			0
$795$	25.5166	+	55.8737i	0.904982	+	1.98163i
$796$		0			0
$797$	−9.29426	+	10.7261i	−0.329219	+	0.379940i	−0.896094	−	0.443865i	$-0.853607\pi$
$797$	−9.29426	+	10.7261i	−0.329219	+	0.379940i	0.566874	+	0.823804i	$0.308153\pi$
$798$		0			0
$799$	−12.4861	−	8.02432i	−0.441726	−	0.283880i
$800$		0			0
$801$	−5.21840	+	3.35366i	−0.184383	+	0.118496i
$802$		0			0
$803$	70.7916	−	20.7863i	2.49818	−	0.733533i
$804$		0			0
$805$	22.8902	−	38.9654i	0.806772	−	1.37335i
$806$		0			0
$807$	−6.31727	+	1.85492i	−0.222379	+	0.0652962i
$808$		0			0
$809$	−42.2013	+	27.1211i	−1.48372	+	0.953529i	−0.486932	+	0.873440i	$0.661884\pi$
$809$	−42.2013	+	27.1211i	−1.48372	+	0.953529i	−0.996788	+	0.0800884i	$0.974480\pi$
$810$		0			0
$811$	29.7149	+	19.0966i	1.04343	+	0.670573i	0.945833	−	0.324653i	$-0.105247\pi$
$811$	29.7149	+	19.0966i	1.04343	+	0.670573i	0.0975986	+	0.995226i	$0.468884\pi$
$812$		0			0
$813$	−13.8105	+	15.9381i	−0.484354	+	0.558974i
$814$		0			0
$815$	−25.7592	−	56.4047i	−0.902304	−	1.97577i
$816$		0			0
$817$	−43.6106	−	12.8052i	−1.52574	−	0.447998i
$818$		0			0
$819$	−2.45331	+	17.0631i	−0.0857255	+	0.596234i
$820$		0			0
$821$	14.0542	−	30.7745i	0.490496	−	1.07404i	−0.488947	−	0.872314i	$-0.662619\pi$
$821$	14.0542	−	30.7745i	0.490496	−	1.07404i	0.979443	−	0.201723i	$-0.0646540\pi$
$822$		0			0
$823$	0.186597	+	1.29781i	0.00650438	+	0.0452389i	0.992815	−	0.119658i	$-0.0381799\pi$
$823$	0.186597	+	1.29781i	0.00650438	+	0.0452389i	−0.986311	+	0.164897i	$0.947271\pi$
$824$		0			0
$825$	−18.7890	−	21.6837i	−0.654150	−	0.754930i
$826$		0			0
$827$	−9.91522			−0.344786			−0.172393	−	0.985028i	$-0.555150\pi$
$827$	−9.91522			−0.344786			−0.172393	+	0.985028i	$0.555150\pi$
$828$		0			0
$829$	39.5179			1.37251			0.686256	−	0.727360i	$-0.259253\pi$
$829$	39.5179			1.37251			0.686256	+	0.727360i	$0.259253\pi$
$830$		0			0
$831$	23.2462	+	26.8276i	0.806403	+	0.930639i
$832$		0			0
$833$	1.42765	+	9.92953i	0.0494652	+	0.344038i
$834$		0			0
$835$	9.95448	−	21.7973i	0.344489	−	0.754326i
$836$		0			0
$837$	0.512079	−	3.56159i	0.0177000	−	0.123106i
$838$		0			0
$839$	−26.0877	−	7.66005i	−0.900649	−	0.264454i	−0.201549	−	0.979478i	$-0.564598\pi$
$839$	−26.0877	−	7.66005i	−0.900649	−	0.264454i	−0.699100	+	0.715024i	$0.746416\pi$
$840$		0			0
$841$	−12.0444	−	26.3736i	−0.415325	−	0.909434i
$842$		0			0
$843$	−6.11067	+	7.05209i	−0.210463	+	0.242887i
$844$		0			0
$845$	−24.1710	−	15.5338i	−0.831509	−	0.534378i
$846$		0			0
$847$	−39.7258	+	25.5302i	−1.36499	+	0.877228i
$848$		0			0
$849$	24.2620	−	7.12397i	0.832671	−	0.244494i
$850$		0			0
$851$	51.1602	+	20.9304i	1.75375	+	0.717486i
$852$		0			0
$853$	28.9603	−	8.50352i	0.991583	−	0.291155i	0.254585	−	0.967050i	$-0.418061\pi$
$853$	28.9603	−	8.50352i	0.991583	−	0.291155i	0.736998	+	0.675895i	$0.236243\pi$
$854$		0			0
$855$	33.8807	−	21.7738i	1.15870	−	0.744649i
$856$		0			0
$857$	14.4861	+	9.30965i	0.494836	+	0.318012i	0.764148	−	0.645041i	$-0.223160\pi$
$857$	14.4861	+	9.30965i	0.494836	+	0.318012i	−0.269312	+	0.963053i	$0.586796\pi$
$858$		0			0
$859$	7.76078	−	8.95642i	0.264794	−	0.305589i	−0.607746	−	0.794132i	$-0.707926\pi$
$859$	7.76078	−	8.95642i	0.264794	−	0.305589i	0.872540	+	0.488543i	$0.162471\pi$
$860$		0			0
$861$	−32.2979	−	70.7225i	−1.10071	−	2.41022i
$862$		0			0
$863$	35.0343	+	10.2870i	1.19258	+	0.350174i	0.817012	−	0.576620i	$-0.195629\pi$
$863$	35.0343	+	10.2870i	1.19258	+	0.350174i	0.375570	+	0.926794i	$0.377447\pi$
$864$		0			0
$865$	5.85481	−	40.7211i	0.199070	−	1.38456i
$866$		0			0
$867$	−13.6278	+	29.8408i	−0.462826	+	1.01345i
$868$		0			0
$869$	4.03037	+	28.0319i	0.136721	+	0.950916i
$870$		0			0
$871$	3.28452	+	3.79054i	0.111292	+	0.128438i
$872$		0			0
$873$	−5.43284			−0.183874
$874$		0			0
$875$	25.2189			0.852555
$876$		0			0
$877$	10.7364	+	12.3904i	0.362542	+	0.418395i	0.907490	−	0.420074i	$-0.137996\pi$
$877$	10.7364	+	12.3904i	0.362542	+	0.418395i	−0.544948	+	0.838470i	$0.683451\pi$
$878$		0			0
$879$	8.78249	+	61.0836i	0.296226	+	2.06030i
$880$		0			0
$881$	−3.91375	+	8.56992i	−0.131858	+	0.288728i	−0.964032	−	0.265786i	$-0.914369\pi$
$881$	−3.91375	+	8.56992i	−0.131858	+	0.288728i	0.832174	+	0.554514i	$0.187096\pi$
$882$		0			0
$883$	−6.96981	+	48.4761i	−0.234553	+	1.63135i	0.443455	+	0.896297i	$0.353753\pi$
$883$	−6.96981	+	48.4761i	−0.234553	+	1.63135i	−0.678008	+	0.735054i	$0.737157\pi$
$884$		0			0
$885$	−52.9968	−	15.5613i	−1.78147	−	0.523087i
$886$		0			0
$887$	−6.36660	−	13.9409i	−0.213770	−	0.468090i	0.772122	−	0.635474i	$-0.219195\pi$
$887$	−6.36660	−	13.9409i	−0.213770	−	0.468090i	−0.985892	+	0.167384i	$0.946468\pi$
$888$		0			0
$889$	−2.20308	+	2.54249i	−0.0738888	+	0.0852723i
$890$		0			0
$891$	−34.7537	−	22.3348i	−1.16429	−	0.748245i
$892$		0			0
$893$	29.5954	−	19.0198i	0.990372	−	0.636473i
$894$		0			0
$895$	−57.9578	+	17.0179i	−1.93732	+	0.568847i
$896$		0			0
$897$	14.4120	+	11.5107i	0.481203	+	0.384330i
$898$		0			0
$899$	0.531582	−	0.156087i	0.0177293	−	0.00520578i
$900$		0			0
$901$	−15.0039	+	9.64244i	−0.499854	+	0.321236i
$902$		0			0
$903$	−71.4832	−	45.9394i	−2.37881	−	1.52877i
$904$		0			0
$905$	23.6492	−	27.2927i	0.786127	−	0.907239i
$906$		0			0
$907$	−12.2248	−	26.7686i	−0.405919	−	0.888838i	−0.996636	−	0.0819590i	$-0.973882\pi$
$907$	−12.2248	−	26.7686i	−0.405919	−	0.888838i	0.590717	−	0.806879i	$-0.298845\pi$
$908$		0			0
$909$	−12.0230	−	3.53026i	−0.398777	−	0.117091i
$910$		0			0
$911$	0.907287	−	6.31032i	0.0300598	−	0.209070i	−0.969256	−	0.246054i	$-0.920866\pi$
$911$	0.907287	−	6.31032i	0.0300598	−	0.209070i	0.999316	+	0.0369838i	$0.0117750\pi$
$912$		0			0
$913$	0.955386	−	2.09200i	0.0316187	−	0.0692352i
$914$		0			0
$915$	7.79487	+	54.2145i	0.257690	+	1.79228i
$916$		0			0
$917$	1.98472	+	2.29049i	0.0655412	+	0.0756385i
$918$		0			0
$919$	−21.7958			−0.718978			−0.359489	−	0.933149i	$-0.617049\pi$
$919$	−21.7958			−0.718978			−0.359489	+	0.933149i	$0.617049\pi$
$920$		0			0
$921$	−75.4861			−2.48735
$922$		0			0
$923$	−4.43813	−	5.12188i	−0.146083	−	0.168589i
$924$		0			0
$925$	−3.81156	−	26.5100i	−0.125323	−	0.871644i
$926$		0			0
$927$	−6.55595	+	14.3555i	−0.215326	+	0.471497i
$928$		0			0
$929$	−2.82208	+	19.6280i	−0.0925895	+	0.643974i	0.889692	+	0.456562i	$0.150919\pi$
$929$	−2.82208	+	19.6280i	−0.0925895	+	0.643974i	−0.982281	+	0.187412i	$0.939990\pi$
$930$		0			0
$931$	−22.8145	−	6.69894i	−0.747715	−	0.219549i
$932$		0			0
$933$	19.8037	+	43.3640i	0.648343	+	1.41967i
$934$		0			0
$935$	17.1946	−	19.8436i	0.562324	−	0.648956i
$936$		0			0
$937$	42.7597	+	27.4800i	1.39690	+	0.897733i	0.999799	−	0.0200420i	$-0.00637999\pi$
$937$	42.7597	+	27.4800i	1.39690	+	0.897733i	0.397101	+	0.917775i	$0.370016\pi$
$938$		0			0
$939$	−70.5111	+	45.3147i	−2.30104	+	1.47879i
$940$		0			0
$941$	37.5474	−	11.0249i	1.22401	−	0.359402i	0.395025	−	0.918670i	$-0.370736\pi$
$941$	37.5474	−	11.0249i	1.22401	−	0.359402i	0.828987	+	0.559268i	$0.188918\pi$
$942$		0			0
$943$	−42.7551	−	4.40821i	−1.39230	−	0.143551i
$944$		0			0
$945$	4.66566	−	1.36996i	0.151774	−	0.0445648i
$946$		0			0
$947$	−41.6890	+	26.7919i	−1.35471	+	0.870620i	−0.997976	−	0.0635852i	$-0.979747\pi$
$947$	−41.6890	+	26.7919i	−1.35471	+	0.870620i	−0.356735	+	0.934206i	$0.616110\pi$
$948$		0			0
$949$	19.3329	+	12.4245i	0.627571	+	0.403315i
$950$		0			0
$951$	−2.19286	+	2.53069i	−0.0711082	+	0.0820632i
$952$		0			0
$953$	−14.0575	−	30.7817i	−0.455368	−	0.997117i	−0.988519	−	0.151097i	$-0.951720\pi$
$953$	−14.0575	−	30.7817i	−0.455368	−	0.997117i	0.533151	−	0.846020i	$-0.321008\pi$
$954$		0			0
$955$	30.0348	+	8.81903i	0.971905	+	0.285377i
$956$		0			0
$957$	−0.139620	+	0.971078i	−0.00451327	+	0.0313905i
$958$		0			0
$959$	4.46049	−	9.76710i	0.144037	−	0.315396i
$960$		0			0
$961$	−2.50757	−	17.4406i	−0.0808895	−	0.562599i
$962$		0			0
$963$	−24.5092	−	28.2851i	−0.789797	−	0.911474i
$964$		0			0
$965$	−38.6937			−1.24559
$966$		0			0
$967$	3.69582			0.118850			0.0594248	−	0.998233i	$-0.481073\pi$
$967$	3.69582			0.118850			0.0594248	+	0.998233i	$0.481073\pi$
$968$		0			0
$969$	14.8213	+	17.1047i	0.476129	+	0.549482i
$970$		0			0
$971$	−8.83525	−	61.4505i	−0.283537	−	1.97204i	−0.228429	−	0.973561i	$-0.573359\pi$
$971$	−8.83525	−	61.4505i	−0.283537	−	1.97204i	−0.0551076	−	0.998480i	$-0.517550\pi$
$972$		0			0
$973$	−6.04474	+	13.2361i	−0.193786	+	0.424331i
$974$		0			0
$975$	1.27185	−	8.84588i	0.0407317	−	0.283295i
$976$		0			0
$977$	−2.26443	−	0.664897i	−0.0724456	−	0.0212719i	0.245309	−	0.969445i	$-0.421111\pi$
$977$	−2.26443	−	0.664897i	−0.0724456	−	0.0212719i	−0.317755	+	0.948173i	$0.602929\pi$
$978$		0			0
$979$	−3.98206	−	8.71949i	−0.127267	−	0.278676i
$980$		0			0
$981$	1.92288	−	2.21912i	0.0613929	−	0.0708511i
$982$		0			0
$983$	37.1004	+	23.8430i	1.18332	+	0.760472i	0.975993	−	0.217800i	$-0.0698880\pi$
$983$	37.1004	+	23.8430i	1.18332	+	0.760472i	0.207325	+	0.978272i	$0.433524\pi$
$984$		0			0
$985$	−32.3237	+	20.7732i	−1.02992	+	0.661888i
$986$		0			0
$987$	63.1053	−	18.5294i	2.00866	−	0.589796i
$988$		0			0
$989$	−41.9144	+	21.2099i	−1.33280	+	0.674434i
$990$		0			0
$991$	14.3205	−	4.20487i	0.454905	−	0.133572i	−0.0462498	−	0.998930i	$-0.514727\pi$
$991$	14.3205	−	4.20487i	0.454905	−	0.133572i	0.501154	+	0.865358i	$0.332909\pi$
$992$		0			0
$993$	0.00687926	−	0.00442103i	0.000218307	−	0.000140297i
$994$		0			0
$995$	−15.1509	−	9.73689i	−0.480316	−	0.308680i
$996$		0			0
$997$	8.73795	−	10.0841i	0.276734	−	0.319368i	−0.600320	−	0.799760i	$-0.704960\pi$
$997$	8.73795	−	10.0841i	0.276734	−	0.319368i	0.877054	+	0.480392i	$0.159506\pi$
$998$		0			0
$999$	2.47079	+	5.41026i	0.0781722	+	0.171173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.2.i.b.9.1	✓	30
4.3	odd	2		368.2.m.e.193.3		30
23.8	even	11		4232.2.a.bb.1.13		15
23.15	odd	22		4232.2.a.ba.1.13		15
23.18	even	11	inner	184.2.i.b.41.1	yes	30
92.15	even	22		8464.2.a.ch.1.3		15
92.31	odd	22		8464.2.a.cg.1.3		15
92.87	odd	22		368.2.m.e.225.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.9.1	✓	30	1.1	even	1	trivial
184.2.i.b.41.1	yes	30	23.18	even	11	inner
368.2.m.e.193.3		30	4.3	odd	2
368.2.m.e.225.3		30	92.87	odd	22
4232.2.a.ba.1.13		15	23.15	odd	22
4232.2.a.bb.1.13		15	23.8	even	11
8464.2.a.cg.1.3		15	92.31	odd	22
8464.2.a.ch.1.3		15	92.15	even	22

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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63153 - 1.88288i) q^{3} +(-0.385137 - 2.67869i) q^{5} +(-1.44647 + 3.16732i) q^{7} +(-0.456422 + 3.17448i) q^{9} +O(q^{10})\)	\(q+(-1.63153 - 1.88288i) q^{3} +(-0.385137 - 2.67869i) q^{5} +(-1.44647 + 3.16732i) q^{7} +(-0.456422 + 3.17448i) q^{9} +(-4.75524 - 1.39626i) q^{11} +(-0.641271 - 1.40419i) q^{13} +(-4.41529 + 5.09552i) q^{15} +(-1.64693 - 1.05842i) q^{17} +(3.90366 - 2.50873i) q^{19} +(8.32364 - 2.44404i) q^{21} +(1.16577 - 4.65199i) q^{23} +(-2.22957 + 0.654662i) q^{25} +(0.434117 - 0.278990i) q^{27} +(0.0668418 + 0.0429566i) q^{29} +(4.56621 - 5.26969i) q^{31} +(5.12930 + 11.2316i) q^{33} +(9.04135 + 2.65478i) q^{35} +(-1.64030 + 11.4085i) q^{37} +(-1.59767 + 3.49841i) q^{39} +(-1.27547 - 8.87110i) q^{41} +(-6.41438 - 7.40258i) q^{43} +8.67923 q^{45} +7.58145 q^{47} +(-3.35562 - 3.87260i) q^{49} +(0.694133 + 4.82780i) q^{51} +(3.78454 - 8.28699i) q^{53} +(-1.90874 + 13.2756i) q^{55} +(-11.0926 - 3.25707i) q^{57} +(3.40314 + 7.45184i) q^{59} +(5.31982 - 6.13940i) q^{61} +(-9.39440 - 6.03742i) q^{63} +(-3.51440 + 2.25857i) q^{65} +(-3.11750 + 0.915379i) q^{67} +(-10.6611 + 5.39483i) q^{69} +(4.21244 - 1.23688i) q^{71} +(-12.5238 + 8.04857i) q^{73} +(4.87026 + 3.12992i) q^{75} +(11.3007 - 13.0417i) q^{77} +(-2.37381 - 5.19793i) q^{79} +(7.99807 + 2.34844i) q^{81} +(-0.0660414 + 0.459328i) q^{83} +(-2.20087 + 4.81924i) q^{85} +(-0.0281720 - 0.195940i) q^{87} +(1.26661 + 1.46175i) q^{89} +5.37509 q^{91} -17.3721 q^{93} +(-8.22354 - 9.49048i) q^{95} +(0.241080 + 1.67675i) q^{97} +(6.60281 - 14.4581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9	\( 30 q + 2 q^{3} - 13 q^{7} + 21 q^{9} + 2 q^{11} - 2 q^{15} - 22 q^{17} + 3 q^{19} + 2 q^{21} + q^{23} + 13 q^{25} - 31 q^{27} + 7 q^{29} + 18 q^{31} - 8 q^{33} + 41 q^{35} - 62 q^{37} + 6 q^{39} - 15 q^{41} - 47 q^{43} + 8 q^{45} - 72 q^{47} - 16 q^{49} - 7 q^{51} - 43 q^{53} - 9 q^{55} - 42 q^{57} - 11 q^{59} + 57 q^{61} - 62 q^{63} + 14 q^{65} - 27 q^{67} - 22 q^{69} + 48 q^{71} - 12 q^{73} + 87 q^{75} - 3 q^{77} + 8 q^{79} + 123 q^{81} - 18 q^{83} + 54 q^{85} + 137 q^{87} - 23 q^{89} + 142 q^{91} - 110 q^{93} + 119 q^{95} + 47 q^{97} - 17 q^{99}+O(q^{100}) \) 30 * q + 2 * q^3 - 13 * q^7 + 21 * q^9 + 2 * q^11 - 2 * q^15 - 22 * q^17 + 3 * q^19 + 2 * q^21 + q^23 + 13 * q^25 - 31 * q^27 + 7 * q^29 + 18 * q^31 - 8 * q^33 + 41 * q^35 - 62 * q^37 + 6 * q^39 - 15 * q^41 - 47 * q^43 + 8 * q^45 - 72 * q^47 - 16 * q^49 - 7 * q^51 - 43 * q^53 - 9 * q^55 - 42 * q^57 - 11 * q^59 + 57 * q^61 - 62 * q^63 + 14 * q^65 - 27 * q^67 - 22 * q^69 + 48 * q^71 - 12 * q^73 + 87 * q^75 - 3 * q^77 + 8 * q^79 + 123 * q^81 - 18 * q^83 + 54 * q^85 + 137 * q^87 - 23 * q^89 + 142 * q^91 - 110 * q^93 + 119 * q^95 + 47 * q^97 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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