LMFDB - Embedded newform 108.4.i.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	108.13
Dual form			108.4.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.52704 + 2.55067i) q^{3} +(-1.73722 - 1.45770i) q^{5} +(-5.32680 - 1.93880i) q^{7} +(13.9881 - 23.0940i) q^{9} +O(q^{10})$	\(q+(-4.52704 + 2.55067i) q^{3} +(-1.73722 - 1.45770i) q^{5} +(-5.32680 - 1.93880i) q^{7} +(13.9881 - 23.0940i) q^{9} +(19.5694 - 16.4207i) q^{11} +(6.38352 - 36.2027i) q^{13} +(11.5826 + 2.16798i) q^{15} +(49.6174 - 85.9398i) q^{17} +(-15.2603 - 26.4317i) q^{19} +(29.0598 - 4.80992i) q^{21} +(55.1467 - 20.0717i) q^{23} +(-20.8130 - 118.036i) q^{25} +(-4.41958 + 140.226i) q^{27} +(-3.73992 - 21.2102i) q^{29} +(-226.385 + 82.3974i) q^{31} +(-46.7076 + 124.252i) q^{33} +(6.42762 + 11.1330i) q^{35} +(-23.8246 + 41.2654i) q^{37} +(63.4429 + 180.173i) q^{39} +(16.7572 - 95.0347i) q^{41} +(-124.156 + 104.179i) q^{43} +(-57.9645 + 19.7288i) q^{45} +(323.003 + 117.563i) q^{47} +(-238.137 - 199.821i) q^{49} +(-5.41531 + 515.610i) q^{51} +343.554 q^{53} -57.9326 q^{55} +(136.503 + 80.7331i) q^{57} +(-212.363 - 178.194i) q^{59} +(-327.611 - 119.241i) q^{61} +(-119.286 + 95.8968i) q^{63} +(-63.8622 + 53.5868i) q^{65} +(-78.4747 + 445.052i) q^{67} +(-198.455 + 231.527i) q^{69} +(407.568 - 705.928i) q^{71} +(71.6513 + 124.104i) q^{73} +(395.293 + 481.268i) q^{75} +(-136.078 + 49.5285i) q^{77} +(-156.000 - 884.718i) q^{79} +(-337.664 - 646.083i) q^{81} +(81.0870 + 459.867i) q^{83} +(-211.470 + 76.9690i) q^{85} +(71.0310 + 86.4799i) q^{87} +(-218.426 - 378.326i) q^{89} +(-104.193 + 180.468i) q^{91} +(814.684 - 950.450i) q^{93} +(-12.0189 + 68.1626i) q^{95} +(1103.50 - 925.949i) q^{97} +(-105.479 - 681.629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.52704	+	2.55067i	−0.871229	+	0.490877i
$3$	−4.52704	+	2.55067i	−0.871229	+	0.490877i
$4$		0			0
$5$	−1.73722	−	1.45770i	−0.155381	−	0.130381i	0.561783	−	0.827285i	$-0.310116\pi$
$5$	−1.73722	−	1.45770i	−0.155381	−	0.130381i	−0.717164	+	0.696904i	$0.754560\pi$
$6$		0			0
$7$	−5.32680	−	1.93880i	−0.287620	−	0.104685i	0.194181	−	0.980966i	$-0.437795\pi$
$7$	−5.32680	−	1.93880i	−0.287620	−	0.104685i	−0.481801	+	0.876281i	$0.660017\pi$
$8$		0			0
$9$	13.9881	−	23.0940i	0.518079	−	0.855333i
$10$		0			0
$11$	19.5694	−	16.4207i	0.536399	−	0.450092i	−0.333905	−	0.942607i	$-0.608367\pi$
$11$	19.5694	−	16.4207i	0.536399	−	0.450092i	0.870304	+	0.492514i	$0.163922\pi$
$12$		0			0
$13$	6.38352	−	36.2027i	0.136190	−	0.772372i	−0.837834	−	0.545926i	$-0.816178\pi$
$13$	6.38352	−	36.2027i	0.136190	−	0.772372i	0.974024	−	0.226446i	$-0.0727108\pi$
$14$		0			0
$15$	11.5826	+	2.16798i	0.199374	+	0.0373180i
$16$		0			0
$17$	49.6174	−	85.9398i	0.707881	−	1.22609i	−0.257761	−	0.966209i	$-0.582985\pi$
$17$	49.6174	−	85.9398i	0.707881	−	1.22609i	0.965642	−	0.259877i	$-0.0836821\pi$
$18$		0			0
$19$	−15.2603	−	26.4317i	−0.184261	−	0.319150i	0.759066	−	0.651014i	$-0.225656\pi$
$19$	−15.2603	−	26.4317i	−0.184261	−	0.319150i	−0.943327	+	0.331864i	$0.892323\pi$
$20$		0			0
$21$	29.0598	−	4.80992i	0.301970	−	0.0499814i
$22$		0			0
$23$	55.1467	−	20.0717i	0.499951	−	0.181967i	−0.0797209	−	0.996817i	$-0.525403\pi$
$23$	55.1467	−	20.0717i	0.499951	−	0.181967i	0.579672	+	0.814850i	$0.303181\pi$
$24$		0			0
$25$	−20.8130	−	118.036i	−0.166504	−	0.944290i
$26$		0			0
$27$	−4.41958	+	140.226i	−0.0315018	+	0.999504i
$28$		0			0
$29$	−3.73992	−	21.2102i	−0.0239478	−	0.135815i	0.970490	−	0.241142i	$-0.0775220\pi$
$29$	−3.73992	−	21.2102i	−0.0239478	−	0.135815i	−0.994438	+	0.105327i	$0.966411\pi$
$30$		0			0
$31$	−226.385	+	82.3974i	−1.31161	+	0.477387i	−0.900761	−	0.434316i	$-0.856990\pi$
$31$	−226.385	+	82.3974i	−1.31161	+	0.477387i	−0.410850	+	0.911703i	$0.634768\pi$
$32$		0			0
$33$	−46.7076	+	124.252i	−0.246386	+	0.655440i
$34$		0			0
$35$	6.42762	+	11.1330i	0.0310419	+	0.0537662i
$36$		0			0
$37$	−23.8246	+	41.2654i	−0.105858	+	0.183351i	−0.914088	−	0.405515i	$-0.867092\pi$
$37$	−23.8246	+	41.2654i	−0.105858	+	0.183351i	0.808230	+	0.588866i	$0.200426\pi$
$38$		0			0
$39$	63.4429	+	180.173i	0.260487	+	0.739765i
$40$		0			0
$41$	16.7572	−	95.0347i	0.0638300	−	0.361998i	−0.936117	−	0.351689i	$-0.885607\pi$
$41$	16.7572	−	95.0347i	0.0638300	−	0.361998i	0.999947	−	0.0103090i	$-0.00328150\pi$
$42$		0			0
$43$	−124.156	+	104.179i	−0.440315	+	0.369468i	−0.835827	−	0.548993i	$-0.815011\pi$
$43$	−124.156	+	104.179i	−0.440315	+	0.369468i	0.395512	+	0.918461i	$0.370567\pi$
$44$		0			0
$45$	−57.9645	+	19.7288i	−0.192019	+	0.0653555i
$46$		0			0
$47$	323.003	+	117.563i	1.00244	+	0.364859i	0.790526	−	0.612429i	$-0.209807\pi$
$47$	323.003	+	117.563i	1.00244	+	0.364859i	0.211916	+	0.977288i	$0.432030\pi$
$48$		0			0
$49$	−238.137	−	199.821i	−0.694278	−	0.582569i
$50$		0			0
$51$	−5.41531	+	515.610i	−0.0148685	+	1.41568i
$52$		0			0
$53$	343.554			0.890391			0.445196	−	0.895433i	$-0.353134\pi$
$53$	343.554			0.890391			0.445196	+	0.895433i	$0.353134\pi$
$54$		0			0
$55$	−57.9326			−0.142030
$56$		0			0
$57$	136.503	+	80.7331i	0.317197	+	0.187603i
$58$		0			0
$59$	−212.363	−	178.194i	−0.468598	−	0.393201i	0.377685	−	0.925934i	$-0.376720\pi$
$59$	−212.363	−	178.194i	−0.468598	−	0.393201i	−0.846283	+	0.532734i	$0.821165\pi$
$60$		0			0
$61$	−327.611	−	119.241i	−0.687643	−	0.250282i	−0.0255176	−	0.999674i	$-0.508123\pi$
$61$	−327.611	−	119.241i	−0.687643	−	0.250282i	−0.662126	+	0.749393i	$0.730346\pi$
$62$		0			0
$63$	−119.286	+	95.8968i	−0.238550	+	0.191776i
$64$		0			0
$65$	−63.8622	+	53.5868i	−0.121864	+	0.102256i
$66$		0			0
$67$	−78.4747	+	445.052i	−0.143093	+	0.811519i	0.825786	+	0.563983i	$0.190732\pi$
$67$	−78.4747	+	445.052i	−0.143093	+	0.811519i	−0.968879	+	0.247536i	$0.920379\pi$
$68$		0			0
$69$	−198.455	+	231.527i	−0.346248	+	0.403950i
$70$		0			0
$71$	407.568	−	705.928i	0.681259	−	1.17998i	−0.293338	−	0.956009i	$-0.594766\pi$
$71$	407.568	−	705.928i	0.681259	−	1.17998i	0.974597	−	0.223967i	$-0.0719007\pi$
$72$		0			0
$73$	71.6513	+	124.104i	0.114879	+	0.198976i	0.917731	−	0.397202i	$-0.130019\pi$
$73$	71.6513	+	124.104i	0.114879	+	0.198976i	−0.802852	+	0.596178i	$0.796685\pi$
$74$		0			0
$75$	395.293	+	481.268i	0.608594	+	0.740960i
$76$		0			0
$77$	−136.078	+	49.5285i	−0.201397	+	0.0733025i
$78$		0			0
$79$	−156.000	−	884.718i	−0.222169	−	1.25998i	−0.868024	−	0.496522i	$-0.834610\pi$
$79$	−156.000	−	884.718i	−0.222169	−	1.25998i	0.645855	−	0.763460i	$-0.276501\pi$
$80$		0			0
$81$	−337.664	−	646.083i	−0.463188	−	0.886260i
$82$		0			0
$83$	81.0870	+	459.867i	0.107234	+	0.608157i	0.990304	+	0.138915i	$0.0443615\pi$
$83$	81.0870	+	459.867i	0.107234	+	0.608157i	−0.883070	+	0.469241i	$0.844527\pi$
$84$		0			0
$85$	−211.470	+	76.9690i	−0.269849	+	0.0982171i
$86$		0			0
$87$	71.0310	+	86.4799i	0.0875324	+	0.106570i
$88$		0			0
$89$	−218.426	−	378.326i	−0.260148	−	0.450589i	0.706133	−	0.708079i	$-0.250438\pi$
$89$	−218.426	−	378.326i	−0.260148	−	0.450589i	−0.966281	+	0.257490i	$0.917105\pi$
$90$		0			0
$91$	−104.193	+	180.468i	−0.120027	+	0.207892i
$92$		0			0
$93$	814.684	−	950.450i	0.908374	−	1.05975i
$94$		0			0
$95$	−12.0189	+	68.1626i	−0.0129801	+	0.0736140i
$96$		0			0
$97$	1103.50	−	925.949i	1.15509	−	0.969236i	0.155264	−	0.987873i	$-0.450377\pi$
$97$	1103.50	−	925.949i	1.15509	−	0.969236i	0.999826	+	0.0186370i	$0.00593269\pi$
$98$		0			0
$99$	−105.479	−	681.629i	−0.107082	−	0.691983i
$100$		0			0
$101$	405.014	+	147.413i	0.399014	+	0.145229i	0.533730	−	0.845655i	$-0.320790\pi$
$101$	405.014	+	147.413i	0.399014	+	0.145229i	−0.134716	+	0.990884i	$0.543012\pi$
$102$		0			0
$103$	−422.424	−	354.456i	−0.404104	−	0.339083i	0.417973	−	0.908459i	$-0.362741\pi$
$103$	−422.424	−	354.456i	−0.404104	−	0.339083i	−0.822077	+	0.569376i	$0.807185\pi$
$104$		0			0
$105$	−57.4947	−	34.0046i	−0.0534372	−	0.0316049i
$106$		0			0
$107$	860.291			0.777266			0.388633	−	0.921393i	$-0.372947\pi$
$107$	860.291			0.777266			0.388633	+	0.921393i	$0.372947\pi$
$108$		0			0
$109$	2113.40			1.85713			0.928563	−	0.371176i	$-0.121045\pi$
$109$	2113.40			1.85713			0.928563	+	0.371176i	$0.121045\pi$
$110$		0			0
$111$	2.60025	−	247.579i	0.00222347	−	0.211704i
$112$		0			0
$113$	−1627.93	−	1366.00i	−1.35525	−	1.13719i	−0.977419	−	0.211313i	$-0.932226\pi$
$113$	−1627.93	−	1366.00i	−1.35525	−	1.13719i	−0.377829	−	0.925875i	$-0.623329\pi$
$114$		0			0
$115$	−125.060	−	45.5182i	−0.101408	−	0.0369095i
$116$		0			0
$117$	−746.772	−	653.830i	−0.590078	−	0.516637i
$118$		0			0
$119$	−430.921	+	361.586i	−0.331954	+	0.278542i
$120$		0			0
$121$	−117.803	+	668.095i	−0.0885072	+	0.501949i
$122$		0			0
$123$	166.542	+	472.968i	0.122086	+	0.346716i
$124$		0			0
$125$	−277.641	+	480.888i	−0.198663	+	0.344095i
$126$		0			0
$127$	1062.08	+	1839.58i	0.742083	+	1.28533i	0.951545	+	0.307509i	$0.0994954\pi$
$127$	1062.08	+	1839.58i	0.742083	+	1.28533i	−0.209462	+	0.977817i	$0.567171\pi$
$128$		0			0
$129$	296.330	−	788.302i	0.202251	−	0.538032i
$130$		0			0
$131$	−1522.41	+	554.114i	−1.01537	+	0.369566i	−0.795494	−	0.605961i	$-0.792789\pi$
$131$	−1522.41	+	554.114i	−1.01537	+	0.369566i	−0.219880	+	0.975527i	$0.570566\pi$
$132$		0			0
$133$	30.0431	+	170.383i	0.0195870	+	0.111083i
$134$		0			0
$135$	212.086	−	237.161i	0.135211	−	0.151197i
$136$		0			0
$137$	498.807	+	2828.87i	0.311065	+	1.76414i	0.593483	+	0.804847i	$0.297752\pi$
$137$	498.807	+	2828.87i	0.311065	+	1.76414i	−0.282418	+	0.959291i	$0.591136\pi$
$138$		0			0
$139$	−2332.30	+	848.889i	−1.42319	+	0.517999i	−0.934971	−	0.354723i	$-0.884575\pi$
$139$	−2332.30	+	848.889i	−1.42319	+	0.517999i	−0.488218	+	0.872722i	$0.662353\pi$
$140$		0			0
$141$	−1762.11	+	291.661i	−1.05246	+	0.174200i
$142$		0			0
$143$	−469.551	−	813.287i	−0.274586	−	0.475598i
$144$		0			0
$145$	−24.4210	+	42.2983i	−0.0139866	+	0.0242254i
$146$		0			0
$147$	1587.74	+	297.186i	0.890845	+	0.166745i
$148$		0			0
$149$	−553.705	+	3140.22i	−0.304438	+	1.72655i	0.321700	+	0.946842i	$0.395746\pi$
$149$	−553.705	+	3140.22i	−0.304438	+	1.72655i	−0.626138	+	0.779712i	$0.715365\pi$
$150$		0			0
$151$	950.851	−	797.859i	0.512445	−	0.429992i	−0.349544	−	0.936920i	$-0.613663\pi$
$151$	950.851	−	797.859i	0.512445	−	0.429992i	0.861989	+	0.506928i	$0.169219\pi$
$152$		0			0
$153$	−1290.64	−	2348.00i	−0.681973	−	1.24068i
$154$		0			0
$155$	513.390	+	186.859i	0.266042	+	0.0968313i
$156$		0			0
$157$	1992.20	+	1671.65i	1.01271	+	0.849761i	0.988693	−	0.149951i	$-0.0479115\pi$
$157$	1992.20	+	1671.65i	1.01271	+	0.849761i	0.0240121	+	0.999712i	$0.492356\pi$
$158$		0			0
$159$	−1555.28	+	876.293i	−0.775734	+	0.437073i
$160$		0			0
$161$	−332.670			−0.162845
$162$		0			0
$163$	1268.83			0.609708			0.304854	−	0.952399i	$-0.401392\pi$
$163$	1268.83			0.609708			0.304854	+	0.952399i	$0.401392\pi$
$164$		0			0
$165$	262.263	−	147.767i	0.123740	−	0.0697192i
$166$		0			0
$167$	−1848.70	−	1551.25i	−0.856628	−	0.718796i	0.104611	−	0.994513i	$-0.466640\pi$
$167$	−1848.70	−	1551.25i	−0.856628	−	0.718796i	−0.961239	+	0.275717i	$0.911085\pi$
$168$		0			0
$169$	794.616	+	289.216i	0.361682	+	0.131642i
$170$		0			0
$171$	−823.877	−	17.3078i	−0.368441	−	0.00774012i
$172$		0			0
$173$	−2855.25	+	2395.84i	−1.25480	+	1.05290i	−0.258587	+	0.965988i	$0.583257\pi$
$173$	−2855.25	+	2395.84i	−1.25480	+	1.05290i	−0.996216	+	0.0869166i	$0.972299\pi$
$174$		0			0
$175$	−117.982	+	669.107i	−0.0509633	+	0.289027i
$176$		0			0
$177$	1415.89	+	265.021i	0.601270	+	0.112543i
$178$		0			0
$179$	1808.10	−	3131.73i	0.754995	−	1.30769i	−0.190382	−	0.981710i	$-0.560973\pi$
$179$	1808.10	−	3131.73i	0.754995	−	1.30769i	0.945377	−	0.325979i	$-0.105694\pi$
$180$		0			0
$181$	1109.38	+	1921.50i	0.455577	+	0.789083i	0.998721	−	0.0505564i	$-0.0160995\pi$
$181$	1109.38	+	1921.50i	0.455577	+	0.789083i	−0.543144	+	0.839640i	$0.682766\pi$
$182$		0			0
$183$	1787.25	−	295.822i	0.721952	−	0.119496i
$184$		0			0
$185$	101.541	−	36.9579i	0.0403538	−	0.0146876i
$186$		0			0
$187$	−440.207	−	2496.54i	−0.172145	−	0.976283i
$188$		0			0
$189$	295.413	−	738.389i	0.113694	−	0.284179i
$190$		0			0
$191$	113.936	+	646.162i	0.0431628	+	0.244789i	0.998754	−	0.0499076i	$-0.0158927\pi$
$191$	113.936	+	646.162i	0.0431628	+	0.244789i	−0.955591	+	0.294696i	$0.904782\pi$
$192$		0			0
$193$	377.376	−	137.354i	0.140747	−	0.0512276i	−0.270686	−	0.962668i	$-0.587251\pi$
$193$	377.376	−	137.354i	0.140747	−	0.0512276i	0.411433	+	0.911440i	$0.365028\pi$
$194$		0			0
$195$	152.424	−	405.481i	0.0559761	−	0.148908i
$196$		0			0
$197$	1359.16	+	2354.14i	0.491555	+	0.851398i	0.999953	−	0.00972432i	$-0.00309540\pi$
$197$	1359.16	+	2354.14i	0.491555	+	0.851398i	−0.508398	+	0.861122i	$0.669762\pi$
$198$		0			0
$199$	262.797	−	455.177i	0.0936138	−	0.162144i	−0.815415	−	0.578876i	$-0.803491\pi$
$199$	262.797	−	455.177i	0.0936138	−	0.162144i	0.909029	+	0.416732i	$0.136825\pi$
$200$		0			0
$201$	−779.925	−	2214.93i	−0.273690	−	0.777260i
$202$		0			0
$203$	−21.2004	+	120.233i	−0.00732992	+	0.0415700i
$204$		0			0
$205$	−167.643	+	140.669i	−0.0571155	+	0.0479256i
$206$		0			0
$207$	307.862	−	1554.32i	0.103372	−	0.521898i
$208$		0			0
$209$	−732.662	−	266.667i	−0.242484	−	0.0882571i
$210$		0			0
$211$	−3546.31	−	2975.70i	−1.15705	−	0.970881i	−0.157190	−	0.987568i	$-0.550244\pi$
$211$	−3546.31	−	2975.70i	−1.15705	−	0.970881i	−0.999861	+	0.0166873i	$0.994688\pi$
$212$		0			0
$213$	−44.4825	+	4235.34i	−0.0143094	+	1.36244i
$214$		0			0
$215$	367.546			0.116588
$216$		0			0
$217$	1365.66			0.427221
$218$		0			0
$219$	−640.916	−	379.063i	−0.197759	−	0.116962i
$220$		0			0
$221$	−2794.52	−	2344.88i	−0.850588	−	0.713728i
$222$		0			0
$223$	−1359.00	−	494.635i	−0.408096	−	0.148535i	0.129812	−	0.991539i	$-0.458563\pi$
$223$	−1359.00	−	494.635i	−0.408096	−	0.148535i	−0.537907	+	0.843004i	$0.680785\pi$
$224$		0			0
$225$	−3017.06	−	1170.45i	−0.893945	−	0.346801i
$226$		0			0
$227$	4668.86	−	3917.63i	1.36512	−	1.14547i	0.390759	−	0.920493i	$-0.372212\pi$
$227$	4668.86	−	3917.63i	1.36512	−	1.14547i	0.974363	−	0.224981i	$-0.0722319\pi$
$228$		0			0
$229$	−184.191	+	1044.60i	−0.0531514	+	0.301437i	−0.999782	−	0.0208842i	$-0.993352\pi$
$229$	−184.191	+	1044.60i	−0.0531514	+	0.301437i	0.946630	+	0.322321i	$0.104463\pi$
$230$		0			0
$231$	489.701	−	571.309i	0.139480	−	0.162725i
$232$		0			0
$233$	444.253	−	769.468i	0.124910	−	0.216350i	−0.796788	−	0.604259i	$-0.793469\pi$
$233$	444.253	−	769.468i	0.124910	−	0.216350i	0.921698	+	0.387909i	$0.126803\pi$
$234$		0			0
$235$	−389.754	−	675.074i	−0.108190	−	0.187391i
$236$		0			0
$237$	2962.84	+	3607.25i	0.812057	+	0.988675i
$238$		0			0
$239$	4785.72	−	1741.86i	1.29524	−	0.471429i	0.399797	−	0.916604i	$-0.369081\pi$
$239$	4785.72	−	1741.86i	1.29524	−	0.471429i	0.895444	+	0.445175i	$0.146858\pi$
$240$		0			0
$241$	−401.648	−	2277.86i	−0.107354	−	0.608837i	−0.990254	−	0.139275i	$-0.955523\pi$
$241$	−401.648	−	2277.86i	−0.107354	−	0.608837i	0.882899	−	0.469562i	$-0.155588\pi$
$242$		0			0
$243$	3176.57	+	2063.57i	0.838588	+	0.544766i
$244$		0			0
$245$	122.418	+	694.265i	0.0319224	+	0.181041i
$246$		0			0
$247$	−1054.31	+	383.739i	−0.271597	+	0.0988532i
$248$		0			0
$249$	−1540.06	−	1875.01i	−0.391956	−	0.477204i
$250$		0			0
$251$	−2065.57	−	3577.67i	−0.519433	−	0.899684i	−0.999745	−	0.0225867i	$-0.992810\pi$
$251$	−2065.57	−	3577.67i	−0.519433	−	0.899684i	0.480312	−	0.877098i	$-0.340524\pi$
$252$		0			0
$253$	749.595	−	1298.34i	0.186271	−	0.322631i
$254$		0			0
$255$	761.012	−	887.833i	0.186888	−	0.218032i
$256$		0			0
$257$	−88.6207	+	502.593i	−0.0215098	+	0.121988i	−0.993672	−	0.112321i	$-0.964172\pi$
$257$	−88.6207	+	502.593i	−0.0215098	+	0.121988i	0.972162	+	0.234309i	$0.0752827\pi$
$258$		0			0
$259$	206.914	−	173.622i	0.0496410	−	0.0416537i
$260$		0			0
$261$	−542.142	−	210.321i	−0.128574	−	0.0498794i
$262$		0			0
$263$	2625.90	+	955.748i	0.615664	+	0.224083i	0.630980	−	0.775799i	$-0.282653\pi$
$263$	2625.90	+	955.748i	0.615664	+	0.224083i	−0.0153157	+	0.999883i	$0.504875\pi$
$264$		0			0
$265$	−596.828	−	500.798i	−0.138350	−	0.116090i
$266$		0			0
$267$	1953.81	+	1155.56i	0.447832	+	0.264866i
$268$		0			0
$269$	4160.31			0.942968			0.471484	−	0.881875i	$-0.343719\pi$
$269$	4160.31			0.942968			0.471484	+	0.881875i	$0.343719\pi$
$270$		0			0
$271$	−5111.90			−1.14585			−0.572926	−	0.819607i	$-0.694192\pi$
$271$	−5111.90			−1.14585			−0.572926	+	0.819607i	$0.694192\pi$
$272$		0			0
$273$	11.3718	−	1082.75i	0.00252107	−	0.240040i
$274$		0			0
$275$	−2345.53	−	1968.13i	−0.514330	−	0.431574i
$276$		0			0
$277$	411.220	+	149.672i	0.0891980	+	0.0324654i	0.386234	−	0.922401i	$-0.373776\pi$
$277$	411.220	+	149.672i	0.0891980	+	0.0324654i	−0.297036	+	0.954866i	$0.595998\pi$
$278$		0			0
$279$	−1263.82	+	6380.71i	−0.271193	+	1.36919i
$280$		0			0
$281$	−533.382	+	447.561i	−0.113235	+	0.0950151i	−0.697647	−	0.716442i	$-0.745770\pi$
$281$	−533.382	+	447.561i	−0.113235	+	0.0950151i	0.584412	+	0.811457i	$0.301325\pi$
$282$		0			0
$283$	−205.873	+	1167.56i	−0.0432433	+	0.245245i	−0.998765	−	0.0496742i	$-0.984182\pi$
$283$	−205.873	+	1167.56i	−0.0432433	+	0.245245i	0.955522	+	0.294919i	$0.0952928\pi$
$284$		0			0
$285$	−119.450	−	339.231i	−0.0248268	−	0.0705063i
$286$		0			0
$287$	−273.515	+	473.742i	−0.0562546	+	0.0974358i
$288$		0			0
$289$	−2467.27	−	4273.43i	−0.502191	−	0.869821i
$290$		0			0
$291$	−2633.81	+	7006.48i	−0.530572	+	1.41143i
$292$		0			0
$293$	6216.76	−	2262.72i	1.23955	−	0.451158i	0.362690	−	0.931910i	$-0.381858\pi$
$293$	6216.76	−	2262.72i	1.23955	−	0.451158i	0.876857	+	0.480752i	$0.159636\pi$
$294$		0			0
$295$	109.168	+	619.122i	0.0215458	+	0.122192i
$296$		0			0
$297$	2216.12	+	2816.72i	0.432971	+	0.550312i
$298$		0			0
$299$	−374.622	−	2124.59i	−0.0724581	−	0.410930i
$300$		0			0
$301$	863.333	−	314.227i	0.165321	−	0.0601720i
$302$		0			0
$303$	−2209.52	+	365.714i	−0.418922	+	0.0693390i
$304$		0			0
$305$	395.314	+	684.704i	0.0742152	+	0.128544i
$306$		0			0
$307$	−2737.00	+	4740.62i	−0.508823	+	0.881308i	0.491124	+	0.871089i	$0.336586\pi$
$307$	−2737.00	+	4740.62i	−0.508823	+	0.881308i	−0.999948	+	0.0102185i	$0.996747\pi$
$308$		0			0
$309$	2816.43	+	527.169i	0.518515	+	0.0970538i
$310$		0			0
$311$	−1849.24	+	10487.6i	−0.337173	+	1.91220i	0.0674546	+	0.997722i	$0.478512\pi$
$311$	−1849.24	+	10487.6i	−0.337173	+	1.91220i	−0.404628	+	0.914482i	$0.632599\pi$
$312$		0			0
$313$	−5515.11	+	4627.73i	−0.995950	+	0.835701i	−0.986418	−	0.164253i	$-0.947479\pi$
$313$	−5515.11	+	4627.73i	−0.995950	+	0.835701i	−0.00953196	+	0.999955i	$0.503034\pi$
$314$		0			0
$315$	347.015	+	7.29001i	0.0620701	+	0.00130395i
$316$		0			0
$317$	82.0633	+	29.8686i	0.0145398	+	0.00529207i	0.349280	−	0.937018i	$-0.386426\pi$
$317$	82.0633	+	29.8686i	0.0145398	+	0.00529207i	−0.334740	+	0.942311i	$0.608648\pi$
$318$		0			0
$319$	−421.473	−	353.658i	−0.0739748	−	0.0620722i
$320$		0			0
$321$	−3894.57	+	2194.32i	−0.677176	+	0.381542i
$322$		0			0
$323$	−3028.71			−0.521740
$324$		0			0
$325$	−4406.10			−0.752019
$326$		0			0
$327$	−9567.42	+	5390.58i	−1.61798	+	0.911621i
$328$		0			0
$329$	−1492.64	−	1252.47i	−0.250127	−	0.209882i
$330$		0			0
$331$	−3752.27	−	1365.71i	−0.623091	−	0.226787i	0.0111304	−	0.999938i	$-0.496457\pi$
$331$	−3752.27	−	1365.71i	−0.623091	−	0.226787i	−0.634221	+	0.773151i	$0.718679\pi$
$332$		0			0
$333$	619.722	+	1127.43i	0.101984	+	0.185534i
$334$		0			0
$335$	785.079	−	658.760i	0.128040	−	0.107438i
$336$		0			0
$337$	1144.62	−	6491.47i	0.185019	−	1.04930i	−0.740911	−	0.671603i	$-0.765606\pi$
$337$	1144.62	−	6491.47i	0.185019	−	1.04930i	0.925931	−	0.377694i	$-0.123283\pi$
$338$		0			0
$339$	10853.9	+	2031.60i	1.73895	+	0.325490i
$340$		0			0
$341$	−3077.19	+	5329.85i	−0.488678	+	0.846416i
$342$		0			0
$343$	1853.27	+	3209.96i	0.291741	+	0.505311i
$344$		0			0
$345$	682.255	−	112.925i	0.106468	−	0.0176223i
$346$		0			0
$347$	9057.25	−	3296.57i	1.40121	−	0.509997i	0.472670	−	0.881240i	$-0.343290\pi$
$347$	9057.25	−	3296.57i	1.40121	−	0.509997i	0.928536	+	0.371242i	$0.121068\pi$
$348$		0			0
$349$	1123.06	+	6369.21i	0.172253	+	0.976895i	0.941267	+	0.337663i	$0.109636\pi$
$349$	1123.06	+	6369.21i	0.172253	+	0.976895i	−0.769014	+	0.639232i	$0.779253\pi$
$350$		0			0
$351$	5048.37	+	1055.14i	0.767698	+	0.160453i
$352$		0			0
$353$	−1919.44	−	10885.7i	−0.289410	−	1.64133i	−0.689093	−	0.724673i	$-0.741991\pi$
$353$	−1919.44	−	10885.7i	−0.289410	−	1.64133i	0.399683	−	0.916653i	$-0.369120\pi$
$354$		0			0
$355$	−1737.06	+	632.240i	−0.259701	+	0.0945234i
$356$		0			0
$357$	1028.51	−	2736.05i	0.152478	−	0.405622i
$358$		0			0
$359$	1362.21	+	2359.42i	0.200264	+	0.346868i	0.948614	−	0.316437i	$-0.102487\pi$
$359$	1362.21	+	2359.42i	0.200264	+	0.346868i	−0.748349	+	0.663305i	$0.769153\pi$
$360$		0			0
$361$	2963.74	−	5133.35i	0.432096	−	0.748411i
$362$		0			0
$363$	−1170.79	−	3324.97i	−0.169286	−	0.480759i
$364$		0			0
$365$	56.4319	−	320.041i	0.00809255	−	0.0458951i
$366$		0			0
$367$	4765.13	−	3998.42i	0.677760	−	0.568708i	−0.237591	−	0.971365i	$-0.576358\pi$
$367$	4765.13	−	3998.42i	0.677760	−	0.568708i	0.915351	+	0.402657i	$0.131913\pi$
$368$		0			0
$369$	−1960.33	−	1716.35i	−0.276560	−	0.242140i
$370$		0			0
$371$	−1830.04	−	666.080i	−0.256094	−	0.0932107i
$372$		0			0
$373$	6859.41	+	5755.73i	0.952190	+	0.798982i	0.979665	−	0.200641i	$-0.0643023\pi$
$373$	6859.41	+	5755.73i	0.952190	+	0.798982i	−0.0274753	+	0.999622i	$0.508747\pi$
$374$		0			0
$375$	30.3021	−	2885.17i	0.00417278	−	0.397305i
$376$		0			0
$377$	−791.740			−0.108161
$378$		0			0
$379$	569.718			0.0772148			0.0386074	−	0.999254i	$-0.487708\pi$
$379$	569.718			0.0772148			0.0386074	+	0.999254i	$0.487708\pi$
$380$		0			0
$381$	−9500.26	−	5618.82i	−1.27746	−	0.755541i
$382$		0			0
$383$	−1839.24	−	1543.30i	−0.245380	−	0.205898i	0.511800	−	0.859105i	$-0.328979\pi$
$383$	−1839.24	−	1543.30i	−0.245380	−	0.205898i	−0.757180	+	0.653206i	$0.773423\pi$
$384$		0			0
$385$	308.595	+	112.320i	0.0408506	+	0.0148684i
$386$		0			0
$387$	669.201	+	4324.51i	0.0879003	+	0.568029i
$388$		0			0
$389$	−2278.94	+	1912.26i	−0.297036	+	0.249243i	−0.779109	−	0.626888i	$-0.784328\pi$
$389$	−2278.94	+	1912.26i	−0.297036	+	0.249243i	0.482073	+	0.876131i	$0.339884\pi$
$390$		0			0
$391$	1011.27	−	5735.20i	0.130798	−	0.741794i
$392$		0			0
$393$	5478.66	−	6391.67i	0.703211	−	0.820400i
$394$		0			0
$395$	−1018.65	+	1764.35i	−0.129756	+	0.224744i
$396$		0			0
$397$	−5487.38	−	9504.43i	−0.693713	−	1.20155i	−0.970613	−	0.240647i	$-0.922640\pi$
$397$	−5487.38	−	9504.43i	−0.693713	−	1.20155i	0.276900	−	0.960899i	$-0.410693\pi$
$398$		0			0
$399$	−570.598	−	694.700i	−0.0715930	−	0.0871641i
$400$		0			0
$401$	12728.6	−	4632.81i	1.58512	−	0.576937i	0.608811	−	0.793315i	$-0.291647\pi$
$401$	12728.6	−	4632.81i	1.58512	−	0.576937i	0.976310	+	0.216378i	$0.0694244\pi$
$402$		0			0
$403$	1537.88	+	8721.74i	0.190092	+	1.07807i
$404$		0			0
$405$	−355.198	+	1614.60i	−0.0435801	+	0.198099i
$406$		0			0
$407$	211.373	+	1198.76i	0.0257429	+	0.145995i
$408$		0			0
$409$	11812.0	−	4299.21i	1.42803	−	0.519761i	0.491665	−	0.870784i	$-0.336388\pi$
$409$	11812.0	−	4299.21i	1.42803	−	0.519761i	0.936367	+	0.351023i	$0.114166\pi$
$410$		0			0
$411$	−9473.65	−	11534.1i	−1.13698	−	1.38427i
$412$		0			0
$413$	785.733	+	1360.93i	0.0936160	+	0.162148i
$414$		0			0
$415$	529.482	−	917.090i	0.0626295	−	0.108478i
$416$		0			0
$417$	8393.18	−	9791.89i	0.985650	−	1.14991i
$418$		0			0
$419$	−2394.23	+	13578.3i	−0.279154	+	1.58316i	0.446294	+	0.894886i	$0.352744\pi$
$419$	−2394.23	+	13578.3i	−0.279154	+	1.58316i	−0.725448	+	0.688277i	$0.758368\pi$
$420$		0			0
$421$	−3826.83	+	3211.09i	−0.443013	+	0.371732i	−0.836835	−	0.547455i	$-0.815597\pi$
$421$	−3826.83	+	3211.09i	−0.443013	+	0.371732i	0.393823	+	0.919186i	$0.371152\pi$
$422$		0			0
$423$	7233.21	−	5814.93i	0.831420	−	0.668396i
$424$		0			0
$425$	−11176.7	−	4067.99i	−1.27565	−	0.464297i
$426$		0			0
$427$	1513.93	+	1270.34i	0.171579	+	0.143972i
$428$		0			0
$429$	4200.11	+	2484.11i	0.472688	+	0.279566i
$430$		0			0
$431$	−13508.3			−1.50968			−0.754838	−	0.655912i	$-0.772284\pi$
$431$	−13508.3			−1.50968			−0.754838	+	0.655912i	$0.772284\pi$
$432$		0			0
$433$	−6126.85			−0.679994			−0.339997	−	0.940427i	$-0.610426\pi$
$433$	−6126.85			−0.679994			−0.339997	+	0.940427i	$0.610426\pi$
$434$		0			0
$435$	2.66534	−	253.776i	0.000293777	−	0.0279716i
$436$		0			0
$437$	−1372.09	−	1151.32i	−0.150196	−	0.126030i
$438$		0			0
$439$	13612.4	+	4954.50i	1.47992	+	0.538646i	0.950774	−	0.309886i	$-0.100291\pi$
$439$	13612.4	+	4954.50i	1.47992	+	0.538646i	0.529144	+	0.848532i	$0.322513\pi$
$440$		0			0
$441$	−7945.76	+	2704.42i	−0.857981	+	0.292022i
$442$		0			0
$443$	3551.99	−	2980.47i	0.380948	−	0.319653i	−0.432126	−	0.901813i	$-0.642237\pi$
$443$	3551.99	−	2980.47i	0.380948	−	0.319653i	0.813074	+	0.582160i	$0.197792\pi$
$444$		0			0
$445$	−172.031	+	975.633i	−0.0183259	+	0.103931i
$446$		0			0
$447$	−5503.02	−	15628.2i	−0.582291	−	1.65367i
$448$		0			0
$449$	−4160.46	+	7206.13i	−0.437292	+	0.757412i	−0.997480	−	0.0709535i	$-0.977396\pi$
$449$	−4160.46	+	7206.13i	−0.437292	+	0.757412i	0.560187	+	0.828366i	$0.310729\pi$
$450$		0			0
$451$	−1232.60	−	2134.93i	−0.128694	−	0.222905i
$452$		0			0
$453$	−2269.46	+	6037.25i	−0.235383	+	0.626169i
$454$		0			0
$455$	444.075	−	161.630i	0.0457551	−	0.0166535i
$456$		0			0
$457$	1535.70	+	8709.37i	0.157192	+	0.891482i	0.956754	+	0.290898i	$0.0939541\pi$
$457$	1535.70	+	8709.37i	0.157192	+	0.891482i	−0.799562	+	0.600584i	$0.794935\pi$
$458$		0			0
$459$	11831.7	+	7337.49i	1.20318	+	0.746154i
$460$		0			0
$461$	−890.872	−	5052.38i	−0.0900044	−	0.510440i	−0.996164	−	0.0875046i	$-0.972111\pi$
$461$	−890.872	−	5052.38i	−0.0900044	−	0.510440i	0.906160	−	0.422936i	$-0.139000\pi$
$462$		0			0
$463$	11339.2	−	4127.13i	1.13818	−	0.414264i	0.296925	−	0.954901i	$-0.404039\pi$
$463$	11339.2	−	4127.13i	1.13818	−	0.414264i	0.841256	+	0.540637i	$0.181817\pi$
$464$		0			0
$465$	−2800.75	+	463.574i	−0.279316	+	0.0462317i
$466$		0			0
$467$	92.2875	+	159.847i	0.00914466	+	0.0158390i	0.870562	−	0.492060i	$-0.163756\pi$
$467$	92.2875	+	159.847i	0.00914466	+	0.0158390i	−0.861417	+	0.507899i	$0.830422\pi$
$468$		0			0
$469$	1280.88	−	2218.56i	0.126110	−	0.218429i
$470$		0			0
$471$	−13282.6	−	2486.19i	−1.29943	−	0.243222i
$472$		0			0
$473$	−718.961	+	4077.43i	−0.0698898	+	0.396365i
$474$		0			0
$475$	−2802.29	+	2351.40i	−0.270690	+	0.227136i
$476$		0			0
$477$	4805.67	−	7934.03i	0.461293	−	0.761581i
$478$		0			0
$479$	85.0550	+	30.9575i	0.00811329	+	0.00295299i	0.346074	−	0.938207i	$-0.387515\pi$
$479$	85.0550	+	30.9575i	0.00811329	+	0.00295299i	−0.337960	+	0.941160i	$0.609737\pi$
$480$		0			0
$481$	1341.84	+	1125.94i	0.127199	+	0.106732i
$482$		0			0
$483$	1506.01	−	848.533i	0.141875	−	0.0799370i
$484$		0			0
$485$	−3266.78			−0.305849
$486$		0			0
$487$	12807.1			1.19167			0.595835	−	0.803107i	$-0.296821\pi$
$487$	12807.1			1.19167			0.595835	+	0.803107i	$0.296821\pi$
$488$		0			0
$489$	−5744.04	+	3236.37i	−0.531195	+	0.299292i
$490$		0			0
$491$	−4314.38	−	3620.19i	−0.396548	−	0.332743i	0.422609	−	0.906312i	$-0.361114\pi$
$491$	−4314.38	−	3620.19i	−0.396548	−	0.332743i	−0.819158	+	0.573568i	$0.805559\pi$
$492$		0			0
$493$	−2008.36	−	730.984i	−0.183473	−	0.0667786i
$494$		0			0
$495$	−810.369	+	1337.90i	−0.0735826	+	0.121483i
$496$		0			0
$497$	−3539.68	+	2970.15i	−0.319470	+	0.268067i
$498$		0			0
$499$	−401.541	+	2277.25i	−0.0360229	+	0.204296i	−0.997507	−	0.0705635i	$-0.977520\pi$
$499$	−401.541	+	2277.25i	−0.0360229	+	0.204296i	0.961484	+	0.274860i	$0.0886314\pi$
$500$		0			0
$501$	12325.9	+	2307.11i	1.09916	+	0.205737i
$502$		0			0
$503$	−7235.56	+	12532.4i	−0.641387	+	1.11092i	0.343736	+	0.939066i	$0.388308\pi$
$503$	−7235.56	+	12532.4i	−0.641387	+	1.11092i	−0.985123	+	0.171849i	$0.945026\pi$
$504$		0			0
$505$	−488.714	−	846.477i	−0.0430643	−	0.0745896i
$506$		0			0
$507$	−4334.95	+	717.511i	−0.379728	+	0.0628517i
$508$		0			0
$509$	12136.9	−	4417.47i	1.05689	−	0.384678i	0.245633	−	0.969363i	$-0.421004\pi$
$509$	12136.9	−	4417.47i	1.05689	−	0.384678i	0.811261	+	0.584685i	$0.198782\pi$
$510$		0			0
$511$	−141.060	−	799.993i	−0.0122116	−	0.0692556i
$512$		0			0
$513$	3773.87	−	2023.09i	0.324796	−	0.174116i
$514$		0			0
$515$	217.153	+	1231.53i	0.0185804	+	0.105375i
$516$		0			0
$517$	8251.43	−	3003.28i	0.701929	−	0.255481i
$518$		0			0
$519$	6814.83	−	18128.9i	0.576373	−	1.53327i
$520$		0			0
$521$	5815.68	+	10073.0i	0.489039	+	0.847041i	0.999920	−	0.0126104i	$-0.00401413\pi$
$521$	5815.68	+	10073.0i	0.489039	+	0.847041i	−0.510881	+	0.859651i	$0.670681\pi$
$522$		0			0
$523$	−7100.15	+	12297.8i	−0.593629	+	1.02820i	0.400110	+	0.916467i	$0.368972\pi$
$523$	−7100.15	+	12297.8i	−0.593629	+	1.02820i	−0.993739	+	0.111728i	$0.964361\pi$
$524$		0			0
$525$	−1172.57	−	3330.01i	−0.0974762	−	0.276826i
$526$		0			0
$527$	−4151.41	+	23543.8i	−0.343147	+	1.94608i
$528$		0			0
$529$	−6682.18	+	5607.02i	−0.549205	+	0.460838i
$530$		0			0
$531$	−7085.76	+	2411.71i	−0.579088	+	0.197099i
$532$		0			0
$533$	−3333.55	−	1213.31i	−0.270904	−	0.0986011i
$534$		0			0
$535$	−1494.51	−	1254.04i	−0.120773	−	0.101340i
$536$		0			0
$537$	−197.339	+	18789.3i	−0.0158581	+	1.50991i
$538$		0			0
$539$	−7941.40			−0.634620
$540$		0			0
$541$	−14803.9			−1.17647			−0.588235	−	0.808690i	$-0.700177\pi$
$541$	−14803.9			−1.17647			−0.588235	+	0.808690i	$0.700177\pi$
$542$		0			0
$543$	−9923.32	−	5869.04i	−0.784255	−	0.463839i
$544$		0			0
$545$	−3671.43	−	3080.69i	−0.288563	−	0.242133i
$546$		0			0
$547$	8475.32	+	3084.76i	0.662483	+	0.241124i	0.651308	−	0.758813i	$-0.274221\pi$
$547$	8475.32	+	3084.76i	0.662483	+	0.241124i	0.0111752	+	0.999938i	$0.496443\pi$
$548$		0			0
$549$	−7336.40	+	5897.88i	−0.570328	+	0.458498i
$550$		0			0
$551$	−503.548	+	422.527i	−0.0389326	+	0.0326683i
$552$		0			0
$553$	−884.309	+	5015.17i	−0.0680012	+	0.385654i
$554$		0			0
$555$	−365.413	+	426.308i	−0.0279476	+	0.0326050i
$556$		0			0
$557$	2010.86	−	3482.91i	0.152967	−	0.264947i	−0.779350	−	0.626589i	$-0.784450\pi$
$557$	2010.86	−	3482.91i	0.152967	−	0.264947i	0.932317	+	0.361642i	$0.117784\pi$
$558$		0			0
$559$	2979.01	+	5159.80i	0.225400	+	0.390405i
$560$		0			0
$561$	8360.69	+	10179.1i	0.629213	+	0.766064i
$562$		0			0
$563$	2100.11	−	764.377i	0.157210	−	0.0572196i	−0.262217	−	0.965009i	$-0.584454\pi$
$563$	2100.11	−	764.377i	0.157210	−	0.0572196i	0.419426	+	0.907789i	$0.362231\pi$
$564$		0			0
$565$	836.860	+	4746.07i	0.0623132	+	0.353396i
$566$		0			0
$567$	546.046	+	4096.22i	0.0404440	+	0.303395i
$568$		0			0
$569$	−1240.71	−	7036.41i	−0.0914117	−	0.518421i	−0.995788	−	0.0916855i	$-0.970775\pi$
$569$	−1240.71	−	7036.41i	−0.0914117	−	0.518421i	0.904376	−	0.426736i	$-0.140337\pi$
$570$		0			0
$571$	−5058.44	+	1841.12i	−0.370734	+	0.134936i	−0.520667	−	0.853760i	$-0.674317\pi$
$571$	−5058.44	+	1841.12i	−0.370734	+	0.134936i	0.149932	+	0.988696i	$0.452094\pi$
$572$		0			0
$573$	−2163.94	−	2634.59i	−0.157766	−	0.192079i
$574$		0			0
$575$	−3516.96	−	6091.56i	−0.255074	−	0.441801i
$576$		0			0
$577$	−869.206	+	1505.51i	−0.0627132	+	0.108622i	−0.895677	−	0.444705i	$-0.853309\pi$
$577$	−869.206	+	1505.51i	−0.0627132	+	0.108622i	0.832964	+	0.553327i	$0.186642\pi$
$578$		0			0
$579$	−1358.05	+	1584.37i	−0.0974761	+	0.113720i
$580$		0			0
$581$	459.655	−	2606.83i	0.0328222	−	0.186144i
$582$		0			0
$583$	6723.13	−	5641.38i	0.477605	−	0.400758i
$584$		0			0
$585$	344.219	+	2224.41i	0.0243277	+	0.157211i
$586$		0			0
$587$	−3342.33	−	1216.51i	−0.235013	−	0.0855379i	0.221829	−	0.975086i	$-0.428797\pi$
$587$	−3342.33	−	1216.51i	−0.235013	−	0.0855379i	−0.456842	+	0.889548i	$0.651020\pi$
$588$		0			0
$589$	5632.61	+	4726.32i	0.394037	+	0.330636i
$590$		0			0
$591$	−12157.6	−	7190.49i	−0.846189	−	0.500469i
$592$		0			0
$593$	1926.38			0.133402			0.0667008	−	0.997773i	$-0.478753\pi$
$593$	1926.38			0.133402			0.0667008	+	0.997773i	$0.478753\pi$
$594$		0			0
$595$	1275.69			0.0878959
$596$		0			0
$597$	−28.6820	+	2730.91i	−0.00196629	+	0.187217i
$598$		0			0
$599$	2265.90	+	1901.31i	0.154561	+	0.129692i	0.716789	−	0.697290i	$-0.245611\pi$
$599$	2265.90	+	1901.31i	0.154561	+	0.129692i	−0.562228	+	0.826982i	$0.690056\pi$
$600$		0			0
$601$	−9704.79	−	3532.26i	−0.658680	−	0.239740i	−0.00901370	−	0.999959i	$-0.502869\pi$
$601$	−9704.79	−	3532.26i	−0.658680	−	0.239740i	−0.649666	+	0.760219i	$0.725091\pi$
$602$		0			0
$603$	9180.31	+	8037.74i	0.619986	+	0.542823i
$604$		0			0
$605$	1178.53	−	988.904i	0.0791968	−	0.0664540i
$606$		0			0
$607$	1586.82	−	8999.33i	0.106107	−	0.601765i	−0.884665	−	0.466228i	$-0.845613\pi$
$607$	1586.82	−	8999.33i	0.106107	−	0.601765i	0.990772	−	0.135537i	$-0.0432761\pi$
$608$		0			0
$609$	−210.701	−	598.375i	−0.0140197	−	0.0398151i
$610$		0			0
$611$	6318.01	−	10943.1i	0.418329	−	0.724568i
$612$		0			0
$613$	−7350.25	−	12731.0i	−0.484296	−	0.838826i	0.515541	−	0.856865i	$-0.327591\pi$
$613$	−7350.25	−	12731.0i	−0.484296	−	0.838826i	−0.999837	+	0.0180389i	$0.994258\pi$
$614$		0			0
$615$	400.124	−	1064.42i	0.0262351	−	0.0697909i
$616$		0			0
$617$	27125.0	−	9872.69i	1.76987	−	0.644181i	0.769890	−	0.638177i	$-0.220311\pi$
$617$	27125.0	−	9872.69i	1.76987	−	0.644181i	0.999982	−	0.00600359i	$-0.00191101\pi$
$618$		0			0
$619$	−4390.06	−	24897.3i	−0.285059	−	1.61665i	−0.705074	−	0.709133i	$-0.749086\pi$
$619$	−4390.06	−	24897.3i	−0.285059	−	1.61665i	0.420015	−	0.907517i	$-0.362025\pi$
$620$		0			0
$621$	2570.87	+	7821.73i	0.166128	+	0.505435i
$622$		0			0
$623$	430.017	+	2438.75i	0.0276537	+	0.156832i
$624$		0			0
$625$	−12895.3	+	4693.51i	−0.825299	+	0.300384i
$626$		0			0
$627$	3996.97	−	661.569i	0.254583	−	0.0421380i
$628$		0			0
$629$	2364.23	+	4094.96i	0.149870	+	0.259582i
$630$		0			0
$631$	8143.24	−	14104.5i	0.513752	−	0.889844i	−0.486121	−	0.873891i	$-0.661589\pi$
$631$	8143.24	−	14104.5i	0.513752	−	0.889844i	0.999873	−	0.0159525i	$-0.00507807\pi$
$632$		0			0
$633$	23644.3	+	4425.65i	1.48464	+	0.277889i
$634$		0			0
$635$	836.486	−	4743.95i	0.0522755	−	0.296469i
$636$		0			0
$637$	−8754.22	+	7345.67i	−0.544513	+	0.456901i
$638$		0			0
$639$	−10601.6	−	19287.0i	−0.656326	−	1.19402i
$640$		0			0
$641$	13181.2	+	4797.57i	0.812211	+	0.295621i	0.714537	−	0.699598i	$-0.246637\pi$
$641$	13181.2	+	4797.57i	0.812211	+	0.295621i	0.0976741	+	0.995218i	$0.468860\pi$
$642$		0			0
$643$	−6177.76	−	5183.75i	−0.378891	−	0.317927i	0.433376	−	0.901213i	$-0.357322\pi$
$643$	−6177.76	−	5183.75i	−0.378891	−	0.317927i	−0.812267	+	0.583286i	$0.801767\pi$
$644$		0			0
$645$	−1663.90	+	937.491i	−0.101575	+	0.0572305i
$646$		0			0
$647$	18799.9			1.14235			0.571175	−	0.820828i	$-0.306488\pi$
$647$	18799.9			1.14235			0.571175	+	0.820828i	$0.306488\pi$
$648$		0			0
$649$	−7081.87			−0.428332
$650$		0			0
$651$	−6182.38	+	3483.35i	−0.372207	+	0.209713i
$652$		0			0
$653$	−22715.5	−	19060.6i	−1.36130	−	1.14226i	−0.975579	−	0.219648i	$-0.929509\pi$
$653$	−22715.5	−	19060.6i	−1.36130	−	1.14226i	−0.385718	−	0.922617i	$-0.626046\pi$
$654$		0			0
$655$	3452.50	+	1256.61i	0.205954	+	0.0749613i
$656$		0			0
$657$	3868.32	+	81.2647i	0.229707	+	0.00482563i
$658$		0			0
$659$	24740.9	−	20760.1i	1.46247	−	1.22716i	0.539679	−	0.841871i	$-0.318546\pi$
$659$	24740.9	−	20760.1i	1.46247	−	1.22716i	0.922795	−	0.385291i	$-0.125899\pi$
$660$		0			0
$661$	2315.53	−	13132.0i	0.136254	−	0.772732i	−0.837725	−	0.546092i	$-0.816115\pi$
$661$	2315.53	−	13132.0i	0.136254	−	0.772732i	0.973979	−	0.226640i	$-0.0727741\pi$
$662$		0			0
$663$	18631.9	+	3487.46i	1.09141	+	0.204286i
$664$		0			0
$665$	196.176	−	339.786i	0.0114396	−	0.0198140i
$666$		0			0
$667$	−631.969	−	1094.60i	−0.0366866	−	0.0635430i
$668$		0			0
$669$	7413.89	−	1227.13i	0.428457	−	0.0709172i
$670$		0			0
$671$	−8369.15	+	3046.12i	−0.481501	+	0.175252i
$672$		0			0
$673$	2027.20	+	11496.8i	0.116111	+	0.658500i	0.986194	+	0.165594i	$0.0529542\pi$
$673$	2027.20	+	11496.8i	0.116111	+	0.658500i	−0.870083	+	0.492906i	$0.835935\pi$
$674$		0			0
$675$	16643.8	−	2396.86i	0.949067	−	0.136674i
$676$		0			0
$677$	789.566	+	4477.85i	0.0448235	+	0.254206i	0.998983	−	0.0450926i	$-0.0143583\pi$
$677$	789.566	+	4477.85i	0.0448235	+	0.254206i	−0.954159	+	0.299299i	$0.903247\pi$
$678$		0			0
$679$	−7673.36	+	2792.88i	−0.433692	+	0.157851i
$680$		0			0
$681$	−11143.5	+	29644.0i	−0.627047	+	1.66808i
$682$		0			0
$683$	−16526.3	−	28624.4i	−0.925859	−	1.60364i	−0.790173	−	0.612884i	$-0.790009\pi$
$683$	−16526.3	−	28624.4i	−0.925859	−	1.60364i	−0.135686	−	0.990752i	$-0.543324\pi$
$684$		0			0
$685$	3257.11	−	5641.48i	0.181675	−	0.314671i
$686$		0			0
$687$	−1830.59	−	5198.74i	−0.101661	−	0.288711i
$688$		0			0
$689$	2193.08	−	12437.6i	0.121262	−	0.687713i
$690$		0			0
$691$	4182.26	−	3509.33i	0.230247	−	0.193200i	−0.520364	−	0.853944i	$-0.674204\pi$
$691$	4182.26	−	3509.33i	0.230247	−	0.193200i	0.750611	+	0.660745i	$0.229759\pi$
$692$		0			0
$693$	−759.672	+	3835.40i	−0.0416415	+	0.210238i
$694$		0			0
$695$	5289.14	+	1925.09i	0.288674	+	0.105069i
$696$		0			0
$697$	−7335.81	−	6155.48i	−0.398657	−	0.334513i
$698$		0			0
$699$	−48.4863	+	4616.55i	−0.00262364	+	0.249806i
$700$		0			0
$701$	27349.1			1.47355			0.736776	−	0.676136i	$-0.236347\pi$
$701$	27349.1			1.47355			0.736776	+	0.676136i	$0.236347\pi$
$702$		0			0
$703$	1454.29			0.0780220
$704$		0			0
$705$	3486.32	+	2061.95i	0.186245	+	0.110152i
$706$		0			0
$707$	−1871.62	−	1570.48i	−0.0995610	−	0.0835416i
$708$		0			0
$709$	−24616.2	−	8959.56i	−1.30392	−	0.474589i	−0.405649	−	0.914029i	$-0.632955\pi$
$709$	−24616.2	−	8959.56i	−1.30392	−	0.474589i	−0.898272	+	0.439440i	$0.855177\pi$
$710$		0			0
$711$	−22613.8	−	8772.90i	−1.19281	−	0.462742i
$712$		0			0
$713$	−10830.5	+	9087.88i	−0.568872	+	0.477340i
$714$		0			0
$715$	−369.814	+	2097.32i	−0.0193430	+	0.109700i
$716$		0			0
$717$	−17222.2	+	20092.3i	−0.897037	+	1.04653i
$718$		0			0
$719$	−356.549	+	617.561i	−0.0184938	+	0.0320322i	−0.875124	−	0.483898i	$-0.839220\pi$
$719$	−356.549	+	617.561i	−0.0184938	+	0.0320322i	0.856630	+	0.515931i	$0.172554\pi$
$720$		0			0
$721$	1562.95	+	2707.11i	0.0807314	+	0.139831i
$722$		0			0
$723$	7628.35	+	9287.48i	0.392395	+	0.477738i
$724$		0			0
$725$	−2425.73	+	882.893i	−0.124261	+	0.0452274i
$726$		0			0
$727$	−1496.29	−	8485.89i	−0.0763334	−	0.432908i	−0.998892	−	0.0470521i	$-0.985017\pi$
$727$	−1496.29	−	8485.89i	−0.0763334	−	0.432908i	0.922559	−	0.385856i	$-0.126094\pi$
$728$		0			0
$729$	−19643.9	−	1239.48i	−0.998015	−	0.0629723i
$730$		0			0
$731$	2792.84	+	15839.0i	0.141309	+	0.801403i
$732$		0			0
$733$	−14280.8	+	5197.80i	−0.719611	+	0.261917i	−0.675761	−	0.737121i	$-0.736185\pi$
$733$	−14280.8	+	5197.80i	−0.719611	+	0.261917i	−0.0438506	+	0.999038i	$0.513963\pi$
$734$		0			0
$735$	−2325.03	−	2830.72i	−0.116680	−	0.142058i
$736$		0			0
$737$	5772.35	+	9998.00i	0.288504	+	0.499703i
$738$		0			0
$739$	−8197.80	+	14199.0i	−0.408066	+	0.706792i	−0.994673	−	0.103080i	$-0.967130\pi$
$739$	−8197.80	+	14199.0i	−0.408066	+	0.706792i	0.586607	+	0.809872i	$0.300463\pi$
$740$		0			0
$741$	3794.13	−	4426.41i	0.188098	−	0.219444i
$742$		0			0
$743$	−2634.69	+	14942.1i	−0.130091	+	0.737781i	0.848063	+	0.529896i	$0.177769\pi$
$743$	−2634.69	+	14942.1i	−0.130091	+	0.737781i	−0.978153	+	0.207885i	$0.933342\pi$
$744$		0			0
$745$	5539.39	−	4648.10i	0.272413	−	0.228582i
$746$		0			0
$747$	11754.4	+	4560.06i	0.575732	+	0.223352i
$748$		0			0
$749$	−4582.59	−	1667.93i	−0.223557	−	0.0813682i
$750$		0			0
$751$	−5652.00	−	4742.59i	−0.274626	−	0.230439i	0.495064	−	0.868857i	$-0.335145\pi$
$751$	−5652.00	−	4742.59i	−0.274626	−	0.230439i	−0.769690	+	0.638418i	$0.779589\pi$
$752$		0			0
$753$	18476.4	+	10927.7i	0.894180	+	0.528853i
$754$		0			0
$755$	−2814.87			−0.135687
$756$		0			0
$757$	23826.1			1.14395			0.571977	−	0.820270i	$-0.306177\pi$
$757$	23826.1			1.14395			0.571977	+	0.820270i	$0.306177\pi$
$758$		0			0
$759$	−81.8118	+	7789.59i	−0.00391249	+	0.372522i
$760$		0			0
$761$	7406.28	+	6214.60i	0.352795	+	0.296030i	0.801911	−	0.597443i	$-0.203817\pi$
$761$	7406.28	+	6214.60i	0.352795	+	0.296030i	−0.449116	+	0.893473i	$0.648261\pi$
$762$		0			0
$763$	−11257.6	−	4097.44i	−0.534146	−	0.194413i
$764$		0			0
$765$	−1180.56	+	5960.35i	−0.0557949	+	0.281695i
$766$		0			0
$767$	−7806.72	+	6550.62i	−0.367515	+	0.308382i
$768$		0			0
$769$	−4584.14	+	25997.9i	−0.214965	+	1.21913i	0.666002	+	0.745950i	$0.268004\pi$
$769$	−4584.14	+	25997.9i	−0.214965	+	1.21913i	−0.880967	+	0.473178i	$0.843107\pi$
$770$		0			0
$771$	−880.761	−	2501.30i	−0.0411412	−	0.116838i
$772$		0			0
$773$	18402.1	−	31873.4i	0.856247	−	1.48306i	−0.0192370	−	0.999815i	$-0.506124\pi$
$773$	18402.1	−	31873.4i	0.856247	−	1.48306i	0.875484	−	0.483248i	$-0.160543\pi$
$774$		0			0
$775$	14437.6	+	25006.7i	0.669180	+	1.15905i
$776$		0			0
$777$	−493.856	+	1313.76i	−0.0228018	+	0.0606576i
$778$		0			0
$779$	−2767.65	+	1007.34i	−0.127293	+	0.0463309i
$780$		0			0
$781$	−3615.96	−	20507.1i	−0.165671	−	0.939567i
$782$		0			0
$783$	2990.76	−	430.696i	0.136502	−	0.0196575i
$784$		0			0
$785$	−1024.12	−	5808.05i	−0.0465634	−	0.264074i
$786$		0			0
$787$	−23907.0	+	8701.45i	−1.08284	+	0.394121i	−0.820963	−	0.570981i	$-0.806563\pi$
$787$	−23907.0	+	8701.45i	−1.08284	+	0.394121i	−0.261875	+	0.965102i	$0.584341\pi$
$788$		0			0
$789$	−14325.3	+	2371.10i	−0.646382	+	0.106988i
$790$		0			0
$791$	6023.28	+	10432.6i	0.270750	+	0.468952i
$792$		0			0
$793$	−6408.14	+	11099.2i	−0.286961	+	0.497031i
$794$		0			0
$795$	3979.23	+	744.818i	0.177521	+	0.0332276i
$796$		0			0
$797$	561.233	−	3182.91i	0.0249434	−	0.141461i	−0.969793	−	0.243930i	$-0.921563\pi$
$797$	561.233	−	3182.91i	0.0249434	−	0.141461i	0.994736	+	0.102469i	$0.0326743\pi$
$798$		0			0
$799$	26129.9	−	21925.6i	1.15696	−	0.970803i
$800$		0			0
$801$	−11792.4	−	247.732i	−0.520181	−	0.0109278i
$802$		0			0
$803$	3440.04	+	1252.07i	0.151178	+	0.0550245i
$804$		0			0
$805$	577.920	+	484.933i	0.0253031	+	0.0212318i
$806$		0			0
$807$	−18833.9	+	10611.6i	−0.821541	+	0.462882i
$808$		0			0
$809$	−5166.02			−0.224509			−0.112254	−	0.993680i	$-0.535807\pi$
$809$	−5166.02			−0.224509			−0.112254	+	0.993680i	$0.535807\pi$
$810$		0			0
$811$	−4953.82			−0.214491			−0.107246	−	0.994233i	$-0.534203\pi$
$811$	−4953.82			−0.214491			−0.107246	+	0.994233i	$0.534203\pi$
$812$		0			0
$813$	23141.8	−	13038.8i	0.998299	−	0.562473i
$814$		0			0
$815$	−2204.23	−	1849.57i	−0.0947373	−	0.0794940i
$816$		0			0
$817$	4648.28	+	1691.84i	0.199049	+	0.0724478i
$818$		0			0
$819$	2710.26	+	4930.66i	0.115634	+	0.210368i
$820$		0			0
$821$	−20677.3	+	17350.3i	−0.878981	+	0.737553i	−0.965969	−	0.258657i	$-0.916720\pi$
$821$	−20677.3	+	17350.3i	−0.878981	+	0.737553i	0.0869882	+	0.996209i	$0.472276\pi$
$822$		0			0
$823$	−4878.12	+	27665.2i	−0.206611	+	1.17175i	0.688274	+	0.725451i	$0.258369\pi$
$823$	−4878.12	+	27665.2i	−0.206611	+	1.17175i	−0.894885	+	0.446297i	$0.852742\pi$
$824$		0			0
$825$	15638.4	+	2927.13i	0.659949	+	0.123527i
$826$		0			0
$827$	10084.8	−	17467.4i	0.424044	−	0.734465i	−0.572287	−	0.820053i	$-0.693944\pi$
$827$	10084.8	−	17467.4i	0.424044	−	0.734465i	0.996331	+	0.0855883i	$0.0272770\pi$
$828$		0			0
$829$	2596.43	+	4497.14i	0.108779	+	0.188410i	0.915276	−	0.402828i	$-0.131973\pi$
$829$	2596.43	+	4497.14i	0.108779	+	0.188410i	−0.806497	+	0.591238i	$0.798639\pi$
$830$		0			0
$831$	−2243.37	+	371.318i	−0.0936484	+	0.0155005i
$832$		0			0
$833$	−28988.3	+	10550.9i	−1.20575	+	0.438855i
$834$		0			0
$835$	950.350	+	5389.70i	0.0393871	+	0.223375i
$836$		0			0
$837$	−10553.8	−	32109.3i	−0.435832	−	1.32600i
$838$		0			0
$839$	6796.07	+	38542.4i	0.279650	+	1.58597i	0.723792	+	0.690018i	$0.242397\pi$
$839$	6796.07	+	38542.4i	0.279650	+	1.58597i	−0.444142	+	0.895956i	$0.646491\pi$
$840$		0			0
$841$	22482.3	−	8182.88i	0.921820	−	0.335515i
$842$		0			0
$843$	1273.06	−	3386.61i	0.0520125	−	0.138364i
$844$		0			0
$845$	−958.830	−	1660.74i	−0.0390352	−	0.0676110i
$846$		0			0
$847$	1922.81	−	3330.41i	0.0780031	−	0.135105i
$848$		0			0
$849$	−2046.08	−	5810.71i	−0.0827105	−	0.234892i
$850$		0			0
$851$	−485.579	+	2753.85i	−0.0195598	+	0.110929i
$852$		0			0
$853$	−10381.3	+	8710.96i	−0.416705	+	0.349657i	−0.826908	−	0.562337i	$-0.809902\pi$
$853$	−10381.3	+	8710.96i	−0.416705	+	0.349657i	0.410203	+	0.911994i	$0.365458\pi$
$854$		0			0
$855$	1406.02	+	1231.03i	0.0562398	+	0.0492402i
$856$		0			0
$857$	28911.2	+	10522.8i	1.15238	+	0.419432i	0.846369	−	0.532596i	$-0.178784\pi$
$857$	28911.2	+	10522.8i	1.15238	+	0.419432i	0.306010	+	0.952028i	$0.401006\pi$
$858$		0			0
$859$	−20278.2	−	17015.4i	−0.805453	−	0.675855i	0.144065	−	0.989568i	$-0.453982\pi$
$859$	−20278.2	−	17015.4i	−0.805453	−	0.675855i	−0.949518	+	0.313713i	$0.898427\pi$
$860$		0			0
$861$	29.8518	−	2842.29i	0.00118159	−	0.112503i
$862$		0			0
$863$	−19823.5			−0.781925			−0.390963	−	0.920407i	$-0.627858\pi$
$863$	−19823.5			−0.781925			−0.390963	+	0.920407i	$0.627858\pi$
$864$		0			0
$865$	8452.61			0.332251
$866$		0			0
$867$	22069.5	+	13052.8i	0.864499	+	0.511299i
$868$		0			0
$869$	−17580.5	−	14751.8i	−0.686280	−	0.575857i
$870$		0			0
$871$	15611.2	+	5682.00i	0.607307	+	0.221042i
$872$		0			0
$873$	−5947.91	−	38436.6i	−0.230591	−	1.49013i
$874$		0			0
$875$	2411.28	−	2023.30i	0.0931612	−	0.0781716i
$876$		0			0
$877$	798.489	−	4528.46i	0.0307446	−	0.174362i	−0.965569	−	0.260147i	$-0.916229\pi$
$877$	798.489	−	4528.46i	0.0307446	−	0.174362i	0.996314	+	0.0857856i	$0.0273400\pi$
$878$		0			0
$879$	−22372.1	+	26100.3i	−0.858466	+	1.00153i
$880$		0			0
$881$	−3156.51	+	5467.23i	−0.120710	+	0.209076i	−0.920048	−	0.391806i	$-0.871850\pi$
$881$	−3156.51	+	5467.23i	−0.120710	+	0.209076i	0.799338	+	0.600882i	$0.205184\pi$
$882$		0			0
$883$	18774.4	+	32518.3i	0.715527	+	1.23933i	0.962756	+	0.270372i	$0.0871467\pi$
$883$	18774.4	+	32518.3i	0.715527	+	1.23933i	−0.247229	+	0.968957i	$0.579520\pi$
$884$		0			0
$885$	−2073.39	−	2524.34i	−0.0787527	−	0.0958810i
$886$		0			0
$887$	−42624.1	+	15513.9i	−1.61350	+	0.587267i	−0.982129	−	0.188211i	$-0.939731\pi$
$887$	−42624.1	+	15513.9i	−1.61350	+	0.587267i	−0.631375	+	0.775478i	$0.717509\pi$
$888$		0			0
$889$	−2090.93	−	11858.2i	−0.0788835	−	0.447370i
$890$		0			0
$891$	−17217.0	−	7098.78i	−0.647353	−	0.266911i
$892$		0			0
$893$	−1821.73	−	10331.6i	−0.0682665	−	0.387159i
$894$		0			0
$895$	−7706.19	+	2804.82i	−0.287809	+	0.104754i
$896$		0			0
$897$	7115.06	+	8662.55i	0.264844	+	0.322446i
$898$		0			0
$899$	2594.32	+	4493.50i	0.0962464	+	0.166704i
$900$		0			0
$901$	17046.2	−	29524.9i	0.630291	−	1.09170i
$902$		0			0
$903$	−3106.85	+	3624.60i	−0.114495	+	0.133576i
$904$		0			0
$905$	873.737	−	4955.21i	0.0320928	−	0.182007i
$906$		0			0
$907$	9498.53	−	7970.21i	0.347732	−	0.291782i	−0.452146	−	0.891944i	$-0.649342\pi$
$907$	9498.53	−	7970.21i	0.347732	−	0.291782i	0.799879	+	0.600162i	$0.204897\pi$
$908$		0			0
$909$	9069.74	−	7291.36i	0.330940	−	0.266050i
$910$		0			0
$911$	14823.9	+	5395.44i	0.539118	+	0.196223i	0.597205	−	0.802089i	$-0.296278\pi$
$911$	14823.9	+	5395.44i	0.539118	+	0.196223i	−0.0580872	+	0.998312i	$0.518500\pi$
$912$		0			0
$913$	9138.15	+	7667.82i	0.331247	+	0.277949i
$914$		0			0
$915$	−3536.06	−	2091.36i	−0.127758	−	0.0755611i
$916$		0			0
$917$	9183.90			0.330730
$918$		0			0
$919$	43295.1			1.55405			0.777025	−	0.629469i	$-0.216728\pi$
$919$	43295.1			1.55405			0.777025	+	0.629469i	$0.216728\pi$
$920$		0			0
$921$	298.720	−	28442.2i	0.0106875	−	1.01759i
$922$		0			0
$923$	−22954.8	−	19261.4i	−0.818599	−	0.686886i
$924$		0			0
$925$	5366.68	+	1953.31i	0.190763	+	0.0694319i
$926$		0			0
$927$	−14094.7	+	4797.28i	−0.499387	+	0.169971i
$928$		0			0
$929$	−18194.5	+	15267.0i	−0.642564	+	0.539176i	−0.904805	−	0.425827i	$-0.859983\pi$
$929$	−18194.5	+	15267.0i	−0.642564	+	0.539176i	0.262240	+	0.965003i	$0.415539\pi$
$930$		0			0
$931$	−1647.55	+	9343.71i	−0.0579981	+	0.328924i
$932$		0			0
$933$	−18378.8	−	52194.4i	−0.644903	−	1.83148i
$934$		0			0
$935$	−2874.47	+	4978.72i	−0.100540	+	0.174141i
$936$		0			0
$937$	1751.71	+	3034.06i	0.0610737	+	0.105783i	0.894946	−	0.446175i	$-0.147214\pi$
$937$	1751.71	+	3034.06i	0.0610737	+	0.105783i	−0.833872	+	0.551958i	$0.813881\pi$
$938$		0			0
$939$	13163.3	−	35017.1i	0.457474	−	1.21698i
$940$		0			0
$941$	−12581.4	+	4579.25i	−0.435857	+	0.158639i	−0.550624	−	0.834754i	$-0.685610\pi$
$941$	−12581.4	+	4579.25i	−0.435857	+	0.158639i	0.114767	+	0.993392i	$0.463388\pi$
$942$		0			0
$943$	−983.409	−	5577.19i	−0.0339599	−	0.192596i
$944$		0			0
$945$	−1589.54	+	852.120i	−0.0547174	+	0.0293328i
$946$		0			0
$947$	2575.71	+	14607.6i	0.0883837	+	0.501249i	0.996575	+	0.0826937i	$0.0263523\pi$
$947$	2575.71	+	14607.6i	0.0883837	+	0.501249i	−0.908191	+	0.418555i	$0.862537\pi$
$948$		0			0
$949$	4950.28	−	1801.76i	0.169329	−	0.0616306i
$950$		0			0
$951$	−447.688	+	74.1004i	−0.0152653	+	0.00252668i
$952$		0			0
$953$	−11115.8	−	19253.1i	−0.377835	−	0.654429i	0.612912	−	0.790151i	$-0.289998\pi$
$953$	−11115.8	−	19253.1i	−0.377835	−	0.654429i	−0.990747	+	0.135722i	$0.956665\pi$
$954$		0			0
$955$	743.978	−	1288.61i	0.0252090	−	0.0436632i
$956$		0			0
$957$	2810.09	+	525.982i	0.0949188	+	0.0177665i
$958$		0			0
$959$	2827.56	−	16035.9i	0.0952104	−	0.539965i
$960$		0			0
$961$	21639.6	−	18157.7i	0.726379	−	0.609504i
$962$		0			0
$963$	12033.9	−	19867.5i	0.402685	−	0.664821i
$964$		0			0
$965$	−855.804	−	311.487i	−0.0285485	−	0.0103908i
$966$		0			0
$967$	13514.4	+	11339.9i	0.449425	+	0.377112i	0.839222	−	0.543788i	$-0.183011\pi$
$967$	13514.4	+	11339.9i	0.449425	+	0.377112i	−0.389798	+	0.920901i	$0.627455\pi$
$968$		0			0
$969$	13711.1	−	7725.26i	0.454555	−	0.256110i
$970$		0			0
$971$	24718.4			0.816944			0.408472	−	0.912771i	$-0.366062\pi$
$971$	24718.4			0.816944			0.408472	+	0.912771i	$0.366062\pi$
$972$		0			0
$973$	14069.5			0.463564
$974$		0			0
$975$	19946.6	−	11238.5i	0.655181	−	0.369149i
$976$		0			0
$977$	14888.2	+	12492.7i	0.487528	+	0.409085i	0.853139	−	0.521683i	$-0.174696\pi$
$977$	14888.2	+	12492.7i	0.487528	+	0.409085i	−0.365611	+	0.930768i	$0.619140\pi$
$978$		0			0
$979$	−10486.8	−	3816.89i	−0.342350	−	0.124605i
$980$		0			0
$981$	29562.5	−	48806.7i	0.962138	−	1.58846i
$982$		0			0
$983$	11737.0	−	9848.53i	0.380827	−	0.319552i	−0.432200	−	0.901778i	$-0.642263\pi$
$983$	11737.0	−	9848.53i	0.380827	−	0.319552i	0.813027	+	0.582226i	$0.197818\pi$
$984$		0			0
$985$	1070.46	−	6070.90i	0.0346272	−	0.196381i
$986$		0			0
$987$	9951.88	+	1862.76i	0.320944	+	0.0600731i
$988$		0			0
$989$	−4755.71	+	8237.13i	−0.152905	+	0.264839i
$990$		0			0
$991$	2778.99	+	4813.35i	0.0890793	+	0.154290i	0.907122	−	0.420867i	$-0.138274\pi$
$991$	2778.99	+	4813.35i	0.0890793	+	0.154290i	−0.818043	+	0.575157i	$0.804941\pi$
$992$		0			0
$993$	20470.1	−	3388.17i	0.654179	−	0.108278i
$994$		0			0
$995$	−1120.05	+	407.663i	−0.0356863	+	0.0129887i
$996$		0			0
$997$	−4994.75	−	28326.6i	−0.158661	−	0.899812i	−0.955362	−	0.295438i	$-0.904534\pi$
$997$	−4994.75	−	28326.6i	−0.158661	−	0.899812i	0.796701	−	0.604374i	$-0.206577\pi$
$998$		0			0
$999$	−5681.21	−	3523.22i	−0.179926	−	0.111581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.13.1	✓	54
3.2	odd	2		324.4.i.a.253.5		54
27.2	odd	18		324.4.i.a.73.5		54
27.25	even	9	inner	108.4.i.a.25.1	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.1	✓	54	1.1	even	1	trivial
108.4.i.a.25.1	yes	54	27.25	even	9	inner
324.4.i.a.73.5		54	27.2	odd	18
324.4.i.a.253.5		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.52704 + 2.55067i) q^{3} +(-1.73722 - 1.45770i) q^{5} +(-5.32680 - 1.93880i) q^{7} +(13.9881 - 23.0940i) q^{9} +O(q^{10})\)	\(q+(-4.52704 + 2.55067i) q^{3} +(-1.73722 - 1.45770i) q^{5} +(-5.32680 - 1.93880i) q^{7} +(13.9881 - 23.0940i) q^{9} +(19.5694 - 16.4207i) q^{11} +(6.38352 - 36.2027i) q^{13} +(11.5826 + 2.16798i) q^{15} +(49.6174 - 85.9398i) q^{17} +(-15.2603 - 26.4317i) q^{19} +(29.0598 - 4.80992i) q^{21} +(55.1467 - 20.0717i) q^{23} +(-20.8130 - 118.036i) q^{25} +(-4.41958 + 140.226i) q^{27} +(-3.73992 - 21.2102i) q^{29} +(-226.385 + 82.3974i) q^{31} +(-46.7076 + 124.252i) q^{33} +(6.42762 + 11.1330i) q^{35} +(-23.8246 + 41.2654i) q^{37} +(63.4429 + 180.173i) q^{39} +(16.7572 - 95.0347i) q^{41} +(-124.156 + 104.179i) q^{43} +(-57.9645 + 19.7288i) q^{45} +(323.003 + 117.563i) q^{47} +(-238.137 - 199.821i) q^{49} +(-5.41531 + 515.610i) q^{51} +343.554 q^{53} -57.9326 q^{55} +(136.503 + 80.7331i) q^{57} +(-212.363 - 178.194i) q^{59} +(-327.611 - 119.241i) q^{61} +(-119.286 + 95.8968i) q^{63} +(-63.8622 + 53.5868i) q^{65} +(-78.4747 + 445.052i) q^{67} +(-198.455 + 231.527i) q^{69} +(407.568 - 705.928i) q^{71} +(71.6513 + 124.104i) q^{73} +(395.293 + 481.268i) q^{75} +(-136.078 + 49.5285i) q^{77} +(-156.000 - 884.718i) q^{79} +(-337.664 - 646.083i) q^{81} +(81.0870 + 459.867i) q^{83} +(-211.470 + 76.9690i) q^{85} +(71.0310 + 86.4799i) q^{87} +(-218.426 - 378.326i) q^{89} +(-104.193 + 180.468i) q^{91} +(814.684 - 950.450i) q^{93} +(-12.0189 + 68.1626i) q^{95} +(1103.50 - 925.949i) q^{97} +(-105.479 - 681.629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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