LMFDB - Embedded newform 125.4.e.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,4,Mod(24,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("125.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, degree $4$, not 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:	$7.37523875072$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	125.49
Dual form			125.4.e.b.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04622 + 2.81638i) q^{2} +(-8.11420 + 2.63646i) q^{3} +(-1.27284 - 3.91740i) q^{4} +(9.17815 - 28.2474i) q^{6} -12.5082i q^{7} +(-12.8494 - 4.17503i) q^{8} +(37.0458 - 26.9153i) q^{9} +O(q^{10})$	\(q+(-2.04622 + 2.81638i) q^{2} +(-8.11420 + 2.63646i) q^{3} +(-1.27284 - 3.91740i) q^{4} +(9.17815 - 28.2474i) q^{6} -12.5082i q^{7} +(-12.8494 - 4.17503i) q^{8} +(37.0458 - 26.9153i) q^{9} +(-30.5650 - 22.2068i) q^{11} +(20.6562 + 28.4308i) q^{12} +(18.7786 + 25.8465i) q^{13} +(35.2278 + 25.5945i) q^{14} +(64.7099 - 47.0145i) q^{16} +(17.8993 + 5.81584i) q^{17} +159.410i q^{18} +(-49.5522 + 152.506i) q^{19} +(32.9774 + 101.494i) q^{21} +(125.085 - 40.6427i) q^{22} +(62.7926 - 86.4266i) q^{23} +115.270 q^{24} -111.218 q^{26} +(-94.2345 + 129.703i) q^{27} +(-48.9997 + 15.9210i) q^{28} +(-33.1890 - 102.145i) q^{29} +(-2.18936 + 6.73816i) q^{31} +170.364i q^{32} +(306.558 + 99.6067i) q^{33} +(-53.0055 + 38.5108i) q^{34} +(-152.592 - 110.864i) q^{36} +(38.0149 + 52.3230i) q^{37} +(-328.120 - 451.619i) q^{38} +(-220.516 - 160.214i) q^{39} +(305.782 - 222.164i) q^{41} +(-353.324 - 114.802i) q^{42} -234.897i q^{43} +(-48.0885 + 148.001i) q^{44} +(114.923 + 353.696i) q^{46} +(101.543 - 32.9933i) q^{47} +(-401.117 + 552.090i) q^{48} +186.545 q^{49} -160.572 q^{51} +(77.3489 - 106.462i) q^{52} +(196.979 - 64.0024i) q^{53} +(-172.467 - 530.800i) q^{54} +(-52.2221 + 160.723i) q^{56} -1368.11i q^{57} +(355.591 + 115.539i) q^{58} +(261.882 - 190.269i) q^{59} +(221.781 + 161.134i) q^{61} +(-14.4973 - 19.9538i) q^{62} +(-336.662 - 463.376i) q^{63} +(37.8690 + 27.5134i) q^{64} +(-907.814 + 659.566i) q^{66} +(134.591 + 43.7313i) q^{67} -77.5215i q^{68} +(-281.651 + 866.833i) q^{69} +(-185.509 - 570.937i) q^{71} +(-588.388 + 191.179i) q^{72} +(-84.9707 + 116.952i) q^{73} -225.148 q^{74} +660.500 q^{76} +(-277.767 + 382.313i) q^{77} +(902.448 - 293.223i) q^{78} +(-98.8328 - 304.176i) q^{79} +(40.6249 - 125.030i) q^{81} +1315.80i q^{82} +(-1059.28 - 344.182i) q^{83} +(355.618 - 258.372i) q^{84} +(661.558 + 480.650i) q^{86} +(538.604 + 741.324i) q^{87} +(300.028 + 412.954i) q^{88} +(-43.7671 - 31.7986i) q^{89} +(323.293 - 234.886i) q^{91} +(-418.493 - 135.977i) q^{92} -60.4469i q^{93} +(-114.857 + 353.495i) q^{94} +(-449.159 - 1382.37i) q^{96} +(1250.98 - 406.468i) q^{97} +(-381.712 + 525.381i) q^{98} -1730.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9}+O(q^{10}) $ 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9	$ 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9} - 178 q^{11} + 34 q^{14} - 414 q^{16} + 230 q^{19} - 288 q^{21} - 1560 q^{24} + 1172 q^{26} + 10 q^{29} - 1278 q^{31} + 1554 q^{34} + 1346 q^{36} + 2266 q^{39} + 682 q^{41} - 1096 q^{44} - 2478 q^{46} - 2688 q^{49} + 4012 q^{51} - 3230 q^{54} - 5820 q^{56} + 3810 q^{59} + 2782 q^{61} + 7192 q^{64} + 7264 q^{66} - 5374 q^{69} - 7438 q^{71} - 9696 q^{74} + 7040 q^{76} - 1550 q^{79} - 7424 q^{81} + 15224 q^{84} + 7782 q^{86} + 10150 q^{89} + 752 q^{91} - 7146 q^{94} - 15508 q^{96} - 13144 q^{99}+O(q^{100}) $ 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9 - 178 * q^11 + 34 * q^14 - 414 * q^16 + 230 * q^19 - 288 * q^21 - 1560 * q^24 + 1172 * q^26 + 10 * q^29 - 1278 * q^31 + 1554 * q^34 + 1346 * q^36 + 2266 * q^39 + 682 * q^41 - 1096 * q^44 - 2478 * q^46 - 2688 * q^49 + 4012 * q^51 - 3230 * q^54 - 5820 * q^56 + 3810 * q^59 + 2782 * q^61 + 7192 * q^64 + 7264 * q^66 - 5374 * q^69 - 7438 * q^71 - 9696 * q^74 + 7040 * q^76 - 1550 * q^79 - 7424 * q^81 + 15224 * q^84 + 7782 * q^86 + 10150 * q^89 + 752 * q^91 - 7146 * q^94 - 15508 * q^96 - 13144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.04622	+	2.81638i	−0.723448	+	0.995740i	0.275955	+	0.961171i	$0.411006\pi$
$2$	−2.04622	+	2.81638i	−0.723448	+	0.995740i	−0.999402	+	0.0345696i	$0.988994\pi$
$3$	−8.11420	+	2.63646i	−1.56158	+	0.507387i	−0.957229	−	0.289332i	$-0.906567\pi$
$3$	−8.11420	+	2.63646i	−1.56158	+	0.507387i	−0.604349	+	0.796720i	$0.706567\pi$
$4$	−1.27284	−	3.91740i	−0.159105	−	0.489676i
$5$		0			0
$5$		0			0
$6$	9.17815	−	28.2474i	0.624494	−	1.92199i
$7$		−	12.5082i		−	0.675379i	−0.941258	−	0.337690i	$-0.890355\pi$
$7$		−	12.5082i		−	0.675379i	0.941258	−	0.337690i	$-0.109645\pi$
$8$	−12.8494	−	4.17503i	−0.567869	−	0.184512i
$9$	37.0458	−	26.9153i	1.37207	−	0.996864i
$10$		0			0
$11$	−30.5650	−	22.2068i	−0.837791	−	0.608691i	0.0839620	−	0.996469i	$-0.473243\pi$
$11$	−30.5650	−	22.2068i	−0.837791	−	0.608691i	−0.921753	+	0.387778i	$0.873243\pi$
$12$	20.6562	+	28.4308i	0.496910	+	0.683938i
$13$	18.7786	+	25.8465i	0.400633	+	0.551424i	0.960903	−	0.276886i	$-0.0893024\pi$
$13$	18.7786	+	25.8465i	0.400633	+	0.551424i	−0.560269	+	0.828310i	$0.689302\pi$
$14$	35.2278	+	25.5945i	0.672502	+	0.488602i
$15$		0			0
$16$	64.7099	−	47.0145i	1.01109	−	0.734602i
$17$	17.8993	+	5.81584i	0.255366	+	0.0829735i	0.433902	−	0.900960i	$-0.357136\pi$
$17$	17.8993	+	5.81584i	0.255366	+	0.0829735i	−0.178536	+	0.983933i	$0.557136\pi$
$18$			159.410i			2.08740i
$19$	−49.5522	+	152.506i	−0.598319	+	1.84144i	−0.0608593	+	0.998146i	$0.519384\pi$
$19$	−49.5522	+	152.506i	−0.598319	+	1.84144i	−0.537459	+	0.843290i	$0.680616\pi$
$20$		0			0
$21$	32.9774	+	101.494i	0.342679	+	1.05466i
$22$	125.085	−	40.6427i	1.21220	−	0.393866i
$23$	62.7926	−	86.4266i	0.569268	−	0.783530i	−0.423200	−	0.906036i	$-0.639093\pi$
$23$	62.7926	−	86.4266i	0.569268	−	0.783530i	0.992468	+	0.122506i	$0.0390931\pi$
$24$	115.270			0.980390
$25$		0			0
$26$	−111.218			−0.838913
$27$	−94.2345	+	129.703i	−0.671683	+	0.924492i
$28$	−48.9997	+	15.9210i	−0.330717	+	0.107456i
$29$	−33.1890	−	102.145i	−0.212519	−	0.654065i	−0.999320	−	0.0368592i	$-0.988265\pi$
$29$	−33.1890	−	102.145i	−0.212519	−	0.654065i	0.786802	−	0.617206i	$-0.211735\pi$
$30$		0			0
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	−0.957198	−	0.289432i	$-0.906533\pi$
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	0.944514	+	0.328471i	$0.106533\pi$
$32$			170.364i			0.941138i
$33$	306.558	+	99.6067i	1.61712	+	0.525433i
$34$	−53.0055	+	38.5108i	−0.267364	+	0.194251i
$35$		0			0
$36$	−152.592	−	110.864i	−0.706443	−	0.513261i
$37$	38.0149	+	52.3230i	0.168908	+	0.232482i	0.885077	−	0.465445i	$-0.154106\pi$
$37$	38.0149	+	52.3230i	0.168908	+	0.232482i	−0.716168	+	0.697928i	$0.754106\pi$
$38$	−328.120	−	451.619i	−1.40074	−	1.92795i
$39$	−220.516	−	160.214i	−0.905406	−	0.657816i
$40$		0			0
$41$	305.782	−	222.164i	1.16476	−	0.846248i	0.174388	−	0.984677i	$-0.444205\pi$
$41$	305.782	−	222.164i	1.16476	−	0.846248i	0.990372	+	0.138429i	$0.0442052\pi$
$42$	−353.324	−	114.802i	−1.29807	−	0.421770i
$43$		−	234.897i		−	0.833056i	−0.909123	−	0.416528i	$-0.863247\pi$
$43$		−	234.897i		−	0.833056i	0.909123	−	0.416528i	$-0.136753\pi$
$44$	−48.0885	+	148.001i	−0.164764	+	0.507091i
$45$		0			0
$46$	114.923	+	353.696i	0.368357	+	1.13369i
$47$	101.543	−	32.9933i	0.315139	−	0.102395i	−0.147177	−	0.989110i	$-0.547019\pi$
$47$	101.543	−	32.9933i	0.315139	−	0.102395i	0.462316	+	0.886715i	$0.347019\pi$
$48$	−401.117	+	552.090i	−1.20617	+	1.66015i
$49$	186.545			0.543863
$50$		0			0
$51$	−160.572			−0.440874
$52$	77.3489	−	106.462i	0.206276	−	0.283915i
$53$	196.979	−	64.0024i	0.510512	−	0.165876i	−0.0424228	−	0.999100i	$-0.513508\pi$
$53$	196.979	−	64.0024i	0.510512	−	0.165876i	0.552935	+	0.833224i	$0.313508\pi$
$54$	−172.467	−	530.800i	−0.434627	−	1.33764i
$55$		0			0
$56$	−52.2221	+	160.723i	−0.124615	+	0.383527i
$57$		−	1368.11i		−	3.17912i
$58$	355.591	+	115.539i	0.805025	+	0.261568i
$59$	261.882	−	190.269i	0.577868	−	0.419845i	−0.260087	−	0.965585i	$-0.583751\pi$
$59$	261.882	−	190.269i	0.577868	−	0.419845i	0.837955	+	0.545740i	$0.183751\pi$
$60$		0			0
$61$	221.781	+	161.134i	0.465511	+	0.338214i	0.795689	−	0.605705i	$-0.207109\pi$
$61$	221.781	+	161.134i	0.465511	+	0.338214i	−0.330178	+	0.943919i	$0.607109\pi$
$62$	−14.4973	−	19.9538i	−0.0296961	−	0.0408732i
$63$	−336.662	−	463.376i	−0.673261	−	0.926665i
$64$	37.8690	+	27.5134i	0.0739629	+	0.0537372i
$65$		0			0
$66$	−907.814	+	659.566i	−1.69309	+	1.23011i
$67$	134.591	+	43.7313i	0.245417	+	0.0797407i	0.429142	−	0.903237i	$-0.358816\pi$
$67$	134.591	+	43.7313i	0.245417	+	0.0797407i	−0.183726	+	0.982978i	$0.558816\pi$
$68$		−	77.5215i		−	0.138248i
$69$	−281.651	+	866.833i	−0.491403	+	1.51238i
$70$		0			0
$71$	−185.509	−	570.937i	−0.310082	−	0.954334i	−0.977732	−	0.209859i	$-0.932700\pi$
$71$	−185.509	−	570.937i	−0.310082	−	0.954334i	0.667650	−	0.744475i	$-0.267300\pi$
$72$	−588.388	+	191.179i	−0.963087	+	0.312926i
$73$	−84.9707	+	116.952i	−0.136234	+	0.187510i	−0.871683	−	0.490070i	$-0.836971\pi$
$73$	−84.9707	+	116.952i	−0.136234	+	0.187510i	0.735449	+	0.677580i	$0.236971\pi$
$74$	−225.148			−0.353688
$75$		0			0
$76$	660.500			0.996902
$77$	−277.767	+	382.313i	−0.411097	+	0.565826i
$78$	902.448	−	293.223i	1.31003	−	0.425654i
$79$	−98.8328	−	304.176i	−0.140754	−	0.433196i	0.855687	−	0.517494i	$-0.173135\pi$
$79$	−98.8328	−	304.176i	−0.140754	−	0.433196i	−0.996441	+	0.0842982i	$0.973135\pi$
$80$		0			0
$81$	40.6249	−	125.030i	0.0557268	−	0.171510i
$82$			1315.80i			1.77202i
$83$	−1059.28	−	344.182i	−1.40086	−	0.455167i	−0.491390	−	0.870939i	$-0.663511\pi$
$83$	−1059.28	−	344.182i	−1.40086	−	0.455167i	−0.909469	+	0.415773i	$0.863511\pi$
$84$	355.618	−	258.372i	0.461918	−	0.335603i
$85$		0			0
$86$	661.558	+	480.650i	0.829507	+	0.602672i
$87$	538.604	+	741.324i	0.663728	+	0.913544i
$88$	300.028	+	412.954i	0.363445	+	0.500239i
$89$	−43.7671	−	31.7986i	−0.0521270	−	0.0378725i	0.561417	−	0.827533i	$-0.310257\pi$
$89$	−43.7671	−	31.7986i	−0.0521270	−	0.0378725i	−0.613544	+	0.789661i	$0.710257\pi$
$90$		0			0
$91$	323.293	−	234.886i	0.372421	−	0.270579i
$92$	−418.493	−	135.977i	−0.474249	−	0.154093i
$93$		−	60.4469i		−	0.0673984i
$94$	−114.857	+	353.495i	−0.126028	+	0.387874i
$95$		0			0
$96$	−449.159	−	1382.37i	−0.477522	−	1.46966i
$97$	1250.98	−	406.468i	1.30946	−	0.425470i	0.430599	−	0.902543i	$-0.358302\pi$
$97$	1250.98	−	406.468i	1.30946	−	0.425470i	0.878863	+	0.477073i	$0.158302\pi$
$98$	−381.712	+	525.381i	−0.393456	+	0.541546i
$99$	−1730.01			−1.75629
$100$		0			0
$101$	−345.232			−0.340117			−0.170059	−	0.985434i	$-0.554396\pi$
$101$	−345.232			−0.340117			−0.170059	+	0.985434i	$0.554396\pi$
$102$	328.565	−	452.231i	0.318949	−	0.438996i
$103$	1387.73	−	450.899i	1.32754	−	0.431344i	0.442463	−	0.896787i	$-0.354105\pi$
$103$	1387.73	−	450.899i	1.32754	−	0.431344i	0.885078	+	0.465443i	$0.154105\pi$
$104$	−133.384	−	410.513i	−0.125763	−	0.387058i
$105$		0			0
$106$	−222.807	+	685.731i	−0.204160	+	0.628340i
$107$			1081.01i			0.976683i	0.872653	+	0.488342i	$0.162398\pi$
$107$			1081.01i			0.976683i	−0.872653	+	0.488342i	$0.837602\pi$
$108$	628.043	+	204.064i	0.559569	+	0.181815i
$109$	1031.20	−	749.212i	0.906158	−	0.658362i	−0.0338823	−	0.999426i	$-0.510787\pi$
$109$	1031.20	−	749.212i	0.906158	−	0.658362i	0.940040	+	0.341064i	$0.110787\pi$
$110$		0			0
$111$	−446.408	−	324.334i	−0.381722	−	0.277337i
$112$	−588.067	−	809.404i	−0.496135	−	0.682871i
$113$	165.207	+	227.388i	0.137535	+	0.189300i	0.872228	−	0.489099i	$-0.162674\pi$
$113$	165.207	+	227.388i	0.137535	+	0.189300i	−0.734694	+	0.678399i	$0.762674\pi$
$114$	3853.11	+	2799.44i	3.16558	+	2.29993i
$115$		0			0
$116$	−357.900	+	260.029i	−0.286467	+	0.208130i
$117$	1391.33	+	452.071i	1.09939	+	0.357214i
$118$			1126.89i			0.879142i
$119$	72.7457	−	223.888i	0.0560386	−	0.172469i
$120$		0			0
$121$	29.7771	+	91.6445i	0.0223720	+	0.0688539i
$122$	−907.627	+	294.906i	−0.673546	+	0.218848i
$123$	−1895.45	+	2608.87i	−1.38949	+	1.91247i
$124$	29.1828			0.0211346
$125$		0			0
$126$	1993.93			1.40979
$127$	114.496	−	157.590i	0.0799990	−	0.110109i	−0.767142	−	0.641477i	$-0.778322\pi$
$127$	114.496	−	157.590i	0.0799990	−	0.110109i	0.847141	+	0.531368i	$0.178322\pi$
$128$	−1451.18	+	471.518i	−1.00209	+	0.325600i
$129$	619.296	+	1906.00i	0.422682	+	1.30088i
$130$		0			0
$131$	766.106	−	2357.83i	0.510954	−	1.57256i	−0.279570	−	0.960125i	$-0.590192\pi$
$131$	766.106	−	2357.83i	0.510954	−	1.57256i	0.790524	−	0.612431i	$-0.209808\pi$
$132$		−	1327.69i		−	0.875462i
$133$	1907.58	+	619.809i	1.24367	+	0.404092i
$134$	−398.567	+	289.576i	−0.256947	+	0.186683i
$135$		0			0
$136$	−205.714	−	149.460i	−0.129705	−	0.0942361i
$137$	−1038.08	−	1428.80i	−0.647369	−	0.891027i	0.351613	−	0.936145i	$-0.385633\pi$
$137$	−1038.08	−	1428.80i	−0.647369	−	0.891027i	−0.998982	+	0.0451188i	$0.985633\pi$
$138$	−1865.01	−	2566.97i	−1.15044	−	1.58344i
$139$	−1897.81	−	1378.84i	−1.15806	−	0.841379i	−0.168528	−	0.985697i	$-0.553901\pi$
$139$	−1897.81	−	1378.84i	−1.15806	−	0.841379i	−0.989531	+	0.144318i	$0.953901\pi$
$140$		0			0
$141$	−736.953	+	535.428i	−0.440160	+	0.319795i
$142$	1987.56	+	645.799i	1.17460	+	0.381650i
$143$		−	1207.01i		−	0.705840i
$144$	1131.82	−	3483.38i	0.654987	−	2.01584i
$145$		0			0
$146$	−155.513	−	478.620i	−0.0881530	−	0.271307i
$147$	−1513.66	+	491.819i	−0.849284	+	0.275949i
$148$	156.583	−	215.519i	0.0869667	−	0.119699i
$149$	−222.823			−0.122513			−0.0612563	−	0.998122i	$-0.519511\pi$
$149$	−222.823			−0.122513			−0.0612563	+	0.998122i	$0.519511\pi$
$150$		0			0
$151$	−1320.15			−0.711471			−0.355735	−	0.934587i	$-0.615770\pi$
$151$	−1320.15			−0.711471			−0.355735	+	0.934587i	$0.615770\pi$
$152$	1273.43	−	1752.73i	0.679533	−	0.935297i
$153$	819.629	−	266.314i	0.433092	−	0.140720i
$154$	−508.367	−	1564.59i	−0.266009	−	0.818692i
$155$		0			0
$156$	−346.942	+	1067.78i	−0.178062	+	0.548017i
$157$			1708.75i			0.868620i	0.900763	+	0.434310i	$0.143008\pi$
$157$			1708.75i			0.868620i	−0.900763	+	0.434310i	$0.856992\pi$
$158$	1058.91	+	344.060i	0.533179	+	0.173240i
$159$	−1429.59	+	1038.66i	−0.713042	+	0.518055i
$160$		0			0
$161$	−1081.04	−	785.423i	−0.529180	−	0.384472i
$162$	269.006	+	370.255i	0.130464	+	0.179568i
$163$	−799.735	−	1100.74i	−0.384295	−	0.528937i	0.572421	−	0.819960i	$-0.306004\pi$
$163$	−799.735	−	1100.74i	−0.384295	−	0.528937i	−0.956716	+	0.291023i	$0.906004\pi$
$164$	−1259.52	−	915.094i	−0.599707	−	0.435712i
$165$		0			0
$166$	3136.87	−	2279.07i	1.46668	−	1.06560i
$167$	−2774.28	−	901.420i	−1.28551	−	0.417688i	−0.414994	−	0.909824i	$-0.636216\pi$
$167$	−2774.28	−	901.420i	−1.28551	−	0.417688i	−0.870518	+	0.492136i	$0.836216\pi$
$168$		−	1441.82i		−	0.662135i
$169$	363.505	−	1118.75i	0.165455	−	0.509218i
$170$		0			0
$171$	2269.05	+	6983.42i	1.01473	+	3.12301i
$172$	−920.185	+	298.986i	−0.407927	+	0.132544i
$173$	1040.70	−	1432.40i	0.457357	−	0.629499i	−0.516601	−	0.856226i	$-0.672803\pi$
$173$	1040.70	−	1432.40i	0.457357	−	0.629499i	0.973958	+	0.226728i	$0.0728028\pi$
$174$	−3189.95			−1.38982
$175$		0			0
$176$	−3021.90			−1.29423
$177$	−1623.33	+	2234.32i	−0.689361	+	0.948824i
$178$	179.114	−	58.1977i	0.0754223	−	0.0245062i
$179$	644.168	+	1982.55i	0.268980	+	0.827835i	0.990750	+	0.135702i	$0.0433289\pi$
$179$	644.168	+	1982.55i	0.268980	+	0.827835i	−0.721770	+	0.692133i	$0.756671\pi$
$180$		0			0
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	−0.978906	−	0.204310i	$-0.934505\pi$
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	0.912042	+	0.410096i	$0.134505\pi$
$182$			1391.14i			0.566584i
$183$	−2224.40	−	722.751i	−0.898538	−	0.291953i
$184$	−1167.68	+	848.370i	−0.467840	+	0.339906i
$185$		0			0
$186$	170.241	+	123.688i	0.0671113	+	0.0487592i
$187$	−417.942	−	575.247i	−0.163438	−	0.224953i
$188$	−258.496	−	355.789i	−0.100281	−	0.138024i
$189$	1622.35	+	1178.70i	0.624383	+	0.453641i
$190$		0			0
$191$	−1872.83	+	1360.69i	−0.709494	+	0.515478i	−0.883011	−	0.469353i	$-0.844487\pi$
$191$	−1872.83	+	1360.69i	−0.709494	+	0.515478i	0.173516	+	0.984831i	$0.444487\pi$
$192$	−379.815	−	123.409i	−0.142764	−	0.0463870i
$193$			2028.97i			0.756727i	0.925657	+	0.378363i	$0.123513\pi$
$193$			2028.97i			0.756727i	−0.925657	+	0.378363i	$0.876487\pi$
$194$	−1415.01	+	4354.96i	−0.523670	+	1.61169i
$195$		0			0
$196$	−237.442	−	730.772i	−0.0865314	−	0.266316i
$197$	2508.61	−	815.098i	0.907265	−	0.294788i	0.182033	−	0.983292i	$-0.441732\pi$
$197$	2508.61	−	815.098i	0.907265	−	0.294788i	0.725232	+	0.688504i	$0.241732\pi$
$198$	3539.97	−	4872.36i	1.27058	−	1.74880i
$199$	−594.340			−0.211717			−0.105858	−	0.994381i	$-0.533759\pi$
$199$	−594.340			−0.211717			−0.105858	+	0.994381i	$0.533759\pi$
$200$		0			0
$201$	−1207.39			−0.423697
$202$	706.420	−	972.304i	0.246057	−	0.338669i
$203$	−1277.65	+	415.134i	−0.441742	+	0.143531i
$204$	204.383	+	629.025i	0.0701453	+	0.215885i
$205$		0			0
$206$	−1569.69	+	4831.00i	−0.530899	+	1.63394i
$207$		−	4891.82i		−	1.64254i
$208$	2430.32	+	789.658i	0.810154	+	0.263235i
$209$	4901.23	−	3560.95i	1.62213	−	1.17855i
$210$		0			0
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	0.808461	−	0.588550i	$-0.200301\pi$
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	−0.309916	+	0.950764i	$0.600301\pi$
$212$	−501.446	−	690.182i	−0.162450	−	0.223594i
$213$	3010.51	+	4143.60i	0.968434	+	1.33293i
$214$	−3044.53	−	2211.98i	−0.972523	−	0.706579i
$215$		0			0
$216$	1752.37	−	1273.17i	0.552008	−	0.401057i
$217$	84.2823	+	27.3850i	0.0263661	+	0.00856688i
$218$			4437.31i			1.37859i
$219$	381.129	−	1173.00i	0.117600	−	0.361935i
$220$		0			0
$221$	185.804	+	571.847i	0.0565546	+	0.174057i
$222$	1826.90	−	593.594i	0.552312	−	0.179457i
$223$	1315.10	−	1810.08i	0.394914	−	0.543553i	−0.564544	−	0.825403i	$-0.690948\pi$
$223$	1315.10	−	1810.08i	0.394914	−	0.543553i	0.959458	+	0.281850i	$0.0909481\pi$
$224$	2130.95			0.635625
$225$		0			0
$226$	−978.462			−0.287993
$227$	987.983	−	1359.84i	0.288875	−	0.397603i	−0.639773	−	0.768564i	$-0.720972\pi$
$227$	987.983	−	1359.84i	0.288875	−	0.397603i	0.928648	+	0.370961i	$0.120972\pi$
$228$	−5359.43	+	1741.38i	−1.55674	+	0.505815i
$229$	−1280.57	−	3941.19i	−0.369531	−	1.13730i	−0.947095	−	0.320953i	$-0.895997\pi$
$229$	−1280.57	−	3941.19i	−0.369531	−	1.13730i	0.577564	−	0.816345i	$-0.304003\pi$
$230$		0			0
$231$	1245.90	−	3834.49i	0.354867	−	1.09217i
$232$			1451.07i			0.410635i
$233$	−4417.38	−	1435.29i	−1.24203	−	0.403559i	−0.386969	−	0.922093i	$-0.626478\pi$
$233$	−4417.38	−	1435.29i	−1.24203	−	0.403559i	−0.855057	+	0.518534i	$0.826478\pi$
$234$	−4120.17	+	2993.48i	−1.15104	+	0.836282i
$235$		0			0
$236$	−1078.69	−	783.717i	−0.297530	−	0.216168i
$237$	1603.90	+	2207.58i	0.439596	+	0.605053i
$238$	481.701	+	663.004i	0.131193	+	0.180572i
$239$	2707.72	+	1967.27i	0.732835	+	0.532436i	0.890459	−	0.455063i	$-0.150383\pi$
$239$	2707.72	+	1967.27i	0.732835	+	0.532436i	−0.157624	+	0.987499i	$0.550383\pi$
$240$		0			0
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.629222	−	0.777226i	$-0.283374\pi$
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.933626	−	0.358250i	$-0.116626\pi$
$242$	−319.036	−	103.661i	−0.0847455	−	0.0275355i
$243$		−	3207.05i		−	0.846635i
$244$	348.933	−	1073.90i	0.0915497	−	0.281761i
$245$		0			0
$246$	−3469.04	−	10676.6i	−0.899098	−	2.76714i
$247$	−4872.26	+	1583.09i	−1.25512	+	0.407813i
$248$	56.2640	−	77.4408i	0.0144063	−	0.0198286i
$249$	9502.64			2.41850
$250$		0			0
$251$	5546.43			1.39477			0.697386	−	0.716696i	$-0.254346\pi$
$251$	5546.43			1.39477			0.697386	+	0.716696i	$0.254346\pi$
$252$	−1386.71	+	1908.65i	−0.346646	+	0.477117i
$253$	−3838.51	+	1247.21i	−0.953855	+	0.309926i
$254$	209.550	+	644.928i	0.0517651	+	0.159317i
$255$		0			0
$256$	1525.75	−	4695.77i	0.372497	−	1.14643i
$257$			56.6174i			0.0137420i	0.999976	+	0.00687100i	$0.00218713\pi$
$257$			56.6174i			0.0137420i	−0.999976	+	0.00687100i	$0.997813\pi$
$258$	−6635.23	−	2155.92i	−1.60113	−	0.520238i
$259$	654.466	−	475.498i	0.157014	−	0.114077i
$260$		0			0
$261$	−3978.78	−	2890.75i	−0.943603	−	0.685568i
$262$	5072.93	+	6982.29i	1.19621	+	1.64644i
$263$	3915.74	+	5389.55i	0.918079	+	1.26363i	0.964332	+	0.264697i	$0.0852720\pi$
$263$	3915.74	+	5389.55i	0.918079	+	1.26363i	−0.0462529	+	0.998930i	$0.514728\pi$
$264$	−3523.23	−	2559.77i	−0.821362	−	0.596754i
$265$		0			0
$266$	−5648.94	+	4104.19i	−1.30210	+	0.946031i
$267$	438.971	+	142.630i	0.100616	+	0.0326922i
$268$		−	582.911i		−	0.132862i
$269$	−1574.21	+	4844.92i	−0.356807	+	1.09814i	0.598147	+	0.801387i	$0.295904\pi$
$269$	−1574.21	+	4844.92i	−0.356807	+	1.09814i	−0.954954	+	0.296754i	$0.904096\pi$
$270$		0			0
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	0.961994	+	0.273072i	$0.0880396\pi$
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	−0.617762	+	0.786365i	$0.711960\pi$
$272$	1431.69	−	465.185i	0.319151	−	0.103698i
$273$	−2003.99	+	2758.26i	−0.444275	+	0.611492i
$274$	6148.19			1.35557
$275$		0			0
$276$	3754.23			0.818762
$277$	−3006.00	+	4137.40i	−0.652032	+	0.897445i	−0.999185	−	0.0403637i	$-0.987148\pi$
$277$	−3006.00	+	4137.40i	−0.652032	+	0.897445i	0.347153	+	0.937808i	$0.387148\pi$
$278$	7766.67	−	2523.55i	1.67559	−	0.544432i
$279$	100.253	+	308.548i	0.0215126	+	0.0662089i
$280$		0			0
$281$	208.142	−	640.597i	0.0441877	−	0.135996i	−0.926529	−	0.376224i	$-0.877222\pi$
$281$	208.142	−	640.597i	0.0441877	−	0.135996i	0.970716	+	0.240228i	$0.0772223\pi$
$282$		−	3171.14i		−	0.669641i
$283$	2706.16	+	879.284i	0.568425	+	0.184693i	0.579109	−	0.815250i	$-0.303401\pi$
$283$	2706.16	+	879.284i	0.568425	+	0.184693i	−0.0106833	+	0.999943i	$0.503401\pi$
$284$	−2000.47	+	1453.42i	−0.417978	+	0.303679i
$285$		0			0
$286$	3399.39	+	2469.80i	0.702833	+	0.510638i
$287$	−2778.87	−	3824.79i	−0.571538	−	0.786655i
$288$	4585.41	+	6311.27i	0.938187	+	1.29130i
$289$	−3688.14	−	2679.59i	−0.750690	−	0.545408i
$290$		0			0
$291$	−9079.06	+	6596.32i	−1.82895	+	1.32881i
$292$	566.303	+	184.003i	0.113495	+	0.0368766i
$293$			208.321i			0.0415367i	0.999784	+	0.0207684i	$0.00661125\pi$
$293$			208.321i			0.0415367i	−0.999784	+	0.0207684i	$0.993389\pi$
$294$	1712.14	−	5269.41i	0.339639	−	1.04530i
$295$		0			0
$296$	−270.019	−	831.032i	−0.0530220	−	0.163185i
$297$	5760.56	−	1871.72i	1.12546	−	0.365684i
$298$	455.945	−	627.554i	0.0886314	−	0.121991i
$299$	3412.98			0.660126
$300$		0			0
$301$	−2938.13			−0.562629
$302$	2701.31	−	3718.04i	0.514712	−	0.708440i
$303$	2801.28	−	910.191i	0.531120	−	0.172571i
$304$	3963.48	+	12198.3i	0.747766	+	2.30139i
$305$		0			0
$306$	−927.101	+	2853.32i	−0.173199	+	0.533051i
$307$		−	661.860i		−	0.123044i	−0.998106	−	0.0615218i	$-0.980405\pi$
$307$		−	661.860i		−	0.123044i	0.998106	−	0.0615218i	$-0.0195954\pi$
$308$	1851.23	+	601.501i	0.342479	+	0.111278i
$309$	−10071.5	+	7317.37i	−1.85420	+	1.34715i
$310$		0			0
$311$	7024.85	+	5103.86i	1.28085	+	0.930589i	0.999578	−	0.0290408i	$-0.00924527\pi$
$311$	7024.85	+	5103.86i	1.28085	+	0.930589i	0.281267	+	0.959629i	$0.409245\pi$
$312$	2164.60	+	2979.32i	0.392777	+	0.540611i
$313$	−2203.89	−	3033.40i	−0.397992	−	0.547788i	0.562247	−	0.826969i	$-0.309937\pi$
$313$	−2203.89	−	3033.40i	−0.397992	−	0.547788i	−0.960238	+	0.279181i	$0.909937\pi$
$314$	−4812.50	−	3496.48i	−0.864920	−	0.628401i
$315$		0			0
$316$	−1065.78	+	774.336i	−0.189731	+	0.137848i
$317$	5946.15	+	1932.02i	1.05353	+	0.342313i	0.784053	−	0.620694i	$-0.213149\pi$
$317$	5946.15	+	1932.02i	1.05353	+	0.342313i	0.269477	+	0.963007i	$0.413149\pi$
$318$		−	6151.58i		−	1.08479i
$319$	−1253.89	+	3859.09i	−0.220077	+	0.677327i
$320$		0			0
$321$	−2850.04	−	8771.52i	−0.495557	−	1.52517i
$322$	4424.10	−	1437.48i	0.765668	−	0.248781i
$323$	−1773.90	+	2441.57i	−0.305581	+	0.420596i
$324$	−541.504			−0.0928505
$325$		0			0
$326$	4736.54			0.804701
$327$	−6392.10	+	8797.98i	−1.08099	+	1.48786i
$328$	−4856.66	+	1578.03i	−0.817574	+	0.265646i
$329$	−412.686	−	1270.12i	−0.0691554	−	0.212839i
$330$		0			0
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	0.730553	+	0.682856i	$0.239262\pi$
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	−0.992402	+	0.123034i	$0.960738\pi$
$332$			4587.72i			0.758386i
$333$	2816.58	+	915.163i	0.463507	+	0.150602i
$334$	8215.53	−	5968.93i	1.34591	−	0.977861i
$335$		0			0
$336$	6905.65	+	5017.25i	1.12123	+	0.814623i
$337$	−3071.24	−	4227.20i	−0.496442	−	0.683294i	0.485118	−	0.874449i	$-0.338777\pi$
$337$	−3071.24	−	4227.20i	−0.496442	−	0.683294i	−0.981560	+	0.191155i	$0.938777\pi$
$338$	2407.02	+	3312.98i	0.387351	+	0.533143i
$339$	−1940.03	−	1409.51i	−0.310819	−	0.225823i
$340$		0			0
$341$	216.551	−	157.333i	0.0343897	−	0.0249856i
$342$	−24310.9	−	7899.10i	−3.84381	−	1.24893i
$343$		−	6623.65i		−	1.04269i
$344$	−980.700	+	3018.28i	−0.153709	+	0.473067i
$345$		0			0
$346$	1904.68	+	5862.00i	0.295943	+	0.910818i
$347$	−748.379	+	243.163i	−0.115778	+	0.0376187i	−0.366333	−	0.930484i	$-0.619387\pi$
$347$	−748.379	+	243.163i	−0.115778	+	0.0376187i	0.250555	+	0.968102i	$0.419387\pi$
$348$	2218.51	−	3053.52i	0.341737	−	0.470361i
$349$	−4031.08			−0.618277			−0.309138	−	0.951017i	$-0.600041\pi$
$349$	−4031.08			−0.618277			−0.309138	+	0.951017i	$0.600041\pi$
$350$		0			0
$351$	−5121.94			−0.778886
$352$	3783.24	−	5207.18i	0.572862	−	0.788477i
$353$	−2248.46	+	730.568i	−0.339018	+	0.110154i	−0.473578	−	0.880752i	$-0.657038\pi$
$353$	−2248.46	+	730.568i	−0.339018	+	0.110154i	0.134560	+	0.990905i	$0.457038\pi$
$354$	−2971.01	−	9143.82i	−0.446066	−	1.37285i
$355$		0			0
$356$	−68.8596	+	211.928i	−0.0102515	+	0.0315510i
$357$			2008.46i			0.297757i
$358$	−6901.71	−	2242.50i	−1.01890	−	0.331061i
$359$	−3962.13	+	2878.66i	−0.582488	+	0.423202i	−0.839620	−	0.543174i	$-0.817222\pi$
$359$	−3962.13	+	2878.66i	−0.582488	+	0.423202i	0.257132	+	0.966376i	$0.417222\pi$
$360$		0			0
$361$	−15253.6	−	11082.4i	−2.22388	−	1.61575i
$362$	−1078.15	−	1483.95i	−0.156537	−	0.215455i
$363$	−483.234	−	665.115i	−0.0698711	−	0.0961694i
$364$	−1331.64	−	967.496i	−0.191750	−	0.139315i
$365$		0			0
$366$	6587.15	−	4785.85i	0.940754	−	0.683498i
$367$	11199.3	+	3638.89i	1.59292	+	0.517570i	0.965343	−	0.260986i	$-0.0840476\pi$
$367$	11199.3	+	3638.89i	1.59292	+	0.517570i	0.627575	+	0.778556i	$0.284048\pi$
$368$		−	8544.82i		−	1.21041i
$369$	5348.33	−	16460.5i	0.754534	−	2.32222i
$370$		0			0
$371$	−800.555	−	2463.85i	−0.112029	−	0.344790i
$372$	−236.795	+	76.9394i	−0.0330034	+	0.0107234i
$373$	7370.66	−	10144.8i	1.02316	−	1.40826i	0.113193	−	0.993573i	$-0.463892\pi$
$373$	7370.66	−	10144.8i	1.02316	−	1.40826i	0.909966	−	0.414684i	$-0.136108\pi$
$374$	2475.32			0.342234
$375$		0			0
$376$	−1442.51			−0.197851
$377$	2016.85	−	2775.96i	0.275525	−	0.379228i
$378$	−6639.35	+	2157.26i	−0.903417	+	0.293538i
$379$	−1673.08	−	5149.21i	−0.226755	−	0.697881i	−0.998109	−	0.0614740i	$-0.980420\pi$
$379$	−1673.08	−	5149.21i	−0.226755	−	0.697881i	0.771353	−	0.636407i	$-0.219580\pi$
$380$		0			0
$381$	−513.562	+	1580.58i	−0.0690567	+	0.212535i
$382$		−	8058.88i		−	1.07939i
$383$	−13497.2	−	4385.52i	−1.80072	−	0.585090i	−0.800817	−	0.598909i	$-0.795601\pi$
$383$	−13497.2	−	4385.52i	−1.80072	−	0.585090i	−0.999905	+	0.0138191i	$0.995601\pi$
$384$	10532.1	−	7651.99i	1.39964	−	1.01690i
$385$		0			0
$386$	−5714.34	−	4151.71i	−0.753503	−	0.547452i
$387$	−6322.32	−	8701.93i	−0.830443	−	1.14301i
$388$	−3184.60	−	4383.23i	−0.416685	−	0.573517i
$389$	191.659	+	139.248i	0.0249807	+	0.0181495i	0.600206	−	0.799846i	$-0.295085\pi$
$389$	191.659	+	139.248i	0.0249807	+	0.0181495i	−0.575225	+	0.817995i	$0.695085\pi$
$390$		0			0
$391$	1626.59	−	1181.79i	0.210384	−	0.152853i
$392$	−2396.99	−	778.830i	−0.308843	−	0.100349i
$393$			21151.7i			2.71492i
$394$	−2837.55	+	8733.07i	−0.362826	+	1.11666i
$395$		0			0
$396$	2202.03	+	6777.14i	0.279434	+	0.860010i
$397$	−10891.6	+	3538.88i	−1.37691	+	0.447384i	−0.901651	−	0.432464i	$-0.857644\pi$
$397$	−10891.6	+	3538.88i	−1.37691	+	0.447384i	−0.475255	+	0.879848i	$0.657644\pi$
$398$	1216.15	−	1673.89i	0.153166	−	0.210815i
$399$	−17112.5			−2.14711
$400$		0			0
$401$	13344.5			1.66183			0.830915	−	0.556399i	$-0.187818\pi$
$401$	13344.5			1.66183			0.830915	+	0.556399i	$0.187818\pi$
$402$	2470.59	−	3400.48i	0.306522	−	0.421892i
$403$	−215.271	+	69.9457i	−0.0266089	+	0.00864576i
$404$	439.426	+	1352.41i	0.0541145	+	0.166547i
$405$		0			0
$406$	1445.18	−	4447.81i	0.176658	−	0.543697i
$407$		−	2443.44i		−	0.297584i
$408$	2063.25	+	670.392i	0.250358	+	0.0813464i
$409$	−6080.01	+	4417.39i	−0.735055	+	0.534048i	−0.891158	−	0.453692i	$-0.850107\pi$
$409$	−6080.01	+	4417.39i	−0.735055	+	0.534048i	0.156104	+	0.987741i	$0.450107\pi$
$410$		0			0
$411$	12190.2	+	8856.70i	1.46301	+	1.06294i
$412$	−3532.71	−	4862.36i	−0.422437	−	0.581435i
$413$	−2379.92	−	3275.68i	−0.283555	−	0.390280i
$414$	13777.2	+	10009.7i	1.63554	+	1.18829i
$415$		0			0
$416$	−4403.31	+	3199.19i	−0.518967	+	0.377051i
$417$	19034.5	+	6184.67i	2.23530	+	0.726294i
$418$			21090.2i			2.46784i
$419$	1980.00	−	6093.82i	0.230858	−	0.710507i	−0.766786	−	0.641903i	$-0.778145\pi$
$419$	1980.00	−	6093.82i	0.230858	−	0.710507i	0.997644	−	0.0686047i	$-0.0218547\pi$
$420$		0			0
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	0.728924	+	0.684594i	$0.240021\pi$
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	−0.187318	+	0.982299i	$0.559979\pi$
$422$	−6253.32	+	2031.83i	−0.721343	+	0.234378i
$423$	2873.71	−	3955.32i	0.330318	−	0.454644i
$424$	−2798.28			−0.320510
$425$		0			0
$426$	−17830.1			−2.02787
$427$	2015.49	−	2774.09i	0.228423	−	0.314397i
$428$	4234.75	−	1375.95i	0.478258	−	0.155395i
$429$	3182.23	+	9793.90i	0.358134	+	1.10222i
$430$		0			0
$431$	3787.43	−	11656.5i	0.423281	−	1.30272i	−0.481350	−	0.876528i	$-0.659853\pi$
$431$	3787.43	−	11656.5i	0.423281	−	1.30272i	0.904631	−	0.426196i	$-0.140147\pi$
$432$			12823.4i			1.42817i
$433$	11869.0	+	3856.48i	1.31730	+	0.428016i	0.881566	−	0.472061i	$-0.156490\pi$
$433$	11869.0	+	3856.48i	1.31730	+	0.428016i	0.435731	+	0.900077i	$0.356490\pi$
$434$	−249.586	+	181.335i	−0.0276049	+	0.0200561i
$435$		0			0
$436$	−4247.52	−	3086.01i	−0.466558	−	0.338974i
$437$	10069.1	+	13858.9i	1.10222	+	1.51707i
$438$	2523.72	+	3473.61i	0.275316	+	0.378939i
$439$	13041.9	+	9475.47i	1.41789	+	1.03016i	0.992115	+	0.125330i	$0.0399990\pi$
$439$	13041.9	+	9475.47i	1.41789	+	1.03016i	0.425776	+	0.904828i	$0.360001\pi$
$440$		0			0
$441$	6910.70	−	5020.92i	0.746215	−	0.542157i
$442$	−1990.73	−	646.829i	−0.214230	−	0.0696075i
$443$		−	11988.6i		−	1.28577i	−0.765963	−	0.642885i	$-0.777737\pi$
$443$		−	11988.6i		−	1.28577i	0.765963	−	0.642885i	$-0.222263\pi$
$444$	−702.342	+	2161.59i	−0.0750713	+	0.231046i
$445$		0			0
$446$	2406.89	+	7407.66i	0.255538	+	0.786464i
$447$	1808.03	−	587.464i	0.191313	−	0.0621613i
$448$	344.144	−	473.673i	0.0362930	−	0.0499530i
$449$	−768.211			−0.0807442			−0.0403721	−	0.999185i	$-0.512854\pi$
$449$	−768.211			−0.0807442			−0.0403721	+	0.999185i	$0.512854\pi$
$450$		0			0
$451$	−14279.8			−1.49093
$452$	680.490	−	936.613i	0.0708131	−	0.0974659i
$453$	10711.9	−	3480.52i	1.11102	−	0.360991i
$454$	1808.20	+	5565.07i	0.186923	+	0.575290i
$455$		0			0
$456$	−5711.88	+	17579.4i	−0.586586	+	1.80533i
$457$		−	13017.8i		−	1.33249i	−0.745732	−	0.666246i	$-0.767900\pi$
$457$		−	13017.8i		−	1.33249i	0.745732	−	0.666246i	$-0.232100\pi$
$458$	13720.2	+	4457.97i	1.39979	+	0.454819i
$459$	−2441.06	+	1773.54i	−0.248233	+	0.180352i
$460$		0			0
$461$	−12600.2	−	9154.58i	−1.27299	−	0.924883i	−0.273675	−	0.961822i	$-0.588239\pi$
$461$	−12600.2	−	9154.58i	−1.27299	−	0.924883i	−0.999318	+	0.0369393i	$0.988239\pi$
$462$	8249.98	+	11355.1i	0.830788	+	1.14348i
$463$	−2392.17	−	3292.54i	−0.240116	−	0.330491i	0.671903	−	0.740639i	$-0.265477\pi$
$463$	−2392.17	−	3292.54i	−0.240116	−	0.330491i	−0.912019	+	0.410148i	$0.865477\pi$
$464$	−6949.96	−	5049.44i	−0.695353	−	0.505203i
$465$		0			0
$466$	13081.3	−	9504.09i	1.30038	−	0.944782i
$467$	−472.706	−	153.591i	−0.0468399	−	0.0152192i	0.285503	−	0.958378i	$-0.407839\pi$
$467$	−472.706	−	153.591i	−0.0468399	−	0.0152192i	−0.332343	+	0.943159i	$0.607839\pi$
$468$		−	6025.82i		−	0.595179i
$469$	547.000	−	1683.49i	0.0538552	−	0.165749i
$470$		0			0
$471$	−4505.06	−	13865.2i	−0.440727	−	1.35642i
$472$	−4159.41	+	1351.47i	−0.405619	+	0.131794i
$473$	−5216.30	+	7179.62i	−0.507073	+	0.697926i
$474$	−9499.30			−0.920500
$475$		0			0
$476$	−969.655			−0.0933698
$477$	5574.60	−	7672.78i	0.535101	−	0.736504i
$478$	−11081.2	+	3600.49i	−1.06034	+	0.344524i
$479$	−1404.36	−	4322.18i	−0.133960	−	0.412287i	0.861467	−	0.507814i	$-0.169546\pi$
$479$	−1404.36	−	4322.18i	−0.133960	−	0.412287i	−0.995427	+	0.0955270i	$0.969546\pi$
$480$		0			0
$481$	−638.500	+	1965.10i	−0.0605261	+	0.186280i
$482$			25160.4i			2.37765i
$483$	10842.5	+	3522.95i	1.02143	+	0.331883i
$484$	321.107	−	233.298i	0.0301566	−	0.0219100i
$485$		0			0
$486$	9032.26	+	6562.32i	0.843028	+	0.612496i
$487$	−9706.02	−	13359.2i	−0.903125	−	1.24304i	−0.969461	−	0.245247i	$-0.921131\pi$
$487$	−9706.02	−	13359.2i	−0.903125	−	1.24304i	0.0663359	−	0.997797i	$-0.478869\pi$
$488$	−2177.02	−	2996.41i	−0.201945	−	0.277954i
$489$	9391.27	+	6823.15i	0.868482	+	0.630989i
$490$		0			0
$491$	1292.08	−	938.748i	0.118759	−	0.0862833i	−0.526821	−	0.849977i	$-0.676616\pi$
$491$	1292.08	−	938.748i	0.118759	−	0.0862833i	0.645579	+	0.763693i	$0.276616\pi$
$492$	12632.6	+	4104.58i	1.15756	+	0.376115i
$493$		−	2021.35i		−	0.184659i
$494$	5511.12	−	16961.5i	0.501937	−	1.54480i
$495$		0			0
$496$	175.118	+	538.958i	0.0158529	+	0.0487901i
$497$	−7141.39	+	2320.38i	−0.644537	+	0.209423i
$498$	−19444.5	+	26763.0i	−1.74966	+	2.40819i
$499$	3319.59			0.297806			0.148903	−	0.988852i	$-0.452426\pi$
$499$	3319.59			0.297806			0.148903	+	0.988852i	$0.452426\pi$
$500$		0			0
$501$	24887.6			2.21936
$502$	−11349.2	+	15620.9i	−1.00904	+	1.38883i
$503$	−6243.29	+	2028.57i	−0.553429	+	0.179820i	−0.572362	−	0.820001i	$-0.693973\pi$
$503$	−6243.29	+	2028.57i	−0.553429	+	0.179820i	0.0189337	+	0.999821i	$0.493973\pi$
$504$	2391.31	+	7359.68i	0.211344	+	0.650449i
$505$		0			0
$506$	4341.83	−	13362.8i	0.381458	−	1.17401i
$507$			10036.1i			0.879134i
$508$	−763.080	−	247.940i	−0.0666461	−	0.0216546i
$509$	12497.0	−	9079.59i	1.08825	−	0.790660i	0.109147	−	0.994026i	$-0.465188\pi$
$509$	12497.0	−	9079.59i	1.08825	−	0.790660i	0.979103	+	0.203366i	$0.0651880\pi$
$510$		0			0
$511$	1462.86	+	1062.83i	0.126640	+	0.0920095i
$512$	2928.01	+	4030.06i	0.252736	+	0.347862i
$513$	−15110.9	−	20798.4i	−1.30051	−	1.79000i
$514$	−159.456	−	115.852i	−0.0136835	−	0.00994162i
$515$		0			0
$516$	6678.30	−	4852.07i	0.569759	−	0.413954i
$517$	−3836.33	−	1246.50i	−0.326348	−	0.106037i
$518$			2816.20i			0.238874i
$519$	−4667.97	+	14366.5i	−0.394800	+	1.21507i
$520$		0			0
$521$	−2533.05	−	7795.93i	−0.213004	−	0.655559i	−0.999289	−	0.0376951i	$-0.987998\pi$
$521$	−2533.05	−	7795.93i	−0.213004	−	0.655559i	0.786285	−	0.617863i	$-0.212002\pi$
$522$	16282.9	−	5290.64i	1.36529	−	0.443611i
$523$	−9649.57	+	13281.5i	−0.806781	+	1.11044i	0.185031	+	0.982733i	$0.440761\pi$
$523$	−9649.57	+	13281.5i	−0.806781	+	1.11044i	−0.991812	+	0.127706i	$0.959239\pi$
$524$	−10211.7			−0.851338
$525$		0			0
$526$	−23191.5			−1.92243
$527$	−78.3762	+	107.876i	−0.00647841	+	0.00891676i
$528$	24520.3	−	7967.12i	2.02104	−	0.656675i
$529$	233.162	+	717.598i	0.0191635	+	0.0589790i
$530$		0			0
$531$	4580.49	−	14097.3i	0.374343	−	1.15211i
$532$		−	8261.66i		−	0.673287i
$533$	11484.3	+	3731.48i	0.933284	+	0.303242i
$534$	−1299.93	+	944.455i	−0.105344	+	0.0765366i
$535$		0			0
$536$	−1546.84	−	1123.84i	−0.124651	−	0.0905646i
$537$	−10453.8	−	14388.4i	−0.840066	−	1.15625i
$538$	−10423.9	−	14347.3i	−0.835331	−	1.14973i
$539$	−5701.75	−	4142.56i	−0.455643	−	0.331044i
$540$		0			0
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.994468	−	0.105043i	$-0.966502\pi$
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.207406	+	0.978255i	$0.566502\pi$
$542$	−16453.7	−	5346.12i	−1.30396	−	0.423682i
$543$		−	4495.38i		−	0.355277i
$544$	−990.811	+	3049.40i	−0.0780895	+	0.240335i
$545$		0			0
$546$	−3667.69	−	11288.0i	−0.287478	−	0.884765i
$547$	11382.1	−	3698.27i	0.889695	−	0.289080i	0.171718	−	0.985146i	$-0.445068\pi$
$547$	11382.1	−	3698.27i	0.889695	−	0.289080i	0.717977	+	0.696067i	$0.245068\pi$
$548$	−4275.87	+	5885.23i	−0.333314	+	0.458768i
$549$	12553.0			0.975865
$550$		0			0
$551$	17222.3			1.33157
$552$	7238.10	−	9962.39i	0.558105	−	0.768166i
$553$	−3804.70	+	1236.22i	−0.292572	+	0.0950623i
$554$	−5501.56	−	16932.0i	−0.421911	−	1.29851i
$555$		0			0
$556$	−2985.86	+	9189.54i	−0.227750	+	0.700941i
$557$			1182.53i			0.0899558i	0.998988	+	0.0449779i	$0.0143217\pi$
$557$			1182.53i			0.0899558i	−0.998988	+	0.0449779i	$0.985678\pi$
$558$	−1074.13	−	349.005i	−0.0814901	−	0.0264777i
$559$	6071.25	−	4411.02i	0.459367	−	0.333750i
$560$		0			0
$561$	4907.88	+	3565.78i	0.369360	+	0.268356i
$562$	1378.26	+	1897.01i	0.103449	+	0.142385i
$563$	4962.58	+	6830.40i	0.371488	+	0.511310i	0.953305	−	0.302011i	$-0.0976578\pi$
$563$	4962.58	+	6830.40i	0.371488	+	0.511310i	−0.581816	+	0.813320i	$0.697658\pi$
$564$	3035.51	+	2205.43i	0.226628	+	0.164655i
$565$		0			0
$566$	−8013.79	+	5822.36i	−0.595132	+	0.432389i
$567$	−1563.91	−	508.144i	−0.115834	−	0.0376368i
$568$			8110.70i			0.599150i
$569$	−1206.03	+	3711.79i	−0.0888568	+	0.273473i	−0.985604	−	0.169070i	$-0.945924\pi$
$569$	−1206.03	+	3711.79i	−0.0888568	+	0.273473i	0.896747	+	0.442543i	$0.145924\pi$
$570$		0			0
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	0.971880	−	0.235478i	$-0.0756656\pi$
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	−0.924678	+	0.380751i	$0.875666\pi$
$572$	−4728.34	+	1536.33i	−0.345633	+	0.112303i
$573$	11609.1	−	15978.6i	0.846384	−	1.16495i
$574$	16458.2			1.19678
$575$		0			0
$576$	2143.42			0.155051
$577$	4251.42	−	5851.58i	0.306740	−	0.422192i	−0.627621	−	0.778519i	$-0.715971\pi$
$577$	4251.42	−	5851.58i	0.306740	−	0.422192i	0.934361	+	0.356327i	$0.115971\pi$
$578$	15093.5	−	4904.17i	1.08617	−	0.352918i
$579$	−5349.29	−	16463.4i	−0.383954	−	1.18169i
$580$		0			0
$581$	−4305.09	+	13249.7i	−0.307410	+	0.946111i
$582$		−	39067.6i		−	2.78248i
$583$	−7441.95	−	2418.04i	−0.528669	−	0.171775i
$584$	1580.10	−	1148.01i	0.111961	−	0.0813443i
$585$		0			0
$586$	−586.712	−	426.271i	−0.0413598	−	0.0300497i
$587$	6218.01	+	8558.36i	0.437214	+	0.601774i	0.969590	−	0.244734i	$-0.0787007\pi$
$587$	6218.01	+	8558.36i	0.437214	+	0.601774i	−0.532376	+	0.846508i	$0.678701\pi$
$588$	3853.30	+	5303.62i	0.270251	+	0.371969i
$589$	−919.123	−	667.782i	−0.0642985	−	0.0467156i
$590$		0			0
$591$	−18206.4	+	13227.7i	−1.26719	+	0.920670i
$592$	4919.88	+	1598.57i	0.341564	+	0.110981i
$593$			7485.02i			0.518335i	0.965832	+	0.259168i	$0.0834482\pi$
$593$			7485.02i			0.518335i	−0.965832	+	0.259168i	$0.916552\pi$
$594$	−6515.89	+	20053.9i	−0.450085	+	1.38522i
$595$		0			0
$596$	283.618	+	872.888i	0.0194924	+	0.0599914i
$597$	4822.59	−	1566.95i	0.330612	−	0.107422i
$598$	−6983.70	+	9612.24i	−0.477566	+	0.657314i
$599$	−16860.4			−1.15008			−0.575039	−	0.818126i	$-0.695013\pi$
$599$	−16860.4			−1.15008			−0.575039	+	0.818126i	$0.695013\pi$
$600$		0			0
$601$	11032.4			0.748788			0.374394	−	0.927270i	$-0.377851\pi$
$601$	11032.4			0.748788			0.374394	+	0.927270i	$0.377851\pi$
$602$	6012.07	−	8274.90i	0.407032	−	0.560232i
$603$	6163.07	−	2002.50i	0.416218	−	0.135238i
$604$	1680.34	+	5171.55i	0.113199	+	0.348390i
$605$		0			0
$606$	−3168.59	+	9751.91i	−0.212401	+	0.653704i
$607$		−	937.076i		−	0.0626602i	−0.999509	−	0.0313301i	$-0.990026\pi$
$607$		−	937.076i		−	0.0626602i	0.999509	−	0.0313301i	$-0.00997432\pi$
$608$	−25981.6	−	8441.92i	−1.73305	−	0.563101i
$609$	9272.63	−	6736.96i	0.616988	−	0.448268i
$610$		0			0
$611$	2759.59	+	2004.96i	0.182718	+	0.132753i
$612$	−2086.52	−	2871.84i	−0.137814	−	0.189685i
$613$	12549.0	+	17272.2i	0.826835	+	1.13804i	0.988504	+	0.151196i	$0.0483124\pi$
$613$	12549.0	+	17272.2i	0.826835	+	1.13804i	−0.161669	+	0.986845i	$0.551688\pi$
$614$	1864.05	+	1354.31i	0.122519	+	0.0890156i
$615$		0			0
$616$	5165.31	−	3752.82i	0.337851	−	0.245463i
$617$	−26253.5	−	8530.27i	−1.71301	−	0.556590i	−0.722177	−	0.691708i	$-0.756858\pi$
$617$	−26253.5	−	8530.27i	−1.71301	−	0.556590i	−0.990829	+	0.135119i	$0.956858\pi$
$618$		−	43338.1i		−	2.82090i
$619$	−3030.03	+	9325.47i	−0.196748	+	0.605529i	0.803204	+	0.595705i	$0.203127\pi$
$619$	−3030.03	+	9325.47i	−0.196748	+	0.605529i	−0.999952	+	0.00982399i	$0.996873\pi$
$620$		0			0
$621$	5292.53	+	16288.7i	0.342000	+	1.05257i
$622$	−28748.8	+	9341.05i	−1.85325	+	0.602157i
$623$	−397.744	+	547.447i	−0.0255783	+	0.0352055i
$624$	−21802.0			−1.39868
$625$		0			0
$626$	13052.8			0.833381
$627$	−30381.2	+	41816.2i	−1.93510	+	2.66344i
$628$	6693.88	−	2174.97i	0.425342	−	0.138202i
$629$	376.138	+	1157.63i	0.0238436	+	0.0733830i
$630$		0			0
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	−1.00000		0.000497352i	$-0.999842\pi$
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	0.809309	+	0.587383i	$0.199842\pi$
$632$			4321.11i			0.271969i
$633$	−15325.5	−	4979.57i	−0.962300	−	0.312670i
$634$	−17608.4	+	12793.3i	−1.10303	+	0.801397i
$635$		0			0
$636$	5888.47	+	4278.23i	0.367128	+	0.266734i
$637$	3503.04	+	4821.53i	0.217890	+	0.299899i
$638$	−8302.91	−	11428.0i	−0.515228	−	0.709150i
$639$	−22239.3	−	16157.8i	−1.37679	−	1.00030i
$640$		0			0
$641$	−18210.1	+	13230.4i	−1.12208	+	0.815242i	−0.984524	−	0.175251i	$-0.943926\pi$
$641$	−18210.1	+	13230.4i	−1.12208	+	0.815242i	−0.137561	+	0.990493i	$0.543926\pi$
$642$	30535.7	+	9921.66i	1.87718	+	0.609932i
$643$		−	649.245i		−	0.0398192i	−0.999802	−	0.0199096i	$-0.993662\pi$
$643$		−	649.245i		−	0.0398192i	0.999802	−	0.0199096i	$-0.00633784\pi$
$644$	−1700.82	+	5234.59i	−0.104071	+	0.320298i
$645$		0			0
$646$	−3246.58	−	9991.96i	−0.197732	−	0.608558i
$647$	30188.5	−	9808.83i	1.83436	−	0.596020i	0.835439	−	0.549584i	$-0.185214\pi$
$647$	30188.5	−	9808.83i	1.83436	−	0.596020i	0.998921	−	0.0464360i	$-0.0147863\pi$
$648$	−1044.01	+	1436.96i	−0.0632911	+	0.0871127i
$649$	−12229.7			−0.739688
$650$		0			0
$651$	−756.082			−0.0455195
$652$	−3294.11	+	4533.95i	−0.197864	+	0.272336i
$653$	5140.54	−	1670.26i	0.308062	−	0.100096i	−0.150906	−	0.988548i	$-0.548219\pi$
$653$	5140.54	−	1670.26i	0.308062	−	0.100096i	0.458968	+	0.888453i	$0.348219\pi$
$654$	−11698.8	−	36005.2i	−0.699478	−	2.15277i
$655$		0			0
$656$	9342.22	−	28752.4i	0.556025	−	1.71127i
$657$			6619.60i			0.393083i
$658$	4421.58	+	1436.66i	0.261962	+	0.0851167i
$659$	2971.87	−	2159.19i	0.175671	−	0.127633i	−0.496475	−	0.868051i	$-0.665373\pi$
$659$	2971.87	−	2159.19i	0.175671	−	0.127633i	0.672146	+	0.740418i	$0.265373\pi$
$660$		0			0
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	0.343698	−	0.939080i	$-0.388320\pi$
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	−0.786910	+	0.617068i	$0.788320\pi$
$662$	−10441.5	−	14371.5i	−0.613023	−	0.843753i
$663$	−3015.31	−	4150.21i	−0.176629	−	0.243108i
$664$	12174.2	+	8845.06i	0.711521	+	0.516950i
$665$		0			0
$666$	−8340.79	+	6059.94i	−0.485284	+	0.352579i
$667$	−10912.1	−	3545.55i	−0.633460	−	0.205823i
$668$			12015.4i			0.695940i
$669$	−5898.79	+	18154.6i	−0.340897	+	1.04917i
$670$		0			0
$671$	−3200.49	−	9850.10i	−0.184134	−	0.566705i
$672$	−17290.9	+	5618.17i	−0.992578	+	0.322508i
$673$	18472.5	−	25425.2i	1.05804	−	1.45627i	0.176422	−	0.984315i	$-0.443548\pi$
$673$	18472.5	−	25425.2i	1.05804	−	1.45627i	0.881621	−	0.471958i	$-0.156452\pi$
$674$	18189.8			1.03953
$675$		0			0
$676$	−4845.29			−0.275677
$677$	−4364.44	+	6007.13i	−0.247768	+	0.341023i	−0.914728	−	0.404070i	$-0.867595\pi$
$677$	−4364.44	+	6007.13i	−0.247768	+	0.341023i	0.666960	+	0.745094i	$0.267595\pi$
$678$	7939.43	−	2579.68i	0.449723	−	0.146124i
$679$	−5084.19	−	15647.5i	−0.287354	−	0.884384i
$680$		0			0
$681$	−4431.51	+	13638.8i	−0.249363	+	0.767459i
$682$			931.827i			0.0523189i
$683$	21384.1	+	6948.13i	1.19801	+	0.389257i	0.839029	−	0.544087i	$-0.183124\pi$
$683$	21384.1	+	6948.13i	1.19801	+	0.389257i	0.358982	+	0.933344i	$0.383124\pi$
$684$	24468.7	−	17777.6i	1.36781	−	0.993776i
$685$		0			0
$686$	18654.7	+	13553.4i	1.03825	+	0.754334i
$687$	20781.6	+	28603.4i	1.15410	+	1.58848i
$688$	−11043.5	−	15200.1i	−0.611964	−	0.842296i
$689$	5353.22	+	3889.34i	0.295996	+	0.215054i
$690$		0			0
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	−0.497794	−	0.867295i	$-0.665857\pi$
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	0.671020	+	0.741439i	$0.265857\pi$
$692$	−6935.93	−	2253.62i	−0.381018	−	0.123800i
$693$			21639.3i			1.18616i
$694$	846.508	−	2605.28i	0.0463012	−	0.142500i
$695$		0			0
$696$	−3825.69	−	11774.3i	−0.208351	−	0.641239i
$697$	6765.37	−	2198.20i	0.367656	−	0.119459i
$698$	8248.47	−	11353.0i	0.447291	−	0.615643i
$699$	39627.6			2.14428
$700$		0			0
$701$	−12744.3			−0.686655			−0.343327	−	0.939216i	$-0.611554\pi$
$701$	−12744.3			−0.686655			−0.343327	+	0.939216i	$0.611554\pi$
$702$	10480.6	−	14425.3i	0.563483	−	0.775568i
$703$	−9863.29	+	3204.78i	−0.529162	+	0.171935i
$704$	−546.482	−	1681.90i	−0.0292561	−	0.0900410i
$705$		0			0
$706$	2543.28	−	7827.41i	0.135577	−	0.417264i
$707$			4318.23i			0.229708i
$708$	10819.0	+	3515.30i	0.574297	+	0.186600i
$709$	−12309.4	+	8943.33i	−0.652032	+	0.473729i	−0.863963	−	0.503556i	$-0.832025\pi$
$709$	−12309.4	+	8943.33i	−0.652032	+	0.473729i	0.211931	+	0.977285i	$0.432025\pi$
$710$		0			0
$711$	−11848.3	−	8608.32i	−0.624961	−	0.454061i
$712$	429.621	+	591.322i	0.0226134	+	0.0311246i
$713$	444.881	+	612.326i	0.0233673	+	0.0321624i
$714$	−5656.60	−	4109.76i	−0.296489	−	0.215412i
$715$		0			0
$716$	6946.51	−	5046.93i	0.362574	−	0.263426i
$717$	−27157.6	−	8824.03i	−1.41453	−	0.459609i
$718$		−	17049.2i		−	0.886172i
$719$	−4155.65	+	12789.8i	−0.215549	+	0.663392i	0.783565	+	0.621310i	$0.213399\pi$
$719$	−4155.65	+	12789.8i	−0.215549	+	0.663392i	−0.999114	+	0.0420821i	$0.986601\pi$
$720$		0			0
$721$	−5639.94	−	17358.0i	−0.291321	−	0.896593i
$722$	62424.5	−	20282.9i	3.21773	−	1.04550i
$723$	−36244.5	+	49886.3i	−1.86438	+	2.56610i
$724$	2170.30			0.111407
$725$		0			0
$726$	2862.02			0.146308
$727$	16933.7	−	23307.2i	0.863871	−	1.18902i	−0.116761	−	0.993160i	$-0.537251\pi$
$727$	16933.7	−	23307.2i	0.863871	−	1.18902i	0.980633	−	0.195857i	$-0.0627487\pi$
$728$	−5134.77	+	1668.39i	−0.261411	+	0.0849377i
$729$	9552.13	+	29398.4i	0.485298	+	1.49360i
$730$		0			0
$731$	1366.12	−	4204.49i	0.0691215	−	0.212734i
$732$			9633.82i			0.486443i
$733$	−13876.0	−	4508.60i	−0.699213	−	0.227188i	−0.0622256	−	0.998062i	$-0.519820\pi$
$733$	−13876.0	−	4508.60i	−0.699213	−	0.227188i	−0.636988	+	0.770874i	$0.719820\pi$
$734$	−33164.8	+	24095.6i	−1.66776	+	1.21170i
$735$		0			0
$736$	14724.0	+	10697.6i	0.737410	+	0.535760i
$737$	−3142.65	−	4325.48i	−0.157070	−	0.216189i
$738$	35415.1	+	48744.6i	1.76646	+	2.43132i
$739$	836.136	+	607.488i	0.0416208	+	0.0302393i	0.608401	−	0.793630i	$-0.291811\pi$
$739$	836.136	+	607.488i	0.0416208	+	0.0302393i	−0.566780	+	0.823869i	$0.691811\pi$
$740$		0			0
$741$	35360.7	−	25691.1i	1.75305	−	1.27366i
$742$	8577.26	+	2786.92i	0.424368	+	0.137885i
$743$		−	3409.57i		−	0.168351i	−0.996451	−	0.0841756i	$-0.973174\pi$
$743$		−	3409.57i		−	0.168351i	0.996451	−	0.0841756i	$-0.0268257\pi$
$744$	−252.367	+	776.707i	−0.0124358	+	0.0382735i
$745$		0			0
$746$	13489.7	+	41517.1i	0.662056	+	2.03760i
$747$	−48505.7	+	15760.5i	−2.37581	+	0.771947i
$748$	−1721.50	+	2369.45i	−0.0841503	+	0.115823i
$749$	13521.5			0.659632
$750$		0			0
$751$	−19553.4			−0.950087			−0.475043	−	0.879962i	$-0.657568\pi$
$751$	−19553.4			−0.950087			−0.475043	+	0.879962i	$0.657568\pi$
$752$	5019.66	−	6908.98i	0.243415	−	0.335032i
$753$	−45004.9	+	14623.0i	−2.17805	+	0.707690i
$754$	3691.23	+	11360.4i	0.178285	+	0.548703i
$755$		0			0
$756$	2552.47	−	7855.69i	0.122794	−	0.377922i
$757$		−	12295.8i		−	0.590353i	−0.955443	−	0.295176i	$-0.904622\pi$
$757$		−	12295.8i		−	0.590353i	0.955443	−	0.295176i	$-0.0953784\pi$
$758$	17925.6	+	5824.38i	0.858954	+	0.279091i
$759$	27858.2	−	20240.2i	1.33227	−	0.967948i
$760$		0			0
$761$	1950.66	+	1417.24i	0.0929190	+	0.0675096i	0.633275	−	0.773927i	$-0.281710\pi$
$761$	1950.66	+	1417.24i	0.0929190	+	0.0675096i	−0.540356	+	0.841437i	$0.681710\pi$
$762$	−3400.66	−	4680.60i	−0.161670	−	0.222520i
$763$	−9371.29	−	12898.5i	−0.444644	−	0.612000i
$764$	7714.20	+	5604.70i	0.365301	+	0.265407i
$765$		0			0
$766$	39969.6	−	29039.6i	1.88533	−	1.36977i
$767$	9835.54	+	3195.76i	0.463026	+	0.150446i
$768$			42125.0i			1.97924i
$769$	8608.70	−	26494.8i	0.403690	−	1.24243i	−0.518294	−	0.855202i	$-0.673433\pi$
$769$	8608.70	−	26494.8i	0.403690	−	1.24243i	0.921984	−	0.387227i	$-0.126567\pi$
$770$		0			0
$771$	−149.270	−	459.404i	−0.00697252	−	0.0214592i
$772$	7948.28	−	2582.55i	0.370551	−	0.120399i
$773$	−14651.0	+	20165.3i	−0.681705	+	0.938287i	−0.999953	−	0.00972064i	$-0.996906\pi$
$773$	−14651.0	+	20165.3i	−0.681705	+	0.938287i	0.318247	+	0.948008i	$0.396906\pi$
$774$	37444.8			1.73892
$775$		0			0
$776$	−17771.4			−0.822107
$777$	−4056.84	+	5583.76i	−0.187308	+	0.257807i
$778$	−784.352	+	254.851i	−0.0361444	+	0.0117440i
$779$	18729.1	+	57642.4i	0.861414	+	2.65116i
$780$		0			0
$781$	−7008.59	+	21570.2i	−0.321110	+	0.988276i
$782$			6999.28i			0.320069i
$783$	16376.0	+	5320.90i	0.747423	+	0.242852i
$784$	12071.3	−	8770.32i	0.549895	−	0.399522i
$785$		0			0
$786$	−59571.3	−	43281.1i	−2.70336	−	1.96410i
$787$	7599.80	+	10460.2i	0.344223	+	0.473782i	0.945669	−	0.325131i	$-0.105408\pi$
$787$	7599.80	+	10460.2i	0.344223	+	0.473782i	−0.601446	+	0.798913i	$0.705408\pi$
$788$	−6386.13	−	8789.76i	−0.288701	−	0.397363i
$789$	−45982.4	−	33408.2i	−2.07480	−	1.50743i
$790$		0			0
$791$	2844.22	−	2066.45i	0.127849	−	0.0928880i
$792$	22229.6	+	7222.82i	0.997340	+	0.324055i
$793$			8758.12i			0.392194i
$794$	12319.7	−	37916.1i	0.550641	−	1.69470i
$795$		0			0
$796$	756.501	+	2328.27i	0.0336852	+	0.103673i
$797$	12314.1	−	4001.08i	0.547285	−	0.177824i	−0.0223070	−	0.999751i	$-0.507101\pi$
$797$	12314.1	−	4001.08i	0.547285	−	0.177824i	0.569592	+	0.821927i	$0.307101\pi$
$798$	35016.0	−	48195.4i	1.55333	−	2.13797i
$799$	2009.43			0.0889719
$800$		0			0
$801$	−2477.26			−0.109275
$802$	−27305.8	+	37583.2i	−1.20225	+	1.65475i
$803$	5194.26	−	1687.72i	0.228271	−	0.0741697i
$804$	1536.82	+	4729.85i	0.0674123	+	0.207474i
$805$		0			0
$806$	243.497	−	749.408i	0.0106412	−	0.0327503i
$807$		−	43462.9i		−	1.89587i
$808$	4436.03	+	1441.35i	0.193142	+	0.0627557i
$809$	−7492.76	+	5443.81i	−0.325626	+	0.236581i	−0.738572	−	0.674174i	$-0.764500\pi$
$809$	−7492.76	+	5443.81i	−0.325626	+	0.236581i	0.412946	+	0.910755i	$0.364500\pi$
$810$		0			0
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	0.645545	−	0.763722i	$-0.276630\pi$
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	−0.526859	+	0.849953i	$0.676630\pi$
$812$	3252.50	+	4476.68i	0.140567	+	0.193474i
$813$	−24921.9	−	34302.0i	−1.07509	−	1.47973i
$814$	6881.65	+	4999.81i	0.296317	+	0.215287i
$815$		0			0
$816$	−10390.6	+	7549.20i	−0.445764	+	0.323866i
$817$	35823.2	+	11639.6i	1.53402	+	0.498433i
$818$		−	26162.6i		−	1.11828i
$819$	5654.60	−	17403.1i	0.241255	−	0.742506i
$820$		0			0
$821$	3816.58	+	11746.2i	0.162241	+	0.499325i	0.998822	−	0.0485169i	$-0.0154495\pi$
$821$	3816.58	+	11746.2i	0.162241	+	0.499325i	−0.836582	+	0.547842i	$0.815449\pi$
$822$	−49887.6	+	16209.5i	−2.11683	+	0.687798i
$823$	17106.4	−	23545.0i	0.724536	−	0.997239i	−0.274825	−	0.961494i	$-0.588620\pi$
$823$	17106.4	−	23545.0i	0.724536	−	0.997239i	0.999361	−	0.0357442i	$-0.0113802\pi$
$824$	−19714.0			−0.833457
$825$		0			0
$826$	14095.4			0.593754
$827$	4728.18	−	6507.78i	0.198809	−	0.273637i	−0.697959	−	0.716137i	$-0.745908\pi$
$827$	4728.18	−	6507.78i	0.198809	−	0.273637i	0.896768	+	0.442500i	$0.145908\pi$
$828$	−19163.3	+	6226.52i	−0.804311	+	0.261336i
$829$	−7849.09	−	24157.0i	−0.328842	−	1.01207i	−0.969676	−	0.244393i	$-0.921411\pi$
$829$	−7849.09	−	24157.0i	−0.328842	−	1.01207i	0.640834	−	0.767679i	$-0.278589\pi$
$830$		0			0
$831$	13483.1	−	41496.9i	0.562846	−	1.73226i
$832$			1495.44i			0.0623139i
$833$	3339.03	+	1084.92i	0.138884	+	0.0451262i
$834$	−56367.1	+	40953.1i	−2.34033	+	1.70035i
$835$		0			0
$836$	−20188.2	−	14667.6i	−0.835195	−	0.606805i
$837$	−667.644	−	918.933i	−0.0275713	−	0.0379486i
$838$	13111.0	+	18045.7i	0.540467	+	0.743889i
$839$	26598.5	+	19324.9i	1.09450	+	0.795198i	0.980153	−	0.198243i	$-0.0635236\pi$
$839$	26598.5	+	19324.9i	1.09450	+	0.795198i	0.114343	+	0.993441i	$0.463524\pi$
$840$		0			0
$841$	10399.0	−	7555.31i	0.426380	−	0.309784i
$842$	−50126.2	−	16287.0i	−2.05162	−	0.666611i
$843$			5746.69i			0.234788i
$844$	2404.06	−	7398.93i	0.0980463	−	0.301756i
$845$		0			0
$846$	5259.44	+	16186.9i	0.213739	+	0.657822i
$847$	1146.31	−	372.458i	0.0465025	−	0.0151096i
$848$	9737.46	−	13402.5i	0.394323	−	0.542739i
$849$	−24276.5			−0.981351
$850$		0			0
$851$	6909.15			0.278311
$852$	12400.3	−	17067.5i	0.498623	−	0.686295i
$853$	8834.96	−	2870.65i	0.354635	−	0.115228i	−0.126281	−	0.991994i	$-0.540304\pi$
$853$	8834.96	−	2870.65i	0.354635	−	0.115228i	0.480916	+	0.876767i	$0.340304\pi$
$854$	3688.74	+	11352.8i	0.147806	+	0.454899i
$855$		0			0
$856$	4513.24	−	13890.3i	0.180210	−	0.554628i
$857$			39874.7i			1.58937i	0.607019	+	0.794687i	$0.292365\pi$
$857$			39874.7i			1.58937i	−0.607019	+	0.794687i	$0.707635\pi$
$858$	−34094.9	−	11078.1i	−1.35662	−	0.440793i
$859$	22161.6	−	16101.3i	0.880261	−	0.639547i	−0.0530595	−	0.998591i	$-0.516897\pi$
$859$	22161.6	−	16101.3i	0.880261	−	0.639547i	0.933321	+	0.359044i	$0.116897\pi$
$860$		0			0
$861$	32632.2	+	23708.7i	1.29164	+	0.938432i
$862$	25079.2	+	34518.6i	0.990953	+	1.36393i
$863$	19467.4	+	26794.6i	0.767879	+	1.05689i	0.996518	+	0.0833829i	$0.0265724\pi$
$863$	19467.4	+	26794.6i	0.767879	+	1.05689i	−0.228639	+	0.973511i	$0.573428\pi$
$864$	−22096.7	−	16054.2i	−0.870075	−	0.632146i
$865$		0			0
$866$	−35148.0	+	25536.5i	−1.37919	+	1.00204i
$867$	36990.9	+	12019.1i	1.44899	+	0.470807i
$868$		−	365.024i		−	0.0142739i
$869$	−3733.95	+	11491.9i	−0.145760	+	0.448603i
$870$		0			0
$871$	1397.13	+	4299.91i	0.0543511	+	0.167276i
$872$	−16378.3	+	5321.64i	−0.636055	+	0.206667i
$873$	35403.3	−	48728.5i	1.37253	−	1.88913i
$874$	−59635.4			−2.30801
$875$		0			0
$876$	−5080.21			−0.195941
$877$	−18581.1	+	25574.8i	−0.715440	+	0.984719i	0.284223	+	0.958758i	$0.408264\pi$
$877$	−18581.1	+	25574.8i	−0.715440	+	0.984719i	−0.999663	+	0.0259603i	$0.991736\pi$
$878$	−53373.0	+	17342.0i	−2.05154	+	0.666586i
$879$	−549.231	−	1690.36i	−0.0210752	−	0.0648629i
$880$		0			0
$881$	−13273.0	+	40850.2i	−0.507583	+	1.56218i	0.288803	+	0.957389i	$0.406743\pi$
$881$	−13273.0	+	40850.2i	−0.507583	+	1.56218i	−0.796385	+	0.604790i	$0.793257\pi$
$882$			29737.1i			1.13526i
$883$	−1948.51	−	633.110i	−0.0742612	−	0.0241289i	0.271651	−	0.962396i	$-0.412430\pi$
$883$	−1948.51	−	633.110i	−0.0742612	−	0.0241289i	−0.345912	+	0.938267i	$0.612430\pi$
$884$	2003.66	−	1455.74i	0.0762333	−	0.0553868i
$885$		0			0
$886$	33764.5	+	24531.3i	1.28029	+	0.930187i
$887$	−7019.42	−	9661.40i	−0.265715	−	0.365725i	0.655222	−	0.755436i	$-0.272575\pi$
$887$	−7019.42	−	9661.40i	−0.265715	−	0.365725i	−0.920937	+	0.389711i	$0.872575\pi$
$888$	4381.97	+	6031.27i	0.165596	+	0.227923i
$889$	−1971.17	−	1432.14i	−0.0743655	−	0.0540297i
$890$		0			0
$891$	−4018.22	+	2919.41i	−0.151084	+	0.109769i
$892$	−8764.75	−	2847.84i	−0.328997	−	0.106898i
$893$			17120.8i			0.641574i
$894$	−2045.10	+	6294.18i	−0.0765083	+	0.235468i
$895$		0			0
$896$	5897.85	+	18151.7i	0.219903	+	0.676792i
$897$	−27693.6	+	8998.18i	−1.03084	+	0.334939i
$898$	1571.93	−	2163.57i	0.0584142	−	0.0804002i
$899$	760.933			0.0282297
$900$		0			0
$901$	3898.02			0.144131
$902$	29219.6	−	40217.3i	1.07861	−	1.48458i
$903$	23840.6	−	7746.28i	0.878588	−	0.285471i
$904$	−1173.46	−	3611.55i	−0.0431735	−	0.132874i
$905$		0			0
$906$	−12116.5	+	37290.8i	−0.444309	+	1.36744i
$907$		−	2447.01i		−	0.0895827i	−0.998996	−	0.0447913i	$-0.985738\pi$
$907$		−	2447.01i		−	0.0895827i	0.998996	−	0.0447913i	$-0.0142623\pi$
$908$	−6584.59	−	2139.46i	−0.240658	−	0.0781945i
$909$	−12789.4	+	9292.03i	−0.466663	+	0.339051i
$910$		0			0
$911$	−19395.7	−	14091.8i	−0.705387	−	0.512493i	0.176296	−	0.984337i	$-0.443589\pi$
$911$	−19395.7	−	14091.8i	−0.705387	−	0.512493i	−0.881682	+	0.471844i	$0.843589\pi$
$912$	−64320.8	−	88530.0i	−2.33539	−	3.21439i
$913$	24733.8	+	34043.2i	0.896571	+	1.23402i
$914$	36663.2	+	26637.3i	1.32682	+	0.963988i
$915$		0			0
$916$	−13809.3	+	10033.0i	−0.498113	+	0.361900i
$917$	−29492.2	−	9582.61i	−1.06207	−	0.345088i
$918$		−	10504.0i		−	0.377651i
$919$	6201.28	−	19085.6i	0.222591	−	0.685066i	−0.775936	−	0.630812i	$-0.782722\pi$
$919$	6201.28	−	19085.6i	0.222591	−	0.685066i	0.998527	−	0.0542539i	$-0.0172780\pi$
$920$		0			0
$921$	1744.97	+	5370.46i	0.0624307	+	0.192142i
$922$	51565.5	−	16754.6i	1.84189	−	0.598465i
$923$	11273.1	−	15516.1i	0.402014	−	0.553325i
$924$	−16607.1			−0.591269
$925$		0			0
$926$	14167.9			0.502794
$927$	39273.3	−	54055.0i	1.39148	−	1.91521i
$928$	17401.9	−	5654.21i	0.615565	−	0.200009i
$929$	−4458.92	−	13723.2i	−0.157473	−	0.484653i	0.840930	−	0.541144i	$-0.182009\pi$
$929$	−4458.92	−	13723.2i	−0.157473	−	0.484653i	−0.998403	+	0.0564915i	$0.982009\pi$
$930$		0			0
$931$	−9243.71	+	28449.2i	−0.325403	+	1.00149i
$932$			19131.6i			0.672398i
$933$	−70457.2	−	22892.9i	−2.47231	−	0.803302i
$934$	1399.83	−	1017.04i	0.0490406	−	0.0356301i
$935$		0			0
$936$	−15990.4	−	11617.7i	−0.558400	−	0.405701i
$937$	−22497.3	−	30964.9i	−0.784371	−	1.07959i	−0.994786	−	0.101981i	$-0.967482\pi$
$937$	−22497.3	−	30964.9i	−0.784371	−	1.07959i	0.210416	−	0.977612i	$-0.432518\pi$
$938$	3622.07	+	4985.35i	0.126082	+	0.173537i
$939$	25880.2	+	18803.1i	0.899435	+	0.653478i
$940$		0			0
$941$	13900.7	−	10099.5i	0.481563	−	0.349876i	−0.320368	−	0.947293i	$-0.603806\pi$
$941$	13900.7	−	10099.5i	0.481563	−	0.349876i	0.801930	+	0.597417i	$0.203806\pi$
$942$	48267.9	+	15683.2i	1.66948	+	0.542448i
$943$		−	40378.0i		−	1.39437i
$944$	8001.00	−	24624.5i	0.275858	−	0.849005i
$945$		0			0
$946$	−9546.84	−	29382.1i	−0.328113	−	1.00983i
$947$	15978.9	−	5191.85i	0.548304	−	0.178155i	−0.0217480	−	0.999763i	$-0.506923\pi$
$947$	15978.9	−	5191.85i	0.548304	−	0.178155i	0.570052	+	0.821609i	$0.306923\pi$
$948$	6606.46	−	9093.01i	0.226337	−	0.311527i
$949$	−4618.43			−0.157977
$950$		0			0
$951$	−53341.9			−1.81885
$952$	−1869.48	+	2573.12i	−0.0636451	+	0.0876000i
$953$	18395.9	−	5977.19i	0.625290	−	0.203169i	0.0208023	−	0.999784i	$-0.493378\pi$
$953$	18395.9	−	5977.19i	0.625290	−	0.203169i	0.604487	+	0.796615i	$0.293378\pi$
$954$	10202.6	+	31400.4i	0.346249	+	1.06564i
$955$		0			0
$956$	4260.10	−	13111.2i	0.144123	−	0.443565i
$957$		−	34619.2i		−	1.16936i
$958$	15046.5	+	4888.92i	0.507444	+	0.164879i
$959$	−17871.7	+	12984.6i	−0.601781	+	0.437219i
$960$		0			0
$961$	24060.8	+	17481.2i	0.807654	+	0.586795i
$962$	−4227.96	−	5819.28i	−0.141699	−	0.195032i
$963$	29095.7	+	40046.8i	0.973620	+	1.34007i
$964$	−24084.3	−	17498.3i	−0.804672	−	0.584628i
$965$		0			0
$966$	−32108.1	+	23327.9i	−1.06942	+	0.776981i
$967$	−37780.0	−	12275.5i	−1.25638	−	0.408224i	−0.396179	−	0.918173i	$-0.629664\pi$
$967$	−37780.0	−	12275.5i	−1.25638	−	0.408224i	−0.860204	+	0.509950i	$0.829664\pi$
$968$		−	1301.90i		−	0.0432279i
$969$	7956.69	−	24488.2i	0.263783	−	0.811840i
$970$		0			0
$971$	3924.88	+	12079.5i	0.129717	+	0.399229i	0.994731	−	0.102520i	$-0.0326904\pi$
$971$	3924.88	+	12079.5i	0.129717	+	0.399229i	−0.865014	+	0.501748i	$0.832690\pi$
$972$	−12563.3	+	4082.06i	−0.414576	+	0.134704i
$973$	−17246.8	+	23738.2i	−0.568250	+	0.782129i
$974$	57485.2			1.89111
$975$		0			0
$976$	21927.1			0.719127
$977$	−8545.44	+	11761.8i	−0.279829	+	0.385152i	−0.925677	−	0.378314i	$-0.876504\pi$
$977$	−8545.44	+	11761.8i	−0.279829	+	0.385152i	0.645848	+	0.763466i	$0.276504\pi$
$978$	−38433.2	+	12487.7i	−1.25660	+	0.408295i
$979$	631.596	+	1943.85i	0.0206189	+	0.0634584i
$980$		0			0
$981$	18036.4	−	55510.3i	0.587011	−	1.80663i
$982$			5559.86i			0.180674i
$983$	−21483.0	−	6980.26i	−0.697053	−	0.226486i	−0.0610068	−	0.998137i	$-0.519431\pi$
$983$	−21483.0	−	6980.26i	−0.697053	−	0.226486i	−0.636046	+	0.771651i	$0.719431\pi$
$984$	35247.5	−	25608.8i	1.14192	−	0.829654i
$985$		0			0
$986$	5692.89	+	4136.13i	0.183873	+	0.133591i
$987$	6697.24	+	9217.95i	0.215983	+	0.297275i
$988$	12403.2	+	17071.6i	0.399392	+	0.549716i
$989$	−20301.3	−	14749.8i	−0.652724	−	0.474232i
$990$		0			0
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	−0.593791	−	0.804619i	$-0.702369\pi$
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	0.581747	+	0.813370i	$0.302369\pi$
$992$	−1147.94	−	372.989i	−0.0367411	−	0.0119379i
$993$		−	43536.2i		−	1.39132i
$994$	8077.78	−	24860.9i	0.257758	−	0.793298i
$995$		0			0
$996$	−12095.4	−	37225.7i	−0.384795	−	1.18428i
$997$	−19413.0	+	6307.66i	−0.616666	+	0.200367i	−0.600659	−	0.799505i	$-0.705095\pi$
$997$	−19413.0	+	6307.66i	−0.616666	+	0.200367i	−0.0160063	+	0.999872i	$0.505095\pi$
$998$	−6792.62	+	9349.23i	−0.215447	+	0.296538i
$999$	−10368.7			−0.328381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.4.e.b.49.3		56
5.2	odd	4		25.4.d.a.16.2	yes	28
5.3	odd	4		125.4.d.a.76.6		28
5.4	even	2	inner	125.4.e.b.49.12		56
15.2	even	4		225.4.h.b.91.6		28
25.2	odd	20		25.4.d.a.11.2	✓	28
25.8	odd	20		625.4.a.d.1.3		14
25.11	even	5	inner	125.4.e.b.74.12		56
25.14	even	10	inner	125.4.e.b.74.3		56
25.17	odd	20		625.4.a.c.1.12		14
25.23	odd	20		125.4.d.a.51.6		28
75.2	even	20		225.4.h.b.136.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.2	✓	28	25.2	odd	20
25.4.d.a.16.2	yes	28	5.2	odd	4
125.4.d.a.51.6		28	25.23	odd	20
125.4.d.a.76.6		28	5.3	odd	4
125.4.e.b.49.3		56	1.1	even	1	trivial
125.4.e.b.49.12		56	5.4	even	2	inner
125.4.e.b.74.3		56	25.14	even	10	inner
125.4.e.b.74.12		56	25.11	even	5	inner
225.4.h.b.91.6		28	15.2	even	4
225.4.h.b.136.6		28	75.2	even	20
625.4.a.c.1.12		14	25.17	odd	20
625.4.a.d.1.3		14	25.8	odd	20

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.04622 + 2.81638i) q^{2} +(-8.11420 + 2.63646i) q^{3} +(-1.27284 - 3.91740i) q^{4} +(9.17815 - 28.2474i) q^{6} -12.5082i q^{7} +(-12.8494 - 4.17503i) q^{8} +(37.0458 - 26.9153i) q^{9} +O(q^{10})\)	\(q+(-2.04622 + 2.81638i) q^{2} +(-8.11420 + 2.63646i) q^{3} +(-1.27284 - 3.91740i) q^{4} +(9.17815 - 28.2474i) q^{6} -12.5082i q^{7} +(-12.8494 - 4.17503i) q^{8} +(37.0458 - 26.9153i) q^{9} +(-30.5650 - 22.2068i) q^{11} +(20.6562 + 28.4308i) q^{12} +(18.7786 + 25.8465i) q^{13} +(35.2278 + 25.5945i) q^{14} +(64.7099 - 47.0145i) q^{16} +(17.8993 + 5.81584i) q^{17} +159.410i q^{18} +(-49.5522 + 152.506i) q^{19} +(32.9774 + 101.494i) q^{21} +(125.085 - 40.6427i) q^{22} +(62.7926 - 86.4266i) q^{23} +115.270 q^{24} -111.218 q^{26} +(-94.2345 + 129.703i) q^{27} +(-48.9997 + 15.9210i) q^{28} +(-33.1890 - 102.145i) q^{29} +(-2.18936 + 6.73816i) q^{31} +170.364i q^{32} +(306.558 + 99.6067i) q^{33} +(-53.0055 + 38.5108i) q^{34} +(-152.592 - 110.864i) q^{36} +(38.0149 + 52.3230i) q^{37} +(-328.120 - 451.619i) q^{38} +(-220.516 - 160.214i) q^{39} +(305.782 - 222.164i) q^{41} +(-353.324 - 114.802i) q^{42} -234.897i q^{43} +(-48.0885 + 148.001i) q^{44} +(114.923 + 353.696i) q^{46} +(101.543 - 32.9933i) q^{47} +(-401.117 + 552.090i) q^{48} +186.545 q^{49} -160.572 q^{51} +(77.3489 - 106.462i) q^{52} +(196.979 - 64.0024i) q^{53} +(-172.467 - 530.800i) q^{54} +(-52.2221 + 160.723i) q^{56} -1368.11i q^{57} +(355.591 + 115.539i) q^{58} +(261.882 - 190.269i) q^{59} +(221.781 + 161.134i) q^{61} +(-14.4973 - 19.9538i) q^{62} +(-336.662 - 463.376i) q^{63} +(37.8690 + 27.5134i) q^{64} +(-907.814 + 659.566i) q^{66} +(134.591 + 43.7313i) q^{67} -77.5215i q^{68} +(-281.651 + 866.833i) q^{69} +(-185.509 - 570.937i) q^{71} +(-588.388 + 191.179i) q^{72} +(-84.9707 + 116.952i) q^{73} -225.148 q^{74} +660.500 q^{76} +(-277.767 + 382.313i) q^{77} +(902.448 - 293.223i) q^{78} +(-98.8328 - 304.176i) q^{79} +(40.6249 - 125.030i) q^{81} +1315.80i q^{82} +(-1059.28 - 344.182i) q^{83} +(355.618 - 258.372i) q^{84} +(661.558 + 480.650i) q^{86} +(538.604 + 741.324i) q^{87} +(300.028 + 412.954i) q^{88} +(-43.7671 - 31.7986i) q^{89} +(323.293 - 234.886i) q^{91} +(-418.493 - 135.977i) q^{92} -60.4469i q^{93} +(-114.857 + 353.495i) q^{94} +(-449.159 - 1382.37i) q^{96} +(1250.98 - 406.468i) q^{97} +(-381.712 + 525.381i) q^{98} -1730.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9}+O(q^{10}) \) 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9	\( 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9} - 178 q^{11} + 34 q^{14} - 414 q^{16} + 230 q^{19} - 288 q^{21} - 1560 q^{24} + 1172 q^{26} + 10 q^{29} - 1278 q^{31} + 1554 q^{34} + 1346 q^{36} + 2266 q^{39} + 682 q^{41} - 1096 q^{44} - 2478 q^{46} - 2688 q^{49} + 4012 q^{51} - 3230 q^{54} - 5820 q^{56} + 3810 q^{59} + 2782 q^{61} + 7192 q^{64} + 7264 q^{66} - 5374 q^{69} - 7438 q^{71} - 9696 q^{74} + 7040 q^{76} - 1550 q^{79} - 7424 q^{81} + 15224 q^{84} + 7782 q^{86} + 10150 q^{89} + 752 q^{91} - 7146 q^{94} - 15508 q^{96} - 13144 q^{99}+O(q^{100}) \) 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9 - 178 * q^11 + 34 * q^14 - 414 * q^16 + 230 * q^19 - 288 * q^21 - 1560 * q^24 + 1172 * q^26 + 10 * q^29 - 1278 * q^31 + 1554 * q^34 + 1346 * q^36 + 2266 * q^39 + 682 * q^41 - 1096 * q^44 - 2478 * q^46 - 2688 * q^49 + 4012 * q^51 - 3230 * q^54 - 5820 * q^56 + 3810 * q^59 + 2782 * q^61 + 7192 * q^64 + 7264 * q^66 - 5374 * q^69 - 7438 * q^71 - 9696 * q^74 + 7040 * q^76 - 1550 * q^79 - 7424 * q^81 + 15224 * q^84 + 7782 * q^86 + 10150 * q^89 + 752 * q^91 - 7146 * q^94 - 15508 * q^96 - 13144 * q^99

Introduction

L-functions

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