LMFDB - Embedded newform 125.4.e.b.74.3

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			74.3
Character	$\chi$	$=$	125.74
Dual form			125.4.e.b.49.3

$q$-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 $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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	−0.999402	−	0.0345696i	$-0.988994\pi$
$2$	−2.04622	−	2.81638i	−0.723448	−	0.995740i	0.275955	−	0.961171i	$-0.411006\pi$
$3$	−8.11420	−	2.63646i	−1.56158	−	0.507387i	−0.604349	−	0.796720i	$-0.706567\pi$
$3$	−8.11420	−	2.63646i	−1.56158	−	0.507387i	−0.957229	+	0.289332i	$0.906567\pi$
$4$	−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	$0.109645\pi$
$7$			12.5082i			0.675379i	−0.941258	+	0.337690i	$0.890355\pi$
$8$	−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	−0.921753	−	0.387778i	$-0.873243\pi$
$11$	−30.5650	+	22.2068i	−0.837791	+	0.608691i	0.0839620	+	0.996469i	$0.473243\pi$
$12$	20.6562	−	28.4308i	0.496910	−	0.683938i
$13$	18.7786	−	25.8465i	0.400633	−	0.551424i	−0.560269	−	0.828310i	$-0.689302\pi$
$13$	18.7786	−	25.8465i	0.400633	−	0.551424i	0.960903	+	0.276886i	$0.0893024\pi$
$14$	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	−0.178536	−	0.983933i	$-0.557136\pi$
$17$	17.8993	−	5.81584i	0.255366	−	0.0829735i	0.433902	+	0.900960i	$0.357136\pi$
$18$		−	159.410i		−	2.08740i
$19$	−49.5522	−	152.506i	−0.598319	−	1.84144i	−0.537459	−	0.843290i	$-0.680616\pi$
$19$	−49.5522	−	152.506i	−0.598319	−	1.84144i	−0.0608593	−	0.998146i	$-0.519384\pi$
$20$		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	0.992468	−	0.122506i	$-0.0390931\pi$
$23$	62.7926	+	86.4266i	0.569268	+	0.783530i	−0.423200	+	0.906036i	$0.639093\pi$
$24$	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	0.786802	+	0.617206i	$0.211735\pi$
$29$	−33.1890	+	102.145i	−0.212519	+	0.654065i	−0.999320	+	0.0368592i	$0.988265\pi$
$30$		0			0
$31$	−2.18936	−	6.73816i	−0.0126845	−	0.0390390i	0.944514	−	0.328471i	$-0.106533\pi$
$31$	−2.18936	−	6.73816i	−0.0126845	−	0.0390390i	−0.957198	+	0.289432i	$0.906533\pi$
$32$		−	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	−0.716168	−	0.697928i	$-0.754106\pi$
$37$	38.0149	−	52.3230i	0.168908	−	0.232482i	0.885077	+	0.465445i	$0.154106\pi$
$38$	−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	0.990372	−	0.138429i	$-0.0442052\pi$
$41$	305.782	+	222.164i	1.16476	+	0.846248i	0.174388	+	0.984677i	$0.444205\pi$
$42$	−353.324	+	114.802i	−1.29807	+	0.421770i
$43$			234.897i			0.833056i	0.909123	+	0.416528i	$0.136753\pi$
$43$			234.897i			0.833056i	−0.909123	+	0.416528i	$0.863247\pi$
$44$	−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	0.462316	−	0.886715i	$-0.347019\pi$
$47$	101.543	+	32.9933i	0.315139	+	0.102395i	−0.147177	+	0.989110i	$0.547019\pi$
$48$	−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	0.552935	−	0.833224i	$-0.313508\pi$
$53$	196.979	+	64.0024i	0.510512	+	0.165876i	−0.0424228	+	0.999100i	$0.513508\pi$
$54$	−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	0.837955	−	0.545740i	$-0.183751\pi$
$59$	261.882	+	190.269i	0.577868	+	0.419845i	−0.260087	+	0.965585i	$0.583751\pi$
$60$		0			0
$61$	221.781	−	161.134i	0.465511	−	0.338214i	−0.330178	−	0.943919i	$-0.607109\pi$
$61$	221.781	−	161.134i	0.465511	−	0.338214i	0.795689	+	0.605705i	$0.207109\pi$
$62$	−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	−0.183726	−	0.982978i	$-0.558816\pi$
$67$	134.591	−	43.7313i	0.245417	−	0.0797407i	0.429142	+	0.903237i	$0.358816\pi$
$68$			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	0.667650	+	0.744475i	$0.267300\pi$
$71$	−185.509	+	570.937i	−0.310082	+	0.954334i	−0.977732	+	0.209859i	$0.932700\pi$
$72$	−588.388	−	191.179i	−0.963087	−	0.312926i
$73$	−84.9707	−	116.952i	−0.136234	−	0.187510i	0.735449	−	0.677580i	$-0.236971\pi$
$73$	−84.9707	−	116.952i	−0.136234	−	0.187510i	−0.871683	+	0.490070i	$0.836971\pi$
$74$	−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	−0.996441	−	0.0842982i	$-0.973135\pi$
$79$	−98.8328	+	304.176i	−0.140754	+	0.433196i	0.855687	+	0.517494i	$0.173135\pi$
$80$		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	−0.909469	−	0.415773i	$-0.863511\pi$
$83$	−1059.28	+	344.182i	−1.40086	+	0.455167i	−0.491390	+	0.870939i	$0.663511\pi$
$84$	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	−0.613544	−	0.789661i	$-0.710257\pi$
$89$	−43.7671	+	31.7986i	−0.0521270	+	0.0378725i	0.561417	+	0.827533i	$0.310257\pi$
$90$		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	0.878863	−	0.477073i	$-0.158302\pi$
$97$	1250.98	+	406.468i	1.30946	+	0.425470i	0.430599	+	0.902543i	$0.358302\pi$
$98$	−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	0.885078	−	0.465443i	$-0.154105\pi$
$103$	1387.73	+	450.899i	1.32754	+	0.431344i	0.442463	+	0.896787i	$0.354105\pi$
$104$	−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	$-0.837602\pi$
$107$		−	1081.01i		−	0.976683i	0.872653	−	0.488342i	$-0.162398\pi$
$108$	628.043	−	204.064i	0.559569	−	0.181815i
$109$	1031.20	+	749.212i	0.906158	+	0.658362i	0.940040	−	0.341064i	$-0.110787\pi$
$109$	1031.20	+	749.212i	0.906158	+	0.658362i	−0.0338823	+	0.999426i	$0.510787\pi$
$110$		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	−0.734694	−	0.678399i	$-0.762674\pi$
$113$	165.207	−	227.388i	0.137535	−	0.189300i	0.872228	+	0.489099i	$0.162674\pi$
$114$	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	0.847141	−	0.531368i	$-0.178322\pi$
$127$	114.496	+	157.590i	0.0799990	+	0.110109i	−0.767142	+	0.641477i	$0.778322\pi$
$128$	−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	0.790524	+	0.612431i	$0.209808\pi$
$131$	766.106	+	2357.83i	0.510954	+	1.57256i	−0.279570	+	0.960125i	$0.590192\pi$
$132$			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	−0.998982	−	0.0451188i	$-0.985633\pi$
$137$	−1038.08	+	1428.80i	−0.647369	+	0.891027i	0.351613	+	0.936145i	$0.385633\pi$
$138$	−1865.01	+	2566.97i	−1.15044	+	1.58344i
$139$	−1897.81	+	1378.84i	−1.15806	+	0.841379i	−0.989531	−	0.144318i	$-0.953901\pi$
$139$	−1897.81	+	1378.84i	−1.15806	+	0.841379i	−0.168528	+	0.985697i	$0.553901\pi$
$140$		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	$-0.856992\pi$
$157$		−	1708.75i		−	0.868620i	0.900763	−	0.434310i	$-0.143008\pi$
$158$	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	−0.956716	−	0.291023i	$-0.906004\pi$
$163$	−799.735	+	1100.74i	−0.384295	+	0.528937i	0.572421	+	0.819960i	$0.306004\pi$
$164$	−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	−0.870518	−	0.492136i	$-0.836216\pi$
$167$	−2774.28	+	901.420i	−1.28551	+	0.417688i	−0.414994	+	0.909824i	$0.636216\pi$
$168$			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	0.973958	−	0.226728i	$-0.0728028\pi$
$173$	1040.70	+	1432.40i	0.457357	+	0.629499i	−0.516601	+	0.856226i	$0.672803\pi$
$174$	−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	−0.721770	−	0.692133i	$-0.756671\pi$
$179$	644.168	−	1982.55i	0.268980	−	0.827835i	0.990750	−	0.135702i	$-0.0433289\pi$
$180$		0			0
$181$	−162.821	−	501.111i	−0.0668639	−	0.205786i	0.912042	−	0.410096i	$-0.134505\pi$
$181$	−162.821	−	501.111i	−0.0668639	−	0.205786i	−0.978906	+	0.204310i	$0.934505\pi$
$182$		−	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	0.173516	−	0.984831i	$-0.444487\pi$
$191$	−1872.83	−	1360.69i	−0.709494	−	0.515478i	−0.883011	+	0.469353i	$0.844487\pi$
$192$	−379.815	+	123.409i	−0.142764	+	0.0463870i
$193$		−	2028.97i		−	0.756727i	−0.925657	−	0.378363i	$-0.876487\pi$
$193$		−	2028.97i		−	0.756727i	0.925657	−	0.378363i	$-0.123513\pi$
$194$	−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	0.725232	−	0.688504i	$-0.241732\pi$
$197$	2508.61	+	815.098i	0.907265	+	0.294788i	0.182033	+	0.983292i	$0.441732\pi$
$198$	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	−0.309916	−	0.950764i	$-0.600301\pi$
$211$	1528.02	−	1110.17i	0.498545	−	0.362214i	0.808461	+	0.588550i	$0.200301\pi$
$212$	−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	0.959458	−	0.281850i	$-0.0909481\pi$
$223$	1315.10	+	1810.08i	0.394914	+	0.543553i	−0.564544	+	0.825403i	$0.690948\pi$
$224$	2130.95			0.635625
$225$		0			0
$226$	−978.462			−0.287993
$227$	987.983	+	1359.84i	0.288875	+	0.397603i	0.928648	−	0.370961i	$-0.120972\pi$
$227$	987.983	+	1359.84i	0.288875	+	0.397603i	−0.639773	+	0.768564i	$0.720972\pi$
$228$	−5359.43	−	1741.38i	−1.55674	−	0.505815i
$229$	−1280.57	+	3941.19i	−0.369531	+	1.13730i	0.577564	+	0.816345i	$0.304003\pi$
$229$	−1280.57	+	3941.19i	−0.369531	+	1.13730i	−0.947095	+	0.320953i	$0.895997\pi$
$230$		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	−0.855057	−	0.518534i	$-0.826478\pi$
$233$	−4417.38	+	1435.29i	−1.24203	+	0.403559i	−0.386969	+	0.922093i	$0.626478\pi$
$234$	−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	−0.157624	−	0.987499i	$-0.550383\pi$
$239$	2707.72	−	1967.27i	0.732835	−	0.532436i	0.890459	+	0.455063i	$0.150383\pi$
$240$		0			0
$241$	5847.12	+	4248.18i	1.56285	+	1.13548i	0.933626	+	0.358250i	$0.116626\pi$
$241$	5847.12	+	4248.18i	1.56285	+	1.13548i	0.629222	+	0.777226i	$0.283374\pi$
$242$	−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	$-0.997813\pi$
$257$		−	56.6174i		−	0.0137420i	0.999976	−	0.00687100i	$-0.00218713\pi$
$258$	−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	−0.0462529	−	0.998930i	$-0.514728\pi$
$263$	3915.74	−	5389.55i	0.918079	−	1.26363i	0.964332	−	0.264697i	$-0.0852720\pi$
$264$	−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	−0.954954	−	0.296754i	$-0.904096\pi$
$269$	−1574.21	−	4844.92i	−0.356807	−	1.09814i	0.598147	−	0.801387i	$-0.295904\pi$
$270$		0			0
$271$	1535.70	−	4726.39i	0.344232	−	1.05944i	−0.617762	−	0.786365i	$-0.711960\pi$
$271$	1535.70	−	4726.39i	0.344232	−	1.05944i	0.961994	−	0.273072i	$-0.0880396\pi$
$272$	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	0.347153	−	0.937808i	$-0.387148\pi$
$277$	−3006.00	−	4137.40i	−0.652032	−	0.897445i	−0.999185	+	0.0403637i	$0.987148\pi$
$278$	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	0.970716	−	0.240228i	$-0.0772223\pi$
$281$	208.142	+	640.597i	0.0441877	+	0.135996i	−0.926529	+	0.376224i	$0.877222\pi$
$282$			3171.14i			0.669641i
$283$	2706.16	−	879.284i	0.568425	−	0.184693i	−0.0106833	−	0.999943i	$-0.503401\pi$
$283$	2706.16	−	879.284i	0.568425	−	0.184693i	0.579109	+	0.815250i	$0.303401\pi$
$284$	−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	$-0.993389\pi$
$293$		−	208.321i		−	0.0415367i	0.999784	−	0.0207684i	$-0.00661125\pi$
$294$	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	$0.0195954\pi$
$307$			661.860i			0.123044i	−0.998106	+	0.0615218i	$0.980405\pi$
$308$	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	0.281267	−	0.959629i	$-0.409245\pi$
$311$	7024.85	−	5103.86i	1.28085	−	0.930589i	0.999578	+	0.0290408i	$0.00924527\pi$
$312$	2164.60	−	2979.32i	0.392777	−	0.540611i
$313$	−2203.89	+	3033.40i	−0.397992	+	0.547788i	−0.960238	−	0.279181i	$-0.909937\pi$
$313$	−2203.89	+	3033.40i	−0.397992	+	0.547788i	0.562247	+	0.826969i	$0.309937\pi$
$314$	−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	0.269477	−	0.963007i	$-0.413149\pi$
$317$	5946.15	−	1932.02i	1.05353	−	0.342313i	0.784053	+	0.620694i	$0.213149\pi$
$318$			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	−0.992402	−	0.123034i	$-0.960738\pi$
$331$	−1576.86	−	4853.08i	−0.261849	−	0.805890i	0.730553	−	0.682856i	$-0.239262\pi$
$332$		−	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	−0.981560	−	0.191155i	$-0.938777\pi$
$337$	−3071.24	+	4227.20i	−0.496442	+	0.683294i	0.485118	+	0.874449i	$0.338777\pi$
$338$	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	0.250555	−	0.968102i	$-0.419387\pi$
$347$	−748.379	−	243.163i	−0.115778	−	0.0376187i	−0.366333	+	0.930484i	$0.619387\pi$
$348$	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	0.134560	−	0.990905i	$-0.457038\pi$
$353$	−2248.46	−	730.568i	−0.339018	−	0.110154i	−0.473578	+	0.880752i	$0.657038\pi$
$354$	−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	0.257132	−	0.966376i	$-0.417222\pi$
$359$	−3962.13	−	2878.66i	−0.582488	−	0.423202i	−0.839620	+	0.543174i	$0.817222\pi$
$360$		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	0.627575	−	0.778556i	$-0.284048\pi$
$367$	11199.3	−	3638.89i	1.59292	−	0.517570i	0.965343	+	0.260986i	$0.0840476\pi$
$368$			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	0.909966	+	0.414684i	$0.136108\pi$
$373$	7370.66	+	10144.8i	1.02316	+	1.40826i	0.113193	+	0.993573i	$0.463892\pi$
$374$	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	0.771353	+	0.636407i	$0.219580\pi$
$379$	−1673.08	+	5149.21i	−0.226755	+	0.697881i	−0.998109	+	0.0614740i	$0.980420\pi$
$380$		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	−0.999905	−	0.0138191i	$-0.995601\pi$
$383$	−13497.2	+	4385.52i	−1.80072	+	0.585090i	−0.800817	+	0.598909i	$0.795601\pi$
$384$	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	−0.575225	−	0.817995i	$-0.695085\pi$
$389$	191.659	−	139.248i	0.0249807	−	0.0181495i	0.600206	+	0.799846i	$0.295085\pi$
$390$		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	−0.475255	−	0.879848i	$-0.657644\pi$
$397$	−10891.6	−	3538.88i	−1.37691	−	0.447384i	−0.901651	+	0.432464i	$0.857644\pi$
$398$	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	0.156104	−	0.987741i	$-0.450107\pi$
$409$	−6080.01	−	4417.39i	−0.735055	−	0.534048i	−0.891158	+	0.453692i	$0.850107\pi$
$410$		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	0.997644	+	0.0686047i	$0.0218547\pi$
$419$	1980.00	+	6093.82i	0.230858	+	0.710507i	−0.766786	+	0.641903i	$0.778145\pi$
$420$		0			0
$421$	4678.50	−	14399.0i	0.541607	−	1.66689i	−0.187318	−	0.982299i	$-0.559979\pi$
$421$	4678.50	−	14399.0i	0.541607	−	1.66689i	0.728924	−	0.684594i	$-0.240021\pi$
$422$	−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	0.904631	+	0.426196i	$0.140147\pi$
$431$	3787.43	+	11656.5i	0.423281	+	1.30272i	−0.481350	+	0.876528i	$0.659853\pi$
$432$		−	12823.4i		−	1.42817i
$433$	11869.0	−	3856.48i	1.31730	−	0.428016i	0.435731	−	0.900077i	$-0.356490\pi$
$433$	11869.0	−	3856.48i	1.31730	−	0.428016i	0.881566	+	0.472061i	$0.156490\pi$
$434$	−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	0.425776	−	0.904828i	$-0.360001\pi$
$439$	13041.9	−	9475.47i	1.41789	−	1.03016i	0.992115	−	0.125330i	$-0.0399990\pi$
$440$		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	$0.222263\pi$
$443$			11988.6i			1.28577i	−0.765963	+	0.642885i	$0.777737\pi$
$444$	−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	$0.232100\pi$
$457$			13017.8i			1.33249i	−0.745732	+	0.666246i	$0.767900\pi$
$458$	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	−0.999318	−	0.0369393i	$-0.988239\pi$
$461$	−12600.2	+	9154.58i	−1.27299	+	0.924883i	−0.273675	+	0.961822i	$0.588239\pi$
$462$	8249.98	−	11355.1i	0.830788	−	1.14348i
$463$	−2392.17	+	3292.54i	−0.240116	+	0.330491i	−0.912019	−	0.410148i	$-0.865477\pi$
$463$	−2392.17	+	3292.54i	−0.240116	+	0.330491i	0.671903	+	0.740639i	$0.265477\pi$
$464$	−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	−0.332343	−	0.943159i	$-0.607839\pi$
$467$	−472.706	+	153.591i	−0.0468399	+	0.0152192i	0.285503	+	0.958378i	$0.407839\pi$
$468$			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	−0.995427	−	0.0955270i	$-0.969546\pi$
$479$	−1404.36	+	4322.18i	−0.133960	+	0.412287i	0.861467	+	0.507814i	$0.169546\pi$
$480$		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	0.0663359	+	0.997797i	$0.478869\pi$
$487$	−9706.02	+	13359.2i	−0.903125	+	1.24304i	−0.969461	+	0.245247i	$0.921131\pi$
$488$	−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	0.645579	−	0.763693i	$-0.276616\pi$
$491$	1292.08	+	938.748i	0.118759	+	0.0862833i	−0.526821	+	0.849977i	$0.676616\pi$
$492$	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	0.0189337	−	0.999821i	$-0.493973\pi$
$503$	−6243.29	−	2028.57i	−0.553429	−	0.179820i	−0.572362	+	0.820001i	$0.693973\pi$
$504$	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	0.979103	−	0.203366i	$-0.0651880\pi$
$509$	12497.0	+	9079.59i	1.08825	+	0.790660i	0.109147	+	0.994026i	$0.465188\pi$
$510$		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	0.786285	+	0.617863i	$0.212002\pi$
$521$	−2533.05	+	7795.93i	−0.213004	+	0.655559i	−0.999289	+	0.0376951i	$0.987998\pi$
$522$	16282.9	+	5290.64i	1.36529	+	0.443611i
$523$	−9649.57	−	13281.5i	−0.806781	−	1.11044i	−0.991812	−	0.127706i	$-0.959239\pi$
$523$	−9649.57	−	13281.5i	−0.806781	−	1.11044i	0.185031	−	0.982733i	$-0.440761\pi$
$524$	−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	−0.207406	−	0.978255i	$-0.566502\pi$
$541$	−15123.6	−	10987.9i	−1.20187	−	0.873212i	−0.994468	+	0.105043i	$0.966502\pi$
$542$	−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	0.717977	−	0.696067i	$-0.245068\pi$
$547$	11382.1	+	3698.27i	0.889695	+	0.289080i	0.171718	+	0.985146i	$0.445068\pi$
$548$	−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	$-0.985678\pi$
$557$		−	1182.53i		−	0.0899558i	0.998988	−	0.0449779i	$-0.0143217\pi$
$558$	−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	−0.581816	−	0.813320i	$-0.697658\pi$
$563$	4962.58	−	6830.40i	0.371488	−	0.511310i	0.953305	+	0.302011i	$0.0976578\pi$
$564$	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	0.896747	−	0.442543i	$-0.145924\pi$
$569$	−1206.03	−	3711.79i	−0.0888568	−	0.273473i	−0.985604	+	0.169070i	$0.945924\pi$
$570$		0			0
$571$	644.040	−	1982.15i	0.0472018	−	0.145272i	−0.924678	−	0.380751i	$-0.875666\pi$
$571$	644.040	−	1982.15i	0.0472018	−	0.145272i	0.971880	+	0.235478i	$0.0756656\pi$
$572$	−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	0.934361	−	0.356327i	$-0.115971\pi$
$577$	4251.42	+	5851.58i	0.306740	+	0.422192i	−0.627621	+	0.778519i	$0.715971\pi$
$578$	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	−0.532376	−	0.846508i	$-0.678701\pi$
$587$	6218.01	−	8558.36i	0.437214	−	0.601774i	0.969590	+	0.244734i	$0.0787007\pi$
$588$	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	$-0.916552\pi$
$593$		−	7485.02i		−	0.518335i	0.965832	−	0.259168i	$-0.0834482\pi$
$594$	−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	$0.00997432\pi$
$607$			937.076i			0.0626602i	−0.999509	+	0.0313301i	$0.990026\pi$
$608$	−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	−0.161669	−	0.986845i	$-0.551688\pi$
$613$	12549.0	−	17272.2i	0.826835	−	1.13804i	0.988504	−	0.151196i	$-0.0483124\pi$
$614$	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	−0.990829	−	0.135119i	$-0.956858\pi$
$617$	−26253.5	+	8530.27i	−1.71301	+	0.556590i	−0.722177	+	0.691708i	$0.756858\pi$
$618$			43338.1i			2.82090i
$619$	−3030.03	−	9325.47i	−0.196748	−	0.605529i	−0.999952	−	0.00982399i	$-0.996873\pi$
$619$	−3030.03	−	9325.47i	−0.196748	−	0.605529i	0.803204	−	0.595705i	$-0.203127\pi$
$620$		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	0.809309	−	0.587383i	$-0.199842\pi$
$631$	−3022.55	−	9302.45i	−0.190691	−	0.586885i	−1.00000		0.000497352i	$0.999842\pi$
$632$		−	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	−0.137561	−	0.990493i	$-0.543926\pi$
$641$	−18210.1	−	13230.4i	−1.12208	−	0.815242i	−0.984524	+	0.175251i	$0.943926\pi$
$642$	30535.7	−	9921.66i	1.87718	−	0.609932i
$643$			649.245i			0.0398192i	0.999802	+	0.0199096i	$0.00633784\pi$
$643$			649.245i			0.0398192i	−0.999802	+	0.0199096i	$0.993662\pi$
$644$	−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	0.998921	+	0.0464360i	$0.0147863\pi$
$647$	30188.5	+	9808.83i	1.83436	+	0.596020i	0.835439	+	0.549584i	$0.185214\pi$
$648$	−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	0.458968	−	0.888453i	$-0.348219\pi$
$653$	5140.54	+	1670.26i	0.308062	+	0.100096i	−0.150906	+	0.988548i	$0.548219\pi$
$654$	−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	0.672146	−	0.740418i	$-0.265373\pi$
$659$	2971.87	+	2159.19i	0.175671	+	0.127633i	−0.496475	+	0.868051i	$0.665373\pi$
$660$		0			0
$661$	−7532.06	+	5472.36i	−0.443212	+	0.322012i	−0.786910	−	0.617068i	$-0.788320\pi$
$661$	−7532.06	+	5472.36i	−0.443212	+	0.322012i	0.343698	+	0.939080i	$0.388320\pi$
$662$	−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	0.881621	+	0.471958i	$0.156452\pi$
$673$	18472.5	+	25425.2i	1.05804	+	1.45627i	0.176422	+	0.984315i	$0.443548\pi$
$674$	18189.8			1.03953
$675$		0			0
$676$	−4845.29			−0.275677
$677$	−4364.44	−	6007.13i	−0.247768	−	0.341023i	0.666960	−	0.745094i	$-0.267595\pi$
$677$	−4364.44	−	6007.13i	−0.247768	−	0.341023i	−0.914728	+	0.404070i	$0.867595\pi$
$678$	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	0.358982	−	0.933344i	$-0.383124\pi$
$683$	21384.1	−	6948.13i	1.19801	−	0.389257i	0.839029	+	0.544087i	$0.183124\pi$
$684$	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	0.671020	−	0.741439i	$-0.265857\pi$
$691$	3146.51	+	2286.07i	0.173225	+	0.125856i	−0.497794	+	0.867295i	$0.665857\pi$
$692$	−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	0.211931	−	0.977285i	$-0.432025\pi$
$709$	−12309.4	−	8943.33i	−0.652032	−	0.473729i	−0.863963	+	0.503556i	$0.832025\pi$
$710$		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	−0.999114	−	0.0420821i	$-0.986601\pi$
$719$	−4155.65	−	12789.8i	−0.215549	−	0.663392i	0.783565	−	0.621310i	$-0.213399\pi$
$720$		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	0.980633	+	0.195857i	$0.0627487\pi$
$727$	16933.7	+	23307.2i	0.863871	+	1.18902i	−0.116761	+	0.993160i	$0.537251\pi$
$728$	−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	−0.636988	−	0.770874i	$-0.719820\pi$
$733$	−13876.0	+	4508.60i	−0.699213	+	0.227188i	−0.0622256	+	0.998062i	$0.519820\pi$
$734$	−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	−0.566780	−	0.823869i	$-0.691811\pi$
$739$	836.136	−	607.488i	0.0416208	−	0.0302393i	0.608401	+	0.793630i	$0.291811\pi$
$740$		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	$0.0268257\pi$
$743$			3409.57i			0.168351i	−0.996451	+	0.0841756i	$0.973174\pi$
$744$	−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	$0.0953784\pi$
$757$			12295.8i			0.590353i	−0.955443	+	0.295176i	$0.904622\pi$
$758$	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	−0.540356	−	0.841437i	$-0.681710\pi$
$761$	1950.66	−	1417.24i	0.0929190	−	0.0675096i	0.633275	+	0.773927i	$0.281710\pi$
$762$	−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	0.921984	+	0.387227i	$0.126567\pi$
$769$	8608.70	+	26494.8i	0.403690	+	1.24243i	−0.518294	+	0.855202i	$0.673433\pi$
$770$		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	0.318247	−	0.948008i	$-0.396906\pi$
$773$	−14651.0	−	20165.3i	−0.681705	−	0.938287i	−0.999953	+	0.00972064i	$0.996906\pi$
$774$	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	−0.601446	−	0.798913i	$-0.705408\pi$
$787$	7599.80	−	10460.2i	0.344223	−	0.473782i	0.945669	+	0.325131i	$0.105408\pi$
$788$	−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	0.569592	−	0.821927i	$-0.307101\pi$
$797$	12314.1	+	4001.08i	0.547285	+	0.177824i	−0.0223070	+	0.999751i	$0.507101\pi$
$798$	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	0.412946	−	0.910755i	$-0.364500\pi$
$809$	−7492.76	−	5443.81i	−0.325626	−	0.236581i	−0.738572	+	0.674174i	$0.764500\pi$
$810$		0			0
$811$	2741.13	−	1991.55i	0.118686	−	0.0862303i	−0.526859	−	0.849953i	$-0.676630\pi$
$811$	2741.13	−	1991.55i	0.118686	−	0.0862303i	0.645545	+	0.763722i	$0.276630\pi$
$812$	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	−0.836582	−	0.547842i	$-0.815449\pi$
$821$	3816.58	−	11746.2i	0.162241	−	0.499325i	0.998822	+	0.0485169i	$0.0154495\pi$
$822$	−49887.6	−	16209.5i	−2.11683	−	0.687798i
$823$	17106.4	+	23545.0i	0.724536	+	0.997239i	0.999361	+	0.0357442i	$0.0113802\pi$
$823$	17106.4	+	23545.0i	0.724536	+	0.997239i	−0.274825	+	0.961494i	$0.588620\pi$
$824$	−19714.0			−0.833457
$825$		0			0
$826$	14095.4			0.593754
$827$	4728.18	+	6507.78i	0.198809	+	0.273637i	0.896768	−	0.442500i	$-0.145908\pi$
$827$	4728.18	+	6507.78i	0.198809	+	0.273637i	−0.697959	+	0.716137i	$0.745908\pi$
$828$	−19163.3	−	6226.52i	−0.804311	−	0.261336i
$829$	−7849.09	+	24157.0i	−0.328842	+	1.01207i	0.640834	+	0.767679i	$0.278589\pi$
$829$	−7849.09	+	24157.0i	−0.328842	+	1.01207i	−0.969676	+	0.244393i	$0.921411\pi$
$830$		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	0.114343	−	0.993441i	$-0.463524\pi$
$839$	26598.5	−	19324.9i	1.09450	−	0.795198i	0.980153	+	0.198243i	$0.0635236\pi$
$840$		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	0.480916	−	0.876767i	$-0.340304\pi$
$853$	8834.96	+	2870.65i	0.354635	+	0.115228i	−0.126281	+	0.991994i	$0.540304\pi$
$854$	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	$-0.707635\pi$
$857$		−	39874.7i		−	1.58937i	0.607019	−	0.794687i	$-0.292365\pi$
$858$	−34094.9	+	11078.1i	−1.35662	+	0.440793i
$859$	22161.6	+	16101.3i	0.880261	+	0.639547i	0.933321	−	0.359044i	$-0.116897\pi$
$859$	22161.6	+	16101.3i	0.880261	+	0.639547i	−0.0530595	+	0.998591i	$0.516897\pi$
$860$		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	−0.228639	−	0.973511i	$-0.573428\pi$
$863$	19467.4	−	26794.6i	0.767879	−	1.05689i	0.996518	−	0.0833829i	$-0.0265724\pi$
$864$	−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	−0.999663	−	0.0259603i	$-0.991736\pi$
$877$	−18581.1	−	25574.8i	−0.715440	−	0.984719i	0.284223	−	0.958758i	$-0.408264\pi$
$878$	−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	−0.796385	−	0.604790i	$-0.793257\pi$
$881$	−13273.0	−	40850.2i	−0.507583	−	1.56218i	0.288803	−	0.957389i	$-0.406743\pi$
$882$		−	29737.1i		−	1.13526i
$883$	−1948.51	+	633.110i	−0.0742612	+	0.0241289i	−0.345912	−	0.938267i	$-0.612430\pi$
$883$	−1948.51	+	633.110i	−0.0742612	+	0.0241289i	0.271651	+	0.962396i	$0.412430\pi$
$884$	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	−0.920937	−	0.389711i	$-0.872575\pi$
$887$	−7019.42	+	9661.40i	−0.265715	+	0.365725i	0.655222	+	0.755436i	$0.272575\pi$
$888$	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	$0.0142623\pi$
$907$			2447.01i			0.0895827i	−0.998996	+	0.0447913i	$0.985738\pi$
$908$	−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	−0.881682	−	0.471844i	$-0.843589\pi$
$911$	−19395.7	+	14091.8i	−0.705387	+	0.512493i	0.176296	+	0.984337i	$0.443589\pi$
$912$	−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	0.998527	+	0.0542539i	$0.0172780\pi$
$919$	6201.28	+	19085.6i	0.222591	+	0.685066i	−0.775936	+	0.630812i	$0.782722\pi$
$920$		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	−0.998403	−	0.0564915i	$-0.982009\pi$
$929$	−4458.92	+	13723.2i	−0.157473	+	0.484653i	0.840930	+	0.541144i	$0.182009\pi$
$930$		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	0.210416	+	0.977612i	$0.432518\pi$
$937$	−22497.3	+	30964.9i	−0.784371	+	1.07959i	−0.994786	+	0.101981i	$0.967482\pi$
$938$	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	0.801930	−	0.597417i	$-0.203806\pi$
$941$	13900.7	+	10099.5i	0.481563	+	0.349876i	−0.320368	+	0.947293i	$0.603806\pi$
$942$	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	0.570052	−	0.821609i	$-0.306923\pi$
$947$	15978.9	+	5191.85i	0.548304	+	0.178155i	−0.0217480	+	0.999763i	$0.506923\pi$
$948$	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	0.604487	−	0.796615i	$-0.293378\pi$
$953$	18395.9	+	5977.19i	0.625290	+	0.203169i	0.0208023	+	0.999784i	$0.493378\pi$
$954$	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	−0.860204	−	0.509950i	$-0.829664\pi$
$967$	−37780.0	+	12275.5i	−1.25638	+	0.408224i	−0.396179	+	0.918173i	$0.629664\pi$
$968$			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	−0.865014	−	0.501748i	$-0.832690\pi$
$971$	3924.88	−	12079.5i	0.129717	−	0.399229i	0.994731	+	0.102520i	$0.0326904\pi$
$972$	−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	0.645848	−	0.763466i	$-0.276504\pi$
$977$	−8545.44	−	11761.8i	−0.279829	−	0.385152i	−0.925677	+	0.378314i	$0.876504\pi$
$978$	−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	−0.636046	−	0.771651i	$-0.719431\pi$
$983$	−21483.0	+	6980.26i	−0.697053	+	0.226486i	−0.0610068	+	0.998137i	$0.519431\pi$
$984$	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	0.581747	−	0.813370i	$-0.302369\pi$
$991$	−375.742	−	272.992i	−0.0120442	−	0.00875064i	−0.593791	+	0.804619i	$0.702369\pi$
$992$	−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	−0.0160063	−	0.999872i	$-0.505095\pi$
$997$	−19413.0	−	6307.66i	−0.616666	−	0.200367i	−0.600659	+	0.799505i	$0.705095\pi$
$998$	−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.74.3		56
5.2	odd	4		125.4.d.a.51.6		28
5.3	odd	4		25.4.d.a.11.2	✓	28
5.4	even	2	inner	125.4.e.b.74.12		56
15.8	even	4		225.4.h.b.136.6		28
25.3	odd	20		625.4.a.c.1.12		14
25.9	even	10	inner	125.4.e.b.49.3		56
25.12	odd	20		125.4.d.a.76.6		28
25.13	odd	20		25.4.d.a.16.2	yes	28
25.16	even	5	inner	125.4.e.b.49.12		56
25.22	odd	20		625.4.a.d.1.3		14
75.38	even	20		225.4.h.b.91.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.2	✓	28	5.3	odd	4
25.4.d.a.16.2	yes	28	25.13	odd	20
125.4.d.a.51.6		28	5.2	odd	4
125.4.d.a.76.6		28	25.12	odd	20
125.4.e.b.49.3		56	25.9	even	10	inner
125.4.e.b.49.12		56	25.16	even	5	inner
125.4.e.b.74.3		56	1.1	even	1	trivial
125.4.e.b.74.12		56	5.4	even	2	inner
225.4.h.b.91.6		28	75.38	even	20
225.4.h.b.136.6		28	15.8	even	4
625.4.a.c.1.12		14	25.3	odd	20
625.4.a.d.1.3		14	25.22	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

Modular forms

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