LMFDB - Embedded newform 250.4.e.b.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	250.49
Dual form			250.4.e.b.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17557 + 1.61803i) q^{2} +(6.75819 - 2.19587i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.39174 + 13.5164i) q^{6} -23.3487i q^{7} +(7.60845 + 2.47214i) q^{8} +(19.0078 - 13.8100i) q^{9} +O(q^{10})$	\(q+(-1.17557 + 1.61803i) q^{2} +(6.75819 - 2.19587i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.39174 + 13.5164i) q^{6} -23.3487i q^{7} +(7.60845 + 2.47214i) q^{8} +(19.0078 - 13.8100i) q^{9} +(-51.2554 - 37.2392i) q^{11} +(-16.7072 - 22.9954i) q^{12} +(3.44706 + 4.74447i) q^{13} +(37.7789 + 27.4480i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-70.6774 - 22.9645i) q^{17} +46.9899i q^{18} +(-3.29893 + 10.1531i) q^{19} +(-51.2706 - 157.795i) q^{21} +(120.509 - 39.1557i) q^{22} +(77.5886 - 106.792i) q^{23} +56.8478 q^{24} -11.7290 q^{26} +(-14.6399 + 20.1502i) q^{27} +(-88.8236 + 28.8605i) q^{28} +(-13.5338 - 41.6528i) q^{29} +(-97.2735 + 299.377i) q^{31} -32.0000i q^{32} +(-428.166 - 139.120i) q^{33} +(120.244 - 87.3621i) q^{34} +(-76.0312 - 55.2399i) q^{36} +(-84.1012 - 115.755i) q^{37} +(-12.5499 - 17.2734i) q^{38} +(33.7141 + 24.4948i) q^{39} +(105.776 - 76.8508i) q^{41} +(315.589 + 102.541i) q^{42} -223.280i q^{43} +(-78.3113 + 241.017i) q^{44} +(81.5815 + 251.082i) q^{46} +(510.915 - 166.006i) q^{47} +(-66.8286 + 91.9817i) q^{48} -202.161 q^{49} -528.078 q^{51} +(13.7883 - 18.9779i) q^{52} +(306.365 - 99.5441i) q^{53} +(-15.3933 - 47.3759i) q^{54} +(57.7211 - 177.647i) q^{56} +75.8604i q^{57} +(83.3056 + 27.0676i) q^{58} +(703.580 - 511.180i) q^{59} +(22.4025 + 16.2764i) q^{61} +(-370.050 - 509.331i) q^{62} +(-322.445 - 443.807i) q^{63} +(51.7771 + 37.6183i) q^{64} +(728.440 - 529.242i) q^{66} +(42.9787 + 13.9646i) q^{67} +297.258i q^{68} +(289.858 - 892.092i) q^{69} +(-206.178 - 634.551i) q^{71} +(178.760 - 58.0827i) q^{72} +(215.194 - 296.189i) q^{73} +286.163 q^{74} +42.7023 q^{76} +(-869.487 + 1196.75i) q^{77} +(-79.2667 + 25.7553i) q^{78} +(103.606 + 318.866i) q^{79} +(-250.721 + 771.641i) q^{81} +261.493i q^{82} +(994.460 + 323.120i) q^{83} +(-536.913 + 390.090i) q^{84} +(361.275 + 262.482i) q^{86} +(-182.928 - 251.779i) q^{87} +(-297.914 - 410.043i) q^{88} +(-224.451 - 163.073i) q^{89} +(110.777 - 80.4843i) q^{91} +(-502.164 - 163.163i) q^{92} +2236.85i q^{93} +(-332.013 + 1021.83i) q^{94} +(-70.2678 - 216.262i) q^{96} +(-509.432 + 165.524i) q^{97} +(237.654 - 327.103i) q^{98} -1488.53 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.17557	+	1.61803i	−0.415627	+	0.572061i
$2$	−1.17557	+	1.61803i	−0.415627	+	0.572061i
$3$	6.75819	−	2.19587i	1.30061	−	0.422595i	0.424819	−	0.905278i	$-0.360338\pi$
$3$	6.75819	−	2.19587i	1.30061	−	0.422595i	0.875795	+	0.482683i	$0.160338\pi$
$4$	−1.23607	−	3.80423i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−4.39174	+	13.5164i	−0.298820	+	0.919673i
$7$		−	23.3487i		−	1.26071i	−0.776307	−	0.630355i	$-0.782909\pi$
$7$		−	23.3487i		−	1.26071i	0.776307	−	0.630355i	$-0.217091\pi$
$8$	7.60845	+	2.47214i	0.336249	+	0.109254i
$9$	19.0078	−	13.8100i	0.703992	−	0.511480i
$10$		0			0
$11$	−51.2554	−	37.2392i	−1.40492	−	1.02073i	−0.994037	−	0.109043i	$-0.965221\pi$
$11$	−51.2554	−	37.2392i	−1.40492	−	1.02073i	−0.410880	−	0.911689i	$-0.634779\pi$
$12$	−16.7072	−	22.9954i	−0.401912	−	0.553184i
$13$	3.44706	+	4.74447i	0.0735418	+	0.101222i	0.844203	−	0.536023i	$-0.180074\pi$
$13$	3.44706	+	4.74447i	0.0735418	+	0.101222i	−0.770661	+	0.637245i	$0.780074\pi$
$14$	37.7789	+	27.4480i	0.721203	+	0.523985i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	−70.6774	−	22.9645i	−1.00834	−	0.327630i	−0.242147	−	0.970240i	$-0.577852\pi$
$17$	−70.6774	−	22.9645i	−1.00834	−	0.327630i	−0.766193	+	0.642610i	$0.777852\pi$
$18$			46.9899i			0.615312i
$19$	−3.29893	+	10.1531i	−0.0398330	+	0.122593i	−0.968996	−	0.247078i	$-0.920530\pi$
$19$	−3.29893	+	10.1531i	−0.0398330	+	0.122593i	0.929163	+	0.369671i	$0.120530\pi$
$20$		0			0
$21$	−51.2706	−	157.795i	−0.532770	−	1.63970i
$22$	120.509	−	39.1557i	1.16784	−	0.379455i
$23$	77.5886	−	106.792i	0.703406	−	0.968156i	−0.296508	−	0.955030i	$-0.595822\pi$
$23$	77.5886	−	106.792i	0.703406	−	0.968156i	0.999914	−	0.0131252i	$-0.00417799\pi$
$24$	56.8478			0.483501
$25$		0			0
$26$	−11.7290			−0.0884709
$27$	−14.6399	+	20.1502i	−0.104350	+	0.143626i
$28$	−88.8236	+	28.8605i	−0.599503	+	0.194790i
$29$	−13.5338	−	41.6528i	−0.0866609	−	0.266715i	0.898330	−	0.439321i	$-0.144781\pi$
$29$	−13.5338	−	41.6528i	−0.0866609	−	0.266715i	−0.984991	+	0.172607i	$0.944781\pi$
$30$		0			0
$31$	−97.2735	+	299.377i	−0.563575	+	1.73451i	0.108572	+	0.994089i	$0.465372\pi$
$31$	−97.2735	+	299.377i	−0.563575	+	1.73451i	−0.672147	+	0.740418i	$0.734628\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−428.166	−	139.120i	−2.25861	−	0.733867i
$34$	120.244	−	87.3621i	0.606518	−	0.440661i
$35$		0			0
$36$	−76.0312	−	55.2399i	−0.351996	−	0.255740i
$37$	−84.1012	−	115.755i	−0.373680	−	0.514326i	0.580217	−	0.814462i	$-0.302968\pi$
$37$	−84.1012	−	115.755i	−0.373680	−	0.514326i	−0.953896	+	0.300136i	$0.902968\pi$
$38$	−12.5499	−	17.2734i	−0.0535753	−	0.0737400i
$39$	33.7141	+	24.4948i	0.138425	+	0.100572i
$40$		0			0
$41$	105.776	−	76.8508i	0.402913	−	0.292733i	−0.367813	−	0.929900i	$-0.619893\pi$
$41$	105.776	−	76.8508i	0.402913	−	0.292733i	0.770726	+	0.637166i	$0.219893\pi$
$42$	315.589	+	102.541i	1.15944	+	0.376725i
$43$		−	223.280i		−	0.791858i	−0.918281	−	0.395929i	$-0.870423\pi$
$43$		−	223.280i		−	0.791858i	0.918281	−	0.395929i	$-0.129577\pi$
$44$	−78.3113	+	241.017i	−0.268315	+	0.825790i
$45$		0			0
$46$	81.5815	+	251.082i	0.261490	+	0.804783i
$47$	510.915	−	166.006i	1.58563	−	0.515202i	0.622131	−	0.782913i	$-0.286267\pi$
$47$	510.915	−	166.006i	1.58563	−	0.515202i	0.963499	+	0.267711i	$0.0862673\pi$
$48$	−66.8286	+	91.9817i	−0.200956	+	0.276592i
$49$	−202.161			−0.589389
$50$		0			0
$51$	−528.078			−1.44992
$52$	13.7883	−	18.9779i	0.0367709	−	0.0506108i
$53$	306.365	−	99.5441i	0.794009	−	0.257989i	0.116199	−	0.993226i	$-0.462929\pi$
$53$	306.365	−	99.5441i	0.794009	−	0.257989i	0.677810	+	0.735237i	$0.262929\pi$
$54$	−15.3933	−	47.3759i	−0.0387920	−	0.119390i
$55$		0			0
$56$	57.7211	−	177.647i	0.137738	−	0.423913i
$57$			75.8604i			0.176280i
$58$	83.3056	+	27.0676i	0.188596	+	0.0612785i
$59$	703.580	−	511.180i	1.55251	−	1.12797i	0.610683	−	0.791875i	$-0.290895\pi$
$59$	703.580	−	511.180i	1.55251	−	1.12797i	0.941829	−	0.336092i	$-0.109105\pi$
$60$		0			0
$61$	22.4025	+	16.2764i	0.0470222	+	0.0341636i	0.611048	−	0.791593i	$-0.290748\pi$
$61$	22.4025	+	16.2764i	0.0470222	+	0.0341636i	−0.564026	+	0.825757i	$0.690748\pi$
$62$	−370.050	−	509.331i	−0.758007	−	1.04331i
$63$	−322.445	−	443.807i	−0.644828	−	0.887530i
$64$	51.7771	+	37.6183i	0.101127	+	0.0734732i
$65$		0			0
$66$	728.440	−	529.242i	1.35856	−	0.987049i
$67$	42.9787	+	13.9646i	0.0783684	+	0.0254634i	0.347939	−	0.937517i	$-0.386882\pi$
$67$	42.9787	+	13.9646i	0.0783684	+	0.0254634i	−0.269570	+	0.962981i	$0.586882\pi$
$68$			297.258i			0.530116i
$69$	289.858	−	892.092i	0.505722	−	1.55645i
$70$		0			0
$71$	−206.178	−	634.551i	−0.344632	−	1.06067i	−0.961781	−	0.273821i	$-0.911712\pi$
$71$	−206.178	−	634.551i	−0.344632	−	1.06067i	0.617149	−	0.786846i	$-0.288288\pi$
$72$	178.760	−	58.0827i	0.292598	−	0.0950709i
$73$	215.194	−	296.189i	0.345021	−	0.474880i	−0.600879	−	0.799340i	$-0.705183\pi$
$73$	215.194	−	296.189i	0.345021	−	0.474880i	0.945899	+	0.324460i	$0.105183\pi$
$74$	286.163			0.449537
$75$		0			0
$76$	42.7023			0.0644511
$77$	−869.487	+	1196.75i	−1.28685	+	1.77119i
$78$	−79.2667	+	25.7553i	−0.115066	+	0.0373874i
$79$	103.606	+	318.866i	0.147552	+	0.454117i	0.997330	−	0.0730225i	$-0.0232645\pi$
$79$	103.606	+	318.866i	0.147552	+	0.454117i	−0.849779	+	0.527140i	$0.823264\pi$
$80$		0			0
$81$	−250.721	+	771.641i	−0.343925	+	1.05849i
$82$			261.493i			0.352159i
$83$	994.460	+	323.120i	1.31513	+	0.427313i	0.880821	−	0.473449i	$-0.156991\pi$
$83$	994.460	+	323.120i	1.31513	+	0.427313i	0.434313	+	0.900762i	$0.356991\pi$
$84$	−536.913	+	390.090i	−0.697405	+	0.506694i
$85$		0			0
$86$	361.275	+	262.482i	0.452992	+	0.329118i
$87$	−182.928	−	251.779i	−0.225425	−	0.310271i
$88$	−297.914	−	410.043i	−0.360883	−	0.496713i
$89$	−224.451	−	163.073i	−0.267323	−	0.194222i	0.446046	−	0.895010i	$-0.352832\pi$
$89$	−224.451	−	163.073i	−0.267323	−	0.194222i	−0.713369	+	0.700788i	$0.752832\pi$
$90$		0			0
$91$	110.777	−	80.4843i	0.127611	−	0.0927149i
$92$	−502.164	−	163.163i	−0.569068	−	0.184901i
$93$			2236.85i			2.49409i
$94$	−332.013	+	1021.83i	−0.364303	+	1.12121i
$95$		0			0
$96$	−70.2678	−	216.262i	−0.0747049	−	0.229918i
$97$	−509.432	+	165.524i	−0.533247	+	0.173262i	−0.563249	−	0.826287i	$-0.690449\pi$
$97$	−509.432	+	165.524i	−0.533247	+	0.173262i	0.0300017	+	0.999550i	$0.490449\pi$
$98$	237.654	−	327.103i	0.244966	−	0.337167i
$99$	−1488.53			−1.51114
$100$		0			0
$101$	567.581			0.559172			0.279586	−	0.960121i	$-0.409803\pi$
$101$	567.581			0.559172			0.279586	+	0.960121i	$0.409803\pi$
$102$	620.793	−	854.448i	0.602624	−	0.829441i
$103$	12.5030	−	4.06247i	0.0119607	−	0.00388628i	−0.303031	−	0.952981i	$-0.597998\pi$
$103$	12.5030	−	4.06247i	0.0119607	−	0.00388628i	0.314991	+	0.949095i	$0.397998\pi$
$104$	14.4978	+	44.6197i	0.0136695	+	0.0420704i
$105$		0			0
$106$	−199.088	+	612.730i	−0.182426	+	0.561449i
$107$			35.7496i			0.0322995i	0.999870	+	0.0161497i	$0.00514084\pi$
$107$			35.7496i			0.0322995i	−0.999870	+	0.0161497i	$0.994859\pi$
$108$	94.7517	+	30.7867i	0.0844212	+	0.0274301i
$109$	−1451.53	+	1054.60i	−1.27552	+	0.926720i	−0.999408	−	0.0344054i	$-0.989046\pi$
$109$	−1451.53	+	1054.60i	−1.27552	+	0.926720i	−0.276113	+	0.961125i	$0.589046\pi$
$110$		0			0
$111$	−822.555	−	597.621i	−0.703364	−	0.511024i
$112$	219.584	+	302.232i	0.185257	+	0.254984i
$113$	−461.504	−	635.206i	−0.384200	−	0.528807i	0.572491	−	0.819911i	$-0.305977\pi$
$113$	−461.504	−	635.206i	−0.384200	−	0.528807i	−0.956691	+	0.291105i	$0.905977\pi$
$114$	−122.745	−	89.1792i	−0.100843	−	0.0732666i
$115$		0			0
$116$	−141.728	+	102.971i	−0.113441	+	0.0824195i
$117$	131.042	+	42.5782i	0.103546	+	0.0336440i
$118$			1739.34i			1.35695i
$119$	−536.190	+	1650.22i	−0.413046	+	1.27122i
$120$		0			0
$121$	829.055	+	2551.57i	0.622881	+	1.91703i
$122$	−52.6716	+	17.1140i	−0.0390874	+	0.0127003i
$123$	546.100	−	751.642i	0.400327	−	0.551002i
$124$	1259.13			0.911884
$125$		0			0
$126$	1097.15			0.775730
$127$	−628.035	+	864.416i	−0.438812	+	0.603973i	−0.969948	−	0.243314i	$-0.921765\pi$
$127$	−628.035	+	864.416i	−0.438812	+	0.603973i	0.531136	+	0.847287i	$0.321765\pi$
$128$	−121.735	+	39.5542i	−0.0840623	+	0.0273135i
$129$	−490.294	−	1508.97i	−0.334635	−	1.02990i
$130$		0			0
$131$	−247.789	+	762.616i	−0.165263	+	0.508627i	−0.999056	−	0.0434510i	$-0.986165\pi$
$131$	−247.789	+	762.616i	−0.165263	+	0.508627i	0.833793	+	0.552078i	$0.186165\pi$
$132$			1800.80i			1.18742i
$133$	237.061	+	77.0257i	0.154555	+	0.0502179i
$134$	−73.1197	+	53.1246i	−0.0471387	+	0.0342482i
$135$		0			0
$136$	−480.974	−	349.448i	−0.303259	−	0.220330i
$137$	1016.56	+	1399.18i	0.633947	+	0.872553i	0.998275	−	0.0587175i	$-0.0187011\pi$
$137$	1016.56	+	1399.18i	0.633947	+	0.872553i	−0.364327	+	0.931271i	$0.618701\pi$
$138$	1102.69	+	1517.72i	0.680195	+	0.936208i
$139$	1749.44	+	1271.04i	1.06752	+	0.775599i	0.975465	−	0.220155i	$-0.0706564\pi$
$139$	1749.44	+	1271.04i	1.06752	+	0.775599i	0.0920552	+	0.995754i	$0.470656\pi$
$140$		0			0
$141$	3088.33	−	2243.80i	1.84457	−	1.34016i
$142$	1269.10	+	412.357i	0.750005	+	0.243691i
$143$		−	371.546i		−	0.217274i
$144$	−116.165	+	357.520i	−0.0672253	+	0.206898i
$145$		0			0
$146$	226.268	+	696.382i	0.128261	+	0.394746i
$147$	−1366.24	+	443.918i	−0.766568	+	0.249073i
$148$	−336.405	+	463.021i	−0.186840	+	0.257163i
$149$	−2077.16			−1.14206			−0.571032	−	0.820928i	$-0.693457\pi$
$149$	−2077.16			−1.14206			−0.571032	+	0.820928i	$0.693457\pi$
$150$		0			0
$151$	529.785			0.285518			0.142759	−	0.989757i	$-0.454403\pi$
$151$	529.785			0.285518			0.142759	+	0.989757i	$0.454403\pi$
$152$	−50.1995	+	69.0937i	−0.0267876	+	0.0368700i
$153$	−1660.56	+	539.549i	−0.877440	+	0.285098i
$154$	−914.233	−	2813.72i	−0.478383	−	1.47231i
$155$		0			0
$156$	51.5106	−	158.533i	0.0264369	−	0.0813643i
$157$		−	2062.25i		−	1.04831i	−0.851622	−	0.524157i	$-0.824381\pi$
$157$		−	2062.25i		−	1.04831i	0.851622	−	0.524157i	$-0.175619\pi$
$158$	−637.733	−	207.212i	−0.321109	−	0.104335i
$159$	1851.89	−	1345.47i	0.923674	−	0.671089i
$160$		0			0
$161$	−2493.44	−	1811.59i	−1.22056	−	0.886791i
$162$	−953.801	−	1312.79i	−0.462578	−	0.636684i
$163$	341.123	+	469.516i	0.163919	+	0.225615i	0.883073	−	0.469235i	$-0.155470\pi$
$163$	341.123	+	469.516i	0.163919	+	0.225615i	−0.719154	+	0.694851i	$0.755470\pi$
$164$	−423.104	−	307.403i	−0.201457	−	0.146367i
$165$		0			0
$166$	−1691.88	+	1229.22i	−0.791055	+	0.574735i
$167$	−3514.49	−	1141.93i	−1.62850	−	0.529131i	−0.654573	−	0.755998i	$-0.727152\pi$
$167$	−3514.49	−	1141.93i	−1.62850	−	0.529131i	−0.973926	+	0.226867i	$0.927152\pi$
$168$		−	1327.32i		−	0.609554i
$169$	668.283	−	2056.76i	0.304180	−	0.936168i
$170$		0			0
$171$	77.5082	+	238.546i	0.0346620	+	0.106679i
$172$	−849.408	+	275.989i	−0.376551	+	0.122349i
$173$	1991.59	−	2741.19i	0.875248	−	1.20468i	−0.102467	−	0.994736i	$-0.532673\pi$
$173$	1991.59	−	2741.19i	0.875248	−	1.20468i	0.977715	−	0.209939i	$-0.0673265\pi$
$174$	622.432			0.271186
$175$		0			0
$176$	1013.68			0.434143
$177$	3632.44	−	4999.62i	1.54255	−	2.12313i
$178$	527.716	−	171.465i	0.222213	−	0.0722015i
$179$	874.381	+	2691.07i	0.365108	+	1.12369i	0.949914	+	0.312513i	$0.101171\pi$
$179$	874.381	+	2691.07i	0.365108	+	1.12369i	−0.584806	+	0.811173i	$0.698829\pi$
$180$		0			0
$181$	112.296	−	345.612i	0.0461155	−	0.141929i	−0.925348	−	0.379120i	$-0.876227\pi$
$181$	112.296	−	345.612i	0.0461155	−	0.141929i	0.971463	+	0.237191i	$0.0762268\pi$
$182$			273.856i			0.111536i
$183$	187.141	+	60.8059i	0.0755951	+	0.0245623i
$184$	854.333	−	620.709i	0.342295	−	0.248692i
$185$		0			0
$186$	−3619.29	−	2629.57i	−1.42677	−	1.03661i
$187$	2767.42	+	3809.03i	1.08221	+	1.48954i
$188$	−1263.05	−	1738.44i	−0.489987	−	0.674409i
$189$	470.479	+	341.823i	0.181071	+	0.131555i
$190$		0			0
$191$	1956.19	−	1421.25i	0.741072	−	0.538421i	−0.151974	−	0.988384i	$-0.548563\pi$
$191$	1956.19	−	1421.25i	0.741072	−	0.538421i	0.893047	+	0.449964i	$0.148563\pi$
$192$	432.524	+	140.536i	0.162577	+	0.0528244i
$193$			1101.32i			0.410750i	0.978683	+	0.205375i	$0.0658415\pi$
$193$			1101.32i			0.410750i	−0.978683	+	0.205375i	$0.934159\pi$
$194$	331.049	−	1018.86i	0.122515	−	0.377063i
$195$		0			0
$196$	249.884	+	769.065i	0.0910657	+	0.280271i
$197$	−1952.44	+	634.387i	−0.706121	+	0.229433i	−0.639995	−	0.768379i	$-0.721064\pi$
$197$	−1952.44	+	634.387i	−0.706121	+	0.229433i	−0.0661254	+	0.997811i	$0.521064\pi$
$198$	1749.87	−	2408.48i	0.628069	−	0.864462i
$199$	1788.40			0.637068			0.318534	−	0.947911i	$-0.396810\pi$
$199$	1788.40			0.637068			0.318534	+	0.947911i	$0.396810\pi$
$200$		0			0
$201$	321.122			0.112688
$202$	−667.231	+	918.365i	−0.232407	+	0.319881i
$203$	−972.538	+	315.997i	−0.336250	+	0.109254i
$204$	652.740	+	2008.93i	0.224024	+	0.689476i
$205$		0			0
$206$	−8.12493	+	25.0060i	−0.00274801	+	0.00845752i
$207$		−	3101.37i		−	1.04135i
$208$	−89.2394	−	28.9956i	−0.0297483	−	0.00966580i
$209$	547.181	−	397.550i	0.181097	−	0.131575i
$210$		0			0
$211$	−2670.08	−	1939.93i	−0.871167	−	0.632940i	0.0597329	−	0.998214i	$-0.480975\pi$
$211$	−2670.08	−	1939.93i	−0.871167	−	0.632940i	−0.930900	+	0.365275i	$0.880975\pi$
$212$	−757.376	−	1042.44i	−0.245362	−	0.337712i
$213$	−2786.78	−	3835.68i	−0.896466	−	1.23388i
$214$	−57.8440	−	42.0261i	−0.0184773	−	0.0134245i
$215$		0			0
$216$	−161.201	+	117.120i	−0.0507794	+	0.0368934i
$217$	6990.06	+	2271.21i	2.18671	+	0.710505i
$218$		−	3588.39i		−	1.11485i
$219$	803.928	−	2474.24i	0.248057	−	0.763440i
$220$		0			0
$221$	−134.675	−	414.487i	−0.0409920	−	0.126160i
$222$	1933.94	−	628.376i	0.584674	−	0.189972i
$223$	−2640.42	+	3634.22i	−0.792894	+	1.09132i	0.200848	+	0.979622i	$0.435630\pi$
$223$	−2640.42	+	3634.22i	−0.792894	+	1.09132i	−0.993742	+	0.111702i	$0.964370\pi$
$224$	−747.158			−0.222864
$225$		0			0
$226$	1570.32			0.462194
$227$	1830.56	−	2519.54i	0.535235	−	0.736687i	−0.452682	−	0.891672i	$-0.649533\pi$
$227$	1830.56	−	2519.54i	0.535235	−	0.736687i	0.987917	+	0.154985i	$0.0495328\pi$
$228$	288.590	−	93.7686i	0.0838260	−	0.0272367i
$229$	475.917	+	1464.72i	0.137334	+	0.422671i	0.995946	−	0.0899558i	$-0.0286726\pi$
$229$	475.917	+	1464.72i	0.137334	+	0.422671i	−0.858612	+	0.512626i	$0.828673\pi$
$230$		0			0
$231$	−3248.26	+	9997.11i	−0.925194	+	2.84745i
$232$		−	350.371i		−	0.0991508i
$233$	1511.27	+	491.040i	0.424920	+	0.138065i	0.513668	−	0.857989i	$-0.328286\pi$
$233$	1511.27	+	491.040i	0.424920	+	0.138065i	−0.0887477	+	0.996054i	$0.528286\pi$
$234$	−222.942	+	161.977i	−0.0622829	+	0.0452511i
$235$		0			0
$236$	−2814.32	−	2044.72i	−0.776256	−	0.563983i
$237$	1400.38	+	1927.45i	0.383815	+	0.528276i
$238$	−2039.79	−	2807.53i	−0.555546	−	0.764643i
$239$	−2305.79	−	1675.26i	−0.624056	−	0.453403i	0.230280	−	0.973124i	$-0.426036\pi$
$239$	−2305.79	−	1675.26i	−0.624056	−	0.453403i	−0.854336	+	0.519721i	$0.826036\pi$
$240$		0			0
$241$	839.653	−	610.044i	0.224427	−	0.163055i	−0.469890	−	0.882725i	$-0.655707\pi$
$241$	839.653	−	610.044i	0.224427	−	0.163055i	0.694317	+	0.719669i	$0.255707\pi$
$242$	−5103.14	−	1658.11i	−1.35555	−	0.440444i
$243$			5092.96i			1.34450i
$244$	34.2280	−	105.343i	0.00898044	−	0.0276389i
$245$		0			0
$246$	574.203	+	1767.22i	0.148821	+	0.458023i
$247$	−59.5426	+	19.3466i	−0.0153385	+	0.00498378i
$248$	−1480.20	+	2037.32i	−0.379004	+	0.521654i
$249$	7430.28			1.89106
$250$		0			0
$251$	2044.25			0.514072			0.257036	−	0.966402i	$-0.417254\pi$
$251$	2044.25			0.514072			0.257036	+	0.966402i	$0.417254\pi$
$252$	−1289.78	+	1775.23i	−0.322414	+	0.443765i
$253$	−7953.67	+	2584.31i	−1.97646	+	0.642189i
$254$	−660.355	−	2032.36i	−0.163127	−	0.502055i
$255$		0			0
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$		−	3870.58i		−	0.939456i	−0.882811	−	0.469728i	$-0.844352\pi$
$257$		−	3870.58i		−	0.939456i	0.882811	−	0.469728i	$-0.155648\pi$
$258$	3017.94	+	980.588i	0.728250	+	0.236623i
$259$	−2702.73	+	1963.65i	−0.648416	+	0.471102i
$260$		0			0
$261$	−832.472	−	604.827i	−0.197428	−	0.143440i
$262$	−942.645	−	1297.44i	−0.222278	−	0.305939i
$263$	856.212	+	1178.47i	0.200746	+	0.276304i	0.897507	−	0.441000i	$-0.145376\pi$
$263$	856.212	+	1178.47i	0.200746	+	0.276304i	−0.696761	+	0.717304i	$0.745376\pi$
$264$	−2913.76	−	2116.97i	−0.679278	−	0.493525i
$265$		0			0
$266$	−403.312	+	293.023i	−0.0929648	+	0.0675429i
$267$	−1874.97	−	609.215i	−0.429761	−	0.139638i
$268$		−	180.762i		−	0.0412007i
$269$	−1136.93	+	3499.11i	−0.257695	+	0.793103i	0.735592	+	0.677425i	$0.236904\pi$
$269$	−1136.93	+	3499.11i	−0.257695	+	0.793103i	−0.993287	+	0.115678i	$0.963096\pi$
$270$		0			0
$271$	−342.338	−	1053.61i	−0.0767363	−	0.236170i	0.905329	−	0.424711i	$-0.139624\pi$
$271$	−342.338	−	1053.61i	−0.0767363	−	0.236170i	−0.982065	+	0.188541i	$0.939624\pi$
$272$	1130.84	−	367.432i	0.252085	−	0.0819074i
$273$	571.920	−	787.180i	0.126792	−	0.174514i
$274$	−3458.96			−0.762640
$275$		0			0
$276$	−3752.00			−0.818276
$277$	248.096	−	341.475i	0.0538146	−	0.0740695i	−0.781262	−	0.624204i	$-0.785423\pi$
$277$	248.096	−	341.475i	0.0538146	−	0.0740695i	0.835076	+	0.550134i	$0.185423\pi$
$278$	−4113.17	+	1336.45i	−0.887380	+	0.288327i
$279$	2285.43	+	7033.84i	0.490413	+	1.50934i
$280$		0			0
$281$	1838.89	−	5659.52i	0.390387	−	1.20149i	−0.542109	−	0.840308i	$-0.682374\pi$
$281$	1838.89	−	5659.52i	0.390387	−	1.20149i	0.932496	−	0.361180i	$-0.117626\pi$
$282$			7634.77i			1.61221i
$283$	8398.74	+	2728.92i	1.76415	+	0.573206i	0.997616	−	0.0690031i	$-0.0219818\pi$
$283$	8398.74	+	2728.92i	1.76415	+	0.573206i	0.766530	+	0.642209i	$0.221982\pi$
$284$	−2159.13	+	1568.70i	−0.451129	+	0.327764i
$285$		0			0
$286$	601.174	+	436.779i	0.124294	+	0.0903051i
$287$	−1794.36	−	2469.73i	−0.369052	−	0.507956i
$288$	−441.919	−	608.249i	−0.0904178	−	0.124449i
$289$	493.226	+	358.349i	0.100392	+	0.0729390i
$290$		0			0
$291$	−3079.37	+	2237.29i	−0.620329	+	0.450695i
$292$	−1392.76	−	452.536i	−0.279128	−	0.0906941i
$293$		−	8009.66i		−	1.59703i	−0.601976	−	0.798514i	$-0.705620\pi$
$293$		−	8009.66i		−	1.59703i	0.601976	−	0.798514i	$-0.294380\pi$
$294$	887.836	−	2732.48i	0.176121	−	0.542045i
$295$		0			0
$296$	−353.717	−	1088.63i	−0.0694573	−	0.213768i
$297$	1500.75	−	487.624i	0.293207	−	0.0952688i
$298$	2441.85	−	3360.91i	0.474672	−	0.653330i
$299$	774.123			0.149728
$300$		0			0
$301$	−5213.30			−0.998304
$302$	−622.799	+	857.209i	−0.118669	+	0.163334i
$303$	3835.82	−	1246.33i	0.727267	−	0.236303i
$304$	−52.7829	−	162.449i	−0.00995825	−	0.0306483i
$305$		0			0
$306$	1079.10	−	3321.12i	0.201594	−	0.620444i
$307$		−	3599.18i		−	0.669107i	−0.942377	−	0.334553i	$-0.891415\pi$
$307$		−	3599.18i		−	0.669107i	0.942377	−	0.334553i	$-0.108585\pi$
$308$	5627.44	+	1828.47i	1.04108	+	0.338268i
$309$	75.5769	−	54.9098i	0.0139140	−	0.0101091i
$310$		0			0
$311$	5819.66	+	4228.23i	1.06110	+	0.770936i	0.974292	−	0.225289i	$-0.0723326\pi$
$311$	5819.66	+	4228.23i	1.06110	+	0.770936i	0.0868104	+	0.996225i	$0.472333\pi$
$312$	195.958	+	269.713i	0.0355575	+	0.0489407i
$313$	−859.220	−	1182.61i	−0.155163	−	0.213563i	0.724358	−	0.689424i	$-0.242136\pi$
$313$	−859.220	−	1182.61i	−0.155163	−	0.213563i	−0.879520	+	0.475861i	$0.842136\pi$
$314$	3336.79	+	2424.32i	0.599700	+	0.435707i
$315$		0			0
$316$	1084.98	−	788.281i	0.193148	−	0.140330i
$317$	760.979	+	247.257i	0.134829	+	0.0438087i	0.375654	−	0.926760i	$-0.377418\pi$
$317$	760.979	+	247.257i	0.134829	+	0.0438087i	−0.240825	+	0.970569i	$0.577418\pi$
$318$			4578.12i			0.807321i
$319$	−857.438	+	2638.92i	−0.150493	+	0.463170i
$320$		0			0
$321$	78.5013	+	241.602i	0.0136496	+	0.0420091i
$322$	5862.43	−	1904.82i	1.01460	−	0.329663i
$323$	466.320	−	641.834i	0.0803304	−	0.110565i
$324$	3245.41			0.556482
$325$		0			0
$326$	−1160.71			−0.197195
$327$	−7493.97	+	10314.6i	−1.26733	+	1.74433i
$328$	994.777	−	323.223i	0.167462	−	0.0544115i
$329$	−3876.03	−	11929.2i	−0.649521	−	1.99902i
$330$		0			0
$331$	136.254	−	419.348i	0.0226261	−	0.0696358i	−0.939106	−	0.343628i	$-0.888344\pi$
$331$	136.254	−	419.348i	0.0226261	−	0.0696358i	0.961732	+	0.273992i	$0.0883442\pi$
$332$		−	4182.55i		−	0.691407i
$333$	−3197.16	−	1038.82i	−0.526135	−	0.170952i
$334$	5979.21	−	4344.15i	0.979544	−	0.711680i
$335$		0			0
$336$	2147.65	+	1560.36i	0.348702	+	0.253347i
$337$	−1929.52	−	2655.75i	−0.311892	−	0.429282i	0.624078	−	0.781362i	$-0.285475\pi$
$337$	−1929.52	−	2655.75i	−0.311892	−	0.429282i	−0.935970	+	0.352080i	$0.885475\pi$
$338$	2542.30	+	3499.17i	0.409121	+	0.563106i
$339$	−4513.76	−	3279.44i	−0.723167	−	0.525412i
$340$		0			0
$341$	16134.4	−	11722.3i	2.56224	−	1.86158i
$342$	−477.091	−	155.016i	−0.0754332	−	0.0245097i
$343$		−	3288.41i		−	0.517661i
$344$	551.979	−	1698.82i	0.0865137	−	0.266262i
$345$		0			0
$346$	2094.08	+	6444.92i	0.325372	+	1.00139i
$347$	−10066.5	+	3270.80i	−1.55734	+	0.506011i	−0.956096	−	0.293052i	$-0.905329\pi$
$347$	−10066.5	+	3270.80i	−1.55734	+	0.506011i	−0.601247	+	0.799064i	$0.705329\pi$
$348$	−731.713	+	1007.12i	−0.112712	+	0.155135i
$349$	−6798.19			−1.04269			−0.521345	−	0.853346i	$-0.674569\pi$
$349$	−6798.19			−1.04269			−0.521345	+	0.853346i	$0.674569\pi$
$350$		0			0
$351$	−146.067			−0.0222121
$352$	−1191.66	+	1640.17i	−0.180442	+	0.248357i
$353$	3477.84	−	1130.02i	0.524381	−	0.170382i	−0.0348515	−	0.999393i	$-0.511096\pi$
$353$	3477.84	−	1130.02i	0.524381	−	0.170382i	0.559233	+	0.829011i	$0.311096\pi$
$354$	3819.37	+	11754.8i	0.573439	+	1.76486i
$355$		0			0
$356$	−342.931	+	1055.43i	−0.0510542	+	0.157129i
$357$			12329.9i			1.82792i
$358$	−5382.14	−	1748.76i	−0.794566	−	0.258170i
$359$	−6563.10	+	4768.37i	−0.964867	+	0.701017i	−0.954276	−	0.298927i	$-0.903371\pi$
$359$	−6563.10	+	4768.37i	−0.964867	+	0.701017i	−0.0105907	+	0.999944i	$0.503371\pi$
$360$		0			0
$361$	5456.85	+	3964.63i	0.795575	+	0.578019i
$362$	427.199	+	587.990i	0.0620252	+	0.0853703i
$363$	11205.8	+	15423.5i	1.62026	+	2.23009i
$364$	−443.109	−	321.937i	−0.0638055	−	0.0463574i
$365$		0			0
$366$	−318.384	+	231.320i	−0.0454705	+	0.0330362i
$367$	1191.88	+	387.265i	0.169525	+	0.0550820i	0.392550	−	0.919731i	$-0.371593\pi$
$367$	1191.88	+	387.265i	0.169525	+	0.0550820i	−0.223025	+	0.974813i	$0.571593\pi$
$368$			2112.03i			0.299177i
$369$	949.262	−	2921.53i	0.133920	−	0.412164i
$370$		0			0
$371$	−2324.22	−	7153.22i	−0.325250	−	1.00102i
$372$	8509.47	−	2764.89i	1.18601	−	0.385358i
$373$	−2536.01	+	3490.52i	−0.352037	+	0.484537i	−0.947909	−	0.318543i	$-0.896807\pi$
$373$	−2536.01	+	3490.52i	−0.352037	+	0.484537i	0.595872	+	0.803080i	$0.296807\pi$
$374$	−9416.43			−1.30190
$375$		0			0
$376$	4297.66			0.589455
$377$	150.969	−	207.791i	0.0206241	−	0.0283866i
$378$	−1106.16	+	359.414i	−0.150516	+	0.0489055i
$379$	−1022.84	−	3147.96i	−0.138627	−	0.426649i	0.857510	−	0.514468i	$-0.172010\pi$
$379$	−1022.84	−	3147.96i	−0.138627	−	0.426649i	−0.996136	+	0.0878185i	$0.972010\pi$
$380$		0			0
$381$	−2346.23	+	7220.97i	−0.315489	+	0.970975i
$382$			4835.96i			0.647721i
$383$	−8764.93	−	2847.90i	−1.16937	−	0.379950i	−0.340960	−	0.940078i	$-0.610752\pi$
$383$	−8764.93	−	2847.90i	−1.16937	−	0.379950i	−0.828406	+	0.560128i	$0.810752\pi$
$384$	−735.854	+	534.629i	−0.0977900	+	0.0710486i
$385$		0			0
$386$	−1781.97	−	1294.68i	−0.234974	−	0.170719i
$387$	−3083.49	−	4244.06i	−0.405020	−	0.557462i
$388$	1259.38	+	1733.39i	0.164782	+	0.226804i
$389$	−3057.70	−	2221.55i	−0.398539	−	0.289555i	0.370407	−	0.928870i	$-0.379218\pi$
$389$	−3057.70	−	2221.55i	−0.398539	−	0.289555i	−0.768946	+	0.639314i	$0.779218\pi$
$390$		0			0
$391$	−7936.17	+	5765.97i	−1.02647	+	0.745774i
$392$	−1538.13	−	499.768i	−0.198182	−	0.0643932i
$393$			5698.01i			0.731366i
$394$	1268.77	−	3904.89i	0.162233	−	0.499303i
$395$		0			0
$396$	1839.92	+	5662.69i	0.233483	+	0.718588i
$397$	3590.32	−	1166.57i	0.453887	−	0.147477i	−0.0731467	−	0.997321i	$-0.523304\pi$
$397$	3590.32	−	1166.57i	0.453887	−	0.147477i	0.527034	+	0.849844i	$0.323304\pi$
$398$	−2102.39	+	2893.70i	−0.264783	+	0.364442i
$399$	1771.24			0.222238
$400$		0			0
$401$	1938.68			0.241429			0.120715	−	0.992687i	$-0.461481\pi$
$401$	1938.68			0.241429			0.120715	+	0.992687i	$0.461481\pi$
$402$	−377.502	+	519.587i	−0.0468361	+	0.0644643i
$403$	−1755.69	+	570.460i	−0.217016	+	0.0705127i
$404$	−701.568	−	2159.21i	−0.0863969	−	0.265902i
$405$		0			0
$406$	631.993	−	1945.08i	0.0772545	−	0.237765i
$407$			9064.95i			1.10401i
$408$	−4017.86	−	1305.48i	−0.487533	−	0.158409i
$409$	4925.34	−	3578.47i	0.595458	−	0.432626i	−0.248806	−	0.968553i	$-0.580038\pi$
$409$	4925.34	−	3578.47i	0.595458	−	0.432626i	0.844264	+	0.535928i	$0.180038\pi$
$410$		0			0
$411$	9942.53	+	7223.67i	1.19326	+	0.866952i
$412$	−30.9091	−	42.5427i	−0.00369607	−	0.00508720i
$413$	−11935.4	−	16427.6i	−1.42204	−	1.95727i
$414$	5018.12	+	3645.88i	0.595718	+	0.432814i
$415$		0			0
$416$	151.823	−	110.306i	0.0178936	−	0.0130005i
$417$	14614.1	+	4748.40i	1.71620	+	0.557626i
$418$			1352.71i			0.158285i
$419$	−4468.35	+	13752.2i	−0.520986	+	1.60343i	0.251134	+	0.967952i	$0.419197\pi$
$419$	−4468.35	+	13752.2i	−0.520986	+	1.60343i	−0.772120	+	0.635477i	$0.780803\pi$
$420$		0			0
$421$	−2520.65	−	7757.76i	−0.291803	−	0.898077i	−0.984277	−	0.176634i	$-0.943479\pi$
$421$	−2520.65	−	7757.76i	−0.291803	−	0.898077i	0.692474	−	0.721443i	$-0.256521\pi$
$422$	6277.75	−	2039.76i	0.724161	−	0.235294i
$423$	7418.82	−	10211.1i	0.852756	−	1.17372i
$424$	2577.05			0.295171
$425$		0			0
$426$	9482.32			1.07845
$427$	380.032	−	523.070i	0.0430704	−	0.0592813i
$428$	135.999	−	44.1889i	0.0153593	−	0.00499054i
$429$	−815.866	−	2510.98i	−0.0918191	−	0.282590i
$430$		0			0
$431$	−2742.25	+	8439.77i	−0.306472	+	0.943224i	0.672652	+	0.739959i	$0.265155\pi$
$431$	−2742.25	+	8439.77i	−0.306472	+	0.943224i	−0.979124	+	0.203265i	$0.934845\pi$
$432$		−	398.511i		−	0.0443828i
$433$	13836.2	+	4495.66i	1.53563	+	0.498955i	0.950166	−	0.311745i	$-0.100914\pi$
$433$	13836.2	+	4495.66i	1.53563	+	0.498955i	0.585461	+	0.810701i	$0.300914\pi$
$434$	−11892.2	+	8640.18i	−1.31531	+	0.955627i
$435$		0			0
$436$	5806.14	+	4218.40i	0.637760	+	0.463360i
$437$	828.303	+	1140.06i	0.0906707	+	0.124797i
$438$	3058.32	+	4209.42i	0.333636	+	0.459210i
$439$	2057.27	+	1494.70i	0.223664	+	0.162501i	0.693974	−	0.720000i	$-0.255858\pi$
$439$	2057.27	+	1494.70i	0.223664	+	0.162501i	−0.470311	+	0.882501i	$0.655858\pi$
$440$		0			0
$441$	−3842.63	+	2791.83i	−0.414926	+	0.301461i
$442$	828.974	+	269.350i	0.0892088	+	0.0289857i
$443$		−	11131.5i		−	1.19385i	−0.802299	−	0.596923i	$-0.796390\pi$
$443$		−	11131.5i		−	1.19385i	0.802299	−	0.596923i	$-0.203610\pi$
$444$	−1256.75	+	3867.88i	−0.134331	+	0.413427i
$445$		0			0
$446$	−2776.30	−	8544.57i	−0.294757	−	0.907168i
$447$	−14037.8	+	4561.17i	−1.48538	+	0.482630i
$448$	878.336	−	1208.93i	0.0926283	−	0.127492i
$449$	2007.71			0.211023			0.105512	−	0.994418i	$-0.466352\pi$
$449$	2007.71			0.211023			0.105512	+	0.994418i	$0.466352\pi$
$450$		0			0
$451$	−8283.46			−0.864862
$452$	−1846.02	+	2540.82i	−0.192100	+	0.264403i
$453$	3580.38	−	1163.34i	0.371349	−	0.120659i
$454$	1924.76	+	5923.80i	0.198972	+	0.612374i
$455$		0			0
$456$	−187.537	+	577.180i	−0.0192593	+	0.0592740i
$457$		−	14907.6i		−	1.52592i	−0.646444	−	0.762961i	$-0.723745\pi$
$457$		−	14907.6i		−	1.52592i	0.646444	−	0.762961i	$-0.276255\pi$
$458$	−2929.45	−	951.834i	−0.298873	−	0.0971098i
$459$	1497.45	−	1087.96i	0.152277	−	0.110636i
$460$		0			0
$461$	−6979.13	−	5070.64i	−0.705099	−	0.512284i	0.176490	−	0.984302i	$-0.443526\pi$
$461$	−6979.13	−	5070.64i	−0.705099	−	0.512284i	−0.881589	+	0.472018i	$0.843526\pi$
$462$	−12357.1	−	17008.1i	−1.24438	−	1.71275i
$463$	4625.89	+	6366.99i	0.464327	+	0.639091i	0.975399	−	0.220447i	$-0.0707516\pi$
$463$	4625.89	+	6366.99i	0.464327	+	0.639091i	−0.511072	+	0.859538i	$0.670752\pi$
$464$	566.912	+	411.886i	0.0567203	+	0.0412097i
$465$		0			0
$466$	−2571.12	+	1868.03i	−0.255590	+	0.185697i
$467$	3578.99	+	1162.89i	0.354638	+	0.115229i	0.480918	−	0.876766i	$-0.340304\pi$
$467$	3578.99	+	1162.89i	0.354638	+	0.115229i	−0.126279	+	0.991995i	$0.540304\pi$
$468$		−	551.143i		−	0.0544372i
$469$	326.055	−	1003.50i	0.0321020	−	0.0987998i
$470$		0			0
$471$	−4528.42	−	13937.0i	−0.443012	−	1.36345i
$472$	6616.86	−	2149.95i	0.645266	−	0.209660i
$473$	−8314.78	+	11444.3i	−0.808275	+	1.11250i
$474$	−4764.93			−0.461731
$475$		0			0
$476$	6940.59			0.668322
$477$	4448.63	−	6123.01i	0.427020	−	0.587743i
$478$	5421.24	−	1761.47i	0.518749	−	0.168552i
$479$	−2390.45	−	7357.04i	−0.228022	−	0.701778i	−0.997971	−	0.0636731i	$-0.979718\pi$
$479$	−2390.45	−	7357.04i	−0.228022	−	0.701778i	0.769949	−	0.638105i	$-0.220282\pi$
$480$		0			0
$481$	259.296	−	798.032i	0.0245798	−	0.0756489i
$482$			2075.74i			0.196156i
$483$	−20829.2	−	6767.80i	−1.96224	−	0.637569i
$484$	8681.98	−	6307.83i	0.815362	−	0.592395i
$485$		0			0
$486$	−8240.58	−	5987.13i	−0.769136	−	0.558810i
$487$	2790.92	+	3841.37i	0.259689	+	0.357431i	0.918875	−	0.394549i	$-0.129099\pi$
$487$	2790.92	+	3841.37i	0.259689	+	0.357431i	−0.659186	+	0.751980i	$0.729099\pi$
$488$	130.211	+	179.220i	0.0120787	+	0.0166248i
$489$	3336.37	+	2424.01i	0.308540	+	0.224167i
$490$		0			0
$491$	−11926.1	+	8664.81i	−1.09616	+	0.796410i	−0.980430	−	0.196870i	$-0.936922\pi$
$491$	−11926.1	+	8664.81i	−1.09616	+	0.796410i	−0.115735	+	0.993280i	$0.536922\pi$
$492$	−3534.43	−	1148.41i	−0.323871	−	0.105232i
$493$			3254.71i			0.297332i
$494$	38.6931	−	119.085i	0.00352406	−	0.0108459i
$495$		0			0
$496$	−1556.38	−	4790.03i	−0.140894	−	0.433627i
$497$	−14815.9	+	4813.99i	−1.33719	+	0.434481i
$498$	−8734.81	+	12022.4i	−0.785977	+	1.08180i
$499$	13757.1			1.23417			0.617086	−	0.786895i	$-0.288313\pi$
$499$	13757.1			1.23417			0.617086	+	0.786895i	$0.288313\pi$
$500$		0			0
$501$	−26259.1			−2.34166
$502$	−2403.16	+	3307.67i	−0.213662	+	0.294081i
$503$	14796.5	−	4807.66i	1.31161	−	0.426169i	0.432006	−	0.901871i	$-0.357806\pi$
$503$	14796.5	−	4807.66i	1.31161	−	0.426169i	0.879607	+	0.475702i	$0.157806\pi$
$504$	−1356.15	−	4173.81i	−0.119857	−	0.368881i
$505$		0			0
$506$	5168.61	−	15907.3i	0.454096	−	1.39756i
$507$		−	15367.4i		−	1.34614i
$508$	4064.73	+	1320.71i	0.355006	+	0.115349i
$509$	3620.57	−	2630.50i	0.315283	−	0.229066i	−0.418877	−	0.908043i	$-0.637576\pi$
$509$	3620.57	−	2630.50i	0.315283	−	0.229066i	0.734160	+	0.678977i	$0.237576\pi$
$510$		0			0
$511$	−6915.62	−	5024.49i	−0.598687	−	0.434971i
$512$	300.946	+	414.217i	0.0259767	+	0.0357538i
$513$	−156.290	−	215.114i	−0.0134510	−	0.0185137i
$514$	6262.73	+	4550.14i	0.537427	+	0.390463i
$515$		0			0
$516$	−5134.42	+	3730.38i	−0.438043	+	0.318257i
$517$	−32369.1	−	10517.4i	−2.75356	−	0.894687i
$518$		−	6681.52i		−	0.566736i
$519$	7440.25	−	22898.7i	0.629270	−	1.93669i
$520$		0			0
$521$	7273.14	+	22384.4i	0.611597	+	1.88230i	0.442705	+	0.896667i	$0.354019\pi$
$521$	7273.14	+	22384.4i	0.611597	+	1.88230i	0.168892	+	0.985635i	$0.445981\pi$
$522$	1957.26	−	635.952i	0.164113	−	0.0533235i
$523$	−5949.18	+	8188.34i	−0.497398	+	0.684610i	−0.981731	−	0.190274i	$-0.939062\pi$
$523$	−5949.18	+	8188.34i	−0.497398	+	0.684610i	0.484333	+	0.874884i	$0.339062\pi$
$524$	3207.45			0.267401
$525$		0			0
$526$	−2913.35			−0.241498
$527$	13750.1	−	18925.3i	1.13655	−	1.56433i
$528$	6850.66	−	2225.91i	0.564653	−	0.183467i
$529$	−1624.64	−	5000.11i	−0.133528	−	0.410957i
$530$		0			0
$531$	6314.11	−	19432.8i	0.516024	−	1.58816i
$532$		−	997.041i		−	0.0812542i
$533$	729.233	+	236.942i	0.0592619	+	0.0192554i
$534$	3189.89	−	2317.59i	0.258502	−	0.187813i
$535$		0			0
$536$	292.479	+	212.498i	0.0235693	+	0.0171241i
$537$	11818.5	+	16266.7i	0.949728	+	1.30719i
$538$	−4325.14	−	5953.05i	−0.346599	−	0.477052i
$539$	10361.8	+	7528.31i	0.828043	+	0.601609i
$540$		0			0
$541$	3855.82	−	2801.42i	0.306423	−	0.222629i	−0.423937	−	0.905692i	$-0.639352\pi$
$541$	3855.82	−	2801.42i	0.306423	−	0.222629i	0.730360	+	0.683062i	$0.239352\pi$
$542$	2107.22	+	684.676i	0.166998	+	0.0542608i
$543$		−	2582.30i		−	0.204083i
$544$	−734.863	+	2261.68i	−0.0579173	+	0.178251i
$545$		0			0
$546$	601.352	+	1850.77i	0.0471346	+	0.145065i
$547$	10532.1	−	3422.10i	0.823256	−	0.267492i	0.133054	−	0.991109i	$-0.457522\pi$
$547$	10532.1	−	3422.10i	0.823256	−	0.267492i	0.690202	+	0.723617i	$0.257522\pi$
$548$	4066.25	−	5596.71i	0.316974	−	0.436277i
$549$	650.600			0.0505773
$550$		0			0
$551$	467.551			0.0361494
$552$	4410.74	−	6070.87i	0.340097	−	0.468104i
$553$	7445.10	−	2419.06i	0.572510	−	0.186020i
$554$	260.864	+	802.856i	0.0200055	+	0.0615705i
$555$		0			0
$556$	2672.90	−	8226.34i	0.203878	−	0.627473i
$557$			1943.11i			0.147813i	0.997265	+	0.0739067i	$0.0235467\pi$
$557$			1943.11i			0.147813i	−0.997265	+	0.0739067i	$0.976453\pi$
$558$	−14067.7	−	4570.87i	−1.06726	−	0.346775i
$559$	1059.35	−	769.661i	0.0801531	−	0.0582347i
$560$		0			0
$561$	27066.9	+	19665.2i	2.03701	+	1.47998i
$562$	6995.55	+	9628.54i	0.525070	+	0.722697i
$563$	−855.195	−	1177.07i	−0.0640181	−	0.0881133i	0.775807	−	0.630970i	$-0.217343\pi$
$563$	−855.195	−	1177.07i	−0.0640181	−	0.0881133i	−0.839826	+	0.542856i	$0.817343\pi$
$564$	−12353.3	−	8975.21i	−0.922285	−	0.670079i
$565$		0			0
$566$	−14288.8	+	10381.4i	−1.06114	+	0.770960i
$567$	18016.8	+	5854.01i	1.33445	+	0.433590i
$568$		−	5337.66i		−	0.394301i
$569$	−1833.32	+	5642.37i	−0.135073	+	0.415713i	−0.995601	−	0.0936902i	$-0.970134\pi$
$569$	−1833.32	+	5642.37i	−0.135073	+	0.415713i	0.860528	+	0.509403i	$0.170134\pi$
$570$		0			0
$571$	−2245.36	−	6910.49i	−0.164563	−	0.506471i	0.834441	−	0.551097i	$-0.185791\pi$
$571$	−2245.36	−	6910.49i	−0.164563	−	0.506471i	−0.999004	+	0.0446256i	$0.985791\pi$
$572$	−1413.45	+	459.256i	−0.103320	+	0.0335707i
$573$	10099.4	−	13900.6i	0.736315	−	1.01345i
$574$	6105.51			0.443970
$575$		0			0
$576$	1503.68			0.108773
$577$	−5002.11	+	6884.81i	−0.360902	+	0.496739i	−0.950400	−	0.311031i	$-0.899326\pi$
$577$	−5002.11	+	6884.81i	−0.360902	+	0.496739i	0.589498	+	0.807770i	$0.299326\pi$
$578$	−1159.64	+	376.791i	−0.0834512	+	0.0271149i
$579$	2418.36	+	7442.93i	0.173581	+	0.534228i
$580$		0			0
$581$	7544.42	−	23219.3i	0.538718	−	1.65800i
$582$		−	7612.61i		−	0.542187i
$583$	−19409.8	−	6306.63i	−1.37886	−	0.448017i
$584$	2369.51	−	1721.55i	0.167896	−	0.121983i
$585$		0			0
$586$	12959.9	+	9415.92i	0.913599	+	0.663768i
$587$	6178.64	+	8504.17i	0.434446	+	0.597964i	0.968967	−	0.247192i	$-0.0795077\pi$
$587$	6178.64	+	8504.17i	0.434446	+	0.597964i	−0.534520	+	0.845156i	$0.679508\pi$
$588$	3377.53	+	4648.77i	0.236883	+	0.326041i
$589$	−2718.70	−	1975.25i	−0.190190	−	0.138181i
$590$		0			0
$591$	−11801.9	+	8574.61i	−0.821433	+	0.596806i
$592$	2177.26	+	707.434i	0.151157	+	0.0491138i
$593$		−	1683.44i		−	0.116578i	−0.998300	−	0.0582890i	$-0.981436\pi$
$593$		−	1683.44i		−	0.116578i	0.998300	−	0.0582890i	$-0.0185645\pi$
$594$	−975.248	+	3001.51i	−0.0673652	+	0.207329i
$595$		0			0
$596$	2567.51	+	7901.98i	0.176459	+	0.543083i
$597$	12086.4	−	3927.10i	0.828579	−	0.269222i
$598$	−910.036	+	1252.56i	−0.0622310	+	0.0856536i
$599$	573.370			0.0391106			0.0195553	−	0.999809i	$-0.493775\pi$
$599$	573.370			0.0391106			0.0195553	+	0.999809i	$0.493775\pi$
$600$		0			0
$601$	−18178.9			−1.23383			−0.616916	−	0.787029i	$-0.711618\pi$
$601$	−18178.9			−1.23383			−0.616916	+	0.787029i	$0.711618\pi$
$602$	6128.60	−	8435.29i	0.414922	−	0.571091i
$603$	1009.78	−	328.098i	0.0681948	−	0.0221578i
$604$	−654.850	−	2015.42i	−0.0441150	−	0.135772i
$605$		0			0
$606$	−2492.66	+	7671.63i	−0.167092	+	0.514255i
$607$		−	336.530i		−	0.0225030i	−0.999937	−	0.0112515i	$-0.996418\pi$
$607$		−	336.530i		−	0.0225030i	0.999937	−	0.0112515i	$-0.00358154\pi$
$608$	324.898	+	105.566i	0.0216716	+	0.00704155i
$609$	−5878.71	+	4271.13i	−0.391161	+	0.284195i
$610$		0			0
$611$	2548.77	+	1851.79i	0.168760	+	0.122611i
$612$	4105.13	+	5650.23i	0.271144	+	0.373198i
$613$	−2302.68	−	3169.37i	−0.151720	−	0.208825i	0.726391	−	0.687282i	$-0.241196\pi$
$613$	−2302.68	−	3169.37i	−0.151720	−	0.208825i	−0.878111	+	0.478457i	$0.841196\pi$
$614$	5823.59	+	4231.08i	0.382770	+	0.278099i
$615$		0			0
$616$	−9573.97	+	6955.89i	−0.626211	+	0.454969i
$617$	6920.81	+	2248.71i	0.451574	+	0.146725i	0.525969	−	0.850503i	$-0.323703\pi$
$617$	6920.81	+	2248.71i	0.451574	+	0.146725i	−0.0743951	+	0.997229i	$0.523703\pi$
$618$			186.836i			0.0121613i
$619$	−10.7010	+	32.9344i	−0.000694848	+	0.00213852i	−0.951403	−	0.307948i	$-0.900358\pi$
$619$	−10.7010	+	32.9344i	−0.000694848	+	0.00213852i	0.950708	+	0.310086i	$0.100358\pi$
$620$		0			0
$621$	1015.97	+	3126.84i	0.0656515	+	0.202055i
$622$	−13682.9	+	4445.83i	−0.882046	+	0.286594i
$623$	−3807.54	+	5240.64i	−0.244857	+	0.337017i
$624$	−666.767			−0.0427757
$625$		0			0
$626$	2923.58			0.186661
$627$	2824.98	−	3888.25i	0.179934	−	0.247659i
$628$	−7845.25	+	2549.08i	−0.498503	+	0.161973i
$629$	3285.79	+	10112.6i	0.208288	+	0.641044i
$630$		0			0
$631$	3257.85	−	10026.6i	0.205536	−	0.632574i	−0.794155	−	0.607715i	$-0.792086\pi$
$631$	3257.85	−	10026.6i	0.205536	−	0.632574i	0.999691	−	0.0248588i	$-0.00791361\pi$
$632$			2682.21i			0.168817i
$633$	−22304.8	−	7247.26i	−1.40053	−	0.455059i
$634$	−1294.66	+	940.622i	−0.0810999	+	0.0589225i
$635$		0			0
$636$	−7407.55	−	5381.90i	−0.461837	−	0.335544i
$637$	−696.860	−	959.146i	−0.0433448	−	0.0596589i
$638$	−3261.89	−	4489.60i	−0.202413	−	0.278597i
$639$	−12682.1	−	9214.11i	−0.785129	−	0.570430i
$640$		0			0
$641$	−18966.8	+	13780.2i	−1.16871	+	0.849120i	−0.990854	−	0.134936i	$-0.956917\pi$
$641$	−18966.8	+	13780.2i	−1.16871	+	0.849120i	−0.177859	+	0.984056i	$0.556917\pi$
$642$	−483.205	−	157.003i	−0.0297049	−	0.00965172i
$643$		−	78.5584i		−	0.00481811i	−0.999997	−	0.00240905i	$-0.999233\pi$
$643$		−	78.5584i		−	0.00481811i	0.999997	−	0.00240905i	$-0.000766826\pi$
$644$	−3809.64	+	11724.9i	−0.233107	+	0.717429i
$645$		0			0
$646$	490.318	+	1509.04i	0.0298627	+	0.0919079i
$647$	−21444.3	+	6967.68i	−1.30303	+	0.423381i	−0.876636	−	0.481154i	$-0.840218\pi$
$647$	−21444.3	+	6967.68i	−1.30303	+	0.423381i	−0.426398	+	0.904536i	$0.640218\pi$
$648$	−3815.20	+	5251.18i	−0.231289	+	0.318342i
$649$	−55098.2			−3.33250
$650$		0			0
$651$	52227.4			3.14432
$652$	1364.49	−	1878.06i	0.0819596	−	0.112808i
$653$	−3890.99	+	1264.26i	−0.233179	+	0.0757645i	−0.423276	−	0.906001i	$-0.639120\pi$
$653$	−3890.99	+	1264.26i	−0.233179	+	0.0757645i	0.190097	+	0.981765i	$0.439120\pi$
$654$	−7879.63	−	24251.0i	−0.471128	−	1.44998i
$655$		0			0
$656$	−646.445	+	1989.55i	−0.0384748	+	0.118413i
$657$		−	8601.72i		−	0.510784i
$658$	23858.4	+	7752.05i	1.41352	+	0.459280i
$659$	15042.9	−	10929.3i	0.889211	−	0.646049i	−0.0464613	−	0.998920i	$-0.514794\pi$
$659$	15042.9	−	10929.3i	0.889211	−	0.646049i	0.935672	+	0.352871i	$0.114794\pi$
$660$		0			0
$661$	4366.40	+	3172.38i	0.256934	+	0.186673i	0.708794	−	0.705415i	$-0.249239\pi$
$661$	4366.40	+	3172.38i	0.256934	+	0.186673i	−0.451860	+	0.892089i	$0.649239\pi$
$662$	518.343	+	713.438i	0.0304320	+	0.0418860i
$663$	−1820.32	−	2505.45i	−0.106629	−	0.146763i
$664$	6767.51	+	4916.88i	0.395527	+	0.287367i
$665$		0			0
$666$	5439.33	−	3951.90i	0.316471	−	0.229930i
$667$	−5498.24	−	1786.49i	−0.319179	−	0.103708i
$668$			14781.4i			0.856153i
$669$	−9864.16	+	30358.7i	−0.570060	+	1.75446i
$670$		0			0
$671$	−542.131	−	1668.51i	−0.0311904	−	0.0959941i
$672$	−5049.43	+	1640.66i	−0.289860	+	0.0941813i
$673$	−2215.56	+	3049.45i	−0.126900	+	0.174662i	−0.867739	−	0.497019i	$-0.834428\pi$
$673$	−2215.56	+	3049.45i	−0.126900	+	0.174662i	0.740840	+	0.671682i	$0.234428\pi$
$674$	6565.38			0.375206
$675$		0			0
$676$	−8650.43			−0.492173
$677$	−4581.89	+	6306.43i	−0.260113	+	0.358014i	−0.919021	−	0.394209i	$-0.871019\pi$
$677$	−4581.89	+	6306.43i	−0.260113	+	0.358014i	0.658908	+	0.752223i	$0.271019\pi$
$678$	10612.5	−	3448.21i	0.601136	−	0.195321i
$679$	3864.78	+	11894.6i	0.218434	+	0.672270i
$680$		0			0
$681$	6838.65	−	21047.2i	0.384813	−	1.18433i
$682$			39886.3i			2.23948i
$683$	19317.5	+	6276.64i	1.08223	+	0.351638i	0.795240	−	0.606295i	$-0.207345\pi$
$683$	19317.5	+	6276.64i	1.08223	+	0.351638i	0.286991	+	0.957933i	$0.407345\pi$
$684$	811.676	−	589.717i	0.0453731	−	0.0329655i
$685$		0			0
$686$	5320.77	+	3865.76i	0.296134	+	0.215154i
$687$	6432.68	+	8853.82i	0.357237	+	0.491695i
$688$	2099.85	+	2890.20i	0.116361	+	0.160157i
$689$	1528.34	+	1110.41i	0.0845069	+	0.0613979i
$690$		0			0
$691$	12909.3	−	9379.16i	0.710700	−	0.516353i	−0.172700	−	0.984975i	$-0.555249\pi$
$691$	12909.3	−	9379.16i	0.710700	−	0.516353i	0.883399	+	0.468621i	$0.155249\pi$
$692$	−12889.8	−	4188.17i	−0.708090	−	0.230073i
$693$			34755.1i			1.90510i
$694$	6541.61	−	20133.0i	0.357804	−	1.10121i
$695$		0			0
$696$	−769.368	−	2367.87i	−0.0419006	−	0.128957i
$697$	−9240.81	+	3002.52i	−0.502182	+	0.163169i
$698$	7991.75	−	10999.7i	0.433370	−	0.596483i
$699$	11291.7			0.611002
$700$		0			0
$701$	31355.4			1.68941			0.844705	−	0.535232i	$-0.179776\pi$
$701$	31355.4			1.68941			0.844705	+	0.535232i	$0.179776\pi$
$702$	171.712	−	236.341i	0.00923197	−	0.0127067i
$703$	1452.72	−	472.016i	0.0779377	−	0.0253235i
$704$	−1252.98	−	3856.28i	−0.0670788	−	0.206447i
$705$		0			0
$706$	−2260.04	+	6955.67i	−0.120478	+	0.370794i
$707$		−	13252.3i		−	0.704954i
$708$	−23509.6	−	7638.74i	−1.24795	−	0.405482i
$709$	21411.2	−	15556.1i	1.13415	−	0.824010i	0.147858	−	0.989009i	$-0.452762\pi$
$709$	21411.2	−	15556.1i	1.13415	−	0.824010i	0.986294	+	0.164999i	$0.0527621\pi$
$710$		0			0
$711$	6372.85	+	4630.15i	0.336147	+	0.244225i
$712$	−1304.59	−	1795.61i	−0.0686677	−	0.0945130i
$713$	24423.6	+	33616.2i	1.28285	+	1.76569i
$714$	−19950.2	−	14494.7i	−1.04568	−	0.759734i
$715$		0			0
$716$	9156.64	−	6652.69i	0.477932	−	0.347238i
$717$	−19261.6	−	6258.48i	−1.00326	−	0.325979i
$718$		−	16224.9i		−	0.843324i
$719$	4896.34	−	15069.4i	0.253967	−	0.781631i	−0.740064	−	0.672537i	$-0.765205\pi$
$719$	4896.34	−	15069.4i	0.253967	−	0.781631i	0.994031	−	0.109095i	$-0.0347952\pi$
$720$		0			0
$721$	−94.8532	−	291.928i	−0.00489947	−	0.0150790i
$722$	−12829.8	+	4168.66i	−0.661324	+	0.214877i
$723$	4334.96	−	5966.56i	0.222986	−	0.306914i
$724$	−1453.59			−0.0746164
$725$		0			0
$726$	−38129.0			−1.94917
$727$	−7266.97	+	10002.1i	−0.370725	+	0.510259i	−0.953098	−	0.302663i	$-0.902124\pi$
$727$	−7266.97	+	10002.1i	−0.370725	+	0.510259i	0.582373	+	0.812922i	$0.302124\pi$
$728$	1041.81	−	338.505i	0.0530386	−	0.0172333i
$729$	4413.99	+	13584.9i	0.224254	+	0.690182i
$730$		0			0
$731$	−5127.51	+	15780.9i	−0.259436	+	0.798463i
$732$		−	787.089i		−	0.0397427i
$733$	15931.9	+	5176.58i	0.802806	+	0.260848i	0.681548	−	0.731773i	$-0.261307\pi$
$733$	15931.9	+	5176.58i	0.802806	+	0.260848i	0.121258	+	0.992621i	$0.461307\pi$
$734$	−2027.75	+	1473.24i	−0.101969	+	0.0740851i
$735$		0			0
$736$	−3417.33	−	2482.84i	−0.171147	−	0.124346i
$737$	−1682.86	−	2316.26i	−0.0841098	−	0.115767i
$738$	3611.21	+	4970.40i	0.180122	+	0.247917i
$739$	24644.7	+	17905.4i	1.22675	+	0.891288i	0.996643	−	0.0818763i	$-0.0260912\pi$
$739$	24644.7	+	17905.4i	1.22675	+	0.891288i	0.230110	+	0.973165i	$0.426091\pi$
$740$		0			0
$741$	−359.918	+	261.495i	−0.0178433	+	0.0129639i
$742$	14306.4	+	4648.44i	0.707825	+	0.229986i
$743$		−	21463.8i		−	1.05980i	−0.848061	−	0.529899i	$-0.822230\pi$
$743$		−	21463.8i		−	1.05980i	0.848061	−	0.529899i	$-0.177770\pi$
$744$	−5529.79	+	17018.9i	−0.272489	+	0.838635i
$745$		0			0
$746$	−2666.52	−	8206.71i	−0.130869	−	0.402773i
$747$	23364.8	−	7591.67i	1.14441	−	0.371840i
$748$	11069.7	−	15236.1i	0.541106	−	0.744769i
$749$	834.705			0.0407202
$750$		0			0
$751$	−9737.29			−0.473128			−0.236564	−	0.971616i	$-0.576021\pi$
$751$	−9737.29			−0.473128			−0.236564	+	0.971616i	$0.576021\pi$
$752$	−5052.20	+	6953.76i	−0.244993	+	0.337204i
$753$	13815.4	−	4488.91i	0.668609	−	0.217244i
$754$	158.738	+	488.545i	0.00766697	+	0.0235965i
$755$		0			0
$756$	718.829	−	2212.33i	0.0345814	−	0.106431i
$757$		−	6890.48i		−	0.330831i	−0.986224	−	0.165415i	$-0.947104\pi$
$757$		−	6890.48i		−	0.330831i	0.986224	−	0.165415i	$-0.0528964\pi$
$758$	6295.93	+	2045.67i	0.301687	+	0.0980239i
$759$	−48077.6	+	34930.4i	−2.29922	+	1.67048i
$760$		0			0
$761$	−3343.32	−	2429.06i	−0.159258	−	0.115707i	0.505302	−	0.862942i	$-0.331381\pi$
$761$	−3343.32	−	2429.06i	−0.159258	−	0.115707i	−0.664560	+	0.747235i	$0.731381\pi$
$762$	−8925.61	−	12285.0i	−0.424332	−	0.584042i
$763$	24623.5	+	33891.4i	1.16832	+	1.60806i
$764$	−7824.75	−	5685.02i	−0.370536	−	0.269210i
$765$		0			0
$766$	14911.8	−	10834.0i	0.703375	−	0.511032i
$767$	4850.57	+	1576.04i	0.228349	+	0.0741951i
$768$		−	1819.13i		−	0.0854716i
$769$	3280.64	−	10096.8i	0.153840	−	0.473471i	−0.844202	−	0.536026i	$-0.819925\pi$
$769$	3280.64	−	10096.8i	0.153840	−	0.473471i	0.998042	+	0.0625552i	$0.0199249\pi$
$770$		0			0
$771$	−8499.29	−	26158.1i	−0.397010	−	1.22187i
$772$	4189.67	−	1361.31i	0.195323	−	0.0634644i
$773$	−13887.3	+	19114.3i	−0.646175	+	0.889383i	−0.998926	−	0.0463341i	$-0.985246\pi$
$773$	−13887.3	+	19114.3i	−0.646175	+	0.889383i	0.352751	+	0.935717i	$0.385246\pi$
$774$	10491.9			0.487240
$775$		0			0
$776$	−4285.19			−0.198234
$777$	−13953.7	+	19205.6i	−0.644253	+	0.886739i
$778$	7189.09	−	2335.88i	0.331287	−	0.107642i
$779$	431.323	+	1327.48i	0.0198379	+	0.0610549i
$780$		0			0
$781$	−13062.5	+	40202.1i	−0.598478	+	1.84193i
$782$		−	19619.3i		−	0.897167i
$783$	1037.44	+	337.086i	0.0473503	+	0.0153850i
$784$	2616.82	−	1901.23i	0.119207	−	0.0866086i
$785$		0			0
$786$	−9219.58	−	6698.42i	−0.418386	−	0.303975i
$787$	−18606.5	−	25609.6i	−0.842756	−	1.15995i	−0.985413	−	0.170182i	$-0.945564\pi$
$787$	−18606.5	−	25609.6i	−0.842756	−	1.15995i	0.142657	−	0.989772i	$-0.454436\pi$
$788$	4826.70	+	6643.39i	0.218203	+	0.300331i
$789$	8374.21	+	6084.22i	0.377858	+	0.274530i
$790$		0			0
$791$	−14831.2	+	10775.5i	−0.666672	+	0.484365i
$792$	−11325.4	−	3679.84i	−0.508118	−	0.165098i
$793$			162.394i			0.00727211i
$794$	−2333.13	+	7180.65i	−0.104282	+	0.320947i
$795$		0			0
$796$	−2210.59	−	6803.49i	−0.0984324	−	0.302944i
$797$	13591.5	−	4416.13i	0.604058	−	0.196270i	0.00900858	−	0.999959i	$-0.497132\pi$
$797$	13591.5	−	4416.13i	0.604058	−	0.196270i	0.595049	+	0.803689i	$0.297132\pi$
$798$	−2082.22	+	2865.92i	−0.0923680	+	0.127134i
$799$	−39922.4			−1.76765
$800$		0			0
$801$	−6518.36			−0.287534
$802$	−2279.06	+	3136.86i	−0.100345	+	0.138112i
$803$	−22059.7	+	7167.63i	−0.969451	+	0.314994i
$804$	−396.929	−	1221.62i	−0.0174112	−	0.0535862i
$805$		0			0
$806$	1140.92	−	3511.39i	0.0498600	−	0.153453i
$807$			26144.2i			1.14042i
$808$	4318.41	+	1403.14i	0.188021	+	0.0610918i
$809$	10002.2	−	7267.04i	0.434684	−	0.315816i	−0.348835	−	0.937184i	$-0.613423\pi$
$809$	10002.2	−	7267.04i	0.434684	−	0.315816i	0.783519	+	0.621368i	$0.213423\pi$
$810$		0			0
$811$	26704.9	+	19402.2i	1.15627	+	0.840080i	0.989302	−	0.145882i	$-0.0466021\pi$
$811$	26704.9	+	19402.2i	1.15627	+	0.840080i	0.166969	+	0.985962i	$0.446602\pi$
$812$	2404.25	+	3309.16i	0.103907	+	0.143016i
$813$	−4627.17	−	6368.75i	−0.199609	−	0.274738i
$814$	−14667.4	−	10656.5i	−0.631563	−	0.458857i
$815$		0			0
$816$	6835.58	−	4966.34i	0.293252	−	0.213060i
$817$	2266.98	+	736.586i	0.0970766	+	0.0315421i
$818$			12176.1i			0.520450i
$819$	994.144	−	3059.66i	0.0424154	−	0.130541i
$820$		0			0
$821$	7646.05	+	23532.1i	0.325029	+	1.00034i	0.971427	+	0.237337i	$0.0762744\pi$
$821$	7646.05	+	23532.1i	0.325029	+	1.00034i	−0.646398	+	0.763000i	$0.723726\pi$
$822$	−23376.3	+	7595.41i	−0.991900	+	0.322288i
$823$	−25385.8	+	34940.5i	−1.07520	+	1.47989i	−0.210509	+	0.977592i	$0.567512\pi$
$823$	−25385.8	+	34940.5i	−1.07520	+	1.47989i	−0.864695	+	0.502298i	$0.832488\pi$
$824$	105.171			0.00444638
$825$		0			0
$826$	40611.4			1.71072
$827$	749.948	−	1032.21i	0.0315335	−	0.0434022i	−0.792959	−	0.609275i	$-0.791461\pi$
$827$	749.948	−	1032.21i	0.0315335	−	0.0434022i	0.824493	+	0.565873i	$0.191461\pi$
$828$	−11798.3	+	3833.50i	−0.495193	+	0.160898i
$829$	10481.4	+	32258.6i	0.439126	+	1.35149i	0.888799	+	0.458298i	$0.151541\pi$
$829$	10481.4	+	32258.6i	0.439126	+	1.35149i	−0.449673	+	0.893193i	$0.648459\pi$
$830$		0			0
$831$	926.846	−	2852.54i	0.0386906	−	0.119078i
$832$			375.328i			0.0156396i
$833$	14288.2	+	4642.51i	0.594305	+	0.193101i
$834$	−24862.9	+	18064.0i	−1.03229	+	0.750005i
$835$		0			0
$836$	−2188.72	−	1590.20i	−0.0905485	−	0.0657874i
$837$	−4608.41	−	6342.94i	−0.190311	−	0.261940i
$838$	−16998.6	−	23396.6i	−0.700724	−	0.964465i
$839$	−29664.7	−	21552.7i	−1.22067	−	0.886866i	−0.224511	−	0.974472i	$-0.572078\pi$
$839$	−29664.7	−	21552.7i	−1.22067	−	0.886866i	−0.996155	+	0.0876059i	$0.972078\pi$
$840$		0			0
$841$	18179.3	−	13208.1i	0.745390	−	0.541558i
$842$	15515.5	+	5041.30i	0.635036	+	0.206336i
$843$		−	42286.0i		−	1.72765i
$844$	−4079.53	+	12555.5i	−0.166378	+	0.512059i
$845$		0			0
$846$	7800.61	+	24007.8i	0.317010	+	0.975657i
$847$	59575.8	−	19357.3i	2.41682	−	0.785273i
$848$	−3029.51	+	4169.76i	−0.122681	+	0.168856i
$849$	62752.6			2.53671
$850$		0			0
$851$	−18887.0			−0.760796
$852$	−11147.1	+	15342.7i	−0.448233	+	0.616940i
$853$	9173.26	−	2980.57i	0.368214	−	0.119640i	−0.119065	−	0.992886i	$-0.537990\pi$
$853$	9173.26	−	2980.57i	0.368214	−	0.119640i	0.487279	+	0.873247i	$0.337990\pi$
$854$	399.590	+	1229.81i	0.0160113	+	0.0492778i
$855$		0			0
$856$	−88.3778	+	271.999i	−0.00352884	+	0.0108607i
$857$			12314.7i			0.490855i	0.969415	+	0.245427i	$0.0789283\pi$
$857$			12314.7i			0.490855i	−0.969415	+	0.245427i	$0.921072\pi$
$858$	5021.96	+	1631.73i	0.199821	+	0.0649259i
$859$	−18157.7	+	13192.3i	−0.721226	+	0.524001i	−0.886776	−	0.462200i	$-0.847060\pi$
$859$	−18157.7	+	13192.3i	−0.721226	+	0.524001i	0.165550	+	0.986201i	$0.447060\pi$
$860$		0			0
$861$	−17549.8	−	12750.7i	−0.694654	−	0.504696i
$862$	−10432.1	−	14358.6i	−0.412204	−	0.567350i
$863$	−16658.4	−	22928.3i	−0.657079	−	0.904391i	0.342302	−	0.939590i	$-0.388794\pi$
$863$	−16658.4	−	22928.3i	−0.657079	−	0.904391i	−0.999380	+	0.0351988i	$0.988794\pi$
$864$	644.805	+	468.478i	0.0253897	+	0.0184467i
$865$		0			0
$866$	−23539.6	+	17102.5i	−0.923681	+	0.671094i
$867$	4120.20	+	1338.73i	0.161395	+	0.0524404i
$868$		−	29399.1i		−	1.14962i
$869$	6563.97	−	20201.8i	0.256234	−	0.788608i
$870$		0			0
$871$	81.8954	+	252.048i	0.00318590	+	0.00980520i
$872$	−13651.0	+	4435.49i	−0.530141	+	0.172253i
$873$	−7397.29	+	10181.5i	−0.286782	+	0.394721i
$874$	−2818.39			−0.109077
$875$		0			0
$876$	−10406.3			−0.401364
$877$	−1419.83	+	1954.23i	−0.0546684	+	0.0752446i	−0.835476	−	0.549527i	$-0.814808\pi$
$877$	−1419.83	+	1954.23i	−0.0546684	+	0.0752446i	0.780808	+	0.624772i	$0.214808\pi$
$878$	−4836.94	+	1571.62i	−0.185921	+	0.0604094i
$879$	−17588.2	−	54130.8i	−0.674896	−	2.07712i
$880$		0			0
$881$	−2814.10	+	8660.91i	−0.107616	+	0.331207i	−0.990335	−	0.138693i	$-0.955710\pi$
$881$	−2814.10	+	8660.91i	−0.107616	+	0.331207i	0.882720	+	0.469900i	$0.155710\pi$
$882$		−	9499.50i		−	0.362658i
$883$	−20713.9	−	6730.34i	−0.789441	−	0.256505i	−0.113575	−	0.993529i	$-0.536230\pi$
$883$	−20713.9	−	6730.34i	−0.789441	−	0.256505i	−0.675866	+	0.737024i	$0.736230\pi$
$884$	−1410.34	+	1024.67i	−0.0536592	+	0.0389857i
$885$		0			0
$886$	18011.1	+	13085.9i	0.682953	+	0.496194i
$887$	25094.3	+	34539.3i	0.949925	+	1.30746i	0.951561	+	0.307461i	$0.0994792\pi$
$887$	25094.3	+	34539.3i	0.949925	+	1.30746i	−0.00163614	+	0.999999i	$0.500521\pi$
$888$	−4780.97	−	6580.44i	−0.180674	−	0.248677i
$889$	20183.0	+	14663.8i	0.761434	+	0.553214i
$890$		0			0
$891$	41586.2	−	30214.1i	1.56362	−	1.13604i
$892$	17089.1	+	5552.60i	0.641465	+	0.208424i
$893$			5735.00i			0.214910i
$894$	9122.33	−	28075.7i	0.341271	−	1.05032i
$895$		0			0
$896$	923.538	+	2842.36i	0.0344344	+	0.105978i
$897$	5231.67	−	1699.87i	0.194738	−	0.0632743i
$898$	−2360.20	+	3248.54i	−0.0877070	+	0.120718i
$899$	13786.4			0.511459
$900$		0			0
$901$	−23939.1			−0.885156
$902$	9737.79	−	13402.9i	0.359460	−	0.494754i
$903$	−35232.4	+	11447.7i	−1.29841	+	0.421878i
$904$	−1941.02	−	5973.83i	−0.0714129	−	0.219786i
$905$		0			0
$906$	−2326.67	+	7160.77i	−0.0853185	+	0.262583i
$907$			23852.3i			0.873211i	0.899653	+	0.436605i	$0.143819\pi$
$907$			23852.3i			0.873211i	−0.899653	+	0.436605i	$0.856181\pi$
$908$	−11847.6	−	3849.52i	−0.433014	−	0.140695i
$909$	10788.5	−	7838.27i	0.393653	−	0.286006i
$910$		0			0
$911$	−10021.8	−	7281.28i	−0.364476	−	0.264807i	0.390440	−	0.920628i	$-0.372323\pi$
$911$	−10021.8	−	7281.28i	−0.364476	−	0.264807i	−0.754917	+	0.655821i	$0.772323\pi$
$912$	−713.434	−	981.957i	−0.0259037	−	0.0356533i
$913$	−38938.7	−	53594.6i	−1.41148	−	1.94274i
$914$	24120.9	+	17524.9i	0.872921	+	0.634214i
$915$		0			0
$916$	4983.87	−	3620.99i	0.179773	−	0.130612i
$917$	17806.1	+	5785.54i	0.641230	+	0.208348i
$918$			3701.90i			0.133095i
$919$	4263.13	−	13120.6i	0.153022	−	0.470954i	−0.844933	−	0.534872i	$-0.820360\pi$
$919$	4263.13	−	13120.6i	0.153022	−	0.470954i	0.997955	+	0.0639181i	$0.0203597\pi$
$920$		0			0
$921$	−7903.32	−	24323.9i	−0.282761	−	0.870250i
$922$	16408.9	−	5331.58i	0.586116	−	0.190441i
$923$	2299.90	−	3165.55i	0.0820176	−	0.112888i
$924$	42046.3			1.49699
$925$		0			0
$926$	−15740.1			−0.558586
$927$	181.552	−	249.884i	0.00643251	−	0.00885359i
$928$	−1332.89	+	433.082i	−0.0471490	+	0.0153196i
$929$	3624.90	+	11156.3i	0.128019	+	0.394001i	0.994439	−	0.105315i	$-0.0335850\pi$
$929$	3624.90	+	11156.3i	0.128019	+	0.394001i	−0.866420	+	0.499315i	$0.833585\pi$
$930$		0			0
$931$	666.914	−	2052.55i	0.0234771	−	0.0722552i
$932$		−	6356.16i		−	0.223394i
$933$	48615.0	+	15796.0i	1.70588	+	0.554273i
$934$	−6088.95	+	4423.88i	−0.213315	+	0.154983i
$935$		0			0
$936$	891.769	+	647.908i	0.0311414	+	0.0226256i
$937$	−28103.4	−	38681.0i	−0.979827	−	1.34862i	−0.936923	−	0.349537i	$-0.886339\pi$
$937$	−28103.4	−	38681.0i	−0.979827	−	1.34862i	−0.0429043	−	0.999079i	$-0.513661\pi$
$938$	1240.39	+	1707.25i	0.0431771	+	0.0594282i
$939$	−8403.63	−	6105.60i	−0.292058	−	0.212192i
$940$		0			0
$941$	12758.9	−	9269.90i	0.442008	−	0.321137i	−0.344425	−	0.938814i	$-0.611926\pi$
$941$	12758.9	−	9269.90i	0.442008	−	0.321137i	0.786432	+	0.617677i	$0.211926\pi$
$942$	27874.1	+	9056.84i	0.964105	+	0.313257i
$943$		−	17258.7i		−	0.595993i
$944$	−4299.90	+	13233.7i	−0.148252	+	0.456272i
$945$		0			0
$946$	−8742.68	−	26907.2i	−0.300475	−	0.924766i
$947$	11795.4	−	3832.56i	0.404752	−	0.131512i	−0.0995641	−	0.995031i	$-0.531745\pi$
$947$	11795.4	−	3832.56i	0.404752	−	0.131512i	0.504316	+	0.863519i	$0.331745\pi$
$948$	5601.51	−	7709.81i	0.191908	−	0.264138i
$949$	2147.05			0.0734416
$950$		0			0
$951$	5685.78			0.193874
$952$	−8159.15	+	11230.1i	−0.277773	+	0.382321i
$953$	25220.9	−	8194.76i	0.857276	−	0.278546i	0.152786	−	0.988259i	$-0.451176\pi$
$953$	25220.9	−	8194.76i	0.857276	−	0.278546i	0.704490	+	0.709714i	$0.251176\pi$
$954$	4677.56	+	14396.1i	0.158744	+	0.488563i
$955$		0			0
$956$	−3522.94	+	10842.5i	−0.119184	+	0.366811i
$957$			19717.1i			0.666003i
$958$	14714.1	+	4780.90i	0.496232	+	0.161236i
$959$	32668.9	−	23735.4i	1.10004	−	0.799223i
$960$		0			0
$961$	−56063.0	−	40732.2i	−1.88188	−	1.36726i
$962$	986.422	+	1357.69i	0.0330598	+	0.0455029i
$963$	493.701	+	679.521i	0.0165205	+	0.0227386i
$964$	−3358.61	−	2440.17i	−0.112213	−	0.0815277i
$965$		0			0
$966$	35436.7	−	25746.3i	1.18029	−	0.857528i
$967$	−40353.9	−	13111.8i	−1.34198	−	0.436036i	−0.451993	−	0.892022i	$-0.649287\pi$
$967$	−40353.9	−	13111.8i	−1.34198	−	0.436036i	−0.889987	+	0.455986i	$0.849287\pi$
$968$			21463.0i			0.712653i
$969$	1742.09	−	5361.61i	0.0577545	−	0.177750i
$970$		0			0
$971$	8372.22	+	25767.0i	0.276702	+	0.851600i	0.988764	+	0.149484i	$0.0477613\pi$
$971$	8372.22	+	25767.0i	0.276702	+	0.851600i	−0.712062	+	0.702116i	$0.752239\pi$
$972$	19374.8	−	6295.24i	0.639348	−	0.207737i
$973$	29677.1	−	40847.0i	0.977805	−	1.34583i
$974$	−9496.38			−0.312406
$975$		0			0
$976$	−443.057			−0.0145307
$977$	22892.8	−	31509.3i	0.749649	−	1.03180i	−0.248357	−	0.968669i	$-0.579890\pi$
$977$	22892.8	−	31509.3i	0.749649	−	1.03180i	0.998005	−	0.0631340i	$-0.0201096\pi$
$978$	−7844.27	+	2548.76i	−0.256475	+	0.0833337i
$979$	5431.61	+	16716.8i	0.177319	+	0.545731i
$980$		0			0
$981$	−13026.4	+	40091.3i	−0.423958	+	1.30481i
$982$		−	29482.9i		−	0.958083i
$983$	17239.4	+	5601.40i	0.559359	+	0.181747i	0.575033	−	0.818130i	$-0.304989\pi$
$983$	17239.4	+	5601.40i	0.559359	+	0.181747i	−0.0156737	+	0.999877i	$0.504989\pi$
$984$	6013.14	−	4368.80i	0.194809	−	0.141537i
$985$		0			0
$986$	−5266.23	−	3826.14i	−0.170092	−	0.123579i
$987$	−52389.8	−	72108.4i	−1.68955	−	2.32547i
$988$	147.197	+	202.600i	0.00473985	+	0.00652385i
$989$	−23844.4	−	17324.0i	−0.766642	−	0.556998i
$990$		0			0
$991$	−10162.9	+	7383.79i	−0.325767	+	0.236684i	−0.738633	−	0.674108i	$-0.764528\pi$
$991$	−10162.9	+	7383.79i	−0.325767	+	0.236684i	0.412865	+	0.910792i	$0.364528\pi$
$992$	9580.06	+	3112.75i	0.306620	+	0.0996270i
$993$		−	3133.23i		−	0.100131i
$994$	9627.98	−	29631.9i	0.307224	−	0.945539i
$995$		0			0
$996$	−9184.33	−	28266.4i	−0.292185	−	0.899254i
$997$	−6667.52	+	2166.41i	−0.211798	+	0.0688173i	−0.412994	−	0.910734i	$-0.635517\pi$
$997$	−6667.52	+	2166.41i	−0.211798	+	0.0688173i	0.201196	+	0.979551i	$0.435517\pi$
$998$	−16172.4	+	22259.4i	−0.512955	+	0.706023i
$999$	3563.72			0.112864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.e.b.49.4		32
5.2	odd	4		250.4.d.c.201.1		32
5.3	odd	4		250.4.d.d.201.8		32
5.4	even	2		50.4.e.a.9.5	✓	32
25.2	odd	20		250.4.d.c.51.1		32
25.8	odd	20		1250.4.a.m.1.14		16
25.11	even	5		50.4.e.a.39.5	yes	32
25.14	even	10	inner	250.4.e.b.199.4		32
25.17	odd	20		1250.4.a.n.1.3		16
25.23	odd	20		250.4.d.d.51.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.5	✓	32	5.4	even	2
50.4.e.a.39.5	yes	32	25.11	even	5
250.4.d.c.51.1		32	25.2	odd	20
250.4.d.c.201.1		32	5.2	odd	4
250.4.d.d.51.8		32	25.23	odd	20
250.4.d.d.201.8		32	5.3	odd	4
250.4.e.b.49.4		32	1.1	even	1	trivial
250.4.e.b.199.4		32	25.14	even	10	inner
1250.4.a.m.1.14		16	25.8	odd	20
1250.4.a.n.1.3		16	25.17	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17557 + 1.61803i) q^{2} +(6.75819 - 2.19587i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.39174 + 13.5164i) q^{6} -23.3487i q^{7} +(7.60845 + 2.47214i) q^{8} +(19.0078 - 13.8100i) q^{9} +O(q^{10})\)	\(q+(-1.17557 + 1.61803i) q^{2} +(6.75819 - 2.19587i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.39174 + 13.5164i) q^{6} -23.3487i q^{7} +(7.60845 + 2.47214i) q^{8} +(19.0078 - 13.8100i) q^{9} +(-51.2554 - 37.2392i) q^{11} +(-16.7072 - 22.9954i) q^{12} +(3.44706 + 4.74447i) q^{13} +(37.7789 + 27.4480i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-70.6774 - 22.9645i) q^{17} +46.9899i q^{18} +(-3.29893 + 10.1531i) q^{19} +(-51.2706 - 157.795i) q^{21} +(120.509 - 39.1557i) q^{22} +(77.5886 - 106.792i) q^{23} +56.8478 q^{24} -11.7290 q^{26} +(-14.6399 + 20.1502i) q^{27} +(-88.8236 + 28.8605i) q^{28} +(-13.5338 - 41.6528i) q^{29} +(-97.2735 + 299.377i) q^{31} -32.0000i q^{32} +(-428.166 - 139.120i) q^{33} +(120.244 - 87.3621i) q^{34} +(-76.0312 - 55.2399i) q^{36} +(-84.1012 - 115.755i) q^{37} +(-12.5499 - 17.2734i) q^{38} +(33.7141 + 24.4948i) q^{39} +(105.776 - 76.8508i) q^{41} +(315.589 + 102.541i) q^{42} -223.280i q^{43} +(-78.3113 + 241.017i) q^{44} +(81.5815 + 251.082i) q^{46} +(510.915 - 166.006i) q^{47} +(-66.8286 + 91.9817i) q^{48} -202.161 q^{49} -528.078 q^{51} +(13.7883 - 18.9779i) q^{52} +(306.365 - 99.5441i) q^{53} +(-15.3933 - 47.3759i) q^{54} +(57.7211 - 177.647i) q^{56} +75.8604i q^{57} +(83.3056 + 27.0676i) q^{58} +(703.580 - 511.180i) q^{59} +(22.4025 + 16.2764i) q^{61} +(-370.050 - 509.331i) q^{62} +(-322.445 - 443.807i) q^{63} +(51.7771 + 37.6183i) q^{64} +(728.440 - 529.242i) q^{66} +(42.9787 + 13.9646i) q^{67} +297.258i q^{68} +(289.858 - 892.092i) q^{69} +(-206.178 - 634.551i) q^{71} +(178.760 - 58.0827i) q^{72} +(215.194 - 296.189i) q^{73} +286.163 q^{74} +42.7023 q^{76} +(-869.487 + 1196.75i) q^{77} +(-79.2667 + 25.7553i) q^{78} +(103.606 + 318.866i) q^{79} +(-250.721 + 771.641i) q^{81} +261.493i q^{82} +(994.460 + 323.120i) q^{83} +(-536.913 + 390.090i) q^{84} +(361.275 + 262.482i) q^{86} +(-182.928 - 251.779i) q^{87} +(-297.914 - 410.043i) q^{88} +(-224.451 - 163.073i) q^{89} +(110.777 - 80.4843i) q^{91} +(-502.164 - 163.163i) q^{92} +2236.85i q^{93} +(-332.013 + 1021.83i) q^{94} +(-70.2678 - 216.262i) q^{96} +(-509.432 + 165.524i) q^{97} +(237.654 - 327.103i) q^{98} -1488.53 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more