LMFDB - Embedded newform 225.4.p.b.32.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.10
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +O(q^{10})$	\(q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +(-31.0214 + 17.9102i) q^{11} +(-20.5500 + 17.9537i) q^{12} +(14.3888 + 53.6997i) q^{13} +(-26.1045 + 45.2143i) q^{14} +(2.79604 + 4.84288i) q^{16} +(29.9510 - 29.9510i) q^{17} +(-27.1155 - 35.6137i) q^{18} -17.7095i q^{19} +(135.890 + 91.1683i) q^{21} +(-57.3607 + 15.3698i) q^{22} +(-101.925 + 27.3107i) q^{23} +(-102.476 + 50.2966i) q^{24} +92.1654i q^{26} +(-117.089 + 77.2859i) q^{27} +(116.945 - 116.945i) q^{28} +(26.5786 + 46.0355i) q^{29} +(-19.1014 + 33.0846i) q^{31} +(47.8872 + 178.717i) q^{32} +(35.9690 + 182.620i) q^{33} +(60.8131 - 35.1104i) q^{34} +(53.7695 + 131.203i) q^{36} +(75.1697 + 75.1697i) q^{37} +(7.59877 - 28.3590i) q^{38} +(288.220 + 19.4346i) q^{39} +(-126.863 - 73.2444i) q^{41} +(178.488 + 204.299i) q^{42} +(-526.075 - 140.961i) q^{43} +188.114 q^{44} -174.935 q^{46} +(-161.279 - 43.2145i) q^{47} +(28.5095 - 5.61527i) q^{48} +(-561.849 - 324.384i) q^{49} +(-96.9742 - 197.579i) q^{51} +(75.5641 - 282.009i) q^{52} +(-170.746 - 170.746i) q^{53} +(-220.661 + 73.5208i) q^{54} +(599.162 - 345.926i) q^{56} +(-87.0821 - 29.7429i) q^{57} +(22.8086 + 85.1228i) q^{58} +(-28.0525 + 48.5883i) q^{59} +(187.285 + 324.386i) q^{61} +(-44.7838 + 44.7838i) q^{62} +(676.522 - 515.089i) q^{63} +261.998i q^{64} +(-20.7596 + 307.870i) q^{66} +(-110.806 + 29.6904i) q^{67} +(-214.863 + 57.5724i) q^{68} +(-36.8879 + 547.058i) q^{69} -921.281i q^{71} +(75.2138 + 588.372i) q^{72} +(-373.434 + 373.434i) q^{73} +(88.1187 + 152.626i) q^{74} +(-46.5016 + 80.5432i) q^{76} +(-291.966 - 1089.63i) q^{77} +(453.200 + 154.791i) q^{78} +(492.922 - 284.589i) q^{79} +(183.385 + 705.557i) q^{81} +(-171.723 - 171.723i) q^{82} +(-117.674 + 439.165i) q^{83} +(-378.640 - 771.455i) q^{84} +(-781.941 - 451.454i) q^{86} +(271.006 - 53.3777i) q^{87} +(760.121 + 203.674i) q^{88} +148.257 q^{89} -1750.79 q^{91} +(535.269 + 143.425i) q^{92} +(130.605 + 149.492i) q^{93} +(-239.720 - 138.402i) q^{94} +(959.224 + 64.6801i) q^{96} +(-83.7049 + 312.391i) q^{97} +(-760.526 - 760.526i) q^{98} +(958.396 + 129.839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.60134	+	0.429078i	0.566160	+	0.151702i	0.530535	−	0.847663i	$-0.321991\pi$
$2$	1.60134	+	0.429078i	0.566160	+	0.151702i	0.0356249	+	0.999365i	$0.488658\pi$
$3$	1.67949	−	4.91725i	0.323217	−	0.946325i
$3$	1.67949	−	4.91725i	0.323217	−	0.946325i
$4$	−4.54802	−	2.62580i	−0.568502	−	0.328225i
$5$		0			0
$5$		0			0
$6$	4.79931	−	7.15356i	0.326552	−	0.486738i
$7$	−8.15082	+	30.4193i	−0.440103	+	1.64249i	0.288449	+	0.957495i	$0.406860\pi$
$7$	−8.15082	+	30.4193i	−0.440103	+	1.64249i	−0.728552	+	0.684991i	$0.759806\pi$
$8$	−15.5344	−	15.5344i	−0.686528	−	0.686528i
$9$	−21.3587	−	16.5169i	−0.791061	−	0.611737i
$10$		0			0
$11$	−31.0214	+	17.9102i	−0.850300	+	0.490921i	−0.860752	−	0.509025i	$-0.830006\pi$
$11$	−31.0214	+	17.9102i	−0.850300	+	0.490921i	0.0104522	+	0.999945i	$0.496673\pi$
$12$	−20.5500	+	17.9537i	−0.494357	+	0.431900i
$13$	14.3888	+	53.6997i	0.306979	+	1.14566i	0.931228	+	0.364437i	$0.118739\pi$
$13$	14.3888	+	53.6997i	0.306979	+	1.14566i	−0.624249	+	0.781226i	$0.714595\pi$
$14$	−26.1045	+	45.2143i	−0.498337	+	0.863145i
$15$		0			0
$16$	2.79604	+	4.84288i	0.0436881	+	0.0756700i
$17$	29.9510	−	29.9510i	0.427305	−	0.427305i	−0.460404	−	0.887709i	$-0.652296\pi$
$17$	29.9510	−	29.9510i	0.427305	−	0.427305i	0.887709	+	0.460404i	$0.152296\pi$
$18$	−27.1155	−	35.6137i	−0.355065	−	0.466346i
$19$		−	17.7095i		−	0.213834i	−0.994268	−	0.106917i	$-0.965902\pi$
$19$		−	17.7095i		−	0.213834i	0.994268	−	0.106917i	$-0.0340979\pi$
$20$		0			0
$21$	135.890	+	91.1683i	1.41208	+	0.947360i
$22$	−57.3607	+	15.3698i	−0.555879	+	0.148947i
$23$	−101.925	+	27.3107i	−0.924036	+	0.247595i	−0.689310	−	0.724467i	$-0.742086\pi$
$23$	−101.925	+	27.3107i	−0.924036	+	0.247595i	−0.234726	+	0.972062i	$0.575419\pi$
$24$	−102.476	+	50.2966i	−0.871576	+	0.427781i
$25$		0			0
$26$			92.1654i			0.695197i
$27$	−117.089	+	77.2859i	−0.834586	+	0.550877i
$28$	116.945	−	116.945i	0.789304	−	0.789304i
$29$	26.5786	+	46.0355i	0.170190	+	0.294779i	0.938486	−	0.345316i	$-0.112228\pi$
$29$	26.5786	+	46.0355i	0.170190	+	0.294779i	−0.768296	+	0.640095i	$0.778895\pi$
$30$		0			0
$31$	−19.1014	+	33.0846i	−0.110668	+	0.191683i	−0.916040	−	0.401087i	$-0.868632\pi$
$31$	−19.1014	+	33.0846i	−0.110668	+	0.191683i	0.805372	+	0.592770i	$0.201966\pi$
$32$	47.8872	+	178.717i	0.264542	+	0.987284i
$33$	35.9690	+	182.620i	0.189739	+	0.963334i
$34$	60.8131	−	35.1104i	0.306746	−	0.177100i
$35$		0			0
$36$	53.7695	+	131.203i	0.248933	+	0.607420i
$37$	75.1697	+	75.1697i	0.333995	+	0.333995i	0.854102	−	0.520106i	$-0.174108\pi$
$37$	75.1697	+	75.1697i	0.333995	+	0.333995i	−0.520106	+	0.854102i	$0.674108\pi$
$38$	7.59877	−	28.3590i	0.0324390	−	0.121064i
$39$	288.220	+	19.4346i	1.18339	+	0.0797955i
$40$		0			0
$41$	−126.863	−	73.2444i	−0.483236	−	0.278996i	0.238528	−	0.971136i	$-0.423335\pi$
$41$	−126.863	−	73.2444i	−0.483236	−	0.278996i	−0.721764	+	0.692139i	$0.756668\pi$
$42$	178.488	+	204.299i	0.655744	+	0.750572i
$43$	−526.075	−	140.961i	−1.86571	−	0.499916i	−0.865712	−	0.500542i	$-0.833134\pi$
$43$	−526.075	−	140.961i	−1.86571	−	0.499916i	−1.00000		0.000626116i	$0.999801\pi$
$44$	188.114			0.644530
$45$		0			0
$46$	−174.935			−0.560712
$47$	−161.279	−	43.2145i	−0.500530	−	0.134117i	−0.000284175	−	1.00000i	$-0.500090\pi$
$47$	−161.279	−	43.2145i	−0.500530	−	0.134117i	−0.500246	+	0.865883i	$0.666757\pi$
$48$	28.5095	−	5.61527i	0.0857291	−	0.0168853i
$49$	−561.849	−	324.384i	−1.63804	−	0.945725i
$50$		0			0
$51$	−96.9742	−	197.579i	−0.266257	−	0.542481i
$52$	75.5641	−	282.009i	0.201517	−	0.752070i
$53$	−170.746	−	170.746i	−0.442525	−	0.442525i	0.450335	−	0.892860i	$-0.351305\pi$
$53$	−170.746	−	170.746i	−0.442525	−	0.442525i	−0.892860	+	0.450335i	$0.851305\pi$
$54$	−220.661	+	73.5208i	−0.556078	+	0.185276i
$55$		0			0
$56$	599.162	−	345.926i	1.42976	−	0.825470i
$57$	−87.0821	−	29.7429i	−0.202356	−	0.0691147i
$58$	22.8086	+	85.1228i	0.0516365	+	0.192710i
$59$	−28.0525	+	48.5883i	−0.0619004	+	0.107215i	−0.895315	−	0.445434i	$-0.853049\pi$
$59$	−28.0525	+	48.5883i	−0.0619004	+	0.107215i	0.833414	+	0.552648i	$0.186383\pi$
$60$		0			0
$61$	187.285	+	324.386i	0.393104	+	0.680876i	0.992857	−	0.119309i	$-0.0380679\pi$
$61$	187.285	+	324.386i	0.393104	+	0.680876i	−0.599753	+	0.800185i	$0.704735\pi$
$62$	−44.7838	+	44.7838i	−0.0917346	+	0.0917346i
$63$	676.522	−	515.089i	1.35292	−	1.03008i
$64$			261.998i			0.511716i
$65$		0			0
$66$	−20.7596	+	307.870i	−0.0387170	+	0.574185i
$67$	−110.806	+	29.6904i	−0.202046	+	0.0541382i	−0.358423	−	0.933559i	$-0.616685\pi$
$67$	−110.806	+	29.6904i	−0.202046	+	0.0541382i	0.156376	+	0.987698i	$0.450019\pi$
$68$	−214.863	+	57.5724i	−0.383176	+	0.102672i
$69$	−36.8879	+	547.058i	−0.0643592	+	0.954465i
$70$		0			0
$71$		−	921.281i		−	1.53994i	−0.638079	−	0.769971i	$-0.720271\pi$
$71$		−	921.281i		−	1.53994i	0.638079	−	0.769971i	$-0.279729\pi$
$72$	75.2138	+	588.372i	0.123111	+	0.963060i
$73$	−373.434	+	373.434i	−0.598729	+	0.598729i	−0.939974	−	0.341246i	$-0.889151\pi$
$73$	−373.434	+	373.434i	−0.598729	+	0.598729i	0.341246	+	0.939974i	$0.389151\pi$
$74$	88.1187	+	152.626i	0.138427	+	0.239762i
$75$		0			0
$76$	−46.5016	+	80.5432i	−0.0701856	+	0.121565i
$77$	−291.966	−	1089.63i	−0.432111	−	1.61266i
$78$	453.200	+	154.791i	0.657883	+	0.224700i
$79$	492.922	−	284.589i	0.702000	−	0.405300i	−0.106092	−	0.994356i	$-0.533834\pi$
$79$	492.922	−	284.589i	0.702000	−	0.405300i	0.808092	+	0.589056i	$0.200500\pi$
$80$		0			0
$81$	183.385	+	705.557i	0.251556	+	0.967843i
$82$	−171.723	−	171.723i	−0.231264	−	0.231264i
$83$	−117.674	+	439.165i	−0.155619	+	0.580779i	0.843432	+	0.537235i	$0.180531\pi$
$83$	−117.674	+	439.165i	−0.155619	+	0.580779i	−0.999052	+	0.0435432i	$0.986135\pi$
$84$	−378.640	−	771.455i	−0.491822	−	1.00205i
$85$		0			0
$86$	−781.941	−	451.454i	−0.980452	−	0.566065i
$87$	271.006	−	53.3777i	0.333965	−	0.0657780i
$88$	760.121	+	203.674i	0.920786	+	0.246724i
$89$	148.257			0.176575			0.0882874	−	0.996095i	$-0.471861\pi$
$89$	148.257			0.176575			0.0882874	+	0.996095i	$0.471861\pi$
$90$		0			0
$91$	−1750.79			−2.01684
$92$	535.269	+	143.425i	0.606583	+	0.162533i
$93$	130.605	+	149.492i	0.145625	+	0.166683i
$94$	−239.720	−	138.402i	−0.263034	−	0.151863i
$95$		0			0
$96$	959.224	+	64.6801i	1.01980	+	0.0687644i
$97$	−83.7049	+	312.391i	−0.0876180	+	0.326995i	−0.995797	−	0.0915871i	$-0.970806\pi$
$97$	−83.7049	+	312.391i	−0.0876180	+	0.326995i	0.908179	+	0.418582i	$0.137473\pi$
$98$	−760.526	−	760.526i	−0.783926	−	0.783926i
$99$	958.396	+	129.839i	0.972954	+	0.131811i
$100$		0			0
$101$	−225.111	+	129.968i	−0.221776	+	0.128043i	−0.606773	−	0.794875i	$-0.707536\pi$
$101$	−225.111	+	129.968i	−0.221776	+	0.128043i	0.384996	+	0.922918i	$0.374203\pi$
$102$	−70.5121	−	358.000i	−0.0684484	−	0.347523i
$103$	304.307	+	1135.69i	0.291109	+	1.08643i	0.944259	+	0.329205i	$0.106781\pi$
$103$	304.307	+	1135.69i	0.291109	+	1.08643i	−0.653149	+	0.757229i	$0.726553\pi$
$104$	610.670	−	1057.71i	0.575780	−	0.997280i
$105$		0			0
$106$	−200.160	−	346.687i	−0.183408	−	0.317671i
$107$	832.828	−	832.828i	0.752453	−	0.752453i	−0.222483	−	0.974937i	$-0.571416\pi$
$107$	832.828	−	832.828i	0.752453	−	0.752453i	0.974937	+	0.222483i	$0.0714162\pi$
$108$	735.461	−	44.0451i	0.655276	−	0.0392430i
$109$		−	494.550i		−	0.434581i	−0.976107	−	0.217290i	$-0.930278\pi$
$109$		−	494.550i		−	0.434581i	0.976107	−	0.217290i	$-0.0697219\pi$
$110$		0			0
$111$	495.874	−	243.382i	0.424021	−	0.208115i
$112$	−170.107	+	45.5800i	−0.143514	+	0.0384545i
$113$	1593.14	−	426.881i	1.32629	−	0.355377i	0.474957	−	0.880009i	$-0.342464\pi$
$113$	1593.14	−	426.881i	1.32629	−	0.355377i	0.851329	+	0.524632i	$0.175797\pi$
$114$	−126.686	−	84.9935i	−0.104081	−	0.0698278i
$115$		0			0
$116$		−	279.160i		−	0.223443i
$117$	579.627	−	1384.61i	0.458004	−	1.09408i
$118$	−65.7698	+	65.7698i	−0.0513102	+	0.0513102i
$119$	666.962	+	1155.21i	0.513784	+	0.889900i
$120$		0			0
$121$	−23.9492	+	41.4813i	−0.0179934	+	0.0311655i
$122$	160.719	+	599.813i	0.119269	+	0.445119i
$123$	−573.225	+	500.804i	−0.420211	+	0.367122i
$124$	173.747	−	100.313i	0.125830	−	0.0726482i
$125$		0			0
$126$	1304.36	−	534.552i	0.922232	−	0.377950i
$127$	−944.231	−	944.231i	−0.659740	−	0.659740i	0.295579	−	0.955318i	$-0.404488\pi$
$127$	−944.231	−	944.231i	−0.659740	−	0.659740i	−0.955318	+	0.295579i	$0.904488\pi$
$128$	270.680	−	1010.19i	0.186914	−	0.697571i
$129$	−1576.68	+	2350.10i	−1.07611	+	1.60399i
$130$		0			0
$131$	1480.35	+	854.679i	0.987317	+	0.570028i	0.904471	−	0.426535i	$-0.140266\pi$
$131$	1480.35	+	854.679i	0.987317	+	0.570028i	0.0828457	+	0.996562i	$0.473599\pi$
$132$	315.935	−	925.005i	0.208323	−	0.609935i
$133$	538.711	+	144.347i	0.351219	+	0.0941089i
$134$	−190.178			−0.122603
$135$		0			0
$136$	−930.539			−0.586714
$137$	1380.02	+	369.776i	0.860608	+	0.230599i	0.662022	−	0.749484i	$-0.269698\pi$
$137$	1380.02	+	369.776i	0.860608	+	0.230599i	0.198586	+	0.980083i	$0.436365\pi$
$138$	−293.801	+	860.199i	−0.181232	+	0.530616i
$139$	−304.149	−	175.600i	−0.185594	−	0.107153i	0.404324	−	0.914616i	$-0.367507\pi$
$139$	−304.149	−	175.600i	−0.185594	−	0.107153i	−0.589918	+	0.807463i	$0.700840\pi$
$140$		0			0
$141$	−483.362	+	720.469i	−0.288698	+	0.430315i
$142$	395.301	−	1475.28i	0.233612	−	0.871853i
$143$	−1408.13	−	1408.13i	−0.823454	−	0.823454i
$144$	20.2697	−	149.619i	0.0117301	−	0.0865852i
$145$		0			0
$146$	−758.228	+	437.763i	−0.429804	+	0.248148i
$147$	−2538.69	+	2217.95i	−1.42441	+	1.24445i
$148$	−144.493	−	539.254i	−0.0802515	−	0.299503i
$149$	817.396	−	1415.77i	0.449421	−	0.778419i	−0.548928	−	0.835870i	$-0.684964\pi$
$149$	817.396	−	1415.77i	0.449421	−	0.778419i	0.998348	+	0.0574504i	$0.0182971\pi$
$150$		0			0
$151$	−238.948	−	413.869i	−0.128777	−	0.223048i	0.794426	−	0.607361i	$-0.207772\pi$
$151$	−238.948	−	413.869i	−0.128777	−	0.223048i	−0.923203	+	0.384313i	$0.874438\pi$
$152$	−275.106	+	275.106i	−0.146803	+	0.146803i
$153$	−1134.41	+	145.016i	−0.599423	+	0.0766263i
$154$		−	1870.15i		−	0.978576i
$155$		0			0
$156$	−1259.80	−	845.198i	−0.646569	−	0.433782i
$157$	−1668.57	+	447.091i	−0.848192	+	0.227272i	−0.656634	−	0.754209i	$-0.728020\pi$
$157$	−1668.57	+	447.091i	−0.848192	+	0.227272i	−0.191557	+	0.981481i	$0.561354\pi$
$158$	911.447	−	244.221i	0.458929	−	0.122970i
$159$	−1126.37	+	552.836i	−0.561804	+	0.275741i
$160$		0			0
$161$		−	3323.09i		−	1.62668i
$162$	−9.07787	+	1208.52i	−0.00440262	+	0.586115i
$163$	−2222.14	+	2222.14i	−1.06780	+	1.06780i	−0.0702721	+	0.997528i	$0.522387\pi$
$163$	−2222.14	+	2222.14i	−1.06780	+	1.06780i	−0.997528	+	0.0702721i	$0.977613\pi$
$164$	384.650	+	666.234i	0.183147	+	0.317220i
$165$		0			0
$166$	−376.872	+	652.762i	−0.176211	+	0.305206i
$167$	436.939	+	1630.68i	0.202463	+	0.755603i	0.990208	+	0.139601i	$0.0445821\pi$
$167$	436.939	+	1630.68i	0.202463	+	0.755603i	−0.787744	+	0.616002i	$0.788751\pi$
$168$	−694.721	−	3527.20i	−0.319041	−	1.61982i
$169$	−773.962	+	446.847i	−0.352281	+	0.203390i
$170$		0			0
$171$	−292.506	+	378.252i	−0.130810	+	0.169156i
$172$	2022.46	+	2022.46i	0.896576	+	0.896576i
$173$	−706.777	+	2637.73i	−0.310609	+	1.15921i	0.617400	+	0.786649i	$0.288186\pi$
$173$	−706.777	+	2637.73i	−0.310609	+	1.15921i	−0.928009	+	0.372558i	$0.878481\pi$
$174$	456.877	+	30.8070i	0.199056	+	0.0134223i
$175$		0			0
$176$	−173.474	−	100.155i	−0.0742959	−	0.0428948i
$177$	191.807	+	219.544i	0.0814526	+	0.0932315i
$178$	237.409	+	63.6136i	0.0999696	+	0.0267868i
$179$	−484.184			−0.202177			−0.101088	−	0.994877i	$-0.532232\pi$
$179$	−484.184			−0.202177			−0.101088	+	0.994877i	$0.532232\pi$
$180$		0			0
$181$	2651.62			1.08891			0.544456	−	0.838789i	$-0.316736\pi$
$181$	2651.62			1.08891			0.544456	+	0.838789i	$0.316736\pi$
$182$	−2803.61	−	751.224i	−1.14185	−	0.305958i
$183$	1909.63	−	376.123i	0.771388	−	0.151933i
$184$	2007.59	+	1159.08i	0.804357	+	0.464396i
$185$		0			0
$186$	144.999	+	295.427i	0.0571606	+	0.116461i
$187$	−392.693	+	1465.55i	−0.153564	+	0.573110i
$188$	620.026	+	620.026i	0.240532	+	0.240532i
$189$	−1396.61	−	4191.71i	−0.537505	−	1.61324i
$190$		0			0
$191$	785.170	−	453.318i	0.297450	−	0.171733i	−0.343847	−	0.939026i	$-0.611730\pi$
$191$	785.170	−	453.318i	0.297450	−	0.171733i	0.641297	+	0.767293i	$0.278397\pi$
$192$	1288.31	+	440.022i	0.484249	+	0.165395i
$193$	−702.651	−	2622.33i	−0.262062	−	0.978028i	−0.964024	−	0.265814i	$-0.914359\pi$
$193$	−702.651	−	2622.33i	−0.262062	−	0.978028i	0.701963	−	0.712214i	$-0.252307\pi$
$194$	−268.080	+	464.328i	−0.0992115	+	0.171839i
$195$		0			0
$196$	1703.53	+	2950.61i	0.620821	+	1.07529i
$197$	749.196	−	749.196i	0.270954	−	0.270954i	−0.558530	−	0.829484i	$-0.688634\pi$
$197$	749.196	−	749.196i	0.270954	−	0.270954i	0.829484	+	0.558530i	$0.188634\pi$
$198$	1479.01	+	619.143i	0.530851	+	0.222225i
$199$			4679.84i			1.66706i	0.552473	+	0.833531i	$0.313684\pi$
$199$			4679.84i			1.66706i	−0.552473	+	0.833531i	$0.686316\pi$
$200$		0			0
$201$	−40.1021	+	594.725i	−0.0140726	+	0.208700i
$202$	−416.247	+	111.533i	−0.144985	+	0.0388487i
$203$	−1617.00	+	433.275i	−0.559071	+	0.149803i
$204$	−77.7616	+	1153.23i	−0.0266882	+	0.395794i
$205$		0			0
$206$			1949.20i			0.659257i
$207$	2628.07	+	1100.16i	0.882432	+	0.369404i
$208$	−219.830	+	219.830i	−0.0732809	+	0.0732809i
$209$	317.181	+	549.374i	0.104975	+	0.181823i
$210$		0			0
$211$	−2264.65	+	3922.50i	−0.738887	+	1.27979i	0.214109	+	0.976810i	$0.431315\pi$
$211$	−2264.65	+	3922.50i	−0.738887	+	1.27979i	−0.952997	+	0.302981i	$0.902018\pi$
$212$	328.212	+	1224.90i	0.106329	+	0.396824i
$213$	−4530.17	−	1547.28i	−1.45729	−	0.497736i
$214$	1690.99	−	976.293i	0.540157	−	0.311860i
$215$		0			0
$216$	3019.49	+	618.318i	0.951160	+	0.194774i
$217$	−850.718	−	850.718i	−0.266131	−	0.266131i
$218$	212.201	−	791.944i	0.0659268	−	0.246042i
$219$	1209.09	+	2463.45i	0.373072	+	0.760111i
$220$		0			0
$221$	2039.32	+	1177.40i	0.620721	+	0.358373i
$222$	898.494	−	176.968i	0.271635	−	0.0535015i
$223$	304.776	+	81.6646i	0.0915217	+	0.0245232i	0.304289	−	0.952580i	$-0.401581\pi$
$223$	304.776	+	81.6646i	0.0915217	+	0.0245232i	−0.212768	+	0.977103i	$0.568248\pi$
$224$	−5826.77			−1.73803
$225$		0			0
$226$	2734.33			0.804801
$227$	−4521.76	−	1211.60i	−1.32211	−	0.354259i	−0.472343	−	0.881415i	$-0.656592\pi$
$227$	−4521.76	−	1211.60i	−1.32211	−	0.354259i	−0.849769	+	0.527156i	$0.823258\pi$
$228$	317.952	+	363.931i	0.0923548	+	0.105710i
$229$	−3088.47	−	1783.13i	−0.891231	−	0.514552i	−0.0168860	−	0.999857i	$-0.505375\pi$
$229$	−3088.47	−	1783.13i	−0.891231	−	0.514552i	−0.874345	+	0.485305i	$0.838709\pi$
$230$		0			0
$231$	−5848.34	−	394.351i	−1.66577	−	0.112322i
$232$	302.250	−	1128.01i	0.0855332	−	0.319214i
$233$	−32.0022	−	32.0022i	−0.00899801	−	0.00899801i	0.702593	−	0.711591i	$-0.252025\pi$
$233$	−32.0022	−	32.0022i	−0.00899801	−	0.00899801i	−0.711591	+	0.702593i	$0.752025\pi$
$234$	1522.29	−	1968.53i	0.425278	−	0.549944i
$235$		0			0
$236$	255.166	−	147.320i	0.0703810	−	0.0406345i
$237$	−571.538	−	2901.78i	−0.156647	−	0.795320i
$238$	572.358	+	2136.07i	0.155884	+	0.581768i
$239$	171.781	−	297.534i	0.0464921	−	0.0805267i	−0.841843	−	0.539723i	$-0.818529\pi$
$239$	171.781	−	297.534i	0.0464921	−	0.0805267i	0.888335	+	0.459196i	$0.151862\pi$
$240$		0			0
$241$	−2279.51	−	3948.22i	−0.609277	−	1.05530i	−0.991360	−	0.131171i	$-0.958126\pi$
$241$	−2279.51	−	3948.22i	−0.609277	−	1.05530i	0.382082	−	0.924128i	$-0.375207\pi$
$242$	−56.1496	+	56.1496i	−0.0149150	+	0.0149150i
$243$	3777.39	+	283.226i	0.997201	+	0.0747692i
$244$		−	1967.09i		−	0.516106i
$245$		0			0
$246$	−1132.81	+	556.000i	−0.293600	+	0.144103i
$247$	950.996	−	254.819i	0.244981	−	0.0656426i
$248$	810.677	−	217.220i	0.207573	−	0.0556189i
$249$	1961.85	+	1316.20i	0.499306	+	0.334984i
$250$		0			0
$251$			6166.99i			1.55083i	0.631455	+	0.775413i	$0.282458\pi$
$251$			6166.99i			1.55083i	−0.631455	+	0.775413i	$0.717542\pi$
$252$	−4429.35	+	566.220i	−1.10723	+	0.141542i
$253$	2672.71	−	2672.71i	0.664158	−	0.664158i
$254$	−1106.89	−	1917.18i	−0.273434	−	0.473602i
$255$		0			0
$256$	1914.90	−	3316.70i	0.467504	−	0.809740i
$257$	1495.68	+	5581.97i	0.363028	+	1.35484i	0.870075	+	0.492920i	$0.164071\pi$
$257$	1495.68	+	5581.97i	0.363028	+	1.35484i	−0.507047	+	0.861919i	$0.669263\pi$
$258$	−3533.17	+	3086.79i	−0.852580	+	0.744865i
$259$	−2899.30	+	1673.91i	−0.695575	+	0.401590i
$260$		0			0
$261$	192.680	−	1422.25i	0.0456957	−	0.337300i
$262$	2003.82	+	2003.82i	0.472505	+	0.472505i
$263$	−639.642	+	2387.18i	−0.149970	+	0.559694i	0.849514	+	0.527566i	$0.176895\pi$
$263$	−639.642	+	2387.18i	−0.149970	+	0.559694i	−0.999484	+	0.0321282i	$0.989772\pi$
$264$	2278.13	−	3395.64i	0.531095	−	0.791617i
$265$		0			0
$266$	800.723	+	462.298i	0.184570	+	0.106561i
$267$	248.995	−	729.014i	0.0570720	−	0.167097i
$268$	581.909	+	155.922i	0.132633	+	0.0355390i
$269$	5983.06			1.35611			0.678055	−	0.735012i	$-0.262823\pi$
$269$	5983.06			1.35611			0.678055	+	0.735012i	$0.262823\pi$
$270$		0			0
$271$	228.531			0.0512260			0.0256130	−	0.999672i	$-0.491846\pi$
$271$	228.531			0.0512260			0.0256130	+	0.999672i	$0.491846\pi$
$272$	228.793	+	61.3049i	0.0510023	+	0.0136660i
$273$	−2940.42	+	8609.05i	−0.651876	+	1.90858i
$274$	2051.22	+	1184.28i	0.452259	+	0.261112i
$275$		0			0
$276$	1604.23	−	2391.17i	0.349867	−	0.521491i
$277$	−877.084	+	3273.32i	−0.190249	+	0.710017i	0.803197	+	0.595713i	$0.203131\pi$
$277$	−877.084	+	3273.32i	−0.190249	+	0.710017i	−0.993446	+	0.114304i	$0.963536\pi$
$278$	−411.700	−	411.700i	−0.0888206	−	0.0888206i
$279$	954.436	−	391.147i	0.204805	−	0.0839332i
$280$		0			0
$281$	−7217.53	+	4167.04i	−1.53225	+	0.884644i	−0.532990	+	0.846122i	$0.678932\pi$
$281$	−7217.53	+	4167.04i	−1.53225	+	0.884644i	−0.999258	+	0.0385220i	$0.987735\pi$
$282$	−1083.16	+	946.317i	−0.228729	+	0.199831i
$283$	−2149.82	−	8023.23i	−0.451567	−	1.68527i	−0.697990	−	0.716107i	$-0.745922\pi$
$283$	−2149.82	−	8023.23i	−0.451567	−	1.68527i	0.246423	−	0.969162i	$-0.420745\pi$
$284$	−2419.10	+	4190.00i	−0.505447	+	0.875461i
$285$		0			0
$286$	−1650.70	−	2859.10i	−0.341287	−	0.591126i
$287$	3262.08	−	3262.08i	0.670921	−	0.670921i
$288$	1929.05	−	4608.11i	0.394689	−	0.942832i
$289$			3118.88i			0.634821i
$290$		0			0
$291$	1395.52	+	936.254i	0.281124	+	0.188605i
$292$	2678.95	−	717.822i	0.536896	−	0.143861i
$293$	8898.62	−	2384.38i	1.77428	−	0.475416i	0.784755	−	0.619806i	$-0.212789\pi$
$293$	8898.62	−	2384.38i	1.77428	−	0.475416i	0.989521	+	0.144390i	$0.0461221\pi$
$294$	−5016.99	+	2462.40i	−0.995227	+	0.488470i
$295$		0			0
$296$		−	2335.43i		−	0.458594i
$297$	2248.06	−	4494.61i	0.439211	−	0.878127i
$298$	1916.41	−	1916.41i	0.372532	−	0.372532i
$299$	−2933.15	−	5080.37i	−0.567320	−	0.982627i
$300$		0			0
$301$	8575.88	−	14853.9i	1.64221	−	2.84439i
$302$	−205.054	−	765.273i	−0.0390714	−	0.145816i
$303$	261.014	+	1325.21i	0.0494881	+	0.251258i
$304$	85.7651	−	49.5165i	0.0161808	−	0.00934199i
$305$		0			0
$306$	−1878.80	−	254.531i	−0.350993	−	0.0475509i
$307$	1803.17	+	1803.17i	0.335219	+	0.335219i	0.854564	−	0.519346i	$-0.173824\pi$
$307$	1803.17	+	1803.17i	0.335219	+	0.335219i	−0.519346	+	0.854564i	$0.673824\pi$
$308$	−1533.29	+	5722.30i	−0.283659	+	1.05863i
$309$	6095.54	+	411.020i	1.12221	+	0.0756702i
$310$		0			0
$311$	−250.629	−	144.701i	−0.0456974	−	0.0263834i	0.476977	−	0.878916i	$-0.341732\pi$
$311$	−250.629	−	144.701i	−0.0456974	−	0.0263834i	−0.522675	+	0.852532i	$0.675066\pi$
$312$	−4175.42	−	4779.22i	−0.757649	−	0.867213i
$313$	−1884.83	−	505.039i	−0.340373	−	0.0912028i	0.0845834	−	0.996416i	$-0.473044\pi$
$313$	−1884.83	−	505.039i	−0.340373	−	0.0912028i	−0.424957	+	0.905214i	$0.639711\pi$
$314$	−2863.78			−0.514690
$315$		0			0
$316$	−2989.09			−0.532118
$317$	−4329.75	−	1160.15i	−0.767139	−	0.205554i	−0.146032	−	0.989280i	$-0.546650\pi$
$317$	−4329.75	−	1160.15i	−0.767139	−	0.205554i	−0.621107	+	0.783726i	$0.713317\pi$
$318$	−2040.91	+	401.979i	−0.359901	+	0.0708864i
$319$	−1649.01	−	952.056i	−0.289426	−	0.167100i
$320$		0			0
$321$	−2696.50	−	5493.94i	−0.468860	−	0.955271i
$322$	1425.86	−	5321.40i	0.246771	−	0.920962i
$323$	−530.418	−	530.418i	−0.0913722	−	0.0913722i
$324$	1018.62	−	3690.42i	0.174660	−	0.632788i
$325$		0			0
$326$	−4511.87	+	2604.93i	−0.766533	+	0.442558i
$327$	−2431.83	−	830.590i	−0.411255	−	0.140464i
$328$	832.931	+	3108.54i	0.140216	+	0.523294i
$329$	2629.11	−	4553.75i	0.440570	−	0.763089i
$330$		0			0
$331$	4301.37	+	7450.20i	0.714274	+	1.23716i	0.963239	+	0.268647i	$0.0865765\pi$
$331$	4301.37	+	7450.20i	0.714274	+	1.23716i	−0.248964	+	0.968513i	$0.580090\pi$
$332$	1688.34	−	1688.34i	0.279096	−	0.279096i
$333$	−363.954	−	2847.09i	−0.0598936	−	0.468528i
$334$			2798.76i			0.458506i
$335$		0			0
$336$	−61.5638	+	913.008i	−0.00999577	+	0.148240i
$337$	6513.21	−	1745.21i	1.05281	−	0.282100i	0.309397	−	0.950933i	$-0.399873\pi$
$337$	6513.21	−	1745.21i	1.05281	−	0.282100i	0.743412	+	0.668833i	$0.233206\pi$
$338$	−1431.11	+	383.465i	−0.230302	+	0.0617093i
$339$	576.579	−	8550.82i	0.0923760	−	1.36996i
$340$		0			0
$341$		−	1368.44i		−	0.217317i
$342$	−630.702	+	480.202i	−0.0997206	+	0.0759250i
$343$	6808.97	−	6808.97i	1.07187	−	1.07187i
$344$	5982.49	+	10362.0i	0.937657	+	1.62407i
$345$		0			0
$346$	−2263.58	+	3920.64i	−0.351708	+	0.609176i
$347$	−3049.05	−	11379.2i	−0.471705	−	1.76043i	−0.633643	−	0.773626i	$-0.718441\pi$
$347$	−3049.05	−	11379.2i	−0.471705	−	1.76043i	0.161938	−	0.986801i	$-0.448226\pi$
$348$	−1372.70	−	468.846i	−0.211450	−	0.0722206i
$349$	6061.28	−	3499.48i	0.929664	−	0.536742i	0.0429588	−	0.999077i	$-0.486322\pi$
$349$	6061.28	−	3499.48i	0.929664	−	0.536742i	0.886705	+	0.462335i	$0.152988\pi$
$350$		0			0
$351$	−5835.00	−	5175.60i	−0.887320	−	0.787046i
$352$	−4686.39	−	4686.39i	−0.709618	−	0.709618i
$353$	−1840.87	+	6870.23i	−0.277563	+	1.03588i	0.676541	+	0.736405i	$0.263478\pi$
$353$	−1840.87	+	6870.23i	−0.277563	+	1.03588i	−0.954104	+	0.299475i	$0.903189\pi$
$354$	212.947	+	433.866i	0.0319718	+	0.0651404i
$355$		0			0
$356$	−674.273	−	389.292i	−0.100383	−	0.0579563i
$357$	6800.62	−	1339.46i	1.00820	−	0.198576i
$358$	−775.344	−	207.753i	−0.114464	−	0.0306706i
$359$	−10744.0			−1.57951			−0.789755	−	0.613422i	$-0.789792\pi$
$359$	−10744.0			−1.57951			−0.789755	+	0.613422i	$0.789792\pi$
$360$		0			0
$361$	6545.37			0.954275
$362$	4246.15	+	1137.75i	0.616498	+	0.165190i
$363$	163.751	+	187.432i	0.0236769	+	0.0271009i
$364$	7962.60	+	4597.21i	1.14658	+	0.661976i
$365$		0			0
$366$	3219.36	+	217.080i	0.459777	+	0.0310026i
$367$	−533.504	+	1991.06i	−0.0758820	+	0.283195i	−0.993432	−	0.114425i	$-0.963497\pi$
$367$	−533.504	+	1991.06i	−0.0758820	+	0.283195i	0.917550	+	0.397621i	$0.130164\pi$
$368$	−417.248	−	417.248i	−0.0591048	−	0.0591048i
$369$	1499.85	+	3659.78i	0.211597	+	0.516316i
$370$		0			0
$371$	6585.70	−	3802.25i	0.921597	−	0.532084i
$372$	−201.458	−	1022.83i	−0.0280783	−	0.142557i
$373$	2043.27	+	7625.58i	0.283637	+	1.05855i	0.949830	+	0.312767i	$0.101256\pi$
$373$	2043.27	+	7625.58i	0.283637	+	1.05855i	−0.666193	+	0.745779i	$0.732077\pi$
$374$	−1257.67	+	2178.35i	−0.173884	+	0.301176i
$375$		0			0
$376$	1834.05	+	3176.67i	0.251553	+	0.435703i
$377$	−2089.66	+	2089.66i	−0.285472	+	0.285472i
$378$	−437.876	−	7311.61i	−0.0595818	−	0.994891i
$379$		−	7547.27i		−	1.02289i	−0.859315	−	0.511447i	$-0.829110\pi$
$379$		−	7547.27i		−	1.02289i	0.859315	−	0.511447i	$-0.170890\pi$
$380$		0			0
$381$	−6228.84	+	3057.20i	−0.837567	+	0.411089i
$382$	1451.83	−	389.018i	0.194456	−	0.0521044i
$383$	5392.00	−	1444.78i	0.719369	−	0.192754i	0.119479	−	0.992837i	$-0.461878\pi$
$383$	5392.00	−	1444.78i	0.719369	−	0.192754i	0.599890	+	0.800082i	$0.295211\pi$
$384$	−4512.76	−	3027.60i	−0.599715	−	0.402348i
$385$		0			0
$386$		−	4500.74i		−	0.593475i
$387$	8908.00	+	11699.9i	1.17008	+	1.53679i
$388$	1200.97	−	1200.97i	0.157139	−	0.157139i
$389$	3919.49	+	6788.76i	0.510864	+	0.884842i	0.999921	+	0.0125902i	$0.00400769\pi$
$389$	3919.49	+	6788.76i	0.510864	+	0.884842i	−0.489057	+	0.872252i	$0.662659\pi$
$390$		0			0
$391$	−2234.77	+	3870.74i	−0.289047	+	0.500643i
$392$	3688.87	+	13767.1i	0.475297	+	1.77383i
$393$	6688.89	−	5843.81i	0.858549	−	0.750080i
$394$	1521.18	−	878.255i	0.194508	−	0.112299i
$395$		0			0
$396$	−4017.87	−	3107.06i	−0.509863	−	0.394283i
$397$	−488.460	−	488.460i	−0.0617509	−	0.0617509i	0.675557	−	0.737308i	$-0.263903\pi$
$397$	−488.460	−	488.460i	−0.0617509	−	0.0617509i	−0.737308	+	0.675557i	$0.763903\pi$
$398$	−2008.02	+	7494.03i	−0.252897	+	0.943823i
$399$	1614.55	−	2406.55i	0.202578	−	0.301950i
$400$		0			0
$401$	7854.07	+	4534.55i	0.978088	+	0.564699i	0.901692	−	0.432378i	$-0.142325\pi$
$401$	7854.07	+	4534.55i	0.978088	+	0.564699i	0.0763957	+	0.997078i	$0.475659\pi$
$402$	−319.401	+	935.151i	−0.0396275	+	0.116023i
$403$	−2051.48	−	549.693i	−0.253577	−	0.0679458i
$404$	1365.08			0.168107
$405$		0			0
$406$	−2775.28			−0.339249
$407$	−3678.17	−	985.563i	−0.447961	−	0.120031i
$408$	−1562.83	+	4575.69i	−0.189636	+	0.555222i
$409$	−1057.59	−	610.597i	−0.127859	−	0.0738193i	0.434706	−	0.900572i	$-0.356852\pi$
$409$	−1057.59	−	610.597i	−0.127859	−	0.0738193i	−0.562565	+	0.826753i	$0.690185\pi$
$410$		0			0
$411$	4136.01	−	6164.88i	0.496385	−	0.739881i
$412$	1598.10	−	5964.18i	0.191098	−	0.713189i
$413$	−1249.37	−	1249.37i	−0.148856	−	0.148856i
$414$	3736.38	+	2889.38i	0.443558	+	0.343008i
$415$		0			0
$416$	−8908.03	+	5143.06i	−1.04989	+	0.606152i
$417$	−1374.28	+	1200.66i	−0.161389	+	0.140999i
$418$	272.191	+	1015.83i	0.0318500	+	0.118866i
$419$	8196.06	−	14196.0i	0.955618	−	1.65518i	0.222670	−	0.974894i	$-0.428523\pi$
$419$	8196.06	−	14196.0i	0.955618	−	1.65518i	0.732948	−	0.680285i	$-0.238144\pi$
$420$		0			0
$421$	−815.167	−	1411.91i	−0.0943677	−	0.163450i	0.814977	−	0.579494i	$-0.196750\pi$
$421$	−815.167	−	1411.91i	−0.0943677	−	0.163450i	−0.909345	+	0.416044i	$0.863416\pi$
$422$	−5309.54	+	5309.54i	−0.612475	+	0.612475i
$423$	2730.93	+	3586.83i	0.313906	+	0.412287i
$424$			5304.87i			0.607611i
$425$		0			0
$426$	−6590.44	−	4421.51i	−0.749549	−	0.502871i
$427$	−11394.1	+	3053.05i	−1.29134	+	0.346012i
$428$	−5974.55	+	1600.88i	−0.674745	+	0.180797i
$429$	−9289.08	+	4559.20i	−1.04541	+	0.513101i
$430$		0			0
$431$			9676.25i			1.08141i	0.841212	+	0.540706i	$0.181843\pi$
$431$			9676.25i			1.08141i	−0.841212	+	0.540706i	$0.818157\pi$
$432$	−701.672	−	350.954i	−0.0781463	−	0.0390863i
$433$	−6547.86	+	6547.86i	−0.726720	+	0.726720i	−0.969965	−	0.243245i	$-0.921788\pi$
$433$	−6547.86	+	6547.86i	−0.726720	+	0.726720i	0.243245	+	0.969965i	$0.421788\pi$
$434$	−997.265	−	1727.31i	−0.110300	−	0.191045i
$435$		0			0
$436$	−1298.59	+	2249.22i	−0.142640	+	0.247060i
$437$	483.660	+	1805.04i	0.0529441	+	0.197590i
$438$	879.158	+	4463.61i	0.0959082	+	0.486940i
$439$	−14231.6	+	8216.60i	−1.54723	+	0.893296i	−0.548882	+	0.835900i	$0.684946\pi$
$439$	−14231.6	+	8216.60i	−1.54723	+	0.893296i	−0.998352	+	0.0573956i	$0.981720\pi$
$440$		0			0
$441$	6642.53	+	16208.4i	0.717259	+	1.75018i
$442$	2760.45	+	2760.45i	0.297061	+	0.297061i
$443$	1837.42	−	6857.35i	0.197062	−	0.735446i	−0.794661	−	0.607053i	$-0.792352\pi$
$443$	1837.42	−	6857.35i	0.197062	−	0.735446i	0.991723	−	0.128393i	$-0.0409818\pi$
$444$	−2894.32	−	195.163i	−0.309365	−	0.0208604i
$445$		0			0
$446$	453.010	+	261.546i	0.0480957	+	0.0277680i
$447$	−5588.89	−	6397.11i	−0.591377	−	0.676896i
$448$	−7969.80	−	2135.50i	−0.840486	−	0.225207i
$449$	−15813.2			−1.66207			−0.831037	−	0.556218i	$-0.812252\pi$
$449$	−15813.2			−1.66207			−0.831037	+	0.556218i	$0.812252\pi$
$450$		0			0
$451$	5247.29			0.547861
$452$	−8366.55	−	2241.81i	−0.870640	−	0.233287i
$453$	−2436.41	+	479.877i	−0.252698	+	0.0497717i
$454$	−6721.00	−	3880.37i	−0.694785	−	0.401134i
$455$		0			0
$456$	890.728	+	1814.80i	0.0914741	+	0.186373i
$457$	−3132.55	+	11690.9i	−0.320645	+	1.19666i	0.597973	+	0.801516i	$0.295973\pi$
$457$	−3132.55	+	11690.9i	−0.320645	+	1.19666i	−0.918618	+	0.395147i	$0.870694\pi$
$458$	−4180.59	−	4180.59i	−0.426520	−	0.426520i
$459$	−1192.15	+	5821.73i	−0.121230	+	0.592015i
$460$		0			0
$461$	8677.59	−	5010.01i	0.876693	−	0.506159i	0.00712658	−	0.999975i	$-0.497732\pi$
$461$	8677.59	−	5010.01i	0.876693	−	0.506159i	0.869567	+	0.493816i	$0.164398\pi$
$462$	−9195.97	−	3140.88i	−0.926051	−	0.316292i
$463$	−2331.25	−	8700.34i	−0.234001	−	0.873303i	−0.978597	−	0.205787i	$-0.934025\pi$
$463$	−2331.25	−	8700.34i	−0.234001	−	0.873303i	0.744596	−	0.667515i	$-0.232642\pi$
$464$	−148.630	+	257.434i	−0.0148706	+	0.0257566i
$465$		0			0
$466$	−37.5150	−	64.9780i	−0.00372929	−	0.00645933i
$467$	−2385.09	+	2385.09i	−0.236336	+	0.236336i	−0.815331	−	0.578995i	$-0.803445\pi$
$467$	−2385.09	+	2385.09i	−0.236336	+	0.236336i	0.578995	+	0.815331i	$0.303445\pi$
$468$	−6271.86	+	4775.25i	−0.619481	+	0.471659i
$469$		−	3612.64i		−	0.355685i
$470$		0			0
$471$	−603.875	+	8955.64i	−0.0590767	+	0.876123i
$472$	1190.57	−	319.011i	0.116102	−	0.0311095i
$473$	18844.2	−	5049.29i	1.83183	−	0.490838i
$474$	329.864	−	4891.98i	0.0319645	−	0.474042i
$475$		0			0
$476$		−	7005.24i		−	0.674547i
$477$	826.714	+	6467.11i	0.0793556	+	0.620773i
$478$	402.746	−	402.746i	0.0385380	−	0.0385380i
$479$	49.6552	+	86.0054i	0.00473654	+	0.00820394i	0.868384	−	0.495892i	$-0.165159\pi$
$479$	49.6552	+	86.0054i	0.00473654	+	0.00820394i	−0.863647	+	0.504096i	$0.831826\pi$
$480$		0			0
$481$	−2954.99	+	5118.19i	−0.280116	+	0.485176i
$482$	−1956.17	−	7300.53i	−0.184857	−	0.689897i
$483$	−16340.4	−	5581.08i	−1.53937	−	0.525772i
$484$	217.843	−	125.772i	0.0204586	−	0.0118118i
$485$		0			0
$486$	5927.37	+	2074.34i	0.553232	+	0.193609i
$487$	752.120	+	752.120i	0.0699831	+	0.0699831i	0.741232	−	0.671249i	$-0.234242\pi$
$487$	752.120	+	752.120i	0.0699831	+	0.0699831i	−0.671249	+	0.741232i	$0.734242\pi$
$488$	2129.79	−	7948.48i	0.197564	−	0.737317i
$489$	7194.76	+	14658.9i	0.665354	+	1.35562i
$490$		0			0
$491$	−3533.78	−	2040.23i	−0.324801	−	0.187524i	0.328729	−	0.944424i	$-0.393380\pi$
$491$	−3533.78	−	2040.23i	−0.324801	−	0.187524i	−0.653531	+	0.756900i	$0.726713\pi$
$492$	3922.05	−	772.491i	0.359390	−	0.0707857i
$493$	2174.86	+	582.753i	0.198684	+	0.0532371i
$494$	1632.21			0.148657
$495$		0			0
$496$	−213.633			−0.0193395
$497$	28024.7	+	7509.19i	2.52933	+	0.677733i
$498$	2576.84	+	2949.48i	0.231869	+	0.265400i
$499$	4377.28	+	2527.22i	0.392693	+	0.226722i	0.683326	−	0.730113i	$-0.260533\pi$
$499$	4377.28	+	2527.22i	0.392693	+	0.226722i	−0.290633	+	0.956835i	$0.593866\pi$
$500$		0			0
$501$	8752.29	+	590.163i	0.780486	+	0.0526279i
$502$	−2646.12	+	9875.46i	−0.235263	+	0.878014i
$503$	−4080.19	−	4080.19i	−0.361683	−	0.361683i	0.502749	−	0.864432i	$-0.332322\pi$
$503$	−4080.19	−	4080.19i	−0.361683	−	0.361683i	−0.864432	+	0.502749i	$0.832322\pi$
$504$	−18510.9	−	2507.77i	−1.63600	−	0.221637i
$505$		0			0
$506$	5426.73	−	3133.12i	0.476774	−	0.275265i
$507$	897.401	+	4556.24i	0.0786094	+	0.399112i
$508$	1815.02	+	6773.74i	0.158521	+	0.591607i
$509$	3668.96	−	6354.83i	0.319497	−	0.553385i	−0.660886	−	0.750486i	$-0.729819\pi$
$509$	3668.96	−	6354.83i	0.319497	−	0.553385i	0.980383	+	0.197101i	$0.0631528\pi$
$510$		0			0
$511$	−8315.80	−	14403.4i	−0.719901	−	1.24691i
$512$	−1426.57	+	1426.57i	−0.123137	+	0.123137i
$513$	1368.70	+	2073.59i	0.117796	+	0.178463i
$514$			9580.40i			0.822127i
$515$		0			0
$516$	13341.6	−	6548.25i	1.13824	−	0.558664i
$517$	5777.07	−	1547.96i	0.491441	−	0.131681i
$518$	−5361.01	+	1436.48i	−0.454728	+	0.121844i
$519$	11783.3	+	7905.43i	0.996592	+	0.668612i
$520$		0			0
$521$			4773.62i			0.401412i	0.979651	+	0.200706i	$0.0643237\pi$
$521$			4773.62i			0.401412i	−0.979651	+	0.200706i	$0.935676\pi$
$522$	918.804	−	2194.84i	0.0770401	−	0.184033i
$523$	−3198.98	+	3198.98i	−0.267460	+	0.267460i	−0.828076	−	0.560616i	$-0.810564\pi$
$523$	−3198.98	+	3198.98i	−0.267460	+	0.267460i	0.560616	+	0.828076i	$0.310564\pi$
$524$	−4488.43	−	7774.19i	−0.374195	−	0.648124i
$525$		0			0
$526$	−2048.57	+	3548.23i	−0.169813	+	0.294125i
$527$	418.811	+	1563.02i	0.0346180	+	0.129196i
$528$	−783.835	+	684.805i	−0.0646061	+	0.0564438i
$529$	−894.110	+	516.215i	−0.0734865	+	0.0424274i
$530$		0			0
$531$	1401.69	−	574.442i	0.114554	−	0.0469466i
$532$	−2071.04	−	2071.04i	−0.168780	−	0.168780i
$533$	2107.80	−	7866.40i	0.171292	−	0.639272i
$534$	711.529	−	1060.56i	0.0576608	−	0.0859457i
$535$		0			0
$536$	2182.52	+	1260.08i	0.175878	+	0.101543i
$537$	−813.181	+	2380.85i	−0.0653470	+	0.191325i
$538$	9580.91	+	2567.20i	0.767774	+	0.205724i
$539$	23239.1			1.85711
$540$		0			0
$541$	−24284.5			−1.92989			−0.964945	−	0.262452i	$-0.915469\pi$
$541$	−24284.5			−1.92989			−0.964945	+	0.262452i	$0.915469\pi$
$542$	365.955	+	98.0575i	0.0290021	+	0.00777109i
$543$	4453.35	−	13038.7i	0.351955	−	1.03047i
$544$	6787.03	+	3918.50i	0.534911	+	0.308831i
$545$		0			0
$546$	−8402.57	+	12524.4i	−0.658602	+	0.981672i
$547$	−1033.92	+	3858.66i	−0.0808180	+	0.301617i	−0.994489	−	0.104837i	$-0.966568\pi$
$547$	−1033.92	+	3858.66i	−0.0808180	+	0.301617i	0.913671	+	0.406454i	$0.133235\pi$
$548$	−5305.41	−	5305.41i	−0.413569	−	0.413569i
$549$	1357.71	−	10021.8i	0.105547	−	0.779091i
$550$		0			0
$551$	815.267	−	470.694i	0.0630336	−	0.0363925i
$552$	9071.23	−	7925.17i	0.699451	−	0.611083i
$553$	4639.26	+	17313.9i	0.356747	+	1.33140i
$554$	−2809.02	+	4865.37i	−0.215422	+	0.373122i
$555$		0			0
$556$	922.183	+	1597.27i	0.0703404	+	0.121833i
$557$	12226.1	−	12226.1i	0.930051	−	0.930051i	−0.0676576	−	0.997709i	$-0.521553\pi$
$557$	12226.1	−	12226.1i	0.930051	−	0.930051i	0.997709	+	0.0676576i	$0.0215526\pi$
$558$	1696.21	−	216.833i	0.128685	−	0.0164503i
$559$		−	30278.3i		−	2.29094i
$560$		0			0
$561$	6546.95	+	4392.34i	0.492714	+	0.330561i
$562$	−13345.7	+	3575.97i	−1.00170	+	0.268404i
$563$	−12639.6	+	3386.78i	−0.946176	+	0.253527i	−0.698739	−	0.715377i	$-0.746255\pi$
$563$	−12639.6	+	3386.78i	−0.946176	+	0.253527i	−0.247437	+	0.968904i	$0.579588\pi$
$564$	4090.15	−	2007.50i	0.305366	−	0.149877i
$565$		0			0
$566$		−	13770.4i		−	1.02264i
$567$	−22957.3	−	172.444i	−1.70038	−	0.0127724i
$568$	−14311.5	+	14311.5i	−1.05721	+	1.05721i
$569$	4163.99	+	7212.24i	0.306790	+	0.531376i	0.977658	−	0.210201i	$-0.0674117\pi$
$569$	4163.99	+	7212.24i	0.306790	+	0.531376i	−0.670868	+	0.741577i	$0.734078\pi$
$570$		0			0
$571$	−4453.29	+	7713.32i	−0.326382	+	0.565311i	−0.981791	−	0.189964i	$-0.939163\pi$
$571$	−4453.29	+	7713.32i	−0.326382	+	0.565311i	0.655409	+	0.755274i	$0.272496\pi$
$572$	2706.74	+	10101.7i	0.197857	+	0.738414i
$573$	−910.396	−	4622.22i	−0.0663741	−	0.336991i
$574$	6623.39	−	3824.01i	0.481629	−	0.278068i
$575$		0			0
$576$	4327.40	−	5595.93i	0.313035	−	0.404798i
$577$	−11134.8	−	11134.8i	−0.803374	−	0.803374i	0.180248	−	0.983621i	$-0.442310\pi$
$577$	−11134.8	−	11134.8i	−0.803374	−	0.803374i	−0.983621	+	0.180248i	$0.942310\pi$
$578$	−1338.24	+	4994.38i	−0.0963036	+	0.359410i
$579$	−14074.7	−	949.054i	−1.01023	−	0.0681198i
$580$		0			0
$581$	−12399.9	−	7159.11i	−0.885432	−	0.511205i
$582$	1832.98	+	2098.05i	0.130549	+	0.149428i
$583$	8354.89	+	2238.68i	0.593523	+	0.159034i
$584$	11602.1			0.822088
$585$		0			0
$586$	15272.8			1.07664
$587$	−16865.3	−	4519.05i	−1.18587	−	0.317753i	−0.388618	−	0.921399i	$-0.627048\pi$
$587$	−16865.3	−	4519.05i	−1.18587	−	0.317753i	−0.797253	+	0.603646i	$0.793714\pi$
$588$	17369.9	−	3421.20i	1.21824	−	0.239945i
$589$	585.913	+	338.277i	0.0409883	+	0.0236646i
$590$		0			0
$591$	−2425.72	−	4942.25i	−0.168834	−	0.343988i
$592$	−153.860	+	574.215i	−0.0106818	+	0.0398650i
$593$	−4464.48	−	4464.48i	−0.309164	−	0.309164i	0.535421	−	0.844585i	$-0.320153\pi$
$593$	−4464.48	−	4464.48i	−0.309164	−	0.309164i	−0.844585	+	0.535421i	$0.820153\pi$
$594$	5528.45	−	6232.81i	0.381877	−	0.430531i
$595$		0			0
$596$	−7435.06	+	4292.63i	−0.510993	+	0.295022i
$597$	23011.9	+	7859.73i	1.57758	+	0.538823i
$598$	−2517.10	−	9393.96i	−0.172127	−	0.642387i
$599$	−7836.14	+	13572.6i	−0.534517	+	0.925811i	0.464669	+	0.885484i	$0.346173\pi$
$599$	−7836.14	+	13572.6i	−0.534517	+	0.925811i	−0.999187	+	0.0403269i	$0.987160\pi$
$600$		0			0
$601$	−3405.59	−	5898.65i	−0.231143	−	0.400351i	0.727002	−	0.686635i	$-0.240913\pi$
$601$	−3405.59	−	5898.65i	−0.231143	−	0.400351i	−0.958145	+	0.286284i	$0.907580\pi$
$602$	20106.4	−	20106.4i	1.36125	−	1.36125i
$603$	2857.06	+	1196.02i	0.192949	+	0.0807726i
$604$			2509.71i			0.169071i
$605$		0			0
$606$	−150.645	+	2234.11i	−0.0100982	+	0.149760i
$607$	832.687	−	223.118i	0.0556800	−	0.0149194i	−0.230872	−	0.972984i	$-0.574158\pi$
$607$	832.687	−	223.118i	0.0556800	−	0.0149194i	0.286552	+	0.958065i	$0.407491\pi$
$608$	3165.00	−	848.059i	0.211115	−	0.0565680i
$609$	−585.214	+	8678.89i	−0.0389393	+	0.577481i
$610$		0			0
$611$		−	9282.42i		−	0.614610i
$612$	5540.10	+	2319.20i	0.365924	+	0.153183i
$613$	−2254.58	+	2254.58i	−0.148551	+	0.148551i	−0.777470	−	0.628920i	$-0.783497\pi$
$613$	−2254.58	+	2254.58i	−0.148551	+	0.148551i	0.628920	+	0.777470i	$0.283497\pi$
$614$	2113.79	+	3661.18i	0.138934	+	0.240641i
$615$		0			0
$616$	−12391.2	+	21462.2i	−0.810481	+	1.40379i
$617$	−5858.87	−	21865.6i	−0.382284	−	1.42670i	−0.842404	−	0.538847i	$-0.818860\pi$
$617$	−5858.87	−	21865.6i	−0.382284	−	1.42670i	0.460120	−	0.887857i	$-0.347806\pi$
$618$	9584.68	+	3273.65i	0.623871	+	0.213083i
$619$	−4224.11	+	2438.79i	−0.274283	+	0.158357i	−0.630832	−	0.775919i	$-0.717286\pi$
$619$	−4224.11	+	2438.79i	−0.274283	+	0.158357i	0.356549	+	0.934276i	$0.383953\pi$
$620$		0			0
$621$	9823.58	−	11075.2i	0.634793	−	0.715669i
$622$	−339.255	−	339.255i	−0.0218696	−	0.0218696i
$623$	−1208.41	+	4509.86i	−0.0777111	+	0.290022i
$624$	711.756	+	1450.16i	0.0456619	+	0.0930332i
$625$		0			0
$626$	−2801.55	−	1617.48i	−0.178870	−	0.103271i
$627$	3234.11	−	636.993i	0.205993	−	0.0405727i
$628$	8762.64	+	2347.94i	0.556795	+	0.149193i
$629$	4502.81			0.285436
$630$		0			0
$631$	3038.06			0.191669			0.0958346	−	0.995397i	$-0.469448\pi$
$631$	3038.06			0.191669			0.0958346	+	0.995397i	$0.469448\pi$
$632$	−12078.1	−	3236.32i	−0.760193	−	0.203693i
$633$	15484.4	+	17723.6i	0.972276	+	1.11288i
$634$	−6435.61	−	3715.60i	−0.403140	−	0.232753i
$635$		0			0
$636$	6574.38	+	443.308i	0.409891	+	0.0276388i
$637$	9334.98	−	34838.6i	0.580636	−	2.16696i
$638$	−2232.12	−	2232.12i	−0.138512	−	0.138512i
$639$	−15216.7	+	19677.3i	−0.942039	+	1.21819i
$640$		0			0
$641$	18662.9	−	10775.1i	1.14999	−	0.663946i	0.201104	−	0.979570i	$-0.435547\pi$
$641$	18662.9	−	10775.1i	1.14999	−	0.663946i	0.948884	+	0.315624i	$0.102214\pi$
$642$	−1960.68	−	9954.69i	−0.120533	−	0.611963i
$643$	−2193.22	−	8185.22i	−0.134514	−	0.502012i	−0.999999	−	0.00107824i	$-0.999657\pi$
$643$	−2193.22	−	8185.22i	−0.134514	−	0.502012i	0.865486	−	0.500933i	$-0.167010\pi$
$644$	−8725.76	+	15113.5i	−0.533918	+	0.924773i
$645$		0			0
$646$	−621.789	−	1076.97i	−0.0378699	−	0.0655926i
$647$	−23205.8	+	23205.8i	−1.41007	+	1.41007i	−0.650953	+	0.759118i	$0.725630\pi$
$647$	−23205.8	+	23205.8i	−1.41007	+	1.41007i	−0.759118	+	0.650953i	$0.774370\pi$
$648$	8111.62	−	13809.1i	0.491751	−	0.837152i
$649$		−	2009.70i		−	0.121553i
$650$		0			0
$651$	−5611.96	+	2754.42i	−0.337865	+	0.165829i
$652$	15941.2	−	4271.44i	0.957525	−	0.256568i
$653$	−22778.0	+	6103.35i	−1.36504	+	0.365762i	−0.865666	−	0.500623i	$-0.833104\pi$
$653$	−22778.0	+	6103.35i	−1.36504	+	0.365762i	−0.499377	+	0.866385i	$0.666438\pi$
$654$	−3537.79	−	2373.50i	−0.211527	−	0.141913i
$655$		0			0
$656$		−	819.176i		−	0.0487553i
$657$	14144.0	−	1808.08i	0.839895	−	0.107367i
$658$	6164.01	−	6164.01i	0.365195	−	0.365195i
$659$	−11587.9	−	20070.8i	−0.684976	−	1.18641i	−0.973444	−	0.228923i	$-0.926480\pi$
$659$	−11587.9	−	20070.8i	−0.684976	−	1.18641i	0.288469	−	0.957489i	$-0.406854\pi$
$660$		0			0
$661$	7538.30	−	13056.7i	0.443580	−	0.768302i	−0.554373	−	0.832269i	$-0.687042\pi$
$661$	7538.30	−	13056.7i	0.443580	−	0.768302i	0.997952	+	0.0639664i	$0.0203750\pi$
$662$	3691.25	+	13775.9i	0.216714	+	0.808787i
$663$	9214.58	−	8050.40i	0.539765	−	0.471571i
$664$	8650.14	−	4994.16i	0.505558	−	0.291884i
$665$		0			0
$666$	638.811	−	4715.33i	0.0371673	−	0.274348i
$667$	−3966.29	−	3966.29i	−0.230248	−	0.230248i
$668$	2294.63	−	8563.67i	0.132907	−	0.496016i
$669$	913.432	−	1361.51i	0.0527882	−	0.0786829i
$670$		0			0
$671$	−11619.7	−	6708.61i	−0.668512	−	0.385966i
$672$	−9785.98	+	28651.7i	−0.561760	+	1.64474i
$673$	−14112.2	−	3781.35i	−0.808298	−	0.216583i	−0.169074	−	0.985603i	$-0.554078\pi$
$673$	−14112.2	−	3781.35i	−0.808298	−	0.216583i	−0.639224	+	0.769021i	$0.720744\pi$
$674$	11178.7			0.638853
$675$		0			0
$676$	4693.32			0.267030
$677$	9881.83	+	2647.83i	0.560989	+	0.150317i	0.528161	−	0.849144i	$-0.322882\pi$
$677$	9881.83	+	2647.83i	0.560989	+	0.150317i	0.0328285	+	0.999461i	$0.489548\pi$
$678$	4592.27	−	13445.4i	0.260125	−	0.761603i
$679$	−8820.44	−	5092.48i	−0.498523	−	0.287823i
$680$		0			0
$681$	−13552.0	+	20199.7i	−0.762573	+	1.13665i
$682$	587.168	−	2191.34i	0.0329675	−	0.123036i
$683$	21858.2	+	21858.2i	1.22457	+	1.22457i	0.965990	+	0.258579i	$0.0832541\pi$
$683$	21858.2	+	21858.2i	1.22457	+	1.22457i	0.258579	+	0.965990i	$0.416746\pi$
$684$	2323.54	−	952.232i	0.129887	−	0.0532303i
$685$		0			0
$686$	13825.1	−	7981.91i	0.769451	−	0.444243i
$687$	−13955.1	+	12192.0i	−0.774995	+	0.677082i
$688$	−788.266	−	2941.85i	−0.0436807	−	0.163019i
$689$	6712.19	−	11625.9i	0.371138	−	0.642830i
$690$		0			0
$691$	7416.99	+	12846.6i	0.408329	+	0.707247i	0.994703	−	0.102794i	$-0.0327782\pi$
$691$	7416.99	+	12846.6i	0.408329	+	0.707247i	−0.586373	+	0.810041i	$0.699445\pi$
$692$	10140.6	−	10140.6i	0.557062	−	0.557062i
$693$	−11761.3	+	28095.4i	−0.644698	+	1.54005i
$694$		−	19530.3i		−	1.06824i
$695$		0			0
$696$	−5039.10	−	3380.72i	−0.274435	−	0.184118i
$697$	−5993.42	+	1605.93i	−0.325706	+	0.0872725i
$698$	11207.7	−	3003.10i	0.607763	−	0.162850i
$699$	−211.110	+	103.616i	−0.0114233	+	0.00560673i
$700$		0			0
$701$		−	29266.1i		−	1.57684i	−0.615136	−	0.788421i	$-0.710899\pi$
$701$		−	29266.1i		−	1.57684i	0.615136	−	0.788421i	$-0.289101\pi$
$702$	−7123.09	−	10791.6i	−0.382968	−	0.580202i
$703$	1331.22	−	1331.22i	0.0714195	−	0.0714195i
$704$	−4692.44	−	8127.55i	−0.251212	−	0.435112i
$705$		0			0
$706$	−5895.73	+	10211.7i	−0.314290	+	0.544366i
$707$	−2118.69	−	7907.07i	−0.112704	−	0.420617i
$708$	−295.863	−	1502.14i	−0.0157051	−	0.0797371i
$709$	−10569.7	+	6102.42i	−0.559878	+	0.323246i	−0.753096	−	0.657910i	$-0.771441\pi$
$709$	−10569.7	+	6102.42i	−0.559878	+	0.323246i	0.193219	+	0.981156i	$0.438107\pi$
$710$		0			0
$711$	−15228.7	−	2063.11i	−0.803262	−	0.108822i
$712$	−2303.07	−	2303.07i	−0.121224	−	0.121224i
$713$	1043.35	−	3893.82i	0.0548017	−	0.204523i
$714$	11464.8	+	773.070i	0.600926	+	0.0405202i
$715$		0			0
$716$	2202.08	+	1271.37i	0.114938	+	0.0663595i
$717$	−1174.54	−	1344.40i	−0.0611774	−	0.0700243i
$718$	−17204.7	−	4609.99i	−0.894255	−	0.239615i
$719$	12947.9			0.671592			0.335796	−	0.941935i	$-0.390995\pi$
$719$	12947.9			0.671592			0.335796	+	0.941935i	$0.390995\pi$
$720$		0			0
$721$	−37027.2			−1.91257
$722$	10481.4	+	2808.48i	0.540272	+	0.144765i
$723$	−23242.8	+	4577.92i	−1.19559	+	0.235484i
$724$	−12059.6	−	6962.62i	−0.619049	−	0.357408i
$725$		0			0
$726$	181.799	+	370.404i	0.00929367	+	0.0189352i
$727$	1058.69	−	3951.09i	0.0540091	−	0.201565i	−0.933649	−	0.358189i	$-0.883394\pi$
$727$	1058.69	−	3951.09i	0.0540091	−	0.201565i	0.987658	+	0.156624i	$0.0500611\pi$
$728$	27197.3	+	27197.3i	1.38462	+	1.38462i
$729$	7736.76	−	18098.7i	0.393068	−	0.919509i
$730$		0			0
$731$	−19978.4	+	11534.5i	−1.01084	+	0.583611i
$732$	−9672.66	−	3303.69i	−0.488404	−	0.166814i
$733$	−2312.48	−	8630.30i	−0.116526	−	0.434881i	0.882871	−	0.469616i	$-0.155608\pi$
$733$	−2312.48	−	8630.30i	−0.116526	−	0.434881i	−0.999397	+	0.0347357i	$0.988941\pi$
$734$	−1708.64	+	2959.46i	−0.0859226	+	0.148822i
$735$		0			0
$736$	−9761.80	−	16907.9i	−0.488892	−	0.846786i
$737$	2905.60	−	2905.60i	0.145223	−	0.145223i
$738$	831.445	+	6504.12i	0.0414714	+	0.324417i
$739$			10810.9i			0.538140i	0.963121	+	0.269070i	$0.0867163\pi$
$739$			10810.9i			0.538140i	−0.963121	+	0.269070i	$0.913284\pi$
$740$		0			0
$741$	344.177	−	5104.25i	0.0170630	−	0.253049i
$742$	12177.4	−	3262.93i	0.602489	−	0.161436i
$743$	−14187.3	+	3801.46i	−0.700511	+	0.187701i	−0.591460	−	0.806335i	$-0.701448\pi$
$743$	−14187.3	+	3801.46i	−0.700511	+	0.187701i	−0.109052	+	0.994036i	$0.534781\pi$
$744$	293.394	−	4351.12i	0.0144575	−	0.214408i
$745$		0			0
$746$			13087.9i			0.642334i
$747$	9767.00	−	7436.37i	0.478388	−	0.364234i
$748$	5634.21	−	5634.21i	0.275411	−	0.275411i
$749$	18545.8	+	32122.2i	0.904737	+	1.56705i
$750$		0			0
$751$	10459.1	−	18115.7i	0.508201	−	0.880229i	−0.491754	−	0.870734i	$-0.663644\pi$
$751$	10459.1	−	18115.7i	0.508201	−	0.880229i	0.999955	−	0.00949541i	$-0.00302253\pi$
$752$	−241.659	−	901.883i	−0.0117186	−	0.0437344i
$753$	30324.6	+	10357.4i	1.46758	+	0.501253i
$754$	−4242.88	+	2449.63i	−0.204929	+	0.118316i
$755$		0			0
$756$	−4654.79	+	22731.2i	−0.223933	+	1.09355i
$757$	18342.1	+	18342.1i	0.880653	+	0.880653i	0.993601	−	0.112948i	$-0.0360293\pi$
$757$	18342.1	+	18342.1i	0.880653	+	0.880653i	−0.112948	+	0.993601i	$0.536029\pi$
$758$	3238.37	−	12085.7i	0.155175	−	0.579121i
$759$	−8653.61	−	17631.2i	−0.413842	−	0.843177i
$760$		0			0
$761$	9287.39	+	5362.08i	0.442402	+	0.255421i	0.704616	−	0.709589i	$-0.251119\pi$
$761$	9287.39	+	5362.08i	0.442402	+	0.255421i	−0.262214	+	0.965010i	$0.584453\pi$
$762$	−11286.3	+	2222.96i	−0.536560	+	0.105681i
$763$	15043.9	+	4030.99i	0.713793	+	0.191260i
$764$	−4761.29			−0.225468
$765$		0			0
$766$	9254.36			0.436519
$767$	−3012.82	−	807.283i	−0.141834	−	0.0380043i
$768$	−13093.0	−	14986.4i	−0.615172	−	0.704132i
$769$	19273.4	+	11127.5i	0.903793	+	0.521805i	0.878429	−	0.477873i	$-0.158592\pi$
$769$	19273.4	+	11127.5i	0.903793	+	0.521805i	0.0253640	+	0.999678i	$0.491926\pi$
$770$		0			0
$771$	29959.9	+	2020.18i	1.39945	+	0.0943647i
$772$	−3690.04	+	13771.4i	−0.172030	+	0.642026i
$773$	−20786.4	−	20786.4i	−0.967184	−	0.967184i	0.0322943	−	0.999478i	$-0.489719\pi$
$773$	−20786.4	−	20786.4i	−0.967184	−	0.967184i	−0.999478	+	0.0322943i	$0.989719\pi$
$774$	9244.60	+	22557.7i	0.429316	+	1.04757i
$775$		0			0
$776$	6153.09	−	3552.49i	0.284643	−	0.164339i
$777$	3361.71	+	17067.9i	0.155213	+	0.788040i
$778$	3363.53	+	12552.9i	0.154998	+	0.578461i
$779$	−1297.12	+	2246.68i	−0.0596589	+	0.103332i
$780$		0			0
$781$	16500.3	+	28579.4i	0.755990	+	1.30941i
$782$	−5239.48	+	5239.48i	−0.239595	+	0.239595i
$783$	−6669.96	−	3336.11i	−0.304425	−	0.152264i
$784$		−	3627.96i		−	0.165268i
$785$		0			0
$786$	13218.6	−	6487.88i	0.599864	−	0.294421i
$787$	−16780.5	+	4496.33i	−0.760053	+	0.203656i	−0.617973	−	0.786200i	$-0.712046\pi$
$787$	−16780.5	+	4496.33i	−0.760053	+	0.203656i	−0.142080	+	0.989855i	$0.545379\pi$
$788$	−5374.60	+	1440.12i	−0.242972	+	0.0651042i
$789$	10664.1	+	7154.50i	0.481180	+	0.322823i
$790$		0			0
$791$			51941.7i			2.33481i
$792$	−12871.1	−	16905.0i	−0.577468	−	0.758452i
$793$	−14724.7	+	14724.7i	−0.659379	+	0.659379i
$794$	−572.604	−	991.779i	−0.0255931	−	0.0443286i
$795$		0			0
$796$	12288.3	−	21284.0i	0.547171	−	0.947728i
$797$	−6123.82	−	22854.4i	−0.272167	−	1.01574i	−0.957716	−	0.287714i	$-0.907105\pi$
$797$	−6123.82	−	22854.4i	−0.272167	−	1.01574i	0.685550	−	0.728026i	$-0.259562\pi$
$798$	3618.04	−	3160.93i	0.160498	−	0.140220i
$799$	−6124.78	+	3536.14i	−0.271188	+	0.156570i
$800$		0			0
$801$	−3166.56	−	2448.74i	−0.139682	−	0.108017i
$802$	10631.4	+	10631.4i	0.468088	+	0.468088i
$803$	4896.16	−	18272.7i	0.215170	−	0.803027i
$804$	1744.01	−	2599.52i	0.0765008	−	0.114027i
$805$		0			0
$806$	−3049.26	−	1760.49i	−0.133258	−	0.0769363i
$807$	10048.5	−	29420.2i	0.438318	−	1.28332i
$808$	5515.93	+	1477.99i	0.240161	+	0.0643509i
$809$	−30629.1			−1.33110			−0.665552	−	0.746352i	$-0.731804\pi$
$809$	−30629.1			−1.33110			−0.665552	+	0.746352i	$0.731804\pi$
$810$		0			0
$811$	16552.9			0.716709			0.358354	−	0.933586i	$-0.383338\pi$
$811$	16552.9			0.716709			0.358354	+	0.933586i	$0.383338\pi$
$812$	8491.85	+	2275.38i	0.367002	+	0.0983379i
$813$	383.814	−	1123.74i	0.0165571	−	0.0484764i
$814$	−5467.13	−	3156.45i	−0.235409	−	0.135913i
$815$		0			0
$816$	685.706	−	1022.07i	0.0294173	−	0.0438476i
$817$	−2496.36	+	9316.53i	−0.106899	+	0.398952i
$818$	−1431.56	−	1431.56i	−0.0611899	−	0.0611899i
$819$	37394.4	+	28917.5i	1.59544	+	1.23377i
$820$		0			0
$821$	−12828.3	+	7406.41i	−0.545323	+	0.314842i	−0.747234	−	0.664562i	$-0.768618\pi$
$821$	−12828.3	+	7406.41i	−0.545323	+	0.314842i	0.201910	+	0.979404i	$0.435285\pi$
$822$	9268.38	−	8097.41i	0.393275	−	0.343588i
$823$	1406.71	+	5249.91i	0.0595806	+	0.222358i	0.989296	−	0.145920i	$-0.0466142\pi$
$823$	1406.71	+	5249.91i	0.0595806	+	0.222358i	−0.929716	+	0.368278i	$0.879948\pi$
$824$	12915.0	−	22369.4i	0.546013	−	0.945722i
$825$		0			0
$826$	−1464.59	−	2536.75i	−0.0616945	−	0.106858i
$827$	−9704.44	+	9704.44i	−0.408049	+	0.408049i	−0.881058	−	0.473009i	$-0.843168\pi$
$827$	−9704.44	+	9704.44i	−0.408049	+	0.408049i	0.473009	+	0.881058i	$0.343168\pi$
$828$	−9063.69	−	11904.3i	−0.380417	−	0.499643i
$829$			44654.1i			1.87081i	0.353581	+	0.935404i	$0.384964\pi$
$829$			44654.1i			1.87081i	−0.353581	+	0.935404i	$0.615036\pi$
$830$		0			0
$831$	14622.7	+	9810.33i	0.610415	+	0.409527i
$832$	−14069.2	+	3769.84i	−0.586253	+	0.157086i
$833$	−26543.6	+	7112.33i	−1.10406	+	0.295831i
$834$	−2715.87	+	1332.99i	−0.112761	+	0.0553448i
$835$		0			0
$836$		−	3331.42i		−	0.137822i
$837$	−320.407	−	5350.12i	−0.0132316	−	0.220941i
$838$	19215.9	−	19215.9i	0.792126	−	0.792126i
$839$	−7021.07	−	12160.9i	−0.288909	−	0.500404i	0.684641	−	0.728880i	$-0.259959\pi$
$839$	−7021.07	−	12160.9i	−0.288909	−	0.500404i	−0.973549	+	0.228476i	$0.926626\pi$
$840$		0			0
$841$	10781.7	−	18674.4i	0.442070	−	0.765688i
$842$	−699.541	−	2610.72i	−0.0286316	−	0.106854i
$843$	8368.65	+	42488.9i	0.341912	+	1.73594i
$844$	20599.4	−	11893.1i	0.840118	−	0.485042i
$845$		0			0
$846$	2834.12	+	6915.52i	0.115176	+	0.281041i
$847$	−1066.63	−	1066.63i	−0.0432700	−	0.0432700i
$848$	349.491	−	1304.32i	0.0141528	−	0.0528189i
$849$	−43062.8	−	2903.71i	−1.74077	−	0.117379i
$850$		0			0
$851$	−9714.61	−	5608.73i	−0.391319	−	0.225928i
$852$	16540.4	+	18932.4i	0.665101	+	0.761281i
$853$	−8502.85	−	2278.33i	−0.341304	−	0.0914521i	0.0840959	−	0.996458i	$-0.473200\pi$
$853$	−8502.85	−	2278.33i	−0.341304	−	0.0914521i	−0.425400	+	0.905006i	$0.639866\pi$
$854$	−19555.9			−0.783593
$855$		0			0
$856$	−25874.9			−1.03316
$857$	−4444.64	−	1190.94i	−0.177160	−	0.0474699i	0.169148	−	0.985591i	$-0.445898\pi$
$857$	−4444.64	−	1190.94i	−0.177160	−	0.0474699i	−0.346308	+	0.938121i	$0.612565\pi$
$858$	−16831.2	+	3315.10i	−0.669707	+	0.131906i
$859$	2297.03	+	1326.19i	0.0912382	+	0.0526764i	0.544925	−	0.838485i	$-0.316558\pi$
$859$	2297.03	+	1326.19i	0.0912382	+	0.0526764i	−0.453687	+	0.891161i	$0.649891\pi$
$860$		0			0
$861$	−10561.8	−	21519.1i	−0.418056	−	0.851763i
$862$	−4151.87	+	15495.0i	−0.164052	+	0.612252i
$863$	−11554.8	−	11554.8i	−0.455770	−	0.455770i	0.441494	−	0.897264i	$-0.354449\pi$
$863$	−11554.8	−	11554.8i	−0.455770	−	0.455770i	−0.897264	+	0.441494i	$0.854449\pi$
$864$	−19419.4	−	17224.9i	−0.764655	−	0.678243i
$865$		0			0
$866$	−13294.9	+	7675.81i	−0.521685	+	0.301195i
$867$	15336.3	+	5238.11i	0.600747	+	0.205185i
$868$	1635.27	+	6102.90i	0.0639453	+	0.238647i
$869$	−10194.1	+	17656.7i	−0.397941	+	0.689253i
$870$		0			0
$871$	−3188.73	−	5523.04i	−0.124048	−	0.214858i
$872$	−7682.52	+	7682.52i	−0.298352	+	0.298352i
$873$	6947.55	−	5289.71i	0.269346	−	0.205074i
$874$			3098.02i			0.119899i
$875$		0			0
$876$	969.546	−	14378.6i	0.0373949	−	0.554576i
$877$	−5920.54	+	1586.40i	−0.227962	+	0.0610821i	−0.370992	−	0.928636i	$-0.620982\pi$
$877$	−5920.54	+	1586.40i	−0.227962	+	0.0610821i	0.143030	+	0.989718i	$0.454315\pi$
$878$	−26315.1	+	7051.12i	−1.01150	+	0.271029i
$879$	3220.52	−	47761.2i	0.123579	−	1.83270i
$880$		0			0
$881$			2309.20i			0.0883075i	0.999025	+	0.0441537i	$0.0140591\pi$
$881$			2309.20i			0.0883075i	−0.999025	+	0.0441537i	$0.985941\pi$
$882$	3682.29	+	28805.4i	0.140577	+	1.09969i
$883$	19660.7	−	19660.7i	0.749303	−	0.749303i	−0.225045	−	0.974348i	$-0.572253\pi$
$883$	19660.7	−	19660.7i	0.749303	−	0.749303i	0.974348	+	0.225045i	$0.0722529\pi$
$884$	−6183.24	−	10709.7i	−0.235254	−	0.407472i
$885$		0			0
$886$	5884.68	−	10192.6i	0.223137	−	0.386485i
$887$	7598.16	+	28356.7i	0.287623	+	1.07342i	0.946902	+	0.321524i	$0.104195\pi$
$887$	7598.16	+	28356.7i	0.287623	+	1.07342i	−0.659279	+	0.751898i	$0.729138\pi$
$888$	−11483.9	−	3922.31i	−0.433979	−	0.148226i
$889$	36419.1	−	21026.6i	1.37397	−	0.793260i
$890$		0			0
$891$	−18325.5	−	18602.9i	−0.689032	−	0.699462i
$892$	−1171.69	−	1171.69i	−0.0439812	−	0.0439812i
$893$	−765.308	+	2856.17i	−0.0286787	+	0.107030i
$894$	−6204.87	−	12642.0i	−0.232127	−	0.472944i
$895$		0			0
$896$	28523.0	+	16467.8i	1.06349	+	0.614006i
$897$	−29907.6	+	5890.64i	−1.11325	+	0.219267i
$898$	−25322.3	−	6785.10i	−0.940999	−	0.252140i
$899$	−2030.76			−0.0753387
$900$		0			0
$901$	−10228.0			−0.378186
$902$	8402.70	+	2251.50i	0.310177	+	0.0831116i
$903$	−58637.0	−	67116.5i	−2.16093	−	2.47342i
$904$	−31379.8	−	18117.1i	−1.15451	−	0.666556i
$905$		0			0
$906$	−4107.42	−	276.962i	−0.150618	−	0.0101561i
$907$	−8789.11	+	32801.4i	−0.321761	+	1.20083i	0.595766	+	0.803158i	$0.296848\pi$
$907$	−8789.11	+	32801.4i	−0.321761	+	1.20083i	−0.917528	+	0.397672i	$0.869818\pi$
$908$	17383.6	+	17383.6i	0.635347	+	0.635347i
$909$	6954.75	+	942.196i	0.253767	+	0.0343792i
$910$		0			0
$911$	−5799.18	+	3348.16i	−0.210906	+	0.121767i	−0.601732	−	0.798698i	$-0.705523\pi$
$911$	−5799.18	+	3348.16i	−0.210906	+	0.121767i	0.390826	+	0.920464i	$0.372189\pi$
$912$	−99.4437	−	504.890i	−0.00361065	−	0.0183318i
$913$	−4215.13	−	15731.1i	−0.152793	−	0.570233i
$914$	−10032.6	+	17376.9i	−0.363072	+	0.628860i
$915$		0			0
$916$	9364.28	+	16219.4i	0.337778	+	0.585048i
$917$	−38064.7	+	38064.7i	−1.37078	+	1.37078i
$918$	−4407.01	+	8811.05i	−0.158446	+	0.316784i
$919$			50724.3i			1.82072i	0.413820	+	0.910359i	$0.364194\pi$
$919$			50724.3i			1.82072i	−0.413820	+	0.910359i	$0.635806\pi$
$920$		0			0
$921$	11895.0	−	5838.23i	0.425574	−	0.208877i
$922$	16045.5	−	4299.37i	0.573134	−	0.153571i
$923$	49472.5	−	13256.1i	1.76425	−	0.472731i
$924$	25562.8	+	17150.1i	0.910125	+	0.610602i
$925$		0			0
$926$		−	14932.5i		−	0.529927i
$927$	12258.5	−	29283.0i	0.434326	−	1.03752i
$928$	−6954.57	+	6954.57i	−0.246008	+	0.246008i
$929$	−18550.3	−	32130.0i	−0.655128	−	1.13472i	−0.981862	−	0.189599i	$-0.939281\pi$
$929$	−18550.3	−	32130.0i	−0.655128	−	1.13472i	0.326733	−	0.945117i	$-0.394052\pi$
$930$		0			0
$931$	−5744.68	+	9950.08i	−0.202228	+	0.350269i
$932$	61.5153	+	229.578i	0.00216202	+	0.00806876i
$933$	−1132.46	+	989.384i	−0.0397374	+	0.0347170i
$934$	−4842.73	+	2795.95i	−0.169656	+	0.0979511i
$935$		0			0
$936$	−30513.2	+	12504.9i	−1.06555	+	0.436684i
$937$	−1098.31	−	1098.31i	−0.0382927	−	0.0382927i	0.687701	−	0.725994i	$-0.258620\pi$
$937$	−1098.31	−	1098.31i	−0.0382927	−	0.0382927i	−0.725994	+	0.687701i	$0.758620\pi$
$938$	1550.10	−	5785.07i	0.0539581	−	0.201374i
$939$	−5648.94	+	8419.97i	−0.196322	+	0.292626i
$940$		0			0
$941$	24281.2	+	14018.8i	0.841175	+	0.485653i	0.857664	−	0.514211i	$-0.171915\pi$
$941$	24281.2	+	14018.8i	0.841175	+	0.485653i	−0.0164881	+	0.999864i	$0.505249\pi$
$942$	−4809.68	+	14081.9i	−0.166356	+	0.487064i
$943$	14930.9	+	4000.71i	0.515605	+	0.138156i
$944$	−313.743			−0.0108172
$945$		0			0
$946$	32342.5			1.11157
$947$	24038.9	+	6441.22i	0.824879	+	0.221026i	0.646479	−	0.762932i	$-0.276241\pi$
$947$	24038.9	+	6441.22i	0.824879	+	0.221026i	0.178401	+	0.983958i	$0.442908\pi$
$948$	−5020.13	+	14698.1i	−0.171990	+	0.503557i
$949$	−25426.6	−	14680.0i	−0.869738	−	0.502144i
$950$		0			0
$951$	−12976.5	+	19342.0i	−0.442474	+	0.659524i
$952$	7584.65	−	28306.3i	0.258214	−	0.963669i
$953$	34055.7	+	34055.7i	1.15758	+	1.15758i	0.984995	+	0.172583i	$0.0552112\pi$
$953$	34055.7	+	34055.7i	1.15758	+	1.15758i	0.172583	+	0.984995i	$0.444789\pi$
$954$	−1451.04	+	10710.8i	−0.0492445	+	0.363495i
$955$		0			0
$956$	−1562.53	+	902.127i	−0.0528617	+	0.0305197i
$957$	−7450.99	+	6509.63i	−0.251678	+	0.219881i
$958$	42.6119	+	159.030i	0.00143709	+	0.00536328i
$959$	−22496.6	+	38965.3i	−0.757512	+	1.31205i
$960$		0			0
$961$	14165.8	+	24535.8i	0.475505	+	0.823599i
$962$	−6928.05	+	6928.05i	−0.232193	+	0.232193i
$963$	−31543.8	+	4032.36i	−1.05554	+	0.134933i
$964$			23942.1i			0.799920i
$965$		0			0
$966$	−23771.9	−	15948.5i	−0.791769	−	0.531196i
$967$	14943.2	−	4004.02i	0.496940	−	0.133155i	−0.00163930	−	0.999999i	$-0.500522\pi$
$967$	14943.2	−	4004.02i	0.496940	−	0.133155i	0.498580	+	0.866844i	$0.333855\pi$
$968$	1016.42	−	272.349i	0.0337490	−	0.00904302i
$969$	−3499.02	+	1717.37i	−0.116001	+	0.0569348i
$970$		0			0
$971$			42148.6i			1.39301i	0.717552	+	0.696505i	$0.245263\pi$
$971$			42148.6i			1.39301i	−0.717552	+	0.696505i	$0.754737\pi$
$972$	−16436.0	−	11206.8i	−0.542370	−	0.369813i
$973$	7820.70	−	7820.70i	0.257677	−	0.257677i
$974$	881.682	+	1527.12i	0.0290050	+	0.0502382i
$975$		0			0
$976$	−1047.31	+	1813.99i	−0.0343479	+	0.0594923i
$977$	−2200.98	−	8214.17i	−0.0720733	−	0.268981i	0.920480	−	0.390789i	$-0.127798\pi$
$977$	−2200.98	−	8214.17i	−0.0720733	−	0.268981i	−0.992554	+	0.121807i	$0.961131\pi$
$978$	5231.47	+	26561.0i	0.171047	+	0.868431i
$979$	−4599.12	+	2655.30i	−0.150142	+	0.0866843i
$980$		0			0
$981$	−8168.43	+	10562.9i	−0.265849	+	0.343780i
$982$	−4783.38	−	4783.38i	−0.155442	−	0.155442i
$983$	−11235.0	+	41929.5i	−0.364537	+	1.36047i	0.503510	+	0.863990i	$0.332042\pi$
$983$	−11235.0	+	41929.5i	−0.364537	+	1.36047i	−0.868047	+	0.496482i	$0.834625\pi$
$984$	16684.4	+	1125.02i	0.540526	+	0.0364475i
$985$		0			0
$986$	3232.65	+	1866.37i	0.104410	+	0.0602814i
$987$	−17976.4	−	20575.9i	−0.579730	−	0.663565i
$988$	−4994.25	−	1338.20i	−0.160818	−	0.0430911i
$989$	57469.9			1.84776
$990$		0			0
$991$	39569.0			1.26837			0.634183	−	0.773183i	$-0.281337\pi$
$991$	39569.0			1.26837			0.634183	+	0.773183i	$0.281337\pi$
$992$	−6827.52	−	1829.43i	−0.218522	−	0.0585528i
$993$	43858.6	−	8638.42i	1.40162	−	0.276064i
$994$	41655.1	+	24049.6i	1.32919	+	0.767410i
$995$		0			0
$996$	−5466.45	−	11137.5i	−0.173907	−	0.354324i
$997$	14488.9	−	54073.3i	0.460249	−	1.71767i	−0.211933	−	0.977284i	$-0.567976\pi$
$997$	14488.9	−	54073.3i	0.460249	−	1.71767i	0.672181	−	0.740387i	$-0.265358\pi$
$998$	5925.14	+	5925.14i	0.187933	+	0.187933i
$999$	−14611.1	−	2992.00i	−0.462738	−	0.0947574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.10		64
5.2	odd	4		45.4.l.a.23.7	yes	64
5.3	odd	4	inner	225.4.p.b.68.10		64
5.4	even	2		45.4.l.a.32.7	yes	64
9.2	odd	6	inner	225.4.p.b.182.10		64
15.2	even	4		135.4.m.a.98.10		64
15.14	odd	2		135.4.m.a.17.10		64
45.2	even	12		45.4.l.a.38.7	yes	64
45.7	odd	12		135.4.m.a.8.10		64
45.29	odd	6		45.4.l.a.2.7	✓	64
45.34	even	6		135.4.m.a.62.10		64
45.38	even	12	inner	225.4.p.b.218.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.7	✓	64	45.29	odd	6
45.4.l.a.23.7	yes	64	5.2	odd	4
45.4.l.a.32.7	yes	64	5.4	even	2
45.4.l.a.38.7	yes	64	45.2	even	12
135.4.m.a.8.10		64	45.7	odd	12
135.4.m.a.17.10		64	15.14	odd	2
135.4.m.a.62.10		64	45.34	even	6
135.4.m.a.98.10		64	15.2	even	4
225.4.p.b.32.10		64	1.1	even	1	trivial
225.4.p.b.68.10		64	5.3	odd	4	inner
225.4.p.b.182.10		64	9.2	odd	6	inner
225.4.p.b.218.10		64	45.38	even	12	inner

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +O(q^{10})\)	\(q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +(-31.0214 + 17.9102i) q^{11} +(-20.5500 + 17.9537i) q^{12} +(14.3888 + 53.6997i) q^{13} +(-26.1045 + 45.2143i) q^{14} +(2.79604 + 4.84288i) q^{16} +(29.9510 - 29.9510i) q^{17} +(-27.1155 - 35.6137i) q^{18} -17.7095i q^{19} +(135.890 + 91.1683i) q^{21} +(-57.3607 + 15.3698i) q^{22} +(-101.925 + 27.3107i) q^{23} +(-102.476 + 50.2966i) q^{24} +92.1654i q^{26} +(-117.089 + 77.2859i) q^{27} +(116.945 - 116.945i) q^{28} +(26.5786 + 46.0355i) q^{29} +(-19.1014 + 33.0846i) q^{31} +(47.8872 + 178.717i) q^{32} +(35.9690 + 182.620i) q^{33} +(60.8131 - 35.1104i) q^{34} +(53.7695 + 131.203i) q^{36} +(75.1697 + 75.1697i) q^{37} +(7.59877 - 28.3590i) q^{38} +(288.220 + 19.4346i) q^{39} +(-126.863 - 73.2444i) q^{41} +(178.488 + 204.299i) q^{42} +(-526.075 - 140.961i) q^{43} +188.114 q^{44} -174.935 q^{46} +(-161.279 - 43.2145i) q^{47} +(28.5095 - 5.61527i) q^{48} +(-561.849 - 324.384i) q^{49} +(-96.9742 - 197.579i) q^{51} +(75.5641 - 282.009i) q^{52} +(-170.746 - 170.746i) q^{53} +(-220.661 + 73.5208i) q^{54} +(599.162 - 345.926i) q^{56} +(-87.0821 - 29.7429i) q^{57} +(22.8086 + 85.1228i) q^{58} +(-28.0525 + 48.5883i) q^{59} +(187.285 + 324.386i) q^{61} +(-44.7838 + 44.7838i) q^{62} +(676.522 - 515.089i) q^{63} +261.998i q^{64} +(-20.7596 + 307.870i) q^{66} +(-110.806 + 29.6904i) q^{67} +(-214.863 + 57.5724i) q^{68} +(-36.8879 + 547.058i) q^{69} -921.281i q^{71} +(75.2138 + 588.372i) q^{72} +(-373.434 + 373.434i) q^{73} +(88.1187 + 152.626i) q^{74} +(-46.5016 + 80.5432i) q^{76} +(-291.966 - 1089.63i) q^{77} +(453.200 + 154.791i) q^{78} +(492.922 - 284.589i) q^{79} +(183.385 + 705.557i) q^{81} +(-171.723 - 171.723i) q^{82} +(-117.674 + 439.165i) q^{83} +(-378.640 - 771.455i) q^{84} +(-781.941 - 451.454i) q^{86} +(271.006 - 53.3777i) q^{87} +(760.121 + 203.674i) q^{88} +148.257 q^{89} -1750.79 q^{91} +(535.269 + 143.425i) q^{92} +(130.605 + 149.492i) q^{93} +(-239.720 - 138.402i) q^{94} +(959.224 + 64.6801i) q^{96} +(-83.7049 + 312.391i) q^{97} +(-760.526 - 760.526i) q^{98} +(958.396 + 129.839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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