LMFDB - Embedded newform 500.4.g.b.201.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [500,4,Mod(101,500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("500.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	500.g (of order $5$, 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:	$29.5009550029$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.5
Character	$\chi$	$=$	500.201
Dual form			500.4.g.b.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53150 - 4.71349i) q^{3} -16.8592 q^{7} +(1.97201 - 1.43275i) q^{9} +O(q^{10})$	\(q+(-1.53150 - 4.71349i) q^{3} -16.8592 q^{7} +(1.97201 - 1.43275i) q^{9} +(-47.8389 - 34.7570i) q^{11} +(5.10901 - 3.71191i) q^{13} +(-40.6606 + 125.140i) q^{17} +(25.3925 - 78.1500i) q^{19} +(25.8199 + 79.4654i) q^{21} +(128.998 + 93.7224i) q^{23} +(-118.031 - 85.7543i) q^{27} +(-15.4646 - 47.5950i) q^{29} +(-13.8066 + 42.4924i) q^{31} +(-90.5611 + 278.718i) q^{33} +(60.7145 - 44.1117i) q^{37} +(-25.3205 - 18.3964i) q^{39} +(-286.091 + 207.857i) q^{41} -79.3703 q^{43} +(94.1857 + 289.874i) q^{47} -58.7686 q^{49} +652.120 q^{51} +(104.844 + 322.676i) q^{53} -407.248 q^{57} +(636.533 - 462.468i) q^{59} +(675.055 + 490.456i) q^{61} +(-33.2464 + 24.1549i) q^{63} +(-187.851 + 578.147i) q^{67} +(244.198 - 751.566i) q^{69} +(-18.9894 - 58.4435i) q^{71} +(-32.0156 - 23.2607i) q^{73} +(806.523 + 585.973i) q^{77} +(178.592 + 549.648i) q^{79} +(-203.100 + 625.077i) q^{81} +(-16.4914 + 50.7554i) q^{83} +(-200.654 + 145.784i) q^{87} +(1170.83 + 850.656i) q^{89} +(-86.1336 + 62.5797i) q^{91} +221.432 q^{93} +(-16.5425 - 50.9127i) q^{97} -144.136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 244 q^{9}+O(q^{10}) $ 64 * q - 244 * q^9	$ 64 q - 244 q^{9} + 40 q^{11} - 4 q^{19} - 216 q^{21} - 124 q^{29} - 756 q^{31} - 1184 q^{39} - 1056 q^{41} + 5592 q^{49} + 3328 q^{51} - 288 q^{59} - 2692 q^{61} - 1912 q^{69} + 1572 q^{71} - 1792 q^{79} + 696 q^{81} + 5024 q^{89} - 4424 q^{91} + 5080 q^{99}+O(q^{100}) $ 64 * q - 244 * q^9 + 40 * q^11 - 4 * q^19 - 216 * q^21 - 124 * q^29 - 756 * q^31 - 1184 * q^39 - 1056 * q^41 + 5592 * q^49 + 3328 * q^51 - 288 * q^59 - 2692 * q^61 - 1912 * q^69 + 1572 * q^71 - 1792 * q^79 + 696 * q^81 + 5024 * q^89 - 4424 * q^91 + 5080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.53150	−	4.71349i	−0.294738	−	0.907111i	−0.983309	−	0.181942i	$-0.941762\pi$
$3$	−1.53150	−	4.71349i	−0.294738	−	0.907111i	0.688571	−	0.725169i	$-0.258238\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−16.8592			−0.910309			−0.455155	−	0.890412i	$-0.650416\pi$
$7$	−16.8592			−0.910309			−0.455155	+	0.890412i	$0.650416\pi$
$8$		0			0
$9$	1.97201	−	1.43275i	0.0730373	−	0.0530647i
$10$		0			0
$11$	−47.8389	−	34.7570i	−1.31127	−	0.952693i	−0.999997	−	0.00237169i	$-0.999245\pi$
$11$	−47.8389	−	34.7570i	−1.31127	−	0.952693i	−0.311272	−	0.950321i	$-0.600755\pi$
$12$		0			0
$13$	5.10901	−	3.71191i	0.108999	−	0.0791922i	−0.531951	−	0.846775i	$-0.678541\pi$
$13$	5.10901	−	3.71191i	0.108999	−	0.0791922i	0.640949	+	0.767583i	$0.278541\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−40.6606	+	125.140i	−0.580097	+	1.78535i	0.0380312	+	0.999277i	$0.487891\pi$
$17$	−40.6606	+	125.140i	−0.580097	+	1.78535i	−0.618128	+	0.786078i	$0.712109\pi$
$18$		0			0
$19$	25.3925	−	78.1500i	0.306602	−	0.943623i	−0.672473	−	0.740122i	$-0.734768\pi$
$19$	25.3925	−	78.1500i	0.306602	−	0.943623i	0.979075	−	0.203501i	$-0.0652321\pi$
$20$		0			0
$21$	25.8199	+	79.4654i	0.268303	+	0.825752i
$22$		0			0
$23$	128.998	+	93.7224i	1.16947	+	0.849672i	0.990946	−	0.134262i	$-0.0428665\pi$
$23$	128.998	+	93.7224i	1.16947	+	0.849672i	0.178528	+	0.983935i	$0.442866\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−118.031	−	85.7543i	−0.841297	−	0.611238i
$28$		0			0
$29$	−15.4646	−	47.5950i	−0.0990240	−	0.304765i	0.889257	−	0.457407i	$-0.151222\pi$
$29$	−15.4646	−	47.5950i	−0.0990240	−	0.304765i	−0.988281	+	0.152642i	$0.951222\pi$
$30$		0			0
$31$	−13.8066	+	42.4924i	−0.0799917	+	0.246189i	−0.983053	−	0.183323i	$-0.941315\pi$
$31$	−13.8066	+	42.4924i	−0.0799917	+	0.246189i	0.903061	+	0.429512i	$0.141315\pi$
$32$		0			0
$33$	−90.5611	+	278.718i	−0.477717	+	1.47026i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	60.7145	−	44.1117i	0.269768	−	0.195998i	−0.444674	−	0.895692i	$-0.646681\pi$
$37$	60.7145	−	44.1117i	0.269768	−	0.195998i	0.714442	+	0.699695i	$0.246681\pi$
$38$		0			0
$39$	−25.3205	−	18.3964i	−0.103962	−	0.0755330i
$40$		0			0
$41$	−286.091	+	207.857i	−1.08975	+	0.791752i	−0.979357	−	0.202136i	$-0.935212\pi$
$41$	−286.091	+	207.857i	−1.08975	+	0.791752i	−0.110395	+	0.993888i	$0.535212\pi$
$42$		0			0
$43$	−79.3703			−0.281485			−0.140743	−	0.990046i	$-0.544949\pi$
$43$	−79.3703			−0.281485			−0.140743	+	0.990046i	$0.544949\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	94.1857	+	289.874i	0.292306	+	0.899626i	0.984113	+	0.177543i	$0.0568150\pi$
$47$	94.1857	+	289.874i	0.292306	+	0.899626i	−0.691807	+	0.722083i	$0.743185\pi$
$48$		0			0
$49$	−58.7686			−0.171337
$50$		0			0
$51$	652.120			1.79049
$52$		0			0
$53$	104.844	+	322.676i	0.271725	+	0.836282i	0.990067	+	0.140593i	$0.0449009\pi$
$53$	104.844	+	322.676i	0.271725	+	0.836282i	−0.718343	+	0.695689i	$0.755099\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−407.248			−0.946338
$58$		0			0
$59$	636.533	−	462.468i	1.40457	−	1.02048i	0.410483	−	0.911868i	$-0.365360\pi$
$59$	636.533	−	462.468i	1.40457	−	1.02048i	0.994084	−	0.108610i	$-0.0346399\pi$
$60$		0			0
$61$	675.055	+	490.456i	1.41692	+	1.02945i	0.992271	+	0.124090i	$0.0396011\pi$
$61$	675.055	+	490.456i	1.41692	+	1.02945i	0.424645	+	0.905360i	$0.360399\pi$
$62$		0			0
$63$	−33.2464	+	24.1549i	−0.0664865	+	0.0483053i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−187.851	+	578.147i	−0.342533	+	1.05421i	0.620359	+	0.784318i	$0.286987\pi$
$67$	−187.851	+	578.147i	−0.342533	+	1.05421i	−0.962891	+	0.269889i	$0.913013\pi$
$68$		0			0
$69$	244.198	−	751.566i	0.426059	−	1.31127i
$70$		0			0
$71$	−18.9894	−	58.4435i	−0.0317413	−	0.0976897i	0.933931	−	0.357454i	$-0.116355\pi$
$71$	−18.9894	−	58.4435i	−0.0317413	−	0.0976897i	−0.965672	+	0.259764i	$0.916355\pi$
$72$		0			0
$73$	−32.0156	−	23.2607i	−0.0513307	−	0.0372940i	0.561824	−	0.827257i	$-0.310100\pi$
$73$	−32.0156	−	23.2607i	−0.0513307	−	0.0372940i	−0.613155	+	0.789963i	$0.710100\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	806.523	+	585.973i	1.19366	+	0.867245i
$78$		0			0
$79$	178.592	+	549.648i	0.254343	+	0.782788i	0.993958	+	0.109758i	$0.0350075\pi$
$79$	178.592	+	549.648i	0.254343	+	0.782788i	−0.739615	+	0.673030i	$0.764992\pi$
$80$		0			0
$81$	−203.100	+	625.077i	−0.278601	+	0.857445i
$82$		0			0
$83$	−16.4914	+	50.7554i	−0.0218093	+	0.0671220i	−0.961369	−	0.275264i	$-0.911235\pi$
$83$	−16.4914	+	50.7554i	−0.0218093	+	0.0671220i	0.939560	+	0.342386i	$0.111235\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−200.654	+	145.784i	−0.247269	+	0.179652i
$88$		0			0
$89$	1170.83	+	850.656i	1.39447	+	1.01314i	0.995359	+	0.0962343i	$0.0306798\pi$
$89$	1170.83	+	850.656i	1.39447	+	1.01314i	0.399107	+	0.916904i	$0.369320\pi$
$90$		0			0
$91$	−86.1336	+	62.5797i	−0.0992226	+	0.0720894i
$92$		0			0
$93$	221.432			0.246898
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−16.5425	−	50.9127i	−0.0173159	−	0.0532928i	0.942025	−	0.335542i	$-0.108919\pi$
$97$	−16.5425	−	50.9127i	−0.0173159	−	0.0532928i	−0.959341	+	0.282249i	$0.908919\pi$
$98$		0			0
$99$	−144.136			−0.146326
$100$		0			0
$101$	−47.2102			−0.0465108			−0.0232554	−	0.999730i	$-0.507403\pi$
$101$	−47.2102			−0.0465108			−0.0232554	+	0.999730i	$0.507403\pi$
$102$		0			0
$103$	45.4731	+	139.952i	0.0435009	+	0.133882i	0.970448	−	0.241310i	$-0.0775769\pi$
$103$	45.4731	+	139.952i	0.0435009	+	0.133882i	−0.926947	+	0.375192i	$0.877577\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1350.74			−1.22038			−0.610192	−	0.792254i	$-0.708908\pi$
$107$	−1350.74			−1.22038			−0.610192	+	0.792254i	$0.708908\pi$
$108$		0			0
$109$	−220.694	+	160.344i	−0.193933	+	0.140900i	−0.680514	−	0.732735i	$-0.738244\pi$
$109$	−220.694	+	160.344i	−0.193933	+	0.140900i	0.486582	+	0.873635i	$0.338244\pi$
$110$		0			0
$111$	−300.904	−	218.620i	−0.257302	−	0.186941i
$112$		0			0
$113$	−511.662	+	371.744i	−0.425957	+	0.309476i	−0.780030	−	0.625742i	$-0.784796\pi$
$113$	−511.662	+	371.744i	−0.425957	+	0.309476i	0.354073	+	0.935218i	$0.384796\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.75677	−	14.6398i	0.00375866	−	0.0115680i
$118$		0			0
$119$	685.504	−	2109.76i	0.528067	−	1.62522i
$120$		0			0
$121$	669.208	+	2059.61i	0.502786	+	1.54742i
$122$		0			0
$123$	1417.88	+	1030.15i	1.03940	+	0.755167i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	741.293	+	538.581i	0.517946	+	0.376310i	0.815829	−	0.578293i	$-0.196281\pi$
$127$	741.293	+	538.581i	0.517946	+	0.376310i	−0.297884	+	0.954602i	$0.596281\pi$
$128$		0			0
$129$	121.556	+	374.111i	0.0829644	+	0.255338i
$130$		0			0
$131$	202.335	−	622.722i	0.134947	−	0.415324i	−0.860635	−	0.509223i	$-0.829933\pi$
$131$	202.335	−	622.722i	0.134947	−	0.415324i	0.995582	+	0.0938986i	$0.0299330\pi$
$132$		0			0
$133$	−428.096	+	1317.54i	−0.279102	+	0.858989i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	459.671	−	333.970i	0.286659	−	0.208270i	−0.435158	−	0.900354i	$-0.643307\pi$
$137$	459.671	−	333.970i	0.286659	−	0.208270i	0.721817	+	0.692084i	$0.243307\pi$
$138$		0			0
$139$	−2079.69	−	1510.98i	−1.26904	−	0.922014i	−0.269879	−	0.962894i	$-0.586984\pi$
$139$	−2079.69	−	1510.98i	−1.26904	−	0.922014i	−0.999164	+	0.0408805i	$0.986984\pi$
$140$		0			0
$141$	1222.07	−	887.886i	0.729907	−	0.530308i
$142$		0			0
$143$	−373.424			−0.218373
$144$		0			0
$145$		0			0
$146$		0			0
$147$	90.0044	+	277.005i	0.0504996	+	0.155422i
$148$		0			0
$149$	−3146.97			−1.73027			−0.865134	−	0.501541i	$-0.832767\pi$
$149$	−3146.97			−1.73027			−0.865134	+	0.501541i	$0.832767\pi$
$150$		0			0
$151$	−1560.39			−0.840946			−0.420473	−	0.907305i	$-0.638136\pi$
$151$	−1560.39			−0.840946			−0.420473	+	0.907305i	$0.638136\pi$
$152$		0			0
$153$	99.1116	+	305.034i	0.0523706	+	0.161180i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2777.66			−1.41198			−0.705992	−	0.708219i	$-0.749499\pi$
$157$	−2777.66			−1.41198			−0.705992	+	0.708219i	$0.749499\pi$
$158$		0			0
$159$	1360.36	−	988.360i	0.678513	−	0.492969i
$160$		0			0
$161$	−2174.79	−	1580.08i	−1.06458	−	0.773465i
$162$		0			0
$163$	439.571	−	319.367i	0.211226	−	0.153465i	−0.477142	−	0.878826i	$-0.658327\pi$
$163$	439.571	−	319.367i	0.211226	−	0.153465i	0.688368	+	0.725361i	$0.258327\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	148.969	−	458.479i	0.0690273	−	0.212444i	−0.910592	−	0.413306i	$-0.864374\pi$
$167$	148.969	−	458.479i	0.0690273	−	0.212444i	0.979620	+	0.200862i	$0.0643741\pi$
$168$		0			0
$169$	−666.587	+	2051.54i	−0.303408	+	0.933793i
$170$		0			0
$171$	−61.8950	−	190.493i	−0.0276797	−	0.0851893i
$172$		0			0
$173$	−2848.28	−	2069.40i	−1.25174	−	0.909442i	−0.253418	−	0.967357i	$-0.581555\pi$
$173$	−2848.28	−	2069.40i	−1.25174	−	0.909442i	−0.998322	+	0.0579150i	$0.981555\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3154.69	−	2292.02i	−1.33967	−	0.973325i
$178$		0			0
$179$	468.991	+	1443.41i	0.195833	+	0.602711i	0.999966	+	0.00826192i	$0.00262988\pi$
$179$	468.991	+	1443.41i	0.195833	+	0.602711i	−0.804133	+	0.594449i	$0.797370\pi$
$180$		0			0
$181$	1017.44	−	3131.37i	0.417823	−	1.28593i	−0.491879	−	0.870664i	$-0.663690\pi$
$181$	1017.44	−	3131.37i	0.417823	−	1.28593i	0.909702	−	0.415262i	$-0.136310\pi$
$182$		0			0
$183$	1277.91	−	3933.00i	0.516206	−	1.58872i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6294.66	−	4573.34i	2.46156	−	1.78843i
$188$		0			0
$189$	1989.90	+	1445.75i	0.765841	+	0.556416i
$190$		0			0
$191$	−3404.02	+	2473.17i	−1.28956	+	0.936922i	−0.999796	−	0.0201762i	$-0.993577\pi$
$191$	−3404.02	+	2473.17i	−1.28956	+	0.936922i	−0.289765	+	0.957098i	$0.593577\pi$
$192$		0			0
$193$	1843.42			0.687524			0.343762	−	0.939057i	$-0.388299\pi$
$193$	1843.42			0.687524			0.343762	+	0.939057i	$0.388299\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1150.87	+	3542.01i	0.416224	+	1.28101i	0.911152	+	0.412071i	$0.135195\pi$
$197$	1150.87	+	3542.01i	0.416224	+	1.28101i	−0.494928	+	0.868934i	$0.664805\pi$
$198$		0			0
$199$	−324.095			−0.115450			−0.0577248	−	0.998333i	$-0.518385\pi$
$199$	−324.095			−0.115450			−0.0577248	+	0.998333i	$0.518385\pi$
$200$		0			0
$201$	3012.78			1.05724
$202$		0			0
$203$	260.720	+	802.412i	0.0901425	+	0.277430i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	388.665			0.130503
$208$		0			0
$209$	−3931.00	+	2856.04i	−1.30102	+	0.945246i
$210$		0			0
$211$	−3043.05	−	2210.91i	−0.992855	−	0.721352i	−0.0323107	−	0.999478i	$-0.510287\pi$
$211$	−3043.05	−	2210.91i	−0.992855	−	0.721352i	−0.960545	+	0.278126i	$0.910287\pi$
$212$		0			0
$213$	−246.390	+	179.013i	−0.0792600	+	0.0575858i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	232.768	−	716.387i	0.0728172	−	0.224108i
$218$		0			0
$219$	−60.6070	+	186.529i	−0.0187006	+	0.0575546i
$220$		0			0
$221$	256.775	+	790.272i	0.0781564	+	0.240541i
$222$		0			0
$223$	−2240.86	−	1628.08i	−0.672911	−	0.488898i	0.198088	−	0.980184i	$-0.436527\pi$
$223$	−2240.86	−	1628.08i	−0.672911	−	0.488898i	−0.870998	+	0.491286i	$0.836527\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1428.96	+	1038.20i	0.417813	+	0.303559i	0.776757	−	0.629800i	$-0.216863\pi$
$227$	1428.96	+	1038.20i	0.417813	+	0.303559i	−0.358945	+	0.933359i	$0.616863\pi$
$228$		0			0
$229$	332.536	+	1023.44i	0.0959588	+	0.295331i	0.987502	−	0.157604i	$-0.0503770\pi$
$229$	332.536	+	1023.44i	0.0959588	+	0.295331i	−0.891544	+	0.452935i	$0.850377\pi$
$230$		0			0
$231$	1526.78	−	4698.96i	0.434870	−	1.33839i
$232$		0			0
$233$	1048.08	−	3225.67i	0.294688	−	0.906955i	−0.688639	−	0.725105i	$-0.741791\pi$
$233$	1048.08	−	3225.67i	0.294688	−	0.906955i	0.983326	−	0.181850i	$-0.0582086\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2317.25	−	1683.58i	0.635111	−	0.461435i
$238$		0			0
$239$	3460.57	+	2514.25i	0.936594	+	0.680475i	0.947598	−	0.319464i	$-0.103503\pi$
$239$	3460.57	+	2514.25i	0.936594	+	0.680475i	−0.0110046	+	0.999939i	$0.503503\pi$
$240$		0			0
$241$	−1761.89	+	1280.09i	−0.470927	+	0.342149i	−0.797803	−	0.602919i	$-0.794004\pi$
$241$	−1761.89	+	1280.09i	−0.470927	+	0.342149i	0.326875	+	0.945067i	$0.394004\pi$
$242$		0			0
$243$	−681.796			−0.179989
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−160.355	−	493.523i	−0.0413084	−	0.127134i
$248$		0			0
$249$	264.492			0.0673152
$250$		0			0
$251$	3829.18			0.962931			0.481465	−	0.876465i	$-0.340105\pi$
$251$	3829.18			0.962931			0.481465	+	0.876465i	$0.340105\pi$
$252$		0			0
$253$	−2913.60	−	8967.14i	−0.724018	−	2.22830i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1052.72			−0.255513			−0.127757	−	0.991806i	$-0.540778\pi$
$257$	−1052.72			−0.255513			−0.127757	+	0.991806i	$0.540778\pi$
$258$		0			0
$259$	−1023.60	+	743.686i	−0.245572	+	0.178419i
$260$		0			0
$261$	−98.6878	−	71.7009i	−0.0234047	−	0.0170045i
$262$		0			0
$263$	3271.97	−	2377.23i	0.767142	−	0.557361i	−0.133951	−	0.990988i	$-0.542766\pi$
$263$	3271.97	−	2377.23i	0.767142	−	0.557361i	0.901093	+	0.433627i	$0.142766\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2216.43	−	6821.46i	0.508027	−	1.56355i
$268$		0			0
$269$	−1125.70	+	3464.56i	−0.255150	+	0.785272i	0.738650	+	0.674090i	$0.235464\pi$
$269$	−1125.70	+	3464.56i	−0.255150	+	0.785272i	−0.993800	+	0.111182i	$0.964536\pi$
$270$		0			0
$271$	−893.315	−	2749.34i	−0.200240	−	0.616275i	−0.999875	−	0.0157892i	$-0.994974\pi$
$271$	−893.315	−	2749.34i	−0.200240	−	0.616275i	0.799635	−	0.600486i	$-0.205026\pi$
$272$		0			0
$273$	426.883	+	310.148i	0.0946378	+	0.0687584i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3663.41	−	2661.63i	−0.794633	−	0.577334i	0.114702	−	0.993400i	$-0.463409\pi$
$277$	−3663.41	−	2661.63i	−0.794633	−	0.577334i	−0.909335	+	0.416066i	$0.863409\pi$
$278$		0			0
$279$	33.6541	+	103.577i	0.00722158	+	0.0222257i
$280$		0			0
$281$	934.864	−	2877.21i	0.198467	−	0.610819i	−0.801451	−	0.598060i	$-0.795938\pi$
$281$	934.864	−	2877.21i	0.198467	−	0.610819i	0.999919	−	0.0127594i	$-0.00406156\pi$
$282$		0			0
$283$	−1762.71	+	5425.06i	−0.370255	+	1.13953i	0.576370	+	0.817189i	$0.304469\pi$
$283$	−1762.71	+	5425.06i	−0.370255	+	1.13953i	−0.946625	+	0.322338i	$0.895531\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4823.25	−	3504.30i	0.992012	−	0.720739i
$288$		0			0
$289$	−10032.2	−	7288.78i	−2.04196	−	1.48357i
$290$		0			0
$291$	−214.641	+	155.946i	−0.0432388	+	0.0314148i
$292$		0			0
$293$	−6874.37			−1.37067			−0.685333	−	0.728230i	$-0.740343\pi$
$293$	−6874.37			−1.37067			−0.685333	+	0.728230i	$0.740343\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2665.89	+	8204.78i	0.520845	+	1.60300i
$298$		0			0
$299$	1006.94			0.194759
$300$		0			0
$301$	1338.12			0.256238
$302$		0			0
$303$	72.3026	+	222.524i	0.0137085	+	0.0421904i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4653.22			−0.865060			−0.432530	−	0.901620i	$-0.642379\pi$
$307$	−4653.22			−0.865060			−0.432530	+	0.901620i	$0.642379\pi$
$308$		0			0
$309$	590.018	−	428.674i	0.108625	−	0.0789203i
$310$		0			0
$311$	−4202.31	−	3053.16i	−0.766210	−	0.556684i	0.134599	−	0.990900i	$-0.457025\pi$
$311$	−4202.31	−	3053.16i	−0.766210	−	0.556684i	−0.900809	+	0.434216i	$0.857025\pi$
$312$		0			0
$313$	−3853.37	+	2799.64i	−0.695863	+	0.505574i	−0.878582	−	0.477591i	$-0.841510\pi$
$313$	−3853.37	+	2799.64i	−0.695863	+	0.505574i	0.182719	+	0.983165i	$0.441510\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1936.73	−	5960.65i	0.343148	−	1.05610i	−0.619420	−	0.785060i	$-0.712632\pi$
$317$	1936.73	−	5960.65i	0.343148	−	1.05610i	0.962568	−	0.271040i	$-0.0873677\pi$
$318$		0			0
$319$	−914.452	+	2814.39i	−0.160500	+	0.493968i
$320$		0			0
$321$	2068.67	+	6366.70i	0.359694	+	1.10702i
$322$		0			0
$323$	8747.25	+	6355.25i	1.50684	+	1.09478i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1093.77	+	794.671i	0.184971	+	0.134390i
$328$		0			0
$329$	−1587.89	−	4887.03i	−0.266089	−	0.818938i
$330$		0			0
$331$	−2918.94	+	8983.56i	−0.484711	+	1.49179i	0.347688	+	0.937610i	$0.386967\pi$
$331$	−2918.94	+	8983.56i	−0.484711	+	1.49179i	−0.832399	+	0.554176i	$0.813033\pi$
$332$		0			0
$333$	56.5285	−	173.977i	0.00930254	−	0.0286303i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8919.14	+	6480.14i	−1.44171	+	1.04746i	−0.454030	+	0.890987i	$0.650014\pi$
$337$	−8919.14	+	6480.14i	−1.44171	+	1.04746i	−0.987681	+	0.156478i	$0.949986\pi$
$338$		0			0
$339$	2535.83	+	1842.39i	0.406275	+	0.295176i
$340$		0			0
$341$	2137.40	−	1552.91i	0.339433	−	0.246613i
$342$		0			0
$343$	6773.48			1.06628
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3117.46	+	9594.55i	0.482288	+	1.48433i	0.835870	+	0.548927i	$0.184964\pi$
$347$	3117.46	+	9594.55i	0.482288	+	1.48433i	−0.353582	+	0.935404i	$0.615036\pi$
$348$		0			0
$349$	7071.09			1.08455			0.542273	−	0.840202i	$-0.317564\pi$
$349$	7071.09			1.08455			0.542273	+	0.840202i	$0.317564\pi$
$350$		0			0
$351$	−921.332			−0.140106
$352$		0			0
$353$	3145.43	+	9680.64i	0.474262	+	1.45963i	0.846951	+	0.531671i	$0.178436\pi$
$353$	3145.43	+	9680.64i	0.474262	+	1.45963i	−0.372689	+	0.927956i	$0.621564\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−10994.2			−1.62990
$358$		0			0
$359$	2756.36	−	2002.61i	0.405223	−	0.294412i	−0.366442	−	0.930441i	$-0.619424\pi$
$359$	2756.36	−	2002.61i	0.405223	−	0.294412i	0.771665	+	0.636029i	$0.219424\pi$
$360$		0			0
$361$	86.4079	+	62.7790i	0.0125977	+	0.00915280i
$362$		0			0
$363$	8683.05	−	6308.61i	1.25549	−	0.912165i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2059.00	−	6336.96i	0.292859	−	0.901326i	−0.691074	−	0.722784i	$-0.742862\pi$
$367$	2059.00	−	6336.96i	0.292859	−	0.901326i	0.983932	−	0.178542i	$-0.0571380\pi$
$368$		0			0
$369$	−266.366	+	819.791i	−0.0375785	+	0.115655i
$370$		0			0
$371$	−1767.58	−	5440.05i	−0.247353	−	0.761275i
$372$		0			0
$373$	−4958.34	−	3602.45i	−0.688293	−	0.500074i	0.187805	−	0.982206i	$-0.439863\pi$
$373$	−4958.34	−	3602.45i	−0.688293	−	0.500074i	−0.876099	+	0.482132i	$0.839863\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−255.677	−	185.760i	−0.0349285	−	0.0253770i
$378$		0			0
$379$	−3610.91	−	11113.2i	−0.489393	−	1.50620i	−0.825517	−	0.564378i	$-0.809116\pi$
$379$	−3610.91	−	11113.2i	−0.489393	−	1.50620i	0.336124	−	0.941818i	$-0.390884\pi$
$380$		0			0
$381$	1403.30	−	4318.91i	0.188696	−	0.580747i
$382$		0			0
$383$	−3165.96	+	9743.83i	−0.422384	+	1.29996i	0.483093	+	0.875569i	$0.339513\pi$
$383$	−3165.96	+	9743.83i	−0.422384	+	1.29996i	−0.905477	+	0.424395i	$0.860487\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−156.519	+	113.718i	−0.0205589	+	0.0149369i
$388$		0			0
$389$	3651.69	+	2653.11i	0.475960	+	0.345805i	0.799759	−	0.600321i	$-0.204960\pi$
$389$	3651.69	+	2653.11i	0.475960	+	0.345805i	−0.323800	+	0.946126i	$0.604960\pi$
$390$		0			0
$391$	−16973.6	+	12332.0i	−2.19537	+	1.59503i
$392$		0			0
$393$	−3245.07			−0.416519
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3635.76	+	11189.7i	0.459631	+	1.41460i	0.865612	+	0.500716i	$0.166930\pi$
$397$	3635.76	+	11189.7i	0.459631	+	1.41460i	−0.405981	+	0.913881i	$0.633070\pi$
$398$		0			0
$399$	6865.85			0.861460
$400$		0			0
$401$	6156.96			0.766743			0.383371	−	0.923594i	$-0.374763\pi$
$401$	6156.96			0.766743			0.383371	+	0.923594i	$0.374763\pi$
$402$		0			0
$403$	87.1900	+	268.343i	0.0107773	+	0.0331690i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4437.70			−0.540463
$408$		0			0
$409$	−4636.63	+	3368.71i	−0.560554	+	0.407266i	−0.831662	−	0.555283i	$-0.812610\pi$
$409$	−4636.63	+	3368.71i	−0.560554	+	0.407266i	0.271108	+	0.962549i	$0.412610\pi$
$410$		0			0
$411$	−2278.15	−	1655.17i	−0.273413	−	0.198647i
$412$		0			0
$413$	−10731.4	+	7796.82i	−1.27859	+	0.928951i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3936.94	+	12116.7i	−0.462333	+	1.42292i
$418$		0			0
$419$	484.018	−	1489.65i	0.0564339	−	0.173686i	−0.918866	−	0.394569i	$-0.870894\pi$
$419$	484.018	−	1489.65i	0.0564339	−	0.173686i	0.975300	+	0.220883i	$0.0708940\pi$
$420$		0			0
$421$	4904.78	+	15095.4i	0.567801	+	1.74751i	0.659479	+	0.751723i	$0.270777\pi$
$421$	4904.78	+	15095.4i	0.567801	+	1.74751i	−0.0916782	+	0.995789i	$0.529223\pi$
$422$		0			0
$423$	601.050	+	436.689i	0.0690876	+	0.0501951i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−11380.9	−	8268.68i	−1.28983	−	0.937118i
$428$		0			0
$429$	571.900	+	1760.13i	0.0643627	+	0.198088i
$430$		0			0
$431$	3851.68	−	11854.2i	0.430461	−	1.32482i	−0.467206	−	0.884149i	$-0.654739\pi$
$431$	3851.68	−	11854.2i	0.430461	−	1.32482i	0.897667	−	0.440674i	$-0.145261\pi$
$432$		0			0
$433$	4530.50	−	13943.4i	0.502822	−	1.54753i	−0.301579	−	0.953441i	$-0.597514\pi$
$433$	4530.50	−	13943.4i	0.502822	−	1.54753i	0.804401	−	0.594086i	$-0.202486\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10600.0	−	7701.33i	1.16033	−	0.843031i
$438$		0			0
$439$	−3142.95	−	2283.49i	−0.341697	−	0.248257i	0.403681	−	0.914900i	$-0.367731\pi$
$439$	−3142.95	−	2283.49i	−0.341697	−	0.248257i	−0.745377	+	0.666643i	$0.767731\pi$
$440$		0			0
$441$	−115.892	+	84.2005i	−0.0125140	+	0.00909194i
$442$		0			0
$443$	4840.23			0.519111			0.259556	−	0.965728i	$-0.416424\pi$
$443$	4840.23			0.519111			0.259556	+	0.965728i	$0.416424\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4819.60	+	14833.2i	0.509976	+	1.56955i
$448$		0			0
$449$	9780.24			1.02797			0.513985	−	0.857799i	$-0.328169\pi$
$449$	9780.24			1.02797			0.513985	+	0.857799i	$0.328169\pi$
$450$		0			0
$451$	20910.7			2.18325
$452$		0			0
$453$	2389.75	+	7354.88i	0.247859	+	0.762831i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3537.61			−0.362106			−0.181053	−	0.983473i	$-0.557950\pi$
$457$	−3537.61			−0.362106			−0.181053	+	0.983473i	$0.557950\pi$
$458$		0			0
$459$	15530.5	−	11283.6i	1.57931	−	1.14744i
$460$		0			0
$461$	9138.35	+	6639.40i	0.923243	+	0.670776i	0.944329	−	0.329002i	$-0.106712\pi$
$461$	9138.35	+	6639.40i	0.923243	+	0.670776i	−0.0210859	+	0.999778i	$0.506712\pi$
$462$		0			0
$463$	−1616.02	+	1174.11i	−0.162209	+	0.117852i	−0.665929	−	0.746015i	$-0.731965\pi$
$463$	−1616.02	+	1174.11i	−0.162209	+	0.117852i	0.503719	+	0.863867i	$0.331965\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3537.19	+	10886.4i	−0.350496	+	1.07872i	0.608079	+	0.793877i	$0.291941\pi$
$467$	−3537.19	+	10886.4i	−0.350496	+	1.07872i	−0.958575	+	0.284840i	$0.908059\pi$
$468$		0			0
$469$	3167.02	−	9747.07i	0.311811	−	0.959655i
$470$		0			0
$471$	4254.00	+	13092.5i	0.416166	+	1.28083i
$472$		0			0
$473$	3796.98	+	2758.67i	0.369103	+	0.268169i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	669.065	+	486.105i	0.0642231	+	0.0466608i
$478$		0			0
$479$	−1357.34	−	4177.45i	−0.129474	−	0.398481i	0.865215	−	0.501401i	$-0.167182\pi$
$479$	−1357.34	−	4177.45i	−0.129474	−	0.398481i	−0.994690	+	0.102919i	$0.967182\pi$
$480$		0			0
$481$	146.452	−	450.734i	0.0138828	−	0.0427270i
$482$		0			0
$483$	−4116.98	+	12670.8i	−0.387845	+	1.19366i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6066.67	−	4407.69i	0.564491	−	0.410127i	−0.268609	−	0.963249i	$-0.586564\pi$
$487$	6066.67	−	4407.69i	0.564491	−	0.410127i	0.833100	+	0.553123i	$0.186564\pi$
$488$		0			0
$489$	−2178.54	−	1582.80i	−0.201466	−	0.146374i
$490$		0			0
$491$	−348.167	+	252.958i	−0.0320011	+	0.0232502i	−0.603671	−	0.797234i	$-0.706296\pi$
$491$	−348.167	+	252.958i	−0.0320011	+	0.0232502i	0.571670	+	0.820484i	$0.306296\pi$
$492$		0			0
$493$	6584.86			0.601556
$494$		0			0
$495$		0			0
$496$		0			0
$497$	320.146	+	985.309i	0.0288944	+	0.0889278i
$498$		0			0
$499$	−1063.14			−0.0953765			−0.0476883	−	0.998862i	$-0.515185\pi$
$499$	−1063.14			−0.0953765			−0.0476883	+	0.998862i	$0.515185\pi$
$500$		0			0
$501$	−2389.18			−0.213055
$502$		0			0
$503$	845.164	+	2601.15i	0.0749185	+	0.230575i	0.981502	−	0.191450i	$-0.0613191\pi$
$503$	845.164	+	2601.15i	0.0749185	+	0.230575i	−0.906584	+	0.422026i	$0.861319\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	10690.8			0.936480
$508$		0			0
$509$	−7550.83	+	5486.00i	−0.657533	+	0.477726i	−0.865829	−	0.500340i	$-0.833208\pi$
$509$	−7550.83	+	5486.00i	−0.657533	+	0.477726i	0.208296	+	0.978066i	$0.433208\pi$
$510$		0			0
$511$	539.757	+	392.156i	0.0467269	+	0.0339490i
$512$		0			0
$513$	−9698.79	+	7046.58i	−0.834721	+	0.606460i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5569.40	−	17140.8i	0.473775	−	1.45813i
$518$		0			0
$519$	−5391.92	+	16594.6i	−0.456029	+	1.40351i
$520$		0			0
$521$	6778.80	+	20863.0i	0.570028	+	1.75437i	0.652517	+	0.757774i	$0.273713\pi$
$521$	6778.80	+	20863.0i	0.570028	+	1.75437i	−0.0824889	+	0.996592i	$0.526287\pi$
$522$		0			0
$523$	−8162.82	−	5930.64i	−0.682477	−	0.495848i	0.191702	−	0.981453i	$-0.438599\pi$
$523$	−8162.82	−	5930.64i	−0.682477	−	0.495848i	−0.874178	+	0.485605i	$0.838599\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4756.14	−	3455.54i	−0.393132	−	0.285627i
$528$		0			0
$529$	4096.74	+	12608.5i	0.336709	+	1.03628i
$530$		0			0
$531$	592.647	−	1823.98i	0.0484344	−	0.149066i
$532$		0			0
$533$	−690.093	+	2123.89i	−0.0560811	+	0.172600i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6085.22	−	4421.17i	0.489007	−	0.355284i
$538$		0			0
$539$	2811.42	+	2042.62i	0.224669	+	0.163232i
$540$		0			0
$541$	3988.34	−	2897.70i	0.316954	−	0.230281i	−0.417920	−	0.908484i	$-0.637241\pi$
$541$	3988.34	−	2897.70i	0.316954	−	0.230281i	0.734875	+	0.678203i	$0.237241\pi$
$542$		0			0
$543$	−16317.9			−1.28963
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5145.67	+	15836.7i	0.402217	+	1.23790i	0.923196	+	0.384328i	$0.125567\pi$
$547$	5145.67	+	15836.7i	0.402217	+	1.23790i	−0.520979	+	0.853569i	$0.674433\pi$
$548$		0			0
$549$	2033.91			0.158115
$550$		0			0
$551$	−4112.23			−0.317944
$552$		0			0
$553$	−3010.90	−	9266.61i	−0.231531	−	0.712579i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13982.7			−1.06367			−0.531836	−	0.846847i	$-0.678498\pi$
$557$	−13982.7			−1.06367			−0.531836	+	0.846847i	$0.678498\pi$
$558$		0			0
$559$	−405.504	+	294.616i	−0.0306815	+	0.0222914i
$560$		0			0
$561$	−31196.7	−	22665.7i	−2.34782	−	1.70579i
$562$		0			0
$563$	8022.71	−	5828.84i	0.600563	−	0.436334i	−0.245516	−	0.969393i	$-0.578957\pi$
$563$	8022.71	−	5828.84i	0.600563	−	0.436334i	0.846079	+	0.533058i	$0.178957\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3424.09	−	10538.3i	0.253613	−	0.780540i
$568$		0			0
$569$	2562.12	−	7885.39i	0.188769	−	0.580972i	−0.811224	−	0.584736i	$-0.801198\pi$
$569$	2562.12	−	7885.39i	0.188769	−	0.580972i	0.999993	+	0.00376415i	$0.00119817\pi$
$570$		0			0
$571$	1824.42	+	5614.99i	0.133712	+	0.411524i	0.995387	−	0.0959364i	$-0.0305845\pi$
$571$	1824.42	+	5614.99i	0.133712	+	0.411524i	−0.861675	+	0.507460i	$0.830585\pi$
$572$		0			0
$573$	16870.5	+	12257.1i	1.22997	+	0.893629i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4866.15	−	3535.47i	−0.351093	−	0.255084i	0.398234	−	0.917284i	$-0.369623\pi$
$577$	−4866.15	−	3535.47i	−0.351093	−	0.255084i	−0.749327	+	0.662200i	$0.769623\pi$
$578$		0			0
$579$	−2823.20	−	8688.92i	−0.202639	−	0.623660i
$580$		0			0
$581$	278.032	−	855.694i	0.0198532	−	0.0611018i
$582$		0			0
$583$	6199.63	−	19080.5i	0.440416	−	1.35546i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6931.13	+	5035.76i	−0.487357	+	0.354085i	−0.804167	−	0.594404i	$-0.797388\pi$
$587$	−6931.13	+	5035.76i	−0.487357	+	0.354085i	0.316810	+	0.948489i	$0.397388\pi$
$588$		0			0
$589$	2970.20	+	2157.97i	0.207784	+	0.150964i
$590$		0			0
$591$	14932.7	−	10849.2i	1.03934	−	0.755123i
$592$		0			0
$593$	19704.6			1.36453			0.682267	−	0.731103i	$-0.260994\pi$
$593$	19704.6			1.36453			0.682267	+	0.731103i	$0.260994\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	496.353	+	1527.62i	0.0340274	+	0.104726i
$598$		0			0
$599$	−2540.05			−0.173262			−0.0866308	−	0.996240i	$-0.527610\pi$
$599$	−2540.05			−0.173262			−0.0866308	+	0.996240i	$0.527610\pi$
$600$		0			0
$601$	−18593.4			−1.26197			−0.630983	−	0.775797i	$-0.717348\pi$
$601$	−18593.4			−1.26197			−0.630983	+	0.775797i	$0.717348\pi$
$602$		0			0
$603$	457.894	+	1409.25i	0.0309235	+	0.0951728i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−22878.6			−1.52984			−0.764922	−	0.644123i	$-0.777222\pi$
$607$	−22878.6			−1.52984			−0.764922	+	0.644123i	$0.777222\pi$
$608$		0			0
$609$	3382.87	−	2457.80i	0.225091	−	0.163538i
$610$		0			0
$611$	1557.18	+	1131.36i	0.103104	+	0.0749098i
$612$		0			0
$613$	11697.2	−	8498.54i	0.770713	−	0.559956i	−0.131464	−	0.991321i	$-0.541968\pi$
$613$	11697.2	−	8498.54i	0.770713	−	0.559956i	0.902178	+	0.431365i	$0.141968\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6038.28	+	18583.9i	−0.393990	+	1.21258i	0.535755	+	0.844373i	$0.320027\pi$
$617$	−6038.28	+	18583.9i	−0.393990	+	1.21258i	−0.929745	+	0.368203i	$0.879973\pi$
$618$		0			0
$619$	5737.53	−	17658.3i	0.372553	−	1.14660i	−0.572561	−	0.819862i	$-0.694050\pi$
$619$	5737.53	−	17658.3i	0.372553	−	1.14660i	0.945114	−	0.326740i	$-0.105950\pi$
$620$		0			0
$621$	−7188.60	−	22124.2i	−0.464523	−	1.42965i
$622$		0			0
$623$	−19739.2	−	14341.3i	−1.26940	−	0.922270i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	19482.3	+	14154.7i	1.24090	+	0.901569i
$628$		0			0
$629$	3051.47	+	9391.45i	0.193434	+	0.595328i
$630$		0			0
$631$	−1938.92	+	5967.39i	−0.122325	+	0.376479i	−0.993404	−	0.114664i	$-0.963421\pi$
$631$	−1938.92	+	5967.39i	−0.122325	+	0.376479i	0.871079	+	0.491143i	$0.163421\pi$
$632$		0			0
$633$	−5760.63	+	17729.4i	−0.361714	+	1.11324i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−300.249	+	218.144i	−0.0186755	+	0.0135686i
$638$		0			0
$639$	−121.182	−	88.0439i	−0.00750217	−	0.00545065i
$640$		0			0
$641$	−5365.30	+	3898.12i	−0.330603	+	0.240197i	−0.740687	−	0.671851i	$-0.765500\pi$
$641$	−5365.30	+	3898.12i	−0.330603	+	0.240197i	0.410083	+	0.912048i	$0.365500\pi$
$642$		0			0
$643$	−12509.7			−0.767240			−0.383620	−	0.923491i	$-0.625323\pi$
$643$	−12509.7			−0.767240			−0.383620	+	0.923491i	$0.625323\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7822.81	−	24076.1i	−0.475342	−	1.46295i	−0.845496	−	0.533982i	$-0.820695\pi$
$647$	−7822.81	−	24076.1i	−0.475342	−	1.46295i	0.370154	−	0.928970i	$-0.379305\pi$
$648$		0			0
$649$	−46525.0			−2.81397
$650$		0			0
$651$	−3733.17			−0.224753
$652$		0			0
$653$	−280.384	−	862.934i	−0.0168029	−	0.0517140i	0.942304	−	0.334760i	$-0.108655\pi$
$653$	−280.384	−	862.934i	−0.0168029	−	0.0517140i	−0.959106	+	0.283046i	$0.908655\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−96.4617			−0.00572805
$658$		0			0
$659$	−9417.94	+	6842.54i	−0.556709	+	0.404473i	−0.830253	−	0.557387i	$-0.811804\pi$
$659$	−9417.94	+	6842.54i	−0.556709	+	0.404473i	0.273544	+	0.961859i	$0.411804\pi$
$660$		0			0
$661$	16022.0	+	11640.7i	0.942791	+	0.684977i	0.949091	−	0.315003i	$-0.102005\pi$
$661$	16022.0	+	11640.7i	0.942791	+	0.684977i	−0.00630023	+	0.999980i	$0.502005\pi$
$662$		0			0
$663$	3331.69	−	2420.61i	0.195161	−	0.141793i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2465.82	−	7589.03i	0.143144	−	0.440552i
$668$		0			0
$669$	−4242.05	+	13055.7i	−0.245152	+	0.754502i
$670$		0			0
$671$	−15247.1	−	46925.7i	−0.877209	−	2.69977i
$672$		0			0
$673$	−3194.22	−	2320.74i	−0.182954	−	0.132924i	0.492538	−	0.870291i	$-0.336069\pi$
$673$	−3194.22	−	2320.74i	−0.182954	−	0.132924i	−0.675493	+	0.737367i	$0.736069\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20291.5	+	14742.6i	1.15194	+	0.836935i	0.988738	−	0.149657i	$-0.0478171\pi$
$677$	20291.5	+	14742.6i	1.15194	+	0.836935i	0.163204	+	0.986592i	$0.447817\pi$
$678$		0			0
$679$	278.893	+	858.345i	0.0157628	+	0.0485129i
$680$		0			0
$681$	2705.09	−	8325.40i	0.152216	−	0.468473i
$682$		0			0
$683$	2278.10	−	7011.29i	0.127627	−	0.392796i	−0.866744	−	0.498754i	$-0.833791\pi$
$683$	2278.10	−	7011.29i	0.127627	−	0.392796i	0.994371	+	0.105959i	$0.0337911\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4314.69	−	3134.80i	0.239615	−	0.174091i
$688$		0			0
$689$	1733.39	+	1259.38i	0.0958447	+	0.0696353i
$690$		0			0
$691$	−24373.2	+	17708.2i	−1.34183	+	0.974894i	−0.342452	+	0.939535i	$0.611257\pi$
$691$	−24373.2	+	17708.2i	−1.34183	+	0.974894i	−0.999375	+	0.0353584i	$0.988743\pi$
$692$		0			0
$693$	2430.02			0.133202
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−14378.7	−	44253.1i	−0.781395	−	2.40489i
$698$		0			0
$699$	−16809.3			−0.909564
$700$		0			0
$701$	275.799			0.0148599			0.00742994	−	0.999972i	$-0.497635\pi$
$701$	275.799			0.0148599			0.00742994	+	0.999972i	$0.497635\pi$
$702$		0			0
$703$	−1905.63	−	5864.94i	−0.102237	−	0.314652i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	795.924			0.0423392
$708$		0			0
$709$	3614.00	−	2625.72i	0.191434	−	0.139085i	−0.487940	−	0.872877i	$-0.662252\pi$
$709$	3614.00	−	2625.72i	0.191434	−	0.139085i	0.679374	+	0.733792i	$0.262252\pi$
$710$		0			0
$711$	1139.69	+	828.033i	0.0601149	+	0.0436760i
$712$		0			0
$713$	−5763.52	+	4187.44i	−0.302728	+	0.219945i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6551.02	−	20162.0i	0.341217	−	1.05016i
$718$		0			0
$719$	1471.37	−	4528.41i	0.0763183	−	0.234883i	−0.905618	−	0.424094i	$-0.860593\pi$
$719$	1471.37	−	4528.41i	0.0763183	−	0.234883i	0.981937	+	0.189210i	$0.0605927\pi$
$720$		0			0
$721$	−766.638	−	2359.47i	−0.0395993	−	0.121874i
$722$		0			0
$723$	8732.03	+	6344.19i	0.449167	+	0.326339i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−16098.8	−	11696.4i	−0.821279	−	0.596694i	0.0957995	−	0.995401i	$-0.469459\pi$
$727$	−16098.8	−	11696.4i	−0.821279	−	0.596694i	−0.917079	+	0.398707i	$0.869459\pi$
$728$		0			0
$729$	6527.87	+	20090.7i	0.331650	+	1.02071i
$730$		0			0
$731$	3227.24	−	9932.44i	0.163289	−	0.502551i
$732$		0			0
$733$	7113.68	−	21893.7i	0.358458	−	1.10322i	−0.595519	−	0.803341i	$-0.703054\pi$
$733$	7113.68	−	21893.7i	0.358458	−	1.10322i	0.953977	−	0.299879i	$-0.0969465\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	29081.2	−	21128.7i	1.45349	−	1.05602i
$738$		0			0
$739$	3899.72	+	2833.31i	0.194119	+	0.141035i	0.680599	−	0.732656i	$-0.261720\pi$
$739$	3899.72	+	2833.31i	0.194119	+	0.141035i	−0.486481	+	0.873691i	$0.661720\pi$
$740$		0			0
$741$	−2080.63	+	1511.67i	−0.103150	+	0.0749426i
$742$		0			0
$743$	−11267.6			−0.556348			−0.278174	−	0.960531i	$-0.589729\pi$
$743$	−11267.6			−0.556348			−0.278174	+	0.960531i	$0.589729\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	40.1984	+	123.718i	0.00196892	+	0.00605971i
$748$		0			0
$749$	22772.4			1.11093
$750$		0			0
$751$	21124.7			1.02643			0.513216	−	0.858259i	$-0.328454\pi$
$751$	21124.7			1.02643			0.513216	+	0.858259i	$0.328454\pi$
$752$		0			0
$753$	−5864.41	−	18048.8i	−0.283813	−	0.873485i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	25198.7			1.20986			0.604929	−	0.796279i	$-0.293201\pi$
$757$	25198.7			1.20986			0.604929	+	0.796279i	$0.293201\pi$
$758$		0			0
$759$	−37804.3	+	27466.4i	−1.80792	+	1.31353i
$760$		0			0
$761$	−7499.45	−	5448.67i	−0.357234	−	0.259546i	0.394664	−	0.918826i	$-0.370861\pi$
$761$	−7499.45	−	5448.67i	−0.357234	−	0.259546i	−0.751897	+	0.659280i	$0.770861\pi$
$762$		0			0
$763$	3720.72	−	2703.26i	0.176539	−	0.128263i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1535.41	−	4725.51i	0.0722822	−	0.222462i
$768$		0			0
$769$	−2189.37	+	6738.20i	−0.102667	+	0.315976i	−0.989176	−	0.146735i	$-0.953123\pi$
$769$	−2189.37	+	6738.20i	−0.102667	+	0.315976i	0.886509	+	0.462712i	$0.153123\pi$
$770$		0			0
$771$	1612.25	+	4961.98i	0.0753095	+	0.231779i
$772$		0			0
$773$	−10867.3	−	7895.59i	−0.505655	−	0.367380i	0.305518	−	0.952186i	$-0.401170\pi$
$773$	−10867.3	−	7895.59i	−0.505655	−	0.367380i	−0.811173	+	0.584806i	$0.801170\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5073.00	+	3685.75i	0.234225	+	0.170174i
$778$		0			0
$779$	8979.47	+	27636.0i	0.412995	+	1.27107i
$780$		0			0
$781$	−1122.89	+	3455.89i	−0.0514469	+	0.158337i
$782$		0			0
$783$	−2256.19	+	6943.83i	−0.102975	+	0.316925i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−10212.9	+	7420.09i	−0.462579	+	0.336084i	−0.794542	−	0.607209i	$-0.792289\pi$
$787$	−10212.9	+	7420.09i	−0.462579	+	0.336084i	0.331963	+	0.943292i	$0.392289\pi$
$788$		0			0
$789$	−16216.1	−	11781.7i	−0.731695	−	0.531607i
$790$		0			0
$791$	8626.20	−	6267.30i	0.387753	−	0.281719i
$792$		0			0
$793$	5269.39			0.235967
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6271.34	+	19301.2i	0.278723	+	0.857822i	0.988210	+	0.153103i	$0.0489267\pi$
$797$	6271.34	+	19301.2i	0.278723	+	0.857822i	−0.709487	+	0.704718i	$0.751073\pi$
$798$		0			0
$799$	−40104.6			−1.77572
$800$		0			0
$801$	3527.65			0.155610
$802$		0			0
$803$	723.119	+	2225.53i	0.0317787	+	0.0978048i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18054.2			0.787531
$808$		0			0
$809$	34293.3	−	24915.5i	1.49034	−	1.08280i	0.516308	−	0.856403i	$-0.327306\pi$
$809$	34293.3	−	24915.5i	1.49034	−	1.08280i	0.974036	−	0.226395i	$-0.0726940\pi$
$810$		0			0
$811$	18821.8	+	13674.9i	0.814949	+	0.592095i	0.915261	−	0.402861i	$-0.131984\pi$
$811$	18821.8	+	13674.9i	0.814949	+	0.592095i	−0.100312	+	0.994956i	$0.531984\pi$
$812$		0			0
$813$	−11590.9	+	8421.25i	−0.500011	+	0.363280i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2015.41	+	6202.79i	−0.0863038	+	0.265616i
$818$		0			0
$819$	−80.1951	+	246.815i	−0.00342154	+	0.0105304i
$820$		0			0
$821$	−6419.92	−	19758.5i	−0.272907	−	0.839921i	−0.989766	−	0.142703i	$-0.954421\pi$
$821$	−6419.92	−	19758.5i	−0.272907	−	0.839921i	0.716859	−	0.697219i	$-0.245579\pi$
$822$		0			0
$823$	2002.18	+	1454.67i	0.0848017	+	0.0616120i	0.629378	−	0.777099i	$-0.283310\pi$
$823$	2002.18	+	1454.67i	0.0848017	+	0.0616120i	−0.544577	+	0.838711i	$0.683310\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8611.12	+	6256.34i	0.362077	+	0.263064i	0.753918	−	0.656969i	$-0.228162\pi$
$827$	8611.12	+	6256.34i	0.362077	+	0.263064i	−0.391841	+	0.920033i	$0.628162\pi$
$828$		0			0
$829$	−6995.29	−	21529.3i	−0.293072	−	0.901982i	−0.983862	−	0.178927i	$-0.942737\pi$
$829$	−6995.29	−	21529.3i	−0.293072	−	0.901982i	0.690791	−	0.723055i	$-0.257263\pi$
$830$		0			0
$831$	−6935.00	+	21343.8i	−0.289498	+	0.890983i
$832$		0			0
$833$	2389.57	−	7354.33i	0.0993920	−	0.305897i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5273.52	−	3831.43i	0.217777	−	0.158224i
$838$		0			0
$839$	27328.7	+	19855.5i	1.12454	+	0.817029i	0.984892	−	0.173171i	$-0.0554014\pi$
$839$	27328.7	+	19855.5i	1.12454	+	0.817029i	0.139653	+	0.990201i	$0.455401\pi$
$840$		0			0
$841$	17705.0	−	12863.4i	0.725941	−	0.527427i
$842$		0			0
$843$	−14993.5			−0.612577
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−11282.3	−	34723.3i	−0.457691	−	1.40863i
$848$		0			0
$849$	28270.5			1.14281
$850$		0			0
$851$	11966.3			0.482020
$852$		0			0
$853$	−11601.1	−	35704.6i	−0.465669	−	1.43318i	−0.858140	−	0.513416i	$-0.828380\pi$
$853$	−11601.1	−	35704.6i	−0.465669	−	1.43318i	0.392471	−	0.919764i	$-0.371620\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24120.1			0.961408			0.480704	−	0.876883i	$-0.340381\pi$
$857$	24120.1			0.961408			0.480704	+	0.876883i	$0.340381\pi$
$858$		0			0
$859$	5422.85	−	3939.93i	0.215396	−	0.156494i	−0.474856	−	0.880064i	$-0.657500\pi$
$859$	5422.85	−	3939.93i	0.215396	−	0.156494i	0.690252	+	0.723569i	$0.257500\pi$
$860$		0			0
$861$	−23904.3	−	17367.5i	−0.946174	−	0.687436i
$862$		0			0
$863$	25270.2	−	18359.9i	0.996766	−	0.724193i	0.0353735	−	0.999374i	$-0.488738\pi$
$863$	25270.2	−	18359.9i	0.996766	−	0.724193i	0.961392	+	0.275181i	$0.0887379\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18991.3	+	58449.2i	−0.743920	+	2.28955i
$868$		0			0
$869$	10560.5	−	32501.8i	0.412244	−	1.26876i
$870$		0			0
$871$	1186.30	+	3651.04i	0.0461494	+	0.142033i
$872$		0			0
$873$	−105.567	−	76.6988i	−0.00409267	−	0.00297350i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19633.2	−	14264.4i	−0.755948	−	0.549228i	0.141717	−	0.989907i	$-0.454738\pi$
$877$	−19633.2	−	14264.4i	−0.755948	−	0.549228i	−0.897665	+	0.440679i	$0.854738\pi$
$878$		0			0
$879$	10528.1	+	32402.3i	0.403988	+	1.24335i
$880$		0			0
$881$	1004.56	−	3091.71i	0.0384159	−	0.118232i	−0.930010	−	0.367535i	$-0.880202\pi$
$881$	1004.56	−	3091.71i	0.0384159	−	0.118232i	0.968425	+	0.249304i	$0.0802017\pi$
$882$		0			0
$883$	3759.01	−	11569.0i	0.143262	−	0.440916i	−0.853521	−	0.521058i	$-0.825537\pi$
$883$	3759.01	−	11569.0i	0.143262	−	0.440916i	0.996783	+	0.0801422i	$0.0255374\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10503.8	+	7631.43i	−0.397612	+	0.288882i	−0.768568	−	0.639768i	$-0.779030\pi$
$887$	−10503.8	+	7631.43i	−0.397612	+	0.288882i	0.370956	+	0.928651i	$0.379030\pi$
$888$		0			0
$889$	−12497.6	−	9080.02i	−0.471491	−	0.342558i
$890$		0			0
$891$	31441.9	−	22843.8i	1.18220	−	0.858920i
$892$		0			0
$893$	25045.2			0.938529
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1542.13	−	4746.20i	−0.0574028	−	0.176668i
$898$		0			0
$899$	2235.94			0.0829509
$900$		0			0
$901$	−44642.8			−1.65069
$902$		0			0
$903$	−2049.33	−	6307.20i	−0.0755233	−	0.232437i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−34569.1			−1.26554			−0.632771	−	0.774339i	$-0.718083\pi$
$907$	−34569.1			−1.26554			−0.632771	+	0.774339i	$0.718083\pi$
$908$		0			0
$909$	−93.0987	+	67.6402i	−0.00339702	+	0.00246808i
$910$		0			0
$911$	−7607.64	−	5527.27i	−0.276676	−	0.201017i	0.440790	−	0.897610i	$-0.354698\pi$
$911$	−7607.64	−	5527.27i	−0.276676	−	0.201017i	−0.717466	+	0.696593i	$0.754698\pi$
$912$		0			0
$913$	2553.03	−	1854.89i	0.0925445	−	0.0672375i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3411.19	+	10498.6i	−0.122843	+	0.378073i
$918$		0			0
$919$	−12428.8	+	38251.9i	−0.446124	+	1.37303i	0.435121	+	0.900372i	$0.356705\pi$
$919$	−12428.8	+	38251.9i	−0.446124	+	1.37303i	−0.881246	+	0.472658i	$0.843295\pi$
$920$		0			0
$921$	7126.43	+	21932.9i	0.254966	+	0.784705i
$922$		0			0
$923$	−313.954	−	228.101i	−0.0111960	−	0.00813439i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	290.189	+	210.834i	0.0102816	+	0.00747002i
$928$		0			0
$929$	4084.78	+	12571.7i	0.144260	+	0.443986i	0.996915	−	0.0784880i	$-0.0250092\pi$
$929$	4084.78	+	12571.7i	0.144260	+	0.443986i	−0.852655	+	0.522474i	$0.825009\pi$
$930$		0			0
$931$	−1492.28	+	4592.76i	−0.0525322	+	0.161677i
$932$		0			0
$933$	−7955.16	+	24483.5i	−0.279143	+	0.859114i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−5460.58	+	3967.34i	−0.190384	+	0.138322i	−0.678894	−	0.734236i	$-0.737540\pi$
$937$	−5460.58	+	3967.34i	−0.190384	+	0.138322i	0.488510	+	0.872558i	$0.337540\pi$
$938$		0			0
$939$	19097.5	+	13875.1i	0.663709	+	0.482213i
$940$		0			0
$941$	−19548.5	+	14202.8i	−0.677219	+	0.492028i	−0.872434	−	0.488732i	$-0.837460\pi$
$941$	−19548.5	+	14202.8i	−0.677219	+	0.492028i	0.195215	+	0.980760i	$0.437460\pi$
$942$		0			0
$943$	−56385.9			−1.94717
$944$		0			0
$945$		0			0
$946$		0			0
$947$	834.834	+	2569.36i	0.0286467	+	0.0881656i	0.964358	−	0.264602i	$-0.0852406\pi$
$947$	834.834	+	2569.36i	0.0286467	+	0.0881656i	−0.935711	+	0.352768i	$0.885241\pi$
$948$		0			0
$949$	−249.910			−0.00854838
$950$		0			0
$951$	−31061.6			−1.05914
$952$		0			0
$953$	10996.2	+	33842.8i	0.373768	+	1.15034i	0.944306	+	0.329069i	$0.106735\pi$
$953$	10996.2	+	33842.8i	0.373768	+	1.15034i	−0.570537	+	0.821272i	$0.693265\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	14666.1			0.495389
$958$		0			0
$959$	−7749.66	+	5630.46i	−0.260948	+	0.189590i
$960$		0			0
$961$	22486.4	+	16337.4i	0.754807	+	0.548399i
$962$		0			0
$963$	−2663.67	+	1935.27i	−0.0891335	+	0.0647593i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1818.77	+	5597.59i	−0.0604836	+	0.186149i	−0.976733	−	0.214459i	$-0.931201\pi$
$967$	−1818.77	+	5597.59i	−0.0604836	+	0.186149i	0.916249	+	0.400608i	$0.131201\pi$
$968$		0			0
$969$	16558.9	−	50963.1i	0.548967	−	1.68955i
$970$		0			0
$971$	12777.2	+	39324.0i	0.422285	+	1.29966i	0.905570	+	0.424196i	$0.139443\pi$
$971$	12777.2	+	39324.0i	0.422285	+	1.29966i	−0.483286	+	0.875463i	$0.660557\pi$
$972$		0			0
$973$	35061.8	+	25473.9i	1.15522	+	0.839318i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22324.9	+	16220.0i	0.731052	+	0.531141i	0.889896	−	0.456163i	$-0.150777\pi$
$977$	22324.9	+	16220.0i	0.731052	+	0.531141i	−0.158844	+	0.987304i	$0.550777\pi$
$978$		0			0
$979$	−26444.8	−	81388.8i	−0.863310	−	2.65699i
$980$		0			0
$981$	−205.478	+	632.397i	−0.00668748	+	0.0205819i
$982$		0			0
$983$	−17534.5	+	53965.8i	−0.568937	+	1.75101i	0.0870170	+	0.996207i	$0.472267\pi$
$983$	−17534.5	+	53965.8i	−0.568937	+	1.75101i	−0.655954	+	0.754801i	$0.727733\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−20603.1	+	14969.0i	−0.664441	+	0.482745i
$988$		0			0
$989$	−10238.6	−	7438.77i	−0.329189	−	0.239170i
$990$		0			0
$991$	−14200.8	+	10317.5i	−0.455200	+	0.330722i	−0.791646	−	0.610981i	$-0.790775\pi$
$991$	−14200.8	+	10317.5i	−0.455200	+	0.330722i	0.336445	+	0.941703i	$0.390775\pi$
$992$		0			0
$993$	46814.3			1.49608
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6569.04	−	20217.4i	−0.208669	−	0.642219i	−0.999543	−	0.0302386i	$-0.990373\pi$
$997$	−6569.04	−	20217.4i	−0.208669	−	0.642219i	0.790873	−	0.611980i	$-0.209627\pi$
$998$		0			0
$999$	−10948.9			−0.346756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.4.g.b.201.5		64
5.2	odd	4		100.4.i.a.9.3	✓	32
5.3	odd	4		500.4.i.a.49.6		32
5.4	even	2	inner	500.4.g.b.201.12		64
25.2	odd	20		500.4.i.a.449.6		32
25.6	even	5		2500.4.a.g.1.9		32
25.11	even	5	inner	500.4.g.b.301.5		64
25.14	even	10	inner	500.4.g.b.301.12		64
25.19	even	10		2500.4.a.g.1.24		32
25.23	odd	20		100.4.i.a.89.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.9.3	✓	32	5.2	odd	4
100.4.i.a.89.3	yes	32	25.23	odd	20
500.4.g.b.201.5		64	1.1	even	1	trivial
500.4.g.b.201.12		64	5.4	even	2	inner
500.4.g.b.301.5		64	25.11	even	5	inner
500.4.g.b.301.12		64	25.14	even	10	inner
500.4.i.a.49.6		32	5.3	odd	4
500.4.i.a.449.6		32	25.2	odd	20
2500.4.a.g.1.9		32	25.6	even	5
2500.4.a.g.1.24		32	25.19	even	10

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:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	500.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53150 - 4.71349i) q^{3} -16.8592 q^{7} +(1.97201 - 1.43275i) q^{9} +O(q^{10})\)	\(q+(-1.53150 - 4.71349i) q^{3} -16.8592 q^{7} +(1.97201 - 1.43275i) q^{9} +(-47.8389 - 34.7570i) q^{11} +(5.10901 - 3.71191i) q^{13} +(-40.6606 + 125.140i) q^{17} +(25.3925 - 78.1500i) q^{19} +(25.8199 + 79.4654i) q^{21} +(128.998 + 93.7224i) q^{23} +(-118.031 - 85.7543i) q^{27} +(-15.4646 - 47.5950i) q^{29} +(-13.8066 + 42.4924i) q^{31} +(-90.5611 + 278.718i) q^{33} +(60.7145 - 44.1117i) q^{37} +(-25.3205 - 18.3964i) q^{39} +(-286.091 + 207.857i) q^{41} -79.3703 q^{43} +(94.1857 + 289.874i) q^{47} -58.7686 q^{49} +652.120 q^{51} +(104.844 + 322.676i) q^{53} -407.248 q^{57} +(636.533 - 462.468i) q^{59} +(675.055 + 490.456i) q^{61} +(-33.2464 + 24.1549i) q^{63} +(-187.851 + 578.147i) q^{67} +(244.198 - 751.566i) q^{69} +(-18.9894 - 58.4435i) q^{71} +(-32.0156 - 23.2607i) q^{73} +(806.523 + 585.973i) q^{77} +(178.592 + 549.648i) q^{79} +(-203.100 + 625.077i) q^{81} +(-16.4914 + 50.7554i) q^{83} +(-200.654 + 145.784i) q^{87} +(1170.83 + 850.656i) q^{89} +(-86.1336 + 62.5797i) q^{91} +221.432 q^{93} +(-16.5425 - 50.9127i) q^{97} -144.136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 244 q^{9}+O(q^{10}) \) 64 * q - 244 * q^9	\( 64 q - 244 q^{9} + 40 q^{11} - 4 q^{19} - 216 q^{21} - 124 q^{29} - 756 q^{31} - 1184 q^{39} - 1056 q^{41} + 5592 q^{49} + 3328 q^{51} - 288 q^{59} - 2692 q^{61} - 1912 q^{69} + 1572 q^{71} - 1792 q^{79} + 696 q^{81} + 5024 q^{89} - 4424 q^{91} + 5080 q^{99}+O(q^{100}) \) 64 * q - 244 * q^9 + 40 * q^11 - 4 * q^19 - 216 * q^21 - 124 * q^29 - 756 * q^31 - 1184 * q^39 - 1056 * q^41 + 5592 * q^49 + 3328 * q^51 - 288 * q^59 - 2692 * q^61 - 1912 * q^69 + 1572 * q^71 - 1792 * q^79 + 696 * q^81 + 5024 * q^89 - 4424 * q^91 + 5080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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