LMFDB - Embedded newform 425.3.t.f.299.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			299.9
Character	$\chi$	$=$	425.299
Dual form			425.3.t.f.199.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.13692 + 0.885142i) q^{2} +(2.78088 - 4.16188i) q^{3} +(0.954534 + 0.954534i) q^{4} +(9.62637 - 6.43213i) q^{6} +(0.193021 - 0.970381i) q^{7} +(-2.34570 - 5.66303i) q^{8} +(-6.14378 - 14.8324i) q^{9} +(0.201395 + 0.301409i) q^{11} +(6.62710 - 1.31821i) q^{12} +(-4.39739 - 4.39739i) q^{13} +(1.27140 - 1.90278i) q^{14} -19.5774i q^{16} +(-1.86536 + 16.8974i) q^{17} -37.1338i q^{18} +(9.20107 - 22.2133i) q^{19} +(-3.50184 - 3.50184i) q^{21} +(0.163576 + 0.822350i) q^{22} +(14.4201 + 21.5813i) q^{23} +(-30.0919 - 5.98565i) q^{24} +(-5.50456 - 13.2892i) q^{26} +(-34.6323 - 6.88880i) q^{27} +(1.11051 - 0.742017i) q^{28} +(8.40610 + 42.2603i) q^{29} +(9.36788 - 14.0200i) q^{31} +(7.94597 - 19.1833i) q^{32} +1.81448 q^{33} +(-18.9427 + 34.4572i) q^{34} +(8.29359 - 20.0225i) q^{36} +(12.0064 - 17.9689i) q^{37} +(39.3239 - 39.3239i) q^{38} +(-30.5300 + 6.07279i) q^{39} +(67.7453 + 13.4754i) q^{41} +(-4.38353 - 10.5828i) q^{42} +(5.12800 - 2.12409i) q^{43} +(-0.0954667 + 0.479943i) q^{44} +(11.7122 + 58.8814i) q^{46} +(-60.9689 - 60.9689i) q^{47} +(-81.4787 - 54.4423i) q^{48} +(44.3657 + 18.3769i) q^{49} +(65.1373 + 54.7528i) q^{51} -8.39491i q^{52} +(14.9763 + 6.20340i) q^{53} +(-67.9091 - 45.3754i) q^{54} +(-5.94806 + 1.18314i) q^{56} +(-66.8621 - 100.066i) q^{57} +(-19.4432 + 97.7476i) q^{58} +(-60.5743 + 25.0907i) q^{59} +(2.42535 - 12.1930i) q^{61} +(32.4281 - 21.6678i) q^{62} +(-15.5790 + 3.09885i) q^{63} +(-21.4134 + 21.4134i) q^{64} +(3.87740 + 1.60607i) q^{66} +39.4771 q^{67} +(-17.9097 + 14.3486i) q^{68} +129.919 q^{69} +(-65.4676 - 43.7440i) q^{71} +(-69.5848 + 69.5848i) q^{72} +(-0.0692193 - 0.347989i) q^{73} +(41.5619 - 27.7708i) q^{74} +(29.9861 - 12.4207i) q^{76} +(0.331355 - 0.137252i) q^{77} +(-70.6154 - 14.0463i) q^{78} +(44.3559 + 66.3833i) q^{79} +(-22.8085 + 22.8085i) q^{81} +(132.839 + 88.7601i) q^{82} +(-32.8738 + 79.3643i) q^{83} -6.68525i q^{84} +12.8383 q^{86} +(199.259 + 82.5356i) q^{87} +(1.23447 - 1.84752i) q^{88} +(120.939 + 120.939i) q^{89} +(-5.11592 + 3.41835i) q^{91} +(-6.83554 + 34.3646i) q^{92} +(-32.2987 - 77.9759i) q^{93} +(-76.3197 - 184.252i) q^{94} +(-57.7416 - 86.4164i) q^{96} +(-86.7371 + 17.2531i) q^{97} +(78.5399 + 78.5399i) q^{98} +(3.23329 - 4.83896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) $ 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	2.13692	+	0.885142i	1.06846	+	0.442571i	0.846447	−	0.532472i	$-0.178737\pi$
$2$	2.13692	+	0.885142i	1.06846	+	0.442571i	0.222014	+	0.975043i	$0.428737\pi$
$3$	2.78088	−	4.16188i	0.926959	−	1.38729i	0.00500688	−	0.999987i	$-0.498406\pi$
$3$	2.78088	−	4.16188i	0.926959	−	1.38729i	0.921952	−	0.387304i	$-0.126594\pi$
$4$	0.954534	+	0.954534i	0.238634	+	0.238634i
$5$		0			0
$5$		0			0
$6$	9.62637	−	6.43213i	1.60440	−	1.07202i
$7$	0.193021	−	0.970381i	0.0275744	−	0.138626i	−0.964546	−	0.263915i	$-0.914986\pi$
$7$	0.193021	−	0.970381i	0.0275744	−	0.138626i	0.992120	+	0.125290i	$0.0399860\pi$
$8$	−2.34570	−	5.66303i	−0.293213	−	0.707878i
$9$	−6.14378	−	14.8324i	−0.682643	−	1.64805i
$10$		0			0
$11$	0.201395	+	0.301409i	0.0183086	+	0.0274008i	0.840511	−	0.541794i	$-0.182255\pi$
$11$	0.201395	+	0.301409i	0.0183086	+	0.0274008i	−0.822202	+	0.569195i	$0.807255\pi$
$12$	6.62710	−	1.31821i	0.552258	−	0.109851i
$13$	−4.39739	−	4.39739i	−0.338260	−	0.338260i	0.517452	−	0.855712i	$-0.326881\pi$
$13$	−4.39739	−	4.39739i	−0.338260	−	0.338260i	−0.855712	+	0.517452i	$0.826881\pi$
$14$	1.27140	−	1.90278i	0.0908140	−	0.135913i
$15$		0			0
$16$		−	19.5774i		−	1.22359i
$17$	−1.86536	+	16.8974i	−0.109727	+	0.993962i
$17$	−1.86536	+	16.8974i	−0.109727	+	0.993962i
$18$		−	37.1338i		−	2.06299i
$19$	9.20107	−	22.2133i	0.484267	−	1.16912i	−0.473297	−	0.880903i	$-0.656936\pi$
$19$	9.20107	−	22.2133i	0.484267	−	1.16912i	0.957564	−	0.288221i	$-0.0930636\pi$
$20$		0			0
$21$	−3.50184	−	3.50184i	−0.166754	−	0.166754i
$22$	0.163576	+	0.822350i	0.00743526	+	0.0373796i
$23$	14.4201	+	21.5813i	0.626963	+	0.938316i	0.999945	+	0.0104775i	$0.00333515\pi$
$23$	14.4201	+	21.5813i	0.626963	+	0.938316i	−0.372982	+	0.927838i	$0.621665\pi$
$24$	−30.0919	−	5.98565i	−1.25383	−	0.249402i
$25$		0			0
$26$	−5.50456	−	13.2892i	−0.211714	−	0.511123i
$27$	−34.6323	−	6.88880i	−1.28268	−	0.255141i
$28$	1.11051	−	0.742017i	0.0396610	−	0.0265006i
$29$	8.40610	+	42.2603i	0.289866	+	1.45725i	0.801472	+	0.598032i	$0.204051\pi$
$29$	8.40610	+	42.2603i	0.289866	+	1.45725i	−0.511606	+	0.859220i	$0.670949\pi$
$30$		0			0
$31$	9.36788	−	14.0200i	0.302190	−	0.452259i	−0.649035	−	0.760759i	$-0.724827\pi$
$31$	9.36788	−	14.0200i	0.302190	−	0.452259i	0.951224	+	0.308500i	$0.0998270\pi$
$32$	7.94597	−	19.1833i	0.248312	−	0.599477i
$33$	1.81448			0.0549842
$34$	−18.9427	+	34.4572i	−0.557138	+	1.01345i
$35$		0			0
$36$	8.29359	−	20.0225i	0.230377	−	0.556180i
$37$	12.0064	−	17.9689i	0.324499	−	0.485646i	−0.632973	−	0.774174i	$-0.718166\pi$
$37$	12.0064	−	17.9689i	0.324499	−	0.485646i	0.957472	+	0.288527i	$0.0931656\pi$
$38$	39.3239	−	39.3239i	1.03484	−	1.03484i
$39$	−30.5300	+	6.07279i	−0.782819	+	0.155712i
$40$		0			0
$41$	67.7453	+	13.4754i	1.65232	+	0.328668i	0.931303	−	0.364245i	$-0.118673\pi$
$41$	67.7453	+	13.4754i	1.65232	+	0.328668i	0.721022	+	0.692913i	$0.243673\pi$
$42$	−4.38353	−	10.5828i	−0.104370	−	0.251971i
$43$	5.12800	−	2.12409i	0.119256	−	0.0493974i	−0.322258	−	0.946652i	$-0.604442\pi$
$43$	5.12800	−	2.12409i	0.119256	−	0.0493974i	0.441513	+	0.897255i	$0.354442\pi$
$44$	−0.0954667	+	0.479943i	−0.00216970	+	0.0109078i
$45$		0			0
$46$	11.7122	+	58.8814i	0.254614	+	1.28003i
$47$	−60.9689	−	60.9689i	−1.29721	−	1.29721i	−0.930227	−	0.366984i	$-0.880390\pi$
$47$	−60.9689	−	60.9689i	−1.29721	−	1.29721i	−0.366984	−	0.930227i	$-0.619610\pi$
$48$	−81.4787	−	54.4423i	−1.69747	−	1.13421i
$49$	44.3657	+	18.3769i	0.905423	+	0.375038i
$50$		0			0
$51$	65.1373	+	54.7528i	1.27720	+	1.07358i
$52$		−	8.39491i		−	0.161441i
$53$	14.9763	+	6.20340i	0.282572	+	0.117045i	0.519468	−	0.854490i	$-0.326130\pi$
$53$	14.9763	+	6.20340i	0.282572	+	0.117045i	−0.236896	+	0.971535i	$0.576130\pi$
$54$	−67.9091	−	45.3754i	−1.25758	−	0.840285i
$55$		0			0
$56$	−5.94806	+	1.18314i	−0.106215	+	0.0211275i
$57$	−66.8621	−	100.066i	−1.17302	−	1.75555i
$58$	−19.4432	+	97.7476i	−0.335228	+	1.68530i
$59$	−60.5743	+	25.0907i	−1.02668	+	0.425266i	−0.831514	−	0.555503i	$-0.812526\pi$
$59$	−60.5743	+	25.0907i	−1.02668	+	0.425266i	−0.195169	+	0.980770i	$0.562526\pi$
$60$		0			0
$61$	2.42535	−	12.1930i	0.0397598	−	0.199886i	−0.955800	−	0.294018i	$-0.905008\pi$
$61$	2.42535	−	12.1930i	0.0397598	−	0.199886i	0.995560	+	0.0941318i	$0.0300075\pi$
$62$	32.4281	−	21.6678i	0.523035	−	0.349481i
$63$	−15.5790	+	3.09885i	−0.247285	+	0.0491881i
$64$	−21.4134	+	21.4134i	−0.334584	+	0.334584i
$65$		0			0
$66$	3.87740	+	1.60607i	0.0587485	+	0.0243344i
$67$	39.4771			0.589210			0.294605	−	0.955619i	$-0.404812\pi$
$67$	39.4771			0.589210			0.294605	+	0.955619i	$0.404812\pi$
$68$	−17.9097	+	14.3486i	−0.263377	+	0.211008i
$69$	129.919			1.88289
$70$		0			0
$71$	−65.4676	−	43.7440i	−0.922079	−	0.616113i	0.00130176	−	0.999999i	$-0.499586\pi$
$71$	−65.4676	−	43.7440i	−0.922079	−	0.616113i	−0.923381	+	0.383886i	$0.874586\pi$
$72$	−69.5848	+	69.5848i	−0.966456	+	0.966456i
$73$	−0.0692193	−	0.347989i	−0.000948210	−	0.00476697i	0.980308	−	0.197473i	$-0.0632736\pi$
$73$	−0.0692193	−	0.347989i	−0.000948210	−	0.00476697i	−0.981256	+	0.192706i	$0.938274\pi$
$74$	41.5619	−	27.7708i	0.561647	−	0.375281i
$75$		0			0
$76$	29.9861	−	12.4207i	0.394554	−	0.163430i
$77$	0.331355	−	0.137252i	0.00430331	−	0.00178249i
$78$	−70.6154	−	14.0463i	−0.905326	−	0.180081i
$79$	44.3559	+	66.3833i	0.561468	+	0.840296i	0.998242	−	0.0592757i	$-0.0188791\pi$
$79$	44.3559	+	66.3833i	0.561468	+	0.840296i	−0.436774	+	0.899571i	$0.643879\pi$
$80$		0			0
$81$	−22.8085	+	22.8085i	−0.281586	+	0.281586i
$82$	132.839	+	88.7601i	1.61999	+	1.08244i
$83$	−32.8738	+	79.3643i	−0.396070	+	0.956197i	0.592519	+	0.805556i	$0.298133\pi$
$83$	−32.8738	+	79.3643i	−0.396070	+	0.956197i	−0.988589	+	0.150640i	$0.951867\pi$
$84$		−	6.68525i		−	0.0795863i
$85$		0			0
$86$	12.8383			0.149282
$87$	199.259	+	82.5356i	2.29033	+	0.948685i
$88$	1.23447	−	1.84752i	0.0140281	−	0.0209945i
$89$	120.939	+	120.939i	1.35887	+	1.35887i	0.875314	+	0.483555i	$0.160655\pi$
$89$	120.939	+	120.939i	1.35887	+	1.35887i	0.483555	+	0.875314i	$0.339345\pi$
$90$		0			0
$91$	−5.11592	+	3.41835i	−0.0562190	+	0.0375643i
$92$	−6.83554	+	34.3646i	−0.0742993	+	0.373528i
$93$	−32.2987	−	77.9759i	−0.347298	−	0.838450i
$94$	−76.3197	−	184.252i	−0.811912	−	1.96013i
$95$		0			0
$96$	−57.7416	−	86.4164i	−0.601475	−	0.900171i
$97$	−86.7371	+	17.2531i	−0.894197	+	0.177867i	−0.620739	−	0.784017i	$-0.713167\pi$
$97$	−86.7371	+	17.2531i	−0.894197	+	0.177867i	−0.273458	+	0.961884i	$0.588167\pi$
$98$	78.5399	+	78.5399i	0.801428	+	0.801428i
$99$	3.23329	−	4.83896i	0.0326595	−	0.0488784i
$100$		0			0
$101$			68.9645i			0.682816i	0.939915	+	0.341408i	$0.110904\pi$
$101$			68.9645i			0.682816i	−0.939915	+	0.341408i	$0.889096\pi$
$102$	90.7294	+	174.658i	0.889504	+	1.71234i
$103$			143.720i			1.39534i	0.716418	+	0.697671i	$0.245780\pi$
$103$			143.720i			1.39534i	−0.716418	+	0.697671i	$0.754220\pi$
$104$	−14.5876	+	35.2175i	−0.140265	+	0.338629i
$105$		0			0
$106$	26.5124	+	26.5124i	0.250117	+	0.250117i
$107$	−37.4541	−	188.295i	−0.350039	−	1.75976i	−0.608319	−	0.793693i	$-0.708156\pi$
$107$	−37.4541	−	188.295i	−0.350039	−	1.75976i	0.258280	−	0.966070i	$-0.416844\pi$
$108$	−26.4822	−	39.6334i	−0.245205	−	0.366975i
$109$	97.4423	+	19.3825i	0.893966	+	0.177821i	0.620635	−	0.784099i	$-0.286875\pi$
$109$	97.4423	+	19.3825i	0.893966	+	0.177821i	0.273330	+	0.961920i	$0.411875\pi$
$110$		0			0
$111$	−41.3960	−	99.9387i	−0.372937	−	0.900348i
$112$	−18.9975	−	3.77884i	−0.169621	−	0.0337397i
$113$	97.9029	−	65.4166i	0.866397	−	0.578908i	−0.0410109	−	0.999159i	$-0.513058\pi$
$113$	97.9029	−	65.4166i	0.866397	−	0.578908i	0.907408	+	0.420251i	$0.138058\pi$
$114$	−54.3063	−	273.016i	−0.476371	−	2.39488i
$115$		0			0
$116$	−32.3150	+	48.3628i	−0.278578	+	0.416921i
$117$	−38.2072	+	92.2404i	−0.326557	+	0.788380i
$118$	−151.652			−1.28518
$119$	16.0368	+	5.07165i	0.134763	+	0.0426189i
$120$		0			0
$121$	46.2544	−	111.668i	0.382268	−	0.922876i
$122$	15.9754	−	23.9088i	0.130946	−	0.195974i
$123$	244.474	−	244.474i	1.98760	−	1.98760i
$124$	22.3246	−	4.44063i	0.180037	−	0.0358115i
$125$		0			0
$126$	−36.0340	−	7.16760i	−0.285984	−	0.0568857i
$127$	45.9034	+	110.821i	0.361444	+	0.872603i	0.995089	+	0.0989792i	$0.0315577\pi$
$127$	45.9034	+	110.821i	0.361444	+	0.872603i	−0.633646	+	0.773623i	$0.718442\pi$
$128$	−141.446	+	58.5887i	−1.10504	+	0.457724i
$129$	5.42014	−	27.2489i	0.0420166	−	0.211232i
$130$		0			0
$131$	41.9499	+	210.896i	0.320228	+	1.60990i	0.720469	+	0.693487i	$0.243926\pi$
$131$	41.9499	+	210.896i	0.320228	+	1.60990i	−0.400241	+	0.916410i	$0.631074\pi$
$132$	1.73198	+	1.73198i	0.0131211	+	0.0131211i
$133$	−19.7794	−	13.2162i	−0.148717	−	0.0993697i
$134$	84.3594	+	34.9428i	0.629548	+	0.260767i
$135$		0			0
$136$	100.066	−	29.0726i	0.735777	−	0.213769i
$137$			82.8569i			0.604795i	0.953182	+	0.302398i	$0.0977870\pi$
$137$			82.8569i			0.604795i	−0.953182	+	0.302398i	$0.902213\pi$
$138$	277.627	+	114.997i	2.01179	+	0.833311i
$139$	−137.679	−	91.9943i	−0.990498	−	0.661829i	−0.0489823	−	0.998800i	$-0.515598\pi$
$139$	−137.679	−	91.9943i	−0.990498	−	0.661829i	−0.941515	+	0.336970i	$0.890598\pi$
$140$		0			0
$141$	−423.292	+	84.1981i	−3.00207	+	0.597149i
$142$	−101.179	−	151.426i	−0.712532	−	1.06638i
$143$	0.439800	−	2.21102i	0.00307552	−	0.0154617i
$144$	−290.380	+	120.279i	−2.01653	+	0.835273i
$145$		0			0
$146$	0.160103	−	0.804894i	0.00109660	−	0.00551298i
$147$	199.858	−	133.541i	1.35958	−	0.908440i
$148$	28.6125	−	5.69138i	0.193328	−	0.0384553i
$149$	−114.653	+	114.653i	−0.769486	+	0.769486i	−0.978016	−	0.208530i	$-0.933132\pi$
$149$	−114.653	+	114.653i	−0.769486	+	0.769486i	0.208530	+	0.978016i	$0.433132\pi$
$150$		0			0
$151$	−144.717	−	59.9439i	−0.958394	−	0.396980i	−0.152014	−	0.988378i	$-0.548576\pi$
$151$	−144.717	−	59.9439i	−0.958394	−	0.396980i	−0.806379	+	0.591399i	$0.798576\pi$
$152$	−147.378			−0.969590
$153$	262.089	−	76.1459i	1.71300	−	0.497686i
$154$	0.829566			0.00538680
$155$		0			0
$156$	−34.9386	−	23.3452i	−0.223965	−	0.149649i
$157$	−88.8938	+	88.8938i	−0.566203	+	0.566203i	−0.931062	−	0.364860i	$-0.881117\pi$
$157$	−88.8938	+	88.8938i	−0.566203	+	0.566203i	0.364860	+	0.931062i	$0.381117\pi$
$158$	36.0265	+	181.117i	0.228016	+	1.14631i
$159$	67.4651	−	45.0787i	0.424309	−	0.283514i
$160$		0			0
$161$	23.7254	−	9.82739i	0.147363	−	0.0610397i
$162$	−68.9287	+	28.5512i	−0.425486	+	0.176242i
$163$	−104.248	−	20.7361i	−0.639556	−	0.127216i	−0.135348	−	0.990798i	$-0.543215\pi$
$163$	−104.248	−	20.7361i	−0.639556	−	0.127216i	−0.504208	+	0.863582i	$0.668215\pi$
$164$	51.8025	+	77.5280i	0.315869	+	0.472731i
$165$		0			0
$166$	−140.497	+	140.497i	−0.846370	+	0.846370i
$167$	−124.453	−	83.1570i	−0.745229	−	0.497946i	0.124045	−	0.992277i	$-0.460413\pi$
$167$	−124.453	−	83.1570i	−0.745229	−	0.497946i	−0.869274	+	0.494331i	$0.835413\pi$
$168$	−11.6167	+	28.0453i	−0.0691472	+	0.166936i
$169$		−	130.326i		−	0.771160i
$170$		0			0
$171$	−386.007			−2.25735
$172$	6.92236	+	2.86734i	0.0402463	+	0.0166706i
$173$	15.1413	−	22.6606i	0.0875220	−	0.130986i	−0.785125	−	0.619337i	$-0.787401\pi$
$173$	15.1413	−	22.6606i	0.0875220	−	0.130986i	0.872647	+	0.488351i	$0.162401\pi$
$174$	352.744	+	352.744i	2.02727	+	2.02727i
$175$		0			0
$176$	5.90080	−	3.94279i	0.0335273	−	0.0224022i
$177$	−64.0253	+	321.877i	−0.361725	+	1.81851i
$178$	151.389	+	365.487i	0.850503	+	2.05330i
$179$	20.5361	+	49.5786i	0.114727	+	0.276976i	0.970805	−	0.239872i	$-0.0771054\pi$
$179$	20.5361	+	49.5786i	0.114727	+	0.276976i	−0.856077	+	0.516847i	$0.827105\pi$
$180$		0			0
$181$	64.7443	+	96.8967i	0.357703	+	0.535341i	0.966058	−	0.258324i	$-0.0831702\pi$
$181$	64.7443	+	96.8967i	0.357703	+	0.535341i	−0.608355	+	0.793665i	$0.708170\pi$
$182$	−13.9581	+	2.77643i	−0.0766927	+	0.0152551i
$183$	−44.0013	−	44.0013i	−0.240445	−	0.240445i
$184$	88.3899	−	132.285i	0.480380	−	0.718939i
$185$		0			0
$186$		−	195.217i		−	1.04956i
$187$	−5.46868	+	2.84080i	−0.0292443	+	0.0151915i
$188$		−	116.394i		−	0.619116i
$189$	−13.3695	+	32.2769i	−0.0707382	+	0.170777i
$190$		0			0
$191$	−54.0250	−	54.0250i	−0.282853	−	0.282853i	0.551393	−	0.834246i	$-0.314097\pi$
$191$	−54.0250	−	54.0250i	−0.282853	−	0.282853i	−0.834246	+	0.551393i	$0.814097\pi$
$192$	29.5719	+	148.668i	0.154020	+	0.774311i
$193$	−120.442	−	180.254i	−0.624052	−	0.933960i	−0.999973	−	0.00730837i	$-0.997674\pi$
$193$	−120.442	−	180.254i	−0.624052	−	0.933960i	0.375921	−	0.926652i	$-0.377326\pi$
$194$	−200.622	−	39.9062i	−1.03413	−	0.205702i
$195$		0			0
$196$	24.8072	+	59.8900i	0.126568	+	0.305561i
$197$	−244.405	−	48.6152i	−1.24064	−	0.246778i	−0.469204	−	0.883090i	$-0.655459\pi$
$197$	−244.405	−	48.6152i	−1.24064	−	0.246778i	−0.771432	+	0.636312i	$0.780459\pi$
$198$	11.1925	−	7.47856i	0.0565276	−	0.0377705i
$199$	−52.4658	−	263.763i	−0.263647	−	1.32544i	−0.854831	−	0.518906i	$-0.826339\pi$
$199$	−52.4658	−	263.763i	−0.263647	−	1.32544i	0.591184	−	0.806537i	$-0.298661\pi$
$200$		0			0
$201$	109.781	−	164.299i	0.546173	−	0.817406i
$202$	−61.0434	+	147.372i	−0.302195	+	0.729563i
$203$	42.6312			0.210006
$204$	9.91237	+	114.439i	0.0485901	+	0.560977i
$205$		0			0
$206$	−127.213	+	307.119i	−0.617538	+	1.49087i
$207$	231.508	−	346.476i	1.11840	−	1.67380i
$208$	−86.0893	+	86.0893i	−0.413891	+	0.413891i
$209$	8.54834	−	1.70037i	0.0409012	−	0.00813575i
$210$		0			0
$211$	199.610	+	39.7050i	0.946021	+	0.188175i	0.643913	−	0.765099i	$-0.277310\pi$
$211$	199.610	+	39.7050i	0.946021	+	0.188175i	0.302107	+	0.953274i	$0.402310\pi$
$212$	8.37406	+	20.2168i	0.0395003	+	0.0953621i
$213$	−364.115	+	150.821i	−1.70946	+	0.708081i
$214$	86.6310	−	435.523i	0.404818	−	2.03516i
$215$		0			0
$216$	42.2257	+	212.283i	0.195489	+	0.982791i
$217$	−11.7966	−	11.7966i	−0.0543620	−	0.0543620i
$218$	191.070	+	127.669i	0.876469	+	0.585638i
$219$	−1.64078	−	0.679632i	−0.00749213	−	0.00310334i
$220$		0			0
$221$	82.5069	−	66.1015i	0.373334	−	0.299102i
$222$		−	250.203i		−	1.12704i
$223$	−301.515	−	124.891i	−1.35208	−	0.560051i	−0.415212	−	0.909725i	$-0.636292\pi$
$223$	−301.515	−	124.891i	−1.35208	−	0.560051i	−0.936872	+	0.349674i	$0.886292\pi$
$224$	−17.0813	−	11.4134i	−0.0762560	−	0.0509526i
$225$		0			0
$226$	267.114	−	53.1323i	1.18192	−	0.235098i
$227$	−86.6828	−	129.730i	−0.381863	−	0.571498i	0.589895	−	0.807480i	$-0.299169\pi$
$227$	−86.6828	−	129.730i	−0.381863	−	0.571498i	−0.971757	+	0.235982i	$0.924169\pi$
$228$	31.6945	−	159.339i	0.139011	−	0.698855i
$229$	−280.820	+	116.319i	−1.22629	+	0.507945i	−0.899403	−	0.437120i	$-0.855999\pi$
$229$	−280.820	+	116.319i	−1.22629	+	0.507945i	−0.326884	+	0.945065i	$0.605999\pi$
$230$		0			0
$231$	0.350232	−	1.76074i	0.00151616	−	0.00762224i
$232$	219.603	−	146.734i	0.946565	−	0.632474i
$233$	−101.530	+	20.1955i	−0.435749	+	0.0866759i	−0.408090	−	0.912942i	$-0.633805\pi$
$233$	−101.530	+	20.1955i	−0.435749	+	0.0866759i	−0.0276587	+	0.999617i	$0.508805\pi$
$234$	−163.292	+	163.292i	−0.697828	+	0.697828i
$235$		0			0
$236$	−81.7702	−	33.8703i	−0.346484	−	0.143518i
$237$	399.628			1.68619
$238$	29.7803	+	25.0326i	0.125127	+	0.105179i
$239$	388.547			1.62572			0.812860	−	0.582459i	$-0.197909\pi$
$239$	388.547			1.62572			0.812860	+	0.582459i	$0.197909\pi$
$240$		0			0
$241$	282.183	+	188.549i	1.17088	+	0.782359i	0.979950	−	0.199244i	$-0.0638486\pi$
$241$	282.183	+	188.549i	1.17088	+	0.782359i	0.190933	+	0.981603i	$0.438849\pi$
$242$	197.684	−	197.684i	0.816877	−	0.816877i
$243$	−30.5007	−	153.337i	−0.125517	−	0.631018i
$244$	13.9538	−	9.32360i	0.0571875	−	0.0382115i
$245$		0			0
$246$	738.817	−	306.028i	3.00332	−	1.24402i
$247$	−138.141	+	57.2200i	−0.559276	+	0.231660i
$248$	−101.370	−	20.1637i	−0.408750	−	0.0813054i
$249$	238.887	+	357.519i	0.959384	+	1.43582i
$250$		0			0
$251$	87.2461	−	87.2461i	0.347594	−	0.347594i	−0.511619	−	0.859213i	$-0.670954\pi$
$251$	87.2461	−	87.2461i	0.347594	−	0.347594i	0.859213	+	0.511619i	$0.170954\pi$
$252$	−17.8286	−	11.9127i	−0.0707485	−	0.0472726i
$253$	−3.60064	+	8.69271i	−0.0142318	+	0.0343585i
$254$			277.446i			1.09231i
$255$		0			0
$256$	−232.986			−0.910100
$257$	71.2832	+	29.5265i	0.277367	+	0.114889i	0.517031	−	0.855967i	$-0.327037\pi$
$257$	71.2832	+	29.5265i	0.277367	+	0.114889i	−0.239664	+	0.970856i	$0.577037\pi$
$258$	35.7016	−	53.4312i	0.138378	−	0.207098i
$259$	−15.1192	−	15.1192i	−0.0583753	−	0.0583753i
$260$		0			0
$261$	575.177	−	384.321i	2.20374	−	1.47249i
$262$	−97.0297	+	487.801i	−0.370342	+	1.86184i
$263$	−28.7756	−	69.4703i	−0.109413	−	0.264146i	0.859684	−	0.510826i	$-0.170660\pi$
$263$	−28.7756	−	69.4703i	−0.109413	−	0.264146i	−0.969097	+	0.246680i	$0.920660\pi$
$264$	−4.25623	−	10.2754i	−0.0161221	−	0.0389221i
$265$		0			0
$266$	−30.5689	−	45.7495i	−0.114921	−	0.171991i
$267$	839.652	−	167.017i	3.14476	−	0.625532i
$268$	37.6822	+	37.6822i	0.140605	+	0.140605i
$269$	100.440	−	150.319i	0.373383	−	0.558807i	−0.596428	−	0.802667i	$-0.703414\pi$
$269$	100.440	−	150.319i	0.373383	−	0.558807i	0.969810	+	0.243860i	$0.0784137\pi$
$270$		0			0
$271$		−	241.430i		−	0.890886i	−0.895310	−	0.445443i	$-0.853046\pi$
$271$		−	241.430i		−	0.890886i	0.895310	−	0.445443i	$-0.146954\pi$
$272$	330.806	+	36.5188i	1.21620	+	0.134260i
$273$			30.7979i			0.112813i
$274$	−73.3402	+	177.059i	−0.267665	+	0.646200i
$275$		0			0
$276$	124.012	+	124.012i	0.449320	+	0.449320i
$277$	60.3707	+	303.504i	0.217945	+	1.09568i	0.922489	+	0.386022i	$0.126151\pi$
$277$	60.3707	+	303.504i	0.217945	+	1.09568i	−0.704545	+	0.709660i	$0.748849\pi$
$278$	−212.782	−	318.450i	−0.765402	−	1.14550i
$279$	−265.505	−	52.8122i	−0.951630	−	0.189291i
$280$		0			0
$281$	−8.71849	−	21.0483i	−0.0310267	−	0.0749050i	0.907607	−	0.419821i	$-0.137907\pi$
$281$	−8.71849	−	21.0483i	−0.0310267	−	0.0749050i	−0.938633	+	0.344916i	$0.887907\pi$
$282$	−979.070	−	194.749i	−3.47188	−	0.690600i
$283$	86.2953	−	57.6606i	0.304930	−	0.203748i	−0.393685	−	0.919245i	$-0.628800\pi$
$283$	86.2953	−	57.6606i	0.304930	−	0.203748i	0.698615	+	0.715498i	$0.253800\pi$
$284$	−20.7359	−	104.246i	−0.0730136	−	0.367064i
$285$		0			0
$286$	2.89689	−	4.33550i	0.0101290	−	0.0151591i
$287$	26.1525	−	63.1377i	0.0911237	−	0.219992i
$288$	−333.352			−1.15747
$289$	−282.041	−	63.0392i	−0.975920	−	0.218129i
$290$		0			0
$291$	−169.400	+	408.968i	−0.582130	+	1.40539i
$292$	0.266095	−	0.398240i	0.000911285	−	0.00136383i
$293$	20.1749	−	20.1749i	0.0688564	−	0.0688564i	−0.671840	−	0.740696i	$-0.734496\pi$
$293$	20.1749	−	20.1749i	0.0688564	−	0.0688564i	0.740696	+	0.671840i	$0.234496\pi$
$294$	545.283	−	108.464i	1.85471	−	0.368924i
$295$		0			0
$296$	−129.922	−	25.8431i	−0.438926	−	0.0873077i
$297$	−4.89843	−	11.8259i	−0.0164930	−	0.0398177i
$298$	−346.490	+	143.521i	−1.16272	+	0.481613i
$299$	31.4902	−	158.312i	0.105318	−	0.529472i
$300$		0			0
$301$	−1.07136	−	5.38610i	−0.00355934	−	0.0178940i
$302$	−256.191	−	256.191i	−0.848315	−	0.848315i
$303$	287.021	+	191.782i	0.947266	+	0.632943i
$304$	−434.879	−	180.133i	−1.43052	−	0.592542i
$305$		0			0
$306$	627.463	+	69.2679i	2.05053	+	0.226366i
$307$		−	178.586i		−	0.581714i	−0.956766	−	0.290857i	$-0.906060\pi$
$307$		−	178.586i		−	0.581714i	0.956766	−	0.290857i	$-0.0939405\pi$
$308$	0.447301	+	0.185278i	0.00145228	+	0.000601552i
$309$	598.146	+	399.668i	1.93575	+	1.29342i
$310$		0			0
$311$	−91.7576	+	18.2517i	−0.295041	+	0.0586872i	−0.340391	−	0.940284i	$-0.610560\pi$
$311$	−91.7576	+	18.2517i	−0.295041	+	0.0586872i	0.0453506	+	0.998971i	$0.485560\pi$
$312$	106.005	+	158.647i	0.339758	+	0.508484i
$313$	−49.0559	+	246.620i	−0.156728	+	0.787925i	0.819819	+	0.572622i	$0.194074\pi$
$313$	−49.0559	+	246.620i	−0.156728	+	0.787925i	−0.976547	+	0.215303i	$0.930926\pi$
$314$	−268.643	+	111.276i	−0.855551	+	0.354381i
$315$		0			0
$316$	−21.0259	+	105.704i	−0.0665377	+	0.334508i
$317$	−439.929	+	293.951i	−1.38779	+	0.927291i	−0.387805	+	0.921742i	$0.626767\pi$
$317$	−439.929	+	293.951i	−1.38779	+	0.927291i	−0.999985	+	0.00554969i	$0.998233\pi$
$318$	184.069	−	36.6135i	0.578832	−	0.115137i
$319$	−11.0447	+	11.0447i	−0.0346228	+	0.0346228i
$320$		0			0
$321$	−887.814	−	367.745i	−2.76578	−	1.14562i
$322$	59.3981			0.184466
$323$	358.183	+	196.910i	1.10893	+	0.609627i
$324$	−43.5429			−0.134392
$325$		0			0
$326$	−204.415	−	136.586i	−0.627039	−	0.418974i
$327$	351.642	−	351.642i	1.07536	−	1.07536i
$328$	−82.5989	−	415.253i	−0.251826	−	1.26601i
$329$	−70.9313	+	47.3948i	−0.215597	+	0.144057i
$330$		0			0
$331$	359.665	−	148.978i	1.08660	−	0.450085i	0.233781	−	0.972289i	$-0.424890\pi$
$331$	359.665	−	148.978i	1.08660	−	0.450085i	0.852821	+	0.522204i	$0.174890\pi$
$332$	−107.135	+	44.3768i	−0.322696	+	0.133665i
$333$	−340.287	−	67.6873i	−1.02188	−	0.203265i
$334$	−192.341	−	287.859i	−0.575871	−	0.861853i
$335$		0			0
$336$	−68.5568	+	68.5568i	−0.204038	+	0.204038i
$337$	−450.870	−	301.262i	−1.33789	−	0.893952i	−0.338991	−	0.940790i	$-0.610085\pi$
$337$	−450.870	−	301.262i	−1.33789	−	0.893952i	−0.998902	+	0.0468383i	$0.985085\pi$
$338$	115.357	−	278.497i	0.341293	−	0.823954i
$339$		−	589.375i		−	1.73857i
$340$		0			0
$341$	6.11240			0.0179249
$342$	−824.867	−	341.671i	−2.41189	−	0.999038i
$343$	53.3302	−	79.8143i	0.155482	−	0.232695i
$344$	−24.0575	−	24.0575i	−0.0699346	−	0.0699346i
$345$		0			0
$346$	52.4136	−	35.0217i	0.151484	−	0.101219i
$347$	−12.2863	+	61.7675i	−0.0354072	+	0.178004i	−0.994442	−	0.105283i	$-0.966425\pi$
$347$	−12.2863	+	61.7675i	−0.0354072	+	0.178004i	0.959035	+	0.283288i	$0.0914251\pi$
$348$	111.416	+	268.982i	0.320161	+	0.772937i
$349$	164.739	+	397.715i	0.472031	+	1.13958i	0.963264	+	0.268556i	$0.0865465\pi$
$349$	164.739	+	397.715i	0.472031	+	1.13958i	−0.491233	+	0.871028i	$0.663454\pi$
$350$		0			0
$351$	121.999	+	182.584i	0.347576	+	0.520184i
$352$	7.38228	−	1.46843i	0.0209724	−	0.00417167i
$353$	27.5316	+	27.5316i	0.0779933	+	0.0779933i	0.745027	−	0.667034i	$-0.232436\pi$
$353$	27.5316	+	27.5316i	0.0779933	+	0.0779933i	−0.667034	+	0.745027i	$0.732436\pi$
$354$	−421.724	+	631.155i	−1.19131	+	1.78292i
$355$		0			0
$356$			230.882i			0.648544i
$357$	65.7039	−	52.6396i	0.184045	−	0.147450i
$358$			124.123i			0.346713i
$359$	−228.318	+	551.208i	−0.635983	+	1.53540i	0.196004	+	0.980603i	$0.437203\pi$
$359$	−228.318	+	551.208i	−0.635983	+	1.53540i	−0.831987	+	0.554795i	$0.812797\pi$
$360$		0			0
$361$	−153.507	−	153.507i	−0.425228	−	0.425228i
$362$	52.5862	+	264.369i	0.145266	+	0.730300i
$363$	−336.121	−	503.040i	−0.925952	−	1.38579i
$364$	−8.14626	−	1.62039i	−0.0223798	−	0.00445163i
$365$		0			0
$366$	−55.0800	−	132.975i	−0.150492	−	0.363319i
$367$	−107.558	−	21.3947i	−0.293074	−	0.0582961i	0.0463633	−	0.998925i	$-0.485237\pi$
$367$	−107.558	−	21.3947i	−0.293074	−	0.0582961i	−0.339438	+	0.940629i	$0.610237\pi$
$368$	422.505	−	282.309i	1.14811	−	0.767143i
$369$	−216.340	−	1087.62i	−0.586288	−	2.94747i
$370$		0			0
$371$	8.91040	−	13.3354i	0.0240172	−	0.0359443i
$372$	43.6005	−	105.261i	0.117206	−	0.282959i
$373$	187.710			0.503243			0.251622	−	0.967826i	$-0.419036\pi$
$373$	187.710			0.503243			0.251622	+	0.967826i	$0.419036\pi$
$374$	−14.2007	+	1.23002i	−0.0379697	+	0.00328882i
$375$		0			0
$376$	−202.254	+	488.284i	−0.537909	+	1.29863i
$377$	148.870	−	222.800i	0.394881	−	0.590981i
$378$	−57.1392	+	57.1392i	−0.151162	+	0.151162i
$379$	33.4960	−	6.66277i	0.0883799	−	0.0175799i	−0.150702	−	0.988579i	$-0.548153\pi$
$379$	33.4960	−	6.66277i	0.0883799	−	0.0175799i	0.239082	+	0.970999i	$0.423153\pi$
$380$		0			0
$381$	588.873	+	117.134i	1.54560	+	0.307439i
$382$	−67.6274	−	163.267i	−0.177035	−	0.427401i
$383$	629.678	−	260.821i	1.64407	−	0.680995i	0.647368	−	0.762178i	$-0.275870\pi$
$383$	629.678	−	260.821i	1.64407	−	0.680995i	0.996699	+	0.0811827i	$0.0258697\pi$
$384$	−149.504	+	751.607i	−0.389333	+	1.95731i
$385$		0			0
$386$	−97.8247	−	491.798i	−0.253432	−	1.27409i
$387$	−63.0106	−	63.0106i	−0.162818	−	0.162818i
$388$	−99.2622	−	66.3249i	−0.255830	−	0.170940i
$389$	10.8240	+	4.48344i	0.0278251	+	0.0115255i	0.396553	−	0.918012i	$-0.370206\pi$
$389$	10.8240	+	4.48344i	0.0278251	+	0.0115255i	−0.368727	+	0.929538i	$0.620206\pi$
$390$		0			0
$391$	−391.565	+	203.405i	−1.00144	+	0.520218i
$392$		−	294.351i		−	0.750895i
$393$	994.382	+	411.887i	2.53024	+	1.04806i
$394$	−479.244	−	320.220i	−1.21635	−	0.812742i
$395$		0			0
$396$	7.70524	−	1.53267i	0.0194577	−	0.00387037i
$397$	11.9231	+	17.8441i	0.0300329	+	0.0449474i	0.846182	−	0.532894i	$-0.178895\pi$
$397$	11.9231	+	17.8441i	0.0300329	+	0.0449474i	−0.816149	+	0.577841i	$0.803895\pi$
$398$	121.353	−	610.081i	0.304906	−	1.53287i
$399$	−110.008	+	45.5669i	−0.275710	+	0.114203i
$400$		0			0
$401$	−6.89278	+	34.6523i	−0.0171890	+	0.0864148i	−0.988428	−	0.151694i	$-0.951527\pi$
$401$	−6.89278	+	34.6523i	−0.0171890	+	0.0864148i	0.971239	+	0.238108i	$0.0765273\pi$
$402$	380.021	−	253.922i	0.945325	−	0.631646i
$403$	−102.846	+	20.4573i	−0.255200	+	0.0507624i
$404$	−65.8289	+	65.8289i	−0.162943	+	0.162943i
$405$		0			0
$406$	91.0995	+	37.7346i	0.224383	+	0.0929425i
$407$	7.83403			0.0192482
$408$	157.274	−	497.308i	0.385475	−	1.21889i
$409$	−280.116			−0.684879			−0.342440	−	0.939540i	$-0.611253\pi$
$409$	−280.116			−0.684879			−0.342440	+	0.939540i	$0.611253\pi$
$410$		0			0
$411$	344.840	+	230.415i	0.839027	+	0.560620i
$412$	−137.186	+	137.186i	−0.332976	+	0.332976i
$413$	12.6554	+	63.6232i	0.0306427	+	0.154051i
$414$	801.395	−	535.475i	1.93574	−	1.29342i
$415$		0			0
$416$	−119.298	+	49.4147i	−0.286773	+	0.118785i
$417$	−765.737	+	317.179i	−1.83630	+	0.760621i
$418$	19.7722	+	3.93294i	0.0473020	+	0.00940895i
$419$	76.3556	+	114.274i	0.182233	+	0.272731i	0.911328	−	0.411682i	$-0.135059\pi$
$419$	76.3556	+	114.274i	0.182233	+	0.272731i	−0.729095	+	0.684413i	$0.760059\pi$
$420$		0			0
$421$	183.297	−	183.297i	0.435385	−	0.435385i	−0.455070	−	0.890455i	$-0.650386\pi$
$421$	183.297	−	183.297i	0.435385	−	0.435385i	0.890455	+	0.455070i	$0.150386\pi$
$422$	391.407	+	261.530i	0.927505	+	0.619739i
$423$	−529.736	+	1278.90i	−1.25233	+	3.02339i
$424$		−	99.3626i		−	0.234346i
$425$		0			0
$426$	−911.583			−2.13987
$427$	−11.3638	−	4.70702i	−0.0266130	−	0.0110235i
$428$	143.982	−	215.485i	0.336408	−	0.503470i
$429$	−7.97897	−	7.97897i	−0.0185990	−	0.0185990i
$430$		0			0
$431$	419.398	−	280.233i	0.973080	−	0.650192i	0.0360172	−	0.999351i	$-0.488533\pi$
$431$	419.398	−	280.233i	0.973080	−	0.650192i	0.937063	+	0.349160i	$0.113533\pi$
$432$	−134.865	+	678.011i	−0.312187	+	1.56947i
$433$	−316.814	−	764.858i	−0.731673	−	1.76641i	−0.636942	−	0.770912i	$-0.719801\pi$
$433$	−316.814	−	764.858i	−0.731673	−	1.76641i	−0.0947312	−	0.995503i	$-0.530199\pi$
$434$	−14.7667	−	35.6500i	−0.0340247	−	0.0821428i
$435$		0			0
$436$	74.5108	+	111.513i	0.170896	+	0.255764i
$437$	612.073	−	121.749i	1.40062	−	0.278601i
$438$	−2.90464	−	2.90464i	−0.00663160	−	0.00663160i
$439$	−37.2714	+	55.7806i	−0.0849006	+	0.127063i	−0.871489	−	0.490415i	$-0.836845\pi$
$439$	−37.2714	+	55.7806i	−0.0849006	+	0.127063i	0.786589	+	0.617477i	$0.211845\pi$
$440$		0			0
$441$		−	770.954i		−	1.74819i
$442$	234.820	−	68.2234i	0.531267	−	0.154352i
$443$			602.890i			1.36093i	0.732783	+	0.680463i	$0.238221\pi$
$443$			602.890i			1.36093i	−0.732783	+	0.680463i	$0.761779\pi$
$444$	55.8810	−	134.909i	0.125858	−	0.303849i
$445$		0			0
$446$	−533.767	−	533.767i	−1.19679	−	1.19679i
$447$	158.336	+	796.010i	0.354220	+	1.78078i
$448$	16.6459	+	24.9124i	0.0371560	+	0.0556079i
$449$	702.019	+	139.640i	1.56352	+	0.311003i	0.899570	−	0.436777i	$-0.143880\pi$
$449$	702.019	+	139.640i	1.56352	+	0.311003i	0.663947	+	0.747780i	$0.268880\pi$
$450$		0			0
$451$	9.58196	+	23.1329i	0.0212460	+	0.0512925i
$452$	155.894	+	31.0093i	0.344898	+	0.0686046i
$453$	−651.920	+	435.599i	−1.43912	+	0.961588i
$454$	−70.4050	−	353.950i	−0.155077	−	0.779625i
$455$		0			0
$456$	−409.839	+	613.368i	−0.898770	+	1.34510i
$457$	−179.878	+	434.264i	−0.393606	+	0.950250i	0.595541	+	0.803325i	$0.296938\pi$
$457$	−179.878	+	434.264i	−0.393606	+	0.950250i	−0.989148	+	0.146925i	$0.953062\pi$
$458$	−703.049			−1.53504
$459$	181.004	−	572.345i	0.394345	−	1.24694i
$460$		0			0
$461$	−152.470	+	368.096i	−0.330739	+	0.798474i	0.667795	+	0.744345i	$0.267238\pi$
$461$	−152.470	+	368.096i	−0.330739	+	0.798474i	−0.998534	+	0.0541287i	$0.982762\pi$
$462$	2.30692	−	3.45255i	0.00499334	−	0.00747306i
$463$	96.2811	−	96.2811i	0.207950	−	0.207950i	−0.595445	−	0.803396i	$-0.703024\pi$
$463$	96.2811	−	96.2811i	0.207950	−	0.207950i	0.803396	+	0.595445i	$0.203024\pi$
$464$	827.347	−	164.570i	1.78307	−	0.354676i
$465$		0			0
$466$	−234.837	−	46.7119i	−0.503941	−	0.100240i
$467$	165.232	+	398.906i	0.353816	+	0.854188i	0.996142	+	0.0877563i	$0.0279697\pi$
$467$	165.232	+	398.906i	0.353816	+	0.854188i	−0.642326	+	0.766432i	$0.722030\pi$
$468$	−124.517	+	51.5765i	−0.266061	+	0.110206i
$469$	7.61989	−	38.3078i	0.0162471	−	0.0816797i
$470$		0			0
$471$	122.762	+	617.168i	0.260642	+	1.31034i
$472$	284.179	+	284.179i	0.602073	+	0.602073i
$473$	1.67297	+	1.11784i	0.00353694	+	0.00236331i
$474$	853.973	+	353.727i	1.80163	+	0.746260i
$475$		0			0
$476$	10.4666	+	20.1487i	0.0219887	+	0.0423293i
$477$		−	260.247i		−	0.545592i
$478$	830.295	+	343.920i	1.73702	+	0.719497i
$479$	−352.426	−	235.484i	−0.735755	−	0.491616i	0.130356	−	0.991467i	$-0.458388\pi$
$479$	−352.426	−	235.484i	−0.735755	−	0.491616i	−0.866111	+	0.499852i	$0.833388\pi$
$480$		0			0
$481$	−131.813	+	26.2193i	−0.274040	+	0.0545099i
$482$	436.111	+	652.686i	0.904794	+	1.35412i
$483$	25.0771	−	126.071i	0.0519194	−	0.261017i
$484$	150.742	−	62.4395i	0.311451	−	0.129007i
$485$		0			0
$486$	70.5478	−	354.668i	0.145160	−	0.729769i
$487$	−398.602	+	266.338i	−0.818486	+	0.546895i	−0.892859	−	0.450336i	$-0.851304\pi$
$487$	−398.602	+	266.338i	−0.818486	+	0.546895i	0.0743736	+	0.997230i	$0.476304\pi$
$488$	−74.7387	+	14.8664i	−0.153153	+	0.0304640i
$489$	−376.201	+	376.201i	−0.769327	+	0.769327i
$490$		0			0
$491$	−2.48118	−	1.02774i	−0.00505332	−	0.00209315i	0.380155	−	0.924923i	$-0.375871\pi$
$491$	−2.48118	−	1.02774i	−0.00505332	−	0.00209315i	−0.385209	+	0.922830i	$0.625871\pi$
$492$	466.718			0.948614
$493$	−729.768	+	63.2102i	−1.48026	+	0.128215i
$494$	−345.845			−0.700091
$495$		0			0
$496$	−274.475	−	183.399i	−0.553378	−	0.369755i
$497$	−55.0850	+	55.0850i	−0.110835	+	0.110835i
$498$	194.027	+	975.439i	0.389612	+	1.95871i
$499$	−300.741	+	200.949i	−0.602688	+	0.402703i	−0.819143	−	0.573589i	$-0.805551\pi$
$499$	−300.741	+	200.949i	−0.602688	+	0.402703i	0.216455	+	0.976293i	$0.430551\pi$
$500$		0			0
$501$	−692.178	+	286.709i	−1.38159	+	0.572274i
$502$	263.663	−	109.213i	0.525226	−	0.217556i
$503$	141.236	+	28.0936i	0.280787	+	0.0558521i	0.333475	−	0.942759i	$-0.391779\pi$
$503$	141.236	+	28.0936i	0.280787	+	0.0558521i	−0.0526876	+	0.998611i	$0.516779\pi$
$504$	54.0924	+	80.9551i	0.107326	+	0.160625i
$505$		0			0
$506$	−15.3886	+	15.3886i	−0.0304122	+	0.0304122i
$507$	−542.401	−	362.420i	−1.06982	−	0.714833i
$508$	−61.9657	+	149.598i	−0.121980	+	0.294485i
$509$		−	281.872i		−	0.553776i	−0.960902	−	0.276888i	$-0.910697\pi$
$509$		−	281.872i		−	0.553776i	0.960902	−	0.276888i	$-0.0893031\pi$
$510$		0			0
$511$	−0.351042			−0.000686972
$512$	67.9107	+	28.1295i	0.132638	+	0.0549405i
$513$	−471.678	+	705.916i	−0.919450	+	1.37605i
$514$	126.192	+	126.192i	0.245509	+	0.245509i
$515$		0			0
$516$	31.1837	−	20.8363i	0.0604336	−	0.0403804i
$517$	6.09774	−	30.6554i	0.0117945	−	0.0592948i
$518$	−18.9259	−	45.6912i	−0.0365365	−	0.0882069i
$519$	−52.2044	−	126.032i	−0.100586	−	0.242837i
$520$		0			0
$521$	−403.558	−	603.967i	−0.774583	−	1.15925i	−0.983428	−	0.181297i	$-0.941971\pi$
$521$	−403.558	−	603.967i	−0.774583	−	1.15925i	0.208846	−	0.977949i	$-0.433029\pi$
$522$	1569.29	−	312.151i	3.00630	−	0.597990i
$523$	658.045	+	658.045i	1.25821	+	1.25821i	0.951946	+	0.306266i	$0.0990796\pi$
$523$	658.045	+	658.045i	1.25821	+	1.25821i	0.306266	+	0.951946i	$0.400920\pi$
$524$	−161.265	+	241.351i	−0.307758	+	0.460593i
$525$		0			0
$526$		−	173.923i		−	0.330652i
$527$	219.427	+	184.445i	0.416370	+	0.349990i
$528$		−	35.5228i		−	0.0672780i
$529$	−55.3710	+	133.677i	−0.104671	+	0.252698i
$530$		0			0
$531$	744.311	+	744.311i	1.40172	+	1.40172i
$532$	−6.26483	−	31.4954i	−0.0117760	−	0.0592019i
$533$	−238.646	−	357.159i	−0.447741	−	0.670091i
$534$	1942.10	+	386.309i	3.63690	+	0.723425i
$535$		0			0
$536$	−92.6014	−	223.560i	−0.172764	−	0.417089i
$537$	263.449	+	52.4032i	0.490593	+	0.0975851i
$538$	347.686	−	232.317i	0.646257	−	0.431815i
$539$	3.39608	+	17.0732i	0.00630070	+	0.0316757i
$540$		0			0
$541$	−190.737	+	285.458i	−0.352563	+	0.527648i	−0.964786	−	0.263037i	$-0.915276\pi$
$541$	−190.737	+	285.458i	−0.352563	+	0.527648i	0.612222	+	0.790686i	$0.290276\pi$
$542$	213.700	−	515.918i	0.394281	−	0.951878i
$543$	583.318			1.07425
$544$	309.324	+	170.049i	0.568611	+	0.312591i
$545$		0			0
$546$	−27.2605	+	65.8126i	−0.0499276	+	0.120536i
$547$	−341.029	+	510.386i	−0.623453	+	0.933064i	0.376525	+	0.926407i	$0.377119\pi$
$547$	−341.029	+	510.386i	−0.623453	+	0.933064i	−0.999978	+	0.00665718i	$0.997881\pi$
$548$	−79.0898	+	79.0898i	−0.144324	+	0.144324i
$549$	−195.753	+	38.9377i	−0.356563	+	0.0709248i
$550$		0			0
$551$	1016.09	+	202.112i	1.84408	+	0.366810i
$552$	−304.752	−	735.736i	−0.552086	−	1.33285i
$553$	72.9787	−	30.2288i	0.131969	−	0.0546633i
$554$	−139.637	+	702.001i	−0.252052	+	1.26715i
$555$		0			0
$556$	−43.6078	−	219.231i	−0.0784313	−	0.394301i
$557$	−41.7424	−	41.7424i	−0.0749415	−	0.0749415i	0.668643	−	0.743584i	$-0.266876\pi$
$557$	−41.7424	−	41.7424i	−0.0749415	−	0.0749415i	−0.743584	+	0.668643i	$0.766876\pi$
$558$	−520.617	−	347.865i	−0.933005	−	0.623414i
$559$	−31.8902	−	13.2094i	−0.0570487	−	0.0236303i
$560$		0			0
$561$	−3.38465	+	30.6599i	−0.00603325	+	0.0546522i
$562$		−	52.6957i		−	0.0937646i
$563$	−474.709	−	196.631i	−0.843177	−	0.349255i	−0.0810717	−	0.996708i	$-0.525834\pi$
$563$	−474.709	−	196.631i	−0.843177	−	0.349255i	−0.762106	+	0.647453i	$0.775834\pi$
$564$	−484.417	−	323.677i	−0.858895	−	0.573895i
$565$		0			0
$566$	235.444	−	46.8328i	0.415979	−	0.0827434i
$567$	17.7304	+	26.5354i	0.0312705	+	0.0467997i
$568$	−94.1562	+	473.355i	−0.165768	+	0.833372i
$569$	327.271	−	135.560i	0.575169	−	0.238243i	−0.0760868	−	0.997101i	$-0.524243\pi$
$569$	327.271	−	135.560i	0.575169	−	0.238243i	0.651256	+	0.758859i	$0.274243\pi$
$570$		0			0
$571$	−160.319	+	805.978i	−0.280769	+	1.41152i	0.540676	+	0.841231i	$0.318169\pi$
$571$	−160.319	+	805.978i	−0.280769	+	1.41152i	−0.821444	+	0.570289i	$0.806831\pi$
$572$	2.53030	−	1.69069i	0.00442360	−	0.00295576i
$573$	−375.082	+	74.6085i	−0.654594	+	0.130207i
$574$	111.772	−	111.772i	0.194724	−	0.194724i
$575$		0			0
$576$	449.171	+	186.053i	0.779811	+	0.323008i
$577$	−337.479			−0.584886			−0.292443	−	0.956283i	$-0.594468\pi$
$577$	−337.479			−0.584886			−0.292443	+	0.956283i	$0.594468\pi$
$578$	−546.901	−	384.356i	−0.946195	−	0.664976i
$579$	−1085.13			−1.87415
$580$		0			0
$581$	70.6683	+	47.2190i	0.121632	+	0.0812720i
$582$	−723.989	+	723.989i	−1.24397	+	1.24397i
$583$	1.14640	+	5.76333i	0.00196638	+	0.00988564i
$584$	−1.80830	+	1.20827i	−0.00309641	+	0.00206895i
$585$		0			0
$586$	60.9699	−	25.2546i	0.104044	−	0.0430965i
$587$	162.837	−	67.4493i	0.277405	−	0.114905i	−0.239644	−	0.970861i	$-0.577031\pi$
$587$	162.837	−	67.4493i	0.277405	−	0.114905i	0.517049	+	0.855956i	$0.327031\pi$
$588$	318.240	+	63.3020i	0.541225	+	0.107656i
$589$	−225.237	−	337.091i	−0.382406	−	0.572311i
$590$		0			0
$591$	−881.991	+	881.991i	−1.49237	+	1.49237i
$592$	−351.784	−	235.055i	−0.594231	−	0.397052i
$593$	−97.6406	+	235.725i	−0.164655	+	0.397513i	−0.984574	−	0.174966i	$-0.944018\pi$
$593$	−97.6406	+	235.725i	−0.164655	+	0.397513i	0.819919	+	0.572479i	$0.194018\pi$
$594$		−	29.6068i		−	0.0498430i
$595$		0			0
$596$	−218.881			−0.367250
$597$	−1243.65	−	515.137i	−2.08317	−	0.862876i
$598$	207.421	−	310.427i	0.346858	−	0.519109i
$599$	−47.8438	−	47.8438i	−0.0798728	−	0.0798728i	0.666042	−	0.745914i	$-0.267987\pi$
$599$	−47.8438	−	47.8438i	−0.0798728	−	0.0798728i	−0.745914	+	0.666042i	$0.767987\pi$
$600$		0			0
$601$	380.371	−	254.155i	0.632896	−	0.422888i	−0.197312	−	0.980341i	$-0.563221\pi$
$601$	380.371	−	254.155i	0.632896	−	0.422888i	0.830208	+	0.557453i	$0.188221\pi$
$602$	2.47805	−	12.4580i	0.00411636	−	0.0206943i
$603$	−242.539	−	585.540i	−0.402220	−	0.971044i
$604$	−80.9192	−	195.356i	−0.133972	−	0.323438i
$605$		0			0
$606$	443.589	+	663.877i	0.731994	+	1.09551i
$607$	258.994	−	51.5172i	0.426679	−	0.0848718i	0.0229205	−	0.999737i	$-0.492704\pi$
$607$	258.994	−	51.5172i	0.426679	−	0.0848718i	0.403759	+	0.914866i	$0.367704\pi$
$608$	−353.013	−	353.013i	−0.580614	−	0.580614i
$609$	118.552	−	177.426i	0.194667	−	0.291339i
$610$		0			0
$611$			536.208i			0.877591i
$612$	322.857	+	177.489i	0.527544	+	0.290014i
$613$			320.858i			0.523422i	0.965146	+	0.261711i	$0.0842868\pi$
$613$			320.858i			0.523422i	−0.965146	+	0.261711i	$0.915713\pi$
$614$	158.074	−	381.625i	0.257450	−	0.621539i
$615$		0			0
$616$	−1.55452	−	1.55452i	−0.00252357	−	0.00252357i
$617$	−109.348	−	549.727i	−0.177225	−	0.890968i	−0.962388	−	0.271679i	$-0.912421\pi$
$617$	−109.348	−	549.727i	−0.177225	−	0.890968i	0.785163	−	0.619289i	$-0.212579\pi$
$618$	924.428	+	1383.50i	1.49584	+	2.23868i
$619$	−102.300	−	20.3487i	−0.165266	−	0.0328735i	0.111764	−	0.993735i	$-0.464350\pi$
$619$	−102.300	−	20.3487i	−0.165266	−	0.0328735i	−0.277030	+	0.960861i	$0.589350\pi$
$620$		0			0
$621$	−350.734	−	846.747i	−0.564789	−	1.36352i
$622$	−212.234	−	42.2160i	−0.341213	−	0.0678715i
$623$	140.701	−	94.0134i	0.225844	−	0.150904i
$624$	118.889	+	597.697i	0.190528	+	0.957848i
$625$		0			0
$626$	−323.123	+	483.587i	−0.516171	+	0.772504i
$627$	16.6952	−	40.3057i	0.0266270	−	0.0642834i
$628$	−169.704			−0.270230
$629$	281.231	+	236.396i	0.447108	+	0.375828i
$630$		0			0
$631$	−141.756	+	342.229i	−0.224652	+	0.542359i	−0.995511	−	0.0946475i	$-0.969828\pi$
$631$	−141.756	+	342.229i	−0.224652	+	0.542359i	0.770858	+	0.637007i	$0.219828\pi$
$632$	271.885	−	406.904i	0.430197	−	0.643836i
$633$	720.339	−	720.339i	1.13798	−	1.13798i
$634$	−1200.28	+	238.751i	−1.89319	+	0.376579i
$635$		0			0
$636$	107.427	+	21.3685i	0.168910	+	0.0335983i
$637$	−114.283	−	275.903i	−0.179408	−	0.433129i
$638$	−33.3778	+	13.8255i	−0.0523162	+	0.0216701i
$639$	−246.611	+	1239.80i	−0.385932	+	1.94021i
$640$		0			0
$641$	−58.4526	−	293.861i	−0.0911897	−	0.458442i	−0.999218	−	0.0395334i	$-0.987413\pi$
$641$	−58.4526	−	293.861i	−0.0911897	−	0.458442i	0.908029	−	0.418908i	$-0.137587\pi$
$642$	−1571.68	−	1571.68i	−2.44811	−	2.44811i
$643$	−220.125	−	147.083i	−0.342341	−	0.228745i	0.372500	−	0.928032i	$-0.378501\pi$
$643$	−220.125	−	147.083i	−0.342341	−	0.228745i	−0.714841	+	0.699287i	$0.753501\pi$
$644$	32.0273	+	13.2662i	0.0497319	+	0.0205996i
$645$		0			0
$646$	591.117	+	737.824i	0.915042	+	1.14214i
$647$			501.378i			0.774927i	0.921885	+	0.387464i	$0.126649\pi$
$647$			501.378i			0.774927i	−0.921885	+	0.387464i	$0.873351\pi$
$648$	182.667	+	75.6631i	0.281893	+	0.116764i
$649$	−19.7619	−	13.2045i	−0.0304498	−	0.0203459i
$650$		0			0
$651$	−81.9006	+	16.2910i	−0.125807	+	0.0250246i
$652$	−79.7146	−	119.301i	−0.122262	−	0.182978i
$653$	−204.042	+	1025.79i	−0.312468	+	1.57088i	0.431152	+	0.902279i	$0.358107\pi$
$653$	−204.042	+	1025.79i	−0.312468	+	1.57088i	−0.743620	+	0.668603i	$0.766893\pi$
$654$	1062.69	−	440.179i	1.62490	−	0.673056i
$655$		0			0
$656$	263.813	−	1326.28i	0.402154	−	2.02176i
$657$	−4.73624	+	3.16466i	−0.00720890	+	0.00481683i
$658$	−193.526	+	38.4947i	−0.294112	+	0.0585026i
$659$	874.251	−	874.251i	1.32663	−	1.32663i	0.418344	−	0.908289i	$-0.362611\pi$
$659$	874.251	−	874.251i	1.32663	−	1.32663i	0.908289	−	0.418344i	$-0.137389\pi$
$660$		0			0
$661$	−1061.36	−	439.631i	−1.60569	−	0.665099i	−0.613486	−	0.789706i	$-0.710233\pi$
$661$	−1061.36	−	439.631i	−1.60569	−	0.665099i	−0.992206	+	0.124607i	$0.960233\pi$
$662$	900.444			1.36019
$663$	−45.6647	−	527.203i	−0.0688759	−	0.795178i
$664$	526.554			0.793003
$665$		0			0
$666$	−667.255	−	445.845i	−1.00188	−	0.669437i
$667$	−790.814	+	790.814i	−1.18563	+	1.18563i
$668$	−39.4187	−	198.171i	−0.0590100	−	0.296663i
$669$	−1358.26	+	907.558i	−2.03028	+	1.35659i
$670$		0			0
$671$	4.16354	−	1.72460i	0.00620498	−	0.00257019i
$672$	−95.0022	+	39.3512i	−0.141372	+	0.0585583i
$673$	1088.11	+	216.439i	1.61681	+	0.321603i	0.918872	−	0.394555i	$-0.129101\pi$
$673$	1088.11	+	216.439i	1.61681	+	0.321603i	0.697938	+	0.716159i	$0.254101\pi$
$674$	−696.815	−	1042.86i	−1.03385	−	1.54727i
$675$		0			0
$676$	124.401	−	124.401i	0.184025	−	0.184025i
$677$	538.907	+	360.086i	0.796023	+	0.531885i	0.885795	−	0.464077i	$-0.153614\pi$
$677$	538.907	+	360.086i	0.796023	+	0.531885i	−0.0897723	+	0.995962i	$0.528614\pi$
$678$	521.681	−	1259.45i	0.769441	−	1.85759i
$679$			87.4982i			0.128863i
$680$		0			0
$681$	−780.974			−1.14681
$682$	13.0617	+	5.41034i	0.0191521	+	0.00793306i
$683$	182.884	−	273.705i	0.267766	−	0.400739i	−0.673083	−	0.739567i	$-0.735030\pi$
$683$	182.884	−	273.705i	0.267766	−	0.400739i	0.940849	+	0.338828i	$0.110030\pi$
$684$	−368.457	−	368.457i	−0.538679	−	0.538679i
$685$		0			0
$686$	184.610	−	123.352i	0.269110	−	0.179814i
$687$	−296.818	+	1492.21i	−0.432050	+	2.17206i
$688$	−41.5841	−	100.393i	−0.0604420	−	0.145920i
$689$	−38.5779	−	93.1354i	−0.0559912	−	0.135175i
$690$		0			0
$691$	−137.814	−	206.253i	−0.199441	−	0.298485i	0.718245	−	0.695790i	$-0.244946\pi$
$691$	−137.814	−	206.253i	−0.199441	−	0.298485i	−0.917687	+	0.397305i	$0.869946\pi$
$692$	36.0832	−	7.17739i	0.0521433	−	0.0103720i
$693$	−4.07154	−	4.07154i	−0.00587524	−	0.00587524i
$694$	−80.9279	+	121.117i	−0.116611	+	0.174520i
$695$		0			0
$696$		−	1322.01i		−	1.89944i
$697$	−354.068	+	1119.58i	−0.507988	+	1.60628i
$698$			995.704i			1.42651i
$699$	−198.290	+	478.714i	−0.283677	+	0.684856i
$700$		0			0
$701$	479.136	+	479.136i	0.683504	+	0.683504i	0.960788	−	0.277284i	$-0.0894342\pi$
$701$	479.136	+	479.136i	0.683504	+	0.683504i	−0.277284	+	0.960788i	$0.589434\pi$
$702$	99.0893	+	498.155i	0.141153	+	0.709623i
$703$	−288.678	−	432.037i	−0.410637	−	0.614561i
$704$	−10.7667	−	2.14163i	−0.0152936	−	0.00304209i
$705$		0			0
$706$	34.4636	+	83.2024i	0.0488152	+	0.117850i
$707$	66.9218	+	13.3116i	0.0946560	+	0.0188282i
$708$	−368.357	+	246.128i	−0.520278	+	0.347639i
$709$	237.118	+	1192.07i	0.334440	+	1.68134i	0.672403	+	0.740185i	$0.265262\pi$
$709$	237.118	+	1192.07i	0.334440	+	1.68134i	−0.337963	+	0.941160i	$0.609738\pi$
$710$		0			0
$711$	712.112	−	1065.75i	1.00156	−	1.49895i
$712$	401.195	−	968.570i	0.563476	−	1.36035i
$713$	437.656			0.613823
$714$	186.998	−	54.3294i	0.261902	−	0.0760916i
$715$		0			0
$716$	−27.7221	+	66.9270i	−0.0387180	+	0.0934734i
$717$	1080.50	−	1617.09i	1.50698	−	2.25535i
$718$	−975.795	+	975.795i	−1.35905	+	1.35905i
$719$	−494.558	+	98.3738i	−0.687842	+	0.136820i	−0.526624	−	0.850099i	$-0.676542\pi$
$719$	−494.558	+	98.3738i	−0.687842	+	0.136820i	−0.161218	+	0.986919i	$0.551542\pi$
$720$		0			0
$721$	139.463	+	27.7410i	0.193430	+	0.0384757i
$722$	−192.158	−	463.909i	−0.266146	−	0.642534i
$723$	1569.43	−	650.080i	2.17072	−	0.899142i
$724$	−30.6906	+	154.292i	−0.0423903	+	0.213110i
$725$		0			0
$726$	−273.002	−	1372.47i	−0.376035	−	1.89046i
$727$	−972.990	−	972.990i	−1.33836	−	1.33836i	−0.897646	−	0.440718i	$-0.854724\pi$
$727$	−972.990	−	972.990i	−1.33836	−	1.33836i	−0.440718	−	0.897646i	$-0.645276\pi$
$728$	31.3586	+	20.9532i	0.0430751	+	0.0287818i
$729$	−991.196	−	410.567i	−1.35967	−	0.563192i
$730$		0			0
$731$	26.3259	+	90.6118i	0.0360135	+	0.123956i
$732$		−	84.0016i		−	0.114756i
$733$	−1328.67	−	550.353i	−1.81265	−	0.750823i	−0.980572	−	0.196159i	$-0.937153\pi$
$733$	−1328.67	−	550.353i	−1.81265	−	0.750823i	−0.832074	−	0.554664i	$-0.812847\pi$
$734$	−210.906	−	140.923i	−0.287339	−	0.191993i
$735$		0			0
$736$	528.581	−	105.141i	0.718181	−	0.142855i
$737$	7.95048	+	11.8987i	0.0107876	+	0.0161448i
$738$	500.393	−	2515.64i	0.678039	−	3.40873i
$739$	347.484	−	143.933i	0.470209	−	0.194767i	−0.134981	−	0.990848i	$-0.543097\pi$
$739$	347.484	−	143.933i	0.470209	−	0.194767i	0.605190	+	0.796081i	$0.293097\pi$
$740$		0			0
$741$	−146.011	+	734.049i	−0.197046	+	0.990619i
$742$	30.8445	−	20.6096i	0.0415694	−	0.0277758i
$743$	865.508	−	172.160i	1.16488	−	0.231710i	0.425477	−	0.904969i	$-0.360107\pi$
$743$	865.508	−	172.160i	1.16488	−	0.231710i	0.739406	+	0.673260i	$0.235107\pi$
$744$	−365.816	+	365.816i	−0.491689	+	0.491689i
$745$		0			0
$746$	401.121	+	166.150i	0.537696	+	0.222721i
$747$	1379.13			1.84623
$748$	−7.93169	−	2.50840i	−0.0106039	−	0.00335348i
$749$	−189.947			−0.253601
$750$		0			0
$751$	−5.26712	−	3.51938i	−0.00701347	−	0.00468625i	0.552059	−	0.833805i	$-0.313842\pi$
$751$	−5.26712	−	3.51938i	−0.00701347	−	0.00468625i	−0.559072	+	0.829119i	$0.688842\pi$
$752$	−1193.61	+	1193.61i	−1.58725	+	1.58725i
$753$	−120.487	−	605.728i	−0.160009	−	0.804420i
$754$	515.333	−	344.335i	0.683466	−	0.456677i
$755$		0			0
$756$	−43.5710	+	18.0477i	−0.0576337	+	0.0238726i
$757$	981.619	−	406.600i	1.29672	−	0.537120i	0.375741	−	0.926725i	$-0.377388\pi$
$757$	981.619	−	406.600i	1.29672	−	0.537120i	0.920982	+	0.389605i	$0.127388\pi$
$758$	77.4758	+	15.4109i	0.102211	+	0.0203310i
$759$	26.1651	+	39.1588i	0.0344731	+	0.0515926i
$760$		0			0
$761$	172.386	−	172.386i	0.226526	−	0.226526i	−0.584714	−	0.811240i	$-0.698793\pi$
$761$	172.386	−	172.386i	0.226526	−	0.226526i	0.811240	+	0.584714i	$0.198793\pi$
$762$	1154.70	+	771.543i	1.51535	+	1.01252i
$763$	37.6168	−	90.8149i	0.0493011	−	0.119023i
$764$		−	103.137i		−	0.134997i
$765$		0			0
$766$	1576.44			2.05801
$767$	376.702	+	156.035i	0.491137	+	0.203436i
$768$	−647.904	+	969.657i	−0.843625	+	1.26257i
$769$	−682.514	−	682.514i	−0.887535	−	0.887535i	0.106751	−	0.994286i	$-0.465955\pi$
$769$	−682.514	−	682.514i	−0.887535	−	0.887535i	−0.994286	+	0.106751i	$0.965955\pi$
$770$		0			0
$771$	321.115	−	214.562i	0.416492	−	0.278291i
$772$	57.0928	−	287.025i	0.0739544	−	0.371794i
$773$	−288.856	−	697.360i	−0.373682	−	0.902147i	−0.993120	−	0.117102i	$-0.962640\pi$
$773$	−288.856	−	697.360i	−0.373682	−	0.902147i	0.619438	−	0.785045i	$-0.287360\pi$
$774$	−78.8755	−	190.422i	−0.101906	−	0.246024i
$775$		0			0
$776$	301.164	+	450.724i	0.388098	+	0.580830i
$777$	−104.969	+	20.8796i	−0.135095	+	0.0268721i
$778$	19.1615	+	19.1615i	0.0246292	+	0.0246292i
$779$	922.663	−	1380.86i	1.18442	−	1.77261i
$780$		0			0
$781$		−	28.5423i		−	0.0365459i
$782$	−1016.79	+	88.0709i	−1.30024	+	0.112623i
$783$		−	1521.48i		−	1.94314i
$784$	359.771	−	868.565i	0.458892	−	1.10786i
$785$		0			0
$786$	1760.34	+	1760.34i	2.23962	+	2.23962i
$787$	−126.416	−	635.538i	−0.160631	−	0.807545i	−0.974132	−	0.225981i	$-0.927441\pi$
$787$	−126.416	−	635.538i	−0.160631	−	0.807545i	0.813501	−	0.581564i	$-0.197559\pi$
$788$	−186.888	−	279.698i	−0.237168	−	0.354947i
$789$	−369.148	−	73.4281i	−0.467868	−	0.0930648i
$790$		0			0
$791$	−44.5817	−	107.630i	−0.0563612	−	0.136068i
$792$	−34.9875	−	6.95945i	−0.0441761	−	0.00878718i
$793$	−64.2827	+	42.9523i	−0.0810627	+	0.0541644i
$794$	9.68407	+	48.6851i	0.0121966	+	0.0613163i
$795$		0			0
$796$	201.691	−	301.851i	0.253380	−	0.379210i
$797$	−511.203	+	1234.15i	−0.641409	+	1.54850i	0.183371	+	0.983044i	$0.441299\pi$
$797$	−511.203	+	1234.15i	−0.641409	+	1.54850i	−0.824780	+	0.565454i	$0.808701\pi$
$798$	−275.412			−0.345128
$799$	1143.94	−	916.485i	1.43172	−	1.14704i
$800$		0			0
$801$	1050.80	−	2536.85i	1.31186	−	3.16710i
$802$	−45.4016	+	67.9483i	−0.0566104	+	0.0847235i
$803$	0.0909465	−	0.0909465i	0.000113258	−	0.000113258i
$804$	261.618	−	52.0391i	0.325396	−	0.0647253i
$805$		0			0
$806$	−237.881	−	47.3174i	−0.295137	−	0.0587065i
$807$	−346.298	−	836.037i	−0.429118	−	1.03598i
$808$	390.547	−	161.770i	0.483351	−	0.200210i
$809$	12.7373	−	64.0346i	0.0157445	−	0.0791528i	−0.972114	−	0.234508i	$-0.924652\pi$
$809$	12.7373	−	64.0346i	0.0157445	−	0.0791528i	0.987859	+	0.155355i	$0.0496522\pi$
$810$		0			0
$811$	−60.0421	−	301.852i	−0.0740347	−	0.372197i	0.925950	−	0.377645i	$-0.123266\pi$
$811$	−60.0421	−	301.852i	−0.0740347	−	0.372197i	−0.999985	+	0.00544749i	$0.998266\pi$
$812$	40.6929	+	40.6929i	0.0501144	+	0.0501144i
$813$	−1004.80	−	671.388i	−1.23592	−	0.825815i
$814$	16.7407	+	6.93423i	0.0205660	+	0.00851871i
$815$		0			0
$816$	1071.92	−	1275.22i	1.31362	−	1.56277i
$817$		−	133.454i		−	0.163346i
$818$	−598.585	−	247.942i	−0.731767	−	0.303108i
$819$	82.1335	+	54.8799i	0.100285	+	0.0670084i
$820$		0			0
$821$	691.877	−	137.623i	0.842725	−	0.167628i	0.245194	−	0.969474i	$-0.421148\pi$
$821$	691.877	−	137.623i	0.842725	−	0.167628i	0.597531	+	0.801846i	$0.296148\pi$
$822$	532.947	+	797.612i	0.648354	+	0.970330i
$823$	116.643	−	586.402i	0.141729	−	0.712517i	−0.842930	−	0.538024i	$-0.819171\pi$
$823$	116.643	−	586.402i	0.141729	−	0.712517i	0.984658	−	0.174494i	$-0.0558289\pi$
$824$	813.892	−	337.125i	0.987732	−	0.409132i
$825$		0			0
$826$	−29.2719	+	147.160i	−0.0354381	+	0.178159i
$827$	423.511	−	282.981i	0.512106	−	0.342178i	−0.272518	−	0.962151i	$-0.587856\pi$
$827$	423.511	−	282.981i	0.512106	−	0.342178i	0.784623	+	0.619973i	$0.212856\pi$
$828$	551.706	−	109.741i	0.666311	−	0.132538i
$829$	−804.169	+	804.169i	−0.970046	+	0.970046i	−0.999564	−	0.0295178i	$-0.990603\pi$
$829$	−804.169	+	804.169i	−0.970046	+	0.970046i	0.0295178	+	0.999564i	$0.490603\pi$
$830$		0			0
$831$	1431.03	+	592.751i	1.72206	+	0.713299i
$832$	188.326			0.226353
$833$	−393.279	+	715.384i	−0.472123	+	0.858804i
$834$	−1917.07			−2.29865
$835$		0			0
$836$	9.78275	+	6.53663i	0.0117019	+	0.00781893i
$837$	−421.013	+	421.013i	−0.503002	+	0.503002i
$838$	62.0171	+	311.781i	0.0740060	+	0.372053i
$839$	−799.310	+	534.082i	−0.952694	+	0.636570i	−0.931707	−	0.363210i	$-0.881681\pi$
$839$	−799.310	+	534.082i	−0.952694	+	0.636570i	−0.0209867	+	0.999780i	$0.506681\pi$
$840$		0			0
$841$	−938.290	+	388.652i	−1.11568	+	0.462131i
$842$	553.936	−	229.448i	0.657881	−	0.272503i
$843$	−111.845	−	22.2475i	−0.132676	−	0.0263908i
$844$	152.635	+	228.435i	0.180847	+	0.270657i
$845$		0			0
$846$	−2264.01	+	2264.01i	−2.67613	+	2.67613i
$847$	−99.4324	−	66.4386i	−0.117394	−	0.0784399i
$848$	121.446	−	293.197i	0.143215	−	0.345752i
$849$		−	519.497i		−	0.611893i
$850$		0			0
$851$	560.927			0.659138
$852$	−491.524	−	203.596i	−0.576906	−	0.238962i
$853$	−702.238	+	1050.97i	−0.823257	+	1.23209i	0.146789	+	0.989168i	$0.453106\pi$
$853$	−702.238	+	1050.97i	−0.823257	+	1.23209i	−0.970046	+	0.242923i	$0.921894\pi$
$854$	−20.1171	−	20.1171i	−0.0235563	−	0.0235563i
$855$		0			0
$856$	−978.461	+	653.787i	−1.14306	+	0.763770i
$857$	195.681	−	983.753i	0.228332	−	1.14790i	−0.681145	−	0.732149i	$-0.738518\pi$
$857$	195.681	−	983.753i	0.228332	−	1.14790i	0.909477	−	0.415754i	$-0.136482\pi$
$858$	−9.98792	−	24.1130i	−0.0116409	−	0.0281037i
$859$	412.502	+	995.868i	0.480212	+	1.15933i	0.959508	+	0.281681i	$0.0908920\pi$
$859$	412.502	+	995.868i	0.480212	+	1.15933i	−0.479296	+	0.877653i	$0.659108\pi$
$860$		0			0
$861$	−190.044	−	284.422i	−0.220725	−	0.330339i
$862$	1144.27	−	227.609i	1.32745	−	0.264047i
$863$	245.882	+	245.882i	0.284915	+	0.284915i	0.835066	−	0.550151i	$-0.185430\pi$
$863$	245.882	+	245.882i	0.284915	+	0.284915i	−0.550151	+	0.835066i	$0.685430\pi$
$864$	−407.337	+	609.623i	−0.471455	+	0.705582i
$865$		0			0
$866$		−	1914.87i		−	2.21116i
$867$	−1046.68	+	998.515i	−1.20725	+	1.15169i
$868$		−	22.5205i		−	0.0259452i
$869$	−11.0755	+	26.7385i	−0.0127451	+	0.0307693i
$870$		0			0
$871$	−173.596	−	173.596i	−0.199306	−	0.199306i
$872$	−118.807	−	597.283i	−0.136247	−	0.684958i
$873$	788.799	+	1180.52i	0.903550	+	1.35226i
$874$	1415.72	+	281.604i	1.61981	+	0.322201i
$875$		0			0
$876$	−0.917446	−	2.21491i	−0.00104731	−	0.00252844i
$877$	−148.338	−	29.5063i	−0.169143	−	0.0336446i	0.109792	−	0.993955i	$-0.464981\pi$
$877$	−148.338	−	29.5063i	−0.169143	−	0.0336446i	−0.278935	+	0.960310i	$0.589981\pi$
$878$	−129.020	+	86.2083i	−0.146947	+	0.0981871i
$879$	−27.8615	−	140.069i	−0.0316969	−	0.159351i
$880$		0			0
$881$	459.227	−	687.281i	0.521256	−	0.780115i	−0.473672	−	0.880701i	$-0.657072\pi$
$881$	459.227	−	687.281i	0.521256	−	0.780115i	0.994928	+	0.100586i	$0.0320719\pi$
$882$	682.404	−	1647.47i	0.773701	−	1.86788i
$883$	−362.947			−0.411038			−0.205519	−	0.978653i	$-0.565888\pi$
$883$	−362.947			−0.411038			−0.205519	+	0.978653i	$0.565888\pi$
$884$	141.852	+	15.6595i	0.160466	+	0.0177144i
$885$		0			0
$886$	−533.643	+	1288.33i	−0.602306	+	1.45410i
$887$	538.457	−	805.857i	0.607054	−	0.908520i	−0.392885	−	0.919588i	$-0.628523\pi$
$887$	538.457	−	805.857i	0.607054	−	0.908520i	0.999939	+	0.0110675i	$0.00352296\pi$
$888$	−468.853	+	468.853i	−0.527987	+	0.527987i
$889$	116.398	−	23.1531i	0.130932	−	0.0260440i
$890$		0			0
$891$	−11.4682	−	2.28116i	−0.0128711	−	0.00256023i
$892$	−168.593	−	407.019i	−0.189005	−	0.456300i
$893$	−1915.30	+	793.345i	−2.14480	+	0.888404i
$894$	−366.230	+	1841.16i	−0.409653	+	2.05946i
$895$		0			0
$896$	29.5514	+	148.565i	0.0329815	+	0.165809i
$897$	−571.305	−	571.305i	−0.636906	−	0.636906i
$898$	1376.56	+	919.787i	1.53292	+	1.02426i
$899$	671.238	+	278.036i	0.746649	+	0.309272i
$900$		0			0
$901$	−132.757	+	241.489i	−0.147344	+	0.268023i
$902$			57.9146i			0.0642069i
$903$	−25.3956	−	10.5192i	−0.0281236	−	0.0116492i
$904$	−600.107	−	400.979i	−0.663835	−	0.443560i
$905$		0			0
$906$	−1778.67	+	353.800i	−1.96321	+	0.390507i
$907$	−20.2068	−	30.2417i	−0.0222788	−	0.0333425i	0.820163	−	0.572130i	$-0.193883\pi$
$907$	−20.2068	−	30.2417i	−0.0222788	−	0.0333425i	−0.842442	+	0.538787i	$0.818883\pi$
$908$	41.0900	−	206.573i	0.0452533	−	0.227504i
$909$	1022.91	−	423.703i	1.12531	−	0.466120i
$910$		0			0
$911$	−294.154	+	1478.81i	−0.322891	+	1.62328i	0.389171	+	0.921166i	$0.372762\pi$
$911$	−294.154	+	1478.81i	−0.322891	+	1.62328i	−0.712062	+	0.702117i	$0.752238\pi$
$912$	−1959.04	+	1308.99i	−2.14807	+	1.43529i
$913$	−30.5417	+	6.07512i	−0.0334520	+	0.00665402i
$914$	−768.771	+	768.771i	−0.841106	+	0.841106i
$915$		0			0
$916$	−379.083	−	157.021i	−0.413846	−	0.171421i
$917$	212.747			0.232003
$918$	893.398	−	1062.84i	0.973201	−	1.15778i
$919$	682.108			0.742229			0.371114	−	0.928587i	$-0.378976\pi$
$919$	682.108			0.742229			0.371114	+	0.928587i	$0.378976\pi$
$920$		0			0
$921$	−743.254	−	496.626i	−0.807008	−	0.539225i
$922$	−651.635	+	651.635i	−0.706763	+	0.706763i
$923$	95.5268	+	480.246i	0.103496	+	0.520310i
$924$	2.01499	−	1.34637i	0.00218073	−	0.00145712i
$925$		0			0
$926$	290.968	−	120.523i	0.314220	−	0.130154i
$927$	2131.72	−	882.986i	2.29959	−	0.952520i
$928$	877.486	+	174.543i	0.945566	+	0.188085i
$929$	−403.390	−	603.716i	−0.434219	−	0.649855i	0.548242	−	0.836320i	$-0.315297\pi$
$929$	−403.390	−	603.716i	−0.434219	−	0.649855i	−0.982462	+	0.186464i	$0.940297\pi$
$930$		0			0
$931$	816.424	−	816.424i	0.876932	−	0.876932i
$932$	−116.191	−	77.6362i	−0.124668	−	0.0833006i
$933$	−179.205	+	432.640i	−0.192074	+	0.463708i
$934$			998.685i			1.06926i
$935$		0			0
$936$	611.983			0.653827
$937$	803.778	+	332.936i	0.857820	+	0.355321i	0.767855	−	0.640624i	$-0.221324\pi$
$937$	803.778	+	332.936i	0.857820	+	0.355321i	0.0899657	+	0.995945i	$0.471324\pi$
$938$	50.1910	−	75.1161i	0.0535085	−	0.0800811i
$939$	889.985	+	889.985i	0.947801	+	0.947801i
$940$		0			0
$941$	−831.285	+	555.447i	−0.883406	+	0.590273i	−0.912397	−	0.409306i	$-0.865771\pi$
$941$	−831.285	+	555.447i	−0.883406	+	0.590273i	0.0289906	+	0.999580i	$0.490771\pi$
$942$	−283.948	+	1427.50i	−0.301431	+	1.51539i
$943$	686.081	+	1656.35i	0.727552	+	1.75647i
$944$	491.211	+	1185.89i	0.520350	+	1.25624i
$945$		0			0
$946$	2.58556	+	3.86956i	0.00273315	+	0.00409045i
$947$	−1739.96	+	346.100i	−1.83734	+	0.365470i	−0.986994	−	0.160754i	$-0.948607\pi$
$947$	−1739.96	+	346.100i	−1.83734	+	0.365470i	−0.850346	+	0.526224i	$0.823607\pi$
$948$	381.458	+	381.458i	0.402382	+	0.402382i
$949$	−1.22586	+	1.83463i	−0.00129174	+	0.00193322i
$950$		0			0
$951$			2648.37i			2.78483i
$952$	−8.89671	−	102.713i	−0.00934529	−	0.107892i
$953$			1184.60i			1.24302i	0.783405	+	0.621512i	$0.213481\pi$
$953$			1184.60i			1.24302i	−0.783405	+	0.621512i	$0.786519\pi$
$954$	230.356	−	556.128i	0.241463	−	0.582944i
$955$		0			0
$956$	370.882	+	370.882i	0.387952	+	0.387952i
$957$	15.2527	+	76.6805i	0.0159380	+	0.0801259i
$958$	−544.671	−	815.158i	−0.568551	−	0.850896i
$959$	80.4028	+	15.9931i	0.0838402	+	0.0166769i
$960$		0			0
$961$	258.955	+	625.173i	0.269464	+	0.650544i
$962$	−304.882	−	60.6449i	−0.316926	−	0.0630404i
$963$	−2562.75	+	1712.38i	−2.66122	+	1.77817i
$964$	89.3772	+	449.329i	0.0927149	+	0.466109i
$965$		0			0
$966$	165.179	−	247.207i	0.170992	−	0.255908i
$967$	−287.336	+	693.690i	−0.297141	+	0.717363i	0.702840	+	0.711348i	$0.251915\pi$
$967$	−287.336	+	693.690i	−0.297141	+	0.717363i	−0.999982	+	0.00601538i	$0.998085\pi$
$968$	−740.878			−0.765370
$969$	1815.58	−	943.134i	1.87366	−	0.973306i
$970$		0			0
$971$	−267.835	+	646.610i	−0.275834	+	0.665922i	−0.999712	−	0.0240064i	$-0.992358\pi$
$971$	−267.835	+	646.610i	−0.275834	+	0.665922i	0.723878	+	0.689928i	$0.242358\pi$
$972$	117.252	−	175.480i	0.120630	−	0.180535i
$973$	−115.844	+	115.844i	−0.119059	+	0.119059i
$974$	−1087.53	+	216.323i	−1.11656	+	0.222098i
$975$		0			0
$976$	−238.708	−	47.4820i	−0.244578	−	0.0486496i
$977$	82.1596	+	198.351i	0.0840938	+	0.203020i	0.960333	−	0.278856i	$-0.0899553\pi$
$977$	82.1596	+	198.351i	0.0840938	+	0.203020i	−0.876239	+	0.481877i	$0.839955\pi$
$978$	−1136.90	+	470.921i	−1.16248	+	0.481514i
$979$	−12.0956	+	60.8087i	−0.0123551	+	0.0621131i
$980$		0			0
$981$	−311.176	−	1564.38i	−0.317202	−	1.59468i
$982$	−4.39240	−	4.39240i	−0.00447291	−	0.00447291i
$983$	1257.79	+	840.427i	1.27954	+	0.854962i	0.994620	−	0.103590i	$-0.0330329\pi$
$983$	1257.79	+	840.427i	1.27954	+	0.854962i	0.284920	+	0.958551i	$0.408033\pi$
$984$	−1957.93	−	811.000i	−1.98976	−	0.824187i
$985$		0			0
$986$	−1615.41	−	510.873i	−1.63834	−	0.518127i
$987$			427.007i			0.432631i
$988$	−186.479	−	77.2422i	−0.188744	−	0.0781803i
$989$	119.787	+	80.0391i	0.121119	+	0.0809293i
$990$		0			0
$991$	1575.69	−	313.425i	1.59000	−	0.316272i	0.680751	−	0.732515i	$-0.261653\pi$
$991$	1575.69	−	313.425i	1.59000	−	0.316272i	0.909253	+	0.416243i	$0.136653\pi$
$992$	−194.513	−	291.109i	−0.196082	−	0.293457i
$993$	380.156	−	1911.17i	0.382836	−	1.92465i
$994$	−166.470	+	68.9543i	−0.167475	+	0.0693705i
$995$		0			0
$996$	−113.239	+	569.290i	−0.113693	+	0.571576i
$997$	959.213	−	640.926i	0.962099	−	0.642854i	0.0279018	−	0.999611i	$-0.491117\pi$
$997$	959.213	−	640.926i	0.962099	−	0.642854i	0.934197	+	0.356757i	$0.116117\pi$
$998$	−820.529	+	163.213i	−0.822174	+	0.163541i
$999$	−539.595	+	539.595i	−0.540136	+	0.540136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.f.299.9		96
5.2	odd	4		425.3.u.c.401.4	yes	96
5.3	odd	4		425.3.u.d.401.9	yes	96
5.4	even	2		425.3.t.g.299.4		96
17.12	odd	16		425.3.t.g.199.4		96
85.12	even	16		425.3.u.c.301.4	✓	96
85.29	odd	16	inner	425.3.t.f.199.9		96
85.63	even	16		425.3.u.d.301.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.3.t.f.199.9		96	85.29	odd	16	inner
425.3.t.f.299.9		96	1.1	even	1	trivial
425.3.t.g.199.4		96	17.12	odd	16
425.3.t.g.299.4		96	5.4	even	2
425.3.u.c.301.4	✓	96	85.12	even	16
425.3.u.c.401.4	yes	96	5.2	odd	4
425.3.u.d.301.9	yes	96	85.63	even	16
425.3.u.d.401.9	yes	96	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.13692 + 0.885142i) q^{2} +(2.78088 - 4.16188i) q^{3} +(0.954534 + 0.954534i) q^{4} +(9.62637 - 6.43213i) q^{6} +(0.193021 - 0.970381i) q^{7} +(-2.34570 - 5.66303i) q^{8} +(-6.14378 - 14.8324i) q^{9} +(0.201395 + 0.301409i) q^{11} +(6.62710 - 1.31821i) q^{12} +(-4.39739 - 4.39739i) q^{13} +(1.27140 - 1.90278i) q^{14} -19.5774i q^{16} +(-1.86536 + 16.8974i) q^{17} -37.1338i q^{18} +(9.20107 - 22.2133i) q^{19} +(-3.50184 - 3.50184i) q^{21} +(0.163576 + 0.822350i) q^{22} +(14.4201 + 21.5813i) q^{23} +(-30.0919 - 5.98565i) q^{24} +(-5.50456 - 13.2892i) q^{26} +(-34.6323 - 6.88880i) q^{27} +(1.11051 - 0.742017i) q^{28} +(8.40610 + 42.2603i) q^{29} +(9.36788 - 14.0200i) q^{31} +(7.94597 - 19.1833i) q^{32} +1.81448 q^{33} +(-18.9427 + 34.4572i) q^{34} +(8.29359 - 20.0225i) q^{36} +(12.0064 - 17.9689i) q^{37} +(39.3239 - 39.3239i) q^{38} +(-30.5300 + 6.07279i) q^{39} +(67.7453 + 13.4754i) q^{41} +(-4.38353 - 10.5828i) q^{42} +(5.12800 - 2.12409i) q^{43} +(-0.0954667 + 0.479943i) q^{44} +(11.7122 + 58.8814i) q^{46} +(-60.9689 - 60.9689i) q^{47} +(-81.4787 - 54.4423i) q^{48} +(44.3657 + 18.3769i) q^{49} +(65.1373 + 54.7528i) q^{51} -8.39491i q^{52} +(14.9763 + 6.20340i) q^{53} +(-67.9091 - 45.3754i) q^{54} +(-5.94806 + 1.18314i) q^{56} +(-66.8621 - 100.066i) q^{57} +(-19.4432 + 97.7476i) q^{58} +(-60.5743 + 25.0907i) q^{59} +(2.42535 - 12.1930i) q^{61} +(32.4281 - 21.6678i) q^{62} +(-15.5790 + 3.09885i) q^{63} +(-21.4134 + 21.4134i) q^{64} +(3.87740 + 1.60607i) q^{66} +39.4771 q^{67} +(-17.9097 + 14.3486i) q^{68} +129.919 q^{69} +(-65.4676 - 43.7440i) q^{71} +(-69.5848 + 69.5848i) q^{72} +(-0.0692193 - 0.347989i) q^{73} +(41.5619 - 27.7708i) q^{74} +(29.9861 - 12.4207i) q^{76} +(0.331355 - 0.137252i) q^{77} +(-70.6154 - 14.0463i) q^{78} +(44.3559 + 66.3833i) q^{79} +(-22.8085 + 22.8085i) q^{81} +(132.839 + 88.7601i) q^{82} +(-32.8738 + 79.3643i) q^{83} -6.68525i q^{84} +12.8383 q^{86} +(199.259 + 82.5356i) q^{87} +(1.23447 - 1.84752i) q^{88} +(120.939 + 120.939i) q^{89} +(-5.11592 + 3.41835i) q^{91} +(-6.83554 + 34.3646i) q^{92} +(-32.2987 - 77.9759i) q^{93} +(-76.3197 - 184.252i) q^{94} +(-57.7416 - 86.4164i) q^{96} +(-86.7371 + 17.2531i) q^{97} +(78.5399 + 78.5399i) q^{98} +(3.23329 - 4.83896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) \) 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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