LMFDB - Embedded newform 425.3.u.d.401.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] 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("425.126"); 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([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == 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			401.9
Character	$\chi$	$=$	425.401
Dual form			425.3.u.d.301.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.885142 - 2.13692i) q^{2} +(4.16188 + 2.78088i) q^{3} +(-0.954534 - 0.954534i) q^{4} +(9.62637 - 6.43213i) q^{6} +(-0.970381 - 0.193021i) q^{7} +(5.66303 - 2.34570i) q^{8} +(6.14378 + 14.8324i) q^{9} +(0.201395 + 0.301409i) q^{11} +(-1.31821 - 6.62710i) q^{12} +(4.39739 - 4.39739i) q^{13} +(-1.27140 + 1.90278i) q^{14} -19.5774i q^{16} +(16.8974 + 1.86536i) q^{17} +37.1338 q^{18} +(-9.20107 + 22.2133i) q^{19} +(-3.50184 - 3.50184i) q^{21} +(0.822350 - 0.163576i) q^{22} +(-21.5813 + 14.4201i) q^{23} +(30.0919 + 5.98565i) q^{24} +(-5.50456 - 13.2892i) q^{26} +(-6.88880 + 34.6323i) q^{27} +(0.742017 + 1.11051i) q^{28} +(-8.40610 - 42.2603i) q^{29} +(9.36788 - 14.0200i) q^{31} +(-19.1833 - 7.94597i) q^{32} +1.81448i q^{33} +(18.9427 - 34.4572i) q^{34} +(8.29359 - 20.0225i) q^{36} +(-17.9689 - 12.0064i) q^{37} +(39.3239 + 39.3239i) q^{38} +(30.5300 - 6.07279i) q^{39} +(67.7453 + 13.4754i) q^{41} +(-10.5828 + 4.38353i) q^{42} +(2.12409 + 5.12800i) q^{43} +(0.0954667 - 0.479943i) q^{44} +(11.7122 + 58.8814i) q^{46} +(-60.9689 + 60.9689i) q^{47} +(54.4423 - 81.4787i) q^{48} +(-44.3657 - 18.3769i) q^{49} +(65.1373 + 54.7528i) q^{51} -8.39491 q^{52} +(-6.20340 + 14.9763i) q^{53} +(67.9091 + 45.3754i) q^{54} +(-5.94806 + 1.18314i) q^{56} +(-100.066 + 66.8621i) q^{57} +(-97.7476 - 19.4432i) q^{58} +(60.5743 - 25.0907i) q^{59} +(2.42535 - 12.1930i) q^{61} +(-21.6678 - 32.4281i) q^{62} +(-3.09885 - 15.5790i) q^{63} +(21.4134 - 21.4134i) q^{64} +(3.87740 + 1.60607i) q^{66} -39.4771i q^{67} +(-14.3486 - 17.9097i) q^{68} -129.919 q^{69} +(-65.4676 - 43.7440i) q^{71} +(69.5848 + 69.5848i) q^{72} +(0.347989 - 0.0692193i) q^{73} +(-41.5619 + 27.7708i) q^{74} +(29.9861 - 12.4207i) q^{76} +(-0.137252 - 0.331355i) q^{77} +(14.0463 - 70.6154i) q^{78} +(-44.3559 - 66.3833i) q^{79} +(-22.8085 + 22.8085i) q^{81} +(88.7601 - 132.839i) q^{82} +(-79.3643 - 32.8738i) q^{83} +6.68525i q^{84} +12.8383 q^{86} +(82.5356 - 199.259i) q^{87} +(1.84752 + 1.23447i) q^{88} +(-120.939 - 120.939i) q^{89} +(-5.11592 + 3.41835i) q^{91} +(34.3646 + 6.83554i) q^{92} +(77.9759 - 32.2987i) q^{93} +(76.3197 + 184.252i) q^{94} +(-57.7416 - 86.4164i) q^{96} +(17.2531 + 86.7371i) q^{97} +(-78.5399 + 78.5399i) q^{98} +(-3.23329 + 4.83896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{12} + 24 q^{13} + 32 q^{14} - 8 q^{17} - 64 q^{18} - 24 q^{19} - 96 q^{22} - 56 q^{23} - 336 q^{24} - 224 q^{26} + 144 q^{27} - 480 q^{28} - 64 q^{31} + 40 q^{32} + 64 q^{34} + 192 q^{36} - 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) $ 96 * q + 96 * q^12 + 24 * q^13 + 32 * q^14 - 8 * q^17 - 64 * q^18 - 24 * q^19 - 96 * q^22 - 56 * q^23 - 336 * q^24 - 224 * q^26 + 144 * q^27 - 480 * q^28 - 64 * q^31 + 40 * q^32 + 64 * q^34 + 192 * q^36 - 128 * q^37 + 496 * q^38 + 16 * q^39 + 216 * q^41 - 432 * q^42 + 592 * q^43 - 32 * q^44 + 336 * q^46 + 160 * q^48 - 32 * q^49 - 32 * q^51 - 96 * q^53 + 584 * q^54 - 40 * q^56 - 1120 * q^57 - 256 * q^58 + 544 * q^59 + 112 * q^61 - 560 * q^62 - 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 + 1040 * q^72 - 336 * q^74 - 1016 * q^76 + 960 * q^77 - 384 * q^79 - 928 * q^81 + 1200 * q^82 + 144 * q^83 + 64 * q^86 + 672 * q^87 + 832 * q^88 + 576 * q^89 + 336 * q^91 + 1008 * q^92 + 512 * q^93 + 672 * q^94 + 768 * q^96 + 128 * 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 $

$2$	0.885142	−	2.13692i	0.442571	−	1.06846i	−0.532472	−	0.846447i	$-0.678737\pi$
$2$	0.885142	−	2.13692i	0.442571	−	1.06846i	0.975043	−	0.222014i	$-0.0712630\pi$
$3$	4.16188	+	2.78088i	1.38729	+	0.926959i	0.999987	+	0.00500688i	$0.00159375\pi$
$3$	4.16188	+	2.78088i	1.38729	+	0.926959i	0.387304	+	0.921952i	$0.373406\pi$
$4$	−0.954534	−	0.954534i	−0.238634	−	0.238634i
$5$		0			0
$5$		0			0
$6$	9.62637	−	6.43213i	1.60440	−	1.07202i
$7$	−0.970381	−	0.193021i	−0.138626	−	0.0275744i	0.125290	−	0.992120i	$-0.460014\pi$
$7$	−0.970381	−	0.193021i	−0.138626	−	0.0275744i	−0.263915	+	0.964546i	$0.585014\pi$
$8$	5.66303	−	2.34570i	0.707878	−	0.293213i
$9$	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	$0.807255\pi$
$12$	−1.31821	−	6.62710i	−0.109851	−	0.552258i
$13$	4.39739	−	4.39739i	0.338260	−	0.338260i	−0.517452	−	0.855712i	$-0.673119\pi$
$13$	4.39739	−	4.39739i	0.338260	−	0.338260i	0.855712	+	0.517452i	$0.173119\pi$
$14$	−1.27140	+	1.90278i	−0.0908140	+	0.135913i
$15$		0			0
$16$		−	19.5774i		−	1.22359i
$17$	16.8974	+	1.86536i	0.993962	+	0.109727i
$17$	16.8974	+	1.86536i	0.993962	+	0.109727i
$18$	37.1338			2.06299
$19$	−9.20107	+	22.2133i	−0.484267	+	1.16912i	0.473297	+	0.880903i	$0.343064\pi$
$19$	−9.20107	+	22.2133i	−0.484267	+	1.16912i	−0.957564	+	0.288221i	$0.906936\pi$
$20$		0			0
$21$	−3.50184	−	3.50184i	−0.166754	−	0.166754i
$22$	0.822350	−	0.163576i	0.0373796	−	0.00743526i
$23$	−21.5813	+	14.4201i	−0.938316	+	0.626963i	−0.927838	−	0.372982i	$-0.878335\pi$
$23$	−21.5813	+	14.4201i	−0.938316	+	0.626963i	−0.0104775	+	0.999945i	$0.503335\pi$
$24$	30.0919	+	5.98565i	1.25383	+	0.249402i
$25$		0			0
$26$	−5.50456	−	13.2892i	−0.211714	−	0.511123i
$27$	−6.88880	+	34.6323i	−0.255141	+	1.28268i
$28$	0.742017	+	1.11051i	0.0265006	+	0.0396610i
$29$	−8.40610	−	42.2603i	−0.289866	−	1.45725i	−0.801472	−	0.598032i	$-0.795949\pi$
$29$	−8.40610	−	42.2603i	−0.289866	−	1.45725i	0.511606	−	0.859220i	$-0.329051\pi$
$30$		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	$0.0998270\pi$
$32$	−19.1833	−	7.94597i	−0.599477	−	0.248312i
$33$			1.81448i			0.0549842i
$34$	18.9427	−	34.4572i	0.557138	−	1.01345i
$35$		0			0
$36$	8.29359	−	20.0225i	0.230377	−	0.556180i
$37$	−17.9689	−	12.0064i	−0.485646	−	0.324499i	0.288527	−	0.957472i	$-0.406834\pi$
$37$	−17.9689	−	12.0064i	−0.485646	−	0.324499i	−0.774174	+	0.632973i	$0.781834\pi$
$38$	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	$0.243673\pi$
$42$	−10.5828	+	4.38353i	−0.251971	+	0.104370i
$43$	2.12409	+	5.12800i	0.0493974	+	0.119256i	0.946652	−	0.322258i	$-0.104442\pi$
$43$	2.12409	+	5.12800i	0.0493974	+	0.119256i	−0.897255	+	0.441513i	$0.854442\pi$
$44$	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	−0.366984	+	0.930227i	$0.619610\pi$
$47$	−60.9689	+	60.9689i	−1.29721	+	1.29721i	−0.930227	+	0.366984i	$0.880390\pi$
$48$	54.4423	−	81.4787i	1.13421	−	1.69747i
$49$	−44.3657	−	18.3769i	−0.905423	−	0.375038i
$50$		0			0
$51$	65.1373	+	54.7528i	1.27720	+	1.07358i
$52$	−8.39491			−0.161441
$53$	−6.20340	+	14.9763i	−0.117045	+	0.282572i	−0.971535	−	0.236896i	$-0.923870\pi$
$53$	−6.20340	+	14.9763i	−0.117045	+	0.282572i	0.854490	+	0.519468i	$0.173870\pi$
$54$	67.9091	+	45.3754i	1.25758	+	0.840285i
$55$		0			0
$56$	−5.94806	+	1.18314i	−0.106215	+	0.0211275i
$57$	−100.066	+	66.8621i	−1.75555	+	1.17302i
$58$	−97.7476	−	19.4432i	−1.68530	−	0.335228i
$59$	60.5743	−	25.0907i	1.02668	−	0.425266i	0.195169	−	0.980770i	$-0.437474\pi$
$59$	60.5743	−	25.0907i	1.02668	−	0.425266i	0.831514	+	0.555503i	$0.187474\pi$
$60$		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	$0.0300075\pi$
$62$	−21.6678	−	32.4281i	−0.349481	−	0.523035i
$63$	−3.09885	−	15.5790i	−0.0491881	−	0.247285i
$64$	21.4134	−	21.4134i	0.334584	−	0.334584i
$65$		0			0
$66$	3.87740	+	1.60607i	0.0587485	+	0.0243344i
$67$		−	39.4771i		−	0.589210i	−0.955619	−	0.294605i	$-0.904812\pi$
$67$		−	39.4771i		−	0.589210i	0.955619	−	0.294605i	$-0.0951880\pi$
$68$	−14.3486	−	17.9097i	−0.211008	−	0.263377i
$69$	−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
$73$	0.347989	−	0.0692193i	0.00476697	−	0.000948210i	−0.192706	−	0.981256i	$-0.561726\pi$
$73$	0.347989	−	0.0692193i	0.00476697	−	0.000948210i	0.197473	+	0.980308i	$0.436726\pi$
$74$	−41.5619	+	27.7708i	−0.561647	+	0.375281i
$75$		0			0
$76$	29.9861	−	12.4207i	0.394554	−	0.163430i
$77$	−0.137252	−	0.331355i	−0.00178249	−	0.00430331i
$78$	14.0463	−	70.6154i	0.180081	−	0.905326i
$79$	−44.3559	−	66.3833i	−0.561468	−	0.840296i	0.436774	−	0.899571i	$-0.356121\pi$
$79$	−44.3559	−	66.3833i	−0.561468	−	0.840296i	−0.998242	+	0.0592757i	$0.981121\pi$
$80$		0			0
$81$	−22.8085	+	22.8085i	−0.281586	+	0.281586i
$82$	88.7601	−	132.839i	1.08244	−	1.61999i
$83$	−79.3643	−	32.8738i	−0.956197	−	0.396070i	−0.150640	−	0.988589i	$-0.548133\pi$
$83$	−79.3643	−	32.8738i	−0.956197	−	0.396070i	−0.805556	+	0.592519i	$0.798133\pi$
$84$			6.68525i			0.0795863i
$85$		0			0
$86$	12.8383			0.149282
$87$	82.5356	−	199.259i	0.948685	−	2.29033i
$88$	1.84752	+	1.23447i	0.0209945	+	0.0140281i
$89$	−120.939	−	120.939i	−1.35887	−	1.35887i	−0.875314	−	0.483555i	$-0.839345\pi$
$89$	−120.939	−	120.939i	−1.35887	−	1.35887i	−0.483555	−	0.875314i	$-0.660655\pi$
$90$		0			0
$91$	−5.11592	+	3.41835i	−0.0562190	+	0.0375643i
$92$	34.3646	+	6.83554i	0.373528	+	0.0742993i
$93$	77.9759	−	32.2987i	0.838450	−	0.347298i
$94$	76.3197	+	184.252i	0.811912	+	1.96013i
$95$		0			0
$96$	−57.7416	−	86.4164i	−0.601475	−	0.900171i
$97$	17.2531	+	86.7371i	0.177867	+	0.894197i	0.961884	+	0.273458i	$0.0881674\pi$
$97$	17.2531	+	86.7371i	0.177867	+	0.894197i	−0.784017	+	0.620739i	$0.786833\pi$
$98$	−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	$0.889096\pi$
$102$	174.658	−	90.7294i	1.71234	−	0.889504i
$103$	−143.720			−1.39534			−0.697671	−	0.716418i	$-0.745780\pi$
$103$	−143.720			−1.39534			−0.697671	+	0.716418i	$0.745780\pi$
$104$	14.5876	−	35.2175i	0.140265	−	0.338629i
$105$		0			0
$106$	26.5124	+	26.5124i	0.250117	+	0.250117i
$107$	−188.295	+	37.4541i	−1.75976	+	0.350039i	−0.966070	−	0.258280i	$-0.916844\pi$
$107$	−188.295	+	37.4541i	−1.75976	+	0.350039i	−0.793693	+	0.608319i	$0.791844\pi$
$108$	39.6334	−	26.4822i	0.366975	−	0.245205i
$109$	−97.4423	−	19.3825i	−0.893966	−	0.177821i	−0.273330	−	0.961920i	$-0.588125\pi$
$109$	−97.4423	−	19.3825i	−0.893966	−	0.177821i	−0.620635	+	0.784099i	$0.713125\pi$
$110$		0			0
$111$	−41.3960	−	99.9387i	−0.372937	−	0.900348i
$112$	−3.77884	+	18.9975i	−0.0337397	+	0.169621i
$113$	65.4166	+	97.9029i	0.578908	+	0.866397i	0.999159	−	0.0410109i	$-0.0130578\pi$
$113$	65.4166	+	97.9029i	0.578908	+	0.866397i	−0.420251	+	0.907408i	$0.638058\pi$
$114$	54.3063	+	273.016i	0.476371	+	2.39488i
$115$		0			0
$116$	−32.3150	+	48.3628i	−0.278578	+	0.416921i
$117$	92.2404	+	38.2072i	0.788380	+	0.326557i
$118$		−	151.652i		−	1.28518i
$119$	−16.0368	−	5.07165i	−0.134763	−	0.0426189i
$120$		0			0
$121$	46.2544	−	111.668i	0.382268	−	0.922876i
$122$	−23.9088	−	15.9754i	−0.195974	−	0.130946i
$123$	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
$127$	110.821	−	45.9034i	0.872603	−	0.361444i	0.0989792	−	0.995089i	$-0.468442\pi$
$127$	110.821	−	45.9034i	0.872603	−	0.361444i	0.773623	+	0.633646i	$0.218442\pi$
$128$	−58.5887	−	141.446i	−0.457724	−	1.10504i
$129$	−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
$133$	13.2162	−	19.7794i	0.0993697	−	0.148717i
$134$	−84.3594	−	34.9428i	−0.629548	−	0.260767i
$135$		0			0
$136$	100.066	−	29.0726i	0.735777	−	0.213769i
$137$	82.8569			0.604795			0.302398	−	0.953182i	$-0.402213\pi$
$137$	82.8569			0.604795			0.302398	+	0.953182i	$0.402213\pi$
$138$	−114.997	+	277.627i	−0.833311	+	2.01179i
$139$	137.679	+	91.9943i	0.990498	+	0.661829i	0.941515	−	0.336970i	$-0.109402\pi$
$139$	137.679	+	91.9943i	0.990498	+	0.661829i	0.0489823	+	0.998800i	$0.484402\pi$
$140$		0			0
$141$	−423.292	+	84.1981i	−3.00207	+	0.597149i
$142$	−151.426	+	101.179i	−1.06638	+	0.712532i
$143$	2.21102	+	0.439800i	0.0154617	+	0.00307552i
$144$	290.380	−	120.279i	2.01653	−	0.835273i
$145$		0			0
$146$	0.160103	−	0.804894i	0.00109660	−	0.00551298i
$147$	−133.541	−	199.858i	−0.908440	−	1.35958i
$148$	5.69138	+	28.6125i	0.0384553	+	0.193328i
$149$	114.653	−	114.653i	0.769486	−	0.769486i	−0.208530	−	0.978016i	$-0.566868\pi$
$149$	114.653	−	114.653i	0.769486	−	0.769486i	0.978016	+	0.208530i	$0.0668680\pi$
$150$		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	$0.798576\pi$
$152$			147.378i			0.969590i
$153$	76.1459	+	262.089i	0.497686	+	1.71300i
$154$	−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	$-0.118883\pi$
$157$	88.8938	+	88.8938i	0.566203	+	0.566203i	−0.364860	+	0.931062i	$0.618883\pi$
$158$	−181.117	+	36.0265i	−1.14631	+	0.228016i
$159$	−67.4651	+	45.0787i	−0.424309	+	0.283514i
$160$		0			0
$161$	23.7254	−	9.82739i	0.147363	−	0.0610397i
$162$	28.5512	+	68.9287i	0.176242	+	0.425486i
$163$	20.7361	−	104.248i	0.127216	−	0.639556i	−0.863582	−	0.504208i	$-0.831785\pi$
$163$	20.7361	−	104.248i	0.127216	−	0.639556i	0.990798	−	0.135348i	$-0.0432154\pi$
$164$	−51.8025	−	77.5280i	−0.315869	−	0.472731i
$165$		0			0
$166$	−140.497	+	140.497i	−0.846370	+	0.846370i
$167$	−83.1570	+	124.453i	−0.497946	+	0.745229i	−0.992277	−	0.124045i	$-0.960413\pi$
$167$	−83.1570	+	124.453i	−0.497946	+	0.745229i	0.494331	+	0.869274i	$0.335413\pi$
$168$	−28.0453	−	11.6167i	−0.166936	−	0.0691472i
$169$			130.326i			0.771160i
$170$		0			0
$171$	−386.007			−2.25735
$172$	2.86734	−	6.92236i	0.0166706	−	0.0402463i
$173$	22.6606	+	15.1413i	0.130986	+	0.0875220i	0.619337	−	0.785125i	$-0.287401\pi$
$173$	22.6606	+	15.1413i	0.130986	+	0.0875220i	−0.488351	+	0.872647i	$0.662401\pi$
$174$	−352.744	−	352.744i	−2.02727	−	2.02727i
$175$		0			0
$176$	5.90080	−	3.94279i	0.0335273	−	0.0224022i
$177$	321.877	+	64.0253i	1.81851	+	0.361725i
$178$	−365.487	+	151.389i	−2.05330	+	0.850503i
$179$	−20.5361	−	49.5786i	−0.114727	−	0.276976i	0.856077	−	0.516847i	$-0.172895\pi$
$179$	−20.5361	−	49.5786i	−0.114727	−	0.276976i	−0.970805	+	0.239872i	$0.922895\pi$
$180$		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	$0.708170\pi$
$182$	2.77643	+	13.9581i	0.0152551	+	0.0766927i
$183$	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
$187$	2.84080	+	5.46868i	0.0151915	+	0.0292443i
$188$	116.394			0.619116
$189$	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	$0.814097\pi$
$192$	148.668	−	29.5719i	0.774311	−	0.154020i
$193$	180.254	−	120.442i	0.933960	−	0.624052i	0.00730837	−	0.999973i	$-0.497674\pi$
$193$	180.254	−	120.442i	0.933960	−	0.624052i	0.926652	+	0.375921i	$0.122674\pi$
$194$	200.622	+	39.9062i	1.03413	+	0.205702i
$195$		0			0
$196$	24.8072	+	59.8900i	0.126568	+	0.305561i
$197$	−48.6152	+	244.405i	−0.246778	+	1.24064i	0.636312	+	0.771432i	$0.280459\pi$
$197$	−48.6152	+	244.405i	−0.246778	+	1.24064i	−0.883090	+	0.469204i	$0.844541\pi$
$198$	7.47856	+	11.1925i	0.0377705	+	0.0565276i
$199$	52.4658	+	263.763i	0.263647	+	1.32544i	0.854831	+	0.518906i	$0.173661\pi$
$199$	52.4658	+	263.763i	0.263647	+	1.32544i	−0.591184	+	0.806537i	$0.701339\pi$
$200$		0			0
$201$	109.781	−	164.299i	0.546173	−	0.817406i
$202$	147.372	+	61.0434i	0.729563	+	0.302195i
$203$			42.6312i			0.210006i
$204$	−9.91237	−	114.439i	−0.0485901	−	0.560977i
$205$		0			0
$206$	−127.213	+	307.119i	−0.617538	+	1.49087i
$207$	−346.476	−	231.508i	−1.67380	−	1.11840i
$208$	−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	$0.402310\pi$
$212$	20.2168	−	8.37406i	0.0953621	−	0.0395003i
$213$	−150.821	−	364.115i	−0.708081	−	1.70946i
$214$	−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
$218$	−127.669	+	191.070i	−0.585638	+	0.876469i
$219$	1.64078	+	0.679632i	0.00749213	+	0.00310334i
$220$		0			0
$221$	82.5069	−	66.1015i	0.373334	−	0.299102i
$222$	−250.203			−1.12704
$223$	124.891	−	301.515i	0.560051	−	1.35208i	−0.349674	−	0.936872i	$-0.613708\pi$
$223$	124.891	−	301.515i	0.560051	−	1.35208i	0.909725	−	0.415212i	$-0.136292\pi$
$224$	17.0813	+	11.4134i	0.0762560	+	0.0509526i
$225$		0			0
$226$	267.114	−	53.1323i	1.18192	−	0.235098i
$227$	−129.730	+	86.6828i	−0.571498	+	0.381863i	−0.807480	−	0.589895i	$-0.799169\pi$
$227$	−129.730	+	86.6828i	−0.571498	+	0.381863i	0.235982	+	0.971757i	$0.424169\pi$
$228$	159.339	+	31.6945i	0.698855	+	0.139011i
$229$	280.820	−	116.319i	1.22629	−	0.507945i	0.326884	−	0.945065i	$-0.394001\pi$
$229$	280.820	−	116.319i	1.22629	−	0.507945i	0.899403	+	0.437120i	$0.144001\pi$
$230$		0			0
$231$	0.350232	−	1.76074i	0.00151616	−	0.00762224i
$232$	−146.734	−	219.603i	−0.632474	−	0.946565i
$233$	−20.1955	−	101.530i	−0.0866759	−	0.435749i	−0.999617	−	0.0276587i	$-0.991195\pi$
$233$	−20.1955	−	101.530i	−0.0866759	−	0.435749i	0.912942	−	0.408090i	$-0.133805\pi$
$234$	163.292	−	163.292i	0.697828	−	0.697828i
$235$		0			0
$236$	−81.7702	−	33.8703i	−0.346484	−	0.143518i
$237$		−	399.628i		−	1.68619i
$238$	−25.0326	+	29.7803i	−0.105179	+	0.125127i
$239$	−388.547			−1.62572			−0.812860	−	0.582459i	$-0.802091\pi$
$239$	−388.547			−1.62572			−0.812860	+	0.582459i	$0.802091\pi$
$240$		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
$243$	153.337	−	30.5007i	0.631018	−	0.125517i
$244$	−13.9538	+	9.32360i	−0.0571875	+	0.0382115i
$245$		0			0
$246$	738.817	−	306.028i	3.00332	−	1.24402i
$247$	57.2200	+	138.141i	0.231660	+	0.559276i
$248$	20.1637	−	101.370i	0.0813054	−	0.408750i
$249$	−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	$0.170954\pi$
$252$	−11.9127	+	17.8286i	−0.0472726	+	0.0707485i
$253$	−8.69271	−	3.60064i	−0.0343585	−	0.0142318i
$254$		−	277.446i		−	1.09231i
$255$		0			0
$256$	−232.986			−0.910100
$257$	29.5265	−	71.2832i	0.114889	−	0.277367i	−0.855967	−	0.517031i	$-0.827037\pi$
$257$	29.5265	−	71.2832i	0.114889	−	0.277367i	0.970856	+	0.239664i	$0.0770373\pi$
$258$	53.4312	+	35.7016i	0.207098	+	0.138378i
$259$	15.1192	+	15.1192i	0.0583753	+	0.0583753i
$260$		0			0
$261$	575.177	−	384.321i	2.20374	−	1.47249i
$262$	487.801	+	97.0297i	1.86184	+	0.370342i
$263$	69.4703	−	28.7756i	0.264146	−	0.109413i	−0.246680	−	0.969097i	$-0.579340\pi$
$263$	69.4703	−	28.7756i	0.264146	−	0.109413i	0.510826	+	0.859684i	$0.329340\pi$
$264$	4.25623	+	10.2754i	0.0161221	+	0.0389221i
$265$		0			0
$266$	−30.5689	−	45.7495i	−0.114921	−	0.171991i
$267$	−167.017	−	839.652i	−0.625532	−	3.14476i
$268$	−37.6822	+	37.6822i	−0.140605	+	0.140605i
$269$	−100.440	+	150.319i	−0.373383	+	0.558807i	−0.969810	−	0.243860i	$-0.921586\pi$
$269$	−100.440	+	150.319i	−0.373383	+	0.558807i	0.596428	+	0.802667i	$0.296586\pi$
$270$		0			0
$271$		−	241.430i		−	0.890886i	−0.895310	−	0.445443i	$-0.853046\pi$
$271$		−	241.430i		−	0.890886i	0.895310	−	0.445443i	$-0.146954\pi$
$272$	36.5188	−	330.806i	0.134260	−	1.21620i
$273$	−30.7979			−0.112813
$274$	73.3402	−	177.059i	0.267665	−	0.646200i
$275$		0			0
$276$	124.012	+	124.012i	0.449320	+	0.449320i
$277$	303.504	−	60.3707i	1.09568	−	0.217945i	0.386022	−	0.922489i	$-0.373849\pi$
$277$	303.504	−	60.3707i	1.09568	−	0.217945i	0.709660	+	0.704545i	$0.248849\pi$
$278$	318.450	−	212.782i	1.14550	−	0.765402i
$279$	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	$0.887907\pi$
$282$	−194.749	+	979.070i	−0.690600	+	3.47188i
$283$	57.6606	+	86.2953i	0.203748	+	0.304930i	0.919245	−	0.393685i	$-0.128800\pi$
$283$	57.6606	+	86.2953i	0.203748	+	0.304930i	−0.715498	+	0.698615i	$0.753800\pi$
$284$	20.7359	+	104.246i	0.0730136	+	0.367064i
$285$		0			0
$286$	2.89689	−	4.33550i	0.0101290	−	0.0151591i
$287$	−63.1377	−	26.1525i	−0.219992	−	0.0911237i
$288$		−	333.352i		−	1.15747i
$289$	282.041	+	63.0392i	0.975920	+	0.218129i
$290$		0			0
$291$	−169.400	+	408.968i	−0.582130	+	1.40539i
$292$	−0.398240	−	0.266095i	−0.00136383	−	0.000911285i
$293$	20.1749	+	20.1749i	0.0688564	+	0.0688564i	0.740696	−	0.671840i	$-0.234496\pi$
$293$	20.1749	+	20.1749i	0.0688564	+	0.0688564i	−0.671840	+	0.740696i	$0.734496\pi$
$294$	−545.283	+	108.464i	−1.85471	+	0.368924i
$295$		0			0
$296$	−129.922	−	25.8431i	−0.438926	−	0.0873077i
$297$	−11.8259	+	4.89843i	−0.0398177	+	0.0164930i
$298$	−143.521	−	346.490i	−0.481613	−	1.16272i
$299$	−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
$303$	−191.782	+	287.021i	−0.632943	+	0.947266i
$304$	434.879	+	180.133i	1.43052	+	0.592542i
$305$		0			0
$306$	627.463	+	69.2679i	2.05053	+	0.226366i
$307$	−178.586			−0.581714			−0.290857	−	0.956766i	$-0.593940\pi$
$307$	−178.586			−0.581714			−0.290857	+	0.956766i	$0.593940\pi$
$308$	−0.185278	+	0.447301i	−0.000601552	+	0.00145228i
$309$	−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	$0.485560\pi$
$312$	158.647	−	106.005i	0.508484	−	0.339758i
$313$	−246.620	−	49.0559i	−0.787925	−	0.156728i	−0.215303	−	0.976547i	$-0.569074\pi$
$313$	−246.620	−	49.0559i	−0.787925	−	0.156728i	−0.572622	+	0.819819i	$0.694074\pi$
$314$	268.643	−	111.276i	0.855551	−	0.354381i
$315$		0			0
$316$	−21.0259	+	105.704i	−0.0665377	+	0.334508i
$317$	293.951	+	439.929i	0.927291	+	1.38779i	0.921742	+	0.387805i	$0.126767\pi$
$317$	293.951	+	439.929i	0.927291	+	1.38779i	0.00554969	+	0.999985i	$0.498233\pi$
$318$	36.6135	+	184.069i	0.115137	+	0.578832i
$319$	11.0447	−	11.0447i	0.0346228	−	0.0346228i
$320$		0			0
$321$	−887.814	−	367.745i	−2.76578	−	1.14562i
$322$		−	59.3981i		−	0.184466i
$323$	−196.910	+	358.183i	−0.609627	+	1.10893i
$324$	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
$328$	415.253	−	82.5989i	1.26601	−	0.251826i
$329$	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	$0.174890\pi$
$332$	44.3768	+	107.135i	0.133665	+	0.322696i
$333$	67.6873	−	340.287i	0.203265	−	1.02188i
$334$	192.341	+	287.859i	0.575871	+	0.861853i
$335$		0			0
$336$	−68.5568	+	68.5568i	−0.204038	+	0.204038i
$337$	−301.262	+	450.870i	−0.893952	+	1.33789i	0.0468383	+	0.998902i	$0.485085\pi$
$337$	−301.262	+	450.870i	−0.893952	+	1.33789i	−0.940790	+	0.338991i	$0.889915\pi$
$338$	278.497	+	115.357i	0.823954	+	0.341293i
$339$			589.375i			1.73857i
$340$		0			0
$341$	6.11240			0.0179249
$342$	−341.671	+	824.867i	−0.999038	+	2.41189i
$343$	79.8143	+	53.3302i	0.232695	+	0.155482i
$344$	24.0575	+	24.0575i	0.0699346	+	0.0699346i
$345$		0			0
$346$	52.4136	−	35.0217i	0.151484	−	0.101219i
$347$	61.7675	+	12.2863i	0.178004	+	0.0354072i	0.283288	−	0.959035i	$-0.408575\pi$
$347$	61.7675	+	12.2863i	0.178004	+	0.0354072i	−0.105283	+	0.994442i	$0.533575\pi$
$348$	−268.982	+	111.416i	−0.772937	+	0.320161i
$349$	−164.739	−	397.715i	−0.472031	−	1.13958i	−0.963264	−	0.268556i	$-0.913454\pi$
$349$	−164.739	−	397.715i	−0.472031	−	1.13958i	0.491233	−	0.871028i	$-0.336546\pi$
$350$		0			0
$351$	121.999	+	182.584i	0.347576	+	0.520184i
$352$	−1.46843	−	7.38228i	−0.00417167	−	0.0209724i
$353$	−27.5316	+	27.5316i	−0.0779933	+	0.0779933i	−0.745027	−	0.667034i	$-0.767564\pi$
$353$	−27.5316	+	27.5316i	−0.0779933	+	0.0779933i	0.667034	+	0.745027i	$0.267564\pi$
$354$	421.724	−	631.155i	1.19131	−	1.78292i
$355$		0			0
$356$			230.882i			0.648544i
$357$	−52.6396	−	65.7039i	−0.147450	−	0.184045i
$358$	−124.123			−0.346713
$359$	228.318	−	551.208i	0.635983	−	1.53540i	−0.196004	−	0.980603i	$-0.562797\pi$
$359$	228.318	−	551.208i	0.635983	−	1.53540i	0.831987	−	0.554795i	$-0.187203\pi$
$360$		0			0
$361$	−153.507	−	153.507i	−0.425228	−	0.425228i
$362$	264.369	−	52.5862i	0.730300	−	0.145266i
$363$	503.040	−	336.121i	1.38579	−	0.925952i
$364$	8.14626	+	1.62039i	0.0223798	+	0.00445163i
$365$		0			0
$366$	−55.0800	−	132.975i	−0.150492	−	0.363319i
$367$	−21.3947	+	107.558i	−0.0582961	+	0.293074i	−0.998925	−	0.0463633i	$-0.985237\pi$
$367$	−21.3947	+	107.558i	−0.0582961	+	0.293074i	0.940629	+	0.339438i	$0.110237\pi$
$368$	282.309	+	422.505i	0.767143	+	1.14811i
$369$	216.340	+	1087.62i	0.586288	+	2.94747i
$370$		0			0
$371$	8.91040	−	13.3354i	0.0240172	−	0.0359443i
$372$	−105.261	−	43.6005i	−0.282959	−	0.117206i
$373$			187.710i			0.503243i	0.967826	+	0.251622i	$0.0809639\pi$
$373$			187.710i			0.503243i	−0.967826	+	0.251622i	$0.919036\pi$
$374$	14.2007	−	1.23002i	0.0379697	−	0.00328882i
$375$		0			0
$376$	−202.254	+	488.284i	−0.537909	+	1.29863i
$377$	−222.800	−	148.870i	−0.590981	−	0.394881i
$378$	−57.1392	−	57.1392i	−0.151162	−	0.151162i
$379$	−33.4960	+	6.66277i	−0.0883799	+	0.0175799i	−0.239082	−	0.970999i	$-0.576847\pi$
$379$	−33.4960	+	6.66277i	−0.0883799	+	0.0175799i	0.150702	+	0.988579i	$0.451847\pi$
$380$		0			0
$381$	588.873	+	117.134i	1.54560	+	0.307439i
$382$	−163.267	+	67.6274i	−0.427401	+	0.177035i
$383$	260.821	+	629.678i	0.680995	+	1.64407i	0.762178	+	0.647368i	$0.224130\pi$
$383$	260.821	+	629.678i	0.680995	+	1.64407i	−0.0811827	+	0.996699i	$0.525870\pi$
$384$	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
$388$	66.3249	−	99.2622i	0.170940	−	0.255830i
$389$	−10.8240	−	4.48344i	−0.0278251	−	0.0115255i	0.368727	−	0.929538i	$-0.379794\pi$
$389$	−10.8240	−	4.48344i	−0.0278251	−	0.0115255i	−0.396553	+	0.918012i	$0.629794\pi$
$390$		0			0
$391$	−391.565	+	203.405i	−1.00144	+	0.520218i
$392$	−294.351			−0.750895
$393$	−411.887	+	994.382i	−1.04806	+	2.53024i
$394$	479.244	+	320.220i	1.21635	+	0.812742i
$395$		0			0
$396$	7.70524	−	1.53267i	0.0194577	−	0.00387037i
$397$	17.8441	−	11.9231i	0.0449474	−	0.0300329i	−0.532894	−	0.846182i	$-0.678895\pi$
$397$	17.8441	−	11.9231i	0.0449474	−	0.0300329i	0.577841	+	0.816149i	$0.303895\pi$
$398$	610.081	+	121.353i	1.53287	+	0.304906i
$399$	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	$0.0765273\pi$
$402$	−253.922	−	380.021i	−0.631646	−	0.945325i
$403$	−20.4573	−	102.846i	−0.0507624	−	0.255200i
$404$	65.8289	−	65.8289i	0.162943	−	0.162943i
$405$		0			0
$406$	91.0995	+	37.7346i	0.224383	+	0.0929425i
$407$		−	7.83403i		−	0.0192482i
$408$	497.308	+	157.274i	1.21889	+	0.385475i
$409$	280.116			0.684879			0.342440	−	0.939540i	$-0.388747\pi$
$409$	280.116			0.684879			0.342440	+	0.939540i	$0.388747\pi$
$410$		0			0
$411$	344.840	+	230.415i	0.839027	+	0.560620i
$412$	137.186	+	137.186i	0.332976	+	0.332976i
$413$	−63.6232	+	12.6554i	−0.154051	+	0.0306427i
$414$	−801.395	+	535.475i	−1.93574	+	1.29342i
$415$		0			0
$416$	−119.298	+	49.4147i	−0.286773	+	0.118785i
$417$	317.179	+	765.737i	0.760621	+	1.83630i
$418$	−3.93294	+	19.7722i	−0.00940895	+	0.0473020i
$419$	−76.3556	−	114.274i	−0.182233	−	0.272731i	0.729095	−	0.684413i	$-0.239941\pi$
$419$	−76.3556	−	114.274i	−0.182233	−	0.272731i	−0.911328	+	0.411682i	$0.864941\pi$
$420$		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	$0.150386\pi$
$422$	261.530	−	391.407i	0.619739	−	0.927505i
$423$	−1278.90	−	529.736i	−3.02339	−	1.25233i
$424$			99.3626i			0.234346i
$425$		0			0
$426$	−911.583			−2.13987
$427$	−4.70702	+	11.3638i	−0.0110235	+	0.0266130i
$428$	215.485	+	143.982i	0.503470	+	0.336408i
$429$	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	$0.113533\pi$
$432$	678.011	+	134.865i	1.56947	+	0.312187i
$433$	764.858	−	316.814i	1.76641	−	0.731673i	0.770912	−	0.636942i	$-0.219801\pi$
$433$	764.858	−	316.814i	1.76641	−	0.731673i	0.995503	−	0.0947312i	$-0.0301991\pi$
$434$	14.7667	+	35.6500i	0.0340247	+	0.0821428i
$435$		0			0
$436$	74.5108	+	111.513i	0.170896	+	0.255764i
$437$	−121.749	−	612.073i	−0.278601	−	1.40062i
$438$	2.90464	−	2.90464i	0.00663160	−	0.00663160i
$439$	37.2714	−	55.7806i	0.0849006	−	0.127063i	−0.786589	−	0.617477i	$-0.788155\pi$
$439$	37.2714	−	55.7806i	0.0849006	−	0.127063i	0.871489	+	0.490415i	$0.163155\pi$
$440$		0			0
$441$		−	770.954i		−	1.74819i
$442$	−68.2234	−	234.820i	−0.154352	−	0.531267i
$443$	−602.890			−1.36093			−0.680463	−	0.732783i	$-0.738221\pi$
$443$	−602.890			−1.36093			−0.680463	+	0.732783i	$0.738221\pi$
$444$	−55.8810	+	134.909i	−0.125858	+	0.303849i
$445$		0			0
$446$	−533.767	−	533.767i	−1.19679	−	1.19679i
$447$	796.010	−	158.336i	1.78078	−	0.354220i
$448$	−24.9124	+	16.6459i	−0.0556079	+	0.0371560i
$449$	−702.019	−	139.640i	−1.56352	−	0.311003i	−0.663947	−	0.747780i	$-0.731120\pi$
$449$	−702.019	−	139.640i	−1.56352	−	0.311003i	−0.899570	+	0.436777i	$0.856120\pi$
$450$		0			0
$451$	9.58196	+	23.1329i	0.0212460	+	0.0512925i
$452$	31.0093	−	155.894i	0.0686046	−	0.344898i
$453$	−435.599	−	651.920i	−0.961588	−	1.43912i
$454$	70.4050	+	353.950i	0.155077	+	0.779625i
$455$		0			0
$456$	−409.839	+	613.368i	−0.898770	+	1.34510i
$457$	434.264	+	179.878i	0.950250	+	0.393606i	0.803325	−	0.595541i	$-0.203062\pi$
$457$	434.264	+	179.878i	0.950250	+	0.393606i	0.146925	+	0.989148i	$0.453062\pi$
$458$		−	703.049i		−	1.53504i
$459$	−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	$0.982762\pi$
$462$	−3.45255	−	2.30692i	−0.00747306	−	0.00499334i
$463$	96.2811	+	96.2811i	0.207950	+	0.207950i	0.803396	−	0.595445i	$-0.203024\pi$
$463$	96.2811	+	96.2811i	0.207950	+	0.207950i	−0.595445	+	0.803396i	$0.703024\pi$
$464$	−827.347	+	164.570i	−1.78307	+	0.354676i
$465$		0			0
$466$	−234.837	−	46.7119i	−0.503941	−	0.100240i
$467$	398.906	−	165.232i	0.854188	−	0.353816i	0.0877563	−	0.996142i	$-0.472030\pi$
$467$	398.906	−	165.232i	0.854188	−	0.353816i	0.766432	+	0.642326i	$0.222030\pi$
$468$	−51.5765	−	124.517i	−0.110206	−	0.266061i
$469$	−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
$473$	−1.11784	+	1.67297i	−0.00236331	+	0.00353694i
$474$	−853.973	−	353.727i	−1.80163	−	0.746260i
$475$		0			0
$476$	10.4666	+	20.1487i	0.0219887	+	0.0423293i
$477$	−260.247			−0.545592
$478$	−343.920	+	830.295i	−0.719497	+	1.73702i
$479$	352.426	+	235.484i	0.735755	+	0.491616i	0.866111	−	0.499852i	$-0.166612\pi$
$479$	352.426	+	235.484i	0.735755	+	0.491616i	−0.130356	+	0.991467i	$0.541612\pi$
$480$		0			0
$481$	−131.813	+	26.2193i	−0.274040	+	0.0545099i
$482$	652.686	−	436.111i	1.35412	−	0.904794i
$483$	126.071	+	25.0771i	0.261017	+	0.0519194i
$484$	−150.742	+	62.4395i	−0.311451	+	0.129007i
$485$		0			0
$486$	70.5478	−	354.668i	0.145160	−	0.729769i
$487$	266.338	+	398.602i	0.546895	+	0.818486i	0.997230	−	0.0743736i	$-0.0236957\pi$
$487$	266.338	+	398.602i	0.546895	+	0.818486i	−0.450336	+	0.892859i	$0.648696\pi$
$488$	−14.8664	−	74.7387i	−0.0304640	−	0.153153i
$489$	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	$0.625871\pi$
$492$		−	466.718i		−	0.948614i
$493$	−63.2102	−	729.768i	−0.128215	−	1.48026i
$494$	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
$498$	−975.439	+	194.027i	−1.95871	+	0.389612i
$499$	300.741	−	200.949i	0.602688	−	0.402703i	−0.216455	−	0.976293i	$-0.569449\pi$
$499$	300.741	−	200.949i	0.602688	−	0.402703i	0.819143	+	0.573589i	$0.194449\pi$
$500$		0			0
$501$	−692.178	+	286.709i	−1.38159	+	0.572274i
$502$	−109.213	−	263.663i	−0.217556	−	0.525226i
$503$	−28.0936	+	141.236i	−0.0558521	+	0.280787i	−0.998611	−	0.0526876i	$-0.983221\pi$
$503$	−28.0936	+	141.236i	−0.0558521	+	0.280787i	0.942759	+	0.333475i	$0.108221\pi$
$504$	−54.0924	−	80.9551i	−0.107326	−	0.160625i
$505$		0			0
$506$	−15.3886	+	15.3886i	−0.0304122	+	0.0304122i
$507$	−362.420	+	542.401i	−0.714833	+	1.06982i
$508$	−149.598	−	61.9657i	−0.294485	−	0.121980i
$509$			281.872i			0.553776i	0.960902	+	0.276888i	$0.0893031\pi$
$509$			281.872i			0.553776i	−0.960902	+	0.276888i	$0.910697\pi$
$510$		0			0
$511$	−0.351042			−0.000686972
$512$	28.1295	−	67.9107i	0.0549405	−	0.132638i
$513$	−705.916	−	471.678i	−1.37605	−	0.919450i
$514$	−126.192	−	126.192i	−0.245509	−	0.245509i
$515$		0			0
$516$	31.1837	−	20.8363i	0.0604336	−	0.0403804i
$517$	−30.6554	−	6.09774i	−0.0592948	−	0.0117945i
$518$	45.6912	−	18.9259i	0.0882069	−	0.0365365i
$519$	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	$-0.433029\pi$
$522$	−312.151	−	1569.29i	−0.597990	−	3.00630i
$523$	−658.045	+	658.045i	−1.25821	+	1.25821i	−0.306266	+	0.951946i	$0.599080\pi$
$523$	−658.045	+	658.045i	−1.25821	+	1.25821i	−0.951946	+	0.306266i	$0.900920\pi$
$524$	161.265	−	241.351i	0.307758	−	0.460593i
$525$		0			0
$526$		−	173.923i		−	0.330652i
$527$	184.445	−	219.427i	0.349990	−	0.416370i
$528$	35.5228			0.0672780
$529$	55.3710	−	133.677i	0.104671	−	0.252698i
$530$		0			0
$531$	744.311	+	744.311i	1.40172	+	1.40172i
$532$	−31.4954	+	6.26483i	−0.0592019	+	0.0117760i
$533$	357.159	−	238.646i	0.670091	−	0.447741i
$534$	−1942.10	−	386.309i	−3.63690	−	0.723425i
$535$		0			0
$536$	−92.6014	−	223.560i	−0.172764	−	0.417089i
$537$	52.4032	−	263.449i	0.0975851	−	0.490593i
$538$	232.317	+	347.686i	0.431815	+	0.646257i
$539$	−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	$0.290276\pi$
$542$	−515.918	−	213.700i	−0.951878	−	0.394281i
$543$			583.318i			1.07425i
$544$	−309.324	−	170.049i	−0.568611	−	0.312591i
$545$		0			0
$546$	−27.2605	+	65.8126i	−0.0499276	+	0.120536i
$547$	510.386	+	341.029i	0.933064	+	0.623453i	0.926407	−	0.376525i	$-0.122881\pi$
$547$	510.386	+	341.029i	0.933064	+	0.623453i	0.00665718	+	0.999978i	$0.497881\pi$
$548$	−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
$552$	−735.736	+	304.752i	−1.33285	+	0.552086i
$553$	30.2288	+	72.9787i	0.0546633	+	0.131969i
$554$	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	−0.743584	−	0.668643i	$-0.766876\pi$
$557$	−41.7424	+	41.7424i	−0.0749415	+	0.0749415i	0.668643	+	0.743584i	$0.266876\pi$
$558$	347.865	−	520.617i	0.623414	−	0.933005i
$559$	31.8902	+	13.2094i	0.0570487	+	0.0236303i
$560$		0			0
$561$	−3.38465	+	30.6599i	−0.00603325	+	0.0546522i
$562$	−52.6957			−0.0937646
$563$	196.631	−	474.709i	0.349255	−	0.843177i	−0.647453	−	0.762106i	$-0.724166\pi$
$563$	196.631	−	474.709i	0.349255	−	0.843177i	0.996708	−	0.0810717i	$-0.0258343\pi$
$564$	484.417	+	323.677i	0.858895	+	0.573895i
$565$		0			0
$566$	235.444	−	46.8328i	0.415979	−	0.0827434i
$567$	26.5354	−	17.7304i	0.0467997	−	0.0312705i
$568$	−473.355	−	94.1562i	−0.833372	−	0.165768i
$569$	−327.271	+	135.560i	−0.575169	+	0.238243i	−0.651256	−	0.758859i	$-0.725757\pi$
$569$	−327.271	+	135.560i	−0.575169	+	0.238243i	0.0760868	+	0.997101i	$0.475757\pi$
$570$		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	$0.806831\pi$
$572$	−1.69069	−	2.53030i	−0.00295576	−	0.00442360i
$573$	−74.6085	−	375.082i	−0.130207	−	0.654594i
$574$	−111.772	+	111.772i	−0.194724	+	0.194724i
$575$		0			0
$576$	449.171	+	186.053i	0.779811	+	0.323008i
$577$			337.479i			0.584886i	0.956283	+	0.292443i	$0.0944682\pi$
$577$			337.479i			0.584886i	−0.956283	+	0.292443i	$0.905532\pi$
$578$	384.356	−	546.901i	0.664976	−	0.946195i
$579$	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
$583$	−5.76333	+	1.14640i	−0.00988564	+	0.00196638i
$584$	1.80830	−	1.20827i	0.00309641	−	0.00206895i
$585$		0			0
$586$	60.9699	−	25.2546i	0.104044	−	0.0430965i
$587$	−67.4493	−	162.837i	−0.114905	−	0.277405i	0.855956	−	0.517049i	$-0.172969\pi$
$587$	−67.4493	−	162.837i	−0.114905	−	0.277405i	−0.970861	+	0.239644i	$0.922969\pi$
$588$	−63.3020	+	318.240i	−0.107656	+	0.541225i
$589$	225.237	+	337.091i	0.382406	+	0.572311i
$590$		0			0
$591$	−881.991	+	881.991i	−1.49237	+	1.49237i
$592$	−235.055	+	351.784i	−0.397052	+	0.594231i
$593$	−235.725	−	97.6406i	−0.397513	−	0.164655i	0.174966	−	0.984574i	$-0.444018\pi$
$593$	−235.725	−	97.6406i	−0.397513	−	0.164655i	−0.572479	+	0.819919i	$0.694018\pi$
$594$			29.6068i			0.0498430i
$595$		0			0
$596$	−218.881			−0.367250
$597$	−515.137	+	1243.65i	−0.862876	+	2.08317i
$598$	310.427	+	207.421i	0.519109	+	0.346858i
$599$	47.8438	+	47.8438i	0.0798728	+	0.0798728i	0.745914	−	0.666042i	$-0.232013\pi$
$599$	47.8438	+	47.8438i	0.0798728	+	0.0798728i	−0.666042	+	0.745914i	$0.732013\pi$
$600$		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	$0.188221\pi$
$602$	−12.4580	−	2.47805i	−0.0206943	−	0.00411636i
$603$	585.540	−	242.539i	0.971044	−	0.402220i
$604$	80.9192	+	195.356i	0.133972	+	0.323438i
$605$		0			0
$606$	443.589	+	663.877i	0.731994	+	1.09551i
$607$	−51.5172	−	258.994i	−0.0848718	−	0.426679i	−0.999737	−	0.0229205i	$-0.992704\pi$
$607$	−51.5172	−	258.994i	−0.0848718	−	0.426679i	0.914866	−	0.403759i	$-0.132296\pi$
$608$	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
$612$	177.489	−	322.857i	0.290014	−	0.527544i
$613$	−320.858			−0.523422			−0.261711	−	0.965146i	$-0.584287\pi$
$613$	−320.858			−0.523422			−0.261711	+	0.965146i	$0.584287\pi$
$614$	−158.074	+	381.625i	−0.257450	+	0.621539i
$615$		0			0
$616$	−1.55452	−	1.55452i	−0.00252357	−	0.00252357i
$617$	−549.727	+	109.348i	−0.890968	+	0.177225i	−0.619289	−	0.785163i	$-0.712579\pi$
$617$	−549.727	+	109.348i	−0.890968	+	0.177225i	−0.271679	+	0.962388i	$0.587579\pi$
$618$	−1383.50	+	924.428i	−2.23868	+	1.49584i
$619$	102.300	+	20.3487i	0.165266	+	0.0328735i	0.277030	−	0.960861i	$-0.410650\pi$
$619$	102.300	+	20.3487i	0.165266	+	0.0328735i	−0.111764	+	0.993735i	$0.535650\pi$
$620$		0			0
$621$	−350.734	−	846.747i	−0.564789	−	1.36352i
$622$	−42.2160	+	212.234i	−0.0678715	+	0.341213i
$623$	94.0134	+	140.701i	0.150904	+	0.225844i
$624$	−118.889	−	597.697i	−0.190528	−	0.957848i
$625$		0			0
$626$	−323.123	+	483.587i	−0.516171	+	0.772504i
$627$	−40.3057	−	16.6952i	−0.0642834	−	0.0266270i
$628$		−	169.704i		−	0.270230i
$629$	−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	$0.219828\pi$
$632$	−406.904	−	271.885i	−0.643836	−	0.430197i
$633$	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
$637$	−275.903	+	114.283i	−0.433129	+	0.179408i
$638$	−13.8255	−	33.3778i	−0.0216701	−	0.0523162i
$639$	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
$643$	147.083	−	220.125i	0.228745	−	0.342341i	−0.699287	−	0.714841i	$-0.746499\pi$
$643$	147.083	−	220.125i	0.228745	−	0.342341i	0.928032	+	0.372500i	$0.121499\pi$
$644$	−32.0273	−	13.2662i	−0.0497319	−	0.0205996i
$645$		0			0
$646$	591.117	+	737.824i	0.915042	+	1.14214i
$647$	501.378			0.774927			0.387464	−	0.921885i	$-0.373351\pi$
$647$	501.378			0.774927			0.387464	+	0.921885i	$0.373351\pi$
$648$	−75.6631	+	182.667i	−0.116764	+	0.281893i
$649$	19.7619	+	13.2045i	0.0304498	+	0.0203459i
$650$		0			0
$651$	−81.9006	+	16.2910i	−0.125807	+	0.0250246i
$652$	−119.301	+	79.7146i	−0.182978	+	0.122262i
$653$	−1025.79	−	204.042i	−1.57088	−	0.312468i	−0.668603	−	0.743620i	$-0.733107\pi$
$653$	−1025.79	−	204.042i	−1.57088	−	0.312468i	−0.902279	+	0.431152i	$0.858107\pi$
$654$	−1062.69	+	440.179i	−1.62490	+	0.673056i
$655$		0			0
$656$	263.813	−	1326.28i	0.402154	−	2.02176i
$657$	3.16466	+	4.73624i	0.00481683	+	0.00720890i
$658$	−38.4947	−	193.526i	−0.0585026	−	0.294112i
$659$	−874.251	+	874.251i	−1.32663	+	1.32663i	−0.418344	+	0.908289i	$0.637389\pi$
$659$	−874.251	+	874.251i	−1.32663	+	1.32663i	−0.908289	+	0.418344i	$0.862611\pi$
$660$		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	$0.960233\pi$
$662$		−	900.444i		−	1.36019i
$663$	527.203	−	45.6647i	0.795178	−	0.0688759i
$664$	−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
$668$	198.171	−	39.4187i	0.296663	−	0.0590100i
$669$	1358.26	−	907.558i	2.03028	−	1.35659i
$670$		0			0
$671$	4.16354	−	1.72460i	0.00620498	−	0.00257019i
$672$	39.3512	+	95.0022i	0.0585583	+	0.141372i
$673$	−216.439	+	1088.11i	−0.321603	+	1.61681i	0.394555	+	0.918872i	$0.370899\pi$
$673$	−216.439	+	1088.11i	−0.321603	+	1.61681i	−0.716159	+	0.697938i	$0.754101\pi$
$674$	696.815	+	1042.86i	1.03385	+	1.54727i
$675$		0			0
$676$	124.401	−	124.401i	0.184025	−	0.184025i
$677$	360.086	−	538.907i	0.531885	−	0.796023i	−0.464077	−	0.885795i	$-0.653614\pi$
$677$	360.086	−	538.907i	0.531885	−	0.796023i	0.995962	+	0.0897723i	$0.0286139\pi$
$678$	1259.45	+	521.681i	1.85759	+	0.769441i
$679$		−	87.4982i		−	0.128863i
$680$		0			0
$681$	−780.974			−1.14681
$682$	5.41034	−	13.0617i	0.00793306	−	0.0191521i
$683$	273.705	+	182.884i	0.400739	+	0.267766i	0.739567	−	0.673083i	$-0.235030\pi$
$683$	273.705	+	182.884i	0.400739	+	0.267766i	−0.338828	+	0.940849i	$0.610030\pi$
$684$	368.457	+	368.457i	0.538679	+	0.538679i
$685$		0			0
$686$	184.610	−	123.352i	0.269110	−	0.179814i
$687$	1492.21	+	296.818i	2.17206	+	0.432050i
$688$	100.393	−	41.5841i	0.145920	−	0.0604420i
$689$	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	$0.869946\pi$
$692$	−7.17739	−	36.0832i	−0.0103720	−	0.0521433i
$693$	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
$697$	1119.58	+	354.068i	1.60628	+	0.507988i
$698$	−995.704			−1.42651
$699$	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	$0.589434\pi$
$702$	498.155	−	99.0893i	0.709623	−	0.141153i
$703$	432.037	−	288.678i	0.614561	−	0.410637i
$704$	10.7667	+	2.14163i	0.0152936	+	0.00304209i
$705$		0			0
$706$	34.4636	+	83.2024i	0.0488152	+	0.117850i
$707$	13.3116	−	66.9218i	0.0188282	−	0.0946560i
$708$	−246.128	−	368.357i	−0.347639	−	0.520278i
$709$	−237.118	−	1192.07i	−0.334440	−	1.68134i	−0.672403	−	0.740185i	$-0.734738\pi$
$709$	−237.118	−	1192.07i	−0.334440	−	1.68134i	0.337963	−	0.941160i	$-0.390262\pi$
$710$		0			0
$711$	712.112	−	1065.75i	1.00156	−	1.49895i
$712$	−968.570	−	401.195i	−1.36035	−	0.563476i
$713$			437.656i			0.613823i
$714$	−186.998	+	54.3294i	−0.261902	+	0.0760916i
$715$		0			0
$716$	−27.7221	+	66.9270i	−0.0387180	+	0.0934734i
$717$	−1617.09	−	1080.50i	−2.25535	−	1.50698i
$718$	−975.795	−	975.795i	−1.35905	−	1.35905i
$719$	494.558	−	98.3738i	0.687842	−	0.136820i	0.161218	−	0.986919i	$-0.448458\pi$
$719$	494.558	−	98.3738i	0.687842	−	0.136820i	0.526624	+	0.850099i	$0.323458\pi$
$720$		0			0
$721$	139.463	+	27.7410i	0.193430	+	0.0384757i
$722$	−463.909	+	192.158i	−0.642534	+	0.266146i
$723$	650.080	+	1569.43i	0.899142	+	2.17072i
$724$	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	−0.440718	+	0.897646i	$0.645276\pi$
$727$	−972.990	+	972.990i	−1.33836	+	1.33836i	−0.897646	+	0.440718i	$0.854724\pi$
$728$	−20.9532	+	31.3586i	−0.0287818	+	0.0430751i
$729$	991.196	+	410.567i	1.35967	+	0.563192i
$730$		0			0
$731$	26.3259	+	90.6118i	0.0360135	+	0.123956i
$732$	−84.0016			−0.114756
$733$	550.353	−	1328.67i	0.750823	−	1.81265i	0.196159	−	0.980572i	$-0.437153\pi$
$733$	550.353	−	1328.67i	0.750823	−	1.81265i	0.554664	−	0.832074i	$-0.312847\pi$
$734$	210.906	+	140.923i	0.287339	+	0.191993i
$735$		0			0
$736$	528.581	−	105.141i	0.718181	−	0.142855i
$737$	11.8987	−	7.95048i	0.0161448	−	0.0107876i
$738$	2515.64	+	500.393i	3.40873	+	0.678039i
$739$	−347.484	+	143.933i	−0.470209	+	0.194767i	−0.605190	−	0.796081i	$-0.706903\pi$
$739$	−347.484	+	143.933i	−0.470209	+	0.194767i	0.134981	+	0.990848i	$0.456903\pi$
$740$		0			0
$741$	−146.011	+	734.049i	−0.197046	+	0.990619i
$742$	−20.6096	−	30.8445i	−0.0277758	−	0.0415694i
$743$	172.160	+	865.508i	0.231710	+	1.16488i	0.904969	+	0.425477i	$0.139893\pi$
$743$	172.160	+	865.508i	0.231710	+	1.16488i	−0.673260	+	0.739406i	$0.735107\pi$
$744$	365.816	−	365.816i	0.491689	−	0.491689i
$745$		0			0
$746$	401.121	+	166.150i	0.537696	+	0.222721i
$747$		−	1379.13i		−	1.84623i
$748$	2.50840	−	7.93169i	0.00335348	−	0.0106039i
$749$	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
$753$	605.728	−	120.487i	0.804420	−	0.160009i
$754$	−515.333	+	344.335i	−0.683466	+	0.456677i
$755$		0			0
$756$	−43.5710	+	18.0477i	−0.0576337	+	0.0238726i
$757$	−406.600	−	981.619i	−0.537120	−	1.29672i	−0.926725	−	0.375741i	$-0.877388\pi$
$757$	−406.600	−	981.619i	−0.537120	−	1.29672i	0.389605	−	0.920982i	$-0.372612\pi$
$758$	−15.4109	+	77.4758i	−0.0203310	+	0.102211i
$759$	−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	$0.198793\pi$
$762$	771.543	−	1154.70i	1.01252	−	1.51535i
$763$	90.8149	+	37.6168i	0.119023	+	0.0493011i
$764$			103.137i			0.134997i
$765$		0			0
$766$	1576.44			2.05801
$767$	156.035	−	376.702i	0.203436	−	0.491137i
$768$	−969.657	−	647.904i	−1.26257	−	0.843625i
$769$	682.514	+	682.514i	0.887535	+	0.887535i	0.994286	−	0.106751i	$-0.0340449\pi$
$769$	682.514	+	682.514i	0.887535	+	0.887535i	−0.106751	+	0.994286i	$0.534045\pi$
$770$		0			0
$771$	321.115	−	214.562i	0.416492	−	0.278291i
$772$	−287.025	−	57.0928i	−0.371794	−	0.0739544i
$773$	697.360	−	288.856i	0.902147	−	0.373682i	0.117102	−	0.993120i	$-0.462640\pi$
$773$	697.360	−	288.856i	0.902147	−	0.373682i	0.785045	+	0.619438i	$0.212640\pi$
$774$	78.8755	+	190.422i	0.101906	+	0.246024i
$775$		0			0
$776$	301.164	+	450.724i	0.388098	+	0.580830i
$777$	20.8796	+	104.969i	0.0268721	+	0.135095i
$778$	−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
$782$	88.0709	+	1016.79i	0.112623	+	1.30024i
$783$	1521.48			1.94314
$784$	−359.771	+	868.565i	−0.458892	+	1.10786i
$785$		0			0
$786$	1760.34	+	1760.34i	2.23962	+	2.23962i
$787$	−635.538	+	126.416i	−0.807545	+	0.160631i	−0.581564	−	0.813501i	$-0.697559\pi$
$787$	−635.538	+	126.416i	−0.807545	+	0.160631i	−0.225981	+	0.974132i	$0.572559\pi$
$788$	279.698	−	186.888i	0.354947	−	0.237168i
$789$	369.148	+	73.4281i	0.467868	+	0.0930648i
$790$		0			0
$791$	−44.5817	−	107.630i	−0.0563612	−	0.136068i
$792$	−6.95945	+	34.9875i	−0.00878718	+	0.0441761i
$793$	−42.9523	−	64.2827i	−0.0541644	−	0.0810627i
$794$	−9.68407	−	48.6851i	−0.0121966	−	0.0613163i
$795$		0			0
$796$	201.691	−	301.851i	0.253380	−	0.379210i
$797$	1234.15	+	511.203i	1.54850	+	0.641409i	0.983044	−	0.183371i	$-0.0587009\pi$
$797$	1234.15	+	511.203i	1.54850	+	0.641409i	0.565454	+	0.824780i	$0.308701\pi$
$798$		−	275.412i		−	0.345128i
$799$	−1143.94	+	916.485i	−1.43172	+	1.14704i
$800$		0			0
$801$	1050.80	−	2536.85i	1.31186	−	3.16710i
$802$	67.9483	+	45.4016i	0.0847235	+	0.0566104i
$803$	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
$807$	−836.037	+	346.298i	−1.03598	+	0.429118i
$808$	161.770	+	390.547i	0.200210	+	0.483351i
$809$	−12.7373	+	64.0346i	−0.0157445	+	0.0791528i	−0.987859	−	0.155355i	$-0.950348\pi$
$809$	−12.7373	+	64.0346i	−0.0157445	+	0.0791528i	0.972114	+	0.234508i	$0.0753478\pi$
$810$		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
$813$	671.388	−	1004.80i	0.825815	−	1.23592i
$814$	−16.7407	−	6.93423i	−0.0205660	−	0.00851871i
$815$		0			0
$816$	1071.92	−	1275.22i	1.31362	−	1.56277i
$817$	−133.454			−0.163346
$818$	247.942	−	598.585i	0.303108	−	0.731767i
$819$	−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	$0.296148\pi$
$822$	797.612	−	532.947i	0.970330	−	0.648354i
$823$	586.402	+	116.643i	0.712517	+	0.141729i	0.538024	−	0.842930i	$-0.319171\pi$
$823$	586.402	+	116.643i	0.712517	+	0.141729i	0.174494	+	0.984658i	$0.444171\pi$
$824$	−813.892	+	337.125i	−0.987732	+	0.409132i
$825$		0			0
$826$	−29.2719	+	147.160i	−0.0354381	+	0.178159i
$827$	−282.981	−	423.511i	−0.342178	−	0.512106i	0.619973	−	0.784623i	$-0.287144\pi$
$827$	−282.981	−	423.511i	−0.342178	−	0.512106i	−0.962151	+	0.272518i	$0.912144\pi$
$828$	109.741	+	551.706i	0.132538	+	0.666311i
$829$	804.169	−	804.169i	0.970046	−	0.970046i	−0.0295178	−	0.999564i	$-0.509397\pi$
$829$	804.169	−	804.169i	0.970046	−	0.970046i	0.999564	+	0.0295178i	$0.00939718\pi$
$830$		0			0
$831$	1431.03	+	592.751i	1.72206	+	0.713299i
$832$		−	188.326i		−	0.226353i
$833$	−715.384	−	393.279i	−0.858804	−	0.472123i
$834$	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
$838$	−311.781	+	62.0171i	−0.372053	+	0.0740060i
$839$	799.310	−	534.082i	0.952694	−	0.636570i	0.0209867	−	0.999780i	$-0.493319\pi$
$839$	799.310	−	534.082i	0.952694	−	0.636570i	0.931707	+	0.363210i	$0.118319\pi$
$840$		0			0
$841$	−938.290	+	388.652i	−1.11568	+	0.462131i
$842$	−229.448	−	553.936i	−0.272503	−	0.657881i
$843$	22.2475	−	111.845i	0.0263908	−	0.132676i
$844$	−152.635	−	228.435i	−0.180847	−	0.270657i
$845$		0			0
$846$	−2264.01	+	2264.01i	−2.67613	+	2.67613i
$847$	−66.4386	+	99.4324i	−0.0784399	+	0.117394i
$848$	293.197	+	121.446i	0.345752	+	0.143215i
$849$			519.497i			0.611893i
$850$		0			0
$851$	560.927			0.659138
$852$	−203.596	+	491.524i	−0.238962	+	0.576906i
$853$	−1050.97	−	702.238i	−1.23209	−	0.823257i	−0.242923	−	0.970046i	$-0.578106\pi$
$853$	−1050.97	−	702.238i	−1.23209	−	0.823257i	−0.989168	+	0.146789i	$0.953106\pi$
$854$	20.1171	+	20.1171i	0.0235563	+	0.0235563i
$855$		0			0
$856$	−978.461	+	653.787i	−1.14306	+	0.763770i
$857$	−983.753	−	195.681i	−1.14790	−	0.228332i	−0.415754	−	0.909477i	$-0.636482\pi$
$857$	−983.753	−	195.681i	−1.14790	−	0.228332i	−0.732149	+	0.681145i	$0.761482\pi$
$858$	24.1130	−	9.98792i	0.0281037	−	0.0116409i
$859$	−412.502	−	995.868i	−0.480212	−	1.15933i	−0.959508	−	0.281681i	$-0.909108\pi$
$859$	−412.502	−	995.868i	−0.480212	−	1.15933i	0.479296	−	0.877653i	$-0.340892\pi$
$860$		0			0
$861$	−190.044	−	284.422i	−0.220725	−	0.330339i
$862$	−227.609	−	1144.27i	−0.264047	−	1.32745i
$863$	−245.882	+	245.882i	−0.284915	+	0.284915i	−0.835066	−	0.550151i	$-0.814570\pi$
$863$	−245.882	+	245.882i	−0.284915	+	0.284915i	0.550151	+	0.835066i	$0.314570\pi$
$864$	407.337	−	609.623i	0.471455	−	0.705582i
$865$		0			0
$866$		−	1914.87i		−	2.21116i
$867$	998.515	+	1046.68i	1.15169	+	1.20725i
$868$	22.5205			0.0259452
$869$	11.0755	−	26.7385i	0.0127451	−	0.0307693i
$870$		0			0
$871$	−173.596	−	173.596i	−0.199306	−	0.199306i
$872$	−597.283	+	118.807i	−0.684958	+	0.136247i
$873$	−1180.52	+	788.799i	−1.35226	+	0.903550i
$874$	−1415.72	−	281.604i	−1.61981	−	0.322201i
$875$		0			0
$876$	−0.917446	−	2.21491i	−0.00104731	−	0.00252844i
$877$	−29.5063	+	148.338i	−0.0336446	+	0.169143i	−0.993955	−	0.109792i	$-0.964981\pi$
$877$	−29.5063	+	148.338i	−0.0336446	+	0.169143i	0.960310	+	0.278935i	$0.0899814\pi$
$878$	−86.2083	−	129.020i	−0.0981871	−	0.146947i
$879$	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	$0.0320719\pi$
$882$	−1647.47	−	682.404i	−1.86788	−	0.773701i
$883$		−	362.947i		−	0.411038i	−0.978653	−	0.205519i	$-0.934112\pi$
$883$		−	362.947i		−	0.411038i	0.978653	−	0.205519i	$-0.0658883\pi$
$884$	−141.852	−	15.6595i	−0.160466	−	0.0177144i
$885$		0			0
$886$	−533.643	+	1288.33i	−0.602306	+	1.45410i
$887$	−805.857	−	538.457i	−0.908520	−	0.607054i	0.0110675	−	0.999939i	$-0.496477\pi$
$887$	−805.857	−	538.457i	−0.908520	−	0.607054i	−0.919588	+	0.392885i	$0.871477\pi$
$888$	−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
$892$	−407.019	+	168.593i	−0.456300	+	0.189005i
$893$	−793.345	−	1915.30i	−0.888404	−	2.14480i
$894$	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
$898$	−919.787	+	1376.56i	−1.02426	+	1.53292i
$899$	−671.238	−	278.036i	−0.746649	−	0.309272i
$900$		0			0
$901$	−132.757	+	241.489i	−0.147344	+	0.268023i
$902$	57.9146			0.0642069
$903$	10.5192	−	25.3956i	0.0116492	−	0.0281236i
$904$	600.107	+	400.979i	0.663835	+	0.443560i
$905$		0			0
$906$	−1778.67	+	353.800i	−1.96321	+	0.390507i
$907$	−30.2417	+	20.2068i	−0.0333425	+	0.0222788i	−0.572130	−	0.820163i	$-0.693883\pi$
$907$	−30.2417	+	20.2068i	−0.0333425	+	0.0222788i	0.538787	+	0.842442i	$0.318883\pi$
$908$	206.573	+	41.0900i	0.227504	+	0.0452533i
$909$	−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	$0.752238\pi$
$912$	1308.99	+	1959.04i	1.43529	+	2.14807i
$913$	−6.07512	−	30.5417i	−0.00665402	−	0.0334520i
$914$	768.771	−	768.771i	0.841106	−	0.841106i
$915$		0			0
$916$	−379.083	−	157.021i	−0.413846	−	0.171421i
$917$		−	212.747i		−	0.232003i
$918$	1062.84	+	893.398i	1.15778	+	0.973201i
$919$	−682.108			−0.742229			−0.371114	−	0.928587i	$-0.621024\pi$
$919$	−682.108			−0.742229			−0.371114	+	0.928587i	$0.621024\pi$
$920$		0			0
$921$	−743.254	−	496.626i	−0.807008	−	0.539225i
$922$	651.635	+	651.635i	0.706763	+	0.706763i
$923$	−480.246	+	95.5268i	−0.520310	+	0.103496i
$924$	−2.01499	+	1.34637i	−0.00218073	+	0.00145712i
$925$		0			0
$926$	290.968	−	120.523i	0.314220	−	0.130154i
$927$	−882.986	−	2131.72i	−0.952520	−	2.29959i
$928$	−174.543	+	877.486i	−0.188085	+	0.945566i
$929$	403.390	+	603.716i	0.434219	+	0.649855i	0.982462	−	0.186464i	$-0.0597028\pi$
$929$	403.390	+	603.716i	0.434219	+	0.649855i	−0.548242	+	0.836320i	$0.684703\pi$
$930$		0			0
$931$	816.424	−	816.424i	0.876932	−	0.876932i
$932$	−77.6362	+	116.191i	−0.0833006	+	0.124668i
$933$	−432.640	−	179.205i	−0.463708	−	0.192074i
$934$		−	998.685i		−	1.06926i
$935$		0			0
$936$	611.983			0.653827
$937$	332.936	−	803.778i	0.355321	−	0.857820i	−0.640624	−	0.767855i	$-0.721324\pi$
$937$	332.936	−	803.778i	0.355321	−	0.857820i	0.995945	−	0.0899657i	$-0.0286758\pi$
$938$	75.1161	+	50.1910i	0.0800811	+	0.0535085i
$939$	−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	$0.490771\pi$
$942$	1427.50	+	283.948i	1.51539	+	0.301431i
$943$	−1656.35	+	686.081i	−1.75647	+	0.727552i
$944$	−491.211	−	1185.89i	−0.520350	−	1.25624i
$945$		0			0
$946$	2.58556	+	3.86956i	0.00273315	+	0.00409045i
$947$	346.100	+	1739.96i	0.365470	+	1.83734i	0.526224	+	0.850346i	$0.323607\pi$
$947$	346.100	+	1739.96i	0.365470	+	1.83734i	−0.160754	+	0.986994i	$0.551393\pi$
$948$	−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
$952$	−102.713	+	8.89671i	−0.107892	+	0.00934529i
$953$	−1184.60			−1.24302			−0.621512	−	0.783405i	$-0.713481\pi$
$953$	−1184.60			−1.24302			−0.621512	+	0.783405i	$0.713481\pi$
$954$	−230.356	+	556.128i	−0.241463	+	0.582944i
$955$		0			0
$956$	370.882	+	370.882i	0.387952	+	0.387952i
$957$	76.6805	−	15.2527i	0.0801259	−	0.0159380i
$958$	815.158	−	544.671i	0.850896	−	0.568551i
$959$	−80.4028	−	15.9931i	−0.0838402	−	0.0166769i
$960$		0			0
$961$	258.955	+	625.173i	0.269464	+	0.650544i
$962$	−60.6449	+	304.882i	−0.0630404	+	0.316926i
$963$	−1712.38	−	2562.75i	−1.77817	−	2.66122i
$964$	−89.3772	−	449.329i	−0.0927149	−	0.466109i
$965$		0			0
$966$	165.179	−	247.207i	0.170992	−	0.255908i
$967$	693.690	+	287.336i	0.717363	+	0.297141i	0.711348	−	0.702840i	$-0.248085\pi$
$967$	693.690	+	287.336i	0.717363	+	0.297141i	0.00601538	+	0.999982i	$0.498085\pi$
$968$		−	740.878i		−	0.765370i
$969$	−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	$0.242358\pi$
$972$	−175.480	−	117.252i	−0.180535	−	0.120630i
$973$	−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
$977$	198.351	−	82.1596i	0.203020	−	0.0840938i	−0.278856	−	0.960333i	$-0.589955\pi$
$977$	198.351	−	82.1596i	0.203020	−	0.0840938i	0.481877	+	0.876239i	$0.339955\pi$
$978$	−470.921	−	1136.90i	−0.481514	−	1.16248i
$979$	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
$983$	−840.427	+	1257.79i	−0.854962	+	1.27954i	0.103590	+	0.994620i	$0.466967\pi$
$983$	−840.427	+	1257.79i	−0.854962	+	1.27954i	−0.958551	+	0.284920i	$0.908033\pi$
$984$	1957.93	+	811.000i	1.98976	+	0.824187i
$985$		0			0
$986$	−1615.41	−	510.873i	−1.63834	−	0.518127i
$987$	427.007			0.432631
$988$	77.2422	−	186.479i	0.0781803	−	0.188744i
$989$	−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	$0.136653\pi$
$992$	−291.109	+	194.513i	−0.293457	+	0.196082i
$993$	1911.17	+	380.156i	1.92465	+	0.382836i
$994$	166.470	−	68.9543i	0.167475	−	0.0693705i
$995$		0			0
$996$	−113.239	+	569.290i	−0.113693	+	0.571576i
$997$	−640.926	−	959.213i	−0.642854	−	0.962099i	−0.999611	−	0.0279018i	$-0.991117\pi$
$997$	−640.926	−	959.213i	−0.642854	−	0.962099i	0.356757	−	0.934197i	$-0.383883\pi$
$998$	−163.213	−	820.529i	−0.163541	−	0.822174i
$999$	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.u.d.401.9	yes	96
5.2	odd	4		425.3.t.f.299.9		96
5.3	odd	4		425.3.t.g.299.4		96
5.4	even	2		425.3.u.c.401.4	yes	96
17.12	odd	16	inner	425.3.u.d.301.9	yes	96
85.12	even	16		425.3.t.g.199.4		96
85.29	odd	16		425.3.u.c.301.4	✓	96
85.63	even	16		425.3.t.f.199.9		96

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

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.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.885142 - 2.13692i) q^{2} +(4.16188 + 2.78088i) q^{3} +(-0.954534 - 0.954534i) q^{4} +(9.62637 - 6.43213i) q^{6} +(-0.970381 - 0.193021i) q^{7} +(5.66303 - 2.34570i) q^{8} +(6.14378 + 14.8324i) q^{9} +(0.201395 + 0.301409i) q^{11} +(-1.31821 - 6.62710i) q^{12} +(4.39739 - 4.39739i) q^{13} +(-1.27140 + 1.90278i) q^{14} -19.5774i q^{16} +(16.8974 + 1.86536i) q^{17} +37.1338 q^{18} +(-9.20107 + 22.2133i) q^{19} +(-3.50184 - 3.50184i) q^{21} +(0.822350 - 0.163576i) q^{22} +(-21.5813 + 14.4201i) q^{23} +(30.0919 + 5.98565i) q^{24} +(-5.50456 - 13.2892i) q^{26} +(-6.88880 + 34.6323i) q^{27} +(0.742017 + 1.11051i) q^{28} +(-8.40610 - 42.2603i) q^{29} +(9.36788 - 14.0200i) q^{31} +(-19.1833 - 7.94597i) q^{32} +1.81448i q^{33} +(18.9427 - 34.4572i) q^{34} +(8.29359 - 20.0225i) q^{36} +(-17.9689 - 12.0064i) q^{37} +(39.3239 + 39.3239i) q^{38} +(30.5300 - 6.07279i) q^{39} +(67.7453 + 13.4754i) q^{41} +(-10.5828 + 4.38353i) q^{42} +(2.12409 + 5.12800i) q^{43} +(0.0954667 - 0.479943i) q^{44} +(11.7122 + 58.8814i) q^{46} +(-60.9689 + 60.9689i) q^{47} +(54.4423 - 81.4787i) q^{48} +(-44.3657 - 18.3769i) q^{49} +(65.1373 + 54.7528i) q^{51} -8.39491 q^{52} +(-6.20340 + 14.9763i) q^{53} +(67.9091 + 45.3754i) q^{54} +(-5.94806 + 1.18314i) q^{56} +(-100.066 + 66.8621i) q^{57} +(-97.7476 - 19.4432i) q^{58} +(60.5743 - 25.0907i) q^{59} +(2.42535 - 12.1930i) q^{61} +(-21.6678 - 32.4281i) q^{62} +(-3.09885 - 15.5790i) q^{63} +(21.4134 - 21.4134i) q^{64} +(3.87740 + 1.60607i) q^{66} -39.4771i q^{67} +(-14.3486 - 17.9097i) q^{68} -129.919 q^{69} +(-65.4676 - 43.7440i) q^{71} +(69.5848 + 69.5848i) q^{72} +(0.347989 - 0.0692193i) q^{73} +(-41.5619 + 27.7708i) q^{74} +(29.9861 - 12.4207i) q^{76} +(-0.137252 - 0.331355i) q^{77} +(14.0463 - 70.6154i) q^{78} +(-44.3559 - 66.3833i) q^{79} +(-22.8085 + 22.8085i) q^{81} +(88.7601 - 132.839i) q^{82} +(-79.3643 - 32.8738i) q^{83} +6.68525i q^{84} +12.8383 q^{86} +(82.5356 - 199.259i) q^{87} +(1.84752 + 1.23447i) q^{88} +(-120.939 - 120.939i) q^{89} +(-5.11592 + 3.41835i) q^{91} +(34.3646 + 6.83554i) q^{92} +(77.9759 - 32.2987i) q^{93} +(76.3197 + 184.252i) q^{94} +(-57.7416 - 86.4164i) q^{96} +(17.2531 + 86.7371i) q^{97} +(-78.5399 + 78.5399i) q^{98} +(-3.23329 + 4.83896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{12} + 24 q^{13} + 32 q^{14} - 8 q^{17} - 64 q^{18} - 24 q^{19} - 96 q^{22} - 56 q^{23} - 336 q^{24} - 224 q^{26} + 144 q^{27} - 480 q^{28} - 64 q^{31} + 40 q^{32} + 64 q^{34} + 192 q^{36} - 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) \) 96 * q + 96 * q^12 + 24 * q^13 + 32 * q^14 - 8 * q^17 - 64 * q^18 - 24 * q^19 - 96 * q^22 - 56 * q^23 - 336 * q^24 - 224 * q^26 + 144 * q^27 - 480 * q^28 - 64 * q^31 + 40 * q^32 + 64 * q^34 + 192 * q^36 - 128 * q^37 + 496 * q^38 + 16 * q^39 + 216 * q^41 - 432 * q^42 + 592 * q^43 - 32 * q^44 + 336 * q^46 + 160 * q^48 - 32 * q^49 - 32 * q^51 - 96 * q^53 + 584 * q^54 - 40 * q^56 - 1120 * q^57 - 256 * q^58 + 544 * q^59 + 112 * q^61 - 560 * q^62 - 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 + 1040 * q^72 - 336 * q^74 - 1016 * q^76 + 960 * q^77 - 384 * q^79 - 928 * q^81 + 1200 * q^82 + 144 * q^83 + 64 * q^86 + 672 * q^87 + 832 * q^88 + 576 * q^89 + 336 * q^91 + 1008 * q^92 + 512 * q^93 + 672 * q^94 + 768 * q^96 + 128 * q^97 + 408 * q^98 - 160 * q^99

Introduction

L-functions

Modular forms

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