LMFDB - Embedded newform 975.2.bn.d.407.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] 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("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.21
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.09662 - 0.561788i) q^{2} +(1.11133 + 1.32851i) q^{3} +(2.34816 - 1.35571i) q^{4} +(3.07638 + 2.16105i) q^{6} +(0.403690 + 0.108168i) q^{7} +(1.09192 - 1.09192i) q^{8} +(-0.529880 + 2.95283i) q^{9} +(0.255945 - 0.443309i) q^{11} +(4.41067 + 1.61291i) q^{12} +(3.55810 - 0.583017i) q^{13} +0.907153 q^{14} +(-1.03551 + 1.79356i) q^{16} +(1.84160 + 0.493455i) q^{17} +(0.547908 + 6.48865i) q^{18} +(-1.50433 - 2.60558i) q^{19} +(0.304931 + 0.656518i) q^{21} +(0.287573 - 1.07324i) q^{22} +(5.61575 - 1.50474i) q^{23} +(2.66411 + 0.237141i) q^{24} +(7.13246 - 3.22126i) q^{26} +(-4.51174 + 2.57763i) q^{27} +(1.09458 - 0.293291i) q^{28} +(-3.99826 + 6.92519i) q^{29} -3.08801i q^{31} +(-1.96282 + 7.32533i) q^{32} +(0.873381 - 0.152639i) q^{33} +4.13835 q^{34} +(2.75895 + 7.65210i) q^{36} +(-1.92109 - 7.16959i) q^{37} +(-4.61780 - 4.61780i) q^{38} +(4.72878 + 4.07905i) q^{39} +(1.77356 - 3.07189i) q^{41} +(1.00815 + 1.20516i) q^{42} +(-6.98963 - 1.87287i) q^{43} -1.38795i q^{44} +(10.9288 - 6.30972i) q^{46} +(5.15313 + 5.15313i) q^{47} +(-3.53356 + 0.617552i) q^{48} +(-5.91091 - 3.41267i) q^{49} +(1.39107 + 2.99498i) q^{51} +(7.56460 - 6.19278i) q^{52} +(-7.15880 - 7.15880i) q^{53} +(-8.01134 + 7.93895i) q^{54} +(0.558908 - 0.322686i) q^{56} +(1.78973 - 4.89419i) q^{57} +(-4.49235 + 16.7657i) q^{58} +(-1.74290 + 1.00626i) q^{59} +(-5.39613 - 9.34638i) q^{61} +(-1.73481 - 6.47438i) q^{62} +(-0.533311 + 1.13471i) q^{63} +12.3191i q^{64} +(1.74540 - 0.810680i) q^{66} +(2.50128 + 9.33491i) q^{67} +(4.99336 - 1.33797i) q^{68} +(8.24002 + 5.78832i) q^{69} +(-2.93620 - 5.08564i) q^{71} +(2.64567 + 3.80284i) q^{72} +(-2.10205 - 2.10205i) q^{73} +(-8.05558 - 13.9527i) q^{74} +(-7.06484 - 4.07889i) q^{76} +(0.151274 - 0.151274i) q^{77} +(12.2060 + 5.89565i) q^{78} -14.3974i q^{79} +(-8.43845 - 3.12930i) q^{81} +(1.99273 - 7.43696i) q^{82} +(-6.15680 + 6.15680i) q^{83} +(1.60608 + 1.12821i) q^{84} -15.7068 q^{86} +(-13.6436 + 2.38446i) q^{87} +(-0.204587 - 0.763529i) q^{88} +(-10.4966 - 6.06022i) q^{89} +(1.49943 + 0.149516i) q^{91} +(11.1467 - 11.1467i) q^{92} +(4.10245 - 3.43180i) q^{93} +(13.6991 + 7.90919i) q^{94} +(-11.9131 + 5.53326i) q^{96} +(15.6563 + 4.19510i) q^{97} +(-14.3101 - 3.83439i) q^{98} +(1.17340 + 0.990663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.09662	−	0.561788i	1.48253	−	0.397244i	0.575326	−	0.817924i	$-0.304875\pi$
$2$	2.09662	−	0.561788i	1.48253	−	0.397244i	0.907209	+	0.420680i	$0.138209\pi$
$3$	1.11133	+	1.32851i	0.641628	+	0.767016i
$3$	1.11133	+	1.32851i	0.641628	+	0.767016i
$4$	2.34816	−	1.35571i	1.17408	−	0.677856i
$5$		0			0
$5$		0			0
$6$	3.07638	+	2.16105i	1.25593	+	0.882245i
$7$	0.403690	+	0.108168i	0.152581	+	0.0408838i	0.334301	−	0.942466i	$-0.391500\pi$
$7$	0.403690	+	0.108168i	0.152581	+	0.0408838i	−0.181720	+	0.983350i	$0.558167\pi$
$8$	1.09192	−	1.09192i	0.386052	−	0.386052i
$9$	−0.529880	+	2.95283i	−0.176627	+	0.984278i
$10$		0			0
$11$	0.255945	−	0.443309i	0.0771702	−	0.133663i	−0.824858	−	0.565340i	$-0.808745\pi$
$11$	0.255945	−	0.443309i	0.0771702	−	0.133663i	0.902028	+	0.431678i	$0.142078\pi$
$12$	4.41067	+	1.61291i	1.27325	+	0.465608i
$13$	3.55810	−	0.583017i	0.986840	−	0.161700i
$13$	3.55810	−	0.583017i	0.986840	−	0.161700i
$14$	0.907153			0.242447
$15$		0			0
$16$	−1.03551	+	1.79356i	−0.258878	+	0.448390i
$17$	1.84160	+	0.493455i	0.446653	+	0.119680i	0.475133	−	0.879914i	$-0.342400\pi$
$17$	1.84160	+	0.493455i	0.446653	+	0.119680i	−0.0284797	+	0.999594i	$0.509067\pi$
$18$	0.547908	+	6.48865i	0.129143	+	1.52939i
$19$	−1.50433	−	2.60558i	−0.345118	−	0.597762i	0.640257	−	0.768161i	$-0.278828\pi$
$19$	−1.50433	−	2.60558i	−0.345118	−	0.597762i	−0.985375	+	0.170399i	$0.945494\pi$
$20$		0			0
$21$	0.304931	+	0.656518i	0.0665414	+	0.143264i
$22$	0.287573	−	1.07324i	0.0613108	−	0.228815i
$23$	5.61575	−	1.50474i	1.17097	−	0.313759i	0.379628	−	0.925139i	$-0.376052\pi$
$23$	5.61575	−	1.50474i	1.17097	−	0.313759i	0.791337	+	0.611380i	$0.209385\pi$
$24$	2.66411	+	0.237141i	0.543809	+	0.0484062i
$25$		0			0
$26$	7.13246	−	3.22126i	1.39879	−	0.631742i
$27$	−4.51174	+	2.57763i	−0.868285	+	0.496065i
$28$	1.09458	−	0.293291i	0.206855	−	0.0554267i
$29$	−3.99826	+	6.92519i	−0.742459	+	1.28598i	0.208914	+	0.977934i	$0.433007\pi$
$29$	−3.99826	+	6.92519i	−0.742459	+	1.28598i	−0.951373	+	0.308042i	$0.900326\pi$
$30$		0			0
$31$		−	3.08801i		−	0.554622i	−0.960780	−	0.277311i	$-0.910557\pi$
$31$		−	3.08801i		−	0.554622i	0.960780	−	0.277311i	$-0.0894433\pi$
$32$	−1.96282	+	7.32533i	−0.346980	+	1.29495i
$33$	0.873381	−	0.152639i	0.152036	−	0.0265710i
$34$	4.13835			0.709722
$35$		0			0
$36$	2.75895	+	7.65210i	0.459825	+	1.27535i
$37$	−1.92109	−	7.16959i	−0.315825	−	1.17867i	−0.923219	−	0.384273i	$-0.874452\pi$
$37$	−1.92109	−	7.16959i	−0.315825	−	1.17867i	0.607395	−	0.794400i	$-0.292215\pi$
$38$	−4.61780	−	4.61780i	−0.749107	−	0.749107i
$39$	4.72878	+	4.07905i	0.757211	+	0.653171i
$40$		0			0
$41$	1.77356	−	3.07189i	0.276983	−	0.479749i	−0.693650	−	0.720312i	$-0.743999\pi$
$41$	1.77356	−	3.07189i	0.276983	−	0.479749i	0.970634	+	0.240563i	$0.0773320\pi$
$42$	1.00815	+	1.20516i	0.155561	+	0.185961i
$43$	−6.98963	−	1.87287i	−1.06591	−	0.285609i	−0.317098	−	0.948393i	$-0.602708\pi$
$43$	−6.98963	−	1.87287i	−1.06591	−	0.285609i	−0.748811	+	0.662783i	$0.769375\pi$
$44$		−	1.38795i		−	0.209241i
$45$		0			0
$46$	10.9288	−	6.30972i	1.61136	−	0.930318i
$47$	5.15313	+	5.15313i	0.751661	+	0.751661i	0.974789	−	0.223128i	$-0.0716268\pi$
$47$	5.15313	+	5.15313i	0.751661	+	0.751661i	−0.223128	+	0.974789i	$0.571627\pi$
$48$	−3.53356	+	0.617552i	−0.510025	+	0.0891360i
$49$	−5.91091	−	3.41267i	−0.844416	−	0.487524i
$50$		0			0
$51$	1.39107	+	2.99498i	0.194789	+	0.419381i
$52$	7.56460	−	6.19278i	1.04902	−	0.858785i
$53$	−7.15880	−	7.15880i	−0.983337	−	0.983337i	0.0165265	−	0.999863i	$-0.494739\pi$
$53$	−7.15880	−	7.15880i	−0.983337	−	0.983337i	−0.999863	+	0.0165265i	$0.994739\pi$
$54$	−8.01134	+	7.93895i	−1.09020	+	1.08035i
$55$		0			0
$56$	0.558908	−	0.322686i	0.0746872	−	0.0431207i
$57$	1.78973	−	4.89419i	0.237055	−	0.648252i
$58$	−4.49235	+	16.7657i	−0.589875	+	2.20144i
$59$	−1.74290	+	1.00626i	−0.226906	+	0.131004i	−0.609144	−	0.793060i	$-0.708487\pi$
$59$	−1.74290	+	1.00626i	−0.226906	+	0.131004i	0.382238	+	0.924064i	$0.375153\pi$
$60$		0			0
$61$	−5.39613	−	9.34638i	−0.690904	−	1.19668i	−0.971542	−	0.236867i	$-0.923879\pi$
$61$	−5.39613	−	9.34638i	−0.690904	−	1.19668i	0.280638	−	0.959814i	$-0.409454\pi$
$62$	−1.73481	−	6.47438i	−0.220320	−	0.822247i
$63$	−0.533311	+	1.13471i	−0.0671909	+	0.142960i
$64$			12.3191i			1.53988i
$65$		0			0
$66$	1.74540	−	0.810680i	0.214844	−	0.0997879i
$67$	2.50128	+	9.33491i	0.305580	+	1.14044i	0.932445	+	0.361312i	$0.117671\pi$
$67$	2.50128	+	9.33491i	0.305580	+	1.14044i	−0.626865	+	0.779128i	$0.715662\pi$
$68$	4.99336	−	1.33797i	0.605534	−	0.162252i
$69$	8.24002	+	5.78832i	0.991982	+	0.696832i
$70$		0			0
$71$	−2.93620	−	5.08564i	−0.348463	−	0.603555i	0.637514	−	0.770439i	$-0.279963\pi$
$71$	−2.93620	−	5.08564i	−0.348463	−	0.603555i	−0.985977	+	0.166884i	$0.946629\pi$
$72$	2.64567	+	3.80284i	0.311795	+	0.448169i
$73$	−2.10205	−	2.10205i	−0.246026	−	0.246026i	0.573311	−	0.819338i	$-0.305659\pi$
$73$	−2.10205	−	2.10205i	−0.246026	−	0.246026i	−0.819338	+	0.573311i	$0.805659\pi$
$74$	−8.05558	−	13.9527i	−0.936442	−	1.62196i
$75$		0			0
$76$	−7.06484	−	4.07889i	−0.810393	−	0.467881i
$77$	0.151274	−	0.151274i	0.0172393	−	0.0172393i
$78$	12.2060	+	5.89565i	1.38206	+	0.667551i
$79$		−	14.3974i		−	1.61983i	−0.586544	−	0.809917i	$-0.699512\pi$
$79$		−	14.3974i		−	1.61983i	0.586544	−	0.809917i	$-0.300488\pi$
$80$		0			0
$81$	−8.43845	−	3.12930i	−0.937606	−	0.347700i
$82$	1.99273	−	7.43696i	0.220060	−	0.821274i
$83$	−6.15680	+	6.15680i	−0.675796	+	0.675796i	−0.959046	−	0.283250i	$-0.908587\pi$
$83$	−6.15680	+	6.15680i	−0.675796	+	0.675796i	0.283250	+	0.959046i	$0.408587\pi$
$84$	1.60608	+	1.12821i	0.175237	+	0.123098i
$85$		0			0
$86$	−15.7068			−1.69370
$87$	−13.6436	+	2.38446i	−1.46275	+	0.255641i
$88$	−0.204587	−	0.763529i	−0.0218090	−	0.0813924i
$89$	−10.4966	−	6.06022i	−1.11264	−	0.642382i	−0.173126	−	0.984900i	$-0.555387\pi$
$89$	−10.4966	−	6.06022i	−1.11264	−	0.642382i	−0.939511	+	0.342518i	$0.888720\pi$
$90$		0			0
$91$	1.49943	+	0.149516i	0.157183	+	0.0156735i
$92$	11.1467	−	11.1467i	1.16212	−	1.16212i
$93$	4.10245	−	3.43180i	0.425404	−	0.355861i
$94$	13.6991	+	7.90919i	1.41296	+	0.815771i
$95$		0			0
$96$	−11.9131	+	5.53326i	−1.21588	+	0.564735i
$97$	15.6563	+	4.19510i	1.58966	+	0.425948i	0.941899	−	0.335895i	$-0.109039\pi$
$97$	15.6563	+	4.19510i	1.58966	+	0.425948i	0.647761	+	0.761843i	$0.275705\pi$
$98$	−14.3101	−	3.83439i	−1.44554	−	0.387332i
$99$	1.17340	+	0.990663i	0.117931	+	0.0995654i
$100$		0			0
$101$	7.56743	+	4.36906i	0.752987	+	0.434737i	0.826772	−	0.562537i	$-0.190175\pi$
$101$	7.56743	+	4.36906i	0.752987	+	0.434737i	−0.0737851	+	0.997274i	$0.523508\pi$
$102$	4.59909	+	5.49784i	0.455377	+	0.544368i
$103$	8.04055	−	8.04055i	0.792259	−	0.792259i	−0.189602	−	0.981861i	$-0.560720\pi$
$103$	8.04055	−	8.04055i	0.792259	−	0.792259i	0.981861	+	0.189602i	$0.0607197\pi$
$104$	3.24855	−	4.52177i	0.318547	−	0.443396i
$105$		0			0
$106$	−19.0310	−	10.9876i	−1.84846	−	1.06721i
$107$	3.12349	+	11.6570i	0.301959	+	1.12693i	0.935531	+	0.353243i	$0.114921\pi$
$107$	3.12349	+	11.6570i	0.301959	+	1.12693i	−0.633572	+	0.773683i	$0.718412\pi$
$108$	−7.09979	+	12.1693i	−0.683177	+	1.17099i
$109$	14.0991			1.35045			0.675225	−	0.737612i	$-0.264047\pi$
$109$	14.0991			1.35045			0.675225	+	0.737612i	$0.264047\pi$
$110$		0			0
$111$	7.38991	−	10.5200i	0.701419	−	0.998512i
$112$	−0.612032	+	0.612032i	−0.0578316	+	0.0578316i
$113$	−0.871189	+	3.25132i	−0.0819545	+	0.305859i	−0.994720	−	0.102625i	$-0.967276\pi$
$113$	−0.871189	+	3.25132i	−0.0819545	+	0.305859i	0.912766	+	0.408484i	$0.133942\pi$
$114$	1.00289	−	11.2667i	0.0939288	−	1.05522i
$115$		0			0
$116$			21.6820i			2.01312i
$117$	−0.163815	+	10.8154i	−0.0151447	+	0.999885i
$118$	−3.08889	+	3.08889i	−0.284355	+	0.284355i
$119$	0.690059	+	0.398406i	0.0632576	+	0.0365218i
$120$		0			0
$121$	5.36898	+	9.29935i	0.488090	+	0.845396i
$122$	−16.5643	−	16.5643i	−1.49966	−	1.49966i
$123$	6.05205	−	1.05770i	0.545695	−	0.0953699i
$124$	−4.18645	−	7.25114i	−0.375954	−	0.651172i
$125$		0			0
$126$	−0.480682	+	2.67867i	−0.0428226	+	0.238635i
$127$	−17.1178	+	4.58670i	−1.51896	+	0.407003i	−0.919399	−	0.393327i	$-0.871324\pi$
$127$	−17.1178	+	4.58670i	−1.51896	+	0.407003i	−0.599559	+	0.800330i	$0.704657\pi$
$128$	2.99508	+	11.1778i	0.264730	+	0.987986i
$129$	−5.27968	−	11.3672i	−0.464850	−	1.00082i
$130$		0			0
$131$		−	3.62886i		−	0.317055i	−0.987355	−	0.158527i	$-0.949325\pi$
$131$		−	3.62886i		−	0.317055i	0.987355	−	0.158527i	$-0.0506746\pi$
$132$	1.84391	−	1.54247i	0.160491	−	0.134255i
$133$	−0.325443	−	1.21457i	−0.0282195	−	0.105317i
$134$	10.4885	+	18.1666i	0.906066	+	1.56935i
$135$		0			0
$136$	2.54969	−	1.47206i	0.218634	−	0.126228i
$137$	0.997998	−	3.72458i	0.0852647	−	0.318212i	−0.910099	−	0.414390i	$-0.863995\pi$
$137$	0.997998	−	3.72458i	0.0852647	−	0.318212i	0.995364	+	0.0961776i	$0.0306617\pi$
$138$	20.5280	+	7.50677i	1.74746	+	0.639019i
$139$	−6.82507	+	3.94046i	−0.578895	+	0.334225i	−0.760694	−	0.649110i	$-0.775141\pi$
$139$	−6.82507	+	3.94046i	−0.578895	+	0.334225i	0.181799	+	0.983336i	$0.441808\pi$
$140$		0			0
$141$	−1.11915	+	12.5728i	−0.0942491	+	1.05882i
$142$	−9.01315	−	9.01315i	−0.756367	−	0.756367i
$143$	0.652221	−	1.72656i	0.0545414	−	0.144382i
$144$	−4.74738	−	4.00807i	−0.395615	−	0.334005i
$145$		0			0
$146$	−5.58811	−	3.22629i	−0.462475	−	0.267010i
$147$	−2.03523	−	11.6453i	−0.167863	−	0.960490i
$148$	−14.2309	−	14.2309i	−1.16977	−	1.16977i
$149$	−4.77688	+	2.75793i	−0.391337	+	0.225938i	−0.682739	−	0.730662i	$-0.739211\pi$
$149$	−4.77688	+	2.75793i	−0.391337	+	0.225938i	0.291402	+	0.956601i	$0.405878\pi$
$150$		0			0
$151$		−	3.50398i		−	0.285150i	−0.989784	−	0.142575i	$-0.954462\pi$
$151$		−	3.50398i		−	0.285150i	0.989784	−	0.142575i	$-0.0455382\pi$
$152$	−4.48770	−	1.20247i	−0.364000	−	0.0975336i
$153$	−2.43292	+	5.17646i	−0.196690	+	0.418492i
$154$	0.232181	−	0.402149i	0.0187097	−	0.0324061i
$155$		0			0
$156$	16.6340	+	3.16741i	1.33178	+	0.253596i
$157$	−1.27066	−	1.27066i	−0.101409	−	0.101409i	0.654582	−	0.755991i	$-0.272845\pi$
$157$	−1.27066	−	1.27066i	−0.101409	−	0.101409i	−0.755991	+	0.654582i	$0.772845\pi$
$158$	−8.08829	−	30.1859i	−0.643470	−	2.40146i
$159$	1.55473	−	17.4663i	0.123298	−	1.38517i
$160$		0			0
$161$	2.42979			0.191494
$162$	−19.4502	−	1.82033i	−1.52816	−	0.143018i
$163$	2.01921	−	7.53579i	0.158157	−	0.590249i	−0.840658	−	0.541567i	$-0.817831\pi$
$163$	2.01921	−	7.53579i	0.158157	−	0.590249i	0.998814	−	0.0486817i	$-0.0155020\pi$
$164$		−	9.61774i		−	0.751019i
$165$		0			0
$166$	−9.44966	+	16.3673i	−0.733436	+	1.27035i
$167$	2.20275	−	0.590226i	0.170454	−	0.0456731i	−0.172583	−	0.984995i	$-0.555211\pi$
$167$	2.20275	−	0.590226i	0.170454	−	0.0456731i	0.343037	+	0.939322i	$0.388544\pi$
$168$	1.04982	+	0.383904i	0.0809957	+	0.0296188i
$169$	12.3202	−	4.14887i	0.947706	−	0.319144i
$170$		0			0
$171$	8.49097	−	3.06140i	0.649321	−	0.234111i
$172$	−18.9519	+	5.07814i	−1.44507	+	0.387204i
$173$	−5.86243	+	21.8789i	−0.445713	+	1.66342i	0.268335	+	0.963326i	$0.413526\pi$
$173$	−5.86243	+	21.8789i	−0.445713	+	1.66342i	−0.714048	+	0.700097i	$0.753140\pi$
$174$	−27.2659	+	12.6641i	−2.06702	+	0.960064i
$175$		0			0
$176$	0.530068	+	0.918104i	0.0399554	+	0.0692047i
$177$	−3.27376	−	1.19716i	−0.246071	−	0.0899844i
$178$	−25.4120	−	6.80911i	−1.90471	−	0.510365i
$179$	4.89863	−	8.48468i	0.366141	−	0.634175i	−0.622818	−	0.782367i	$-0.714012\pi$
$179$	4.89863	−	8.48468i	0.366141	−	0.634175i	0.988959	+	0.148192i	$0.0473454\pi$
$180$		0			0
$181$	1.50768			0.112065			0.0560325	−	0.998429i	$-0.482155\pi$
$181$	1.50768			0.112065			0.0560325	+	0.998429i	$0.482155\pi$
$182$	3.22774	−	0.528886i	0.239256	−	0.0392036i
$183$	6.41986	−	17.5557i	0.474570	−	1.29776i
$184$	4.48890	−	7.77499i	0.330926	−	0.573180i
$185$		0			0
$186$	6.67334	−	9.49990i	0.489313	−	0.696566i
$187$	0.690101	−	0.690101i	0.0504652	−	0.0504652i
$188$	19.0865	+	5.11423i	1.39203	+	0.372993i
$189$	−2.10016	+	0.552535i	−0.152764	+	0.0401910i
$190$		0			0
$191$	−3.89212	+	2.24712i	−0.281624	+	0.162596i	−0.634158	−	0.773203i	$-0.718653\pi$
$191$	−3.89212	+	2.24712i	−0.281624	+	0.162596i	0.352534	+	0.935799i	$0.385320\pi$
$192$	−16.3660	+	13.6906i	−1.18112	+	0.988033i
$193$	15.3024	−	4.10026i	1.10149	−	0.295143i	0.338118	−	0.941104i	$-0.390210\pi$
$193$	15.3024	−	4.10026i	1.10149	−	0.295143i	0.763371	+	0.645960i	$0.223543\pi$
$194$	35.1822			2.52593
$195$		0			0
$196$	−18.5064			−1.32188
$197$	11.8903	−	3.18600i	0.847150	−	0.226993i	0.190968	−	0.981596i	$-0.438837\pi$
$197$	11.8903	−	3.18600i	0.847150	−	0.226993i	0.656181	+	0.754603i	$0.272171\pi$
$198$	3.01671	+	1.41784i	0.214389	+	0.100762i
$199$	−19.5208	+	11.2703i	−1.38379	+	0.798933i	−0.992606	−	0.121378i	$-0.961269\pi$
$199$	−19.5208	+	11.2703i	−1.38379	+	0.798933i	−0.391187	+	0.920311i	$0.627935\pi$
$200$		0			0
$201$	−9.62177	+	13.6972i	−0.678667	+	0.966124i
$202$	18.3205	+	4.90897i	1.28903	+	0.345394i
$203$	−2.36315	+	2.36315i	−0.165860	+	0.165860i
$204$	7.32678	+	5.14680i	0.512977	+	0.360348i
$205$		0			0
$206$	12.3409	−	21.3751i	0.859832	−	1.48927i
$207$	1.46756	+	17.3797i	0.102002	+	1.20797i
$208$	−2.63878	+	6.98539i	−0.182967	+	0.484349i
$209$	−1.54011			−0.106531
$210$		0			0
$211$	1.99042	−	3.44751i	0.137026	−	0.237336i	−0.789344	−	0.613952i	$-0.789579\pi$
$211$	1.99042	−	3.44751i	0.137026	−	0.237336i	0.926370	+	0.376616i	$0.122912\pi$
$212$	−26.5153	−	7.10476i	−1.82108	−	0.487957i
$213$	3.49324	−	9.55261i	0.239353	−	0.654534i
$214$	13.0975	+	22.6856i	0.895330	+	1.55076i
$215$		0			0
$216$	−2.11190	+	7.74102i	−0.143696	+	0.526710i
$217$	0.334025	−	1.24660i	0.0226751	−	0.0846246i
$218$	29.5605	−	7.92071i	2.00209	−	0.536458i
$219$	0.456519	−	5.12867i	0.0308487	−	0.346563i
$220$		0			0
$221$	6.84029	+	0.682079i	0.460128	+	0.0458816i
$222$	9.58384	−	26.2080i	0.643225	−	1.75896i
$223$	−13.5539	+	3.63175i	−0.907635	+	0.243200i	−0.682292	−	0.731080i	$-0.739017\pi$
$223$	−13.5539	+	3.63175i	−0.907635	+	0.243200i	−0.225342	+	0.974280i	$0.572350\pi$
$224$	−1.58474	+	2.74485i	−0.105885	+	0.183398i
$225$		0			0
$226$			7.30621i			0.486002i
$227$	−2.30516	+	8.60297i	−0.152999	+	0.570999i	0.846270	+	0.532755i	$0.178843\pi$
$227$	−2.30516	+	8.60297i	−0.152999	+	0.570999i	−0.999268	+	0.0382445i	$0.987823\pi$
$228$	−2.43254	−	13.9187i	−0.161099	−	0.921790i
$229$	−13.9049			−0.918865			−0.459432	−	0.888213i	$-0.651947\pi$
$229$	−13.9049			−0.918865			−0.459432	+	0.888213i	$0.651947\pi$
$230$		0			0
$231$	0.369086	+	0.0328535i	0.0242841	+	0.00216160i
$232$	3.19597	+	11.9275i	0.209826	+	0.783081i
$233$	10.6874	+	10.6874i	0.700154	+	0.700154i	0.964443	−	0.264289i	$-0.0851374\pi$
$233$	10.6874	+	10.6874i	0.700154	+	0.700154i	−0.264289	+	0.964443i	$0.585137\pi$
$234$	5.73251	+	22.7679i	0.374746	+	1.48838i
$235$		0			0
$236$	−2.72840	+	4.72573i	−0.177604	+	0.307619i
$237$	19.1271	−	16.0003i	1.24244	−	1.03933i
$238$	1.67061	+	0.447639i	0.108290	+	0.0290161i
$239$		−	2.14533i		−	0.138770i	−0.997590	−	0.0693849i	$-0.977896\pi$
$239$		−	2.14533i		−	0.138770i	0.997590	−	0.0693849i	$-0.0221036\pi$
$240$		0			0
$241$	4.50245	−	2.59949i	0.290028	−	0.167448i	−0.347926	−	0.937522i	$-0.613114\pi$
$241$	4.50245	−	2.59949i	0.290028	−	0.167448i	0.637955	+	0.770074i	$0.279781\pi$
$242$	16.4810	+	16.4810i	1.05944	+	1.05944i
$243$	−5.22062	−	14.6883i	−0.334903	−	0.942253i
$244$	−25.3420	−	14.6312i	−1.62236	−	0.936667i
$245$		0			0
$246$	12.0947	−	5.61757i	0.771127	−	0.358163i
$247$	−6.87167	−	8.39388i	−0.437234	−	0.534090i
$248$	−3.37185	−	3.37185i	−0.214113	−	0.214113i
$249$	−15.0216	−	1.33712i	−0.951957	−	0.0847366i
$250$		0			0
$251$	−3.01039	+	1.73805i	−0.190014	+	0.109705i	−0.591989	−	0.805946i	$-0.701657\pi$
$251$	−3.01039	+	1.73805i	−0.190014	+	0.109705i	0.401975	+	0.915651i	$0.368324\pi$
$252$	0.286045	+	3.38751i	0.0180191	+	0.213393i
$253$	0.770259	−	2.87464i	0.0484257	−	0.180727i
$254$	−33.3128	+	19.2331i	−2.09023	+	1.20679i
$255$		0			0
$256$	0.240005	+	0.415700i	0.0150003	+	0.0259813i
$257$	−1.03229	−	3.85254i	−0.0643922	−	0.240315i	0.926227	−	0.376966i	$-0.123033\pi$
$257$	−1.03229	−	3.85254i	−0.0643922	−	0.240315i	−0.990619	+	0.136651i	$0.956366\pi$
$258$	−17.4554	−	20.8666i	−1.08673	−	1.29910i
$259$		−	3.10209i		−	0.192755i
$260$		0			0
$261$	−18.3303	−	15.4757i	−1.13462	−	0.957924i
$262$	−2.03865	−	7.60834i	−0.125948	−	0.470045i
$263$	23.3298	−	6.25119i	1.43857	−	0.385465i	0.546540	−	0.837433i	$-0.315945\pi$
$263$	23.3298	−	6.25119i	1.43857	−	0.385465i	0.892034	+	0.451968i	$0.149278\pi$
$264$	0.786992	−	1.12033i	0.0484360	−	0.0689516i
$265$		0			0
$266$	−1.36466	−	2.36366i	−0.0836727	−	0.144925i
$267$	−3.61415	−	20.6798i	−0.221183	−	1.26558i
$268$	18.5289	+	18.5289i	1.13183	+	1.13183i
$269$	12.4058	+	21.4875i	0.756397	+	1.31012i	0.944677	+	0.328003i	$0.106375\pi$
$269$	12.4058	+	21.4875i	0.756397	+	1.31012i	−0.188280	+	0.982115i	$0.560291\pi$
$270$		0			0
$271$	18.7408	+	10.8200i	1.13842	+	0.657270i	0.946040	−	0.324050i	$-0.105045\pi$
$271$	18.7408	+	10.8200i	1.13842	+	0.657270i	0.192385	+	0.981320i	$0.438378\pi$
$272$	−2.79204	+	2.79204i	−0.169292	+	0.169292i
$273$	1.46774	+	2.15818i	0.0888315	+	0.130619i
$274$		−	8.36970i		−	0.505632i
$275$		0			0
$276$	27.1962	+	2.42082i	1.63702	+	0.145716i
$277$	0.115159	−	0.429778i	0.00691921	−	0.0258228i	−0.962380	−	0.271707i	$-0.912412\pi$
$277$	0.115159	−	0.429778i	0.00691921	−	0.0258228i	0.969299	+	0.245885i	$0.0790784\pi$
$278$	−12.0959	+	12.0959i	−0.725463	+	0.725463i
$279$	9.11837	+	1.63627i	0.545903	+	0.0979612i
$280$		0			0
$281$	10.2114			0.609162			0.304581	−	0.952486i	$-0.401484\pi$
$281$	10.2114			0.609162			0.304581	+	0.952486i	$0.401484\pi$
$282$	4.71684	+	26.9892i	0.280883	+	1.60718i
$283$	2.14169	+	7.99290i	0.127310	+	0.475129i	0.999911	−	0.0133048i	$-0.00423516\pi$
$283$	2.14169	+	7.99290i	0.127310	+	0.475129i	−0.872601	+	0.488433i	$0.837568\pi$
$284$	−13.7893	−	7.96128i	−0.818247	−	0.472415i
$285$		0			0
$286$	0.397499	−	3.98635i	0.0235046	−	0.235718i
$287$	1.04825	−	1.04825i	0.0618762	−	0.0618762i
$288$	−20.5904	−	9.67742i	−1.21330	−	0.570247i
$289$	−11.5744	−	6.68251i	−0.680850	−	0.393089i
$290$		0			0
$291$	11.8262	+	25.4618i	0.693262	+	1.49260i
$292$	−7.78573	−	2.08618i	−0.455625	−	0.122084i
$293$	−17.1295	−	4.58984i	−1.00072	−	0.268141i	−0.278971	−	0.960300i	$-0.589993\pi$
$293$	−17.1295	−	4.58984i	−1.00072	−	0.268141i	−0.721745	+	0.692159i	$0.756660\pi$
$294$	−10.8093	−	23.2725i	−0.630411	−	1.35728i
$295$		0			0
$296$	−9.92628	−	5.73094i	−0.576953	−	0.333104i
$297$	−0.0120704	+	2.65983i	−0.000700396	+	0.154339i
$298$	−8.46593	+	8.46593i	−0.490418	+	0.490418i
$299$	19.1041	−	8.62808i	1.10482	−	0.498975i
$300$		0			0
$301$	−2.61906	−	1.51212i	−0.150960	−	0.0871569i
$302$	−1.96850	−	7.34652i	−0.113274	−	0.422745i
$303$	2.60559	+	14.9089i	0.149687	+	0.856493i
$304$	6.23102			0.357374
$305$		0			0
$306$	−2.19283	+	12.2199i	−0.125356	+	0.698563i
$307$	−18.0565	+	18.0565i	−1.03054	+	1.03054i	−0.0310201	+	0.999519i	$0.509876\pi$
$307$	−18.0565	+	18.0565i	−1.03054	+	1.03054i	−0.999519	+	0.0310201i	$0.990124\pi$
$308$	0.150132	−	0.560302i	0.00855459	−	0.0319262i
$309$	19.6177	+	1.74623i	1.11601	+	0.0993396i
$310$		0			0
$311$			25.9620i			1.47217i	0.676890	+	0.736084i	$0.263327\pi$
$311$			25.9620i			1.47217i	−0.676890	+	0.736084i	$0.736673\pi$
$312$	9.61744	−	0.709451i	0.544480	−	0.0401648i
$313$	−1.24977	+	1.24977i	−0.0706415	+	0.0706415i	−0.741545	−	0.670903i	$-0.765907\pi$
$313$	−1.24977	+	1.24977i	−0.0706415	+	0.0706415i	0.670903	+	0.741545i	$0.265907\pi$
$314$	−3.37793	−	1.95025i	−0.190627	−	0.110059i
$315$		0			0
$316$	−19.5187	−	33.8075i	−1.09802	−	1.90182i
$317$	12.6999	+	12.6999i	0.713299	+	0.713299i	0.967224	−	0.253925i	$-0.0817216\pi$
$317$	12.6999	+	12.6999i	0.713299	+	0.713299i	−0.253925	+	0.967224i	$0.581722\pi$
$318$	−6.55270	−	37.4937i	−0.367457	−	2.10254i
$319$	2.04667	+	3.54493i	0.114591	+	0.198478i
$320$		0			0
$321$	−12.0152	+	17.1044i	−0.670625	+	0.954675i
$322$	5.09435	−	1.36503i	0.283897	−	0.0760699i
$323$	−1.48464	−	5.54076i	−0.0826077	−	0.308296i
$324$	−24.0573	+	4.09202i	−1.33652	+	0.227334i
$325$		0			0
$326$		−	16.9341i		−	0.937891i
$327$	15.6688	+	18.7308i	0.866487	+	1.03582i
$328$	−1.41768	−	5.29084i	−0.0782780	−	0.292138i
$329$	1.52286	+	2.63767i	0.0839581	+	0.145420i
$330$		0			0
$331$	−7.74634	+	4.47235i	−0.425777	+	0.245823i	−0.697546	−	0.716540i	$-0.745725\pi$
$331$	−7.74634	+	4.47235i	−0.425777	+	0.245823i	0.271769	+	0.962363i	$0.412391\pi$
$332$	−6.11032	+	22.8040i	−0.335347	+	1.25153i
$333$	22.1885	−	1.87362i	1.21592	−	0.102674i
$334$	4.28676	−	2.47496i	0.234561	−	0.135424i
$335$		0			0
$336$	−1.49326	−	0.132920i	−0.0814642	−	0.00725138i
$337$	−1.08661	−	1.08661i	−0.0591915	−	0.0591915i	0.676891	−	0.736083i	$-0.263327\pi$
$337$	−1.08661	−	1.08661i	−0.0591915	−	0.0591915i	−0.736083	+	0.676891i	$0.763327\pi$
$338$	23.5000	−	15.6199i	1.27823	−	0.849613i
$339$	−5.28759	+	2.45591i	−0.287183	+	0.133387i
$340$		0			0
$341$	−1.36894	−	0.790359i	−0.0741324	−	0.0428004i
$342$	16.0825	−	11.1887i	0.869641	−	0.605017i
$343$	−4.08569	−	4.08569i	−0.220606	−	0.220606i
$344$	−9.67713	+	5.58709i	−0.521756	+	0.301236i
$345$		0			0
$346$			49.1652i			2.64314i
$347$	−34.3656	−	9.20824i	−1.84484	−	0.494324i	−0.845622	−	0.533782i	$-0.820770\pi$
$347$	−34.3656	−	9.20824i	−1.84484	−	0.494324i	−0.999221	+	0.0394575i	$0.987437\pi$
$348$	−28.8047	+	24.0959i	−1.54410	+	1.29168i
$349$	−0.580105	+	1.00477i	−0.0310523	+	0.0537841i	−0.881134	−	0.472867i	$-0.843219\pi$
$349$	−0.580105	+	1.00477i	−0.0310523	+	0.0537841i	0.850082	+	0.526651i	$0.176553\pi$
$350$		0			0
$351$	−14.5504	+	11.8019i	−0.776645	+	0.629938i
$352$	2.74501	+	2.74501i	0.146310	+	0.146310i
$353$	8.13026	+	30.3425i	0.432730	+	1.61497i	0.746440	+	0.665452i	$0.231761\pi$
$353$	8.13026	+	30.3425i	0.432730	+	1.61497i	−0.313710	+	0.949519i	$0.601572\pi$
$354$	−7.53640	−	0.670838i	−0.400555	−	0.0356546i
$355$		0			0
$356$	−32.8636			−1.74177
$357$	0.237599	+	1.35951i	0.0125751	+	0.0719530i
$358$	5.50399	−	20.5412i	0.290895	−	1.08563i
$359$			18.5415i			0.978582i	0.872120	+	0.489291i	$0.162744\pi$
$359$			18.5415i			0.978582i	−0.872120	+	0.489291i	$0.837256\pi$
$360$		0			0
$361$	4.97396	−	8.61515i	0.261787	−	0.453429i
$362$	3.16104	−	0.846997i	0.166140	−	0.0445172i
$363$	−6.38756	+	17.4674i	−0.335260	+	0.916802i
$364$	3.72362	−	1.68171i	0.195171	−	0.0881458i
$365$		0			0
$366$	3.59741	−	40.4144i	0.188039	−	2.11249i
$367$	−5.91325	+	1.58445i	−0.308669	+	0.0827076i	−0.409828	−	0.912163i	$-0.634411\pi$
$367$	−5.91325	+	1.58445i	−0.308669	+	0.0827076i	0.101159	+	0.994870i	$0.467745\pi$
$368$	−3.11634	+	11.6304i	−0.162451	+	0.606274i
$369$	8.13101	+	6.86475i	0.423284	+	0.357365i
$370$		0			0
$371$	−2.11558	−	3.66429i	−0.109835	−	0.190241i
$372$	4.98068	−	13.6202i	0.258236	−	0.706173i
$373$	25.0927	+	6.72356i	1.29925	+	0.348133i	0.841167	−	0.540776i	$-0.181869\pi$
$373$	25.0927	+	6.72356i	1.29925	+	0.348133i	0.458083	+	0.888909i	$0.348536\pi$
$374$	1.05919	−	1.83457i	0.0547694	−	0.0948634i
$375$		0			0
$376$	11.2536			0.580360
$377$	−10.1887	+	26.9716i	−0.524746	+	1.38911i
$378$	−4.09284	+	2.33830i	−0.210513	+	0.120269i
$379$	10.9047	−	18.8876i	0.560139	−	0.970189i	−0.437345	−	0.899294i	$-0.644081\pi$
$379$	10.9047	−	18.8876i	0.560139	−	0.970189i	0.997484	−	0.0708954i	$-0.0225857\pi$
$380$		0			0
$381$	−25.1170	−	17.6438i	−1.28678	−	0.903920i
$382$	−6.89790	+	6.89790i	−0.352927	+	0.352927i
$383$	11.4935	+	3.07967i	0.587290	+	0.157364i	0.540215	−	0.841527i	$-0.318343\pi$
$383$	11.4935	+	3.07967i	0.587290	+	0.157364i	0.0470758	+	0.998891i	$0.485010\pi$
$384$	−11.5213	+	16.4012i	−0.587942	+	0.836971i
$385$		0			0
$386$	29.7798	−	17.1934i	1.51575	−	0.875120i
$387$	9.23393	−	19.6468i	0.469387	−	0.998704i
$388$	42.4510	−	11.3747i	2.15512	−	0.577463i
$389$	18.6519			0.945690			0.472845	−	0.881146i	$-0.343227\pi$
$389$	18.6519			0.945690			0.472845	+	0.881146i	$0.343227\pi$
$390$		0			0
$391$	11.0845			0.560566
$392$	−10.1806	+	2.72788i	−0.514198	+	0.137779i
$393$	4.82098	−	4.03287i	0.243186	−	0.203431i
$394$	23.1396	−	13.3597i	1.16576	−	0.673050i
$395$		0			0
$396$	4.09839	+	0.735447i	0.205952	+	0.0369576i
$397$	16.8034	+	4.50246i	0.843340	+	0.225972i	0.654525	−	0.756041i	$-0.272869\pi$
$397$	16.8034	+	4.50246i	0.843340	+	0.225972i	0.188815	+	0.982013i	$0.439535\pi$
$398$	−34.5962	+	34.5962i	−1.73415	+	1.73415i
$399$	1.25189	−	1.78215i	0.0626731	−	0.0892188i
$400$		0			0
$401$	2.63268	−	4.55994i	0.131470	−	0.227712i	−0.792774	−	0.609516i	$-0.791364\pi$
$401$	2.63268	−	4.55994i	0.131470	−	0.227712i	0.924243	+	0.381804i	$0.124697\pi$
$402$	−12.4783	+	34.1232i	−0.622361	+	1.70191i
$403$	−1.80036	−	10.9874i	−0.0896824	−	0.547324i
$404$	23.6927			1.17876
$405$		0			0
$406$	−3.62704	+	6.28221i	−0.180007	+	0.311781i
$407$	−3.67004	−	0.983383i	−0.181917	−	0.0487445i
$408$	4.78921	+	1.75134i	0.237101	+	0.0867041i
$409$	4.97625	+	8.61911i	0.246060	+	0.426188i	0.962429	−	0.271534i	$-0.0875308\pi$
$409$	4.97625	+	8.61911i	0.246060	+	0.426188i	−0.716369	+	0.697721i	$0.754197\pi$
$410$		0			0
$411$	6.05725	−	2.81340i	0.298782	−	0.138775i
$412$	7.97985	−	29.7812i	0.393139	−	1.46721i
$413$	−0.812435	+	0.217691i	−0.0399773	+	0.0107119i
$414$	12.8406	+	35.6142i	0.631082	+	1.75034i
$415$		0			0
$416$	−2.71311	+	27.2086i	−0.133021	+	1.33401i
$417$	−12.8199	−	4.68802i	−0.627791	−	0.229573i
$418$	−3.22902	+	0.865213i	−0.157936	+	0.0423189i
$419$	8.67323	−	15.0225i	0.423715	−	0.733896i	−0.572584	−	0.819846i	$-0.694059\pi$
$419$	8.67323	−	15.0225i	0.423715	−	0.733896i	0.996299	+	0.0859496i	$0.0273924\pi$
$420$		0			0
$421$		−	9.95497i		−	0.485175i	−0.970129	−	0.242588i	$-0.922004\pi$
$421$		−	9.95497i		−	0.485175i	0.970129	−	0.242588i	$-0.0779962\pi$
$422$	2.23639	−	8.34631i	0.108866	−	0.406292i
$423$	−17.9469	+	12.4858i	−0.872607	+	0.607080i
$424$	−15.6337			−0.759238
$425$		0			0
$426$	1.95746	−	21.9907i	0.0948391	−	1.06545i
$427$	−1.16738	−	4.35673i	−0.0564936	−	0.210837i
$428$	23.1380	+	23.1380i	1.11842	+	1.11842i
$429$	3.01859	−	1.05230i	0.145739	−	0.0508055i
$430$		0			0
$431$	−6.30631	+	10.9229i	−0.303764	+	0.526135i	−0.976985	−	0.213306i	$-0.931577\pi$
$431$	−6.30631	+	10.9229i	−0.303764	+	0.526135i	0.673221	+	0.739441i	$0.264910\pi$
$432$	0.0488349	−	10.7612i	0.00234957	−	0.517751i
$433$	−21.8390	−	5.85174i	−1.04952	−	0.281217i	−0.307464	−	0.951560i	$-0.599480\pi$
$433$	−21.8390	−	5.85174i	−1.04952	−	0.281217i	−0.742052	+	0.670343i	$0.766147\pi$
$434$		−	2.80129i		−	0.134466i
$435$		0			0
$436$	33.1070	−	19.1143i	1.58554	−	0.915411i
$437$	−12.3687	−	12.3687i	−0.591674	−	0.591674i
$438$	−1.92408	−	11.0093i	−0.0919360	−	0.526047i
$439$	10.2958	+	5.94428i	0.491391	+	0.283705i	0.725152	−	0.688589i	$-0.241770\pi$
$439$	10.2958	+	5.94428i	0.491391	+	0.283705i	−0.233760	+	0.972294i	$0.575103\pi$
$440$		0			0
$441$	13.2091	−	15.6456i	0.629005	−	0.745030i
$442$	14.7247	−	2.41273i	0.700382	−	0.114762i
$443$	−14.0199	−	14.0199i	−0.666105	−	0.666105i	0.290707	−	0.956812i	$-0.406109\pi$
$443$	−14.0199	−	14.0199i	−0.666105	−	0.666105i	−0.956812	+	0.290707i	$0.906109\pi$
$444$	3.09064	−	34.7212i	0.146675	−	1.64780i
$445$		0			0
$446$	−26.3771	+	15.2288i	−1.24899	+	0.721105i
$447$	−8.97264	−	3.28115i	−0.424391	−	0.155193i
$448$	−1.33254	+	4.97309i	−0.0629564	+	0.234956i
$449$	3.69387	−	2.13266i	0.174324	−	0.100646i	−0.410299	−	0.911951i	$-0.634576\pi$
$449$	3.69387	−	2.13266i	0.174324	−	0.100646i	0.584623	+	0.811305i	$0.301242\pi$
$450$		0			0
$451$	−0.907865	−	1.57247i	−0.0427497	−	0.0740447i
$452$	2.36216	+	8.81571i	0.111107	+	0.414656i
$453$	4.65508	−	3.89409i	0.218715	−	0.182960i
$454$			19.3322i			0.907304i
$455$		0			0
$456$	−3.38982	−	7.29830i	−0.158743	−	0.341774i
$457$	−6.74076	−	25.1569i	−0.315320	−	1.17679i	−0.923692	−	0.383137i	$-0.874844\pi$
$457$	−6.74076	−	25.1569i	−0.315320	−	1.17679i	0.608372	−	0.793652i	$-0.291823\pi$
$458$	−29.1534	+	7.81163i	−1.36225	+	0.365014i
$459$	−9.58077	+	2.52062i	−0.447192	+	0.117652i
$460$		0			0
$461$	6.68465	+	11.5782i	0.311335	+	0.539249i	0.978652	−	0.205526i	$-0.0658904\pi$
$461$	6.68465	+	11.5782i	0.311335	+	0.539249i	−0.667316	+	0.744774i	$0.732557\pi$
$462$	0.792290	−	0.138467i	0.0368607	−	0.00644205i
$463$	−3.79477	−	3.79477i	−0.176358	−	0.176358i	0.613408	−	0.789766i	$-0.289798\pi$
$463$	−3.79477	−	3.79477i	−0.176358	−	0.176358i	−0.789766	+	0.613408i	$0.789798\pi$
$464$	−8.28050	−	14.3422i	−0.384412	−	0.665822i
$465$		0			0
$466$	28.4115	+	16.4034i	1.31614	+	0.759871i
$467$	15.8650	−	15.8650i	0.734143	−	0.734143i	−0.237294	−	0.971438i	$-0.576261\pi$
$467$	15.8650	−	15.8650i	0.734143	−	0.734143i	0.971438	+	0.237294i	$0.0762606\pi$
$468$	14.2779	+	25.6184i	0.659997	+	1.18421i
$469$			4.03897i			0.186502i
$470$		0			0
$471$	0.275959	−	3.10020i	0.0127155	−	0.142850i
$472$	−0.804345	+	3.00186i	−0.0370230	+	0.138172i
$473$	−2.61922	+	2.61922i	−0.120432	+	0.120432i
$474$	31.1135	−	44.2920i	1.42909	−	2.03440i
$475$		0			0
$476$	2.16050			0.0990261
$477$	24.9321	−	17.3454i	1.14156	−	0.794193i
$478$	−1.20522	−	4.49794i	−0.0551254	−	0.205731i
$479$	−17.3730	−	10.0303i	−0.793793	−	0.458297i	0.0475029	−	0.998871i	$-0.484874\pi$
$479$	−17.3730	−	10.0303i	−0.793793	−	0.458297i	−0.841296	+	0.540574i	$0.818207\pi$
$480$		0			0
$481$	−11.0154	−	24.3901i	−0.502260	−	1.11209i
$482$	7.97957	−	7.97957i	0.363460	−	0.363460i
$483$	2.70030	+	3.22800i	0.122868	+	0.146879i
$484$	25.2145	+	14.5576i	1.14611	+	0.661709i
$485$		0			0
$486$	−19.1974	−	27.8628i	−0.870810	−	1.26388i
$487$	27.5972	+	7.39466i	1.25055	+	0.335084i	0.822549	−	0.568694i	$-0.192551\pi$
$487$	27.5972	+	7.39466i	1.25055	+	0.335084i	0.428001	+	0.903778i	$0.359218\pi$
$488$	−16.0976	−	4.31335i	−0.728705	−	0.195256i
$489$	12.2554	−	5.69223i	0.554208	−	0.257411i
$490$		0			0
$491$	−25.1585	−	14.5253i	−1.13539	−	0.655516i	−0.190103	−	0.981764i	$-0.560882\pi$
$491$	−25.1585	−	14.5253i	−1.13539	−	0.655516i	−0.945284	+	0.326248i	$0.894215\pi$
$492$	12.7773	−	10.6885i	0.576044	−	0.481875i
$493$	−10.7805	+	10.7805i	−0.485528	+	0.485528i
$494$	−19.1229	−	13.7384i	−0.860379	−	0.618118i
$495$		0			0
$496$	5.53852	+	3.19767i	0.248687	+	0.143580i
$497$	−0.635208	−	2.37063i	−0.0284930	−	0.106337i
$498$	−32.2458	+	5.63553i	−1.44497	+	0.252534i
$499$	−20.0887			−0.899294			−0.449647	−	0.893206i	$-0.648450\pi$
$499$	−20.0887			−0.899294			−0.449647	+	0.893206i	$0.648450\pi$
$500$		0			0
$501$	3.23211	+	2.27044i	0.144400	+	0.101436i
$502$	−5.33523	+	5.33523i	−0.238123	+	0.238123i
$503$	−2.45860	+	9.17562i	−0.109624	+	0.409121i	−0.998829	−	0.0483882i	$-0.984592\pi$
$503$	−2.45860	+	9.17562i	−0.109624	+	0.409121i	0.889205	+	0.457509i	$0.151258\pi$
$504$	0.656683	+	1.82135i	0.0292510	+	0.0811293i
$505$		0			0
$506$		−	6.45976i		−	0.287171i
$507$	19.2036	+	11.7567i	0.852863	+	0.522134i
$508$	−33.9771	+	33.9771i	−1.50749	+	1.50749i
$509$	35.0026	+	20.2088i	1.55146	+	0.895738i	0.998023	+	0.0628499i	$0.0200189\pi$
$509$	35.0026	+	20.2088i	1.55146	+	0.895738i	0.553441	+	0.832888i	$0.313314\pi$
$510$		0			0
$511$	−0.621201	−	1.07595i	−0.0274803	−	0.0475973i
$512$	−15.6287	−	15.6287i	−0.690696	−	0.690696i
$513$	13.5034	+	7.87811i	0.596189	+	0.347827i
$514$	−4.32863	−	7.49740i	−0.190927	−	0.330696i
$515$		0			0
$516$	−27.8082	−	19.5343i	−1.22419	−	0.859948i
$517$	3.60335	−	0.965514i	0.158475	−	0.0424632i
$518$	−1.74272	−	6.50391i	−0.0765707	−	0.285766i
$519$	−35.5815	+	16.5264i	−1.56185	+	0.725430i
$520$		0			0
$521$		−	3.29710i		−	0.144448i	−0.997388	−	0.0722242i	$-0.976990\pi$
$521$		−	3.29710i		−	0.144448i	0.997388	−	0.0722242i	$-0.0230097\pi$
$522$	−47.1259	−	22.1490i	−2.06264	−	0.969434i
$523$	−2.08910	−	7.79663i	−0.0913500	−	0.340923i	0.905091	−	0.425218i	$-0.139803\pi$
$523$	−2.08910	−	7.79663i	−0.0913500	−	0.340923i	−0.996441	+	0.0842956i	$0.973136\pi$
$524$	−4.91969	−	8.52115i	−0.214918	−	0.372248i
$525$		0			0
$526$	45.4018	−	26.2127i	1.97961	−	1.14293i
$527$	1.52379	−	5.68687i	0.0663774	−	0.247724i
$528$	−0.630630	+	1.72452i	−0.0274446	+	0.0750501i
$529$	9.35384	−	5.40044i	0.406689	−	0.234802i
$530$		0			0
$531$	−2.04780	−	5.67968i	−0.0888668	−	0.246477i
$532$	−2.41080	−	2.41080i	−0.104521	−	0.104521i
$533$	4.51953	−	11.9641i	0.195763	−	0.518224i
$534$	−19.1952	−	41.3272i	−0.830655	−	1.78840i
$535$		0			0
$536$	12.9242	+	7.46177i	0.558239	+	0.322299i
$537$	16.7160	−	2.92142i	0.721349	−	0.126068i
$538$	38.0818	+	38.0818i	1.64182	+	1.64182i
$539$	−3.02573	+	1.74691i	−0.130328	+	0.0752447i
$540$		0			0
$541$			20.9027i			0.898677i	0.893362	+	0.449338i	$0.148340\pi$
$541$			20.9027i			0.898677i	−0.893362	+	0.449338i	$0.851660\pi$
$542$	45.3710	+	12.1571i	1.94885	+	0.522193i
$543$	1.67553	+	2.00297i	0.0719041	+	0.0859557i
$544$	−7.22944	+	12.5218i	−0.309960	+	0.536866i
$545$		0			0
$546$	4.28973	+	3.70032i	0.183583	+	0.158359i
$547$	4.29605	+	4.29605i	0.183686	+	0.183686i	0.792960	−	0.609274i	$-0.208539\pi$
$547$	4.29605	+	4.29605i	0.183686	+	0.183686i	−0.609274	+	0.792960i	$0.708539\pi$
$548$	−2.70600	−	10.0989i	−0.115594	−	0.431404i
$549$	30.4576	−	10.9814i	1.29990	−	0.468676i
$550$		0			0
$551$	24.0589			1.02494
$552$	15.3178	−	2.67706i	0.651970	−	0.113943i
$553$	1.55735	−	5.81209i	0.0662251	−	0.247155i
$554$		−	0.965776i		−	0.0410319i
$555$		0			0
$556$	−10.6843	+	18.5057i	−0.453113	+	0.784815i
$557$	18.7339	−	5.01972i	0.793779	−	0.212692i	0.160928	−	0.986966i	$-0.448551\pi$
$557$	18.7339	−	5.01972i	0.793779	−	0.212692i	0.632851	+	0.774274i	$0.281885\pi$
$558$	20.0370	−	1.69194i	0.848234	−	0.0716257i
$559$	−25.9617	−	2.58877i	−1.09806	−	0.109493i
$560$		0			0
$561$	1.68374	+	0.149875i	0.0710875	+	0.00632772i
$562$	21.4095	−	5.73665i	0.903104	−	0.241986i
$563$	10.7184	−	40.0016i	0.451727	−	1.68587i	−0.245809	−	0.969318i	$-0.579054\pi$
$563$	10.7184	−	40.0016i	0.451727	−	1.68587i	0.697536	−	0.716550i	$-0.254280\pi$
$564$	14.4172	+	31.0403i	0.607074	+	1.30703i
$565$		0			0
$566$	8.98063	+	15.5549i	0.377484	+	0.653822i
$567$	−3.06803	−	2.17604i	−0.128845	−	0.0913851i
$568$	−8.75920	−	2.34702i	−0.367528	−	0.0984788i
$569$	8.79437	−	15.2323i	0.368679	−	0.638571i	−0.620680	−	0.784064i	$-0.713143\pi$
$569$	8.79437	−	15.2323i	0.368679	−	0.638571i	0.989359	+	0.145493i	$0.0464767\pi$
$570$		0			0
$571$	−28.6479			−1.19888			−0.599439	−	0.800420i	$-0.704610\pi$
$571$	−28.6479			−1.19888			−0.599439	+	0.800420i	$0.704610\pi$
$572$	−0.809199	−	4.93847i	−0.0338343	−	0.206488i
$573$	−7.31076	−	2.67343i	−0.305411	−	0.111684i
$574$	1.60889	−	2.78668i	0.0671537	−	0.116314i
$575$		0			0
$576$	−36.3762	−	6.52764i	−1.51567	−	0.271985i
$577$	7.73617	−	7.73617i	0.322061	−	0.322061i	−0.527496	−	0.849557i	$-0.676869\pi$
$577$	7.73617	−	7.73617i	0.322061	−	0.322061i	0.849557	+	0.527496i	$0.176869\pi$
$578$	−28.0214	−	7.50830i	−1.16554	−	0.312304i
$579$	22.4533	+	15.7726i	0.933126	+	0.655488i
$580$		0			0
$581$	−3.15141	+	1.81947i	−0.130743	+	0.0754842i
$582$	39.0991	+	46.7399i	1.62071	+	1.93743i
$583$	−5.00582	+	1.34131i	−0.207320	+	0.0555512i
$584$	−4.59053			−0.189958
$585$		0			0
$586$	−38.4926			−1.59011
$587$	27.6328	−	7.40419i	1.14053	−	0.305604i	0.361365	−	0.932425i	$-0.382311\pi$
$587$	27.6328	−	7.40419i	1.14053	−	0.305604i	0.779163	+	0.626821i	$0.215644\pi$
$588$	−20.5667	−	24.5859i	−0.848158	−	1.01391i
$589$	−8.04606	+	4.64539i	−0.331532	+	0.191410i
$590$		0			0
$591$	17.4467	+	12.2557i	0.717662	+	0.504132i
$592$	14.8484	+	3.97861i	0.610265	+	0.163520i
$593$	0.767325	−	0.767325i	0.0315103	−	0.0315103i	−0.691176	−	0.722686i	$-0.742907\pi$
$593$	0.767325	−	0.767325i	0.0315103	−	0.0315103i	0.722686	+	0.691176i	$0.242907\pi$
$594$	1.46895	+	5.58343i	0.0602718	+	0.229091i
$595$		0			0
$596$	−7.47792	+	12.9521i	−0.306308	+	0.530540i
$597$	−36.6669	−	13.4085i	−1.50068	−	0.548773i
$598$	35.2070	−	28.8223i	1.43972	−	1.17863i
$599$	−28.3284			−1.15747			−0.578734	−	0.815516i	$-0.696453\pi$
$599$	−28.3284			−1.15747			−0.578734	+	0.815516i	$0.696453\pi$
$600$		0			0
$601$	8.57196	−	14.8471i	0.349658	−	0.605625i	−0.636531	−	0.771251i	$-0.719631\pi$
$601$	8.57196	−	14.8471i	0.349658	−	0.605625i	0.986189	+	0.165626i	$0.0529646\pi$
$602$	−6.34067	−	1.69898i	−0.258426	−	0.0692451i
$603$	−28.8898	+	2.43948i	−1.17648	+	0.0993435i
$604$	−4.75039	−	8.22792i	−0.193291	−	0.334789i
$605$		0			0
$606$	13.8386	+	29.7945i	0.562153	+	1.21032i
$607$	−2.05233	+	7.65942i	−0.0833017	+	0.310886i	−0.994987	−	0.100003i	$-0.968115\pi$
$607$	−2.05233	+	7.65942i	−0.0833017	+	0.310886i	0.911685	+	0.410889i	$0.134782\pi$
$608$	22.0395	−	5.90546i	0.893819	−	0.239498i
$609$	−5.76571	−	0.513224i	−0.233638	−	0.0207969i
$610$		0			0
$611$	21.3397	+	15.3310i	0.863313	+	0.620226i
$612$	1.30491	+	15.4535i	0.0527479	+	0.624671i
$613$	36.5885	−	9.80387i	1.47780	−	0.395975i	0.572200	−	0.820114i	$-0.306090\pi$
$613$	36.5885	−	9.80387i	1.47780	−	0.395975i	0.905597	+	0.424139i	$0.139423\pi$
$614$	−27.7137	+	48.0016i	−1.11843	+	1.93719i
$615$		0			0
$616$		−	0.330359i		−	0.0133105i
$617$	0.539359	−	2.01292i	0.0217138	−	0.0810369i	−0.954219	−	0.299110i	$-0.903310\pi$
$617$	0.539359	−	2.01292i	0.0217138	−	0.0810369i	0.975933	+	0.218073i	$0.0699770\pi$
$618$	42.1119	−	7.35979i	1.69399	−	0.296054i
$619$	−30.7890			−1.23751			−0.618757	−	0.785583i	$-0.712363\pi$
$619$	−30.7890			−1.23751			−0.618757	+	0.785583i	$0.712363\pi$
$620$		0			0
$621$	−21.4582	+	21.2643i	−0.861087	+	0.853307i
$622$	14.5851	+	54.4324i	0.584810	+	2.18254i
$623$	−3.58185	−	3.58185i	−0.143504	−	0.143504i
$624$	−12.2127	+	4.25744i	−0.488900	+	0.170434i
$625$		0			0
$626$	−1.91820	+	3.32241i	−0.0766665	+	0.132790i
$627$	−1.71157	−	2.04605i	−0.0683535	−	0.0817112i
$628$	−4.70636	−	1.26106i	−0.187804	−	0.0503219i
$629$		−	14.1515i		−	0.564256i
$630$		0			0
$631$	−25.0094	+	14.4392i	−0.995608	+	0.574815i	−0.906946	−	0.421247i	$-0.861593\pi$
$631$	−25.0094	+	14.4392i	−0.995608	+	0.574815i	−0.0886624	+	0.996062i	$0.528259\pi$
$632$	−15.7208	−	15.7208i	−0.625340	−	0.625340i
$633$	6.79207	−	1.18703i	0.269960	−	0.0471803i
$634$	33.7616	+	19.4923i	1.34084	+	0.774137i
$635$		0			0
$636$	−20.0286	−	43.1216i	−0.794185	−	1.70988i
$637$	−23.0213	−	8.69645i	−0.912136	−	0.344566i
$638$	6.28259	+	6.28259i	0.248730	+	0.248730i
$639$	16.5729	−	5.97532i	0.655614	−	0.236380i
$640$		0			0
$641$	36.8548	−	21.2782i	1.45568	−	0.840437i	0.456885	−	0.889526i	$-0.348965\pi$
$641$	36.8548	−	21.2782i	1.45568	−	0.840437i	0.998794	+	0.0490894i	$0.0156319\pi$
$642$	−15.5824	+	42.6115i	−0.614986	+	1.68174i
$643$	−11.0203	+	41.1282i	−0.434597	+	1.62194i	0.307432	+	0.951570i	$0.400530\pi$
$643$	−11.0203	+	41.1282i	−0.434597	+	1.62194i	−0.742029	+	0.670368i	$0.766136\pi$
$644$	5.70554	−	3.29409i	0.224830	−	0.129806i
$645$		0			0
$646$	−6.22546	−	10.7828i	−0.244938	−	0.424244i
$647$	−0.566681	−	2.11488i	−0.0222785	−	0.0831446i	0.953892	−	0.300152i	$-0.0970373\pi$
$647$	−0.566681	−	2.11488i	−0.0222785	−	0.0831446i	−0.976170	+	0.217007i	$0.930371\pi$
$648$	−12.6310	+	5.79717i	−0.496194	+	0.227734i
$649$			1.03019i			0.0404385i
$650$		0			0
$651$	2.02733	−	0.941629i	0.0794574	−	0.0369054i
$652$	−5.47493	−	20.4327i	−0.214415	−	0.800207i
$653$	−20.0829	+	5.38119i	−0.785904	+	0.210582i	−0.629386	−	0.777093i	$-0.716694\pi$
$653$	−20.0829	+	5.38119i	−0.785904	+	0.210582i	−0.156518	+	0.987675i	$0.550027\pi$
$654$	43.3743	+	30.4689i	1.69607	+	1.19143i
$655$		0			0
$656$	3.67308	+	6.36196i	0.143410	+	0.248393i
$657$	7.32084	−	5.09317i	0.285613	−	0.198703i
$658$	4.67468	+	4.67468i	0.182238	+	0.182238i
$659$	6.20566	+	10.7485i	0.241738	+	0.418703i	0.961210	−	0.275819i	$-0.0889491\pi$
$659$	6.20566	+	10.7485i	0.241738	+	0.418703i	−0.719471	+	0.694522i	$0.755616\pi$
$660$		0			0
$661$	6.32611	+	3.65238i	0.246057	+	0.142061i	0.617957	−	0.786212i	$-0.287960\pi$
$661$	6.32611	+	3.65238i	0.246057	+	0.142061i	−0.371900	+	0.928273i	$0.621294\pi$
$662$	−13.7286	+	13.7286i	−0.533578	+	0.533578i
$663$	6.69569	+	9.84541i	0.260039	+	0.382364i
$664$			13.4454i			0.521785i
$665$		0			0
$666$	45.4684	−	16.3935i	1.76186	−	0.635237i
$667$	−12.0327	+	44.9065i	−0.465906	+	1.73879i
$668$	4.37225	−	4.37225i	0.169167	−	0.169167i
$669$	−19.8877	−	13.9704i	−0.768902	−	0.540126i
$670$		0			0
$671$	−5.52445			−0.213269
$672$	−5.40773	+	0.945097i	−0.208608	+	0.0364579i
$673$	0.383129	+	1.42986i	0.0147685	+	0.0551169i	0.972917	−	0.231155i	$-0.0742505\pi$
$673$	0.383129	+	1.42986i	0.0147685	+	0.0551169i	−0.958148	+	0.286272i	$0.907584\pi$
$674$	−2.88866	−	1.66777i	−0.111267	−	0.0642400i
$675$		0			0
$676$	23.3051	−	26.4448i	0.896351	−	1.01711i
$677$	−13.3487	+	13.3487i	−0.513033	+	0.513033i	−0.915455	−	0.402421i	$-0.868169\pi$
$677$	−13.3487	+	13.3487i	−0.513033	+	0.513033i	0.402421	+	0.915455i	$0.368169\pi$
$678$	−9.70638	+	8.11963i	−0.372771	+	0.311832i
$679$	5.86653	+	3.38704i	0.225137	+	0.129983i
$680$		0			0
$681$	−13.9909	+	6.49834i	−0.536134	+	0.249017i
$682$	−3.31417	−	0.888028i	−0.126906	−	0.0340044i
$683$	−10.7061	−	2.86868i	−0.409656	−	0.109767i	0.0481050	−	0.998842i	$-0.484682\pi$
$683$	−10.7061	−	2.86868i	−0.409656	−	0.109767i	−0.457761	+	0.889075i	$0.651348\pi$
$684$	15.7878	−	18.7000i	0.603662	−	0.715012i
$685$		0			0
$686$	−10.8614	−	6.27085i	−0.414691	−	0.239422i
$687$	−15.4530	−	18.4729i	−0.589569	−	0.704784i
$688$	10.5969	−	10.5969i	0.404005	−	0.404005i
$689$	−29.6454	−	21.2980i	−1.12940	−	0.811391i
$690$		0			0
$691$	7.29352	+	4.21092i	0.277459	+	0.160191i	0.632272	−	0.774746i	$-0.282122\pi$
$691$	7.29352	+	4.21092i	0.277459	+	0.160191i	−0.354814	+	0.934937i	$0.615456\pi$
$692$	15.8956	+	59.3230i	0.604258	+	2.25512i
$693$	0.366531	+	0.526846i	0.0139234	+	0.0200132i
$694$	−77.2248			−2.93141
$695$		0			0
$696$	−12.2941	+	17.5013i	−0.466005	+	0.663386i
$697$	4.78202	−	4.78202i	0.181132	−	0.181132i
$698$	−0.651792	+	2.43252i	−0.0246707	+	0.0920722i
$699$	−2.32107	+	26.0756i	−0.0877908	+	0.986268i
$700$		0			0
$701$		−	9.61731i		−	0.363241i	−0.983369	−	0.181620i	$-0.941866\pi$
$701$		−	9.61731i		−	0.363241i	0.983369	−	0.181620i	$-0.0581342\pi$
$702$	−23.8766	+	32.9184i	−0.901164	+	1.24242i
$703$	−15.7910	+	15.7910i	−0.595569	+	0.595569i
$704$	5.46116	+	3.15300i	0.205825	+	0.118833i
$705$		0			0
$706$	34.0922	+	59.0493i	1.28308	+	2.22235i
$707$	2.58230	+	2.58230i	0.0971174	+	0.0971174i
$708$	−9.31034	+	1.62715i	−0.349904	+	0.0611519i
$709$	15.7072	+	27.2057i	0.589896	+	1.02173i	0.994246	+	0.107125i	$0.0341647\pi$
$709$	15.7072	+	27.2057i	0.589896	+	1.02173i	−0.404349	+	0.914605i	$0.632502\pi$
$710$		0			0
$711$	42.5131	+	7.62890i	1.59437	+	0.286106i
$712$	−18.0787	+	4.84417i	−0.677528	+	0.181543i
$713$	−4.64664	−	17.3415i	−0.174018	−	0.649443i
$714$	1.26191	+	2.71690i	0.0472259	+	0.101677i
$715$		0			0
$716$		−	26.5646i		−	0.992764i
$717$	2.85009	−	2.38417i	0.106439	−	0.0890385i
$718$	10.4164	+	38.8745i	0.388736	+	1.45078i
$719$	6.02748	+	10.4399i	0.224787	+	0.389342i	0.956256	−	0.292533i	$-0.0944980\pi$
$719$	6.02748	+	10.4399i	0.224787	+	0.389342i	−0.731469	+	0.681875i	$0.761165\pi$
$720$		0			0
$721$	4.11563	−	2.37616i	0.153274	−	0.0884927i
$722$	5.58862	−	20.8570i	0.207987	−	0.776218i
$723$	8.45717	+	3.09265i	0.314526	+	0.115017i
$724$	3.54028	−	2.04398i	0.131573	−	0.0759640i
$725$		0			0
$726$	−3.57931	+	40.2110i	−0.132841	+	1.49237i
$727$	1.96600	+	1.96600i	0.0729151	+	0.0729151i	0.742624	−	0.669709i	$-0.233581\pi$
$727$	1.96600	+	1.96600i	0.0729151	+	0.0729151i	−0.669709	+	0.742624i	$0.733581\pi$
$728$	1.80052	−	1.47400i	0.0667317	−	0.0546301i
$729$	13.7117	−	23.2592i	0.507839	−	0.861452i
$730$		0			0
$731$	−11.9479	−	6.89814i	−0.441910	−	0.255137i
$732$	−8.72567	−	49.9272i	−0.322510	−	1.84536i
$733$	29.6853	+	29.6853i	1.09645	+	1.09645i	0.994822	+	0.101628i	$0.0324051\pi$
$733$	29.6853	+	29.6853i	1.09645	+	1.09645i	0.101628	+	0.994822i	$0.467595\pi$
$734$	−11.5077	+	6.64398i	−0.424757	+	0.245234i
$735$		0			0
$736$			44.0907i			1.62521i
$737$	4.77844	+	1.28038i	0.176016	+	0.0471634i
$738$	20.9042	+	9.82489i	0.769494	+	0.361659i
$739$	16.6414	−	28.8238i	0.612164	−	1.06030i	−0.378711	−	0.925515i	$-0.623633\pi$
$739$	16.6414	−	28.8238i	0.612164	−	1.06030i	0.990875	−	0.134784i	$-0.0430340\pi$
$740$		0			0
$741$	3.51464	−	18.4575i	0.129114	−	0.678052i
$742$	−6.49413	−	6.49413i	−0.238407	−	0.238407i
$743$	0.258881	+	0.966155i	0.00949741	+	0.0354448i	0.970512	−	0.241053i	$-0.0774928\pi$
$743$	0.258881	+	0.966155i	0.00949741	+	0.0354448i	−0.961015	+	0.276498i	$0.910826\pi$
$744$	0.732292	−	8.22679i	0.0268471	−	0.301609i
$745$		0			0
$746$	56.3871			2.06448
$747$	−14.9176	−	21.4424i	−0.545808	−	0.784535i
$748$	0.684891	−	2.55605i	0.0250421	−	0.0934584i
$749$			5.04369i			0.184292i
$750$		0			0
$751$	−8.71518	+	15.0951i	−0.318022	+	0.550829i	−0.980075	−	0.198627i	$-0.936352\pi$
$751$	−8.71518	+	15.0951i	−0.318022	+	0.550829i	0.662054	+	0.749456i	$0.269685\pi$
$752$	−14.5786	+	3.90632i	−0.531626	+	0.142449i
$753$	−5.65456	−	2.06778i	−0.206063	−	0.0753542i
$754$	−6.20956	+	62.2731i	−0.226139	+	2.26785i
$755$		0			0
$756$	−4.18245	+	4.14466i	−0.152114	+	0.150740i
$757$	−15.6903	+	4.20419i	−0.570272	+	0.152804i	−0.532422	−	0.846479i	$-0.678718\pi$
$757$	−15.6903	+	4.20419i	−0.570272	+	0.152804i	−0.0378509	+	0.999283i	$0.512051\pi$
$758$	12.2523	−	45.7262i	0.445024	−	1.66085i
$759$	4.67501	−	2.17139i	0.169692	−	0.0788164i
$760$		0			0
$761$	−7.90134	−	13.6855i	−0.286423	−	0.496100i	0.686530	−	0.727101i	$-0.259133\pi$
$761$	−7.90134	−	13.6855i	−0.286423	−	0.496100i	−0.972953	+	0.231002i	$0.925800\pi$
$762$	−62.5730	−	22.8819i	−2.26678	−	0.828925i
$763$	5.69167	+	1.52508i	0.206052	+	0.0552116i
$764$	−6.09289	+	10.5532i	−0.220433	+	0.381801i
$765$		0			0
$766$	25.8276			0.933190
$767$	−5.61473	+	4.59652i	−0.202736	+	0.165971i
$768$	−0.285537	+	0.780830i	−0.0103034	+	0.0281758i
$769$	8.96855	−	15.5340i	0.323414	−	0.560170i	−0.657776	−	0.753214i	$-0.728503\pi$
$769$	8.96855	−	15.5340i	0.323414	−	0.560170i	0.981190	+	0.193044i	$0.0618360\pi$
$770$		0			0
$771$	3.97093	−	5.65286i	0.143010	−	0.203583i
$772$	30.3737	−	30.3737i	1.09317	−	1.09317i
$773$	−15.7622	−	4.22347i	−0.566927	−	0.151908i	−0.0360399	−	0.999350i	$-0.511474\pi$
$773$	−15.7622	−	4.22347i	−0.566927	−	0.151908i	−0.530887	+	0.847443i	$0.678141\pi$
$774$	8.32270	−	46.3795i	0.299153	−	1.66708i
$775$		0			0
$776$	21.6762	−	12.5147i	0.778129	−	0.449253i
$777$	4.12116	−	3.44746i	0.147846	−	0.123677i
$778$	39.1060	−	10.4784i	1.40202	−	0.375670i
$779$	−10.6721			−0.382367
$780$		0			0
$781$	−3.00602			−0.107564
$782$	23.2400	−	6.22713i	0.831059	−	0.222682i
$783$	0.188559	−	41.5507i	0.00673854	−	1.48490i
$784$	12.2416	−	7.06771i	0.437201	−	0.252418i
$785$		0			0
$786$	7.84214	−	11.1638i	0.279720	−	0.398198i
$787$	7.64525	+	2.04854i	0.272524	+	0.0730225i	0.392493	−	0.919755i	$-0.371613\pi$
$787$	7.64525	+	2.04854i	0.272524	+	0.0730225i	−0.119969	+	0.992778i	$0.538280\pi$
$788$	23.6011	−	23.6011i	0.840754	−	0.840754i
$789$	34.2319	+	24.0467i	1.21869	+	0.856084i
$790$		0			0
$791$	−0.703381	+	1.21829i	−0.0250093	+	0.0433174i
$792$	2.36298	−	0.199532i	0.0839648	−	0.00709007i
$793$	−24.6491	−	30.1093i	−0.875315	−	1.06921i
$794$	37.7598			1.34005
$795$		0			0
$796$	−30.5587	+	52.9292i	−1.08312	+	1.87603i
$797$	−6.26020	−	1.67742i	−0.221748	−	0.0594171i	0.146234	−	0.989250i	$-0.453285\pi$
$797$	−6.26020	−	1.67742i	−0.221748	−	0.0594171i	−0.367982	+	0.929833i	$0.619951\pi$
$798$	1.62356	−	4.43978i	0.0574733	−	0.157167i
$799$	6.94716	+	12.0328i	0.245773	+	0.425691i
$800$		0			0
$801$	23.4568	−	27.7835i	0.828804	−	0.981683i
$802$	2.95802	−	11.0395i	0.104451	−	0.389817i
$803$	−1.46987	+	0.393850i	−0.0518705	+	0.0138986i
$804$	−4.02406	+	45.2075i	−0.141918	+	1.59435i
$805$		0			0
$806$	−9.94729	−	22.0251i	−0.350378	−	0.775801i
$807$	−14.7594	+	40.3611i	−0.519556	+	1.42078i
$808$	13.0337	−	3.49236i	0.458523	−	0.122861i
$809$	−7.98528	+	13.8309i	−0.280748	+	0.486269i	−0.971569	−	0.236756i	$-0.923916\pi$
$809$	−7.98528	+	13.8309i	−0.280748	+	0.486269i	0.690821	+	0.723025i	$0.257249\pi$
$810$		0			0
$811$		−	8.00665i		−	0.281151i	−0.990070	−	0.140576i	$-0.955105\pi$
$811$		−	8.00665i		−	0.281151i	0.990070	−	0.140576i	$-0.0448953\pi$
$812$	−2.34531	+	8.75280i	−0.0823041	+	0.307163i
$813$	6.45278	+	36.9220i	0.226309	+	1.29491i
$814$	−8.24713			−0.289062
$815$		0			0
$816$	−6.81214	−	0.606369i	−0.238472	−	0.0212272i
$817$	5.63483	+	21.0295i	0.197138	+	0.735728i
$818$	15.2754	+	15.2754i	0.534092	+	0.534092i
$819$	−1.23602	+	4.34836i	−0.0431899	+	0.151944i
$820$		0			0
$821$	25.1045	−	43.4822i	0.876152	−	1.51754i	0.0206220	−	0.999787i	$-0.493435\pi$
$821$	25.1045	−	43.4822i	0.876152	−	1.51754i	0.855530	−	0.517753i	$-0.173231\pi$
$822$	11.1192	−	9.30151i	0.387828	−	0.324428i
$823$	−47.1413	−	12.6315i	−1.64324	−	0.440306i	−0.685534	−	0.728041i	$-0.740431\pi$
$823$	−47.1413	−	12.6315i	−1.64324	−	0.440306i	−0.957710	+	0.287735i	$0.907098\pi$
$824$		−	17.5593i		−	0.611706i
$825$		0			0
$826$	−1.58107	+	0.912833i	−0.0550126	+	0.0317615i
$827$	30.0940	+	30.0940i	1.04647	+	1.04647i	0.998866	+	0.0476050i	$0.0151589\pi$
$827$	30.0940	+	30.0940i	1.04647	+	1.04647i	0.0476050	+	0.998866i	$0.484841\pi$
$828$	27.0080	+	38.8208i	0.938591	+	1.34912i
$829$	9.32181	+	5.38195i	0.323760	+	0.186923i	0.653067	−	0.757300i	$-0.273482\pi$
$829$	9.32181	+	5.38195i	0.323760	+	0.186923i	−0.329307	+	0.944223i	$0.606815\pi$
$830$		0			0
$831$	0.698944	−	0.324637i	0.0242461	−	0.0112615i
$832$	7.18224	+	43.8325i	0.248999	+	1.51962i
$833$	−9.20153	−	9.20153i	−0.318814	−	0.318814i
$834$	−29.5121	−	2.62696i	−1.02192	−	0.0909642i
$835$		0			0
$836$	−3.61642	+	2.08794i	−0.125076	+	0.0722129i
$837$	7.95974	+	13.9323i	0.275129	+	0.481571i
$838$	9.74504	−	36.3690i	0.336637	−	1.25635i
$839$	−24.9640	+	14.4130i	−0.861854	+	0.497592i	−0.864633	−	0.502405i	$-0.832449\pi$
$839$	−24.9640	+	14.4130i	−0.861854	+	0.497592i	0.00277877	+	0.999996i	$0.499115\pi$
$840$		0			0
$841$	−17.4722	−	30.2628i	−0.602490	−	1.04354i
$842$	−5.59258	−	20.8718i	−0.192733	−	0.719289i
$843$	11.3483	+	13.5660i	0.390855	+	0.467237i
$844$		−	10.7937i		−	0.371536i
$845$		0			0
$846$	−30.6134	+	36.2603i	−1.05251	+	1.24666i
$847$	1.16151	+	4.33481i	0.0399099	+	0.148946i
$848$	20.2528	−	5.42671i	0.695482	−	0.186354i
$849$	−8.23852	+	11.7280i	−0.282745	+	0.402505i
$850$		0			0
$851$	−21.5767	−	37.3719i	−0.739639	−	1.28109i
$852$	−4.74790	−	27.1669i	−0.162660	−	0.930723i
$853$	−18.6086	−	18.6086i	−0.637146	−	0.637146i	0.312704	−	0.949851i	$-0.398765\pi$
$853$	−18.6086	−	18.6086i	−0.637146	−	0.637146i	−0.949851	+	0.312704i	$0.898765\pi$
$854$	−4.89512	−	8.47859i	−0.167507	−	0.290131i
$855$		0			0
$856$	16.1391	+	9.31793i	0.551624	+	0.318480i
$857$	4.26135	−	4.26135i	0.145565	−	0.145565i	−0.630569	−	0.776134i	$-0.717178\pi$
$857$	4.26135	−	4.26135i	0.145565	−	0.145565i	0.776134	+	0.630569i	$0.217178\pi$
$858$	5.73766	−	3.90208i	0.195881	−	0.133215i
$859$			29.4002i			1.00312i	0.865122	+	0.501561i	$0.167241\pi$
$859$			29.4002i			1.00312i	−0.865122	+	0.501561i	$0.832759\pi$
$860$		0			0
$861$	2.55756	+	0.227657i	0.0871615	+	0.00775852i
$862$	−7.08562	+	26.4439i	−0.241337	+	0.900683i
$863$	23.1832	−	23.1832i	0.789164	−	0.789164i	−0.192193	−	0.981357i	$-0.561560\pi$
$863$	23.1832	−	23.1832i	0.789164	−	0.789164i	0.981357	+	0.192193i	$0.0615601\pi$
$864$	−10.0263	−	38.1094i	−0.341100	−	1.29651i
$865$		0			0
$866$	−49.0756			−1.66766
$867$	−3.98527	−	22.8033i	−0.135347	−	0.774439i
$868$	−0.905684	−	3.38006i	−0.0307409	−	0.114727i
$869$	−6.38250	−	3.68494i	−0.216512	−	0.125003i
$870$		0			0
$871$	14.3422	+	31.7563i	0.485968	+	1.07602i
$872$	15.3951	−	15.3951i	0.521343	−	0.521343i
$873$	−20.6834	+	44.0077i	−0.700028	+	1.48943i
$874$	−32.8810	−	18.9839i	−1.11222	−	0.642139i
$875$		0			0
$876$	−5.88102	−	12.6619i	−0.198701	−	0.427805i
$877$	−43.6039	−	11.6836i	−1.47240	−	0.394529i	−0.568647	−	0.822582i	$-0.692533\pi$
$877$	−43.6039	−	11.6836i	−1.47240	−	0.394529i	−0.903754	+	0.428053i	$0.859200\pi$
$878$	24.9258	+	6.67885i	0.841205	+	0.225400i
$879$	−12.9389	−	27.8576i	−0.436419	−	0.939612i
$880$		0			0
$881$	12.6778	+	7.31952i	0.427125	+	0.246601i	0.698121	−	0.715980i	$-0.254020\pi$
$881$	12.6778	+	7.31952i	0.427125	+	0.246601i	−0.270996	+	0.962580i	$0.587353\pi$
$882$	18.9050	−	40.2237i	0.636564	−	1.35440i
$883$	−8.31854	+	8.31854i	−0.279941	+	0.279941i	−0.833086	−	0.553144i	$-0.813428\pi$
$883$	−8.31854	+	8.31854i	−0.279941	+	0.279941i	0.553144	+	0.833086i	$0.313428\pi$
$884$	16.9868	−	7.67183i	0.571329	−	0.258032i
$885$		0			0
$886$	−37.2706	−	21.5182i	−1.25213	−	0.722917i
$887$	−13.7391	−	51.2751i	−0.461314	−	1.72165i	−0.668829	−	0.743416i	$-0.733204\pi$
$887$	−13.7391	−	51.2751i	−0.461314	−	1.72165i	0.207515	−	0.978232i	$-0.433462\pi$
$888$	−3.41778	−	19.5561i	−0.114693	−	0.656261i
$889$	−7.40642			−0.248403
$890$		0			0
$891$	−3.54702	+	2.93992i	−0.118830	+	0.0984910i
$892$	−26.9031	+	26.9031i	−0.900782	+	0.900782i
$893$	5.67488	−	21.1789i	0.189903	−	0.708726i
$894$	−20.6555	−	1.83861i	−0.690824	−	0.0614924i
$895$		0			0
$896$			4.83633i			0.161571i
$897$	32.6935	+	15.7914i	1.09161	+	0.527258i
$898$	6.54654	−	6.54654i	0.218461	−	0.218461i
$899$	21.3850	+	12.3467i	0.713231	+	0.411784i
$900$		0			0
$901$	−9.65110	−	16.7162i	−0.321525	−	0.556897i
$902$	−2.78684	−	2.78684i	−0.0927918	−	0.0927918i
$903$	−0.901786	−	5.15991i	−0.0300096	−	0.171711i
$904$	2.59891	+	4.50145i	0.0864385	+	0.149716i
$905$		0			0
$906$	7.57228	−	10.7796i	0.251572	−	0.358128i
$907$	−16.3128	+	4.37099i	−0.541657	+	0.145136i	−0.519266	−	0.854613i	$-0.673794\pi$
$907$	−16.3128	+	4.37099i	−0.541657	+	0.145136i	−0.0223908	+	0.999749i	$0.507128\pi$
$908$	6.25027	+	23.3263i	0.207422	+	0.774111i
$909$	−16.9109	+	20.0303i	−0.560900	+	0.664362i
$910$		0			0
$911$			52.3968i			1.73598i	0.496579	+	0.867992i	$0.334589\pi$
$911$			52.3968i			1.73598i	−0.496579	+	0.867992i	$0.665411\pi$
$912$	6.92474	+	8.27798i	0.229301	+	0.274111i
$913$	1.15357	+	4.30517i	0.0381775	+	0.142480i
$914$	−28.2656	−	48.9575i	−0.934945	−	1.61937i
$915$		0			0
$916$	−32.6511	+	18.8511i	−1.07882	+	0.622858i
$917$	0.392528	−	1.46493i	0.0129624	−	0.0483764i
$918$	−18.6712	+	10.6671i	−0.616241	+	0.352068i
$919$	12.0636	−	6.96489i	0.397940	−	0.229751i	−0.287655	−	0.957734i	$-0.592876\pi$
$919$	12.0636	−	6.96489i	0.397940	−	0.229751i	0.685595	+	0.727983i	$0.259542\pi$
$920$		0			0
$921$	−44.0550	−	3.92147i	−1.45166	−	0.129217i
$922$	20.5197	+	20.5197i	0.675779	+	0.675779i
$923$	−13.4123	−	16.3834i	−0.441472	−	0.539266i
$924$	0.911214	−	0.423229i	0.0299767	−	0.0139232i
$925$		0			0
$926$	−10.0880	−	5.82433i	−0.331514	−	0.191400i
$927$	19.4819	+	28.0029i	0.639869	+	0.919737i
$928$	−42.8815	−	42.8815i	−1.40765	−	1.40765i
$929$	−0.125289	+	0.0723356i	−0.00411060	+	0.00237325i	−0.502054	−	0.864836i	$-0.667422\pi$
$929$	−0.125289	+	0.0723356i	−0.00411060	+	0.00237325i	0.497943	+	0.867210i	$0.334089\pi$
$930$		0			0
$931$			20.5352i			0.673013i
$932$	39.5848	+	10.6067i	1.29664	+	0.347434i
$933$	−34.4908	+	28.8524i	−1.12918	+	0.944585i
$934$	24.3501	−	42.1756i	0.796759	−	1.38003i
$935$		0			0
$936$	11.6307	+	11.9884i	0.380161	+	0.391854i
$937$	−35.9634	−	35.9634i	−1.17487	−	1.17487i	−0.981033	−	0.193841i	$-0.937905\pi$
$937$	−35.9634	−	35.9634i	−1.17487	−	1.17487i	−0.193841	−	0.981033i	$-0.562095\pi$
$938$	2.26904	+	8.46819i	0.0740869	+	0.276496i
$939$	−3.04925	−	0.271424i	−0.0995087	−	0.00885758i
$940$		0			0
$941$	−28.4119			−0.926201			−0.463101	−	0.886306i	$-0.653263\pi$
$941$	−28.4119			−0.926201			−0.463101	+	0.886306i	$0.653263\pi$
$942$	−1.16308	−	6.65498i	−0.0378951	−	0.216831i
$943$	5.33747	−	19.9197i	0.173812	−	0.648675i
$944$		−	4.16798i		−	0.135656i
$945$		0			0
$946$	−4.02006	+	6.96295i	−0.130704	+	0.226385i
$947$	−49.3529	+	13.2241i	−1.60375	+	0.429725i	−0.946174	−	0.323659i	$-0.895087\pi$
$947$	−49.3529	+	13.2241i	−1.60375	+	0.429725i	−0.657581	+	0.753384i	$0.728420\pi$
$948$	23.2217	−	63.5022i	0.754207	−	2.06246i
$949$	−8.70484	−	6.25377i	−0.282571	−	0.203006i
$950$		0			0
$951$	−2.75814	+	30.9858i	−0.0894390	+	1.00478i
$952$	1.18852	−	0.318462i	0.0385200	−	0.0103214i
$953$	−3.42531	+	12.7834i	−0.110957	+	0.414095i	−0.998953	−	0.0457555i	$-0.985430\pi$
$953$	−3.42531	+	12.7834i	−0.110957	+	0.414095i	0.887996	+	0.459851i	$0.152097\pi$
$954$	42.5286	−	50.3733i	1.37691	−	1.63090i
$955$		0			0
$956$	−2.90845	−	5.03758i	−0.0940659	−	0.162927i
$957$	−2.43495	+	6.65862i	−0.0787108	+	0.215243i
$958$	−42.0595	−	11.2698i	−1.35888	−	0.364111i
$959$	0.805764	−	1.39562i	0.0260195	−	0.0450671i
$960$		0			0
$961$	21.4642			0.692394
$962$	−36.7972	−	44.9485i	−1.18639	−	1.44920i
$963$	−36.0763	+	3.04632i	−1.16254	+	0.0981663i
$964$	7.04833	−	12.2081i	0.227011	−	0.393195i
$965$		0			0
$966$	7.47496	+	5.25089i	0.240503	+	0.168945i
$967$	11.1974	−	11.1974i	0.360084	−	0.360084i	−0.503760	−	0.863844i	$-0.668050\pi$
$967$	11.1974	−	11.1974i	0.360084	−	0.360084i	0.863844	+	0.503760i	$0.168050\pi$
$968$	16.0166	+	4.29165i	0.514794	+	0.137939i
$969$	5.71103	−	8.12999i	0.183465	−	0.261173i
$970$		0			0
$971$	−28.5582	+	16.4881i	−0.916478	+	0.529129i	−0.882510	−	0.470294i	$-0.844148\pi$
$971$	−28.5582	+	16.4881i	−0.916478	+	0.529129i	−0.0339681	+	0.999423i	$0.510814\pi$
$972$	−32.1719	−	27.4128i	−1.03192	−	0.879265i
$973$	−3.18145	+	0.852466i	−0.101993	+	0.0273288i
$974$	62.0152			1.98710
$975$		0			0
$976$	22.3510			0.715439
$977$	18.7761	−	5.03105i	0.600701	−	0.160957i	0.0543619	−	0.998521i	$-0.482688\pi$
$977$	18.7761	−	5.03105i	0.600701	−	0.160957i	0.546339	+	0.837564i	$0.316021\pi$
$978$	22.4971	−	18.8194i	0.719377	−	0.601777i
$979$	−5.37310	+	3.10216i	−0.171725	+	0.0991455i
$980$		0			0
$981$	−7.47084	+	41.6323i	−0.238526	+	1.32922i
$982$	−60.9079	−	16.3202i	−1.94365	−	0.520799i
$983$	−33.5020	+	33.5020i	−1.06855	+	1.06855i	−0.0710772	+	0.997471i	$0.522644\pi$
$983$	−33.5020	+	33.5020i	−1.06855	+	1.06855i	−0.997471	+	0.0710772i	$0.977356\pi$
$984$	5.45342	−	7.76328i	0.173849	−	0.247484i
$985$		0			0
$986$	−16.5462	+	28.6589i	−0.526939	+	0.912685i
$987$	−1.81177	+	4.95447i	−0.0576693	+	0.157702i
$988$	−27.5155	−	10.3942i	−0.875385	−	0.330683i
$989$	−42.0702			−1.33775
$990$		0			0
$991$	27.1809	−	47.0787i	0.863431	−	1.49551i	−0.00516644	−	0.999987i	$-0.501645\pi$
$991$	27.1809	−	47.0787i	0.863431	−	1.49551i	0.868597	−	0.495519i	$-0.165022\pi$
$992$	22.6207	+	6.06119i	0.718207	+	0.192443i
$993$	−14.5503	−	5.32082i	−0.461741	−	0.168851i
$994$	−2.66358	−	4.61346i	−0.0844837	−	0.146330i
$995$		0			0
$996$	−37.0860	+	17.2252i	−1.17511	+	0.545802i
$997$	4.05645	−	15.1389i	0.128469	−	0.479453i	−0.871471	−	0.490448i	$-0.836833\pi$
$997$	4.05645	−	15.1389i	0.128469	−	0.479453i	0.999940	+	0.0109949i	$0.00349985\pi$
$998$	−42.1184	+	11.2856i	−1.33323	+	0.357239i
$999$	27.1480	+	27.3955i	0.858924	+	0.866755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.407.21		96
3.2	odd	2	inner	975.2.bn.d.407.4		96
5.2	odd	4		195.2.bf.a.173.21	yes	96
5.3	odd	4	inner	975.2.bn.d.368.4		96
5.4	even	2		195.2.bf.a.17.4	✓	96
13.10	even	6	inner	975.2.bn.d.257.21		96
15.2	even	4		195.2.bf.a.173.4	yes	96
15.8	even	4	inner	975.2.bn.d.368.21		96
15.14	odd	2		195.2.bf.a.17.21	yes	96
39.23	odd	6	inner	975.2.bn.d.257.4		96
65.23	odd	12	inner	975.2.bn.d.218.4		96
65.49	even	6		195.2.bf.a.62.4	yes	96
65.62	odd	12		195.2.bf.a.23.21	yes	96
195.23	even	12	inner	975.2.bn.d.218.21		96
195.62	even	12		195.2.bf.a.23.4	yes	96
195.179	odd	6		195.2.bf.a.62.21	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.4	✓	96	5.4	even	2
195.2.bf.a.17.21	yes	96	15.14	odd	2
195.2.bf.a.23.4	yes	96	195.62	even	12
195.2.bf.a.23.21	yes	96	65.62	odd	12
195.2.bf.a.62.4	yes	96	65.49	even	6
195.2.bf.a.62.21	yes	96	195.179	odd	6
195.2.bf.a.173.4	yes	96	15.2	even	4
195.2.bf.a.173.21	yes	96	5.2	odd	4
975.2.bn.d.218.4		96	65.23	odd	12	inner
975.2.bn.d.218.21		96	195.23	even	12	inner
975.2.bn.d.257.4		96	39.23	odd	6	inner
975.2.bn.d.257.21		96	13.10	even	6	inner
975.2.bn.d.368.4		96	5.3	odd	4	inner
975.2.bn.d.368.21		96	15.8	even	4	inner
975.2.bn.d.407.4		96	3.2	odd	2	inner
975.2.bn.d.407.21		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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.09662 - 0.561788i) q^{2} +(1.11133 + 1.32851i) q^{3} +(2.34816 - 1.35571i) q^{4} +(3.07638 + 2.16105i) q^{6} +(0.403690 + 0.108168i) q^{7} +(1.09192 - 1.09192i) q^{8} +(-0.529880 + 2.95283i) q^{9} +(0.255945 - 0.443309i) q^{11} +(4.41067 + 1.61291i) q^{12} +(3.55810 - 0.583017i) q^{13} +0.907153 q^{14} +(-1.03551 + 1.79356i) q^{16} +(1.84160 + 0.493455i) q^{17} +(0.547908 + 6.48865i) q^{18} +(-1.50433 - 2.60558i) q^{19} +(0.304931 + 0.656518i) q^{21} +(0.287573 - 1.07324i) q^{22} +(5.61575 - 1.50474i) q^{23} +(2.66411 + 0.237141i) q^{24} +(7.13246 - 3.22126i) q^{26} +(-4.51174 + 2.57763i) q^{27} +(1.09458 - 0.293291i) q^{28} +(-3.99826 + 6.92519i) q^{29} -3.08801i q^{31} +(-1.96282 + 7.32533i) q^{32} +(0.873381 - 0.152639i) q^{33} +4.13835 q^{34} +(2.75895 + 7.65210i) q^{36} +(-1.92109 - 7.16959i) q^{37} +(-4.61780 - 4.61780i) q^{38} +(4.72878 + 4.07905i) q^{39} +(1.77356 - 3.07189i) q^{41} +(1.00815 + 1.20516i) q^{42} +(-6.98963 - 1.87287i) q^{43} -1.38795i q^{44} +(10.9288 - 6.30972i) q^{46} +(5.15313 + 5.15313i) q^{47} +(-3.53356 + 0.617552i) q^{48} +(-5.91091 - 3.41267i) q^{49} +(1.39107 + 2.99498i) q^{51} +(7.56460 - 6.19278i) q^{52} +(-7.15880 - 7.15880i) q^{53} +(-8.01134 + 7.93895i) q^{54} +(0.558908 - 0.322686i) q^{56} +(1.78973 - 4.89419i) q^{57} +(-4.49235 + 16.7657i) q^{58} +(-1.74290 + 1.00626i) q^{59} +(-5.39613 - 9.34638i) q^{61} +(-1.73481 - 6.47438i) q^{62} +(-0.533311 + 1.13471i) q^{63} +12.3191i q^{64} +(1.74540 - 0.810680i) q^{66} +(2.50128 + 9.33491i) q^{67} +(4.99336 - 1.33797i) q^{68} +(8.24002 + 5.78832i) q^{69} +(-2.93620 - 5.08564i) q^{71} +(2.64567 + 3.80284i) q^{72} +(-2.10205 - 2.10205i) q^{73} +(-8.05558 - 13.9527i) q^{74} +(-7.06484 - 4.07889i) q^{76} +(0.151274 - 0.151274i) q^{77} +(12.2060 + 5.89565i) q^{78} -14.3974i q^{79} +(-8.43845 - 3.12930i) q^{81} +(1.99273 - 7.43696i) q^{82} +(-6.15680 + 6.15680i) q^{83} +(1.60608 + 1.12821i) q^{84} -15.7068 q^{86} +(-13.6436 + 2.38446i) q^{87} +(-0.204587 - 0.763529i) q^{88} +(-10.4966 - 6.06022i) q^{89} +(1.49943 + 0.149516i) q^{91} +(11.1467 - 11.1467i) q^{92} +(4.10245 - 3.43180i) q^{93} +(13.6991 + 7.90919i) q^{94} +(-11.9131 + 5.53326i) q^{96} +(15.6563 + 4.19510i) q^{97} +(-14.3101 - 3.83439i) q^{98} +(1.17340 + 0.990663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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