LMFDB - Embedded newform 975.2.bn.d.368.21

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			368.21
Character	$\chi$	$=$	975.368
Dual form			975.2.bn.d.257.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.561788 + 2.09662i) q^{2} +(-1.70619 - 0.298187i) q^{3} +(-2.34816 + 1.35571i) q^{4} +(-0.333332 - 3.74475i) q^{6} +(0.108168 - 0.403690i) q^{7} +(-1.09192 - 1.09192i) q^{8} +(2.82217 + 1.01753i) q^{9} +(-0.255945 + 0.443309i) q^{11} +(4.41067 - 1.61291i) q^{12} +(0.583017 + 3.55810i) q^{13} +0.907153 q^{14} +(-1.03551 + 1.79356i) q^{16} +(-0.493455 + 1.84160i) q^{17} +(-0.547908 + 6.48865i) q^{18} +(1.50433 + 2.60558i) q^{19} +(-0.304931 + 0.656518i) q^{21} +(-1.07324 - 0.287573i) q^{22} +(-1.50474 - 5.61575i) q^{23} +(1.53743 + 2.18862i) q^{24} +(-7.13246 + 3.22126i) q^{26} +(-4.51174 - 2.57763i) q^{27} +(0.293291 + 1.09458i) q^{28} +(-3.99826 + 6.92519i) q^{29} -3.08801i q^{31} +(-7.32533 - 1.96282i) q^{32} +(0.568879 - 0.680051i) q^{33} -4.13835 q^{34} +(-8.00639 + 1.43673i) q^{36} +(-7.16959 + 1.92109i) q^{37} +(-4.61780 + 4.61780i) q^{38} +(0.0662412 - 6.24465i) q^{39} +(-1.77356 + 3.07189i) q^{41} +(-1.54778 - 0.270501i) q^{42} +(1.87287 - 6.98963i) q^{43} -1.38795i q^{44} +(10.9288 - 6.30972i) q^{46} +(-5.15313 + 5.15313i) q^{47} +(2.30160 - 2.75138i) q^{48} +(5.91091 + 3.41267i) q^{49} +(1.39107 - 2.99498i) q^{51} +(-6.19278 - 7.56460i) q^{52} +(-7.15880 + 7.15880i) q^{53} +(2.86967 - 10.9075i) q^{54} +(-0.558908 + 0.322686i) q^{56} +(-1.78973 - 4.89419i) q^{57} +(-16.7657 - 4.49235i) q^{58} +(-1.74290 + 1.00626i) q^{59} +(-5.39613 - 9.34638i) q^{61} +(6.47438 - 1.73481i) q^{62} +(0.716035 - 1.02922i) q^{63} -12.3191i q^{64} +(1.74540 + 0.810680i) q^{66} +(9.33491 - 2.50128i) q^{67} +(-1.33797 - 4.99336i) q^{68} +(0.892822 + 10.0302i) q^{69} +(2.93620 + 5.08564i) q^{71} +(-1.97052 - 4.19264i) 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} +(13.1299 - 3.36928i) q^{78} +14.3974i q^{79} +(6.92928 + 5.74327i) q^{81} +(-7.43696 - 1.99273i) q^{82} +(6.15680 + 6.15680i) q^{83} +(-0.174021 - 1.95501i) q^{84} +15.7068 q^{86} +(8.88680 - 10.6235i) q^{87} +(0.763529 - 0.204587i) q^{88} +(-10.4966 - 6.06022i) q^{89} +(1.49943 + 0.149516i) q^{91} +(11.1467 + 11.1467i) q^{92} +(-0.920803 + 5.26873i) q^{93} +(-13.6991 - 7.90919i) q^{94} +(11.9131 + 5.53326i) q^{96} +(4.19510 - 15.6563i) q^{97} +(-3.83439 + 14.3101i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.561788	+	2.09662i	0.397244	+	1.48253i	0.817924	+	0.575326i	$0.195125\pi$
$2$	0.561788	+	2.09662i	0.397244	+	1.48253i	−0.420680	+	0.907209i	$0.638209\pi$
$3$	−1.70619	−	0.298187i	−0.985069	−	0.172158i
$3$	−1.70619	−	0.298187i	−0.985069	−	0.172158i
$4$	−2.34816	+	1.35571i	−1.17408	+	0.677856i
$5$		0			0
$5$		0			0
$6$	−0.333332	−	3.74475i	−0.136082	−	1.52879i
$7$	0.108168	−	0.403690i	0.0408838	−	0.152581i	−0.942466	−	0.334301i	$-0.891500\pi$
$7$	0.108168	−	0.403690i	0.0408838	−	0.152581i	0.983350	+	0.181720i	$0.0581665\pi$
$8$	−1.09192	−	1.09192i	−0.386052	−	0.386052i
$9$	2.82217	+	1.01753i	0.940723	+	0.339176i
$10$		0			0
$11$	−0.255945	+	0.443309i	−0.0771702	+	0.133663i	−0.902028	−	0.431678i	$-0.857922\pi$
$11$	−0.255945	+	0.443309i	−0.0771702	+	0.133663i	0.824858	+	0.565340i	$0.191255\pi$
$12$	4.41067	−	1.61291i	1.27325	−	0.465608i
$13$	0.583017	+	3.55810i	0.161700	+	0.986840i
$13$	0.583017	+	3.55810i	0.161700	+	0.986840i
$14$	0.907153			0.242447
$15$		0			0
$16$	−1.03551	+	1.79356i	−0.258878	+	0.448390i
$17$	−0.493455	+	1.84160i	−0.119680	+	0.446653i	−0.999594	−	0.0284797i	$-0.990933\pi$
$17$	−0.493455	+	1.84160i	−0.119680	+	0.446653i	0.879914	+	0.475133i	$0.157600\pi$
$18$	−0.547908	+	6.48865i	−0.129143	+	1.52939i
$19$	1.50433	+	2.60558i	0.345118	+	0.597762i	0.985375	−	0.170399i	$-0.0545056\pi$
$19$	1.50433	+	2.60558i	0.345118	+	0.597762i	−0.640257	+	0.768161i	$0.721172\pi$
$20$		0			0
$21$	−0.304931	+	0.656518i	−0.0665414	+	0.143264i
$22$	−1.07324	−	0.287573i	−0.228815	−	0.0613108i
$23$	−1.50474	−	5.61575i	−0.313759	−	1.17097i	−0.925139	−	0.379628i	$-0.876052\pi$
$23$	−1.50474	−	5.61575i	−0.313759	−	1.17097i	0.611380	−	0.791337i	$-0.290615\pi$
$24$	1.53743	+	2.18862i	0.313826	+	0.446750i
$25$		0			0
$26$	−7.13246	+	3.22126i	−1.39879	+	0.631742i
$27$	−4.51174	−	2.57763i	−0.868285	−	0.496065i
$28$	0.293291	+	1.09458i	0.0554267	+	0.206855i
$29$	−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	$-0.0894433\pi$
$32$	−7.32533	−	1.96282i	−1.29495	−	0.346980i
$33$	0.568879	−	0.680051i	0.0990292	−	0.118382i
$34$	−4.13835			−0.709722
$35$		0			0
$36$	−8.00639	+	1.43673i	−1.33440	+	0.239455i
$37$	−7.16959	+	1.92109i	−1.17867	+	0.315825i	−0.794400	−	0.607395i	$-0.792215\pi$
$37$	−7.16959	+	1.92109i	−1.17867	+	0.315825i	−0.384273	+	0.923219i	$0.625548\pi$
$38$	−4.61780	+	4.61780i	−0.749107	+	0.749107i
$39$	0.0662412	−	6.24465i	0.0106071	−	0.999944i
$40$		0			0
$41$	−1.77356	+	3.07189i	−0.276983	+	0.479749i	−0.970634	−	0.240563i	$-0.922668\pi$
$41$	−1.77356	+	3.07189i	−0.276983	+	0.479749i	0.693650	+	0.720312i	$0.256001\pi$
$42$	−1.54778	−	0.270501i	−0.238827	−	0.0417392i
$43$	1.87287	−	6.98963i	0.285609	−	1.06591i	−0.662783	−	0.748811i	$-0.730625\pi$
$43$	1.87287	−	6.98963i	0.285609	−	1.06591i	0.948393	−	0.317098i	$-0.102708\pi$
$44$		−	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	$-0.928373\pi$
$47$	−5.15313	+	5.15313i	−0.751661	+	0.751661i	0.223128	+	0.974789i	$0.428373\pi$
$48$	2.30160	−	2.75138i	0.332207	−	0.397127i
$49$	5.91091	+	3.41267i	0.844416	+	0.487524i
$50$		0			0
$51$	1.39107	−	2.99498i	0.194789	−	0.419381i
$52$	−6.19278	−	7.56460i	−0.858785	−	1.04902i
$53$	−7.15880	+	7.15880i	−0.983337	+	0.983337i	−0.999863	−	0.0165265i	$-0.994739\pi$
$53$	−7.15880	+	7.15880i	−0.983337	+	0.983337i	0.0165265	+	0.999863i	$0.494739\pi$
$54$	2.86967	−	10.9075i	0.390512	−	1.48432i
$55$		0			0
$56$	−0.558908	+	0.322686i	−0.0746872	+	0.0431207i
$57$	−1.78973	−	4.89419i	−0.237055	−	0.648252i
$58$	−16.7657	−	4.49235i	−2.20144	−	0.589875i
$59$	−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	$-0.409454\pi$
$62$	6.47438	−	1.73481i	0.822247	−	0.220320i
$63$	0.716035	−	1.02922i	0.0902120	−	0.129669i
$64$		−	12.3191i		−	1.53988i
$65$		0			0
$66$	1.74540	+	0.810680i	0.214844	+	0.0997879i
$67$	9.33491	−	2.50128i	1.14044	−	0.305580i	0.361312	−	0.932445i	$-0.382329\pi$
$67$	9.33491	−	2.50128i	1.14044	−	0.305580i	0.779128	+	0.626865i	$0.215662\pi$
$68$	−1.33797	−	4.99336i	−0.162252	−	0.605534i
$69$	0.892822	+	10.0302i	0.107483	+	1.20750i
$70$		0			0
$71$	2.93620	+	5.08564i	0.348463	+	0.603555i	0.985977	−	0.166884i	$-0.0533705\pi$
$71$	2.93620	+	5.08564i	0.348463	+	0.603555i	−0.637514	+	0.770439i	$0.720037\pi$
$72$	−1.97052	−	4.19264i	−0.232228	−	0.494107i
$73$	2.10205	−	2.10205i	0.246026	−	0.246026i	−0.573311	−	0.819338i	$-0.694341\pi$
$73$	2.10205	−	2.10205i	0.246026	−	0.246026i	0.819338	+	0.573311i	$0.194341\pi$
$74$	−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
$78$	13.1299	−	3.36928i	1.48667	−	0.381496i
$79$			14.3974i			1.61983i	0.586544	+	0.809917i	$0.300488\pi$
$79$			14.3974i			1.61983i	−0.586544	+	0.809917i	$0.699512\pi$
$80$		0			0
$81$	6.92928	+	5.74327i	0.769920	+	0.638141i
$82$	−7.43696	−	1.99273i	−0.821274	−	0.220060i
$83$	6.15680	+	6.15680i	0.675796	+	0.675796i	0.959046	−	0.283250i	$-0.0914125\pi$
$83$	6.15680	+	6.15680i	0.675796	+	0.675796i	−0.283250	+	0.959046i	$0.591413\pi$
$84$	−0.174021	−	1.95501i	−0.0189873	−	0.213309i
$85$		0			0
$86$	15.7068			1.69370
$87$	8.88680	−	10.6235i	0.952765	−	1.13896i
$88$	0.763529	−	0.204587i	0.0813924	−	0.0218090i
$89$	−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
$93$	−0.920803	+	5.26873i	−0.0954829	+	0.546342i
$94$	−13.6991	−	7.90919i	−1.41296	−	0.815771i
$95$		0			0
$96$	11.9131	+	5.53326i	1.21588	+	0.564735i
$97$	4.19510	−	15.6563i	0.425948	−	1.58966i	−0.335895	−	0.941899i	$-0.609039\pi$
$97$	4.19510	−	15.6563i	0.425948	−	1.58966i	0.761843	−	0.647761i	$-0.224295\pi$
$98$	−3.83439	+	14.3101i	−0.387332	+	1.44554i
$99$	−1.17340	+	0.990663i	−0.117931	+	0.0995654i
$100$		0			0
$101$	−7.56743	−	4.36906i	−0.752987	−	0.434737i	0.0737851	−	0.997274i	$-0.476492\pi$
$101$	−7.56743	−	4.36906i	−0.752987	−	0.434737i	−0.826772	+	0.562537i	$0.809825\pi$
$102$	7.06082	+	1.23400i	0.699125	+	0.122184i
$103$	8.04055	+	8.04055i	0.792259	+	0.792259i	0.981861	−	0.189602i	$-0.0607197\pi$
$103$	8.04055	+	8.04055i	0.792259	+	0.792259i	−0.189602	+	0.981861i	$0.560720\pi$
$104$	3.24855	−	4.52177i	0.318547	−	0.443396i
$105$		0			0
$106$	−19.0310	−	10.9876i	−1.84846	−	1.06721i
$107$	−11.6570	+	3.12349i	−1.12693	+	0.301959i	−0.773683	−	0.633572i	$-0.781588\pi$
$107$	−11.6570	+	3.12349i	−1.12693	+	0.301959i	−0.353243	+	0.935531i	$0.614921\pi$
$108$	14.0888	−	0.0639357i	1.35570	−	0.00615221i
$109$	−14.0991			−1.35045			−0.675225	−	0.737612i	$-0.735953\pi$
$109$	−14.0991			−1.35045			−0.675225	+	0.737612i	$0.735953\pi$
$110$		0			0
$111$	12.8055	−	1.13986i	1.21545	−	0.108191i
$112$	0.612032	+	0.612032i	0.0578316	+	0.0578316i
$113$	3.25132	+	0.871189i	0.305859	+	0.0819545i	0.408484	−	0.912766i	$-0.366058\pi$
$113$	3.25132	+	0.871189i	0.305859	+	0.0819545i	−0.102625	+	0.994720i	$0.532724\pi$
$114$	9.25582	−	6.50188i	0.866887	−	0.608957i
$115$		0			0
$116$		−	21.6820i		−	2.01312i
$117$	−1.97509	+	10.6348i	−0.182597	+	0.983188i
$118$	−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
$123$	3.94202	−	4.71238i	0.355440	−	0.424901i
$124$	4.18645	+	7.25114i	0.375954	+	0.651172i
$125$		0			0
$126$	2.56014	+	0.923053i	0.228075	+	0.0822321i
$127$	4.58670	+	17.1178i	0.407003	+	1.51896i	0.800330	+	0.599559i	$0.204657\pi$
$127$	4.58670	+	17.1178i	0.407003	+	1.51896i	−0.393327	+	0.919399i	$0.628676\pi$
$128$	11.1778	−	2.99508i	0.987986	−	0.264730i
$129$	−5.27968	+	11.3672i	−0.464850	+	1.00082i
$130$		0			0
$131$			3.62886i			0.317055i	0.987355	+	0.158527i	$0.0506746\pi$
$131$			3.62886i			0.317055i	−0.987355	+	0.158527i	$0.949325\pi$
$132$	−0.413869	+	2.36811i	−0.0360226	+	0.206117i
$133$	1.21457	−	0.325443i	0.105317	−	0.0282195i
$134$	10.4885	+	18.1666i	0.906066	+	1.56935i
$135$		0			0
$136$	2.54969	−	1.47206i	0.218634	−	0.126228i
$137$	3.72458	+	0.997998i	0.318212	+	0.0852647i	0.414390	−	0.910099i	$-0.363995\pi$
$137$	3.72458	+	0.997998i	0.318212	+	0.0852647i	−0.0961776	+	0.995364i	$0.530662\pi$
$138$	−20.5280	+	7.50677i	−1.74746	+	0.639019i
$139$	6.82507	−	3.94046i	0.578895	−	0.334225i	−0.181799	−	0.983336i	$-0.558192\pi$
$139$	6.82507	−	3.94046i	0.578895	−	0.334225i	0.760694	+	0.649110i	$0.224859\pi$
$140$		0			0
$141$	10.3288	−	7.25562i	0.869843	−	0.611034i
$142$	−9.01315	+	9.01315i	−0.756367	+	0.756367i
$143$	−1.72656	−	0.652221i	−0.144382	−	0.0545414i
$144$	−4.74738	+	4.00807i	−0.395615	+	0.334005i
$145$		0			0
$146$	5.58811	+	3.22629i	0.462475	+	0.267010i
$147$	−9.06753	−	7.58522i	−0.747877	−	0.625618i
$148$	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	$-0.0455382\pi$
$152$	1.20247	−	4.48770i	0.0975336	−	0.364000i
$153$	−3.26649	+	4.69520i	−0.264080	+	0.379584i
$154$	−0.232181	+	0.402149i	−0.0187097	+	0.0324061i
$155$		0			0
$156$	8.31040	+	14.7533i	0.665365	+	1.18121i
$157$	−1.27066	+	1.27066i	−0.101409	+	0.101409i	−0.755991	−	0.654582i	$-0.772845\pi$
$157$	−1.27066	+	1.27066i	−0.101409	+	0.101409i	0.654582	+	0.755991i	$0.272845\pi$
$158$	−30.1859	+	8.08829i	−2.40146	+	0.643470i
$159$	14.3489	−	10.0796i	1.13794	−	0.799365i
$160$		0			0
$161$	−2.42979			−0.191494
$162$	−8.14867	+	17.7546i	−0.640220	+	1.39493i
$163$	7.53579	+	2.01921i	0.590249	+	0.158157i	0.541567	−	0.840658i	$-0.317831\pi$
$163$	7.53579	+	2.01921i	0.590249	+	0.158157i	0.0486817	+	0.998814i	$0.484498\pi$
$164$		−	9.61774i		−	0.751019i
$165$		0			0
$166$	−9.44966	+	16.3673i	−0.733436	+	1.27035i
$167$	0.590226	+	2.20275i	0.0456731	+	0.170454i	0.984995	−	0.172583i	$-0.0552111\pi$
$167$	0.590226	+	2.20275i	0.0456731	+	0.170454i	−0.939322	+	0.343037i	$0.888544\pi$
$168$	1.04982	−	0.383904i	0.0809957	−	0.0296188i
$169$	−12.3202	+	4.14887i	−0.947706	+	0.319144i
$170$		0			0
$171$	1.59423	+	8.88410i	0.121914	+	0.679384i
$172$	5.07814	+	18.9519i	0.387204	+	1.44507i
$173$	21.8789	+	5.86243i	1.66342	+	0.445713i	0.963326	−	0.268335i	$-0.0864736\pi$
$173$	21.8789	+	5.86243i	1.66342	+	0.445713i	0.700097	+	0.714048i	$0.253140\pi$
$174$	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
$178$	6.80911	−	25.4120i	0.510365	−	1.90471i
$179$	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	$0.482155\pi$
$182$	0.528886	+	3.22774i	0.0392036	+	0.239256i
$183$	6.41986	+	17.5557i	0.474570	+	1.29776i
$184$	−4.48890	+	7.77499i	−0.330926	+	0.573180i
$185$		0			0
$186$	−11.5638	+	1.02933i	−0.847900	+	0.0754743i
$187$	−0.690101	−	0.690101i	−0.0504652	−	0.0504652i
$188$	5.11423	−	19.0865i	0.372993	−	1.39203i
$189$	−1.52859	+	1.54253i	−0.111189	+	0.112202i
$190$		0			0
$191$	3.89212	−	2.24712i	0.281624	−	0.162596i	−0.352534	−	0.935799i	$-0.614680\pi$
$191$	3.89212	−	2.24712i	0.281624	−	0.162596i	0.634158	+	0.773203i	$0.281347\pi$
$192$	−3.67339	+	21.0187i	−0.265104	+	1.51689i
$193$	4.10026	+	15.3024i	0.295143	+	1.10149i	0.941104	+	0.338118i	$0.109790\pi$
$193$	4.10026	+	15.3024i	0.295143	+	1.10149i	−0.645960	+	0.763371i	$0.723543\pi$
$194$	35.1822			2.52593
$195$		0			0
$196$	−18.5064			−1.32188
$197$	3.18600	+	11.8903i	0.226993	+	0.847150i	0.981596	+	0.190968i	$0.0611628\pi$
$197$	3.18600	+	11.8903i	0.226993	+	0.847150i	−0.754603	+	0.656181i	$0.772171\pi$
$198$	−2.73625	−	1.90363i	−0.194457	−	0.135285i
$199$	19.5208	−	11.2703i	1.38379	−	0.798933i	0.391187	−	0.920311i	$-0.372065\pi$
$199$	19.5208	−	11.2703i	1.38379	−	0.798933i	0.992606	+	0.121378i	$0.0387313\pi$
$200$		0			0
$201$	−16.6730	+	1.48411i	−1.17602	+	0.104681i
$202$	4.90897	−	18.3205i	0.345394	−	1.28903i
$203$	2.36315	+	2.36315i	0.165860	+	0.165860i
$204$	0.793871	+	8.91858i	0.0555821	+	0.624426i
$205$		0			0
$206$	−12.3409	+	21.3751i	−0.859832	+	1.48927i
$207$	1.46756	−	17.3797i	0.102002	−	1.20797i
$208$	−6.98539	−	2.63878i	−0.484349	−	0.182967i
$209$	−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	$0.122912\pi$
$212$	7.10476	−	26.5153i	0.487957	−	1.82108i
$213$	−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
$217$	−1.24660	−	0.334025i	−0.0846246	−	0.0226751i
$218$	−7.92071	−	29.5605i	−0.536458	−	2.00209i
$219$	−4.21330	+	2.95969i	−0.284708	+	0.199997i
$220$		0			0
$221$	−6.84029	−	0.682079i	−0.460128	−	0.0458816i
$222$	9.58384	+	26.2080i	0.643225	+	1.75896i
$223$	−3.63175	−	13.5539i	−0.243200	−	0.907635i	−0.974280	−	0.225342i	$-0.927650\pi$
$223$	−3.63175	−	13.5539i	−0.243200	−	0.907635i	0.731080	−	0.682292i	$-0.239017\pi$
$224$	−1.58474	+	2.74485i	−0.105885	+	0.183398i
$225$		0			0
$226$			7.30621i			0.486002i
$227$	−8.60297	−	2.30516i	−0.570999	−	0.152999i	−0.0382445	−	0.999268i	$-0.512177\pi$
$227$	−8.60297	−	2.30516i	−0.570999	−	0.152999i	−0.532755	+	0.846270i	$0.678843\pi$
$228$	10.8377	+	9.06600i	0.717744	+	0.600411i
$229$	13.9049			0.918865			0.459432	−	0.888213i	$-0.348053\pi$
$229$	13.9049			0.918865			0.459432	+	0.888213i	$0.348053\pi$
$230$		0			0
$231$	−0.212995	−	0.303211i	−0.0140140	−	0.0199498i
$232$	11.9275	−	3.19597i	0.783081	−	0.209826i
$233$	10.6874	−	10.6874i	0.700154	−	0.700154i	−0.264289	−	0.964443i	$-0.585137\pi$
$233$	10.6874	−	10.6874i	0.700154	−	0.700154i	0.964443	+	0.264289i	$0.0851374\pi$
$234$	−23.4067	+	1.83348i	−1.53015	+	0.119859i
$235$		0			0
$236$	2.72840	−	4.72573i	0.177604	−	0.307619i
$237$	4.29312	−	24.5647i	0.278868	−	1.59565i
$238$	−0.447639	+	1.67061i	−0.0290161	+	0.108290i
$239$		−	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
$243$	−10.1101	−	11.8653i	−0.648563	−	0.761161i
$244$	25.3420	+	14.6312i	1.62236	+	0.936667i
$245$		0			0
$246$	12.0947	+	5.61757i	0.771127	+	0.358163i
$247$	−8.39388	+	6.87167i	−0.534090	+	0.437234i
$248$	−3.37185	+	3.37185i	−0.214113	+	0.214113i
$249$	−8.66879	−	12.3405i	−0.549362	−	0.782050i
$250$		0			0
$251$	3.01039	−	1.73805i	0.190014	−	0.109705i	−0.401975	−	0.915651i	$-0.631676\pi$
$251$	3.01039	−	1.73805i	0.190014	−	0.109705i	0.591989	+	0.805946i	$0.298343\pi$
$252$	−0.286045	+	3.38751i	−0.0180191	+	0.213393i
$253$	2.87464	+	0.770259i	0.180727	+	0.0484257i
$254$	−33.3128	+	19.2331i	−2.09023	+	1.20679i
$255$		0			0
$256$	0.240005	+	0.415700i	0.0150003	+	0.0259813i
$257$	3.85254	−	1.03229i	0.240315	−	0.0643922i	−0.136651	−	0.990619i	$-0.543634\pi$
$257$	3.85254	−	1.03229i	0.240315	−	0.0643922i	0.376966	+	0.926227i	$0.376967\pi$
$258$	−26.7987	−	4.68355i	−1.66842	−	0.291585i
$259$			3.10209i			0.192755i
$260$		0			0
$261$	−18.3303	+	15.4757i	−1.13462	+	0.957924i
$262$	−7.60834	+	2.03865i	−0.470045	+	0.125948i
$263$	−6.25119	−	23.3298i	−0.385465	−	1.43857i	−0.837433	−	0.546540i	$-0.815945\pi$
$263$	−6.25119	−	23.3298i	−0.385465	−	1.43857i	0.451968	−	0.892034i	$-0.350722\pi$
$264$	−1.36373	+	0.121390i	−0.0839318	+	0.00747103i
$265$		0			0
$266$	1.36466	+	2.36366i	0.0836727	+	0.144925i
$267$	16.1021	+	13.4698i	0.985434	+	0.824340i
$268$	−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
$273$	−2.51374	−	0.702215i	−0.152138	−	0.0425000i
$274$			8.36970i			0.505632i
$275$		0			0
$276$	−15.6946	−	22.3422i	−0.944704	−	1.34484i
$277$	−0.429778	−	0.115159i	−0.0258228	−	0.00691921i	0.245885	−	0.969299i	$-0.420922\pi$
$277$	−0.429778	−	0.115159i	−0.0258228	−	0.00691921i	−0.271707	+	0.962380i	$0.587588\pi$
$278$	12.0959	+	12.0959i	0.725463	+	0.725463i
$279$	3.14213	−	8.71488i	0.188114	−	0.521746i
$280$		0			0
$281$	−10.2114			−0.609162			−0.304581	−	0.952486i	$-0.598516\pi$
$281$	−10.2114			−0.609162			−0.304581	+	0.952486i	$0.598516\pi$
$282$	21.0149	+	17.5795i	1.25142	+	1.04684i
$283$	−7.99290	+	2.14169i	−0.475129	+	0.127310i	−0.488433	−	0.872601i	$-0.662432\pi$
$283$	−7.99290	+	2.14169i	−0.475129	+	0.127310i	0.0133048	+	0.999911i	$0.495765\pi$
$284$	−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
$288$	−18.6761	−	12.9931i	−1.10050	−	0.765627i
$289$	11.5744	+	6.68251i	0.680850	+	0.393089i
$290$		0			0
$291$	−11.8262	+	25.4618i	−0.693262	+	1.49260i
$292$	−2.08618	+	7.78573i	−0.122084	+	0.455625i
$293$	−4.58984	+	17.1295i	−0.268141	+	1.00072i	0.692159	+	0.721745i	$0.256660\pi$
$293$	−4.58984	+	17.1295i	−0.268141	+	1.00072i	−0.960300	+	0.278971i	$0.910007\pi$
$294$	10.8093	−	23.2725i	0.630411	−	1.35728i
$295$		0			0
$296$	9.92628	+	5.73094i	0.576953	+	0.333104i
$297$	2.29744	−	1.34037i	0.133311	−	0.0777760i
$298$	−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
$302$	7.34652	−	1.96850i	0.422745	−	0.113274i
$303$	11.6087	+	9.71095i	0.666901	+	0.557879i
$304$	−6.23102			−0.357374
$305$		0			0
$306$	−11.6791	−	4.21089i	−0.667651	−	0.240720i
$307$	18.0565	+	18.0565i	1.03054	+	1.03054i	0.999519	+	0.0310201i	$0.00987558\pi$
$307$	18.0565	+	18.0565i	1.03054	+	1.03054i	0.0310201	+	0.999519i	$0.490124\pi$
$308$	−0.560302	−	0.150132i	−0.0319262	−	0.00855459i
$309$	−11.3211	−	16.1163i	−0.644036	−	0.916824i
$310$		0			0
$311$		−	25.9620i		−	1.47217i	−0.676890	−	0.736084i	$-0.736673\pi$
$311$		−	25.9620i		−	1.47217i	0.676890	−	0.736084i	$-0.263327\pi$
$312$	−6.89098	+	6.74632i	−0.390125	+	0.381935i
$313$	−1.24977	−	1.24977i	−0.0706415	−	0.0706415i	0.670903	−	0.741545i	$-0.265907\pi$
$313$	−1.24977	−	1.24977i	−0.0706415	−	0.0706415i	−0.741545	+	0.670903i	$0.765907\pi$
$314$	−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	$-0.918278\pi$
$317$	−12.6999	+	12.6999i	−0.713299	+	0.713299i	0.253925	+	0.967224i	$0.418278\pi$
$318$	29.1942	+	24.4217i	1.63713	+	1.36950i
$319$	−2.04667	−	3.54493i	−0.114591	−	0.198478i
$320$		0			0
$321$	20.8205	−	1.85330i	1.16209	−	0.103441i
$322$	−1.36503	−	5.09435i	−0.0760699	−	0.283897i
$323$	−5.54076	+	1.48464i	−0.308296	+	0.0826077i
$324$	−24.0573	−	4.09202i	−1.33652	−	0.227334i
$325$		0			0
$326$			16.9341i			0.937891i
$327$	24.0558	+	4.20417i	1.33029	+	0.232491i
$328$	5.29084	−	1.41768i	0.292138	−	0.0782780i
$329$	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	$0.412391\pi$
$332$	−22.8040	−	6.11032i	−1.25153	−	0.335347i
$333$	−22.1885	−	1.87362i	−1.21592	−	0.102674i
$334$	−4.28676	+	2.47496i	−0.234561	+	0.135424i
$335$		0			0
$336$	−0.861744	−	1.22674i	−0.0470120	−	0.0669244i
$337$	−1.08661	+	1.08661i	−0.0591915	+	0.0591915i	−0.736083	−	0.676891i	$-0.763327\pi$
$337$	−1.08661	+	1.08661i	−0.0591915	+	0.0591915i	0.676891	+	0.736083i	$0.263327\pi$
$338$	−15.6199	−	23.5000i	−0.849613	−	1.27823i
$339$	−5.28759	−	2.45591i	−0.287183	−	0.133387i
$340$		0			0
$341$	1.36894	+	0.790359i	0.0741324	+	0.0428004i
$342$	−17.7310	+	8.33348i	−0.958781	+	0.450623i
$343$	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
$347$	9.20824	−	34.3656i	0.494324	−	1.84484i	−0.0394575	−	0.999221i	$-0.512563\pi$
$347$	9.20824	−	34.3656i	0.494324	−	1.84484i	0.533782	−	0.845622i	$-0.320770\pi$
$348$	−6.46528	+	36.9936i	−0.346576	+	1.98306i
$349$	0.580105	−	1.00477i	0.0310523	−	0.0537841i	−0.850082	−	0.526651i	$-0.823447\pi$
$349$	0.580105	−	1.00477i	0.0310523	−	0.0537841i	0.881134	+	0.472867i	$0.156781\pi$
$350$		0			0
$351$	6.54104	−	17.5560i	0.349135	−	0.937072i
$352$	2.74501	−	2.74501i	0.146310	−	0.146310i
$353$	30.3425	−	8.13026i	1.61497	−	0.432730i	0.665452	−	0.746440i	$-0.268239\pi$
$353$	30.3425	−	8.13026i	1.61497	−	0.432730i	0.949519	+	0.313710i	$0.101572\pi$
$354$	4.34916	+	6.19129i	0.231155	+	0.329063i
$355$		0			0
$356$	32.8636			1.74177
$357$	−1.05857	−	0.885523i	−0.0560256	−	0.0468668i
$358$	20.5412	+	5.50399i	1.08563	+	0.290895i
$359$			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
$362$	0.846997	+	3.16104i	0.0445172	+	0.166140i
$363$	−6.38756	−	17.4674i	−0.335260	−	0.916802i
$364$	−3.72362	+	1.68171i	−0.195171	+	0.0881458i
$365$		0			0
$366$	−33.2012	+	23.3226i	−1.73545	+	1.21909i
$367$	1.58445	+	5.91325i	0.0827076	+	0.308669i	0.994870	−	0.101159i	$-0.0322552\pi$
$367$	1.58445	+	5.91325i	0.0827076	+	0.308669i	−0.912163	+	0.409828i	$0.865589\pi$
$368$	11.6304	+	3.11634i	0.606274	+	0.162451i
$369$	−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
$373$	−6.72356	+	25.0927i	−0.348133	+	1.29925i	0.540776	+	0.841167i	$0.318131\pi$
$373$	−6.72356	+	25.0927i	−0.348133	+	1.29925i	−0.888909	+	0.458083i	$0.848536\pi$
$374$	1.05919	−	1.83457i	0.0547694	−	0.0948634i
$375$		0			0
$376$	11.2536			0.580360
$377$	−26.9716	−	10.1887i	−1.38911	−	0.524746i
$378$	−4.09284	−	2.33830i	−0.210513	−	0.120269i
$379$	−10.9047	+	18.8876i	−0.560139	+	0.970189i	0.437345	+	0.899294i	$0.355919\pi$
$379$	−10.9047	+	18.8876i	−0.560139	+	0.970189i	−0.997484	+	0.0708954i	$0.977414\pi$
$380$		0			0
$381$	−2.72148	−	30.5739i	−0.139425	−	1.56635i
$382$	6.89790	+	6.89790i	0.352927	+	0.352927i
$383$	3.07967	−	11.4935i	0.157364	−	0.587290i	−0.841527	−	0.540215i	$-0.818343\pi$
$383$	3.07967	−	11.4935i	0.157364	−	0.587290i	0.998891	−	0.0470758i	$-0.0149902\pi$
$384$	−19.9645	+	1.77710i	−1.01881	+	0.0906874i
$385$		0			0
$386$	−29.7798	+	17.1934i	−1.51575	+	0.875120i
$387$	12.3977	−	17.8202i	0.630210	−	0.905853i
$388$	11.3747	+	42.4510i	0.577463	+	2.15512i
$389$	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
$392$	−2.72788	−	10.1806i	−0.137779	−	0.514198i
$393$	1.08208	−	6.19152i	0.0545836	−	0.312321i
$394$	−23.1396	+	13.3597i	−1.16576	+	0.673050i
$395$		0			0
$396$	1.41228	−	3.91703i	0.0709696	−	0.196838i
$397$	4.50246	−	16.8034i	0.225972	−	0.843340i	−0.756041	−	0.654525i	$-0.772869\pi$
$397$	4.50246	−	16.8034i	0.225972	−	0.843340i	0.982013	−	0.188815i	$-0.0604646\pi$
$398$	34.5962	+	34.5962i	1.73415	+	1.73415i
$399$	−2.16933	+	0.193099i	−0.108602	+	0.00966703i
$400$		0			0
$401$	−2.63268	+	4.55994i	−0.131470	+	0.227712i	−0.924243	−	0.381804i	$-0.875303\pi$
$401$	−2.63268	+	4.55994i	−0.131470	+	0.227712i	0.792774	+	0.609516i	$0.208636\pi$
$402$	−12.4783	−	34.1232i	−0.622361	−	1.70191i
$403$	10.9874	−	1.80036i	0.547324	−	0.0896824i
$404$	23.6927			1.17876
$405$		0			0
$406$	−3.62704	+	6.28221i	−0.180007	+	0.311781i
$407$	0.983383	−	3.67004i	0.0487445	−	0.181917i
$408$	−4.78921	+	1.75134i	−0.237101	+	0.0867041i
$409$	−4.97625	−	8.61911i	−0.246060	−	0.426188i	0.716369	−	0.697721i	$-0.245803\pi$
$409$	−4.97625	−	8.61911i	−0.246060	−	0.426188i	−0.962429	+	0.271534i	$0.912469\pi$
$410$		0			0
$411$	−6.05725	−	2.81340i	−0.298782	−	0.138775i
$412$	−29.7812	−	7.97985i	−1.46721	−	0.393139i
$413$	0.217691	+	0.812435i	0.0107119	+	0.0399773i
$414$	37.2631	−	6.68679i	1.83138	−	0.328638i
$415$		0			0
$416$	2.71311	−	27.2086i	0.133021	−	1.33401i
$417$	−12.8199	+	4.68802i	−0.627791	+	0.229573i
$418$	−0.865213	−	3.22902i	−0.0423189	−	0.157936i
$419$	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	$-0.0779962\pi$
$422$	8.34631	+	2.23639i	0.406292	+	0.108866i
$423$	−19.7864	+	9.29955i	−0.962050	+	0.452160i
$424$	15.6337			0.759238
$425$		0			0
$426$	18.0657	−	12.6905i	0.875288	−	0.614859i
$427$	−4.35673	+	1.16738i	−0.210837	+	0.0564936i
$428$	23.1380	−	23.1380i	1.11842	−	1.11842i
$429$	2.75136	+	1.62765i	0.132837	+	0.0785837i
$430$		0			0
$431$	6.30631	−	10.9229i	0.303764	−	0.526135i	−0.673221	−	0.739441i	$-0.735090\pi$
$431$	6.30631	−	10.9229i	0.303764	−	0.526135i	0.976985	+	0.213306i	$0.0684231\pi$
$432$	9.29509	−	5.42291i	0.447210	−	0.260910i
$433$	5.85174	−	21.8390i	0.281217	−	1.04952i	−0.670343	−	0.742052i	$-0.733853\pi$
$433$	5.85174	−	21.8390i	0.281217	−	1.04952i	0.951560	−	0.307464i	$-0.0994804\pi$
$434$		−	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
$438$	−8.57233	−	7.17097i	−0.409602	−	0.342642i
$439$	−10.2958	−	5.94428i	−0.491391	−	0.283705i	0.233760	−	0.972294i	$-0.424897\pi$
$439$	−10.2958	−	5.94428i	−0.491391	−	0.283705i	−0.725152	+	0.688589i	$0.758230\pi$
$440$		0			0
$441$	13.2091	+	15.6456i	0.629005	+	0.745030i
$442$	−2.41273	−	14.7247i	−0.114762	−	0.700382i
$443$	−14.0199	+	14.0199i	−0.666105	+	0.666105i	−0.956812	−	0.290707i	$-0.906109\pi$
$443$	−14.0199	+	14.0199i	−0.666105	+	0.666105i	0.290707	+	0.956812i	$0.406109\pi$
$444$	−28.5241	+	20.0372i	−1.35370	+	0.950923i
$445$		0			0
$446$	26.3771	−	15.2288i	1.24899	−	0.721105i
$447$	8.97264	−	3.28115i	0.424391	−	0.155193i
$448$	−4.97309	−	1.33254i	−0.234956	−	0.0629564i
$449$	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
$452$	−8.81571	+	2.36216i	−0.414656	+	0.111107i
$453$	−1.04484	+	5.97846i	−0.0490910	+	0.280893i
$454$		−	19.3322i		−	0.907304i
$455$		0			0
$456$	−3.38982	+	7.29830i	−0.158743	+	0.341774i
$457$	−25.1569	+	6.74076i	−1.17679	+	0.315320i	−0.793652	−	0.608372i	$-0.791823\pi$
$457$	−25.1569	+	6.74076i	−1.17679	+	0.315320i	−0.383137	+	0.923692i	$0.625156\pi$
$458$	7.81163	+	29.1534i	0.365014	+	1.36225i
$459$	6.97330	−	7.03688i	0.325486	−	0.328453i
$460$		0			0
$461$	−6.68465	−	11.5782i	−0.311335	−	0.539249i	0.667316	−	0.744774i	$-0.267443\pi$
$461$	−6.68465	−	11.5782i	−0.311335	−	0.539249i	−0.978652	+	0.205526i	$0.934110\pi$
$462$	0.516061	−	0.616910i	0.0240093	−	0.0287012i
$463$	3.79477	−	3.79477i	0.176358	−	0.176358i	−0.613408	−	0.789766i	$-0.710202\pi$
$463$	3.79477	−	3.79477i	0.176358	−	0.176358i	0.789766	+	0.613408i	$0.210202\pi$
$464$	−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	0.971438	−	0.237294i	$-0.0762606\pi$
$467$	15.8650	+	15.8650i	0.734143	+	0.734143i	−0.237294	+	0.971438i	$0.576261\pi$
$468$	−9.77990	−	27.6499i	−0.452076	−	1.27812i
$469$		−	4.03897i		−	0.186502i
$470$		0			0
$471$	2.54688	−	1.78909i	0.117354	−	0.0824369i
$472$	3.00186	+	0.804345i	0.138172	+	0.0370230i
$473$	2.61922	+	2.61922i	0.120432	+	0.120432i
$474$	53.9147	−	4.79912i	2.47638	−	0.220431i
$475$		0			0
$476$	−2.16050			−0.0990261
$477$	−27.4876	+	12.9191i	−1.25857	+	0.591524i
$478$	4.49794	−	1.20522i	0.205731	−	0.0551254i
$479$	−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
$483$	4.14568	+	0.724531i	0.188635	+	0.0329673i
$484$	−25.2145	−	14.5576i	−1.14611	−	0.661709i
$485$		0			0
$486$	19.1974	−	27.8628i	0.870810	−	1.26388i
$487$	7.39466	−	27.5972i	0.335084	−	1.25055i	−0.568694	−	0.822549i	$-0.692551\pi$
$487$	7.39466	−	27.5972i	0.335084	−	1.25055i	0.903778	−	0.428001i	$-0.140782\pi$
$488$	−4.31335	+	16.0976i	−0.195256	+	0.728705i
$489$	−12.2554	−	5.69223i	−0.554208	−	0.257411i
$490$		0			0
$491$	25.1585	+	14.5253i	1.13539	+	0.655516i	0.945284	−	0.326248i	$-0.105785\pi$
$491$	25.1585	+	14.5253i	1.13539	+	0.655516i	0.190103	+	0.981764i	$0.439118\pi$
$492$	−2.86788	+	16.4097i	−0.129294	+	0.739806i
$493$	−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
$497$	2.37063	−	0.635208i	0.106337	−	0.0284930i
$498$	21.0034	−	25.1079i	0.941186	−	1.12511i
$499$	20.0887			0.899294			0.449647	−	0.893206i	$-0.351550\pi$
$499$	20.0887			0.899294			0.449647	+	0.893206i	$0.351550\pi$
$500$		0			0
$501$	−0.350205	−	3.93431i	−0.0156460	−	0.175772i
$502$	5.33523	+	5.33523i	0.238123	+	0.238123i
$503$	9.17562	+	2.45860i	0.409121	+	0.109624i	0.457509	−	0.889205i	$-0.348742\pi$
$503$	9.17562	+	2.45860i	0.409121	+	0.109624i	−0.0483882	+	0.998829i	$0.515408\pi$
$504$	−1.90567	+	0.341970i	−0.0848855	+	0.0152325i
$505$		0			0
$506$			6.45976i			0.287171i
$507$	22.2577	−	3.40504i	0.988500	−	0.151223i
$508$	−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
$513$	−0.0709447	−	15.6333i	−0.00313228	−	0.690229i
$514$	4.32863	+	7.49740i	0.190927	+	0.330696i
$515$		0			0
$516$	−3.01307	−	33.8497i	−0.132643	−	1.49015i
$517$	−0.965514	−	3.60335i	−0.0424632	−	0.158475i
$518$	−6.50391	+	1.74272i	−0.285766	+	0.0765707i
$519$	−35.5815	−	16.5264i	−1.56185	−	0.725430i
$520$		0			0
$521$			3.29710i			0.144448i	0.997388	+	0.0722242i	$0.0230097\pi$
$521$			3.29710i			0.144448i	−0.997388	+	0.0722242i	$0.976990\pi$
$522$	−42.7445	−	29.7377i	−1.87088	−	1.30158i
$523$	7.79663	−	2.08910i	0.340923	−	0.0913500i	−0.0842956	−	0.996441i	$-0.526864\pi$
$523$	7.79663	−	2.08910i	0.340923	−	0.0913500i	0.425218	+	0.905091i	$0.360197\pi$
$524$	−4.91969	−	8.52115i	−0.214918	−	0.372248i
$525$		0			0
$526$	45.4018	−	26.2127i	1.97961	−	1.14293i
$527$	5.68687	+	1.52379i	0.247724	+	0.0663774i
$528$	0.630630	+	1.72452i	0.0274446	+	0.0750501i
$529$	−9.35384	+	5.40044i	−0.406689	+	0.234802i
$530$		0			0
$531$	−5.94264	+	1.06640i	−0.257889	+	0.0462776i
$532$	−2.41080	+	2.41080i	−0.104521	+	0.104521i
$533$	−11.9641	−	4.51953i	−0.518224	−	0.195763i
$534$	−19.1952	+	41.3272i	−0.830655	+	1.78840i
$535$		0			0
$536$	−12.9242	−	7.46177i	−0.558239	−	0.322299i
$537$	−10.8880	+	13.0158i	−0.469853	+	0.561672i
$538$	−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	$0.851660\pi$
$542$	−12.1571	+	45.3710i	−0.522193	+	1.94885i
$543$	−2.57239	−	0.449571i	−0.110392	−	0.0192929i
$544$	7.22944	−	12.5218i	0.309960	−	0.536866i
$545$		0			0
$546$	0.0600909	−	5.66485i	0.00257165	−	0.242433i
$547$	4.29605	−	4.29605i	0.183686	−	0.183686i	−0.609274	−	0.792960i	$-0.708539\pi$
$547$	4.29605	−	4.29605i	0.183686	−	0.183686i	0.792960	+	0.609274i	$0.208539\pi$
$548$	−10.0989	+	2.70600i	−0.431404	+	0.115594i
$549$	−5.71861	−	31.8678i	−0.244064	−	1.36008i
$550$		0			0
$551$	−24.0589			−1.02494
$552$	9.97731	−	11.9271i	0.424663	−	0.507651i
$553$	5.81209	+	1.55735i	0.247155	+	0.0662251i
$554$		−	0.965776i		−	0.0410319i
$555$		0			0
$556$	−10.6843	+	18.5057i	−0.453113	+	0.784815i
$557$	5.01972	+	18.7339i	0.212692	+	0.793779i	0.986966	+	0.160928i	$0.0514487\pi$
$557$	5.01972	+	18.7339i	0.212692	+	0.793779i	−0.774274	+	0.632851i	$0.781885\pi$
$558$	20.0370	+	1.69194i	0.848234	+	0.0716257i
$559$	25.9617	+	2.58877i	1.09806	+	0.109493i
$560$		0			0
$561$	0.971664	+	1.38322i	0.0410237	+	0.0583997i
$562$	−5.73665	−	21.4095i	−0.241986	−	0.903104i
$563$	−40.0016	−	10.7184i	−1.68587	−	0.451727i	−0.716550	−	0.697536i	$-0.754280\pi$
$563$	−40.0016	−	10.7184i	−1.68587	−	0.451727i	−0.969318	+	0.245809i	$0.920946\pi$
$564$	−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
$568$	2.34702	−	8.75920i	0.0984788	−	0.367528i
$569$	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	$0.704610\pi$
$572$	4.93847	−	0.809199i	0.206488	−	0.0338343i
$573$	−7.31076	+	2.67343i	−0.305411	+	0.111684i
$574$	−1.60889	+	2.78668i	−0.0671537	+	0.116314i
$575$		0			0
$576$	12.5350	−	34.7665i	0.522292	−	1.44861i
$577$	−7.73617	−	7.73617i	−0.322061	−	0.322061i	0.527496	−	0.849557i	$-0.323131\pi$
$577$	−7.73617	−	7.73617i	−0.322061	−	0.322061i	−0.849557	+	0.527496i	$0.823131\pi$
$578$	−7.50830	+	28.0214i	−0.312304	+	1.16554i
$579$	−2.43285	−	27.3314i	−0.101106	−	1.13585i
$580$		0			0
$581$	3.15141	−	1.81947i	0.130743	−	0.0754842i
$582$	−60.0275	−	10.4909i	−2.48822	−	0.434860i
$583$	−1.34131	−	5.00582i	−0.0555512	−	0.207320i
$584$	−4.59053			−0.189958
$585$		0			0
$586$	−38.4926			−1.59011
$587$	7.40419	+	27.6328i	0.305604	+	1.14053i	0.932425	+	0.361365i	$0.117689\pi$
$587$	7.40419	+	27.6328i	0.305604	+	1.14053i	−0.626821	+	0.779163i	$0.715644\pi$
$588$	31.5754	+	5.51836i	1.30215	+	0.227573i
$589$	8.04606	−	4.64539i	0.331532	−	0.191410i
$590$		0			0
$591$	−1.89039	−	21.2372i	−0.0777601	−	0.873580i
$592$	3.97861	−	14.8484i	0.163520	−	0.610265i
$593$	−0.767325	−	0.767325i	−0.0315103	−	0.0315103i	0.691176	−	0.722686i	$-0.257093\pi$
$593$	−0.767325	−	0.767325i	−0.0315103	−	0.0315103i	−0.722686	+	0.691176i	$0.757093\pi$
$594$	4.10092	+	4.06387i	0.168263	+	0.166742i
$595$		0			0
$596$	7.47792	−	12.9521i	0.306308	−	0.530540i
$597$	−36.6669	+	13.4085i	−1.50068	+	0.548773i
$598$	28.8223	+	35.2070i	1.17863	+	1.43972i
$599$	−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	$0.0529646\pi$
$602$	1.69898	−	6.34067i	0.0692451	−	0.258426i
$603$	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
$607$	7.65942	+	2.05233i	0.310886	+	0.0833017i	0.410889	−	0.911685i	$-0.365218\pi$
$607$	7.65942	+	2.05233i	0.310886	+	0.0833017i	−0.100003	+	0.994987i	$0.531885\pi$
$608$	−5.90546	−	22.0395i	−0.239498	−	0.893819i
$609$	−3.32732	−	4.73664i	−0.134830	−	0.191938i
$610$		0			0
$611$	−21.3397	−	15.3310i	−0.863313	−	0.620226i
$612$	1.30491	−	15.4535i	0.0527479	−	0.624671i
$613$	9.80387	+	36.5885i	0.395975	+	1.47780i	0.820114	+	0.572200i	$0.193910\pi$
$613$	9.80387	+	36.5885i	0.395975	+	1.47780i	−0.424139	+	0.905597i	$0.639423\pi$
$614$	−27.7137	+	48.0016i	−1.11843	+	1.93719i
$615$		0			0
$616$		−	0.330359i		−	0.0133105i
$617$	2.01292	+	0.539359i	0.0810369	+	0.0217138i	0.299110	−	0.954219i	$-0.403310\pi$
$617$	2.01292	+	0.539359i	0.0810369	+	0.0217138i	−0.218073	+	0.975933i	$0.569977\pi$
$618$	27.4297	−	32.7900i	1.10338	−	1.31901i
$619$	30.7890			1.23751			0.618757	−	0.785583i	$-0.287637\pi$
$619$	30.7890			1.23751			0.618757	+	0.785583i	$0.287637\pi$
$620$		0			0
$621$	−7.68634	+	29.2155i	−0.308442	+	1.17238i
$622$	54.4324	−	14.5851i	2.18254	−	0.584810i
$623$	−3.58185	+	3.58185i	−0.143504	+	0.143504i
$624$	11.1315	+	6.58521i	0.445619	+	0.263620i
$625$		0			0
$626$	1.91820	−	3.32241i	0.0766665	−	0.132790i
$627$	2.62771	+	0.459239i	0.104941	+	0.0183403i
$628$	1.26106	−	4.70636i	0.0503219	−	0.187804i
$629$		−	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
$633$	−4.42403	+	5.28858i	−0.175840	+	0.210202i
$634$	−33.7616	−	19.4923i	−1.34084	−	0.774137i
$635$		0			0
$636$	−20.0286	+	43.1216i	−0.794185	+	1.70988i
$637$	−8.69645	+	23.0213i	−0.344566	+	0.912136i
$638$	6.28259	−	6.28259i	0.248730	−	0.248730i
$639$	3.11167	+	17.3402i	0.123096	+	0.685968i
$640$		0			0
$641$	−36.8548	+	21.2782i	−1.45568	+	0.840437i	−0.998794	−	0.0490894i	$-0.984368\pi$
$641$	−36.8548	+	21.2782i	−1.45568	+	0.840437i	−0.456885	+	0.889526i	$0.651035\pi$
$642$	15.5824	+	42.6115i	0.614986	+	1.68174i
$643$	−41.1282	−	11.0203i	−1.62194	−	0.434597i	−0.670368	−	0.742029i	$-0.733864\pi$
$643$	−41.1282	−	11.0203i	−1.62194	−	0.434597i	−0.951570	+	0.307432i	$0.900530\pi$
$644$	5.70554	−	3.29409i	0.224830	−	0.129806i
$645$		0			0
$646$	−6.22546	−	10.7828i	−0.244938	−	0.424244i
$647$	2.11488	−	0.566681i	0.0831446	−	0.0222785i	−0.217007	−	0.976170i	$-0.569629\pi$
$647$	2.11488	−	0.566681i	0.0831446	−	0.0222785i	0.300152	+	0.953892i	$0.402963\pi$
$648$	−1.29503	−	13.8374i	−0.0508735	−	0.543584i
$649$		−	1.03019i		−	0.0404385i
$650$		0			0
$651$	2.02733	+	0.941629i	0.0794574	+	0.0369054i
$652$	−20.4327	+	5.47493i	−0.800207	+	0.214415i
$653$	5.38119	+	20.0829i	0.210582	+	0.785904i	0.987675	+	0.156518i	$0.0500268\pi$
$653$	5.38119	+	20.0829i	0.210582	+	0.785904i	−0.777093	+	0.629386i	$0.783306\pi$
$654$	4.69969	+	52.7977i	0.183772	+	2.06455i
$655$		0			0
$656$	−3.67308	−	6.36196i	−0.143410	−	0.248393i
$657$	8.07123	−	3.79345i	0.314889	−	0.147996i
$658$	−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
$663$	11.4674	+	3.20344i	0.445359	+	0.124411i
$664$		−	13.4454i		−	0.521785i
$665$		0			0
$666$	−8.53698	−	47.5736i	−0.330801	−	1.84344i
$667$	44.9065	+	12.0327i	1.73879	+	0.465906i
$668$	−4.37225	−	4.37225i	−0.169167	−	0.169167i
$669$	2.15487	+	24.2084i	0.0833120	+	0.935952i
$670$		0			0
$671$	5.52445			0.213269
$672$	3.52234	−	4.21069i	0.135877	−	0.162431i
$673$	−1.42986	+	0.383129i	−0.0551169	+	0.0147685i	−0.286272	−	0.958148i	$-0.592416\pi$
$673$	−1.42986	+	0.383129i	−0.0551169	+	0.0147685i	0.231155	+	0.972917i	$0.425749\pi$
$674$	−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	0.402421	−	0.915455i	$-0.368169\pi$
$677$	−13.3487	−	13.3487i	−0.513033	−	0.513033i	−0.915455	+	0.402421i	$0.868169\pi$
$678$	2.17862	−	12.4658i	0.0836693	−	0.478746i
$679$	−5.86653	−	3.38704i	−0.225137	−	0.129983i
$680$		0			0
$681$	13.9909	+	6.49834i	0.536134	+	0.249017i
$682$	−0.888028	+	3.31417i	−0.0340044	+	0.126906i
$683$	−2.86868	+	10.7061i	−0.109767	+	0.409656i	−0.998842	−	0.0481050i	$-0.984682\pi$
$683$	−2.86868	+	10.7061i	−0.109767	+	0.409656i	0.889075	+	0.457761i	$0.151348\pi$
$684$	−15.7878	−	18.7000i	−0.603662	−	0.715012i
$685$		0			0
$686$	10.8614	+	6.27085i	0.414691	+	0.239422i
$687$	−23.7245	−	4.14627i	−0.905145	−	0.158190i
$688$	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	$0.615456\pi$
$692$	−59.3230	+	15.8956i	−2.25512	+	0.604258i
$693$	0.272996	+	0.580848i	0.0103703	+	0.0220646i
$694$	77.2248			2.93141
$695$		0			0
$696$	−21.3036	+	1.89630i	−0.807512	+	0.0718792i
$697$	−4.78202	−	4.78202i	−0.181132	−	0.181132i
$698$	2.43252	+	0.651792i	0.0920722	+	0.0246707i
$699$	−21.4216	+	15.0479i	−0.810238	+	0.569163i
$700$		0			0
$701$			9.61731i			0.363241i	0.983369	+	0.181620i	$0.0581342\pi$
$701$			9.61731i			0.363241i	−0.983369	+	0.181620i	$0.941866\pi$
$702$	40.4831	+	3.85131i	1.52793	+	0.145358i
$703$	−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
$708$	−6.06432	+	7.24942i	−0.227911	+	0.272450i
$709$	−15.7072	−	27.2057i	−0.589896	−	1.02173i	−0.994246	−	0.107125i	$-0.965835\pi$
$709$	−15.7072	−	27.2057i	−0.589896	−	1.02173i	0.404349	−	0.914605i	$-0.367498\pi$
$710$		0			0
$711$	−14.6498	+	40.6319i	−0.549409	+	1.52382i
$712$	4.84417	+	18.0787i	0.181543	+	0.677528i
$713$	−17.3415	+	4.64664i	−0.649443	+	0.174018i
$714$	1.26191	−	2.71690i	0.0472259	−	0.101677i
$715$		0			0
$716$			26.5646i			0.992764i
$717$	−0.639709	+	3.66034i	−0.0238904	+	0.136698i
$718$	−38.8745	+	10.4164i	−1.45078	+	0.388736i
$719$	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
$722$	20.8570	+	5.58862i	0.776218	+	0.207987i
$723$	−8.45717	+	3.09265i	−0.314526	+	0.115017i
$724$	−3.54028	+	2.04398i	−0.131573	+	0.0759640i
$725$		0			0
$726$	33.0341	−	23.2053i	1.22601	−	0.861229i
$727$	1.96600	−	1.96600i	0.0729151	−	0.0729151i	−0.669709	−	0.742624i	$-0.733581\pi$
$727$	1.96600	−	1.96600i	0.0729151	−	0.0729151i	0.742624	+	0.669709i	$0.233581\pi$
$728$	−1.47400	−	1.80052i	−0.0546301	−	0.0667317i
$729$	13.7117	+	23.2592i	0.507839	+	0.861452i
$730$		0			0
$731$	11.9479	+	6.89814i	0.441910	+	0.255137i
$732$	−38.8754	−	32.5203i	−1.43688	−	1.20198i
$733$	−29.6853	+	29.6853i	−1.09645	+	1.09645i	−0.101628	+	0.994822i	$0.532405\pi$
$733$	−29.6853	+	29.6853i	−1.09645	+	1.09645i	−0.994822	+	0.101628i	$0.967595\pi$
$734$	−11.5077	+	6.64398i	−0.424757	+	0.245234i
$735$		0			0
$736$			44.0907i			1.62521i
$737$	−1.28038	+	4.77844i	−0.0471634	+	0.176016i
$738$	−18.9607	−	13.1911i	−0.697953	−	0.485572i
$739$	−16.6414	+	28.8238i	−0.612164	+	1.06030i	0.378711	+	0.925515i	$0.376367\pi$
$739$	−16.6414	+	28.8238i	−0.612164	+	1.06030i	−0.990875	+	0.134784i	$0.956966\pi$
$740$		0			0
$741$	16.3706	−	9.22144i	0.601389	−	0.338758i
$742$	−6.49413	+	6.49413i	−0.238407	+	0.238407i
$743$	0.966155	−	0.258881i	0.0354448	−	0.00949741i	−0.241053	−	0.970512i	$-0.577493\pi$
$743$	0.966155	−	0.258881i	0.0354448	−	0.00949741i	0.276498	+	0.961015i	$0.410826\pi$
$744$	6.75847	−	4.74758i	0.247777	−	0.174055i
$745$		0			0
$746$	−56.3871			−2.06448
$747$	11.1108	+	23.6402i	0.406524	+	0.864951i
$748$	2.55605	+	0.684891i	0.0934584	+	0.0250421i
$749$			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	$0.269685\pi$
$752$	−3.90632	−	14.5786i	−0.142449	−	0.531626i
$753$	−5.65456	+	2.06778i	−0.206063	+	0.0753542i
$754$	6.20956	−	62.2731i	0.226139	−	2.26785i
$755$		0			0
$756$	1.49816	−	5.69444i	0.0544874	−	0.207105i
$757$	4.20419	+	15.6903i	0.152804	+	0.570272i	0.999283	+	0.0378509i	$0.0120512\pi$
$757$	4.20419	+	15.6903i	0.152804	+	0.570272i	−0.846479	+	0.532422i	$0.821282\pi$
$758$	−45.7262	−	12.2523i	−1.66085	−	0.445024i
$759$	−4.67501	−	2.17139i	−0.169692	−	0.0788164i
$760$		0			0
$761$	7.90134	+	13.6855i	0.286423	+	0.496100i	0.972953	−	0.231002i	$-0.0742003\pi$
$761$	7.90134	+	13.6855i	0.286423	+	0.496100i	−0.686530	+	0.727101i	$0.740867\pi$
$762$	62.5730	−	22.8819i	2.26678	−	0.828925i
$763$	−1.52508	+	5.69167i	−0.0552116	+	0.206052i
$764$	−6.09289	+	10.5532i	−0.220433	+	0.381801i
$765$		0			0
$766$	25.8276			0.933190
$767$	−4.59652	−	5.61473i	−0.165971	−	0.202736i
$768$	−0.285537	−	0.780830i	−0.0103034	−	0.0281758i
$769$	−8.96855	+	15.5340i	−0.323414	+	0.560170i	−0.981190	−	0.193044i	$-0.938164\pi$
$769$	−8.96855	+	15.5340i	−0.323414	+	0.560170i	0.657776	+	0.753214i	$0.271497\pi$
$770$		0			0
$771$	−6.88099	+	0.612498i	−0.247813	+	0.0220586i
$772$	−30.3737	−	30.3737i	−1.09317	−	1.09317i
$773$	−4.22347	+	15.7622i	−0.151908	+	0.566927i	0.847443	+	0.530887i	$0.178141\pi$
$773$	−4.22347	+	15.7622i	−0.151908	+	0.566927i	−0.999350	+	0.0360399i	$0.988526\pi$
$774$	44.3271	+	15.9821i	1.59331	+	0.574463i
$775$		0			0
$776$	−21.6762	+	12.5147i	−0.778129	+	0.449253i
$777$	0.925004	−	5.29276i	0.0331843	−	0.189877i
$778$	10.4784	+	39.1060i	0.375670	+	1.40202i
$779$	−10.6721			−0.382367
$780$		0			0
$781$	−3.00602			−0.107564
$782$	6.22713	+	23.2400i	0.222682	+	0.831059i
$783$	35.8897	−	20.9387i	1.28259	−	0.748287i
$784$	−12.2416	+	7.06771i	−0.437201	+	0.252418i
$785$		0			0
$786$	13.5892	−	1.20961i	0.484710	−	0.0431455i
$787$	2.04854	−	7.64525i	0.0730225	−	0.272524i	−0.919755	−	0.392493i	$-0.871613\pi$
$787$	2.04854	−	7.64525i	0.0730225	−	0.272524i	0.992778	+	0.119969i	$0.0382795\pi$
$788$	−23.6011	−	23.6011i	−0.840754	−	0.840754i
$789$	3.70909	+	41.6690i	0.132047	+	1.48346i
$790$		0			0
$791$	0.703381	−	1.21829i	0.0250093	−	0.0433174i
$792$	2.36298	+	0.199532i	0.0839648	+	0.00709007i
$793$	30.1093	−	24.6491i	1.06921	−	0.875315i
$794$	37.7598			1.34005
$795$		0			0
$796$	−30.5587	+	52.9292i	−1.08312	+	1.87603i
$797$	1.67742	−	6.26020i	0.0594171	−	0.221748i	−0.929833	−	0.367982i	$-0.880049\pi$
$797$	1.67742	−	6.26020i	0.0594171	−	0.221748i	0.989250	+	0.146234i	$0.0467154\pi$
$798$	−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
$802$	−11.0395	−	2.95802i	−0.389817	−	0.104451i
$803$	0.393850	+	1.46987i	0.0138986	+	0.0518705i
$804$	37.1388	−	26.0887i	1.30979	−	0.920078i
$805$		0			0
$806$	9.94729	+	22.0251i	0.350378	+	0.775801i
$807$	−14.7594	−	40.3611i	−0.519556	−	1.42078i
$808$	3.49236	+	13.0337i	0.122861	+	0.458523i
$809$	−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	$-0.0448953\pi$
$812$	−8.75280	−	2.34531i	−0.307163	−	0.0823041i
$813$	−28.7490	−	24.0493i	−1.00827	−	0.843445i
$814$	8.24713			0.289062
$815$		0			0
$816$	3.93120	+	5.59630i	0.137619	+	0.195910i
$817$	21.0295	−	5.63483i	0.735728	−	0.197138i
$818$	15.2754	−	15.2754i	0.534092	−	0.534092i
$819$	4.07952	+	1.94768i	0.142550	+	0.0680573i
$820$		0			0
$821$	−25.1045	+	43.4822i	−0.876152	+	1.51754i	−0.0206220	+	0.999787i	$0.506565\pi$
$821$	−25.1045	+	43.4822i	−0.876152	+	1.51754i	−0.855530	+	0.517753i	$0.826769\pi$
$822$	2.49573	−	14.2803i	0.0870487	−	0.498082i
$823$	12.6315	−	47.1413i	0.440306	−	1.64324i	−0.287735	−	0.957710i	$-0.592902\pi$
$823$	12.6315	−	47.1413i	0.440306	−	1.64324i	0.728041	−	0.685534i	$-0.240431\pi$
$824$		−	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	−0.0476050	+	0.998866i	$0.515159\pi$
$827$	−30.0940	+	30.0940i	−1.04647	+	1.04647i	−0.998866	+	0.0476050i	$0.984841\pi$
$828$	20.1158	+	42.8000i	0.699073	+	1.48740i
$829$	−9.32181	−	5.38195i	−0.323760	−	0.186923i	0.329307	−	0.944223i	$-0.393185\pi$
$829$	−9.32181	−	5.38195i	−0.323760	−	0.186923i	−0.653067	+	0.757300i	$0.726518\pi$
$830$		0			0
$831$	0.698944	+	0.324637i	0.0242461	+	0.0112615i
$832$	43.8325	−	7.18224i	1.51962	−	0.248999i
$833$	−9.20153	+	9.20153i	−0.318814	+	0.318814i
$834$	−17.0310	−	24.2447i	−0.589737	−	0.839526i
$835$		0			0
$836$	3.61642	−	2.08794i	0.125076	−	0.0722129i
$837$	−7.95974	+	13.9323i	−0.275129	+	0.481571i
$838$	36.3690	+	9.74504i	1.25635	+	0.336637i
$839$	−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
$842$	20.8718	−	5.59258i	0.719289	−	0.192733i
$843$	17.4226	+	3.04491i	0.600067	+	0.104872i
$844$			10.7937i			0.371536i
$845$		0			0
$846$	−30.6134	−	36.2603i	−1.05251	−	1.24666i
$847$	4.33481	−	1.16151i	0.148946	−	0.0399099i
$848$	−5.42671	−	20.2528i	−0.186354	−	0.695482i
$849$	14.2760	−	1.27075i	0.489952	−	0.0436122i
$850$		0			0
$851$	21.5767	+	37.3719i	0.739639	+	1.28109i
$852$	21.1533	+	17.6953i	0.724700	+	0.606230i
$853$	18.6086	−	18.6086i	0.637146	−	0.637146i	−0.312704	−	0.949851i	$-0.601235\pi$
$853$	18.6086	−	18.6086i	0.637146	−	0.637146i	0.949851	+	0.312704i	$0.101235\pi$
$854$	−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	0.776134	−	0.630569i	$-0.217178\pi$
$857$	4.26135	+	4.26135i	0.145565	+	0.145565i	−0.630569	+	0.776134i	$0.717178\pi$
$858$	−1.86689	+	6.68294i	−0.0637345	+	0.228152i
$859$		−	29.4002i		−	1.00312i	−0.865122	−	0.501561i	$-0.832759\pi$
$859$		−	29.4002i		−	1.00312i	0.865122	−	0.501561i	$-0.167241\pi$
$860$		0			0
$861$	−1.47594	−	2.10109i	−0.0502999	−	0.0716049i
$862$	26.4439	+	7.08562i	0.900683	+	0.241337i
$863$	−23.1832	−	23.1832i	−0.789164	−	0.789164i	0.192193	−	0.981357i	$-0.438440\pi$
$863$	−23.1832	−	23.1832i	−0.789164	−	0.789164i	−0.981357	+	0.192193i	$0.938440\pi$
$864$	27.9906	+	27.7377i	0.952260	+	0.943656i
$865$		0			0
$866$	49.0756			1.66766
$867$	−17.7556	−	14.8530i	−0.603011	−	0.504433i
$868$	3.38006	−	0.905684i	0.114727	−	0.0307409i
$869$	−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
$873$	27.7700	−	39.9162i	0.939874	−	1.35096i
$874$	32.8810	+	18.9839i	1.11222	+	0.642139i
$875$		0			0
$876$	5.88102	−	12.6619i	0.198701	−	0.427805i
$877$	−11.6836	+	43.6039i	−0.394529	+	1.47240i	0.428053	+	0.903754i	$0.359200\pi$
$877$	−11.6836	+	43.6039i	−0.394529	+	1.47240i	−0.822582	+	0.568647i	$0.807467\pi$
$878$	6.67885	−	24.9258i	0.225400	−	0.841205i
$879$	12.9389	−	27.8576i	0.436419	−	0.939612i
$880$		0			0
$881$	−12.6778	−	7.31952i	−0.427125	−	0.246601i	0.270996	−	0.962580i	$-0.412647\pi$
$881$	−12.6778	−	7.31952i	−0.427125	−	0.246601i	−0.698121	+	0.715980i	$0.745980\pi$
$882$	−25.3823	+	36.4840i	−0.854665	+	1.22848i
$883$	−8.31854	−	8.31854i	−0.279941	−	0.279941i	0.553144	−	0.833086i	$-0.313428\pi$
$883$	−8.31854	−	8.31854i	−0.279941	−	0.279941i	−0.833086	+	0.553144i	$0.813428\pi$
$884$	16.9868	−	7.67183i	0.571329	−	0.258032i
$885$		0			0
$886$	−37.2706	−	21.5182i	−1.25213	−	0.722917i
$887$	51.2751	−	13.7391i	1.72165	−	0.461314i	0.743416	−	0.668829i	$-0.233204\pi$
$887$	51.2751	−	13.7391i	1.72165	−	0.461314i	0.978232	+	0.207515i	$0.0665375\pi$
$888$	−15.2272	−	12.7380i	−0.510992	−	0.427458i
$889$	7.40642			0.248403
$890$		0			0
$891$	−4.31956	+	1.60185i	−0.144711	+	0.0536641i
$892$	26.9031	+	26.9031i	0.900782	+	0.900782i
$893$	−21.1789	−	5.67488i	−0.708726	−	0.189903i
$894$	11.9201	+	16.9689i	0.398666	+	0.567525i
$895$		0			0
$896$		−	4.83633i		−	0.161571i
$897$	−35.1681	+	9.02455i	−1.17423	+	0.301321i
$898$	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
$903$	4.01772	+	3.36093i	0.133701	+	0.111845i
$904$	−2.59891	−	4.50145i	−0.0864385	−	0.149716i
$905$		0			0
$906$	−13.1215	+	1.16799i	−0.435934	+	0.0388039i
$907$	4.37099	+	16.3128i	0.145136	+	0.541657i	0.999749	+	0.0223908i	$0.00712782\pi$
$907$	4.37099	+	16.3128i	0.145136	+	0.541657i	−0.854613	+	0.519266i	$0.826206\pi$
$908$	23.3263	−	6.25027i	0.774111	−	0.207422i
$909$	−16.9109	−	20.0303i	−0.560900	−	0.664362i
$910$		0			0
$911$		−	52.3968i		−	1.73598i	−0.496579	−	0.867992i	$-0.665411\pi$
$911$		−	52.3968i		−	1.73598i	0.496579	−	0.867992i	$-0.334589\pi$
$912$	10.6313	+	1.85801i	0.352038	+	0.0615248i
$913$	−4.30517	+	1.15357i	−0.142480	+	0.0381775i
$914$	−28.2656	−	48.9575i	−0.934945	−	1.61937i
$915$		0			0
$916$	−32.6511	+	18.8511i	−1.07882	+	0.622858i
$917$	1.46493	+	0.392528i	0.0483764	+	0.0129624i
$918$	18.6712	+	10.6671i	0.616241	+	0.352068i
$919$	−12.0636	+	6.96489i	−0.397940	+	0.229751i	−0.685595	−	0.727983i	$-0.740458\pi$
$919$	−12.0636	+	6.96489i	−0.397940	+	0.229751i	0.287655	+	0.957734i	$0.407124\pi$
$920$		0			0
$921$	−25.4236	−	36.1920i	−0.837736	−	1.19257i
$922$	20.5197	−	20.5197i	0.675779	−	0.675779i
$923$	−16.3834	+	13.4123i	−0.539266	+	0.441472i
$924$	0.911214	+	0.423229i	0.0299767	+	0.0139232i
$925$		0			0
$926$	10.0880	+	5.82433i	0.331514	+	0.191400i
$927$	14.5103	+	30.8733i	0.476581	+	1.01401i
$928$	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
$932$	−10.6067	+	39.5848i	−0.347434	+	1.29664i
$933$	−7.74152	+	44.2961i	−0.253446	+	1.45019i
$934$	−24.3501	+	42.1756i	−0.796759	+	1.38003i
$935$		0			0
$936$	13.7690	−	9.45570i	0.450053	−	0.309069i
$937$	−35.9634	+	35.9634i	−1.17487	+	1.17487i	−0.193841	+	0.981033i	$0.562095\pi$
$937$	−35.9634	+	35.9634i	−1.17487	+	1.17487i	−0.981033	+	0.193841i	$0.937905\pi$
$938$	8.46819	−	2.26904i	0.276496	−	0.0740869i
$939$	1.75969	+	2.50502i	0.0574252	+	0.0817482i
$940$		0			0
$941$	28.4119			0.926201			0.463101	−	0.886306i	$-0.346737\pi$
$941$	28.4119			0.926201			0.463101	+	0.886306i	$0.346737\pi$
$942$	5.18185	+	4.33474i	0.168834	+	0.141234i
$943$	19.9197	+	5.33747i	0.648675	+	0.173812i
$944$		−	4.16798i		−	0.135656i
$945$		0			0
$946$	−4.02006	+	6.96295i	−0.130704	+	0.226385i
$947$	−13.2241	−	49.3529i	−0.429725	−	1.60375i	−0.753384	−	0.657581i	$-0.771580\pi$
$947$	−13.2241	−	49.3529i	−0.429725	−	1.60375i	0.323659	−	0.946174i	$-0.395087\pi$
$948$	23.2217	+	63.5022i	0.754207	+	2.06246i
$949$	8.70484	+	6.25377i	0.282571	+	0.203006i
$950$		0			0
$951$	25.4554	−	17.8815i	0.825449	−	0.579849i
$952$	−0.318462	−	1.18852i	−0.0103214	−	0.0385200i
$953$	12.7834	+	3.42531i	0.414095	+	0.110957i	0.459851	−	0.887996i	$-0.347903\pi$
$953$	12.7834	+	3.42531i	0.414095	+	0.110957i	−0.0457555	+	0.998953i	$0.514570\pi$
$954$	−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
$958$	11.2698	−	42.0595i	0.364111	−	1.35888i
$959$	0.805764	−	1.39562i	0.0260195	−	0.0450671i
$960$		0			0
$961$	21.4642			0.692394
$962$	44.9485	−	36.7972i	1.44920	−	1.18639i
$963$	−36.0763	−	3.04632i	−1.16254	−	0.0981663i
$964$	−7.04833	+	12.2081i	−0.227011	+	0.393195i
$965$		0			0
$966$	0.809926	+	9.09895i	0.0260589	+	0.292754i
$967$	−11.1974	−	11.1974i	−0.360084	−	0.360084i	0.503760	−	0.863844i	$-0.331950\pi$
$967$	−11.1974	−	11.1974i	−0.360084	−	0.360084i	−0.863844	+	0.503760i	$0.831950\pi$
$968$	4.29165	−	16.0166i	0.137939	−	0.514794i
$969$	9.89629	−	0.880900i	0.317915	−	0.0282986i
$970$		0			0
$971$	28.5582	−	16.4881i	0.916478	−	0.529129i	0.0339681	−	0.999423i	$-0.489186\pi$
$971$	28.5582	−	16.4881i	0.916478	−	0.529129i	0.882510	+	0.470294i	$0.155852\pi$
$972$	39.8261	+	14.1553i	1.27742	+	0.454033i
$973$	−0.852466	−	3.18145i	−0.0273288	−	0.101993i
$974$	62.0152			1.98710
$975$		0			0
$976$	22.3510			0.715439
$977$	5.03105	+	18.7761i	0.160957	+	0.600701i	0.998521	+	0.0543619i	$0.0173125\pi$
$977$	5.03105	+	18.7761i	0.160957	+	0.600701i	−0.837564	+	0.546339i	$0.816021\pi$
$978$	5.04952	−	28.8927i	0.161466	−	0.923887i
$979$	5.37310	−	3.10216i	0.171725	−	0.0991455i
$980$		0			0
$981$	−39.7901	−	14.3462i	−1.27040	−	0.458040i
$982$	−16.3202	+	60.9079i	−0.520799	+	1.94365i
$983$	33.5020	+	33.5020i	1.06855	+	1.06855i	0.997471	+	0.0710772i	$0.0226437\pi$
$983$	33.5020	+	33.5020i	1.06855	+	1.06855i	0.0710772	+	0.997471i	$0.477356\pi$
$984$	−9.44991	+	0.841166i	−0.301252	+	0.0268154i
$985$		0			0
$986$	16.5462	−	28.6589i	0.526939	−	0.912685i
$987$	−1.81177	−	4.95447i	−0.0576693	−	0.157702i
$988$	10.3942	−	27.5155i	0.330683	−	0.875385i
$989$	−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	$-0.165022\pi$
$992$	−6.06119	+	22.6207i	−0.192443	+	0.718207i
$993$	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
$997$	−15.1389	−	4.05645i	−0.479453	−	0.128469i	0.0109949	−	0.999940i	$-0.496500\pi$
$997$	−15.1389	−	4.05645i	−0.479453	−	0.128469i	−0.490448	+	0.871471i	$0.663167\pi$
$998$	11.2856	+	42.1184i	0.357239	+	1.33323i
$999$	37.2992	+	9.81309i	1.18009	+	0.310472i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(0.561788 + 2.09662i) q^{2} +(-1.70619 - 0.298187i) q^{3} +(-2.34816 + 1.35571i) q^{4} +(-0.333332 - 3.74475i) q^{6} +(0.108168 - 0.403690i) q^{7} +(-1.09192 - 1.09192i) q^{8} +(2.82217 + 1.01753i) q^{9} +(-0.255945 + 0.443309i) q^{11} +(4.41067 - 1.61291i) q^{12} +(0.583017 + 3.55810i) q^{13} +0.907153 q^{14} +(-1.03551 + 1.79356i) q^{16} +(-0.493455 + 1.84160i) q^{17} +(-0.547908 + 6.48865i) q^{18} +(1.50433 + 2.60558i) q^{19} +(-0.304931 + 0.656518i) q^{21} +(-1.07324 - 0.287573i) q^{22} +(-1.50474 - 5.61575i) q^{23} +(1.53743 + 2.18862i) q^{24} +(-7.13246 + 3.22126i) q^{26} +(-4.51174 - 2.57763i) q^{27} +(0.293291 + 1.09458i) q^{28} +(-3.99826 + 6.92519i) q^{29} -3.08801i q^{31} +(-7.32533 - 1.96282i) q^{32} +(0.568879 - 0.680051i) q^{33} -4.13835 q^{34} +(-8.00639 + 1.43673i) q^{36} +(-7.16959 + 1.92109i) q^{37} +(-4.61780 + 4.61780i) q^{38} +(0.0662412 - 6.24465i) q^{39} +(-1.77356 + 3.07189i) q^{41} +(-1.54778 - 0.270501i) q^{42} +(1.87287 - 6.98963i) q^{43} -1.38795i q^{44} +(10.9288 - 6.30972i) q^{46} +(-5.15313 + 5.15313i) q^{47} +(2.30160 - 2.75138i) q^{48} +(5.91091 + 3.41267i) q^{49} +(1.39107 - 2.99498i) q^{51} +(-6.19278 - 7.56460i) q^{52} +(-7.15880 + 7.15880i) q^{53} +(2.86967 - 10.9075i) q^{54} +(-0.558908 + 0.322686i) q^{56} +(-1.78973 - 4.89419i) q^{57} +(-16.7657 - 4.49235i) q^{58} +(-1.74290 + 1.00626i) q^{59} +(-5.39613 - 9.34638i) q^{61} +(6.47438 - 1.73481i) q^{62} +(0.716035 - 1.02922i) q^{63} -12.3191i q^{64} +(1.74540 + 0.810680i) q^{66} +(9.33491 - 2.50128i) q^{67} +(-1.33797 - 4.99336i) q^{68} +(0.892822 + 10.0302i) q^{69} +(2.93620 + 5.08564i) q^{71} +(-1.97052 - 4.19264i) 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} +(13.1299 - 3.36928i) q^{78} +14.3974i q^{79} +(6.92928 + 5.74327i) q^{81} +(-7.43696 - 1.99273i) q^{82} +(6.15680 + 6.15680i) q^{83} +(-0.174021 - 1.95501i) q^{84} +15.7068 q^{86} +(8.88680 - 10.6235i) q^{87} +(0.763529 - 0.204587i) q^{88} +(-10.4966 - 6.06022i) q^{89} +(1.49943 + 0.149516i) q^{91} +(11.1467 + 11.1467i) q^{92} +(-0.920803 + 5.26873i) q^{93} +(-13.6991 - 7.90919i) q^{94} +(11.9131 + 5.53326i) q^{96} +(4.19510 - 15.6563i) q^{97} +(-3.83439 + 14.3101i) 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

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Database

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