LMFDB - Embedded newform 375.3.k.b.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(7,375)] 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("375.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 17])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.k (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,-4,0,0,0,0,4,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	375.7
Dual form			375.3.k.b.268.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.22224 + 1.13229i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.30514 - 1.79637i) q^{4} +(-3.49485 + 2.53916i) q^{6} +(-3.10232 - 3.10232i) q^{7} +(0.694313 - 4.38372i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-2.50856 + 7.72057i) q^{11} +(1.74601 - 3.42674i) q^{12} +(2.93716 + 1.49656i) q^{13} +(10.4068 + 3.38139i) q^{14} +(6.16532 + 18.9749i) q^{16} +(-27.8560 - 4.41196i) q^{17} +(-5.29075 + 5.29075i) q^{18} +(15.2294 + 20.9615i) q^{19} +(-6.14781 - 4.46664i) q^{21} +(-3.16728 - 19.9974i) q^{22} +(8.88304 + 17.4339i) q^{23} -7.68747i q^{24} -8.22163 q^{26} +(4.62981 - 2.35900i) q^{27} +(-9.62191 + 1.52396i) q^{28} +(-20.3892 + 28.0633i) q^{29} +(8.77688 - 6.37677i) q^{31} +(-22.6323 - 22.6323i) q^{32} +(-2.19956 + 13.8875i) q^{33} +(66.8985 - 21.7366i) q^{34} +(2.05846 - 6.33529i) q^{36} +(-11.0377 + 21.6628i) q^{37} +(-57.5779 - 29.3374i) q^{38} +(5.43018 + 1.76437i) q^{39} +(13.9284 + 42.8673i) q^{41} +(18.7195 + 2.96487i) q^{42} +(8.53203 - 8.53203i) q^{43} +(10.5950 + 14.5828i) q^{44} +(-39.4805 - 28.6843i) q^{46} +(6.30548 + 39.8112i) q^{47} +(15.6885 + 30.7904i) q^{48} -29.7512i q^{49} -48.8495 q^{51} +(6.52180 - 3.32302i) q^{52} +(-90.1725 + 14.2819i) q^{53} +(-7.61748 + 10.4846i) q^{54} +(-15.7537 + 11.4457i) q^{56} +(31.7329 + 31.7329i) q^{57} +(13.5339 - 85.4499i) q^{58} +(-101.152 + 32.8662i) q^{59} +(-4.73879 + 14.5845i) q^{61} +(-12.2840 + 24.1087i) q^{62} +(-11.7275 - 5.97544i) q^{63} +(0.0212563 + 0.00690660i) q^{64} +(-10.8367 - 33.3519i) q^{66} +(-26.4335 - 4.18666i) q^{67} +(-44.2816 + 44.2816i) q^{68} +(19.9202 + 27.4178i) q^{69} +(-41.3332 - 30.0303i) q^{71} +(-2.08294 - 13.1512i) q^{72} +(51.7793 + 101.623i) q^{73} -60.6378i q^{74} +57.5312 q^{76} +(31.7341 - 16.1693i) q^{77} +(-14.0650 + 2.22767i) q^{78} +(-21.7607 + 29.9510i) q^{79} +(7.28115 - 5.29007i) q^{81} +(-79.4905 - 79.4905i) q^{82} +(16.2002 - 102.284i) q^{83} +(-16.0475 + 5.21416i) q^{84} +(-9.29951 + 28.6210i) q^{86} +(-27.2765 + 53.5331i) q^{87} +(32.1031 + 16.3573i) q^{88} +(-108.616 - 35.2914i) q^{89} +(-4.46922 - 13.7548i) q^{91} +(42.9115 + 6.79652i) q^{92} +(13.2870 - 13.2870i) q^{93} +(-59.0902 - 81.3306i) q^{94} +(-44.8500 - 32.5855i) q^{96} +(9.20986 + 58.1488i) q^{97} +(33.6869 + 66.1143i) q^{98} +24.3537i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} + 4 q^{7} + 72 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} - 40 q^{17} + 48 q^{18} + 100 q^{19} - 280 q^{22} - 264 q^{23} - 40 q^{26} + 44 q^{28} - 200 q^{29} - 636 q^{32} - 36 q^{33} - 100 q^{34}+ \cdots - 828 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 + 4 * q^7 + 72 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 - 40 * q^17 + 48 * q^18 + 100 * q^19 - 280 * q^22 - 264 * q^23 - 40 * q^26 + 44 * q^28 - 200 * q^29 - 636 * q^32 - 36 * q^33 - 100 * q^34 - 120 * q^36 + 124 * q^37 - 96 * q^38 + 160 * q^41 + 252 * q^42 + 472 * q^43 + 700 * q^44 + 128 * q^47 + 48 * q^48 + 620 * q^52 + 76 * q^53 - 72 * q^57 + 108 * q^58 - 800 * q^59 - 240 * q^61 + 328 * q^62 - 168 * q^63 - 100 * q^64 + 1240 * q^67 - 104 * q^68 - 216 * q^72 - 244 * q^73 + 648 * q^77 + 120 * q^78 - 200 * q^79 + 180 * q^81 + 168 * q^82 + 44 * q^83 + 1200 * q^84 - 84 * q^87 - 1008 * q^88 + 1500 * q^89 - 2236 * q^92 + 648 * q^93 + 200 * q^94 + 60 * q^96 - 200 * q^97 - 828 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$1$

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 $

$2$	−2.22224	+	1.13229i	−1.11112	+	0.566145i	−0.910494	−	0.413523i	$-0.864298\pi$
$2$	−2.22224	+	1.13229i	−1.11112	+	0.566145i	−0.200628	+	0.979668i	$0.564298\pi$
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$4$	1.30514	−	1.79637i	0.326286	−	0.449094i
$5$		0			0
$5$		0			0
$6$	−3.49485	+	2.53916i	−0.582475	+	0.423193i
$7$	−3.10232	−	3.10232i	−0.443189	−	0.443189i	0.449893	−	0.893082i	$-0.351462\pi$
$7$	−3.10232	−	3.10232i	−0.443189	−	0.443189i	−0.893082	+	0.449893i	$0.851462\pi$
$8$	0.694313	−	4.38372i	0.0867892	−	0.547965i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$		0			0
$11$	−2.50856	+	7.72057i	−0.228051	+	0.701870i	0.769916	+	0.638145i	$0.220298\pi$
$11$	−2.50856	+	7.72057i	−0.228051	+	0.701870i	−0.997968	+	0.0637248i	$0.979702\pi$
$12$	1.74601	−	3.42674i	0.145501	−	0.285561i
$13$	2.93716	+	1.49656i	0.225936	+	0.115120i	0.563295	−	0.826256i	$-0.309534\pi$
$13$	2.93716	+	1.49656i	0.225936	+	0.115120i	−0.337359	+	0.941376i	$0.609534\pi$
$14$	10.4068	+	3.38139i	0.743346	+	0.241528i
$15$		0			0
$16$	6.16532	+	18.9749i	0.385333	+	1.18593i
$17$	−27.8560	−	4.41196i	−1.63859	−	0.259527i	−0.731927	−	0.681383i	$-0.761379\pi$
$17$	−27.8560	−	4.41196i	−1.63859	−	0.259527i	−0.906663	+	0.421856i	$0.861379\pi$
$18$	−5.29075	+	5.29075i	−0.293930	+	0.293930i
$19$	15.2294	+	20.9615i	0.801547	+	1.10324i	0.992573	+	0.121650i	$0.0388186\pi$
$19$	15.2294	+	20.9615i	0.801547	+	1.10324i	−0.191026	+	0.981585i	$0.561181\pi$
$20$		0			0
$21$	−6.14781	−	4.46664i	−0.292753	−	0.212697i
$22$	−3.16728	−	19.9974i	−0.143967	−	0.908972i
$23$	8.88304	+	17.4339i	0.386219	+	0.757997i	0.999492	−	0.0318737i	$-0.0101474\pi$
$23$	8.88304	+	17.4339i	0.386219	+	0.757997i	−0.613273	+	0.789871i	$0.710147\pi$
$24$		−	7.68747i		−	0.320311i
$25$		0			0
$26$	−8.22163			−0.316216
$27$	4.62981	−	2.35900i	0.171474	−	0.0873705i
$28$	−9.62191	+	1.52396i	−0.343640	+	0.0544272i
$29$	−20.3892	+	28.0633i	−0.703075	+	0.967699i	0.296844	+	0.954926i	$0.404066\pi$
$29$	−20.3892	+	28.0633i	−0.703075	+	0.967699i	−0.999918	+	0.0127733i	$0.995934\pi$
$30$		0			0
$31$	8.77688	−	6.37677i	0.283125	−	0.205702i	−0.437154	−	0.899387i	$-0.644014\pi$
$31$	8.77688	−	6.37677i	0.283125	−	0.205702i	0.720279	+	0.693684i	$0.244014\pi$
$32$	−22.6323	−	22.6323i	−0.707261	−	0.707261i
$33$	−2.19956	+	13.8875i	−0.0666534	+	0.420833i
$34$	66.8985	−	21.7366i	1.96760	−	0.639313i
$35$		0			0
$36$	2.05846	−	6.33529i	0.0571795	−	0.175980i
$37$	−11.0377	+	21.6628i	−0.298317	+	0.585480i	−0.990702	−	0.136048i	$-0.956560\pi$
$37$	−11.0377	+	21.6628i	−0.298317	+	0.585480i	0.692385	+	0.721528i	$0.256560\pi$
$38$	−57.5779	−	29.3374i	−1.51521	−	0.772037i
$39$	5.43018	+	1.76437i	0.139235	+	0.0452403i
$40$		0			0
$41$	13.9284	+	42.8673i	0.339718	+	1.04554i	0.964351	+	0.264626i	$0.0852484\pi$
$41$	13.9284	+	42.8673i	0.339718	+	1.04554i	−0.624634	+	0.780918i	$0.714752\pi$
$42$	18.7195	+	2.96487i	0.445701	+	0.0705921i
$43$	8.53203	−	8.53203i	0.198419	−	0.198419i	−0.600903	−	0.799322i	$-0.705192\pi$
$43$	8.53203	−	8.53203i	0.198419	−	0.198419i	0.799322	+	0.600903i	$0.205192\pi$
$44$	10.5950	+	14.5828i	0.240795	+	0.331426i
$45$		0			0
$46$	−39.4805	−	28.6843i	−0.858272	−	0.623571i
$47$	6.30548	+	39.8112i	0.134159	+	0.847048i	0.959355	+	0.282201i	$0.0910646\pi$
$47$	6.30548	+	39.8112i	0.134159	+	0.847048i	−0.825196	+	0.564846i	$0.808935\pi$
$48$	15.6885	+	30.7904i	0.326843	+	0.641466i
$49$		−	29.7512i		−	0.607167i
$50$		0			0
$51$	−48.8495			−0.957833
$52$	6.52180	−	3.32302i	0.125419	−	0.0639042i
$53$	−90.1725	+	14.2819i	−1.70137	+	0.269470i	−0.930171	−	0.367127i	$-0.880341\pi$
$53$	−90.1725	+	14.2819i	−1.70137	+	0.269470i	−0.771197	+	0.636597i	$0.780341\pi$
$54$	−7.61748	+	10.4846i	−0.141064	+	0.194158i
$55$		0			0
$56$	−15.7537	+	11.4457i	−0.281316	+	0.204388i
$57$	31.7329	+	31.7329i	0.556718	+	0.556718i
$58$	13.5339	−	85.4499i	0.233344	−	1.47327i
$59$	−101.152	+	32.8662i	−1.71444	+	0.557055i	−0.991062	−	0.133399i	$-0.957411\pi$
$59$	−101.152	+	32.8662i	−1.71444	+	0.557055i	−0.723377	+	0.690454i	$0.757411\pi$
$60$		0			0
$61$	−4.73879	+	14.5845i	−0.0776851	+	0.239090i	−0.982356	−	0.187021i	$-0.940117\pi$
$61$	−4.73879	+	14.5845i	−0.0776851	+	0.239090i	0.904671	+	0.426111i	$0.140117\pi$
$62$	−12.2840	+	24.1087i	−0.198129	+	0.388850i
$63$	−11.7275	−	5.97544i	−0.186150	−	0.0948483i
$64$	0.0212563	+	0.00690660i	0.000332130	+	0.000107916i
$65$		0			0
$66$	−10.8367	−	33.3519i	−0.164192	−	0.505332i
$67$	−26.4335	−	4.18666i	−0.394530	−	0.0624874i	−0.0439823	−	0.999032i	$-0.514005\pi$
$67$	−26.4335	−	4.18666i	−0.394530	−	0.0624874i	−0.350548	+	0.936545i	$0.614005\pi$
$68$	−44.2816	+	44.2816i	−0.651200	+	0.651200i
$69$	19.9202	+	27.4178i	0.288699	+	0.397360i
$70$		0			0
$71$	−41.3332	−	30.0303i	−0.582158	−	0.422963i	0.257343	−	0.966320i	$-0.417153\pi$
$71$	−41.3332	−	30.0303i	−0.582158	−	0.422963i	−0.839501	+	0.543357i	$0.817153\pi$
$72$	−2.08294	−	13.1512i	−0.0289297	−	0.182655i
$73$	51.7793	+	101.623i	0.709306	+	1.39209i	0.910902	+	0.412622i	$0.135387\pi$
$73$	51.7793	+	101.623i	0.709306	+	1.39209i	−0.201596	+	0.979469i	$0.564613\pi$
$74$		−	60.6378i		−	0.819430i
$75$		0			0
$76$	57.5312			0.756989
$77$	31.7341	−	16.1693i	0.412131	−	0.209991i
$78$	−14.0650	+	2.22767i	−0.180320	+	0.0285599i
$79$	−21.7607	+	29.9510i	−0.275452	+	0.379127i	−0.924221	−	0.381859i	$-0.875284\pi$
$79$	−21.7607	+	29.9510i	−0.275452	+	0.379127i	0.648769	+	0.760985i	$0.275284\pi$
$80$		0			0
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	−79.4905	−	79.4905i	−0.969396	−	0.969396i
$83$	16.2002	−	102.284i	0.195183	−	1.23234i	−0.674332	−	0.738429i	$-0.735568\pi$
$83$	16.2002	−	102.284i	0.195183	−	1.23234i	0.869514	−	0.493907i	$-0.164432\pi$
$84$	−16.0475	+	5.21416i	−0.191042	+	0.0620733i
$85$		0			0
$86$	−9.29951	+	28.6210i	−0.108134	+	0.332802i
$87$	−27.2765	+	53.5331i	−0.313523	+	0.615323i
$88$	32.1031	+	16.3573i	0.364808	+	0.185879i
$89$	−108.616	−	35.2914i	−1.22040	−	0.396533i	−0.373175	−	0.927761i	$-0.621731\pi$
$89$	−108.616	−	35.2914i	−1.22040	−	0.396533i	−0.847229	+	0.531228i	$0.821731\pi$
$90$		0			0
$91$	−4.46922	−	13.7548i	−0.0491123	−	0.151152i
$92$	42.9115	+	6.79652i	0.466429	+	0.0738752i
$93$	13.2870	−	13.2870i	0.142871	−	0.142871i
$94$	−59.0902	−	81.3306i	−0.628619	−	0.865219i
$95$		0			0
$96$	−44.8500	−	32.5855i	−0.467188	−	0.339432i
$97$	9.20986	+	58.1488i	0.0949470	+	0.599472i	0.988583	+	0.150679i	$0.0481460\pi$
$97$	9.20986	+	58.1488i	0.0949470	+	0.599472i	−0.893636	+	0.448793i	$0.851854\pi$
$98$	33.6869	+	66.1143i	0.343744	+	0.674636i
$99$			24.3537i			0.245997i
$100$		0			0
$101$	76.1042			0.753507			0.376754	−	0.926313i	$-0.377040\pi$
$101$	76.1042			0.753507			0.376754	+	0.926313i	$0.377040\pi$
$102$	108.555	−	55.3117i	1.06427	−	0.542272i
$103$	3.16859	−	0.501856i	0.0307631	−	0.00487239i	−0.141034	−	0.990005i	$-0.545043\pi$
$103$	3.16859	−	0.501856i	0.0307631	−	0.00487239i	0.171797	+	0.985132i	$0.445043\pi$
$104$	8.59981	−	11.8366i	0.0826905	−	0.113814i
$105$		0			0
$106$	184.214	−	133.839i	1.73787	−	1.26263i
$107$	93.9432	+	93.9432i	0.877974	+	0.877974i	0.993325	−	0.115351i	$-0.0367993\pi$
$107$	93.9432	+	93.9432i	0.877974	+	0.877974i	−0.115351	+	0.993325i	$0.536799\pi$
$108$	1.80490	−	11.3957i	0.0167121	−	0.105516i
$109$	203.328	−	66.0652i	1.86539	−	0.606103i	0.872269	−	0.489026i	$-0.162648\pi$
$109$	203.328	−	66.0652i	1.86539	−	0.606103i	0.993123	−	0.117076i	$-0.0373523\pi$
$110$		0			0
$111$	−13.0130	+	40.0498i	−0.117234	+	0.360809i
$112$	39.7395	−	77.9931i	0.354817	−	0.696367i
$113$	125.909	+	64.1541i	1.11424	+	0.567735i	0.911419	−	0.411480i	$-0.134988\pi$
$113$	125.909	+	64.1541i	1.11424	+	0.567735i	0.202824	+	0.979215i	$0.434988\pi$
$114$	−106.449	−	34.5874i	−0.933763	−	0.303398i
$115$		0			0
$116$	23.8014	+	73.2532i	0.205184	+	0.631493i
$117$	9.76761	+	1.54704i	0.0834838	+	0.0132225i
$118$	187.570	−	187.570i	1.58958	−	1.58958i
$119$	72.7311	+	100.106i	0.611185	+	0.841224i
$120$		0			0
$121$	44.5768	+	32.3869i	0.368403	+	0.267661i
$122$	−5.98312	−	37.7760i	−0.0490420	−	0.309639i
$123$	35.4427	+	69.5603i	0.288152	+	0.565531i
$124$		−	24.0892i		−	0.194267i
$125$		0			0
$126$	32.8272			0.260533
$127$	−166.206	+	84.6861i	−1.30871	+	0.666820i	−0.962486	−	0.271332i	$-0.912536\pi$
$127$	−166.206	+	84.6861i	−1.30871	+	0.666820i	−0.346222	+	0.938152i	$0.612536\pi$
$128$	126.397	−	20.0193i	0.987473	−	0.156400i
$129$	12.2842	−	16.9077i	0.0952263	−	0.131068i
$130$		0			0
$131$	132.639	−	96.3682i	1.01251	−	0.735635i	0.0477795	−	0.998858i	$-0.484786\pi$
$131$	132.639	−	96.3682i	1.01251	−	0.735635i	0.964735	+	0.263223i	$0.0847855\pi$
$132$	22.0764	+	22.0764i	0.167245	+	0.167245i
$133$	17.7827	−	112.276i	0.133705	−	0.844179i
$134$	63.4822	−	20.6266i	0.473748	−	0.153930i
$135$		0			0
$136$	−38.6816	+	119.050i	−0.284424	+	0.875366i
$137$	57.9190	−	113.672i	0.422766	−	0.829726i	−0.577148	−	0.816640i	$-0.695834\pi$
$137$	57.9190	−	113.672i	0.422766	−	0.829726i	0.999914	−	0.0130861i	$-0.00416557\pi$
$138$	−75.3124	−	38.3736i	−0.545742	−	0.278070i
$139$	17.6523	+	5.73557i	0.126995	+	0.0412631i	0.371825	−	0.928303i	$-0.378732\pi$
$139$	17.6523	+	5.73557i	0.126995	+	0.0412631i	−0.244830	+	0.969566i	$0.578732\pi$
$140$		0			0
$141$	21.5739	+	66.3977i	0.153006	+	0.470905i
$142$	125.855	+	19.9335i	0.886306	+	0.140377i
$143$	−18.9223	+	18.9223i	−0.132324	+	0.132324i
$144$	35.1814	+	48.4231i	0.244315	+	0.336271i
$145$		0			0
$146$	−230.132	−	167.201i	−1.57625	−	1.14521i
$147$	−8.06116	−	50.8961i	−0.0548378	−	0.346232i
$148$	24.5086	+	48.1009i	0.165599	+	0.325006i
$149$			10.5645i			0.0709024i	0.999371	+	0.0354512i	$0.0112868\pi$
$149$			10.5645i			0.0709024i	−0.999371	+	0.0354512i	$0.988713\pi$
$150$		0			0
$151$	119.808			0.793433			0.396716	−	0.917941i	$-0.370150\pi$
$151$	119.808			0.793433			0.396716	+	0.917941i	$0.370150\pi$
$152$	102.463	−	52.2076i	0.674100	−	0.343471i
$153$	−83.5681	+	13.2359i	−0.546197	+	0.0865090i
$154$	−52.2125	+	71.8643i	−0.339042	+	0.466651i
$155$		0			0
$156$	10.2566	−	7.45188i	0.0657476	−	0.0477684i
$157$	−61.8710	−	61.8710i	−0.394083	−	0.394083i	0.482057	−	0.876140i	$-0.339890\pi$
$157$	−61.8710	−	61.8710i	−0.394083	−	0.394083i	−0.876140	+	0.482057i	$0.839890\pi$
$158$	14.4443	−	91.1978i	0.0914197	−	0.577202i
$159$	−150.391	+	48.8649i	−0.945854	+	0.307326i
$160$		0			0
$161$	26.5277	−	81.6438i	0.164768	−	0.507104i
$162$	−10.1906	+	20.0002i	−0.0629050	+	0.123458i
$163$	−262.372	−	133.685i	−1.60964	−	0.820153i	−0.999614	−	0.0277732i	$-0.991158\pi$
$163$	−262.372	−	133.685i	−1.60964	−	0.820153i	−0.610028	−	0.792380i	$-0.708842\pi$
$164$	95.1843	+	30.9272i	0.580392	+	0.188581i
$165$		0			0
$166$	79.8142	+	245.643i	0.480809	+	1.47978i
$167$	−27.9969	−	4.43427i	−0.167646	−	0.0265525i	0.0720471	−	0.997401i	$-0.477047\pi$
$167$	−27.9969	−	4.43427i	−0.167646	−	0.0265525i	−0.239693	+	0.970849i	$0.577047\pi$
$168$	−23.8490	+	23.8490i	−0.141958	+	0.141958i
$169$	−92.9485	−	127.933i	−0.549991	−	0.756998i
$170$		0			0
$171$	62.8844	+	45.6882i	0.367745	+	0.267182i
$172$	−4.19120	−	26.4622i	−0.0243675	−	0.153850i
$173$	21.3003	+	41.8042i	0.123123	+	0.241643i	0.944338	−	0.328976i	$-0.106703\pi$
$173$	21.3003	+	41.8042i	0.123123	+	0.241643i	−0.821215	+	0.570619i	$0.806703\pi$
$174$		−	149.848i		−	0.861198i
$175$		0			0
$176$	−161.963			−0.920246
$177$	−164.138	+	83.6325i	−0.927334	+	0.472500i
$178$	281.331	−	44.5585i	1.58051	−	0.250328i
$179$	65.0062	−	89.4733i	0.363163	−	0.499851i	−0.587864	−	0.808960i	$-0.700031\pi$
$179$	65.0062	−	89.4733i	0.363163	−	0.499851i	0.951027	+	0.309109i	$0.100031\pi$
$180$		0			0
$181$	152.214	−	110.590i	0.840962	−	0.610995i	−0.0816769	−	0.996659i	$-0.526028\pi$
$181$	152.214	−	110.590i	0.840962	−	0.610995i	0.922639	+	0.385664i	$0.126028\pi$
$182$	25.5061	+	25.5061i	0.140144	+	0.140144i
$183$	−4.15507	+	26.2341i	−0.0227053	+	0.143356i
$184$	82.5931	−	26.8361i	0.448876	−	0.145849i
$185$		0			0
$186$	−14.4822	+	44.5718i	−0.0778615	+	0.239633i
$187$	103.941	−	203.997i	0.555837	−	1.09089i
$188$	79.7455	+	40.6323i	0.424178	+	0.216129i
$189$	−21.6815	−	7.04476i	−0.114717	−	0.0372739i
$190$		0			0
$191$	−47.3319	−	145.673i	−0.247811	−	0.762683i	−0.995161	−	0.0982534i	$-0.968674\pi$
$191$	−47.3319	−	145.673i	−0.247811	−	0.762683i	0.747351	−	0.664430i	$-0.231326\pi$
$192$	0.0382351	+	0.00605585i	0.000199141	+	3.15409e-5i
$193$	−243.828	+	243.828i	−1.26336	+	1.26336i	−0.313901	+	0.949456i	$0.601636\pi$
$193$	−243.828	+	243.828i	−1.26336	+	1.26336i	−0.949456	+	0.313901i	$0.898364\pi$
$194$	−86.3078	−	118.792i	−0.444885	−	0.612332i
$195$		0			0
$196$	−53.4443	−	38.8295i	−0.272675	−	0.198110i
$197$	33.5989	+	212.135i	0.170553	+	1.07683i	0.913309	+	0.407266i	$0.133518\pi$
$197$	33.5989	+	212.135i	0.170553	+	1.07683i	−0.742757	+	0.669562i	$0.766482\pi$
$198$	−27.5754	−	54.1197i	−0.139270	−	0.273332i
$199$			261.788i			1.31552i	0.753228	+	0.657760i	$0.228496\pi$
$199$			261.788i			1.31552i	−0.753228	+	0.657760i	$0.771504\pi$
$200$		0			0
$201$	−46.3549			−0.230621
$202$	−169.122	+	86.1720i	−0.837238	+	0.426594i
$203$	150.315	−	23.8076i	0.740469	−	0.117279i
$204$	−63.7555	+	87.7519i	−0.312527	+	0.430157i
$205$		0			0
$206$	−6.47314	+	4.70301i	−0.0314230	+	0.0228302i
$207$	41.5070	+	41.5070i	0.200517	+	0.200517i
$208$	−10.2885	+	64.9592i	−0.0494641	+	0.312304i
$209$	−200.038	+	64.9964i	−0.957121	+	0.310988i
$210$		0			0
$211$	−5.06063	+	15.5750i	−0.0239840	+	0.0738152i	−0.962332	−	0.271877i	$-0.912356\pi$
$211$	−5.06063	+	15.5750i	−0.0239840	+	0.0738152i	0.938348	+	0.345692i	$0.112356\pi$
$212$	−92.0323	+	180.623i	−0.434114	+	0.851997i
$213$	−78.8466	−	40.1744i	−0.370172	−	0.188612i
$214$	−315.135	−	102.394i	−1.47260	−	0.478475i
$215$		0			0
$216$	−7.12668	−	21.9337i	−0.0329939	−	0.101545i
$217$	−47.0115	−	7.44589i	−0.216643	−	0.0343129i
$218$	−377.039	+	377.039i	−1.72954	+	1.72954i
$219$	116.115	+	159.819i	0.530206	+	0.729766i
$220$		0			0
$221$	−75.2149	−	54.6468i	−0.340339	−	0.247271i
$222$	−16.4300	−	103.735i	−0.0740089	−	0.467274i
$223$	−19.6834	−	38.6309i	−0.0882664	−	0.173233i	0.842653	−	0.538457i	$-0.180992\pi$
$223$	−19.6834	−	38.6309i	−0.0882664	−	0.173233i	−0.930920	+	0.365224i	$0.880992\pi$
$224$			140.426i			0.626900i
$225$		0			0
$226$	−352.442			−1.55948
$227$	145.293	−	74.0305i	0.640058	−	0.326126i	−0.103667	−	0.994612i	$-0.533058\pi$
$227$	145.293	−	74.0305i	0.640058	−	0.326126i	0.743724	+	0.668486i	$0.233058\pi$
$228$	98.4201	−	15.5882i	0.431667	−	0.0683694i
$229$	5.52850	−	7.60933i	0.0241419	−	0.0332285i	−0.796775	−	0.604276i	$-0.793463\pi$
$229$	5.52850	−	7.60933i	0.0241419	−	0.0332285i	0.820917	+	0.571047i	$0.193463\pi$
$230$		0			0
$231$	49.9072	−	36.2597i	0.216048	−	0.156968i
$232$	108.865	+	108.865i	0.469246	+	0.469246i
$233$	−4.20377	+	26.5415i	−0.0180419	+	0.113912i	−0.995066	−	0.0992181i	$-0.968366\pi$
$233$	−4.20377	+	26.5415i	−0.0180419	+	0.113912i	0.977024	+	0.213130i	$0.0683659\pi$
$234$	−23.4577	+	7.62187i	−0.100247	+	0.0325721i
$235$		0			0
$236$	−72.9776	+	224.602i	−0.309227	+	0.951703i
$237$	−29.1113	+	57.1341i	−0.122832	+	0.241072i
$238$	−274.975	−	140.107i	−1.15536	−	0.588683i
$239$	325.106	+	105.633i	1.36028	+	0.441981i	0.896135	−	0.443781i	$-0.146363\pi$
$239$	325.106	+	105.633i	1.36028	+	0.441981i	0.464141	+	0.885761i	$0.346363\pi$
$240$		0			0
$241$	−27.6920	−	85.2271i	−0.114904	−	0.353639i	0.877023	−	0.480449i	$-0.159526\pi$
$241$	−27.6920	−	85.2271i	−0.114904	−	0.353639i	−0.991927	+	0.126810i	$0.959526\pi$
$242$	−135.732	−	21.4978i	−0.560875	−	0.0888339i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	20.0144	+	27.5475i	0.0820263	+	0.112900i
$245$		0			0
$246$	−157.525	−	114.448i	−0.640344	−	0.465237i
$247$	13.3611	+	84.3589i	0.0540937	+	0.341534i
$248$	−21.8601	−	42.9029i	−0.0881456	−	0.172995i
$249$		−	179.369i		−	0.720358i
$250$		0			0
$251$	−259.732			−1.03479			−0.517394	−	0.855747i	$-0.673098\pi$
$251$	−259.732			−1.03479			−0.517394	+	0.855747i	$0.673098\pi$
$252$	−26.0401	+	13.2681i	−0.103334	+	0.0526513i
$253$	−156.884	+	24.8479i	−0.620093	+	0.0982131i
$254$	273.461	−	376.386i	1.07662	−	1.48184i
$255$		0			0
$256$	−258.289	+	187.658i	−1.00894	+	0.733038i
$257$	124.723	+	124.723i	0.485305	+	0.485305i	0.906821	−	0.421516i	$-0.138502\pi$
$257$	124.723	+	124.723i	0.485305	+	0.485305i	−0.421516	+	0.906821i	$0.638502\pi$
$258$	−8.15400	+	51.4823i	−0.0316047	+	0.199544i
$259$	101.448	−	32.9623i	0.391689	−	0.127268i
$260$		0			0
$261$	−32.1577	+	98.9711i	−0.123209	+	0.379200i
$262$	−185.640	+	364.340i	−0.708551	+	1.39061i
$263$	−79.8979	−	40.7100i	−0.303794	−	0.154791i	0.295448	−	0.955359i	$-0.404531\pi$
$263$	−79.8979	−	40.7100i	−0.303794	−	0.154791i	−0.599242	+	0.800568i	$0.704531\pi$
$264$	59.3517	+	19.2845i	0.224817	+	0.0730474i
$265$		0			0
$266$	87.6111	+	269.639i	0.329365	+	1.01368i
$267$	−195.374	−	30.9443i	−0.731739	−	0.115896i
$268$	−42.0203	+	42.0203i	−0.156792	+	0.156792i
$269$	−29.3157	−	40.3496i	−0.108980	−	0.149999i	0.751043	−	0.660253i	$-0.229551\pi$
$269$	−29.3157	−	40.3496i	−0.108980	−	0.149999i	−0.860023	+	0.510255i	$0.829551\pi$
$270$		0			0
$271$	−176.269	−	128.067i	−0.650439	−	0.472571i	0.212982	−	0.977056i	$-0.431682\pi$
$271$	−176.269	−	128.067i	−0.650439	−	0.472571i	−0.863421	+	0.504485i	$0.831682\pi$
$272$	−88.0248	−	555.767i	−0.323621	−	2.04326i
$273$	−11.3725	−	22.3198i	−0.0416576	−	0.0817576i
$274$			318.189i			1.16127i
$275$		0			0
$276$	75.2514			0.272650
$277$	−31.6907	+	16.1472i	−0.114407	+	0.0582933i	−0.510257	−	0.860022i	$-0.670450\pi$
$277$	−31.6907	+	16.1472i	−0.114407	+	0.0582933i	0.395850	+	0.918315i	$0.370450\pi$
$278$	−45.7220	+	7.24165i	−0.164467	+	0.0260491i
$279$	19.1303	−	26.3306i	0.0685675	−	0.0943750i
$280$		0			0
$281$	300.785	−	218.533i	1.07041	−	0.777697i	0.0944226	−	0.995532i	$-0.469900\pi$
$281$	300.785	−	218.533i	1.07041	−	0.777697i	0.975986	+	0.217835i	$0.0698995\pi$
$282$	−123.124	−	123.124i	−0.436609	−	0.436609i
$283$	−39.1052	+	246.901i	−0.138181	+	0.872441i	0.817047	+	0.576571i	$0.195609\pi$
$283$	−39.1052	+	246.901i	−0.138181	+	0.872441i	−0.955228	+	0.295870i	$0.904391\pi$
$284$	−107.891	+	35.0561i	−0.379900	+	0.123437i
$285$		0			0
$286$	20.6245	−	63.4756i	0.0721136	−	0.221943i
$287$	89.7777	−	176.199i	0.312814	−	0.613933i
$288$	−85.5552	−	43.5926i	−0.297067	−	0.151363i
$289$	481.637	+	156.493i	1.66657	+	0.541500i
$290$		0			0
$291$	31.5111	+	96.9812i	0.108286	+	0.333269i
$292$	250.132	+	39.6170i	0.856615	+	0.135675i
$293$	28.4897	−	28.4897i	0.0972346	−	0.0972346i	−0.656816	−	0.754051i	$-0.728097\pi$
$293$	28.4897	−	28.4897i	0.0972346	−	0.0972346i	0.754051	+	0.656816i	$0.228097\pi$
$294$	75.5430	+	103.976i	0.256949	+	0.353660i
$295$		0			0
$296$	87.2999	+	63.4271i	0.294932	+	0.214281i
$297$	6.59868	+	41.6624i	0.0222178	+	0.140278i
$298$	−11.9620	−	23.4768i	−0.0401410	−	0.0787812i
$299$			64.5003i			0.215720i
$300$		0			0
$301$	−52.9382			−0.175874
$302$	−266.243	+	135.658i	−0.881600	+	0.449198i
$303$	130.194	−	20.6206i	0.429682	−	0.0680549i
$304$	−303.848	+	418.211i	−0.999500	+	1.37569i
$305$		0			0
$306$	170.722	−	124.037i	0.557914	−	0.405348i
$307$	−395.674	−	395.674i	−1.28884	−	1.28884i	−0.935491	−	0.353351i	$-0.885042\pi$
$307$	−395.674	−	395.674i	−1.28884	−	1.28884i	−0.353351	−	0.935491i	$-0.614958\pi$
$308$	12.3713	−	78.1095i	0.0401667	−	0.253602i
$309$	5.28462	−	1.71708i	0.0171023	−	0.00555688i
$310$		0			0
$311$	−149.055	+	458.744i	−0.479276	+	1.47506i	0.360826	+	0.932633i	$0.382495\pi$
$311$	−149.055	+	458.744i	−0.479276	+	1.47506i	−0.840102	+	0.542428i	$0.817505\pi$
$312$	11.5048	−	22.5794i	0.0368742	−	0.0723697i
$313$	195.466	+	99.5948i	0.624492	+	0.318194i	0.737446	−	0.675406i	$-0.236032\pi$
$313$	195.466	+	99.5948i	0.624492	+	0.318194i	−0.112955	+	0.993600i	$0.536032\pi$
$314$	207.548	+	67.4365i	0.660982	+	0.214766i
$315$		0			0
$316$	25.4025	+	78.1807i	0.0803875	+	0.247407i
$317$	−260.197	−	41.2111i	−0.820809	−	0.130003i	−0.268114	−	0.963387i	$-0.586401\pi$
$317$	−260.197	−	41.2111i	−0.820809	−	0.130003i	−0.552695	+	0.833384i	$0.686401\pi$
$318$	278.875	−	278.875i	0.876967	−	0.876967i
$319$	−165.517	−	227.814i	−0.518862	−	0.714152i
$320$		0			0
$321$	186.165	+	135.257i	0.579954	+	0.421361i
$322$	33.4934	+	211.469i	0.104017	+	0.656737i
$323$	−331.749	−	651.095i	−1.02709	−	2.01577i
$324$		−	19.9840i		−	0.0616789i
$325$		0			0
$326$	734.423			2.25283
$327$	329.938	−	168.112i	1.00898	−	0.514103i
$328$	197.589	−	31.2950i	0.602405	−	0.0954116i
$329$	103.946	−	143.069i	0.315944	−	0.434860i
$330$		0			0
$331$	42.7419	−	31.0538i	0.129130	−	0.0938181i	−0.521346	−	0.853346i	$-0.674570\pi$
$331$	42.7419	−	31.0538i	0.129130	−	0.0938181i	0.650475	+	0.759527i	$0.274570\pi$
$332$	−162.597	−	162.597i	−0.489749	−	0.489749i
$333$	−11.4100	+	72.0401i	−0.0342644	+	0.216337i
$334$	67.2367	−	21.8465i	0.201307	−	0.0654088i
$335$		0			0
$336$	46.8510	−	144.192i	0.139437	−	0.429144i
$337$	283.573	−	556.543i	0.841463	−	1.65146i	0.0859789	−	0.996297i	$-0.472598\pi$
$337$	283.573	−	556.543i	0.841463	−	1.65146i	0.755484	−	0.655167i	$-0.227402\pi$
$338$	351.411	+	179.053i	1.03968	+	0.529742i
$339$	232.779	+	75.6346i	0.686664	+	0.223111i
$340$		0			0
$341$	27.2150	+	83.7590i	0.0798092	+	0.245628i
$342$	−191.477	−	30.3269i	−0.559873	−	0.0886752i
$343$	−244.312	+	244.312i	−0.712279	+	0.712279i
$344$	−31.4781	−	43.3259i	−0.0915062	−	0.125947i
$345$		0			0
$346$	−94.6688	−	68.7809i	−0.273609	−	0.198789i
$347$	−14.2223	−	89.7958i	−0.0409863	−	0.258777i	0.958683	−	0.284475i	$-0.0918193\pi$
$347$	−14.2223	−	89.7958i	−0.0409863	−	0.258777i	−0.999670	+	0.0256976i	$0.991819\pi$
$348$	60.5658	+	118.867i	0.174040	+	0.341572i
$349$		−	481.591i		−	1.37992i	−0.723849	−	0.689958i	$-0.757629\pi$
$349$		−	481.591i		−	1.37992i	0.723849	−	0.689958i	$-0.242371\pi$
$350$		0			0
$351$	17.1289			0.0488002
$352$	231.509	−	117.960i	0.657697	−	0.335113i
$353$	323.170	−	51.1852i	0.915497	−	0.145000i	0.319129	−	0.947711i	$-0.396610\pi$
$353$	323.170	−	51.1852i	0.915497	−	0.145000i	0.596368	+	0.802711i	$0.296610\pi$
$354$	270.058	−	371.703i	0.762877	−	1.05001i
$355$		0			0
$356$	−205.156	+	149.054i	−0.576281	+	0.418692i
$357$	151.547	+	151.547i	0.424501	+	0.424501i
$358$	−43.1498	+	272.437i	−0.120530	+	0.760998i
$359$	−661.981	+	215.091i	−1.84396	+	0.599138i	−0.846152	+	0.532942i	$0.821086\pi$
$359$	−661.981	+	215.091i	−1.84396	+	0.599138i	−0.997807	+	0.0661963i	$0.978914\pi$
$360$		0			0
$361$	−95.8935	+	295.130i	−0.265633	+	0.817534i
$362$	−213.037	+	418.109i	−0.588500	+	1.15500i
$363$	85.0340	+	43.3270i	0.234253	+	0.119358i
$364$	−30.5418	−	9.92363i	−0.0839061	−	0.0272627i
$365$		0			0
$366$	−20.4710	−	63.0032i	−0.0559316	−	0.172140i
$367$	438.510	+	69.4532i	1.19485	+	0.189246i	0.721997	−	0.691896i	$-0.243224\pi$
$367$	438.510	+	69.4532i	1.19485	+	0.189246i	0.472853	+	0.881141i	$0.343224\pi$
$368$	−276.041	+	276.041i	−0.750111	+	0.750111i
$369$	79.4803	+	109.395i	0.215394	+	0.296464i
$370$		0			0
$371$	324.051	+	235.437i	0.873454	+	0.634601i
$372$	−6.52702	−	41.2100i	−0.0175457	−	0.110779i
$373$	106.315	+	208.656i	0.285028	+	0.559399i	0.988481	−	0.151342i	$-0.0483596\pi$
$373$	106.315	+	208.656i	0.285028	+	0.559399i	−0.703453	+	0.710741i	$0.748360\pi$
$374$			571.022i			1.52680i
$375$		0			0
$376$	178.899			0.475796
$377$	−101.885	+	51.9128i	−0.270251	+	0.137700i
$378$	56.1584	−	8.89461i	0.148567	−	0.0235307i
$379$	−45.5534	+	62.6989i	−0.120194	+	0.165432i	−0.864874	−	0.501989i	$-0.832602\pi$
$379$	−45.5534	+	62.6989i	−0.120194	+	0.165432i	0.744680	+	0.667421i	$0.232602\pi$
$380$		0			0
$381$	−261.387	+	189.909i	−0.686055	+	0.498448i
$382$	270.126	+	270.126i	0.707137	+	0.707137i
$383$	76.7271	−	484.436i	0.200332	−	1.26485i	−0.658497	−	0.752583i	$-0.728808\pi$
$383$	76.7271	−	484.436i	0.200332	−	1.26485i	0.858829	−	0.512262i	$-0.171192\pi$
$384$	210.806	−	68.4949i	0.548973	−	0.178372i
$385$		0			0
$386$	265.761	−	817.928i	0.688500	−	2.11898i
$387$	16.4337	−	32.2529i	0.0424643	−	0.0833409i
$388$	116.477	+	59.3481i	0.300199	+	0.152959i
$389$	229.887	+	74.6949i	0.590970	+	0.192018i	0.589209	−	0.807981i	$-0.299439\pi$
$389$	229.887	+	74.6949i	0.590970	+	0.192018i	0.00176103	+	0.999998i	$0.499439\pi$
$390$		0			0
$391$	−170.528	−	524.832i	−0.436134	−	1.34228i
$392$	−130.421	−	20.6566i	−0.332706	−	0.0526955i
$393$	200.799	−	200.799i	0.510938	−	0.510938i
$394$	−314.863	−	433.372i	−0.799145	−	1.09993i
$395$		0			0
$396$	43.7483	+	31.7850i	0.110475	+	0.0802651i
$397$	56.6087	+	357.414i	0.142591	+	0.900286i	0.950443	+	0.310900i	$0.100630\pi$
$397$	56.6087	+	357.414i	0.142591	+	0.900286i	−0.807851	+	0.589386i	$0.799370\pi$
$398$	−296.420	−	581.757i	−0.744774	−	1.46170i
$399$		−	196.891i		−	0.493462i
$400$		0			0
$401$	−41.2205			−0.102794			−0.0513972	−	0.998678i	$-0.516367\pi$
$401$	−41.2205			−0.102794			−0.0513972	+	0.998678i	$0.516367\pi$
$402$	103.012	−	52.4871i	0.256248	−	0.130565i
$403$	35.3223	−	5.59451i	0.0876485	−	0.0138822i
$404$	99.3269	−	136.712i	0.245859	−	0.338395i
$405$		0			0
$406$	−307.080	+	223.106i	−0.756354	+	0.549523i
$407$	−139.560	−	139.560i	−0.342899	−	0.342899i
$408$	−33.9168	+	214.142i	−0.0831295	+	0.524859i
$409$	11.1021	−	3.60730i	0.0271446	−	0.00881980i	−0.295413	−	0.955370i	$-0.595457\pi$
$409$	11.1021	−	3.60730i	0.0271446	−	0.00881980i	0.322558	+	0.946550i	$0.395457\pi$
$410$		0			0
$411$	68.2837	−	210.156i	0.166140	−	0.511328i
$412$	3.23395	−	6.34698i	0.00784938	−	0.0154053i
$413$	415.768	+	211.844i	1.00670	+	0.512940i
$414$	−139.236	−	45.2407i	−0.336320	−	0.109277i
$415$		0			0
$416$	−32.6042	−	100.346i	−0.0783756	−	0.241215i
$417$	31.7523	+	5.02907i	0.0761445	+	0.0120601i
$418$	370.939	−	370.939i	0.887414	−	0.887414i
$419$	−172.247	−	237.078i	−0.411091	−	0.565818i	0.552393	−	0.833584i	$-0.313715\pi$
$419$	−172.247	−	237.078i	−0.411091	−	0.565818i	−0.963484	+	0.267766i	$0.913715\pi$
$420$		0			0
$421$	−180.537	−	131.168i	−0.428830	−	0.311563i	0.352351	−	0.935868i	$-0.385382\pi$
$421$	−180.537	−	131.168i	−0.428830	−	0.311563i	−0.781181	+	0.624305i	$0.785382\pi$
$422$	−6.38947	−	40.3415i	−0.0151409	−	0.0955960i
$423$	54.8977	+	107.743i	0.129782	+	0.254711i
$424$			405.207i			0.955677i
$425$		0			0
$426$	220.705			0.518088
$427$	59.9471	−	30.5446i	0.140391	−	0.0715329i
$428$	291.366	−	46.1479i	0.680763	−	0.107822i
$429$	−27.2439	+	37.4980i	−0.0635056	+	0.0874080i
$430$		0			0
$431$	−251.983	+	183.076i	−0.584647	+	0.424771i	−0.840396	−	0.541972i	$-0.817678\pi$
$431$	−251.983	+	183.076i	−0.584647	+	0.424771i	0.255750	+	0.966743i	$0.417678\pi$
$432$	73.3061	+	73.3061i	0.169690	+	0.169690i
$433$	−60.9708	+	384.955i	−0.140810	+	0.889041i	0.811598	+	0.584216i	$0.198598\pi$
$433$	−60.9708	+	384.955i	−0.140810	+	0.889041i	−0.952408	+	0.304825i	$0.901402\pi$
$434$	112.902	−	36.6841i	0.260143	−	0.0845255i
$435$		0			0
$436$	146.694	−	451.477i	0.336454	−	1.03550i
$437$	−230.158	+	451.710i	−0.526677	+	1.03366i
$438$	−438.997	−	223.680i	−1.00228	−	0.510685i
$439$	−648.013	−	210.552i	−1.47611	−	0.479617i	−0.543162	−	0.839628i	$-0.682773\pi$
$439$	−648.013	−	210.552i	−1.47611	−	0.479617i	−0.932948	+	0.360010i	$0.882773\pi$
$440$		0			0
$441$	−27.5809	−	84.8852i	−0.0625416	−	0.192483i
$442$	229.022	+	36.2735i	0.518149	+	0.0820667i
$443$	−109.896	+	109.896i	−0.248072	+	0.248072i	−0.820179	−	0.572107i	$-0.806126\pi$
$443$	−109.896	+	109.896i	−0.248072	+	0.248072i	0.572107	+	0.820179i	$0.306126\pi$
$444$	54.9606	+	75.6468i	0.123785	+	0.170376i
$445$		0			0
$446$	87.4826	+	63.5598i	0.196149	+	0.142511i
$447$	2.86246	+	18.0729i	0.00640372	+	0.0404315i
$448$	−0.0445175	−	0.0873705i	−9.93694e−5	−	0.000195023i
$449$		−	352.558i		−	0.785208i	−0.919708	−	0.392604i	$-0.871574\pi$
$449$		−	352.558i		−	0.785208i	0.919708	−	0.392604i	$-0.128426\pi$
$450$		0			0
$451$	−365.900			−0.811308
$452$	279.574	−	142.450i	0.618527	−	0.315156i
$453$	204.959	−	32.4624i	0.452449	−	0.0716609i
$454$	−239.053	+	329.028i	−0.526547	+	0.724730i
$455$		0			0
$456$	161.141	−	117.076i	0.353379	−	0.256745i
$457$	453.981	+	453.981i	0.993395	+	0.993395i	0.999978	−	0.00658340i	$-0.00209558\pi$
$457$	453.981	+	453.981i	0.993395	+	0.993395i	−0.00658340	+	0.999978i	$0.502096\pi$
$458$	−3.66971	+	23.1696i	−0.00801247	+	0.0505887i
$459$	−139.376	+	45.2859i	−0.303651	+	0.0986622i
$460$		0			0
$461$	20.3868	−	62.7440i	0.0442229	−	0.136104i	−0.926507	−	0.376277i	$-0.877204\pi$
$461$	20.3868	−	62.7440i	0.0442229	−	0.136104i	0.970730	+	0.240173i	$0.0772041\pi$
$462$	−69.8494	+	137.087i	−0.151189	+	0.296726i
$463$	−366.287	−	186.633i	−0.791117	−	0.403094i	0.0112413	−	0.999937i	$-0.496422\pi$
$463$	−366.287	−	186.633i	−0.791117	−	0.403094i	−0.802358	+	0.596843i	$0.796422\pi$
$464$	−658.204	−	213.863i	−1.41854	−	0.460913i
$465$		0			0
$466$	−20.7109	−	63.7416i	−0.0444440	−	0.136785i
$467$	222.934	+	35.3093i	0.477375	+	0.0756088i	0.390485	−	0.920609i	$-0.372307\pi$
$467$	222.934	+	35.3093i	0.477375	+	0.0756088i	0.0868898	+	0.996218i	$0.472307\pi$
$468$	15.5272	−	15.5272i	0.0331777	−	0.0331777i
$469$	69.0169	+	94.9936i	0.147158	+	0.202545i
$470$		0			0
$471$	−122.608	−	89.0803i	−0.260315	−	0.189130i
$472$	73.8454	+	466.241i	0.156452	+	0.987799i
$473$	44.4689	+	87.2752i	0.0940147	+	0.184514i
$474$		−	159.928i		−	0.337401i
$475$		0			0
$476$	274.752			0.577210
$477$	−244.037	+	124.343i	−0.511609	+	0.260678i
$478$	−842.072	+	133.371i	−1.76166	+	0.279019i
$479$	−107.714	+	148.256i	−0.224874	+	0.309512i	−0.906514	−	0.422175i	$-0.861267\pi$
$479$	−107.714	+	148.256i	−0.224874	+	0.309512i	0.681641	+	0.731687i	$0.261267\pi$
$480$		0			0
$481$	−64.8392	+	47.1084i	−0.134801	+	0.0979386i
$482$	158.040	+	158.040i	0.327884	+	0.327884i
$483$	23.2600	−	146.858i	0.0481574	−	0.304054i
$484$	116.358	−	37.8070i	0.240409	−	0.0781137i
$485$		0			0
$486$	−12.0142	+	36.9760i	−0.0247206	+	0.0760823i
$487$	198.241	−	389.069i	0.407065	−	0.798910i	−0.592915	−	0.805265i	$-0.702023\pi$
$487$	198.241	−	389.069i	0.407065	−	0.798910i	0.999980	+	0.00635532i	$0.00202297\pi$
$488$	60.6441	+	30.8997i	0.124271	+	0.0633191i
$489$	−485.068	−	157.608i	−0.991960	−	0.322307i
$490$		0			0
$491$	−58.5836	−	180.302i	−0.119315	−	0.367213i	0.873508	−	0.486810i	$-0.161840\pi$
$491$	−58.5836	−	180.302i	−0.119315	−	0.367213i	−0.992823	+	0.119597i	$0.961840\pi$
$492$	171.214	+	27.1176i	0.347996	+	0.0551172i
$493$	691.775	−	691.775i	1.40320	−	1.40320i
$494$	−125.210	−	172.337i	−0.253462	−	0.348861i
$495$		0			0
$496$	175.111	+	127.226i	0.353046	+	0.256503i
$497$	35.0652	+	221.393i	0.0705537	+	0.445458i
$498$	203.098	+	398.602i	0.407827	+	0.800406i
$499$		−	326.118i		−	0.653543i	−0.945103	−	0.326772i	$-0.894039\pi$
$499$		−	326.118i		−	0.653543i	0.945103	−	0.326772i	$-0.105961\pi$
$500$		0			0
$501$	−49.0964			−0.0979969
$502$	577.187	−	294.091i	1.14977	−	0.585839i
$503$	−256.945	+	40.6961i	−0.510826	+	0.0809069i	−0.406526	−	0.913639i	$-0.633260\pi$
$503$	−256.945	+	40.6961i	−0.510826	+	0.0809069i	−0.104299	+	0.994546i	$0.533260\pi$
$504$	−34.3372	+	47.2611i	−0.0681294	+	0.0937720i
$505$		0			0
$506$	320.498	−	232.856i	0.633396	−	0.460189i
$507$	−193.673	−	193.673i	−0.381998	−	0.381998i
$508$	−64.7944	+	409.096i	−0.127548	+	0.805306i
$509$	−592.785	+	192.608i	−1.16461	+	0.378404i	−0.826627	−	0.562750i	$-0.809744\pi$
$509$	−592.785	+	192.608i	−1.16461	+	0.378404i	−0.337980	+	0.941153i	$0.609744\pi$
$510$		0			0
$511$	154.630	−	475.902i	0.302603	−	0.931316i
$512$	129.105	−	253.382i	0.252158	−	0.494887i
$513$	119.957	+	61.1213i	0.233835	+	0.119145i
$514$	−418.388	−	135.943i	−0.813985	−	0.264480i
$515$		0			0
$516$	−14.3400	−	44.1340i	−0.0277907	−	0.0855310i
$517$	−323.183	−	51.1872i	−0.625112	−	0.0990081i
$518$	−188.118	+	188.118i	−0.363162	+	0.363162i
$519$	47.7659	+	65.7441i	0.0920345	+	0.126675i
$520$		0			0
$521$	632.041	+	459.205i	1.21313	+	0.881391i	0.995511	−	0.0946427i	$-0.0301709\pi$
$521$	632.041	+	459.205i	1.21313	+	0.881391i	0.217619	+	0.976034i	$0.430171\pi$
$522$	−40.6018	−	256.350i	−0.0777812	−	0.491091i
$523$	−32.3892	−	63.5674i	−0.0619296	−	0.121544i	0.857967	−	0.513705i	$-0.171727\pi$
$523$	−32.3892	−	63.5674i	−0.0619296	−	0.121544i	−0.919896	+	0.392161i	$0.871727\pi$
$524$		−	364.044i		−	0.694741i
$525$		0			0
$526$	223.648			0.425186
$527$	−272.623	+	138.908i	−0.517311	+	0.263583i
$528$	−277.075	+	43.8843i	−0.524763	+	0.0831143i
$529$	85.9045	−	118.237i	0.162390	−	0.223511i
$530$		0			0
$531$	−258.135	+	187.546i	−0.486130	+	0.353194i
$532$	−178.480	−	178.480i	−0.335489	−	0.335489i
$533$	−23.2434	+	146.753i	−0.0436086	+	0.275334i
$534$	469.207	−	152.455i	0.878665	−	0.285496i
$535$		0			0
$536$	−36.7063	+	112.970i	−0.0684818	+	0.210765i
$537$	86.9648	−	170.678i	0.161946	−	0.317836i
$538$	110.834	+	56.4728i	0.206011	+	0.104968i
$539$	229.696	+	74.6328i	0.426152	+	0.138465i
$540$		0			0
$541$	146.082	+	449.594i	0.270022	+	0.831042i	0.990494	+	0.137558i	$0.0439252\pi$
$541$	146.082	+	449.594i	0.270022	+	0.831042i	−0.720472	+	0.693484i	$0.756075\pi$
$542$	536.721	+	85.0083i	0.990260	+	0.156842i
$543$	230.432	−	230.432i	0.424369	−	0.424369i
$544$	530.594	+	730.300i	0.975357	+	1.34246i
$545$		0			0
$546$	50.5450	+	36.7231i	0.0925732	+	0.0672584i
$547$	3.82493	+	24.1496i	0.00699255	+	0.0441492i	0.990938	−	0.134321i	$-0.0428853\pi$
$547$	3.82493	+	24.1496i	0.00699255	+	0.0441492i	−0.983945	+	0.178470i	$0.942885\pi$
$548$	−128.606	−	252.403i	−0.234682	−	0.460589i
$549$			46.0051i			0.0837981i
$550$		0			0
$551$	−898.762			−1.63115
$552$	134.023	−	68.2881i	0.242795	−	0.123710i
$553$	160.426	−	25.4091i	0.290102	−	0.0459477i
$554$	52.1412	−	71.7662i	0.0941176	−	0.129542i
$555$		0			0
$556$	33.3420	−	24.2244i	0.0599676	−	0.0435690i
$557$	−361.027	−	361.027i	−0.648163	−	0.648163i	0.304385	−	0.952549i	$-0.401549\pi$
$557$	−361.027	−	361.027i	−0.648163	−	0.648163i	−0.952549	+	0.304385i	$0.901549\pi$
$558$	−12.6983	+	80.1741i	−0.0227569	+	0.143681i
$559$	37.8286	−	12.2913i	0.0676720	−	0.0219880i
$560$		0			0
$561$	122.542	−	377.146i	0.218435	−	0.672274i
$562$	−420.974	+	826.208i	−0.749064	+	1.47012i
$563$	808.836	+	412.123i	1.43665	+	0.732012i	0.986929	−	0.161155i	$-0.0515219\pi$
$563$	808.836	+	412.123i	1.43665	+	0.732012i	0.449725	+	0.893167i	$0.351522\pi$
$564$	147.432	+	47.9036i	0.261404	+	0.0849354i
$565$		0			0
$566$	−192.662	−	592.952i	−0.340392	−	1.04762i
$567$	−39.0000	−	6.17699i	−0.0687830	−	0.0108942i
$568$	−160.343	+	160.343i	−0.282294	+	0.282294i
$569$	100.389	+	138.174i	0.176430	+	0.242836i	0.888069	−	0.459710i	$-0.152047\pi$
$569$	100.389	+	138.174i	0.176430	+	0.242836i	−0.711639	+	0.702546i	$0.752047\pi$
$570$		0			0
$571$	−18.3779	−	13.3524i	−0.0321855	−	0.0233842i	0.571576	−	0.820549i	$-0.306332\pi$
$571$	−18.3779	−	13.3524i	−0.0321855	−	0.0233842i	−0.603762	+	0.797165i	$0.706332\pi$
$572$	9.29526	+	58.6880i	0.0162505	+	0.102601i
$573$	−120.442	−	236.381i	−0.210196	−	0.412533i
$574$			493.210i			0.859252i
$575$		0			0
$576$	0.0670507			0.000116407
$577$	−408.355	+	208.067i	−0.707721	+	0.360602i	−0.770512	−	0.637425i	$-0.780000\pi$
$577$	−408.355	+	208.067i	−0.707721	+	0.360602i	0.0627918	+	0.998027i	$0.480000\pi$
$578$	−1247.51	+	197.586i	−2.15832	+	0.341845i
$579$	−351.057	+	483.188i	−0.606316	+	0.834522i
$580$		0			0
$581$	−367.576	+	267.059i	−0.632661	+	0.459655i
$582$	−179.836	−	179.836i	−0.308997	−	0.308997i
$583$	115.939	−	732.010i	0.198866	−	1.25559i
$584$	481.436	−	156.428i	0.824377	−	0.267856i
$585$		0			0
$586$	−31.0525	+	95.5697i	−0.0529906	+	0.163088i
$587$	409.786	−	804.250i	0.698102	−	1.37010i	−0.220683	−	0.975346i	$-0.570829\pi$
$587$	409.786	−	804.250i	0.698102	−	1.37010i	0.918785	−	0.394757i	$-0.129171\pi$
$588$	−101.949	−	51.9459i	−0.173383	−	0.0883433i
$589$	267.333	+	86.8618i	0.453876	+	0.147473i
$590$		0			0
$591$	114.957	+	353.801i	0.194513	+	0.598649i
$592$	−479.100	−	75.8820i	−0.809291	−	0.128179i
$593$	244.551	−	244.551i	0.412397	−	0.412397i	−0.470176	−	0.882573i	$-0.655810\pi$
$593$	244.551	−	244.551i	0.412397	−	0.412397i	0.882573	+	0.470176i	$0.155810\pi$
$594$	−61.8378	−	85.1124i	−0.104104	−	0.143287i
$595$		0			0
$596$	18.9777	+	13.7881i	0.0318418	+	0.0231344i
$597$	70.9322	+	447.848i	0.118814	+	0.750164i
$598$	−73.0330	−	143.335i	−0.122129	−	0.239691i
$599$		−	40.7095i		−	0.0679624i	−0.999422	−	0.0339812i	$-0.989181\pi$
$599$		−	40.7095i		−	0.0679624i	0.999422	−	0.0339812i	$-0.0108186\pi$
$600$		0			0
$601$	713.924			1.18789			0.593947	−	0.804504i	$-0.297569\pi$
$601$	713.924			1.18789			0.593947	+	0.804504i	$0.297569\pi$
$602$	117.642	−	59.9414i	0.195418	−	0.0995704i
$603$	−79.3005	+	12.5600i	−0.131510	+	0.0208291i
$604$	156.367	−	215.221i	0.258886	−	0.356326i
$605$		0			0
$606$	−265.973	+	193.241i	−0.438900	+	0.318879i
$607$	−374.723	−	374.723i	−0.617337	−	0.617337i	0.327511	−	0.944847i	$-0.393790\pi$
$607$	−374.723	−	374.723i	−0.617337	−	0.617337i	−0.944847	+	0.327511i	$0.893790\pi$
$608$	129.730	−	819.084i	0.213372	−	1.34718i
$609$	250.697	−	81.4565i	0.411654	−	0.133755i
$610$		0			0
$611$	−41.0597	+	126.369i	−0.0672007	+	0.206823i
$612$	−85.2916	+	167.394i	−0.139365	+	0.273520i
$613$	−230.186	−	117.286i	−0.375508	−	0.191331i	0.256043	−	0.966665i	$-0.417581\pi$
$613$	−230.186	−	117.286i	−0.375508	−	0.191331i	−0.631551	+	0.775335i	$0.717581\pi$
$614$	1327.30	+	431.267i	2.16173	+	0.702389i
$615$		0			0
$616$	−48.8484	−	150.340i	−0.0792993	−	0.244058i
$617$	403.258	+	63.8697i	0.653578	+	0.103517i	0.474413	−	0.880302i	$-0.342660\pi$
$617$	403.258	+	63.8697i	0.653578	+	0.103517i	0.179165	+	0.983819i	$0.442660\pi$
$618$	−9.79948	+	9.79948i	−0.0158568	+	0.0158568i
$619$	400.379	+	551.074i	0.646816	+	0.890265i	0.998956	−	0.0456817i	$-0.0145460\pi$
$619$	400.379	+	551.074i	0.646816	+	0.890265i	−0.352140	+	0.935947i	$0.614546\pi$
$620$		0			0
$621$	82.2535	+	59.7606i	0.132453	+	0.0962329i
$622$	−188.195	−	1188.21i	−0.302564	−	1.91031i
$623$	227.476	+	446.447i	0.365130	+	0.716608i
$624$			113.915i			0.182556i
$625$		0			0
$626$	−547.143			−0.874030
$627$	−324.600	+	165.392i	−0.517703	+	0.263783i
$628$	−191.894	+	30.3930i	−0.305564	+	0.0483965i
$629$	403.043	−	554.741i	0.640767	−	0.881940i
$630$		0			0
$631$	−395.032	+	287.008i	−0.626042	+	0.454846i	−0.855027	−	0.518584i	$-0.826459\pi$
$631$	−395.032	+	287.008i	−0.626042	+	0.454846i	0.228985	+	0.973430i	$0.426459\pi$
$632$	116.188	+	116.188i	0.183842	+	0.183842i
$633$	−4.43726	+	28.0158i	−0.00700989	+	0.0442587i
$634$	624.883	−	203.037i	0.985620	−	0.320247i
$635$		0			0
$636$	−108.502	+	333.934i	−0.170600	+	0.525053i
$637$	44.5244	−	87.3841i	0.0698970	−	0.137181i
$638$	625.771	+	318.846i	0.980832	+	0.499759i
$639$	−145.770	−	47.3637i	−0.228123	−	0.0741215i
$640$		0			0
$641$	17.7948	+	54.7668i	0.0277610	+	0.0854396i	0.963977	−	0.265985i	$-0.0856973\pi$
$641$	17.7948	+	54.7668i	0.0277610	+	0.0854396i	−0.936216	+	0.351425i	$0.885697\pi$
$642$	−566.854	−	89.7809i	−0.882951	−	0.139846i
$643$	178.471	−	178.471i	0.277560	−	0.277560i	−0.554575	−	0.832134i	$-0.687119\pi$
$643$	178.471	−	178.471i	0.277560	−	0.277560i	0.832134	+	0.554575i	$0.187119\pi$
$644$	−112.040	−	154.210i	−0.173976	−	0.239457i
$645$		0			0
$646$	1474.46	+	1071.25i	2.28244	+	1.65829i
$647$	51.1811	+	323.144i	0.0791052	+	0.499450i	0.995150	+	0.0983735i	$0.0313640\pi$
$647$	51.1811	+	323.144i	0.0791052	+	0.499450i	−0.916044	+	0.401077i	$0.868636\pi$
$648$	−18.1348	−	35.5915i	−0.0279858	−	0.0549252i
$649$		−	863.397i		−	1.33035i
$650$		0			0
$651$	−82.4413			−0.126638
$652$	−582.581	+	296.840i	−0.893529	+	0.455276i
$653$	−327.898	+	51.9339i	−0.502141	+	0.0795313i	−0.402366	−	0.915479i	$-0.631812\pi$
$653$	−327.898	+	51.9339i	−0.502141	+	0.0795313i	−0.0997745	+	0.995010i	$0.531812\pi$
$654$	−542.850	+	747.170i	−0.830047	+	1.14246i
$655$		0			0
$656$	−727.530	+	528.581i	−1.10904	+	0.805764i
$657$	241.945	+	241.945i	0.368257	+	0.368257i
$658$	−68.9971	+	435.631i	−0.104859	+	0.662053i
$659$	1028.88	−	334.304i	1.56128	−	0.507290i	0.604129	−	0.796887i	$-0.293521\pi$
$659$	1028.88	−	334.304i	1.56128	−	0.507290i	0.957149	+	0.289597i	$0.0935212\pi$
$660$		0			0
$661$	−277.189	+	853.099i	−0.419348	+	1.29062i	0.488956	+	0.872308i	$0.337378\pi$
$661$	−277.189	+	853.099i	−0.419348	+	1.29062i	−0.908304	+	0.418311i	$0.862622\pi$
$662$	−59.8209	+	117.405i	−0.0903640	+	0.177349i
$663$	−143.479	−	73.1061i	−0.216408	−	0.110266i
$664$	−437.136	−	142.034i	−0.658337	−	0.213907i
$665$		0			0
$666$	−56.2144	−	173.010i	−0.0844059	−	0.259775i
$667$	−670.371	−	106.176i	−1.00505	−	0.159185i
$668$	−44.5055	+	44.5055i	−0.0666250	+	0.0666250i
$669$	−44.1400	−	60.7536i	−0.0659791	−	0.0908125i
$670$		0			0
$671$	−100.713	−	73.1723i	−0.150094	−	0.109050i
$672$	38.0487	+	240.230i	0.0566201	+	0.357485i
$673$	514.734	+	1010.22i	0.764834	+	1.50107i	0.862613	+	0.505864i	$0.168826\pi$
$673$	514.734	+	1010.22i	0.764834	+	1.50107i	−0.0977789	+	0.995208i	$0.531174\pi$
$674$			1557.86i			2.31137i
$675$		0			0
$676$	−351.126			−0.519417
$677$	−6.84418	+	3.48729i	−0.0101096	+	0.00515109i	−0.459038	−	0.888417i	$-0.651806\pi$
$677$	−6.84418	+	3.48729i	−0.0101096	+	0.00515109i	0.448928	+	0.893568i	$0.351806\pi$
$678$	−602.932	+	95.4951i	−0.889281	+	0.140848i
$679$	151.824	−	208.968i	0.223600	−	0.307759i
$680$		0			0
$681$	228.498	−	166.013i	0.335533	−	0.243779i
$682$	−155.318	−	155.318i	−0.227738	−	0.227738i
$683$	−64.3583	+	406.342i	−0.0942289	+	0.594938i	0.894714	+	0.446640i	$0.147379\pi$
$683$	−64.3583	+	406.342i	−0.0942289	+	0.594938i	−0.988943	+	0.148298i	$0.952621\pi$
$684$	164.146	−	53.3343i	0.239980	−	0.0779742i
$685$		0			0
$686$	266.288	−	819.551i	0.388175	−	1.19468i
$687$	7.39599	−	14.5154i	0.0107656	−	0.0211287i
$688$	214.497	+	109.292i	0.311769	+	0.158854i
$689$	−286.225	−	93.0001i	−0.415421	−	0.134978i
$690$		0			0
$691$	−336.357	−	1035.20i	−0.486769	−	1.49812i	−0.829402	−	0.558652i	$-0.811319\pi$
$691$	−336.357	−	1035.20i	−0.486769	−	1.49812i	0.342633	−	0.939469i	$-0.388681\pi$
$692$	102.896	+	16.2971i	0.148693	+	0.0235507i
$693$	75.5529	−	75.5529i	0.109023	−	0.109023i
$694$	133.280	+	183.444i	0.192046	+	0.264329i
$695$		0			0
$696$	215.736	+	156.741i	0.309965	+	0.225203i
$697$	−198.862	−	1255.56i	−0.285311	−	1.80138i
$698$	545.300	+	1070.21i	0.781232	+	1.53325i
$699$			46.5443i			0.0665870i
$700$		0			0
$701$	356.852			0.509061			0.254530	−	0.967065i	$-0.418079\pi$
$701$	356.852			0.509061			0.254530	+	0.967065i	$0.418079\pi$
$702$	−38.0645	+	19.3948i	−0.0542230	+	0.0276280i
$703$	−622.181	+	98.5439i	−0.885038	+	0.140176i
$704$	−0.106646	+	0.146785i	−0.000151485	+	0.000208502i
$705$		0			0
$706$	−660.207	+	479.668i	−0.935137	+	0.679417i
$707$	−236.100	−	236.100i	−0.333946	−	0.333946i
$708$	−63.9882	+	404.006i	−0.0903788	+	0.570630i
$709$	−449.573	+	146.075i	−0.634095	+	0.206030i	−0.608388	−	0.793640i	$-0.708184\pi$
$709$	−449.573	+	146.075i	−0.634095	+	0.206030i	−0.0257068	+	0.999670i	$0.508184\pi$
$710$		0			0
$711$	−34.3208	+	105.629i	−0.0482712	+	0.148563i
$712$	−230.121	+	451.639i	−0.323204	+	0.634324i
$713$	189.138	+	96.3704i	0.265270	+	0.135162i
$714$	−508.369	−	165.179i	−0.712001	−	0.231343i
$715$		0			0
$716$	−75.8853	−	233.551i	−0.105985	−	0.326188i
$717$	584.789	+	92.6215i	0.815606	+	0.129179i
$718$	1227.54	−	1227.54i	1.70966	−	1.70966i
$719$	396.460	+	545.680i	0.551404	+	0.758943i	0.990202	−	0.139643i	$-0.0445955\pi$
$719$	396.460	+	545.680i	0.551404	+	0.758943i	−0.438798	+	0.898586i	$0.644596\pi$
$720$		0			0
$721$	−11.3869	−	8.27308i	−0.0157932	−	0.0114745i
$722$	−121.074	−	764.429i	−0.167692	−	1.05877i
$723$	−70.4658	−	138.297i	−0.0974631	−	0.191282i
$724$		−	417.770i		−	0.577030i
$725$		0			0
$726$	−238.025			−0.327858
$727$	3.06318	−	1.56077i	0.00421345	−	0.00214686i	−0.451883	−	0.892077i	$-0.649247\pi$
$727$	3.06318	−	1.56077i	0.00421345	−	0.00214686i	0.456096	+	0.889931i	$0.349247\pi$
$728$	−63.4004	+	10.0416i	−0.0870885	+	0.0137935i
$729$	15.8702	−	21.8435i	0.0217698	−	0.0299636i
$730$		0			0
$731$	−275.311	+	200.025i	−0.376623	+	0.273633i
$732$	41.7032	+	41.7032i	0.0569716	+	0.0569716i
$733$	34.5462	−	218.116i	0.0471299	−	0.297566i	−0.952853	−	0.303433i	$-0.901867\pi$
$733$	34.5462	−	218.116i	0.0471299	−	0.297566i	0.999983	+	0.00586626i	$0.00186730\pi$
$734$	−1053.12	+	342.178i	−1.43476	+	0.466183i
$735$		0			0
$736$	193.527	−	595.615i	0.262944	−	0.809259i
$737$	98.6335	−	193.579i	0.133831	−	0.262658i
$738$	−300.492	−	153.108i	−0.407170	−	0.207464i
$739$	218.413	+	70.9668i	0.295553	+	0.0960308i	0.453040	−	0.891490i	$-0.350339\pi$
$739$	218.413	+	70.9668i	0.295553	+	0.0960308i	−0.157488	+	0.987521i	$0.550339\pi$
$740$		0			0
$741$	45.7145	+	140.695i	0.0616930	+	0.189872i
$742$	−986.703	−	156.278i	−1.32979	−	0.210618i
$743$	−308.291	+	308.291i	−0.414927	+	0.414927i	−0.883451	−	0.468524i	$-0.844786\pi$
$743$	−308.291	+	308.291i	−0.414927	+	0.414927i	0.468524	+	0.883451i	$0.344786\pi$
$744$	−49.0213	−	67.4720i	−0.0658888	−	0.0906882i
$745$		0			0
$746$	−472.518	−	343.304i	−0.633401	−	0.460193i
$747$	−48.6005	−	306.852i	−0.0650610	−	0.410779i
$748$	−230.796	−	452.962i	−0.308551	−	0.605565i
$749$		−	582.884i		−	0.778217i
$750$		0			0
$751$	158.526			0.211087			0.105544	−	0.994415i	$-0.466342\pi$
$751$	158.526			0.211087			0.105544	+	0.994415i	$0.466342\pi$
$752$	−716.540	+	365.095i	−0.952845	+	0.485499i
$753$	−444.330	+	70.3749i	−0.590079	+	0.0934594i
$754$	167.632	−	230.726i	0.222324	−	0.306002i
$755$		0			0
$756$	−40.9525	+	29.7538i	−0.0541700	+	0.0393568i
$757$	211.358	+	211.358i	0.279205	+	0.279205i	0.832792	−	0.553587i	$-0.186741\pi$
$757$	211.358	+	211.358i	0.279205	+	0.279205i	−0.553587	+	0.832792i	$0.686741\pi$
$758$	30.2375	−	190.912i	0.0398911	−	0.251863i
$759$	−261.652	+	85.0160i	−0.344733	+	0.112011i
$760$		0			0
$761$	−124.883	+	384.349i	−0.164103	+	0.505058i	−0.998969	−	0.0453953i	$-0.985545\pi$
$761$	−124.883	+	384.349i	−0.164103	+	0.505058i	0.834866	+	0.550454i	$0.185545\pi$
$762$	365.834	−	717.989i	0.480097	−	0.942243i
$763$	−835.744	−	425.833i	−1.09534	−	0.558103i
$764$	−323.457	−	105.098i	−0.423373	−	0.137562i
$765$		0			0
$766$	378.015	+	1163.41i	0.493493	+	1.51881i
$767$	−346.286	−	54.8463i	−0.451481	−	0.0715076i
$768$	−391.015	+	391.015i	−0.509134	+	0.509134i
$769$	278.600	+	383.460i	0.362289	+	0.498647i	0.950785	−	0.309853i	$-0.100280\pi$
$769$	278.600	+	383.460i	0.362289	+	0.498647i	−0.588496	+	0.808500i	$0.700280\pi$
$770$		0			0
$771$	247.162	+	179.573i	0.320573	+	0.232910i
$772$	119.776	+	756.236i	0.155150	+	0.979580i
$773$	−364.589	−	715.546i	−0.471655	−	0.925674i	−0.997191	−	0.0749030i	$-0.976135\pi$
$773$	−364.589	−	715.546i	−0.471655	−	0.925674i	0.525536	−	0.850771i	$-0.323865\pi$
$774$			90.2816i			0.116643i
$775$		0			0
$776$	261.303			0.336730
$777$	164.618	−	83.8769i	0.211863	−	0.107950i
$778$	−595.442	+	94.3087i	−0.765349	+	0.121219i
$779$	−686.440	+	944.803i	−0.881181	+	1.21284i
$780$		0			0
$781$	335.538	−	243.783i	0.429626	−	0.312142i
$782$	973.216	+	973.216i	1.24452	+	1.24452i
$783$	−28.1965	+	178.026i	−0.0360108	+	0.227364i
$784$	564.526	−	183.426i	0.720059	−	0.233961i
$785$		0			0
$786$	−218.861	+	673.585i	−0.278449	+	0.856978i
$787$	−222.389	+	436.463i	−0.282578	+	0.554591i	−0.988048	−	0.154150i	$-0.950736\pi$
$787$	−222.389	+	436.463i	−0.282578	+	0.554591i	0.705469	+	0.708740i	$0.250736\pi$
$788$	424.925	+	216.510i	0.539246	+	0.274759i
$789$	−147.714	−	47.9951i	−0.187217	−	0.0608303i
$790$		0			0
$791$	−191.585	−	589.638i	−0.242206	−	0.745434i
$792$	106.760	+	16.9091i	0.134798	+	0.0213498i
$793$	−35.7451	+	35.7451i	−0.0450758	+	0.0450758i
$794$	−530.494	−	730.162i	−0.668128	−	0.919600i
$795$		0			0
$796$	470.270	+	341.671i	0.590791	+	0.429235i
$797$	238.720	+	1507.22i	0.299523	+	1.89111i	0.435156	+	0.900355i	$0.356693\pi$
$797$	238.720	+	1507.22i	0.299523	+	1.89111i	−0.135633	+	0.990759i	$0.543307\pi$
$798$	222.938	+	437.540i	0.279371	+	0.548296i
$799$		−	1136.80i		−	1.42278i
$800$		0			0
$801$	−342.617			−0.427736
$802$	91.6020	−	46.6736i	0.114217	−	0.0581964i
$803$	−914.476	+	144.839i	−1.13882	+	0.180372i
$804$	−60.4997	+	83.2707i	−0.0752484	+	0.103571i
$805$		0			0
$806$	−72.1602	+	52.4274i	−0.0895288	+	0.0650465i
$807$	−61.0840	−	61.0840i	−0.0756927	−	0.0756927i
$808$	52.8402	−	333.620i	0.0653963	−	0.412896i
$809$	687.263	−	223.305i	0.849522	−	0.276026i	0.148276	−	0.988946i	$-0.452628\pi$
$809$	687.263	−	223.305i	0.849522	−	0.276026i	0.701246	+	0.712920i	$0.252628\pi$
$810$		0			0
$811$	268.108	−	825.153i	0.330590	−	1.01745i	−0.638264	−	0.769818i	$-0.720347\pi$
$811$	268.108	−	825.153i	0.330590	−	1.01745i	0.968854	−	0.247634i	$-0.0796529\pi$
$812$	153.415	−	301.095i	0.188935	−	0.370806i
$813$	−336.248	−	171.327i	−0.413589	−	0.210734i
$814$	468.158	+	152.114i	0.575133	+	0.186872i
$815$		0			0
$816$	−301.173	−	926.914i	−0.369084	−	1.13592i
$817$	308.781	+	48.9062i	0.377945	+	0.0598607i
$818$	−20.5871	+	20.5871i	−0.0251676	+	0.0251676i
$819$	−25.5029	−	35.1017i	−0.0311390	−	0.0428592i
$820$		0			0
$821$	−114.066	−	82.8741i	−0.138936	−	0.100943i	0.516146	−	0.856500i	$-0.327366\pi$
$821$	−114.066	−	82.8741i	−0.138936	−	0.100943i	−0.655082	+	0.755558i	$0.727366\pi$
$822$	86.2140	+	544.334i	0.104883	+	0.662207i
$823$	−404.846	−	794.555i	−0.491915	−	0.965437i	−0.994874	−	0.101127i	$-0.967755\pi$
$823$	−404.846	−	794.555i	−0.491915	−	0.965437i	0.502959	−	0.864311i	$-0.332245\pi$
$824$		−	14.2387i		−	0.0172800i
$825$		0			0
$826$	−1163.81			−1.40897
$827$	258.953	−	131.943i	0.313124	−	0.159545i	−0.290365	−	0.956916i	$-0.593777\pi$
$827$	258.953	−	131.943i	0.313124	−	0.159545i	0.603489	+	0.797371i	$0.293777\pi$
$828$	128.735	−	20.3895i	0.155476	−	0.0246251i
$829$	−320.933	+	441.726i	−0.387133	+	0.532842i	−0.957457	−	0.288578i	$-0.906818\pi$
$829$	−320.933	+	441.726i	−0.387133	+	0.532842i	0.570324	+	0.821420i	$0.306818\pi$
$830$		0			0
$831$	−49.8391	+	36.2102i	−0.0599748	+	0.0435742i
$832$	0.0520972	+	0.0520972i	6.26168e−5	+	6.26168e-5i
$833$	−131.261	+	828.750i	−0.157576	+	0.994898i
$834$	−76.2556	+	24.7770i	−0.0914336	+	0.0297086i
$835$		0			0
$836$	−144.321	+	444.173i	−0.172632	+	0.531308i
$837$	25.5924	−	50.2279i	0.0305763	−	0.0600095i
$838$	651.215	+	331.811i	0.777107	+	0.395956i
$839$	400.077	+	129.993i	0.476849	+	0.154938i	0.537574	−	0.843217i	$-0.319341\pi$
$839$	400.077	+	129.993i	0.476849	+	0.154938i	−0.0607243	+	0.998155i	$0.519341\pi$
$840$		0			0
$841$	−111.946	−	344.535i	−0.133111	−	0.409673i
$842$	549.718	+	87.0668i	0.652872	+	0.103405i
$843$	455.348	−	455.348i	0.540152	−	0.540152i
$844$	21.3737	+	29.4184i	0.0253243	+	0.0348559i
$845$		0			0
$846$	−243.992	−	177.270i	−0.288406	−	0.209540i
$847$	−37.8169	−	238.766i	−0.0446480	−	0.281897i
$848$	−826.941	−	1622.96i	−0.975166	−	1.91387i
$849$			432.975i			0.509983i
$850$		0			0
$851$	−475.716			−0.559008
$852$	−175.074	+	89.2048i	−0.205486	+	0.104700i
$853$	209.883	−	33.2422i	0.246053	−	0.0389709i	−0.0321898	−	0.999482i	$-0.510248\pi$
$853$	209.883	−	33.2422i	0.246053	−	0.0389709i	0.278242	+	0.960511i	$0.410248\pi$
$854$	−98.6316	+	135.755i	−0.115494	+	0.158963i
$855$		0			0
$856$	477.047	−	346.595i	0.557298	−	0.404900i
$857$	549.525	+	549.525i	0.641220	+	0.641220i	0.950855	−	0.309636i	$-0.100207\pi$
$857$	549.525	+	549.525i	0.641220	+	0.641220i	−0.309636	+	0.950855i	$0.600207\pi$
$858$	18.0840	−	114.178i	0.0210769	−	0.133074i
$859$	−1586.71	+	515.554i	−1.84716	+	0.600179i	−0.849839	+	0.527043i	$0.823301\pi$
$859$	−1586.71	+	515.554i	−1.84716	+	0.600179i	−0.997322	+	0.0731359i	$0.976699\pi$
$860$		0			0
$861$	105.844	−	325.753i	0.122931	−	0.378343i
$862$	352.671	−	692.157i	0.409132	−	0.802966i
$863$	−61.9038	−	31.5416i	−0.0717310	−	0.0365488i	0.417757	−	0.908559i	$-0.362816\pi$
$863$	−61.9038	−	31.5416i	−0.0717310	−	0.0365488i	−0.489488	+	0.872010i	$0.662816\pi$
$864$	−158.173	−	51.3936i	−0.183071	−	0.0594833i
$865$		0			0
$866$	−300.388	−	924.499i	−0.346868	−	1.06755i
$867$	866.352	+	137.217i	0.999253	+	0.158266i
$868$	−74.7323	+	74.7323i	−0.0860972	+	0.0860972i
$869$	−176.651	−	243.139i	−0.203281	−	0.279792i
$870$		0			0
$871$	−71.3739	−	51.8562i	−0.0819448	−	0.0595364i
$872$	−148.438	−	937.202i	−0.170227	−	1.07477i
$873$	80.1842	+	157.370i	0.0918490	+	0.180264i
$874$		−	1264.41i		−	1.44670i
$875$		0			0
$876$	438.641			0.500732
$877$	303.375	−	154.577i	0.345923	−	0.176257i	−0.272393	−	0.962186i	$-0.587815\pi$
$877$	303.375	−	154.577i	0.345923	−	0.176257i	0.618316	+	0.785929i	$0.287815\pi$
$878$	1678.45	−	265.840i	1.91167	−	0.302779i
$879$	41.0188	−	56.4575i	0.0466653	−	0.0642292i
$880$		0			0
$881$	−130.707	+	94.9645i	−0.148362	+	0.107792i	−0.659490	−	0.751713i	$-0.729228\pi$
$881$	−130.707	+	94.9645i	−0.148362	+	0.107792i	0.511128	+	0.859505i	$0.329228\pi$
$882$	157.406	+	157.406i	0.178465	+	0.178465i
$883$	−12.9653	+	81.8594i	−0.0146832	+	0.0927060i	−0.993942	−	0.109909i	$-0.964944\pi$
$883$	−12.9653	+	81.8594i	−0.0146832	+	0.0927060i	0.979258	+	0.202615i	$0.0649440\pi$
$884$	−196.332	+	63.7922i	−0.222095	+	0.0721632i
$885$		0			0
$886$	119.782	−	368.650i	0.135194	−	0.416083i
$887$	−331.311	+	650.234i	−0.373518	+	0.733071i	−0.998883	−	0.0472620i	$-0.984950\pi$
$887$	−331.311	+	650.234i	−0.373518	+	0.733071i	0.625364	+	0.780333i	$0.284950\pi$
$888$	166.532	+	84.8523i	0.187536	+	0.0955543i
$889$	778.348	+	252.901i	0.875532	+	0.284478i
$890$		0			0
$891$	22.5771	+	69.4851i	0.0253390	+	0.0779855i
$892$	−95.0851	−	15.0600i	−0.106598	−	0.0168834i
$893$	−738.474	+	738.474i	−0.826958	+	0.826958i
$894$	−26.8248	−	36.9212i	−0.0300054	−	0.0412989i
$895$		0			0
$896$	−454.229	−	330.017i	−0.506952	−	0.368322i
$897$	17.4765	+	110.342i	0.0194833	+	0.123013i
$898$	399.198	+	783.470i	0.444541	+	0.872461i
$899$			376.325i			0.418604i
$900$		0			0
$901$	2574.86			2.85778
$902$	813.119	−	414.305i	0.901462	−	0.459318i
$903$	−90.5628	+	14.3437i	−0.100291	+	0.0158845i
$904$	368.654	−	507.409i	0.407803	−	0.561293i
$905$		0			0
$906$	−418.713	+	304.212i	−0.462155	+	0.335775i
$907$	592.187	+	592.187i	0.652907	+	0.652907i	0.953692	−	0.300785i	$-0.0972486\pi$
$907$	592.187	+	592.187i	0.652907	+	0.652907i	−0.300785	+	0.953692i	$0.597249\pi$
$908$	56.6416	−	357.621i	0.0623806	−	0.393856i
$909$	217.138	−	70.5525i	0.238876	−	0.0776155i
$910$		0			0
$911$	470.455	−	1447.91i	0.516416	−	1.58936i	−0.264276	−	0.964447i	$-0.585133\pi$
$911$	470.455	−	1447.91i	0.516416	−	1.58936i	0.780691	−	0.624917i	$-0.214867\pi$
$912$	−406.485	+	797.773i	−0.445708	+	0.874751i
$913$	749.050	+	381.660i	0.820428	+	0.418029i
$914$	−1522.90	−	494.819i	−1.66619	−	0.541377i
$915$		0			0
$916$	−6.45372	−	19.8625i	−0.00704555	−	0.0216840i
$917$	−710.455	−	112.525i	−0.774761	−	0.122710i
$918$	258.450	−	258.450i	0.281536	−	0.281536i
$919$	808.788	+	1113.20i	0.880074	+	1.21132i	0.976400	+	0.215968i	$0.0692906\pi$
$919$	808.788	+	1113.20i	0.880074	+	1.21132i	−0.0963268	+	0.995350i	$0.530709\pi$
$920$		0			0
$921$	−784.099	−	569.682i	−0.851357	−	0.618547i
$922$	25.7400	+	162.516i	0.0279176	+	0.176265i
$923$	−76.4602	−	150.062i	−0.0828388	−	0.162580i
$924$		−	136.976i		−	0.148243i
$925$		0			0
$926$	1025.30			1.10724
$927$	8.57529	−	4.36933i	0.00925058	−	0.00471341i
$928$	1096.59	−	173.683i	1.18167	−	0.187159i
$929$	18.7994	−	25.8751i	0.0202361	−	0.0278526i	−0.798779	−	0.601624i	$-0.794520\pi$
$929$	18.7994	−	25.8751i	0.0202361	−	0.0278526i	0.819015	+	0.573772i	$0.194520\pi$
$930$		0			0
$931$	623.629	−	453.093i	0.669848	−	0.486673i
$932$	42.1920	+	42.1920i	0.0452704	+	0.0452704i
$933$	−130.694	+	825.172i	−0.140080	+	0.884429i
$934$	−535.394	+	173.960i	−0.573227	+	0.186253i
$935$		0			0
$936$	13.5636	−	41.7443i	0.0144910	−	0.0445987i
$937$	−105.454	+	206.965i	−0.112544	+	0.220880i	−0.940408	−	0.340049i	$-0.889556\pi$
$937$	−105.454	+	206.965i	−0.112544	+	0.220880i	0.827863	+	0.560930i	$0.189556\pi$
$938$	−260.933	−	132.952i	−0.278180	−	0.141740i
$939$	361.374	+	117.418i	0.384850	+	0.125045i
$940$		0			0
$941$	503.761	+	1550.42i	0.535347	+	1.64763i	0.742899	+	0.669404i	$0.233450\pi$
$941$	503.761	+	1550.42i	0.535347	+	1.64763i	−0.207552	+	0.978224i	$0.566550\pi$
$942$	373.330	+	59.1297i	0.396317	+	0.0627704i
$943$	−623.619	+	623.619i	−0.661314	+	0.661314i
$944$	−1247.27	−	1716.72i	−1.32126	−	1.81856i
$945$		0			0
$946$	−197.642	−	143.595i	−0.208923	−	0.151792i
$947$	−28.3129	−	178.761i	−0.0298975	−	0.188765i	0.968220	−	0.250101i	$-0.0804639\pi$
$947$	−28.3129	−	178.761i	−0.0298975	−	0.188765i	−0.998117	+	0.0613359i	$0.980464\pi$
$948$	64.6399	+	126.863i	0.0681855	+	0.133822i
$949$			375.973i			0.396178i
$950$		0			0
$951$	−456.291			−0.479802
$952$	489.334	−	249.328i	0.514006	−	0.261899i
$953$	−213.634	+	33.8363i	−0.224170	+	0.0355050i	−0.267509	−	0.963555i	$-0.586200\pi$
$953$	−213.634	+	33.8363i	−0.224170	+	0.0355050i	0.0433390	+	0.999060i	$0.486200\pi$
$954$	401.518	−	552.642i	0.420878	−	0.579289i
$955$		0			0
$956$	614.067	−	446.146i	0.642329	−	0.466680i
$957$	−344.881	−	344.881i	−0.360377	−	0.360377i
$958$	71.4988	−	451.425i	0.0746334	−	0.471216i
$959$	−532.332	+	172.965i	−0.555091	+	0.180360i
$960$		0			0
$961$	−260.595	+	802.029i	−0.271171	+	0.834578i
$962$	90.7481	−	178.103i	0.0943327	−	0.185138i
$963$	355.126	+	180.946i	0.368770	+	0.187898i
$964$	−189.242	−	61.4883i	−0.196309	−	0.0637846i
$965$		0			0
$966$	114.596	+	352.691i	0.118630	+	0.365104i
$967$	1448.08	+	229.353i	1.49749	+	0.237180i	0.850767	−	0.525543i	$-0.176138\pi$
$967$	1448.08	+	229.353i	1.49749	+	0.237180i	0.646726	+	0.762723i	$0.276138\pi$
$968$	172.926	−	172.926i	0.178642	−	0.178642i
$969$	−743.948	−	1023.96i	−0.767748	−	1.05671i
$970$		0			0
$971$	1546.53	+	1123.62i	1.59272	+	1.15718i	0.899925	+	0.436044i	$0.143621\pi$
$971$	1546.53	+	1123.62i	1.59272	+	1.15718i	0.692795	+	0.721135i	$0.256379\pi$
$972$	−5.41471	−	34.1871i	−0.00557068	−	0.0351719i
$973$	−36.9695	−	72.5567i	−0.0379953	−	0.0745700i
$974$			1089.07i			1.11814i
$975$		0			0
$976$	−305.956			−0.313479
$977$	90.8290	−	46.2797i	0.0929673	−	0.0473692i	−0.406889	−	0.913478i	$-0.633386\pi$
$977$	90.8290	−	46.2797i	0.0929673	−	0.0473692i	0.499856	+	0.866109i	$0.333386\pi$
$978$	1256.40	−	198.994i	1.28466	−	0.203470i
$979$	544.940	−	750.046i	0.556629	−	0.766134i
$980$		0			0
$981$	518.883	−	376.990i	0.528932	−	0.384292i
$982$	334.341	+	334.341i	0.340469	+	0.340469i
$983$	31.0320	−	195.928i	0.0315687	−	0.199317i	−0.966863	−	0.255295i	$-0.917828\pi$
$983$	31.0320	−	195.928i	0.0315687	−	0.199317i	0.998432	+	0.0559777i	$0.0178276\pi$
$984$	329.541	−	107.074i	0.334900	−	0.108815i
$985$		0			0
$986$	−754.003	+	2320.58i	−0.764709	+	2.35353i
$987$	139.058	−	272.916i	0.140889	−	0.276511i
$988$	168.978	+	86.0988i	0.171031	+	0.0871446i
$989$	224.537	+	72.9565i	0.227034	+	0.0737680i
$990$		0			0
$991$	−126.479	−	389.263i	−0.127628	−	0.392798i	0.866743	−	0.498755i	$-0.166209\pi$
$991$	−126.479	−	389.263i	−0.127628	−	0.392798i	−0.994371	+	0.105957i	$0.966209\pi$
$992$	−342.963	−	54.3199i	−0.345728	−	0.0547580i
$993$	64.7056	−	64.7056i	0.0651617	−	0.0651617i
$994$	−328.604	−	452.285i	−0.330588	−	0.455015i
$995$		0			0
$996$	−322.214	−	234.102i	−0.323508	−	0.235043i
$997$	−147.130	−	928.943i	−0.147573	−	0.931738i	−0.944702	−	0.327929i	$-0.893649\pi$
$997$	−147.130	−	928.943i	−0.147573	−	0.931738i	0.797129	−	0.603808i	$-0.206351\pi$
$998$	369.260	+	724.714i	0.370000	+	0.726166i
$999$			126.332i			0.126459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.b.7.2		80
5.2	odd	4		75.3.k.a.28.2	✓	80
5.3	odd	4		375.3.k.a.118.9		80
5.4	even	2		375.3.k.c.7.9		80
15.2	even	4		225.3.r.b.28.9		80
25.6	even	5		375.3.k.a.232.9		80
25.8	odd	20	inner	375.3.k.b.268.2		80
25.17	odd	20		375.3.k.c.268.9		80
25.19	even	10		75.3.k.a.67.2	yes	80
75.44	odd	10		225.3.r.b.217.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.2	✓	80	5.2	odd	4
75.3.k.a.67.2	yes	80	25.19	even	10
225.3.r.b.28.9		80	15.2	even	4
225.3.r.b.217.9		80	75.44	odd	10
375.3.k.a.118.9		80	5.3	odd	4
375.3.k.a.232.9		80	25.6	even	5
375.3.k.b.7.2		80	1.1	even	1	trivial
375.3.k.b.268.2		80	25.8	odd	20	inner
375.3.k.c.7.9		80	5.4	even	2
375.3.k.c.268.9		80	25.17	odd	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.k (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22224 + 1.13229i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.30514 - 1.79637i) q^{4} +(-3.49485 + 2.53916i) q^{6} +(-3.10232 - 3.10232i) q^{7} +(0.694313 - 4.38372i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-2.50856 + 7.72057i) q^{11} +(1.74601 - 3.42674i) q^{12} +(2.93716 + 1.49656i) q^{13} +(10.4068 + 3.38139i) q^{14} +(6.16532 + 18.9749i) q^{16} +(-27.8560 - 4.41196i) q^{17} +(-5.29075 + 5.29075i) q^{18} +(15.2294 + 20.9615i) q^{19} +(-6.14781 - 4.46664i) q^{21} +(-3.16728 - 19.9974i) q^{22} +(8.88304 + 17.4339i) q^{23} -7.68747i q^{24} -8.22163 q^{26} +(4.62981 - 2.35900i) q^{27} +(-9.62191 + 1.52396i) q^{28} +(-20.3892 + 28.0633i) q^{29} +(8.77688 - 6.37677i) q^{31} +(-22.6323 - 22.6323i) q^{32} +(-2.19956 + 13.8875i) q^{33} +(66.8985 - 21.7366i) q^{34} +(2.05846 - 6.33529i) q^{36} +(-11.0377 + 21.6628i) q^{37} +(-57.5779 - 29.3374i) q^{38} +(5.43018 + 1.76437i) q^{39} +(13.9284 + 42.8673i) q^{41} +(18.7195 + 2.96487i) q^{42} +(8.53203 - 8.53203i) q^{43} +(10.5950 + 14.5828i) q^{44} +(-39.4805 - 28.6843i) q^{46} +(6.30548 + 39.8112i) q^{47} +(15.6885 + 30.7904i) q^{48} -29.7512i q^{49} -48.8495 q^{51} +(6.52180 - 3.32302i) q^{52} +(-90.1725 + 14.2819i) q^{53} +(-7.61748 + 10.4846i) q^{54} +(-15.7537 + 11.4457i) q^{56} +(31.7329 + 31.7329i) q^{57} +(13.5339 - 85.4499i) q^{58} +(-101.152 + 32.8662i) q^{59} +(-4.73879 + 14.5845i) q^{61} +(-12.2840 + 24.1087i) q^{62} +(-11.7275 - 5.97544i) q^{63} +(0.0212563 + 0.00690660i) q^{64} +(-10.8367 - 33.3519i) q^{66} +(-26.4335 - 4.18666i) q^{67} +(-44.2816 + 44.2816i) q^{68} +(19.9202 + 27.4178i) q^{69} +(-41.3332 - 30.0303i) q^{71} +(-2.08294 - 13.1512i) q^{72} +(51.7793 + 101.623i) q^{73} -60.6378i q^{74} +57.5312 q^{76} +(31.7341 - 16.1693i) q^{77} +(-14.0650 + 2.22767i) q^{78} +(-21.7607 + 29.9510i) q^{79} +(7.28115 - 5.29007i) q^{81} +(-79.4905 - 79.4905i) q^{82} +(16.2002 - 102.284i) q^{83} +(-16.0475 + 5.21416i) q^{84} +(-9.29951 + 28.6210i) q^{86} +(-27.2765 + 53.5331i) q^{87} +(32.1031 + 16.3573i) q^{88} +(-108.616 - 35.2914i) q^{89} +(-4.46922 - 13.7548i) q^{91} +(42.9115 + 6.79652i) q^{92} +(13.2870 - 13.2870i) q^{93} +(-59.0902 - 81.3306i) q^{94} +(-44.8500 - 32.5855i) q^{96} +(9.20986 + 58.1488i) q^{97} +(33.6869 + 66.1143i) q^{98} +24.3537i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} + 4 q^{7} + 72 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} - 40 q^{17} + 48 q^{18} + 100 q^{19} - 280 q^{22} - 264 q^{23} - 40 q^{26} + 44 q^{28} - 200 q^{29} - 636 q^{32} - 36 q^{33} - 100 q^{34}+ \cdots - 828 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 + 4 * q^7 + 72 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 - 40 * q^17 + 48 * q^18 + 100 * q^19 - 280 * q^22 - 264 * q^23 - 40 * q^26 + 44 * q^28 - 200 * q^29 - 636 * q^32 - 36 * q^33 - 100 * q^34 - 120 * q^36 + 124 * q^37 - 96 * q^38 + 160 * q^41 + 252 * q^42 + 472 * q^43 + 700 * q^44 + 128 * q^47 + 48 * q^48 + 620 * q^52 + 76 * q^53 - 72 * q^57 + 108 * q^58 - 800 * q^59 - 240 * q^61 + 328 * q^62 - 168 * q^63 - 100 * q^64 + 1240 * q^67 - 104 * q^68 - 216 * q^72 - 244 * q^73 + 648 * q^77 + 120 * q^78 - 200 * q^79 + 180 * q^81 + 168 * q^82 + 44 * q^83 + 1200 * q^84 - 84 * q^87 - 1008 * q^88 + 1500 * q^89 - 2236 * q^92 + 648 * q^93 + 200 * q^94 + 60 * q^96 - 200 * q^97 - 828 * q^98

Introduction

L-functions

Modular forms

Varieties

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