LMFDB - Embedded newform 475.2.l.f.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	475.101
Dual form			475.2.l.f.301.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05812 - 1.72697i) q^{2} +(2.01713 + 0.734175i) q^{3} +(0.906145 - 5.13900i) q^{4} +(5.41939 - 1.97250i) q^{6} +(-1.39152 + 2.41018i) q^{7} +(-4.32326 - 7.48810i) q^{8} +(1.23166 + 1.03349i) q^{9} +O(q^{10})$	\(q+(2.05812 - 1.72697i) q^{2} +(2.01713 + 0.734175i) q^{3} +(0.906145 - 5.13900i) q^{4} +(5.41939 - 1.97250i) q^{6} +(-1.39152 + 2.41018i) q^{7} +(-4.32326 - 7.48810i) q^{8} +(1.23166 + 1.03349i) q^{9} +(1.19000 + 2.06113i) q^{11} +(5.60074 - 9.70076i) q^{12} +(-0.0380504 + 0.0138492i) q^{13} +(1.29839 + 7.36354i) q^{14} +(-12.0223 - 4.37577i) q^{16} +(-1.39094 + 1.16714i) q^{17} +4.31971 q^{18} +(-4.07652 - 1.54336i) q^{19} +(-4.57636 + 3.84002i) q^{21} +(6.00867 + 2.18698i) q^{22} +(-0.441819 + 2.50568i) q^{23} +(-3.22299 - 18.2785i) q^{24} +(-0.0543952 + 0.0942153i) q^{26} +(-1.49422 - 2.58806i) q^{27} +(11.1250 + 9.33498i) q^{28} +(2.25845 + 1.89507i) q^{29} +(1.44307 - 2.49947i) q^{31} +(-16.0501 + 5.84176i) q^{32} +(0.887142 + 5.03123i) q^{33} +(-0.847116 + 4.80423i) q^{34} +(6.42716 - 5.39302i) q^{36} -0.227089 q^{37} +(-11.0553 + 3.86361i) q^{38} -0.0869204 q^{39} +(-7.55269 - 2.74896i) q^{41} +(-2.78710 + 15.8065i) q^{42} +(0.891282 + 5.05471i) q^{43} +(11.6705 - 4.24771i) q^{44} +(3.41791 + 5.92000i) q^{46} +(8.48501 + 7.11977i) q^{47} +(-21.0380 - 17.6530i) q^{48} +(-0.372635 - 0.645423i) q^{49} +(-3.66260 + 1.33308i) q^{51} +(0.0366920 + 0.208091i) q^{52} +(0.992310 - 5.62767i) q^{53} +(-7.54477 - 2.74607i) q^{54} +24.0635 q^{56} +(-7.08978 - 6.10603i) q^{57} +7.92088 q^{58} +(8.89878 - 7.46696i) q^{59} +(0.795974 - 4.51419i) q^{61} +(-1.34649 - 7.63635i) q^{62} +(-4.20476 + 1.53041i) q^{63} +(-10.1506 + 17.5814i) q^{64} +(10.5146 + 8.82282i) q^{66} +(3.71745 + 3.11931i) q^{67} +(4.73754 + 8.20566i) q^{68} +(-2.73081 + 4.72991i) q^{69} +(-1.34912 - 7.65124i) q^{71} +(2.41406 - 13.6908i) q^{72} +(3.99151 + 1.45279i) q^{73} +(-0.467377 + 0.392176i) q^{74} +(-11.6252 + 19.5508i) q^{76} -6.62359 q^{77} +(-0.178893 + 0.150109i) q^{78} +(-10.9102 - 3.97100i) q^{79} +(-1.95152 - 11.0676i) q^{81} +(-20.2917 + 7.38558i) q^{82} +(-2.23528 + 3.87161i) q^{83} +(15.5870 + 26.9975i) q^{84} +(10.5637 + 8.86399i) q^{86} +(3.16428 + 5.48069i) q^{87} +(10.2893 - 17.8216i) q^{88} +(-14.4648 + 5.26476i) q^{89} +(0.0195687 - 0.110980i) q^{91} +(12.4764 + 4.54102i) q^{92} +(4.74590 - 3.98229i) q^{93} +29.7588 q^{94} -36.6640 q^{96} +(4.28633 - 3.59666i) q^{97} +(-1.88155 - 0.684829i) q^{98} +(-0.664482 + 3.76846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	2.05812	−	1.72697i	1.45531	−	1.22115i	0.526724	−	0.850036i	$-0.323420\pi$
$2$	2.05812	−	1.72697i	1.45531	−	1.22115i	0.928587	−	0.371115i	$-0.121024\pi$
$3$	2.01713	+	0.734175i	1.16459	+	0.423876i	0.850735	−	0.525595i	$-0.176157\pi$
$3$	2.01713	+	0.734175i	1.16459	+	0.423876i	0.313855	+	0.949471i	$0.398379\pi$
$4$	0.906145	−	5.13900i	0.453073	−	2.56950i
$5$		0			0
$5$		0			0
$6$	5.41939	−	1.97250i	2.21246	−	0.805269i
$7$	−1.39152	+	2.41018i	−0.525944	+	0.910961i	0.473600	+	0.880740i	$0.342954\pi$
$7$	−1.39152	+	2.41018i	−0.525944	+	0.910961i	−0.999543	+	0.0302209i	$0.990379\pi$
$8$	−4.32326	−	7.48810i	−1.52850	−	2.64744i
$9$	1.23166	+	1.03349i	0.410554	+	0.344496i
$10$		0			0
$11$	1.19000	+	2.06113i	0.358797	+	0.621455i	0.987760	−	0.155980i	$-0.0498536\pi$
$11$	1.19000	+	2.06113i	0.358797	+	0.621455i	−0.628963	+	0.777435i	$0.716520\pi$
$12$	5.60074	−	9.70076i	1.61679	−	2.80037i
$13$	−0.0380504	+	0.0138492i	−0.0105533	+	0.00384108i	−0.347291	−	0.937757i	$-0.612899\pi$
$13$	−0.0380504	+	0.0138492i	−0.0105533	+	0.00384108i	0.336738	+	0.941598i	$0.390676\pi$
$14$	1.29839	+	7.36354i	0.347010	+	1.96799i
$15$		0			0
$16$	−12.0223	−	4.37577i	−3.00558	−	1.09394i
$17$	−1.39094	+	1.16714i	−0.337353	+	0.283073i	−0.795688	−	0.605707i	$-0.792891\pi$
$17$	−1.39094	+	1.16714i	−0.337353	+	0.283073i	0.458335	+	0.888780i	$0.348446\pi$
$18$	4.31971			1.01816
$19$	−4.07652	−	1.54336i	−0.935219	−	0.354071i
$19$	−4.07652	−	1.54336i	−0.935219	−	0.354071i
$20$		0			0
$21$	−4.57636	+	3.84002i	−0.998643	+	0.837961i
$22$	6.00867	+	2.18698i	1.28105	+	0.466265i
$23$	−0.441819	+	2.50568i	−0.0921257	+	0.522471i	0.903465	+	0.428663i	$0.141015\pi$
$23$	−0.441819	+	2.50568i	−0.0921257	+	0.522471i	−0.995590	+	0.0938080i	$0.970096\pi$
$24$	−3.22299	−	18.2785i	−0.657890	−	3.73108i
$25$		0			0
$26$	−0.0543952	+	0.0942153i	−0.0106678	+	0.0184771i
$27$	−1.49422	−	2.58806i	−0.287562	−	0.498072i
$28$	11.1250	+	9.33498i	2.10243	+	1.76414i
$29$	2.25845	+	1.89507i	0.419384	+	0.351905i	0.827929	−	0.560833i	$-0.189519\pi$
$29$	2.25845	+	1.89507i	0.419384	+	0.351905i	−0.408545	+	0.912738i	$0.633964\pi$
$30$		0			0
$31$	1.44307	−	2.49947i	0.259183	−	0.448918i	−0.706840	−	0.707373i	$-0.749880\pi$
$31$	1.44307	−	2.49947i	0.259183	−	0.448918i	0.966023	+	0.258455i	$0.0832134\pi$
$32$	−16.0501	+	5.84176i	−2.83728	+	1.03269i
$33$	0.887142	+	5.03123i	0.154432	+	0.875826i
$34$	−0.847116	+	4.80423i	−0.145279	+	0.823919i
$35$		0			0
$36$	6.42716	−	5.39302i	1.07119	−	0.898837i
$37$	−0.227089			−0.0373333			−0.0186666	−	0.999826i	$-0.505942\pi$
$37$	−0.227089			−0.0373333			−0.0186666	+	0.999826i	$0.505942\pi$
$38$	−11.0553	+	3.86361i	−1.79341	+	0.626761i
$39$	−0.0869204			−0.0139184
$40$		0			0
$41$	−7.55269	−	2.74896i	−1.17953	−	0.429315i	−0.323496	−	0.946230i	$-0.604858\pi$
$41$	−7.55269	−	2.74896i	−1.17953	−	0.429315i	−0.856037	+	0.516915i	$0.827080\pi$
$42$	−2.78710	+	15.8065i	−0.430059	+	2.43899i
$43$	0.891282	+	5.05471i	0.135919	+	0.770836i	0.974215	+	0.225621i	$0.0724410\pi$
$43$	0.891282	+	5.05471i	0.135919	+	0.770836i	−0.838296	+	0.545215i	$0.816448\pi$
$44$	11.6705	−	4.24771i	1.75939	−	0.640366i
$45$		0			0
$46$	3.41791	+	5.92000i	0.503944	+	0.872857i
$47$	8.48501	+	7.11977i	1.23767	+	1.03853i	0.997703	+	0.0677434i	$0.0215799\pi$
$47$	8.48501	+	7.11977i	1.23767	+	1.03853i	0.239964	+	0.970782i	$0.422865\pi$
$48$	−21.0380	−	17.6530i	−3.03657	−	2.54799i
$49$	−0.372635	−	0.645423i	−0.0532336	−	0.0922032i
$50$		0			0
$51$	−3.66260	+	1.33308i	−0.512866	+	0.186668i
$52$	0.0366920	+	0.208091i	0.00508827	+	0.0288570i
$53$	0.992310	−	5.62767i	0.136304	−	0.773020i	−0.837638	−	0.546225i	$-0.816064\pi$
$53$	0.992310	−	5.62767i	0.136304	−	0.773020i	0.973943	−	0.226794i	$-0.0728246\pi$
$54$	−7.54477	−	2.74607i	−1.02671	−	0.373693i
$55$		0			0
$56$	24.0635			3.21562
$57$	−7.08978	−	6.10603i	−0.939064	−	0.808764i
$58$	7.92088			1.04006
$59$	8.89878	−	7.46696i	1.15852	−	0.972116i	0.158638	−	0.987337i	$-0.449290\pi$
$59$	8.89878	−	7.46696i	1.15852	−	0.972116i	0.999884	+	0.0152208i	$0.00484512\pi$
$60$		0			0
$61$	0.795974	−	4.51419i	0.101914	−	0.577983i	−0.890494	−	0.454995i	$-0.849641\pi$
$61$	0.795974	−	4.51419i	0.101914	−	0.577983i	0.992408	−	0.122988i	$-0.0392477\pi$
$62$	−1.34649	−	7.63635i	−0.171005	−	0.969817i
$63$	−4.20476	+	1.53041i	−0.529750	+	0.192813i
$64$	−10.1506	+	17.5814i	−1.26883	+	2.19767i
$65$		0			0
$66$	10.5146	+	8.82282i	1.29426	+	1.08601i
$67$	3.71745	+	3.11931i	0.454159	+	0.381084i	0.840976	−	0.541072i	$-0.181981\pi$
$67$	3.71745	+	3.11931i	0.454159	+	0.381084i	−0.386818	+	0.922156i	$0.626426\pi$
$68$	4.73754	+	8.20566i	0.574511	+	0.995083i
$69$	−2.73081	+	4.72991i	−0.328751	+	0.569414i
$70$		0			0
$71$	−1.34912	−	7.65124i	−0.160111	−	0.908035i	−0.953963	−	0.299924i	$-0.903039\pi$
$71$	−1.34912	−	7.65124i	−0.160111	−	0.908035i	0.793852	−	0.608111i	$-0.208072\pi$
$72$	2.41406	−	13.6908i	0.284500	−	1.61348i
$73$	3.99151	+	1.45279i	0.467171	+	0.170036i	0.564870	−	0.825180i	$-0.308926\pi$
$73$	3.99151	+	1.45279i	0.467171	+	0.170036i	−0.0976997	+	0.995216i	$0.531148\pi$
$74$	−0.467377	+	0.392176i	−0.0543315	+	0.0455896i
$75$		0			0
$76$	−11.6252	+	19.5508i	−1.33351	+	2.24263i
$77$	−6.62359			−0.754828
$78$	−0.178893	+	0.150109i	−0.0202556	+	0.0169965i
$79$	−10.9102	−	3.97100i	−1.22750	−	0.446773i	−0.354758	−	0.934958i	$-0.615437\pi$
$79$	−10.9102	−	3.97100i	−1.22750	−	0.446773i	−0.872740	+	0.488185i	$0.837659\pi$
$80$		0			0
$81$	−1.95152	−	11.0676i	−0.216836	−	1.22974i
$82$	−20.2917	+	7.38558i	−2.24085	+	0.815601i
$83$	−2.23528	+	3.87161i	−0.245354	+	0.424965i	−0.962231	−	0.272234i	$-0.912237\pi$
$83$	−2.23528	+	3.87161i	−0.245354	+	0.424965i	0.716877	+	0.697199i	$0.245571\pi$
$84$	15.5870	+	26.9975i	1.70069	+	2.94567i
$85$		0			0
$86$	10.5637	+	8.86399i	1.13911	+	0.955828i
$87$	3.16428	+	5.48069i	0.339246	+	0.587592i
$88$	10.2893	−	17.8216i	1.09684	−	1.89979i
$89$	−14.4648	+	5.26476i	−1.53327	+	0.558064i	−0.964419	−	0.264378i	$-0.914833\pi$
$89$	−14.4648	+	5.26476i	−1.53327	+	0.558064i	−0.568849	+	0.822442i	$0.692611\pi$
$90$		0			0
$91$	0.0195687	−	0.110980i	0.00205136	−	0.0116338i
$92$	12.4764	+	4.54102i	1.30075	+	0.473434i
$93$	4.74590	−	3.98229i	0.492127	−	0.412944i
$94$	29.7588			3.06939
$95$		0			0
$96$	−36.6640			−3.74200
$97$	4.28633	−	3.59666i	0.435211	−	0.365185i	−0.398703	−	0.917080i	$-0.630540\pi$
$97$	4.28633	−	3.59666i	0.435211	−	0.365185i	0.833914	+	0.551895i	$0.186095\pi$
$98$	−1.88155	−	0.684829i	−0.190066	−	0.0691782i
$99$	−0.664482	+	3.76846i	−0.0667829	+	0.378745i
$100$		0			0
$101$	−11.2361	+	4.08961i	−1.11804	+	0.406932i	−0.833935	−	0.551863i	$-0.813917\pi$
$101$	−11.2361	+	4.08961i	−1.11804	+	0.406932i	−0.284101	+	0.958794i	$0.591695\pi$
$102$	−5.23589	+	9.06882i	−0.518430	+	0.897947i
$103$	7.04702	+	12.2058i	0.694363	+	1.20267i	0.970395	+	0.241524i	$0.0776473\pi$
$103$	7.04702	+	12.2058i	0.694363	+	1.20267i	−0.276031	+	0.961149i	$0.589019\pi$
$104$	0.268206	+	0.225052i	0.0262998	+	0.0220681i
$105$		0			0
$106$	−7.67651	−	13.2961i	−0.745609	−	1.29143i
$107$	5.86249	−	10.1541i	0.566748	−	0.981637i	−0.430137	−	0.902764i	$-0.641535\pi$
$107$	5.86249	−	10.1541i	0.566748	−	0.981637i	0.996885	−	0.0788727i	$-0.0251321\pi$
$108$	−14.6540	+	5.33362i	−1.41008	+	0.513228i
$109$	−1.16558	−	6.61032i	−0.111642	−	0.633154i	−0.988358	−	0.152145i	$-0.951382\pi$
$109$	−1.16558	−	6.61032i	−0.111642	−	0.633154i	0.876716	−	0.481008i	$-0.159729\pi$
$110$		0			0
$111$	−0.458068	−	0.166723i	−0.0434779	−	0.0158247i
$112$	27.2757	−	22.8870i	2.57731	−	2.16262i
$113$	2.46603			0.231985			0.115992	−	0.993250i	$-0.462995\pi$
$113$	2.46603			0.231985			0.115992	+	0.993250i	$0.462995\pi$
$114$	−25.1365	−	0.323128i	−2.35425	−	0.0302637i
$115$		0			0
$116$	11.7852	−	9.88899i	1.09423	−	0.918169i
$117$	−0.0611783	−	0.0222671i	−0.00565593	−	0.00205859i
$118$	5.41956	−	30.7358i	0.498911	−	2.82946i
$119$	−0.877494	−	4.97651i	−0.0804397	−	0.456196i
$120$		0			0
$121$	2.66782	−	4.62080i	0.242529	−	0.420073i
$122$	−6.15765	−	10.6654i	−0.557488	−	0.965597i
$123$	−13.2165	−	11.0900i	−1.19170	−	0.999951i
$124$	−11.5372	−	9.68082i	−1.03607	−	0.869364i
$125$		0			0
$126$	−6.01094	+	10.4113i	−0.535497	+	0.927509i
$127$	−0.694456	+	0.252761i	−0.0616230	+	0.0224289i	−0.372648	−	0.927973i	$-0.621550\pi$
$127$	−0.694456	+	0.252761i	−0.0616230	+	0.0224289i	0.311025	+	0.950402i	$0.399328\pi$
$128$	3.53942	+	20.0731i	0.312844	+	1.77423i
$129$	−1.91321	+	10.8504i	−0.168449	+	0.955320i
$130$		0			0
$131$	−8.35925	+	7.01424i	−0.730351	+	0.612837i	−0.930227	−	0.366984i	$-0.880390\pi$
$131$	−8.35925	+	7.01424i	−0.730351	+	0.612837i	0.199876	+	0.979821i	$0.435946\pi$
$132$	26.6594			2.32040
$133$	9.39231	−	7.67754i	0.814417	−	0.665727i
$134$	13.0379			1.12630
$135$		0			0
$136$	14.7531	+	5.36968i	1.26506	+	0.460446i
$137$	0.797114	−	4.52066i	0.0681021	−	0.386226i	−0.931637	−	0.363390i	$-0.881619\pi$
$137$	0.797114	−	4.52066i	0.0681021	−	0.386226i	0.999739	−	0.0228361i	$-0.00726959\pi$
$138$	2.54806	+	14.4508i	0.216905	+	1.23013i
$139$	7.37217	−	2.68325i	0.625299	−	0.227590i	−0.00988487	−	0.999951i	$-0.503147\pi$
$139$	7.37217	−	2.68325i	0.625299	−	0.227590i	0.635184	+	0.772361i	$0.280924\pi$
$140$		0			0
$141$	11.8882	+	20.5910i	1.00117	+	1.73407i
$142$	−15.9901	−	13.4173i	−1.34186	−	1.12595i
$143$	−0.0738250	−	0.0619465i	−0.00617355	−	0.00518023i
$144$	−10.2851	−	17.8144i	−0.857095	−	1.48453i
$145$		0			0
$146$	10.7239	−	3.90319i	0.887518	−	0.323030i
$147$	−0.277800	−	1.57548i	−0.0229125	−	0.129943i
$148$	−0.205776	+	1.16701i	−0.0169147	+	0.0959279i
$149$	20.4289	+	7.43550i	1.67360	+	0.609140i	0.992411	−	0.122968i	$-0.0392412\pi$
$149$	20.4289	+	7.43550i	1.67360	+	0.609140i	0.681188	+	0.732108i	$0.261463\pi$
$150$		0			0
$151$	9.68916			0.788493			0.394247	−	0.919005i	$-0.371006\pi$
$151$	9.68916			0.788493			0.394247	+	0.919005i	$0.371006\pi$
$152$	6.06704	+	37.1977i	0.492102	+	3.01714i
$153$	−2.91940			−0.236019
$154$	−13.6322	+	11.4387i	−1.09851	+	0.921760i
$155$		0			0
$156$	−0.0787625	+	0.446684i	−0.00630604	+	0.0357634i
$157$	1.28145	+	7.26744i	0.102271	+	0.580005i	0.992275	+	0.124054i	$0.0395897\pi$
$157$	1.28145	+	7.26744i	0.102271	+	0.580005i	−0.890005	+	0.455951i	$0.849299\pi$
$158$	−29.3124	+	10.6688i	−2.33197	+	0.848767i
$159$	6.13331	−	10.6232i	0.486403	−	0.842474i
$160$		0			0
$161$	−5.42434	−	4.55156i	−0.427498	−	0.358713i
$162$	−23.1299	−	19.4083i	−1.81726	−	1.52486i
$163$	−2.45155	−	4.24622i	−0.192021	−	0.332589i	0.753899	−	0.656990i	$-0.228171\pi$
$163$	−2.45155	−	4.24622i	−0.192021	−	0.332589i	−0.945920	+	0.324401i	$0.894837\pi$
$164$	−20.9707	+	36.3224i	−1.63754	+	2.83630i
$165$		0			0
$166$	2.08568	+	11.8285i	0.161880	+	0.918070i
$167$	−1.75241	+	9.93844i	−0.135606	+	0.769059i	0.838830	+	0.544394i	$0.183240\pi$
$167$	−1.75241	+	9.93844i	−0.135606	+	0.769059i	−0.974436	+	0.224666i	$0.927871\pi$
$168$	48.5392	+	17.6668i	3.74488	+	1.36303i
$169$	−9.95732	+	8.35518i	−0.765948	+	0.642707i
$170$		0			0
$171$	−3.42586	−	6.11393i	−0.261982	−	0.467544i
$172$	26.7838			2.04225
$173$	−3.73777	+	3.13636i	−0.284177	+	0.238453i	−0.773722	−	0.633525i	$-0.781607\pi$
$173$	−3.73777	+	3.13636i	−0.284177	+	0.238453i	0.489545	+	0.871978i	$0.337163\pi$
$174$	15.9774	+	5.81531i	1.21125	+	0.440858i
$175$		0			0
$176$	−5.28748	−	29.9868i	−0.398559	−	2.26034i
$177$	23.4320	−	8.52857i	1.76126	−	0.641046i
$178$	−20.6783	+	35.8158i	−1.54990	+	2.68451i
$179$	−11.9422	−	20.6845i	−0.892604	−	1.54604i	−0.836743	−	0.547597i	$-0.815543\pi$
$179$	−11.9422	−	20.6845i	−0.892604	−	1.54604i	−0.0558613	−	0.998439i	$-0.517790\pi$
$180$		0			0
$181$	1.96682	+	1.65036i	0.146193	+	0.122670i	0.712951	−	0.701214i	$-0.247358\pi$
$181$	1.96682	+	1.65036i	0.146193	+	0.122670i	−0.566758	+	0.823884i	$0.691803\pi$
$182$	−0.151384	−	0.262204i	−0.0112213	−	0.0194359i
$183$	4.91979	−	8.52132i	0.363681	−	0.629914i
$184$	20.6729	−	7.52431i	1.52403	−	0.554700i
$185$		0			0
$186$	2.89036	−	16.3921i	0.211932	−	1.20192i
$187$	−4.06085	−	1.47803i	−0.296959	−	0.108084i
$188$	44.2772	−	37.1530i	3.22925	−	2.70966i
$189$	8.31690			0.604965
$190$		0			0
$191$	9.28746			0.672017			0.336008	−	0.941859i	$-0.390923\pi$
$191$	9.28746			0.672017			0.336008	+	0.941859i	$0.390923\pi$
$192$	−33.3829	+	28.0116i	−2.40920	+	2.02156i
$193$	−23.3341	−	8.49293i	−1.67963	−	0.611334i	−0.686368	−	0.727254i	$-0.740796\pi$
$193$	−23.3341	−	8.49293i	−1.67963	−	0.611334i	−0.993259	+	0.115920i	$0.963018\pi$
$194$	2.61047	−	14.8047i	0.187421	−	1.06292i
$195$		0			0
$196$	−3.65449	+	1.33013i	−0.261035	+	0.0950090i
$197$	2.08658	−	3.61406i	0.148663	−	0.257491i	−0.782071	−	0.623190i	$-0.785836\pi$
$197$	2.08658	−	3.61406i	0.148663	−	0.257491i	0.930733	+	0.365698i	$0.119170\pi$
$198$	5.14043	+	8.90349i	0.365315	+	0.632744i
$199$	17.1492	+	14.3899i	1.21567	+	1.02007i	0.999039	+	0.0438194i	$0.0139526\pi$
$199$	17.1492	+	14.3899i	1.21567	+	1.02007i	0.216635	+	0.976253i	$0.430492\pi$
$200$		0			0
$201$	5.20845	+	9.02131i	0.367376	+	0.636314i
$202$	−16.0627	+	27.8213i	−1.13016	+	1.95750i
$203$	−7.71012	+	2.80625i	−0.541144	+	0.196960i
$204$	3.53184	+	20.0301i	0.247278	+	1.40238i
$205$		0			0
$206$	35.5826	+	12.9510i	2.47916	+	0.902340i
$207$	−3.13376	+	2.62954i	−0.217811	+	0.182765i
$208$	0.518056			0.0359207
$209$	−1.66998	−	10.2388i	−0.115515	−	0.708236i
$210$		0			0
$211$	1.28817	−	1.08090i	0.0886814	−	0.0744125i	−0.597369	−	0.801966i	$-0.703787\pi$
$211$	1.28817	−	1.08090i	0.0886814	−	0.0744125i	0.686051	+	0.727554i	$0.259343\pi$
$212$	−28.0214	−	10.1990i	−1.92452	−	0.700468i
$213$	2.89600	−	16.4240i	0.198431	−	1.12536i
$214$	−5.47015	−	31.0228i	−0.373932	−	2.12067i
$215$		0			0
$216$	−12.9197	+	22.3777i	−0.879078	+	1.52261i
$217$	4.01611	+	6.95611i	0.272631	+	0.472211i
$218$	−13.8147	−	11.5919i	−0.935650	−	0.785104i
$219$	6.98478	+	5.86093i	0.471988	+	0.396045i
$220$		0			0
$221$	0.0367620	−	0.0636737i	0.00247288	−	0.00428316i
$222$	−1.23069	+	0.447933i	−0.0825982	+	0.0300633i
$223$	1.66903	+	9.46555i	0.111767	+	0.633860i	0.988300	+	0.152520i	$0.0487388\pi$
$223$	1.66903	+	9.46555i	0.111767	+	0.633860i	−0.876534	+	0.481340i	$0.840150\pi$
$224$	8.25431	−	46.8125i	0.551514	−	3.12779i
$225$		0			0
$226$	5.07539	−	4.25876i	0.337610	−	0.283288i
$227$	−23.4650			−1.55743			−0.778714	−	0.627379i	$-0.784128\pi$
$227$	−23.4650			−1.55743			−0.778714	+	0.627379i	$0.784128\pi$
$228$	−37.8033	+	30.9014i	−2.50358	+	2.04650i
$229$	−1.19088			−0.0786952			−0.0393476	−	0.999226i	$-0.512528\pi$
$229$	−1.19088			−0.0786952			−0.0393476	+	0.999226i	$0.512528\pi$
$230$		0			0
$231$	−13.3606	−	4.86287i	−0.879065	−	0.319954i
$232$	4.42658	−	25.1044i	0.290619	−	1.64818i
$233$	−4.01831	−	22.7889i	−0.263248	−	1.49295i	−0.773978	−	0.633212i	$-0.781736\pi$
$233$	−4.01831	−	22.7889i	−0.263248	−	1.49295i	0.510730	−	0.859741i	$-0.329375\pi$
$234$	−0.164367	+	0.0598246i	−0.0107450	+	0.00391086i
$235$		0			0
$236$	−30.3092	−	52.4970i	−1.97296	−	3.41727i
$237$	−19.0920	−	16.0200i	−1.24016	−	1.04061i
$238$	−10.4003	−	8.72686i	−0.674149	−	0.565679i
$239$	−4.84358	−	8.38932i	−0.313305	−	0.542660i	0.665771	−	0.746156i	$-0.268103\pi$
$239$	−4.84358	−	8.38932i	−0.313305	−	0.542660i	−0.979076	+	0.203496i	$0.934770\pi$
$240$		0			0
$241$	−14.8334	+	5.39891i	−0.955503	+	0.347775i	−0.772270	−	0.635295i	$-0.780879\pi$
$241$	−14.8334	+	5.39891i	−0.955503	+	0.347775i	−0.183233	+	0.983070i	$0.558656\pi$
$242$	−2.48928	−	14.1174i	−0.160017	−	0.907502i
$243$	2.63230	−	14.9285i	0.168862	−	0.957665i
$244$	−22.4772	−	8.18102i	−1.43895	−	0.523736i
$245$		0			0
$246$	−46.3533			−2.95538
$247$	0.176488	+	0.00226874i	0.0112297	+	0.000144356i
$248$	−24.9550			−1.58465
$249$	−7.35128	+	6.16846i	−0.465869	+	0.390910i
$250$		0			0
$251$	0.951469	−	5.39605i	0.0600562	−	0.340596i	−0.939944	−	0.341330i	$-0.889123\pi$
$251$	0.951469	−	5.39605i	0.0600562	−	0.340596i	1.00000		0.000734411i	$0.000233770\pi$
$252$	4.05465	+	22.9951i	0.255419	+	1.44855i
$253$	−5.69030	+	2.07110i	−0.357746	+	0.130209i
$254$	−0.992764	+	1.71952i	−0.0622915	+	0.107892i
$255$		0			0
$256$	10.8468	+	9.10155i	0.677926	+	0.568847i
$257$	−2.71792	−	2.28060i	−0.169539	−	0.142260i	0.554070	−	0.832470i	$-0.313074\pi$
$257$	−2.71792	−	2.28060i	−0.169539	−	0.142260i	−0.723609	+	0.690210i	$0.757518\pi$
$258$	14.8006	+	25.6354i	0.921445	+	1.59599i
$259$	0.315999	−	0.547326i	0.0196352	−	0.0340092i
$260$		0			0
$261$	0.823122	+	4.66816i	0.0509500	+	0.288952i
$262$	−5.09097	+	28.8723i	−0.314521	+	1.78374i
$263$	24.7587	+	9.01141i	1.52668	+	0.555668i	0.962807	−	0.270191i	$-0.0870868\pi$
$263$	24.7587	+	9.01141i	1.52668	+	0.555668i	0.563877	+	0.825858i	$0.309309\pi$
$264$	33.8390	−	28.3943i	2.08265	−	1.74755i
$265$		0			0
$266$	6.07166	−	32.0215i	0.372277	−	1.96337i
$267$	−33.0427			−2.02218
$268$	19.3987	−	16.2774i	1.18496	−	0.994303i
$269$	−21.7224	−	7.90629i	−1.32444	−	0.482055i	−0.419559	−	0.907728i	$-0.637815\pi$
$269$	−21.7224	−	7.90629i	−1.32444	−	0.482055i	−0.904877	+	0.425673i	$0.860037\pi$
$270$		0			0
$271$	3.20656	+	18.1853i	0.194785	+	1.10468i	0.912725	+	0.408574i	$0.133974\pi$
$271$	3.20656	+	18.1853i	0.194785	+	1.10468i	−0.717941	+	0.696104i	$0.754915\pi$
$272$	21.8295	−	7.94530i	1.32361	−	0.481754i
$273$	0.120951	−	0.209493i	0.00732029	−	0.0126791i
$274$	−6.16648	−	10.6807i	−0.372531	−	0.645242i
$275$		0			0
$276$	21.8325	+	18.3196i	1.31416	+	1.10271i
$277$	14.9854	+	25.9554i	0.900384	+	1.55951i	0.826996	+	0.562208i	$0.190048\pi$
$277$	14.9854	+	25.9554i	0.900384	+	1.55951i	0.0733885	+	0.997303i	$0.476619\pi$
$278$	10.5389	−	18.2540i	0.632083	−	1.09480i
$279$	4.36054	−	1.58711i	0.261059	−	0.0950177i
$280$		0			0
$281$	−0.690977	+	3.91872i	−0.0412202	+	0.233771i	−0.998457	−	0.0555351i	$-0.982314\pi$
$281$	−0.690977	+	3.91872i	−0.0412202	+	0.233771i	0.957237	+	0.289306i	$0.0934247\pi$
$282$	60.0273	+	21.8482i	3.57458	+	1.30104i
$283$	−6.93217	+	5.81678i	−0.412075	+	0.345772i	−0.825139	−	0.564930i	$-0.808903\pi$
$283$	−6.93217	+	5.81678i	−0.412075	+	0.345772i	0.413064	+	0.910702i	$0.364459\pi$
$284$	−40.5423			−2.40574
$285$		0			0
$286$	−0.258920			−0.0153103
$287$	17.1352	−	14.3781i	1.01146	−	0.848713i
$288$	−25.8057	−	9.39250i	−1.52061	−	0.553458i
$289$	−2.37951	+	13.4949i	−0.139971	+	0.793816i
$290$		0			0
$291$	11.2867	−	4.10800i	0.661635	−	0.240816i
$292$	11.0828	−	19.1959i	0.648570	−	1.12336i
$293$	−1.16822	−	2.02341i	−0.0682479	−	0.118209i	0.829882	−	0.557939i	$-0.188408\pi$
$293$	−1.16822	−	2.02341i	−0.0682479	−	0.118209i	−0.898130	+	0.439730i	$0.855074\pi$
$294$	−3.29255	−	2.76278i	−0.192025	−	0.161128i
$295$		0			0
$296$	0.981765	+	1.70047i	0.0570640	+	0.0988377i
$297$	3.55622	−	6.15955i	0.206353	−	0.357413i
$298$	54.8860	−	19.9769i	3.17946	−	1.15723i
$299$	−0.0178903	−	0.101461i	−0.00103462	−	0.00586765i
$300$		0			0
$301$	−13.4230	−	4.88556i	−0.773687	−	0.281599i
$302$	19.9415	−	16.7329i	1.14750	−	0.962869i
$303$	−25.6672			−1.47454
$304$	42.2559	+	36.3927i	2.42354	+	2.08726i
$305$		0			0
$306$	−6.00847	+	5.04170i	−0.343481	+	0.288215i
$307$	−7.14274	−	2.59974i	−0.407658	−	0.148375i	0.130048	−	0.991508i	$-0.458487\pi$
$307$	−7.14274	−	2.59974i	−0.407658	−	0.148375i	−0.537706	+	0.843132i	$0.680709\pi$
$308$	−6.00194	+	34.0387i	−0.341992	+	1.93953i
$309$	5.25356	+	29.7944i	0.298864	+	1.69494i
$310$		0			0
$311$	9.41207	−	16.3022i	0.533709	−	0.924412i	−0.465515	−	0.885040i	$-0.654131\pi$
$311$	9.41207	−	16.3022i	0.533709	−	0.924412i	0.999225	−	0.0393720i	$-0.0125357\pi$
$312$	0.375779	+	0.650868i	0.0212743	+	0.0368482i
$313$	17.0147	+	14.2771i	0.961729	+	0.806987i	0.981234	−	0.192823i	$-0.0617643\pi$
$313$	17.0147	+	14.2771i	0.961729	+	0.806987i	−0.0195042	+	0.999810i	$0.506209\pi$
$314$	15.1880	+	12.7443i	0.857109	+	0.719200i
$315$		0			0
$316$	−30.2933	+	52.4695i	−1.70413	+	2.95164i
$317$	−3.82711	+	1.39295i	−0.214952	+	0.0782360i	−0.447252	−	0.894408i	$-0.647597\pi$
$317$	−3.82711	+	1.39295i	−0.214952	+	0.0782360i	0.232300	+	0.972644i	$0.425375\pi$
$318$	−5.72284	−	32.4559i	−0.320921	−	1.82003i
$319$	−1.21843	+	6.91009i	−0.0682193	+	0.386891i
$320$		0			0
$321$	19.2803	−	16.1781i	1.07612	−	0.902973i
$322$	−19.0243			−1.06018
$323$	7.47153	−	2.61115i	0.415727	−	0.145288i
$324$	−58.6450			−3.25806
$325$		0			0
$326$	−12.3787	−	4.50547i	−0.685591	−	0.249535i
$327$	2.50201	−	14.1896i	0.138361	−	0.784687i
$328$	12.0678	+	68.4398i	0.666331	+	3.77895i
$329$	−28.9669	+	10.5431i	−1.59700	+	0.581260i
$330$		0			0
$331$	−10.3939	−	18.0028i	−0.571301	−	0.989523i	−0.996433	−	0.0843910i	$-0.973106\pi$
$331$	−10.3939	−	18.0028i	−0.571301	−	0.989523i	0.425132	−	0.905132i	$-0.360228\pi$
$332$	17.8708	+	14.9953i	0.980785	+	0.822976i
$333$	−0.279697	−	0.234694i	−0.0153273	−	0.0128611i
$334$	13.5567	+	23.4809i	0.741789	+	1.28482i
$335$		0			0
$336$	71.8215	−	26.1409i	3.91819	−	1.42610i
$337$	4.54476	+	25.7746i	0.247569	+	1.40403i	0.814450	+	0.580234i	$0.197039\pi$
$337$	4.54476	+	25.7746i	0.247569	+	1.40403i	−0.566881	+	0.823800i	$0.691850\pi$
$338$	−6.06423	+	34.3920i	−0.329851	+	1.87068i
$339$	4.97430	+	1.81050i	0.270167	+	0.0983328i
$340$		0			0
$341$	6.86899			0.371976
$342$	−17.6094	−	6.66685i	−0.952207	−	0.360502i
$343$	−17.4071			−0.939896
$344$	33.9969	−	28.5268i	1.83299	−	1.53806i
$345$		0			0
$346$	−2.27639	+	12.9100i	−0.122379	+	0.694047i
$347$	−3.57695	−	20.2859i	−0.192021	−	1.08901i	−0.916598	−	0.399811i	$-0.869076\pi$
$347$	−3.57695	−	20.2859i	−0.192021	−	1.08901i	0.724577	−	0.689194i	$-0.242035\pi$
$348$	31.0326	−	11.2949i	1.66352	−	0.605472i
$349$	12.5153	−	21.6772i	0.669929	−	1.16035i	−0.307994	−	0.951388i	$-0.599658\pi$
$349$	12.5153	−	21.6772i	0.669929	−	1.16035i	0.977924	−	0.208963i	$-0.0670089\pi$
$350$		0			0
$351$	0.0926981	+	0.0777830i	0.00494786	+	0.00415175i
$352$	−31.1402	−	26.1297i	−1.65978	−	1.39272i
$353$	−3.60628	−	6.24627i	−0.191943	−	0.332455i	0.753951	−	0.656931i	$-0.228146\pi$
$353$	−3.60628	−	6.24627i	−0.191943	−	0.332455i	−0.945894	+	0.324475i	$0.894812\pi$
$354$	33.4974	−	58.0192i	1.78037	−	3.08369i
$355$		0			0
$356$	13.9484	+	79.1054i	0.739265	+	4.19258i
$357$	1.88361	−	10.6825i	0.0996914	−	0.565378i
$358$	−60.3001	−	21.9474i	−3.18696	−	1.15996i
$359$	12.1097	−	10.1613i	0.639128	−	0.536292i	−0.264622	−	0.964352i	$-0.585247\pi$
$359$	12.1097	−	10.1613i	0.639128	−	0.536292i	0.903750	+	0.428060i	$0.140803\pi$
$360$		0			0
$361$	14.2361	+	12.5831i	0.749268	+	0.662267i
$362$	6.89807			0.362554
$363$	8.77381	−	7.36210i	0.460506	−	0.386410i
$364$	−0.552593	−	0.201127i	−0.0289637	−	0.0105419i
$365$		0			0
$366$	−4.59053	−	26.0342i	−0.239951	−	1.36083i
$367$	−2.48326	+	0.903831i	−0.129625	+	0.0471796i	−0.406018	−	0.913865i	$-0.633083\pi$
$367$	−2.48326	+	0.903831i	−0.129625	+	0.0471796i	0.276393	+	0.961045i	$0.410861\pi$
$368$	16.2760	−	28.1908i	0.848444	−	1.46955i
$369$	−6.46135	−	11.1914i	−0.336365	−	0.582601i
$370$		0			0
$371$	12.1829	+	10.2226i	0.632502	+	0.530733i
$372$	−16.1645	−	27.9978i	−0.838091	−	1.45162i
$373$	−3.08220	+	5.33853i	−0.159590	+	0.276419i	−0.934721	−	0.355382i	$-0.884351\pi$
$373$	−3.08220	+	5.33853i	−0.159590	+	0.276419i	0.775131	+	0.631801i	$0.217684\pi$
$374$	−10.9102	+	3.97100i	−0.564154	+	0.205335i
$375$		0			0
$376$	16.6307	−	94.3172i	0.857661	−	4.86404i
$377$	−0.112180	−	0.0408303i	−0.00577758	−	0.00210287i
$378$	17.1172	−	14.3630i	0.880413	−	0.738754i
$379$	0.156142			0.00802047			0.00401024	−	0.999992i	$-0.498723\pi$
$379$	0.156142			0.00802047			0.00401024	+	0.999992i	$0.498723\pi$
$380$		0			0
$381$	−1.58638			−0.0812726
$382$	19.1147	−	16.0391i	0.977993	−	0.820634i
$383$	15.1497	+	5.51405i	0.774115	+	0.281755i	0.698716	−	0.715399i	$-0.253755\pi$
$383$	15.1497	+	5.51405i	0.774115	+	0.281755i	0.0753983	+	0.997153i	$0.475977\pi$
$384$	−7.59767	+	43.0885i	−0.387717	+	2.19885i
$385$		0			0
$386$	−62.6915	+	22.8178i	−3.19091	+	1.16140i
$387$	−4.12622	+	7.14682i	−0.209747	+	0.363293i
$388$	−14.5992	−	25.2866i	−0.741162	−	1.28373i
$389$	2.07987	+	1.74521i	0.105453	+	0.0884859i	0.693990	−	0.719985i	$-0.255851\pi$
$389$	2.07987	+	1.74521i	0.105453	+	0.0884859i	−0.588537	+	0.808471i	$0.700296\pi$
$390$		0			0
$391$	−2.30994	−	4.00093i	−0.116818	−	0.202336i
$392$	−3.22199	+	5.58065i	−0.162735	+	0.281866i
$393$	−22.0114	+	8.01148i	−1.11033	+	0.404126i
$394$	−1.94694	−	11.0416i	−0.0980854	−	0.556270i
$395$		0			0
$396$	18.7640	+	6.82955i	0.942928	+	0.343198i
$397$	−12.1440	+	10.1900i	−0.609488	+	0.511422i	−0.894480	−	0.447109i	$-0.852454\pi$
$397$	−12.1440	+	10.1900i	−0.609488	+	0.511422i	0.284991	+	0.958530i	$0.408009\pi$
$398$	60.1460			3.01485
$399$	24.5822	−	8.59098i	1.23065	−	0.430087i
$400$		0			0
$401$	−2.54746	+	2.13757i	−0.127214	+	0.106745i	−0.704175	−	0.710026i	$-0.748683\pi$
$401$	−2.54746	+	2.13757i	−0.127214	+	0.106745i	0.576961	+	0.816772i	$0.304239\pi$
$402$	26.2991	+	9.57210i	1.31168	+	0.477413i
$403$	−0.0202937	+	0.115091i	−0.00101090	+	0.00573311i
$404$	10.8350	+	61.4483i	0.539061	+	3.05717i
$405$		0			0
$406$	−11.0220	+	19.0907i	−0.547015	+	0.947457i
$407$	−0.270235	−	0.468061i	−0.0133951	−	0.0232009i
$408$	25.8165	+	21.6627i	1.27811	+	1.07246i
$409$	5.73789	+	4.81466i	0.283720	+	0.238070i	0.773530	−	0.633760i	$-0.218489\pi$
$409$	5.73789	+	4.81466i	0.283720	+	0.238070i	−0.489809	+	0.871830i	$0.662934\pi$
$410$		0			0
$411$	4.92684	−	8.53353i	0.243023	−	0.420928i
$412$	69.1113	−	25.1544i	3.40487	−	1.23927i
$413$	5.61391	+	31.8380i	0.276242	+	1.56665i
$414$	−1.90853	+	10.8238i	−0.0937991	+	0.531961i
$415$		0			0
$416$	0.529810	−	0.444563i	0.0259761	−	0.0217965i
$417$	16.8406			0.824687
$418$	−21.1192	−	18.1888i	−1.03297	−	0.889642i
$419$	14.4108			0.704012			0.352006	−	0.935998i	$-0.385500\pi$
$419$	14.4108			0.704012			0.352006	+	0.935998i	$0.385500\pi$
$420$		0			0
$421$	33.6092	+	12.2327i	1.63801	+	0.596187i	0.986690	−	0.162614i	$-0.0519927\pi$
$421$	33.6092	+	12.2327i	1.63801	+	0.596187i	0.651322	+	0.758802i	$0.274215\pi$
$422$	0.784525	−	4.44926i	0.0381901	−	0.216587i
$423$	3.09247	+	17.5383i	0.150361	+	0.852741i
$424$	−46.4305	+	16.8993i	−2.25487	+	0.820704i
$425$		0			0
$426$	−22.4035	−	38.8039i	−1.08545	−	1.88006i
$427$	9.77239	+	8.20001i	0.472919	+	0.396826i
$428$	−46.8698	−	39.3285i	−2.26554	−	1.90101i
$429$	−0.103435	−	0.179154i	−0.00499388	−	0.00864966i
$430$		0			0
$431$	−9.76286	+	3.55339i	−0.470260	+	0.171161i	−0.566270	−	0.824220i	$-0.691614\pi$
$431$	−9.76286	+	3.55339i	−0.470260	+	0.171161i	0.0960100	+	0.995380i	$0.469392\pi$
$432$	6.63921	+	37.6528i	0.319429	+	1.81157i
$433$	−6.09178	+	34.5482i	−0.292752	+	1.66028i	0.383448	+	0.923563i	$0.374737\pi$
$433$	−6.09178	+	34.5482i	−0.292752	+	1.66028i	−0.676200	+	0.736718i	$0.736374\pi$
$434$	20.2786	+	7.38081i	0.973405	+	0.354290i
$435$		0			0
$436$	−35.0266			−1.67747
$437$	5.66825	−	9.53258i	0.271149	−	0.456005i
$438$	24.4972			1.17052
$439$	14.6520	−	12.2945i	0.699303	−	0.586785i	−0.222272	−	0.974985i	$-0.571347\pi$
$439$	14.6520	−	12.2945i	0.699303	−	0.586785i	0.921575	+	0.388199i	$0.126903\pi$
$440$		0			0
$441$	0.208076	−	1.18006i	0.00990836	−	0.0561931i
$442$	−0.0343018	−	0.194535i	−0.00163157	−	0.00925309i
$443$	21.6050	−	7.86358i	1.02649	−	0.373610i	0.226744	−	0.973954i	$-0.427192\pi$
$443$	21.6050	−	7.86358i	1.02649	−	0.373610i	0.799742	+	0.600344i	$0.204970\pi$
$444$	−1.27187	+	2.20294i	−0.0603602	+	0.104547i
$445$		0			0
$446$	19.7818	+	16.5989i	0.936694	+	0.785980i
$447$	35.7487	+	29.9967i	1.69086	+	1.41880i
$448$	−28.2495	−	48.9296i	−1.33466	−	2.31171i
$449$	−7.88692	+	13.6605i	−0.372207	+	0.644681i	−0.989905	−	0.141734i	$-0.954732\pi$
$449$	−7.88692	+	13.6605i	−0.372207	+	0.644681i	0.617698	+	0.786415i	$0.288065\pi$
$450$		0			0
$451$	−3.32171	−	18.8384i	−0.156413	−	0.887063i
$452$	2.23458	−	12.6729i	0.105106	−	0.596085i
$453$	19.5443	+	7.11354i	0.918271	+	0.334223i
$454$	−48.2939	+	40.5234i	−2.26654	+	1.90186i
$455$		0			0
$456$	−15.0716	+	79.4869i	−0.705794	+	3.72231i
$457$	−34.6414			−1.62046			−0.810229	−	0.586114i	$-0.800657\pi$
$457$	−34.6414			−1.62046			−0.810229	+	0.586114i	$0.800657\pi$
$458$	−2.45096	+	2.05660i	−0.114526	+	0.0960988i
$459$	5.09899	+	1.85588i	0.238001	+	0.0866252i
$460$		0			0
$461$	4.26528	+	24.1896i	0.198654	+	1.12662i	0.907119	+	0.420875i	$0.138277\pi$
$461$	4.26528	+	24.1896i	0.198654	+	1.12662i	−0.708465	+	0.705746i	$0.750612\pi$
$462$	−35.8958	+	13.0650i	−1.67003	+	0.607840i
$463$	3.85305	−	6.67368i	0.179067	−	0.310152i	−0.762495	−	0.646995i	$-0.776026\pi$
$463$	3.85305	−	6.67368i	0.179067	−	0.310152i	0.941561	+	0.336842i	$0.109359\pi$
$464$	−18.8595	−	32.6656i	−0.875529	−	1.51646i
$465$		0			0
$466$	−47.6260	−	39.9629i	−2.20623	−	1.85125i
$467$	3.25944	+	5.64552i	0.150829	+	0.261243i	0.931532	−	0.363658i	$-0.118472\pi$
$467$	3.25944	+	5.64552i	0.150829	+	0.261243i	−0.780704	+	0.624902i	$0.785139\pi$
$468$	−0.169867	+	0.294218i	−0.00785210	+	0.0136002i
$469$	−12.6910	+	4.61914i	−0.586015	+	0.213292i
$470$		0			0
$471$	−2.75073	+	15.6002i	−0.126747	+	0.718818i
$472$	−94.3851	−	34.3534i	−4.34442	−	1.58124i
$473$	−9.35781	+	7.85213i	−0.430272	+	0.361041i
$474$	−66.9597			−3.07556
$475$		0			0
$476$	−26.3695			−1.20864
$477$	7.03831	−	5.90584i	0.322262	−	0.270410i
$478$	−24.4568	−	8.90153i	−1.11863	−	0.407147i
$479$	2.14887	−	12.1868i	0.0981842	−	0.556830i	−0.895541	−	0.444979i	$-0.853211\pi$
$479$	2.14887	−	12.1868i	0.0981842	−	0.556830i	0.993725	−	0.111851i	$-0.0356779\pi$
$480$		0			0
$481$	0.00864085	−	0.00314501i	0.000393989	−	0.000143400i
$482$	−21.2052	+	36.7284i	−0.965868	+	1.67293i
$483$	−7.59994	−	13.1635i	−0.345809	−	0.598959i
$484$	−21.3289	−	17.8971i	−0.969495	−	0.813503i
$485$		0			0
$486$	−20.3635	−	35.2706i	−0.923707	−	1.59991i
$487$	19.3605	−	33.5333i	0.877306	−	1.51954i	0.0230209	−	0.999735i	$-0.492672\pi$
$487$	19.3605	−	33.5333i	0.877306	−	1.51954i	0.854285	−	0.519804i	$-0.173995\pi$
$488$	−37.2439	+	13.5557i	−1.68595	+	0.613636i
$489$	−1.82763	−	10.3650i	−0.0826485	−	0.468723i
$490$		0			0
$491$	29.5147	+	10.7425i	1.33198	+	0.484802i	0.907278	−	0.420531i	$-0.138156\pi$
$491$	29.5147	+	10.7425i	1.33198	+	0.484802i	0.424704	+	0.905332i	$0.360378\pi$
$492$	−68.9676	+	57.8707i	−3.10930	+	2.60901i
$493$	−5.35319			−0.241095
$494$	0.367151	−	0.300120i	0.0165189	−	0.0135030i
$495$		0			0
$496$	−28.2862	+	23.7349i	−1.27009	+	1.06573i
$497$	20.3182	+	7.39521i	0.911394	+	0.331720i
$498$	−4.47709	+	25.3909i	−0.200623	+	1.13779i
$499$	3.37331	+	19.1310i	0.151010	+	0.856422i	0.962343	+	0.271837i	$0.0876312\pi$
$499$	3.37331	+	19.1310i	0.151010	+	0.856422i	−0.811333	+	0.584584i	$0.801258\pi$
$500$		0			0
$501$	−10.8314	+	18.7605i	−0.483911	+	0.838158i
$502$	−7.36057	−	12.7489i	−0.328518	−	0.569010i
$503$	3.26190	+	2.73706i	0.145441	+	0.122039i	0.712605	−	0.701565i	$-0.247515\pi$
$503$	3.26190	+	2.73706i	0.145441	+	0.122039i	−0.567164	+	0.823605i	$0.691960\pi$
$504$	29.6381	+	24.8693i	1.32019	+	1.10777i
$505$		0			0
$506$	−8.13461	+	14.0896i	−0.361627	+	0.626357i
$507$	−26.2194	+	9.54307i	−1.16444	+	0.423823i
$508$	0.669664	+	3.79785i	0.0297115	+	0.168502i
$509$	−1.27413	+	7.22597i	−0.0564750	+	0.320286i	−0.999937	−	0.0111941i	$-0.996437\pi$
$509$	−1.27413	+	7.22597i	−0.0564750	+	0.320286i	0.943462	+	0.331480i	$0.107548\pi$
$510$		0			0
$511$	−9.05573	+	7.59866i	−0.400602	+	0.336145i
$512$	−2.72331			−0.120354
$513$	2.09691	+	12.8564i	0.0925807	+	0.567623i
$514$	−9.53234			−0.420453
$515$		0			0
$516$	54.0264	+	19.6640i	2.37838	+	0.865659i
$517$	−4.57767	+	25.9612i	−0.201326	+	1.14177i
$518$	−0.294851	−	1.67218i	−0.0129550	−	0.0734714i
$519$	−9.84220	+	3.58227i	−0.432025	+	0.157244i
$520$		0			0
$521$	3.98404	+	6.90057i	0.174544	+	0.302319i	0.940003	−	0.341165i	$-0.110822\pi$
$521$	3.98404	+	6.90057i	0.174544	+	0.302319i	−0.765459	+	0.643484i	$0.777488\pi$
$522$	9.75585	+	8.18613i	0.427002	+	0.358297i
$523$	12.0080	+	10.0759i	0.525075	+	0.440590i	0.866397	−	0.499357i	$-0.166430\pi$
$523$	12.0080	+	10.0759i	0.525075	+	0.440590i	−0.341322	+	0.939946i	$0.610875\pi$
$524$	28.4715	+	49.3141i	1.24378	+	2.15430i
$525$		0			0
$526$	66.5187	−	24.2108i	2.90035	−	1.05564i
$527$	0.910003	+	5.16089i	0.0396404	+	0.224812i
$528$	11.3500	−	64.3691i	0.493946	−	2.80131i
$529$	15.5297	+	5.65235i	0.675204	+	0.245754i
$530$		0			0
$531$	18.6773			0.810526
$532$	−30.9441	−	55.2241i	−1.34160	−	2.39427i
$533$	0.325454			0.0140970
$534$	−68.0058	+	57.0636i	−2.94290	+	2.46938i
$535$		0			0
$536$	7.28622	−	41.3222i	0.314717	−	1.78485i
$537$	−8.90294	−	50.4911i	−0.384190	−	2.17885i
$538$	−58.3612	+	21.2417i	−2.51613	+	0.915796i
$539$	0.886868	−	1.53610i	0.0382001	−	0.0661645i
$540$		0			0
$541$	22.3123	+	18.7223i	0.959283	+	0.804934i	0.980836	−	0.194834i	$-0.0624168\pi$
$541$	22.3123	+	18.7223i	0.959283	+	0.804934i	−0.0215537	+	0.999768i	$0.506861\pi$
$542$	38.0049	+	31.8899i	1.63245	+	1.36979i
$543$	2.75568	+	4.77297i	0.118257	+	0.204828i
$544$	15.5066	−	26.8583i	0.664841	−	1.15154i
$545$		0			0
$546$	−0.112857	−	0.640042i	−0.00482982	−	0.0273913i
$547$	−2.51214	+	14.2470i	−0.107411	+	0.609160i	0.882818	+	0.469714i	$0.155643\pi$
$547$	−2.51214	+	14.2470i	−0.107411	+	0.609160i	−0.990230	+	0.139445i	$0.955468\pi$
$548$	−22.5094	−	8.19275i	−0.961553	−	0.349977i
$549$	5.64573	−	4.73733i	0.240954	−	0.202184i
$550$		0			0
$551$	−6.28187	−	11.2109i	−0.267617	−	0.477599i
$552$	47.2240			2.00999
$553$	24.7526	−	20.7699i	1.05259	−	0.883226i
$554$	75.6660	+	27.5402i	3.21474	+	1.17007i
$555$		0			0
$556$	−7.10898	−	40.3170i	−0.301488	−	1.70982i
$557$	−31.6465	+	11.5184i	−1.34090	+	0.488049i	−0.910097	−	0.414395i	$-0.863993\pi$
$557$	−31.6465	+	11.5184i	−1.34090	+	0.488049i	−0.430807	+	0.902444i	$0.641771\pi$
$558$	6.23364	−	10.7970i	0.263891	−	0.457073i
$559$	−0.103917	−	0.179990i	−0.00439524	−	0.00761278i
$560$		0			0
$561$	−7.10612	−	5.96274i	−0.300021	−	0.251747i
$562$	5.34540	+	9.25850i	0.225482	+	0.390546i
$563$	12.4577	−	21.5774i	0.525030	−	0.909378i	−0.474545	−	0.880231i	$-0.657387\pi$
$563$	12.4577	−	21.5774i	0.525030	−	0.909378i	0.999575	−	0.0291473i	$-0.00927920\pi$
$564$	116.590	−	42.4351i	4.90931	−	1.78684i
$565$		0			0
$566$	−4.22185	+	23.9433i	−0.177457	+	1.00641i
$567$	29.3905	+	10.6973i	1.23429	+	0.449244i
$568$	−51.4607	+	43.1806i	−2.15924	+	1.81182i
$569$	19.7304			0.827141			0.413571	−	0.910472i	$-0.364281\pi$
$569$	19.7304			0.827141			0.413571	+	0.910472i	$0.364281\pi$
$570$		0			0
$571$	−13.8463			−0.579452			−0.289726	−	0.957110i	$-0.593564\pi$
$571$	−13.8463			−0.579452			−0.289726	+	0.957110i	$0.593564\pi$
$572$	−0.385239	+	0.323254i	−0.0161077	+	0.0135159i
$573$	18.7340	+	6.81862i	0.782624	+	0.284852i
$574$	10.4357	−	59.1838i	0.435578	−	2.47028i
$575$		0			0
$576$	−30.6723	+	11.1638i	−1.27801	+	0.465158i
$577$	−20.8327	+	36.0832i	−0.867275	+	1.50216i	−0.00250405	+	0.999997i	$0.500797\pi$
$577$	−20.8327	+	36.0832i	−0.867275	+	1.50216i	−0.864771	+	0.502167i	$0.832536\pi$
$578$	18.4079	+	31.8834i	0.765668	+	1.32618i
$579$	−40.8326	−	34.2626i	−1.69695	−	1.42391i
$580$		0			0
$581$	−6.22085	−	10.7748i	−0.258084	−	0.447015i
$582$	16.1349	−	27.9465i	0.668813	−	1.15842i
$583$	12.7802	−	4.65162i	0.529302	−	0.192650i
$584$	−6.37767	−	36.1696i	−0.263910	−	1.49671i
$585$		0			0
$586$	−5.89869	−	2.14695i	−0.243673	−	0.0886896i
$587$	12.3875	−	10.3943i	0.511286	−	0.429020i	−0.350296	−	0.936639i	$-0.613919\pi$
$587$	12.3875	−	10.3943i	0.511286	−	0.429020i	0.861581	+	0.507619i	$0.169474\pi$
$588$	−8.34812			−0.344271
$589$	−9.74028	+	7.96198i	−0.401341	+	0.328068i
$590$		0			0
$591$	6.86226	−	5.75812i	0.282276	−	0.236857i
$592$	2.73014	+	0.993691i	0.112208	+	0.0408405i
$593$	−3.90122	+	22.1249i	−0.160204	+	0.908562i	0.793669	+	0.608350i	$0.208168\pi$
$593$	−3.90122	+	22.1249i	−0.160204	+	0.908562i	−0.953873	+	0.300212i	$0.902943\pi$
$594$	−3.31822	−	18.8186i	−0.136148	−	0.772136i
$595$		0			0
$596$	56.7226	−	98.2464i	2.32345	−	4.02433i
$597$	24.0274	+	41.6168i	0.983378	+	1.70326i
$598$	−0.212041	−	0.177923i	−0.00867099	−	0.00727582i
$599$	1.65472	+	1.38847i	0.0676099	+	0.0567314i	0.675966	−	0.736932i	$-0.263726\pi$
$599$	1.65472	+	1.38847i	0.0676099	+	0.0567314i	−0.608356	+	0.793664i	$0.708171\pi$
$600$		0			0
$601$	8.52974	−	14.7739i	0.347935	−	0.602641i	−0.637947	−	0.770080i	$-0.720216\pi$
$601$	8.52974	−	14.7739i	0.347935	−	0.602641i	0.985883	+	0.167439i	$0.0535496\pi$
$602$	−36.0633	+	13.1260i	−1.46983	+	0.534975i
$603$	1.35487	+	7.68387i	0.0551747	+	0.312911i
$604$	8.77979	−	49.7927i	0.357245	−	2.02603i
$605$		0			0
$606$	−52.8262	+	44.3264i	−2.14592	+	1.80064i
$607$	−3.47625			−0.141097			−0.0705483	−	0.997508i	$-0.522475\pi$
$607$	−3.47625			−0.141097			−0.0705483	+	0.997508i	$0.522475\pi$
$608$	74.4446	+	0.956978i	3.01913	+	0.0388106i
$609$	−17.6126			−0.713697
$610$		0			0
$611$	−0.421462	−	0.153400i	−0.0170505	−	0.00620588i
$612$	−2.64540	+	15.0028i	−0.106934	+	0.606452i
$613$	−3.22691	−	18.3007i	−0.130334	−	0.739159i	−0.977996	−	0.208623i	$-0.933102\pi$
$613$	−3.22691	−	18.3007i	−0.130334	−	0.739159i	0.847663	−	0.530536i	$-0.178009\pi$
$614$	−19.1903	+	6.98470i	−0.774457	+	0.281879i
$615$		0			0
$616$	28.6355	+	49.5981i	1.15376	+	1.99837i
$617$	−15.2199	−	12.7710i	−0.612729	−	0.514141i	0.282779	−	0.959185i	$-0.408744\pi$
$617$	−15.2199	−	12.7710i	−0.612729	−	0.514141i	−0.895509	+	0.445044i	$0.853188\pi$
$618$	62.2664	+	52.2478i	2.50472	+	2.10171i
$619$	4.21208	+	7.29553i	0.169298	+	0.293232i	0.938173	−	0.346166i	$-0.112517\pi$
$619$	4.21208	+	7.29553i	0.169298	+	0.293232i	−0.768875	+	0.639399i	$0.779183\pi$
$620$		0			0
$621$	7.14502	−	2.60057i	0.286720	−	0.104357i
$622$	−8.78218	−	49.8062i	−0.352133	−	1.99705i
$623$	7.43902	−	42.1888i	0.298038	−	1.69026i
$624$	1.04499	+	0.380344i	0.0418329	+	0.0152259i
$625$		0			0
$626$	59.6744			2.38507
$627$	4.14854	−	21.8791i	0.165677	−	0.873768i
$628$	38.5086			1.53666
$629$	0.315868	−	0.265045i	0.0125945	−	0.0105680i
$630$		0			0
$631$	0.278838	−	1.58137i	0.0111004	−	0.0629534i	−0.978754	−	0.205036i	$-0.934269\pi$
$631$	0.278838	−	1.58137i	0.0111004	−	0.0629534i	0.989855	+	0.142083i	$0.0453799\pi$
$632$	17.4325	+	98.8646i	0.693428	+	3.93262i
$633$	3.39198	−	1.23458i	0.134819	−	0.0490701i
$634$	−5.47106	+	9.47616i	−0.217284	+	0.376346i
$635$		0			0
$636$	−49.0350	−	41.1452i	−1.94436	−	1.63152i
$637$	0.0231175	+	0.0193979i	0.000915950	+	0.000768573i
$638$	9.42582	+	16.3260i	0.373172	+	0.646352i
$639$	6.24580	−	10.8180i	0.247080	−	0.427955i
$640$		0			0
$641$	−7.96102	−	45.1492i	−0.314442	−	1.78329i	−0.575334	−	0.817919i	$-0.695128\pi$
$641$	−7.96102	−	45.1492i	−0.314442	−	1.78329i	0.260892	−	0.965368i	$-0.415983\pi$
$642$	11.7421	−	66.5929i	0.463425	−	2.62821i
$643$	−17.2221	−	6.26834i	−0.679175	−	0.247199i	−0.0206816	−	0.999786i	$-0.506584\pi$
$643$	−17.2221	−	6.26834i	−0.679175	−	0.247199i	−0.658493	+	0.752587i	$0.728806\pi$
$644$	−28.3057	+	23.7513i	−1.11540	+	0.935933i
$645$		0			0
$646$	10.8679	−	18.2772i	0.427593	−	0.719105i
$647$	25.1770			0.989808			0.494904	−	0.868948i	$-0.335203\pi$
$647$	25.1770			0.989808			0.494904	+	0.868948i	$0.335203\pi$
$648$	−74.4386	+	62.4614i	−2.92423	+	2.45372i
$649$	25.9799	+	9.45592i	1.01980	+	0.371177i
$650$		0			0
$651$	2.99401	+	16.9799i	0.117345	+	0.665494i
$652$	−24.0428	+	8.75086i	−0.941588	+	0.342710i
$653$	−0.349290	+	0.604989i	−0.0136688	+	0.0236750i	−0.872779	−	0.488116i	$-0.837684\pi$
$653$	−0.349290	+	0.604989i	−0.0136688	+	0.0236750i	0.859110	+	0.511791i	$0.171018\pi$
$654$	−19.3556	−	33.5248i	−0.756862	−	1.31092i
$655$		0			0
$656$	78.7722	+	66.0977i	3.07554	+	2.58068i
$657$	3.41475	+	5.91451i	0.133222	+	0.230747i
$658$	−41.4099	+	71.7240i	−1.61432	+	2.79609i
$659$	−19.1350	+	6.96458i	−0.745395	+	0.271301i	−0.686667	−	0.726973i	$-0.740927\pi$
$659$	−19.1350	+	6.96458i	−0.745395	+	0.271301i	−0.0587281	+	0.998274i	$0.518705\pi$
$660$		0			0
$661$	−6.03199	+	34.2091i	−0.234617	+	1.33058i	0.608801	+	0.793323i	$0.291651\pi$
$661$	−6.03199	+	34.2091i	−0.234617	+	1.33058i	−0.843418	+	0.537258i	$0.819460\pi$
$662$	−52.4822	−	19.1019i	−2.03978	−	0.742418i
$663$	0.120901	−	0.101448i	0.00469542	−	0.00393992i
$664$	38.6547			1.50009
$665$		0			0
$666$	−0.980960			−0.0380114
$667$	−5.74626	+	4.82168i	−0.222496	+	0.186696i
$668$	49.4857	+	18.0113i	1.91466	+	0.696879i
$669$	−3.58272	+	20.3186i	−0.138516	+	0.785562i
$670$		0			0
$671$	10.2516	−	3.73126i	0.395757	−	0.144044i
$672$	51.0185	−	88.3667i	1.96808	−	3.40882i
$673$	12.7767	+	22.1298i	0.492505	+	0.853043i	0.999963	−	0.00863342i	$-0.00274814\pi$
$673$	12.7767	+	22.1298i	0.492505	+	0.853043i	−0.507458	+	0.861676i	$0.669415\pi$
$674$	53.8656	+	45.1986i	2.07483	+	1.74099i
$675$		0			0
$676$	33.9146	+	58.7417i	1.30441	+	2.25930i
$677$	19.0216	−	32.9463i	0.731058	−	1.26623i	−0.225373	−	0.974273i	$-0.572360\pi$
$677$	19.0216	−	32.9463i	0.731058	−	1.26623i	0.956431	−	0.291957i	$-0.0943066\pi$
$678$	13.3644	−	4.86424i	0.513256	−	0.186810i
$679$	2.70408	+	15.3356i	0.103773	+	0.588527i
$680$		0			0
$681$	−47.3320	−	17.2274i	−1.81376	−	0.660156i
$682$	14.1372	−	11.8625i	0.541342	−	0.454239i
$683$	−31.7070			−1.21324			−0.606618	−	0.794994i	$-0.707474\pi$
$683$	−31.7070			−1.21324			−0.606618	+	0.794994i	$0.707474\pi$
$684$	−34.5238	+	12.0654i	−1.32005	+	0.461332i
$685$		0			0
$686$	−35.8260	+	30.0615i	−1.36784	+	1.14775i
$687$	−2.40215	−	0.874310i	−0.0916477	−	0.0333570i
$688$	11.4030	−	64.6694i	0.434734	−	2.46550i
$689$	0.0401810	+	0.227878i	0.00153078	+	0.00868146i
$690$		0			0
$691$	−2.05528	+	3.55984i	−0.0781864	+	0.135423i	−0.902467	−	0.430758i	$-0.858246\pi$
$691$	−2.05528	+	3.55984i	−0.0781864	+	0.135423i	0.824281	+	0.566181i	$0.191580\pi$
$692$	12.7308	+	22.0504i	0.483953	+	0.838231i
$693$	−8.15802	−	6.84540i	−0.309898	−	0.260035i
$694$	−42.3949	−	35.5736i	−1.60929	−	1.35035i
$695$		0			0
$696$	27.3600	−	47.3888i	1.03708	−	1.79627i
$697$	13.7138	−	4.99141i	0.519447	−	0.189063i
$698$	−11.6777	−	66.2277i	−0.442009	−	2.50676i
$699$	8.62563	−	48.9184i	0.326251	−	1.85026i
$700$		0			0
$701$	−3.40592	+	2.85791i	−0.128640	+	0.107942i	−0.704838	−	0.709369i	$-0.748980\pi$
$701$	−3.40592	+	2.85791i	−0.128640	+	0.107942i	0.576198	+	0.817310i	$0.304536\pi$
$702$	0.325113			0.0122706
$703$	0.925735	+	0.350480i	0.0349148	+	0.0132186i
$704$	−48.3168			−1.82101
$705$		0			0
$706$	−18.2093	−	6.62763i	−0.685315	−	0.249434i
$707$	5.77855	−	32.7718i	0.217325	−	1.23251i
$708$	−22.5955	−	128.145i	−0.849191	−	4.81600i
$709$	−3.15334	+	1.14772i	−0.118426	+	0.0431036i	−0.400554	−	0.916273i	$-0.631182\pi$
$709$	−3.15334	+	1.14772i	−0.118426	+	0.0431036i	0.282127	+	0.959377i	$0.408960\pi$
$710$		0			0
$711$	−9.33375	−	16.1665i	−0.350043	−	0.606292i
$712$	101.958	+	85.5531i	3.82104	+	3.20624i
$713$	5.62530	+	4.72019i	0.210669	+	0.176772i
$714$	−14.5716	−	25.2388i	−0.545330	−	0.944539i
$715$		0			0
$716$	−117.119	+	42.6279i	−4.37695	+	1.59308i
$717$	−3.61089	−	20.4784i	−0.134851	−	0.764779i
$718$	7.37510	−	41.8263i	0.275236	−	1.56094i
$719$	−38.6145	−	14.0545i	−1.44008	−	0.524145i	−0.500275	−	0.865866i	$-0.666768\pi$
$719$	−38.6145	−	14.0545i	−1.44008	−	0.524145i	−0.939801	+	0.341721i	$0.888990\pi$
$720$		0			0
$721$	−39.2242			−1.46078
$722$	51.0302	+	1.31219i	1.89915	+	0.0488348i
$723$	−33.8846			−1.26018
$724$	10.2634	−	8.61203i	0.381437	−	0.320064i
$725$		0			0
$726$	5.34345	−	30.3042i	0.198314	−	1.12469i
$727$	2.09533	+	11.8832i	0.0777114	+	0.440723i	0.998693	+	0.0511164i	$0.0162780\pi$
$727$	2.09533	+	11.8832i	0.0777114	+	0.440723i	−0.920981	+	0.389607i	$0.872611\pi$
$728$	−0.915628	+	0.333261i	−0.0339354	+	0.0123515i
$729$	−0.587731	+	1.01798i	−0.0217678	+	0.0377029i
$730$		0			0
$731$	−7.13928	−	5.99056i	−0.264056	−	0.221569i
$732$	−39.3330	−	33.0043i	−1.45379	−	1.21988i
$733$	−6.81748	−	11.8082i	−0.251809	−	0.436147i	0.712215	−	0.701962i	$-0.247692\pi$
$733$	−6.81748	−	11.8082i	−0.251809	−	0.436147i	−0.964024	+	0.265815i	$0.914359\pi$
$734$	−3.54995	+	6.14870i	−0.131031	+	0.226953i
$735$		0			0
$736$	−7.54634	−	42.7974i	−0.278162	−	1.57753i
$737$	−2.00556	+	11.3741i	−0.0738759	+	0.418971i
$738$	−32.6254	−	11.8747i	−1.20096	−	0.437113i
$739$	29.2757	−	24.5652i	1.07692	−	0.903645i	0.0812609	−	0.996693i	$-0.474105\pi$
$739$	29.2757	−	24.5652i	1.07692	−	0.903645i	0.995662	+	0.0930476i	$0.0296609\pi$
$740$		0			0
$741$	0.354333	+	0.134149i	0.0130167	+	0.00492810i
$742$	42.7280			1.56859
$743$	−4.65236	+	3.90379i	−0.170679	+	0.143216i	−0.724126	−	0.689668i	$-0.757757\pi$
$743$	−4.65236	+	3.90379i	−0.170679	+	0.143216i	0.553447	+	0.832884i	$0.313312\pi$
$744$	−50.3375	−	18.3214i	−1.84546	−	0.671694i
$745$		0			0
$746$	2.87593	+	16.3102i	0.105295	+	0.597159i
$747$	−6.75437	+	2.45839i	−0.247129	+	0.0899477i
$748$	−11.2753	+	19.5294i	−0.412266	+	0.714066i
$749$	16.3155	+	28.2593i	0.596155	+	1.03257i
$750$		0			0
$751$	0.156655	+	0.131449i	0.00571641	+	0.00479664i	0.645641	−	0.763641i	$-0.276590\pi$
$751$	0.156655	+	0.131449i	0.00571641	+	0.00479664i	−0.639925	+	0.768437i	$0.721035\pi$
$752$	−70.8551	−	122.725i	−2.58382	−	4.47531i
$753$	5.88088	−	10.1860i	0.214311	−	0.371198i
$754$	−0.301393	+	0.109698i	−0.0109761	+	0.00399497i
$755$		0			0
$756$	7.53632	−	42.7406i	0.274093	−	1.55446i
$757$	17.2765	+	6.28814i	0.627926	+	0.228546i	0.636328	−	0.771418i	$-0.280452\pi$
$757$	17.2765	+	6.28814i	0.627926	+	0.228546i	−0.00840229	+	0.999965i	$0.502675\pi$
$758$	0.321359	−	0.269652i	0.0116723	−	0.00979421i
$759$	−12.9986			−0.471820
$760$		0			0
$761$	−31.4304			−1.13935			−0.569675	−	0.821870i	$-0.692931\pi$
$761$	−31.4304			−1.13935			−0.569675	+	0.821870i	$0.692931\pi$
$762$	−3.26496	+	2.73963i	−0.118277	+	0.0992461i
$763$	17.5540	+	6.38912i	0.635496	+	0.231302i
$764$	8.41578	−	47.7283i	0.304472	−	1.72675i
$765$		0			0
$766$	40.7026	−	14.8145i	1.47064	−	0.535270i
$767$	−0.235191	+	0.407363i	−0.00849225	+	0.0147090i
$768$	15.1973	+	26.3225i	0.548385	+	0.949830i
$769$	−16.5419	−	13.8803i	−0.596516	−	0.500537i	0.293807	−	0.955865i	$-0.405078\pi$
$769$	−16.5419	−	13.8803i	−0.596516	−	0.500537i	−0.890324	+	0.455328i	$0.849522\pi$
$770$		0			0
$771$	−3.80803	−	6.59570i	−0.137143	−	0.237538i
$772$	−64.7893	+	112.218i	−2.33182	+	4.03883i
$773$	−34.8529	+	12.6854i	−1.25357	+	0.456263i	−0.881607	−	0.471983i	$-0.843538\pi$
$773$	−34.8529	+	12.6854i	−1.25357	+	0.456263i	−0.371965	+	0.928247i	$0.621316\pi$
$774$	3.85008	+	21.8349i	0.138388	+	0.784838i
$775$		0			0
$776$	−45.4630	−	16.5472i	−1.63203	−	0.594009i
$777$	1.03924	−	0.872028i	0.0372826	−	0.0312838i
$778$	7.29454			0.261522
$779$	26.5461	+	22.8627i	0.951113	+	0.819141i
$780$		0			0
$781$	14.1648	−	11.8857i	0.506856	−	0.425302i
$782$	−11.6636	−	4.24520i	−0.417089	−	0.151808i
$783$	1.52993	−	8.67664i	0.0546751	−	0.310078i
$784$	1.65572	+	9.39005i	0.0591328	+	0.335359i
$785$		0			0
$786$	−31.4665	+	54.5015i	−1.12237	+	1.94401i
$787$	1.00158	+	1.73479i	0.0357025	+	0.0618385i	0.883325	−	0.468762i	$-0.155300\pi$
$787$	1.00158	+	1.73479i	0.0357025	+	0.0618385i	−0.847622	+	0.530600i	$0.821966\pi$
$788$	−16.6819	−	13.9978i	−0.594270	−	0.498652i
$789$	43.3254	+	36.3544i	1.54243	+	1.29425i
$790$		0			0
$791$	−3.43152	+	5.94357i	−0.122011	+	0.211329i
$792$	31.0913	−	11.3163i	1.10478	−	0.402108i
$793$	0.0322309	+	0.182791i	0.00114455	+	0.00649108i
$794$	−7.39595	+	41.9445i	−0.262472	+	1.48856i
$795$		0			0
$796$	89.4894	−	75.0905i	3.17187	−	2.66151i
$797$	−12.8587			−0.455480			−0.227740	−	0.973722i	$-0.573134\pi$
$797$	−12.8587			−0.455480			−0.227740	+	0.973722i	$0.573134\pi$
$798$	35.7567	−	60.1339i	1.26577	−	2.12872i
$799$	−20.1119			−0.711509
$800$		0			0
$801$	−23.2568	−	8.46479i	−0.821739	−	0.299089i
$802$	−1.55146	+	8.79877i	−0.0547840	+	0.310695i
$803$	1.75548	+	9.95584i	0.0619496	+	0.351334i
$804$	51.0801	−	18.5917i	1.80146	−	0.655677i
$805$		0			0
$806$	0.156992	+	0.271918i	0.00552981	+	0.00957792i
$807$	−38.0122	−	31.8960i	−1.33809	−	1.12279i
$808$	79.2001	+	66.4567i	2.78625	+	2.33794i
$809$	−10.5986	−	18.3573i	−0.372627	−	0.645410i	0.617341	−	0.786695i	$-0.288210\pi$
$809$	−10.5986	−	18.3573i	−0.372627	−	0.645410i	−0.989969	+	0.141286i	$0.954876\pi$
$810$		0			0
$811$	8.40909	−	3.06066i	0.295283	−	0.107474i	−0.190131	−	0.981759i	$-0.560891\pi$
$811$	8.40909	−	3.06066i	0.295283	−	0.107474i	0.485414	+	0.874284i	$0.338669\pi$
$812$	7.43486	+	42.1652i	0.260912	+	1.47971i
$813$	−6.88314	+	39.0362i	−0.241402	+	1.36906i
$814$	−1.36450	−	0.496639i	−0.0478258	−	0.0174072i
$815$		0			0
$816$	49.8662			1.74567
$817$	4.16789	−	21.9812i	0.145816	−	0.769025i
$818$	20.1240			0.703621
$819$	0.138798	−	0.116465i	0.00485000	−	0.00406963i
$820$		0			0
$821$	−0.600509	+	3.40566i	−0.0209579	+	0.118858i	−0.993492	−	0.113903i	$-0.963665\pi$
$821$	−0.600509	+	3.40566i	−0.0209579	+	0.118858i	0.972534	+	0.232761i	$0.0747759\pi$
$822$	−4.59711	−	26.0715i	−0.160343	−	0.909349i
$823$	17.0350	−	6.20022i	0.593801	−	0.216126i	−0.0275992	−	0.999619i	$-0.508786\pi$
$823$	17.0350	−	6.20022i	0.593801	−	0.216126i	0.621401	+	0.783493i	$0.286564\pi$
$824$	60.9321	−	105.538i	2.12267	−	3.67657i
$825$		0			0
$826$	66.5374	+	55.8315i	2.31513	+	1.94263i
$827$	22.5132	+	18.8909i	0.782862	+	0.656899i	0.943968	−	0.330038i	$-0.107061\pi$
$827$	22.5132	+	18.8909i	0.782862	+	0.656899i	−0.161105	+	0.986937i	$0.551506\pi$
$828$	10.6736	+	18.4871i	0.370932	+	0.642473i
$829$	1.73389	−	3.00318i	0.0602204	−	0.104305i	−0.834343	−	0.551245i	$-0.814153\pi$
$829$	1.73389	−	3.00318i	0.0602204	−	0.104305i	0.894564	+	0.446940i	$0.147486\pi$
$830$		0			0
$831$	11.1716	+	63.3574i	0.387539	+	2.19784i
$832$	0.142747	−	0.809558i	0.00494886	−	0.0280664i
$833$	1.27161	+	0.462829i	0.0440588	+	0.0160361i
$834$	34.6600	−	29.0832i	1.20018	−	1.00707i
$835$		0			0
$836$	−54.1307	−	0.695845i	−1.87215	−	0.0240663i
$837$	−8.62503			−0.298125
$838$	29.6591	−	24.8869i	1.02456	−	0.859705i
$839$	−37.4283	−	13.6228i	−1.29217	−	0.470311i	−0.397730	−	0.917503i	$-0.630202\pi$
$839$	−37.4283	−	13.6228i	−1.29217	−	0.470311i	−0.894438	+	0.447192i	$0.852424\pi$
$840$		0			0
$841$	−3.52647	−	19.9996i	−0.121602	−	0.689641i
$842$	90.2973	−	32.8655i	3.11185	−	1.13262i
$843$	−4.27082	+	7.39727i	−0.147095	+	0.254775i
$844$	−4.38750	−	7.59938i	−0.151024	−	0.261581i
$845$		0			0
$846$	36.6528	+	30.7553i	1.26015	+	1.05739i
$847$	7.42463	+	12.8598i	0.255113	+	0.441869i
$848$	−36.5553	+	63.3156i	−1.25531	+	2.17427i
$849$	−18.2536	+	6.64377i	−0.626462	+	0.228014i
$850$		0			0
$851$	0.100332	−	0.569014i	0.00343935	−	0.0195055i
$852$	−81.7789	−	29.7651i	−2.80170	−	1.01974i
$853$	−12.2652	+	10.2917i	−0.419953	+	0.352383i	−0.828145	−	0.560513i	$-0.810604\pi$
$853$	−12.2652	+	10.2917i	−0.419953	+	0.352383i	0.408192	+	0.912896i	$0.366159\pi$
$854$	34.2739			1.17283
$855$		0			0
$856$	−101.380			−3.46510
$857$	12.4439	−	10.4417i	0.425075	−	0.356680i	−0.405015	−	0.914310i	$-0.632734\pi$
$857$	12.4439	−	10.4417i	0.425075	−	0.356680i	0.830090	+	0.557630i	$0.188289\pi$
$858$	−0.522276	−	0.190093i	−0.0178302	−	0.00648966i
$859$	−9.76555	+	55.3832i	−0.333196	+	1.88965i	0.111163	+	0.993802i	$0.464542\pi$
$859$	−9.76555	+	55.3832i	−0.333196	+	1.88965i	−0.444360	+	0.895849i	$0.646569\pi$
$860$		0			0
$861$	45.1199	−	16.4223i	1.53768	−	0.559670i
$862$	−13.9565	+	24.1734i	−0.475362	+	0.823351i
$863$	−7.07944	−	12.2619i	−0.240987	−	0.417402i	0.720009	−	0.693965i	$-0.244138\pi$
$863$	−7.07944	−	12.2619i	−0.240987	−	0.417402i	−0.960996	+	0.276563i	$0.910804\pi$
$864$	39.1011	+	32.8097i	1.33025	+	1.11621i
$865$		0			0
$866$	47.1260	+	81.6247i	1.60141	+	2.77372i
$867$	−14.7074	+	25.4739i	−0.499489	+	0.865140i
$868$	39.3866	−	14.3356i	1.33687	−	0.486581i
$869$	−4.79838	−	27.2129i	−0.162774	−	0.923136i
$870$		0			0
$871$	−0.184651	−	0.0672073i	−0.00625665	−	0.00227723i
$872$	−44.4596	+	37.3061i	−1.50559	+	1.26334i
$873$	8.99640			0.304482
$874$	−4.79653	−	29.4081i	−0.162245	−	0.994744i
$875$		0			0
$876$	36.4485	−	30.5840i	1.23148	−	1.03334i
$877$	−6.02143	−	2.19162i	−0.203329	−	0.0740058i	0.238348	−	0.971180i	$-0.423394\pi$
$877$	−6.02143	−	2.19162i	−0.203329	−	0.0740058i	−0.441677	+	0.897174i	$0.645616\pi$
$878$	8.92342	−	50.6072i	0.301151	−	1.70791i
$879$	−0.870905	−	4.93915i	−0.0293749	−	0.166593i
$880$		0			0
$881$	5.80585	−	10.0560i	0.195604	−	0.338796i	−0.751494	−	0.659740i	$-0.770667\pi$
$881$	5.80585	−	10.0560i	0.195604	−	0.338796i	0.947098	+	0.320943i	$0.104000\pi$
$882$	−1.60967	−	2.78804i	−0.0542005	−	0.0938781i
$883$	−20.2430	−	16.9859i	−0.681231	−	0.571620i	0.235135	−	0.971963i	$-0.424447\pi$
$883$	−20.2430	−	16.9859i	−0.681231	−	0.571620i	−0.916366	+	0.400342i	$0.868891\pi$
$884$	−0.293908	−	0.246618i	−0.00988518	−	0.00829465i
$885$		0			0
$886$	30.8856	−	53.4954i	1.03762	−	1.79721i
$887$	−36.7051	+	13.3596i	−1.23244	+	0.448570i	−0.874431	−	0.485149i	$-0.838765\pi$
$887$	−36.7051	+	13.3596i	−1.23244	+	0.448570i	−0.358005	+	0.933720i	$0.616543\pi$
$888$	0.731907	+	4.15085i	0.0245612	+	0.139293i
$889$	0.357147	−	2.02548i	0.0119783	−	0.0679325i
$890$		0			0
$891$	20.4896	−	17.1928i	0.686426	−	0.575980i
$892$	50.1559			1.67934
$893$	−23.6010	−	42.1193i	−0.789777	−	1.40947i
$894$	125.379			4.19329
$895$		0			0
$896$	−53.3048	−	19.4014i	−1.78079	−	0.648154i
$897$	0.0384031	−	0.217795i	0.00128224	−	0.00727196i
$898$	7.35910	+	41.7355i	0.245576	+	1.39273i
$899$	7.99576	−	2.91022i	0.266674	−	0.0970613i
$900$		0			0
$901$	5.18803	+	8.98593i	0.172838	+	0.299365i
$902$	−39.3697	−	33.0351i	−1.31087	−	1.09995i
$903$	−23.4890	−	19.7096i	−0.781665	−	0.655895i
$904$	−10.6613	−	18.4659i	−0.354589	−	0.614166i
$905$		0			0
$906$	52.5094	−	19.1118i	1.74451	−	0.634949i
$907$	−9.95684	−	56.4681i	−0.330612	−	1.87499i	−0.466882	−	0.884320i	$-0.654623\pi$
$907$	−9.95684	−	56.4681i	−0.330612	−	1.87499i	0.136270	−	0.990672i	$-0.456489\pi$
$908$	−21.2627	+	120.587i	−0.705628	+	4.00182i
$909$	−18.0657	−	6.57536i	−0.599200	−	0.218091i
$910$		0			0
$911$	22.2118			0.735909			0.367954	−	0.929844i	$-0.380058\pi$
$911$	22.2118			0.735909			0.367954	+	0.929844i	$0.380058\pi$
$912$	58.5171	+	104.432i	1.93769	+	3.45809i
$913$	−10.6399			−0.352129
$914$	−71.2962	+	59.8247i	−2.35827	+	1.97882i
$915$		0			0
$916$	−1.07911	+	6.11991i	−0.0356546	+	0.202208i
$917$	−5.27354	−	29.9077i	−0.174148	−	0.987640i
$918$	13.6994	−	4.98617i	0.452147	−	0.164568i
$919$	−24.0265	+	41.6150i	−0.792560	+	1.37275i	0.131817	+	0.991274i	$0.457919\pi$
$919$	−24.0265	+	41.6150i	−0.792560	+	1.37275i	−0.924377	+	0.381480i	$0.875415\pi$
$920$		0			0
$921$	−12.4992	−	10.4880i	−0.411861	−	0.345593i
$922$	50.5531	+	42.4191i	1.66488	+	1.39700i
$923$	0.157298	+	0.272449i	0.00517754	+	0.00896776i
$924$	−37.0970	+	64.2539i	−1.22040	+	2.11380i
$925$		0			0
$926$	−3.59519	−	20.3893i	−0.118145	−	0.670035i
$927$	−3.93499	+	22.3164i	−0.129242	+	0.732967i
$928$	−47.3189	−	17.2227i	−1.55332	−	0.565362i
$929$	6.24472	−	5.23994i	0.204883	−	0.171917i	−0.534573	−	0.845122i	$-0.679528\pi$
$929$	6.24472	−	5.23994i	0.204883	−	0.171917i	0.739455	+	0.673205i	$0.235083\pi$
$930$		0			0
$931$	0.522937	+	3.20619i	0.0171386	+	0.105079i
$932$	−120.754			−3.95542
$933$	30.9540	−	25.9735i	1.01339	−	0.850334i
$934$	16.4579	+	5.99020i	0.538521	+	0.196005i
$935$		0			0
$936$	0.0977513	+	0.554375i	0.00319510	+	0.0181203i
$937$	−33.0325	+	12.0229i	−1.07913	+	0.392770i	−0.819582	−	0.572962i	$-0.805794\pi$
$937$	−33.0325	+	12.0229i	−1.07913	+	0.392770i	−0.259544	+	0.965731i	$0.583572\pi$
$938$	−18.1425	+	31.4237i	−0.592372	+	1.02602i
$939$	23.8390	+	41.2904i	0.777958	+	1.34746i
$940$		0			0
$941$	−11.4837	−	9.63598i	−0.374358	−	0.314124i	0.436124	−	0.899886i	$-0.356351\pi$
$941$	−11.4837	−	9.63598i	−0.374358	−	0.314124i	−0.810483	+	0.585762i	$0.800795\pi$
$942$	21.2797	+	36.8575i	0.693329	+	1.20088i
$943$	10.2249	−	17.7101i	0.332970	−	0.576720i
$944$	−139.658	+	50.8313i	−4.54547	+	1.65442i
$945$		0			0
$946$	−5.69911	+	32.3213i	−0.185294	+	1.05086i
$947$	30.9978	+	11.2823i	1.00729	+	0.366625i	0.792393	−	0.610011i	$-0.208835\pi$
$947$	30.9978	+	11.2823i	1.00729	+	0.366625i	0.214901	+	0.976636i	$0.431057\pi$
$948$	−99.6272	+	83.5971i	−3.23574	+	2.71511i
$949$	−0.171999			−0.00558331
$950$		0			0
$951$	−8.74244			−0.283493
$952$	−33.4710	+	28.0855i	−1.08480	+	0.910256i
$953$	−27.2039	−	9.90142i	−0.881222	−	0.320739i	−0.138519	−	0.990360i	$-0.544234\pi$
$953$	−27.2039	−	9.90142i	−0.881222	−	0.320739i	−0.742703	+	0.669621i	$0.766456\pi$
$954$	4.28649	−	24.3099i	0.138780	−	0.787061i
$955$		0			0
$956$	−47.5017	+	17.2892i	−1.53632	+	0.559173i
$957$	−7.53095	+	13.0440i	−0.243441	+	0.421652i
$958$	−16.6236	−	28.7930i	−0.537085	−	0.930259i
$959$	9.78639	+	8.21176i	0.316019	+	0.265171i
$960$		0			0
$961$	11.3351	+	19.6330i	0.365648	+	0.633322i
$962$	0.0123526	−	0.0213953i	0.000398263	−	0.000689812i
$963$	17.7148	−	6.44764i	0.570850	−	0.207772i
$964$	14.3038	+	81.1210i	0.460695	+	2.61273i
$965$		0			0
$966$	−38.3745	−	13.9672i	−1.23468	−	0.449387i
$967$	−25.5597	+	21.4472i	−0.821945	+	0.689694i	−0.953427	−	0.301625i	$-0.902471\pi$
$967$	−25.5597	+	21.4472i	−0.821945	+	0.689694i	0.131481	+	0.991319i	$0.458027\pi$
$968$	−46.1347			−1.48283
$969$	16.9881	+	0.218380i	0.545736	+	0.00701538i
$970$		0			0
$971$	−5.21562	+	4.37643i	−0.167377	+	0.140446i	−0.722629	−	0.691236i	$-0.757066\pi$
$971$	−5.21562	+	4.37643i	−0.167377	+	0.140446i	0.555252	+	0.831682i	$0.312622\pi$
$972$	−74.3325	−	27.0548i	−2.38422	−	0.867783i
$973$	−3.79138	+	21.5020i	−0.121546	+	0.689323i
$974$	−18.0648	−	102.451i	−0.578833	−	3.28273i
$975$		0			0
$976$	−29.3225	+	50.7881i	−0.938591	+	1.62569i
$977$	−0.0334665	−	0.0579657i	−0.00107069	−	0.00185449i	0.865490	−	0.500927i	$-0.167007\pi$
$977$	−0.0334665	−	0.0579657i	−0.00107069	−	0.00185449i	−0.866560	+	0.499072i	$0.833674\pi$
$978$	−21.6616	−	18.1762i	−0.692661	−	0.581211i
$979$	−28.0644	−	23.5489i	−0.896944	−	0.752625i
$980$		0			0
$981$	5.39608	−	9.34629i	0.172284	−	0.298404i
$982$	79.2969	−	28.8617i	2.53046	−	0.921014i
$983$	−8.73556	−	49.5418i	−0.278621	−	1.58014i	−0.727220	−	0.686405i	$-0.759188\pi$
$983$	−8.73556	−	49.5418i	−0.278621	−	1.58014i	0.448599	−	0.893733i	$-0.351923\pi$
$984$	−25.9045	+	146.912i	−0.825805	+	4.68337i
$985$		0			0
$986$	−11.0175	+	9.24478i	−0.350869	+	0.294414i
$987$	−66.1705			−2.10623
$988$	0.171583	−	0.904916i	0.00545877	−	0.0287892i
$989$	−13.0593			−0.415261
$990$		0			0
$991$	−3.99186	−	1.45292i	−0.126806	−	0.0461534i	0.277838	−	0.960628i	$-0.410382\pi$
$991$	−3.99186	−	1.45292i	−0.126806	−	0.0461534i	−0.404644	+	0.914475i	$0.632604\pi$
$992$	−8.56011	+	48.5468i	−0.271784	+	1.54136i
$993$	−7.74867	−	43.9449i	−0.245897	−	1.39455i
$994$	54.5885	−	19.8686i	1.73144	−	0.630194i
$995$		0			0
$996$	25.0384	+	43.3678i	0.793372	+	1.37416i
$997$	−35.2540	−	29.5816i	−1.11650	−	0.936858i	−0.118082	−	0.993004i	$-0.537674\pi$
$997$	−35.2540	−	29.5816i	−1.11650	−	0.936858i	−0.998423	+	0.0561457i	$0.982119\pi$
$998$	39.9813	+	33.5483i	1.26559	+	1.06195i
$999$	0.339320	+	0.587720i	0.0107356	+	0.0185946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.101.8		48
5.2	odd	4		95.2.p.a.44.8	yes	48
5.3	odd	4		95.2.p.a.44.1	✓	48
5.4	even	2	inner	475.2.l.f.101.1		48
15.2	even	4		855.2.da.b.424.1		48
15.8	even	4		855.2.da.b.424.8		48
19.4	even	9		9025.2.a.cu.1.24		24
19.15	odd	18		9025.2.a.ct.1.1		24
19.16	even	9	inner	475.2.l.f.301.8		48
95.4	even	18		9025.2.a.cu.1.1		24
95.23	odd	36		1805.2.b.k.1084.1		24
95.34	odd	18		9025.2.a.ct.1.24		24
95.42	odd	36		1805.2.b.k.1084.24		24
95.53	even	36		1805.2.b.l.1084.24		24
95.54	even	18	inner	475.2.l.f.301.1		48
95.72	even	36		1805.2.b.l.1084.1		24
95.73	odd	36		95.2.p.a.54.8	yes	48
95.92	odd	36		95.2.p.a.54.1	yes	48
285.92	even	36		855.2.da.b.244.8		48
285.263	even	36		855.2.da.b.244.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.1	✓	48	5.3	odd	4
95.2.p.a.44.8	yes	48	5.2	odd	4
95.2.p.a.54.1	yes	48	95.92	odd	36
95.2.p.a.54.8	yes	48	95.73	odd	36
475.2.l.f.101.1		48	5.4	even	2	inner
475.2.l.f.101.8		48	1.1	even	1	trivial
475.2.l.f.301.1		48	95.54	even	18	inner
475.2.l.f.301.8		48	19.16	even	9	inner
855.2.da.b.244.1		48	285.263	even	36
855.2.da.b.244.8		48	285.92	even	36
855.2.da.b.424.1		48	15.2	even	4
855.2.da.b.424.8		48	15.8	even	4
1805.2.b.k.1084.1		24	95.23	odd	36
1805.2.b.k.1084.24		24	95.42	odd	36
1805.2.b.l.1084.1		24	95.72	even	36
1805.2.b.l.1084.24		24	95.53	even	36
9025.2.a.ct.1.1		24	19.15	odd	18
9025.2.a.ct.1.24		24	95.34	odd	18
9025.2.a.cu.1.1		24	95.4	even	18
9025.2.a.cu.1.24		24	19.4	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05812 - 1.72697i) q^{2} +(2.01713 + 0.734175i) q^{3} +(0.906145 - 5.13900i) q^{4} +(5.41939 - 1.97250i) q^{6} +(-1.39152 + 2.41018i) q^{7} +(-4.32326 - 7.48810i) q^{8} +(1.23166 + 1.03349i) q^{9} +O(q^{10})\)	\(q+(2.05812 - 1.72697i) q^{2} +(2.01713 + 0.734175i) q^{3} +(0.906145 - 5.13900i) q^{4} +(5.41939 - 1.97250i) q^{6} +(-1.39152 + 2.41018i) q^{7} +(-4.32326 - 7.48810i) q^{8} +(1.23166 + 1.03349i) q^{9} +(1.19000 + 2.06113i) q^{11} +(5.60074 - 9.70076i) q^{12} +(-0.0380504 + 0.0138492i) q^{13} +(1.29839 + 7.36354i) q^{14} +(-12.0223 - 4.37577i) q^{16} +(-1.39094 + 1.16714i) q^{17} +4.31971 q^{18} +(-4.07652 - 1.54336i) q^{19} +(-4.57636 + 3.84002i) q^{21} +(6.00867 + 2.18698i) q^{22} +(-0.441819 + 2.50568i) q^{23} +(-3.22299 - 18.2785i) q^{24} +(-0.0543952 + 0.0942153i) q^{26} +(-1.49422 - 2.58806i) q^{27} +(11.1250 + 9.33498i) q^{28} +(2.25845 + 1.89507i) q^{29} +(1.44307 - 2.49947i) q^{31} +(-16.0501 + 5.84176i) q^{32} +(0.887142 + 5.03123i) q^{33} +(-0.847116 + 4.80423i) q^{34} +(6.42716 - 5.39302i) q^{36} -0.227089 q^{37} +(-11.0553 + 3.86361i) q^{38} -0.0869204 q^{39} +(-7.55269 - 2.74896i) q^{41} +(-2.78710 + 15.8065i) q^{42} +(0.891282 + 5.05471i) q^{43} +(11.6705 - 4.24771i) q^{44} +(3.41791 + 5.92000i) q^{46} +(8.48501 + 7.11977i) q^{47} +(-21.0380 - 17.6530i) q^{48} +(-0.372635 - 0.645423i) q^{49} +(-3.66260 + 1.33308i) q^{51} +(0.0366920 + 0.208091i) q^{52} +(0.992310 - 5.62767i) q^{53} +(-7.54477 - 2.74607i) q^{54} +24.0635 q^{56} +(-7.08978 - 6.10603i) q^{57} +7.92088 q^{58} +(8.89878 - 7.46696i) q^{59} +(0.795974 - 4.51419i) q^{61} +(-1.34649 - 7.63635i) q^{62} +(-4.20476 + 1.53041i) q^{63} +(-10.1506 + 17.5814i) q^{64} +(10.5146 + 8.82282i) q^{66} +(3.71745 + 3.11931i) q^{67} +(4.73754 + 8.20566i) q^{68} +(-2.73081 + 4.72991i) q^{69} +(-1.34912 - 7.65124i) q^{71} +(2.41406 - 13.6908i) q^{72} +(3.99151 + 1.45279i) q^{73} +(-0.467377 + 0.392176i) q^{74} +(-11.6252 + 19.5508i) q^{76} -6.62359 q^{77} +(-0.178893 + 0.150109i) q^{78} +(-10.9102 - 3.97100i) q^{79} +(-1.95152 - 11.0676i) q^{81} +(-20.2917 + 7.38558i) q^{82} +(-2.23528 + 3.87161i) q^{83} +(15.5870 + 26.9975i) q^{84} +(10.5637 + 8.86399i) q^{86} +(3.16428 + 5.48069i) q^{87} +(10.2893 - 17.8216i) q^{88} +(-14.4648 + 5.26476i) q^{89} +(0.0195687 - 0.110980i) q^{91} +(12.4764 + 4.54102i) q^{92} +(4.74590 - 3.98229i) q^{93} +29.7588 q^{94} -36.6640 q^{96} +(4.28633 - 3.59666i) q^{97} +(-1.88155 - 0.684829i) q^{98} +(-0.664482 + 3.76846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more