LMFDB - Embedded newform 425.3.t.f.24.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			24.6
Character	$\chi$	$=$	425.24
Dual form			425.3.t.f.124.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.387390 - 0.160462i) q^{2} +(-1.40425 - 0.938292i) q^{3} +(-2.70410 - 2.70410i) q^{4} +(0.393433 + 0.588815i) q^{6} +(-1.84965 - 0.367918i) q^{7} +(1.25549 + 3.03101i) q^{8} +(-2.35262 - 5.67972i) q^{9} +(-16.4446 + 10.9879i) q^{11} +(1.26001 + 6.33449i) q^{12} +(4.15401 + 4.15401i) q^{13} +(0.657498 + 0.439326i) q^{14} +13.9211i q^{16} +(9.03903 - 14.3978i) q^{17} +2.57777i q^{18} +(-0.863349 + 2.08431i) q^{19} +(2.25216 + 2.25216i) q^{21} +(8.13362 - 1.61788i) q^{22} +(14.1508 - 9.45525i) q^{23} +(1.08095 - 5.43432i) q^{24} +(-0.942660 - 2.27578i) q^{26} +(-4.99092 + 25.0911i) q^{27} +(4.00675 + 5.99653i) q^{28} +(8.72414 - 1.73534i) q^{29} +(-4.59107 - 3.06766i) q^{31} +(7.25575 - 17.5169i) q^{32} +33.4023 q^{33} +(-5.81193 + 4.12713i) q^{34} +(-8.99683 + 21.7203i) q^{36} +(47.8471 + 31.9704i) q^{37} +(0.668906 - 0.668906i) q^{38} +(-1.93561 - 9.73095i) q^{39} +(-12.0488 + 60.5735i) q^{41} +(-0.511078 - 1.23385i) q^{42} +(-14.5262 + 6.01694i) q^{43} +(74.1804 + 14.7554i) q^{44} +(-6.99908 + 1.39220i) q^{46} +(47.7291 + 47.7291i) q^{47} +(13.0620 - 19.5487i) q^{48} +(-41.9843 - 17.3905i) q^{49} +(-26.2024 + 11.7369i) q^{51} -22.4657i q^{52} +(66.3355 + 27.4771i) q^{53} +(5.95960 - 8.91917i) q^{54} +(-1.20704 - 6.06822i) q^{56} +(3.16805 - 2.11682i) q^{57} +(-3.65810 - 0.727641i) q^{58} +(11.8299 - 4.90011i) q^{59} +(77.9573 + 15.5067i) q^{61} +(1.28629 + 1.92507i) q^{62} +(2.26184 + 11.3710i) q^{63} +(33.7532 - 33.7532i) q^{64} +(-12.9397 - 5.35980i) q^{66} -121.122 q^{67} +(-63.3756 + 14.4906i) q^{68} -28.7431 q^{69} +(2.12776 - 3.18442i) q^{71} +(14.2616 - 14.2616i) q^{72} +(-13.2164 + 2.62891i) q^{73} +(-13.4055 - 20.0627i) q^{74} +(7.97078 - 3.30160i) q^{76} +(34.4594 - 14.2735i) q^{77} +(-0.811615 + 4.08026i) q^{78} +(-45.3705 + 30.3156i) q^{79} +(-8.57232 + 8.57232i) q^{81} +(14.3873 - 21.5322i) q^{82} +(-20.1994 + 48.7656i) q^{83} -12.1802i q^{84} +6.59279 q^{86} +(-13.8792 - 5.74893i) q^{87} +(-53.9504 - 36.0485i) q^{88} +(-60.0205 - 60.0205i) q^{89} +(-6.15512 - 9.21178i) q^{91} +(-63.8331 - 12.6972i) q^{92} +(3.56867 + 8.61554i) q^{93} +(-10.8311 - 26.1485i) q^{94} +(-26.6249 + 17.7902i) q^{96} +(7.28522 + 36.6253i) q^{97} +(13.4738 + 13.4738i) q^{98} +(101.096 + 67.5502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) $ 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	−0.387390	−	0.160462i	−0.193695	−	0.0802311i	0.283728	−	0.958905i	$-0.408429\pi$
$2$	−0.387390	−	0.160462i	−0.193695	−	0.0802311i	−0.477423	+	0.878674i	$0.658429\pi$
$3$	−1.40425	−	0.938292i	−0.468084	−	0.312764i	0.299065	−	0.954233i	$-0.403325\pi$
$3$	−1.40425	−	0.938292i	−0.468084	−	0.312764i	−0.767149	+	0.641469i	$0.778325\pi$
$4$	−2.70410	−	2.70410i	−0.676026	−	0.676026i
$5$		0			0
$5$		0			0
$6$	0.393433	+	0.588815i	0.0655722	+	0.0981358i
$7$	−1.84965	−	0.367918i	−0.264235	−	0.0525597i	0.0611945	−	0.998126i	$-0.480509\pi$
$7$	−1.84965	−	0.367918i	−0.264235	−	0.0525597i	−0.325430	+	0.945566i	$0.605509\pi$
$8$	1.25549	+	3.03101i	0.156936	+	0.378876i
$9$	−2.35262	−	5.67972i	−0.261402	−	0.631080i
$10$		0			0
$11$	−16.4446	+	10.9879i	−1.49496	+	0.998902i	−0.504157	+	0.863612i	$0.668197\pi$
$11$	−16.4446	+	10.9879i	−1.49496	+	0.998902i	−0.990806	+	0.135290i	$0.956803\pi$
$12$	1.26001	+	6.33449i	0.105001	+	0.527874i
$13$	4.15401	+	4.15401i	0.319539	+	0.319539i	0.848590	−	0.529051i	$-0.177452\pi$
$13$	4.15401	+	4.15401i	0.319539	+	0.319539i	−0.529051	+	0.848590i	$0.677452\pi$
$14$	0.657498	+	0.439326i	0.0469642	+	0.0313804i
$15$		0			0
$16$			13.9211i			0.870068i
$17$	9.03903	−	14.3978i	0.531708	−	0.846928i
$17$	9.03903	−	14.3978i	0.531708	−	0.846928i
$18$			2.57777i			0.143209i
$19$	−0.863349	+	2.08431i	−0.0454394	+	0.109700i	−0.944970	−	0.327158i	$-0.893909\pi$
$19$	−0.863349	+	2.08431i	−0.0454394	+	0.109700i	0.899530	+	0.436859i	$0.143909\pi$
$20$		0			0
$21$	2.25216	+	2.25216i	0.107246	+	0.107246i
$22$	8.13362	−	1.61788i	0.369710	−	0.0735399i
$23$	14.1508	−	9.45525i	0.615251	−	0.411098i	−0.208522	−	0.978018i	$-0.566865\pi$
$23$	14.1508	−	9.45525i	0.615251	−	0.411098i	0.823773	+	0.566920i	$0.191865\pi$
$24$	1.08095	−	5.43432i	0.0450397	−	0.226430i
$25$		0			0
$26$	−0.942660	−	2.27578i	−0.0362561	−	0.0875301i
$27$	−4.99092	+	25.0911i	−0.184849	+	0.929299i
$28$	4.00675	+	5.99653i	0.143098	+	0.214162i
$29$	8.72414	−	1.73534i	0.300832	−	0.0598393i	−0.0423662	−	0.999102i	$-0.513490\pi$
$29$	8.72414	−	1.73534i	0.300832	−	0.0598393i	0.343199	+	0.939263i	$0.388490\pi$
$30$		0			0
$31$	−4.59107	−	3.06766i	−0.148099	−	0.0989567i	0.479313	−	0.877644i	$-0.340886\pi$
$31$	−4.59107	−	3.06766i	−0.148099	−	0.0989567i	−0.627412	+	0.778687i	$0.715886\pi$
$32$	7.25575	−	17.5169i	0.226742	−	0.547404i
$33$	33.4023			1.01219
$34$	−5.81193	+	4.12713i	−0.170939	+	0.121386i
$35$		0			0
$36$	−8.99683	+	21.7203i	−0.249912	+	0.603341i
$37$	47.8471	+	31.9704i	1.29317	+	0.864066i	0.995876	−	0.0907218i	$-0.0289174\pi$
$37$	47.8471	+	31.9704i	1.29317	+	0.864066i	0.297289	+	0.954787i	$0.403917\pi$
$38$	0.668906	−	0.668906i	0.0176028	−	0.0176028i
$39$	−1.93561	−	9.73095i	−0.0496309	−	0.249512i
$40$		0			0
$41$	−12.0488	+	60.5735i	−0.293873	+	1.47740i	0.498246	+	0.867036i	$0.333978\pi$
$41$	−12.0488	+	60.5735i	−0.293873	+	1.47740i	−0.792120	+	0.610366i	$0.791022\pi$
$42$	−0.511078	−	1.23385i	−0.0121685	−	0.0293774i
$43$	−14.5262	+	6.01694i	−0.337818	+	0.139929i	−0.545142	−	0.838343i	$-0.683524\pi$
$43$	−14.5262	+	6.01694i	−0.337818	+	0.139929i	0.207324	+	0.978272i	$0.433524\pi$
$44$	74.1804	+	14.7554i	1.68592	+	0.335350i
$45$		0			0
$46$	−6.99908	+	1.39220i	−0.152154	+	0.0302653i
$47$	47.7291	+	47.7291i	1.01551	+	1.01551i	0.999878	+	0.0156344i	$0.00497680\pi$
$47$	47.7291	+	47.7291i	1.01551	+	1.01551i	0.0156344	+	0.999878i	$0.495023\pi$
$48$	13.0620	−	19.5487i	0.272126	−	0.407265i
$49$	−41.9843	−	17.3905i	−0.856822	−	0.354907i
$50$		0			0
$51$	−26.2024	+	11.7369i	−0.513773	+	0.230135i
$52$		−	22.4657i		−	0.432033i
$53$	66.3355	+	27.4771i	1.25161	+	0.518435i	0.907326	−	0.420429i	$-0.138120\pi$
$53$	66.3355	+	27.4771i	1.25161	+	0.518435i	0.344288	+	0.938864i	$0.388120\pi$
$54$	5.95960	−	8.91917i	0.110363	−	0.165170i
$55$		0			0
$56$	−1.20704	−	6.06822i	−0.0215543	−	0.108361i
$57$	3.16805	−	2.11682i	0.0555799	−	0.0371373i
$58$	−3.65810	−	0.727641i	−0.0630707	−	0.0125455i
$59$	11.8299	−	4.90011i	0.200507	−	0.0830527i	−0.280170	−	0.959950i	$-0.590391\pi$
$59$	11.8299	−	4.90011i	0.200507	−	0.0830527i	0.480677	+	0.876898i	$0.340391\pi$
$60$		0			0
$61$	77.9573	+	15.5067i	1.27799	+	0.254208i	0.786997	−	0.616956i	$-0.211635\pi$
$61$	77.9573	+	15.5067i	1.27799	+	0.254208i	0.490992	+	0.871164i	$0.336635\pi$
$62$	1.28629	+	1.92507i	0.0207467	+	0.0310496i
$63$	2.26184	+	11.3710i	0.0359022	+	0.180493i
$64$	33.7532	−	33.7532i	0.527393	−	0.527393i
$65$		0			0
$66$	−12.9397	−	5.35980i	−0.196056	−	0.0812091i
$67$	−121.122			−1.80780			−0.903898	−	0.427748i	$-0.859307\pi$
$67$	−121.122			−1.80780			−0.903898	+	0.427748i	$0.859307\pi$
$68$	−63.3756	+	14.4906i	−0.931994	+	0.213097i
$69$	−28.7431			−0.416566
$70$		0			0
$71$	2.12776	−	3.18442i	0.0299685	−	0.0448510i	−0.816183	−	0.577794i	$-0.803914\pi$
$71$	2.12776	−	3.18442i	0.0299685	−	0.0448510i	0.846151	+	0.532943i	$0.178914\pi$
$72$	14.2616	−	14.2616i	0.198078	−	0.198078i
$73$	−13.2164	+	2.62891i	−0.181047	+	0.0360125i	−0.284781	−	0.958593i	$-0.591921\pi$
$73$	−13.2164	+	2.62891i	−0.181047	+	0.0360125i	0.103734	+	0.994605i	$0.466921\pi$
$74$	−13.4055	−	20.0627i	−0.181155	−	0.271117i
$75$		0			0
$76$	7.97078	−	3.30160i	0.104879	−	0.0434421i
$77$	34.4594	−	14.2735i	0.447524	−	0.185371i
$78$	−0.811615	+	4.08026i	−0.0104053	+	0.0523111i
$79$	−45.3705	+	30.3156i	−0.574311	+	0.383742i	−0.808542	−	0.588439i	$-0.799743\pi$
$79$	−45.3705	+	30.3156i	−0.574311	+	0.383742i	0.234231	+	0.972181i	$0.424743\pi$
$80$		0			0
$81$	−8.57232	+	8.57232i	−0.105831	+	0.105831i
$82$	14.3873	−	21.5322i	0.175455	−	0.262587i
$83$	−20.1994	+	48.7656i	−0.243366	+	0.587537i	−0.997613	−	0.0690534i	$-0.978002\pi$
$83$	−20.1994	+	48.7656i	−0.243366	+	0.587537i	0.754247	+	0.656591i	$0.228002\pi$
$84$		−	12.1802i		−	0.145002i
$85$		0			0
$86$	6.59279			0.0766603
$87$	−13.8792	−	5.74893i	−0.159531	−	0.0660797i
$88$	−53.9504	−	36.0485i	−0.613073	−	0.409642i
$89$	−60.0205	−	60.0205i	−0.674388	−	0.674388i	0.284336	−	0.958725i	$-0.408227\pi$
$89$	−60.0205	−	60.0205i	−0.674388	−	0.674388i	−0.958725	+	0.284336i	$0.908227\pi$
$90$		0			0
$91$	−6.15512	−	9.21178i	−0.0676387	−	0.101228i
$92$	−63.8331	−	12.6972i	−0.693839	−	0.138013i
$93$	3.56867	+	8.61554i	0.0383728	+	0.0926402i
$94$	−10.8311	−	26.1485i	−0.115224	−	0.278175i
$95$		0			0
$96$	−26.6249	+	17.7902i	−0.277343	+	0.185314i
$97$	7.28522	+	36.6253i	0.0751053	+	0.377580i	0.999996	−	0.00265195i	$-0.000844143\pi$
$97$	7.28522	+	36.6253i	0.0751053	+	0.377580i	−0.924891	+	0.380232i	$0.875844\pi$
$98$	13.4738	+	13.4738i	0.137487	+	0.137487i
$99$	101.096	+	67.5502i	1.02117	+	0.682326i
$100$		0			0
$101$		−	10.0641i		−	0.0996450i	−0.998758	−	0.0498225i	$-0.984134\pi$
$101$		−	10.0641i		−	0.0996450i	0.998758	−	0.0498225i	$-0.0158656\pi$
$102$	12.0339	−	0.342249i	0.117979	−	0.00335539i
$103$			62.2752i			0.604614i	0.953211	+	0.302307i	$0.0977567\pi$
$103$			62.2752i			0.604614i	−0.953211	+	0.302307i	$0.902243\pi$
$104$	−7.37554	+	17.8061i	−0.0709187	+	0.171213i
$105$		0			0
$106$	−21.2887	−	21.2887i	−0.200837	−	0.200837i
$107$	−3.60240	+	0.716562i	−0.0336673	+	0.00669684i	−0.211895	−	0.977292i	$-0.567964\pi$
$107$	−3.60240	+	0.716562i	−0.0336673	+	0.00669684i	0.178228	+	0.983989i	$0.442964\pi$
$108$	81.3448	−	54.3529i	0.753193	−	0.503268i
$109$	−24.8584	+	124.971i	−0.228058	+	1.14653i	0.681778	+	0.731559i	$0.261207\pi$
$109$	−24.8584	+	124.971i	−0.228058	+	1.14653i	−0.909836	+	0.414967i	$0.863793\pi$
$110$		0			0
$111$	−37.1919	−	89.7892i	−0.335062	−	0.808911i
$112$	5.12181	−	25.7491i	0.0457305	−	0.229903i
$113$	−76.9038	−	115.095i	−0.680564	−	1.01854i	−0.997540	−	0.0701028i	$-0.977667\pi$
$113$	−76.9038	−	115.095i	−0.680564	−	1.01854i	0.316975	−	0.948434i	$-0.397333\pi$
$114$	−1.56694	+	0.311684i	−0.0137451	+	0.00273407i
$115$		0			0
$116$	−28.2835	−	18.8984i	−0.243823	−	0.162918i
$117$	13.8208	−	33.3664i	0.118126	−	0.285183i
$118$	−5.36907			−0.0455006
$119$	−22.0162	+	23.3052i	−0.185010	+	0.195842i
$120$		0			0
$121$	103.385	−	249.594i	0.854425	−	2.06276i
$122$	−27.7117	−	18.5163i	−0.227145	−	0.151773i
$123$	73.7552	−	73.7552i	0.599636	−	0.599636i
$124$	4.11948	+	20.7100i	0.0332216	+	0.167016i
$125$		0			0
$126$	0.948408	−	4.76797i	0.00752705	−	0.0378410i
$127$	−44.3856	−	107.156i	−0.349493	−	0.843751i	−0.996680	−	0.0814193i	$-0.974055\pi$
$127$	−44.3856	−	107.156i	−0.349493	−	0.843751i	0.647187	−	0.762331i	$-0.275945\pi$
$128$	−88.5594	+	36.6825i	−0.691871	+	0.286582i
$129$	26.0441	+	5.18049i	0.201892	+	0.0401588i
$130$		0			0
$131$	87.2129	−	17.3477i	0.665747	−	0.132425i	0.149363	−	0.988782i	$-0.452278\pi$
$131$	87.2129	−	17.3477i	0.665747	−	0.132425i	0.516384	+	0.856357i	$0.327278\pi$
$132$	−90.3232	−	90.3232i	−0.684267	−	0.684267i
$133$	2.36375	−	3.53760i	0.0177725	−	0.0265985i
$134$	46.9216	+	19.4356i	0.350161	+	0.145041i
$135$		0			0
$136$	54.9882	+	9.32120i	0.404325	+	0.0685383i
$137$			10.5646i			0.0771141i	0.999256	+	0.0385571i	$0.0122761\pi$
$137$			10.5646i			0.0771141i	−0.999256	+	0.0385571i	$0.987724\pi$
$138$	11.1348	+	4.61217i	0.0806868	+	0.0334216i
$139$	−122.408	+	183.196i	−0.880631	+	1.31796i	0.0667236	+	0.997771i	$0.478745\pi$
$139$	−122.408	+	183.196i	−0.880631	+	1.31796i	−0.947355	+	0.320186i	$0.896255\pi$
$140$		0			0
$141$	−22.2399	−	111.808i	−0.157730	−	0.792961i
$142$	−1.33525	+	0.892188i	−0.00940319	+	0.00628301i
$143$	−113.955	−	22.6670i	−0.796887	−	0.158511i
$144$	79.0678	−	32.7510i	0.549082	−	0.227437i
$145$		0			0
$146$	5.54176	+	1.10232i	0.0379572	+	0.00755016i
$147$	42.6392	+	63.8141i	0.290063	+	0.434110i
$148$	−42.9322	−	215.835i	−0.290083	−	1.45834i
$149$	−124.308	+	124.308i	−0.834279	+	0.834279i	−0.988099	−	0.153820i	$-0.950843\pi$
$149$	−124.308	+	124.308i	−0.834279	+	0.834279i	0.153820	+	0.988099i	$0.450843\pi$
$150$		0			0
$151$	110.054	+	45.5858i	0.728833	+	0.301893i	0.716072	−	0.698026i	$-0.245938\pi$
$151$	110.054	+	45.5858i	0.728833	+	0.301893i	0.0127607	+	0.999919i	$0.495938\pi$
$152$	−7.40148			−0.0486940
$153$	−103.041	−	17.4667i	−0.673468	−	0.114162i
$154$	−15.6396			−0.101556
$155$		0			0
$156$	−21.0794	+	31.5476i	−0.135125	+	0.202228i
$157$	−125.113	+	125.113i	−0.796896	+	0.796896i	−0.982605	−	0.185709i	$-0.940542\pi$
$157$	−125.113	+	125.113i	−0.796896	+	0.796896i	0.185709	+	0.982605i	$0.440542\pi$
$158$	22.4406	−	4.46371i	0.142029	−	0.0282514i
$159$	−67.3704	−	100.827i	−0.423713	−	0.634131i
$160$		0			0
$161$	−29.6527	+	12.2826i	−0.184178	+	0.0762892i
$162$	4.69636	−	1.94530i	0.0289899	−	0.0120080i
$163$	−45.3079	+	227.778i	−0.277963	+	1.39741i	0.549313	+	0.835617i	$0.314889\pi$
$163$	−45.3079	+	227.778i	−0.277963	+	1.39741i	−0.827276	+	0.561796i	$0.810111\pi$
$164$	196.378	−	131.216i	1.19743	−	0.800096i
$165$		0			0
$166$	15.6501	−	15.6501i	0.0942775	−	0.0942775i
$167$	−44.6539	+	66.8292i	−0.267388	+	0.400175i	−0.940730	−	0.339156i	$-0.889858\pi$
$167$	−44.6539	+	66.8292i	−0.267388	+	0.400175i	0.673342	+	0.739332i	$0.264858\pi$
$168$	−3.99876	+	9.65387i	−0.0238022	+	0.0574635i
$169$		−	134.488i		−	0.795790i
$170$		0			0
$171$	13.8694			0.0811077
$172$	55.5507	+	23.0099i	0.322969	+	0.133778i
$173$	138.960	+	92.8500i	0.803236	+	0.536705i	0.888080	−	0.459689i	$-0.152039\pi$
$173$	138.960	+	92.8500i	0.803236	+	0.536705i	−0.0848437	+	0.996394i	$0.527039\pi$
$174$	4.45416	+	4.45416i	0.0255986	+	0.0255986i
$175$		0			0
$176$	−152.964	−	228.927i	−0.869113	−	1.30072i
$177$	−21.2099	−	4.21891i	−0.119830	−	0.0238357i
$178$	13.6203	+	32.8824i	0.0765187	+	0.184732i
$179$	−14.8103	−	35.7552i	−0.0827390	−	0.199750i	0.877096	−	0.480316i	$-0.159478\pi$
$179$	−14.8103	−	35.7552i	−0.0827390	−	0.199750i	−0.959835	+	0.280566i	$0.909478\pi$
$180$		0			0
$181$	53.8192	−	35.9608i	0.297344	−	0.198679i	−0.397945	−	0.917409i	$-0.630277\pi$
$181$	53.8192	−	35.9608i	0.297344	−	0.198679i	0.695289	+	0.718731i	$0.255277\pi$
$182$	0.906288	+	4.55622i	0.00497960	+	0.0250342i
$183$	−94.9221	−	94.9221i	−0.518700	−	0.518700i
$184$	46.4250	+	31.0202i	0.252310	+	0.168588i
$185$		0			0
$186$		−	3.91021i		−	0.0210226i
$187$	9.55844	+	336.086i	0.0511147	+	1.79725i
$188$		−	258.129i		−	1.37303i
$189$	18.4629	−	44.5734i	0.0976873	−	0.235838i
$190$		0			0
$191$	0.0431974	+	0.0431974i	0.000226164	+	0.000226164i	0.707220	−	0.706994i	$-0.249949\pi$
$191$	0.0431974	+	0.0431974i	0.000226164	+	0.000226164i	−0.706994	+	0.707220i	$0.749949\pi$
$192$	−79.0683	+	15.7277i	−0.411814	+	0.0819149i
$193$	−174.041	+	116.290i	−0.901767	+	0.602541i	−0.917675	−	0.397332i	$-0.869936\pi$
$193$	−174.041	+	116.290i	−0.901767	+	0.602541i	0.0159081	+	0.999873i	$0.494936\pi$
$194$	3.05475	−	15.3573i	0.0157461	−	0.0791611i
$195$		0			0
$196$	66.5042	+	160.555i	0.339307	+	0.819160i
$197$	45.8195	−	230.350i	0.232586	−	1.16929i	−0.671190	−	0.741286i	$-0.734216\pi$
$197$	45.8195	−	230.350i	0.232586	−	1.16929i	0.903776	−	0.428005i	$-0.140784\pi$
$198$	−28.3244	−	42.3904i	−0.143052	−	0.214093i
$199$	−205.980	+	40.9720i	−1.03508	+	0.205889i	−0.683256	−	0.730179i	$-0.739437\pi$
$199$	−205.980	+	40.9720i	−1.03508	+	0.205889i	−0.351819	+	0.936068i	$0.614437\pi$
$200$		0			0
$201$	170.086	+	113.648i	0.846201	+	0.565414i
$202$	−1.61491	+	3.89875i	−0.00799463	+	0.0193007i
$203$	−16.7750			−0.0826357
$204$	102.592	+	39.1163i	0.502901	+	0.191747i
$205$		0			0
$206$	9.99282	−	24.1248i	0.0485088	−	0.117111i
$207$	−86.9944	−	58.1278i	−0.420263	−	0.280811i
$208$	−57.8283	+	57.8283i	−0.278021	+	0.278021i
$209$	−8.70481	−	43.7620i	−0.0416498	−	0.209388i
$210$		0			0
$211$	15.1489	−	76.1587i	0.0717957	−	0.360942i	−0.928141	−	0.372230i	$-0.878593\pi$
$211$	15.1489	−	76.1587i	0.0717957	−	0.360942i	0.999936	+	0.0112884i	$0.00359328\pi$
$212$	−105.077	−	253.679i	−0.495648	−	1.19660i
$213$	−5.97584	+	2.47527i	−0.0280556	+	0.0116210i
$214$	1.51051	+	0.300460i	0.00705848	+	0.00140402i
$215$		0			0
$216$	−82.3173	+	16.3739i	−0.381099	+	0.0758052i
$217$	7.36322	+	7.36322i	0.0339319	+	0.0339319i
$218$	29.6831	−	44.4238i	0.136161	−	0.203779i
$219$	21.0259	+	8.70922i	0.0960087	+	0.0397681i
$220$		0			0
$221$	97.3567	−	22.2602i	0.440528	−	0.100725i
$222$			40.7513i			0.183564i
$223$	339.240	+	140.518i	1.52126	+	0.630125i	0.977843	−	0.209341i	$-0.0671319\pi$
$223$	339.240	+	140.518i	1.52126	+	0.630125i	0.543413	+	0.839466i	$0.317132\pi$
$224$	−19.8654	+	29.7306i	−0.0886847	+	0.132726i
$225$		0			0
$226$	11.3234	+	56.9267i	0.0501036	+	0.251888i
$227$	240.374	−	160.613i	1.05892	−	0.707546i	0.101086	−	0.994878i	$-0.467768\pi$
$227$	240.374	−	160.613i	1.05892	−	0.707546i	0.957831	+	0.287332i	$0.0927683\pi$
$228$	−14.2909	−	2.84263i	−0.0626792	−	0.0124677i
$229$	−255.217	+	105.714i	−1.11448	+	0.461635i	−0.862480	−	0.506091i	$-0.831090\pi$
$229$	−255.217	+	105.714i	−1.11448	+	0.461635i	−0.252005	+	0.967726i	$0.581090\pi$
$230$		0			0
$231$	−61.7824	−	12.2893i	−0.267456	−	0.0532004i
$232$	16.2129	+	24.2642i	0.0698830	+	0.104587i
$233$	−12.9165	−	64.9355i	−0.0554355	−	0.278693i	0.943118	−	0.332458i	$-0.107878\pi$
$233$	−12.9165	−	64.9355i	−0.0554355	−	0.278693i	−0.998554	+	0.0537648i	$0.982878\pi$
$234$	−10.7081	+	10.7081i	−0.0457610	+	0.0457610i
$235$		0			0
$236$	−45.2397	−	18.7389i	−0.191694	−	0.0794021i
$237$	92.1566			0.388847
$238$	12.2685	−	5.49543i	0.0515482	−	0.0230900i
$239$	341.209			1.42765			0.713826	−	0.700323i	$-0.246961\pi$
$239$	341.209			1.42765			0.713826	+	0.700323i	$0.246961\pi$
$240$		0			0
$241$	−195.177	+	292.104i	−0.809865	+	1.21205i	0.164344	+	0.986403i	$0.447449\pi$
$241$	−195.177	+	292.104i	−0.809865	+	1.21205i	−0.974209	+	0.225646i	$0.927551\pi$
$242$	−80.1009	+	80.1009i	−0.330996	+	0.330996i
$243$	245.901	−	48.9127i	1.01194	−	0.201287i
$244$	−168.873	−	252.736i	−0.692103	−	1.03580i
$245$		0			0
$246$	−40.4069	+	16.7371i	−0.164256	+	0.0680370i
$247$	−12.2446	+	5.07188i	−0.0495733	+	0.0205339i
$248$	3.53407	−	17.7670i	0.0142503	−	0.0716411i
$249$	74.1214	−	49.5264i	0.297676	−	0.198901i
$250$		0			0
$251$	−242.068	+	242.068i	−0.964413	+	0.964413i	−0.999388	−	0.0349756i	$-0.988865\pi$
$251$	−242.068	+	242.068i	−0.964413	+	0.964413i	0.0349756	+	0.999388i	$0.488865\pi$
$252$	24.6322	−	36.8647i	0.0977470	−	0.146289i
$253$	−128.810	+	310.975i	−0.509131	+	1.22915i
$254$			48.6335i			0.191470i
$255$		0			0
$256$	−150.744			−0.588842
$257$	176.767	+	73.2192i	0.687808	+	0.284899i	0.699087	−	0.715037i	$-0.253590\pi$
$257$	176.767	+	73.2192i	0.687808	+	0.284899i	−0.0112785	+	0.999936i	$0.503590\pi$
$258$	−9.25794	−	6.18596i	−0.0358835	−	0.0239766i
$259$	−76.7378	−	76.7378i	−0.296285	−	0.296285i
$260$		0			0
$261$	−30.3808	−	45.4680i	−0.116401	−	0.174207i
$262$	−36.5691	−	7.27404i	−0.139577	−	0.0277635i
$263$	84.5519	+	204.126i	0.321490	+	0.776145i	0.999168	+	0.0407866i	$0.0129864\pi$
$263$	84.5519	+	204.126i	0.321490	+	0.776145i	−0.677678	+	0.735359i	$0.737014\pi$
$264$	41.9360	+	101.243i	0.158849	+	0.383495i
$265$		0			0
$266$	−1.48334	+	0.991137i	−0.00557647	+	0.00372608i
$267$	27.9672	+	140.601i	0.104746	+	0.526595i
$268$	327.527	+	327.527i	1.22212	+	1.22212i
$269$	375.222	+	250.715i	1.39488	+	0.932028i	0.999911	+	0.0133326i	$0.00424401\pi$
$269$	375.222	+	250.715i	1.39488	+	0.932028i	0.394967	+	0.918695i	$0.370756\pi$
$270$		0			0
$271$			262.055i			0.966991i	0.875347	+	0.483496i	$0.160633\pi$
$271$			262.055i			0.966991i	−0.875347	+	0.483496i	$0.839367\pi$
$272$	200.433	+	125.833i	0.736885	+	0.462622i
$273$			18.7110i			0.0685384i
$274$	1.69522	−	4.09263i	0.00618695	−	0.0149366i
$275$		0			0
$276$	77.7242	+	77.7242i	0.281610	+	0.281610i
$277$	398.485	−	79.2635i	1.43857	−	0.286150i	0.586660	−	0.809834i	$-0.300443\pi$
$277$	398.485	−	79.2635i	1.43857	−	0.286150i	0.851913	+	0.523684i	$0.175443\pi$
$278$	76.8156	−	51.3265i	0.276315	−	0.184628i
$279$	−6.62239	+	33.2930i	−0.0237362	+	0.119330i
$280$		0			0
$281$	13.1151	+	31.6626i	0.0466728	+	0.112678i	0.945497	−	0.325632i	$-0.105577\pi$
$281$	13.1151	+	31.6626i	0.0466728	+	0.112678i	−0.898824	+	0.438310i	$0.855577\pi$
$282$	−9.32537	+	46.8818i	−0.0330687	+	0.166247i
$283$	−56.2418	−	84.1717i	−0.198734	−	0.297427i	0.718695	−	0.695325i	$-0.244740\pi$
$283$	−56.2418	−	84.1717i	−0.198734	−	0.297427i	−0.917429	+	0.397899i	$0.869740\pi$
$284$	−14.3647	+	2.85732i	−0.0505799	+	0.0100610i
$285$		0			0
$286$	40.5078	+	27.0664i	0.141636	+	0.0946379i
$287$	44.5721	−	107.607i	0.155304	−	0.374936i
$288$	−116.561			−0.404726
$289$	−125.592	−	260.284i	−0.434574	−	0.900636i
$290$		0			0
$291$	24.1349	−	58.2668i	0.0829378	−	0.200230i
$292$	42.8475	+	28.6298i	0.146738	+	0.0980472i
$293$	309.797	−	309.797i	1.05733	−	1.05733i	0.0590734	−	0.998254i	$-0.481185\pi$
$293$	309.797	−	309.797i	1.05733	−	1.05733i	0.998254	−	0.0590734i	$-0.0188146\pi$
$294$	−6.27826	−	31.5629i	−0.0213546	−	0.107357i
$295$		0			0
$296$	−36.8313	+	185.163i	−0.124430	+	0.625552i
$297$	−193.625	−	467.452i	−0.651936	−	1.57391i
$298$	68.1022	−	28.2089i	0.228531	−	0.0946606i
$299$	98.0596	+	19.5053i	0.327959	+	0.0652350i
$300$		0			0
$301$	29.0821	−	5.78478i	0.0966181	−	0.0192185i
$302$	−35.3189	−	35.3189i	−0.116950	−	0.116950i
$303$	−9.44311	+	14.1326i	−0.0311654	+	0.0466423i
$304$	−29.0158	−	12.0188i	−0.0954468	−	0.0395354i
$305$		0			0
$306$	37.1142	+	23.3006i	0.121288	+	0.0761456i
$307$			379.484i			1.23610i	0.786138	+	0.618052i	$0.212078\pi$
$307$			379.484i			1.23610i	−0.786138	+	0.618052i	$0.787922\pi$
$308$	−131.779	−	54.5846i	−0.427853	−	0.177223i
$309$	58.4323	−	87.4502i	0.189101	−	0.283010i
$310$		0			0
$311$	−30.2155	−	151.903i	−0.0971559	−	0.488436i	−0.998471	−	0.0552722i	$-0.982397\pi$
$311$	−30.2155	−	151.903i	−0.0971559	−	0.488436i	0.901315	−	0.433163i	$-0.142603\pi$
$312$	27.0645	−	18.0839i	0.0867451	−	0.0579612i
$313$	226.477	+	45.0492i	0.723570	+	0.143927i	0.543117	−	0.839657i	$-0.317244\pi$
$313$	226.477	+	45.0492i	0.723570	+	0.143927i	0.180452	+	0.983584i	$0.442244\pi$
$314$	68.5432	−	28.3915i	0.218290	−	0.0904189i
$315$		0			0
$316$	204.663	+	40.7101i	0.647669	+	0.128829i
$317$	64.7874	+	96.9612i	0.204377	+	0.305871i	0.919472	−	0.393156i	$-0.128617\pi$
$317$	64.7874	+	96.9612i	0.204377	+	0.305871i	−0.715095	+	0.699027i	$0.753617\pi$
$318$	9.91970	+	49.8697i	0.0311940	+	0.156823i
$319$	−124.397	+	124.397i	−0.389960	+	0.389960i
$320$		0			0
$321$	5.73103	+	2.37387i	0.0178537	+	0.00739523i
$322$	13.4580			0.0417952
$323$	22.2056	+	31.2704i	0.0687479	+	0.0968125i
$324$	46.3609			0.143089
$325$		0			0
$326$	54.1016	−	80.9688i	0.165956	−	0.248371i
$327$	152.167	−	152.167i	0.465343	−	0.465343i
$328$	−198.726	+	39.5290i	−0.605871	+	0.120515i
$329$	−70.7216	−	105.842i	−0.214959	−	0.321709i
$330$		0			0
$331$	−546.440	+	226.343i	−1.65087	+	0.683815i	−0.997327	−	0.0730702i	$-0.976720\pi$
$331$	−546.440	+	226.343i	−1.65087	+	0.683815i	−0.653548	+	0.756885i	$0.726720\pi$
$332$	186.488	−	77.2461i	0.561712	−	0.232669i
$333$	69.0171	−	346.972i	0.207258	−	1.04196i
$334$	28.0220	−	18.7237i	0.0838983	−	0.0560590i
$335$		0			0
$336$	−31.3525	+	31.3525i	−0.0933110	+	0.0933110i
$337$	−248.770	+	372.311i	−0.738190	+	1.10478i	0.252360	+	0.967633i	$0.418793\pi$
$337$	−248.770	+	372.311i	−0.738190	+	1.10478i	−0.990551	+	0.137147i	$0.956207\pi$
$338$	−21.5803	+	52.0995i	−0.0638471	+	0.154140i
$339$			233.780i			0.689617i
$340$		0			0
$341$	109.206			0.320251
$342$	−5.37287	−	2.22552i	−0.0157101	−	0.00650736i
$343$	148.093	+	98.9523i	0.431757	+	0.288491i
$344$	−36.4748	−	36.4748i	−0.106031	−	0.106031i
$345$		0			0
$346$	−38.9327	−	58.2670i	−0.112522	−	0.168402i
$347$	−210.083	−	41.7882i	−0.605427	−	0.120427i	−0.117148	−	0.993114i	$-0.537375\pi$
$347$	−210.083	−	41.7882i	−0.605427	−	0.120427i	−0.488279	+	0.872687i	$0.662375\pi$
$348$	21.9850	+	53.0764i	0.0631752	+	0.152518i
$349$	−201.268	−	485.904i	−0.576699	−	1.39228i	−0.895759	−	0.444541i	$-0.853367\pi$
$349$	−201.268	−	485.904i	−0.576699	−	1.39228i	0.319059	−	0.947735i	$-0.396633\pi$
$350$		0			0
$351$	−124.961	+	83.4962i	−0.356014	+	0.237881i
$352$	73.1568	+	367.784i	0.207832	+	1.04484i
$353$	−270.213	−	270.213i	−0.765475	−	0.765475i	0.211831	−	0.977306i	$-0.432057\pi$
$353$	−270.213	−	270.213i	−0.765475	−	0.765475i	−0.977306	+	0.211831i	$0.932057\pi$
$354$	7.53953	+	5.03775i	0.0212981	+	0.0142309i
$355$		0			0
$356$			324.604i			0.911808i
$357$	52.7834	−	12.0687i	0.147853	−	0.0338060i
$358$			16.2277i			0.0453287i
$359$	89.6379	−	216.405i	0.249688	−	0.602800i	−0.748490	−	0.663146i	$-0.769221\pi$
$359$	89.6379	−	216.405i	0.249688	−	0.602800i	0.998177	+	0.0603467i	$0.0192206\pi$
$360$		0			0
$361$	251.667	+	251.667i	0.697137	+	0.697137i
$362$	−26.6194	+	5.29492i	−0.0735342	+	0.0146269i
$363$	−379.372	+	253.488i	−1.04510	+	0.698315i
$364$	−8.26555	+	41.5537i	−0.0227075	+	0.114159i
$365$		0			0
$366$	21.5405	+	52.0033i	0.0588537	+	0.142085i
$367$	−120.703	+	606.816i	−0.328892	+	1.65345i	0.363252	+	0.931691i	$0.381666\pi$
$367$	−120.703	+	606.816i	−0.328892	+	1.65345i	−0.692144	+	0.721759i	$0.743334\pi$
$368$	131.627	+	196.994i	0.357683	+	0.535310i
$369$	372.386	−	74.0722i	1.00918	−	0.200738i
$370$		0			0
$371$	−112.588	−	75.2289i	−0.303472	−	0.202773i
$372$	13.6472	−	32.9474i	0.0366862	−	0.0885682i
$373$	439.311			1.17778			0.588889	−	0.808214i	$-0.299566\pi$
$373$	439.311			1.17778			0.588889	+	0.808214i	$0.299566\pi$
$374$	50.2262	−	131.730i	0.134295	−	0.352219i
$375$		0			0
$376$	−84.7441	+	204.590i	−0.225383	+	0.544123i
$377$	43.4487	+	29.0315i	0.115249	+	0.0770067i
$378$	−14.3047	+	14.3047i	−0.0378431	+	0.0378431i
$379$	17.8942	+	89.9601i	0.0472142	+	0.237362i	0.997185	−	0.0749759i	$-0.0238880\pi$
$379$	17.8942	+	89.9601i	0.0472142	+	0.237362i	−0.949971	+	0.312338i	$0.898888\pi$
$380$		0			0
$381$	−38.2153	+	192.121i	−0.100303	+	0.504255i
$382$	−0.00980269	−	0.0236658i	−2.56615e−5	−	6.19523e-5i
$383$	−385.118	+	159.521i	−1.00553	+	0.416505i	−0.823823	−	0.566848i	$-0.808163\pi$
$383$	−385.118	+	159.521i	−1.00553	+	0.416505i	−0.181709	+	0.983352i	$0.558163\pi$
$384$	158.779	+	31.5831i	0.413487	+	0.0822476i
$385$		0			0
$386$	86.0820	−	17.1228i	0.223010	−	0.0443595i
$387$	68.3490	+	68.3490i	0.176612	+	0.176612i
$388$	79.3385	−	118.739i	0.204481	−	0.306027i
$389$	−623.992	−	258.466i	−1.60409	−	0.664437i	−0.612105	−	0.790776i	$-0.709677\pi$
$389$	−623.992	−	258.466i	−1.60409	−	0.664437i	−0.991987	+	0.126339i	$0.959677\pi$
$390$		0			0
$391$	−8.22516	−	289.206i	−0.0210362	−	0.739657i
$392$		−	149.088i		−	0.380327i
$393$	−138.746	−	57.4706i	−0.353044	−	0.146236i
$394$	−54.7125	+	81.8831i	−0.138864	+	0.207825i
$395$		0			0
$396$	−90.7115	−	456.037i	−0.229069	−	1.15161i
$397$	474.265	−	316.894i	1.19462	−	0.798221i	0.210828	−	0.977523i	$-0.432384\pi$
$397$	474.265	−	316.894i	1.19462	−	0.798221i	0.983794	+	0.179302i	$0.0573839\pi$
$398$	86.3690	+	17.1799i	0.217008	+	0.0431655i
$399$	−6.63860	+	2.74980i	−0.0166381	+	0.00689172i
$400$		0			0
$401$	387.307	+	77.0401i	0.965852	+	0.192120i	0.652728	−	0.757592i	$-0.273624\pi$
$401$	387.307	+	77.0401i	0.965852	+	0.192120i	0.313124	+	0.949712i	$0.398624\pi$
$402$	−47.6536	−	71.3186i	−0.118541	−	0.177409i
$403$	−6.32828	−	31.8144i	−0.0157029	−	0.0789440i
$404$	−27.2145	+	27.2145i	−0.0673626	+	0.0673626i
$405$		0			0
$406$	6.49848	+	2.69176i	0.0160061	+	0.00662995i
$407$	−1138.12			−2.79635
$408$	−68.4713	−	64.6843i	−0.167822	−	0.158540i
$409$	−269.952			−0.660030			−0.330015	−	0.943976i	$-0.607054\pi$
$409$	−269.952			−0.660030			−0.330015	+	0.943976i	$0.607054\pi$
$410$		0			0
$411$	9.91271	−	14.8354i	0.0241185	−	0.0360959i
$412$	168.399	−	168.399i	0.408735	−	0.408735i
$413$	−23.6840	+	4.71104i	−0.0573462	+	0.0114069i
$414$	24.3735	+	36.4775i	0.0588731	+	0.0881098i
$415$		0			0
$416$	102.906	−	42.6250i	0.247370	−	0.102464i
$417$	343.783	−	142.400i	0.824419	−	0.341486i
$418$	−3.64999	+	18.3498i	−0.00873205	+	0.0438990i
$419$	209.349	−	139.883i	0.499640	−	0.333849i	−0.280080	−	0.959977i	$-0.590361\pi$
$419$	209.349	−	139.883i	0.499640	−	0.333849i	0.779721	+	0.626128i	$0.215361\pi$
$420$		0			0
$421$	322.754	−	322.754i	0.766636	−	0.766636i	−0.210877	−	0.977513i	$-0.567632\pi$
$421$	322.754	−	322.754i	0.766636	−	0.766636i	0.977513	+	0.210877i	$0.0676318\pi$
$422$	−18.0891	+	27.0723i	−0.0428652	+	0.0641523i
$423$	158.799	−	383.376i	0.375412	−	0.906326i
$424$			235.561i			0.555568i
$425$		0			0
$426$	2.71217			0.00636659
$427$	−138.488	−	57.3638i	−0.324329	−	0.134341i
$428$	11.6789	+	7.80361i	0.0272872	+	0.0182327i
$429$	138.753	+	138.753i	0.323434	+	0.323434i
$430$		0			0
$431$	−224.535	−	336.041i	−0.520964	−	0.779677i	0.473935	−	0.880560i	$-0.342833\pi$
$431$	−224.535	−	336.041i	−0.520964	−	0.779677i	−0.994898	+	0.100883i	$0.967833\pi$
$432$	−349.295	−	69.4791i	−0.808553	−	0.160831i
$433$	−151.364	−	365.424i	−0.349569	−	0.843935i	−0.996671	−	0.0815313i	$-0.974019\pi$
$433$	−151.364	−	365.424i	−0.349569	−	0.843935i	0.647101	−	0.762404i	$-0.275981\pi$
$434$	−1.67092	−	4.03396i	−0.00385005	−	0.00929483i
$435$		0			0
$436$	405.155	−	270.716i	0.929255	−	0.620908i
$437$	7.49060	+	37.6578i	0.0171410	+	0.0861734i
$438$	−6.74773	−	6.74773i	−0.0154058	−	0.0154058i
$439$	158.154	+	105.675i	0.360260	+	0.240718i	0.722506	−	0.691365i	$-0.242990\pi$
$439$	158.154	+	105.675i	0.360260	+	0.240718i	−0.362246	+	0.932082i	$0.617990\pi$
$440$		0			0
$441$			279.372i			0.633496i
$442$	−41.2869	−	6.99867i	−0.0934093	−	0.0158341i
$443$		−	13.9070i		−	0.0313928i	−0.999877	−	0.0156964i	$-0.995003\pi$
$443$		−	13.9070i		−	0.0313928i	0.999877	−	0.0156964i	$-0.00499653\pi$
$444$	−142.229	+	343.370i	−0.320335	+	0.773356i
$445$		0			0
$446$	−108.870	−	108.870i	−0.244104	−	0.244104i
$447$	291.196	−	57.9225i	0.651446	−	0.129581i
$448$	−74.8499	+	50.0131i	−0.167076	+	0.111636i
$449$	−126.722	+	637.075i	−0.282232	+	1.41887i	0.536113	+	0.844146i	$0.319892\pi$
$449$	−126.722	+	637.075i	−0.282232	+	1.41887i	−0.818345	+	0.574728i	$0.805108\pi$
$450$		0			0
$451$	−467.439	−	1128.50i	−1.03645	−	2.50221i
$452$	−103.272	+	519.184i	−0.228478	+	1.14864i
$453$	−111.771	−	167.277i	−0.246734	−	0.369264i
$454$	−118.891	+	23.6489i	−0.261874	+	0.0520900i
$455$		0			0
$456$	10.3936	+	6.94475i	0.0227929	+	0.0152297i
$457$	217.862	−	525.964i	0.476721	−	1.15091i	−0.484416	−	0.874838i	$-0.660968\pi$
$457$	217.862	−	525.964i	0.476721	−	1.15091i	0.961138	−	0.276069i	$-0.0890320\pi$
$458$	115.832			0.252908
$459$	316.142	+	298.657i	0.688763	+	0.650669i
$460$		0			0
$461$	−50.8038	+	122.651i	−0.110204	+	0.266055i	−0.969354	−	0.245668i	$-0.920993\pi$
$461$	−50.8038	+	122.651i	−0.110204	+	0.266055i	0.859150	+	0.511723i	$0.170993\pi$
$462$	21.9619	+	14.6745i	0.0475366	+	0.0317630i
$463$	−508.784	+	508.784i	−1.09888	+	1.09888i	−0.104343	+	0.994541i	$0.533274\pi$
$463$	−508.784	+	508.784i	−1.09888	+	1.09888i	−0.994541	+	0.104343i	$0.966726\pi$
$464$	24.1578	+	121.449i	0.0520642	+	0.261744i
$465$		0			0
$466$	−5.41598	+	27.2280i	−0.0116223	+	0.0584291i
$467$	−309.814	−	747.957i	−0.663413	−	1.60162i	−0.792419	−	0.609977i	$-0.791178\pi$
$467$	−309.814	−	747.957i	−0.663413	−	1.60162i	0.129005	−	0.991644i	$-0.458822\pi$
$468$	−127.599	+	52.8532i	−0.272647	+	0.112934i
$469$	224.034	+	44.5631i	0.477684	+	0.0950172i
$470$		0			0
$471$	293.082	−	58.2976i	0.622255	−	0.123774i
$472$	29.7045	+	29.7045i	0.0629333	+	0.0629333i
$473$	172.763	−	258.559i	0.365250	−	0.546636i
$474$	−35.7006	−	14.7877i	−0.0753176	−	0.0311976i
$475$		0			0
$476$	122.554	−	3.48549i	0.257466	−	0.00732246i
$477$		−	441.410i		−	0.925388i
$478$	−132.181	−	54.7511i	−0.276529	−	0.114542i
$479$	205.016	−	306.828i	0.428008	−	0.640559i	−0.553305	−	0.832979i	$-0.686634\pi$
$479$	205.016	−	306.828i	0.428008	−	0.640559i	0.981313	+	0.192420i	$0.0616336\pi$
$480$		0			0
$481$	65.9519	+	331.563i	0.137114	+	0.689320i
$482$	122.481	−	81.8395i	0.254111	−	0.169791i
$483$	53.1645	+	10.5751i	0.110072	+	0.0218946i
$484$	−954.494	+	395.365i	−1.97210	+	0.816869i
$485$		0			0
$486$	−103.108	−	20.5095i	−0.212157	−	0.0422006i
$487$	298.584	+	446.863i	0.613109	+	0.917583i	0.999990	−	0.00454704i	$-0.00144737\pi$
$487$	298.584	+	446.863i	0.613109	+	0.917583i	−0.386880	+	0.922130i	$0.626447\pi$
$488$	50.8734	+	255.758i	0.104249	+	0.524094i
$489$	277.346	−	277.346i	0.567170	−	0.567170i
$490$		0			0
$491$	−654.145	−	270.956i	−1.33227	−	0.551845i	−0.400969	−	0.916092i	$-0.631327\pi$
$491$	−654.145	−	270.956i	−1.33227	−	0.551845i	−0.931303	+	0.364247i	$0.881327\pi$
$492$	−398.883			−0.810739
$493$	53.8728	−	141.294i	0.109275	−	0.286600i
$494$	5.55728			0.0112495
$495$		0			0
$496$	42.7051	−	63.9127i	0.0860990	−	0.128856i
$497$	−5.10722	+	5.10722i	−0.0102761	+	0.0102761i
$498$	−36.6610	+	7.29233i	−0.0736165	+	0.0146432i
$499$	10.2364	+	15.3199i	0.0205139	+	0.0307012i	0.841585	−	0.540125i	$-0.181623\pi$
$499$	10.2364	+	15.3199i	0.0205139	+	0.0307012i	−0.821071	+	0.570826i	$0.806623\pi$
$500$		0			0
$501$	125.411	−	51.9468i	0.250321	−	0.103686i
$502$	132.617	−	54.9319i	0.264178	−	0.109426i
$503$	154.344	−	775.937i	0.306846	−	1.54262i	−0.452400	−	0.891815i	$-0.649432\pi$
$503$	154.344	−	775.937i	0.306846	−	1.54262i	0.759246	−	0.650804i	$-0.225568\pi$
$504$	−31.6260	+	21.1318i	−0.0627501	+	0.0419282i
$505$		0			0
$506$	99.7996	−	99.7996i	0.197232	−	0.197232i
$507$	−126.189	+	188.856i	−0.248894	+	0.372497i
$508$	−169.739	+	409.785i	−0.334131	+	0.806664i
$509$			563.079i			1.10625i	0.833100	+	0.553123i	$0.186564\pi$
$509$			563.079i			1.10625i	−0.833100	+	0.553123i	$0.813436\pi$
$510$		0			0
$511$	25.4130			0.0497319
$512$	412.634	+	170.919i	0.805926	+	0.333826i
$513$	−47.9886	−	32.0650i	−0.0935451	−	0.0625048i
$514$	−56.7287	−	56.7287i	−0.110367	−	0.110367i
$515$		0			0
$516$	−56.4173	−	84.4345i	−0.109336	−	0.163633i
$517$	−1309.33	−	260.442i	−2.53255	−	0.503756i
$518$	17.4139	+	42.0410i	0.0336177	+	0.0811602i
$519$	−108.014	−	260.770i	−0.208120	−	0.502447i
$520$		0			0
$521$	204.589	−	136.702i	0.392685	−	0.262384i	−0.343516	−	0.939147i	$-0.611618\pi$
$521$	204.589	−	136.702i	0.392685	−	0.262384i	0.736201	+	0.676763i	$0.236618\pi$
$522$	4.47331	+	22.4888i	0.00856955	+	0.0430820i
$523$	375.197	+	375.197i	0.717394	+	0.717394i	0.968071	−	0.250677i	$-0.0806532\pi$
$523$	375.197	+	375.197i	0.717394	+	0.717394i	−0.250677	+	0.968071i	$0.580653\pi$
$524$	−282.743	−	188.923i	−0.539585	−	0.360539i
$525$		0			0
$526$		−	92.6438i		−	0.176129i
$527$	−85.6663	+	38.3726i	−0.162555	+	0.0728132i
$528$			464.996i			0.880674i
$529$	−91.5967	+	221.134i	−0.173151	+	0.418023i
$530$		0			0
$531$	−55.6624	−	55.6624i	−0.104826	−	0.104826i
$532$	−15.9578	+	3.17421i	−0.0299960	+	0.00596657i
$533$	−301.673	+	201.572i	−0.565991	+	0.378183i
$534$	11.7269	−	58.9550i	0.0219605	−	0.110403i
$535$		0			0
$536$	−152.067	−	367.123i	−0.283708	−	0.684931i
$537$	−12.7514	+	64.1057i	−0.0237457	+	0.119377i
$538$	−105.127	−	157.334i	−0.195403	−	0.292442i
$539$	881.499	−	175.341i	1.63543	−	0.325308i
$540$		0			0
$541$	320.302	+	214.019i	0.592056	+	0.395599i	0.815194	−	0.579187i	$-0.196630\pi$
$541$	320.302	+	214.019i	0.592056	+	0.395599i	−0.223138	+	0.974787i	$0.571630\pi$
$542$	42.0499	−	101.517i	0.0775828	−	0.187301i
$543$	−109.318			−0.201321
$544$	−186.620	−	262.803i	−0.343051	−	0.483093i
$545$		0			0
$546$	3.00240	−	7.24845i	0.00549891	−	0.0132755i
$547$	−446.787	−	298.533i	−0.816795	−	0.545765i	0.0755382	−	0.997143i	$-0.475933\pi$
$547$	−446.787	−	298.533i	−0.816795	−	0.545765i	−0.892333	+	0.451378i	$0.850933\pi$
$548$	28.5679	−	28.5679i	0.0521311	−	0.0521311i
$549$	−95.3301	−	479.257i	−0.173643	−	0.872963i
$550$		0			0
$551$	−3.91499	+	19.6820i	−0.00710525	+	0.0357205i
$552$	−36.0865	−	87.1205i	−0.0653741	−	0.157827i
$553$	95.0732	−	39.3806i	0.171923	−	0.0712127i
$554$	−167.088	−	33.2358i	−0.301602	−	0.0599924i
$555$		0			0
$556$	826.385	−	164.378i	1.48630	−	0.295644i
$557$	−369.217	−	369.217i	−0.662868	−	0.662868i	0.293187	−	0.956055i	$-0.405284\pi$
$557$	−369.217	−	369.217i	−0.662868	−	0.662868i	−0.956055	+	0.293187i	$0.905284\pi$
$558$	7.90772	−	11.8347i	0.0141715	−	0.0212092i
$559$	−85.3363	−	35.3474i	−0.152659	−	0.0632333i
$560$		0			0
$561$	301.924	−	480.918i	0.538189	−	0.857252i
$562$		−	14.3702i		−	0.0255698i
$563$	−927.087	−	384.012i	−1.64669	−	0.682082i	−0.649743	−	0.760154i	$-0.725124\pi$
$563$	−927.087	−	384.012i	−1.64669	−	0.682082i	−0.996948	+	0.0780721i	$0.975124\pi$
$564$	−242.200	+	362.478i	−0.429433	+	0.642692i
$565$		0			0
$566$	8.28111	+	41.6320i	0.0146309	+	0.0735547i
$567$	19.0097	−	12.7019i	0.0335268	−	0.0224019i
$568$	12.3234	+	2.45127i	0.0216961	+	0.00431562i
$569$	−332.996	+	137.931i	−0.585230	+	0.242410i	−0.655597	−	0.755111i	$-0.727583\pi$
$569$	−332.996	+	137.931i	−0.585230	+	0.242410i	0.0703670	+	0.997521i	$0.477583\pi$
$570$		0			0
$571$	258.662	+	51.4510i	0.452998	+	0.0901069i	0.416316	−	0.909220i	$-0.363321\pi$
$571$	258.662	+	51.4510i	0.452998	+	0.0901069i	0.0366821	+	0.999327i	$0.488321\pi$
$572$	246.852	+	369.440i	0.431559	+	0.645874i
$573$	−0.0201283	−	0.101192i	−3.51279e−5	−	0.000176600i
$574$	−34.5336	+	34.5336i	−0.0601630	+	0.0601630i
$575$		0			0
$576$	−271.117	−	112.300i	−0.470688	−	0.194966i
$577$	−342.604			−0.593768			−0.296884	−	0.954914i	$-0.595947\pi$
$577$	−342.604			−0.593768			−0.296884	+	0.954914i	$0.595947\pi$
$578$	6.88727	+	120.984i	0.0119157	+	0.209315i
$579$	353.512			0.610556
$580$		0			0
$581$	55.3035	−	82.7675i	0.0951867	−	0.142457i
$582$	−18.6992	+	18.6992i	−0.0321293	+	0.0321293i
$583$	−1392.78	+	277.040i	−2.38898	+	0.475198i
$584$	−24.5613	−	36.7586i	−0.0420570	−	0.0629428i
$585$		0			0
$586$	−169.723	+	70.3015i	−0.289629	+	0.119968i
$587$	924.930	−	383.118i	1.57569	−	0.652672i	0.587966	−	0.808886i	$-0.299929\pi$
$587$	924.930	−	383.118i	1.57569	−	0.652672i	0.987723	+	0.156214i	$0.0499288\pi$
$588$	57.2591	−	287.861i	0.0973794	−	0.489559i
$589$	10.3576	−	6.92076i	0.0175851	−	0.0117500i
$590$		0			0
$591$	−280.478	+	280.478i	−0.474582	+	0.474582i
$592$	−445.063	+	666.084i	−0.751796	+	1.12514i
$593$	339.173	−	818.835i	0.571961	−	1.38084i	−0.327923	−	0.944705i	$-0.606349\pi$
$593$	339.173	−	818.835i	0.571961	−	1.38084i	0.899883	−	0.436131i	$-0.143651\pi$
$594$			212.156i			0.357165i
$595$		0			0
$596$	672.281			1.12799
$597$	327.692	+	135.734i	0.548897	+	0.227361i
$598$	−34.8574	−	23.2910i	−0.0582900	−	0.0389482i
$599$	288.858	+	288.858i	0.482234	+	0.482234i	0.905844	−	0.423611i	$-0.139238\pi$
$599$	288.858	+	288.858i	0.482234	+	0.482234i	−0.423611	+	0.905844i	$0.639238\pi$
$600$		0			0
$601$	−109.235	−	163.481i	−0.181755	−	0.272015i	0.729393	−	0.684095i	$-0.239803\pi$
$601$	−109.235	−	163.481i	−0.181755	−	0.272015i	−0.911148	+	0.412079i	$0.864803\pi$
$602$	−12.1943	−	2.42560i	−0.0202564	−	0.00402924i
$603$	284.954	+	687.940i	0.472561	+	1.14086i
$604$	−174.328	−	420.866i	−0.288623	−	0.696797i
$605$		0			0
$606$	5.92591	−	3.95957i	0.00977874	−	0.00653394i
$607$	58.1380	+	292.279i	0.0957792	+	0.481515i	0.998666	+	0.0516361i	$0.0164436\pi$
$607$	58.1380	+	292.279i	0.0957792	+	0.481515i	−0.902887	+	0.429878i	$0.858556\pi$
$608$	30.2464	+	30.2464i	0.0497474	+	0.0497474i
$609$	23.5564	+	15.7399i	0.0386805	+	0.0258455i
$610$		0			0
$611$			396.534i			0.648992i
$612$	231.401	+	325.864i	0.378106	+	0.532458i
$613$		−	376.625i		−	0.614397i	−0.951645	−	0.307199i	$-0.900608\pi$
$613$		−	376.625i		−	0.614397i	0.951645	−	0.307199i	$-0.0993916\pi$
$614$	60.8928	−	147.008i	0.0991739	−	0.239427i
$615$		0			0
$616$	86.5264	+	86.5264i	0.140465	+	0.140465i
$617$	−223.361	+	44.4293i	−0.362012	+	0.0720086i	−0.372745	−	0.927934i	$-0.621583\pi$
$617$	−223.361	+	44.4293i	−0.362012	+	0.0720086i	0.0107334	+	0.999942i	$0.496583\pi$
$618$	−36.6686	+	24.5011i	−0.0593342	+	0.0396459i
$619$	64.5005	−	324.266i	0.104201	−	0.523854i	−0.893063	−	0.449932i	$-0.851448\pi$
$619$	64.5005	−	324.266i	0.104201	−	0.523854i	0.997264	−	0.0739224i	$-0.0235517\pi$
$620$		0			0
$621$	166.617	+	402.249i	0.268304	+	0.647743i
$622$	−12.6696	+	63.6943i	−0.0203691	+	0.102402i
$623$	88.9342	+	133.099i	0.142752	+	0.213643i
$624$	135.465	−	26.9457i	0.217092	−	0.0431823i
$625$		0			0
$626$	−80.5064	−	53.7926i	−0.128604	−	0.0859307i
$627$	−28.8378	+	69.6206i	−0.0459933	+	0.111038i
$628$	676.635			1.07744
$629$	892.795	−	399.910i	1.41939	−	0.635787i
$630$		0			0
$631$	116.241	−	280.631i	0.184217	−	0.444740i	−0.804610	−	0.593803i	$-0.797626\pi$
$631$	116.241	−	280.631i	0.184217	−	0.444740i	0.988828	+	0.149063i	$0.0476258\pi$
$632$	−148.849	−	99.4577i	−0.235521	−	0.157370i
$633$	−92.7320	+	92.7320i	−0.146496	+	0.146496i
$634$	−9.53938	−	47.9577i	−0.0150463	−	0.0756431i
$635$		0			0
$636$	−90.4699	+	454.823i	−0.142248	+	0.715130i
$637$	−102.163	−	246.643i	−0.160381	−	0.387195i
$638$	68.1512	−	28.2292i	0.106820	−	0.0442463i
$639$	−23.0924	−	4.59337i	−0.0361384	−	0.00718837i
$640$		0			0
$641$	344.400	−	68.5054i	0.537285	−	0.106873i	0.0810131	−	0.996713i	$-0.474184\pi$
$641$	344.400	−	68.5054i	0.537285	−	0.106873i	0.456272	+	0.889840i	$0.349184\pi$
$642$	−1.83923	−	1.83923i	−0.00286484	−	0.00286484i
$643$	129.923	−	194.444i	0.202058	−	0.302402i	−0.716577	−	0.697508i	$-0.754292\pi$
$643$	129.923	−	194.444i	0.202058	−	0.302402i	0.918635	+	0.395106i	$0.129292\pi$
$644$	113.397	+	46.9707i	0.176083	+	0.0729359i
$645$		0			0
$646$	−3.58449	−	15.6770i	−0.00554875	−	0.0242678i
$647$			877.981i			1.35700i	0.734599	+	0.678502i	$0.237370\pi$
$647$			877.981i			1.35700i	−0.734599	+	0.678502i	$0.762630\pi$
$648$	−36.7452	−	15.2204i	−0.0567055	−	0.0234882i
$649$	−140.696	+	210.566i	−0.216789	+	0.324447i
$650$		0			0
$651$	−3.43098	−	17.2487i	−0.00527032	−	0.0264957i
$652$	738.454	−	493.419i	1.13260	−	0.756777i
$653$	841.416	+	167.368i	1.28854	+	0.256306i	0.791365	−	0.611345i	$-0.209371\pi$
$653$	841.416	+	167.368i	1.28854	+	0.256306i	0.497174	+	0.867651i	$0.334371\pi$
$654$	−83.3651	+	34.5309i	−0.127470	+	0.0527996i
$655$		0			0
$656$	−843.248	−	167.732i	−1.28544	−	0.255690i
$657$	46.0247	+	68.8808i	0.0700528	+	0.104841i
$658$	10.4131	+	52.3504i	0.0158254	+	0.0795599i
$659$	−73.9544	+	73.9544i	−0.112222	+	0.112222i	−0.760988	−	0.648766i	$-0.775285\pi$
$659$	−73.9544	+	73.9544i	−0.112222	+	0.112222i	0.648766	+	0.760988i	$0.275285\pi$
$660$		0			0
$661$	−33.3477	−	13.8131i	−0.0504504	−	0.0208972i	0.357316	−	0.933984i	$-0.383692\pi$
$661$	−33.3477	−	13.8131i	−0.0504504	−	0.0208972i	−0.407766	+	0.913086i	$0.633692\pi$
$662$	248.005			0.374629
$663$	−157.600	−	60.0900i	−0.237707	−	0.0906334i
$664$	−173.169			−0.260797
$665$		0			0
$666$	−82.4124	+	123.339i	−0.123742	+	0.185194i
$667$	107.045	−	107.045i	0.160488	−	0.160488i
$668$	301.462	−	59.9645i	0.451290	−	0.0897672i
$669$	−344.532	−	515.629i	−0.514996	−	0.770745i
$670$		0			0
$671$	−1452.36	+	601.588i	−2.16447	+	0.896555i
$672$	55.7920	−	23.1098i	0.0830238	−	0.0343896i
$673$	−75.0718	+	377.412i	−0.111548	+	0.560790i	0.884076	+	0.467343i	$0.154789\pi$
$673$	−75.0718	+	377.412i	−0.111548	+	0.560790i	−0.995624	+	0.0934470i	$0.970211\pi$
$674$	156.113	−	104.311i	0.231621	−	0.154765i
$675$		0			0
$676$	−363.671	+	363.671i	−0.537975	+	0.537975i
$677$	−498.196	+	745.603i	−0.735887	+	1.10133i	0.255040	+	0.966931i	$0.417912\pi$
$677$	−498.196	+	745.603i	−0.735887	+	1.10133i	−0.990927	+	0.134403i	$0.957088\pi$
$678$	37.5129	−	90.5641i	0.0553287	−	0.133575i
$679$		−	70.4242i		−	0.103718i
$680$		0			0
$681$	−488.248			−0.716958
$682$	−42.3051	−	17.5234i	−0.0620310	−	0.0256941i
$683$	673.860	+	450.259i	0.986618	+	0.659237i	0.940534	−	0.339701i	$-0.110326\pi$
$683$	673.860	+	450.259i	0.986618	+	0.659237i	0.0460841	+	0.998938i	$0.485326\pi$
$684$	−37.5043	−	37.5043i	−0.0548309	−	0.0548309i
$685$		0			0
$686$	−41.4915	−	62.0964i	−0.0604832	−	0.0905195i
$687$	457.580	+	91.0184i	0.666056	+	0.132487i
$688$	−83.7623	−	202.220i	−0.121748	−	0.293925i
$689$	161.418	+	389.698i	0.234279	+	0.565600i
$690$		0			0
$691$	503.216	−	336.238i	0.728243	−	0.486597i	−0.135342	−	0.990799i	$-0.543213\pi$
$691$	503.216	−	336.238i	0.728243	−	0.486597i	0.863586	+	0.504202i	$0.168213\pi$
$692$	−124.686	−	626.838i	−0.180182	−	0.905835i
$693$	−162.139	−	162.139i	−0.233967	−	0.233967i
$694$	74.6787	+	49.8987i	0.107606	+	0.0719002i
$695$		0			0
$696$		−	49.2855i		−	0.0708126i
$697$	763.213	+	721.001i	1.09500	+	1.03444i
$698$			220.530i			0.315946i
$699$	−42.7904	+	103.305i	−0.0612167	+	0.147790i
$700$		0			0
$701$	654.391	+	654.391i	0.933510	+	0.933510i	0.997923	−	0.0644129i	$-0.0205175\pi$
$701$	654.391	+	654.391i	0.933510	+	0.933510i	−0.0644129	+	0.997923i	$0.520517\pi$
$702$	61.8065	−	12.2941i	0.0880435	−	0.0175129i
$703$	−107.945	+	72.1266i	−0.153549	+	0.102598i
$704$	−184.180	+	925.934i	−0.261619	+	1.31525i
$705$		0			0
$706$	61.3188	+	148.037i	0.0868538	+	0.209684i
$707$	−3.70278	+	18.6151i	−0.00523731	+	0.0263297i
$708$	45.9454	+	68.7622i	0.0648947	+	0.0971218i
$709$	534.037	−	106.227i	0.753226	−	0.149826i	0.196479	−	0.980508i	$-0.437049\pi$
$709$	534.037	−	106.227i	0.753226	−	0.149826i	0.556747	+	0.830682i	$0.312049\pi$
$710$		0			0
$711$	278.924	+	186.371i	0.392298	+	0.262125i
$712$	106.568	−	257.278i	0.149674	−	0.361345i
$713$	−93.9727			−0.131799
$714$	−22.3844	−	3.79444i	−0.0313506	−	0.00531434i
$715$		0			0
$716$	−56.6372	+	136.734i	−0.0791022	+	0.190970i
$717$	−479.144	−	320.154i	−0.668262	−	0.446518i
$718$	−69.4497	+	69.4497i	−0.0967266	+	0.0967266i
$719$	−39.1006	−	196.572i	−0.0543819	−	0.273396i	0.944021	−	0.329884i	$-0.107010\pi$
$719$	−39.1006	−	196.572i	−0.0543819	−	0.273396i	−0.998403	+	0.0564880i	$0.982010\pi$
$720$		0			0
$721$	22.9122	−	115.187i	0.0317783	−	0.159760i
$722$	−57.1101	−	137.876i	−0.0790999	−	0.190964i
$723$	548.157	−	227.054i	0.758171	−	0.314045i
$724$	−242.775	−	48.2909i	−0.335324	−	0.0667001i
$725$		0			0
$726$	187.640	−	37.3239i	0.258457	−	0.0514104i
$727$	−623.022	−	623.022i	−0.856977	−	0.856977i	0.134004	−	0.990981i	$-0.457216\pi$
$727$	−623.022	−	623.022i	−0.856977	−	0.856977i	−0.990981	+	0.134004i	$0.957216\pi$
$728$	20.1933	−	30.2215i	0.0277381	−	0.0415130i
$729$	−290.399	−	120.287i	−0.398352	−	0.165003i
$730$		0			0
$731$	−44.6721	+	263.532i	−0.0611109	+	0.360509i
$732$			513.358i			0.701309i
$733$	−509.805	−	211.168i	−0.695505	−	0.288088i	0.00678636	−	0.999977i	$-0.497840\pi$
$733$	−509.805	−	211.168i	−0.695505	−	0.288088i	−0.702292	+	0.711889i	$0.747840\pi$
$734$	144.130	−	215.706i	0.196363	−	0.293878i
$735$		0			0
$736$	−62.9524	−	316.483i	−0.0855331	−	0.430004i
$737$	1991.81	−	1330.88i	2.70259	−	1.80581i
$738$	−156.144	−	31.0591i	−0.211578	−	0.0420855i
$739$	−1115.79	+	462.177i	−1.50987	+	0.625409i	−0.975531	−	0.219861i	$-0.929440\pi$
$739$	−1115.79	+	462.177i	−1.50987	+	0.625409i	−0.534340	+	0.845270i	$0.679440\pi$
$740$		0			0
$741$	21.9534	+	4.36681i	0.0296267	+	0.00589313i
$742$	31.5441	+	47.2091i	0.0425122	+	0.0636241i
$743$	−46.2789	−	232.660i	−0.0622865	−	0.313136i	0.937065	−	0.349156i	$-0.113532\pi$
$743$	−46.2789	−	232.660i	−0.0622865	−	0.313136i	−0.999351	+	0.0360207i	$0.988532\pi$
$744$	−21.6334	+	21.6334i	−0.0290771	+	0.0290771i
$745$		0			0
$746$	−170.185	−	70.4928i	−0.228130	−	0.0944944i
$747$	324.496			0.434399
$748$	882.964	−	934.658i	1.18043	−	1.24954i
$749$	6.92681			0.00924807
$750$		0			0
$751$	−611.599	+	915.323i	−0.814380	+	1.21881i	0.158469	+	0.987364i	$0.449344\pi$
$751$	−611.599	+	915.323i	−0.814380	+	1.21881i	−0.972849	+	0.231442i	$0.925656\pi$
$752$	−664.440	+	664.440i	−0.883564	+	0.883564i
$753$	567.054	−	112.794i	0.753060	−	0.149793i
$754$	−12.1731	−	18.2184i	−0.0161448	−	0.0241623i
$755$		0			0
$756$	−170.457	+	70.6055i	−0.225472	+	0.0933935i
$757$	−552.363	+	228.796i	−0.729674	+	0.302241i	−0.716418	−	0.697671i	$-0.754220\pi$
$757$	−552.363	+	228.796i	−0.729674	+	0.302241i	−0.0132561	+	0.999912i	$0.504220\pi$
$758$	7.50317	−	37.7210i	0.00989864	−	0.0497638i
$759$	472.668	−	315.827i	0.622751	−	0.416109i
$760$		0			0
$761$	−334.015	+	334.015i	−0.438916	+	0.438916i	−0.891647	−	0.452731i	$-0.850450\pi$
$761$	−334.015	+	334.015i	−0.438916	+	0.438916i	0.452731	+	0.891647i	$0.350450\pi$
$762$	45.6324	−	68.2938i	0.0598851	−	0.0896244i
$763$	91.9584	−	222.007i	0.120522	−	0.290966i
$764$		−	0.233620i		−	0.000305786i
$765$		0			0
$766$	174.788			0.228183
$767$	69.4966	+	28.7864i	0.0906083	+	0.0375312i
$768$	211.682	+	141.441i	0.275628	+	0.184169i
$769$	796.827	+	796.827i	1.03619	+	1.03619i	0.999320	+	0.0368659i	$0.0117374\pi$
$769$	796.827	+	796.827i	1.03619	+	1.03619i	0.0368659	+	0.999320i	$0.488263\pi$
$770$		0			0
$771$	−179.524	−	268.677i	−0.232846	−	0.348479i
$772$	785.087	+	156.163i	1.01695	+	0.202284i
$773$	387.361	+	935.171i	0.501113	+	1.20979i	0.948878	+	0.315643i	$0.102220\pi$
$773$	387.361	+	935.171i	0.501113	+	1.20979i	−0.447765	+	0.894151i	$0.647780\pi$
$774$	−15.5103	−	37.4452i	−0.0200391	−	0.0483788i
$775$		0			0
$776$	−101.865	+	68.0640i	−0.131269	+	0.0877114i
$777$	35.7569	+	179.762i	0.0460191	+	0.231354i
$778$	200.254	+	200.254i	0.257396	+	0.257396i
$779$	−115.851	−	77.4095i	−0.148718	−	0.0993703i
$780$		0			0
$781$			75.7462i			0.0969862i
$782$	−43.2203	+	113.355i	−0.0552689	+	0.144956i
$783$			227.559i			0.290624i
$784$	242.094	−	584.466i	0.308793	−	0.745493i
$785$		0			0
$786$	44.5270	+	44.5270i	0.0566502	+	0.0566502i
$787$	1101.19	−	219.041i	1.39923	−	0.278323i	0.562886	−	0.826534i	$-0.309691\pi$
$787$	1101.19	−	219.041i	1.39923	−	0.278323i	0.836340	+	0.548211i	$0.184691\pi$
$788$	−746.792	+	498.991i	−0.947706	+	0.633237i
$789$	72.7978	−	365.979i	0.0922659	−	0.463852i
$790$		0			0
$791$	99.8995	+	241.179i	0.126295	+	0.304904i
$792$	−77.8208	+	391.232i	−0.0982586	+	0.493979i
$793$	259.420	+	388.250i	0.327138	+	0.489597i
$794$	−234.575	+	46.6599i	−0.295435	+	0.0587656i
$795$		0			0
$796$	667.784	+	446.199i	0.838924	+	0.560551i
$797$	84.7173	−	204.526i	0.106295	−	0.256620i	−0.861779	−	0.507285i	$-0.830649\pi$
$797$	84.7173	−	204.526i	0.106295	−	0.256620i	0.968074	+	0.250665i	$0.0806493\pi$
$798$	3.01296			0.00377565
$799$	1118.62	−	255.768i	1.40002	−	0.320110i
$800$		0			0
$801$	−199.694	+	482.105i	−0.249306	+	0.601879i
$802$	−137.677	−	91.9927i	−0.171667	−	0.114704i
$803$	188.453	−	188.453i	0.234686	−	0.234686i
$804$	−152.615	−	767.248i	−0.189820	−	0.954289i
$805$		0			0
$806$	−2.65350	+	13.3400i	−0.00329218	+	0.0165509i
$807$	−291.663	−	704.136i	−0.361416	−	0.872536i
$808$	30.5045	−	12.6354i	0.0377531	−	0.0156378i
$809$	−751.667	−	149.516i	−0.929132	−	0.184816i	−0.292749	−	0.956189i	$-0.594570\pi$
$809$	−751.667	−	149.516i	−0.929132	−	0.184816i	−0.636383	+	0.771374i	$0.719570\pi$
$810$		0			0
$811$	−1340.74	+	266.689i	−1.65319	+	0.328840i	−0.931601	−	0.363481i	$-0.881588\pi$
$811$	−1340.74	+	266.689i	−1.65319	+	0.328840i	−0.721589	+	0.692322i	$0.756588\pi$
$812$	45.3615	+	45.3615i	0.0558639	+	0.0558639i
$813$	245.884	−	367.991i	0.302440	−	0.452634i
$814$	440.894	+	182.624i	0.541639	+	0.224354i
$815$		0			0
$816$	−163.390	−	364.766i	−0.200233	−	0.447017i
$817$		−	35.4718i		−	0.0434171i
$818$	104.577	+	43.3171i	0.127844	+	0.0529549i
$819$	−37.8397	+	56.6311i	−0.0462023	+	0.0691466i
$820$		0			0
$821$	183.972	+	924.890i	0.224083	+	1.12654i	0.914952	+	0.403562i	$0.132228\pi$
$821$	183.972	+	924.890i	0.224083	+	1.12654i	−0.690869	+	0.722980i	$0.742772\pi$
$822$	−6.22061	+	4.15648i	−0.00756765	+	0.00505654i
$823$	823.095	+	163.724i	1.00012	+	0.198935i	0.667886	−	0.744263i	$-0.267199\pi$
$823$	823.095	+	163.724i	1.00012	+	0.198935i	0.332229	+	0.943199i	$0.392199\pi$
$824$	−188.757	+	78.1856i	−0.229074	+	0.0948854i
$825$		0			0
$826$	9.93089	+	1.97538i	0.0120229	+	0.00239150i
$827$	656.015	+	981.796i	0.793247	+	1.18718i	0.978855	+	0.204554i	$0.0655743\pi$
$827$	656.015	+	981.796i	0.793247	+	1.18718i	−0.185609	+	0.982624i	$0.559426\pi$
$828$	78.0583	+	392.426i	0.0942734	+	0.473944i
$829$	121.810	−	121.810i	0.146936	−	0.146936i	−0.629812	−	0.776748i	$-0.716868\pi$
$829$	121.810	−	121.810i	0.146936	−	0.146936i	0.776748	+	0.629812i	$0.216868\pi$
$830$		0			0
$831$	−633.946	−	262.589i	−0.762871	−	0.315991i
$832$	280.422			0.337045
$833$	−629.881	+	447.287i	−0.756160	+	0.536959i
$834$	−156.028			−0.187084
$835$		0			0
$836$	−94.7984	+	141.876i	−0.113395	+	0.169708i
$837$	99.8845	−	99.8845i	0.119336	−	0.119336i
$838$	−103.546	+	20.5965i	−0.123563	+	0.0245782i
$839$	−720.467	−	1078.26i	−0.858722	−	1.28517i	−0.957023	−	0.290011i	$-0.906341\pi$
$839$	−720.467	−	1078.26i	−0.858722	−	1.28517i	0.0983016	−	0.995157i	$-0.468659\pi$
$840$		0			0
$841$	−703.884	+	291.558i	−0.836960	+	0.346680i
$842$	−176.821	+	73.2418i	−0.210002	+	0.0869855i
$843$	11.2919	−	56.7680i	0.0133949	−	0.0673405i
$844$	−246.905	+	164.977i	−0.292542	+	0.195470i
$845$		0			0
$846$	−123.035	+	123.035i	−0.145431	+	0.145431i
$847$	−283.057	+	423.625i	−0.334188	+	0.500147i
$848$	−382.511	+	923.462i	−0.451074	+	1.08899i
$849$			170.970i			0.201378i
$850$		0			0
$851$	979.362			1.15084
$852$	22.8527	+	9.46589i	0.0268224	+	0.0111102i
$853$	−317.095	−	211.876i	−0.371740	−	0.248389i	0.355641	−	0.934623i	$-0.384263\pi$
$853$	−317.095	−	211.876i	−0.371740	−	0.248389i	−0.727381	+	0.686234i	$0.759263\pi$
$854$	44.4443	+	44.4443i	0.0520425	+	0.0520425i
$855$		0			0
$856$	−6.69467	−	10.0193i	−0.00782087	−	0.0117048i
$857$	−1462.52	−	290.914i	−1.70656	−	0.339456i	−0.757089	−	0.653311i	$-0.773379\pi$
$857$	−1462.52	−	290.914i	−1.70656	−	0.339456i	−0.949471	+	0.313855i	$0.898379\pi$
$858$	−31.4870	−	76.0163i	−0.0366981	−	0.0885970i
$859$	104.148	+	251.434i	0.121243	+	0.292706i	0.972835	−	0.231498i	$-0.0743628\pi$
$859$	104.148	+	251.434i	0.121243	+	0.292706i	−0.851592	+	0.524204i	$0.824363\pi$
$860$		0			0
$861$	−163.557	+	109.285i	−0.189962	+	0.126928i
$862$	33.0609	+	166.208i	0.0383537	+	0.192817i
$863$	299.499	+	299.499i	0.347044	+	0.347044i	0.859007	−	0.511963i	$-0.171082\pi$
$863$	299.499	+	299.499i	0.347044	+	0.347044i	−0.511963	+	0.859007i	$0.671082\pi$
$864$	403.306	+	269.480i	0.466789	+	0.311898i
$865$		0			0
$866$			165.850i			0.191512i
$867$	−67.8597	+	483.346i	−0.0782695	+	0.557493i
$868$		−	39.8218i		−	0.0458777i
$869$	412.994	−	997.056i	0.475252	−	1.14736i
$870$		0			0
$871$	−503.143	−	503.143i	−0.577661	−	0.577661i
$872$	−409.999	+	81.5538i	−0.470182	+	0.0935250i
$873$	190.882	−	127.543i	0.218650	−	0.146098i
$874$	3.14087	−	15.7902i	0.00359367	−	0.0180666i
$875$		0			0
$876$	−33.3056	−	80.4069i	−0.0380201	−	0.0917887i
$877$	51.3586	−	258.197i	0.0585617	−	0.294410i	−0.940395	−	0.340085i	$-0.889544\pi$
$877$	51.3586	−	258.197i	0.0585617	−	0.294410i	0.998956	+	0.0456757i	$0.0145441\pi$
$878$	−44.3104	−	66.3152i	−0.0504674	−	0.0755299i
$879$	−725.713	+	144.353i	−0.825612	+	0.164224i
$880$		0			0
$881$	1188.52	+	794.144i	1.34906	+	0.901412i	0.999371	−	0.0354553i	$-0.0112881\pi$
$881$	1188.52	+	794.144i	1.34906	+	0.901412i	0.349686	+	0.936867i	$0.386288\pi$
$882$	44.8286	−	108.226i	0.0508261	−	0.122705i
$883$	−898.781			−1.01787			−0.508936	−	0.860804i	$-0.669961\pi$
$883$	−898.781			−1.01787			−0.508936	+	0.860804i	$0.669961\pi$
$884$	−323.457	−	203.069i	−0.365901	−	0.229716i
$885$		0			0
$886$	−2.23155	+	5.38744i	−0.00251868	+	0.00608063i
$887$	56.3214	+	37.6327i	0.0634965	+	0.0424270i	0.586913	−	0.809650i	$-0.300343\pi$
$887$	56.3214	+	37.6327i	0.0634965	+	0.0424270i	−0.523417	+	0.852077i	$0.675343\pi$
$888$	225.458	−	225.458i	0.253894	−	0.253894i
$889$	42.6730	+	214.532i	0.0480011	+	0.241318i
$890$		0			0
$891$	46.7763	−	235.160i	0.0524986	−	0.263928i
$892$	−537.365	−	1297.31i	−0.602428	−	1.45439i
$893$	−140.689	+	58.2753i	−0.157546	+	0.0652579i
$894$	−122.101	−	24.2874i	−0.136578	−	0.0271671i
$895$		0			0
$896$	177.300	−	35.2671i	0.197879	−	0.0393607i
$897$	−119.399	−	119.399i	−0.133109	−	0.133109i
$898$	151.317	−	226.462i	0.168505	−	0.252185i
$899$	−45.3766	−	18.7956i	−0.0504745	−	0.0209072i
$900$		0			0
$901$	995.218	−	706.718i	1.10457	−	0.784370i
$902$			512.175i			0.567821i
$903$	−46.2664	−	19.1642i	−0.0512363	−	0.0212228i
$904$	252.301	−	377.596i	0.279094	−	0.417694i
$905$		0			0
$906$	16.4573	+	82.7362i	0.0181647	+	0.0913203i
$907$	−18.1601	+	12.1342i	−0.0200222	+	0.0133784i	−0.565541	−	0.824720i	$-0.691333\pi$
$907$	−18.1601	+	12.1342i	−0.0200222	+	0.0133784i	0.545519	+	0.838099i	$0.316333\pi$
$908$	−1084.31	−	215.683i	−1.19417	−	0.237536i
$909$	−57.1615	+	23.6771i	−0.0628839	+	0.0260474i
$910$		0			0
$911$	473.629	+	94.2107i	0.519901	+	0.103415i	0.448063	−	0.894002i	$-0.352114\pi$
$911$	473.629	+	94.2107i	0.519901	+	0.103415i	0.0718370	+	0.997416i	$0.477114\pi$
$912$	29.4685	+	44.1027i	0.0323119	+	0.0483582i
$913$	−203.662	−	1023.88i	−0.223069	−	1.12145i
$914$	−168.795	+	168.795i	−0.184677	+	0.184677i
$915$		0			0
$916$	975.996	+	404.271i	1.06550	+	0.441344i
$917$	−167.696			−0.182874
$918$	−74.5472	−	166.426i	−0.0812061	−	0.181292i
$919$	77.0647			0.0838572			0.0419286	−	0.999121i	$-0.486650\pi$
$919$	77.0647			0.0838572			0.0419286	+	0.999121i	$0.486650\pi$
$920$		0			0
$921$	356.067	−	532.891i	0.386609	−	0.578601i
$922$	39.3618	−	39.3618i	0.0426917	−	0.0426917i
$923$	22.0669	−	4.38937i	0.0239077	−	0.00475555i
$924$	133.835	+	200.298i	0.144843	+	0.216772i
$925$		0			0
$926$	278.738	−	115.457i	0.301013	−	0.124684i
$927$	353.705	−	146.510i	0.381559	−	0.158047i
$928$	32.9023	−	165.411i	0.0354551	−	0.178245i
$929$	−596.669	+	398.682i	−0.642271	+	0.429151i	−0.833596	−	0.552375i	$-0.813722\pi$
$929$	−596.669	+	398.682i	−0.642271	+	0.429151i	0.191325	+	0.981527i	$0.438722\pi$
$930$		0			0
$931$	72.4942	−	72.4942i	0.0778670	−	0.0778670i
$932$	−140.665	+	210.520i	−0.150928	+	0.225880i
$933$	−100.100	+	241.662i	−0.107288	+	0.259016i
$934$			339.465i			0.363452i
$935$		0			0
$936$	118.486			0.126587
$937$	215.009	+	89.0595i	0.229465	+	0.0950475i	0.494454	−	0.869204i	$-0.335368\pi$
$937$	215.009	+	89.0595i	0.229465	+	0.0950475i	−0.264989	+	0.964252i	$0.585368\pi$
$938$	−79.6377	−	53.2122i	−0.0849016	−	0.0567294i
$939$	−275.762	−	275.762i	−0.293677	−	0.293677i
$940$		0			0
$941$	−580.541	−	868.841i	−0.616940	−	0.923317i	0.383059	−	0.923724i	$-0.374870\pi$
$941$	−580.541	−	868.841i	−0.616940	−	0.923317i	−1.00000		0.000407033i	$0.999870\pi$
$942$	−122.892	−	24.4447i	−0.130458	−	0.0259497i
$943$	402.237	+	971.086i	0.426550	+	1.02978i
$944$	68.2148	+	164.685i	0.0722614	+	0.174455i
$945$		0			0
$946$	−108.416	+	72.4410i	−0.114604	+	0.0765762i
$947$	242.166	+	1217.45i	0.255719	+	1.28559i	0.868640	+	0.495444i	$0.164994\pi$
$947$	242.166	+	1217.45i	0.255719	+	1.28559i	−0.612921	+	0.790144i	$0.710006\pi$
$948$	−249.201	−	249.201i	−0.262870	−	0.262870i
$949$	−65.8217	−	43.9807i	−0.0693590	−	0.0463442i
$950$		0			0
$951$		−	196.948i		−	0.207095i
$952$	−98.2793	−	37.4721i	−0.103235	−	0.0393614i
$953$		−	1337.30i		−	1.40325i	−0.712545	−	0.701626i	$-0.752458\pi$
$953$		−	1337.30i		−	1.40325i	0.712545	−	0.701626i	$-0.247542\pi$
$954$	−70.8296	+	170.998i	−0.0742449	+	0.179243i
$955$		0			0
$956$	−922.665	−	922.665i	−0.965130	−	0.965130i
$957$	291.406	−	57.9642i	0.304499	−	0.0605687i
$958$	−128.655	+	85.9647i	−0.134296	+	0.0897335i
$959$	3.88692	−	19.5408i	0.00405309	−	0.0203763i
$960$		0			0
$961$	−356.091	−	859.681i	−0.370542	−	0.894569i
$962$	27.6542	−	139.027i	0.0287465	−	0.144519i
$963$	12.5449	+	18.7748i	0.0130269	+	0.0194962i
$964$	1317.66	−	262.099i	1.36687	−	0.271887i
$965$		0			0
$966$	−18.8985	−	12.6276i	−0.0195637	−	0.0130720i
$967$	86.2341	−	208.188i	0.0891770	−	0.215292i	−0.872998	−	0.487723i	$-0.837828\pi$
$967$	86.2341	−	208.188i	0.0891770	−	0.215292i	0.962175	+	0.272431i	$0.0878276\pi$
$968$	886.322			0.915622
$969$	−1.84143	−	64.7469i	−0.00190035	−	0.0668183i
$970$		0			0
$971$	190.485	−	459.871i	0.196174	−	0.473605i	−0.794929	−	0.606702i	$-0.792492\pi$
$971$	190.485	−	459.871i	0.196174	−	0.473605i	0.991103	+	0.133097i	$0.0424921\pi$
$972$	−797.206	−	532.676i	−0.820171	−	0.548021i
$973$	293.812	−	293.812i	0.301965	−	0.301965i
$974$	−43.9639	−	221.022i	−0.0451375	−	0.226922i
$975$		0			0
$976$	−215.870	+	1085.25i	−0.221178	+	1.11194i
$977$	230.443	+	556.340i	0.235868	+	0.569437i	0.996848	−	0.0793394i	$-0.0252811\pi$
$977$	230.443	+	556.340i	0.235868	+	0.569437i	−0.760979	+	0.648776i	$0.775281\pi$
$978$	−151.945	+	62.9376i	−0.155363	+	0.0643534i
$979$	1646.51	+	327.512i	1.68183	+	0.334537i
$980$		0			0
$981$	768.284	−	152.821i	0.783164	−	0.155781i
$982$	209.931	+	209.931i	0.213779	+	0.213779i
$983$	−1007.10	+	1507.23i	−1.02452	+	1.53330i	−0.190400	+	0.981707i	$0.560979\pi$
$983$	−1007.10	+	1507.23i	−1.02452	+	1.53330i	−0.834116	+	0.551590i	$0.814021\pi$
$984$	316.151	+	130.954i	0.321292	+	0.133083i
$985$		0			0
$986$	−43.5421	+	46.0913i	−0.0441603	+	0.0467458i
$987$			214.987i			0.217819i
$988$	46.8255	+	19.3958i	0.0473943	+	0.0196314i
$989$	−148.665	+	222.493i	−0.150319	+	0.224968i
$990$		0			0
$991$	−141.139	−	709.553i	−0.142421	−	0.715997i	−0.984324	−	0.176369i	$-0.943565\pi$
$991$	−141.139	−	709.553i	−0.142421	−	0.715997i	0.841903	−	0.539628i	$-0.181435\pi$
$992$	−87.0476	+	58.1633i	−0.0877496	+	0.0586324i
$993$	979.715	+	194.877i	0.986622	+	0.196251i
$994$	2.79800	−	1.15897i	0.00281489	−	0.00116597i
$995$		0			0
$996$	−334.356	−	66.5076i	−0.335699	−	0.0667747i
$997$	−333.769	−	499.520i	−0.334773	−	0.501024i	0.625447	−	0.780266i	$-0.284917\pi$
$997$	−333.769	−	499.520i	−0.334773	−	0.501024i	−0.960220	+	0.279243i	$0.909917\pi$
$998$	−1.50723	−	7.57734i	−0.00151025	−	0.00759253i
$999$	−1040.97	+	1040.97i	−1.04202	+	1.04202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.f.24.6		96
5.2	odd	4		425.3.u.c.126.7	✓	96
5.3	odd	4		425.3.u.d.126.6	yes	96
5.4	even	2		425.3.t.g.24.7		96
17.5	odd	16		425.3.t.g.124.7		96
85.22	even	16		425.3.u.c.226.7	yes	96
85.39	odd	16	inner	425.3.t.f.124.6		96
85.73	even	16		425.3.u.d.226.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.3.t.f.24.6		96	1.1	even	1	trivial
425.3.t.f.124.6		96	85.39	odd	16	inner
425.3.t.g.24.7		96	5.4	even	2
425.3.t.g.124.7		96	17.5	odd	16
425.3.u.c.126.7	✓	96	5.2	odd	4
425.3.u.c.226.7	yes	96	85.22	even	16
425.3.u.d.126.6	yes	96	5.3	odd	4
425.3.u.d.226.6	yes	96	85.73	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.387390 - 0.160462i) q^{2} +(-1.40425 - 0.938292i) q^{3} +(-2.70410 - 2.70410i) q^{4} +(0.393433 + 0.588815i) q^{6} +(-1.84965 - 0.367918i) q^{7} +(1.25549 + 3.03101i) q^{8} +(-2.35262 - 5.67972i) q^{9} +(-16.4446 + 10.9879i) q^{11} +(1.26001 + 6.33449i) q^{12} +(4.15401 + 4.15401i) q^{13} +(0.657498 + 0.439326i) q^{14} +13.9211i q^{16} +(9.03903 - 14.3978i) q^{17} +2.57777i q^{18} +(-0.863349 + 2.08431i) q^{19} +(2.25216 + 2.25216i) q^{21} +(8.13362 - 1.61788i) q^{22} +(14.1508 - 9.45525i) q^{23} +(1.08095 - 5.43432i) q^{24} +(-0.942660 - 2.27578i) q^{26} +(-4.99092 + 25.0911i) q^{27} +(4.00675 + 5.99653i) q^{28} +(8.72414 - 1.73534i) q^{29} +(-4.59107 - 3.06766i) q^{31} +(7.25575 - 17.5169i) q^{32} +33.4023 q^{33} +(-5.81193 + 4.12713i) q^{34} +(-8.99683 + 21.7203i) q^{36} +(47.8471 + 31.9704i) q^{37} +(0.668906 - 0.668906i) q^{38} +(-1.93561 - 9.73095i) q^{39} +(-12.0488 + 60.5735i) q^{41} +(-0.511078 - 1.23385i) q^{42} +(-14.5262 + 6.01694i) q^{43} +(74.1804 + 14.7554i) q^{44} +(-6.99908 + 1.39220i) q^{46} +(47.7291 + 47.7291i) q^{47} +(13.0620 - 19.5487i) q^{48} +(-41.9843 - 17.3905i) q^{49} +(-26.2024 + 11.7369i) q^{51} -22.4657i q^{52} +(66.3355 + 27.4771i) q^{53} +(5.95960 - 8.91917i) q^{54} +(-1.20704 - 6.06822i) q^{56} +(3.16805 - 2.11682i) q^{57} +(-3.65810 - 0.727641i) q^{58} +(11.8299 - 4.90011i) q^{59} +(77.9573 + 15.5067i) q^{61} +(1.28629 + 1.92507i) q^{62} +(2.26184 + 11.3710i) q^{63} +(33.7532 - 33.7532i) q^{64} +(-12.9397 - 5.35980i) q^{66} -121.122 q^{67} +(-63.3756 + 14.4906i) q^{68} -28.7431 q^{69} +(2.12776 - 3.18442i) q^{71} +(14.2616 - 14.2616i) q^{72} +(-13.2164 + 2.62891i) q^{73} +(-13.4055 - 20.0627i) q^{74} +(7.97078 - 3.30160i) q^{76} +(34.4594 - 14.2735i) q^{77} +(-0.811615 + 4.08026i) q^{78} +(-45.3705 + 30.3156i) q^{79} +(-8.57232 + 8.57232i) q^{81} +(14.3873 - 21.5322i) q^{82} +(-20.1994 + 48.7656i) q^{83} -12.1802i q^{84} +6.59279 q^{86} +(-13.8792 - 5.74893i) q^{87} +(-53.9504 - 36.0485i) q^{88} +(-60.0205 - 60.0205i) q^{89} +(-6.15512 - 9.21178i) q^{91} +(-63.8331 - 12.6972i) q^{92} +(3.56867 + 8.61554i) q^{93} +(-10.8311 - 26.1485i) q^{94} +(-26.6249 + 17.7902i) q^{96} +(7.28522 + 36.6253i) q^{97} +(13.4738 + 13.4738i) q^{98} +(101.096 + 67.5502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) \) 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more