LMFDB - Embedded newform 750.2.m.a.481.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			481.2
Character	$\chi$	$=$	750.481
Dual form			750.2.m.a.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(0.728969 - 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.13314 + 1.92769i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.320263 + 0.232684i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(0.728969 - 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.13314 + 1.92769i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.320263 + 0.232684i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(1.02044 + 1.98965i) q^{10} +(3.00612 - 4.73688i) q^{11} +(-0.929776 - 0.368125i) q^{12} +(0.111605 - 1.77391i) q^{13} +(0.0248566 + 0.395085i) q^{14} +(0.493572 + 2.18091i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(2.07911 - 4.41833i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.950777 - 0.892839i) q^{19} +(2.22669 + 0.204525i) q^{20} +(-0.0741779 + 0.388854i) q^{21} +(-2.38873 - 5.07630i) q^{22} +(-0.573179 - 0.147167i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-2.43199 - 4.36869i) q^{25} +(-1.43796 - 1.04474i) q^{26} +(-0.637424 - 0.770513i) q^{27} +(0.346900 + 0.190710i) q^{28} +(5.31918 + 2.92424i) q^{29} +(2.10588 + 0.751856i) q^{30} +(3.17128 - 6.73932i) q^{31} +(0.309017 + 0.951057i) q^{32} +(-1.05125 - 5.51087i) q^{33} +(-2.61648 - 4.12291i) q^{34} +(-0.0856414 - 0.881031i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(1.51057 - 1.82596i) q^{37} +(-1.26330 + 0.324361i) q^{38} +(-1.13297 - 1.36952i) q^{39} +(1.36581 - 1.77047i) q^{40} +(-5.52041 + 1.41740i) q^{41} +(0.288574 + 0.270989i) q^{42} +(0.526586 - 1.62066i) q^{43} +(-5.56600 - 0.703150i) q^{44} +(1.85274 + 1.25194i) q^{45} +(-0.431382 + 0.405095i) q^{46} +(5.65248 - 0.714075i) q^{47} +(0.0627905 + 0.998027i) q^{48} +(-2.11469 + 6.50836i) q^{49} +(-4.99173 - 0.287465i) q^{50} +(-1.50895 - 4.64408i) q^{51} +(-1.65260 + 0.654310i) q^{52} +(-1.79149 + 9.39130i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(5.72490 + 11.1624i) q^{55} +(0.346900 - 0.190710i) q^{56} -1.30428 q^{57} +(5.31918 - 2.92424i) q^{58} +(6.00561 + 2.37779i) q^{59} +(1.76320 - 1.37519i) q^{60} +(-6.23523 - 1.60093i) q^{61} +(-3.99094 - 6.28871i) q^{62} +(0.212116 + 0.334241i) q^{63} +(0.968583 + 0.248690i) q^{64} +(3.29308 + 2.22523i) q^{65} +(-5.21627 - 2.06527i) q^{66} +(-13.2502 + 7.28435i) q^{67} -4.88307 q^{68} +(-0.518573 + 0.285088i) q^{69} +(-0.789768 - 0.399771i) q^{70} +(10.4147 - 1.31568i) q^{71} +(-0.187381 + 0.982287i) q^{72} +(-8.27049 + 3.27452i) q^{73} +(-0.732308 - 2.25381i) q^{74} +(-4.76342 - 1.51983i) q^{75} +(-0.403044 + 1.24044i) q^{76} +(0.139452 + 2.21652i) q^{77} +(-1.76340 + 0.222769i) q^{78} +(-0.538206 + 0.505409i) q^{79} +(-0.763021 - 2.10186i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-1.76123 + 5.42052i) q^{82} +(8.25842 + 7.75517i) q^{83} +(0.383429 - 0.0984479i) q^{84} +(6.16126 + 9.01447i) q^{85} +(-1.08621 - 1.31301i) q^{86} +(5.87930 - 1.50955i) q^{87} +(-3.57610 + 4.32277i) q^{88} +(-2.93208 + 1.16089i) q^{89} +(2.04980 - 0.893492i) q^{90} +(0.377018 + 0.594085i) q^{91} +(0.110887 + 0.581289i) q^{92} +(-2.30162 - 7.08365i) q^{93} +(2.42584 - 5.15517i) q^{94} +(2.79848 - 0.821093i) q^{95} +(0.876307 + 0.481754i) q^{96} +(-8.68881 - 4.77671i) q^{97} +(4.36208 + 5.27285i) q^{98} +(-4.53878 - 3.29762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 20 q^{5} + 5 q^{7}+O(q^{10}) $ 100 * q - 20 * q^5 + 5 * q^7	$ 100 q - 20 q^{5} + 5 q^{7} - 20 q^{10} + 10 q^{11} + 10 q^{13} - 20 q^{14} - 20 q^{15} + 15 q^{17} - 25 q^{18} + 15 q^{19} + 5 q^{20} + 5 q^{21} + 10 q^{22} - 5 q^{23} - 25 q^{24} + 10 q^{26} + 5 q^{28} + 25 q^{29} + 5 q^{30} - 25 q^{31} - 25 q^{32} + 10 q^{33} - 10 q^{34} + 40 q^{35} + 30 q^{37} - 35 q^{38} + 10 q^{39} + 5 q^{40} - 15 q^{41} + 5 q^{42} + 35 q^{43} - 15 q^{44} + 5 q^{45} + 20 q^{46} - 110 q^{47} + 20 q^{49} + 15 q^{51} - 40 q^{52} + 45 q^{53} + 60 q^{55} + 5 q^{56} - 60 q^{57} + 25 q^{58} - 20 q^{60} + 25 q^{62} + 5 q^{63} + 70 q^{65} - 15 q^{66} - 45 q^{67} - 60 q^{68} + 20 q^{69} - 10 q^{70} + 10 q^{71} + 60 q^{73} + 30 q^{74} - 25 q^{75} + 15 q^{76} + 5 q^{77} + 10 q^{78} - 10 q^{79} + 5 q^{80} - 15 q^{82} - 5 q^{83} + 5 q^{84} - 10 q^{85} + 35 q^{86} + 25 q^{87} + 10 q^{88} + 5 q^{90} + 15 q^{91} - 55 q^{92} + 40 q^{94} - 125 q^{95} + 80 q^{97} - 5 q^{98} + 10 q^{99}+O(q^{100}) $ 100 * q - 20 * q^5 + 5 * q^7 - 20 * q^10 + 10 * q^11 + 10 * q^13 - 20 * q^14 - 20 * q^15 + 15 * q^17 - 25 * q^18 + 15 * q^19 + 5 * q^20 + 5 * q^21 + 10 * q^22 - 5 * q^23 - 25 * q^24 + 10 * q^26 + 5 * q^28 + 25 * q^29 + 5 * q^30 - 25 * q^31 - 25 * q^32 + 10 * q^33 - 10 * q^34 + 40 * q^35 + 30 * q^37 - 35 * q^38 + 10 * q^39 + 5 * q^40 - 15 * q^41 + 5 * q^42 + 35 * q^43 - 15 * q^44 + 5 * q^45 + 20 * q^46 - 110 * q^47 + 20 * q^49 + 15 * q^51 - 40 * q^52 + 45 * q^53 + 60 * q^55 + 5 * q^56 - 60 * q^57 + 25 * q^58 - 20 * q^60 + 25 * q^62 + 5 * q^63 + 70 * q^65 - 15 * q^66 - 45 * q^67 - 60 * q^68 + 20 * q^69 - 10 * q^70 + 10 * q^71 + 60 * q^73 + 30 * q^74 - 25 * q^75 + 15 * q^76 + 5 * q^77 + 10 * q^78 - 10 * q^79 + 5 * q^80 - 15 * q^82 - 5 * q^83 + 5 * q^84 - 10 * q^85 + 35 * q^86 + 25 * q^87 + 10 * q^88 + 5 * q^90 + 15 * q^91 - 55 * q^92 + 40 * q^94 - 125 * q^95 + 80 * q^97 - 5 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{25}\right)$	$1$

Coefficient data

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

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

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

$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$3$	0.728969	−	0.684547i	0.420870	−	0.395223i
$3$	0.728969	−	0.684547i	0.420870	−	0.395223i
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	−1.13314	+	1.92769i	−0.506756	+	0.862090i
$5$	−1.13314	+	1.92769i	−0.506756	+	0.862090i
$6$	−0.187381	−	0.982287i	−0.0764981	−	0.401017i
$7$	−0.320263	+	0.232684i	−0.121048	+	0.0879464i	−0.646662	−	0.762777i	$-0.723836\pi$
$7$	−0.320263	+	0.232684i	−0.121048	+	0.0879464i	0.525614	+	0.850723i	$0.323836\pi$
$8$	−0.992115	−	0.125333i	−0.350766	−	0.0443120i
$9$	0.0627905	−	0.998027i	0.0209302	−	0.332676i
$10$	1.02044	+	1.98965i	0.322690	+	0.629183i
$11$	3.00612	−	4.73688i	0.906379	−	1.42822i	0.00270807	−	0.999996i	$-0.499138\pi$
$11$	3.00612	−	4.73688i	0.906379	−	1.42822i	0.903671	−	0.428228i	$-0.140862\pi$
$12$	−0.929776	−	0.368125i	−0.268403	−	0.106268i
$13$	0.111605	−	1.77391i	0.0309536	−	0.491994i	−0.951758	−	0.306850i	$-0.900725\pi$
$13$	0.111605	−	1.77391i	0.0309536	−	0.491994i	0.982711	−	0.185144i	$-0.0592750\pi$
$14$	0.0248566	+	0.395085i	0.00664322	+	0.105591i
$15$	0.493572	+	2.18091i	0.127440	+	0.563110i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	2.07911	−	4.41833i	0.504258	−	1.07160i	−0.476999	−	0.878904i	$-0.658276\pi$
$17$	2.07911	−	4.41833i	0.504258	−	1.07160i	0.981258	−	0.192700i	$-0.0617244\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−0.950777	−	0.892839i	−0.218123	−	0.204831i	0.567781	−	0.823180i	$-0.307802\pi$
$19$	−0.950777	−	0.892839i	−0.218123	−	0.204831i	−0.785904	+	0.618348i	$0.787802\pi$
$20$	2.22669	+	0.204525i	0.497904	+	0.0457331i
$21$	−0.0741779	+	0.388854i	−0.0161870	+	0.0848550i
$22$	−2.38873	−	5.07630i	−0.509278	−	1.08227i
$23$	−0.573179	−	0.147167i	−0.119516	−	0.0306865i	0.188458	−	0.982081i	$-0.439651\pi$
$23$	−0.573179	−	0.147167i	−0.119516	−	0.0306865i	−0.307974	+	0.951395i	$0.599651\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−2.43199	−	4.36869i	−0.486398	−	0.873738i
$26$	−1.43796	−	1.04474i	−0.282007	−	0.204890i
$27$	−0.637424	−	0.770513i	−0.122672	−	0.148285i
$28$	0.346900	+	0.190710i	0.0655580	+	0.0360408i
$29$	5.31918	+	2.92424i	0.987747	+	0.543018i	0.891830	−	0.452371i	$-0.149422\pi$
$29$	5.31918	+	2.92424i	0.987747	+	0.543018i	0.0959170	+	0.995389i	$0.469422\pi$
$30$	2.10588	+	0.751856i	0.384479	+	0.137269i
$31$	3.17128	−	6.73932i	0.569579	−	1.21042i	−0.387842	−	0.921726i	$-0.626780\pi$
$31$	3.17128	−	6.73932i	0.569579	−	1.21042i	0.957422	−	0.288692i	$-0.0932205\pi$
$32$	0.309017	+	0.951057i	0.0546270	+	0.168125i
$33$	−1.05125	−	5.51087i	−0.183000	−	0.959319i
$34$	−2.61648	−	4.12291i	−0.448723	−	0.707074i
$35$	−0.0856414	−	0.881031i	−0.0144760	−	0.148921i
$36$	−0.929776	+	0.368125i	−0.154963	+	0.0613541i
$37$	1.51057	−	1.82596i	0.248336	−	0.300186i	−0.631585	−	0.775306i	$-0.717595\pi$
$37$	1.51057	−	1.82596i	0.248336	−	0.300186i	0.879921	+	0.475120i	$0.157595\pi$
$38$	−1.26330	+	0.324361i	−0.204934	+	0.0526182i
$39$	−1.13297	−	1.36952i	−0.181420	−	0.219299i
$40$	1.36581	−	1.77047i	0.215953	−	0.279936i
$41$	−5.52041	+	1.41740i	−0.862143	+	0.221361i	−0.653774	−	0.756690i	$-0.726815\pi$
$41$	−5.52041	+	1.41740i	−0.862143	+	0.221361i	−0.208369	+	0.978050i	$0.566815\pi$
$42$	0.288574	+	0.270989i	0.0445280	+	0.0418145i
$43$	0.526586	−	1.62066i	0.0803036	−	0.247149i	−0.902842	−	0.429972i	$-0.858523\pi$
$43$	0.526586	−	1.62066i	0.0803036	−	0.247149i	0.983146	+	0.182823i	$0.0585235\pi$
$44$	−5.56600	−	0.703150i	−0.839107	−	0.106004i
$45$	1.85274	+	1.25194i	0.276190	+	0.186629i
$46$	−0.431382	+	0.405095i	−0.0636039	+	0.0597280i
$47$	5.65248	−	0.714075i	0.824499	−	0.104159i	0.298249	−	0.954488i	$-0.403597\pi$
$47$	5.65248	−	0.714075i	0.824499	−	0.104159i	0.526250	+	0.850330i	$0.323597\pi$
$48$	0.0627905	+	0.998027i	0.00906303	+	0.144053i
$49$	−2.11469	+	6.50836i	−0.302099	+	0.929765i
$50$	−4.99173	−	0.287465i	−0.705937	−	0.0406536i
$51$	−1.50895	−	4.64408i	−0.211295	−	0.650301i
$52$	−1.65260	+	0.654310i	−0.229174	+	0.0907365i
$53$	−1.79149	+	9.39130i	−0.246080	+	1.28999i	0.617816	+	0.786323i	$0.288018\pi$
$53$	−1.79149	+	9.39130i	−0.246080	+	1.28999i	−0.863895	+	0.503671i	$0.831982\pi$
$54$	−0.992115	+	0.125333i	−0.135010	+	0.0170557i
$55$	5.72490	+	11.1624i	0.771945	+	1.50514i
$56$	0.346900	−	0.190710i	0.0463565	−	0.0254847i
$57$	−1.30428			−0.172756
$58$	5.31918	−	2.92424i	0.698443	−	0.383972i
$59$	6.00561	+	2.37779i	0.781864	+	0.309562i	0.724936	−	0.688817i	$-0.241869\pi$
$59$	6.00561	+	2.37779i	0.781864	+	0.309562i	0.0569279	+	0.998378i	$0.481869\pi$
$60$	1.76320	−	1.37519i	0.227628	−	0.177536i
$61$	−6.23523	−	1.60093i	−0.798339	−	0.204979i	−0.172581	−	0.984995i	$-0.555211\pi$
$61$	−6.23523	−	1.60093i	−0.798339	−	0.204979i	−0.625759	+	0.780017i	$0.715211\pi$
$62$	−3.99094	−	6.28871i	−0.506850	−	0.798667i
$63$	0.212116	+	0.334241i	0.0267241	+	0.0421104i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	3.29308	+	2.22523i	0.408457	+	0.276005i
$66$	−5.21627	−	2.06527i	−0.642079	−	0.254217i
$67$	−13.2502	+	7.28435i	−1.61877	+	0.889925i	−0.624736	+	0.780836i	$0.714793\pi$
$67$	−13.2502	+	7.28435i	−1.61877	+	0.889925i	−0.994032	+	0.109089i	$0.965207\pi$
$68$	−4.88307			−0.592159
$69$	−0.518573	+	0.285088i	−0.0624288	+	0.0343205i
$70$	−0.789768	−	0.399771i	−0.0943954	−	0.0477817i
$71$	10.4147	−	1.31568i	1.23600	−	0.156142i	0.519950	−	0.854197i	$-0.325951\pi$
$71$	10.4147	−	1.31568i	1.23600	−	0.156142i	0.716045	+	0.698054i	$0.245951\pi$
$72$	−0.187381	+	0.982287i	−0.0220831	+	0.115764i
$73$	−8.27049	+	3.27452i	−0.967988	+	0.383253i	−0.798310	−	0.602246i	$-0.794273\pi$
$73$	−8.27049	+	3.27452i	−0.967988	+	0.383253i	−0.169677	+	0.985500i	$0.554273\pi$
$74$	−0.732308	−	2.25381i	−0.0851291	−	0.262000i
$75$	−4.76342	−	1.51983i	−0.550032	−	0.175494i
$76$	−0.403044	+	1.24044i	−0.0462323	+	0.142288i
$77$	0.139452	+	2.21652i	0.0158920	+	0.252596i
$78$	−1.76340	+	0.222769i	−0.199666	+	0.0252236i
$79$	−0.538206	+	0.505409i	−0.0605529	+	0.0568630i	−0.714233	−	0.699908i	$-0.753224\pi$
$79$	−0.538206	+	0.505409i	−0.0605529	+	0.0568630i	0.653680	+	0.756771i	$0.273224\pi$
$80$	−0.763021	−	2.10186i	−0.0853084	−	0.234995i
$81$	−0.992115	−	0.125333i	−0.110235	−	0.0139259i
$82$	−1.76123	+	5.42052i	−0.194496	+	0.598596i
$83$	8.25842	+	7.75517i	0.906480	+	0.851241i	0.989385	−	0.145316i	$-0.0464200\pi$
$83$	8.25842	+	7.75517i	0.906480	+	0.851241i	−0.0829057	+	0.996557i	$0.526420\pi$
$84$	0.383429	−	0.0984479i	0.0418356	−	0.0107416i
$85$	6.16126	+	9.01447i	0.668283	+	0.977757i
$86$	−1.08621	−	1.31301i	−0.117129	−	0.141585i
$87$	5.87930	−	1.50955i	0.630327	−	0.161840i
$88$	−3.57610	+	4.32277i	−0.381214	+	0.460808i
$89$	−2.93208	+	1.16089i	−0.310800	+	0.123054i	−0.518346	−	0.855171i	$-0.673452\pi$
$89$	−2.93208	+	1.16089i	−0.310800	+	0.123054i	0.207546	+	0.978225i	$0.433452\pi$
$90$	2.04980	−	0.893492i	0.216068	−	0.0941823i
$91$	0.377018	+	0.594085i	0.0395222	+	0.0622770i
$92$	0.110887	+	0.581289i	0.0115608	+	0.0606036i
$93$	−2.30162	−	7.08365i	−0.238667	−	0.734540i
$94$	2.42584	−	5.15517i	0.250206	−	0.531715i
$95$	2.79848	−	0.821093i	0.287118	−	0.0842424i
$96$	0.876307	+	0.481754i	0.0894377	+	0.0491688i
$97$	−8.68881	−	4.77671i	−0.882215	−	0.485002i	−0.0248382	−	0.999691i	$-0.507907\pi$
$97$	−8.68881	−	4.77671i	−0.882215	−	0.485002i	−0.857376	+	0.514690i	$0.827907\pi$
$98$	4.36208	+	5.27285i	0.440636	+	0.532638i
$99$	−4.53878	−	3.29762i	−0.456165	−	0.331423i
$100$	−2.91742	+	4.06063i	−0.291742	+	0.406063i
$101$	8.28091	−	6.01643i	0.823981	−	0.598657i	−0.0938690	−	0.995585i	$-0.529923\pi$
$101$	8.28091	−	6.01643i	0.823981	−	0.598657i	0.917850	+	0.396927i	$0.129923\pi$
$102$	−4.72966	−	1.21437i	−0.468306	−	0.120241i
$103$	6.91021	+	14.6850i	0.680884	+	1.44695i	0.883852	+	0.467766i	$0.154941\pi$
$103$	6.91021	+	14.6850i	0.680884	+	1.44695i	−0.202969	+	0.979185i	$0.565059\pi$
$104$	−0.333054	+	1.74593i	−0.0326587	+	0.171203i
$105$	−0.665537	−	0.583619i	−0.0649498	−	0.0569553i
$106$	6.96941	+	6.54471i	0.676929	+	0.635679i
$107$	−2.94608	−	2.14045i	−0.284808	−	0.206925i	0.436204	−	0.899848i	$-0.356323\pi$
$107$	−2.94608	−	2.14045i	−0.284808	−	0.206925i	−0.721012	+	0.692923i	$0.756323\pi$
$108$	−0.425779	+	0.904827i	−0.0409706	+	0.0870670i
$109$	2.81171	−	3.39877i	0.269313	−	0.325543i	−0.618468	−	0.785810i	$-0.712246\pi$
$109$	2.81171	−	3.39877i	0.269313	−	0.325543i	0.887781	+	0.460267i	$0.152246\pi$
$110$	12.4923	+	1.14743i	1.19109	+	0.109403i
$111$	−0.148801	−	2.36512i	−0.0141236	−	0.224487i
$112$	0.0248566	−	0.395085i	0.00234873	−	0.0373320i
$113$	5.10856	+	2.02262i	0.480573	+	0.190272i	0.595905	−	0.803055i	$-0.296793\pi$
$113$	5.10856	+	2.02262i	0.480573	+	0.190272i	−0.115333	+	0.993327i	$0.536793\pi$
$114$	−0.698867	+	1.10124i	−0.0654549	+	0.103140i
$115$	0.933186	−	0.938152i	0.0870200	−	0.0874831i
$116$	0.381138	−	6.05802i	0.0353878	−	0.562473i
$117$	−1.76340	−	0.222769i	−0.163026	−	0.0205950i
$118$	5.22560	−	3.79662i	0.481055	−	0.349507i
$119$	0.362216	+	1.89880i	0.0332043	+	0.174063i
$120$	−0.216339	−	2.22558i	−0.0197490	−	0.203167i
$121$	−8.71775	−	18.5262i	−0.792523	−	1.68420i
$122$	−4.69272	+	4.40675i	−0.424859	+	0.398969i
$123$	−3.05393	+	4.81222i	−0.275363	+	0.433903i
$124$	−7.44819			−0.668867
$125$	11.1773	+	0.262212i	0.999725	+	0.0234530i
$126$	0.395866			0.0352666
$127$	−3.11865	+	4.91420i	−0.276735	+	0.436065i	−0.954058	−	0.299621i	$-0.903140\pi$
$127$	−3.11865	+	4.91420i	−0.276735	+	0.436065i	0.677323	+	0.735685i	$0.263140\pi$
$128$	0.728969	−	0.684547i	0.0644323	−	0.0605060i
$129$	−0.725557	−	1.54189i	−0.0638817	−	0.135756i
$130$	3.64334	−	1.58811i	0.319542	−	0.139286i
$131$	−3.81852	−	20.0174i	−0.333626	−	1.74893i	−0.614251	−	0.789111i	$-0.710542\pi$
$131$	−3.81852	−	20.0174i	−0.333626	−	1.74893i	0.280625	−	0.959817i	$-0.409458\pi$
$132$	−4.53878	+	3.29762i	−0.395050	+	0.287021i
$133$	0.512248	+	0.0647120i	0.0444175	+	0.00561124i
$134$	−0.949423	+	15.0907i	−0.0820177	+	1.30363i
$135$	2.20760	−	0.355657i	0.190000	−	0.0306101i
$136$	−2.61648	+	4.12291i	−0.224361	+	0.353537i
$137$	16.2154	+	6.42014i	1.38538	+	0.548510i	0.938249	−	0.345960i	$-0.112447\pi$
$137$	16.2154	+	6.42014i	1.38538	+	0.548510i	0.447128	+	0.894470i	$0.352447\pi$
$138$	−0.0371576	+	0.590603i	−0.00316307	+	0.0502755i
$139$	0.572533	+	9.10015i	0.0485616	+	0.771864i	0.944669	+	0.328026i	$0.106383\pi$
$139$	0.572533	+	9.10015i	0.0485616	+	0.771864i	−0.896107	+	0.443838i	$0.853617\pi$
$140$	−0.760717	+	0.452616i	−0.0642923	+	0.0382530i
$141$	3.63167	−	4.38993i	0.305841	−	0.369699i
$142$	4.46960	−	9.49838i	0.375080	−	0.797086i
$143$	−8.06730	−	5.86124i	−0.674622	−	0.490141i
$144$	0.728969	+	0.684547i	0.0607474	+	0.0570456i
$145$	−11.6644	+	6.94016i	−0.968677	+	0.576349i
$146$	−1.66678	+	8.73758i	−0.137944	+	0.723127i
$147$	2.91373	+	6.19199i	0.240320	+	0.510707i
$148$	−2.29535	−	0.589345i	−0.188676	−	0.0484439i
$149$	−1.59128	+	1.15613i	−0.130363	+	0.0947140i	−0.651056	−	0.759030i	$-0.725674\pi$
$149$	−1.59128	+	1.15613i	−0.130363	+	0.0947140i	0.520693	+	0.853744i	$0.325674\pi$
$150$	−3.83560	+	3.20752i	−0.313175	+	0.261893i
$151$	16.9917	+	12.3452i	1.38276	+	1.00464i	0.996616	+	0.0822004i	$0.0261947\pi$
$151$	16.9917	+	12.3452i	1.38276	+	1.00464i	0.386148	+	0.922437i	$0.373805\pi$
$152$	0.831378	+	1.00496i	0.0674336	+	0.0815133i
$153$	−4.27907	−	2.35244i	−0.345942	−	0.190183i
$154$	1.94619	+	1.06993i	0.156829	+	0.0862174i
$155$	9.39782	+	13.7499i	0.754851	+	1.10441i
$156$	−0.756787	+	1.60825i	−0.0605914	+	0.128763i
$157$	−5.32098	−	16.3763i	−0.424660	−	1.30697i	−0.903319	−	0.428969i	$-0.858877\pi$
$157$	−5.32098	−	16.3763i	−0.424660	−	1.30697i	0.478659	−	0.878001i	$-0.341123\pi$
$158$	0.138346	+	0.725235i	0.0110062	+	0.0576966i
$159$	5.12285	+	8.07232i	0.406268	+	0.640177i
$160$	−2.18350	−	0.481991i	−0.172621	−	0.0381047i
$161$	0.217811	−	0.0862377i	0.0171659	−	0.00679648i
$162$	−0.637424	+	0.770513i	−0.0500808	+	0.0605372i
$163$	−18.3662	+	4.71563i	−1.43855	+	0.369357i	−0.885830	−	0.464011i	$-0.846410\pi$
$163$	−18.3662	+	4.71563i	−1.43855	+	0.369357i	−0.552719	+	0.833367i	$0.686410\pi$
$164$	3.63298	+	4.39152i	0.283688	+	0.342920i
$165$	11.8145	+	4.21809i	0.919756	+	0.328378i
$166$	10.9730	−	2.81739i	0.851670	−	0.218672i
$167$	−3.16911	−	2.97600i	−0.245233	−	0.230290i	0.552177	−	0.833727i	$-0.313797\pi$
$167$	−3.16911	−	2.97600i	−0.245233	−	0.230290i	−0.797410	+	0.603437i	$0.793797\pi$
$168$	0.122329	−	0.376491i	0.00943792	−	0.0290469i
$169$	9.76320	+	1.23338i	0.751015	+	0.0948753i
$170$	10.9125	−	0.371929i	0.836954	−	0.0285256i
$171$	−0.950777	+	0.892839i	−0.0727078	+	0.0682771i
$172$	−1.69063	+	0.213576i	−0.128909	+	0.0162850i
$173$	−0.536449	−	8.52661i	−0.0407854	−	0.648266i	−0.964318	−	0.264746i	$-0.914712\pi$
$173$	−0.536449	−	8.52661i	−0.0407854	−	0.648266i	0.923533	−	0.383520i	$-0.125288\pi$
$174$	1.87573	−	5.77291i	0.142199	−	0.437643i
$175$	1.79540	+	0.833242i	0.135719	+	0.0629871i
$176$	1.73366	+	5.33566i	0.130680	+	0.402190i
$177$	6.00561	−	2.37779i	0.451409	−	0.178726i
$178$	−0.590913	+	3.09767i	−0.0442908	+	0.232180i
$179$	0.0630597	−	0.00796629i	0.00471330	−	0.000595429i	−0.122976	−	0.992410i	$-0.539244\pi$
$179$	0.0630597	−	0.00796629i	0.00471330	−	0.000595429i	0.127690	+	0.991814i	$0.459244\pi$
$180$	0.343936	−	2.20946i	0.0256355	−	0.164683i
$181$	18.6449	−	10.2501i	1.38587	−	0.761886i	0.398028	−	0.917373i	$-0.369695\pi$
$181$	18.6449	−	10.2501i	1.38587	−	0.761886i	0.987838	+	0.155487i	$0.0496946\pi$
$182$	0.703619			0.0521557
$183$	−5.64120	+	3.10128i	−0.417010	+	0.229253i
$184$	0.550215	+	0.217845i	0.0405624	+	0.0160598i
$185$	1.80821	+	4.98097i	0.132942	+	0.366209i
$186$	−7.21419	−	1.85229i	−0.528970	−	0.135816i
$187$	−14.6791	−	23.1305i	−1.07344	−	1.69147i
$188$	−3.05282	−	4.81048i	−0.222650	−	0.350840i
$189$	0.383429	+	0.0984479i	0.0278904	+	0.00716103i
$190$	0.806230	−	2.80280i	0.0584901	−	0.203337i
$191$	−3.01399	−	1.19332i	−0.218085	−	0.0863459i	0.256542	−	0.966533i	$-0.417417\pi$
$191$	−3.01399	−	1.19332i	−0.218085	−	0.0863459i	−0.474627	+	0.880187i	$0.657417\pi$
$192$	0.876307	−	0.481754i	0.0632420	−	0.0347676i
$193$	−15.9464			−1.14785			−0.573924	−	0.818909i	$-0.694579\pi$
$193$	−15.9464			−1.14785			−0.573924	+	0.818909i	$0.694579\pi$
$194$	−8.68881	+	4.77671i	−0.623820	+	0.342948i
$195$	3.92383	−	0.632151i	0.280991	−	0.0452693i
$196$	6.78933	−	0.857692i	0.484952	−	0.0612637i
$197$	−3.94810	+	20.6967i	−0.281290	+	1.47458i	0.508427	+	0.861105i	$0.330227\pi$
$197$	−3.94810	+	20.6967i	−0.281290	+	1.47458i	−0.789717	+	0.613471i	$0.789773\pi$
$198$	−5.21627	+	2.06527i	−0.370704	+	0.146772i
$199$	0.456721	+	1.40564i	0.0323761	+	0.0996433i	0.965939	−	0.258771i	$-0.0833175\pi$
$199$	0.456721	+	1.40564i	0.0323761	+	0.0996433i	−0.933563	+	0.358414i	$0.883318\pi$
$200$	1.86527	+	4.63905i	0.131894	+	0.328030i
$201$	−4.67249	+	14.3804i	−0.329572	+	1.01432i
$202$	−0.642709	−	10.2156i	−0.0452208	−	0.718765i
$203$	−2.38396	+	0.301164i	−0.167321	+	0.0211376i
$204$	−3.55960	+	3.34269i	−0.249222	+	0.234035i
$205$	3.52309	−	12.2478i	0.246063	−	0.855421i
$206$	16.1016	+	2.03410i	1.12185	+	0.141723i
$207$	−0.182867	+	0.562808i	−0.0127102	+	0.0391178i
$208$	1.29568	+	1.21672i	0.0898393	+	0.0843647i
$209$	−7.08743	+	1.81974i	−0.490247	+	0.125874i
$210$	−0.849378	+	0.249213i	−0.0586127	+	0.0171973i
$211$	13.1391	+	15.8825i	0.904534	+	1.09339i	0.995234	+	0.0975157i	$0.0310896\pi$
$211$	13.1391	+	15.8825i	0.904534	+	1.09339i	−0.0906998	+	0.995878i	$0.528910\pi$
$212$	9.26028	−	2.37764i	0.635999	−	0.163297i
$213$	6.69133	−	8.08843i	0.458482	−	0.554210i
$214$	−3.38583	+	1.34054i	−0.231450	+	0.0916377i
$215$	2.52745	+	2.85153i	0.172370	+	0.194473i
$216$	0.535827	+	0.844328i	0.0364584	+	0.0574492i
$217$	0.552491	+	2.89626i	0.0375056	+	0.196611i
$218$	−1.36309	−	4.19515i	−0.0923200	−	0.284132i
$219$	−3.78737	+	8.04856i	−0.255926	+	0.543871i
$220$	7.66252	−	9.93277i	0.516607	−	0.669667i
$221$	−7.60568	−	4.18126i	−0.511613	−	0.281262i
$222$	−2.07667	−	1.14166i	−0.139377	−	0.0766231i
$223$	−1.97920	−	2.39245i	−0.132537	−	0.160210i	0.700069	−	0.714075i	$-0.253152\pi$
$223$	−1.97920	−	2.39245i	−0.132537	−	0.160210i	−0.832607	+	0.553865i	$0.813152\pi$
$224$	−0.320263	−	0.232684i	−0.0213984	−	0.0155469i
$225$	−4.51277	+	2.15288i	−0.300852	+	0.143525i
$226$	4.44506	−	3.22952i	0.295681	−	0.214825i
$227$	18.5054	+	4.75137i	1.22825	+	0.315360i	0.806434	−	0.591324i	$-0.201395\pi$
$227$	18.5054	+	4.75137i	1.22825	+	0.315360i	0.421811	+	0.906684i	$0.361395\pi$
$228$	0.555334	+	1.18015i	0.0367779	+	0.0781570i
$229$	0.979186	−	5.13307i	0.0647064	−	0.339203i	−0.935182	−	0.354169i	$-0.884764\pi$
$229$	0.979186	−	5.13307i	0.0647064	−	0.339203i	0.999888	+	0.0149657i	$0.00476391\pi$
$230$	−0.292082	−	1.29060i	−0.0192593	−	0.0850998i
$231$	1.61897	+	1.52031i	0.106520	+	0.100029i
$232$	−4.91073	−	3.56786i	−0.322405	−	0.234241i
$233$	−0.0451188	+	0.0958824i	−0.00295583	+	0.00628146i	−0.906300	−	0.422636i	$-0.861105\pi$
$233$	−0.0451188	+	0.0958824i	−0.00295583	+	0.00628146i	0.903344	+	0.428917i	$0.141105\pi$
$234$	−1.13297	+	1.36952i	−0.0740644	+	0.0895285i
$235$	−5.02854	+	11.7054i	−0.328026	+	0.763575i
$236$	−0.405576	−	6.44645i	−0.0264008	−	0.419628i
$237$	−0.0463590	+	0.736855i	−0.00301134	+	0.0478639i
$238$	1.79730	+	0.711601i	0.116502	+	0.0461262i
$239$	−13.0778	+	20.6073i	−0.845934	+	1.33298i	0.0953781	+	0.995441i	$0.469594\pi$
$239$	−13.0778	+	20.6073i	−0.845934	+	1.33298i	−0.941312	+	0.337537i	$0.890406\pi$
$240$	−1.99504	−	1.00986i	−0.128779	−	0.0651864i
$241$	−0.235644	+	3.74545i	−0.0151791	+	0.241266i	0.983120	+	0.182963i	$0.0585688\pi$
$241$	−0.235644	+	3.74545i	−0.0151791	+	0.241266i	−0.998299	+	0.0583026i	$0.981431\pi$
$242$	−20.3134	−	2.56618i	−1.30579	−	0.164960i
$243$	−0.809017	+	0.587785i	−0.0518985	+	0.0377064i
$244$	1.20626	+	6.32345i	0.0772230	+	0.404817i
$245$	−10.1499	−	11.4514i	−0.648451	−	0.731600i
$246$	2.42672	+	5.15703i	0.154722	+	0.328801i
$247$	−1.68993	+	1.58695i	−0.107527	+	0.100975i
$248$	−3.99094	+	6.28871i	−0.253425	+	0.399334i
$249$	11.3289			0.717941
$250$	6.21047	−	9.29678i	0.392785	−	0.587980i
$251$	−11.0601			−0.698106			−0.349053	−	0.937103i	$-0.613497\pi$
$251$	−11.0601			−0.698106			−0.349053	+	0.937103i	$0.613497\pi$
$252$	0.212116	−	0.334241i	0.0133620	−	0.0210552i
$253$	−2.42016	+	2.27268i	−0.152154	+	0.142882i
$254$	2.47814	+	5.26632i	0.155492	+	0.330438i
$255$	10.6622	+	2.35359i	0.667693	+	0.147388i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	−12.8212	+	9.31514i	−0.799764	+	0.581062i	−0.910845	−	0.412749i	$-0.864569\pi$
$257$	−12.8212	+	9.31514i	−0.799764	+	0.581062i	0.111081	+	0.993811i	$0.464569\pi$
$258$	−1.69063	−	0.213576i	−0.105254	−	0.0132967i
$259$	−0.0589052	+	0.936272i	−0.00366019	+	0.0581771i
$260$	0.611318	−	3.92713i	0.0379123	−	0.243550i
$261$	3.25247	−	5.12507i	0.201323	−	0.317234i
$262$	−18.9473	−	7.50177i	−1.17057	−	0.463461i
$263$	−1.17307	+	18.6454i	−0.0723347	+	1.14973i	0.779669	+	0.626191i	$0.215387\pi$
$263$	−1.17307	+	18.6454i	−0.0723347	+	1.14973i	−0.852004	+	0.523535i	$0.824613\pi$
$264$	0.352270	+	5.59917i	0.0216807	+	0.344605i
$265$	−16.0735	−	14.0951i	−0.987389	−	0.865854i
$266$	0.329114	−	0.397831i	0.0201793	−	0.0243926i
$267$	−1.34271	+	2.85340i	−0.0821724	+	0.174625i
$268$	12.2327	+	8.88760i	0.747233	+	0.542897i
$269$	18.3529	+	17.2345i	1.11900	+	1.05081i	0.998310	+	0.0581163i	$0.0185094\pi$
$269$	18.3529	+	17.2345i	1.11900	+	1.05081i	0.120686	+	0.992691i	$0.461491\pi$
$270$	0.882601	−	2.05451i	0.0537134	−	0.125034i
$271$	0.00198508	−	0.0104061i	0.000120585	−	0.000632128i	−0.982227	−	0.187697i	$-0.939898\pi$
$271$	0.00198508	−	0.0104061i	0.000120585	−	0.000632128i	0.982347	+	0.187065i	$0.0598976\pi$
$272$	2.07911	+	4.41833i	0.126065	+	0.267901i
$273$	0.681513	+	0.174983i	0.0412471	+	0.0105904i
$274$	14.1094	−	10.2511i	0.852378	−	0.619289i
$275$	−28.0048	−	1.61275i	−1.68875	−	0.0972523i
$276$	0.478753	+	0.347834i	0.0288175	+	0.0209372i
$277$	0.939606	+	1.13579i	0.0564555	+	0.0682429i	0.797985	−	0.602677i	$-0.205899\pi$
$277$	0.939606	+	1.13579i	0.0564555	+	0.0682429i	−0.741530	+	0.670920i	$0.765899\pi$
$278$	7.99029	+	4.39270i	0.479226	+	0.263457i
$279$	−6.52690	−	3.58819i	−0.390755	−	0.214819i
$280$	−0.0254564	+	0.884818i	−0.00152131	+	0.0528780i
$281$	8.62855	−	18.3366i	0.514736	−	1.09387i	−0.463447	−	0.886125i	$-0.653388\pi$
$281$	8.62855	−	18.3366i	0.514736	−	1.09387i	0.978183	−	0.207745i	$-0.0666124\pi$
$282$	−1.76060	−	5.41856i	−0.104842	−	0.322670i
$283$	−2.89706	−	15.1869i	−0.172212	−	0.902769i	−0.958540	−	0.284959i	$-0.908020\pi$
$283$	−2.89706	−	15.1869i	−0.172212	−	0.902769i	0.786327	−	0.617810i	$-0.211980\pi$
$284$	−5.62482	−	8.86329i	−0.333772	−	0.525940i
$285$	1.47793	−	2.51424i	0.0875449	−	0.148931i
$286$	−9.27148	+	3.67084i	−0.548234	+	0.217061i
$287$	1.43817	−	1.73845i	0.0848927	−	0.102618i
$288$	0.968583	−	0.248690i	0.0570743	−	0.0146542i
$289$	−4.36277	−	5.27368i	−0.256633	−	0.310216i
$290$	−0.390335	+	13.5673i	−0.0229213	+	0.796700i
$291$	−9.60375	+	2.46582i	−0.562982	+	0.144549i
$292$	6.48428	+	6.08914i	0.379464	+	0.356340i
$293$	3.78851	−	11.6598i	0.221327	−	0.681175i	−0.777317	−	0.629110i	$-0.783420\pi$
$293$	3.78851	−	11.6598i	0.221327	−	0.681175i	0.998644	−	0.0520653i	$-0.0165804\pi$
$294$	6.78933	+	0.857692i	0.395962	+	0.0500216i
$295$	−11.3888	+	8.88259i	−0.663084	+	0.517164i
$296$	−1.72751	+	1.62224i	−0.100409	+	0.0942907i
$297$	−5.56600	+	0.703150i	−0.322972	+	0.0408009i
$298$	0.123505	+	1.96305i	0.00715443	+	0.113716i
$299$	−0.325031	+	1.00034i	−0.0187970	+	0.0578513i
$300$	0.652984	+	4.95718i	0.0377000	+	0.286203i
$301$	0.208458	+	0.641566i	0.0120153	+	0.0369793i
$302$	19.5280	−	7.73168i	1.12371	−	0.444908i
$303$	1.91799	−	10.0545i	0.110186	−	0.577614i
$304$	1.29399	−	0.163469i	0.0742156	−	0.00937561i
$305$	10.1515	−	10.2055i	0.581273	−	0.584366i
$306$	−4.27907	+	2.35244i	−0.244618	+	0.134480i
$307$	10.9971			0.627639			0.313819	−	0.949483i	$-0.398391\pi$
$307$	10.9971			0.627639			0.313819	+	0.949483i	$0.398391\pi$
$308$	1.94619	−	1.06993i	0.110895	−	0.0609649i
$309$	15.0899	+	5.97450i	0.858433	+	0.339878i
$310$	16.6450	−	0.567306i	0.945372	−	0.0322208i
$311$	7.88158	+	2.02365i	0.446924	+	0.114750i	0.465443	−	0.885078i	$-0.345895\pi$
$311$	7.88158	+	2.02365i	0.446924	+	0.114750i	−0.0185190	+	0.999829i	$0.505895\pi$
$312$	0.952387	+	1.50072i	0.0539183	+	0.0849616i
$313$	5.79923	+	9.13813i	0.327792	+	0.516518i	0.967757	−	0.251887i	$-0.0810511\pi$
$313$	5.79923	+	9.13813i	0.327792	+	0.516518i	−0.639965	+	0.768404i	$0.721051\pi$
$314$	−16.6781	−	4.28220i	−0.941198	−	0.241659i
$315$	−0.884670	+	0.0301520i	−0.0498455	+	0.00169887i
$316$	0.686465	+	0.271791i	0.0386167	+	0.0152894i
$317$	−11.9675	+	6.57922i	−0.672164	+	0.369526i	−0.780997	−	0.624535i	$-0.785289\pi$
$317$	−11.9675	+	6.57922i	−0.672164	+	0.369526i	0.108833	+	0.994060i	$0.465289\pi$
$318$	9.56065			0.536134
$319$	29.8419	−	16.4057i	1.67083	−	0.918544i
$320$	−1.57694	+	1.58533i	−0.0881535	+	0.0886226i
$321$	−3.61284	+	0.456407i	−0.201649	+	0.0254742i
$322$	0.0438964	−	0.230113i	0.00244625	−	0.0128237i
$323$	−5.92163	+	2.34454i	−0.329488	+	0.130454i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−8.02107	+	3.82656i	−0.444929	+	0.212259i
$326$	−5.85954	+	18.0338i	−0.324530	+	0.998801i
$327$	−0.276972	−	4.40234i	−0.0153166	−	0.243450i
$328$	5.65453	−	0.714333i	0.312219	−	0.0394424i
$329$	−1.64412	+	1.54394i	−0.0906435	+	0.0851199i
$330$	9.89196	−	7.71512i	0.544535	−	0.424704i
$331$	26.8245	+	3.38872i	1.47441	+	0.186261i	0.821079	−	0.570815i	$-0.193373\pi$
$331$	26.8245	+	3.38872i	1.47441	+	0.186261i	0.653327	+	0.757076i	$0.273373\pi$
$332$	3.50083	−	10.7744i	0.192133	−	0.591324i
$333$	−1.72751	−	1.62224i	−0.0946669	−	0.0888981i
$334$	−4.21081	+	1.08115i	−0.230405	+	0.0591581i
$335$	0.972333	−	33.7965i	0.0531242	−	1.84650i
$336$	−0.252335	−	0.305020i	−0.0137660	−	0.0166402i
$337$	−8.24591	+	2.11719i	−0.449183	+	0.115331i	−0.466504	−	0.884519i	$-0.654487\pi$
$337$	−8.24591	+	2.11719i	−0.449183	+	0.115331i	0.0173203	+	0.999850i	$0.494487\pi$
$338$	6.27276	−	7.58246i	0.341193	−	0.412432i
$339$	5.10856	−	2.02262i	0.277459	−	0.109854i
$340$	5.53320	−	9.41305i	0.300080	−	0.510494i
$341$	−22.3901	−	35.2812i	−1.21249	−	1.91058i
$342$	0.244397	+	1.28117i	0.0132155	+	0.0692780i
$343$	−1.69344	−	5.21188i	−0.0914372	−	0.281415i
$344$	−0.725557	+	1.54189i	−0.0391194	+	0.0831329i
$345$	0.0380542	−	1.32269i	0.00204877	−	0.0712114i
$346$	−7.48670	−	4.11585i	−0.402487	−	0.221269i
$347$	8.04668	+	4.42370i	0.431969	+	0.237477i	0.682876	−	0.730534i	$-0.260729\pi$
$347$	8.04668	+	4.42370i	0.431969	+	0.237477i	−0.250907	+	0.968011i	$0.580729\pi$
$348$	−3.86916	−	4.67701i	−0.207409	−	0.250714i
$349$	−16.5615	−	12.0327i	−0.886518	−	0.644093i	0.0484495	−	0.998826i	$-0.484572\pi$
$349$	−16.5615	−	12.0327i	−0.886518	−	0.644093i	−0.934968	+	0.354732i	$0.884572\pi$
$350$	1.66555	−	1.06943i	0.0890275	−	0.0571636i
$351$	−1.43796	+	1.04474i	−0.0767526	+	0.0557640i
$352$	5.43399	+	1.39521i	0.289632	+	0.0743650i
$353$	−11.5573	−	24.5606i	−0.615134	−	1.30723i	−0.933268	−	0.359181i	$-0.883056\pi$
$353$	−11.5573	−	24.5606i	−0.615134	−	1.30723i	0.318134	−	0.948046i	$-0.396944\pi$
$354$	1.21033	−	6.34479i	0.0643284	−	0.337222i
$355$	−9.26506	+	21.5671i	−0.491739	+	1.14466i
$356$	2.29883	+	2.15874i	0.121838	+	0.114413i
$357$	1.56386	+	1.13621i	0.0827685	+	0.0601348i
$358$	0.0270629	−	0.0575116i	0.00143032	−	0.00303958i
$359$	−11.1140	+	13.4345i	−0.586575	+	0.709048i	−0.977395	−	0.211419i	$-0.932191\pi$
$359$	−11.1140	+	13.4345i	−0.586575	+	0.709048i	0.390820	+	0.920467i	$0.372191\pi$
$360$	−1.68122	−	1.47428i	−0.0886079	−	0.0777015i
$361$	−1.08620	−	17.2647i	−0.0571687	−	0.908670i
$362$	1.33598	−	21.2347i	0.0702173	−	1.11607i
$363$	−19.0370	−	7.53728i	−0.999184	−	0.395605i
$364$	0.377018	−	0.594085i	0.0197611	−	0.0311385i
$365$	3.05936	−	19.6534i	0.160134	−	1.02871i
$366$	−0.404212	+	6.42477i	−0.0211285	+	0.335828i
$367$	−27.0133	−	3.41258i	−1.41008	−	0.178135i	−0.616864	−	0.787070i	$-0.711597\pi$
$367$	−27.0133	−	3.41258i	−1.41008	−	0.178135i	−0.793220	+	0.608935i	$0.791597\pi$
$368$	0.478753	−	0.347834i	0.0249567	−	0.0181321i
$369$	1.06797	+	5.59852i	0.0555965	+	0.291447i
$370$	5.17446	+	1.14222i	0.269007	+	0.0593812i
$371$	−1.61146	−	3.42453i	−0.0836630	−	0.177793i
$372$	−5.42950	+	5.09864i	−0.281506	+	0.264352i
$373$	−8.77339	+	13.8247i	−0.454269	+	0.715813i	−0.991852	−	0.127398i	$-0.959338\pi$
$373$	−8.77339	+	13.8247i	−0.454269	+	0.715813i	0.537583	+	0.843211i	$0.319338\pi$
$374$	−27.3952			−1.41657
$375$	8.32737	−	7.46022i	0.430024	−	0.385244i
$376$	−5.69741			−0.293821
$377$	5.78099	−	9.10938i	0.297736	−	0.469157i
$378$	0.288574	−	0.270989i	0.0148427	−	0.0139382i
$379$	2.90149	+	6.16599i	0.149040	+	0.316725i	0.965381	−	0.260845i	$-0.0840010\pi$
$379$	2.90149	+	6.16599i	0.149040	+	0.316725i	−0.816341	+	0.577570i	$0.804001\pi$
$380$	−1.93448	−	2.18254i	−0.0992369	−	0.111962i
$381$	1.09061	+	5.71716i	0.0558734	+	0.292899i
$382$	−2.62253	+	1.90538i	−0.134181	+	0.0974879i
$383$	−5.17679	−	0.653981i	−0.264522	−	0.0334169i	−0.00804631	−	0.999968i	$-0.502561\pi$
$383$	−5.17679	−	0.653981i	−0.264522	−	0.0334169i	−0.256475	+	0.966551i	$0.582561\pi$
$384$	0.0627905	−	0.998027i	0.00320427	−	0.0509303i
$385$	−4.43079	−	2.24281i	−0.225814	−	0.114304i
$386$	−8.54451	+	13.4640i	−0.434904	+	0.685300i
$387$	−1.58440	−	0.627309i	−0.0805397	−	0.0318879i
$388$	−0.622584	+	9.89569i	−0.0316069	+	0.502378i
$389$	0.377047	+	5.99300i	0.0191171	+	0.303857i	0.995954	+	0.0898698i	$0.0286451\pi$
$389$	0.377047	+	5.99300i	0.0191171	+	0.303857i	−0.976836	+	0.213987i	$0.931355\pi$
$390$	1.56875	−	3.65172i	0.0794367	−	0.184912i
$391$	−1.84194	+	2.22652i	−0.0931508	+	0.112600i
$392$	2.91373	−	6.19199i	0.147166	−	0.312743i
$393$	−16.4864	−	11.9781i	−0.831631	−	0.604215i
$394$	15.3593	+	14.4233i	0.773789	+	0.726636i
$395$	−0.364410	−	1.61020i	−0.0183355	−	0.0810177i
$396$	−1.05125	+	5.51087i	−0.0528275	+	0.276932i
$397$	6.30670	+	13.4024i	0.316524	+	0.672648i	0.998261	−	0.0589495i	$-0.0187751\pi$
$397$	6.30670	+	13.4024i	0.316524	+	0.672648i	−0.681737	+	0.731597i	$0.738775\pi$
$398$	1.43155	+	0.367559i	0.0717569	+	0.0184240i
$399$	0.417711	−	0.303485i	0.0209117	−	0.0151933i
$400$	4.91634	+	0.910828i	0.245817	+	0.0455414i
$401$	15.2888	+	11.1080i	0.763488	+	0.554706i	0.899978	−	0.435935i	$-0.143582\pi$
$401$	15.2888	+	11.1080i	0.763488	+	0.554706i	−0.136490	+	0.990641i	$0.543582\pi$
$402$	9.63816	+	11.6505i	0.480708	+	0.581076i
$403$	−11.6010	−	6.37771i	−0.577887	−	0.317696i
$404$	−8.96967	−	4.93112i	−0.446258	−	0.245332i
$405$	1.36581	−	1.77047i	0.0678676	−	0.0879754i
$406$	−1.02311	+	2.17422i	−0.0507760	+	0.107905i
$407$	−4.10843	−	12.6444i	−0.203647	−	0.626761i
$408$	0.914996	+	4.79658i	0.0452991	+	0.237466i
$409$	−11.0796	−	17.4587i	−0.547853	−	0.863278i	0.451730	−	0.892155i	$-0.350807\pi$
$409$	−11.0796	−	17.4587i	−0.547853	−	0.863278i	−0.999583	+	0.0288770i	$0.990807\pi$
$410$	−8.45336	−	9.53732i	−0.417482	−	0.471015i
$411$	16.2154	−	6.42014i	0.799848	−	0.316682i
$412$	10.3451	−	12.5051i	0.509667	−	0.616082i
$413$	−2.47665	+	0.635894i	−0.121868	+	0.0312903i
$414$	0.377209	+	0.455967i	0.0185388	+	0.0224096i
$415$	−24.3075	+	7.13199i	−1.19321	+	0.350096i
$416$	1.72157	−	0.442025i	0.0844071	−	0.0216721i
$417$	6.64684	+	6.24180i	0.325497	+	0.305662i
$418$	−2.26117	+	6.95918i	−0.110598	+	0.340384i
$419$	31.1093	+	3.93002i	1.51979	+	0.191994i	0.840475	−	0.541851i	$-0.182276\pi$
$419$	31.1093	+	3.93002i	1.51979	+	0.191994i	0.679317	+	0.733845i	$0.262276\pi$
$420$	−0.244702	+	0.850689i	−0.0119402	+	0.0415094i
$421$	−0.685297	+	0.643537i	−0.0333993	+	0.0313641i	−0.701067	−	0.713095i	$-0.747293\pi$
$421$	−0.685297	+	0.643537i	−0.0333993	+	0.0313641i	0.667668	+	0.744459i	$0.267293\pi$
$422$	20.4503	−	2.58347i	0.995505	−	0.125762i
$423$	−0.357743	−	5.68617i	−0.0173941	−	0.276471i
$424$	2.95440	−	9.09271i	0.143478	−	0.441581i
$425$	−24.3587	+	1.66235i	−1.18157	+	0.0806359i
$426$	−3.24389	−	9.98367i	−0.157167	−	0.483711i
$427$	2.36942	−	0.938121i	0.114664	−	0.0453988i
$428$	−0.682359	+	3.57705i	−0.0329830	+	0.172903i
$429$	−9.89310	+	1.24979i	−0.477643	+	0.0603404i
$430$	3.76190	−	0.606064i	0.181415	−	0.0292270i
$431$	−24.9311	+	13.7060i	−1.20089	+	0.660194i	−0.951332	−	0.308167i	$-0.900285\pi$
$431$	−24.9311	+	13.7060i	−1.20089	+	0.660194i	−0.249556	+	0.968360i	$0.580285\pi$
$432$	1.00000			0.0481125
$433$	5.77467	−	3.17465i	0.277513	−	0.152564i	−0.336920	−	0.941533i	$-0.609385\pi$
$433$	5.77467	−	3.17465i	0.277513	−	0.152564i	0.614432	+	0.788969i	$0.289385\pi$
$434$	2.74143	+	1.08541i	0.131593	+	0.0521014i
$435$	−3.75213	+	13.0440i	−0.179901	+	0.625412i
$436$	−4.27247	−	1.09698i	−0.204614	−	0.0525359i
$437$	0.413569	+	0.651681i	0.0197837	+	0.0311741i
$438$	4.76625	+	7.51041i	0.227740	+	0.358861i
$439$	7.52090	+	1.93104i	0.358953	+	0.0921634i	0.423860	−	0.905728i	$-0.360675\pi$
$439$	7.52090	+	1.93104i	0.358953	+	0.0921634i	−0.0649068	+	0.997891i	$0.520675\pi$
$440$	−4.28073	−	11.7919i	−0.204076	−	0.562158i
$441$	6.36273	+	2.51918i	0.302987	+	0.119961i
$442$	−7.60568	+	4.18126i	−0.361765	+	0.198882i
$443$	−9.33775			−0.443650			−0.221825	−	0.975087i	$-0.571201\pi$
$443$	−9.33775			−0.443650			−0.221825	+	0.975087i	$0.571201\pi$
$444$	−2.07667	+	1.14166i	−0.0985544	+	0.0541807i
$445$	1.08461	−	6.96760i	0.0514156	−	0.330296i
$446$	−3.08052	+	0.389160i	−0.145867	+	0.0184273i
$447$	−0.368566	+	1.93209i	−0.0174326	+	0.0913847i
$448$	−0.368067	+	0.145728i	−0.0173895	+	0.00688501i
$449$	−10.6967	−	32.9212i	−0.504811	−	1.55365i	−0.801089	−	0.598546i	$-0.795745\pi$
$449$	−10.6967	−	32.9212i	−0.504811	−	1.55365i	0.296278	−	0.955102i	$-0.404255\pi$
$450$	−0.600331	+	4.96383i	−0.0282999	+	0.233997i
$451$	−9.88095	+	30.4104i	−0.465276	+	1.43197i
$452$	−0.344996	−	5.48355i	−0.0162272	−	0.257924i
$453$	20.8373	−	2.63236i	0.979020	−	0.123679i
$454$	13.9274	−	13.0787i	0.653645	−	0.613814i
$455$	−1.57243	+	0.0535926i	−0.0737165	+	0.00251246i
$456$	1.29399	+	0.163469i	0.0605968	+	0.00765515i
$457$	5.79042	−	17.8211i	0.270864	−	0.833634i	−0.719420	−	0.694575i	$-0.755592\pi$
$457$	5.79042	−	17.8211i	0.270864	−	0.833634i	0.990284	−	0.139059i	$-0.0444077\pi$
$458$	−3.80932	−	3.57719i	−0.177998	−	0.167151i
$459$	−4.72966	+	1.21437i	−0.220762	+	0.0566819i
$460$	−1.24620	−	0.444926i	−0.0581042	−	0.0207448i
$461$	−8.53613	−	10.3184i	−0.397567	−	0.480576i	0.533304	−	0.845924i	$-0.320950\pi$
$461$	−8.53613	−	10.3184i	−0.397567	−	0.480576i	−0.930871	+	0.365347i	$0.880950\pi$
$462$	2.15113	−	0.552317i	0.100080	−	0.0256961i
$463$	−7.20965	+	8.71497i	−0.335061	+	0.405019i	−0.910955	−	0.412505i	$-0.864654\pi$
$463$	−7.20965	+	8.71497i	−0.335061	+	0.405019i	0.575894	+	0.817524i	$0.304654\pi$
$464$	−5.64374	+	2.23452i	−0.262004	+	0.103735i
$465$	16.2631	+	3.58996i	0.754185	+	0.166480i
$466$	0.0567803	+	0.0894714i	0.00263030	+	0.00414468i
$467$	1.71640	+	8.99768i	0.0794255	+	0.416363i	0.999686	+	0.0250569i	$0.00797670\pi$
$467$	1.71640	+	8.99768i	0.0794255	+	0.416363i	−0.920260	+	0.391306i	$0.872023\pi$
$468$	0.549252	+	1.69042i	0.0253892	+	0.0781398i
$469$	2.54858	−	5.41602i	0.117683	−	0.250088i
$470$	7.18876	+	10.5178i	0.331593	+	0.485150i
$471$	−15.0892	−	8.29534i	−0.695272	−	0.382229i
$472$	−5.66024	−	3.11174i	−0.260533	−	0.143229i
$473$	−6.09392	−	7.36628i	−0.280199	−	0.338702i
$474$	0.597307	+	0.433969i	0.0274352	+	0.0199329i
$475$	−1.58826	+	6.32502i	−0.0728742	+	0.290212i
$476$	1.56386	−	1.13621i	0.0716796	−	0.0520783i
$477$	9.26028	+	2.37764i	0.423999	+	0.108864i
$478$	10.3919	+	22.0839i	0.475315	+	1.01010i
$479$	1.90468	−	9.98470i	0.0870272	−	0.456212i	−0.911921	−	0.410365i	$-0.865401\pi$
$479$	1.90468	−	9.98470i	0.0870272	−	0.456212i	0.998948	−	0.0458473i	$-0.0145988\pi$
$480$	−1.92165	+	1.14335i	−0.0877109	+	0.0521868i
$481$	−3.07050	−	2.88339i	−0.140003	−	0.131471i
$482$	3.03612	+	2.20587i	0.138292	+	0.100475i
$483$	0.0997440	−	0.211967i	0.00453851	−	0.00964482i
$484$	−13.0511	+	15.7761i	−0.593234	+	0.717096i
$485$	19.0537	−	11.3367i	0.865182	−	0.514771i
$486$	0.0627905	+	0.998027i	0.00284824	+	0.0452714i
$487$	1.05150	−	16.7130i	0.0476478	−	0.757340i	−0.899575	−	0.436765i	$-0.856124\pi$
$487$	1.05150	−	16.7130i	0.0476478	−	0.757340i	0.947223	−	0.320575i	$-0.103876\pi$
$488$	5.98541	+	2.36979i	0.270947	+	0.107275i
$489$	−10.1603	+	16.0100i	−0.459464	+	0.723999i
$490$	−15.1073	+	2.43387i	−0.682477	+	0.109951i
$491$	−0.361761	+	5.75003i	−0.0163261	+	0.259495i	0.981394	+	0.192005i	$0.0614991\pi$
$491$	−0.361761	+	5.75003i	−0.0163261	+	0.259495i	−0.997720	+	0.0674900i	$0.978501\pi$
$492$	5.65453	+	0.714333i	0.254926	+	0.0322046i
$493$	23.9794	−	17.4221i	1.07998	−	0.784651i
$494$	0.434395	+	2.27718i	0.0195444	+	0.102455i
$495$	11.4999	−	5.01271i	0.516880	−	0.225304i
$496$	3.17128	+	6.73932i	0.142395	+	0.302604i
$497$	−3.02929	+	2.84470i	−0.135882	+	0.127602i
$498$	6.07033	−	9.56532i	0.272018	−	0.428632i
$499$	44.4080			1.98798			0.993988	−	0.109486i	$-0.0349205\pi$
$499$	44.4080			1.98798			0.993988	+	0.109486i	$0.0349205\pi$
$500$	−4.52179	−	10.2251i	−0.202221	−	0.457282i
$501$	−4.34740			−0.194227
$502$	−5.92629	+	9.33834i	−0.264503	+	0.416790i
$503$	−26.3697	+	24.7628i	−1.17577	+	1.10412i	−0.183120	+	0.983091i	$0.558620\pi$
$503$	−26.3697	+	24.7628i	−1.17577	+	1.10412i	−0.992649	+	0.121029i	$0.961380\pi$
$504$	−0.168552	−	0.358191i	−0.00750789	−	0.0159551i
$505$	2.21440	+	22.7805i	0.0985393	+	1.01372i
$506$	0.622102	+	3.26117i	0.0276558	+	0.144977i
$507$	7.96137	−	5.78427i	0.353577	−	0.256889i
$508$	5.77435	+	0.729471i	0.256196	+	0.0323650i
$509$	0.726760	−	11.5515i	0.0322131	−	0.512012i	−0.948527	−	0.316696i	$-0.897427\pi$
$509$	0.726760	−	11.5515i	0.0322131	−	0.512012i	0.980740	−	0.195316i	$-0.0625734\pi$
$510$	7.70030	−	7.74127i	0.340975	−	0.342789i
$511$	1.88680	−	2.97312i	0.0834671	−	0.131523i
$512$	−0.929776	−	0.368125i	−0.0410907	−	0.0162690i
$513$	−0.0818962	+	1.30170i	−0.00361581	+	0.0574716i
$514$	0.995096	+	15.8166i	0.0438918	+	0.697640i
$515$	−36.1383	−	3.31935i	−1.59244	−	0.146268i
$516$	−1.08621	+	1.31301i	−0.0478179	+	0.0578019i
$517$	13.6095	−	28.9218i	0.598547	−	1.27198i
$518$	0.758958	+	0.551415i	0.0333467	+	0.0242278i
$519$	−6.22792	−	5.84841i	−0.273375	−	0.256717i
$520$	−2.98822	−	2.62041i	−0.131042	−	0.114913i
$521$	−0.487085	+	2.55339i	−0.0213396	+	0.111866i	−0.991363	−	0.131144i	$-0.958135\pi$
$521$	−0.487085	+	2.55339i	−0.0213396	+	0.111866i	0.970024	+	0.243010i	$0.0781349\pi$
$522$	−2.58448	−	5.49230i	−0.113120	−	0.240391i
$523$	−32.0818	−	8.23721i	−1.40284	−	0.360188i	−0.529919	−	0.848048i	$-0.677778\pi$
$523$	−32.0818	−	8.23721i	−1.40284	−	0.360188i	−0.872922	+	0.487860i	$0.837778\pi$
$524$	−16.4864	+	11.9781i	−0.720213	+	0.523265i
$525$	1.87918	−	0.621629i	0.0820143	−	0.0271301i
$526$	15.1143	+	10.9812i	0.659015	+	0.478802i
$527$	−23.1831	−	28.0236i	−1.00987	−	1.22073i
$528$	4.91629	+	2.70275i	0.213954	+	0.117622i
$529$	−19.8482	−	10.9116i	−0.862964	−	0.474419i
$530$	−20.5135	+	6.01880i	−0.891050	+	0.261440i
$531$	2.75019	−	5.84445i	0.119348	−	0.253628i
$532$	−0.159551	−	0.491049i	−0.00691743	−	0.0212897i
$533$	1.89823	+	9.95089i	0.0822216	+	0.431021i
$534$	1.68975	+	2.66261i	0.0731225	+	0.115223i
$535$	7.46444	−	3.25370i	0.322716	−	0.140670i
$536$	14.0587	−	5.56622i	0.607242	−	0.240424i
$537$	0.0405152	−	0.0489745i	0.00174836	−	0.00211341i
$538$	24.3856	−	6.26115i	1.05134	−	0.269937i
$539$	24.4723	+	29.5819i	1.05410	+	1.27418i
$540$	−1.26176	−	1.84607i	−0.0542975	−	0.0794421i
$541$	7.12640	−	1.82975i	0.306388	−	0.0786671i	−0.0923656	−	0.995725i	$-0.529443\pi$
$541$	7.12640	−	1.82975i	0.306388	−	0.0786671i	0.398754	+	0.917058i	$0.369443\pi$
$542$	−0.00772253	−	0.00725194i	−0.000331711	−	0.000311498i
$543$	6.57486	−	20.2354i	0.282154	−	0.868382i
$544$	4.84457	+	0.612011i	0.207709	+	0.0262398i
$545$	3.36572	+	9.27139i	0.144172	+	0.397143i
$546$	0.512916	−	0.481660i	0.0219508	−	0.0206132i
$547$	14.7114	−	1.85848i	0.629013	−	0.0794628i	0.195637	−	0.980676i	$-0.437322\pi$
$547$	14.7114	−	1.85848i	0.629013	−	0.0794628i	0.433375	+	0.901213i	$0.357322\pi$
$548$	−1.09507	−	17.4057i	−0.0467793	−	0.743535i
$549$	−1.98929	+	6.12240i	−0.0849008	+	0.261298i
$550$	−16.3674	+	22.7811i	−0.697909	+	0.971389i
$551$	−2.44648	−	7.52948i	−0.104223	−	0.320767i
$552$	0.550215	−	0.217845i	0.0234187	−	0.00927212i
$553$	0.0547665	−	0.287096i	0.00232891	−	0.0122086i
$554$	1.46244	−	0.184750i	0.0621333	−	0.00784926i
$555$	4.72784	+	2.39317i	0.200686	+	0.101584i
$556$	7.99029	−	4.39270i	0.338864	−	0.186292i
$557$	26.2009			1.11017			0.555083	−	0.831795i	$-0.312686\pi$
$557$	26.2009			1.11017			0.555083	+	0.831795i	$0.312686\pi$
$558$	−6.52690	+	3.58819i	−0.276306	+	0.151900i
$559$	−2.81614	−	1.11499i	−0.119110	−	0.0471590i
$560$	0.733436	+	0.495603i	0.0309933	+	0.0209430i
$561$	−26.5345	−	6.81291i	−1.12029	−	0.287641i
$562$	−10.8587	−	17.1106i	−0.458046	−	0.721765i
$563$	−10.5875	−	16.6833i	−0.446211	−	0.703117i	0.544551	−	0.838728i	$-0.316700\pi$
$563$	−10.5875	−	16.6833i	−0.446211	−	0.703117i	−0.990762	+	0.135611i	$0.956700\pi$
$564$	−5.51841	−	1.41689i	−0.232367	−	0.0596618i
$565$	−9.68770	+	7.55581i	−0.407564	+	0.317875i
$566$	−14.3751	−	5.69149i	−0.604229	−	0.239231i
$567$	0.346900	−	0.190710i	0.0145684	−	0.00800907i
$568$	−10.4975			−0.440463
$569$	34.4121	−	18.9182i	1.44263	−	0.793092i	0.447750	−	0.894159i	$-0.352225\pi$
$569$	34.4121	−	18.9182i	1.44263	−	0.793092i	0.994880	+	0.101066i	$0.0322254\pi$
$570$	−1.33093	−	2.59506i	−0.0557466	−	0.108695i
$571$	16.0623	−	2.02914i	0.672185	−	0.0849167i	0.218170	−	0.975911i	$-0.429991\pi$
$571$	16.0623	−	2.02914i	0.672185	−	0.0849167i	0.454015	+	0.890994i	$0.349991\pi$
$572$	−1.86852	+	9.79511i	−0.0781266	+	0.409554i
$573$	−3.01399	+	1.19332i	−0.125911	+	0.0498518i
$574$	−0.697213	−	2.14580i	−0.0291011	−	0.0895640i
$575$	0.751037	+	2.86195i	0.0313204	+	0.119352i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	2.58908	+	41.1522i	0.107785	+	1.71319i	0.566047	+	0.824373i	$0.308472\pi$
$577$	2.58908	+	41.1522i	0.107785	+	1.71319i	−0.458263	+	0.888817i	$0.651528\pi$
$578$	−6.79040	+	0.857827i	−0.282444	+	0.0356809i
$579$	−11.6244	+	10.9161i	−0.483095	+	0.453656i
$580$	11.2461	+	7.59930i	0.466969	+	0.315544i
$581$	−4.44937	−	0.562086i	−0.184591	−	0.0233193i
$582$	−3.06398	+	9.42997i	−0.127006	+	0.390885i
$583$	39.1001	+	36.7174i	1.61936	+	1.52068i
$584$	8.61568	−	2.21213i	0.356519	−	0.0915386i
$585$	2.42761	−	3.14686i	0.100369	−	0.130107i
$586$	−7.81474	−	9.44640i	−0.322824	−	0.390227i
$587$	34.3108	−	8.80952i	1.41616	−	0.363608i	0.538392	−	0.842695i	$-0.319032\pi$
$587$	34.3108	−	8.80952i	1.41616	−	0.363608i	0.877768	+	0.479087i	$0.159032\pi$
$588$	4.36208	−	5.27285i	0.179889	−	0.217448i
$589$	−9.03232	+	3.57615i	−0.372170	+	0.147353i
$590$	1.39738	+	14.3754i	0.0575291	+	0.591828i
$591$	11.2898	+	17.7899i	0.464400	+	0.731778i
$592$	0.444056	+	2.32782i	0.0182506	+	0.0956729i
$593$	−8.04537	−	24.7611i	−0.330384	−	1.01682i	−0.968951	−	0.247251i	$-0.920473\pi$
$593$	−8.04537	−	24.7611i	−0.330384	−	1.01682i	0.638568	−	0.769566i	$-0.279527\pi$
$594$	−2.38873	+	5.07630i	−0.0980106	+	0.208283i
$595$	−4.07075	−	1.45337i	−0.166884	−	0.0595823i
$596$	1.72363	+	0.947576i	0.0706028	+	0.0388142i
$597$	1.29516	+	0.712022i	0.0530075	+	0.0291411i
$598$	0.670457	+	0.810443i	0.0274170	+	0.0331415i
$599$	−0.697920	−	0.507069i	−0.0285162	−	0.0207183i	0.573436	−	0.819250i	$-0.305610\pi$
$599$	−0.697920	−	0.507069i	−0.0285162	−	0.0207183i	−0.601952	+	0.798532i	$0.705610\pi$
$600$	4.53537	+	2.10486i	0.185156	+	0.0859304i
$601$	−14.5776	+	10.5912i	−0.594631	+	0.432025i	−0.843969	−	0.536392i	$-0.819787\pi$
$601$	−14.5776	+	10.5912i	−0.594631	+	0.432025i	0.249338	+	0.968416i	$0.419787\pi$
$602$	0.653389	+	0.167762i	0.0266302	+	0.00683746i
$603$	6.43799	+	13.6814i	0.262175	+	0.557151i
$604$	3.93555	−	20.6309i	0.160135	−	0.839458i
$605$	45.5912	+	4.18760i	1.85354	+	0.170250i
$606$	−7.46155	−	7.00686i	−0.303105	−	0.284634i
$607$	31.3156	+	22.7521i	1.27106	+	0.923479i	0.999244	−	0.0388697i	$-0.0123757\pi$
$607$	31.3156	+	22.7521i	1.27106	+	0.923479i	0.271816	+	0.962349i	$0.412376\pi$
$608$	0.555334	−	1.18015i	0.0225218	−	0.0478612i
$609$	−1.53167	+	1.85147i	−0.0620664	+	0.0750254i
$610$	−3.17736	−	14.0396i	−0.128647	−	0.568446i
$611$	−0.635858	−	10.1067i	−0.0257241	−	0.408873i
$612$	−0.306611	+	4.87343i	−0.0123940	+	0.196997i
$613$	5.22019	+	2.06682i	0.210841	+	0.0834780i	0.471171	−	0.882042i	$-0.343831\pi$
$613$	5.22019	+	2.06682i	0.210841	+	0.0834780i	−0.260330	+	0.965520i	$0.583831\pi$
$614$	5.89255	−	9.28517i	0.237804	−	0.374719i
$615$	−5.81595	−	11.3400i	−0.234522	−	0.457271i
$616$	0.139452	−	2.21652i	0.00561867	−	0.0893063i
$617$	−39.6857	−	5.01347i	−1.59769	−	0.201835i	−0.724520	−	0.689254i	$-0.757938\pi$
$617$	−39.6857	−	5.01347i	−1.59769	−	0.201835i	−0.873168	+	0.487419i	$0.837938\pi$
$618$	13.1300	−	9.53950i	0.528166	−	0.383735i
$619$	−2.54075	−	13.3191i	−0.102121	−	0.535340i	−0.996175	−	0.0873796i	$-0.972151\pi$
$619$	−2.54075	−	13.3191i	−0.102121	−	0.535340i	0.894054	−	0.447960i	$-0.147849\pi$
$620$	8.43984	−	14.3578i	0.338952	−	0.576623i
$621$	0.251964	+	0.535450i	0.0101110	+	0.0214869i
$622$	5.93179	−	5.57032i	0.237843	−	0.223349i
$623$	0.668914	−	1.05404i	0.0267995	−	0.0422292i
$624$	1.77742			0.0711536
$625$	−13.1709	+	21.2492i	−0.526835	+	0.849968i
$626$	10.8230			0.432572
$627$	−3.92081	+	6.17821i	−0.156582	+	0.246734i
$628$	−12.5521	+	11.7872i	−0.500885	+	0.470362i
$629$	−4.92707	−	10.4706i	−0.196455	−	0.417489i
$630$	−0.448572	+	0.763108i	−0.0178715	+	0.0304030i
$631$	7.79026	+	40.8380i	0.310126	+	1.62573i	0.706547	+	0.707666i	$0.250252\pi$
$631$	7.79026	+	40.8380i	0.310126	+	1.62573i	−0.396421	+	0.918069i	$0.629748\pi$
$632$	0.597307	−	0.433969i	0.0237596	−	0.0172624i
$633$	20.4503	+	2.58347i	0.812826	+	0.102684i
$634$	−0.857518	+	13.6299i	−0.0340564	+	0.541311i
$635$	−5.93920	−	11.5803i	−0.235690	−	0.459549i
$636$	5.12285	−	8.07232i	0.203134	−	0.320088i
$637$	11.3092	+	4.47764i	0.448087	+	0.177410i
$638$	2.13828	−	33.9870i	0.0846553	−	1.34556i
$639$	−0.659141	−	10.4767i	−0.0260752	−	0.414453i
$640$	0.493572	+	2.18091i	0.0195102	+	0.0862082i
$641$	−24.2414	+	29.3028i	−0.957478	+	1.15739i	0.0299867	+	0.999550i	$0.490454\pi$
$641$	−24.2414	+	29.3028i	−0.957478	+	1.15739i	−0.987464	+	0.157841i	$0.949546\pi$
$642$	−1.55050	+	3.29497i	−0.0611932	+	0.130042i
$643$	8.90643	+	6.47090i	0.351235	+	0.255187i	0.749387	−	0.662132i	$-0.230348\pi$
$643$	8.90643	+	6.47090i	0.351235	+	0.255187i	−0.398152	+	0.917320i	$0.630348\pi$
$644$	−0.170770	−	0.160363i	−0.00672927	−	0.00631921i
$645$	3.79444	+	0.348524i	0.149406	+	0.0137231i
$646$	−1.19341	+	6.25607i	−0.0469540	+	0.246142i
$647$	17.9609	+	38.1688i	0.706115	+	1.50057i	0.858809	+	0.512296i	$0.171205\pi$
$647$	17.9609	+	38.1688i	0.706115	+	1.50057i	−0.152694	+	0.988273i	$0.548795\pi$
$648$	0.968583	+	0.248690i	0.0380495	+	0.00976946i
$649$	29.3169	−	21.3000i	1.15079	−	0.836096i
$650$	−1.06704	+	8.82279i	−0.0418526	+	0.346058i
$651$	2.38538	+	1.73308i	0.0934902	+	0.0679246i
$652$	12.0868	+	14.6104i	0.473354	+	0.572187i
$653$	39.9341	+	21.9540i	1.56274	+	0.859125i	0.999460	+	0.0328606i	$0.0104618\pi$
$653$	39.9341	+	21.9540i	1.56274	+	0.859125i	0.563283	+	0.826264i	$0.309538\pi$
$654$	−3.86543	−	2.12504i	−0.151150	−	0.0830956i
$655$	42.9143	+	15.3216i	1.67680	+	0.598664i
$656$	2.42672	−	5.15703i	0.0947474	−	0.201348i
$657$	2.74875	+	8.45978i	0.107239	+	0.330047i
$658$	0.422622	+	2.21546i	0.0164755	+	0.0863677i
$659$	−13.8625	−	21.8438i	−0.540007	−	0.850914i	0.459295	−	0.888284i	$-0.348102\pi$
$659$	−13.8625	−	21.8438i	−0.540007	−	0.850914i	−0.999302	+	0.0373696i	$0.988102\pi$
$660$	−1.21371	−	12.4860i	−0.0472438	−	0.486018i
$661$	−5.30317	+	2.09967i	−0.206269	+	0.0816678i	−0.468988	−	0.883205i	$-0.655381\pi$
$661$	−5.30317	+	2.09967i	−0.206269	+	0.0816678i	0.262718	+	0.964873i	$0.415381\pi$
$662$	17.2345	−	20.8329i	0.669836	−	0.809693i
$663$	−8.40657	+	2.15844i	−0.326484	+	0.0838269i
$664$	−7.22132	−	8.72908i	−0.280242	−	0.338754i
$665$	−0.705193	+	0.914128i	−0.0273462	+	0.0354484i
$666$	−2.29535	+	0.589345i	−0.0889429	+	0.0228367i
$667$	−2.61849	−	2.45893i	−0.101388	−	0.0952100i
$668$	−1.34342	+	4.13462i	−0.0519784	+	0.159973i
$669$	−3.08052	−	0.389160i	−0.119100	−	0.0150458i
$670$	−28.0143	−	18.9300i	−1.08229	−	0.731330i
$671$	−26.3273	+	24.7230i	−1.01635	+	0.954419i
$672$	−0.392745	+	0.0496152i	−0.0151505	+	0.00191395i
$673$	2.19449	+	34.8803i	0.0845912	+	1.34454i	0.779935	+	0.625861i	$0.215252\pi$
$673$	2.19449	+	34.8803i	0.0845912	+	1.34454i	−0.695343	+	0.718678i	$0.744748\pi$
$674$	−2.63078	+	8.09670i	−0.101334	+	0.311873i
$675$	−1.81592	+	4.65859i	−0.0698950	+	0.179309i
$676$	−3.04097	−	9.35915i	−0.116960	−	0.359967i
$677$	−15.5874	+	6.17150i	−0.599074	+	0.237190i	−0.648035	−	0.761610i	$-0.724409\pi$
$677$	−15.5874	+	6.17150i	−0.599074	+	0.237190i	0.0489610	+	0.998801i	$0.484409\pi$
$678$	1.02955	−	5.39707i	0.0395395	−	0.207273i
$679$	3.89417	−	0.491948i	0.149444	−	0.0188792i
$680$	−4.98286	−	9.71560i	−0.191084	−	0.372576i
$681$	16.7424	−	9.20420i	0.641569	−	0.352706i
$682$	−41.7861			−1.60007
$683$	33.9810	−	18.6812i	1.30025	−	0.714816i	0.327097	−	0.944991i	$-0.393930\pi$
$683$	33.9810	−	18.6812i	1.30025	−	0.714816i	0.973149	+	0.230175i	$0.0739297\pi$
$684$	1.21269	+	0.480136i	0.0463682	+	0.0183585i
$685$	−30.7504	+	23.9834i	−1.17491	+	0.916359i
$686$	−5.30792	−	1.36284i	−0.202658	−	0.0520336i
$687$	−2.80003	−	4.41215i	−0.106828	−	0.168334i
$688$	0.913085	+	1.43879i	0.0348110	+	0.0548534i
$689$	16.4594	+	4.22605i	0.627052	+	0.161000i
$690$	−1.09640	−	0.740864i	−0.0417391	−	0.0282042i
$691$	−26.0305	−	10.3062i	−0.990246	−	0.392066i	−0.183536	−	0.983013i	$-0.558754\pi$
$691$	−26.0305	−	10.3062i	−0.990246	−	0.392066i	−0.806711	+	0.590947i	$0.798754\pi$
$692$	−7.48670	+	4.11585i	−0.284602	+	0.156461i
$693$	2.22091			0.0843652
$694$	8.04668	−	4.42370i	0.305448	−	0.167921i
$695$	−18.1910	−	9.20807i	−0.690025	−	0.349282i
$696$	−6.02213	+	0.760773i	−0.228268	+	0.0288370i
$697$	−5.21499	+	27.3380i	−0.197532	+	1.03550i
$698$	−19.0336	+	7.53594i	−0.720433	+	0.285240i
$699$	0.0327458	+	0.100781i	0.00123856	+	0.00381189i
$700$	−0.0105046	−	1.97930i	−0.000397038	−	0.0748106i
$701$	−2.74954	+	8.46223i	−0.103849	+	0.319614i	−0.989459	−	0.144816i	$-0.953741\pi$
$701$	−2.74954	+	8.46223i	−0.103849	+	0.319614i	0.885610	+	0.464430i	$0.153741\pi$
$702$	0.111605	+	1.77391i	0.00421225	+	0.0669519i
$703$	−3.06650	+	0.387389i	−0.115655	+	0.0146107i
$704$	4.08969	−	3.84048i	0.154136	−	0.144743i
$705$	4.34724	+	11.9751i	0.163727	+	0.451010i
$706$	−26.9299	−	3.40204i	−1.01352	−	0.128037i
$707$	−1.25213	+	3.85368i	−0.0470914	+	0.144932i
$708$	−4.70855	−	4.42162i	−0.176958	−	0.166175i
$709$	2.21513	−	0.568750i	0.0831911	−	0.0213599i	−0.206865	−	0.978370i	$-0.566326\pi$
$709$	2.21513	−	0.568750i	0.0831911	−	0.0213599i	0.290056	+	0.957010i	$0.406326\pi$
$710$	13.2453	+	19.3790i	0.497086	+	0.727281i
$711$	0.470618	+	0.568879i	0.0176495	+	0.0213346i
$712$	3.05446	−	0.784251i	0.114471	−	0.0293911i
$713$	−2.80952	+	3.39613i	−0.105217	+	0.127186i
$714$	1.79730	−	0.711601i	0.0672622	−	0.0266310i
$715$	20.4400	−	8.90966i	0.764414	−	0.333203i
$716$	−0.0340576	−	0.0536662i	−0.00127279	−	0.00200560i
$717$	4.57338	+	23.9745i	0.170796	+	0.895344i
$718$	5.38797	+	16.5825i	0.201077	+	0.618852i
$719$	−0.349411	+	0.742537i	−0.0130308	+	0.0276919i	−0.911237	−	0.411883i	$-0.864871\pi$
$719$	−0.349411	+	0.742537i	−0.0130308	+	0.0276919i	0.898206	+	0.439575i	$0.144871\pi$
$720$	−2.14562	+	0.629539i	−0.0799625	+	0.0234615i
$721$	−5.63004	−	3.09514i	−0.209674	−	0.115269i
$722$	−15.1591	−	8.33379i	−0.564164	−	0.310152i
$723$	2.39216	+	2.89162i	0.0889654	+	0.107541i
$724$	−17.2132	−	12.5061i	−0.639724	−	0.464787i
$725$	−0.161073	−	30.3496i	−0.00598208	−	1.12715i
$726$	−16.5645	+	12.0348i	−0.614765	+	0.446653i
$727$	18.8005	+	4.82714i	0.697271	+	0.179029i	0.580657	−	0.814149i	$-0.302796\pi$
$727$	18.8005	+	4.82714i	0.697271	+	0.179029i	0.116614	+	0.993177i	$0.462796\pi$
$728$	−0.299586	−	0.636653i	−0.0111034	−	0.0235959i
$729$	−0.187381	+	0.982287i	−0.00694005	+	0.0363810i
$730$	−14.9547	−	13.1139i	−0.553497	−	0.485369i
$731$	−6.06581	−	5.69617i	−0.224352	−	0.210680i
$732$	5.20803	+	3.78385i	0.192494	+	0.139855i
$733$	19.7265	−	41.9209i	0.728614	−	1.54838i	−0.104030	−	0.994574i	$-0.533174\pi$
$733$	19.7265	−	41.9209i	0.728614	−	1.54838i	0.832644	−	0.553809i	$-0.186826\pi$
$734$	−17.3558	+	20.9795i	−0.640614	+	0.774369i
$735$	−15.2379	−	1.39962i	−0.562059	−	0.0516258i
$736$	−0.0371576	−	0.590603i	−0.00136965	−	0.0217699i
$737$	−5.32650	+	84.6622i	−0.196204	+	3.11857i
$738$	5.29923	+	2.09811i	0.195067	+	0.0772327i
$739$	15.5950	−	24.5738i	0.573672	−	0.903963i	−0.426327	−	0.904569i	$-0.640193\pi$
$739$	15.5950	−	24.5738i	0.573672	−	0.903963i	1.00000		0.000605786i	$0.000192828\pi$
$740$	3.73702	−	3.75691i	0.137376	−	0.138107i
$741$	−0.145564	+	2.31367i	−0.00534741	+	0.0849947i
$742$	−3.75489	−	0.474353i	−0.137846	−	0.0174141i
$743$	14.7314	−	10.7030i	0.540441	−	0.392653i	−0.283808	−	0.958881i	$-0.591598\pi$
$743$	14.7314	−	10.7030i	0.540441	−	0.392653i	0.824249	+	0.566228i	$0.191598\pi$
$744$	1.39565	+	7.31626i	0.0511671	+	0.268227i
$745$	−0.425524	−	4.37756i	−0.0155900	−	0.160381i
$746$	6.97152	+	14.8152i	0.255246	+	0.542424i
$747$	8.25842	−	7.75517i	0.302160	−	0.283747i
$748$	−14.6791	+	23.1305i	−0.536721	+	0.845736i
$749$	1.44157			0.0526737
$750$	−1.83684	−	11.0284i	−0.0670720	−	0.402701i
$751$	51.5868			1.88243			0.941214	−	0.337812i	$-0.109687\pi$
$751$	51.5868			1.88243			0.941214	+	0.337812i	$0.109687\pi$
$752$	−3.05282	+	4.81048i	−0.111325	+	0.175420i
$753$	−8.06245	+	7.57115i	−0.293812	+	0.275908i
$754$	−4.59369	−	9.76210i	−0.167292	−	0.355515i
$755$	−43.0517	+	18.7659i	−1.56681	+	0.682962i
$756$	−0.0741779	−	0.388854i	−0.00269783	−	0.0141425i
$757$	−16.7073	+	12.1386i	−0.607237	+	0.441184i	−0.848440	−	0.529291i	$-0.822458\pi$
$757$	−16.7073	+	12.1386i	−0.607237	+	0.441184i	0.241203	+	0.970475i	$0.422458\pi$
$758$	6.76081	+	0.854089i	0.245564	+	0.0310219i
$759$	−0.208463	+	3.31343i	−0.00756673	+	0.120270i
$760$	−2.87933	+	0.463876i	−0.104444	+	0.0168265i
$761$	−24.5635	+	38.7059i	−0.890427	+	1.40309i	0.0246000	+	0.999697i	$0.492169\pi$
$761$	−24.5635	+	38.7059i	−0.890427	+	1.40309i	−0.915027	+	0.403392i	$0.867831\pi$
$762$	5.41153	+	2.14258i	0.196039	+	0.0776174i
$763$	−0.109644	+	1.74274i	−0.00396937	+	0.0630914i
$764$	0.203544	+	3.23523i	0.00736395	+	0.117047i
$765$	9.38355	−	5.58308i	0.339263	−	0.201857i
$766$	−3.32604	+	4.02049i	−0.120175	+	0.145266i
$767$	4.88823	−	10.3880i	0.176504	−	0.375090i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	−18.5861	−	17.4535i	−0.670232	−	0.629390i	0.272808	−	0.962069i	$-0.412048\pi$
$769$	−18.5861	−	17.4535i	−0.670232	−	0.629390i	−0.943040	+	0.332678i	$0.892048\pi$
$770$	−4.26780	+	2.53928i	−0.153801	+	0.0915094i
$771$	−2.96959	+	15.5672i	−0.106947	+	0.560637i
$772$	6.78965	+	14.4287i	0.244365	+	0.519302i
$773$	32.4894	+	8.34186i	1.16856	+	0.300036i	0.782628	−	0.622490i	$-0.213879\pi$
$773$	32.4894	+	8.34186i	1.16856	+	0.300036i	0.385935	+	0.922526i	$0.373879\pi$
$774$	−1.37862	+	1.00163i	−0.0495534	+	0.0360027i
$775$	−37.1545	+	2.53560i	−1.33463	+	0.0910814i
$776$	8.02161	+	5.82804i	0.287959	+	0.209215i
$777$	0.597982	+	0.722836i	0.0214525	+	0.0259316i
$778$	5.26209	+	2.89286i	0.188655	+	0.103714i
$779$	6.51419	+	3.58121i	0.233395	+	0.128310i
$780$	−2.24267	−	3.28123i	−0.0803005	−	0.117487i
$781$	25.0755	−	53.2882i	0.897273	−	1.90680i
$782$	0.892954	+	2.74823i	0.0319320	+	0.0982765i
$783$	−1.13740	−	5.96248i	−0.0406475	−	0.213082i
$784$	−3.66682	−	5.77798i	−0.130958	−	0.206356i
$785$	37.5978	+	8.29942i	1.34192	+	0.296219i
$786$	−18.9473	+	7.50177i	−0.675828	+	0.267579i
$787$	9.15439	−	11.0658i	0.326319	−	0.394452i	−0.581685	−	0.813414i	$-0.697606\pi$
$787$	9.15439	−	11.0658i	0.326319	−	0.394452i	0.908003	+	0.418963i	$0.137606\pi$
$788$	20.4079	−	5.23986i	0.727002	−	0.186662i
$789$	11.9085	+	14.3950i	0.423955	+	0.512474i
$790$	−1.55479	−	0.555104i	−0.0553171	−	0.0197497i
$791$	−2.10671	+	0.540912i	−0.0749060	+	0.0192326i
$792$	4.08969	+	3.84048i	0.145321	+	0.136465i
$793$	−3.53579	+	10.8821i	−0.125560	+	0.386433i
$794$	14.6953	+	1.85645i	0.521518	+	0.0658830i
$795$	−21.3658	+	0.728206i	−0.757769	+	0.0258268i
$796$	1.07740	−	1.01175i	0.0381875	−	0.0358604i
$797$	−43.9131	+	5.54752i	−1.55548	+	0.196503i	−0.855556	−	0.517711i	$-0.826784\pi$
$797$	−43.9131	+	5.54752i	−1.55548	+	0.196503i	−0.699927	+	0.714214i	$0.746784\pi$
$798$	−0.0324200	−	0.515301i	−0.00114765	−	0.0182414i
$799$	8.59711	−	26.4592i	0.304144	−	0.936059i
$800$	3.40334	−	3.66296i	0.120326	−	0.129505i
$801$	0.974495	+	2.99919i	0.0344321	+	0.105971i
$802$	17.5710	−	6.95683i	0.620452	−	0.245654i
$803$	−9.35106	+	49.0200i	−0.329992	+	1.72988i
$804$	15.0013	−	1.89510i	0.529054	−	0.0668350i
$805$	−0.0805713	+	0.517593i	−0.00283976	+	0.0182427i
$806$	−11.6010	+	6.37771i	−0.408628	+	0.224645i
$807$	25.1765			0.886256
$808$	−8.96967	+	4.93112i	−0.315552	+	0.173476i
$809$	−40.2554	−	15.9382i	−1.41530	−	0.560359i	−0.468873	−	0.883265i	$-0.655340\pi$
$809$	−40.2554	−	15.9382i	−1.41530	−	0.560359i	−0.946431	+	0.322907i	$0.895340\pi$
$810$	−0.763021	−	2.10186i	−0.0268098	−	0.0738517i
$811$	−1.71560	−	0.440492i	−0.0602429	−	0.0154677i	0.218448	−	0.975849i	$-0.429901\pi$
$811$	−1.71560	−	0.440492i	−0.0602429	−	0.0154677i	−0.278691	+	0.960381i	$0.589901\pi$
$812$	1.28754	+	2.02884i	0.0451839	+	0.0711984i
$813$	−0.00567643	−	0.00894462i	−0.000199081	−	0.000313702i
$814$	−12.8775	−	3.30637i	−0.451354	−	0.115888i
$815$	11.7212	−	40.7478i	0.410574	−	1.42733i
$816$	4.54016	+	1.79758i	0.158938	+	0.0629278i
$817$	−1.94766	+	1.07073i	−0.0681399	+	0.0374602i
$818$	−20.6776			−0.722977
$819$	0.616586	−	0.338971i	0.0215453	−	0.0118446i
$820$	−12.5822	+	2.02706i	−0.439388	+	0.0707880i
$821$	−41.1991	+	5.20465i	−1.43786	+	0.181644i	−0.805299	−	0.592869i	$-0.797995\pi$
$821$	−41.1991	+	5.20465i	−1.43786	+	0.181644i	−0.632559	+	0.774512i	$0.717995\pi$
$822$	3.26795	−	17.1312i	0.113983	−	0.597520i
$823$	−23.2411	+	9.20181i	−0.810134	+	0.320755i	−0.736420	−	0.676525i	$-0.763485\pi$
$823$	−23.2411	+	9.20181i	−0.810134	+	0.320755i	−0.0737143	+	0.997279i	$0.523485\pi$
$824$	−5.01521	−	15.4352i	−0.174713	−	0.537712i
$825$	−21.5186	+	17.9950i	−0.749183	+	0.626505i
$826$	−0.790150	+	2.43183i	−0.0274928	+	0.0846142i
$827$	−0.135702	−	2.15692i	−0.00471883	−	0.0750036i	0.994962	−	0.100248i	$-0.0319636\pi$
$827$	−0.135702	−	2.15692i	−0.00471883	−	0.0750036i	−0.999681	+	0.0252444i	$0.991964\pi$
$828$	0.587105	−	0.0741686i	0.0204033	−	0.00257754i
$829$	−36.2261	+	34.0186i	−1.25819	+	1.18151i	−0.283246	+	0.959047i	$0.591411\pi$
$829$	−36.2261	+	34.0186i	−1.25819	+	1.18151i	−0.974940	+	0.222468i	$0.928589\pi$
$830$	−7.00289	+	24.3450i	−0.243074	+	0.845029i
$831$	1.46244	+	0.184750i	0.0507316	+	0.00640889i
$832$	0.549252	−	1.69042i	0.0190419	−	0.0586049i
$833$	24.3594	+	22.8750i	0.844003	+	0.792572i
$834$	8.83168	−	2.26759i	0.305816	−	0.0785202i
$835$	9.32785	−	2.73685i	0.322804	−	0.0947128i
$836$	4.66423	+	5.63809i	0.161316	+	0.194997i
$837$	−7.21419	+	1.85229i	−0.249359	+	0.0640245i
$838$	19.9875	−	24.1607i	0.690455	−	0.834617i
$839$	−3.06657	+	1.21414i	−0.105870	+	0.0419167i	−0.420462	−	0.907310i	$-0.638132\pi$
$839$	−3.06657	+	1.21414i	−0.105870	+	0.0419167i	0.314593	+	0.949227i	$0.398132\pi$
$840$	0.587143	+	0.662431i	0.0202583	+	0.0228560i
$841$	4.20350	+	6.62365i	0.144948	+	0.228402i
$842$	0.176156	+	0.923440i	0.00607072	+	0.0318238i
$843$	−6.26232	−	19.2734i	−0.215686	−	0.663813i
$844$	8.77652	−	18.6511i	0.302100	−	0.641996i
$845$	−13.4406	+	17.4228i	−0.462372	+	0.599364i
$846$	−4.99268	−	2.74475i	−0.171652	−	0.0943664i
$847$	7.10272	+	3.90475i	0.244052	+	0.134169i
$848$	−6.09419	−	7.36660i	−0.209275	−	0.252970i
$849$	−12.5080	−	9.08762i	−0.429275	−	0.311886i
$850$	−11.6485	+	21.4575i	−0.399539	+	0.735985i
$851$	−1.13455	+	0.824297i	−0.0388918	+	0.0282565i
$852$	−10.1677	−	2.61061i	−0.348338	−	0.0894381i
$853$	−1.27260	−	2.70441i	−0.0435729	−	0.0925971i	0.881855	−	0.471520i	$-0.156295\pi$
$853$	−1.27260	−	2.70441i	−0.0435729	−	0.0925971i	−0.925428	+	0.378923i	$0.876295\pi$
$854$	0.477519	−	2.50324i	0.0163403	−	0.0856591i
$855$	−0.643755	−	2.84452i	−0.0220160	−	0.0972804i
$856$	2.65458	+	2.49281i	0.0907315	+	0.0852026i
$857$	43.8401	+	31.8517i	1.49755	+	1.08803i	0.971344	+	0.237677i	$0.0763860\pi$
$857$	43.8401	+	31.8517i	1.49755	+	1.08803i	0.526206	+	0.850357i	$0.323614\pi$
$858$	−4.24576	+	9.02269i	−0.144948	+	0.308030i
$859$	21.1697	−	25.5898i	0.722301	−	0.873112i	−0.273758	−	0.961799i	$-0.588267\pi$
$859$	21.1697	−	25.5898i	0.722301	−	0.873112i	0.996060	+	0.0886861i	$0.0282668\pi$
$860$	1.50401	−	3.50102i	0.0512864	−	0.119384i
$861$	−0.141670	−	2.25178i	−0.00482809	−	0.0767403i
$862$	−1.78640	+	28.3940i	−0.0608451	+	0.967105i
$863$	4.68166	+	1.85360i	0.159365	+	0.0630972i	0.446453	−	0.894807i	$-0.352687\pi$
$863$	4.68166	+	1.85360i	0.159365	+	0.0630972i	−0.287087	+	0.957904i	$0.592687\pi$
$864$	0.535827	−	0.844328i	0.0182292	−	0.0287246i
$865$	17.0445	+	8.62773i	0.579532	+	0.293352i
$866$	0.413776	−	6.57678i	0.0140607	−	0.223488i
$867$	−6.79040	−	0.857827i	−0.230614	−	0.0291333i
$868$	2.38538	−	1.73308i	0.0809649	−	0.0588245i
$869$	0.776154	+	4.06874i	0.0263292	+	0.138023i
$870$	9.00292	+	10.1573i	0.305228	+	0.344366i
$871$	11.4430	+	24.3176i	0.387731	+	0.823970i
$872$	−3.21551	+	3.01957i	−0.108891	+	0.102256i
$873$	−5.31286	+	8.37173i	−0.179813	+	0.283340i
$874$	0.771833			0.0261077
$875$	−3.64067	+	2.51680i	−0.123077	+	0.0850833i
$876$	8.89514			0.300539
$877$	12.6086	−	19.8680i	0.425763	−	0.670896i	−0.561950	−	0.827171i	$-0.689949\pi$
$877$	12.6086	−	19.8680i	0.425763	−	0.670896i	0.987714	+	0.156275i	$0.0499487\pi$
$878$	5.66033	−	5.31540i	0.191027	−	0.179386i
$879$	−5.22000	−	11.0931i	−0.176066	−	0.374160i
$880$	−12.2500	−	2.70408i	−0.412947	−	0.0911547i
$881$	−8.55579	−	44.8510i	−0.288252	−	1.51107i	−0.771864	−	0.635787i	$-0.780676\pi$
$881$	−8.55579	−	44.8510i	−0.288252	−	1.51107i	0.483612	−	0.875282i	$-0.339324\pi$
$882$	5.53634	−	4.02238i	0.186418	−	0.135441i
$883$	−18.5975	−	2.34941i	−0.625856	−	0.0790640i	−0.193993	−	0.981003i	$-0.562144\pi$
$883$	−18.5975	−	2.34941i	−0.625856	−	0.0790640i	−0.431864	+	0.901939i	$0.642144\pi$
$884$	−0.544974	+	8.66212i	−0.0183295	+	0.291339i
$885$	−2.22155	+	14.2713i	−0.0746766	+	0.479725i
$886$	−5.00342	+	7.88412i	−0.168093	+	0.264872i
$887$	2.24372	+	0.888354i	0.0753369	+	0.0298280i	0.405491	−	0.914099i	$-0.367101\pi$
$887$	2.24372	+	0.888354i	0.0753369	+	0.0298280i	−0.330154	+	0.943927i	$0.607101\pi$
$888$	−0.148801	+	2.36512i	−0.00499343	+	0.0793683i
$889$	−0.144672	−	2.29949i	−0.00485214	−	0.0771225i
$890$	−5.30177	−	4.64920i	−0.177716	−	0.155841i
$891$	−3.57610	+	4.32277i	−0.119804	+	0.144818i
$892$	−1.32205	+	2.80949i	−0.0442654	+	0.0940688i
$893$	−6.01181	−	4.36783i	−0.201177	−	0.146164i
$894$	1.43383	+	1.34646i	0.0479544	+	0.0450322i
$895$	−0.0560989	+	0.130587i	−0.00187518	+	0.00436503i
$896$	−0.0741779	+	0.388854i	−0.00247811	+	0.0129907i
$897$	0.447844	+	0.951718i	0.0149531	+	0.0317769i
$898$	−33.5279	−	8.60850i	−1.11884	−	0.287269i
$899$	36.5761	−	26.5741i	1.21988	−	0.886294i
$900$	3.86943	+	3.16663i	0.128981	+	0.105554i
$901$	37.7692	+	27.4409i	1.25827	+	0.914190i
$902$	20.3819	+	24.6375i	0.678643	+	0.820338i
$903$	0.591141	+	0.324983i	0.0196720	+	0.0108147i
$904$	−4.81477	−	2.64694i	−0.160137	−	0.0880360i
$905$	−1.36821	+	47.5565i	−0.0454809	+	1.58083i
$906$	8.94259	−	19.0040i	0.297098	−	0.631365i
$907$	1.75622	+	5.40508i	0.0583142	+	0.179473i	0.975971	−	0.217902i	$-0.0699213\pi$
$907$	1.75622	+	5.40508i	0.0583142	+	0.179473i	−0.917656	+	0.397375i	$0.869921\pi$
$908$	−3.58004	−	18.7672i	−0.118808	−	0.622812i
$909$	−5.48460	−	8.64234i	−0.181913	−	0.286648i
$910$	−0.797299	+	1.35636i	−0.0264302	+	0.0449629i
$911$	30.9747	−	12.2638i	1.02624	−	0.406317i	0.206130	−	0.978525i	$-0.433913\pi$
$911$	30.9747	−	12.2638i	1.02624	−	0.406317i	0.820109	+	0.572208i	$0.193913\pi$
$912$	0.831378	−	1.00496i	0.0275297	−	0.0332776i
$913$	61.5612	−	15.8062i	2.03738	−	0.523109i
$914$	−11.9442	−	14.4380i	−0.395078	−	0.477567i
$915$	0.413966	−	14.3887i	0.0136853	−	0.475675i
$916$	−5.06146	+	1.29956i	−0.167235	+	0.0429387i
$917$	5.88066	+	5.52231i	0.194197	+	0.182363i
$918$	−1.50895	+	4.64408i	−0.0498028	+	0.153277i
$919$	−13.5751	−	1.71494i	−0.447802	−	0.0565705i	−0.101801	−	0.994805i	$-0.532461\pi$
$919$	−13.5751	−	1.71494i	−0.447802	−	0.0565705i	−0.346001	+	0.938234i	$0.612461\pi$
$920$	−1.04341	+	0.813795i	−0.0344002	+	0.0268300i
$921$	8.01655	−	7.52804i	0.264154	−	0.248058i
$922$	−13.2860	+	1.67841i	−0.437551	+	0.0552756i
$923$	−1.17157	−	18.6215i	−0.0385626	−	0.612935i
$924$	0.686298	−	2.11221i	0.0225775	−	0.0694865i
$925$	−11.6507	−	2.15848i	−0.383074	−	0.0709703i
$926$	3.49517	+	10.7570i	0.114858	+	0.353498i
$927$	15.0899	−	5.97450i	0.495616	−	0.196228i
$928$	−1.13740	+	5.96248i	−0.0373371	+	0.195728i
$929$	−33.2468	+	4.20005i	−1.09079	+	0.137799i	−0.650092	−	0.759855i	$-0.725270\pi$
$929$	−33.2468	+	4.20005i	−1.09079	+	0.137799i	−0.440700	+	0.897654i	$0.645270\pi$
$930$	11.7453	−	11.8078i	0.385144	−	0.387194i
$931$	7.82152	−	4.29992i	0.256340	−	0.140924i
$932$	0.105968			0.00347108
$933$	7.13071	−	3.92014i	0.233449	−	0.128340i
$934$	8.51669	+	3.37200i	0.278675	+	0.110335i
$935$	61.2220	−	2.08661i	2.00217	−	0.0682395i
$936$	1.72157	+	0.442025i	0.0562714	+	0.0144480i
$937$	−9.62237	−	15.1624i	−0.314349	−	0.495335i	0.650012	−	0.759924i	$-0.274764\pi$
$937$	−9.62237	−	15.1624i	−0.314349	−	0.495335i	−0.964361	+	0.264589i	$0.914764\pi$
$938$	−3.20729	−	5.05389i	−0.104722	−	0.165015i
$939$	10.4829	+	2.69156i	0.342098	+	0.0878358i
$940$	12.7324	−	0.433955i	0.415285	−	0.0141540i
$941$	6.65391	+	2.63447i	0.216911	+	0.0858812i	0.474067	−	0.880489i	$-0.342785\pi$
$941$	6.65391	+	2.63447i	0.216911	+	0.0858812i	−0.257156	+	0.966370i	$0.582785\pi$
$942$	−15.0892	+	8.29534i	−0.491632	+	0.270277i
$943$	3.37278			0.109833
$944$	−5.66024	+	3.11174i	−0.184225	+	0.101279i
$945$	−0.624256	+	0.627578i	−0.0203071	+	0.0204151i
$946$	−9.48485	+	1.19821i	−0.308379	+	0.0389573i
$947$	−0.792304	+	4.15340i	−0.0257464	+	0.134967i	−0.992840	−	0.119455i	$-0.961885\pi$
$947$	−0.792304	+	4.15340i	−0.0257464	+	0.134967i	0.967093	+	0.254422i	$0.0818853\pi$
$948$	0.686465	−	0.271791i	0.0222954	−	0.00882735i
$949$	4.88567	+	15.0365i	0.158596	+	0.488107i
$950$	4.48936	+	4.73013i	0.145654	+	0.153466i
$951$	−4.22018	+	12.9884i	−0.136849	+	0.421177i
$952$	−0.121377	−	1.92923i	−0.00393384	−	0.0625267i
$953$	−23.7983	+	3.00642i	−0.770902	+	0.0973876i	−0.500939	−	0.865483i	$-0.667012\pi$
$953$	−23.7983	+	3.00642i	−0.770902	+	0.0973876i	−0.269964	+	0.962870i	$0.587012\pi$
$954$	6.96941	−	6.54471i	0.225643	−	0.211893i
$955$	5.71564	−	4.45784i	0.184954	−	0.144252i
$956$	24.2144	+	3.05898i	0.783148	+	0.0989346i
$957$	10.5233	−	32.3874i	0.340170	−	1.04694i
$958$	−7.40978	−	6.95825i	−0.239399	−	0.224811i
$959$	−6.68706	+	1.71695i	−0.215936	+	0.0554430i
$960$	−0.0643057	+	2.23514i	−0.00207546	+	0.0721389i
$961$	−15.6013	−	18.8587i	−0.503267	−	0.608345i
$962$	−4.07979	+	1.04751i	−0.131538	+	0.0337731i
$963$	−2.32121	+	2.80586i	−0.0748000	+	0.0904177i
$964$	3.48932	−	1.38152i	0.112383	−	0.0444957i
$965$	18.0695	−	30.7398i	0.581678	−	0.989548i
$966$	−0.125524	−	0.197794i	−0.00403867	−	0.00636392i
$967$	−10.7687	−	56.4517i	−0.346299	−	1.81536i	−0.548652	−	0.836051i	$-0.684859\pi$
$967$	−10.7687	−	56.4517i	−0.346299	−	1.81536i	0.202353	−	0.979313i	$-0.435141\pi$
$968$	6.32707	+	19.4727i	0.203360	+	0.625877i
$969$	−2.71174	+	5.76273i	−0.0871135	+	0.185126i
$970$	0.637607	−	22.1620i	0.0204723	−	0.711580i
$971$	45.9425	+	25.2571i	1.47436	+	0.810538i	0.997650	−	0.0685199i	$-0.0218277\pi$
$971$	45.9425	+	25.2571i	1.47436	+	0.810538i	0.476714	+	0.879058i	$0.341828\pi$
$972$	0.876307	+	0.481754i	0.0281075	+	0.0154523i
$973$	−2.30082	−	2.78122i	−0.0737610	−	0.0891617i
$974$	−13.5479	−	9.84310i	−0.434102	−	0.315393i
$975$	−3.22765	+	8.28024i	−0.103368	+	0.265180i
$976$	5.20803	−	3.78385i	0.166705	−	0.121118i
$977$	−7.29825	−	1.87387i	−0.233492	−	0.0599505i	0.130131	−	0.991497i	$-0.458460\pi$
$977$	−7.29825	−	1.87387i	−0.233492	−	0.0599505i	−0.363623	+	0.931546i	$0.618460\pi$
$978$	8.07358	+	17.1572i	0.258165	+	0.548628i
$979$	−3.31516	+	17.3787i	−0.105953	+	0.555426i
$980$	−6.03989	+	14.0596i	−0.192937	+	0.449118i
$981$	−3.21551	−	3.01957i	−0.102663	−	0.0964074i
$982$	4.66107	+	3.38647i	0.148741	+	0.108066i
$983$	10.2682	−	21.8211i	0.327506	−	0.695986i	−0.671479	−	0.741023i	$-0.734341\pi$
$983$	10.2682	−	21.8211i	0.327506	−	0.695986i	0.998985	+	0.0450376i	$0.0143408\pi$
$984$	3.63298	−	4.39152i	0.115815	−	0.139996i
$985$	−35.4230	−	31.0629i	−1.12867	−	0.989747i
$986$	−1.86113	−	29.5817i	−0.0592703	−	0.942074i
$987$	−0.141619	+	2.25096i	−0.00450777	+	0.0716489i
$988$	2.15545	+	0.853402i	0.0685739	+	0.0271503i
$989$	−0.540337	+	0.851435i	−0.0171817	+	0.0270741i
$990$	1.92957	−	12.3956i	0.0613256	−	0.393958i
$991$	−2.93477	+	46.6468i	−0.0932260	+	1.48178i	0.622069	+	0.782962i	$0.286292\pi$
$991$	−2.93477	+	46.6468i	−0.0932260	+	1.48178i	−0.715295	+	0.698822i	$0.753708\pi$
$992$	7.38946	+	0.933505i	0.234615	+	0.0296388i
$993$	21.8739	−	15.8923i	0.694148	−	0.504328i
$994$	0.778680	+	4.08198i	0.0246982	+	0.129473i
$995$	−3.22717	−	0.712372i	−0.102308	−	0.0225837i
$996$	−4.82362	−	10.2507i	−0.152842	−	0.324806i
$997$	−0.812351	+	0.762848i	−0.0257274	+	0.0241596i	−0.697304	−	0.716775i	$-0.745617\pi$
$997$	−0.812351	+	0.762848i	−0.0257274	+	0.0241596i	0.671577	+	0.740935i	$0.265617\pi$
$998$	23.7950	−	37.4949i	0.753218	−	1.18688i
$999$	−2.36980			−0.0749771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.a.481.2	yes	100
125.46	even	25	inner	750.2.m.a.421.2	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.a.421.2	✓	100	125.46	even	25	inner
750.2.m.a.481.2	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(0.728969 - 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.13314 + 1.92769i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.320263 + 0.232684i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(0.728969 - 0.684547i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.13314 + 1.92769i) q^{5} +(-0.187381 - 0.982287i) q^{6} +(-0.320263 + 0.232684i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(1.02044 + 1.98965i) q^{10} +(3.00612 - 4.73688i) q^{11} +(-0.929776 - 0.368125i) q^{12} +(0.111605 - 1.77391i) q^{13} +(0.0248566 + 0.395085i) q^{14} +(0.493572 + 2.18091i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(2.07911 - 4.41833i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.950777 - 0.892839i) q^{19} +(2.22669 + 0.204525i) q^{20} +(-0.0741779 + 0.388854i) q^{21} +(-2.38873 - 5.07630i) q^{22} +(-0.573179 - 0.147167i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-2.43199 - 4.36869i) q^{25} +(-1.43796 - 1.04474i) q^{26} +(-0.637424 - 0.770513i) q^{27} +(0.346900 + 0.190710i) q^{28} +(5.31918 + 2.92424i) q^{29} +(2.10588 + 0.751856i) q^{30} +(3.17128 - 6.73932i) q^{31} +(0.309017 + 0.951057i) q^{32} +(-1.05125 - 5.51087i) q^{33} +(-2.61648 - 4.12291i) q^{34} +(-0.0856414 - 0.881031i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(1.51057 - 1.82596i) q^{37} +(-1.26330 + 0.324361i) q^{38} +(-1.13297 - 1.36952i) q^{39} +(1.36581 - 1.77047i) q^{40} +(-5.52041 + 1.41740i) q^{41} +(0.288574 + 0.270989i) q^{42} +(0.526586 - 1.62066i) q^{43} +(-5.56600 - 0.703150i) q^{44} +(1.85274 + 1.25194i) q^{45} +(-0.431382 + 0.405095i) q^{46} +(5.65248 - 0.714075i) q^{47} +(0.0627905 + 0.998027i) q^{48} +(-2.11469 + 6.50836i) q^{49} +(-4.99173 - 0.287465i) q^{50} +(-1.50895 - 4.64408i) q^{51} +(-1.65260 + 0.654310i) q^{52} +(-1.79149 + 9.39130i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(5.72490 + 11.1624i) q^{55} +(0.346900 - 0.190710i) q^{56} -1.30428 q^{57} +(5.31918 - 2.92424i) q^{58} +(6.00561 + 2.37779i) q^{59} +(1.76320 - 1.37519i) q^{60} +(-6.23523 - 1.60093i) q^{61} +(-3.99094 - 6.28871i) q^{62} +(0.212116 + 0.334241i) q^{63} +(0.968583 + 0.248690i) q^{64} +(3.29308 + 2.22523i) q^{65} +(-5.21627 - 2.06527i) q^{66} +(-13.2502 + 7.28435i) q^{67} -4.88307 q^{68} +(-0.518573 + 0.285088i) q^{69} +(-0.789768 - 0.399771i) q^{70} +(10.4147 - 1.31568i) q^{71} +(-0.187381 + 0.982287i) q^{72} +(-8.27049 + 3.27452i) q^{73} +(-0.732308 - 2.25381i) q^{74} +(-4.76342 - 1.51983i) q^{75} +(-0.403044 + 1.24044i) q^{76} +(0.139452 + 2.21652i) q^{77} +(-1.76340 + 0.222769i) q^{78} +(-0.538206 + 0.505409i) q^{79} +(-0.763021 - 2.10186i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-1.76123 + 5.42052i) q^{82} +(8.25842 + 7.75517i) q^{83} +(0.383429 - 0.0984479i) q^{84} +(6.16126 + 9.01447i) q^{85} +(-1.08621 - 1.31301i) q^{86} +(5.87930 - 1.50955i) q^{87} +(-3.57610 + 4.32277i) q^{88} +(-2.93208 + 1.16089i) q^{89} +(2.04980 - 0.893492i) q^{90} +(0.377018 + 0.594085i) q^{91} +(0.110887 + 0.581289i) q^{92} +(-2.30162 - 7.08365i) q^{93} +(2.42584 - 5.15517i) q^{94} +(2.79848 - 0.821093i) q^{95} +(0.876307 + 0.481754i) q^{96} +(-8.68881 - 4.77671i) q^{97} +(4.36208 + 5.27285i) q^{98} +(-4.53878 - 3.29762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 20 q^{5} + 5 q^{7}+O(q^{10}) \) 100 * q - 20 * q^5 + 5 * q^7	\( 100 q - 20 q^{5} + 5 q^{7} - 20 q^{10} + 10 q^{11} + 10 q^{13} - 20 q^{14} - 20 q^{15} + 15 q^{17} - 25 q^{18} + 15 q^{19} + 5 q^{20} + 5 q^{21} + 10 q^{22} - 5 q^{23} - 25 q^{24} + 10 q^{26} + 5 q^{28} + 25 q^{29} + 5 q^{30} - 25 q^{31} - 25 q^{32} + 10 q^{33} - 10 q^{34} + 40 q^{35} + 30 q^{37} - 35 q^{38} + 10 q^{39} + 5 q^{40} - 15 q^{41} + 5 q^{42} + 35 q^{43} - 15 q^{44} + 5 q^{45} + 20 q^{46} - 110 q^{47} + 20 q^{49} + 15 q^{51} - 40 q^{52} + 45 q^{53} + 60 q^{55} + 5 q^{56} - 60 q^{57} + 25 q^{58} - 20 q^{60} + 25 q^{62} + 5 q^{63} + 70 q^{65} - 15 q^{66} - 45 q^{67} - 60 q^{68} + 20 q^{69} - 10 q^{70} + 10 q^{71} + 60 q^{73} + 30 q^{74} - 25 q^{75} + 15 q^{76} + 5 q^{77} + 10 q^{78} - 10 q^{79} + 5 q^{80} - 15 q^{82} - 5 q^{83} + 5 q^{84} - 10 q^{85} + 35 q^{86} + 25 q^{87} + 10 q^{88} + 5 q^{90} + 15 q^{91} - 55 q^{92} + 40 q^{94} - 125 q^{95} + 80 q^{97} - 5 q^{98} + 10 q^{99}+O(q^{100}) \) 100 * q - 20 * q^5 + 5 * q^7 - 20 * q^10 + 10 * q^11 + 10 * q^13 - 20 * q^14 - 20 * q^15 + 15 * q^17 - 25 * q^18 + 15 * q^19 + 5 * q^20 + 5 * q^21 + 10 * q^22 - 5 * q^23 - 25 * q^24 + 10 * q^26 + 5 * q^28 + 25 * q^29 + 5 * q^30 - 25 * q^31 - 25 * q^32 + 10 * q^33 - 10 * q^34 + 40 * q^35 + 30 * q^37 - 35 * q^38 + 10 * q^39 + 5 * q^40 - 15 * q^41 + 5 * q^42 + 35 * q^43 - 15 * q^44 + 5 * q^45 + 20 * q^46 - 110 * q^47 + 20 * q^49 + 15 * q^51 - 40 * q^52 + 45 * q^53 + 60 * q^55 + 5 * q^56 - 60 * q^57 + 25 * q^58 - 20 * q^60 + 25 * q^62 + 5 * q^63 + 70 * q^65 - 15 * q^66 - 45 * q^67 - 60 * q^68 + 20 * q^69 - 10 * q^70 + 10 * q^71 + 60 * q^73 + 30 * q^74 - 25 * q^75 + 15 * q^76 + 5 * q^77 + 10 * q^78 - 10 * q^79 + 5 * q^80 - 15 * q^82 - 5 * q^83 + 5 * q^84 - 10 * q^85 + 35 * q^86 + 25 * q^87 + 10 * q^88 + 5 * q^90 + 15 * q^91 - 55 * q^92 + 40 * q^94 - 125 * q^95 + 80 * q^97 - 5 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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