LMFDB - Embedded newform 380.2.d.b.379.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.13
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 + 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 - 1.64479i) q^{6} -4.13073 q^{7} +(2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +O(q^{10})$	\(q+(-0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 + 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 - 1.64479i) q^{6} -4.13073 q^{7} +(2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +(-3.06322 + 0.785308i) q^{10} +0.681732i q^{11} +(-4.23583 - 3.70165i) q^{12} -3.19485 q^{13} +(2.41557 + 5.31892i) q^{14} +(6.19289 + 1.09710i) q^{15} +(-0.535953 - 3.96393i) q^{16} -2.93351i q^{17} +(2.87192 + 6.32377i) q^{18} +(2.23259 - 3.74374i) q^{19} +(2.80251 + 3.48510i) q^{20} -11.6184i q^{21} +(0.877829 - 0.398663i) q^{22} -6.41181 q^{23} +(-2.28939 + 7.61890i) q^{24} +(-4.69571 - 1.71763i) q^{25} +(1.86829 + 4.11384i) q^{26} -5.37533i q^{27} +(5.43630 - 6.22080i) q^{28} -0.928351i q^{29} +(-2.20881 - 8.61581i) q^{30} -6.68773 q^{31} +(-4.79072 + 3.00815i) q^{32} -1.91749 q^{33} +(-3.77732 + 1.71546i) q^{34} +(-1.61121 + 9.09498i) q^{35} +(6.46334 - 7.39604i) q^{36} -6.63253 q^{37} +(-6.12618 - 0.685517i) q^{38} -8.98606i q^{39} +(2.84873 - 5.64666i) q^{40} +4.89391i q^{41} +(-14.9604 + 6.79420i) q^{42} +7.02309 q^{43} +(-1.02667 - 0.897202i) q^{44} +(-1.91560 + 10.8132i) q^{45} +(3.74950 + 8.25615i) q^{46} +6.74187 q^{47} +(11.1492 - 1.50746i) q^{48} +10.0629 q^{49} +(0.534257 + 7.05086i) q^{50} +8.25100 q^{51} +(4.20463 - 4.81138i) q^{52} +7.60467 q^{53} +(-6.92152 + 3.14339i) q^{54} +(1.50103 + 0.265913i) q^{55} +(-11.1892 - 3.36223i) q^{56} +(10.5299 + 6.27953i) q^{57} +(-1.19539 + 0.542882i) q^{58} -13.1971 q^{59} +(-9.80245 + 7.88253i) q^{60} -5.76313 q^{61} +(3.91085 + 8.61143i) q^{62} +20.2865 q^{63} +(6.67495 + 4.40965i) q^{64} +(-1.24617 + 7.03438i) q^{65} +(1.12131 + 2.46904i) q^{66} +5.12809i q^{67} +(4.41781 + 3.86069i) q^{68} -18.0343i q^{69} +(12.6533 - 3.24390i) q^{70} -7.43972 q^{71} +(-13.3031 - 3.99743i) q^{72} +10.1531i q^{73} +(3.87857 + 8.54034i) q^{74} +(4.83114 - 13.2075i) q^{75} +(2.69977 + 8.28923i) q^{76} -2.81605i q^{77} +(-11.5709 + 5.25487i) q^{78} +4.94607 q^{79} +(-8.93678 - 0.366097i) q^{80} +0.385683 q^{81} +(6.30163 - 2.86187i) q^{82} -9.74393 q^{83} +(17.4970 + 15.2905i) q^{84} +(-6.45896 - 1.14423i) q^{85} +(-4.10697 - 9.04326i) q^{86} +2.61115 q^{87} +(-0.554899 + 1.84666i) q^{88} +7.65281i q^{89} +(15.0438 - 3.85674i) q^{90} +13.1971 q^{91} +(8.43836 - 9.65607i) q^{92} -18.8104i q^{93} +(-3.94252 - 8.68115i) q^{94} +(-7.37207 - 6.37594i) q^{95} +(-8.46093 - 13.4747i) q^{96} +15.0798 q^{97} +(-5.88460 - 12.9575i) q^{98} -3.34806i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.584780	−	1.28765i	−0.413502	−	0.910503i
$2$	−0.584780	−	1.28765i	−0.413502	−	0.910503i
$3$			2.81267i			1.62390i	0.583730	+	0.811948i	$0.301593\pi$
$3$			2.81267i			1.62390i	−0.583730	+	0.811948i	$0.698407\pi$
$4$	−1.31606	+	1.50598i	−0.658032	+	0.752990i
$5$	0.390055	−	2.20178i	0.174438	−	0.984668i
$5$	0.390055	−	2.20178i	0.174438	−	0.984668i
$6$	3.62172	−	1.64479i	1.47856	−	0.671485i
$7$	−4.13073			−1.56127			−0.780634	−	0.624988i	$-0.785104\pi$
$7$	−4.13073			−1.56127			−0.780634	+	0.624988i	$0.785104\pi$
$8$	2.70878	+	0.813956i	0.957697	+	0.287777i
$9$	−4.91111			−1.63704
$10$	−3.06322	+	0.785308i	−0.968674	+	0.248336i
$11$			0.681732i			0.205550i	0.994705	+	0.102775i	$0.0327721\pi$
$11$			0.681732i			0.205550i	−0.994705	+	0.102775i	$0.967228\pi$
$12$	−4.23583	−	3.70165i	−1.22278	−	1.06857i
$13$	−3.19485			−0.886092			−0.443046	−	0.896499i	$-0.646102\pi$
$13$	−3.19485			−0.886092			−0.443046	+	0.896499i	$0.646102\pi$
$14$	2.41557	+	5.31892i	0.645588	+	1.42154i
$15$	6.19289	+	1.09710i	1.59900	+	0.283269i
$16$	−0.535953	−	3.96393i	−0.133988	−	0.990983i
$17$		−	2.93351i		−	0.711481i	−0.934585	−	0.355741i	$-0.884229\pi$
$17$		−	2.93351i		−	0.711481i	0.934585	−	0.355741i	$-0.115771\pi$
$18$	2.87192	+	6.32377i	0.676919	+	1.49053i
$19$	2.23259	−	3.74374i	0.512190	−	0.858872i
$19$	2.23259	−	3.74374i	0.512190	−	0.858872i
$20$	2.80251	+	3.48510i	0.626660	+	0.779293i
$21$		−	11.6184i		−	2.53534i
$22$	0.877829	−	0.398663i	0.187154	−	0.0849953i
$23$	−6.41181			−1.33696			−0.668478	−	0.743732i	$-0.733054\pi$
$23$	−6.41181			−1.33696			−0.668478	+	0.743732i	$0.733054\pi$
$24$	−2.28939	+	7.61890i	−0.467320	+	1.55520i
$25$	−4.69571	−	1.71763i	−0.939143	−	0.343527i
$26$	1.86829	+	4.11384i	0.366401	+	0.806790i
$27$		−	5.37533i		−	1.03448i
$28$	5.43630	−	6.22080i	1.02736	−	1.17562i
$29$		−	0.928351i		−	0.172391i	−0.996278	−	0.0861953i	$-0.972529\pi$
$29$		−	0.928351i		−	0.172391i	0.996278	−	0.0861953i	$-0.0274709\pi$
$30$	−2.20881	−	8.61581i	−0.403272	−	1.57303i
$31$	−6.68773			−1.20115			−0.600576	−	0.799568i	$-0.705062\pi$
$31$	−6.68773			−1.20115			−0.600576	+	0.799568i	$0.705062\pi$
$32$	−4.79072	+	3.00815i	−0.846889	+	0.531770i
$33$	−1.91749			−0.333791
$34$	−3.77732	+	1.71546i	−0.647806	+	0.294199i
$35$	−1.61121	+	9.09498i	−0.272344	+	1.53733i
$36$	6.46334	−	7.39604i	1.07722	−	1.23267i
$37$	−6.63253			−1.09038			−0.545190	−	0.838312i	$-0.683543\pi$
$37$	−6.63253			−1.09038			−0.545190	+	0.838312i	$0.683543\pi$
$38$	−6.12618	−	0.685517i	−0.993797	−	0.111205i
$39$		−	8.98606i		−	1.43892i
$40$	2.84873	−	5.64666i	0.450423	−	0.892815i
$41$			4.89391i			0.764301i	0.924100	+	0.382151i	$0.124816\pi$
$41$			4.89391i			0.764301i	−0.924100	+	0.382151i	$0.875184\pi$
$42$	−14.9604	+	6.79420i	−2.30843	+	1.04837i
$43$	7.02309			1.07101			0.535506	−	0.844532i	$-0.320121\pi$
$43$	7.02309			1.07101			0.535506	+	0.844532i	$0.320121\pi$
$44$	−1.02667	−	0.897202i	−0.154777	−	0.135258i
$45$	−1.91560	+	10.8132i	−0.285561	+	1.61194i
$46$	3.74950	+	8.25615i	0.552834	+	1.21730i
$47$	6.74187			0.983404			0.491702	−	0.870764i	$-0.336375\pi$
$47$	6.74187			0.983404			0.491702	+	0.870764i	$0.336375\pi$
$48$	11.1492	−	1.50746i	1.60925	−	0.217583i
$49$	10.0629			1.43756
$50$	0.534257	+	7.05086i	0.0755553	+	0.997142i
$51$	8.25100			1.15537
$52$	4.20463	−	4.81138i	0.583077	−	0.667219i
$53$	7.60467			1.04458			0.522291	−	0.852767i	$-0.325077\pi$
$53$	7.60467			1.04458			0.522291	+	0.852767i	$0.325077\pi$
$54$	−6.92152	+	3.14339i	−0.941899	+	0.427761i
$55$	1.50103	+	0.265913i	0.202398	+	0.0358557i
$56$	−11.1892	−	3.36223i	−1.49522	−	0.449297i
$57$	10.5299	+	6.27953i	1.39472	+	0.831744i
$58$	−1.19539	+	0.542882i	−0.156962	+	0.0712839i
$59$	−13.1971			−1.71811			−0.859056	−	0.511882i	$-0.828949\pi$
$59$	−13.1971			−1.71811			−0.859056	+	0.511882i	$0.828949\pi$
$60$	−9.80245	+	7.88253i	−1.26549	+	1.01763i
$61$	−5.76313			−0.737893			−0.368947	−	0.929451i	$-0.620281\pi$
$61$	−5.76313			−0.737893			−0.368947	+	0.929451i	$0.620281\pi$
$62$	3.91085	+	8.61143i	0.496679	+	1.09365i
$63$	20.2865			2.55586
$64$	6.67495	+	4.40965i	0.834369	+	0.551206i
$65$	−1.24617	+	7.03438i	−0.154568	+	0.872507i
$66$	1.12131	+	2.46904i	0.138024	+	0.303918i
$67$			5.12809i			0.626496i	0.949671	+	0.313248i	$0.101417\pi$
$67$			5.12809i			0.626496i	−0.949671	+	0.313248i	$0.898583\pi$
$68$	4.41781	+	3.86069i	0.535738	+	0.468177i
$69$		−	18.0343i		−	2.17108i
$70$	12.6533	−	3.24390i	1.51236	−	0.387720i
$71$	−7.43972			−0.882933			−0.441466	−	0.897278i	$-0.645542\pi$
$71$	−7.43972			−0.882933			−0.441466	+	0.897278i	$0.645542\pi$
$72$	−13.3031	−	3.99743i	−1.56779	−	0.471101i
$73$			10.1531i			1.18833i	0.804342	+	0.594167i	$0.202518\pi$
$73$			10.1531i			1.18833i	−0.804342	+	0.594167i	$0.797482\pi$
$74$	3.87857	+	8.54034i	0.450875	+	0.992795i
$75$	4.83114	−	13.2075i	0.557852	−	1.52507i
$76$	2.69977	+	8.28923i	0.309685	+	0.950839i
$77$		−	2.81605i		−	0.320919i
$78$	−11.5709	+	5.25487i	−1.31014	+	0.594997i
$79$	4.94607			0.556476			0.278238	−	0.960512i	$-0.410250\pi$
$79$	4.94607			0.556476			0.278238	+	0.960512i	$0.410250\pi$
$80$	−8.93678	−	0.366097i	−0.999162	−	0.0409309i
$81$	0.385683			0.0428536
$82$	6.30163	−	2.86187i	0.695899	−	0.316040i
$83$	−9.74393			−1.06954			−0.534768	−	0.844999i	$-0.679601\pi$
$83$	−9.74393			−1.06954			−0.534768	+	0.844999i	$0.679601\pi$
$84$	17.4970	+	15.2905i	1.90908	+	1.66833i
$85$	−6.45896	−	1.14423i	−0.700573	−	0.124109i
$86$	−4.10697	−	9.04326i	−0.442866	−	0.975159i
$87$	2.61115			0.279944
$88$	−0.554899	+	1.84666i	−0.0591525	+	0.196855i
$89$			7.65281i			0.811197i	0.914051	+	0.405598i	$0.132937\pi$
$89$			7.65281i			0.811197i	−0.914051	+	0.405598i	$0.867063\pi$
$90$	15.0438	−	3.85674i	1.58576	−	0.406536i
$91$	13.1971			1.38343
$92$	8.43836	−	9.65607i	0.879759	−	1.00671i
$93$		−	18.8104i		−	1.95054i
$94$	−3.94252	−	8.68115i	−0.406640	−	0.895392i
$95$	−7.37207	−	6.37594i	−0.756358	−	0.654157i
$96$	−8.46093	−	13.4747i	−0.863540	−	1.37526i
$97$	15.0798			1.53113			0.765563	−	0.643361i	$-0.222461\pi$
$97$	15.0798			1.53113			0.765563	+	0.643361i	$0.222461\pi$
$98$	−5.88460	−	12.9575i	−0.594434	−	1.30890i
$99$		−	3.34806i		−	0.336493i
$100$	8.76658	−	4.81114i	0.876658	−	0.481114i
$101$	7.45052			0.741355			0.370677	−	0.928762i	$-0.379126\pi$
$101$	7.45052			0.741355			0.370677	+	0.928762i	$0.379126\pi$
$102$	−4.82502	−	10.6244i	−0.477749	−	1.05197i
$103$			0.817949i			0.0805950i	0.999188	+	0.0402975i	$0.0128306\pi$
$103$			0.817949i			0.0805950i	−0.999188	+	0.0402975i	$0.987169\pi$
$104$	−8.65414	−	2.60047i	−0.848609	−	0.254997i
$105$	−25.5812	−	4.53181i	−2.49647	−	0.442259i
$106$	−4.44707	−	9.79213i	−0.431937	−	0.951095i
$107$			11.1238i			1.07538i	0.843143	+	0.537689i	$0.180702\pi$
$107$			11.1238i			1.07538i	−0.843143	+	0.537689i	$0.819298\pi$
$108$	8.09514	+	7.07427i	0.778955	+	0.680722i
$109$		−	3.24135i		−	0.310465i	−0.987878	−	0.155232i	$-0.950387\pi$
$109$		−	3.24135i		−	0.310465i	0.987878	−	0.155232i	$-0.0496126\pi$
$110$	−0.535369	−	2.08829i	−0.0510455	−	0.199111i
$111$		−	18.6551i		−	1.77066i
$112$	2.21388	+	16.3739i	0.209192	+	1.54719i
$113$	1.55514			0.146295			0.0731476	−	0.997321i	$-0.476696\pi$
$113$	1.55514			0.146295			0.0731476	+	0.997321i	$0.476696\pi$
$114$	1.92813	−	17.2309i	0.180586	−	1.61382i
$115$	−2.50096	+	14.1174i	−0.233216	+	1.31646i
$116$	1.39808	+	1.22177i	0.129808	+	0.113438i
$117$	15.6903			1.45057
$118$	7.71739	+	16.9931i	0.710443	+	1.56435i
$119$			12.1175i			1.11081i
$120$	15.8822	+	8.01253i	1.44984	+	0.731441i
$121$	10.5352			0.957749
$122$	3.37017	+	7.42087i	0.305120	+	0.671854i
$123$	−13.7650			−1.24115
$124$	8.80148	−	10.0716i	0.790396	−	0.904455i
$125$	−5.61345	+	9.66898i	−0.502082	+	0.864820i
$126$	−11.8631	−	26.1218i	−1.05685	−	2.32711i
$127$		−	16.2908i		−	1.44557i	−0.691071	−	0.722787i	$-0.742861\pi$
$127$		−	16.2908i		−	1.44557i	0.691071	−	0.722787i	$-0.257139\pi$
$128$	1.77469	−	11.1737i	0.156862	−	0.987621i
$129$			19.7536i			1.73921i
$130$	9.78652	−	2.50894i	0.858335	−	0.220049i
$131$		−	5.44773i		−	0.475970i	−0.971269	−	0.237985i	$-0.923513\pi$
$131$		−	5.44773i		−	0.475970i	0.971269	−	0.237985i	$-0.0764870\pi$
$132$	2.52353	−	2.88770i	0.219645	−	0.251342i
$133$	−9.22221	+	15.4644i	−0.799667	+	1.34093i
$134$	6.60316	−	2.99881i	0.570427	−	0.259058i
$135$	−11.8353	−	2.09667i	−1.01862	−	0.180453i
$136$	2.38775	−	7.94623i	0.204748	−	0.681384i
$137$		−	21.1247i		−	1.80480i	−0.430897	−	0.902401i	$-0.641803\pi$
$137$		−	21.1247i		−	1.80480i	0.430897	−	0.902401i	$-0.358197\pi$
$138$	−23.2218	+	10.5461i	−1.97677	+	0.897745i
$139$		−	9.05531i		−	0.768062i	−0.923320	−	0.384031i	$-0.874536\pi$
$139$		−	9.05531i		−	0.768062i	0.923320	−	0.384031i	$-0.125464\pi$
$140$	−11.5764	−	14.3960i	−0.978384	−	1.21669i
$141$			18.9627i			1.59694i
$142$	4.35060	+	9.57973i	0.365095	+	0.803913i
$143$		−	2.17803i		−	0.182136i
$144$	2.63213	+	19.4673i	0.219344	+	1.62228i
$145$	−2.04403	−	0.362108i	−0.169747	−	0.0300714i
$146$	13.0736	−	5.93735i	1.08198	−	0.491379i
$147$			28.3037i			2.33445i
$148$	8.72883	−	9.98845i	0.717505	−	0.821046i
$149$	−1.55447			−0.127348			−0.0636738	−	0.997971i	$-0.520282\pi$
$149$	−1.55447			−0.127348			−0.0636738	+	0.997971i	$0.520282\pi$
$150$	−19.8317	+	1.50269i	−1.61925	+	0.122694i
$151$	−4.46517			−0.363371			−0.181685	−	0.983357i	$-0.558155\pi$
$151$	−4.46517			−0.363371			−0.181685	+	0.983357i	$0.558155\pi$
$152$	9.09482	−	8.32372i	0.737687	−	0.675143i
$153$			14.4068i			1.16472i
$154$	−3.62607	+	1.64677i	−0.292197	+	0.132701i
$155$	−2.60858	+	14.7249i	−0.209526	+	1.18274i
$156$	13.5328	+	11.8262i	1.08349	+	0.946856i
$157$		−	0.527586i		−	0.0421060i	−0.999778	−	0.0210530i	$-0.993298\pi$
$157$		−	0.527586i		−	0.0421060i	0.999778	−	0.0210530i	$-0.00670187\pi$
$158$	−2.89236	−	6.36878i	−0.230104	−	0.506673i
$159$			21.3894i			1.69629i
$160$	4.75465	+	11.7215i	0.375888	+	0.926665i
$161$	26.4855			2.08735
$162$	−0.225540	−	0.496623i	−0.0177201	−	0.0390184i
$163$	−23.5089			−1.84136			−0.920679	−	0.390320i	$-0.872364\pi$
$163$	−23.5089			−1.84136			−0.920679	+	0.390320i	$0.872364\pi$
$164$	−7.37014	−	6.44070i	−0.575511	−	0.502934i
$165$	−0.747925	+	4.22189i	−0.0582259	+	0.328674i
$166$	5.69806	+	12.5467i	0.442255	+	0.973815i
$167$			14.4543i			1.11851i	0.828996	+	0.559254i	$0.188912\pi$
$167$			14.4543i			1.11851i	−0.828996	+	0.559254i	$0.811088\pi$
$168$	9.45685	−	31.4716i	0.729611	−	2.42809i
$169$	−2.79292			−0.214840
$170$	2.30371	+	8.98598i	0.176687	+	0.689193i
$171$	−10.9645	+	18.3859i	−0.838475	+	1.40601i
$172$	−9.24284	+	10.5766i	−0.704760	+	0.806461i
$173$	−17.4795			−1.32894			−0.664469	−	0.747315i	$-0.731342\pi$
$173$	−17.4795			−1.32894			−0.664469	+	0.747315i	$0.731342\pi$
$174$	−1.52695	−	3.36223i	−0.115758	−	0.254890i
$175$	19.3967	+	7.09508i	1.46625	+	0.536338i
$176$	2.70234	−	0.365376i	0.203696	−	0.0275413i
$177$		−	37.1190i		−	2.79003i
$178$	9.85411	−	4.47522i	0.738597	−	0.335432i
$179$	3.96422			0.296300			0.148150	−	0.988965i	$-0.452668\pi$
$179$	3.96422			0.296300			0.148150	+	0.988965i	$0.452668\pi$
$180$	−13.7634	−	17.1157i	−1.02587	−	1.27573i
$181$		−	16.7164i		−	1.24252i	−0.783604	−	0.621261i	$-0.786621\pi$
$181$		−	16.7164i		−	1.24252i	0.783604	−	0.621261i	$-0.213379\pi$
$182$	−7.71739	−	16.9931i	−0.572051	−	1.25962i
$183$		−	16.2098i		−	1.19826i
$184$	−17.3682	−	5.21893i	−1.28040	−	0.384745i
$185$	−2.58705	+	14.6034i	−0.190204	+	1.07366i
$186$	−24.2211	+	10.9999i	−1.77598	+	0.806555i
$187$	1.99987			0.146245
$188$	−8.87274	+	10.1531i	−0.647111	+	0.740493i
$189$			22.2040i			1.61510i
$190$	−3.89891	+	13.2211i	−0.282856	+	0.959162i
$191$			2.74091i			0.198325i	0.995071	+	0.0991625i	$0.0316164\pi$
$191$			2.74091i			0.198325i	−0.995071	+	0.0991625i	$0.968384\pi$
$192$	−12.4029	+	18.7744i	−0.895102	+	1.35493i
$193$	−4.92107			−0.354226			−0.177113	−	0.984191i	$-0.556676\pi$
$193$	−4.92107			−0.354226			−0.177113	+	0.984191i	$0.556676\pi$
$194$	−8.81840	−	19.4175i	−0.633124	−	1.39409i
$195$	−19.7854	−	3.50506i	−1.41686	−	0.251003i
$196$	−13.2434	+	15.1546i	−0.945960	+	1.08247i
$197$			6.48624i			0.462126i	0.972939	+	0.231063i	$0.0742203\pi$
$197$			6.48624i			0.462126i	−0.972939	+	0.231063i	$0.925780\pi$
$198$	−4.31112	+	1.95788i	−0.306378	+	0.139141i
$199$		−	4.63007i		−	0.328217i	−0.986442	−	0.164109i	$-0.947525\pi$
$199$		−	4.63007i		−	0.328217i	0.986442	−	0.164109i	$-0.0524747\pi$
$200$	−11.3216	−	8.47479i	−0.800556	−	0.599258i
$201$	−14.4236			−1.01736
$202$	−4.35692	−	9.59363i	−0.306552	−	0.675006i
$203$			3.83477i			0.269148i
$204$	−10.8588	+	12.4258i	−0.760271	+	0.869983i
$205$	10.7753	+	1.90890i	0.752583	+	0.133323i
$206$	1.05323	−	0.478321i	0.0733820	−	0.0333262i
$207$	31.4891			2.18865
$208$	1.71229	+	12.6642i	0.118726	+	0.878102i
$209$	2.55222	+	1.52202i	0.176541	+	0.105281i
$210$	9.12401	+	35.5896i	0.629616	+	2.45592i
$211$	−14.4300			−0.993399			−0.496699	−	0.867923i	$-0.665455\pi$
$211$	−14.4300			−0.993399			−0.496699	+	0.867923i	$0.665455\pi$
$212$	−10.0082	+	11.4525i	−0.687368	+	0.786560i
$213$		−	20.9255i		−	1.43379i
$214$	14.3235	−	6.50498i	0.979135	−	0.444671i
$215$	2.73939	−	15.4633i	0.186825	−	1.05459i
$216$	4.37528	−	14.5606i	0.297700	−	0.990721i
$217$	27.6252			1.87532
$218$	−4.17371	+	1.89548i	−0.282679	+	0.128378i
$219$	−28.5574			−1.92973
$220$	−2.37591	+	1.91056i	−0.160184	+	0.128810i
$221$			9.37214i			0.630438i
$222$	−24.0212	+	10.9091i	−1.61220	+	0.732174i
$223$		−	18.6603i		−	1.24959i	−0.780790	−	0.624794i	$-0.785183\pi$
$223$		−	18.6603i		−	1.24959i	0.780790	−	0.624794i	$-0.214817\pi$
$224$	19.7892	−	12.4258i	1.32222	−	0.830237i
$225$	23.0612	+	8.43550i	1.53741	+	0.562366i
$226$	−0.909415	−	2.00247i	−0.0604934	−	0.133202i
$227$			2.50907i			0.166533i	0.996527	+	0.0832663i	$0.0265352\pi$
$227$			2.50907i			0.166533i	−0.996527	+	0.0832663i	$0.973465\pi$
$228$	−23.3149	+	7.59355i	−1.54406	+	0.502895i
$229$	−14.8673			−0.982461			−0.491231	−	0.871030i	$-0.663453\pi$
$229$	−14.8673			−0.982461			−0.491231	+	0.871030i	$0.663453\pi$
$230$	19.6408	−	5.03525i	1.29507	−	0.332015i
$231$	7.92062			0.521138
$232$	0.755637	−	2.51470i	0.0496100	−	0.165098i
$233$		−	3.78435i		−	0.247921i	−0.992287	−	0.123960i	$-0.960440\pi$
$233$		−	3.78435i		−	0.247921i	0.992287	−	0.123960i	$-0.0395596\pi$
$234$	−9.17537	−	20.2035i	−0.599812	−	1.32075i
$235$	2.62970	−	14.8442i	0.171543	−	0.968326i
$236$	17.3682	−	19.8745i	1.13057	−	1.29372i
$237$			13.9117i			0.903659i
$238$	15.6031	−	7.08610i	1.01140	−	0.459324i
$239$			23.0185i			1.48894i	0.667654	+	0.744472i	$0.267299\pi$
$239$			23.0185i			1.48894i	−0.667654	+	0.744472i	$0.732701\pi$
$240$	1.02971	−	25.1362i	0.0664676	−	1.62253i
$241$		−	2.24624i		−	0.144693i	−0.997380	−	0.0723466i	$-0.976951\pi$
$241$		−	2.24624i		−	0.144693i	0.997380	−	0.0723466i	$-0.0230488\pi$
$242$	−6.16080	−	13.5657i	−0.396031	−	0.872034i
$243$		−	15.0412i		−	0.964892i
$244$	7.58464	−	8.67916i	0.485557	−	0.555626i
$245$	3.92509	−	22.1564i	0.250765	−	1.41552i
$246$	8.04948	+	17.7244i	0.513216	+	1.13007i
$247$	−7.13278	+	11.9607i	−0.453848	+	0.761040i
$248$	−18.1156	−	5.44352i	−1.15034	−	0.345664i
$249$		−	27.4065i		−	1.73681i
$250$	15.7329	+	1.57390i	0.995033	+	0.0995424i
$251$		−	8.81332i		−	0.556292i	−0.960539	−	0.278146i	$-0.910280\pi$
$251$		−	8.81332i		−	0.556292i	0.960539	−	0.278146i	$-0.0897199\pi$
$252$	−26.6983	+	30.5510i	−1.68183	+	1.92453i
$253$		−	4.37114i		−	0.274811i
$254$	−20.9768	+	9.52654i	−1.31620	+	0.597748i
$255$	3.21834	−	18.1669i	0.201541	−	1.13766i
$256$	−15.4255	+	4.24897i	−0.964094	+	0.265560i
$257$	7.30009			0.455367			0.227684	−	0.973735i	$-0.426885\pi$
$257$	7.30009			0.455367			0.227684	+	0.973735i	$0.426885\pi$
$258$	25.4357	−	11.5515i	1.58356	−	0.719168i
$259$	27.3972			1.70238
$260$	−8.95360	−	11.1344i	−0.555278	−	0.690526i
$261$			4.55924i			0.282210i
$262$	−7.01474	+	3.18573i	−0.433372	+	0.196815i
$263$	19.0639			1.17553			0.587766	−	0.809031i	$-0.300008\pi$
$263$	19.0639			1.17553			0.587766	+	0.809031i	$0.300008\pi$
$264$	−5.19404	−	1.56075i	−0.319671	−	0.0960575i
$265$	2.96624	−	16.7439i	0.182215	−	1.02857i
$266$	25.3056	+	2.83168i	1.55158	+	0.173622i
$267$	−21.5248			−1.31730
$268$	−7.72280	−	6.74889i	−0.471745	−	0.412254i
$269$			18.9627i			1.15617i	0.815975	+	0.578087i	$0.196201\pi$
$269$			18.9627i			1.15617i	−0.815975	+	0.578087i	$0.803799\pi$
$270$	4.22129	+	16.4658i	0.256899	+	1.00208i
$271$		−	25.7581i		−	1.56469i	−0.622844	−	0.782346i	$-0.714023\pi$
$271$		−	25.7581i		−	1.56469i	0.622844	−	0.782346i	$-0.285977\pi$
$272$	−11.6282	+	1.57223i	−0.705066	+	0.0953302i
$273$			37.1190i			2.24654i
$274$	−27.2011	+	12.3533i	−1.64328	+	0.746290i
$275$	1.17097	−	3.20122i	0.0706119	−	0.193041i
$276$	27.1593	+	23.7343i	1.63480	+	1.42864i
$277$			23.2139i			1.39479i	0.716687	+	0.697395i	$0.245658\pi$
$277$			23.2139i			1.39479i	−0.716687	+	0.697395i	$0.754342\pi$
$278$	−11.6600	+	5.29537i	−0.699323	+	0.317595i
$279$	32.8442			1.96633
$280$	−11.7673	+	23.3248i	−0.703232	+	1.39392i
$281$		−	9.45315i		−	0.563928i	−0.959425	−	0.281964i	$-0.909014\pi$
$281$		−	9.45315i		−	0.563928i	0.959425	−	0.281964i	$-0.0909858\pi$
$282$	24.4172	−	11.0890i	1.45402	−	0.660340i
$283$	21.0074			1.24876			0.624381	−	0.781120i	$-0.285351\pi$
$283$	21.0074			1.24876			0.624381	+	0.781120i	$0.285351\pi$
$284$	9.79115	−	11.2041i	0.580998	−	0.664840i
$285$	17.9334	−	20.7352i	1.06228	−	1.22825i
$286$	−2.80453	+	1.27367i	−0.165836	+	0.0753137i
$287$		−	20.2154i		−	1.19328i
$288$	23.5278	−	14.7734i	1.38639	−	0.870528i
$289$	8.39451			0.493795
$290$	0.729042	+	2.84374i	0.0428108	+	0.166990i
$291$			42.4146i			2.48639i
$292$	−15.2904	−	13.3622i	−0.894804	−	0.781962i
$293$	−32.7375			−1.91255			−0.956274	−	0.292474i	$-0.905522\pi$
$293$	−32.7375			−1.91255			−0.956274	+	0.292474i	$0.905522\pi$
$294$	36.4451	−	16.5514i	2.12552	−	0.965299i
$295$	−5.14758	+	29.0571i	−0.299704	+	1.69177i
$296$	−17.9660	−	5.39858i	−1.04425	−	0.313786i
$297$	3.66453			0.212638
$298$	0.909026	+	2.00161i	0.0526585	+	0.115950i
$299$	20.4848			1.18467
$300$	13.5321	+	24.6575i	0.781278	+	1.42360i
$301$	−29.0105			−1.67214
$302$	2.61115	+	5.74956i	0.150255	+	0.330850i
$303$			20.9559i			1.20388i
$304$	−16.0365	−	6.84335i	−0.919755	−	0.392493i
$305$	−2.24794	+	12.6892i	−0.128717	+	0.726580i
$306$	18.5509	−	8.42482i	1.06048	−	0.481615i
$307$		−	24.7134i		−	1.41047i	−0.708975	−	0.705233i	$-0.750842\pi$
$307$		−	24.7134i		−	1.41047i	0.708975	−	0.705233i	$-0.249158\pi$
$308$	4.24091	+	3.70610i	0.241649	+	0.211175i
$309$	−2.30062			−0.130878
$310$	20.4860	−	5.25193i	1.16352	−	0.298289i
$311$		−	18.3688i		−	1.04160i	−0.853679	−	0.520800i	$-0.825634\pi$
$311$		−	18.3688i		−	1.04160i	0.853679	−	0.520800i	$-0.174366\pi$
$312$	7.31426	−	24.3412i	0.414088	−	1.37805i
$313$		−	13.0608i		−	0.738241i	−0.929382	−	0.369120i	$-0.879659\pi$
$313$		−	13.0608i		−	0.738241i	0.929382	−	0.369120i	$-0.120341\pi$
$314$	−0.679345	+	0.308522i	−0.0383376	+	0.0174109i
$315$	7.91284	−	44.6664i	0.445838	−	2.51667i
$316$	−6.50934	+	7.44868i	−0.366179	+	0.419021i
$317$	5.67220			0.318583			0.159291	−	0.987232i	$-0.449079\pi$
$317$	5.67220			0.318583			0.159291	+	0.987232i	$0.449079\pi$
$318$	27.5420	−	12.5081i	1.54448	−	0.701421i
$319$	0.632887			0.0354348
$320$	12.3127	−	12.9768i	0.688301	−	0.725425i
$321$	−31.2876			−1.74630
$322$	−15.4882	−	34.1039i	−0.863123	−	1.90054i
$323$	−10.9823	−	6.54932i	−0.611071	−	0.364414i
$324$	−0.507583	+	0.580830i	−0.0281990	+	0.0322684i
$325$	15.0021	+	5.48759i	0.832167	+	0.304397i
$326$	13.7475	+	30.2711i	0.761406	+	1.67656i
$327$	9.11684			0.504162
$328$	−3.98343	+	13.2565i	−0.219948	+	0.731969i
$329$	−27.8489			−1.53536
$330$	5.87367	−	1.50582i	0.323335	−	0.0828925i
$331$	−3.78583			−0.208088			−0.104044	−	0.994573i	$-0.533178\pi$
$331$	−3.78583			−0.208088			−0.104044	+	0.994573i	$0.533178\pi$
$332$	12.8236	−	14.6742i	0.703788	−	0.805349i
$333$	32.5731			1.78499
$334$	18.6120	−	8.45260i	1.01840	−	0.462505i
$335$	11.2910	+	2.00024i	0.616891	+	0.109285i
$336$	−46.0545	+	6.22691i	−2.51248	+	0.339706i
$337$	−28.8626			−1.57225			−0.786123	−	0.618070i	$-0.787915\pi$
$337$	−28.8626			−1.57225			−0.786123	+	0.618070i	$0.787915\pi$
$338$	1.63325	+	3.59629i	0.0888369	+	0.195613i
$339$			4.37410i			0.237568i
$340$	10.2236	−	8.22119i	0.554452	−	0.445857i
$341$		−	4.55924i		−	0.246897i
$342$	30.0863	+	3.36665i	1.62688	+	0.182048i
$343$	−12.6521			−0.683149
$344$	19.0240	+	5.71649i	1.02571	+	0.308212i
$345$	−39.7077	−	7.03438i	−2.13779	−	0.378718i
$346$	10.2216	+	22.5074i	0.549519	+	1.21000i
$347$	−5.58017			−0.299559			−0.149780	−	0.988719i	$-0.547856\pi$
$347$	−5.58017			−0.299559			−0.149780	+	0.988719i	$0.547856\pi$
$348$	−3.43643	+	3.93233i	−0.184212	+	0.210795i
$349$	12.5906			0.673959			0.336980	−	0.941512i	$-0.390595\pi$
$349$	12.5906			0.673959			0.336980	+	0.941512i	$0.390595\pi$
$350$	−2.20687	−	29.1252i	−0.117962	−	1.55681i
$351$			17.1734i			0.916647i
$352$	−2.05075	−	3.26599i	−0.109305	−	0.174078i
$353$		−	0.501758i		−	0.0267059i	−0.999911	−	0.0133529i	$-0.995750\pi$
$353$		−	0.501758i		−	0.0267059i	0.999911	−	0.0133529i	$-0.00425050\pi$
$354$	−47.7961	+	21.7065i	−2.54033	+	1.15369i
$355$	−2.90190	+	16.3807i	−0.154017	+	0.869396i
$356$	−11.5250	−	10.0716i	−0.610823	−	0.533793i
$357$	−34.0826			−1.80384
$358$	−2.31820	−	5.10451i	−0.122521	−	0.269782i
$359$			17.0054i			0.897509i	0.893655	+	0.448754i	$0.148132\pi$
$359$			17.0054i			0.897509i	−0.893655	+	0.448754i	$0.851868\pi$
$360$	−13.9904	+	27.7314i	−0.737360	+	1.46157i
$361$	−9.03112	−	16.7164i	−0.475322	−	0.879812i
$362$	−21.5248	+	9.77544i	−1.13132	+	0.513786i
$363$			29.6322i			1.55528i
$364$	−17.3682	+	19.8745i	−0.910340	+	1.04171i
$365$	22.3550	+	3.96028i	1.17011	+	0.207291i
$366$	−20.8725	+	9.47916i	−1.09102	+	0.495484i
$367$	0.980882			0.0512016			0.0256008	−	0.999672i	$-0.491850\pi$
$367$	0.980882			0.0512016			0.0256008	+	0.999672i	$0.491850\pi$
$368$	3.43643	+	25.4160i	0.179136	+	1.32490i
$369$		−	24.0346i		−	1.25119i
$370$	20.3169	−	5.20858i	1.05622	−	0.270781i
$371$	−31.4128			−1.63087
$372$	28.3281	+	24.7556i	1.46874	+	1.28352i
$373$	2.73331			0.141526			0.0707628	−	0.997493i	$-0.477457\pi$
$373$	2.73331			0.141526			0.0707628	+	0.997493i	$0.477457\pi$
$374$	−1.16948	−	2.57512i	−0.0604726	−	0.133156i
$375$	−27.1957	−	15.7888i	−1.40438	−	0.815329i
$376$	18.2622	+	5.48759i	0.941803	+	0.283001i
$377$			2.96594i			0.152754i
$378$	28.5909	−	12.9845i	1.47056	−	0.667849i
$379$	−4.89460			−0.251419			−0.125709	−	0.992067i	$-0.540121\pi$
$379$	−4.89460			−0.251419			−0.125709	+	0.992067i	$0.540121\pi$
$380$	19.3041	−	2.71105i	0.990282	−	0.139074i
$381$	45.8206			2.34746
$382$	3.52932	−	1.60283i	0.180576	−	0.0820079i
$383$		−	0.855884i		−	0.0437336i	−0.999761	−	0.0218668i	$-0.993039\pi$
$383$		−	0.855884i		−	0.0437336i	0.999761	−	0.0218668i	$-0.00696098\pi$
$384$	31.4278	+	4.99161i	1.60379	+	0.254727i
$385$	−6.20033	−	1.09841i	−0.315998	−	0.0559804i
$386$	2.87774	+	6.33659i	0.146473	+	0.322524i
$387$	−34.4912			−1.75329
$388$	−19.8460	+	22.7099i	−1.00753	+	1.15292i
$389$	1.53950			0.0780560			0.0390280	−	0.999238i	$-0.487574\pi$
$389$	1.53950			0.0780560			0.0390280	+	0.999238i	$0.487574\pi$
$390$	7.05683	+	27.5263i	0.357336	+	1.39385i
$391$			18.8091i			0.951219i
$392$	27.2582	+	8.19077i	1.37675	+	0.413697i
$393$	15.3227			0.772926
$394$	8.35199	−	3.79303i	0.420767	−	0.191090i
$395$	1.92924	−	10.8902i	0.0970705	−	0.547944i
$396$	5.04211	+	4.40626i	0.253376	+	0.221423i
$397$		−	34.3640i		−	1.72468i	−0.506330	−	0.862340i	$-0.668998\pi$
$397$		−	34.3640i		−	1.72468i	0.506330	−	0.862340i	$-0.331002\pi$
$398$	−5.96189	+	2.70758i	−0.298843	+	0.135718i
$399$	−43.4961	−	25.9390i	−2.17753	−	1.29858i
$400$	−4.29190	+	19.5341i	−0.214595	+	0.976703i
$401$			25.1483i			1.25585i	0.778275	+	0.627924i	$0.216095\pi$
$401$			25.1483i			1.25585i	−0.778275	+	0.627924i	$0.783905\pi$
$402$	8.43466	+	18.5725i	0.420682	+	0.926313i
$403$	21.3663			1.06433
$404$	−9.80536	+	11.2203i	−0.487835	+	0.558233i
$405$	0.150437	−	0.849190i	0.00747530	−	0.0421966i
$406$	4.93782	−	2.24250i	0.245060	−	0.111293i
$407$		−	4.52160i		−	0.224128i
$408$	22.3501	+	6.71595i	1.10650	+	0.332489i
$409$		−	7.36766i		−	0.364307i	−0.983270	−	0.182154i	$-0.941693\pi$
$409$		−	7.36766i		−	0.364307i	0.983270	−	0.182154i	$-0.0583069\pi$
$410$	−3.84323	−	14.9911i	−0.189804	−	0.740359i
$411$	59.4167			2.93081
$412$	−1.23182	−	1.07647i	−0.0606872	−	0.0530340i
$413$	54.5135			2.68243
$414$	−18.4142	−	40.5469i	−0.905010	−	1.99277i
$415$	−3.80067	+	21.4540i	−0.186567	+	1.05314i
$416$	15.3057	−	9.61059i	0.750422	−	0.471198i
$417$	25.4696			1.24725
$418$	0.467338	−	4.17641i	0.0228583	−	0.204275i
$419$		−	6.90117i		−	0.337144i	−0.985689	−	0.168572i	$-0.946084\pi$
$419$		−	6.90117i		−	0.337144i	0.985689	−	0.168572i	$-0.0539156\pi$
$420$	40.4913	−	32.5606i	1.97577	−	1.58879i
$421$			1.83055i			0.0892154i	0.999005	+	0.0446077i	$0.0142038\pi$
$421$			1.83055i			0.0892154i	−0.999005	+	0.0446077i	$0.985796\pi$
$422$	8.43836	+	18.5807i	0.410773	+	0.904493i
$423$	−33.1101			−1.60987
$424$	20.5994	+	6.18987i	1.00039	+	0.300607i
$425$	−5.03870	+	13.7749i	−0.244413	+	0.668182i
$426$	−26.9446	+	12.2368i	−1.30547	+	0.592876i
$427$	23.8059			1.15205
$428$	−16.7522	−	14.6396i	−0.809749	−	0.707633i
$429$	6.12608			0.295770
$430$	−21.5132	+	5.51529i	−1.03746	+	0.265971i
$431$	14.0996			0.679152			0.339576	−	0.940579i	$-0.389716\pi$
$431$	14.0996			0.679152			0.339576	+	0.940579i	$0.389716\pi$
$432$	−21.3074	+	2.88092i	−1.02515	+	0.138609i
$433$	−16.9499			−0.814561			−0.407280	−	0.913303i	$-0.633523\pi$
$433$	−16.9499			−0.814561			−0.407280	+	0.913303i	$0.633523\pi$
$434$	−16.1547	−	35.5715i	−0.775449	−	1.70749i
$435$	1.01849	−	5.74918i	0.0488329	−	0.275652i
$436$	4.88141	+	4.26582i	0.233777	+	0.204296i
$437$	−14.3149	+	24.0041i	−0.684776	+	1.14827i
$438$	16.6998	+	36.7718i	0.797948	+	1.75703i
$439$	24.5284			1.17067			0.585337	−	0.810790i	$-0.300962\pi$
$439$	24.5284			1.17067			0.585337	+	0.810790i	$0.300962\pi$
$440$	3.84951	+	1.94207i	0.183518	+	0.0925845i
$441$	−49.4201			−2.35334
$442$	12.0680	−	5.48064i	0.574016	−	0.260688i
$443$	−6.36297			−0.302314			−0.151157	−	0.988510i	$-0.548300\pi$
$443$	−6.36297			−0.302314			−0.151157	+	0.988510i	$0.548300\pi$
$444$	28.0942	+	24.5513i	1.33329	+	1.16515i
$445$	16.8498	+	2.98502i	0.798759	+	0.141503i
$446$	−24.0279	+	10.9122i	−1.13775	+	0.516707i
$447$		−	4.37222i		−	0.206799i
$448$	−27.5724	−	18.2151i	−1.30267	−	0.860581i
$449$			24.8083i			1.17078i	0.810753	+	0.585388i	$0.199058\pi$
$449$			24.8083i			1.17078i	−0.810753	+	0.585388i	$0.800942\pi$
$450$	−2.62379	−	34.6275i	−0.123687	−	1.63236i
$451$	−3.33634			−0.157102
$452$	−2.04666	+	2.34201i	−0.0962669	+	0.110159i
$453$		−	12.5591i		−	0.590076i
$454$	3.23079	−	1.46725i	0.151628	−	0.0688616i
$455$	5.14758	−	29.0571i	0.241322	−	1.36222i
$456$	23.4119	+	25.5807i	1.09636	+	1.19793i
$457$			6.10142i			0.285413i	0.989765	+	0.142706i	$0.0455804\pi$
$457$			6.10142i			0.285413i	−0.989765	+	0.142706i	$0.954420\pi$
$458$	8.69413	+	19.1439i	0.406250	+	0.894534i
$459$	−15.7686			−0.736014
$460$	−17.9692	−	22.3458i	−0.837816	−	1.04188i
$461$	4.88681			0.227601			0.113801	−	0.993504i	$-0.463697\pi$
$461$	4.88681			0.227601			0.113801	+	0.993504i	$0.463697\pi$
$462$	−4.63182	−	10.1989i	−0.215492	−	0.474498i
$463$	−0.798615			−0.0371148			−0.0185574	−	0.999828i	$-0.505907\pi$
$463$	−0.798615			−0.0371148			−0.0185574	+	0.999828i	$0.505907\pi$
$464$	−3.67992	+	0.497553i	−0.170836	+	0.0230983i
$465$	−41.4164	−	7.33708i	−1.92064	−	0.340249i
$466$	−4.87290	+	2.21301i	−0.225733	+	0.102516i
$467$	8.83970			0.409053			0.204526	−	0.978861i	$-0.434435\pi$
$467$	8.83970			0.409053			0.204526	+	0.978861i	$0.434435\pi$
$468$	−20.6494	+	23.6292i	−0.954519	+	1.09226i
$469$		−	21.1828i		−	0.978129i
$470$	−20.6518	+	5.29445i	−0.952597	+	0.244215i
$471$	1.48393			0.0683757
$472$	−35.7479	−	10.7418i	−1.64543	−	0.494433i
$473$			4.78786i			0.220146i
$474$	17.9133	−	8.13526i	0.822784	−	0.373665i
$475$	−16.9140	+	13.7447i	−0.776066	+	0.630652i
$476$	−18.2488	−	15.9475i	−0.836432	−	0.730950i
$477$	−37.3474			−1.71002
$478$	29.6397	−	13.4608i	1.35569	−	0.615681i
$479$			9.69477i			0.442966i	0.975164	+	0.221483i	$0.0710897\pi$
$479$			9.69477i			0.442966i	−0.975164	+	0.221483i	$0.928910\pi$
$480$	−32.9687	+	13.3733i	−1.50481	+	0.610403i
$481$	21.1899			0.966178
$482$	−2.89236	+	1.31356i	−0.131744	+	0.0598309i
$483$			74.4949i			3.38963i
$484$	−13.8650	+	15.8659i	−0.630229	+	0.721176i
$485$	5.88197	−	33.2026i	0.267086	−	1.50765i
$486$	−19.3677	+	8.79579i	−0.878537	+	0.398985i
$487$		−	12.6428i		−	0.572902i	−0.958095	−	0.286451i	$-0.907524\pi$
$487$		−	12.6428i		−	0.572902i	0.958095	−	0.286451i	$-0.0924755\pi$
$488$	−15.6110	−	4.69093i	−0.706678	−	0.212349i
$489$		−	66.1228i		−	2.99017i
$490$	−30.8249	+	7.90249i	−1.39253	+	0.356998i
$491$		−	3.36009i		−	0.151639i	−0.997122	−	0.0758193i	$-0.975843\pi$
$491$		−	3.36009i		−	0.151639i	0.997122	−	0.0758193i	$-0.0241572\pi$
$492$	18.1156	−	20.7298i	0.816713	−	0.934570i
$493$	−2.72333			−0.122653
$494$	19.5722	+	2.19012i	0.880596	+	0.0985383i
$495$	−7.37171	−	1.30593i	−0.331334	−	0.0586971i
$496$	3.58431	+	26.5097i	0.160940	+	1.19032i
$497$	30.7315			1.37850
$498$	−35.2898	+	16.0268i	−1.58137	+	0.718176i
$499$			2.61776i			0.117187i	0.998282	+	0.0585935i	$0.0186616\pi$
$499$			2.61776i			0.117187i	−0.998282	+	0.0585935i	$0.981338\pi$
$500$	−7.17364	−	21.1787i	−0.320815	−	0.947142i
$501$	−40.6552			−1.81634
$502$	−11.3484	+	5.15386i	−0.506505	+	0.230028i
$503$	33.9417			1.51339			0.756694	−	0.653769i	$-0.226813\pi$
$503$	33.9417			1.51339			0.756694	+	0.653769i	$0.226813\pi$
$504$	54.9515	+	16.5123i	2.44774	+	0.735516i
$505$	2.90611	−	16.4044i	0.129320	−	0.729988i
$506$	−5.62848	+	2.55616i	−0.250216	+	0.113635i
$507$		−	7.85557i		−	0.348878i
$508$	24.5336	+	21.4397i	1.08850	+	0.951234i
$509$		−	1.44843i		−	0.0642006i	−0.999485	−	0.0321003i	$-0.989780\pi$
$509$		−	1.44843i		−	0.0642006i	0.999485	−	0.0321003i	$-0.0102196\pi$
$510$	−25.2746	+	6.47958i	−1.11918	+	0.286921i
$511$		−	41.9398i		−	1.85531i
$512$	14.4917	+	17.3779i	0.640449	+	0.768001i
$513$	−20.1238	−	12.0009i	−0.888488	−	0.529852i
$514$	−4.26895	−	9.39993i	−0.188295	−	0.414613i
$515$	1.80095	+	0.319045i	0.0793593	+	0.0140588i
$516$	−29.7486	−	25.9970i	−1.30961	−	1.14446i
$517$			4.59615i			0.202138i
$518$	−16.0213	−	35.2778i	−0.703937	−	1.55002i
$519$		−	49.1640i		−	2.15806i
$520$	−9.10126	+	18.0402i	−0.399117	+	0.791117i
$521$		−	33.3661i		−	1.46180i	−0.682487	−	0.730898i	$-0.739102\pi$
$521$		−	33.3661i		−	1.46180i	0.682487	−	0.730898i	$-0.260898\pi$
$522$	5.87068	−	2.66615i	0.256953	−	0.116694i
$523$		−	37.3100i		−	1.63145i	−0.578437	−	0.815727i	$-0.696337\pi$
$523$		−	37.3100i		−	1.63145i	0.578437	−	0.815727i	$-0.303663\pi$
$524$	8.20417	+	7.16956i	0.358401	+	0.313204i
$525$	−19.9561	+	54.5566i	−0.870957	+	2.38104i
$526$	−11.1482	−	24.5476i	−0.486085	−	1.07032i
$527$			19.6185i			0.854597i
$528$	1.02768	+	7.60078i	0.0447242	+	0.330782i
$529$	18.1114			0.787451
$530$	−23.2948	+	5.97201i	−1.01186	+	0.259408i
$531$	64.8123			2.81261
$532$	−11.1520	−	34.2405i	−0.483501	−	1.48452i
$533$		−	15.6353i		−	0.677241i
$534$	12.5873	+	27.7164i	0.544706	+	1.19940i
$535$	24.4922	+	4.33889i	1.05889	+	0.187587i
$536$	−4.17404	+	13.8909i	−0.180291	+	0.599994i
$537$			11.1500i			0.481160i
$538$	24.4172	−	11.0890i	1.05270	−	0.478081i
$539$			6.86021i			0.295490i
$540$	18.7336	−	15.0644i	0.806165	−	0.648268i
$541$	0.420141			0.0180633			0.00903163	−	0.999959i	$-0.497125\pi$
$541$	0.420141			0.0180633			0.00903163	+	0.999959i	$0.497125\pi$
$542$	−33.1673	+	15.0628i	−1.42466	+	0.647004i
$543$	47.0178			2.01773
$544$	8.82444	+	14.0536i	0.378345	+	0.602545i
$545$	−7.13675	−	1.26430i	−0.305705	−	0.0541568i
$546$	47.7961	−	21.7065i	2.04548	−	0.928951i
$547$		−	1.24302i		−	0.0531479i	−0.999647	−	0.0265739i	$-0.991540\pi$
$547$		−	1.24302i		−	0.0531479i	0.999647	−	0.0265739i	$-0.00845974\pi$
$548$	31.8133	+	27.8014i	1.35900	+	1.18762i
$549$	28.3034			1.20796
$550$	−4.80679	+	0.364220i	−0.204962	+	0.0155304i
$551$	−3.47550	−	2.07262i	−0.148061	−	0.0882968i
$552$	14.6791	−	48.8510i	0.624786	−	2.07923i
$553$	−20.4309			−0.868809
$554$	29.8913	−	13.5751i	1.26996	−	0.576749i
$555$	−41.0745	−	7.27652i	−1.74352	−	0.308871i
$556$	13.6371	+	11.9174i	0.578343	+	0.505409i
$557$			24.3255i			1.03071i	0.856978	+	0.515353i	$0.172339\pi$
$557$			24.3255i			1.03071i	−0.856978	+	0.515353i	$0.827661\pi$
$558$	−19.2066	−	42.2917i	−0.813082	−	1.79035i
$559$	−22.4377			−0.949015
$560$	36.9154	+	1.51225i	1.55996	+	0.0639042i
$561$			5.62497i			0.237486i
$562$	−12.1723	+	5.52802i	−0.513458	+	0.233185i
$563$		−	17.4856i		−	0.736928i	−0.929642	−	0.368464i	$-0.879884\pi$
$563$		−	17.4856i		−	0.736928i	0.929642	−	0.368464i	$-0.120116\pi$
$564$	−28.5574	−	24.9561i	−1.20248	−	1.05084i
$565$	0.606590	−	3.42408i	0.0255194	−	0.144052i
$566$	−12.2847	−	27.0501i	−0.516366	−	1.13700i
$567$	−1.59315			−0.0669060
$568$	−20.1526	−	6.05561i	−0.845582	−	0.254088i
$569$			42.2662i			1.77189i	0.463790	+	0.885945i	$0.346489\pi$
$569$			42.2662i			1.77189i	−0.463790	+	0.885945i	$0.653511\pi$
$570$	−37.1867	−	10.9663i	−1.55758	−	0.459329i
$571$			20.7425i			0.868047i	0.900902	+	0.434023i	$0.142907\pi$
$571$			20.7425i			0.868047i	−0.900902	+	0.434023i	$0.857093\pi$
$572$	3.28007	+	2.86643i	0.137147	+	0.119851i
$573$	−7.70927			−0.322059
$574$	−26.0303	+	11.8216i	−1.08648	+	0.493424i
$575$	30.1080	+	11.0132i	1.25559	+	0.459280i
$576$	−32.7814	−	21.6563i	−1.36589	−	0.902345i
$577$		−	3.16844i		−	0.131904i	−0.997823	−	0.0659519i	$-0.978992\pi$
$577$		−	3.16844i		−	0.131904i	0.997823	−	0.0659519i	$-0.0210084\pi$
$578$	−4.90894	−	10.8092i	−0.204185	−	0.449601i
$579$		−	13.8413i		−	0.575226i
$580$	3.23540	−	2.60171i	0.134343	−	0.108030i
$581$	40.2495			1.66983
$582$	54.6150	−	24.8032i	2.26386	−	1.02813i
$583$			5.18435i			0.214714i
$584$	−8.26420	+	27.5026i	−0.341975	+	1.13806i
$585$	6.12007	−	34.5466i	0.253034	−	1.42833i
$586$	19.1443	+	42.1544i	0.790843	+	1.74138i
$587$	−23.4852			−0.969336			−0.484668	−	0.874698i	$-0.661060\pi$
$587$	−23.4852			−0.969336			−0.484668	+	0.874698i	$0.661060\pi$
$588$	−42.6248	−	37.2494i	−1.75782	−	1.53614i
$589$	−14.9309	+	25.0371i	−0.615218	+	1.03164i
$590$	40.4255	−	10.3638i	1.66429	−	0.426669i
$591$	−18.2437			−0.750444
$592$	3.55472	+	26.2909i	0.146098	+	1.08055i
$593$			30.3518i			1.24640i	0.782062	+	0.623200i	$0.214168\pi$
$593$			30.3518i			1.24640i	−0.782062	+	0.623200i	$0.785832\pi$
$594$	−2.14295	−	4.71862i	−0.0879261	−	0.193607i
$595$	26.6802	+	4.72651i	1.09378	+	0.193768i
$596$	2.04579	−	2.34101i	0.0837987	−	0.0958914i
$597$	13.0229			0.532990
$598$	−11.9791	−	26.3772i	−0.489862	−	1.07864i
$599$	−22.8129			−0.932109			−0.466055	−	0.884756i	$-0.654325\pi$
$599$	−22.8129			−0.932109			−0.466055	+	0.884756i	$0.654325\pi$
$600$	23.8368	−	31.8438i	0.973133	−	1.30002i
$601$			34.9549i			1.42584i	0.701246	+	0.712920i	$0.252628\pi$
$601$			34.9549i			1.42584i	−0.701246	+	0.712920i	$0.747372\pi$
$602$	16.9648	+	37.3552i	0.691432	+	1.52249i
$603$		−	25.1846i		−	1.02560i
$604$	5.87645	−	6.72446i	0.239109	−	0.273614i
$605$	4.10932	−	23.1963i	0.167068	−	0.943065i
$606$	26.9837	−	12.2546i	1.09614	−	0.497808i
$607$			39.4409i			1.60085i	0.599430	+	0.800427i	$0.295394\pi$
$607$			39.4409i			1.60085i	−0.599430	+	0.800427i	$0.704606\pi$
$608$	0.566005	+	24.6512i	0.0229545	+	0.999737i
$609$	−10.7859			−0.437068
$610$	17.6537	−	4.52583i	0.714778	−	0.183246i
$611$	−21.5393			−0.871386
$612$	−21.6964	−	18.9603i	−0.877024	−	0.766424i
$613$			26.3466i			1.06413i	0.846703	+	0.532065i	$0.178584\pi$
$613$			26.3466i			1.06413i	−0.846703	+	0.532065i	$0.821416\pi$
$614$	−31.8221	+	14.4519i	−1.28423	+	0.583231i
$615$	−5.36910	+	30.3075i	−0.216503	+	1.22212i
$616$	2.29214	−	7.62805i	0.0923529	−	0.307343i
$617$		−	13.0674i		−	0.526074i	−0.964786	−	0.263037i	$-0.915276\pi$
$617$		−	13.0674i		−	0.526074i	0.964786	−	0.263037i	$-0.0847242\pi$
$618$	1.34536	+	2.96239i	0.0541183	+	0.119165i
$619$		−	10.7709i		−	0.432917i	−0.976292	−	0.216459i	$-0.930549\pi$
$619$		−	10.7709i		−	0.432917i	0.976292	−	0.216459i	$-0.0694506\pi$
$620$	−18.7424	−	23.3074i	−0.752713	−	0.936049i
$621$			34.4656i			1.38306i
$622$	−23.6525	+	10.7417i	−0.948380	+	0.430704i
$623$		−	31.6117i		−	1.26650i
$624$	−35.6201	+	4.81611i	−1.42595	+	0.192799i
$625$	19.0995	+	16.1310i	0.763978	+	0.645242i
$626$	−16.8177	+	7.63771i	−0.672171	+	0.305264i
$627$	−4.28095	+	7.17856i	−0.170965	+	0.286684i
$628$	0.794535	+	0.694337i	0.0317054	+	0.0277071i
$629$			19.4566i			0.775785i
$630$	−62.1418	+	15.9311i	−2.47579	+	0.634711i
$631$			10.0679i			0.400795i	0.979715	+	0.200397i	$0.0642233\pi$
$631$			10.0679i			0.400795i	−0.979715	+	0.200397i	$0.935777\pi$
$632$	13.3978	+	4.02588i	0.532936	+	0.160141i
$633$		−	40.5867i		−	1.61318i
$634$	−3.31699	−	7.30379i	−0.131735	−	0.290071i
$635$	−35.8688	−	6.35431i	−1.42341	−	0.252163i
$636$	−32.2121	−	28.1499i	−1.27729	−	1.11621i
$637$	−32.1495			−1.27381
$638$	−0.370100	−	0.814934i	−0.0146524	−	0.0322635i
$639$	36.5373			1.44539
$640$	−23.9098	−	8.26582i	−0.945116	−	0.326735i
$641$			13.1666i			0.520048i	0.965602	+	0.260024i	$0.0837304\pi$
$641$			13.1666i			0.520048i	−0.965602	+	0.260024i	$0.916270\pi$
$642$	18.2964	+	40.2873i	0.722099	+	1.59001i
$643$	−31.8875			−1.25752			−0.628761	−	0.777599i	$-0.716438\pi$
$643$	−31.8875			−1.25752			−0.628761	+	0.777599i	$0.716438\pi$
$644$	−34.8566	+	39.8866i	−1.37354	+	1.57175i
$645$	43.4933	+	7.70501i	1.71255	+	0.303384i
$646$	−2.01097	+	17.9712i	−0.0791206	+	0.707068i
$647$	20.6536			0.811979			0.405989	−	0.913878i	$-0.366927\pi$
$647$	20.6536			0.811979			0.405989	+	0.913878i	$0.366927\pi$
$648$	1.04473	+	0.313929i	0.0410408	+	0.0123323i
$649$		−	8.99686i		−	0.353158i
$650$	−1.70687	−	22.5264i	−0.0669490	−	0.883560i
$651$			77.7006i			3.04533i
$652$	30.9392	−	35.4039i	1.21167	−	1.38653i
$653$		−	29.4300i		−	1.15169i	−0.817560	−	0.575843i	$-0.804674\pi$
$653$		−	29.4300i		−	1.15169i	0.817560	−	0.575843i	$-0.195326\pi$
$654$	−5.33135	−	11.7393i	−0.208472	−	0.459041i
$655$	−11.9947	−	2.12491i	−0.468673	−	0.0830273i
$656$	19.3991	−	2.62291i	0.757409	−	0.102407i
$657$		−	49.8632i		−	1.94535i
$658$	16.2855	+	35.8595i	0.634874	+	1.39795i
$659$	−11.5946			−0.451660			−0.225830	−	0.974167i	$-0.572509\pi$
$659$	−11.5946			−0.451660			−0.225830	+	0.974167i	$0.572509\pi$
$660$	−5.37377	−	6.68264i	−0.209174	−	0.260121i
$661$			29.8500i			1.16103i	0.814250	+	0.580515i	$0.197149\pi$
$661$			29.8500i			1.16103i	−0.814250	+	0.580515i	$0.802851\pi$
$662$	2.21388	+	4.87481i	0.0860448	+	0.189465i
$663$	−26.3607			−1.02377
$664$	−26.3941	−	7.93113i	−1.02429	−	0.307787i
$665$	30.4520	+	26.3373i	1.18088	+	1.02132i
$666$	−19.0481	−	41.9426i	−0.738099	−	1.62524i
$667$			5.95242i			0.230478i
$668$	−21.7679	−	19.0228i	−0.842225	−	0.736014i
$669$	52.4853			2.02920
$670$	−4.02713	−	15.7084i	−0.155582	−	0.606870i
$671$		−	3.92891i		−	0.151674i
$672$	34.9498	+	55.6604i	1.34822	+	2.14715i
$673$	−41.0916			−1.58396			−0.791982	−	0.610545i	$-0.790950\pi$
$673$	−41.0916			−1.58396			−0.791982	+	0.610545i	$0.790950\pi$
$674$	16.8783	+	37.1648i	0.650128	+	1.43154i
$675$	−9.23285	+	25.2410i	−0.355372	+	0.971526i
$676$	3.67566	−	4.20609i	0.141372	−	0.161773i
$677$	32.6916			1.25644			0.628220	−	0.778036i	$-0.283784\pi$
$677$	32.6916			1.25644			0.628220	+	0.778036i	$0.283784\pi$
$678$	5.63229	−	2.55789i	0.216307	−	0.0982350i
$679$	−62.2907			−2.39050
$680$	−16.5645	−	8.35678i	−0.635221	−	0.320468i
$681$	−7.05718			−0.270432
$682$	−5.87068	+	2.66615i	−0.224800	+	0.102092i
$683$			7.06028i			0.270154i	0.990835	+	0.135077i	$0.0431282\pi$
$683$			7.06028i			0.270154i	−0.990835	+	0.135077i	$0.956872\pi$
$684$	−13.2589	−	40.7093i	−0.506965	−	1.55656i
$685$	−46.5120	−	8.23978i	−1.77713	−	0.314826i
$686$	7.39870	+	16.2914i	0.282484	+	0.622010i
$687$		−	41.8169i		−	1.59541i
$688$	−3.76405	−	27.8391i	−0.143503	−	1.06135i
$689$	−24.2958			−0.925597
$690$	14.1625	+	55.2430i	0.539157	+	2.10307i
$691$		−	11.1247i		−	0.423203i	−0.977356	−	0.211602i	$-0.932132\pi$
$691$		−	11.1247i		−	0.423203i	0.977356	−	0.211602i	$-0.0678679\pi$
$692$	23.0041	−	26.3237i	0.874484	−	1.00068i
$693$			13.8299i			0.525356i
$694$	3.26317	+	7.18528i	0.123868	+	0.272749i
$695$	−19.9379	−	3.53207i	−0.756286	−	0.133979i
$696$	7.07301	+	2.12536i	0.268102	+	0.0805615i
$697$	14.3564			0.543786
$698$	−7.36274	−	16.2122i	−0.278684	−	0.613642i
$699$	10.6441			0.402598
$700$	−36.2124	+	19.8735i	−1.36870	+	0.751148i
$701$	−0.945903			−0.0357263			−0.0178631	−	0.999840i	$-0.505686\pi$
$701$	−0.945903			−0.0357263			−0.0178631	+	0.999840i	$0.505686\pi$
$702$	22.1132	−	10.0427i	0.834610	−	0.379035i
$703$	−14.8077	+	24.8304i	−0.558482	+	0.936497i
$704$	−3.00620	+	4.55053i	−0.113300	+	0.171504i
$705$	41.7517	+	7.39648i	1.57246	+	0.278568i
$706$	−0.646086	+	0.293418i	−0.0243158	+	0.0110429i
$707$	−30.7761			−1.15745
$708$	55.9005	+	48.8510i	2.10087	+	1.83593i
$709$	−20.0593			−0.753342			−0.376671	−	0.926347i	$-0.622931\pi$
$709$	−20.0593			−0.753342			−0.376671	+	0.926347i	$0.622931\pi$
$710$	22.7895	−	5.84247i	0.855274	−	0.219264i
$711$	−24.2907			−0.910972
$712$	−6.22905	+	20.7298i	−0.233444	+	0.776881i
$713$	42.8805			1.60589
$714$	19.9309	+	43.8864i	0.745894	+	1.64241i
$715$	−4.79556	−	0.849552i	−0.179344	−	0.0317715i
$716$	−5.21717	+	5.97004i	−0.194975	+	0.223111i
$717$	−64.7434			−2.41789
$718$	21.8969	−	9.94440i	0.817184	−	0.371122i
$719$		−	31.0420i		−	1.15767i	−0.815444	−	0.578836i	$-0.803507\pi$
$719$		−	31.0420i		−	1.15767i	0.815444	−	0.578836i	$-0.196493\pi$
$720$	43.8895	+	1.79795i	1.63567	+	0.0670055i
$721$		−	3.37873i		−	0.125830i
$722$	−16.2436	+	21.4043i	−0.604525	+	0.796586i
$723$	6.31793			0.234967
$724$	25.1746	+	21.9999i	0.935607	+	0.817619i
$725$	−1.59457	+	4.35927i	−0.0592208	+	0.161899i
$726$	38.1557	−	17.3283i	1.41609	−	0.643114i
$727$	−10.7341			−0.398106			−0.199053	−	0.979989i	$-0.563787\pi$
$727$	−10.7341			−0.398106			−0.199053	+	0.979989i	$0.563787\pi$
$728$	35.7479	+	10.7418i	1.32491	+	0.398119i
$729$	43.4629			1.60974
$730$	−7.97334	−	31.1012i	−0.295106	−	1.15111i
$731$		−	20.6023i		−	0.762004i
$732$	24.4116	+	21.3331i	0.902279	+	0.788494i
$733$			39.1519i			1.44611i	0.690792	+	0.723053i	$0.257262\pi$
$733$			39.1519i			1.44611i	−0.690792	+	0.723053i	$0.742738\pi$
$734$	−0.573601	−	1.26303i	−0.0211720	−	0.0466193i
$735$	62.3186	+	11.0400i	2.29866	+	0.407216i
$736$	30.7172	−	19.2877i	1.13225	−	0.710954i
$737$	−3.49598			−0.128776
$738$	−30.9480	+	14.0549i	−1.13921	+	0.517370i
$739$			10.7025i			0.393697i	0.980434	+	0.196849i	$0.0630707\pi$
$739$			10.7025i			0.393697i	−0.980434	+	0.196849i	$0.936929\pi$
$740$	−18.5877	−	23.1150i	−0.683298	−	0.849726i
$741$	−33.6414	−	20.0622i	−1.23585	−	0.737002i
$742$	18.3696	+	40.4486i	0.674370	+	1.48492i
$743$			30.9024i			1.13370i	0.823822	+	0.566849i	$0.191838\pi$
$743$			30.9024i			1.13370i	−0.823822	+	0.566849i	$0.808162\pi$
$744$	15.3108	−	50.9531i	0.561322	−	1.86803i
$745$	−0.606331	+	3.42262i	−0.0222142	+	0.125395i
$746$	−1.59839	−	3.51954i	−0.0585212	−	0.128860i
$747$	47.8535			1.75087
$748$	−2.63195	+	3.01176i	−0.0962338	+	0.110121i
$749$		−	45.9494i		−	1.67895i
$750$	−4.42687	+	44.2513i	−0.161646	+	1.61583i
$751$	−10.3152			−0.376408			−0.188204	−	0.982130i	$-0.560267\pi$
$751$	−10.3152			−0.376408			−0.188204	+	0.982130i	$0.560267\pi$
$752$	−3.61333	−	26.7243i	−0.131765	−	0.974536i
$753$	24.7890			0.903360
$754$	3.81909	−	1.73443i	0.139083	−	0.0631641i
$755$	−1.74166	+	9.83135i	−0.0633856	+	0.357799i
$756$	−33.4388	−	29.2219i	−1.21616	−	1.06279i
$757$		−	12.5915i		−	0.457645i	−0.973468	−	0.228823i	$-0.926512\pi$
$757$		−	12.5915i		−	0.457645i	0.973468	−	0.228823i	$-0.0734876\pi$
$758$	2.86227	+	6.30252i	0.103962	+	0.228918i
$759$	12.2946			0.446264
$760$	−14.7796	−	23.2715i	−0.536111	−	0.844147i
$761$	31.3117			1.13505			0.567523	−	0.823357i	$-0.307902\pi$
$761$	31.3117			1.13505			0.567523	+	0.823357i	$0.307902\pi$
$762$	−26.7950	−	59.0008i	−0.970681	−	2.13737i
$763$			13.3891i			0.484719i
$764$	−4.12775	−	3.60721i	−0.149337	−	0.130504i
$765$	31.7207	+	5.61945i	1.14686	+	0.203172i
$766$	−1.10208	+	0.500504i	−0.0398196	+	0.0180840i
$767$	42.1627			1.52241
$768$	−11.9509	−	43.3869i	−0.431242	−	1.56559i
$769$	0.105528			0.00380544			0.00190272	−	0.999998i	$-0.499394\pi$
$769$	0.105528			0.00380544			0.00190272	+	0.999998i	$0.499394\pi$
$770$	2.21147	+	8.62617i	0.0796957	+	0.310865i
$771$			20.5327i			0.739469i
$772$	6.47644	−	7.41103i	0.233092	−	0.266729i
$773$	−13.6012			−0.489200			−0.244600	−	0.969624i	$-0.578657\pi$
$773$	−13.6012			−0.489200			−0.244600	+	0.969624i	$0.578657\pi$
$774$	20.1698	+	44.4124i	0.724988	+	1.59637i
$775$	31.4037	+	11.4871i	1.12805	+	0.412628i
$776$	40.8479	+	12.2743i	1.46636	+	0.440623i
$777$			77.0592i			2.76448i
$778$	−0.900272	−	1.98234i	−0.0322763	−	0.0710702i
$779$	18.3215	+	10.9261i	0.656437	+	0.391468i
$780$	31.3174	−	25.1835i	1.12134	−	0.901714i
$781$		−	5.07189i		−	0.181487i
$782$	24.2195	−	10.9992i	0.866088	−	0.393331i
$783$	−4.99019			−0.178335
$784$	−5.39326	−	39.8887i	−0.192616	−	1.42460i
$785$	−1.16163	−	0.205788i	−0.0414604	−	0.00734488i
$786$	−8.96039	−	19.7302i	−0.319607	−	0.703752i
$787$		−	38.3007i		−	1.36527i	−0.730758	−	0.682637i	$-0.760833\pi$
$787$		−	38.3007i		−	1.36527i	0.730758	−	0.682637i	$-0.239167\pi$
$788$	−9.76816	−	8.53631i	−0.347976	−	0.304093i
$789$			53.6205i			1.90894i
$790$	−15.1509	+	3.88419i	−0.539044	+	0.138193i
$791$	−6.42386			−0.228406
$792$	2.72517	−	9.06915i	0.0968348	−	0.322258i
$793$	18.4123			0.653841
$794$	−44.2486	+	20.0954i	−1.57033	+	0.713159i
$795$	47.0949	+	8.34306i	1.67029	+	0.295898i
$796$	6.97280	+	6.09347i	0.247144	+	0.215977i
$797$	−35.6646			−1.26330			−0.631652	−	0.775252i	$-0.717623\pi$
$797$	−35.6646			−1.26330			−0.631652	+	0.775252i	$0.717623\pi$
$798$	−7.96459	+	71.1763i	−0.281943	+	2.51961i
$799$		−	19.7774i		−	0.699673i
$800$	27.6628	−	5.89669i	0.978027	−	0.208479i
$801$		−	37.5838i		−	1.32796i
$802$	32.3821	−	14.7062i	1.14345	−	0.519296i
$803$	−6.92171			−0.244262
$804$	18.9824	−	21.7217i	0.669458	−	0.766065i
$805$	10.3308	−	58.3153i	0.364113	−	2.05534i
$806$	−12.4946	−	27.5122i	−0.440103	−	0.969077i
$807$	−53.3357			−1.87751
$808$	20.1818	+	6.06440i	0.709994	+	0.213345i
$809$	−6.99766			−0.246024			−0.123012	−	0.992405i	$-0.539255\pi$
$809$	−6.99766			−0.246024			−0.123012	+	0.992405i	$0.539255\pi$
$810$	−1.18143	+	0.302880i	−0.0415112	+	0.0106421i
$811$	−7.46612			−0.262171			−0.131085	−	0.991371i	$-0.541846\pi$
$811$	−7.46612			−0.262171			−0.131085	+	0.991371i	$0.541846\pi$
$812$	−5.77508	−	5.04680i	−0.202666	−	0.177108i
$813$	72.4490			2.54090
$814$	−5.82222	+	2.64415i	−0.204069	+	0.0926772i
$815$	−9.16976	+	51.7615i	−0.321203	+	1.81313i
$816$	−4.42215	−	32.7064i	−0.154806	−	1.14495i
$817$	15.6797	−	26.2926i	0.548562	−	0.919862i
$818$	−9.48694	+	4.30847i	−0.331703	+	0.150642i
$819$	−64.8123			−2.26472
$820$	−17.0558	+	13.7152i	−0.595614	+	0.478957i
$821$	−45.6471			−1.59310			−0.796548	−	0.604576i	$-0.793343\pi$
$821$	−45.6471			−1.59310			−0.796548	+	0.604576i	$0.793343\pi$
$822$	−34.7457	−	76.5077i	−1.21190	−	2.66851i
$823$	−17.1790			−0.598821			−0.299410	−	0.954124i	$-0.596790\pi$
$823$	−17.1790			−0.598821			−0.299410	+	0.954124i	$0.596790\pi$
$824$	−0.665775	+	2.21564i	−0.0231934	+	0.0771856i
$825$	9.00397	+	3.29354i	0.313478	+	0.114666i
$826$	−31.8784	−	70.1941i	−1.10919	−	2.44236i
$827$			15.8191i			0.550084i	0.961432	+	0.275042i	$0.0886917\pi$
$827$			15.8191i			0.550084i	−0.961432	+	0.275042i	$0.911308\pi$
$828$	−41.4417	+	47.4220i	−1.44020	+	1.64803i
$829$		−	37.5577i		−	1.30443i	−0.758033	−	0.652216i	$-0.773840\pi$
$829$		−	37.5577i		−	1.30443i	0.758033	−	0.652216i	$-0.226160\pi$
$830$	29.8478	−	7.65199i	1.03603	−	0.265604i
$831$	−65.2932			−2.26499
$832$	−21.3255	−	14.0882i	−0.739328	−	0.488420i
$833$		−	29.5197i		−	1.02280i
$834$	−14.8941	−	32.7958i	−0.515742	−	1.13563i
$835$	31.8253	+	5.63798i	1.10136	+	0.195110i
$836$	−5.65103	+	1.84052i	−0.195445	+	0.0636556i
$837$			35.9487i			1.24257i
$838$	−8.88627	+	4.03567i	−0.306971	+	0.139410i
$839$	26.3813			0.910784			0.455392	−	0.890291i	$-0.349499\pi$
$839$	26.3813			0.910784			0.455392	+	0.890291i	$0.349499\pi$
$840$	−65.6050	−	33.0976i	−2.26359	−	1.14198i
$841$	28.1382			0.970282
$842$	2.35710	−	1.07047i	0.0812309	−	0.0368908i
$843$	26.5886			0.915760
$844$	18.9907	−	21.7312i	0.653688	−	0.748020i
$845$	−1.08939	+	6.14941i	−0.0374763	+	0.211546i
$846$	19.3621	+	42.6341i	0.665684	+	1.46579i
$847$	−43.5182			−1.49530
$848$	−4.07575	−	30.1444i	−0.139962	−	1.03516i
$849$			59.0870i			2.02786i
$850$	20.6838	−	1.56725i	0.709447	−	0.0537562i
$851$	42.5265			1.45779
$852$	31.5134	+	27.5393i	1.07963	+	0.943480i
$853$		−	3.94363i		−	0.135027i	−0.997718	−	0.0675137i	$-0.978493\pi$
$853$		−	3.94363i		−	0.135027i	0.997718	−	0.0675137i	$-0.0215066\pi$
$854$	−13.9212	−	30.6536i	−0.476375	−	1.04894i
$855$	36.2051	+	31.3129i	1.23819	+	1.07088i
$856$	−9.05428	+	30.1319i	−0.309469	+	1.02989i
$857$	−51.9532			−1.77469			−0.887344	−	0.461109i	$-0.847452\pi$
$857$	−51.9532			−1.77469			−0.887344	+	0.461109i	$0.847452\pi$
$858$	−3.58241	−	7.88823i	−0.122302	−	0.269300i
$859$			16.6922i			0.569532i	0.958597	+	0.284766i	$0.0919159\pi$
$859$			16.6922i			0.569532i	−0.958597	+	0.284766i	$0.908084\pi$
$860$	19.6823	+	24.4762i	0.671160	+	0.834632i
$861$	56.8593			1.93776
$862$	−8.24515	−	18.1553i	−0.280831	−	0.618370i
$863$			21.9125i			0.745910i	0.927849	+	0.372955i	$0.121655\pi$
$863$			21.9125i			0.745910i	−0.927849	+	0.372955i	$0.878345\pi$
$864$	16.1698	+	25.7517i	0.550107	+	0.876091i
$865$	−6.81795	+	38.4860i	−0.231817	+	1.30856i
$866$	9.91198	+	21.8255i	0.336823	+	0.741660i
$867$			23.6110i			0.801871i
$868$	−36.3565	+	41.6030i	−1.23402	+	1.41210i
$869$			3.37189i			0.114384i
$870$	−7.99850	+	2.05055i	−0.271175	+	0.0695203i
$871$		−	16.3835i		−	0.555133i
$872$	2.63831	−	8.78009i	0.0893446	−	0.297331i
$873$	−74.0588			−2.50651
$874$	39.2799	+	4.39541i	1.32866	+	0.148677i
$875$	23.1876	−	39.9399i	0.783885	−	1.35022i
$876$	37.5834	−	43.0069i	1.26982	−	1.45307i
$877$	−10.8819			−0.367455			−0.183728	−	0.982977i	$-0.558816\pi$
$877$	−10.8819			−0.367455			−0.183728	+	0.982977i	$0.558816\pi$
$878$	−14.3437	−	31.5838i	−0.484077	−	1.06590i
$879$		−	92.0799i		−	3.10578i
$880$	0.249580	−	6.09248i	0.00841335	−	0.205378i
$881$	3.53485			0.119092			0.0595460	−	0.998226i	$-0.481035\pi$
$881$	3.53485			0.119092			0.0595460	+	0.998226i	$0.481035\pi$
$882$	28.8999	+	63.6356i	0.973111	+	2.14272i
$883$	6.96126			0.234265			0.117132	−	0.993116i	$-0.462630\pi$
$883$	6.96126			0.234265			0.117132	+	0.993116i	$0.462630\pi$
$884$	−14.1143	−	12.3343i	−0.474714	−	0.414848i
$885$	−81.7280	−	14.4785i	−2.74726	−	0.486688i
$886$	3.72094	+	8.19325i	0.125007	+	0.275258i
$887$		−	12.1852i		−	0.409138i	−0.978852	−	0.204569i	$-0.934421\pi$
$887$		−	12.1852i		−	0.409138i	0.978852	−	0.204569i	$-0.0655792\pi$
$888$	15.1844	−	50.5325i	0.509556	−	1.69576i
$889$			67.2929i			2.25693i
$890$	−6.00982	−	23.4422i	−0.201450	−	0.785785i
$891$			0.262932i			0.00880855i
$892$	28.1021	+	24.5582i	0.940927	+	0.822268i
$893$	15.0518	−	25.2398i	0.503690	−	0.844618i
$894$	−5.62988	+	2.55679i	−0.188291	+	0.0855119i
$895$	1.54626	−	8.72836i	0.0516859	−	0.291757i
$896$	−7.33075	+	46.1553i	−0.244903	+	1.54194i
$897$			57.6170i			1.92377i
$898$	31.9443	−	14.5074i	1.06600	−	0.484119i
$899$			6.20856i			0.207067i
$900$	−43.0537	+	23.6280i	−1.43512	+	0.787601i
$901$		−	22.3084i		−	0.743201i
$902$	1.95102	+	4.29602i	0.0649620	+	0.143042i
$903$		−	81.5969i		−	2.71538i
$904$	4.21253	+	1.26582i	0.140107	+	0.0421004i
$905$	−36.8060	−	6.52033i	−1.22347	−	0.216743i
$906$	−16.1716	+	7.34429i	−0.537266	+	0.243998i
$907$		−	31.9261i		−	1.06009i	−0.847970	−	0.530044i	$-0.822175\pi$
$907$		−	31.9261i		−	1.06009i	0.847970	−	0.530044i	$-0.177825\pi$
$908$	−3.77861	−	3.30209i	−0.125397	−	0.109584i
$909$	−36.5903			−1.21363
$910$	−40.4255	+	10.3638i	−1.34009	+	0.343555i
$911$	−35.0406			−1.16095			−0.580473	−	0.814280i	$-0.697132\pi$
$911$	−35.0406			−1.16095			−0.580473	+	0.814280i	$0.697132\pi$
$912$	19.2481	−	45.1053i	0.637368	−	1.49359i
$913$		−	6.64274i		−	0.219843i
$914$	7.85647	−	3.56799i	0.259869	−	0.118019i
$915$	−35.6904	−	6.32271i	−1.17989	−	0.209022i
$916$	19.5664	−	22.3899i	0.646491	−	0.739784i
$917$			22.5031i			0.743117i
$918$	9.22116	+	20.3044i	0.304344	+	0.670143i
$919$			31.1838i			1.02866i	0.857592	+	0.514330i	$0.171959\pi$
$919$			31.1838i			1.02866i	−0.857592	+	0.514330i	$0.828041\pi$
$920$	−18.2655	+	36.2053i	−0.602196	+	1.19365i
$921$	69.5105			2.29045
$922$	−2.85771	−	6.29248i	−0.0941137	−	0.207232i
$923$	23.7688			0.782360
$924$	−10.4240	+	11.9283i	−0.342926	+	0.392412i
$925$	31.1444	+	11.3923i	1.02402	+	0.374575i
$926$	0.467015	+	1.02833i	0.0153471	+	0.0337931i
$927$		−	4.01704i		−	0.131937i
$928$	2.79262	+	4.44748i	0.0916722	+	0.145996i
$929$	2.93575			0.0963188			0.0481594	−	0.998840i	$-0.484664\pi$
$929$	2.93575			0.0963188			0.0481594	+	0.998840i	$0.484664\pi$
$930$	14.7719	+	57.6202i	0.484391	+	1.88944i
$931$	22.4663	−	37.6729i	0.736305	−	1.23468i
$932$	5.69916	+	4.98044i	0.186682	+	0.163140i
$933$	51.6654			1.69145
$934$	−5.16929	−	11.3824i	−0.169144	−	0.372444i
$935$	0.780059	−	4.40328i	0.0255106	−	0.144003i
$936$	42.5015	+	12.7712i	1.38920	+	0.417439i
$937$			36.6167i			1.19622i	0.801416	+	0.598108i	$0.204081\pi$
$937$			36.6167i			1.19622i	−0.801416	+	0.598108i	$0.795919\pi$
$938$	−27.2759	+	12.3873i	−0.890589	+	0.404458i
$939$	36.7358			1.19883
$940$	18.8942	+	23.4961i	0.616259	+	0.766359i
$941$		−	34.9115i		−	1.13808i	−0.822309	−	0.569041i	$-0.807315\pi$
$941$		−	34.9115i		−	1.13808i	0.822309	−	0.569041i	$-0.192685\pi$
$942$	−0.867771	−	1.91077i	−0.0282735	−	0.0622563i
$943$		−	31.3789i		−	1.02184i
$944$	7.07301	+	52.3123i	0.230207	+	1.70262i
$945$	48.8885	+	8.66079i	1.59034	+	0.281735i
$946$	6.16507	−	2.79985i	0.200444	−	0.0910310i
$947$	43.7796			1.42264			0.711322	−	0.702866i	$-0.248097\pi$
$947$	43.7796			1.42264			0.711322	+	0.702866i	$0.248097\pi$
$948$	−20.9507	−	18.3086i	−0.680446	−	0.594636i
$949$		−	32.4377i		−	1.05297i
$950$	27.5893	+	13.7415i	0.895116	+	0.445834i
$951$			15.9540i			0.517345i
$952$	−9.86314	+	32.8237i	−0.319666	+	1.06382i
$953$	34.1942			1.10766			0.553830	−	0.832630i	$-0.313166\pi$
$953$	34.1942			1.10766			0.553830	+	0.832630i	$0.313166\pi$
$954$	21.8400	+	48.0902i	0.707097	+	1.55698i
$955$	6.03489	+	1.06910i	0.195284	+	0.0345954i
$956$	−34.6654	−	30.2938i	−1.12116	−	0.979772i
$957$			1.78010i			0.0575425i
$958$	12.4834	−	5.66932i	0.403322	−	0.183167i
$959$			87.2603i			2.81778i
$960$	36.4995	+	34.6316i	1.17801	+	1.11773i
$961$	13.7257			0.442765
$962$	−12.3915	−	27.2851i	−0.399517	−	0.879708i
$963$		−	54.6302i		−	1.76043i
$964$	3.38279	+	2.95620i	0.108952	+	0.0952127i
$965$	−1.91949	+	10.8351i	−0.0617905	+	0.348795i
$966$	95.9230	−	43.5631i	3.08627	−	1.40162i
$967$	−17.9312			−0.576627			−0.288314	−	0.957536i	$-0.593095\pi$
$967$	−17.9312			−0.576627			−0.288314	+	0.957536i	$0.593095\pi$
$968$	28.5376	+	8.57522i	0.917234	+	0.275618i
$969$	18.4211	−	30.8896i	0.591770	−	0.992316i
$970$	−46.1928	+	11.8423i	−1.48316	+	0.380234i
$971$	−33.5761			−1.07751			−0.538754	−	0.842463i	$-0.681105\pi$
$971$	−33.5761			−1.07751			−0.538754	+	0.842463i	$0.681105\pi$
$972$	22.6517	+	19.7951i	0.726554	+	0.634930i
$973$			37.4050i			1.19915i
$974$	−16.2795	+	7.39329i	−0.521629	+	0.236896i
$975$	−15.4348	+	42.1960i	−0.494308	+	1.35135i
$976$	3.08877	+	22.8446i	0.0988691	+	0.731239i
$977$	−44.2614			−1.41605			−0.708024	−	0.706189i	$-0.750413\pi$
$977$	−44.2614			−1.41605			−0.708024	+	0.706189i	$0.750413\pi$
$978$	−85.1427	+	38.6673i	−2.72256	+	1.23644i
$979$	−5.21717			−0.166741
$980$	28.2014	+	35.0703i	0.900861	+	1.12028i
$981$			15.9186i			0.508242i
$982$	−4.32660	+	1.96491i	−0.138067	+	0.0627029i
$983$			44.5179i			1.41990i	0.704252	+	0.709950i	$0.251282\pi$
$983$			44.5179i			1.41990i	−0.704252	+	0.709950i	$0.748718\pi$
$984$	−37.2862	−	11.2041i	−1.18864	−	0.357173i
$985$	14.2813	+	2.52999i	0.455041	+	0.0806123i
$986$	1.59255	+	3.50668i	0.0507171	+	0.111676i
$987$		−	78.3296i		−	2.49326i
$988$	−8.62536	−	26.4828i	−0.274409	−	0.842532i
$989$	−45.0308			−1.43189
$990$	2.62926	+	10.2558i	0.0835633	+	0.325952i
$991$	35.8187			1.13782			0.568910	−	0.822400i	$-0.307365\pi$
$991$	35.8187			1.13782			0.568910	+	0.822400i	$0.307365\pi$
$992$	32.0391	−	20.1177i	1.01724	−	0.638737i
$993$		−	10.6483i		−	0.337913i
$994$	−17.9712	−	39.5713i	−0.570011	−	1.25512i
$995$	−10.1944	−	1.80598i	−0.323185	−	0.0572535i
$996$	41.2736	+	36.0686i	1.30780	+	1.14288i
$997$		−	34.3781i		−	1.08876i	−0.838837	−	0.544382i	$-0.816764\pi$
$997$		−	34.3781i		−	1.08876i	0.838837	−	0.544382i	$-0.183236\pi$
$998$	3.37074	−	1.53081i	0.106699	−	0.0484570i
$999$			35.6520i			1.12798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.13	✓	40
4.3	odd	2	inner	380.2.d.b.379.15	yes	40
5.4	even	2	inner	380.2.d.b.379.28	yes	40
19.18	odd	2	inner	380.2.d.b.379.27	yes	40
20.19	odd	2	inner	380.2.d.b.379.26	yes	40
76.75	even	2	inner	380.2.d.b.379.25	yes	40
95.94	odd	2	inner	380.2.d.b.379.14	yes	40
380.379	even	2	inner	380.2.d.b.379.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.13	✓	40	1.1	even	1	trivial
380.2.d.b.379.14	yes	40	95.94	odd	2	inner
380.2.d.b.379.15	yes	40	4.3	odd	2	inner
380.2.d.b.379.16	yes	40	380.379	even	2	inner
380.2.d.b.379.25	yes	40	76.75	even	2	inner
380.2.d.b.379.26	yes	40	20.19	odd	2	inner
380.2.d.b.379.27	yes	40	19.18	odd	2	inner
380.2.d.b.379.28	yes	40	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 + 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 - 1.64479i) q^{6} -4.13073 q^{7} +(2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +O(q^{10})\)	\(q+(-0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 + 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 - 1.64479i) q^{6} -4.13073 q^{7} +(2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +(-3.06322 + 0.785308i) q^{10} +0.681732i q^{11} +(-4.23583 - 3.70165i) q^{12} -3.19485 q^{13} +(2.41557 + 5.31892i) q^{14} +(6.19289 + 1.09710i) q^{15} +(-0.535953 - 3.96393i) q^{16} -2.93351i q^{17} +(2.87192 + 6.32377i) q^{18} +(2.23259 - 3.74374i) q^{19} +(2.80251 + 3.48510i) q^{20} -11.6184i q^{21} +(0.877829 - 0.398663i) q^{22} -6.41181 q^{23} +(-2.28939 + 7.61890i) q^{24} +(-4.69571 - 1.71763i) q^{25} +(1.86829 + 4.11384i) q^{26} -5.37533i q^{27} +(5.43630 - 6.22080i) q^{28} -0.928351i q^{29} +(-2.20881 - 8.61581i) q^{30} -6.68773 q^{31} +(-4.79072 + 3.00815i) q^{32} -1.91749 q^{33} +(-3.77732 + 1.71546i) q^{34} +(-1.61121 + 9.09498i) q^{35} +(6.46334 - 7.39604i) q^{36} -6.63253 q^{37} +(-6.12618 - 0.685517i) q^{38} -8.98606i q^{39} +(2.84873 - 5.64666i) q^{40} +4.89391i q^{41} +(-14.9604 + 6.79420i) q^{42} +7.02309 q^{43} +(-1.02667 - 0.897202i) q^{44} +(-1.91560 + 10.8132i) q^{45} +(3.74950 + 8.25615i) q^{46} +6.74187 q^{47} +(11.1492 - 1.50746i) q^{48} +10.0629 q^{49} +(0.534257 + 7.05086i) q^{50} +8.25100 q^{51} +(4.20463 - 4.81138i) q^{52} +7.60467 q^{53} +(-6.92152 + 3.14339i) q^{54} +(1.50103 + 0.265913i) q^{55} +(-11.1892 - 3.36223i) q^{56} +(10.5299 + 6.27953i) q^{57} +(-1.19539 + 0.542882i) q^{58} -13.1971 q^{59} +(-9.80245 + 7.88253i) q^{60} -5.76313 q^{61} +(3.91085 + 8.61143i) q^{62} +20.2865 q^{63} +(6.67495 + 4.40965i) q^{64} +(-1.24617 + 7.03438i) q^{65} +(1.12131 + 2.46904i) q^{66} +5.12809i q^{67} +(4.41781 + 3.86069i) q^{68} -18.0343i q^{69} +(12.6533 - 3.24390i) q^{70} -7.43972 q^{71} +(-13.3031 - 3.99743i) q^{72} +10.1531i q^{73} +(3.87857 + 8.54034i) q^{74} +(4.83114 - 13.2075i) q^{75} +(2.69977 + 8.28923i) q^{76} -2.81605i q^{77} +(-11.5709 + 5.25487i) q^{78} +4.94607 q^{79} +(-8.93678 - 0.366097i) q^{80} +0.385683 q^{81} +(6.30163 - 2.86187i) q^{82} -9.74393 q^{83} +(17.4970 + 15.2905i) q^{84} +(-6.45896 - 1.14423i) q^{85} +(-4.10697 - 9.04326i) q^{86} +2.61115 q^{87} +(-0.554899 + 1.84666i) q^{88} +7.65281i q^{89} +(15.0438 - 3.85674i) q^{90} +13.1971 q^{91} +(8.43836 - 9.65607i) q^{92} -18.8104i q^{93} +(-3.94252 - 8.68115i) q^{94} +(-7.37207 - 6.37594i) q^{95} +(-8.46093 - 13.4747i) q^{96} +15.0798 q^{97} +(-5.88460 - 12.9575i) q^{98} -3.34806i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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