LMFDB - Embedded newform 380.2.d.b.379.14

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			379.14
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.15

$q$-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} +(2.60702 - 1.78981i) 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} +(-3.82918 - 2.31027i) 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} +(5.03415 + 7.33269i) 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} +(-3.51503 + 5.06404i) q^{38} -8.98606i q^{39} +(-0.735583 + 6.28163i) 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} +(4.95767 + 5.04198i) 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} +(6.49804 - 10.7702i) 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} +(10.7689 - 7.39324i) 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} +(8.57622 + 1.56476i) q^{76} +2.81605i q^{77} +(-11.5709 + 5.25487i) q^{78} -4.94607 q^{79} +(8.51867 - 2.72621i) 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} +(-12.8034 + 8.78997i) 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	$-0.214896\pi$
$7$	4.13073			1.56127			0.780634	+	0.624988i	$0.214896\pi$
$8$	2.70878	+	0.813956i	0.957697	+	0.287777i
$9$	−4.91111			−1.63704
$10$	2.60702	−	1.78981i	0.824413	−	0.565989i
$11$			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	$0.115771\pi$
$17$			2.93351i			0.711481i	−0.934585	+	0.355741i	$0.884229\pi$
$18$	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
$20$	−3.82918	−	2.31027i	−0.856231	−	0.516593i
$21$			11.6184i			2.53534i
$22$	0.877829	−	0.398663i	0.187154	−	0.0849953i
$23$	6.41181			1.33696			0.668478	−	0.743732i	$-0.266946\pi$
$23$	6.41181			1.33696			0.668478	+	0.743732i	$0.266946\pi$
$24$	−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	$0.0274709\pi$
$29$			0.928351i			0.172391i	−0.996278	+	0.0861953i	$0.972529\pi$
$30$	5.03415	+	7.33269i	0.919107	+	1.33876i
$31$	6.68773			1.20115			0.600576	−	0.799568i	$-0.294938\pi$
$31$	6.68773			1.20115			0.600576	+	0.799568i	$0.294938\pi$
$32$	−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	$0.683543\pi$
$38$	−3.51503	+	5.06404i	−0.570214	+	0.821496i
$39$		−	8.98606i		−	1.43892i
$40$	−0.735583	+	6.28163i	−0.116306	+	0.993213i
$41$		−	4.89391i		−	0.764301i	−0.924100	−	0.382151i	$-0.875184\pi$
$41$		−	4.89391i		−	0.764301i	0.924100	−	0.382151i	$-0.124816\pi$
$42$	14.9604	−	6.79420i	2.30843	−	1.04837i
$43$	−7.02309			−1.07101			−0.535506	−	0.844532i	$-0.679879\pi$
$43$	−7.02309			−1.07101			−0.535506	+	0.844532i	$0.679879\pi$
$44$	−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	$-0.663625\pi$
$47$	−6.74187			−0.983404			−0.491702	+	0.870764i	$0.663625\pi$
$48$	11.1492	−	1.50746i	1.60925	−	0.217583i
$49$	10.0629			1.43756
$50$	4.95767	+	5.04198i	0.701120	+	0.713043i
$51$	−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	$-0.171051\pi$
$59$	13.1971			1.71811			0.859056	+	0.511882i	$0.171051\pi$
$60$	6.49804	−	10.7702i	0.838893	−	1.39043i
$61$	−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
$70$	10.7689	−	7.39324i	1.28713	−	0.883661i
$71$	7.43972			0.882933			0.441466	−	0.897278i	$-0.354458\pi$
$71$	7.43972			0.882933			0.441466	+	0.897278i	$0.354458\pi$
$72$	−13.3031	−	3.99743i	−1.56779	−	0.471101i
$73$		−	10.1531i		−	1.18833i	−0.804342	−	0.594167i	$-0.797482\pi$
$73$		−	10.1531i		−	1.18833i	0.804342	−	0.594167i	$-0.202518\pi$
$74$	3.87857	+	8.54034i	0.450875	+	0.992795i
$75$	−4.83114	−	13.2075i	−0.557852	−	1.52507i
$76$	8.57622	+	1.56476i	0.983760	+	0.179491i
$77$			2.81605i			0.320919i
$78$	−11.5709	+	5.25487i	−1.31014	+	0.594997i
$79$	−4.94607			−0.556476			−0.278238	−	0.960512i	$-0.589750\pi$
$79$	−4.94607			−0.556476			−0.278238	+	0.960512i	$0.589750\pi$
$80$	8.51867	−	2.72621i	0.952417	−	0.304799i
$81$	0.385683			0.0428536
$82$	−6.30163	+	2.86187i	−0.695899	+	0.316040i
$83$	9.74393			1.06954			0.534768	−	0.844999i	$-0.320399\pi$
$83$	9.74393			1.06954			0.534768	+	0.844999i	$0.320399\pi$
$84$	−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	$-0.867063\pi$
$89$		−	7.65281i		−	0.811197i	0.914051	−	0.405598i	$-0.132937\pi$
$90$	−12.8034	+	8.78997i	−1.34959	+	0.926545i
$91$	−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
$100$	3.59313	−	9.33217i	0.359313	−	0.933217i
$101$	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	$0.0496126\pi$
$109$			3.24135i			0.310465i	−0.987878	+	0.155232i	$0.950387\pi$
$110$	1.22017	+	1.77729i	0.116339	+	0.169458i
$111$		−	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	$0.476696\pi$
$114$	−14.2435	−	9.88663i	−1.33402	−	0.925967i
$115$	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
$120$	−17.6682	−	2.06895i	−1.61288	−	0.188869i
$121$	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
$130$	−8.32905	+	5.71819i	−0.730506	+	0.501518i
$131$		−	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	$0.358197\pi$
$137$			21.1247i			1.80480i	−0.430897	+	0.902401i	$0.641803\pi$
$138$	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	$-0.125464\pi$
$140$	−15.8173	−	9.54311i	−1.33681	−	0.806540i
$141$		−	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	$0.520282\pi$
$150$	−14.1814	+	13.9443i	−1.15791	+	1.13855i
$151$	4.46517			0.363371			0.181685	−	0.983357i	$-0.441845\pi$
$151$	4.46517			0.363371			0.181685	+	0.983357i	$0.441845\pi$
$152$	−3.00034	−	11.9582i	−0.243360	−	0.969936i
$153$		−	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	$0.00670187\pi$
$157$			0.527586i			0.0421060i	−0.999778	+	0.0210530i	$0.993298\pi$
$158$	2.89236	+	6.36878i	0.230104	+	0.506673i
$159$			21.3894i			1.69629i
$160$	−8.49194	−	9.37480i	−0.671347	−	0.741143i
$161$	26.4855			2.08735
$162$	−0.225540	−	0.496623i	−0.0177201	−	0.0390184i
$163$	23.5089			1.84136			0.920679	−	0.390320i	$-0.127636\pi$
$163$	23.5089			1.84136			0.920679	+	0.390320i	$0.127636\pi$
$164$	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
$170$	5.25044	+	7.64773i	0.402690	+	0.586554i
$171$	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	$-0.547332\pi$
$179$	−3.96422			−0.296300			−0.148150	+	0.988965i	$0.547332\pi$
$180$	18.8055	+	11.3460i	1.40168	+	0.845682i
$181$			16.7164i			1.24252i	0.783604	+	0.621261i	$0.213379\pi$
$181$			16.7164i			1.24252i	−0.783604	+	0.621261i	$0.786621\pi$
$182$	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
$190$	−12.5210	−	5.76409i	−0.908368	−	0.418171i
$191$			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	$-0.925780\pi$
$197$		−	6.48624i		−	0.462126i	0.972939	−	0.231063i	$-0.0742203\pi$
$198$	−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	$-0.0524747\pi$
$200$	−14.1177	+	0.830587i	−0.998274	+	0.0587313i
$201$	−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
$210$	20.7947	+	30.2894i	1.43497	+	2.09017i
$211$	14.4300			0.993399			0.496699	−	0.867923i	$-0.334545\pi$
$211$	14.4300			0.993399			0.496699	+	0.867923i	$0.334545\pi$
$212$	−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
$220$	1.57499	−	2.61047i	0.106186	−	0.175998i
$221$		−	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	$0.973465\pi$
$228$	−4.40116	+	24.1221i	−0.291474	+	1.59752i
$229$	−14.8673			−0.982461			−0.491231	−	0.871030i	$-0.663453\pi$
$229$	−14.8673			−0.982461			−0.491231	+	0.871030i	$0.663453\pi$
$230$	16.7157	−	11.4760i	1.10220	−	0.756702i
$231$	−7.92062			−0.521138
$232$	−0.755637	+	2.51470i	−0.0496100	+	0.165098i
$233$			3.78435i			0.247921i	0.992287	+	0.123960i	$0.0395596\pi$
$233$			3.78435i			0.247921i	−0.992287	+	0.123960i	$0.960440\pi$
$234$	−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	$0.732701\pi$
$240$	7.66792	+	23.9602i	0.494962	+	1.54663i
$241$			2.24624i			0.144693i	0.997380	+	0.0723466i	$0.0230488\pi$
$241$			2.24624i			0.144693i	−0.997380	+	0.0723466i	$0.976951\pi$
$242$	−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
$250$	−9.16759	+	12.8824i	−0.579809	+	0.814752i
$251$		−	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
$260$	12.2337	+	7.38098i	0.758700	+	0.457749i
$261$		−	4.55924i		−	0.282210i
$262$	−7.01474	+	3.18573i	−0.433372	+	0.196815i
$263$	−19.0639			−1.17553			−0.587766	−	0.809031i	$-0.699992\pi$
$263$	−19.0639			−1.17553			−0.587766	+	0.809031i	$0.699992\pi$
$264$	−5.19404	−	1.56075i	−0.319671	−	0.0960575i
$265$	2.96624	+	16.7439i	0.182215	+	1.02857i
$266$	−14.5196	+	20.9182i	−0.890257	+	1.28258i
$267$	21.5248			1.31730
$268$	−7.72280	−	6.74889i	−0.471745	−	0.412254i
$269$		−	18.9627i		−	1.15617i	−0.815975	−	0.578087i	$-0.803799\pi$
$269$		−	18.9627i		−	1.15617i	0.815975	−	0.578087i	$-0.196201\pi$
$270$	−9.62083	−	14.0136i	−0.585505	−	0.852840i
$271$		−	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	$-0.754342\pi$
$277$		−	23.2139i		−	1.39479i	0.716687	−	0.697395i	$-0.245658\pi$
$278$	−11.6600	+	5.29537i	−0.699323	+	0.317595i
$279$	−32.8442			−1.96633
$280$	−3.03850	+	25.9477i	−0.181585	+	1.55067i
$281$			9.45315i			0.563928i	0.959425	+	0.281964i	$0.0909858\pi$
$281$			9.45315i			0.563928i	−0.959425	+	0.281964i	$0.909014\pi$
$282$	−24.4172	+	11.0890i	−1.45402	+	0.660340i
$283$	−21.0074			−1.24876			−0.624381	−	0.781120i	$-0.714649\pi$
$283$	−21.0074			−1.24876			−0.624381	+	0.781120i	$0.714649\pi$
$284$	−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
$290$	1.66158	+	2.42023i	0.0975711	+	0.142121i
$291$			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
$300$	26.2483	+	10.1063i	1.51545	+	0.583487i
$301$	−29.0105			−1.67214
$302$	−2.61115	−	5.74956i	−0.150255	−	0.330850i
$303$			20.9559i			1.20388i
$304$	−13.6434	+	10.8563i	−0.782500	+	0.622651i
$305$	−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
$310$	17.4351	−	11.9698i	0.990245	−	0.679838i
$311$		−	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	$0.120341\pi$
$313$			13.0608i			0.738241i	−0.929382	+	0.369120i	$0.879659\pi$
$314$	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
$320$	−7.10550	+	16.4168i	−0.397210	+	0.917728i
$321$	−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
$330$	−4.99893	+	3.43194i	−0.275182	+	0.188922i
$331$	3.78583			0.208088			0.104044	−	0.994573i	$-0.466822\pi$
$331$	3.78583			0.208088			0.104044	+	0.994573i	$0.466822\pi$
$332$	−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
$340$	6.77722	−	11.2330i	0.367546	−	0.609192i
$341$			4.55924i			0.246897i
$342$	17.2627	−	24.8701i	0.933461	−	1.34482i
$343$	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	$-0.452144\pi$
$347$	5.58017			0.299559			0.149780	+	0.988719i	$0.452144\pi$
$348$	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	$0.390595\pi$
$350$	20.4788	+	20.8270i	1.09464	+	1.11325i
$351$			17.1734i			0.916647i
$352$	−2.05075	−	3.26599i	−0.109305	−	0.174078i
$353$			0.501758i			0.0267059i	0.999911	+	0.0133529i	$0.00425050\pi$
$353$			0.501758i			0.0267059i	−0.999911	+	0.0133529i	$0.995750\pi$
$354$	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	$0.851868\pi$
$360$	3.61253	−	30.8498i	0.190397	−	1.62593i
$361$	−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	$-0.508150\pi$
$367$	−0.980882			−0.0512016			−0.0256008	+	0.999672i	$0.508150\pi$
$368$	−3.43643	−	25.4160i	−0.179136	−	1.32490i
$369$			24.0346i			1.25119i
$370$	−17.2911	+	11.8710i	−0.898924	+	0.617143i
$371$	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	$-0.459879\pi$
$379$	4.89460			0.251419			0.125709	+	0.992067i	$0.459879\pi$
$380$	−0.100075	+	19.4933i	−0.00513375	+	0.999987i
$381$	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	$0.487574\pi$
$390$	−16.0834	−	23.4269i	−0.814414	−	1.18627i
$391$			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	$0.331002\pi$
$397$			34.3640i			1.72468i	−0.506330	+	0.862340i	$0.668998\pi$
$398$	−5.96189	+	2.70758i	−0.298843	+	0.135718i
$399$	43.4961	−	25.9390i	2.17753	−	1.29858i
$400$	9.32527	+	17.6929i	0.466264	+	0.884646i
$401$		−	25.1483i		−	1.25585i	−0.778275	−	0.627924i	$-0.783905\pi$
$401$		−	25.1483i		−	1.25585i	0.778275	−	0.627924i	$-0.216095\pi$
$402$	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	$0.0583069\pi$
$409$			7.36766i			0.364307i	−0.983270	+	0.182154i	$0.941693\pi$
$410$	−8.75920	−	12.7585i	−0.432586	−	0.630100i
$411$	−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
$418$	−3.45232	−	2.39631i	−0.168858	−	0.117207i
$419$		−	6.90117i		−	0.337144i	−0.985689	−	0.168572i	$-0.946084\pi$
$419$		−	6.90117i		−	0.337144i	0.985689	−	0.168572i	$-0.0539156\pi$
$420$	26.8416	−	44.4889i	1.30974	−	2.17084i
$421$		−	1.83055i		−	0.0892154i	−0.999005	−	0.0446077i	$-0.985796\pi$
$421$		−	1.83055i		−	0.0892154i	0.999005	−	0.0446077i	$-0.0142038\pi$
$422$	−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
$430$	−18.3094	+	12.5700i	−0.882956	+	0.606180i
$431$	−14.0996			−0.679152			−0.339576	−	0.940579i	$-0.610284\pi$
$431$	−14.0996			−0.679152			−0.339576	+	0.940579i	$0.610284\pi$
$432$	−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	$-0.699038\pi$
$439$	−24.5284			−1.17067			−0.585337	+	0.810790i	$0.699038\pi$
$440$	−4.28239	−	0.501470i	−0.204155	−	0.0239067i
$441$	−49.4201			−2.35334
$442$	−12.0680	+	5.48064i	−0.574016	+	0.260688i
$443$	6.36297			0.302314			0.151157	−	0.988510i	$-0.451700\pi$
$443$	6.36297			0.302314			0.151157	+	0.988510i	$0.451700\pi$
$444$	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	$-0.800942\pi$
$449$		−	24.8083i		−	1.17078i	0.810753	−	0.585388i	$-0.199058\pi$
$450$	−24.3477	−	24.7617i	−1.14776	−	1.16728i
$451$	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
$456$	33.6344	−	8.43898i	1.57507	−	0.395191i
$457$		−	6.10142i		−	0.285413i	−0.989765	−	0.142706i	$-0.954420\pi$
$457$		−	6.10142i		−	0.285413i	0.989765	−	0.142706i	$-0.0455804\pi$
$458$	8.69413	+	19.1439i	0.406250	+	0.894534i
$459$	15.7686			0.736014
$460$	−24.5520	−	14.8130i	−1.14474	−	0.690662i
$461$	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	$-0.494093\pi$
$463$	0.798615			0.0371148			0.0185574	+	0.999828i	$0.494093\pi$
$464$	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	$-0.565565\pi$
$467$	−8.83970			−0.409053			−0.204526	+	0.978861i	$0.565565\pi$
$468$	−20.6494	+	23.6292i	−0.954519	+	1.09226i
$469$			21.1828i			0.978129i
$470$	−17.5762	+	12.0667i	−0.810731	+	0.556595i
$471$	−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	$0.928910\pi$
$480$	26.3682	−	23.8850i	1.20354	−	1.09020i
$481$	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
$490$	26.2343	−	18.0108i	1.18514	−	0.813643i
$491$		−	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
$494$	11.2300	−	16.1789i	0.505262	−	0.727922i
$495$	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	$0.981338\pi$
$500$	21.9490	+	4.27125i	0.981587	+	0.191016i
$501$	−40.6552			−1.81634
$502$	−11.3484	+	5.15386i	−0.506505	+	0.230028i
$503$	−33.9417			−1.51339			−0.756694	−	0.653769i	$-0.773187\pi$
$503$	−33.9417			−1.51339			−0.756694	+	0.653769i	$0.773187\pi$
$504$	−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	$0.0102196\pi$
$509$			1.44843i			0.0642006i	−0.999485	+	0.0321003i	$0.989780\pi$
$510$	−21.5105	+	14.7678i	−0.952503	+	0.653927i
$511$		−	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
$520$	2.35008	−	20.0689i	0.103058	−	0.880079i
$521$			33.3661i			1.46180i	0.682487	+	0.730898i	$0.260898\pi$
$521$			33.3661i			1.46180i	−0.682487	+	0.730898i	$0.739102\pi$
$522$	−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
$530$	19.8256	−	13.6109i	0.861167	−	0.591222i
$531$	−64.8123			−2.81261
$532$	35.4260	+	6.46361i	1.53591	+	0.280233i
$533$			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
$540$	−12.4185	+	20.5831i	−0.534406	+	0.885756i
$541$	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
$550$	−3.43728	+	3.37980i	−0.146566	+	0.144115i
$551$	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	$-0.827661\pi$
$557$		−	24.3255i		−	1.03071i	0.856978	−	0.515353i	$-0.172339\pi$
$558$	19.2066	+	42.2917i	0.813082	+	1.79035i
$559$	22.4377			0.949015
$560$	35.1883	−	11.2612i	1.48698	−	0.475873i
$561$		−	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	$-0.653511\pi$
$569$		−	42.2662i		−	1.77189i	0.463790	−	0.885945i	$-0.346489\pi$
$570$	16.2125	−	35.2174i	0.679066	−	1.47510i
$571$			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	$0.0210084\pi$
$577$			3.16844i			0.131904i	−0.997823	+	0.0659519i	$0.978992\pi$
$578$	−4.90894	−	10.8092i	−0.204185	−	0.449601i
$579$		−	13.8413i		−	0.575226i
$580$	2.14475	−	3.55483i	0.0890557	−	0.147606i
$581$	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	$-0.338940\pi$
$587$	23.4852			0.969336			0.484668	+	0.874698i	$0.338940\pi$
$588$	−42.6248	−	37.2494i	−1.75782	−	1.53614i
$589$	−14.9309	−	25.0371i	−0.615218	−	1.03164i
$590$	34.4051	−	23.6203i	1.41643	−	0.972432i
$591$	18.2437			0.750444
$592$	3.55472	+	26.2909i	0.146098	+	1.08055i
$593$		−	30.3518i		−	1.24640i	−0.782062	−	0.623200i	$-0.785832\pi$
$593$		−	30.3518i		−	1.24640i	0.782062	−	0.623200i	$-0.214168\pi$
$594$	−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	$-0.345675\pi$
$599$	22.8129			0.932109			0.466055	+	0.884756i	$0.345675\pi$
$600$	−2.33617	−	39.7085i	−0.0953736	−	1.62109i
$601$		−	34.9549i		−	1.42584i	−0.701246	−	0.712920i	$-0.747372\pi$
$601$		−	34.9549i		−	1.42584i	0.701246	−	0.712920i	$-0.252628\pi$
$602$	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	$0.704606\pi$
$608$	21.9574	+	11.2193i	0.890491	+	0.455001i
$609$	−10.7859			−0.437068
$610$	−15.0246	+	10.3149i	−0.608329	+	0.417639i
$611$	21.5393			0.871386
$612$	21.6964	+	18.9603i	0.877024	+	0.766424i
$613$		−	26.3466i		−	1.06413i	−0.846703	−	0.532065i	$-0.821416\pi$
$613$		−	26.3466i		−	1.06413i	0.846703	−	0.532065i	$-0.178584\pi$
$614$	−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	$0.0847242\pi$
$617$			13.0674i			0.526074i	−0.964786	+	0.263037i	$0.915276\pi$
$618$	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	$-0.0694506\pi$
$620$	−25.6085	−	15.4505i	−1.02846	−	0.620506i
$621$		−	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
$630$	−52.8873	+	36.3090i	−2.10708	+	1.44659i
$631$			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
$640$	25.2942	−	0.450861i	0.999841	−	0.0178218i
$641$		−	13.1666i		−	0.520048i	−0.965602	−	0.260024i	$-0.916270\pi$
$641$		−	13.1666i		−	0.520048i	0.965602	−	0.260024i	$-0.0837304\pi$
$642$	18.2964	+	40.2873i	0.722099	+	1.59001i
$643$	31.8875			1.25752			0.628761	−	0.777599i	$-0.283562\pi$
$643$	31.8875			1.25752			0.628761	+	0.777599i	$0.283562\pi$
$644$	−34.8566	+	39.8866i	−1.37354	+	1.57175i
$645$	43.4933	−	7.70501i	1.71255	−	0.303384i
$646$	−14.8554	−	10.3114i	−0.584479	−	0.405696i
$647$	−20.6536			−0.811979			−0.405989	−	0.913878i	$-0.633073\pi$
$647$	−20.6536			−0.811979			−0.405989	+	0.913878i	$0.633073\pi$
$648$	1.04473	+	0.313929i	0.0410408	+	0.0123323i
$649$			8.99686i			0.353158i
$650$	−15.8390	−	16.1084i	−0.621257	−	0.631822i
$651$			77.7006i			3.04533i
$652$	−30.9392	+	35.4039i	−1.21167	+	1.38653i
$653$			29.4300i			1.15169i	0.817560	+	0.575843i	$0.195326\pi$
$653$			29.4300i			1.15169i	−0.817560	+	0.575843i	$0.804674\pi$
$654$	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	$-0.427491\pi$
$659$	11.5946			0.451660			0.225830	+	0.974167i	$0.427491\pi$
$660$	7.34240	+	4.42992i	0.285803	+	0.172434i
$661$		−	29.8500i		−	1.16103i	−0.814250	−	0.580515i	$-0.802851\pi$
$661$		−	29.8500i		−	1.16103i	0.814250	−	0.580515i	$-0.197149\pi$
$662$	−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
$670$	9.17833	+	13.3690i	0.354590	+	0.516491i
$671$		−	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
$680$	−18.4272	−	2.15784i	−0.706653	−	0.0827495i
$681$	−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	$0.956872\pi$
$684$	−42.1188	−	7.68473i	−1.61045	−	0.293833i
$685$	−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
$690$	32.2781	+	47.0159i	1.22880	+	1.78986i
$691$		−	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
$700$	14.8423	−	38.5487i	0.560985	−	1.45700i
$701$	−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	$0.622931\pi$
$710$	19.3955	−	13.3157i	0.727901	−	0.499730i
$711$	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	$-0.196493\pi$
$720$	−41.8362	+	13.3887i	−1.55914	+	0.498967i
$721$			3.37873i			0.125830i
$722$	26.8061	+	1.85344i	0.997618	+	0.0689779i
$723$	−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	$-0.436213\pi$
$727$	10.7341			0.398106			0.199053	+	0.979989i	$0.436213\pi$
$728$	−35.7479	−	10.7418i	−1.32491	−	0.398119i
$729$	43.4629			1.60974
$730$	−18.1722	−	26.4694i	−0.672584	−	0.979678i
$731$		−	20.6023i		−	0.762004i
$732$	24.4116	+	21.3331i	0.902279	+	0.788494i
$733$		−	39.1519i		−	1.44611i	−0.690792	−	0.723053i	$-0.742738\pi$
$733$		−	39.1519i		−	1.44611i	0.690792	−	0.723053i	$-0.257262\pi$
$734$	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	$0.936929\pi$
$740$	25.3971	+	15.3229i	0.933618	+	0.563283i
$741$	−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
$750$	−36.2338	−	25.7854i	−1.32307	−	0.941549i
$751$	10.3152			0.376408			0.188204	−	0.982130i	$-0.439733\pi$
$751$	10.3152			0.376408			0.188204	+	0.982130i	$0.439733\pi$
$752$	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	$0.0734876\pi$
$757$			12.5915i			0.457645i	−0.973468	+	0.228823i	$0.926512\pi$
$758$	−2.86227	−	6.30252i	−0.103962	−	0.228918i
$759$	−12.2946			−0.446264
$760$	25.1590	−	11.2705i	0.912614	−	0.408823i
$761$	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	$0.499394\pi$
$770$	5.04020	+	7.34150i	0.181636	+	0.264569i
$771$			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
$780$	−20.7603	+	34.4093i	−0.743337	+	1.23205i
$781$			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
$790$	−12.8945	+	8.85254i	−0.458766	+	0.314959i
$791$	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	$0.717623\pi$
$798$	−58.8360	−	40.8390i	−2.08277	−	1.44568i
$799$		−	19.7774i		−	0.699673i
$800$	17.3290	−	22.3541i	0.612672	−	0.790337i
$801$			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	$0.539255\pi$
$810$	1.00548	−	0.690300i	0.0353291	−	0.0242547i
$811$	7.46612			0.262171			0.131085	−	0.991371i	$-0.458154\pi$
$811$	7.46612			0.262171			0.131085	+	0.991371i	$0.458154\pi$
$812$	−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
$820$	−11.3063	+	18.7397i	−0.394833	+	0.654418i
$821$	−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	$-0.403210\pi$
$823$	17.1790			0.598821			0.299410	+	0.954124i	$0.403210\pi$
$824$	−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	$0.226160\pi$
$829$			37.5577i			1.30443i	−0.758033	+	0.652216i	$0.773840\pi$
$830$	25.4026	−	17.4398i	0.881739	−	0.605345i
$831$	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
$836$	−1.06675	+	5.84668i	−0.0368943	+	0.202212i
$837$		−	35.9487i		−	1.24257i
$838$	−8.88627	+	4.03567i	−0.306971	+	0.139410i
$839$	−26.3813			−0.910784			−0.455392	−	0.890291i	$-0.650501\pi$
$839$	−26.3813			−0.910784			−0.455392	+	0.890291i	$0.650501\pi$
$840$	−72.9824	−	8.54628i	−2.51813	−	0.294875i
$841$	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
$850$	−14.7907	+	14.5434i	−0.507317	+	0.498834i
$851$	−42.5265			−1.45779
$852$	−31.5134	−	27.5393i	−1.07963	−	0.943480i
$853$			3.94363i			0.135027i	0.997718	+	0.0675137i	$0.0215066\pi$
$853$			3.94363i			0.135027i	−0.997718	+	0.0675137i	$0.978493\pi$
$854$	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	$0.908084\pi$
$860$	26.8927	+	16.2253i	0.917033	+	0.553277i
$861$	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
$870$	−6.80732	+	4.67346i	−0.230790	+	0.158445i
$871$		−	16.3835i		−	0.555133i
$872$	−2.63831	+	8.78009i	−0.0893446	+	0.297331i
$873$	−74.0588			−2.50651
$874$	−22.5377	+	32.4697i	−0.762350	+	1.09830i
$875$	−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
$880$	1.85854	+	5.80745i	0.0626514	+	0.195769i
$881$	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	$-0.537370\pi$
$883$	−6.96126			−0.234265			−0.117132	+	0.993116i	$0.537370\pi$
$884$	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
$890$	−13.6971	−	19.9511i	−0.459128	−	0.668761i
$891$			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
$900$	−17.6463	+	45.8313i	−0.588209	+	1.52771i
$901$			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
$910$	−34.4051	+	23.6203i	−1.14052	+	0.783005i
$911$	35.0406			1.16095			0.580473	−	0.814280i	$-0.302868\pi$
$911$	35.0406			1.16095			0.580473	+	0.814280i	$0.302868\pi$
$912$	−30.5352	−	38.3742i	−1.01112	−	1.27070i
$913$			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	$0.828041\pi$
$920$	−4.71642	+	40.2767i	−0.155496	+	1.32788i
$921$	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	$0.484664\pi$
$930$	33.6671	+	49.0391i	1.10399	+	1.60805i
$931$	−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	$-0.795919\pi$
$937$		−	36.6167i		−	1.19622i	0.801416	−	0.598108i	$-0.204081\pi$
$938$	27.2759	−	12.3873i	0.890589	−	0.404458i
$939$	−36.7358			−1.19883
$940$	25.8159	+	15.5756i	0.842021	+	0.508019i
$941$			34.9115i			1.13808i	0.822309	+	0.569041i	$0.192685\pi$
$941$			34.9115i			1.13808i	−0.822309	+	0.569041i	$0.807315\pi$
$942$	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	$-0.751903\pi$
$947$	−43.7796			−1.42264			−0.711322	+	0.702866i	$0.751903\pi$
$948$	20.9507	+	18.3086i	0.680446	+	0.594636i
$949$			32.4377i			1.05297i
$950$	7.80741	−	29.8168i	0.253306	−	0.967386i
$951$			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
$960$	−46.1751	−	19.9854i	−1.49029	−	0.645027i
$961$	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	$-0.406905\pi$
$967$	17.9312			0.576627			0.288314	+	0.957536i	$0.406905\pi$
$968$	28.5376	+	8.57522i	0.917234	+	0.275618i
$969$	18.4211	+	30.8896i	0.591770	+	0.992316i
$970$	39.3135	−	26.9901i	1.26228	−	0.866600i
$971$	33.5761			1.07751			0.538754	−	0.842463i	$-0.318895\pi$
$971$	33.5761			1.07751			0.538754	+	0.842463i	$0.318895\pi$
$972$	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
$980$	−38.5328	−	23.2481i	−1.23088	−	0.742633i
$981$		−	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
$988$	−27.3997	−	4.99919i	−0.871702	−	0.159045i
$989$	−45.0308			−1.43189
$990$	−5.99240	−	8.72847i	−0.190451	−	0.277409i
$991$	−35.8187			−1.13782			−0.568910	−	0.822400i	$-0.692635\pi$
$991$	−35.8187			−1.13782			−0.568910	+	0.822400i	$0.692635\pi$
$992$	−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	$0.183236\pi$
$997$			34.3781i			1.08876i	−0.838837	+	0.544382i	$0.816764\pi$
$998$	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.379.14	yes	40
4.3	odd	2	inner	380.2.d.b.379.16	yes	40
5.4	even	2	inner	380.2.d.b.379.27	yes	40
19.18	odd	2	inner	380.2.d.b.379.28	yes	40
20.19	odd	2	inner	380.2.d.b.379.25	yes	40
76.75	even	2	inner	380.2.d.b.379.26	yes	40
95.94	odd	2	inner	380.2.d.b.379.13	✓	40
380.379	even	2	inner	380.2.d.b.379.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.13	✓	40	95.94	odd	2	inner
380.2.d.b.379.14	yes	40	1.1	even	1	trivial
380.2.d.b.379.15	yes	40	380.379	even	2	inner
380.2.d.b.379.16	yes	40	4.3	odd	2	inner
380.2.d.b.379.25	yes	40	20.19	odd	2	inner
380.2.d.b.379.26	yes	40	76.75	even	2	inner
380.2.d.b.379.27	yes	40	5.4	even	2	inner
380.2.d.b.379.28	yes	40	19.18	odd	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} +(2.60702 - 1.78981i) 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} +(-3.82918 - 2.31027i) 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} +(5.03415 + 7.33269i) 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} +(-3.51503 + 5.06404i) q^{38} -8.98606i q^{39} +(-0.735583 + 6.28163i) 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} +(4.95767 + 5.04198i) 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} +(6.49804 - 10.7702i) 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} +(10.7689 - 7.39324i) 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} +(8.57622 + 1.56476i) q^{76} +2.81605i q^{77} +(-11.5709 + 5.25487i) q^{78} -4.94607 q^{79} +(8.51867 - 2.72621i) 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} +(-12.8034 + 8.78997i) 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

Groups

Database

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