LMFDB - Embedded newform 62.7.f.a.29.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	62.29
Dual form			62.7.f.a.15.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.57649 + 3.32502i) q^{2} +(15.4410 + 21.2527i) q^{3} +(9.88854 + 30.4338i) q^{4} +6.26454 q^{5} +148.604i q^{6} +(109.443 + 336.831i) q^{7} +(-55.9381 + 172.160i) q^{8} +(12.0203 - 36.9947i) q^{9} +(28.6696 + 20.8297i) q^{10} +(-988.558 + 321.202i) q^{11} +(-494.112 + 680.086i) q^{12} +(1598.75 + 2200.48i) q^{13} +(-619.103 + 1905.40i) q^{14} +(96.7308 + 133.138i) q^{15} +(-828.433 + 601.892i) q^{16} +(576.948 + 187.462i) q^{17} +(178.019 - 129.338i) q^{18} +(-9178.28 - 6668.41i) q^{19} +(61.9472 + 190.654i) q^{20} +(-5468.66 + 7526.96i) q^{21} +(-5592.13 - 1816.99i) q^{22} +(12987.6 + 4219.91i) q^{23} +(-4522.60 + 1469.48i) q^{24} -15585.8 q^{25} +15386.3i q^{26} +(19185.2 - 6233.65i) q^{27} +(-9168.81 + 6661.53i) q^{28} +(-3018.28 + 4154.30i) q^{29} +930.938i q^{30} +(9749.41 + 28150.5i) q^{31} -5792.62 q^{32} +(-22090.7 - 16049.8i) q^{33} +(2017.08 + 2776.28i) q^{34} +(685.610 + 2110.09i) q^{35} +1244.75 q^{36} +20798.0i q^{37} +(-19831.8 - 61035.9i) q^{38} +(-22080.0 + 67955.3i) q^{39} +(-350.426 + 1078.50i) q^{40} +(21655.4 + 15733.6i) q^{41} +(-50054.5 + 16263.7i) q^{42} +(78114.4 - 107515. i) q^{43} +(-19550.8 - 26909.4i) q^{44} +(75.3017 - 231.755i) q^{45} +(45406.2 + 62496.2i) q^{46} +(69915.4 - 50796.5i) q^{47} +(-25583.7 - 8312.64i) q^{48} +(-6297.21 + 4575.19i) q^{49} +(-71328.1 - 51822.9i) q^{50} +(4924.58 + 15156.3i) q^{51} +(-51159.8 + 70415.5i) q^{52} +(165534. + 53785.2i) q^{53} +(108528. + 35262.9i) q^{54} +(-6192.86 + 2012.18i) q^{55} -64110.7 q^{56} -298030. i q^{57} +(-27626.3 + 8976.31i) q^{58} +(213614. - 155200. i) q^{59} +(-3095.38 + 4260.43i) q^{60} -240009. i q^{61} +(-48982.9 + 161248. i) q^{62} +13776.5 q^{63} +(-26509.9 - 19260.5i) q^{64} +(10015.4 + 13785.0i) q^{65} +(-47732.0 - 146904. i) q^{66} +135109. q^{67} +19412.4i q^{68} +(110856. + 341180. i) q^{69} +(-3878.40 + 11936.5i) q^{70} +(24551.9 - 75563.1i) q^{71} +(5696.60 + 4138.82i) q^{72} +(87800.2 - 28528.0i) q^{73} +(-69153.8 + 95182.0i) q^{74} +(-240660. - 331239. i) q^{75} +(112185. - 345271. i) q^{76} +(-216381. - 297823. i) q^{77} +(-327001. + 237580. i) q^{78} +(206942. + 67239.7i) q^{79} +(-5189.76 + 3770.58i) q^{80} +(405779. + 294816. i) q^{81} +(46791.4 + 144009. i) q^{82} +(23542.5 - 32403.4i) q^{83} +(-283151. - 92001.4i) q^{84} +(3614.31 + 1174.36i) q^{85} +(714980. - 232311. i) q^{86} -134895. q^{87} -188157. i q^{88} +(-1.25555e6 + 407954. i) q^{89} +(1115.21 - 810.245i) q^{90} +(-566219. + 779334. i) q^{91} +436989. i q^{92} +(-447734. + 641874. i) q^{93} +488867. q^{94} +(-57497.8 - 41774.6i) q^{95} +(-89443.8 - 123109. i) q^{96} +(-21348.5 - 65703.9i) q^{97} -44031.7 q^{98} +40432.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	4.57649	+	3.32502i	0.572061	+	0.415627i
$2$	4.57649	+	3.32502i	0.572061	+	0.415627i
$3$	15.4410	+	21.2527i	0.571889	+	0.787137i	0.992777	−	0.119975i	$-0.0382816\pi$
$3$	15.4410	+	21.2527i	0.571889	+	0.787137i	−0.420888	+	0.907112i	$0.638282\pi$
$4$	9.88854	+	30.4338i	0.154508	+	0.475528i
$5$	6.26454			0.0501163			0.0250582	−	0.999686i	$-0.492023\pi$
$5$	6.26454			0.0501163			0.0250582	+	0.999686i	$0.492023\pi$
$6$			148.604i			0.687983i
$7$	109.443	+	336.831i	0.319076	+	0.982014i	0.974044	+	0.226358i	$0.0726819\pi$
$7$	109.443	+	336.831i	0.319076	+	0.982014i	−0.654968	+	0.755656i	$0.727318\pi$
$8$	−55.9381	+	172.160i	−0.109254	+	0.336249i
$9$	12.0203	−	36.9947i	0.0164888	−	0.0507472i
$10$	28.6696	+	20.8297i	0.0286696	+	0.0208297i
$11$	−988.558	+	321.202i	−0.742718	+	0.241324i	−0.655845	−	0.754896i	$-0.727687\pi$
$11$	−988.558	+	321.202i	−0.742718	+	0.241324i	−0.0868731	+	0.996219i	$0.527687\pi$
$12$	−494.112	+	680.086i	−0.285944	+	0.393569i
$13$	1598.75	+	2200.48i	0.727695	+	1.00159i	0.999233	+	0.0391581i	$0.0124676\pi$
$13$	1598.75	+	2200.48i	0.727695	+	1.00159i	−0.271538	+	0.962428i	$0.587532\pi$
$14$	−619.103	+	1905.40i	−0.225621	+	0.694389i
$15$	96.7308	+	133.138i	0.0286610	+	0.0394484i
$16$	−828.433	+	601.892i	−0.202254	+	0.146946i
$17$	576.948	+	187.462i	0.117433	+	0.0381562i	0.367144	−	0.930164i	$-0.380336\pi$
$17$	576.948	+	187.462i	0.117433	+	0.0381562i	−0.249711	+	0.968320i	$0.580336\pi$
$18$	178.019	−	129.338i	0.0305245	−	0.0221773i
$19$	−9178.28	−	6668.41i	−1.33814	−	0.972214i	−0.999510	−	0.0312929i	$-0.990038\pi$
$19$	−9178.28	−	6668.41i	−1.33814	−	0.972214i	−0.338627	−	0.940921i	$-0.609962\pi$
$20$	61.9472	+	190.654i	0.00774340	+	0.0238317i
$21$	−5468.66	+	7526.96i	−0.590504	+	0.812759i
$22$	−5592.13	−	1816.99i	−0.525181	−	0.170642i
$23$	12987.6	+	4219.91i	1.06744	+	0.346833i	0.789490	−	0.613763i	$-0.210345\pi$
$23$	12987.6	+	4219.91i	1.06744	+	0.346833i	0.277950	+	0.960595i	$0.410345\pi$
$24$	−4522.60	+	1469.48i	−0.327155	+	0.106299i
$25$	−15585.8			−0.997488
$26$			15386.3i			0.875418i
$27$	19185.2	−	6233.65i	0.974710	−	0.316702i
$28$	−9168.81	+	6661.53i	−0.417676	+	0.303459i
$29$	−3018.28	+	4154.30i	−0.123756	+	0.170335i	−0.866399	−	0.499352i	$-0.833572\pi$
$29$	−3018.28	+	4154.30i	−0.123756	+	0.170335i	0.742644	+	0.669687i	$0.233572\pi$
$30$			930.938i			0.0344792i
$31$	9749.41	+	28150.5i	0.327260	+	0.944934i
$31$	9749.41	+	28150.5i	0.327260	+	0.944934i
$32$	−5792.62			−0.176777
$33$	−22090.7	−	16049.8i	−0.614707	−	0.446611i
$34$	2017.08	+	2776.28i	0.0513200	+	0.0706360i
$35$	685.610	+	2110.09i	0.0159909	+	0.0492150i
$36$	1244.75			0.0266794
$37$			20798.0i			0.410598i	0.978699	+	0.205299i	$0.0658167\pi$
$37$			20798.0i			0.410598i	−0.978699	+	0.205299i	$0.934183\pi$
$38$	−19831.8	−	61035.9i	−0.361419	−	1.11233i
$39$	−22080.0	+	67955.3i	−0.372225	+	1.14559i
$40$	−350.426	+	1078.50i	−0.00547541	+	0.0168516i
$41$	21655.4	+	15733.6i	0.314206	+	0.228284i	0.733699	−	0.679474i	$-0.237792\pi$
$41$	21655.4	+	15733.6i	0.314206	+	0.228284i	−0.419493	+	0.907759i	$0.637792\pi$
$42$	−50054.5	+	16263.7i	−0.675609	+	0.219519i
$43$	78114.4	−	107515.i	0.982484	−	1.35227i	0.0470043	−	0.998895i	$-0.485033\pi$
$43$	78114.4	−	107515.i	0.982484	−	1.35227i	0.935480	−	0.353379i	$-0.114967\pi$
$44$	−19550.8	−	26909.4i	−0.229512	−	0.315897i
$45$	75.3017	−	231.755i	0.000826357	−	0.00254326i
$46$	45406.2	+	62496.2i	0.466489	+	0.642067i
$47$	69915.4	−	50796.5i	0.673410	−	0.489261i	−0.197755	−	0.980251i	$-0.563365\pi$
$47$	69915.4	−	50796.5i	0.673410	−	0.489261i	0.871165	+	0.490990i	$0.163365\pi$
$48$	−25583.7	−	8312.64i	−0.231334	−	0.0751649i
$49$	−6297.21	+	4575.19i	−0.0535254	+	0.0388885i
$50$	−71328.1	−	51822.9i	−0.570625	−	0.414583i
$51$	4924.58	+	15156.3i	0.0371243	+	0.114257i
$52$	−51159.8	+	70415.5i	−0.363847	+	0.500793i
$53$	165534.	+	53785.2i	1.11188	+	0.361273i	0.806665	−	0.591009i	$-0.201270\pi$
$53$	165534.	+	53785.2i	1.11188	+	0.361273i	0.305219	+	0.952282i	$0.401270\pi$
$54$	108528.	+	35262.9i	0.689224	+	0.223942i
$55$	−6192.86	+	2012.18i	−0.0372223	+	0.0120943i
$56$	−64110.7			−0.365062
$57$		−	298030.i		−	1.60930i
$58$	−27626.3	+	8976.31i	−0.141592	+	0.0460060i
$59$	213614.	−	155200.i	1.04010	−	0.755674i	0.0697919	−	0.997562i	$-0.477766\pi$
$59$	213614.	−	155200.i	1.04010	−	0.755674i	0.970304	+	0.241887i	$0.0777665\pi$
$60$	−3095.38	+	4260.43i	−0.0143305	+	0.0197242i
$61$		−	240009.i		−	1.05740i	−0.848809	−	0.528699i	$-0.822680\pi$
$61$		−	240009.i		−	1.05740i	0.848809	−	0.528699i	$-0.177320\pi$
$62$	−48982.9	+	161248.i	−0.205527	+	0.676579i
$63$	13776.5			0.0550956
$64$	−26509.9	−	19260.5i	−0.101127	−	0.0734732i
$65$	10015.4	+	13785.0i	0.0364694	+	0.0501958i
$66$	−47732.0	−	146904.i	−0.166027	−	0.510977i
$67$	135109.			0.449220			0.224610	−	0.974449i	$-0.427889\pi$
$67$	135109.			0.449220			0.224610	+	0.974449i	$0.427889\pi$
$68$			19412.4i			0.0617381i
$69$	110856.	+	341180.i	0.337452	+	1.03857i
$70$	−3878.40	+	11936.5i	−0.0113073	+	0.0348002i
$71$	24551.9	−	75563.1i	0.0685979	−	0.211123i	−0.910881	−	0.412669i	$-0.864597\pi$
$71$	24551.9	−	75563.1i	0.0685979	−	0.211123i	0.979479	+	0.201546i	$0.0645967\pi$
$72$	5696.60	+	4138.82i	0.0152622	+	0.0110887i
$73$	87800.2	−	28528.0i	0.225697	−	0.0733336i	−0.193985	−	0.981004i	$-0.562141\pi$
$73$	87800.2	−	28528.0i	0.225697	−	0.0733336i	0.419683	+	0.907671i	$0.362141\pi$
$74$	−69153.8	+	95182.0i	−0.170656	+	0.234887i
$75$	−240660.	−	331239.i	−0.570452	−	0.785160i
$76$	112185.	−	345271.i	0.255561	−	0.786537i
$77$	−216381.	−	297823.i	−0.473967	−	0.652359i
$78$	−327001.	+	237580.i	−0.689074	+	0.500642i
$79$	206942.	+	67239.7i	0.419728	+	0.136378i	0.511264	−	0.859424i	$-0.329178\pi$
$79$	206942.	+	67239.7i	0.419728	+	0.136378i	−0.0915355	+	0.995802i	$0.529178\pi$
$80$	−5189.76	+	3770.58i	−0.0101362	+	0.00736441i
$81$	405779.	+	294816.i	0.763545	+	0.554748i
$82$	46791.4	+	144009.i	0.0848642	+	0.261185i
$83$	23542.5	−	32403.4i	0.0411735	−	0.0566704i	−0.787934	−	0.615760i	$-0.788849\pi$
$83$	23542.5	−	32403.4i	0.0411735	−	0.0566704i	0.829107	+	0.559089i	$0.188849\pi$
$84$	−283151.	−	92001.4i	−0.477728	−	0.155223i
$85$	3614.31	+	1174.36i	0.00588531	+	0.00191225i
$86$	714980.	−	232311.i	1.12408	−	0.365237i
$87$	−134895.			−0.204852
$88$		−	188157.i		−	0.276104i
$89$	−1.25555e6	+	407954.i	−1.78101	+	0.578684i	−0.999005	−	0.0445922i	$-0.985801\pi$
$89$	−1.25555e6	+	407954.i	−1.78101	+	0.578684i	−0.782002	+	0.623276i	$0.785801\pi$
$90$	1115.21	−	810.245i	0.00152978	−	0.00111145i
$91$	−566219.	+	779334.i	−0.751382	+	1.03419i
$92$			436989.i			0.561187i
$93$	−447734.	+	641874.i	−0.556636	+	0.797996i
$94$	488867.			0.588582
$95$	−57497.8	−	41774.6i	−0.0670625	−	0.0487238i
$96$	−89443.8	−	123109.i	−0.101097	−	0.139147i
$97$	−21348.5	−	65703.9i	−0.0233912	−	0.0719907i	0.938680	−	0.344791i	$-0.112050\pi$
$97$	−21348.5	−	65703.9i	−0.0233912	−	0.0719907i	−0.962071	+	0.272800i	$0.912050\pi$
$98$	−44031.7			−0.0467829
$99$			40432.3i			0.0416700i
$100$	−154120.	−	474334.i	−0.154120	−	0.474334i
$101$	−362158.	+	1.11461e6i	−0.351507	+	1.08183i	0.606501	+	0.795083i	$0.292573\pi$
$101$	−362158.	+	1.11461e6i	−0.351507	+	1.08183i	−0.958007	+	0.286743i	$0.907427\pi$
$102$	−27857.6	+	85736.9i	−0.0262508	+	0.0807918i
$103$	473233.	+	343824.i	0.433075	+	0.314647i	0.782877	−	0.622176i	$-0.213751\pi$
$103$	473233.	+	343824.i	0.433075	+	0.314647i	−0.349802	+	0.936824i	$0.613751\pi$
$104$	−468265.	+	152149.i	−0.416286	+	0.135260i
$105$	−34258.6	+	47153.0i	−0.0295939	+	0.0407325i
$106$	578728.	+	796551.i	0.485911	+	0.668799i
$107$	−158399.	+	487503.i	−0.129301	+	0.397948i	−0.994660	−	0.103205i	$-0.967090\pi$
$107$	−158399.	+	487503.i	−0.129301	+	0.397948i	0.865359	+	0.501152i	$0.167090\pi$
$108$	379428.	+	522237.i	0.301202	+	0.414569i
$109$	−605771.	+	440118.i	−0.467766	+	0.339852i	−0.796570	−	0.604546i	$-0.793354\pi$
$109$	−605771.	+	440118.i	−0.467766	+	0.339852i	0.328804	+	0.944398i	$0.393354\pi$
$110$	−35032.1	−	11382.6i	−0.0263201	−	0.00855193i
$111$	−442014.	+	321142.i	−0.323197	+	0.234816i
$112$	−293402.	−	213169.i	−0.208838	−	0.151730i
$113$	−61359.8	−	188846.i	−0.0425254	−	0.130880i	0.927540	−	0.373724i	$-0.121919\pi$
$113$	−61359.8	−	188846.i	−0.0425254	−	0.130880i	−0.970065	+	0.242845i	$0.921919\pi$
$114$	990955.	−	1.36393e6i	0.668866	−	0.920616i
$115$	81361.1	+	26435.8i	0.0534962	+	0.0173820i
$116$	−156278.	−	50777.7i	−0.100121	−	0.0325311i
$117$	100624.	−	32694.6i	0.0628265	−	0.0204136i
$118$	1.49364e6			0.909077
$119$			214850.i			0.127495i
$120$	−28332.0	+	9205.62i	−0.0163958	+	0.00532733i
$121$	−559148.	+	406244.i	−0.315624	+	0.229314i
$122$	798035.	−	1.09840e6i	0.439483	−	0.604897i
$123$			703178.i			0.377877i
$124$	−760320.	+	575080.i	−0.398778	+	0.301622i
$125$	−195521.			−0.100107
$126$	63048.0	+	45807.1i	0.0315181	+	0.0228992i
$127$	−1.84382e6	−	2.53780e6i	−0.900135	−	1.23893i	−0.970425	−	0.241403i	$-0.922393\pi$
$127$	−1.84382e6	−	2.53780e6i	−0.900135	−	1.23893i	0.0702901	−	0.997527i	$-0.477607\pi$
$128$	−57280.6	−	176291.i	−0.0273135	−	0.0840623i
$129$	3.49115e6			1.62630
$130$			96388.4i			0.0438728i
$131$	−1.34441e6	−	4.13767e6i	−0.598023	−	1.84053i	−0.539064	−	0.842265i	$-0.681222\pi$
$131$	−1.34441e6	−	4.13767e6i	−0.598023	−	1.84053i	−0.0589594	−	0.998260i	$-0.518778\pi$
$132$	270013.	−	831014.i	0.117399	−	0.361316i
$133$	1.24163e6	−	3.82134e6i	0.527760	−	1.62428i
$134$	618324.	+	449239.i	0.256981	+	0.186708i
$135$	120187.	−	39051.0i	0.0488489	−	0.0158720i
$136$	−64546.6	+	88840.8i	−0.0256600	+	0.0353180i
$137$	1.03409e6	+	1.42330e6i	0.402158	+	0.553523i	0.961284	−	0.275560i	$-0.0888632\pi$
$137$	1.03409e6	+	1.42330e6i	0.402158	+	0.553523i	−0.559126	+	0.829083i	$0.688863\pi$
$138$	−627097.	+	1.93001e6i	−0.238615	+	0.734381i
$139$	−2.69709e6	−	3.71223e6i	−1.00427	−	1.38226i	−0.922668	−	0.385596i	$-0.873996\pi$
$139$	−2.69709e6	−	3.71223e6i	−1.00427	−	1.38226i	−0.0816039	−	0.996665i	$-0.526004\pi$
$140$	−57438.4	+	41731.5i	−0.0209324	+	0.0152083i
$141$	2.15913e6	+	701543.i	0.770231	+	0.250263i
$142$	363610.	−	264178.i	0.126990	−	0.0922639i
$143$	−2.28725e6	−	1.66179e6i	−0.782178	−	0.568286i
$144$	12308.8	+	37882.6i	0.00412219	+	0.0126868i
$145$	−18908.1	+	26024.8i	−0.00620219	+	0.00853658i
$146$	496673.	+	161379.i	0.159592	+	0.0518547i
$147$	−194470.	−	63187.2i	−0.0612211	−	0.0198919i
$148$	−632963.	+	205662.i	−0.195251	+	0.0634409i
$149$	2.05914e6			0.622484			0.311242	−	0.950331i	$-0.399255\pi$
$149$	2.05914e6			0.622484			0.311242	+	0.950331i	$0.399255\pi$
$150$		−	2.31611e6i		−	0.686255i
$151$	2.62771e6	−	853795.i	0.763215	−	0.247984i	0.0985570	−	0.995131i	$-0.468577\pi$
$151$	2.62771e6	−	853795.i	0.763215	−	0.247984i	0.664658	+	0.747148i	$0.268577\pi$
$152$	1.66145e6	−	1.20711e6i	0.473103	−	0.343729i
$153$	13870.2	−	19090.7i	0.00387265	−	0.00533024i
$154$		−	2.08246e6i		−	0.570183i
$155$	61075.6	+	176350.i	0.0164011	+	0.0473566i
$156$	−2.28648e6			−0.602273
$157$	2.03205e6	+	1.47637e6i	0.525091	+	0.381501i	0.818518	−	0.574480i	$-0.194796\pi$
$157$	2.03205e6	+	1.47637e6i	0.525091	+	0.381501i	−0.293427	+	0.955981i	$0.594796\pi$
$158$	723497.	+	995808.i	0.183428	+	0.252467i
$159$	1.41293e6	+	4.34854e6i	0.351502	+	1.08181i
$160$	−36288.1			−0.00885940
$161$			4.83645e6i			1.15891i
$162$	876778.	+	2.69845e6i	0.206227	+	0.634700i
$163$	−1.01988e6	+	3.13888e6i	−0.235498	+	0.724788i	0.761557	+	0.648098i	$0.224435\pi$
$163$	−1.01988e6	+	3.13888e6i	−0.235498	+	0.724788i	−0.997055	+	0.0766904i	$0.975565\pi$
$164$	−264692.	+	814639.i	−0.0600081	+	0.184686i
$165$	−138388.	−	100545.i	−0.0308069	−	0.0223825i
$166$	215484.	−	70014.9i	0.0471075	−	0.0153062i
$167$	−1.68494e6	+	2.31911e6i	−0.361771	+	0.497935i	−0.950641	−	0.310293i	$-0.899573\pi$
$167$	−1.68494e6	+	2.31911e6i	−0.361771	+	0.497935i	0.588870	+	0.808228i	$0.299573\pi$
$168$	−989933.	−	1.36253e6i	−0.208775	−	0.287354i
$169$	−794577.	+	2.44546e6i	−0.164617	+	0.506641i
$170$	12636.1	+	17392.1i	0.00257197	+	0.00354002i
$171$	−357022.	+	259392.i	−0.0714014	+	0.0518761i
$172$	4.04454e6	+	1.31415e6i	0.794847	+	0.258261i
$173$	−357880.	+	260015.i	−0.0691192	+	0.0502180i	−0.621808	−	0.783169i	$-0.713602\pi$
$173$	−357880.	+	260015.i	−0.0691192	+	0.0502180i	0.552689	+	0.833388i	$0.313602\pi$
$174$	−617348.	−	448529.i	−0.117188	−	0.0851419i
$175$	−1.70575e6	−	5.24976e6i	−0.318274	−	0.979548i
$176$	625625.	−	861099.i	0.114756	−	0.157948i
$177$	6.59682e6	+	2.14344e6i	1.18964	+	0.386537i
$178$	−7.10249e6	−	2.30774e6i	−1.25936	−	0.409192i
$179$	−2.73323e6	+	888081.i	−0.476560	+	0.154844i	−0.537441	−	0.843301i	$-0.680609\pi$
$179$	−2.73323e6	+	888081.i	−0.476560	+	0.154844i	0.0608813	+	0.998145i	$0.480609\pi$
$180$	7797.81			0.00133707
$181$			791395.i			0.133462i	0.997771	+	0.0667310i	$0.0212569\pi$
$181$			791395.i			0.133462i	−0.997771	+	0.0667310i	$0.978743\pi$
$182$	−5.18260e6	+	1.68393e6i	−0.859673	+	0.279325i
$183$	5.10085e6	−	3.70598e6i	0.832318	−	0.604714i
$184$	−1.45300e6	+	1.99988e6i	−0.233244	+	0.321033i
$185$			130290.i			0.0205777i
$186$	−4.18329e6	+	1.44880e6i	−0.650099	+	0.225150i
$187$	−630559.			−0.0964275
$188$	2.23729e6	+	1.62549e6i	0.336705	+	0.244630i
$189$	4.19937e6	+	5.77994e6i	0.622012	+	0.856127i
$190$	−124237.	−	382362.i	−0.0181130	−	0.0557460i
$191$	−9.56901e6			−1.37331			−0.686653	−	0.726986i	$-0.740921\pi$
$191$	−9.56901e6			−1.37331			−0.686653	+	0.726986i	$0.740921\pi$
$192$		−	860808.i		−	0.121619i
$193$	−3.30078e6	−	1.01588e7i	−0.459139	−	1.41309i	−0.866206	−	0.499687i	$-0.833448\pi$
$193$	−3.30078e6	−	1.01588e7i	−0.459139	−	1.41309i	0.407067	−	0.913398i	$-0.366552\pi$
$194$	120765.	−	371678.i	0.0165401	−	0.0509051i
$195$	−138321.	+	425709.i	−0.0186546	+	0.0574128i
$196$	−201511.	−	146406.i	−0.0267627	−	0.0194442i
$197$	3.22409e6	−	1.04757e6i	0.421704	−	0.137020i	−0.0904746	−	0.995899i	$-0.528838\pi$
$197$	3.22409e6	−	1.04757e6i	0.421704	−	0.137020i	0.512179	+	0.858879i	$0.328838\pi$
$198$	−134438.	+	185038.i	−0.0173192	+	0.0238378i
$199$	−5.88687e6	−	8.10258e6i	−0.747008	−	1.02817i	−0.998185	−	0.0602269i	$-0.980818\pi$
$199$	−5.88687e6	−	8.10258e6i	−0.747008	−	1.02817i	0.251177	−	0.967941i	$-0.419182\pi$
$200$	871837.	−	2.68324e6i	0.108980	−	0.335405i
$201$	2.08621e6	+	2.87143e6i	0.256904	+	0.353598i
$202$	−5.36350e6	+	3.89681e6i	−0.650720	+	0.472775i
$203$	−1.72963e6	−	561990.i	−0.206759	−	0.0671801i
$204$	−412567.	+	299747.i	−0.0485963	+	0.0353073i
$205$	135661.	+	98563.7i	0.0157469	+	0.0114408i
$206$	1.02253e6	+	3.14701e6i	0.116970	+	0.359995i
$207$	312229.	−	429746.i	0.0352016	−	0.0484508i
$208$	−2.64891e6	−	860682.i	−0.294359	−	0.0956429i
$209$	1.12152e7	+	3.64403e6i	1.22848	+	0.399156i
$210$	−313569.	+	101885.i	−0.0338591	+	0.0110015i
$211$	−882678.			−0.0939626			−0.0469813	−	0.998896i	$-0.514960\pi$
$211$	−882678.			−0.0939626			−0.0469813	+	0.998896i	$0.514960\pi$
$212$			5.56969e6i			0.584552i
$213$	1.98503e6	−	644974.i	0.205413	−	0.0667426i
$214$	−2.34587e6	+	1.70437e6i	−0.239366	+	0.173910i
$215$	489351.	−	673534.i	0.0492385	−	0.0677710i
$216$			3.65162e6i			0.362346i
$217$	−8.41496e6	+	6.36478e6i	−0.823518	+	0.622880i
$218$	−4.23570e6			−0.408843
$219$	1.96202e6	+	1.42549e6i	0.186797	+	0.135716i
$220$	−122477.	−	168575.i	−0.0115023	−	0.0158316i
$221$	509886.	+	1.56927e6i	0.0472385	+	0.145385i
$222$	−3.09068e6			−0.282485
$223$		−	1.70298e7i		−	1.53566i	−0.640656	−	0.767828i	$-0.721337\pi$
$223$		−	1.70298e7i		−	1.53566i	0.640656	−	0.767828i	$-0.278663\pi$
$224$	−633961.	−	1.95113e6i	−0.0564052	−	0.173597i
$225$	−187346.	+	576590.i	−0.0164474	+	0.0506197i
$226$	347103.	−	1.06827e6i	0.0300700	−	0.0925459i
$227$	1.70260e7	+	1.23701e7i	1.45557	+	1.05754i	0.984489	+	0.175447i	$0.0561369\pi$
$227$	1.70260e7	+	1.23701e7i	1.45557	+	1.05754i	0.471083	+	0.882089i	$0.343863\pi$
$228$	9.07019e6	−	2.94708e6i	0.765265	−	0.248650i
$229$	−1.10877e7	+	1.52610e7i	−0.923286	+	1.27079i	0.0391348	+	0.999234i	$0.487540\pi$
$229$	−1.10877e7	+	1.52610e7i	−0.923286	+	1.27079i	−0.962421	+	0.271561i	$0.912460\pi$
$230$	284449.	+	391510.i	0.0233787	+	0.0321780i
$231$	2.98841e6	−	9.19738e6i	0.242440	−	0.746153i
$232$	−546367.	−	752009.i	−0.0437543	−	0.0602226i
$233$	−1.14034e6	+	828503.i	−0.0901499	+	0.0654977i	−0.631947	−	0.775011i	$-0.717744\pi$
$233$	−1.14034e6	+	828503.i	−0.0901499	+	0.0654977i	0.541797	+	0.840509i	$0.317744\pi$
$234$	569213.	+	184949.i	0.0444250	+	0.0144346i
$235$	437988.	−	318217.i	0.0337488	−	0.0245200i
$236$	6.83565e6	+	4.96639e6i	0.520048	+	0.377837i
$237$	1.76637e6	+	5.43633e6i	0.132690	+	0.408377i
$238$	−714380.	+	983260.i	−0.0529905	+	0.0729352i
$239$	8.07698e6	+	2.62437e6i	0.591637	+	0.192235i	0.589507	−	0.807763i	$-0.299322\pi$
$239$	8.07698e6	+	2.62437e6i	0.591637	+	0.192235i	0.00212998	+	0.999998i	$0.499322\pi$
$240$	−160270.	−	52074.9i	−0.0115936	−	0.00376699i
$241$	−2.41756e6	+	785513.i	−0.172713	+	0.0561180i	−0.394097	−	0.919069i	$-0.628943\pi$
$241$	−2.41756e6	+	785513.i	−0.172713	+	0.0561180i	0.221384	+	0.975187i	$0.428943\pi$
$242$	−3.90970e6			−0.275866
$243$		−	1.52961e6i		−	0.106601i
$244$	7.30440e6	−	2.37334e6i	0.502823	−	0.163377i
$245$	−39449.1	+	28661.5i	−0.00268250	+	0.00194895i
$246$	−2.33808e6	+	3.21809e6i	−0.157056	+	0.216169i
$247$		−	3.08578e7i		−	2.04773i
$248$	−5.39175e6	+	103769.i	−0.353488	+	0.00680320i
$249$	1.05218e6			0.0681540
$250$	−894801.	−	650111.i	−0.0572672	−	0.0416071i
$251$	1.66371e7	+	2.28990e7i	1.05210	+	1.44809i	0.886974	+	0.461819i	$0.152803\pi$
$251$	1.66371e7	+	2.28990e7i	1.05210	+	1.44809i	0.165126	+	0.986272i	$0.447197\pi$
$252$	136229.	+	419271.i	0.00851274	+	0.0261995i
$253$	−1.41944e7			−0.876506
$254$		−	1.77450e7i		−	1.08286i
$255$	30850.2	+	94947.2i	0.00186053	+	0.00572614i
$256$	324028.	−	997255.i	0.0193136	−	0.0594410i
$257$	3.92374e6	−	1.20760e7i	0.231154	−	0.711418i	−0.766455	−	0.642298i	$-0.777981\pi$
$257$	3.92374e6	−	1.20760e7i	0.231154	−	0.711418i	0.997608	−	0.0691196i	$-0.0220190\pi$
$258$	1.59772e7	+	1.16081e7i	0.930341	+	0.675933i
$259$	−7.00542e6	+	2.27620e6i	−0.403213	+	0.131012i
$260$	−320493.	+	441121.i	−0.0182347	+	0.0250979i
$261$	117407.	+	161596.i	0.00660345	+	0.00908887i
$262$	7.60513e6	−	2.34062e7i	0.422866	−	1.30145i
$263$	440394.	+	606151.i	0.0242089	+	0.0333206i	0.820950	−	0.571000i	$-0.193444\pi$
$263$	440394.	+	606151.i	0.0242089	+	0.0333206i	−0.796741	+	0.604321i	$0.793444\pi$
$264$	3.99885e6	−	2.90533e6i	0.217332	−	0.157901i
$265$	1.03699e6	+	336940.i	0.0557236	+	0.0181057i
$266$	1.83883e7	−	1.33599e7i	0.977006	−	0.709836i
$267$	−2.80571e7	−	2.03847e7i	−1.47404	−	1.07095i
$268$	1.33603e6	+	4.11187e6i	0.0694083	+	0.213617i
$269$	1.25749e7	−	1.73079e7i	0.646024	−	0.889176i	−0.352894	−	0.935663i	$-0.614803\pi$
$269$	1.25749e7	−	1.73079e7i	0.646024	−	0.889176i	0.998919	+	0.0464867i	$0.0148025\pi$
$270$	679878.	+	220906.i	0.0345414	+	0.0112232i
$271$	−2.85813e7	−	9.28663e6i	−1.43607	−	0.466606i	−0.515397	−	0.856951i	$-0.672356\pi$
$271$	−2.85813e7	−	9.28663e6i	−1.43607	−	0.466606i	−0.920669	+	0.390345i	$0.872356\pi$
$272$	−590794.	+	191961.i	−0.0293582	+	0.00953906i
$273$	−2.53059e7			−1.24375
$274$			9.95210e6i			0.483797i
$275$	1.54074e7	−	5.00617e6i	0.740852	−	0.240718i
$276$	−9.28721e6	+	6.74755e6i	−0.441731	+	0.320936i
$277$	1.32419e7	−	1.82260e7i	0.623035	−	0.857534i	−0.374535	−	0.927213i	$-0.622198\pi$
$277$	1.32419e7	−	1.82260e7i	0.623035	−	0.857534i	0.997569	+	0.0696791i	$0.0221975\pi$
$278$		−	2.59568e7i		−	1.20814i
$279$	1.15861e6	−	22298.6i	0.0533489	−	0.00102675i
$280$	−401624.			−0.0182956
$281$	2.93637e7	+	2.13340e7i	1.32340	+	0.961507i	0.999883	+	0.0152849i	$0.00486553\pi$
$281$	2.93637e7	+	2.13340e7i	1.32340	+	0.961507i	0.323518	+	0.946222i	$0.395134\pi$
$282$	7.54859e6	+	1.03897e7i	0.336603	+	0.463295i
$283$	3.05347e6	+	9.39761e6i	0.134721	+	0.414627i	0.995546	−	0.0942722i	$-0.0300524\pi$
$283$	3.05347e6	+	9.39761e6i	0.134721	+	0.414627i	−0.860826	+	0.508900i	$0.830052\pi$
$284$	2.54245e6			0.110994
$285$		−	1.86702e6i		−	0.0806520i
$286$	−4.94212e6	−	1.52103e7i	−0.211259	−	0.650189i
$287$	−2.92952e6	+	9.01614e6i	−0.123923	+	0.381395i
$288$	−69629.1	+	214296.i	−0.00291483	+	0.00897092i
$289$	−1.92300e7	−	1.39714e7i	−0.796682	−	0.578824i
$290$	−173066.	+	56232.5i	−0.00709606	+	0.00230565i
$291$	1.06674e6	−	1.46825e6i	0.0432894	−	0.0595827i
$292$	1.73643e6	+	2.38999e6i	0.0697444	+	0.0959949i
$293$	−1.50704e7	+	4.63820e7i	−0.599132	+	1.84394i	−0.0661517	+	0.997810i	$0.521072\pi$
$293$	−1.50704e7	+	4.63820e7i	−0.599132	+	1.84394i	−0.532980	+	0.846128i	$0.678928\pi$
$294$	−679893.	−	935792.i	−0.0267546	−	0.0368246i
$295$	1.33819e6	−	972255.i	0.0521258	−	0.0378716i
$296$	−3.58058e6	−	1.16340e6i	−0.138063	−	0.0448595i
$297$	−1.69634e7	+	1.23247e7i	−0.647507	+	0.470441i
$298$	9.42366e6	+	6.84669e6i	0.356099	+	0.258721i
$299$	1.14779e7	+	3.53255e7i	0.429388	+	1.32152i
$300$	7.70110e6	−	1.05997e7i	0.285226	−	0.392580i
$301$	4.47635e7	+	1.45445e7i	1.64144	+	0.533336i
$302$	1.48646e7	+	4.82980e6i	0.539674	+	0.175351i
$303$	−2.92805e7	+	9.51380e6i	−1.05257	+	0.342000i
$304$	1.16173e7			0.413507
$305$		−	1.50355e6i		−	0.0529930i
$306$	126953.	−	41249.7i	0.00443078	−	0.00143965i
$307$	3.03442e7	−	2.20464e7i	1.04872	−	0.761942i	0.0767535	−	0.997050i	$-0.475545\pi$
$307$	3.03442e7	−	2.20464e7i	1.04872	−	0.761942i	0.971969	+	0.235108i	$0.0755445\pi$
$308$	6.92420e6	−	9.53035e6i	0.236983	−	0.326179i
$309$			1.53665e7i			0.520833i
$310$	−306855.	+	1.01014e6i	−0.0103003	+	0.0339076i
$311$	−5.92155e7			−1.96859			−0.984293	−	0.176545i	$-0.943508\pi$
$311$	−5.92155e7			−1.96859			−0.984293	+	0.176545i	$0.943508\pi$
$312$	−1.04640e7	−	7.60257e6i	−0.344537	−	0.250321i
$313$	−5.18842e6	−	7.14125e6i	−0.169201	−	0.232885i	0.715993	−	0.698108i	$-0.245974\pi$
$313$	−5.18842e6	−	7.14125e6i	−0.169201	−	0.232885i	−0.885194	+	0.465223i	$0.845974\pi$
$314$	4.39070e6	+	1.35132e7i	0.141822	+	0.436484i
$315$	86303.5			0.00276119
$316$			6.96295e6i			0.220664i
$317$	−8.63019e6	−	2.65610e7i	−0.270921	−	0.833809i	−0.990270	−	0.139160i	$-0.955560\pi$
$317$	−8.63019e6	−	2.65610e7i	−0.270921	−	0.833809i	0.719349	−	0.694649i	$-0.244440\pi$
$318$	−7.99272e6	+	2.45991e7i	−0.248550	+	0.764957i
$319$	1.64937e6	−	5.07625e6i	0.0508097	−	0.156376i
$320$	−166072.	−	120659.i	−0.00506812	−	0.00368221i
$321$	−1.28066e7	+	4.16112e6i	−0.387185	+	0.125804i
$322$	−1.60813e7	+	2.21340e7i	−0.481673	+	0.662966i
$323$	−4.04532e6	−	5.56790e6i	−0.120045	−	0.165228i
$324$	−4.95981e6	+	1.52647e7i	−0.145824	+	0.448801i
$325$	−2.49176e7	−	3.42962e7i	−0.725867	−	0.999070i
$326$	−1.51043e7	+	1.09739e7i	−0.435961	+	0.316744i
$327$	−1.87074e7	−	6.07840e6i	−0.535020	−	0.173839i
$328$	−3.92005e6	+	2.84808e6i	−0.111089	+	0.0807107i
$329$	2.47616e7	+	1.79904e7i	0.695330	+	0.505187i
$330$	−299019.	−	920286.i	−0.00832065	−	0.0256083i
$331$	−2.21209e7	+	3.04469e7i	−0.609986	+	0.839573i	−0.996576	−	0.0826780i	$-0.973653\pi$
$331$	−2.21209e7	+	3.04469e7i	−0.609986	+	0.839573i	0.386591	+	0.922251i	$0.373653\pi$
$332$	1.21896e6	+	396064.i	0.0333100	+	0.0108231i
$333$	769417.	+	249999.i	0.0208367	+	0.00677026i
$334$	−1.54222e7	+	5.01097e6i	−0.413910	+	0.134488i
$335$	846395.			0.0225133
$336$		−	9.52713e6i		−	0.251156i
$337$	177764.	−	57759.1i	0.00464467	−	0.00150914i	−0.306694	−	0.951808i	$-0.599223\pi$
$337$	177764.	−	57759.1i	0.00464467	−	0.00150914i	0.311338	+	0.950299i	$0.399223\pi$
$338$	−1.17676e7	+	8.54963e6i	−0.304745	+	0.221410i
$339$	3.06603e6	−	4.22003e6i	0.0787005	−	0.108322i
$340$			121610.i			0.00309409i
$341$	−1.86799e7	−	2.46969e7i	−0.471097	−	0.622844i
$342$	−2.49639e6			−0.0624071
$343$	3.14792e7	+	2.28710e7i	0.780083	+	0.566764i
$344$	1.41402e7	+	1.94623e7i	0.347361	+	0.478101i
$345$	694463.	+	2.13734e6i	0.0169119	+	0.0520494i
$346$	−2.50239e6			−0.0604124
$347$			4.32261e6i			0.103456i	0.998661	+	0.0517282i	$0.0164730\pi$
$347$			4.32261e6i			0.103456i	−0.998661	+	0.0517282i	$0.983527\pi$
$348$	−1.33392e6	−	4.10538e6i	−0.0316513	−	0.0974127i
$349$	7.84988e6	−	2.41595e7i	0.184666	−	0.568344i	−0.815276	−	0.579072i	$-0.803415\pi$
$349$	7.84988e6	−	2.41595e7i	0.184666	−	0.568344i	0.999942	+	0.0107284i	$0.00341502\pi$
$350$	9.64919e6	−	2.96971e7i	0.225054	−	0.692645i
$351$	4.43893e7	+	3.22507e7i	1.02650	+	0.745793i
$352$	5.72634e6	−	1.86060e6i	0.131295	−	0.0426604i
$353$	−3.20799e7	+	4.41542e7i	−0.729305	+	1.00380i	0.269859	+	0.962900i	$0.413023\pi$
$353$	−3.20799e7	+	4.41542e7i	−0.729305	+	1.00380i	−0.999163	+	0.0409017i	$0.986977\pi$
$354$	2.30633e7	+	3.17440e7i	0.519891	+	0.715569i
$355$	153807.	−	473368.i	0.00343787	−	0.0105807i
$356$	−2.48312e7	−	3.41772e7i	−0.550361	−	0.757507i
$357$	−4.56614e6	+	3.31750e6i	−0.100356	+	0.0729132i
$358$	−1.54615e7	−	5.02374e6i	−0.336979	−	0.109491i
$359$	4.25900e7	−	3.09434e7i	0.920501	−	0.668783i	−0.0231480	−	0.999732i	$-0.507369\pi$
$359$	4.25900e7	−	3.09434e7i	0.920501	−	0.668783i	0.943649	+	0.330949i	$0.107369\pi$
$360$	35686.6	+	25927.8i	0.000764888	+	0.000555724i
$361$	2.52352e7	+	7.76659e7i	0.536395	+	1.65085i
$362$	−2.63140e6	+	3.62181e6i	−0.0554704	+	0.0763484i
$363$	−1.72676e7	−	5.61058e6i	−0.361004	−	0.117297i
$364$	−2.93172e7	−	9.52573e6i	−0.607880	−	0.197512i
$365$	550028.	−	178715.i	0.0113111	−	0.00367521i
$366$	3.56664e7			0.727472
$367$		−	3.52991e7i		−	0.714111i	−0.934083	−	0.357056i	$-0.883781\pi$
$367$		−	3.52991e7i		−	0.714111i	0.934083	−	0.357056i	$-0.116219\pi$
$368$	−1.32993e7	+	4.32119e6i	−0.266860	+	0.0867081i
$369$	842364.	−	612013.i	0.0167657	−	0.0121810i
$370$	−433217.	+	596272.i	−0.00855264	+	0.0117717i
$371$			6.16433e7i			1.20716i
$372$	−2.39621e7	−	7.27907e6i	−0.465475	−	0.141399i
$373$	6.10315e7			1.17606			0.588028	−	0.808841i	$-0.299905\pi$
$373$	6.10315e7			1.17606			0.588028	+	0.808841i	$0.299905\pi$
$374$	−2.88575e6	−	2.09662e6i	−0.0551624	−	0.0400779i
$375$	−3.01904e6	−	4.15535e6i	−0.0572499	−	0.0787978i
$376$	4.83418e6	+	1.48781e7i	0.0909409	+	0.279887i
$377$	−1.39669e7			−0.260662
$378$			4.04148e7i			0.748282i
$379$	−1.82306e7	−	5.61081e7i	−0.334876	−	1.03064i	−0.966783	−	0.255598i	$-0.917728\pi$
$379$	−1.82306e7	−	5.61081e7i	−0.334876	−	1.03064i	0.631907	−	0.775044i	$-0.282272\pi$
$380$	702790.	−	2.16297e6i	0.0128078	−	0.0394184i
$381$	2.54647e7	−	7.83723e7i	0.460430	−	1.41706i
$382$	−4.37925e7	−	3.18171e7i	−0.785615	−	0.570783i
$383$	1.39293e7	−	4.52592e6i	0.247933	−	0.0805583i	−0.182414	−	0.983222i	$-0.558391\pi$
$383$	1.39293e7	−	4.52592e6i	0.247933	−	0.0805583i	0.430347	+	0.902663i	$0.358391\pi$
$384$	2.86220e6	−	3.93948e6i	0.0505483	−	0.0695737i
$385$	−1.35553e6	−	1.86573e6i	−0.0237535	−	0.0326938i
$386$	1.86720e7	−	5.74666e7i	0.324661	−	0.999202i
$387$	−3.03854e6	−	4.18219e6i	−0.0524242	−	0.0721557i
$388$	1.78852e6	−	1.29943e6i	0.0306195	−	0.0222463i
$389$	−6.21268e7	−	2.01862e7i	−1.05543	−	0.342930i	−0.270634	−	0.962682i	$-0.587233\pi$
$389$	−6.21268e7	−	2.01862e7i	−1.05543	−	0.342930i	−0.784798	+	0.619752i	$0.787233\pi$
$390$	−2.04851e6	+	1.48833e6i	−0.0345339	+	0.0250903i
$391$	6.70207e6	+	4.86934e6i	0.112119	+	0.0814591i
$392$	−435409.	−	1.34005e6i	−0.00722836	−	0.0222466i
$393$	6.71776e7	−	9.24620e7i	1.10674	−	1.52330i
$394$	1.82382e7	+	5.92595e6i	0.298190	+	0.0968878i
$395$	1.29640e6	+	421226.i	0.0210352	+	0.00683477i
$396$	−1.23051e6	+	399817.i	−0.0198153	+	0.00643837i
$397$	2.36574e7			0.378090			0.189045	−	0.981968i	$-0.439461\pi$
$397$	2.36574e7			0.378090			0.189045	+	0.981968i	$0.439461\pi$
$398$		−	5.66553e7i		−	0.898652i
$399$	1.00386e8	−	3.26173e7i	1.58035	−	0.513487i
$400$	1.29118e7	−	9.38094e6i	0.201746	−	0.146577i
$401$	−1.81406e7	+	2.49684e7i	−0.281331	+	0.387219i	−0.926174	−	0.377096i	$-0.876923\pi$
$401$	−1.81406e7	+	2.49684e7i	−0.281331	+	0.387219i	0.644843	+	0.764315i	$0.276923\pi$
$402$			2.00778e7i			0.309056i
$403$	−4.63580e7	+	6.64590e7i	−0.708287	+	1.01540i
$404$	−3.75029e7			−0.568750
$405$	2.54202e6	+	1.84689e6i	0.0382661	+	0.0278020i
$406$	−6.04700e6	−	8.32298e6i	−0.0903570	−	0.124366i
$407$	−6.68037e6	−	2.05601e7i	−0.0990871	−	0.304959i
$408$	−2.88477e6			−0.0424748
$409$		−	4.95623e7i		−	0.724406i	−0.932099	−	0.362203i	$-0.882025\pi$
$409$		−	4.95623e7i		−	0.724406i	0.932099	−	0.362203i	$-0.117975\pi$
$410$	293127.	+	902152.i	0.00425309	+	0.0130897i
$411$	−1.42817e7	+	4.39544e7i	−0.205709	+	0.633107i
$412$	−5.78428e6	+	1.78022e7i	−0.0827100	+	0.254555i
$413$	7.56546e7	+	5.49662e7i	1.07395	+	0.780272i
$414$	2.85782e6	−	928564.i	0.0402749	−	0.0130861i
$415$	147483.	−	202993.i	0.00206346	−	0.00284011i
$416$	−9.26092e6	−	1.27466e7i	−0.128639	−	0.177057i
$417$	3.72491e7	−	1.14641e8i	0.513698	−	1.58100i
$418$	3.92097e7	+	5.39675e7i	0.536864	+	0.738930i
$419$	7.11602e7	−	5.17009e7i	0.967376	−	0.702840i	0.0125239	−	0.999922i	$-0.496013\pi$
$419$	7.11602e7	−	5.17009e7i	0.967376	−	0.702840i	0.954852	+	0.297082i	$0.0960134\pi$
$420$	−1.77381e6	−	576347.i	−0.0239420	−	0.00777922i
$421$	−1.59652e7	+	1.15994e7i	−0.213957	+	0.155449i	−0.689602	−	0.724188i	$-0.742215\pi$
$421$	−1.59652e7	+	1.15994e7i	−0.213957	+	0.155449i	0.475645	+	0.879637i	$0.342215\pi$
$422$	−4.03957e6	−	2.93492e6i	−0.0537524	−	0.0390534i
$423$	−1.03880e6	−	3.19709e6i	−0.0137249	−	0.0422410i
$424$	−1.85193e7	+	2.54896e7i	−0.242956	+	0.334400i
$425$	−8.99216e6	−	2.92173e6i	−0.117138	−	0.0380604i
$426$	1.12290e7	+	3.64852e6i	0.145249	+	0.0471942i
$427$	8.08426e7	−	2.62673e7i	1.03838	−	0.337390i
$428$	−1.64029e7			−0.209214
$429$		−	7.42699e7i		−	0.940678i
$430$	4.47902e6	−	1.45532e6i	0.0563349	−	0.0183043i
$431$	−4.46391e7	+	3.24322e7i	−0.557550	+	0.405083i	−0.830561	−	0.556927i	$-0.811980\pi$
$431$	−4.46391e7	+	3.24322e7i	−0.557550	+	0.405083i	0.273012	+	0.962011i	$0.411980\pi$
$432$	−1.21417e7	+	1.67116e7i	−0.150601	+	0.207284i
$433$			4.17540e7i			0.514321i	0.966369	+	0.257161i	$0.0827869\pi$
$433$			4.17540e7i			0.514321i	−0.966369	+	0.257161i	$0.917213\pi$
$434$	−5.96740e7	+	1.14848e6i	−0.729988	+	0.0140493i
$435$	−845058.			−0.0102664
$436$	−1.93847e7	−	1.40838e7i	−0.233883	−	0.169926i
$437$	−9.10633e7	−	1.25338e8i	−1.09119	−	1.50189i
$438$	4.23938e6	+	1.30475e7i	0.0504522	+	0.155276i
$439$	−1.94430e6			−0.0229811			−0.0114905	−	0.999934i	$-0.503658\pi$
$439$	−1.94430e6			−0.0229811			−0.0114905	+	0.999934i	$0.503658\pi$
$440$		−	1.17872e6i		−	0.0138373i
$441$	93563.4	+	287959.i	0.00109091	+	0.00335749i
$442$	−2.88435e6	+	8.87712e6i	−0.0334027	+	0.102803i
$443$	−2.81522e7	+	8.66435e7i	−0.323818	+	0.996609i	0.648154	+	0.761510i	$0.275541\pi$
$443$	−2.81522e7	+	8.66435e7i	−0.323818	+	0.996609i	−0.971971	+	0.235099i	$0.924459\pi$
$444$	−1.41445e7	−	1.02766e7i	−0.161599	−	0.117408i
$445$	−7.86548e6	+	2.55565e6i	−0.0892576	+	0.0290015i
$446$	5.66242e7	−	7.79366e7i	0.638260	−	0.878490i
$447$	3.17952e7	+	4.37624e7i	0.355991	+	0.489980i
$448$	3.58623e6	−	1.10373e7i	0.0398845	−	0.122752i
$449$	−1.21239e7	−	1.66871e7i	−0.133938	−	0.184349i	0.736780	−	0.676132i	$-0.236345\pi$
$449$	−1.21239e7	−	1.66871e7i	−0.133938	−	0.184349i	−0.870718	+	0.491783i	$0.836345\pi$
$450$	−2.77456e6	+	2.01583e6i	−0.0304478	+	0.0221216i
$451$	−2.64613e7	−	8.59779e6i	−0.288457	−	0.0937254i
$452$	5.14054e6	−	3.73482e6i	0.0556665	−	0.0404440i
$453$	5.87199e7	+	4.26625e7i	0.631671	+	0.458936i
$454$	3.67884e7	+	1.13223e8i	0.393137	+	1.20995i
$455$	−3.54711e6	+	4.88217e6i	−0.0376565	+	0.0518297i
$456$	5.13088e7	+	1.66712e7i	0.541124	+	0.175822i
$457$	−1.07330e8	−	3.48738e7i	−1.12454	−	0.365385i	−0.313041	−	0.949740i	$-0.601348\pi$
$457$	−1.07330e8	−	3.48738e7i	−1.12454	−	0.365385i	−0.811498	+	0.584355i	$0.801348\pi$
$458$	−1.01486e8	+	3.29748e7i	−1.05635	+	0.343230i
$459$	1.22374e7			0.126547
$460$			2.73754e6i			0.0281246i
$461$	5.70840e6	−	1.85477e6i	0.0582655	−	0.0189316i	−0.279739	−	0.960076i	$-0.590248\pi$
$461$	5.70840e6	−	1.85477e6i	0.0582655	−	0.0189316i	0.338005	+	0.941144i	$0.390248\pi$
$462$	4.42578e7	−	3.21552e7i	0.448812	−	0.326081i
$463$	−8.08475e7	+	1.11277e8i	−0.814561	+	1.12115i	0.176043	+	0.984383i	$0.443670\pi$
$463$	−8.08475e7	+	1.11277e8i	−0.814561	+	1.12115i	−0.990604	+	0.136764i	$0.956330\pi$
$464$		−	5.25824e6i		−	0.0526365i
$465$	−2.80485e6	+	4.02104e6i	−0.0278966	+	0.0399926i
$466$	−7.97352e6			−0.0787939
$467$	−2.37257e7	−	1.72377e7i	−0.232953	−	0.169250i	0.465185	−	0.885214i	$-0.345988\pi$
$467$	−2.37257e7	−	1.72377e7i	−0.232953	−	0.169250i	−0.698138	+	0.715963i	$0.745988\pi$
$468$	1.99004e6	+	2.73906e6i	0.0194144	+	0.0267217i
$469$	1.47867e7	+	4.55088e7i	0.143335	+	0.441140i
$470$	3.06253e6			0.0294976
$471$			6.59831e7i			0.631495i
$472$	1.47700e7	+	4.54573e7i	0.140460	+	0.432292i
$473$	−4.26865e7	+	1.31375e8i	−0.403373	+	1.24145i
$474$	−9.99211e6	+	3.07525e7i	−0.0938257	+	0.288766i
$475$	1.43050e8	+	1.03932e8i	1.33478	+	0.969772i
$476$	−6.53871e6	+	2.12455e6i	−0.0606277	+	0.0196991i
$477$	3.97954e6	−	5.47736e6i	0.0366672	−	0.0504680i
$478$	2.82382e7	+	3.88665e7i	0.258555	+	0.355870i
$479$	−8.31136e6	+	2.55797e7i	−0.0756250	+	0.232750i	−0.981722	−	0.190320i	$-0.939047\pi$
$479$	−8.31136e6	+	2.55797e7i	−0.0756250	+	0.232750i	0.906097	+	0.423070i	$0.139047\pi$
$480$	−560324.	−	771220.i	−0.00506659	−	0.00697356i
$481$	−4.57657e7	+	3.32508e7i	−0.411249	+	0.298790i
$482$	−1.36758e7	−	4.44353e6i	−0.122127	−	0.0396814i
$483$	−1.02788e8	+	7.46795e7i	−0.912219	+	0.662766i
$484$	−1.78927e7	−	1.29998e7i	−0.157812	−	0.114657i
$485$	−133739.	−	411605.i	−0.00117228	−	0.00360791i
$486$	5.08599e6	−	7.00027e6i	0.0443065	−	0.0609826i
$487$	1.14559e8	+	3.72224e7i	0.991839	+	0.322268i	0.759600	−	0.650391i	$-0.225395\pi$
$487$	1.14559e8	+	3.72224e7i	0.991839	+	0.322268i	0.232239	+	0.972659i	$0.425395\pi$
$488$	4.13199e7	+	1.34257e7i	0.355550	+	0.115525i
$489$	−8.24576e7	+	2.67921e7i	−0.705186	+	0.229129i
$490$	−275838.			−0.00234459
$491$		−	1.97602e8i		−	1.66935i	−0.550744	−	0.834674i	$-0.685656\pi$
$491$		−	1.97602e8i		−	1.66935i	0.550744	−	0.834674i	$-0.314344\pi$
$492$	−2.14004e7	+	6.95341e6i	−0.179691	+	0.0583852i
$493$	−2.52016e6	+	1.83100e6i	−0.0210323	+	0.0152809i
$494$	1.02603e8	−	1.41220e8i	0.851093	−	1.17143i
$495$			253290.i			0.00208835i
$496$	−2.50203e7	−	1.74527e7i	−0.205044	−	0.143027i
$497$	2.81390e7			0.229213
$498$	4.81529e6	+	3.49851e6i	0.0389883	+	0.0283266i
$499$	−1.24648e8	−	1.71563e8i	−1.00319	−	1.38077i	−0.923348	−	0.383964i	$-0.874559\pi$
$499$	−1.24648e8	−	1.71563e8i	−1.00319	−	1.38077i	−0.0798409	−	0.996808i	$-0.525441\pi$
$500$	−1.93342e6	−	5.95045e6i	−0.0154674	−	0.0476036i
$501$	−7.53045e7			−0.598836
$502$			1.60116e8i			1.26568i
$503$	5.98242e7	+	1.84120e8i	0.470081	+	1.44676i	0.852478	+	0.522763i	$0.175099\pi$
$503$	5.98242e7	+	1.84120e8i	0.470081	+	1.44676i	−0.382397	+	0.923998i	$0.624901\pi$
$504$	−770630.	+	2.37176e6i	−0.00601942	+	0.0185259i
$505$	−2.26875e6	+	6.98250e6i	−0.0176162	+	0.0542172i
$506$	−6.49605e7	−	4.71966e7i	−0.501415	−	0.364300i
$507$	−6.42416e7	+	2.08734e7i	−0.492938	+	0.160165i
$508$	5.90023e7	−	8.12097e7i	0.450067	−	0.619465i
$509$	−4.29893e7	−	5.91697e7i	−0.325992	−	0.448690i	0.614293	−	0.789078i	$-0.289441\pi$
$509$	−4.29893e7	−	5.91697e7i	−0.325992	−	0.448690i	−0.940285	+	0.340389i	$0.889441\pi$
$510$	−174515.	+	537103.i	−0.00131560	+	0.00404899i
$511$	1.92182e7	+	2.64516e7i	0.144029	+	0.198239i
$512$	4.79880e6	−	3.48653e6i	0.0357538	−	0.0259767i
$513$	−2.17656e8	−	7.07207e7i	−1.61220	−	0.523835i
$514$	5.81099e7	−	4.22193e7i	0.427919	−	0.310901i
$515$	2.96459e6	+	2.15390e6i	0.0217041	+	0.0157690i
$516$	3.45224e7	+	1.06249e8i	0.251277	+	0.773350i
$517$	−5.27995e7	+	7.26723e7i	−0.382083	+	0.525893i
$518$	−3.96286e7	−	1.28761e7i	−0.285115	−	0.0926394i
$519$	−1.10520e7	−	3.59102e6i	−0.0790570	−	0.0256872i
$520$	−2.93347e6	+	953141.i	−0.0208627	+	0.00677871i
$521$	−2.58662e8			−1.82902			−0.914510	−	0.404562i	$-0.867424\pi$
$521$	−2.58662e8			−1.82902			−0.914510	+	0.404562i	$0.867424\pi$
$522$			1.12992e6i			0.00794397i
$523$	1.39387e8	−	4.52895e7i	0.974353	−	0.316586i	0.221781	−	0.975096i	$-0.428813\pi$
$523$	1.39387e8	−	4.52895e7i	0.974353	−	0.316586i	0.752572	+	0.658510i	$0.228813\pi$
$524$	1.12631e8	−	8.18310e7i	0.782822	−	0.568754i
$525$	8.52331e7	−	1.17313e8i	0.589021	−	0.810718i
$526$			4.23836e6i			0.0291233i
$527$	347755.	+	1.80690e7i	0.00237597	+	0.123453i
$528$	2.79610e7			0.189955
$529$	3.11053e7	+	2.25993e7i	0.210120	+	0.152661i
$530$	3.62547e6	+	4.99003e6i	0.0243521	+	0.0335178i
$531$	−3.17386e6	−	9.76813e6i	−0.0211984	−	0.0652421i
$532$	1.28576e8			0.853934
$533$			7.28064e7i			0.480826i
$534$	−6.06238e7	−	1.86581e8i	−0.398125	−	1.22530i
$535$	−992300.	+	3.05398e6i	−0.00648010	+	0.0199437i
$536$	−7.55772e6	+	2.32603e7i	−0.0490791	+	0.151050i
$537$	−6.10779e7	−	4.43757e7i	−0.394422	−	0.286564i
$538$	1.15098e8	−	3.73977e7i	0.739131	−	0.240158i
$539$	4.75559e6	−	6.54551e6i	0.0303696	−	0.0418001i
$540$	2.37694e6	+	3.27158e6i	0.0150951	+	0.0207767i
$541$	8.12656e7	−	2.50110e8i	0.513233	−	1.57957i	−0.273240	−	0.961946i	$-0.588095\pi$
$541$	8.12656e7	−	2.50110e8i	0.513233	−	1.57957i	0.786473	−	0.617624i	$-0.211905\pi$
$542$	−9.99240e7	−	1.37534e8i	−0.627584	−	0.863795i
$543$	−1.68193e7	+	1.22199e7i	−0.105053	+	0.0763254i
$544$	−3.34204e6	−	1.08589e6i	−0.0207594	−	0.00674514i
$545$	−3.79488e6	+	2.75714e6i	−0.0234427	+	0.0170321i
$546$	−1.15812e8	−	8.41427e7i	−0.711504	−	0.516938i
$547$	8.24126e7	+	2.53640e8i	0.503538	+	1.54973i	0.803215	+	0.595689i	$0.203121\pi$
$547$	8.24126e7	+	2.53640e8i	0.503538	+	1.54973i	−0.299678	+	0.954040i	$0.596879\pi$
$548$	−3.30909e7	+	4.55457e7i	−0.201079	+	0.276761i
$549$	−8.87908e6	−	2.88499e6i	−0.0536600	−	0.0174352i
$550$	8.71575e7	+	2.83192e7i	0.523862	+	0.170213i
$551$	5.54052e7	−	1.80023e7i	0.331204	−	0.107615i
$552$	−6.49385e7			−0.386087
$553$			7.70635e7i			0.455694i
$554$	1.21203e8	−	3.93813e7i	0.712828	−	0.231612i
$555$	−2.76902e6	+	2.01181e6i	−0.0161975	+	0.0117681i
$556$	8.63069e7	−	1.18791e8i	0.502136	−	0.691131i
$557$			1.85682e8i			1.07449i	0.843425	+	0.537247i	$0.180536\pi$
$557$			1.85682e8i			1.07449i	−0.843425	+	0.537247i	$0.819464\pi$
$558$	5.37652e6	+	3.75035e6i	0.0309456	+	0.0215859i
$559$	3.61471e8			2.06937
$560$	−1.83803e6	−	1.33541e6i	−0.0104662	−	0.00760413i
$561$	−9.73645e6	−	1.34011e7i	−0.0551458	−	0.0759016i
$562$	6.34469e7	+	1.95269e8i	0.357438	+	1.10008i
$563$	−1.04279e8			−0.584348			−0.292174	−	0.956365i	$-0.594379\pi$
$563$	−1.04279e8			−0.584348			−0.292174	+	0.956365i	$0.594379\pi$
$564$			7.26477e7i			0.404934i
$565$	−384391.	−	1.18303e6i	−0.00213122	−	0.00655921i
$566$	−1.72730e7	+	5.31609e7i	−0.0952619	+	0.293186i
$567$	−5.48934e7	+	1.68945e8i	−0.301142	+	0.926819i
$568$	1.16355e7	+	8.45370e6i	0.0634952	+	0.0461320i
$569$	1.11367e8	−	3.61855e7i	0.604535	−	0.196425i	0.00927278	−	0.999957i	$-0.497048\pi$
$569$	1.11367e8	−	3.61855e7i	0.604535	−	0.196425i	0.595262	+	0.803532i	$0.297048\pi$
$570$	6.20788e6	−	8.54441e6i	0.0335211	−	0.0461379i
$571$	−6.51079e7	−	8.96133e7i	−0.349724	−	0.481353i	0.597526	−	0.801849i	$-0.296150\pi$
$571$	−6.51079e7	−	8.96133e7i	−0.349724	−	0.481353i	−0.947250	+	0.320496i	$0.896150\pi$
$572$	2.79569e7	−	8.60424e7i	0.149383	−	0.459753i
$573$	−1.47755e8	−	2.03367e8i	−0.785377	−	1.08098i
$574$	−4.33858e7	+	3.15216e7i	−0.229410	+	0.166676i
$575$	−2.02421e8	−	6.57705e7i	−1.06476	−	0.345961i
$576$	−1.03120e6	+	749207.i	−0.00539602	+	0.00392044i
$577$	5.79376e7	+	4.20941e7i	0.301601	+	0.219126i	0.728284	−	0.685275i	$-0.240318\pi$
$577$	5.79376e7	+	4.20941e7i	0.301601	+	0.219126i	−0.426683	+	0.904401i	$0.640318\pi$
$578$	−4.15507e7	−	1.27880e8i	−0.215177	−	0.662245i
$579$	1.64934e8	−	2.27012e8i	0.849715	−	1.16953i
$580$	−979008.	−	318099.i	−0.00501767	−	0.00163034i
$581$	1.34910e7	+	4.38350e6i	0.0687886	+	0.0223508i
$582$	9.76389e6	−	3.17248e6i	0.0495284	−	0.0160927i
$583$	−1.80916e8			−0.913000
$584$			1.67114e7i			0.0839026i
$585$	630361.	−	204817.i	0.00314863	−	0.00102305i
$586$	−2.23190e8	+	1.62157e8i	−1.10913	+	0.805830i
$587$	1.58240e8	−	2.17799e8i	0.782353	−	1.07682i	−0.212666	−	0.977125i	$-0.568214\pi$
$587$	1.58240e8	−	2.17799e8i	0.782353	−	1.07682i	0.995018	−	0.0996913i	$-0.0317855\pi$
$588$		−	6.54330e6i		−	0.0321858i
$589$	9.82365e7	−	3.23387e8i	0.480759	−	1.58262i
$590$	9.35699e6			0.0455596
$591$	7.20468e7	+	5.23451e7i	0.349022	+	0.253579i
$592$	−1.25182e7	−	1.72298e7i	−0.0603359	−	0.0830452i
$593$	1.24008e8	+	3.81657e8i	0.594683	+	1.83024i	0.556300	+	0.830982i	$0.312221\pi$
$593$	1.24008e8	+	3.81657e8i	0.594683	+	1.83024i	0.0383830	+	0.999263i	$0.487779\pi$
$594$	−1.18613e8			−0.565942
$595$			1.34594e6i			0.00638961i
$596$	2.03619e7	+	6.26676e7i	0.0961790	+	0.296009i
$597$	8.13026e7	−	2.50224e8i	0.382104	−	1.17600i
$598$	−6.49290e7	+	1.99831e8i	−0.303623	+	0.934457i
$599$	9.94286e7	+	7.22391e7i	0.462627	+	0.336118i	0.794561	−	0.607185i	$-0.207701\pi$
$599$	9.94286e7	+	7.22391e7i	0.462627	+	0.336118i	−0.331934	+	0.943303i	$0.607701\pi$
$600$	7.04881e7	−	2.29030e7i	0.326334	−	0.106032i
$601$	−1.08361e8	+	1.49145e8i	−0.499169	+	0.687047i	−0.982046	−	0.188641i	$-0.939592\pi$
$601$	−1.08361e8	+	1.49145e8i	−0.499169	+	0.687047i	0.482877	+	0.875688i	$0.339592\pi$
$602$	1.56499e8	+	2.15402e8i	0.717335	+	0.987327i
$603$	1.62405e6	−	4.99831e6i	0.00740708	−	0.0227967i
$604$	5.19685e7	+	7.15285e7i	0.235846	+	0.324615i
$605$	−3.50280e6	+	2.54494e6i	−0.0158179	+	0.0114924i
$606$	−1.65635e8	−	5.38182e7i	−0.744278	−	0.241831i
$607$	2.06271e8	−	1.49865e8i	0.922299	−	0.670089i	−0.0217962	−	0.999762i	$-0.506938\pi$
$607$	2.06271e8	−	1.49865e8i	0.922299	−	0.670089i	0.944095	+	0.329673i	$0.106938\pi$
$608$	5.31663e7	+	3.86276e7i	0.236551	+	0.171865i
$609$	−1.47634e7	−	4.54369e7i	−0.0653632	−	0.201167i
$610$	4.99933e6	−	6.88098e6i	0.0220253	−	0.0303152i
$611$	2.23554e8	+	7.26371e7i	0.980074	+	0.318445i
$612$	718157.	+	233343.i	0.00313304	+	0.00101799i
$613$	−1.70671e8	+	5.54543e7i	−0.740931	+	0.240743i	−0.655074	−	0.755564i	$-0.727363\pi$
$613$	−1.70671e8	+	5.54543e7i	−0.740931	+	0.240743i	−0.0858568	+	0.996307i	$0.527363\pi$
$614$	2.12174e8			0.916617
$615$			4.40509e6i			0.0189378i
$616$	6.33771e7	−	2.05925e7i	0.271138	−	0.0880981i
$617$	2.05705e7	−	1.49453e7i	0.0875767	−	0.0636282i	−0.543135	−	0.839645i	$-0.682763\pi$
$617$	2.05705e7	−	1.49453e7i	0.0875767	−	0.0636282i	0.630712	+	0.776017i	$0.282763\pi$
$618$	−5.10937e7	+	7.03244e7i	−0.216472	+	0.297948i
$619$			6.26056e6i			0.0263962i	0.999913	+	0.0131981i	$0.00420120\pi$
$619$			6.26056e6i			0.0263962i	−0.999913	+	0.0131981i	$0.995799\pi$
$620$	−4.76306e6	+	3.60261e6i	−0.0199853	+	0.0151162i
$621$	2.75474e8			1.15029
$622$	−2.70999e8	−	1.96892e8i	−1.12615	−	0.818197i
$623$	−2.74823e8	−	3.78262e8i	−1.13655	−	1.56433i
$624$	−2.26099e7	−	6.95862e7i	−0.0930563	−	0.286398i
$625$	2.42303e8			0.992471
$626$		−	4.99335e7i		−	0.203549i
$627$	9.57278e7	+	2.94620e8i	0.388361	+	1.19525i
$628$	−2.48375e7	+	7.64421e7i	−0.100284	+	0.308641i
$629$	−3.89883e6	+	1.19994e7i	−0.0156669	+	0.0482177i
$630$	394967.	+	286960.i	0.00157957	+	0.00114763i
$631$	−2.68870e8	+	8.73612e7i	−1.07017	+	0.347721i	−0.790555	−	0.612390i	$-0.790208\pi$
$631$	−2.68870e8	+	8.73612e7i	−1.07017	+	0.347721i	−0.279619	+	0.960111i	$0.590208\pi$
$632$	−2.31519e7	+	3.18659e7i	−0.0917140	+	0.126233i
$633$	−1.36294e7	−	1.87593e7i	−0.0537361	−	0.0739614i
$634$	4.88197e7	−	1.50252e8i	0.191570	−	0.589592i
$635$	−1.15507e7	−	1.58982e7i	−0.0451115	−	0.0620906i
$636$	−1.18371e8	+	8.60015e7i	−0.460122	+	0.334299i
$637$	−2.01353e7	−	6.54234e6i	−0.0779003	−	0.0253113i
$638$	2.44269e7	−	1.77472e7i	0.0940604	−	0.0683389i
$639$	−2.50031e6	−	1.81658e6i	−0.00958278	−	0.00696230i
$640$	−358837.	−	1.10439e6i	−0.00136885	−	0.00421290i
$641$	2.12974e8	−	2.93133e8i	0.808634	−	1.11299i	−0.182899	−	0.983132i	$-0.558548\pi$
$641$	2.12974e8	−	2.93133e8i	0.808634	−	1.11299i	0.991533	−	0.129857i	$-0.0414518\pi$
$642$	−7.24451e7	−	2.35388e7i	−0.273781	−	0.0889569i
$643$	−1.81979e8	−	5.91285e7i	−0.684523	−	0.222415i	−0.0539487	−	0.998544i	$-0.517181\pi$
$643$	−1.81979e8	−	5.91285e7i	−0.684523	−	0.222415i	−0.630575	+	0.776129i	$0.717181\pi$
$644$	−1.47192e8	+	4.78254e7i	−0.551093	+	0.179061i
$645$	2.18705e7			0.0815040
$646$		−	3.89322e7i		−	0.144415i
$647$	6.28574e7	−	2.04236e7i	0.232083	−	0.0754084i	−0.190667	−	0.981655i	$-0.561065\pi$
$647$	6.28574e7	−	2.04236e7i	0.232083	−	0.0754084i	0.422750	+	0.906246i	$0.361065\pi$
$648$	−7.34539e7	+	5.33674e7i	−0.269954	+	0.196133i
$649$	−1.61319e8	+	2.22037e8i	−0.590136	+	0.812253i
$650$		−	2.39808e8i		−	0.873219i
$651$	−2.65204e8	−	8.05622e7i	−0.961252	−	0.292004i
$652$	−1.05613e8			−0.381044
$653$	−3.27100e7	−	2.37652e7i	−0.117474	−	0.0853496i	0.527497	−	0.849557i	$-0.323131\pi$
$653$	−3.27100e7	−	2.37652e7i	−0.117474	−	0.0853496i	−0.644971	+	0.764207i	$0.723131\pi$
$654$	−6.54035e7	−	9.00201e7i	−0.233812	−	0.321815i
$655$	−8.42211e6	−	2.59206e7i	−0.0299707	−	0.0922404i
$656$	−2.74100e7			−0.0970951
$657$		−	3.59106e6i		−	0.0126627i
$658$	5.35030e7	+	1.64665e8i	0.187802	+	0.577996i
$659$	1.59121e8	−	4.89724e8i	0.555996	−	1.71118i	−0.137304	−	0.990529i	$-0.543844\pi$
$659$	1.59121e8	−	4.89724e8i	0.555996	−	1.71118i	0.693299	−	0.720650i	$-0.256156\pi$
$660$	1.69151e6	−	5.20592e6i	0.00588359	−	0.0181078i
$661$	2.24779e8	+	1.63311e8i	0.778307	+	0.565473i	0.904470	−	0.426536i	$-0.140266\pi$
$661$	2.24779e8	+	1.63311e8i	0.778307	+	0.565473i	−0.126164	+	0.992009i	$0.540266\pi$
$662$	−2.02473e8	+	6.57873e7i	−0.697899	+	0.226761i
$663$	−2.54780e7	+	3.50675e7i	−0.0874229	+	0.120327i
$664$	4.26164e6	+	5.86564e6i	0.0145570	+	0.0200360i
$665$	7.77824e6	−	2.39389e7i	0.0264494	−	0.0814029i
$666$	2.68998e6	+	3.70244e6i	0.00910598	+	0.0125333i
$667$	−5.67309e7	+	4.12174e7i	−0.191180	+	0.138900i
$668$	−8.72410e7	−	2.83463e7i	−0.292679	−	0.0950971i
$669$	3.61928e8	−	2.62956e8i	1.20877	−	0.878224i
$670$	3.87352e6	+	2.81428e6i	0.0128790	+	0.00935712i
$671$	7.70915e7	+	2.37263e8i	0.255175	+	0.785349i
$672$	3.16778e7	−	4.36008e7i	0.104387	−	0.143677i
$673$	−2.61337e8	−	8.49134e7i	−0.857344	−	0.278568i	−0.152825	−	0.988253i	$-0.548837\pi$
$673$	−2.61337e8	−	8.49134e7i	−0.857344	−	0.278568i	−0.704519	+	0.709685i	$0.748837\pi$
$674$	1.00559e6	+	326735.i	0.00328428	+	0.00106713i
$675$	−2.99016e8	+	9.71562e7i	−0.972262	+	0.315907i
$676$	−8.22818e7			−0.266357
$677$			2.91443e8i			0.939263i	0.882862	+	0.469632i	$0.155613\pi$
$677$			2.91443e8i			0.939263i	−0.882862	+	0.469632i	$0.844387\pi$
$678$	2.80633e7	−	9.11832e6i	0.0900430	−	0.0292567i
$679$	1.97947e7	−	1.43817e7i	0.0632323	−	0.0459410i
$680$	−404355.	+	556547.i	−0.00128599	+	0.00177001i
$681$			5.52854e8i			1.75053i
$682$	−3.37065e6	−	1.75136e8i	−0.0106258	−	0.552106i
$683$	1.34558e8			0.422325			0.211163	−	0.977451i	$-0.432275\pi$
$683$	1.34558e8			0.422325			0.211163	+	0.977451i	$0.432275\pi$
$684$	−1.14247e7	−	8.30053e6i	−0.0357007	−	0.0259381i
$685$	6.47810e6	+	8.91634e6i	0.0201547	+	0.0277405i
$686$	6.80179e7	+	2.09338e8i	0.210693	+	0.648447i
$687$	−4.95542e8			−1.52831
$688$			1.36086e8i			0.417876i
$689$	1.46293e8	+	4.50244e8i	0.447266	+	1.37654i
$690$	−3.92848e6	+	1.20906e7i	−0.0119585	+	0.0368045i
$691$	−1.68776e8	+	5.19440e8i	−0.511537	+	1.57435i	0.277958	+	0.960593i	$0.410342\pi$
$691$	−1.68776e8	+	5.19440e8i	−0.511537	+	1.57435i	−0.789495	+	0.613757i	$0.789658\pi$
$692$	−1.14522e7	−	8.32047e6i	−0.0345596	−	0.0251090i
$693$	−1.36189e7	+	4.42504e6i	−0.0409205	+	0.0132959i
$694$	−1.43727e7	+	1.97824e7i	−0.0429993	+	0.0591834i
$695$	−1.68960e7	−	2.32554e7i	−0.0503304	−	0.0692739i
$696$	7.54579e6	−	2.32235e7i	0.0223809	−	0.0688812i
$697$	9.54460e6	+	1.31370e7i	0.0281877	+	0.0387970i
$698$	1.16256e8	−	8.44646e7i	0.341859	−	0.248375i
$699$	−3.52158e7	−	1.14423e7i	−0.103111	−	0.0335029i
$700$	1.42903e8	−	1.03825e8i	0.416626	−	0.302697i
$701$	−1.07961e8	−	7.84380e7i	−0.313409	−	0.227705i	0.419949	−	0.907548i	$-0.362048\pi$
$701$	−1.07961e8	−	7.84380e7i	−0.313409	−	0.227705i	−0.733358	+	0.679843i	$0.762048\pi$
$702$	9.59132e7	+	2.95190e8i	0.277247	+	0.853279i
$703$	1.38690e8	−	1.90890e8i	0.399189	−	0.549437i
$704$	3.23931e7	+	1.05251e7i	0.0928397	+	0.0301655i
$705$	1.35259e7	+	4.39485e6i	0.0386012	+	0.0125423i
$706$	−2.93627e8	+	9.54051e7i	−0.834414	+	0.271118i
$707$	−4.15070e8			−1.17453
$708$			2.21962e8i			0.625430i
$709$	6.49174e8	−	2.10930e8i	1.82147	−	0.591832i	0.821713	−	0.569901i	$-0.193019\pi$
$709$	6.49174e8	−	2.10930e8i	1.82147	−	0.591832i	0.999759	−	0.0219309i	$-0.00698137\pi$
$710$	2.27785e6	−	1.65496e6i	0.00636429	−	0.00462393i
$711$	4.97502e6	−	6.84753e6i	0.0138416	−	0.0190513i
$712$		−	2.38976e8i		−	0.662086i
$713$	7.82824e6	+	4.06748e8i	0.0215971	+	1.12217i
$714$	−3.19277e7			−0.0877147
$715$	−1.43286e7	−	1.04103e7i	−0.0391999	−	0.0284804i
$716$	−5.40554e7	−	7.44008e7i	−0.147265	−	0.202693i
$717$	6.89416e7	+	2.12181e8i	0.187036	+	0.575636i
$718$	2.97800e8			0.804547
$719$			5.43051e8i			1.46101i	0.682906	+	0.730506i	$0.260716\pi$
$719$			5.43051e8i			1.46101i	−0.682906	+	0.730506i	$0.739284\pi$
$720$	77109.0	+	237317.i	0.000206589	+	0.000635816i
$721$	−6.40184e7	+	1.97028e8i	−0.170804	+	0.525682i
$722$	−1.42752e8	+	4.39345e8i	−0.379289	+	1.16733i
$723$	−5.40238e7	−	3.92506e7i	−0.142945	−	0.103856i
$724$	−2.40852e7	+	7.82574e6i	−0.0634649	+	0.0206210i
$725$	4.70422e7	−	6.47480e7i	0.123445	−	0.169907i
$726$	−6.03697e7	−	8.30917e7i	−0.157764	−	0.217144i
$727$	−7.31991e7	+	2.25284e8i	−0.190503	+	0.586309i	−1.00000		0.000815931i	$-0.999740\pi$
$727$	−7.31991e7	+	2.25284e8i	−0.190503	+	0.586309i	0.809496	+	0.587125i	$0.199740\pi$
$728$	−1.02497e8	−	1.41075e8i	−0.265654	−	0.365641i
$729$	3.28322e8	−	2.38540e8i	0.847455	−	0.615712i
$730$	3.11143e6	+	1.01096e6i	0.00799818	+	0.00259877i
$731$	6.52229e7	−	4.73872e7i	0.166974	−	0.121313i
$732$	1.63227e8	+	1.18591e8i	0.416159	+	0.302357i
$733$	1.99090e7	+	6.12737e7i	0.0505520	+	0.155583i	0.973146	−	0.230190i	$-0.0739348\pi$
$733$	1.99090e7	+	6.12737e7i	0.0505520	+	0.155583i	−0.922594	+	0.385773i	$0.873935\pi$
$734$	1.17370e8	−	1.61546e8i	0.296804	−	0.408515i
$735$	−1.21827e6	−	395839.i	−0.00306818	−	0.000996911i
$736$	−7.52319e7	−	2.44443e7i	−0.188699	−	0.0613119i
$737$	−1.33563e8	+	4.33972e7i	−0.333644	+	0.108407i
$738$	5.89003e6			0.0146537
$739$		−	4.61963e8i		−	1.14465i	−0.820026	−	0.572327i	$-0.806041\pi$
$739$		−	4.61963e8i		−	1.14465i	0.820026	−	0.572327i	$-0.193959\pi$
$740$	−3.96523e6	+	1.28838e6i	−0.00978527	+	0.00317943i
$741$	6.55811e8	−	4.76474e8i	1.61185	−	1.17108i
$742$	−2.04965e8	+	2.82110e8i	−0.501728	+	0.690569i
$743$		−	2.93405e8i		−	0.715320i	−0.933852	−	0.357660i	$-0.883575\pi$
$743$		−	2.93405e8i		−	0.715320i	0.933852	−	0.357660i	$-0.116425\pi$
$744$	−8.54593e7	−	1.12987e8i	−0.207511	−	0.274353i
$745$	1.28996e7			0.0311966
$746$	2.79310e8	+	2.02931e8i	0.672776	+	0.488800i
$747$	−915767.	−	1.26045e6i	−0.00219697	−	0.00302386i
$748$	−6.23531e6	−	1.91903e7i	−0.0148989	−	0.0458540i
$749$	−1.81542e8			−0.432047
$750$		−	2.90553e7i		−	0.0688718i
$751$	−2.23930e8	−	6.89187e8i	−0.528680	−	1.62711i	−0.756921	−	0.653506i	$-0.773297\pi$
$751$	−2.23930e8	−	6.89187e8i	−0.528680	−	1.62711i	0.228241	−	0.973605i	$-0.426703\pi$
$752$	−2.73463e7	+	8.41631e7i	−0.0643049	+	0.197910i
$753$	−2.29773e8	+	7.07168e8i	−0.538163	+	1.65629i
$754$	−6.39196e7	−	4.64403e7i	−0.149114	−	0.108338i
$755$	1.64614e7	−	5.34864e6i	0.0382495	−	0.0124280i
$756$	−1.34380e8	+	1.84958e8i	−0.311006	+	0.428063i
$757$	−2.55932e8	−	3.52260e8i	−0.589980	−	0.812038i	0.404765	−	0.914421i	$-0.367353\pi$
$757$	−2.55932e8	−	3.52260e8i	−0.589980	−	0.812038i	−0.994745	+	0.102383i	$0.967353\pi$
$758$	1.03128e8	−	3.17395e8i	0.236793	−	0.728774i
$759$	−2.19175e8	−	3.01669e8i	−0.501264	−	0.689931i
$760$	1.04082e7	−	7.56200e6i	0.0237102	−	0.0172265i
$761$	−3.03823e8	−	9.87182e7i	−0.689394	−	0.223998i	−0.0566903	−	0.998392i	$-0.518055\pi$
$761$	−3.03823e8	−	9.87182e7i	−0.689394	−	0.223998i	−0.632703	+	0.774394i	$0.718055\pi$
$762$	3.77128e8	−	2.74000e8i	0.852362	−	0.619277i
$763$	−2.14543e8	−	1.55874e8i	−0.482992	−	0.350914i
$764$	−9.46236e7	−	2.91222e8i	−0.212187	−	0.653045i
$765$	86890.3	−	119594.i	0.000194083	−	0.000267132i
$766$	7.87963e7	+	2.56025e7i	0.175315	+	0.0569633i
$767$	6.83028e8	+	2.21929e8i	1.51374	+	0.491846i
$768$	2.61977e7	−	8.51214e6i	0.0578334	−	0.0187912i
$769$	−3.68523e8			−0.810374			−0.405187	−	0.914234i	$-0.632794\pi$
$769$	−3.68523e8			−0.810374			−0.405187	+	0.914234i	$0.632794\pi$
$770$		−	1.30456e7i		−	0.0285755i
$771$	3.17235e8	−	1.03076e8i	0.692178	−	0.224902i
$772$	2.76530e8	−	2.00911e8i	0.601021	−	0.436667i
$773$	−8.39558e7	+	1.15555e8i	−0.181766	+	0.250179i	−0.890171	−	0.455627i	$-0.849415\pi$
$773$	−8.39558e7	+	1.15555e8i	−0.181766	+	0.250179i	0.708405	+	0.705806i	$0.249415\pi$
$774$		−	2.92429e7i		−	0.0630664i
$775$	−1.51952e8	−	4.38747e8i	−0.326438	−	0.942561i
$776$	1.25058e7			0.0267624
$777$	−1.56546e8	−	1.13737e8i	−0.333717	−	0.242460i
$778$	−2.17203e8	−	2.98955e8i	−0.461240	−	0.634843i
$779$	−9.38415e7	−	2.88815e8i	−0.198510	−	0.610951i
$780$	−1.43237e7			−0.0301837
$781$			8.25846e7i			0.173359i
$782$	1.44813e7	+	4.45689e7i	0.0302823	+	0.0931992i
$783$	−3.20098e7	+	9.85161e7i	−0.0666804	+	0.205221i
$784$	2.46305e6	−	7.58048e6i	0.00511122	−	0.0157307i
$785$	1.27298e7	+	9.24878e6i	0.0263157	+	0.0191194i
$786$	6.14875e8	−	1.99785e8i	1.26625	−	0.411430i
$787$	1.88288e8	−	2.59156e8i	0.386277	−	0.531665i	−0.570957	−	0.820980i	$-0.693428\pi$
$787$	1.88288e8	−	2.59156e8i	0.386277	−	0.531665i	0.957234	+	0.289315i	$0.0934276\pi$
$788$	6.37631e7	+	8.77623e7i	0.130314	+	0.179362i
$789$	−6.08222e6	+	1.87191e7i	−0.0123831	+	0.0381114i
$790$	4.53238e6	+	6.23828e6i	0.00919274	+	0.0126527i
$791$	5.68937e7	−	4.13357e7i	0.114957	−	0.0835211i
$792$	−6.96082e6	−	2.26171e6i	−0.0140115	−	0.00455261i
$793$	5.28137e8	−	3.83714e8i	1.05908	−	0.769463i
$794$	1.08268e8	+	7.86611e7i	0.216291	+	0.157144i
$795$	8.85134e6	+	2.72416e7i	0.0176160	+	0.0542165i
$796$	1.88380e8	−	2.59283e8i	0.373504	−	0.514084i
$797$	6.41920e8	+	2.08572e8i	1.26796	+	0.411985i	0.864325	−	0.502934i	$-0.167746\pi$
$797$	6.41920e8	+	2.08572e8i	1.26796	+	0.411985i	0.403636	+	0.914920i	$0.367746\pi$
$798$	5.67868e8	+	1.84511e8i	1.11748	+	0.363090i
$799$	4.98600e7	−	1.62005e7i	0.0977488	−	0.0317605i
$800$	9.02823e7			0.176333
$801$			5.13526e7i			0.0999229i
$802$	−1.66040e8	+	5.39498e7i	−0.321877	+	0.104584i
$803$	−7.76323e7	+	5.64031e7i	−0.149932	+	0.108932i
$804$	−6.67588e7	+	9.18857e7i	−0.128452	+	0.176799i
$805$			3.02981e7i			0.0580802i
$806$	−4.33134e8	+	1.50008e8i	−0.827212	+	0.286490i
$807$	5.62009e8			1.06936
$808$	−1.71632e8	−	1.24698e8i	−0.325360	−	0.236388i
$809$	−5.22976e8	−	7.19814e8i	−0.987724	−	1.35949i	−0.932562	−	0.361009i	$-0.882432\pi$
$809$	−5.22976e8	−	7.19814e8i	−0.987724	−	1.35949i	−0.0551620	−	0.998477i	$-0.517568\pi$
$810$	5.49261e6	+	1.69045e7i	0.0103353	+	0.0318088i
$811$	−6.32571e8			−1.18590			−0.592948	−	0.805241i	$-0.702036\pi$
$811$	−6.32571e8			−1.18590			−0.592948	+	0.805241i	$0.702036\pi$
$812$		−	5.81964e7i		−	0.108700i
$813$	−2.43958e8	−	7.50825e8i	−0.453987	−	1.39723i
$814$	3.77899e7	−	1.16305e8i	0.0700651	−	0.215638i
$815$	−6.38910e6	+	1.96636e7i	−0.0118023	+	0.0363237i
$816$	−1.32021e7	−	9.59191e6i	−0.0242982	−	0.0176537i
$817$	−1.43391e9	+	4.65906e8i	−2.62940	+	0.854343i
$818$	1.64796e8	−	2.26822e8i	0.301082	−	0.414404i
$819$	2.20251e7	+	3.03150e7i	0.0400928	+	0.0551830i
$820$	−1.65818e6	+	5.10334e6i	−0.00300739	+	0.00925578i
$821$	−8.30312e7	−	1.14283e8i	−0.150042	−	0.206515i	0.727380	−	0.686235i	$-0.240738\pi$
$821$	−8.30312e7	−	1.14283e8i	−0.150042	−	0.206515i	−0.877421	+	0.479721i	$0.840738\pi$
$822$	−2.11509e8	+	1.53670e8i	−0.380814	+	0.276678i
$823$	1.20451e8	+	3.91369e7i	0.216078	+	0.0702081i	0.415056	−	0.909796i	$-0.363762\pi$
$823$	1.20451e8	+	3.91369e7i	0.216078	+	0.0702081i	−0.198977	+	0.980004i	$0.563762\pi$
$824$	−8.56643e7	+	6.22387e7i	−0.153115	+	0.111245i
$825$	3.44300e8	+	2.50149e8i	0.613163	+	0.445489i
$826$	1.63469e8	+	5.03105e8i	0.290065	+	0.892727i
$827$	2.68378e8	−	3.69390e8i	0.474493	−	0.653084i	−0.502942	−	0.864320i	$-0.667749\pi$
$827$	2.68378e8	−	3.69390e8i	0.474493	−	0.653084i	0.977435	+	0.211236i	$0.0677490\pi$
$828$	1.61663e7	+	5.25275e6i	0.0284787	+	0.00925328i
$829$	9.26903e8	+	3.01169e8i	1.62694	+	0.528624i	0.973565	−	0.228412i	$-0.0733534\pi$
$829$	9.26903e8	+	3.01169e8i	1.62694	+	0.528624i	0.653373	+	0.757036i	$0.273353\pi$
$830$	1.34991e6	−	438611.i	0.00236086	−	0.000767089i
$831$	5.91820e8			1.03130
$832$		−	8.91272e7i		−	0.154754i
$833$	−4.49083e6	+	1.45916e6i	−0.00776948	+	0.00252446i
$834$	5.51653e8	−	4.00799e8i	0.950972	−	0.690922i
$835$	−1.05553e7	+	1.45282e7i	−0.0181306	+	0.0249547i
$836$			3.77354e8i			0.645848i
$837$	3.62525e8	+	4.79300e8i	0.618247	+	0.817393i
$838$	4.97571e8			0.845518
$839$	−8.56647e8	−	6.22390e8i	−1.45049	−	1.05385i	−0.985716	−	0.168418i	$-0.946134\pi$
$839$	−8.56647e8	−	6.22390e8i	−1.45049	−	1.05385i	−0.464778	−	0.885427i	$-0.653866\pi$
$840$	−6.20148e6	−	8.53560e6i	−0.0104630	−	0.0144011i
$841$	1.75662e8	+	5.40633e8i	0.295318	+	0.908897i
$842$	−1.11633e8			−0.187006
$843$			9.53475e8i			1.59157i
$844$	−8.72840e6	−	2.68633e7i	−0.0145180	−	0.0446819i
$845$	−4.97766e6	+	1.53197e7i	−0.00825003	+	0.0253910i
$846$	5.87633e6	−	1.80855e7i	0.00970499	−	0.0298689i
$847$	−1.98030e8	−	1.43878e8i	−0.325898	−	0.236779i
$848$	−1.69507e8	+	5.50761e7i	−0.277971	+	0.0903182i
$849$	−1.52576e8	+	2.10003e8i	−0.249323	+	0.343164i
$850$	−3.14378e7	−	4.32704e7i	−0.0511911	−	0.0704586i
$851$	−8.77659e7	+	2.70116e8i	−0.142409	+	0.438289i
$852$	3.92580e7	+	5.40340e7i	0.0634760	+	0.0873672i
$853$	−8.30445e8	+	6.03354e8i	−1.33802	+	0.972131i	−0.338510	+	0.940963i	$0.609923\pi$
$853$	−8.30445e8	+	6.03354e8i	−1.33802	+	0.972131i	−0.999514	+	0.0311687i	$0.990077\pi$
$854$	4.57315e8	+	1.48591e8i	0.734246	+	0.238571i
$855$	−2.23658e6	+	1.62497e6i	−0.00357837	+	0.00259984i
$856$	−7.50678e7	−	5.45399e7i	−0.119683	−	0.0869548i
$857$	2.03496e8	+	6.26295e8i	0.323305	+	0.995031i	0.972200	+	0.234153i	$0.0752315\pi$
$857$	2.03496e8	+	6.26295e8i	0.323305	+	0.995031i	−0.648895	+	0.760878i	$0.724768\pi$
$858$	2.46948e8	−	3.39895e8i	0.390971	−	0.538125i
$859$	4.73102e8	+	1.53720e8i	0.746406	+	0.242522i	0.657434	−	0.753512i	$-0.271642\pi$
$859$	4.73102e8	+	1.53720e8i	0.746406	+	0.242522i	0.0889718	+	0.996034i	$0.471642\pi$
$860$	2.53372e7	+	8.23255e6i	0.0398348	+	0.0129431i
$861$	−2.36852e8	+	7.69579e7i	−0.371080	+	0.120571i
$862$	−3.12128e8			−0.487316
$863$			4.13182e8i			0.642849i	0.946935	+	0.321425i	$0.104162\pi$
$863$			4.13182e8i			0.642849i	−0.946935	+	0.321425i	$0.895838\pi$
$864$	−1.11133e8	+	3.61092e7i	−0.172306	+	0.0559856i
$865$	−2.24195e6	+	1.62887e6i	−0.00346400	+	0.00251674i
$866$	−1.38833e8	+	1.91087e8i	−0.213766	+	0.294223i
$867$		−	6.24421e8i		−	0.958121i
$868$	−2.76916e8	−	1.93161e8i	−0.423437	−	0.295366i
$869$	−2.26172e8			−0.344651
$870$	−3.86740e6	−	2.80983e6i	−0.00587302	−	0.00426700i
$871$	2.16005e8	+	2.97305e8i	0.326895	+	0.449932i
$872$	−4.18849e7	−	1.28909e8i	−0.0631697	−	0.194416i
$873$	−2.68731e6			−0.00403902
$874$		−	8.76395e8i		−	1.31270i
$875$	−2.13984e7	−	6.58575e7i	−0.0319417	−	0.0983063i
$876$	−2.39816e7	+	7.38077e7i	−0.0356751	+	0.109797i
$877$	−1.60026e7	+	4.92510e7i	−0.0237242	+	0.0730157i	−0.962218	−	0.272281i	$-0.912222\pi$
$877$	−1.60026e7	+	4.92510e7i	−0.0237242	+	0.0730157i	0.938493	+	0.345297i	$0.112222\pi$
$878$	−8.89809e6	−	6.46484e6i	−0.0131466	−	0.00955156i
$879$	−1.21844e9	+	3.95896e8i	−1.79407	+	0.582928i
$880$	3.91926e6	−	5.39439e6i	0.00575116	−	0.00791580i
$881$	3.96965e8	+	5.46375e8i	0.580530	+	0.799030i	0.993753	−	0.111599i	$-0.0355972\pi$
$881$	3.96965e8	+	5.46375e8i	0.580530	+	0.799030i	−0.413224	+	0.910630i	$0.635597\pi$
$882$	−529275.	+	1.62894e6i	−0.000771392	+	0.00237410i
$883$	−6.70105e8	−	9.22321e8i	−0.973332	−	1.33968i	−0.940346	−	0.340220i	$-0.889498\pi$
$883$	−6.70105e8	−	9.22321e8i	−0.973332	−	1.33968i	−0.0329860	−	0.999456i	$-0.510502\pi$
$884$	−4.27167e7	+	3.10355e7i	−0.0618360	+	0.0449265i
$885$	4.13261e7	+	1.34277e7i	0.0596203	+	0.0193718i
$886$	−4.16929e8	+	3.02917e8i	−0.599461	+	0.435534i
$887$	1.91999e8	+	1.39496e8i	0.275124	+	0.199889i	0.716788	−	0.697291i	$-0.245612\pi$
$887$	1.91999e8	+	1.39496e8i	0.275124	+	0.199889i	−0.441664	+	0.897181i	$0.645612\pi$
$888$	−3.05623e7	−	9.40611e7i	−0.0436463	−	0.134329i
$889$	6.53017e8	−	8.98800e8i	0.929435	−	1.27926i
$890$	−4.44939e7	−	1.44569e7i	−0.0631146	−	0.0205072i
$891$	−4.95832e8	−	1.61105e8i	−0.700973	−	0.227760i
$892$	5.18281e8	−	1.68400e8i	0.730248	−	0.237272i
$893$	−9.80436e8			−1.37678
$894$			3.05998e8i			0.428258i
$895$	−1.71224e7	+	5.56342e6i	−0.0238834	+	0.00776020i
$896$	5.31114e7	−	3.85877e7i	0.0738353	−	0.0536445i
$897$	−5.73531e8	+	7.89397e8i	−0.794656	+	1.09375i
$898$		−	1.16680e8i		−	0.161127i
$899$	−1.46372e8	−	4.44641e7i	−0.201456	−	0.0611971i
$900$	−1.94004e7			−0.0266124
$901$	8.54217e7	+	6.20625e7i	0.116787	+	0.0848506i
$902$	−9.25120e7	−	1.27332e8i	−0.126060	−	0.173507i
$903$	3.82082e8	+	1.17593e9i	0.518912	+	1.59705i
$904$	3.59440e7			0.0486543
$905$			4.95773e6i			0.00668863i
$906$	1.26878e8	+	3.90489e8i	0.170608	+	0.525079i
$907$	−2.84630e8	+	8.76002e8i	−0.381469	+	1.17404i	0.557541	+	0.830150i	$0.311745\pi$
$907$	−2.84630e8	+	8.76002e8i	−0.381469	+	1.17404i	−0.939010	+	0.343891i	$0.888255\pi$
$908$	−2.08107e8	+	6.40487e8i	−0.277990	+	0.855564i
$909$	3.68813e7	+	2.67958e7i	0.0491037	+	0.0356760i
$910$	−3.24666e7	+	1.05490e7i	−0.0430837	+	0.0139987i
$911$	−1.10181e8	+	1.51652e8i	−0.145731	+	0.200582i	−0.875642	−	0.482960i	$-0.839562\pi$
$911$	−1.10181e8	+	1.51652e8i	−0.145731	+	0.200582i	0.729911	+	0.683542i	$0.239562\pi$
$912$	1.79382e8	+	2.46898e8i	0.236480	+	0.325487i
$913$	−1.28650e7	+	3.95945e7i	−0.0169044	+	0.0520263i
$914$	−3.75241e8	−	5.16475e8i	−0.491441	−	0.676411i
$915$	3.19545e7	−	2.32163e7i	0.0417127	−	0.0303061i
$916$	−5.74091e8	−	1.86533e8i	−0.746954	−	0.242700i
$917$	1.24656e9	−	9.05678e8i	1.61661	−	1.17453i
$918$	5.60045e7	+	4.06897e7i	0.0723927	+	0.0525964i
$919$	−1.57496e8	−	4.84723e8i	−0.202919	−	0.624521i	−0.999792	−	0.0203744i	$-0.993514\pi$
$919$	−1.57496e8	−	4.84723e8i	−0.202919	−	0.624521i	0.796873	−	0.604146i	$-0.206486\pi$
$920$	−9.10236e6	+	1.25283e7i	−0.0116894	+	0.0160890i
$921$	9.37089e8	+	3.04479e8i	1.19950	+	0.389743i
$922$	3.22916e7	+	1.04922e7i	0.0412000	+	0.0133867i
$923$	2.05528e8	−	6.67800e7i	0.261376	−	0.0849261i
$924$	3.09462e8			0.392276
$925$		−	3.24153e8i		−	0.409567i
$926$	−7.39996e8	+	2.40439e8i	−0.931958	+	0.302811i
$927$	1.84081e7	−	1.33742e7i	0.0231083	−	0.0167892i
$928$	1.74837e7	−	2.40643e7i	0.0218771	−	0.0301113i
$929$			1.19101e7i			0.0148548i	0.999972	+	0.00742740i	$0.00236424\pi$
$929$			1.19101e7i			0.0148548i	−0.999972	+	0.00742740i	$0.997636\pi$
$930$	−2.62064e7	+	9.07610e6i	−0.0325806	+	0.0112837i
$931$	8.83068e7			0.109432
$932$	−3.64908e7	−	2.65121e7i	−0.0450749	−	0.0327489i
$933$	−9.14346e8	−	1.25849e9i	−1.12581	−	1.54955i
$934$	−5.12648e7	−	1.57777e8i	−0.0629185	−	0.193643i
$935$	−3.95016e6			−0.00483259
$936$			1.91522e7i			0.0233556i
$937$	1.44335e8	+	4.44216e8i	0.175449	+	0.539977i	0.999654	−	0.0263151i	$-0.00837731\pi$
$937$	1.44335e8	+	4.44216e8i	0.175449	+	0.539977i	−0.824204	+	0.566292i	$0.808377\pi$
$938$	−8.36462e7	+	2.57437e8i	−0.101353	+	0.311933i
$939$	7.16565e7	−	2.20536e8i	0.0865483	−	0.266368i
$940$	1.40156e7	+	1.01829e7i	0.0168744	+	0.0122600i
$941$	4.90776e8	−	1.59463e8i	0.588998	−	0.191377i	0.000670626	−	1.00000i	$-0.499787\pi$
$941$	4.90776e8	−	1.59463e8i	0.588998	−	0.191377i	0.588328	+	0.808623i	$0.299787\pi$
$942$	−2.19395e8	+	3.01971e8i	−0.262466	+	0.361254i
$943$	2.14857e8	+	2.95725e8i	0.256220	+	0.352657i
$944$	−8.35515e7	+	2.57145e8i	−0.0993203	+	0.305677i
$945$	2.63072e7	+	3.62087e7i	0.0311730	+	0.0429059i
$946$	−6.32180e8	+	4.59306e8i	−0.746736	+	0.542536i
$947$	1.02564e9	+	3.33251e8i	1.20766	+	0.392394i	0.842575	−	0.538579i	$-0.181039\pi$
$947$	1.02564e9	+	3.33251e8i	1.20766	+	0.392394i	0.365088	+	0.930973i	$0.381039\pi$
$948$	−1.47981e8	+	1.07515e8i	−0.173693	+	0.126195i
$949$	2.03145e8	+	1.47594e8i	0.237689	+	0.172691i
$950$	3.09093e8	+	9.51290e8i	0.360511	+	1.10954i
$951$	4.31234e8	−	5.93543e8i	0.501385	−	0.690098i
$952$	−3.69885e7	−	1.20183e7i	−0.0428702	−	0.0139294i
$953$	−1.15679e9	−	3.75864e8i	−1.33652	−	0.434262i	−0.448385	−	0.893841i	$-0.648000\pi$
$953$	−1.15679e9	−	3.75864e8i	−1.33652	−	0.434262i	−0.888137	+	0.459579i	$0.848000\pi$
$954$	3.64246e7	−	1.18351e7i	0.0419518	−	0.0136310i
$955$	−5.99455e7			−0.0688250
$956$			2.71765e8i			0.311042i
$957$	1.33352e8	−	4.33286e7i	0.152147	−	0.0494355i
$958$	−1.23090e8	+	8.94300e7i	−0.139999	+	0.101715i
$959$	−3.66238e8	+	5.04084e8i	−0.415248	+	0.571540i
$960$		−	5.39257e6i		−	0.00609512i
$961$	−6.97402e8	+	5.48902e8i	−0.785801	+	0.618479i
$962$	−3.20006e8			−0.359445
$963$	1.61310e7	+	1.17199e7i	0.0180627	+	0.0131233i
$964$	−4.78123e7	−	6.58080e7i	−0.0533714	−	0.0734594i
$965$	−2.06779e7	−	6.36399e7i	−0.0230104	−	0.0708187i
$966$	−7.18717e8			−0.797309
$967$		−	6.81085e8i		−	0.753220i	−0.926372	−	0.376610i	$-0.877090\pi$
$967$		−	6.81085e8i		−	0.753220i	0.926372	−	0.376610i	$-0.122910\pi$
$968$	−3.86613e7	−	1.18987e8i	−0.0426236	−	0.131182i
$969$	5.58692e7	−	1.71948e8i	0.0614047	−	0.188984i
$970$	756540.	−	2.32839e6i	0.000828928	−	0.00255118i
$971$	8.49860e8	+	6.17460e8i	0.928303	+	0.674452i	0.945577	−	0.325399i	$-0.105499\pi$
$971$	8.49860e8	+	6.17460e8i	0.928303	+	0.674452i	−0.0172737	+	0.999851i	$0.505499\pi$
$972$	4.65520e7	−	1.51257e7i	0.0506920	−	0.0164708i
$973$	9.55215e8	−	1.31474e9i	1.03696	−	1.42725i
$974$	4.00512e8	+	5.51257e8i	0.433449	+	0.596592i
$975$	3.44134e8	−	1.05913e9i	0.371290	−	1.14271i
$976$	1.44460e8	+	1.98832e8i	0.155381	+	0.213863i
$977$	−1.22070e9	+	8.86893e8i	−1.30896	+	0.951016i	−1.00000		5.92014e-5i	$-0.999981\pi$
$977$	−1.22070e9	+	8.86893e8i	−1.30896	+	0.951016i	−0.308961	+	0.951075i	$0.599981\pi$
$978$	−4.66450e8	−	1.51559e8i	−0.498642	−	0.162019i
$979$	1.11015e9	−	8.06573e8i	1.18314	−	0.859598i
$980$	−1.26237e6	−	917167.i	−0.00134125	−	0.000974474i
$981$	9.00049e6	+	2.77007e7i	0.00953365	+	0.0293416i
$982$	6.57030e8	−	9.04324e8i	0.693826	−	0.954970i
$983$	9.52039e8	+	3.09336e8i	1.00229	+	0.325664i	0.763781	−	0.645475i	$-0.223341\pi$
$983$	9.52039e8	+	3.09336e8i	1.00229	+	0.325664i	0.238511	+	0.971140i	$0.423341\pi$
$984$	−1.21059e8	−	3.93344e7i	−0.127061	−	0.0412845i
$985$	2.01974e7	−	6.56254e6i	0.0211343	−	0.00686695i
$986$	−1.76216e7			−0.0183829
$987$			8.04040e8i			0.836231i
$988$	9.39119e8	−	3.05138e8i	0.973755	−	0.316392i
$989$	1.46822e9	−	1.06672e9i	1.51776	−	1.10271i
$990$	−842194.	+	1.15918e6i	−0.000867973	+	0.00119466i
$991$			5.54183e8i			0.569419i	0.958614	+	0.284710i	$0.0918972\pi$
$991$			5.54183e8i			0.569419i	−0.958614	+	0.284710i	$0.908103\pi$
$992$	−5.64746e7	−	1.63065e8i	−0.0578520	−	0.167042i
$993$	−9.88648e8			−1.00970
$994$	1.28778e8	+	9.35626e7i	0.131124	+	0.0952672i
$995$	−3.68785e7	−	5.07590e7i	−0.0374373	−	0.0515280i
$996$	1.04045e7	+	3.20218e7i	0.0105304	+	0.0324092i
$997$	−9.29473e8			−0.937889			−0.468944	−	0.883228i	$-0.655366\pi$
$997$	−9.29473e8			−0.937889			−0.468944	+	0.883228i	$0.655366\pi$
$998$		−	1.19961e9i		−	1.20684i
$999$	1.29648e8	+	3.99015e8i	0.130037	+	0.400214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.29.14	yes	64
31.15	odd	10	inner	62.7.f.a.15.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.14	✓	64	31.15	odd	10	inner
62.7.f.a.29.14	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.57649 + 3.32502i) q^{2} +(15.4410 + 21.2527i) q^{3} +(9.88854 + 30.4338i) q^{4} +6.26454 q^{5} +148.604i q^{6} +(109.443 + 336.831i) q^{7} +(-55.9381 + 172.160i) q^{8} +(12.0203 - 36.9947i) q^{9} +(28.6696 + 20.8297i) q^{10} +(-988.558 + 321.202i) q^{11} +(-494.112 + 680.086i) q^{12} +(1598.75 + 2200.48i) q^{13} +(-619.103 + 1905.40i) q^{14} +(96.7308 + 133.138i) q^{15} +(-828.433 + 601.892i) q^{16} +(576.948 + 187.462i) q^{17} +(178.019 - 129.338i) q^{18} +(-9178.28 - 6668.41i) q^{19} +(61.9472 + 190.654i) q^{20} +(-5468.66 + 7526.96i) q^{21} +(-5592.13 - 1816.99i) q^{22} +(12987.6 + 4219.91i) q^{23} +(-4522.60 + 1469.48i) q^{24} -15585.8 q^{25} +15386.3i q^{26} +(19185.2 - 6233.65i) q^{27} +(-9168.81 + 6661.53i) q^{28} +(-3018.28 + 4154.30i) q^{29} +930.938i q^{30} +(9749.41 + 28150.5i) q^{31} -5792.62 q^{32} +(-22090.7 - 16049.8i) q^{33} +(2017.08 + 2776.28i) q^{34} +(685.610 + 2110.09i) q^{35} +1244.75 q^{36} +20798.0i q^{37} +(-19831.8 - 61035.9i) q^{38} +(-22080.0 + 67955.3i) q^{39} +(-350.426 + 1078.50i) q^{40} +(21655.4 + 15733.6i) q^{41} +(-50054.5 + 16263.7i) q^{42} +(78114.4 - 107515. i) q^{43} +(-19550.8 - 26909.4i) q^{44} +(75.3017 - 231.755i) q^{45} +(45406.2 + 62496.2i) q^{46} +(69915.4 - 50796.5i) q^{47} +(-25583.7 - 8312.64i) q^{48} +(-6297.21 + 4575.19i) q^{49} +(-71328.1 - 51822.9i) q^{50} +(4924.58 + 15156.3i) q^{51} +(-51159.8 + 70415.5i) q^{52} +(165534. + 53785.2i) q^{53} +(108528. + 35262.9i) q^{54} +(-6192.86 + 2012.18i) q^{55} -64110.7 q^{56} -298030. i q^{57} +(-27626.3 + 8976.31i) q^{58} +(213614. - 155200. i) q^{59} +(-3095.38 + 4260.43i) q^{60} -240009. i q^{61} +(-48982.9 + 161248. i) q^{62} +13776.5 q^{63} +(-26509.9 - 19260.5i) q^{64} +(10015.4 + 13785.0i) q^{65} +(-47732.0 - 146904. i) q^{66} +135109. q^{67} +19412.4i q^{68} +(110856. + 341180. i) q^{69} +(-3878.40 + 11936.5i) q^{70} +(24551.9 - 75563.1i) q^{71} +(5696.60 + 4138.82i) q^{72} +(87800.2 - 28528.0i) q^{73} +(-69153.8 + 95182.0i) q^{74} +(-240660. - 331239. i) q^{75} +(112185. - 345271. i) q^{76} +(-216381. - 297823. i) q^{77} +(-327001. + 237580. i) q^{78} +(206942. + 67239.7i) q^{79} +(-5189.76 + 3770.58i) q^{80} +(405779. + 294816. i) q^{81} +(46791.4 + 144009. i) q^{82} +(23542.5 - 32403.4i) q^{83} +(-283151. - 92001.4i) q^{84} +(3614.31 + 1174.36i) q^{85} +(714980. - 232311. i) q^{86} -134895. q^{87} -188157. i q^{88} +(-1.25555e6 + 407954. i) q^{89} +(1115.21 - 810.245i) q^{90} +(-566219. + 779334. i) q^{91} +436989. i q^{92} +(-447734. + 641874. i) q^{93} +488867. q^{94} +(-57497.8 - 41774.6i) q^{95} +(-89443.8 - 123109. i) q^{96} +(-21348.5 - 65703.9i) q^{97} -44031.7 q^{98} +40432.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more