LMFDB - Embedded newform 76.7.b.a.39.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.b (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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.9
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.15940 - 3.56973i) q^{2} -19.3279i q^{3} +(38.5141 + 51.1142i) q^{4} -43.0893 q^{5} +(-68.9953 + 138.376i) q^{6} +282.338i q^{7} +(-93.2744 - 503.432i) q^{8} +355.433 q^{9} +O(q^{10})$	\(q+(-7.15940 - 3.56973i) q^{2} -19.3279i q^{3} +(38.5141 + 51.1142i) q^{4} -43.0893 q^{5} +(-68.9953 + 138.376i) q^{6} +282.338i q^{7} +(-93.2744 - 503.432i) q^{8} +355.433 q^{9} +(308.494 + 153.817i) q^{10} -1423.66i q^{11} +(987.930 - 744.397i) q^{12} -64.5564 q^{13} +(1007.87 - 2021.37i) q^{14} +832.825i q^{15} +(-1129.32 + 3937.24i) q^{16} +6845.77 q^{17} +(-2544.69 - 1268.80i) q^{18} -1573.56i q^{19} +(-1659.55 - 2202.48i) q^{20} +5457.00 q^{21} +(-5082.09 + 10192.6i) q^{22} -8610.09i q^{23} +(-9730.28 + 1802.80i) q^{24} -13768.3 q^{25} +(462.185 + 230.449i) q^{26} -20959.8i q^{27} +(-14431.5 + 10874.0i) q^{28} -37754.8 q^{29} +(2972.96 - 5962.53i) q^{30} -16053.5i q^{31} +(22140.2 - 24156.9i) q^{32} -27516.4 q^{33} +(-49011.6 - 24437.5i) q^{34} -12165.7i q^{35} +(13689.2 + 18167.7i) q^{36} -89414.3 q^{37} +(-5617.19 + 11265.8i) q^{38} +1247.74i q^{39} +(4019.13 + 21692.5i) q^{40} +53959.7 q^{41} +(-39068.8 - 19480.0i) q^{42} -97929.6i q^{43} +(72769.5 - 54831.2i) q^{44} -15315.3 q^{45} +(-30735.6 + 61643.1i) q^{46} -23989.0i q^{47} +(76098.5 + 21827.5i) q^{48} +37934.2 q^{49} +(98572.9 + 49149.1i) q^{50} -132314. i q^{51} +(-2486.33 - 3299.75i) q^{52} -80853.1 q^{53} +(-74820.7 + 150060. i) q^{54} +61344.7i q^{55} +(142138. - 26334.9i) q^{56} -30413.6 q^{57} +(270302. + 134774. i) q^{58} +102427. i q^{59} +(-42569.2 + 32075.5i) q^{60} -66372.6 q^{61} +(-57306.6 + 114933. i) q^{62} +100352. i q^{63} +(-244744. + 93914.7i) q^{64} +2781.69 q^{65} +(197001. + 98226.1i) q^{66} -178825. i q^{67} +(263659. + 349916. i) q^{68} -166415. q^{69} +(-43428.4 + 87099.5i) q^{70} -536228. i q^{71} +(-33152.8 - 178936. i) q^{72} +727200. q^{73} +(640153. + 319184. i) q^{74} +266112. i q^{75} +(80431.4 - 60604.4i) q^{76} +401955. q^{77} +(4454.08 - 8933.06i) q^{78} -514579. i q^{79} +(48661.8 - 169653. i) q^{80} -145998. q^{81} +(-386319. - 192621. i) q^{82} -560472. i q^{83} +(210171. + 278930. i) q^{84} -294980. q^{85} +(-349582. + 701117. i) q^{86} +729721. i q^{87} +(-716718. + 132791. i) q^{88} -310222. q^{89} +(109649. + 54671.6i) q^{90} -18226.7i q^{91} +(440098. - 331610. i) q^{92} -310280. q^{93} +(-85634.1 + 171747. i) q^{94} +67803.7i q^{95} +(-466902. - 427922. i) q^{96} -475542. q^{97} +(-271587. - 135415. i) q^{98} -506017. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−7.15940	−	3.56973i	−0.894925	−	0.446216i
$2$	−7.15940	−	3.56973i	−0.894925	−	0.446216i
$3$		−	19.3279i		−	0.715848i	−0.933751	−	0.357924i	$-0.883485\pi$
$3$		−	19.3279i		−	0.715848i	0.933751	−	0.357924i	$-0.116515\pi$
$4$	38.5141	+	51.1142i	0.601783	+	0.798660i
$5$	−43.0893			−0.344714			−0.172357	−	0.985035i	$-0.555138\pi$
$5$	−43.0893			−0.344714			−0.172357	+	0.985035i	$0.555138\pi$
$6$	−68.9953	+	138.376i	−0.319422	+	0.640630i
$7$			282.338i			0.823143i	0.911377	+	0.411571i	$0.135020\pi$
$7$			282.338i			0.823143i	−0.911377	+	0.411571i	$0.864980\pi$
$8$	−93.2744	−	503.432i	−0.182177	−	0.983266i
$9$	355.433			0.487562
$10$	308.494	+	153.817i	0.308494	+	0.153817i
$11$		−	1423.66i		−	1.06962i	−0.844972	−	0.534810i	$-0.820383\pi$
$11$		−	1423.66i		−	1.06962i	0.844972	−	0.534810i	$-0.179617\pi$
$12$	987.930	−	744.397i	0.571719	−	0.430785i
$13$	−64.5564			−0.0293839			−0.0146919	−	0.999892i	$-0.504677\pi$
$13$	−64.5564			−0.0293839			−0.0146919	+	0.999892i	$0.504677\pi$
$14$	1007.87	−	2021.37i	0.367299	−	0.736652i
$15$			832.825i			0.246763i
$16$	−1129.32	+	3937.24i	−0.275714	+	0.961240i
$17$	6845.77			1.39340			0.696700	−	0.717363i	$-0.254651\pi$
$17$	6845.77			1.39340			0.696700	+	0.717363i	$0.254651\pi$
$18$	−2544.69	−	1268.80i	−0.436332	−	0.217558i
$19$		−	1573.56i		−	0.229416i
$19$		−	1573.56i		−	0.229416i
$20$	−1659.55	−	2202.48i	−0.207443	−	0.275309i
$21$	5457.00			0.589245
$22$	−5082.09	+	10192.6i	−0.477281	+	0.957230i
$23$		−	8610.09i		−	0.707659i	−0.935310	−	0.353829i	$-0.884879\pi$
$23$		−	8610.09i		−	0.707659i	0.935310	−	0.353829i	$-0.115121\pi$
$24$	−9730.28	+	1802.80i	−0.703869	+	0.130411i
$25$	−13768.3			−0.881172
$26$	462.185	+	230.449i	0.0262964	+	0.0131115i
$27$		−	20959.8i		−	1.06487i
$28$	−14431.5	+	10874.0i	−0.657411	+	0.495354i
$29$	−37754.8			−1.54803			−0.774013	−	0.633170i	$-0.781754\pi$
$29$	−37754.8			−1.54803			−0.774013	+	0.633170i	$0.781754\pi$
$30$	2972.96	−	5962.53i	0.110110	−	0.220835i
$31$		−	16053.5i		−	0.538871i	−0.963018	−	0.269435i	$-0.913163\pi$
$31$		−	16053.5i		−	0.538871i	0.963018	−	0.269435i	$-0.0868370\pi$
$32$	22140.2	−	24156.9i	0.675664	−	0.737210i
$33$	−27516.4			−0.765685
$34$	−49011.6	−	24437.5i	−1.24699	−	0.621757i
$35$		−	12165.7i		−	0.283749i
$36$	13689.2	+	18167.7i	0.293407	+	0.389396i
$37$	−89414.3			−1.76523			−0.882616	−	0.470095i	$-0.844220\pi$
$37$	−89414.3			−1.76523			−0.882616	+	0.470095i	$0.844220\pi$
$38$	−5617.19	+	11265.8i	−0.102369	+	0.205310i
$39$			1247.74i			0.0210344i
$40$	4019.13	+	21692.5i	0.0627989	+	0.338946i
$41$	53959.7			0.782921			0.391460	−	0.920195i	$-0.371970\pi$
$41$	53959.7			0.782921			0.391460	+	0.920195i	$0.371970\pi$
$42$	−39068.8	−	19480.0i	−0.527330	−	0.262930i
$43$		−	97929.6i		−	1.23171i	−0.787859	−	0.615855i	$-0.788811\pi$
$43$		−	97929.6i		−	1.23171i	0.787859	−	0.615855i	$-0.211189\pi$
$44$	72769.5	−	54831.2i	0.854262	−	0.643679i
$45$	−15315.3			−0.168070
$46$	−30735.6	+	61643.1i	−0.315769	+	0.633302i
$47$		−	23989.0i		−	0.231057i	−0.993304	−	0.115528i	$-0.963144\pi$
$47$		−	23989.0i		−	0.231057i	0.993304	−	0.115528i	$-0.0368561\pi$
$48$	76098.5	+	21827.5i	0.688101	+	0.197369i
$49$	37934.2			0.322436
$50$	98572.9	+	49149.1i	0.788583	+	0.393193i
$51$		−	132314.i		−	0.997462i
$52$	−2486.33	−	3299.75i	−0.0176827	−	0.0234677i
$53$	−80853.1			−0.543087			−0.271543	−	0.962426i	$-0.587534\pi$
$53$	−80853.1			−0.543087			−0.271543	+	0.962426i	$0.587534\pi$
$54$	−74820.7	+	150060.i	−0.475161	+	0.952977i
$55$			61344.7i			0.368713i
$56$	142138.	−	26334.9i	0.809368	−	0.149957i
$57$	−30413.6			−0.164227
$58$	270302.	+	134774.i	1.38537	+	0.690753i
$59$			102427.i			0.498720i	0.968411	+	0.249360i	$0.0802203\pi$
$59$			102427.i			0.498720i	−0.968411	+	0.249360i	$0.919780\pi$
$60$	−42569.2	+	32075.5i	−0.197080	+	0.148498i
$61$	−66372.6			−0.292415			−0.146207	−	0.989254i	$-0.546707\pi$
$61$	−66372.6			−0.292415			−0.146207	+	0.989254i	$0.546707\pi$
$62$	−57306.6	+	114933.i	−0.240453	+	0.482249i
$63$			100352.i			0.401333i
$64$	−244744.	+	93914.7i	−0.933623	+	0.358256i
$65$	2781.69			0.0101290
$66$	197001.	+	98226.1i	0.685231	+	0.341661i
$67$		−	178825.i		−	0.594571i	−0.954789	−	0.297286i	$-0.903919\pi$
$67$		−	178825.i		−	0.594571i	0.954789	−	0.297286i	$-0.0960814\pi$
$68$	263659.	+	349916.i	0.838524	+	1.11285i
$69$	−166415.			−0.506576
$70$	−43428.4	+	87099.5i	−0.126613	+	0.253934i
$71$		−	536228.i		−	1.49822i	−0.662447	−	0.749108i	$-0.730482\pi$
$71$		−	536228.i		−	1.49822i	0.662447	−	0.749108i	$-0.269518\pi$
$72$	−33152.8	−	178936.i	−0.0888224	−	0.479403i
$73$	727200.			1.86933			0.934663	−	0.355535i	$-0.115701\pi$
$73$	727200.			1.86933			0.934663	+	0.355535i	$0.115701\pi$
$74$	640153.	+	319184.i	1.57975	+	0.787674i
$75$			266112.i			0.630785i
$76$	80431.4	−	60604.4i	0.183225	−	0.138059i
$77$	401955.			0.880450
$78$	4454.08	−	8933.06i	0.00938587	−	0.0188242i
$79$		−	514579.i		−	1.04369i	−0.853041	−	0.521844i	$-0.825244\pi$
$79$		−	514579.i		−	1.04369i	0.853041	−	0.521844i	$-0.174756\pi$
$80$	48661.8	−	169653.i	0.0950426	−	0.331353i
$81$	−145998.			−0.274721
$82$	−386319.	−	192621.i	−0.700656	−	0.349351i
$83$		−	560472.i		−	0.980210i	−0.871663	−	0.490105i	$-0.836958\pi$
$83$		−	560472.i		−	0.980210i	0.871663	−	0.490105i	$-0.163042\pi$
$84$	210171.	+	278930.i	0.354598	+	0.470606i
$85$	−294980.			−0.480325
$86$	−349582.	+	701117.i	−0.549608	+	1.10229i
$87$			729721.i			1.10815i
$88$	−716718.	+	132791.i	−1.05172	+	0.194860i
$89$	−310222.			−0.440051			−0.220025	−	0.975494i	$-0.570614\pi$
$89$	−310222.			−0.440051			−0.220025	+	0.975494i	$0.570614\pi$
$90$	109649.	+	54671.6i	0.150410	+	0.0749953i
$91$		−	18226.7i		−	0.0241871i
$92$	440098.	−	331610.i	0.565179	−	0.425857i
$93$	−310280.			−0.385749
$94$	−85634.1	+	171747.i	−0.103101	+	0.206778i
$95$			67803.7i			0.0790829i
$96$	−466902.	−	427922.i	−0.527730	−	0.483672i
$97$	−475542.			−0.521043			−0.260521	−	0.965468i	$-0.583894\pi$
$97$	−475542.			−0.521043			−0.260521	+	0.965468i	$0.583894\pi$
$98$	−271587.	−	135415.i	−0.288556	−	0.143876i
$99$		−	506017.i		−	0.521506i
$100$	−530274.	−	703756.i	−0.530274	−	0.703756i
$101$	366846.			0.356057			0.178028	−	0.984025i	$-0.443028\pi$
$101$	366846.			0.356057			0.178028	+	0.984025i	$0.443028\pi$
$102$	−472326.	+	947292.i	−0.445083	+	0.892654i
$103$		−	662397.i		−	0.606187i	−0.952961	−	0.303094i	$-0.901981\pi$
$103$		−	662397.i		−	0.606187i	0.952961	−	0.303094i	$-0.0980195\pi$
$104$	6021.46	+	32499.8i	0.00535306	+	0.0288922i
$105$	−235138.			−0.203121
$106$	578860.	+	288623.i	0.486022	+	0.242334i
$107$			638219.i			0.520977i	0.965477	+	0.260489i	$0.0838836\pi$
$107$			638219.i			0.520977i	−0.965477	+	0.260489i	$0.916116\pi$
$108$	1.07134e6	−	807248.i	0.850467	−	0.640820i
$109$	−1.54663e6			−1.19428			−0.597139	−	0.802138i	$-0.703696\pi$
$109$	−1.54663e6			−1.19428			−0.597139	+	0.802138i	$0.703696\pi$
$110$	218984.	−	439191.i	0.164526	−	0.329971i
$111$			1.72819e6i			1.26364i
$112$	−1.11163e6	−	318851.i	−0.791238	−	0.226952i
$113$	985871.			0.683258			0.341629	−	0.939835i	$-0.389021\pi$
$113$	985871.			0.683258			0.341629	+	0.939835i	$0.389021\pi$
$114$	217744.	+	108568.i	0.146971	+	0.0732805i
$115$			371003.i			0.243940i
$116$	−1.45409e6	−	1.92981e6i	−0.931576	−	1.23635i
$117$	−22945.4			−0.0143265
$118$	365635.	−	733314.i	0.222537	−	0.446317i
$119$			1.93282e6i			1.14697i
$120$	419271.	−	77681.3i	0.242634	−	0.0449545i
$121$	−255259.			−0.144087
$122$	475188.	+	236932.i	0.261689	+	0.130480i
$123$		−	1.04293e6i		−	0.560452i
$124$	820562.	−	618286.i	0.430374	−	0.324283i
$125$	1.26654e6			0.648467
$126$	358230.	−	718462.i	0.179081	−	0.359163i
$127$		−	1.79774e6i		−	0.877640i	−0.898575	−	0.438820i	$-0.855397\pi$
$127$		−	1.79774e6i		−	0.877640i	0.898575	−	0.438820i	$-0.144603\pi$
$128$	2.08747e6	+	201295.i	0.995383	+	0.0959848i
$129$	−1.89277e6			−0.881717
$130$	−19915.2	−	9929.87i	−0.00906474	−	0.00451974i
$131$		−	2.43254e6i		−	1.08205i	−0.841007	−	0.541024i	$-0.818037\pi$
$131$		−	2.43254e6i		−	1.08205i	0.841007	−	0.541024i	$-0.181963\pi$
$132$	−1.05977e6	−	1.40648e6i	−0.460776	−	0.611522i
$133$	444277.			0.188842
$134$	−638357.	+	1.28028e6i	−0.265307	+	0.532097i
$135$			903143.i			0.367075i
$136$	−638536.	−	3.44638e6i	−0.253845	−	1.37008i
$137$	3.44256e6			1.33881			0.669406	−	0.742897i	$-0.266549\pi$
$137$	3.44256e6			1.33881			0.669406	+	0.742897i	$0.266549\pi$
$138$	1.19143e6	+	594055.i	0.453348	+	0.226042i
$139$			5.01559e6i			1.86757i	0.357831	+	0.933787i	$0.383517\pi$
$139$			5.01559e6i			1.86757i	−0.357831	+	0.933787i	$0.616483\pi$
$140$	621843.	−	468553.i	0.226619	−	0.170755i
$141$	−463657.			−0.165401
$142$	−1.91419e6	+	3.83907e6i	−0.668528	+	1.34079i
$143$			91906.6i			0.0314296i
$144$	−401399.	+	1.39942e6i	−0.134428	+	0.468664i
$145$	1.62683e6			0.533627
$146$	−5.20632e6	−	2.59590e6i	−1.67291	−	0.834123i
$147$		−	733189.i		−	0.230815i
$148$	−3.44371e6	−	4.57034e6i	−1.06229	−	1.40982i
$149$	−2.90677e6			−0.878723			−0.439362	−	0.898310i	$-0.644795\pi$
$149$	−2.90677e6			−0.878723			−0.439362	+	0.898310i	$0.644795\pi$
$150$	949948.	−	1.90521e6i	0.281466	−	0.564506i
$151$			1.83580e6i			0.533206i	0.963806	+	0.266603i	$0.0859013\pi$
$151$			1.83580e6i			0.533206i	−0.963806	+	0.266603i	$0.914099\pi$
$152$	−792182.	+	146773.i	−0.225577	+	0.0417942i
$153$	2.43321e6			0.679369
$154$	−2.87775e6	−	1.43487e6i	−0.787937	−	0.392871i
$155$			691734.i			0.185756i
$156$	−63777.2	+	48055.5i	−0.0167993	+	0.0126581i
$157$	351824.			0.0909131			0.0454566	−	0.998966i	$-0.485526\pi$
$157$	351824.			0.0909131			0.0454566	+	0.998966i	$0.485526\pi$
$158$	−1.83691e6	+	3.68408e6i	−0.465710	+	0.934024i
$159$			1.56272e6i			0.388767i
$160$	−954004.	+	1.04090e6i	−0.232911	+	0.254127i
$161$	2.43095e6			0.582504
$162$	1.04526e6	+	521173.i	0.245855	+	0.122585i
$163$			5.22903e6i			1.20742i	0.797204	+	0.603710i	$0.206312\pi$
$163$			5.22903e6i			1.20742i	−0.797204	+	0.603710i	$0.793688\pi$
$164$	2.07821e6	+	2.75811e6i	0.471148	+	0.625287i
$165$	1.18566e6			0.263943
$166$	−2.00073e6	+	4.01264e6i	−0.437385	+	0.877215i
$167$			611903.i			0.131381i	0.997840	+	0.0656906i	$0.0209250\pi$
$167$			611903.i			0.131381i	−0.997840	+	0.0656906i	$0.979075\pi$
$168$	−508998.	−	2.74723e6i	−0.107347	−	0.579384i
$169$	−4.82264e6			−0.999137
$170$	2.11188e6	+	1.05300e6i	0.429855	+	0.214329i
$171$		−	559296.i		−	0.111854i
$172$	5.00559e6	−	3.77167e6i	0.983717	−	0.741223i
$173$	4.58401e6			0.885335			0.442667	−	0.896686i	$-0.354032\pi$
$173$	4.58401e6			0.885335			0.442667	+	0.896686i	$0.354032\pi$
$174$	2.60490e6	−	5.22437e6i	0.494474	−	0.991712i
$175$		−	3.88732e6i		−	0.725330i
$176$	5.60530e6	+	1.60778e6i	1.02816	+	0.294909i
$177$	1.97969e6			0.357008
$178$	2.22101e6	+	1.10741e6i	0.393813	+	0.196358i
$179$			8.95423e6i			1.56124i	0.625008	+	0.780619i	$0.285096\pi$
$179$			8.95423e6i			1.56124i	−0.625008	+	0.780619i	$0.714904\pi$
$180$	−589857.	−	782832.i	−0.101141	−	0.134230i
$181$	−1.98646e6			−0.334999			−0.167499	−	0.985872i	$-0.553569\pi$
$181$	−1.98646e6			−0.334999			−0.167499	+	0.985872i	$0.553569\pi$
$182$	−65064.4	+	130492.i	−0.0107927	+	0.0216457i
$183$			1.28284e6i			0.209325i
$184$	−4.33459e6	+	803101.i	−0.695817	+	0.128919i
$185$	3.85280e6			0.608501
$186$	2.22142e6	+	1.10761e6i	0.345217	+	0.172127i
$187$		−	9.74608e6i		−	1.49041i
$188$	1.22618e6	−	923915.i	0.184536	−	0.139046i
$189$	5.91775e6			0.876538
$190$	242041.	−	485434.i	0.0352880	−	0.0707733i
$191$			6.05943e6i			0.869625i	0.900521	+	0.434812i	$0.143185\pi$
$191$			6.05943e6i			0.869625i	−0.900521	+	0.434812i	$0.856815\pi$
$192$	1.81517e6	+	4.73038e6i	0.256457	+	0.668332i
$193$	5.78772e6			0.805073			0.402537	−	0.915404i	$-0.368129\pi$
$193$	5.78772e6			0.805073			0.402537	+	0.915404i	$0.368129\pi$
$194$	3.40460e6	+	1.69755e6i	0.466294	+	0.232497i
$195$		−	53764.2i		−	0.00725085i
$196$	1.46100e6	+	1.93898e6i	0.194036	+	0.257516i
$197$	−4.55224e6			−0.595424			−0.297712	−	0.954656i	$-0.596224\pi$
$197$	−4.55224e6			−0.595424			−0.297712	+	0.954656i	$0.596224\pi$
$198$	−1.80634e6	+	3.62278e6i	−0.232704	+	0.466709i
$199$		−	5.21399e6i		−	0.661624i	−0.943697	−	0.330812i	$-0.892677\pi$
$199$		−	5.21399e6i		−	0.661624i	0.943697	−	0.330812i	$-0.107323\pi$
$200$	1.28423e6	+	6.93141e6i	0.160529	+	0.866426i
$201$	−3.45631e6			−0.425623
$202$	−2.62640e6	−	1.30954e6i	−0.318644	−	0.158878i
$203$		−	1.06596e7i		−	1.27425i
$204$	6.76314e6	−	5.09597e6i	0.796632	−	0.600256i
$205$	−2.32508e6			−0.269884
$206$	−2.36458e6	+	4.74237e6i	−0.270490	+	0.542492i
$207$		−	3.06031e6i		−	0.345028i
$208$	72905.1	−	254174.i	0.00810155	−	0.0282449i
$209$	−2.24022e6			−0.245388
$210$	1.68345e6	+	839379.i	0.181778	+	0.0906359i
$211$			6.10836e6i			0.650245i	0.945672	+	0.325123i	$0.105406\pi$
$211$			6.10836e6i			0.650245i	−0.945672	+	0.325123i	$0.894594\pi$
$212$	−3.11399e6	−	4.13274e6i	−0.326820	−	0.433741i
$213$	−1.03642e7			−1.07250
$214$	2.27827e6	−	4.56927e6i	0.232468	−	0.466236i
$215$			4.21972e6i			0.424588i
$216$	−1.05518e7	+	1.95501e6i	−1.04705	+	0.193994i
$217$	4.53251e6			0.443568
$218$	1.10729e7	+	5.52103e6i	1.06879	+	0.532906i
$219$		−	1.40552e7i		−	1.33815i
$220$	−3.13559e6	+	2.36264e6i	−0.294476	+	0.221886i
$221$	−441938.			−0.0409435
$222$	6.16916e6	−	1.23728e7i	0.563855	−	1.13086i
$223$			3.06268e6i			0.276177i	0.990420	+	0.138088i	$0.0440958\pi$
$223$			3.06268e6i			0.276177i	−0.990420	+	0.138088i	$0.955904\pi$
$224$	6.82041e6	+	6.25101e6i	0.606829	+	0.556168i
$225$	−4.89371e6			−0.429626
$226$	−7.05825e6	−	3.51929e6i	−0.611465	−	0.304880i
$227$		−	6.97393e6i		−	0.596211i	−0.954533	−	0.298106i	$-0.903645\pi$
$227$		−	6.97393e6i		−	0.596211i	0.954533	−	0.298106i	$-0.0963548\pi$
$228$	−1.17135e6	−	1.55457e6i	−0.0988289	−	0.131161i
$229$	−8.36599e6			−0.696644			−0.348322	−	0.937375i	$-0.613248\pi$
$229$	−8.36599e6			−0.696644			−0.348322	+	0.937375i	$0.613248\pi$
$230$	1.32438e6	−	2.65616e6i	0.108850	−	0.218308i
$231$		−	7.76893e6i		−	0.630268i
$232$	3.52156e6	+	1.90070e7i	0.282014	+	1.52212i
$233$	−778446.			−0.0615404			−0.0307702	−	0.999526i	$-0.509796\pi$
$233$	−778446.			−0.0615404			−0.0307702	+	0.999526i	$0.509796\pi$
$234$	164276.	+	81908.9i	0.0128211	+	0.00639269i
$235$			1.03367e6i			0.0796486i
$236$	−5.23546e6	+	3.94487e6i	−0.398308	+	0.300121i
$237$	−9.94573e6			−0.747122
$238$	6.89964e6	−	1.38379e7i	0.511795	−	1.02645i
$239$			1.27720e7i			0.935546i	0.883849	+	0.467773i	$0.154944\pi$
$239$			1.27720e7i			0.935546i	−0.883849	+	0.467773i	$0.845056\pi$
$240$	−3.27903e6	−	940530.i	−0.237198	−	0.0680360i
$241$	−2.50051e7			−1.78639			−0.893197	−	0.449666i	$-0.851543\pi$
$241$	−2.50051e7			−1.78639			−0.893197	+	0.449666i	$0.851543\pi$
$242$	1.82750e6	+	911203.i	0.128947	+	0.0642938i
$243$		−	1.24579e7i		−	0.868209i
$244$	−2.55628e6	−	3.39258e6i	−0.175970	−	0.233540i
$245$	−1.63456e6			−0.111148
$246$	−3.72296e6	+	7.46673e6i	−0.250082	+	0.501563i
$247$			101583.i			0.00674112i
$248$	−8.08184e6	+	1.49738e6i	−0.529853	+	0.0981696i
$249$	−1.08327e7			−0.701681
$250$	−9.06765e6	−	4.52119e6i	−0.580330	−	0.289356i
$251$		−	1.95555e7i		−	1.23665i	−0.785921	−	0.618327i	$-0.787811\pi$
$251$		−	1.95555e7i		−	1.23665i	0.785921	−	0.618327i	$-0.212189\pi$
$252$	−5.12942e6	+	3.86498e6i	−0.320529	+	0.241516i
$253$	−1.22579e7			−0.756926
$254$	−6.41745e6	+	1.28708e7i	−0.391617	+	0.785422i
$255$			5.70133e6i			0.343839i
$256$	−1.42265e7	−	8.89284e6i	−0.847963	−	0.530055i
$257$	2.98305e7			1.75736			0.878682	−	0.477408i	$-0.158423\pi$
$257$	2.98305e7			1.75736			0.878682	+	0.477408i	$0.158423\pi$
$258$	1.35511e7	+	6.75668e6i	0.789071	+	0.393436i
$259$		−	2.52451e7i		−	1.45304i
$260$	107134.	+	142184.i	0.00609549	+	0.00808966i
$261$	−1.34193e7			−0.754759
$262$	−8.68351e6	+	1.74156e7i	−0.482827	+	0.968352i
$263$		−	2.07385e7i		−	1.14002i	−0.821639	−	0.570008i	$-0.806940\pi$
$263$		−	2.07385e7i		−	1.14002i	0.821639	−	0.570008i	$-0.193060\pi$
$264$	2.56658e6	+	1.38527e7i	0.139490	+	0.752872i
$265$	3.48390e6			0.187210
$266$	−3.18075e6	−	1.58595e6i	−0.168999	−	0.0842642i
$267$			5.99594e6i			0.315009i
$268$	9.14050e6	−	6.88729e6i	0.474860	−	0.357803i
$269$	2.53362e7			1.30162			0.650811	−	0.759240i	$-0.274429\pi$
$269$	2.53362e7			1.30162			0.650811	+	0.759240i	$0.274429\pi$
$270$	3.22397e6	−	6.46596e6i	0.163795	−	0.328505i
$271$		−	2.55619e7i		−	1.28435i	−0.766556	−	0.642177i	$-0.778031\pi$
$271$		−	2.55619e7i		−	1.28435i	0.766556	−	0.642177i	$-0.221969\pi$
$272$	−7.73110e6	+	2.69534e7i	−0.384180	+	1.33939i
$273$	−352284.			−0.0173143
$274$	−2.46467e7	−	1.22890e7i	−1.19814	−	0.597399i
$275$			1.96015e7i			0.942519i
$276$	−6.40932e6	−	8.50616e6i	−0.304849	−	0.404582i
$277$	2.15062e7			1.01187			0.505935	−	0.862572i	$-0.331148\pi$
$277$	2.15062e7			1.01187			0.505935	+	0.862572i	$0.331148\pi$
$278$	1.79043e7	−	3.59086e7i	0.833340	−	1.67134i
$279$		−	5.70594e6i		−	0.262733i
$280$	−6.12463e6	+	1.13475e6i	−0.279001	+	0.0516925i
$281$	−1.14760e7			−0.517216			−0.258608	−	0.965982i	$-0.583264\pi$
$281$	−1.14760e7			−0.517216			−0.258608	+	0.965982i	$0.583264\pi$
$282$	3.31951e6	+	1.65513e6i	0.148022	+	0.0738047i
$283$			2.77075e7i			1.22247i	0.791450	+	0.611234i	$0.209326\pi$
$283$			2.77075e7i			1.22247i	−0.791450	+	0.611234i	$0.790674\pi$
$284$	2.74089e7	−	2.06524e7i	1.19657	−	0.901602i
$285$	1.31050e6			0.0566113
$286$	328081.	−	657996.i	0.0140244	−	0.0281271i
$287$			1.52349e7i			0.644456i
$288$	7.86933e6	−	8.58615e6i	0.329428	−	0.359436i
$289$	2.27270e7			0.941562
$290$	−1.16471e7	−	5.80733e6i	−0.477556	−	0.238113i
$291$			9.19122e6i			0.372987i
$292$	2.80075e7	+	3.71702e7i	1.12493	+	1.49296i
$293$	−951701.			−0.0378353			−0.0189177	−	0.999821i	$-0.506022\pi$
$293$	−951701.			−0.0378353			−0.0189177	+	0.999821i	$0.506022\pi$
$294$	−2.61728e6	+	5.24920e6i	−0.102993	+	0.206562i
$295$		−	4.41349e6i		−	0.171916i
$296$	8.34007e6	+	4.50140e7i	0.321584	+	1.73569i
$297$	−2.98397e7			−1.13900
$298$	2.08108e7	+	1.03764e7i	0.786392	+	0.392100i
$299$			555836.i			0.0207938i
$300$	−1.36021e7	+	1.02491e7i	−0.503782	+	0.379596i
$301$	2.76492e7			1.01387
$302$	6.55331e6	−	1.31433e7i	0.237925	−	0.477180i
$303$		−	7.09035e6i		−	0.254882i
$304$	6.19549e6	+	1.77706e6i	0.220524	+	0.0632532i
$305$	2.85995e6			0.100800
$306$	−1.74203e7	−	8.68590e6i	−0.607984	−	0.303145i
$307$			5.68676e6i			0.196539i	0.995160	+	0.0982697i	$0.0313308\pi$
$307$			5.68676e6i			0.196539i	−0.995160	+	0.0982697i	$0.968669\pi$
$308$	1.54809e7	+	2.05456e7i	0.529840	+	0.703180i
$309$	−1.28027e7			−0.433938
$310$	2.46930e6	−	4.95240e6i	0.0828874	−	0.166238i
$311$			3.40240e7i			1.13111i	0.824711	+	0.565554i	$0.191338\pi$
$311$			3.40240e7i			1.13111i	−0.824711	+	0.565554i	$0.808662\pi$
$312$	628152.	−	116382.i	0.0206824	−	0.00383197i
$313$	1.98948e7			0.648795			0.324398	−	0.945921i	$-0.394838\pi$
$313$	1.98948e7			0.648795			0.324398	+	0.945921i	$0.394838\pi$
$314$	−2.51885e6	−	1.25592e6i	−0.0813605	−	0.0405669i
$315$		−	4.32410e6i		−	0.138345i
$316$	2.63023e7	−	1.98186e7i	0.833552	−	0.628074i
$317$	4.51404e7			1.41706			0.708530	−	0.705681i	$-0.249359\pi$
$317$	4.51404e7			1.41706			0.708530	+	0.705681i	$0.249359\pi$
$318$	5.57848e6	−	1.11881e7i	0.173474	−	0.347918i
$319$			5.37502e7i			1.65580i
$320$	1.05458e7	−	4.04672e6i	0.321833	−	0.123496i
$321$	1.23354e7			0.372940
$322$	−1.74042e7	−	8.67784e6i	−0.521298	−	0.259923i
$323$		−	1.07723e7i		−	0.319668i
$324$	−5.62299e6	−	7.46258e6i	−0.165323	−	0.219409i
$325$	888832.			0.0258922
$326$	1.86662e7	−	3.74367e7i	0.538770	−	1.08055i
$327$			2.98930e7i			0.854922i
$328$	−5.03306e6	−	2.71650e7i	−0.142630	−	0.769819i
$329$	6.77301e6			0.190193
$330$	−8.48864e6	−	4.23249e6i	−0.236209	−	0.117775i
$331$			2.76425e7i			0.762243i	0.924525	+	0.381121i	$0.124462\pi$
$331$			2.76425e7i			0.762243i	−0.924525	+	0.381121i	$0.875538\pi$
$332$	2.86481e7	−	2.15861e7i	0.782854	−	0.589874i
$333$	−3.17808e7			−0.860660
$334$	2.18432e6	−	4.38086e6i	0.0586243	−	0.117576i
$335$			7.70545e6i			0.204957i
$336$	−6.16272e6	+	2.14855e7i	−0.162463	+	0.566406i
$337$	3.15251e7			0.823696			0.411848	−	0.911253i	$-0.364883\pi$
$337$	3.15251e7			0.823696			0.411848	+	0.911253i	$0.364883\pi$
$338$	3.45272e7	+	1.72155e7i	0.894153	+	0.445830i
$339$		−	1.90548e7i		−	0.489109i
$340$	−1.13609e7	−	1.50776e7i	−0.289051	−	0.383616i
$341$	−2.28548e7			−0.576387
$342$	−1.99653e6	+	4.00422e6i	−0.0499112	+	0.100101i
$343$			4.39271e7i			1.08855i
$344$	−4.93009e7	+	9.13433e6i	−1.21110	+	0.224389i
$345$	7.17070e6			0.174624
$346$	−3.28188e7	−	1.63637e7i	−0.792309	−	0.395050i
$347$		−	4.77274e7i		−	1.14230i	−0.820846	−	0.571149i	$-0.806498\pi$
$347$		−	4.77274e7i		−	1.14230i	0.820846	−	0.571149i	$-0.193502\pi$
$348$	−3.72991e7	+	2.81046e7i	−0.885035	+	0.666867i
$349$	−4.37619e7			−1.02949			−0.514743	−	0.857345i	$-0.672112\pi$
$349$	−4.37619e7			−1.02949			−0.514743	+	0.857345i	$0.672112\pi$
$350$	−1.38767e7	+	2.78309e7i	−0.323654	+	0.649117i
$351$			1.35309e6i			0.0312899i
$352$	−3.43913e7	−	3.15201e7i	−0.788534	−	0.722703i
$353$	−6.05613e7			−1.37680			−0.688401	−	0.725331i	$-0.741687\pi$
$353$	−6.05613e7			−1.37680			−0.688401	+	0.725331i	$0.741687\pi$
$354$	−1.41734e7	−	7.06695e6i	−0.319495	−	0.159302i
$355$			2.31057e7i			0.516457i
$356$	−1.19479e7	−	1.58568e7i	−0.264815	−	0.351451i
$357$	3.73574e7			0.821054
$358$	3.19641e7	−	6.41069e7i	0.696649	−	1.39719i
$359$			6.33798e7i			1.36983i	0.728622	+	0.684916i	$0.240161\pi$
$359$			6.33798e7i			1.36983i	−0.728622	+	0.684916i	$0.759839\pi$
$360$	1.42853e6	+	7.71024e6i	0.0306184	+	0.165257i
$361$	−2.47610e6			−0.0526316
$362$	1.42218e7	+	7.09110e6i	0.299799	+	0.149482i
$363$			4.93361e6i			0.103144i
$364$	931644.	−	701986.i	0.0193173	−	0.0145554i
$365$	−3.13345e7			−0.644384
$366$	4.57940e6	−	9.18439e6i	0.0934039	−	0.187330i
$367$			7.53606e7i			1.52457i	0.647244	+	0.762283i	$0.275921\pi$
$367$			7.53606e7i			1.52457i	−0.647244	+	0.762283i	$0.724079\pi$
$368$	3.39000e7	+	9.72359e6i	0.680230	+	0.195112i
$369$	1.91790e7			0.381722
$370$	−2.75837e7	−	1.37534e7i	−0.544563	−	0.271523i
$371$		−	2.28279e7i		−	0.447038i
$372$	−1.19502e7	−	1.58597e7i	−0.232137	−	0.308082i
$373$	9.87750e7			1.90336			0.951679	−	0.307096i	$-0.0993571\pi$
$373$	9.87750e7			1.90336			0.951679	+	0.307096i	$0.0993571\pi$
$374$	−3.47908e7	+	6.97761e7i	−0.665043	+	1.33380i
$375$		−	2.44795e7i		−	0.464204i
$376$	−1.20768e7	+	2.23756e6i	−0.227190	+	0.0420931i
$377$	2.43731e6			0.0454870
$378$	−4.23675e7	−	2.11247e7i	−0.784437	−	0.391125i
$379$		−	9.59013e7i		−	1.76160i	−0.473491	−	0.880799i	$-0.657006\pi$
$379$		−	9.59013e7i		−	1.76160i	0.473491	−	0.880799i	$-0.342994\pi$
$380$	−3.46573e6	+	2.61140e6i	−0.0631603	+	0.0475908i
$381$	−3.47466e7			−0.628256
$382$	2.16305e7	−	4.33819e7i	0.388040	−	0.778249i
$383$		−	4.83660e7i		−	0.860882i	−0.902619	−	0.430441i	$-0.858358\pi$
$383$		−	4.83660e7i		−	0.860882i	0.902619	−	0.430441i	$-0.141642\pi$
$384$	3.89060e6	−	4.03464e7i	0.0687105	−	0.712543i
$385$	−1.73199e7			−0.303504
$386$	−4.14366e7	−	2.06606e7i	−0.720481	−	0.359236i
$387$		−	3.48074e7i		−	0.600535i
$388$	−1.83151e7	−	2.43069e7i	−0.313555	−	0.416136i
$389$	2.77967e7			0.472220			0.236110	−	0.971726i	$-0.424127\pi$
$389$	2.77967e7			0.472220			0.236110	+	0.971726i	$0.424127\pi$
$390$	−191923.	+	384919.i	−0.00323544	+	0.00648897i
$391$		−	5.89427e7i		−	0.986052i
$392$	−3.53830e6	−	1.90973e7i	−0.0587403	−	0.317040i
$393$	−4.70159e7			−0.774582
$394$	3.25913e7	+	1.62502e7i	0.532860	+	0.265688i
$395$			2.21729e7i			0.359775i
$396$	2.58646e7	−	1.94888e7i	0.416506	−	0.313834i
$397$	8.91953e7			1.42551			0.712756	−	0.701412i	$-0.247447\pi$
$397$	8.91953e7			1.42551			0.712756	+	0.701412i	$0.247447\pi$
$398$	−1.86125e7	+	3.73291e7i	−0.295227	+	0.592104i
$399$		−	8.58693e6i		−	0.135182i
$400$	1.55489e7	−	5.42091e7i	0.242952	−	0.847017i
$401$	−2.66394e6			−0.0413134			−0.0206567	−	0.999787i	$-0.506576\pi$
$401$	−2.66394e6			−0.0413134			−0.0206567	+	0.999787i	$0.506576\pi$
$402$	2.47451e7	+	1.23381e7i	0.380901	+	0.189920i
$403$			1.03636e6i			0.0158341i
$404$	1.41287e7	+	1.87510e7i	0.214269	+	0.284368i
$405$	6.29096e6			0.0947004
$406$	−3.80519e7	+	7.63165e7i	−0.568589	+	1.14036i
$407$			1.27296e8i			1.88813i
$408$	−6.66113e7	+	1.23415e7i	−0.980770	+	0.181714i
$409$	−8.84457e7			−1.29273			−0.646364	−	0.763030i	$-0.723711\pi$
$409$	−8.84457e7			−1.29273			−0.646364	+	0.763030i	$0.723711\pi$
$410$	1.66462e7	+	8.29991e6i	0.241526	+	0.120426i
$411$		−	6.65374e7i		−	0.958385i
$412$	3.38579e7	−	2.55116e7i	0.484137	−	0.364793i
$413$	−2.89189e7			−0.410518
$414$	−1.09245e7	+	2.19100e7i	−0.153957	+	0.308774i
$415$			2.41503e7i			0.337893i
$416$	−1.42929e6	+	1.55948e6i	−0.0198536	+	0.0216621i
$417$	9.69408e7			1.33690
$418$	1.60387e7	+	7.99699e6i	0.219604	+	0.109496i
$419$			2.40174e7i			0.326500i	0.986585	+	0.163250i	$0.0521978\pi$
$419$			2.40174e7i			0.326500i	−0.986585	+	0.163250i	$0.947802\pi$
$420$	−9.05614e6	−	1.20189e7i	−0.122235	−	0.162225i
$421$	1.78676e7			0.239453			0.119726	−	0.992807i	$-0.461798\pi$
$421$	1.78676e7			0.239453			0.119726	+	0.992807i	$0.461798\pi$
$422$	2.18052e7	−	4.37322e7i	0.290150	−	0.581921i
$423$		−	8.52647e6i		−	0.112654i
$424$	7.54153e6	+	4.07040e7i	0.0989377	+	0.533998i
$425$	−9.42547e7			−1.22782
$426$	7.42012e7	+	3.69972e7i	0.959803	+	0.478564i
$427$		−	1.87395e7i		−	0.240699i
$428$	−3.26221e7	+	2.45805e7i	−0.416083	+	0.313515i
$429$	1.77636e6			0.0224988
$430$	1.50632e7	−	3.02107e7i	0.189458	−	0.379975i
$431$		−	1.36332e8i		−	1.70281i	−0.524506	−	0.851407i	$-0.675750\pi$
$431$		−	1.36332e8i		−	1.70281i	0.524506	−	0.851407i	$-0.324250\pi$
$432$	8.25237e7	+	2.36704e7i	1.02359	+	0.293599i
$433$	−6.16047e7			−0.758840			−0.379420	−	0.925225i	$-0.623876\pi$
$433$	−6.16047e7			−0.758840			−0.379420	+	0.925225i	$0.623876\pi$
$434$	−3.24501e7	−	1.61798e7i	−0.396960	−	0.197927i
$435$		−	3.14432e7i		−	0.381996i
$436$	−5.95669e7	−	7.90545e7i	−0.718697	−	0.953822i
$437$	−1.35485e7			−0.162348
$438$	−5.01733e7	+	1.00627e8i	−0.597105	+	1.19755i
$439$			1.61483e8i			1.90869i	0.298713	+	0.954343i	$0.403443\pi$
$439$			1.61483e8i			1.90869i	−0.298713	+	0.954343i	$0.596557\pi$
$440$	3.08829e7	−	5.72189e6i	0.362543	−	0.0671710i
$441$	1.34831e7			0.157207
$442$	3.16401e6	+	1.57760e6i	0.0366414	+	0.0182696i
$443$			5.94878e7i			0.684252i	0.939654	+	0.342126i	$0.111147\pi$
$443$			5.94878e7i			0.684252i	−0.939654	+	0.342126i	$0.888853\pi$
$444$	−8.83350e7	+	6.65597e7i	−1.00922	+	0.760436i
$445$	1.33673e7			0.151692
$446$	1.09329e7	−	2.19270e7i	0.123234	−	0.247157i
$447$			5.61818e7i			0.629032i
$448$	−2.65157e7	−	6.91005e7i	−0.294896	−	0.768505i
$449$	5.06345e7			0.559381			0.279690	−	0.960090i	$-0.409768\pi$
$449$	5.06345e7			0.559381			0.279690	+	0.960090i	$0.409768\pi$
$450$	3.50360e7	+	1.74692e7i	0.384483	+	0.191706i
$451$		−	7.68204e7i		−	0.837427i
$452$	3.79700e7	+	5.03920e7i	0.411173	+	0.545690i
$453$	3.54822e7			0.381695
$454$	−2.48950e7	+	4.99292e7i	−0.266039	+	0.533565i
$455$			785377.i			0.00833765i
$456$	2.83682e6	+	1.53112e7i	0.0299183	+	0.161479i
$457$	−1.24003e8			−1.29922			−0.649610	−	0.760267i	$-0.725068\pi$
$457$	−1.24003e8			−1.29922			−0.649610	+	0.760267i	$0.725068\pi$
$458$	5.98955e7	+	2.98643e7i	0.623445	+	0.310854i
$459$		−	1.43486e8i		−	1.48379i
$460$	−1.89635e7	+	1.42888e7i	−0.194825	+	0.146799i
$461$	4.15495e7			0.424095			0.212047	−	0.977259i	$-0.431987\pi$
$461$	4.15495e7			0.424095			0.212047	+	0.977259i	$0.431987\pi$
$462$	−2.77330e7	+	5.56209e7i	−0.281236	+	0.564043i
$463$			3.90890e7i			0.393832i	0.980420	+	0.196916i	$0.0630927\pi$
$463$			3.90890e7i			0.393832i	−0.980420	+	0.196916i	$0.936907\pi$
$464$	4.26374e7	−	1.48650e8i	0.426813	−	1.48802i
$465$	1.33698e7			0.132973
$466$	5.57321e6	+	2.77884e6i	0.0550741	+	0.0274603i
$467$		−	1.69657e8i		−	1.66580i	−0.553425	−	0.832899i	$-0.686680\pi$
$467$		−	1.69657e8i		−	1.66580i	0.553425	−	0.832899i	$-0.313320\pi$
$468$	−883724.	−	1.17284e6i	−0.00862142	−	0.0114420i
$469$	5.04891e7			0.489417
$470$	3.68991e6	−	7.40045e6i	0.0355404	−	0.0712795i
$471$		−	6.80002e6i		−	0.0650799i
$472$	5.15649e7	−	9.55379e6i	0.490374	−	0.0908551i
$473$	−1.39419e8			−1.31746
$474$	7.12055e7	+	3.55035e7i	0.668619	+	0.333378i
$475$			2.16653e7i			0.202155i
$476$	−9.87947e7	+	7.44409e7i	−0.916036	+	0.690225i
$477$	−2.87378e7			−0.264788
$478$	4.55925e7	−	9.14399e7i	0.417455	−	0.837244i
$479$		−	1.19896e8i		−	1.09093i	−0.838134	−	0.545465i	$-0.816353\pi$
$479$		−	1.19896e8i		−	1.09093i	0.838134	−	0.545465i	$-0.183647\pi$
$480$	2.01185e7	+	1.84389e7i	0.181916	+	0.166729i
$481$	5.77226e6			0.0518694
$482$	1.79021e8	+	8.92613e7i	1.59869	+	0.797117i
$483$		−	4.69852e7i		−	0.416985i
$484$	−9.83106e6	−	1.30473e7i	−0.0867090	−	0.115076i
$485$	2.04908e7			0.179611
$486$	−4.44711e7	+	8.91908e7i	−0.387409	+	0.776983i
$487$			9.71669e7i			0.841262i	0.907232	+	0.420631i	$0.138191\pi$
$487$			9.71669e7i			0.841262i	−0.907232	+	0.420631i	$0.861809\pi$
$488$	6.19087e6	+	3.34141e7i	0.0532712	+	0.287522i
$489$	1.01066e8			0.864329
$490$	1.17025e7	+	5.83493e6i	0.0994694	+	0.0495961i
$491$		−	1.28590e8i		−	1.08634i	−0.839624	−	0.543168i	$-0.817225\pi$
$491$		−	1.28590e8i		−	1.08634i	0.839624	−	0.543168i	$-0.182775\pi$
$492$	5.33084e7	−	4.01674e7i	0.447610	−	0.337271i
$493$	−2.58461e8			−2.15702
$494$	362625.	−	727277.i	0.00300799	−	0.00603280i
$495$			2.18039e7i			0.179771i
$496$	6.32064e7	+	1.81296e7i	0.517984	+	0.148574i
$497$	1.51398e8			1.23325
$498$	7.75559e7	+	3.86699e7i	0.627953	+	0.313101i
$499$			5.54855e7i			0.446558i	0.974755	+	0.223279i	$0.0716761\pi$
$499$			5.54855e7i			0.446558i	−0.974755	+	0.223279i	$0.928324\pi$
$500$	4.87796e7	+	6.47381e7i	0.390237	+	0.517904i
$501$	1.18268e7			0.0940489
$502$	−6.98078e7	+	1.40006e8i	−0.551814	+	1.10671i
$503$		−	4.66881e7i		−	0.366861i	−0.983033	−	0.183431i	$-0.941280\pi$
$503$		−	4.66881e7i		−	0.366861i	0.983033	−	0.183431i	$-0.0587203\pi$
$504$	5.05205e7	−	9.36029e6i	0.394617	−	0.0731135i
$505$	−1.58071e7			−0.122738
$506$	8.77591e7	+	4.37572e7i	0.677392	+	0.337752i
$507$			9.32115e7i			0.715230i
$508$	9.18902e7	−	6.92384e7i	0.700935	−	0.528149i
$509$	−6.56054e7			−0.497492			−0.248746	−	0.968569i	$-0.580019\pi$
$509$	−6.56054e7			−0.497492			−0.248746	+	0.968569i	$0.580019\pi$
$510$	2.03522e7	−	4.08181e7i	0.153427	−	0.307711i
$511$			2.05316e8i			1.53872i
$512$	7.01080e7	+	1.14452e8i	0.522345	+	0.852734i
$513$	−3.29815e7			−0.244297
$514$	−2.13569e8	−	1.06487e8i	−1.57271	−	0.784163i
$515$			2.85422e7i			0.208961i
$516$	−7.28985e7	−	9.67476e7i	−0.530602	−	0.704192i
$517$	−3.41523e7			−0.247143
$518$	−9.01179e7	+	1.80740e8i	−0.648368	+	1.30036i
$519$		−	8.85993e7i		−	0.633765i
$520$	−259460.	−	1.40039e6i	−0.00184528	−	0.00995954i
$521$	−3.52168e7			−0.249021			−0.124511	−	0.992218i	$-0.539736\pi$
$521$	−3.52168e7			−0.249021			−0.124511	+	0.992218i	$0.539736\pi$
$522$	9.60741e7	+	4.79032e7i	0.675453	+	0.336785i
$523$			1.22732e8i			0.857933i	0.903320	+	0.428967i	$0.141122\pi$
$523$			1.22732e8i			0.857933i	−0.903320	+	0.428967i	$0.858878\pi$
$524$	1.24337e8	−	9.36872e7i	0.864188	−	0.651158i
$525$	−7.51336e7			−0.519226
$526$	−7.40309e7	+	1.48476e8i	−0.508693	+	1.02023i
$527$		−	1.09899e8i		−	0.750862i
$528$	3.10750e7	−	1.08339e8i	0.211110	−	0.736007i
$529$	7.39023e7			0.499219
$530$	−2.49427e7	−	1.24366e7i	−0.167539	−	0.0835359i
$531$			3.64058e7i			0.243157i
$532$	1.71109e7	+	2.27088e7i	0.113642	+	0.150820i
$533$	−3.48344e6			−0.0230052
$534$	2.14039e7	−	4.29273e7i	0.140562	−	0.281910i
$535$		−	2.75004e7i		−	0.179588i
$536$	−9.00263e7	+	1.66798e7i	−0.584622	+	0.108317i
$537$	1.73066e8			1.11761
$538$	−1.81392e8	−	9.04434e7i	−1.16486	−	0.580804i
$539$		−	5.40056e7i		−	0.344884i
$540$	−4.61634e7	+	3.47838e7i	−0.293168	+	0.220900i
$541$	1.84803e8			1.16712			0.583562	−	0.812068i	$-0.301658\pi$
$541$	1.84803e8			1.16712			0.583562	+	0.812068i	$0.301658\pi$
$542$	−9.12489e7	+	1.83008e8i	−0.573099	+	1.14940i
$543$			3.83940e7i			0.239808i
$544$	1.51566e8	−	1.65373e8i	0.941470	−	1.02723i
$545$	6.66430e7			0.411685
$546$	2.52214e6	+	1.25756e6i	0.0154950	+	0.00772591i
$547$		−	1.70180e8i		−	1.03979i	−0.854230	−	0.519895i	$-0.825971\pi$
$547$		−	1.70180e8i		−	1.03979i	0.854230	−	0.519895i	$-0.174029\pi$
$548$	1.32587e8	+	1.75964e8i	0.805674	+	1.06925i
$549$	−2.35910e7			−0.142570
$550$	6.99718e7	−	1.40335e8i	0.420567	−	0.843484i
$551$			5.94095e7i			0.355142i
$552$	1.55222e7	+	8.37786e7i	0.0922863	+	0.498099i
$553$	1.45285e8			0.859105
$554$	−1.53972e8	−	7.67712e7i	−0.905547	−	0.451512i
$555$		−	7.44665e7i		−	0.435594i
$556$	−2.56368e8	+	1.93171e8i	−1.49156	+	1.12387i
$557$	−1.27648e8			−0.738664			−0.369332	−	0.929298i	$-0.620413\pi$
$557$	−1.27648e8			−0.738664			−0.369332	+	0.929298i	$0.620413\pi$
$558$	−2.03686e7	+	4.08511e7i	−0.117236	+	0.235126i
$559$			6.32198e6i			0.0361924i
$560$	4.78994e7	+	1.37391e7i	0.272751	+	0.0782337i
$561$	−1.88371e8			−1.06691
$562$	8.21614e7	+	4.09662e7i	0.462870	+	0.230790i
$563$		−	1.68278e8i		−	0.942978i	−0.881872	−	0.471489i	$-0.843717\pi$
$563$		−	1.68278e8i		−	0.942978i	0.881872	−	0.471489i	$-0.156283\pi$
$564$	−1.78573e7	−	2.36994e7i	−0.0995358	−	0.132099i
$565$	−4.24805e7			−0.235529
$566$	9.89080e7	−	1.98369e8i	0.545484	−	1.09402i
$567$		−	4.12208e7i		−	0.226135i
$568$	−2.69955e8	+	5.00164e7i	−1.47315	+	0.272940i
$569$	2.36146e8			1.28187			0.640933	−	0.767597i	$-0.278547\pi$
$569$	2.36146e8			1.28187			0.640933	+	0.767597i	$0.278547\pi$
$570$	−9.38242e6	−	4.67813e6i	−0.0506629	−	0.0252609i
$571$			1.96411e8i			1.05501i	0.849551	+	0.527506i	$0.176873\pi$
$571$			1.96411e8i			1.05501i	−0.849551	+	0.527506i	$0.823127\pi$
$572$	−4.69773e6	+	3.53970e6i	−0.0251015	+	0.0189138i
$573$	1.17116e8			0.622519
$574$	5.43843e7	−	1.09073e8i	0.287566	−	0.576740i
$575$			1.18546e8i			0.623569i
$576$	−8.69899e7	+	3.33804e7i	−0.455199	+	0.174672i
$577$	1.75233e8			0.912198			0.456099	−	0.889929i	$-0.349246\pi$
$577$	1.75233e8			0.912198			0.456099	+	0.889929i	$0.349246\pi$
$578$	−1.62712e8	−	8.11292e7i	−0.842628	−	0.420140i
$579$		−	1.11864e8i		−	0.576310i
$580$	6.26559e7	+	8.31540e7i	0.321128	+	0.426186i
$581$	1.58242e8			0.806853
$582$	3.28101e7	−	6.58036e7i	0.166433	−	0.333796i
$583$			1.15108e8i			0.580896i
$584$	−6.78291e7	−	3.66096e8i	−0.340548	−	1.83804i
$585$	988703.			0.00493854
$586$	6.81361e6	+	3.39731e6i	0.0338598	+	0.0168827i
$587$		−	2.00189e8i		−	0.989751i	−0.868964	−	0.494875i	$-0.835214\pi$
$587$		−	2.00189e8i		−	0.989751i	0.868964	−	0.494875i	$-0.164786\pi$
$588$	3.74764e7	−	2.82381e7i	0.184343	−	0.138901i
$589$	−2.52612e7			−0.123625
$590$	−1.57550e7	+	3.15980e7i	−0.0767116	+	0.153852i
$591$			8.79852e7i			0.426233i
$592$	1.00978e8	−	3.52045e8i	0.486699	−	1.69681i
$593$	−3.18572e8			−1.52772			−0.763860	−	0.645382i	$-0.776698\pi$
$593$	−3.18572e8			−1.52772			−0.763860	+	0.645382i	$0.776698\pi$
$594$	2.13635e8	+	1.06520e8i	1.01932	+	0.508241i
$595$		−	8.32839e7i		−	0.395376i
$596$	−1.11952e8	−	1.48577e8i	−0.528801	−	0.701801i
$597$	−1.00776e8			−0.473622
$598$	1.98418e6	−	3.97945e6i	0.00927850	−	0.0186089i
$599$			2.78200e8i			1.29442i	0.762311	+	0.647211i	$0.224065\pi$
$599$			2.78200e8i			1.29442i	−0.762311	+	0.647211i	$0.775935\pi$
$600$	1.33970e8	−	2.48215e7i	0.620229	−	0.114914i
$601$	3.80068e6			0.0175080			0.00875402	−	0.999962i	$-0.497213\pi$
$601$	3.80068e6			0.0175080			0.00875402	+	0.999962i	$0.497213\pi$
$602$	−1.97952e8	−	9.87002e7i	−0.907341	−	0.452406i
$603$		−	6.35603e7i		−	0.289890i
$604$	−9.38356e7	+	7.07043e7i	−0.425850	+	0.320875i
$605$	1.09989e7			0.0496688
$606$	−2.53106e7	+	5.07627e7i	−0.113733	+	0.228101i
$607$			1.91879e8i			0.857950i	0.903316	+	0.428975i	$0.141125\pi$
$607$			1.91879e8i			0.857950i	−0.903316	+	0.428975i	$0.858875\pi$
$608$	−3.80124e7	−	3.48389e7i	−0.169128	−	0.155008i
$609$	−2.06028e8			−0.912167
$610$	−2.04755e7	−	1.02092e7i	−0.0902081	−	0.0449784i
$611$			1.54864e6i			0.00678934i
$612$	9.37130e7	+	1.24372e8i	0.408833	+	0.542584i
$613$	1.79924e7			0.0781104			0.0390552	−	0.999237i	$-0.487565\pi$
$613$	1.79924e7			0.0781104			0.0390552	+	0.999237i	$0.487565\pi$
$614$	2.03002e7	−	4.07138e7i	0.0876989	−	0.175888i
$615$			4.49390e7i			0.193196i
$616$	−3.74921e7	−	2.02357e8i	−0.160397	−	0.865716i
$617$	873438.			0.00371858			0.00185929	−	0.999998i	$-0.499408\pi$
$617$	873438.			0.00371858			0.00185929	+	0.999998i	$0.499408\pi$
$618$	9.16600e7	+	4.57023e7i	0.388342	+	0.193630i
$619$			6.52368e7i			0.275056i	0.990498	+	0.137528i	$0.0439157\pi$
$619$			6.52368e7i			0.275056i	−0.990498	+	0.137528i	$0.956084\pi$
$620$	−3.53574e7	+	2.66415e7i	−0.148356	+	0.111785i
$621$	−1.80466e8			−0.753563
$622$	1.21456e8	−	2.43592e8i	0.504718	−	1.01226i
$623$		−	8.75875e7i		−	0.362225i
$624$	−4.91264e6	−	1.40910e6i	−0.0202191	−	0.00579948i
$625$	1.60556e8			0.657636
$626$	−1.42435e8	−	7.10191e7i	−0.580623	−	0.289503i
$627$			4.32988e7i			0.175660i
$628$	1.35502e7	+	1.79832e7i	0.0547100	+	0.0726086i
$629$	−6.12110e8			−2.45967
$630$	−1.54359e7	+	3.09580e7i	−0.0617319	+	0.123809i
$631$		−	9.10812e7i		−	0.362527i	−0.983435	−	0.181264i	$-0.941981\pi$
$631$		−	9.10812e7i		−	0.362527i	0.983435	−	0.181264i	$-0.0580187\pi$
$632$	−2.59056e8	+	4.79971e7i	−1.02622	+	0.190136i
$633$	1.18062e8			0.465476
$634$	−3.23179e8	−	1.61139e8i	−1.26816	−	0.632314i
$635$			7.74634e7i			0.302535i
$636$	−7.98772e7	+	6.01868e7i	−0.310493	+	0.233954i
$637$	−2.44890e6			−0.00947441
$638$	1.91873e8	−	3.84819e8i	0.738844	−	1.48182i
$639$		−	1.90593e8i		−	0.730474i
$640$	−8.99476e7	−	8.67365e6i	−0.343123	−	0.0330874i
$641$	−5.68906e7			−0.216006			−0.108003	−	0.994151i	$-0.534446\pi$
$641$	−5.68906e7			−0.216006			−0.108003	+	0.994151i	$0.534446\pi$
$642$	−8.83144e7	−	4.40341e7i	−0.333754	−	0.166412i
$643$			1.16275e8i			0.437374i	0.975795	+	0.218687i	$0.0701773\pi$
$643$			1.16275e8i			0.437374i	−0.975795	+	0.218687i	$0.929823\pi$
$644$	9.36261e7	+	1.24256e8i	0.350541	+	0.465223i
$645$	8.15582e7			0.303941
$646$	−3.84540e7	+	7.71229e7i	−0.142641	+	0.286079i
$647$			4.90342e8i			1.81045i	0.424932	+	0.905225i	$0.360298\pi$
$647$			4.90342e8i			1.81045i	−0.424932	+	0.905225i	$0.639702\pi$
$648$	1.36179e7	+	7.35002e7i	0.0500478	+	0.270124i
$649$	1.45821e8			0.533441
$650$	−6.36351e6	−	3.17289e6i	−0.0231716	−	0.0115535i
$651$		−	8.76039e7i		−	0.317527i
$652$	−2.67278e8	+	2.01392e8i	−0.964317	+	0.726605i
$653$	−4.41624e8			−1.58604			−0.793018	−	0.609199i	$-0.791491\pi$
$653$	−4.41624e8			−1.58604			−0.793018	+	0.609199i	$0.791491\pi$
$654$	1.06710e8	−	2.14016e8i	0.381479	−	0.765091i
$655$			1.04817e8i			0.372998i
$656$	−6.09380e7	+	2.12452e8i	−0.215862	+	0.752574i
$657$	2.58471e8			0.911412
$658$	−4.84907e7	−	2.41778e7i	−0.170208	−	0.0848669i
$659$		−	3.14533e7i		−	0.109903i	−0.998489	−	0.0549516i	$-0.982500\pi$
$659$		−	3.14533e7i		−	0.109903i	0.998489	−	0.0549516i	$-0.0175004\pi$
$660$	4.56648e7	+	6.06042e7i	0.158836	+	0.210800i
$661$	1.10180e8			0.381504			0.190752	−	0.981638i	$-0.438907\pi$
$661$	1.10180e8			0.381504			0.190752	+	0.981638i	$0.438907\pi$
$662$	9.86761e7	−	1.97904e8i	0.340125	−	0.682150i
$663$			8.54173e6i			0.0293093i
$664$	−2.82159e8	+	5.22777e7i	−0.963807	+	0.178571i
$665$	−1.91436e7			−0.0650965
$666$	2.27531e8	+	1.13449e8i	0.770227	+	0.384040i
$667$			3.25072e8i			1.09547i
$668$	−3.12769e7	+	2.35669e7i	−0.104929	+	0.0790629i
$669$	5.91951e7			0.197700
$670$	2.75063e7	−	5.51664e7i	0.0914552	−	0.183422i
$671$			9.44923e7i			0.312773i
$672$	1.20819e8	−	1.31824e8i	0.398131	−	0.434397i
$673$	1.37869e8			0.452296			0.226148	−	0.974093i	$-0.427387\pi$
$673$	1.37869e8			0.452296			0.226148	+	0.974093i	$0.427387\pi$
$674$	−2.25701e8	−	1.12536e8i	−0.737147	−	0.367546i
$675$			2.88581e8i			0.938332i
$676$	−1.85740e8	−	2.46506e8i	−0.601264	−	0.797970i
$677$	4.07109e8			1.31203			0.656017	−	0.754746i	$-0.272240\pi$
$677$	4.07109e8			1.31203			0.656017	+	0.754746i	$0.272240\pi$
$678$	−6.80204e7	+	1.36421e8i	−0.218248	+	0.437716i
$679$		−	1.34264e8i		−	0.428893i
$680$	2.75141e7	+	1.48502e8i	0.0875040	+	0.472287i
$681$	−1.34791e8			−0.426796
$682$	1.63627e8	+	8.15853e7i	0.515823	+	0.257193i
$683$		−	3.44159e8i		−	1.08018i	−0.841606	−	0.540091i	$-0.818390\pi$
$683$		−	3.44159e8i		−	1.08018i	0.841606	−	0.540091i	$-0.181610\pi$
$684$	2.85880e7	−	2.15408e7i	0.0893336	−	0.0673121i
$685$	−1.48337e8			−0.461508
$686$	1.56808e8	−	3.14492e8i	0.485730	−	0.974174i
$687$			1.61697e8i			0.498691i
$688$	3.85572e8	+	1.10594e8i	1.18397	+	0.339600i
$689$	5.21958e6			0.0159580
$690$	−5.13379e7	−	2.55974e7i	−0.156276	−	0.0779200i
$691$			1.55237e8i			0.470502i	0.971935	+	0.235251i	$0.0755912\pi$
$691$			1.55237e8i			0.470502i	−0.971935	+	0.235251i	$0.924409\pi$
$692$	1.76549e8	+	2.34308e8i	0.532780	+	0.707081i
$693$	1.42868e8			0.429274
$694$	−1.70374e8	+	3.41700e8i	−0.509711	+	1.02227i
$695$		−	2.16118e8i		−	0.643779i
$696$	3.67365e8	−	6.80643e7i	1.08961	−	0.201879i
$697$	3.69396e8			1.09092
$698$	3.13309e8	+	1.56218e8i	0.921312	+	0.459372i
$699$			1.50457e7i			0.0440536i
$700$	1.98697e8	−	1.49717e8i	0.579292	−	0.436492i
$701$	7.17366e7			0.208251			0.104125	−	0.994564i	$-0.466796\pi$
$701$	7.17366e7			0.208251			0.104125	+	0.994564i	$0.466796\pi$
$702$	4.83015e6	−	9.68731e6i	0.0139621	−	0.0280022i
$703$			1.40699e8i			0.404972i
$704$	1.33703e8	+	3.48433e8i	0.383198	+	0.998622i
$705$	1.99786e7			0.0570162
$706$	4.33583e8	+	2.16187e8i	1.23213	+	0.614350i
$707$			1.03574e8i			0.293086i
$708$	7.62460e7	+	1.01190e8i	0.214841	+	0.285128i
$709$	6.55343e8			1.83878			0.919390	−	0.393347i	$-0.128683\pi$
$709$	6.55343e8			1.83878			0.919390	+	0.393347i	$0.128683\pi$
$710$	8.24810e7	−	1.65423e8i	0.230451	−	0.462190i
$711$		−	1.82898e8i		−	0.508863i
$712$	2.89358e7	+	1.56176e8i	0.0801670	+	0.432687i
$713$	−1.38222e8			−0.381337
$714$	−2.67456e8	−	1.33356e8i	−0.734782	−	0.366367i
$715$		−	3.96019e6i		−	0.0108342i
$716$	−4.57688e8	+	3.44864e8i	−1.24690	+	0.939526i
$717$	2.46856e8			0.669709
$718$	2.26248e8	−	4.53761e8i	0.611240	−	1.22590i
$719$		−	3.54721e8i		−	0.954334i	−0.878813	−	0.477167i	$-0.841664\pi$
$719$		−	3.54721e8i		−	0.954334i	0.878813	−	0.477167i	$-0.158336\pi$
$720$	1.72960e7	−	6.03002e7i	0.0463392	−	0.161555i
$721$	1.87020e8			0.498979
$722$	1.77274e7	+	8.83899e6i	0.0471013	+	0.0234850i
$723$			4.83295e8i			1.27879i
$724$	−7.65066e7	−	1.01536e8i	−0.201597	−	0.267550i
$725$	5.19820e8			1.36408
$726$	1.76116e7	−	3.53217e7i	0.0460246	−	0.0923064i
$727$			6.62723e8i			1.72476i	0.506260	+	0.862381i	$0.331027\pi$
$727$			6.62723e8i			1.72476i	−0.506260	+	0.862381i	$0.668973\pi$
$728$	−9.17592e6	+	1.70009e6i	−0.0237824	+	0.00440633i
$729$	−3.47217e8			−0.896227
$730$	2.24337e8	+	1.11856e8i	0.576675	+	0.287534i
$731$		−	6.70404e8i		−	1.71626i
$732$	−6.55715e7	+	4.94076e7i	−0.167179	+	0.125968i
$733$	4.71983e8			1.19844			0.599218	−	0.800586i	$-0.295478\pi$
$733$	4.71983e8			1.19844			0.599218	+	0.800586i	$0.295478\pi$
$734$	2.69017e8	−	5.39537e8i	0.680285	−	1.36437i
$735$			3.15926e7i			0.0795652i
$736$	−2.07993e8	−	1.90629e8i	−0.521693	−	0.478140i
$737$	−2.54587e8			−0.635966
$738$	−1.37310e8	−	6.84639e7i	−0.341613	−	0.170330i
$739$		−	1.09317e8i		−	0.270866i	−0.990786	−	0.135433i	$-0.956757\pi$
$739$		−	1.09317e8i		−	0.270866i	0.990786	−	0.135433i	$-0.0432426\pi$
$740$	1.48387e8	+	1.96933e8i	0.366186	+	0.485985i
$741$	1.96339e6			0.00482562
$742$	−8.14893e7	+	1.63434e8i	−0.199475	+	0.400066i
$743$		−	3.61211e8i		−	0.880632i	−0.897843	−	0.440316i	$-0.854866\pi$
$743$		−	3.61211e8i		−	0.880632i	0.897843	−	0.440316i	$-0.145134\pi$
$744$	2.89412e7	+	1.56205e8i	0.0702745	+	0.379294i
$745$	1.25251e8			0.302909
$746$	−7.07170e8	−	3.52599e8i	−1.70336	−	0.849308i
$747$		−	1.99210e8i		−	0.477913i
$748$	4.98163e8	−	3.75362e8i	1.19033	−	0.896902i
$749$	−1.80194e8			−0.428839
$750$	−8.73851e7	+	1.75259e8i	−0.207135	+	0.415428i
$751$			3.77340e7i			0.0890867i	0.999007	+	0.0445434i	$0.0141833\pi$
$751$			3.77340e7i			0.0890867i	−0.999007	+	0.0445434i	$0.985817\pi$
$752$	9.44504e7	+	2.70914e7i	0.222101	+	0.0637056i
$753$	−3.77967e8			−0.885256
$754$	−1.74497e7	−	8.70054e6i	−0.0407075	−	0.0202970i
$755$		−	7.91035e7i		−	0.183804i
$756$	2.27917e8	+	3.02481e8i	0.527486	+	0.700056i
$757$	−5.14247e7			−0.118545			−0.0592726	−	0.998242i	$-0.518878\pi$
$757$	−5.14247e7			−0.118545			−0.0592726	+	0.998242i	$0.518878\pi$
$758$	−3.42341e8	+	6.86596e8i	−0.786053	+	1.57650i
$759$			2.36919e8i			0.541844i
$760$	3.41346e7	−	6.32435e6i	0.0777595	−	0.0144071i
$761$	−3.37064e8			−0.764818			−0.382409	−	0.923993i	$-0.624905\pi$
$761$	−3.37064e8			−0.764818			−0.382409	+	0.923993i	$0.624905\pi$
$762$	2.48765e8	+	1.24036e8i	0.562243	+	0.280338i
$763$		−	4.36671e8i		−	0.983062i
$764$	−3.09723e8	+	2.33374e8i	−0.694534	+	0.523326i
$765$	−1.04845e8			−0.234188
$766$	−1.72653e8	+	3.46272e8i	−0.384139	+	0.770425i
$767$		−	6.61229e6i		−	0.0146543i
$768$	−1.71880e8	+	2.74968e8i	−0.379438	+	0.607013i
$769$	1.89775e8			0.417312			0.208656	−	0.977989i	$-0.433091\pi$
$769$	1.89775e8			0.417312			0.208656	+	0.977989i	$0.433091\pi$
$770$	1.24000e8	+	6.18274e7i	0.271613	+	0.135428i
$771$		−	5.76561e8i		−	1.25801i
$772$	2.22909e8	+	2.95835e8i	0.484480	+	0.642980i
$773$	−3.47147e8			−0.751580			−0.375790	−	0.926705i	$-0.622629\pi$
$773$	−3.47147e8			−0.751580			−0.375790	+	0.926705i	$0.622629\pi$
$774$	−1.24253e8	+	2.49200e8i	−0.267968	+	0.537434i
$775$			2.21030e8i			0.474838i
$776$	4.43559e7	+	2.39403e8i	0.0949218	+	0.512324i
$777$	−4.87934e8			−1.04015
$778$	−1.99008e8	−	9.92265e7i	−0.422601	−	0.210712i
$779$		−	8.49089e7i		−	0.179614i
$780$	2.74811e6	−	2.07068e6i	0.00579096	−	0.00436344i
$781$	−7.63409e8			−1.60252
$782$	−2.10409e8	+	4.21995e8i	−0.439992	+	0.882443i
$783$			7.91333e8i			1.64844i
$784$	−4.28401e7	+	1.49356e8i	−0.0889001	+	0.309938i
$785$	−1.51599e7			−0.0313391
$786$	3.36606e8	+	1.67834e8i	0.693193	+	0.345630i
$787$		−	7.77357e8i		−	1.59476i	−0.603476	−	0.797381i	$-0.706218\pi$
$787$		−	7.77357e8i		−	1.59476i	0.603476	−	0.797381i	$-0.293782\pi$
$788$	−1.75325e8	−	2.32684e8i	−0.358316	−	0.475541i
$789$	−4.00832e8			−0.816078
$790$	7.91510e7	−	1.58744e8i	0.160537	−	0.321971i
$791$			2.78349e8i			0.562419i
$792$	−2.54745e8	+	4.71984e7i	−0.512779	+	0.0950062i
$793$	4.28478e6			0.00859228
$794$	−6.38585e8	−	3.18403e8i	−1.27573	−	0.636085i
$795$		−	6.73365e7i		−	0.134014i
$796$	2.66509e8	−	2.00812e8i	0.528412	−	0.398154i
$797$	5.55254e8			1.09677			0.548387	−	0.836225i	$-0.315242\pi$
$797$	5.55254e8			1.09677			0.548387	+	0.836225i	$0.315242\pi$
$798$	−3.06530e7	+	6.14773e7i	−0.0603204	+	0.120978i
$799$		−	1.64223e8i		−	0.321954i
$800$	−3.04833e8	+	3.32600e8i	−0.595376	+	0.649609i
$801$	−1.10263e8			−0.214552
$802$	1.90722e7	+	9.50954e6i	0.0369725	+	0.0184347i
$803$		−	1.03529e9i		−	1.99947i
$804$	−1.33117e8	−	1.76667e8i	−0.256133	−	0.339928i
$805$	−1.04748e8			−0.200798
$806$	3.69950e6	−	7.41969e6i	0.00706543	−	0.0141703i
$807$		−	4.89696e8i		−	0.931763i
$808$	−3.42173e7	−	1.84682e8i	−0.0648652	−	0.350098i
$809$	−8.19417e8			−1.54760			−0.773801	−	0.633429i	$-0.781647\pi$
$809$	−8.19417e8			−1.54760			−0.773801	+	0.633429i	$0.781647\pi$
$810$	−4.50395e7	−	2.24570e7i	−0.0847498	−	0.0422568i
$811$			6.14350e8i			1.15174i	0.817542	+	0.575868i	$0.195336\pi$
$811$			6.14350e8i			1.15174i	−0.817542	+	0.575868i	$0.804664\pi$
$812$	5.44858e8	−	4.10546e8i	1.01769	−	0.766820i
$813$	−4.94057e8			−0.919402
$814$	4.54411e8	−	9.11363e8i	0.842512	−	1.68973i
$815$		−	2.25315e8i		−	0.416215i
$816$	5.20953e8	+	1.49426e8i	0.958800	+	0.275014i
$817$	−1.54098e8			−0.282574
$818$	6.33219e8	+	3.15727e8i	1.15689	+	0.576835i
$819$		−	6.47837e6i		−	0.0117927i
$820$	−8.95486e7	−	1.18845e8i	−0.162412	−	0.215545i
$821$	8.00270e8			1.44613			0.723065	−	0.690780i	$-0.242733\pi$
$821$	8.00270e8			1.44613			0.723065	+	0.690780i	$0.242733\pi$
$822$	−2.37520e8	+	4.76368e8i	−0.427646	+	0.857683i
$823$		−	8.94897e8i		−	1.60536i	−0.596408	−	0.802682i	$-0.703406\pi$
$823$		−	8.94897e8i		−	1.60536i	0.596408	−	0.802682i	$-0.296594\pi$
$824$	−3.33472e8	+	6.17847e7i	−0.596043	+	0.110433i
$825$	3.78855e8			0.674700
$826$	2.07042e8	+	1.03233e8i	0.367383	+	0.183180i
$827$			3.99694e8i			0.706661i	0.935499	+	0.353330i	$0.114951\pi$
$827$			3.99694e8i			0.706661i	−0.935499	+	0.353330i	$0.885049\pi$
$828$	1.56425e8	−	1.17865e8i	0.275560	−	0.207632i
$829$	−1.02755e9			−1.80360			−0.901798	−	0.432158i	$-0.857752\pi$
$829$	−1.02755e9			−1.80360			−0.901798	+	0.432158i	$0.857752\pi$
$830$	8.62100e7	−	1.72902e8i	0.150773	−	0.302389i
$831$		−	4.15669e8i		−	0.724344i
$832$	1.57998e7	−	6.06279e6i	0.0274335	−	0.0105270i
$833$	2.59689e8			0.449282
$834$	−6.94038e8	−	3.46052e8i	−1.19642	−	0.596545i
$835$		−	2.63665e7i		−	0.0452890i
$836$	−8.62803e7	−	1.14507e8i	−0.147670	−	0.195981i
$837$	−3.36478e8			−0.573826
$838$	8.57354e7	−	1.71950e8i	0.145690	−	0.292193i
$839$		−	6.44404e8i		−	1.09112i	−0.838072	−	0.545560i	$-0.816317\pi$
$839$		−	6.44404e8i		−	1.09112i	0.838072	−	0.545560i	$-0.183683\pi$
$840$	2.19324e7	+	1.18376e8i	0.0370039	+	0.199722i
$841$	8.30602e8			1.39638
$842$	−1.27921e8	−	6.37824e7i	−0.214292	−	0.106848i
$843$			2.21807e8i			0.370248i
$844$	−3.12224e8	+	2.35258e8i	−0.519324	+	0.391306i
$845$	2.07804e8			0.344417
$846$	−3.04372e7	+	6.10445e7i	−0.0502682	+	0.100817i
$847$		−	7.20692e7i		−	0.118604i
$848$	9.13094e7	−	3.18338e8i	0.149737	−	0.522036i
$849$	5.35527e8			0.875101
$850$	6.74808e8	+	3.36463e8i	1.09881	+	0.547875i
$851$			7.69865e8i			1.24918i
$852$	−3.99167e8	−	5.29756e8i	−0.645410	−	0.856559i
$853$	−3.67847e8			−0.592680			−0.296340	−	0.955083i	$-0.595766\pi$
$853$	−3.67847e8			−0.592680			−0.296340	+	0.955083i	$0.595766\pi$
$854$	−6.68949e7	+	1.34164e8i	−0.107404	+	0.215408i
$855$			2.40997e7i			0.0385578i
$856$	3.21300e8	−	5.95296e7i	0.512259	−	0.0949099i
$857$	−1.15746e9			−1.83892			−0.919461	−	0.393182i	$-0.871374\pi$
$857$	−1.15746e9			−1.83892			−0.919461	+	0.393182i	$0.871374\pi$
$858$	−1.27177e7	−	6.34112e6i	−0.0201347	−	0.0100393i
$859$			6.82772e8i			1.07720i	0.842561	+	0.538600i	$0.181047\pi$
$859$			6.82772e8i			1.07720i	−0.842561	+	0.538600i	$0.818953\pi$
$860$	−2.15688e8	+	1.62519e8i	−0.339101	+	0.255510i
$861$	2.94458e8			0.461332
$862$	−4.86669e8	+	9.76059e8i	−0.759822	+	1.52389i
$863$		−	2.21195e8i		−	0.344146i	−0.985084	−	0.172073i	$-0.944953\pi$
$863$		−	2.21195e8i		−	0.344146i	0.985084	−	0.172073i	$-0.0550465\pi$
$864$	−5.06324e8	−	4.64053e8i	−0.785031	−	0.719493i
$865$	−1.97522e8			−0.305188
$866$	4.41053e8	+	2.19912e8i	0.679105	+	0.338606i
$867$		−	4.39265e8i		−	0.674015i
$868$	1.74566e8	+	2.31676e8i	0.266931	+	0.354259i
$869$	−7.32588e8			−1.11635
$870$	−1.12243e8	+	2.25114e8i	−0.170452	+	0.341858i
$871$			1.15443e7i			0.0174708i
$872$	1.44261e8	+	7.78621e8i	0.217570	+	1.17429i
$873$	−1.69023e8			−0.254041
$874$	9.69993e7	+	4.83645e7i	0.145289	+	0.0724423i
$875$			3.57592e8i			0.533781i
$876$	7.18422e8	−	5.41325e8i	1.06873	−	0.805278i
$877$	1.91647e8			0.284121			0.142061	−	0.989858i	$-0.454627\pi$
$877$	1.91647e8			0.284121			0.142061	+	0.989858i	$0.454627\pi$
$878$	5.76452e8	−	1.15613e9i	0.851686	−	1.70813i
$879$			1.83944e7i			0.0270843i
$880$	−2.41529e8	−	6.92781e7i	−0.354422	−	0.101659i
$881$	5.07899e8			0.742763			0.371381	−	0.928480i	$-0.378884\pi$
$881$	5.07899e8			0.742763			0.371381	+	0.928480i	$0.378884\pi$
$882$	−9.65308e7	−	4.81309e7i	−0.140689	−	0.0701484i
$883$		−	1.96495e8i		−	0.285410i	−0.989765	−	0.142705i	$-0.954420\pi$
$883$		−	1.96495e8i		−	0.285410i	0.989765	−	0.142705i	$-0.0455800\pi$
$884$	−1.70209e7	−	2.25893e7i	−0.0246391	−	0.0326999i
$885$	−8.53035e7			−0.123066
$886$	2.12355e8	−	4.25897e8i	0.305324	−	0.612355i
$887$		−	6.08868e8i		−	0.872473i	−0.899832	−	0.436237i	$-0.856311\pi$
$887$		−	6.08868e8i		−	0.872473i	0.899832	−	0.436237i	$-0.143689\pi$
$888$	8.70026e8	−	1.61196e8i	1.24249	−	0.230205i
$889$	5.07571e8			0.722423
$890$	−9.57016e7	−	4.77174e7i	−0.135753	−	0.0676873i
$891$			2.07852e8i			0.293847i
$892$	−1.56546e8	+	1.17956e8i	−0.220571	+	0.166198i
$893$	−3.77482e7			−0.0530080
$894$	2.00553e8	−	4.02228e8i	0.280684	−	0.562937i
$895$		−	3.85831e8i		−	0.538181i
$896$	−5.68332e7	+	5.89372e8i	−0.0790092	+	0.819342i
$897$	1.07431e7			0.0148852
$898$	−3.62513e8	−	1.80751e8i	−0.500604	−	0.249605i
$899$			6.06097e8i			0.834186i
$900$	−1.88477e8	−	2.50138e8i	−0.258542	−	0.343125i
$901$	−5.53502e8			−0.756737
$902$	−2.74228e8	+	5.49989e8i	−0.373673	+	0.749435i
$903$		−	5.34402e8i		−	0.725779i
$904$	−9.19566e7	−	4.96319e8i	−0.124474	−	0.671824i
$905$	8.55950e7			0.115479
$906$	−2.54031e8	−	1.26662e8i	−0.341588	−	0.170318i
$907$			1.36257e9i			1.82615i	0.407786	+	0.913077i	$0.366301\pi$
$907$			1.36257e9i			1.82615i	−0.407786	+	0.913077i	$0.633699\pi$
$908$	3.56467e8	−	2.68595e8i	0.476170	−	0.358790i
$909$	1.30389e8			0.173600
$910$	2.80358e6	−	5.62283e6i	0.00372039	−	0.00746158i
$911$			2.01475e8i			0.266481i	0.991084	+	0.133241i	$0.0425383\pi$
$911$			2.01475e8i			0.266481i	−0.991084	+	0.133241i	$0.957462\pi$
$912$	3.43469e7	−	1.19746e8i	0.0452796	−	0.157861i
$913$	−7.97923e8			−1.04845
$914$	8.87786e8	+	4.42656e8i	1.16271	+	0.579733i
$915$		−	5.52768e7i		−	0.0721572i
$916$	−3.22209e8	−	4.27621e8i	−0.419229	−	0.556381i
$917$	6.86799e8			0.890680
$918$	−5.12206e8	+	1.02727e9i	−0.662089	+	1.32788i
$919$			9.53855e8i			1.22895i	0.788935	+	0.614477i	$0.210633\pi$
$919$			9.53855e8i			1.22895i	−0.788935	+	0.614477i	$0.789367\pi$
$920$	1.86775e8	−	3.46051e7i	0.239858	−	0.0444402i
$921$	1.09913e8			0.140692
$922$	−2.97470e8	−	1.48320e8i	−0.379533	−	0.189238i
$923$			3.46170e7i			0.0440234i
$924$	3.97103e8	−	2.99214e8i	0.503370	−	0.379285i
$925$	1.23108e9			1.55547
$926$	1.39537e8	−	2.79854e8i	0.175734	−	0.352451i
$927$		−	2.35438e8i		−	0.295554i
$928$	−8.35897e8	+	9.12039e8i	−1.04595	+	1.14122i
$929$	1.08935e9			1.35869			0.679345	−	0.733819i	$-0.262264\pi$
$929$	1.08935e9			1.35869			0.679345	+	0.733819i	$0.262264\pi$
$930$	−9.57195e7	−	4.77264e7i	−0.119001	−	0.0593348i
$931$		−	5.96919e7i		−	0.0739718i
$932$	−2.99811e7	−	3.97896e7i	−0.0370340	−	0.0491498i
$933$	6.57612e8			0.809701
$934$	−6.05630e8	+	1.21465e9i	−0.743305	+	1.49076i
$935$			4.19952e8i			0.513765i
$936$	2.14022e6	+	1.15515e7i	0.00260995	+	0.0140867i
$937$	1.91934e8			0.233310			0.116655	−	0.993173i	$-0.462783\pi$
$937$	1.91934e8			0.233310			0.116655	+	0.993173i	$0.462783\pi$
$938$	−3.61472e8	−	1.80232e8i	−0.437992	−	0.218386i
$939$		−	3.84525e8i		−	0.464439i
$940$	−5.28352e7	+	3.98109e7i	−0.0636121	+	0.0479312i
$941$	8.75876e8			1.05117			0.525586	−	0.850740i	$-0.323846\pi$
$941$	8.75876e8			1.05117			0.525586	+	0.850740i	$0.323846\pi$
$942$	−2.42742e7	+	4.86841e7i	−0.0290397	+	0.0582417i
$943$		−	4.64597e8i		−	0.554041i
$944$	−4.03278e8	−	1.15673e8i	−0.479390	−	0.137504i
$945$	−2.54992e8			−0.302155
$946$	9.98156e8	+	4.97687e8i	1.17903	+	0.587872i
$947$			5.39757e8i			0.635548i	0.948166	+	0.317774i	$0.102935\pi$
$947$			5.39757e8i			0.635548i	−0.948166	+	0.317774i	$0.897065\pi$
$948$	−3.83051e8	−	5.08368e8i	−0.449606	−	0.596696i
$949$	−4.69454e7			−0.0549281
$950$	7.73392e7	−	1.55111e8i	0.0902046	−	0.180913i
$951$		−	8.72469e8i		−	1.01440i
$952$	9.73044e8	−	1.80283e8i	1.12777	−	0.208951i
$953$	1.58037e7			0.0182592			0.00912958	−	0.999958i	$-0.497094\pi$
$953$	1.58037e7			0.0182592			0.00912958	+	0.999958i	$0.497094\pi$
$954$	2.05746e8	+	1.02586e8i	0.236966	+	0.118153i
$955$		−	2.61097e8i		−	0.299772i
$956$	−6.52831e8	+	4.91902e8i	−0.747183	+	0.562996i
$957$	1.03888e9			1.18530
$958$	−4.27994e8	+	8.58381e8i	−0.486790	+	0.976301i
$959$			9.71965e8i			1.10203i
$960$	−7.82145e7	−	2.03829e8i	−0.0884044	−	0.230384i
$961$	6.29789e8			0.709618
$962$	−4.13260e7	−	2.06054e7i	−0.0464192	−	0.0231449i
$963$			2.26844e8i			0.254009i
$964$	−9.63049e8	−	1.27811e9i	−1.07502	−	1.42672i
$965$	−2.49389e8			−0.277520
$966$	−1.67724e8	+	3.36386e8i	−0.186065	+	0.373170i
$967$			9.26100e8i			1.02419i	0.858930	+	0.512093i	$0.171130\pi$
$967$			9.26100e8i			1.02419i	−0.858930	+	0.512093i	$0.828870\pi$
$968$	2.38091e7	+	1.28505e8i	0.0262492	+	0.141676i
$969$	−2.08205e8			−0.228833
$970$	−1.46702e8	−	7.31464e7i	−0.160738	−	0.0801452i
$971$			7.96889e8i			0.870443i	0.900323	+	0.435221i	$0.143330\pi$
$971$			7.96889e8i			0.870443i	−0.900323	+	0.435221i	$0.856670\pi$
$972$	6.36773e8	−	4.79803e8i	0.693404	−	0.522474i
$973$	−1.41609e9			−1.53728
$974$	3.46859e8	−	6.95657e8i	0.375384	−	0.752867i
$975$		−	1.71793e7i		−	0.0185349i
$976$	7.49563e7	−	2.61325e8i	0.0806229	−	0.281081i
$977$	4.11830e8			0.441605			0.220803	−	0.975319i	$-0.429132\pi$
$977$	4.11830e8			0.441605			0.220803	+	0.975319i	$0.429132\pi$
$978$	−7.23573e8	−	3.60778e8i	−0.773510	−	0.385677i
$979$			4.41652e8i			0.470687i
$980$	−6.29536e7	−	8.35492e7i	−0.0668871	−	0.0887696i
$981$	−5.49721e8			−0.582285
$982$	−4.59032e8	+	9.20630e8i	−0.484740	+	0.972189i
$983$			4.34128e8i			0.457043i	0.973539	+	0.228522i	$0.0733892\pi$
$983$			4.34128e8i			0.457043i	−0.973539	+	0.228522i	$0.926611\pi$
$984$	−5.25043e8	+	9.72784e7i	−0.551073	+	0.102101i
$985$	1.96153e8			0.205251
$986$	1.85043e9	+	9.22634e8i	1.93037	+	0.962496i
$987$		−	1.30908e8i		−	0.136149i
$988$	−5.19236e6	+	3.91240e6i	−0.00538386	+	0.00405669i
$989$	−8.43182e8			−0.871631
$990$	7.78340e7	−	1.56103e8i	0.0802165	−	0.160881i
$991$		−	1.87758e9i		−	1.92920i	−0.263725	−	0.964598i	$-0.584951\pi$
$991$		−	1.87758e9i		−	1.92920i	0.263725	−	0.964598i	$-0.415049\pi$
$992$	−3.87803e8	−	3.55427e8i	−0.397261	−	0.364095i
$993$	5.34271e8			0.545650
$994$	−1.08392e9	−	5.40448e8i	−1.10366	−	0.550294i
$995$			2.24667e8i			0.228071i
$996$	−4.17213e8	−	5.53707e8i	−0.422260	−	0.560405i
$997$	1.35522e9			1.36749			0.683744	−	0.729722i	$-0.260350\pi$
$997$	1.35522e9			1.36749			0.683744	+	0.729722i	$0.260350\pi$
$998$	1.98068e8	−	3.97243e8i	0.199261	−	0.399636i
$999$			1.87411e9i			1.87974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.9	✓	54
4.3	odd	2	inner	76.7.b.a.39.10	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.9	✓	54	1.1	even	1	trivial
76.7.b.a.39.10	yes	54	4.3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.15940 - 3.56973i) q^{2} -19.3279i q^{3} +(38.5141 + 51.1142i) q^{4} -43.0893 q^{5} +(-68.9953 + 138.376i) q^{6} +282.338i q^{7} +(-93.2744 - 503.432i) q^{8} +355.433 q^{9} +O(q^{10})\)	\(q+(-7.15940 - 3.56973i) q^{2} -19.3279i q^{3} +(38.5141 + 51.1142i) q^{4} -43.0893 q^{5} +(-68.9953 + 138.376i) q^{6} +282.338i q^{7} +(-93.2744 - 503.432i) q^{8} +355.433 q^{9} +(308.494 + 153.817i) q^{10} -1423.66i q^{11} +(987.930 - 744.397i) q^{12} -64.5564 q^{13} +(1007.87 - 2021.37i) q^{14} +832.825i q^{15} +(-1129.32 + 3937.24i) q^{16} +6845.77 q^{17} +(-2544.69 - 1268.80i) q^{18} -1573.56i q^{19} +(-1659.55 - 2202.48i) q^{20} +5457.00 q^{21} +(-5082.09 + 10192.6i) q^{22} -8610.09i q^{23} +(-9730.28 + 1802.80i) q^{24} -13768.3 q^{25} +(462.185 + 230.449i) q^{26} -20959.8i q^{27} +(-14431.5 + 10874.0i) q^{28} -37754.8 q^{29} +(2972.96 - 5962.53i) q^{30} -16053.5i q^{31} +(22140.2 - 24156.9i) q^{32} -27516.4 q^{33} +(-49011.6 - 24437.5i) q^{34} -12165.7i q^{35} +(13689.2 + 18167.7i) q^{36} -89414.3 q^{37} +(-5617.19 + 11265.8i) q^{38} +1247.74i q^{39} +(4019.13 + 21692.5i) q^{40} +53959.7 q^{41} +(-39068.8 - 19480.0i) q^{42} -97929.6i q^{43} +(72769.5 - 54831.2i) q^{44} -15315.3 q^{45} +(-30735.6 + 61643.1i) q^{46} -23989.0i q^{47} +(76098.5 + 21827.5i) q^{48} +37934.2 q^{49} +(98572.9 + 49149.1i) q^{50} -132314. i q^{51} +(-2486.33 - 3299.75i) q^{52} -80853.1 q^{53} +(-74820.7 + 150060. i) q^{54} +61344.7i q^{55} +(142138. - 26334.9i) q^{56} -30413.6 q^{57} +(270302. + 134774. i) q^{58} +102427. i q^{59} +(-42569.2 + 32075.5i) q^{60} -66372.6 q^{61} +(-57306.6 + 114933. i) q^{62} +100352. i q^{63} +(-244744. + 93914.7i) q^{64} +2781.69 q^{65} +(197001. + 98226.1i) q^{66} -178825. i q^{67} +(263659. + 349916. i) q^{68} -166415. q^{69} +(-43428.4 + 87099.5i) q^{70} -536228. i q^{71} +(-33152.8 - 178936. i) q^{72} +727200. q^{73} +(640153. + 319184. i) q^{74} +266112. i q^{75} +(80431.4 - 60604.4i) q^{76} +401955. q^{77} +(4454.08 - 8933.06i) q^{78} -514579. i q^{79} +(48661.8 - 169653. i) q^{80} -145998. q^{81} +(-386319. - 192621. i) q^{82} -560472. i q^{83} +(210171. + 278930. i) q^{84} -294980. q^{85} +(-349582. + 701117. i) q^{86} +729721. i q^{87} +(-716718. + 132791. i) q^{88} -310222. q^{89} +(109649. + 54671.6i) q^{90} -18226.7i q^{91} +(440098. - 331610. i) q^{92} -310280. q^{93} +(-85634.1 + 171747. i) q^{94} +67803.7i q^{95} +(-466902. - 427922. i) q^{96} -475542. q^{97} +(-271587. - 135415. i) q^{98} -506017. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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