LMFDB - Embedded newform 16.7.f.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,7,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68086533792$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	16.11
Dual form			16.7.f.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.99319 + 6.93213i) q^{2} +(31.6770 + 31.6770i) q^{3} +(-32.1089 - 55.3626i) q^{4} +(69.9376 + 69.9376i) q^{5} +(-346.081 + 93.0969i) q^{6} -445.243 q^{7} +(511.998 - 1.51028i) q^{8} +1277.86i q^{9} +O(q^{10})$	\(q+(-3.99319 + 6.93213i) q^{2} +(31.6770 + 31.6770i) q^{3} +(-32.1089 - 55.3626i) q^{4} +(69.9376 + 69.9376i) q^{5} +(-346.081 + 93.0969i) q^{6} -445.243 q^{7} +(511.998 - 1.51028i) q^{8} +1277.86i q^{9} +(-764.090 + 205.543i) q^{10} +(365.568 - 365.568i) q^{11} +(736.605 - 2770.83i) q^{12} +(1786.18 - 1786.18i) q^{13} +(1777.94 - 3086.49i) q^{14} +4430.82i q^{15} +(-2034.03 + 3555.27i) q^{16} +2879.01 q^{17} +(-8858.29 - 5102.73i) q^{18} +(8638.45 + 8638.45i) q^{19} +(1626.30 - 6117.55i) q^{20} +(-14103.9 - 14103.9i) q^{21} +(1074.38 + 3993.95i) q^{22} -8375.32 q^{23} +(16266.4 + 16170.7i) q^{24} -5842.47i q^{25} +(5249.49 + 19514.6i) q^{26} +(-17386.2 + 17386.2i) q^{27} +(14296.3 + 24649.8i) q^{28} +(13847.6 - 13847.6i) q^{29} +(-30715.0 - 17693.1i) q^{30} -20606.0i q^{31} +(-16523.3 - 28297.0i) q^{32} +23160.2 q^{33} +(-11496.4 + 19957.7i) q^{34} +(-31139.2 - 31139.2i) q^{35} +(70745.6 - 41030.7i) q^{36} +(-3701.07 - 3701.07i) q^{37} +(-94377.8 + 25387.9i) q^{38} +113162. q^{39} +(35913.5 + 35702.3i) q^{40} -45867.1i q^{41} +(154090. - 41450.8i) q^{42} +(-100322. + 100322. i) q^{43} +(-31976.8 - 8500.79i) q^{44} +(-89370.4 + 89370.4i) q^{45} +(33444.2 - 58058.8i) q^{46} -36756.6i q^{47} +(-177052. + 48188.1i) q^{48} +80592.5 q^{49} +(40500.8 + 23330.1i) q^{50} +(91198.3 + 91198.3i) q^{51} +(-156240. - 41535.2i) q^{52} +(-83859.8 - 83859.8i) q^{53} +(-51097.1 - 189950. i) q^{54} +51133.9 q^{55} +(-227964. + 672.443i) q^{56} +547279. i q^{57} +(40697.3 + 151289. i) q^{58} +(43125.2 - 43125.2i) q^{59} +(245302. - 142269. i) q^{60} +(79012.6 - 79012.6i) q^{61} +(142843. + 82283.5i) q^{62} -568958. i q^{63} +(262139. - 1546.52i) q^{64} +249842. q^{65} +(-92482.8 + 160549. i) q^{66} +(-151377. - 151377. i) q^{67} +(-92442.0 - 159390. i) q^{68} +(-265305. - 265305. i) q^{69} +(340206. - 91516.6i) q^{70} -383594. q^{71} +(1929.93 + 654261. i) q^{72} -101689. i q^{73} +(40435.4 - 10877.3i) q^{74} +(185072. - 185072. i) q^{75} +(200875. - 755618. i) q^{76} +(-162767. + 162767. i) q^{77} +(-451875. + 784451. i) q^{78} +380802. i q^{79} +(-390902. + 106391. i) q^{80} -169923. q^{81} +(317957. + 183156. i) q^{82} +(43960.4 + 43960.4i) q^{83} +(-327968. + 1.23369e6i) q^{84} +(201351. + 201351. i) q^{85} +(-294841. - 1.09605e6i) q^{86} +877297. q^{87} +(186618. - 187722. i) q^{88} -631244. i q^{89} +(-262655. - 976400. i) q^{90} +(-795285. + 795285. i) q^{91} +(268923. + 463680. i) q^{92} +(652735. - 652735. i) q^{93} +(254801. + 146776. i) q^{94} +1.20830e6i q^{95} +(372955. - 1.41977e6i) q^{96} -1.05819e6 q^{97} +(-321821. + 558678. i) q^{98} +(467144. + 467144. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) $ 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.99319	+	6.93213i	−0.499148	+	0.866517i
$2$	−3.99319	+	6.93213i	−0.499148	+	0.866517i
$3$	31.6770	+	31.6770i	1.17322	+	1.17322i	0.981437	+	0.191783i	$0.0614271\pi$
$3$	31.6770	+	31.6770i	1.17322	+	1.17322i	0.191783	+	0.981437i	$0.438573\pi$
$4$	−32.1089	−	55.3626i	−0.501702	−	0.865040i
$5$	69.9376	+	69.9376i	0.559501	+	0.559501i	0.929165	−	0.369665i	$-0.120527\pi$
$5$	69.9376	+	69.9376i	0.559501	+	0.559501i	−0.369665	+	0.929165i	$0.620527\pi$
$6$	−346.081	+	93.0969i	−1.60223	+	0.431004i
$7$	−445.243			−1.29809			−0.649043	−	0.760752i	$-0.724830\pi$
$7$	−445.243			−1.29809			−0.649043	+	0.760752i	$0.724830\pi$
$8$	511.998	−	1.51028i	0.999996	−	0.00294977i
$9$			1277.86i			1.75289i
$10$	−764.090	+	205.543i	−0.764090	+	0.205543i
$11$	365.568	−	365.568i	0.274657	−	0.274657i	−0.556315	−	0.830972i	$-0.687785\pi$
$11$	365.568	−	365.568i	0.274657	−	0.274657i	0.830972	+	0.556315i	$0.187785\pi$
$12$	736.605	−	2770.83i	0.426276	−	1.60349i
$13$	1786.18	−	1786.18i	0.813009	−	0.813009i	−0.172075	−	0.985084i	$-0.555047\pi$
$13$	1786.18	−	1786.18i	0.813009	−	0.813009i	0.985084	+	0.172075i	$0.0550470\pi$
$14$	1777.94	−	3086.49i	0.647937	−	1.12481i
$15$			4430.82i			1.31284i
$16$	−2034.03	+	3555.27i	−0.496590	+	0.867985i
$17$	2879.01			0.585999			0.292999	−	0.956113i	$-0.405347\pi$
$17$	2879.01			0.585999			0.292999	+	0.956113i	$0.405347\pi$
$18$	−8858.29	−	5102.73i	−1.51891	−	0.874953i
$19$	8638.45	+	8638.45i	1.25943	+	1.25943i	0.951364	+	0.308068i	$0.0996825\pi$
$19$	8638.45	+	8638.45i	1.25943	+	1.25943i	0.308068	+	0.951364i	$0.400318\pi$
$20$	1626.30	−	6117.55i	0.203288	−	0.764693i
$21$	−14103.9	−	14103.9i	−1.52294	−	1.52294i
$22$	1074.38	+	3993.95i	0.100900	+	0.375089i
$23$	−8375.32			−0.688364			−0.344182	−	0.938903i	$-0.611844\pi$
$23$	−8375.32			−0.688364			−0.344182	+	0.938903i	$0.611844\pi$
$24$	16266.4	+	16170.7i	1.17668	+	1.16975i
$25$		−	5842.47i		−	0.373918i
$26$	5249.49	+	19514.6i	0.298674	+	1.11030i
$27$	−17386.2	+	17386.2i	−0.883309	+	0.883309i
$28$	14296.3	+	24649.8i	0.651252	+	1.12290i
$29$	13847.6	−	13847.6i	0.567779	−	0.567779i	−0.363727	−	0.931506i	$-0.618496\pi$
$29$	13847.6	−	13847.6i	0.567779	−	0.567779i	0.931506	+	0.363727i	$0.118496\pi$
$30$	−30715.0	−	17693.1i	−1.13759	−	0.655299i
$31$		−	20606.0i		−	0.691685i	−0.938293	−	0.345842i	$-0.887593\pi$
$31$		−	20606.0i		−	0.691685i	0.938293	−	0.345842i	$-0.112407\pi$
$32$	−16523.3	−	28297.0i	−0.504252	−	0.863557i
$33$	23160.2			0.644466
$34$	−11496.4	+	19957.7i	−0.292500	+	0.507778i
$35$	−31139.2	−	31139.2i	−0.726279	−	0.726279i
$36$	70745.6	−	41030.7i	1.51632	−	0.879430i
$37$	−3701.07	−	3701.07i	−0.0730672	−	0.0730672i	0.669629	−	0.742696i	$-0.266453\pi$
$37$	−3701.07	−	3701.07i	−0.0730672	−	0.0730672i	−0.742696	+	0.669629i	$0.766453\pi$
$38$	−94377.8	+	25387.9i	−1.71996	+	0.462676i
$39$	113162.			1.90768
$40$	35913.5	+	35702.3i	0.561149	+	0.557848i
$41$		−	45867.1i		−	0.665503i	−0.943015	−	0.332752i	$-0.892023\pi$
$41$		−	45867.1i		−	0.665503i	0.943015	−	0.332752i	$-0.107977\pi$
$42$	154090.	−	41450.8i	2.07983	−	0.559480i
$43$	−100322.	+	100322.i	−1.26180	+	1.26180i	−0.311580	+	0.950220i	$0.600858\pi$
$43$	−100322.	+	100322.i	−1.26180	+	1.26180i	−0.950220	+	0.311580i	$0.899142\pi$
$44$	−31976.8	−	8500.79i	−0.375385	−	0.0997933i
$45$	−89370.4	+	89370.4i	−0.980745	+	0.980745i
$46$	33444.2	−	58058.8i	0.343596	−	0.596479i
$47$		−	36756.6i		−	0.354031i	−0.984208	−	0.177016i	$-0.943356\pi$
$47$		−	36756.6i		−	0.354031i	0.984208	−	0.177016i	$-0.0566443\pi$
$48$	−177052.	+	48188.1i	−1.60095	+	0.435728i
$49$	80592.5			0.685025
$50$	40500.8	+	23330.1i	0.324006	+	0.186641i
$51$	91198.3	+	91198.3i	0.687506	+	0.687506i
$52$	−156240.	−	41535.2i	−1.11117	−	0.295397i
$53$	−83859.8	−	83859.8i	−0.563283	−	0.563283i	0.366956	−	0.930238i	$-0.380400\pi$
$53$	−83859.8	−	83859.8i	−0.563283	−	0.563283i	−0.930238	+	0.366956i	$0.880400\pi$
$54$	−51097.1	−	189950.i	−0.324500	−	1.20630i
$55$	51133.9			0.307341
$56$	−227964.	+	672.443i	−1.29808	+	0.00382905i
$57$			547279.i			2.95518i
$58$	40697.3	+	151289.i	0.208584	+	0.775396i
$59$	43125.2	−	43125.2i	0.209979	−	0.209979i	−0.594280	−	0.804258i	$-0.702563\pi$
$59$	43125.2	−	43125.2i	0.209979	−	0.209979i	0.804258	+	0.594280i	$0.202563\pi$
$60$	245302.	−	142269.i	1.13566	−	0.658652i
$61$	79012.6	−	79012.6i	0.348102	−	0.348102i	−0.511300	−	0.859402i	$-0.670836\pi$
$61$	79012.6	−	79012.6i	0.348102	−	0.348102i	0.859402	+	0.511300i	$0.170836\pi$
$62$	142843.	+	82283.5i	0.599356	+	0.345253i
$63$		−	568958.i		−	2.27540i
$64$	262139.	−	1546.52i	0.999983	−	0.00589952i
$65$	249842.			0.909758
$66$	−92482.8	+	160549.i	−0.321684	+	0.558440i
$67$	−151377.	−	151377.i	−0.503311	−	0.503311i	0.409154	−	0.912465i	$-0.365824\pi$
$67$	−151377.	−	151377.i	−0.503311	−	0.503311i	−0.912465	+	0.409154i	$0.865824\pi$
$68$	−92442.0	−	159390.i	−0.293997	−	0.506913i
$69$	−265305.	−	265305.i	−0.807603	−	0.807603i
$70$	340206.	−	91516.6i	0.991854	−	0.266812i
$71$	−383594.			−1.07176			−0.535880	−	0.844294i	$-0.680020\pi$
$71$	−383594.			−1.07176			−0.535880	+	0.844294i	$0.680020\pi$
$72$	1929.93	+	654261.i	0.00517063	+	1.75289i
$73$		−	101689.i		−	0.261400i	−0.991422	−	0.130700i	$-0.958277\pi$
$73$		−	101689.i		−	0.261400i	0.991422	−	0.130700i	$-0.0417225\pi$
$74$	40435.4	−	10877.3i	0.0997853	−	0.0268426i
$75$	185072.	−	185072.i	0.438688	−	0.438688i
$76$	200875.	−	755618.i	0.457600	−	1.72132i
$77$	−162767.	+	162767.i	−0.356528	+	0.356528i
$78$	−451875.	+	784451.i	−0.952214	+	1.65303i
$79$			380802.i			0.772356i	0.922424	+	0.386178i	$0.126205\pi$
$79$			380802.i			0.772356i	−0.922424	+	0.386178i	$0.873795\pi$
$80$	−390902.	+	106391.i	−0.763481	+	0.207796i
$81$	−169923.			−0.319741
$82$	317957.	+	183156.i	0.576670	+	0.332185i
$83$	43960.4	+	43960.4i	0.0768825	+	0.0768825i	0.744502	−	0.667620i	$-0.232687\pi$
$83$	43960.4	+	43960.4i	0.0768825	+	0.0768825i	−0.667620	+	0.744502i	$0.732687\pi$
$84$	−327968.	+	1.23369e6i	−0.553343	+	2.08147i
$85$	201351.	+	201351.i	0.327867	+	0.327867i
$86$	−294841.	−	1.09605e6i	−0.463545	−	1.72320i
$87$	877297.			1.33226
$88$	186618.	−	187722.i	0.273845	−	0.275466i
$89$		−	631244.i		−	0.895421i	−0.894179	−	0.447710i	$-0.852240\pi$
$89$		−	631244.i		−	0.895421i	0.894179	−	0.447710i	$-0.147760\pi$
$90$	−262655.	−	976400.i	−0.360295	−	1.33937i
$91$	−795285.	+	795285.i	−1.05536	+	1.05536i
$92$	268923.	+	463680.i	0.345354	+	0.595463i
$93$	652735.	−	652735.i	0.811499	−	0.811499i
$94$	254801.	+	146776.i	0.306774	+	0.176714i
$95$			1.20830e6i			1.40931i
$96$	372955.	−	1.41977e6i	0.421544	−	1.60474i
$97$	−1.05819e6			−1.15944			−0.579719	−	0.814817i	$-0.696838\pi$
$97$	−1.05819e6			−1.15944			−0.579719	+	0.814817i	$0.696838\pi$
$98$	−321821.	+	558678.i	−0.341929	+	0.593586i
$99$	467144.	+	467144.i	0.481444	+	0.481444i
$100$	−323454.	+	187596.i	−0.323454	+	0.187596i
$101$	414918.	+	414918.i	0.402715	+	0.402715i	0.879189	−	0.476474i	$-0.158085\pi$
$101$	414918.	+	414918.i	0.402715	+	0.402715i	−0.476474	+	0.879189i	$0.658085\pi$
$102$	−996371.	+	268027.i	−0.938903	+	0.252568i
$103$	−497799.			−0.455557			−0.227779	−	0.973713i	$-0.573146\pi$
$103$	−497799.			−0.455557			−0.227779	+	0.973713i	$0.573146\pi$
$104$	911823.	−	917218.i	0.810608	−	0.815404i
$105$		−	1.97279e6i		−	1.70417i
$106$	916195.	−	246460.i	0.769255	−	0.206932i
$107$	486860.	−	486860.i	0.397423	−	0.397423i	−0.479900	−	0.877323i	$-0.659327\pi$
$107$	486860.	−	486860.i	0.397423	−	0.397423i	0.877323	+	0.479900i	$0.159327\pi$
$108$	1.52080e6	+	404292.i	1.20726	+	0.320940i
$109$	−1.15792e6	+	1.15792e6i	−0.894128	+	0.894128i	−0.994909	−	0.100780i	$-0.967866\pi$
$109$	−1.15792e6	+	1.15792e6i	−0.894128	+	0.894128i	0.100780	+	0.994909i	$0.467866\pi$
$110$	−204187.	+	354467.i	−0.153409	+	0.266316i
$111$		−	234477.i		−	0.171448i
$112$	905639.	−	1.58296e6i	0.644616	−	1.12672i
$113$	2.35083e6			1.62925			0.814623	−	0.579991i	$-0.196944\pi$
$113$	2.35083e6			1.62925			0.814623	+	0.579991i	$0.196944\pi$
$114$	−3.79381e6	−	2.18539e6i	−2.56072	−	1.47507i
$115$	−585750.	−	585750.i	−0.385140	−	0.385140i
$116$	−1.21127e6	−	322007.i	−0.776008	−	0.206296i
$117$	2.28249e6	+	2.28249e6i	1.42512	+	1.42512i
$118$	126743.	+	471157.i	0.0771395	+	0.286761i
$119$	−1.28186e6			−0.760676
$120$	6691.79	+	2.26857e6i	0.00387256	+	1.31283i
$121$			1.50428e6i			0.849127i
$122$	232214.	+	863238.i	0.127882	+	0.475391i
$123$	1.45293e6	−	1.45293e6i	0.780782	−	0.780782i
$124$	−1.14080e6	+	661636.i	−0.598335	+	0.347020i
$125$	1.50138e6	−	1.50138e6i	0.768708	−	0.768708i
$126$	3.94409e6	+	2.27196e6i	1.97168	+	1.13576i
$127$			2.20742e6i			1.07764i	0.842420	+	0.538821i	$0.181130\pi$
$127$			2.20742e6i			1.07764i	−0.842420	+	0.538821i	$0.818870\pi$
$128$	−1.03605e6	+	1.82336e6i	−0.494028	+	0.869446i
$129$	−6.35579e6			−2.96074
$130$	−997667.	+	1.73194e6i	−0.454104	+	0.788321i
$131$	−853575.	−	853575.i	−0.379689	−	0.379689i	0.491301	−	0.870990i	$-0.336522\pi$
$131$	−853575.	−	853575.i	−0.379689	−	0.379689i	−0.870990	+	0.491301i	$0.836522\pi$
$132$	−743648.	−	1.28221e6i	−0.323330	−	0.557489i
$133$	−3.84621e6	−	3.84621e6i	−1.63485	−	1.63485i
$134$	1.65385e6	−	444890.i	0.687354	−	0.184901i
$135$	−2.43189e6			−0.988424
$136$	1.47405e6	−	4348.12i	0.585996	−	0.00172856i
$137$		−	164889.i		−	0.0641254i	−0.999486	−	0.0320627i	$-0.989792\pi$
$137$		−	164889.i		−	0.0641254i	0.999486	−	0.0320627i	$-0.0102076\pi$
$138$	2.89854e6	−	779717.i	1.10291	−	0.296688i
$139$	3.09039e6	−	3.09039e6i	1.15072	−	1.15072i	0.164310	−	0.986409i	$-0.447460\pi$
$139$	3.09039e6	−	3.09039e6i	1.15072	−	1.15072i	0.986409	−	0.164310i	$-0.0525399\pi$
$140$	−724101.	+	2.72380e6i	−0.263885	+	0.992637i
$141$	1.16434e6	−	1.16434e6i	0.415357	−	0.415357i
$142$	1.53176e6	−	2.65913e6i	0.534967	−	0.928697i
$143$		−	1.30594e6i		−	0.446597i
$144$	−4.54313e6	−	2.59921e6i	−1.52149	−	0.870469i
$145$	1.93693e6			0.635346
$146$	704923.	+	406064.i	0.226508	+	0.130478i
$147$	2.55293e6	+	2.55293e6i	0.803685	+	0.803685i
$148$	−86063.5	+	323738.i	−0.0265481	+	0.0998640i
$149$	3.60789e6	+	3.60789e6i	1.09067	+	1.09067i	0.995457	+	0.0952145i	$0.0303537\pi$
$149$	3.60789e6	+	3.60789e6i	1.09067	+	1.09067i	0.0952145	+	0.995457i	$0.469646\pi$
$150$	543916.	+	2.02197e6i	0.161160	+	0.599101i
$151$	63331.8			0.0183946			0.00919731	−	0.999958i	$-0.497072\pi$
$151$	63331.8			0.0183946			0.00919731	+	0.999958i	$0.497072\pi$
$152$	4.43591e6	+	4.40982e6i	1.26314	+	1.25571i
$153$			3.67897e6i			1.02719i
$154$	−478363.	−	1.77828e6i	−0.130977	−	0.486897i
$155$	1.44113e6	−	1.44113e6i	0.386998	−	0.386998i
$156$	−3.63350e6	−	6.26492e6i	−0.957086	−	1.65022i
$157$	−3.03025e6	+	3.03025e6i	−0.783033	+	0.783033i	−0.980341	−	0.197308i	$-0.936780\pi$
$157$	−3.03025e6	+	3.03025e6i	−0.783033	+	0.783033i	0.197308	+	0.980341i	$0.436780\pi$
$158$	−2.63977e6	−	1.52061e6i	−0.669259	−	0.385520i
$159$		−	5.31285e6i		−	1.32171i
$160$	823425.	−	3.13463e6i	0.201031	−	0.765290i
$161$	3.72906e6			0.893555
$162$	678535.	−	1.17793e6i	0.159598	−	0.277061i
$163$	−3.10014e6	−	3.10014e6i	−0.715844	−	0.715844i	0.251908	−	0.967751i	$-0.418942\pi$
$163$	−3.10014e6	−	3.10014e6i	−0.715844	−	0.715844i	−0.967751	+	0.251908i	$0.918942\pi$
$164$	−2.53932e6	+	1.47274e6i	−0.575687	+	0.333884i
$165$	1.61977e6	+	1.61977e6i	0.360579	+	0.360579i
$166$	−480282.	+	129197.i	−0.104996	+	0.0282442i
$167$	5.22136e6			1.12107			0.560537	−	0.828130i	$-0.310595\pi$
$167$	5.22136e6			1.12107			0.560537	+	0.828130i	$0.310595\pi$
$168$	−7.24249e6	−	7.19989e6i	−1.52743	−	1.51844i
$169$		−	1.55408e6i		−	0.321968i
$170$	−2.19983e6	+	591760.i	−0.447756	+	0.120448i
$171$	−1.10387e7	+	1.10387e7i	−2.20765	+	2.20765i
$172$	8.77531e6	+	2.33285e6i	1.72456	+	0.458460i
$173$	−5.78163e6	+	5.78163e6i	−1.11664	+	1.11664i	−0.124405	+	0.992232i	$0.539702\pi$
$173$	−5.78163e6	+	5.78163e6i	−1.11664	+	1.11664i	−0.992232	+	0.124405i	$0.960298\pi$
$174$	−3.50321e6	+	6.08154e6i	−0.664995	+	1.15443i
$175$			2.60132e6i			0.485378i
$176$	556115.	+	2.04327e6i	0.102006	+	0.374790i
$177$	2.73215e6			0.492703
$178$	4.37587e6	+	2.52067e6i	0.775897	+	0.446948i
$179$	−2.90396e6	−	2.90396e6i	−0.506328	−	0.506328i	0.407069	−	0.913397i	$-0.366551\pi$
$179$	−2.90396e6	−	2.90396e6i	−0.506328	−	0.506328i	−0.913397	+	0.407069i	$0.866551\pi$
$180$	7.81736e6	+	2.07819e6i	1.34043	+	0.356342i
$181$	−1.14159e6	−	1.14159e6i	−0.192519	−	0.192519i	0.604265	−	0.796784i	$-0.293467\pi$
$181$	−1.14159e6	−	1.14159e6i	−0.192519	−	0.192519i	−0.796784	+	0.604265i	$0.793467\pi$
$182$	−2.33730e6	−	8.68874e6i	−0.387704	−	1.44126i
$183$	5.00576e6			0.816801
$184$	−4.28815e6	+	12649.1i	−0.688361	+	0.00203052i
$185$		−	517688.i		−	0.0817623i
$186$	1.91835e6	+	7.13134e6i	0.298119	+	1.10824i
$187$	1.05247e6	−	1.05247e6i	0.160948	−	0.160948i
$188$	−2.03494e6	+	1.18021e6i	−0.306251	+	0.177618i
$189$	7.74108e6	−	7.74108e6i	1.14661	−	1.14661i
$190$	−8.37612e6	−	4.82498e6i	−1.22119	−	0.703453i
$191$			2.75166e6i			0.394907i	0.980312	+	0.197453i	$0.0632671\pi$
$191$			2.75166e6i			0.394907i	−0.980312	+	0.197453i	$0.936733\pi$
$192$	8.35277e6	+	8.25479e6i	1.18012	+	1.16628i
$193$	−3.25985e6			−0.453446			−0.226723	−	0.973959i	$-0.572801\pi$
$193$	−3.25985e6			−0.453446			−0.226723	+	0.973959i	$0.572801\pi$
$194$	4.22554e6	−	7.33549e6i	0.578731	−	1.00467i
$195$	7.91425e6	+	7.91425e6i	1.06735	+	1.06735i
$196$	−2.58774e6	−	4.46181e6i	−0.343678	−	0.592574i
$197$	−9.02475e6	−	9.02475e6i	−1.18042	−	1.18042i	−0.979636	−	0.200784i	$-0.935651\pi$
$197$	−9.02475e6	−	9.02475e6i	−1.18042	−	1.18042i	−0.200784	−	0.979636i	$-0.564349\pi$
$198$	−5.10370e6	+	1.37291e6i	−0.657491	+	0.176867i
$199$	5.33669e6			0.677193			0.338596	−	0.940932i	$-0.390048\pi$
$199$	5.33669e6			0.677193			0.338596	+	0.940932i	$0.390048\pi$
$200$	−8823.79	−	2.99133e6i	−0.00110297	−	0.373916i
$201$		−	9.59035e6i		−	1.18099i
$202$	−4.53311e6	+	1.21942e6i	−0.549974	+	0.147945i
$203$	−6.16553e6	+	6.16553e6i	−0.737026	+	0.737026i
$204$	2.12069e6	−	7.97726e6i	0.249797	−	0.939644i
$205$	3.20784e6	−	3.20784e6i	0.372349	−	0.372349i
$206$	1.98781e6	−	3.45081e6i	0.227390	−	0.394748i
$207$		−	1.07025e7i		−	1.20663i
$208$	2.71720e6	+	9.98350e6i	0.301948	+	1.10941i
$209$	6.31588e6			0.691823
$210$	1.36757e7	+	7.87773e6i	1.47669	+	0.850634i
$211$	4.02283e6	+	4.02283e6i	0.428237	+	0.428237i	0.888027	−	0.459791i	$-0.152076\pi$
$211$	4.02283e6	+	4.02283e6i	0.428237	+	0.428237i	−0.459791	+	0.888027i	$0.652076\pi$
$212$	−1.95005e6	+	7.33535e6i	−0.204662	+	0.769862i
$213$	−1.21511e7	−	1.21511e7i	−1.25741	−	1.25741i
$214$	1.43086e6	+	5.31910e6i	0.146001	+	0.542747i
$215$	−1.40325e7			−1.41196
$216$	−8.87543e6	+	8.92794e6i	−0.880700	+	0.885911i
$217$			9.17467e6i			0.897866i
$218$	−3.40307e6	−	1.26507e7i	−0.328474	−	1.22108i
$219$	3.22120e6	−	3.22120e6i	0.306680	−	0.306680i
$220$	−1.64185e6	−	2.83090e6i	−0.154194	−	0.265862i
$221$	5.14244e6	−	5.14244e6i	0.476422	−	0.476422i
$222$	1.62543e6	+	936312.i	0.148562	+	0.0855779i
$223$			8.82481e6i			0.795776i	0.917434	+	0.397888i	$0.130257\pi$
$223$			8.82481e6i			0.795776i	−0.917434	+	0.397888i	$0.869743\pi$
$224$	7.35689e6	+	1.25991e7i	0.654561	+	1.12097i
$225$	7.46585e6			0.655438
$226$	−9.38731e6	+	1.62963e7i	−0.813235	+	1.41177i
$227$	−1.01370e7	−	1.01370e7i	−0.866629	−	0.866629i	0.125469	−	0.992098i	$-0.459957\pi$
$227$	−1.01370e7	−	1.01370e7i	−0.866629	−	0.866629i	−0.992098	+	0.125469i	$0.959957\pi$
$228$	3.02988e7	−	1.75726e7i	2.55635	−	1.48262i
$229$	3.89615e6	+	3.89615e6i	0.324436	+	0.324436i	0.850466	−	0.526030i	$-0.176320\pi$
$229$	3.89615e6	+	3.89615e6i	0.324436	+	0.324436i	−0.526030	+	0.850466i	$0.676320\pi$
$230$	6.39950e6	−	1.72149e6i	0.525972	−	0.141488i
$231$	−1.03119e7			−0.836571
$232$	7.06901e6	−	7.11084e6i	0.566102	−	0.569451i
$233$			1.91488e7i			1.51382i	0.653519	+	0.756911i	$0.273292\pi$
$233$			1.91488e7i			1.51382i	−0.653519	+	0.756911i	$0.726708\pi$
$234$	−2.49369e7	+	6.70811e6i	−1.94623	+	0.523543i
$235$	2.57067e6	−	2.57067e6i	0.198081	−	0.198081i
$236$	−3.77223e6	−	1.00282e6i	−0.286987	−	0.0762933i
$237$	−1.20626e7	+	1.20626e7i	−0.906144	+	0.906144i
$238$	5.11871e6	−	8.88603e6i	0.379690	−	0.659139i
$239$		−	1.17598e7i		−	0.861405i	−0.902494	−	0.430702i	$-0.858266\pi$
$239$		−	1.17598e7i		−	0.861405i	0.902494	−	0.430702i	$-0.141734\pi$
$240$	−1.57527e7	−	9.01243e6i	−1.13952	−	0.651941i
$241$	−4.96712e6			−0.354857			−0.177429	−	0.984134i	$-0.556778\pi$
$241$	−4.96712e6			−0.354857			−0.177429	+	0.984134i	$0.556778\pi$
$242$	−1.04279e7	−	6.00687e6i	−0.735783	−	0.423840i
$243$	7.29187e6	+	7.29187e6i	0.508183	+	0.508183i
$244$	−6.91135e6	−	1.83733e6i	−0.475766	−	0.126479i
$245$	5.63644e6	+	5.63644e6i	0.383272	+	0.383272i
$246$	4.27009e6	+	1.58737e7i	0.286835	+	1.06629i
$247$	3.08597e7			2.04786
$248$	−31120.9	−	1.05502e7i	−0.00204031	−	0.691682i
$249$			2.78506e6i			0.180400i
$250$	4.41248e6	+	1.64031e7i	0.282399	+	1.04980i
$251$	−4.79277e6	+	4.79277e6i	−0.303086	+	0.303086i	−0.842220	−	0.539134i	$-0.818752\pi$
$251$	−4.79277e6	+	4.79277e6i	−0.303086	+	0.303086i	0.539134	+	0.842220i	$0.318752\pi$
$252$	−3.14990e7	+	1.82686e7i	−1.96832	+	1.14158i
$253$	−3.06175e6	+	3.06175e6i	−0.189064	+	0.189064i
$254$	−1.53022e7	−	8.81465e6i	−0.933795	−	0.537903i
$255$			1.27564e7i			0.769320i
$256$	−8.50264e6	−	1.44631e7i	−0.506797	−	0.862066i
$257$	1.57504e7			0.927883			0.463942	−	0.885866i	$-0.346435\pi$
$257$	1.57504e7			0.927883			0.463942	+	0.885866i	$0.346435\pi$
$258$	2.53798e7	−	4.40592e7i	1.47785	−	2.56553i
$259$	1.64788e6	+	1.64788e6i	0.0948474	+	0.0948474i
$260$	−8.02217e6	−	1.38319e7i	−0.456428	−	0.786978i
$261$	1.76952e7	+	1.76952e7i	0.995256	+	0.995256i
$262$	9.32558e6	−	2.50861e6i	0.518528	−	0.139486i
$263$	−3.10288e7			−1.70568			−0.852840	−	0.522172i	$-0.825122\pi$
$263$	−3.10288e7			−1.70568			−0.852840	+	0.522172i	$0.825122\pi$
$264$	1.18579e7	−	34978.4i	0.644463	−	0.00190103i
$265$		−	1.17299e7i		−	0.630314i
$266$	4.20211e7	−	1.13038e7i	2.23266	−	0.600592i
$267$	1.99959e7	−	1.99959e7i	1.05053	−	1.05053i
$268$	−3.52008e6	+	1.32412e7i	−0.182872	+	0.687897i
$269$	1.07031e7	−	1.07031e7i	0.549860	−	0.549860i	−0.376540	−	0.926400i	$-0.622886\pi$
$269$	1.07031e7	−	1.07031e7i	0.549860	−	0.549860i	0.926400	+	0.376540i	$0.122886\pi$
$270$	9.71101e6	−	1.68582e7i	0.493370	−	0.856486i
$271$		−	1.71206e7i		−	0.860223i	−0.902776	−	0.430112i	$-0.858474\pi$
$271$		−	1.71206e7i		−	0.860223i	0.902776	−	0.430112i	$-0.141526\pi$
$272$	−5.85601e6	+	1.02357e7i	−0.291001	+	0.508638i
$273$	−5.03844e7			−2.47633
$274$	1.14303e6	+	658433.i	0.0555658	+	0.0320081i
$275$	−2.13582e6	−	2.13582e6i	−0.102699	−	0.102699i
$276$	−6.16930e6	+	2.32066e7i	−0.293433	+	1.10378i
$277$	4.38225e6	+	4.38225e6i	0.206185	+	0.206185i	0.802644	−	0.596459i	$-0.203426\pi$
$277$	4.38225e6	+	4.38225e6i	0.206185	+	0.206185i	−0.596459	+	0.802644i	$0.703426\pi$
$278$	9.08250e6	+	3.37635e7i	0.422738	+	1.57150i
$279$	2.63315e7			1.21245
$280$	−1.59902e7	−	1.58962e7i	−0.728419	−	0.724134i
$281$		−	4.01434e7i		−	1.80924i	−0.426223	−	0.904618i	$-0.640156\pi$
$281$		−	4.01434e7i		−	1.80924i	0.426223	−	0.904618i	$-0.359844\pi$
$282$	3.42192e6	+	1.27207e7i	0.152589	+	0.567238i
$283$	6.60823e6	−	6.60823e6i	0.291558	−	0.291558i	−0.546137	−	0.837696i	$-0.683902\pi$
$283$	6.60823e6	−	6.60823e6i	0.291558	−	0.291558i	0.837696	+	0.546137i	$0.183902\pi$
$284$	1.23168e7	+	2.12368e7i	0.537704	+	0.927115i
$285$	−3.82754e7	+	3.82754e7i	−1.65343	+	1.65343i
$286$	9.05296e6	+	5.21487e6i	0.386983	+	0.222918i
$287$			2.04220e7i			0.863880i
$288$	3.61596e7	−	2.11145e7i	1.51372	−	0.883899i
$289$	−1.58489e7			−0.656605
$290$	−7.73452e6	+	1.34271e7i	−0.317132	+	0.550537i
$291$	−3.35201e7	−	3.35201e7i	−1.36028	−	1.36028i
$292$	−5.62978e6	+	3.26513e6i	−0.226122	+	0.131145i
$293$	2.91677e7	+	2.91677e7i	1.15957	+	1.15957i	0.984567	+	0.175008i	$0.0559951\pi$
$293$	2.91677e7	+	2.91677e7i	1.15957	+	1.15957i	0.175008	+	0.984567i	$0.444005\pi$
$294$	−2.78915e7	+	7.50291e6i	−1.09756	+	0.295249i
$295$	6.03215e6			0.234966
$296$	−1.90053e6	−	1.88935e6i	−0.0732824	−	0.0728513i
$297$			1.27117e7i			0.485214i
$298$	−3.94173e7	+	1.06034e7i	−1.48949	+	0.400678i
$299$	−1.49598e7	+	1.49598e7i	−0.559646	+	0.559646i
$300$	−1.61885e7	−	4.30359e6i	−0.599574	−	0.159392i
$301$	4.46677e7	−	4.46677e7i	1.63792	−	1.63792i
$302$	−252896.	+	439024.i	−0.00918165	+	0.0159392i
$303$			2.62867e7i			0.944947i
$304$	−4.82829e7	+	1.31411e7i	−1.71859	+	0.467747i
$305$	1.10519e7			0.389527
$306$	−2.55031e7	−	1.46908e7i	−0.890080	−	0.512722i
$307$	−8.34441e6	−	8.34441e6i	−0.288390	−	0.288390i	0.548053	−	0.836443i	$-0.315369\pi$
$307$	−8.34441e6	−	8.34441e6i	−0.288390	−	0.288390i	−0.836443	+	0.548053i	$0.815369\pi$
$308$	1.42374e7	+	3.78492e6i	0.487282	+	0.129540i
$309$	−1.57688e7	−	1.57688e7i	−0.534469	−	0.534469i
$310$	4.23541e6	+	1.57448e7i	0.142171	+	0.528510i
$311$	−2.89591e7			−0.962728			−0.481364	−	0.876521i	$-0.659858\pi$
$311$	−2.89591e7			−0.962728			−0.481364	+	0.876521i	$0.659858\pi$
$312$	5.79385e7	−	170906.i	1.90767	−	0.00562722i
$313$		−	1.44783e7i		−	0.472155i	−0.971734	−	0.236078i	$-0.924138\pi$
$313$		−	1.44783e7i		−	0.472155i	0.971734	−	0.236078i	$-0.0758620\pi$
$314$	−8.90576e6	−	3.31065e7i	−0.287662	−	1.06936i
$315$	3.97915e7	−	3.97915e7i	1.27309	−	1.27309i
$316$	2.10822e7	−	1.22271e7i	0.668119	−	0.387493i
$317$	−1.37295e7	+	1.37295e7i	−0.431001	+	0.431001i	−0.888969	−	0.457968i	$-0.848578\pi$
$317$	−1.37295e7	+	1.37295e7i	−0.431001	+	0.431001i	0.457968	+	0.888969i	$0.348578\pi$
$318$	3.68294e7	+	2.12152e7i	1.14528	+	0.659729i
$319$		−	1.01245e7i		−	0.311889i
$320$	1.84416e7	+	1.82252e7i	0.562792	+	0.556190i
$321$	3.08445e7			0.932530
$322$	−1.48908e7	+	2.58503e7i	−0.446016	+	0.774280i
$323$	2.48702e7	+	2.48702e7i	0.738026	+	0.738026i
$324$	5.45606e6	+	9.40739e6i	0.160415	+	0.276589i
$325$	−1.04357e7	−	1.04357e7i	−0.303999	−	0.303999i
$326$	3.38700e7	−	9.11114e6i	0.977603	−	0.262978i
$327$	−7.33589e7			−2.09802
$328$	−69272.4	−	2.34839e7i	−0.00196308	−	0.665500i
$329$			1.63656e7i			0.459562i
$330$	−1.76965e7	+	4.76040e6i	−0.492430	+	0.132465i
$331$	−1.79822e7	+	1.79822e7i	−0.495860	+	0.495860i	−0.910146	−	0.414287i	$-0.864031\pi$
$331$	−1.79822e7	+	1.79822e7i	−0.495860	+	0.495860i	0.414287	+	0.910146i	$0.364031\pi$
$332$	1.02224e6	−	3.84528e6i	0.0279344	−	0.105079i
$333$	4.72945e6	−	4.72945e6i	0.128079	−	0.128079i
$334$	−2.08499e7	+	3.61952e7i	−0.559582	+	0.971429i
$335$		−	2.11739e7i		−	0.563206i
$336$	7.88312e7	−	2.14554e7i	2.07817	−	0.565613i
$337$	−2.03899e7			−0.532751			−0.266376	−	0.963869i	$-0.585826\pi$
$337$	−2.03899e7			−0.532751			−0.266376	+	0.963869i	$0.585826\pi$
$338$	1.07731e7	+	6.20572e6i	0.278991	+	0.160710i
$339$	7.44672e7	+	7.44672e7i	1.91146	+	1.91146i
$340$	4.68215e6	−	1.76125e7i	0.119127	−	0.448109i
$341$	−7.53289e6	−	7.53289e6i	−0.189976	−	0.189976i
$342$	−3.24422e7	−	1.20601e8i	−0.811021	−	3.01491i
$343$	1.64992e7			0.408864
$344$	−5.12131e7	+	5.15161e7i	−1.25807	+	1.26552i
$345$		−	3.71095e7i		−	0.903708i
$346$	−1.69919e7	−	6.31661e7i	−0.410217	−	1.52495i
$347$	1.33068e7	−	1.33068e7i	0.318482	−	0.318482i	−0.529702	−	0.848184i	$-0.677696\pi$
$347$	1.33068e7	−	1.33068e7i	0.318482	−	0.318482i	0.848184	+	0.529702i	$0.177696\pi$
$348$	−2.81691e7	−	4.85695e7i	−0.668398	−	1.15246i
$349$	4.91437e7	−	4.91437e7i	1.15609	−	1.15609i	0.170779	−	0.985309i	$-0.445371\pi$
$349$	4.91437e7	−	4.91437e7i	1.15609	−	1.15609i	0.985309	−	0.170779i	$-0.0546285\pi$
$350$	−1.80327e7	−	1.03876e7i	−0.420588	−	0.242275i
$351$			6.21097e7i			1.43628i
$352$	−1.63849e7	−	4.30409e6i	−0.375678	−	0.0986856i
$353$	−1.93651e7			−0.440245			−0.220123	−	0.975472i	$-0.570646\pi$
$353$	−1.93651e7			−0.440245			−0.220123	+	0.975472i	$0.570646\pi$
$354$	−1.09100e7	+	1.89396e7i	−0.245932	+	0.426935i
$355$	−2.68277e7	−	2.68277e7i	−0.599650	−	0.599650i
$356$	−3.49473e7	+	2.02686e7i	−0.774575	+	0.449235i
$357$	−4.06054e7	−	4.06054e7i	−0.892441	−	0.892441i
$358$	3.17267e7	−	8.53460e6i	0.691475	−	0.186009i
$359$	3.01978e7			0.652668			0.326334	−	0.945255i	$-0.394187\pi$
$359$	3.01978e7			0.652668			0.326334	+	0.945255i	$0.394187\pi$
$360$	−4.56224e7	+	4.58924e7i	−0.977847	+	0.983633i
$361$			1.02200e8i			2.17234i
$362$	1.24722e7	−	3.35506e6i	0.262916	−	0.0707253i
$363$	−4.76510e7	+	4.76510e7i	−0.996214	+	0.996214i
$364$	6.95648e7	+	1.84933e7i	1.44240	+	0.383451i
$365$	7.11190e6	−	7.11190e6i	0.146254	−	0.146254i
$366$	−1.99889e7	+	3.47006e7i	−0.407705	+	0.707772i
$367$			9.00756e7i			1.82225i	0.412127	+	0.911127i	$0.364786\pi$
$367$			9.00756e7i			1.82225i	−0.412127	+	0.911127i	$0.635214\pi$
$368$	1.70357e7	−	2.97765e7i	0.341835	−	0.597490i
$369$	5.86117e7			1.16656
$370$	3.58868e6	+	2.06722e6i	0.0708484	+	0.0408115i
$371$	3.73380e7	+	3.73380e7i	0.731189	+	0.731189i
$372$	−5.70957e7	−	1.51785e7i	−1.10911	−	0.294849i
$373$	−5.03209e6	−	5.03209e6i	−0.0969666	−	0.0969666i	0.656959	−	0.753926i	$-0.271842\pi$
$373$	−5.03209e6	−	5.03209e6i	−0.0969666	−	0.0969666i	−0.753926	+	0.656959i	$0.771842\pi$
$374$	3.09317e6	+	1.14986e7i	0.0591274	+	0.219802i
$375$	9.51185e7			1.80373
$376$	−55512.8	−	1.88193e7i	−0.00104431	−	0.354030i
$377$		−	4.94685e7i		−	0.923219i
$378$	2.27506e7	+	8.45737e7i	0.421229	+	1.56589i
$379$	−1.26716e7	+	1.26716e7i	−0.232762	+	0.232762i	−0.813845	−	0.581083i	$-0.802629\pi$
$379$	−1.26716e7	+	1.26716e7i	−0.232762	+	0.232762i	0.581083	+	0.813845i	$0.302629\pi$
$380$	6.68948e7	−	3.87974e7i	1.21911	−	0.707052i
$381$	−6.99245e7	+	6.99245e7i	−1.26431	+	1.26431i
$382$	−1.90749e7	−	1.09879e7i	−0.342193	−	0.197117i
$383$		−	8.72854e7i		−	1.55362i	−0.629734	−	0.776811i	$-0.716836\pi$
$383$		−	8.72854e7i		−	1.55362i	0.629734	−	0.776811i	$-0.283164\pi$
$384$	−9.05775e7	+	2.49396e7i	−1.59966	+	0.440449i
$385$	−2.27670e7			−0.398955
$386$	1.30172e7	−	2.25977e7i	0.226337	−	0.392918i
$387$	−1.28197e8	−	1.28197e8i	−2.21180	−	2.21180i
$388$	3.39773e7	+	5.85840e7i	0.581692	+	1.00296i
$389$	6.56082e7	+	6.56082e7i	1.11458	+	1.11458i	0.992524	+	0.122052i	$0.0389473\pi$
$389$	6.56082e7	+	6.56082e7i	1.11458	+	1.11458i	0.122052	+	0.992524i	$0.461053\pi$
$390$	−8.64657e7	+	2.32595e7i	−1.45764	+	0.392110i
$391$	−2.41127e7			−0.403380
$392$	4.12632e7	−	121718.i	0.685022	−	0.00202067i
$393$		−	5.40773e7i		−	0.890918i
$394$	9.85982e7	−	2.65233e7i	1.61206	−	0.433649i
$395$	−2.66324e7	+	2.66324e7i	−0.432134	+	0.432134i
$396$	1.08628e7	−	4.08618e7i	0.174927	−	0.658010i
$397$	−3.86742e7	+	3.86742e7i	−0.618087	+	0.618087i	−0.945040	−	0.326954i	$-0.893978\pi$
$397$	−3.86742e7	+	3.86742e7i	−0.618087	+	0.618087i	0.326954	+	0.945040i	$0.393978\pi$
$398$	−2.13104e7	+	3.69946e7i	−0.338020	+	0.586799i
$399$		−	2.43672e8i		−	3.83608i
$400$	2.07715e7	+	1.18838e7i	0.324555	+	0.185684i
$401$	−5.72006e6			−0.0887090			−0.0443545	−	0.999016i	$-0.514123\pi$
$401$	−5.72006e6			−0.0887090			−0.0443545	+	0.999016i	$0.514123\pi$
$402$	6.64816e7	+	3.82960e7i	1.02335	+	0.589489i
$403$	−3.68060e7	−	3.68060e7i	−0.562346	−	0.562346i
$404$	9.64835e6	−	3.62935e7i	0.146322	−	0.550408i
$405$	−1.18840e7	−	1.18840e7i	−0.178895	−	0.178895i
$406$	−1.81202e7	−	6.73604e7i	−0.270760	−	1.00653i
$407$	−2.70599e6			−0.0401368
$408$	4.68311e7	+	4.65556e7i	0.689531	+	0.685475i
$409$			8.57443e7i			1.25324i	0.779324	+	0.626622i	$0.215563\pi$
$409$			8.57443e7i			1.25324i	−0.779324	+	0.626622i	$0.784437\pi$
$410$	9.42766e6	+	3.50466e7i	0.136789	+	0.508504i
$411$	5.22319e6	−	5.22319e6i	0.0752333	−	0.0752333i
$412$	1.59838e7	+	2.75595e7i	0.228554	+	0.394075i
$413$	−1.92012e7	+	1.92012e7i	−0.272570	+	0.272570i
$414$	7.41910e7	+	4.27370e7i	1.04556	+	0.602286i
$415$			6.14897e6i			0.0860316i
$416$	−8.00573e7	−	2.10300e7i	−1.11204	−	0.292118i
$417$	1.95788e8			2.70009
$418$	−2.52205e7	+	4.37825e7i	−0.345322	+	0.599476i
$419$	5.70718e7	+	5.70718e7i	0.775853	+	0.775853i	0.979123	−	0.203270i	$-0.0651568\pi$
$419$	5.70718e7	+	5.70718e7i	0.775853	+	0.775853i	−0.203270	+	0.979123i	$0.565157\pi$
$420$	−1.09219e8	+	6.33442e7i	−1.47418	+	0.854987i
$421$	−4.29554e7	−	4.29554e7i	−0.575668	−	0.575668i	0.358039	−	0.933707i	$-0.383445\pi$
$421$	−4.29554e7	−	4.29554e7i	−0.575668	−	0.575668i	−0.933707	+	0.358039i	$0.883445\pi$
$422$	−4.39506e7	+	1.18229e7i	−0.584828	+	0.157321i
$423$	4.69697e7			0.620579
$424$	−4.30627e7	−	4.28094e7i	−0.564942	−	0.561619i
$425$		−	1.68205e7i		−	0.219116i
$426$	1.32755e8	−	3.57115e7i	1.71720	−	0.461933i
$427$	−3.51798e7	+	3.51798e7i	−0.451866	+	0.451866i
$428$	−4.25864e7	−	1.13213e7i	−0.543175	−	0.144399i
$429$	4.13682e7	−	4.13682e7i	0.523956	−	0.523956i
$430$	5.60346e7	−	9.72755e7i	0.704775	−	1.22348i
$431$		−	7.22248e7i		−	0.902100i	−0.892499	−	0.451050i	$-0.851050\pi$
$431$		−	7.22248e7i		−	0.902100i	0.892499	−	0.451050i	$-0.148950\pi$
$432$	−2.64485e7	−	9.71766e7i	−0.328057	−	1.20534i
$433$	−1.23758e8			−1.52444			−0.762219	−	0.647320i	$-0.775890\pi$
$433$	−1.23758e8			−1.52444			−0.762219	+	0.647320i	$0.775890\pi$
$434$	−6.36001e7	−	3.66362e7i	−0.778016	−	0.448168i
$435$	6.13561e7	+	6.13561e7i	0.745400	+	0.745400i
$436$	1.01285e8	+	2.69259e7i	1.22204	+	0.324871i
$437$	−7.23498e7	−	7.23498e7i	−0.866948	−	0.866948i
$438$	9.46695e6	+	3.51927e7i	0.112665	+	0.418823i
$439$	1.18874e8			1.40506			0.702529	−	0.711655i	$-0.252054\pi$
$439$	1.18874e8			1.40506			0.702529	+	0.711655i	$0.252054\pi$
$440$	2.61804e7	−	77226.6i	0.307340	−	0.000906586i
$441$			1.02986e8i			1.20078i
$442$	1.51134e7	+	5.61828e7i	0.175023	+	0.650633i
$443$	5.32806e7	−	5.32806e7i	0.612855	−	0.612855i	−0.330834	−	0.943689i	$-0.607330\pi$
$443$	5.32806e7	−	5.32806e7i	0.612855	−	0.612855i	0.943689	+	0.330834i	$0.107330\pi$
$444$	−1.29813e7	+	7.52882e6i	−0.148309	+	0.0860158i
$445$	4.41477e7	−	4.41477e7i	0.500989	−	0.500989i
$446$	−6.11748e7	−	3.52391e7i	−0.689553	−	0.397210i
$447$			2.28574e8i			2.55920i
$448$	−1.16716e8	+	688579.i	−1.29806	+	0.00765808i
$449$	−9.20149e7			−1.01653			−0.508264	−	0.861202i	$-0.669712\pi$
$449$	−9.20149e7			−1.01653			−0.508264	+	0.861202i	$0.669712\pi$
$450$	−2.98125e7	+	5.17543e7i	−0.327161	+	0.567948i
$451$	−1.67676e7	−	1.67676e7i	−0.182785	−	0.182785i
$452$	−7.54827e7	−	1.30148e8i	−0.817396	−	1.40936i
$453$	2.00616e6	+	2.00616e6i	0.0215810	+	0.0215810i
$454$	1.10750e8	−	2.97922e7i	1.18352	−	0.318372i
$455$	−1.11241e8			−1.18094
$456$	826547.	+	2.80206e8i	0.00871712	+	2.95517i
$457$			2.53067e7i			0.265147i	0.991173	+	0.132573i	$0.0423240\pi$
$457$			2.53067e7i			0.265147i	−0.991173	+	0.132573i	$0.957676\pi$
$458$	−4.25666e7	+	1.14506e7i	−0.443071	+	0.119187i
$459$	−5.00550e7	+	5.00550e7i	−0.517618	+	0.517618i
$460$	−1.36208e7	+	5.12364e7i	−0.139936	+	0.526387i
$461$	−1.16422e8	+	1.16422e8i	−1.18832	+	1.18832i	−0.210785	+	0.977532i	$0.567602\pi$
$461$	−1.16422e8	+	1.16422e8i	−1.18832	+	1.18832i	−0.977532	+	0.210785i	$0.932398\pi$
$462$	4.11773e7	−	7.14835e7i	0.417573	−	0.724903i
$463$		−	7.86453e7i		−	0.792373i	−0.918170	−	0.396187i	$-0.870333\pi$
$463$		−	7.86453e7i		−	0.792373i	0.918170	−	0.396187i	$-0.129667\pi$
$464$	2.10654e7	+	7.73982e7i	0.210870	+	0.774777i
$465$	9.13014e7			0.908068
$466$	−1.32742e8	−	7.64648e7i	−1.31175	−	0.755621i
$467$	−1.07909e7	−	1.07909e7i	−0.105951	−	0.105951i	0.652144	−	0.758095i	$-0.273870\pi$
$467$	−1.07909e7	−	1.07909e7i	−0.105951	−	0.105951i	−0.758095	+	0.652144i	$0.773870\pi$
$468$	5.30762e7	−	1.99653e8i	0.517800	−	1.94777i
$469$	6.73998e7	+	6.73998e7i	0.653341	+	0.653341i
$470$	7.55505e6	+	2.80853e7i	0.0727685	+	0.270512i
$471$	−1.91978e8			−1.83734
$472$	2.20149e7	−	2.21451e7i	0.209358	−	0.210597i
$473$			7.33490e7i			0.693123i
$474$	−3.54515e7	−	1.31788e8i	−0.332889	−	1.23749i
$475$	5.04699e7	−	5.04699e7i	0.470925	−	0.470925i
$476$	4.11592e7	+	7.09671e7i	0.381633	+	0.658016i
$477$	1.07161e8	−	1.07161e8i	0.987374	−	0.987374i
$478$	8.15207e7	+	4.69592e7i	0.746421	+	0.429969i
$479$			1.33349e8i			1.21334i	0.794954	+	0.606670i	$0.207495\pi$
$479$			1.33349e8i			1.21334i	−0.794954	+	0.606670i	$0.792505\pi$
$480$	1.25379e8	−	7.32118e7i	1.13371	−	0.661999i
$481$	−1.32216e7			−0.118809
$482$	1.98347e7	−	3.44328e7i	0.177126	−	0.307490i
$483$	1.18125e8	+	1.18125e8i	1.04834	+	1.04834i
$484$	8.32809e7	−	4.83009e7i	0.734530	−	0.426009i
$485$	−7.40070e7	−	7.40070e7i	−0.648706	−	0.648706i
$486$	−7.96660e7	+	2.14304e7i	−0.694008	+	0.186690i
$487$	−2.41097e7			−0.208740			−0.104370	−	0.994539i	$-0.533283\pi$
$487$	−2.41097e7			−0.208740			−0.104370	+	0.994539i	$0.533283\pi$
$488$	4.03349e7	−	4.05736e7i	0.347074	−	0.349128i
$489$		−	1.96406e8i		−	1.67969i
$490$	−6.15800e7	+	1.65652e7i	−0.523421	+	0.140802i
$491$	8.96839e7	−	8.96839e7i	0.757652	−	0.757652i	−0.218242	−	0.975895i	$-0.570032\pi$
$491$	8.96839e7	−	8.96839e7i	0.757652	−	0.757652i	0.975895	+	0.218242i	$0.0700323\pi$
$492$	−1.27090e8	−	3.37860e7i	−1.06713	−	0.283688i
$493$	3.98673e7	−	3.98673e7i	0.332718	−	0.332718i
$494$	−1.23228e8	+	2.13923e8i	−1.02219	+	1.77451i
$495$			6.53419e7i			0.538736i
$496$	7.32598e7	+	4.19132e7i	0.600372	+	0.343484i
$497$	1.70793e8			1.39123
$498$	−1.93064e7	−	1.11213e7i	−0.156320	−	0.0900465i
$499$	−8.57130e7	−	8.57130e7i	−0.689835	−	0.689835i	0.272360	−	0.962195i	$-0.412196\pi$
$499$	−8.57130e7	−	8.57130e7i	−0.689835	−	0.689835i	−0.962195	+	0.272360i	$0.912196\pi$
$500$	−1.31328e8	−	3.49126e7i	−1.05063	−	0.279301i
$501$	1.65397e8	+	1.65397e8i	1.31527	+	1.31527i
$502$	−1.40857e7	−	5.23625e7i	−0.111344	−	0.413913i
$503$	2.43799e8			1.91570			0.957849	−	0.287270i	$-0.0927479\pi$
$503$	2.43799e8			1.91570			0.957849	+	0.287270i	$0.0927479\pi$
$504$	−859288.	−	2.91305e8i	−0.00671192	−	2.27539i
$505$			5.80367e7i			0.450639i
$506$	−8.99832e6	−	3.34506e7i	−0.0694560	−	0.258198i
$507$	4.92285e7	−	4.92285e7i	0.377740	−	0.377740i
$508$	1.22209e8	−	7.08780e7i	0.932204	−	0.540655i
$509$	1.11805e8	−	1.11805e8i	0.847831	−	0.847831i	−0.142032	−	0.989862i	$-0.545363\pi$
$509$	1.11805e8	−	1.11805e8i	0.847831	−	0.847831i	0.989862	+	0.142032i	$0.0453635\pi$
$510$	−8.84289e7	−	5.09386e7i	−0.666628	−	0.384005i
$511$			4.52764e7i			0.339320i
$512$	1.34212e8	−	1.18772e6i	0.999961	−	0.00884921i
$513$	−3.00379e8			−2.22494
$514$	−6.28944e7	+	1.09184e8i	−0.463151	+	0.804026i
$515$	−3.48149e7	−	3.48149e7i	−0.254884	−	0.254884i
$516$	2.04078e8	+	3.51873e8i	1.48541	+	2.56116i
$517$	−1.34370e7	−	1.34370e7i	−0.0972370	−	0.0972370i
$518$	−1.80036e7	+	4.84302e6i	−0.129530	+	0.0348440i
$519$	−3.66289e8			−2.62012
$520$	1.27919e8	−	377333.i	0.909754	−	0.00268358i
$521$		−	2.19388e8i		−	1.55131i	−0.631155	−	0.775657i	$-0.717419\pi$
$521$		−	2.19388e8i		−	1.55131i	0.631155	−	0.775657i	$-0.282581\pi$
$522$	−1.93326e8	+	5.20054e7i	−1.35919	+	0.365626i
$523$	−1.56561e8	+	1.56561e8i	−1.09441	+	1.09441i	−0.0993576	+	0.995052i	$0.531679\pi$
$523$	−1.56561e8	+	1.56561e8i	−1.09441	+	1.09441i	−0.995052	+	0.0993576i	$0.968321\pi$
$524$	−1.98487e7	+	7.46635e7i	−0.137956	+	0.518937i
$525$	−8.24019e7	+	8.24019e7i	−0.569455	+	0.569455i
$526$	1.23904e8	−	2.15096e8i	0.851387	−	1.47800i
$527$		−	5.93249e7i		−	0.405327i
$528$	−4.71085e7	+	8.23406e7i	−0.320035	+	0.559387i
$529$	−7.78899e7			−0.526155
$530$	8.13133e7	+	4.68397e7i	0.546178	+	0.314620i
$531$	5.51079e7	+	5.51079e7i	0.368070	+	0.368070i
$532$	−8.94384e7	+	3.36434e8i	−0.594004	+	2.23442i
$533$	−8.19270e7	−	8.19270e7i	−0.541060	−	0.541060i
$534$	5.87669e7	+	2.18461e8i	0.385930	+	1.43467i
$535$	6.80997e7			0.444717
$536$	−7.77335e7	−	7.72763e7i	−0.504794	−	0.501824i
$537$		−	1.83977e8i		−	1.18807i
$538$	3.14558e7	+	1.16935e8i	0.202001	+	0.750924i
$539$	2.94620e7	−	2.94620e7i	0.188147	−	0.188147i
$540$	7.80855e7	+	1.34636e8i	0.495895	+	0.855027i
$541$	3.53897e7	−	3.53897e7i	0.223504	−	0.223504i	−0.586468	−	0.809972i	$-0.699482\pi$
$541$	3.53897e7	−	3.53897e7i	0.223504	−	0.223504i	0.809972	+	0.586468i	$0.199482\pi$
$542$	1.18682e8	+	6.83658e7i	0.745398	+	0.429379i
$543$		−	7.23240e7i		−	0.451734i
$544$	−4.75708e7	−	8.14675e7i	−0.295491	−	0.506043i
$545$	−1.61965e8			−1.00053
$546$	2.01194e8	−	3.49271e8i	1.23606	−	2.14578i
$547$	−2.11041e8	−	2.11041e8i	−1.28945	−	1.28945i	−0.935122	−	0.354327i	$-0.884710\pi$
$547$	−2.11041e8	−	2.11041e8i	−1.28945	−	1.28945i	−0.354327	−	0.935122i	$-0.615290\pi$
$548$	−9.12869e6	+	5.29441e6i	−0.0554711	+	0.0321719i
$549$	1.00967e8	+	1.00967e8i	0.610186	+	0.610186i
$550$	2.33345e7	−	6.27706e6i	0.140253	−	0.0377284i
$551$	2.39243e8			1.43016
$552$	−1.36236e8	−	1.35435e8i	−0.809981	−	0.805217i
$553$		−	1.69549e8i		−	1.00258i
$554$	−4.78774e7	+	1.28792e7i	−0.281580	+	0.0757459i
$555$	1.63988e7	−	1.63988e7i	0.0959252	−	0.0959252i
$556$	−2.70321e8	−	7.18629e7i	−1.57274	−	0.418100i
$557$	−1.98247e8	+	1.98247e8i	−1.14720	+	1.14720i	−0.160103	+	0.987100i	$0.551183\pi$
$557$	−1.98247e8	+	1.98247e8i	−1.14720	+	1.14720i	−0.987100	+	0.160103i	$0.948817\pi$
$558$	−1.05147e8	+	1.82534e8i	−0.605192	+	1.05061i
$559$			3.58386e8i			2.05171i
$560$	1.74047e8	−	4.73701e7i	0.991063	−	0.269737i
$561$	6.66784e7			0.377656
$562$	2.78279e8	+	1.60300e8i	1.56773	+	0.903077i
$563$	2.27999e8	+	2.27999e8i	1.27764	+	1.27764i	0.941987	+	0.335649i	$0.108956\pi$
$563$	2.27999e8	+	2.27999e8i	1.27764	+	1.27764i	0.335649	+	0.941987i	$0.391044\pi$
$564$	−1.01846e8	−	2.70751e7i	−0.567685	−	0.150915i
$565$	1.64412e8	+	1.64412e8i	0.911564	+	0.911564i
$566$	1.94212e7	+	7.21970e7i	0.107109	+	0.398171i
$567$	7.56572e7			0.415051
$568$	−1.96399e8	+	579336.i	−1.07175	+	0.00316145i
$569$		−	4.46686e7i		−	0.242474i	−0.992624	−	0.121237i	$-0.961314\pi$
$569$		−	4.46686e7i		−	0.242474i	0.992624	−	0.121237i	$-0.0386861\pi$
$570$	−1.12489e8	−	4.18171e8i	−0.607417	−	2.25803i
$571$	9.20376e7	−	9.20376e7i	0.494376	−	0.494376i	−0.415306	−	0.909682i	$-0.636326\pi$
$571$	9.20376e7	−	9.20376e7i	0.494376	−	0.494376i	0.909682	+	0.415306i	$0.136326\pi$
$572$	−7.23003e7	+	4.19324e7i	−0.386324	+	0.224059i
$573$	−8.71642e7	+	8.71642e7i	−0.463313	+	0.463313i
$574$	−1.41568e8	−	8.15490e7i	−0.748566	−	0.431204i
$575$			4.89326e7i			0.257392i
$576$	1.97624e6	+	3.34977e8i	0.0103412	+	1.75286i
$577$	2.08860e8			1.08725			0.543623	−	0.839329i	$-0.317052\pi$
$577$	2.08860e8			1.08725			0.543623	+	0.839329i	$0.317052\pi$
$578$	6.32874e7	−	1.09866e8i	0.327743	−	0.568959i
$579$	−1.03262e8	−	1.03262e8i	−0.531992	−	0.531992i
$580$	−6.21928e7	−	1.07233e8i	−0.318754	−	0.549600i
$581$	−1.95731e7	−	1.95731e7i	−0.0998000	−	0.0998000i
$582$	3.66218e8	−	9.85139e7i	1.85768	−	0.499722i
$583$	−6.13129e7			−0.309419
$584$	−153580.	−	5.20647e7i	−0.000771072	−	0.261399i
$585$			3.19263e8i			1.59471i
$586$	−3.18666e8	+	8.57222e7i	−1.58359	+	0.425991i
$587$	2.21507e7	−	2.21507e7i	0.109515	−	0.109515i	−0.650226	−	0.759741i	$-0.725326\pi$
$587$	2.21507e7	−	2.21507e7i	0.109515	−	0.109515i	0.759741	+	0.650226i	$0.225326\pi$
$588$	5.93648e7	−	2.23308e8i	0.292010	−	1.09843i
$589$	1.78004e8	−	1.78004e8i	0.871130	−	0.871130i
$590$	−2.40875e7	+	4.18156e7i	−0.117283	+	0.203602i
$591$		−	5.71753e8i		−	2.76978i
$592$	2.06864e7	−	5.63020e6i	0.0997057	−	0.0271368i
$593$	6.69338e7			0.320982			0.160491	−	0.987037i	$-0.448692\pi$
$593$	6.69338e7			0.320982			0.160491	+	0.987037i	$0.448692\pi$
$594$	−8.81189e7	−	5.07600e7i	−0.420446	−	0.242193i
$595$	−8.96502e7	−	8.96502e7i	−0.425599	−	0.425599i
$596$	8.38965e7	−	3.15587e8i	0.396283	−	1.49067i
$597$	1.69050e8	+	1.69050e8i	0.794497	+	0.794497i
$598$	−4.39662e7	−	1.63441e8i	−0.205596	−	0.764289i
$599$	−3.45050e8			−1.60547			−0.802734	−	0.596337i	$-0.796622\pi$
$599$	−3.45050e8			−1.60547			−0.802734	+	0.596337i	$0.796622\pi$
$600$	9.44768e7	−	9.50358e7i	0.437392	−	0.439981i
$601$			2.86015e8i			1.31754i	0.752343	+	0.658772i	$0.228924\pi$
$601$			2.86015e8i			1.31754i	−0.752343	+	0.658772i	$0.771076\pi$
$602$	1.31276e8	+	4.88008e8i	0.601721	+	2.23685i
$603$	1.93439e8	−	1.93439e8i	0.882251	−	0.882251i
$604$	−2.03352e6	−	3.50621e6i	−0.00922862	−	0.0159121i
$605$	−1.05206e8	+	1.05206e8i	−0.475087	+	0.475087i
$606$	−1.82223e8	−	1.04967e8i	−0.818812	−	0.471669i
$607$			1.24729e8i			0.557700i	0.960335	+	0.278850i	$0.0899532\pi$
$607$			1.24729e8i			0.557700i	−0.960335	+	0.278850i	$0.910047\pi$
$608$	1.01707e8	−	3.87178e8i	0.452521	−	1.72266i
$609$	−3.90611e8			−1.72939
$610$	−4.41323e7	+	7.66132e7i	−0.194432	+	0.337531i
$611$	−6.56539e7	−	6.56539e7i	−0.287831	−	0.287831i
$612$	2.03677e8	−	1.18128e8i	0.888564	−	0.515345i
$613$	−1.38969e8	−	1.38969e8i	−0.603305	−	0.603305i	0.337883	−	0.941188i	$-0.390289\pi$
$613$	−1.38969e8	−	1.38969e8i	−0.603305	−	0.603305i	−0.941188	+	0.337883i	$0.890289\pi$
$614$	9.11654e7	−	2.45238e7i	0.393844	−	0.105945i
$615$	2.03229e8			0.873696
$616$	−8.30903e7	+	8.35820e7i	−0.355474	+	0.357578i
$617$			4.35555e8i			1.85433i	0.374650	+	0.927166i	$0.377763\pi$
$617$			4.35555e8i			1.85433i	−0.374650	+	0.927166i	$0.622237\pi$
$618$	1.72279e8	−	4.63436e7i	0.729905	−	0.196347i
$619$	8.97072e7	−	8.97072e7i	0.378229	−	0.378229i	−0.492234	−	0.870463i	$-0.663819\pi$
$619$	8.97072e7	−	8.97072e7i	0.378229	−	0.378229i	0.870463	+	0.492234i	$0.163819\pi$
$620$	−1.26058e8	−	3.35116e7i	−0.528927	−	0.140611i
$621$	1.45615e8	−	1.45615e8i	0.608038	−	0.608038i
$622$	1.15639e8	−	2.00748e8i	0.480544	−	0.834219i
$623$			2.81057e8i			1.16233i
$624$	−2.30174e8	+	4.02320e8i	−0.947334	+	1.65584i
$625$	1.18718e8			0.486267
$626$	1.00366e8	+	5.78146e7i	0.409130	+	0.235675i
$627$	2.00068e8	+	2.00068e8i	0.811661	+	0.811661i
$628$	2.65061e8	+	7.04645e7i	1.07020	+	0.284506i
$629$	−1.06554e7	−	1.06554e7i	−0.0428173	−	0.0428173i
$630$	1.16945e8	+	4.34735e8i	0.467693	+	1.73861i
$631$	−1.31795e8			−0.524579			−0.262289	−	0.964989i	$-0.584478\pi$
$631$	−1.31795e8			−0.524579			−0.262289	+	0.964989i	$0.584478\pi$
$632$	575118.	+	1.94970e8i	0.00227827	+	0.772353i
$633$			2.54862e8i			1.00483i
$634$	−4.03504e7	−	1.50000e8i	−0.158336	−	0.588603i
$635$	−1.54382e8	+	1.54382e8i	−0.602942	+	0.602942i
$636$	−2.94133e8	+	1.70590e8i	−1.14333	+	0.663104i
$637$	1.43953e8	−	1.43953e8i	0.556932	−	0.556932i
$638$	7.01840e7	+	4.04288e7i	0.270257	+	0.155679i
$639$		−	4.90180e8i		−	1.87868i
$640$	−1.99980e8	+	5.50626e7i	−0.762864	+	0.210047i
$641$	3.68404e8			1.39878			0.699392	−	0.714739i	$-0.253454\pi$
$641$	3.68404e8			1.39878			0.699392	+	0.714739i	$0.253454\pi$
$642$	−1.23168e8	+	2.13818e8i	−0.465471	+	0.808053i
$643$	6.99010e7	+	6.99010e7i	0.262936	+	0.262936i	0.826246	−	0.563310i	$-0.190472\pi$
$643$	6.99010e7	+	6.99010e7i	0.262936	+	0.262936i	−0.563310	+	0.826246i	$0.690472\pi$
$644$	−1.19736e8	−	2.06450e8i	−0.448298	−	0.772961i
$645$	−4.44508e8	−	4.44508e8i	−1.65654	−	1.65654i
$646$	−2.71715e8	+	7.30922e7i	−1.00790	+	0.271127i
$647$	−2.51486e8			−0.928540			−0.464270	−	0.885694i	$-0.653683\pi$
$647$	−2.51486e8			−0.928540			−0.464270	+	0.885694i	$0.653683\pi$
$648$	−8.70003e7	+	256632.i	−0.319739	+	0.000943162i
$649$		−	3.15304e7i		−	0.115344i
$650$	1.14013e8	−	3.06700e7i	0.415161	−	0.111680i
$651$	−2.90626e8	+	2.90626e8i	−1.05339	+	1.05339i
$652$	−7.20895e7	+	2.71174e8i	−0.260094	+	0.978374i
$653$	−1.46710e8	+	1.46710e8i	−0.526889	+	0.526889i	−0.919643	−	0.392755i	$-0.871522\pi$
$653$	−1.46710e8	+	1.46710e8i	−0.526889	+	0.526889i	0.392755	+	0.919643i	$0.371522\pi$
$654$	2.92936e8	−	5.08534e8i	1.04722	−	1.81797i
$655$		−	1.19394e8i		−	0.424872i
$656$	1.63070e8	+	9.32953e7i	0.577647	+	0.330482i
$657$	1.29944e8			0.458207
$658$	−1.13449e8	−	6.53509e7i	−0.398219	−	0.229390i
$659$	7.83557e7	+	7.83557e7i	0.273788	+	0.273788i	0.830623	−	0.556835i	$-0.187984\pi$
$659$	7.83557e7	+	7.83557e7i	0.273788	+	0.273788i	−0.556835	+	0.830623i	$0.687984\pi$
$660$	3.76655e7	−	1.41683e8i	0.131012	−	0.492819i
$661$	−2.26847e8	−	2.26847e8i	−0.785470	−	0.785470i	0.195278	−	0.980748i	$-0.437439\pi$
$661$	−2.26847e8	−	2.26847e8i	−0.785470	−	0.785470i	−0.980748	+	0.195278i	$0.937439\pi$
$662$	−5.28487e7	−	1.96461e8i	−0.182163	−	0.677178i
$663$	3.25794e8			1.11790
$664$	2.25740e7	+	2.24412e7i	0.0771090	+	0.0766554i
$665$		−	5.37989e8i		−	1.82940i
$666$	1.38996e7	+	5.16707e7i	0.0470522	+	0.174913i
$667$	−1.15978e8	+	1.15978e8i	−0.390839	+	0.390839i
$668$	−1.67652e8	−	2.89068e8i	−0.562445	−	0.969774i
$669$	−2.79543e8	+	2.79543e8i	−0.933621	+	0.933621i
$670$	1.46781e8	+	8.45515e7i	0.488027	+	0.281123i
$671$		−	5.77689e7i		−	0.191217i
$672$	−1.66056e8	+	6.32144e8i	−0.547200	+	2.08309i
$673$	1.89781e8			0.622597			0.311299	−	0.950312i	$-0.399236\pi$
$673$	1.89781e8			0.622597			0.311299	+	0.950312i	$0.399236\pi$
$674$	8.14205e7	−	1.41345e8i	0.265922	−	0.461638i
$675$	1.01578e8	+	1.01578e8i	0.330285	+	0.330285i
$676$	−8.60378e7	+	4.98998e7i	−0.278515	+	0.161532i
$677$	1.21554e8	+	1.21554e8i	0.391744	+	0.391744i	0.875309	−	0.483565i	$-0.160658\pi$
$677$	1.21554e8	+	1.21554e8i	0.391744	+	0.391744i	−0.483565	+	0.875309i	$0.660658\pi$
$678$	−8.13578e8	+	2.18855e8i	−2.61042	+	0.702211i
$679$	4.71151e8			1.50505
$680$	1.03395e8	+	1.02787e8i	0.328832	+	0.326898i
$681$		−	6.42220e8i		−	2.03349i
$682$	8.22992e7	−	2.21388e7i	0.259443	−	0.0697911i
$683$	1.24044e8	−	1.24044e8i	0.389325	−	0.389325i	−0.485122	−	0.874447i	$-0.661225\pi$
$683$	1.24044e8	−	1.24044e8i	0.389325	−	0.389325i	0.874447	+	0.485122i	$0.161225\pi$
$684$	9.65573e8	+	2.56691e8i	3.01729	+	0.802124i
$685$	1.15319e7	−	1.15319e7i	0.0358782	−	0.0358782i
$686$	−6.58842e7	+	1.14374e8i	−0.204084	+	0.354288i
$687$			2.46836e8i			0.761270i
$688$	−1.52613e8	−	5.60729e8i	−0.468626	−	1.72182i
$689$	−2.99578e8			−0.915908
$690$	2.57248e8	+	1.48185e8i	0.783078	+	0.451084i
$691$	−2.26281e8	−	2.26281e8i	−0.685827	−	0.685827i	0.275480	−	0.961307i	$-0.411163\pi$
$691$	−2.26281e8	−	2.26281e8i	−0.685827	−	0.685827i	−0.961307	+	0.275480i	$0.911163\pi$
$692$	5.05728e8	+	1.34444e8i	1.52615	+	0.405717i
$693$	−2.07993e8	−	2.07993e8i	−0.624955	−	0.624955i
$694$	3.91079e7	+	1.45381e8i	0.117000	+	0.434940i
$695$	4.32269e8			1.28766
$696$	4.49174e8	−	1.32497e6i	1.33225	−	0.00392986i
$697$		−	1.32052e8i		−	0.389984i
$698$	1.44431e8	+	5.36910e8i	0.424710	+	1.57883i
$699$	−6.06577e8	+	6.06577e8i	−1.77605	+	1.77605i
$700$	1.44016e8	−	8.35256e7i	0.419871	−	0.243515i
$701$	1.92569e8	−	1.92569e8i	0.559027	−	0.559027i	−0.370004	−	0.929030i	$-0.620644\pi$
$701$	1.92569e8	−	1.92569e8i	0.559027	−	0.559027i	0.929030	+	0.370004i	$0.120644\pi$
$702$	−4.30553e8	−	2.48016e8i	−1.24456	−	0.716915i
$703$		−	6.39430e7i		−	0.184046i
$704$	9.52644e7	−	9.63951e7i	0.273031	−	0.276272i
$705$	1.62862e8			0.464784
$706$	7.73283e7	−	1.34241e8i	0.219748	−	0.381480i
$707$	−1.84739e8	−	1.84739e8i	−0.522758	−	0.522758i
$708$	−8.77265e7	−	1.51259e8i	−0.247190	−	0.426208i
$709$	5.57023e7	+	5.57023e7i	0.156291	+	0.156291i	0.780921	−	0.624630i	$-0.214750\pi$
$709$	5.57023e7	+	5.57023e7i	0.156291	+	0.156291i	−0.624630	+	0.780921i	$0.714750\pi$
$710$	2.93101e8	−	7.88451e7i	0.818921	−	0.220292i
$711$	−4.86611e8			−1.35386
$712$	−953357.	−	3.23196e8i	−0.00264129	−	0.895417i
$713$			1.72582e8i			0.476131i
$714$	4.43627e8	−	1.19337e8i	1.21878	−	0.327855i
$715$	9.13344e7	−	9.13344e7i	0.249871	−	0.249871i
$716$	−6.75278e7	+	2.54014e8i	−0.183968	+	0.692020i
$717$	3.72515e8	−	3.72515e8i	1.01062	−	1.01062i
$718$	−1.20586e8	+	2.09335e8i	−0.325778	+	0.565548i
$719$		−	1.66500e8i		−	0.447949i	−0.974595	−	0.223974i	$-0.928097\pi$
$719$		−	1.66500e8i		−	0.447949i	0.974595	−	0.223974i	$-0.0719032\pi$
$720$	−1.35953e8	−	4.99518e8i	−0.364244	−	1.33830i
$721$	2.21642e8			0.591352
$722$	−7.08462e8	−	4.08102e8i	−1.88237	−	1.08432i
$723$	−1.57343e8	−	1.57343e8i	−0.416326	−	0.416326i
$724$	−2.65461e7	+	9.98564e7i	−0.0699495	+	0.263124i
$725$	−8.09040e7	−	8.09040e7i	−0.212303	−	0.212303i
$726$	−1.40044e8	−	5.20603e8i	−0.365977	−	1.36049i
$727$	3.56157e8			0.926911			0.463456	−	0.886120i	$-0.346609\pi$
$727$	3.56157e8			0.926911			0.463456	+	0.886120i	$0.346609\pi$
$728$	−4.05983e8	+	4.08385e8i	−1.05224	+	1.05846i
$729$			5.85843e8i			1.51216i
$730$	2.09015e7	+	7.76997e7i	0.0537290	+	0.199734i
$731$	−2.88828e8	+	2.88828e8i	−0.739413	+	0.739413i
$732$	−1.60730e8	−	2.77132e8i	−0.409791	−	0.706566i
$733$	−9.61641e7	+	9.61641e7i	−0.244175	+	0.244175i	−0.818575	−	0.574400i	$-0.805235\pi$
$733$	−9.61641e7	+	9.61641e7i	−0.244175	+	0.244175i	0.574400	+	0.818575i	$0.305235\pi$
$734$	−6.24416e8	−	3.59688e8i	−1.57901	−	0.909574i
$735$			3.57091e8i			0.899325i
$736$	1.38388e8	+	2.36997e8i	0.347109	+	0.594441i
$737$	−1.10677e8			−0.276476
$738$	−2.34048e8	+	4.06304e8i	−0.582284	+	1.01084i
$739$	3.01036e8	+	3.01036e8i	0.745908	+	0.745908i	0.973708	−	0.227800i	$-0.0731533\pi$
$739$	3.01036e8	+	3.01036e8i	0.745908	+	0.745908i	−0.227800	+	0.973708i	$0.573153\pi$
$740$	−2.86606e7	+	1.66224e7i	−0.0707277	+	0.0410203i
$741$	9.77540e8	+	9.77540e8i	2.40259	+	2.40259i
$742$	−4.07930e8	+	1.09734e8i	−0.998559	+	0.268616i
$743$	−9.23940e7			−0.225257			−0.112628	−	0.993637i	$-0.535927\pi$
$743$	−9.23940e7			−0.225257			−0.112628	+	0.993637i	$0.535927\pi$
$744$	3.33213e8	−	3.35185e8i	0.809102	−	0.813889i
$745$			5.04653e8i			1.22046i
$746$	5.49772e7	−	1.47890e7i	0.132424	−	0.0356224i
$747$	−5.61752e7	+	5.61752e7i	−0.134767	+	0.134767i
$748$	−9.20616e7	−	2.44739e7i	−0.219975	−	0.0584788i
$749$	−2.16771e8	+	2.16771e8i	−0.515889	+	0.515889i
$750$	−3.79826e8	+	6.59374e8i	−0.900328	+	1.56296i
$751$			7.07334e7i			0.166996i	0.996508	+	0.0834978i	$0.0266091\pi$
$751$			7.07334e7i			0.166996i	−0.996508	+	0.0834978i	$0.973391\pi$
$752$	1.30679e8	+	7.47641e7i	0.307294	+	0.175808i
$753$	−3.03641e8			−0.711173
$754$	3.42922e8	+	1.97537e8i	0.799985	+	0.460823i
$755$	4.42927e6	+	4.42927e6i	0.0102918	+	0.0102918i
$756$	−6.77124e8	−	1.80008e8i	−1.56712	−	0.416608i
$757$	−1.47342e8	−	1.47342e8i	−0.339655	−	0.339655i	0.516583	−	0.856237i	$-0.327204\pi$
$757$	−1.47342e8	−	1.47342e8i	−0.339655	−	0.339655i	−0.856237	+	0.516583i	$0.827204\pi$
$758$	−3.72410e7	−	1.38441e8i	−0.0855094	−	0.317875i
$759$	−1.93974e8			−0.443627
$760$	1.82488e6	+	6.18649e8i	0.00415713	+	1.40930i
$761$		−	7.47889e8i		−	1.69701i	−0.529190	−	0.848503i	$-0.677504\pi$
$761$		−	7.47889e8i		−	1.69701i	0.529190	−	0.848503i	$-0.322496\pi$
$762$	−2.05504e8	−	7.63947e8i	−0.464468	−	1.72663i
$763$	5.15557e8	−	5.15557e8i	1.16065	−	1.16065i
$764$	1.52339e8	−	8.83529e7i	0.341610	−	0.198126i
$765$	−2.57298e8	+	2.57298e8i	−0.574715	+	0.574715i
$766$	6.05074e8	+	3.48547e8i	1.34624	+	0.775488i
$767$		−	1.54059e8i		−	0.341429i
$768$	1.88808e8	−	7.27483e8i	0.416809	−	1.60598i
$769$	3.04514e8			0.669620			0.334810	−	0.942286i	$-0.391328\pi$
$769$	3.04514e8			0.669620			0.334810	+	0.942286i	$0.391328\pi$
$770$	9.09129e7	−	1.57824e8i	0.199138	−	0.345701i
$771$	4.98926e8	+	4.98926e8i	1.08861	+	1.08861i
$772$	1.04670e8	+	1.80474e8i	0.227495	+	0.392249i
$773$	−1.66527e8	−	1.66527e8i	−0.360534	−	0.360534i	0.503475	−	0.864010i	$-0.332054\pi$
$773$	−1.66527e8	−	1.66527e8i	−0.360534	−	0.360534i	−0.864010	+	0.503475i	$0.832054\pi$
$774$	1.40060e9	−	3.76765e8i	3.02058	−	0.812545i
$775$	−1.20390e8			−0.258634
$776$	−5.41789e8	+	1.59816e6i	−1.15943	+	0.00342007i
$777$			1.04399e8i			0.222554i
$778$	−7.16791e8	+	1.92819e8i	−1.52214	+	0.409460i
$779$	3.96221e8	−	3.96221e8i	0.838156	−	0.838156i
$780$	1.84035e8	−	6.92271e8i	0.387808	−	1.45879i
$781$	−1.40230e8	+	1.40230e8i	−0.294366	+	0.294366i
$782$	9.62863e7	−	1.67152e8i	0.201347	−	0.349536i
$783$			4.81513e8i			1.00305i
$784$	−1.63928e8	+	2.86528e8i	−0.340177	+	0.594592i
$785$	−4.23857e8			−0.876215
$786$	3.74871e8	+	2.15941e8i	0.771995	+	0.444700i
$787$	−1.36572e7	−	1.36572e7i	−0.0280181	−	0.0280181i	0.692959	−	0.720977i	$-0.256307\pi$
$787$	−1.36572e7	−	1.36572e7i	−0.0280181	−	0.0280181i	−0.720977	+	0.692959i	$0.756307\pi$
$788$	−2.09858e8	+	7.89408e8i	−0.428892	+	1.61333i
$789$	−9.82897e8	−	9.82897e8i	−2.00114	−	2.00114i
$790$	−7.82711e7	−	2.90967e8i	−0.158752	−	0.590150i
$791$	−1.04669e9			−2.11490
$792$	2.39882e8	+	2.38471e8i	0.482862	+	0.480021i
$793$		−	2.82262e8i		−	0.566021i
$794$	−1.13661e8	−	4.22528e8i	−0.227066	−	0.844099i
$795$	3.71568e8	−	3.71568e8i	0.739497	−	0.739497i
$796$	−1.71355e8	−	2.95453e8i	−0.339749	−	0.585799i
$797$	2.89625e8	−	2.89625e8i	0.572086	−	0.572086i	−0.360625	−	0.932711i	$-0.617437\pi$
$797$	2.89625e8	−	2.89625e8i	0.572086	−	0.572086i	0.932711	+	0.360625i	$0.117437\pi$
$798$	1.68917e9	+	9.73029e8i	3.32403	+	1.91477i
$799$		−	1.05823e8i		−	0.207462i
$800$	−1.65325e8	+	9.65370e7i	−0.322900	+	0.188549i
$801$	8.06641e8			1.56958
$802$	2.28413e7	−	3.96522e7i	0.0442789	−	0.0768678i
$803$	−3.71743e7	−	3.71743e7i	−0.0717954	−	0.0717954i
$804$	−5.30947e8	+	3.07936e8i	−1.02160	+	0.592505i
$805$	2.60801e8	+	2.60801e8i	0.499944	+	0.499944i
$806$	4.02118e8	−	1.08171e8i	0.767976	−	0.206588i
$807$	6.78082e8			1.29021
$808$	2.13064e8	+	2.11810e8i	0.403901	+	0.401525i
$809$			6.32786e8i			1.19512i	0.801824	+	0.597560i	$0.203863\pi$
$809$			6.32786e8i			1.19512i	−0.801824	+	0.597560i	$0.796137\pi$
$810$	1.29837e8	−	3.49265e7i	0.244311	−	0.0657204i
$811$	−1.36555e8	+	1.36555e8i	−0.256004	+	0.256004i	−0.823427	−	0.567423i	$-0.807940\pi$
$811$	−1.36555e8	+	1.36555e8i	−0.256004	+	0.256004i	0.567423	+	0.823427i	$0.307940\pi$
$812$	5.39309e8	+	1.43371e8i	1.00732	+	0.267790i
$813$	5.42329e8	−	5.42329e8i	1.00923	−	1.00923i
$814$	1.08055e7	−	1.87583e7i	0.0200342	−	0.0347792i
$815$		−	4.33632e8i		−	0.801030i
$816$	−5.09735e8	+	1.38734e8i	−0.938153	+	0.255336i
$817$	−1.73325e9			−3.17830
$818$	−5.94391e8	−	3.42393e8i	−1.08596	−	0.625554i
$819$	−1.01626e9	−	1.01626e9i	−1.84992	−	1.84992i
$820$	−2.80594e8	−	7.45939e7i	−0.508906	−	0.135289i
$821$	6.18278e8	+	6.18278e8i	1.11726	+	1.11726i	0.992142	+	0.125118i	$0.0399310\pi$
$821$	6.18278e8	+	6.18278e8i	1.11726	+	1.11726i	0.125118	+	0.992142i	$0.460069\pi$
$822$	1.53507e7	+	5.70650e7i	0.0276383	+	0.102743i
$823$	−1.80420e8			−0.323658			−0.161829	−	0.986819i	$-0.551739\pi$
$823$	−1.80420e8			−0.323658			−0.161829	+	0.986819i	$0.551739\pi$
$824$	−2.54872e8	+	751818.i	−0.455555	+	0.00134379i
$825$		−	1.35313e8i		−	0.240977i
$826$	−5.64313e7	−	2.09779e8i	−0.100134	−	0.372240i
$827$	3.14397e8	−	3.14397e8i	0.555856	−	0.555856i	−0.372269	−	0.928125i	$-0.621420\pi$
$827$	3.14397e8	−	3.14397e8i	0.555856	−	0.555856i	0.928125	+	0.372269i	$0.121420\pi$
$828$	−5.92517e8	+	3.43645e8i	−1.04378	+	0.605368i
$829$	−3.11145e8	+	3.11145e8i	−0.546135	+	0.546135i	−0.925321	−	0.379186i	$-0.876204\pi$
$829$	−3.11145e8	+	3.11145e8i	−0.546135	+	0.546135i	0.379186	+	0.925321i	$0.376204\pi$
$830$	−4.26255e7	−	2.45540e7i	−0.0745478	−	0.0429425i
$831$			2.77632e8i			0.483801i
$832$	4.65466e8	−	4.70991e8i	0.808199	−	0.817791i
$833$	2.32027e8			0.401424
$834$	−7.81820e8	+	1.35723e9i	−1.34775	+	2.33968i
$835$	3.65169e8	+	3.65169e8i	0.627241	+	0.627241i
$836$	−2.02796e8	−	3.49663e8i	−0.347089	−	0.598455i
$837$	3.58259e8	+	3.58259e8i	0.610972	+	0.610972i
$838$	−6.23528e8	+	1.67731e8i	−1.05956	+	0.285024i
$839$	4.21133e8			0.713073			0.356536	−	0.934281i	$-0.383958\pi$
$839$	4.21133e8			0.713073			0.356536	+	0.934281i	$0.383958\pi$
$840$	−2.97947e6	−	1.01007e9i	−0.00502692	−	1.70416i
$841$			2.11313e8i			0.355254i
$842$	4.69302e8	−	1.26244e8i	0.786169	−	0.211482i
$843$	1.27162e9	−	1.27162e9i	2.12263	−	2.12263i
$844$	9.35454e7	−	3.51883e8i	0.155595	−	0.585289i
$845$	1.08688e8	−	1.08688e8i	0.180141	−	0.180141i
$846$	−1.87559e8	+	3.25600e8i	−0.309761	+	0.537742i
$847$		−	6.69771e8i		−	1.10224i
$848$	4.68718e8	−	1.27570e8i	0.768642	−	0.209200i
$849$	4.18657e8			0.684125
$850$	1.16602e8	+	6.71676e7i	0.189867	+	0.109371i
$851$	3.09977e7	+	3.09977e7i	0.0502968	+	0.0502968i
$852$	−2.82558e8	+	1.06288e9i	−0.456865	+	1.71856i
$853$	5.46609e8	+	5.46609e8i	0.880703	+	0.880703i	0.993606	−	0.112903i	$-0.0360150\pi$
$853$	5.46609e8	+	5.46609e8i	0.880703	+	0.880703i	−0.112903	+	0.993606i	$0.536015\pi$
$854$	−1.03392e8	−	3.84351e8i	−0.166001	−	0.617098i
$855$	−1.54404e9			−2.47036
$856$	2.48536e8	−	2.50007e8i	0.396249	−	0.398594i
$857$			7.20599e8i			1.14486i	0.819955	+	0.572428i	$0.193998\pi$
$857$			7.20599e8i			1.14486i	−0.819955	+	0.572428i	$0.806002\pi$
$858$	1.21579e8	+	4.51961e8i	0.192485	+	0.715549i
$859$	−5.23143e8	+	5.23143e8i	−0.825356	+	0.825356i	−0.986870	−	0.161515i	$-0.948362\pi$
$859$	−5.23143e8	+	5.23143e8i	−0.825356	+	0.825356i	0.161515	+	0.986870i	$0.448362\pi$
$860$	4.50570e8	+	7.76878e8i	0.708381	+	1.22140i
$861$	−6.46908e8	+	6.46908e8i	−1.01352	+	1.01352i
$862$	5.00672e8	+	2.88407e8i	0.781685	+	0.450282i
$863$		−	3.04904e8i		−	0.474384i	−0.971463	−	0.237192i	$-0.923773\pi$
$863$		−	3.04904e8i		−	0.474384i	0.971463	−	0.237192i	$-0.0762271\pi$
$864$	7.79255e8	+	2.04700e8i	1.20820	+	0.317378i
$865$	−8.08706e8			−1.24952
$866$	4.94189e8	−	8.57907e8i	0.760920	−	1.32095i
$867$	−5.02044e8	−	5.02044e8i	−0.770343	−	0.770343i
$868$	5.07934e8	−	2.94589e8i	0.776690	−	0.450461i
$869$	1.39209e8	+	1.39209e8i	0.212133	+	0.212133i
$870$	−6.70334e8	+	1.80322e8i	−1.01797	+	0.273837i
$871$	−5.40775e8			−0.818393
$872$	−5.91105e8	+	5.94602e8i	−0.891487	+	0.896762i
$873$		−	1.35221e9i		−	2.03237i
$874$	7.90444e8	−	2.12632e8i	1.18396	−	0.318489i
$875$	−6.68481e8	+	6.68481e8i	−0.997848	+	0.997848i
$876$	−2.81764e8	−	7.49048e7i	−0.419153	−	0.111429i
$877$	1.43156e8	−	1.43156e8i	0.212231	−	0.212231i	−0.592983	−	0.805215i	$-0.702050\pi$
$877$	1.43156e8	−	1.43156e8i	0.212231	−	0.212231i	0.805215	+	0.592983i	$0.202050\pi$
$878$	−4.74687e8	+	8.24052e8i	−0.701332	+	1.21751i
$879$			1.84789e9i			2.72087i
$880$	−1.04008e8	+	1.81795e8i	−0.152623	+	0.266768i
$881$	6.20837e8			0.907924			0.453962	−	0.891021i	$-0.350010\pi$
$881$	6.20837e8			0.907924			0.453962	+	0.891021i	$0.350010\pi$
$882$	−7.13912e8	−	4.11242e8i	−1.04049	−	0.599365i
$883$	3.63776e8	+	3.63776e8i	0.528386	+	0.528386i	0.920091	−	0.391705i	$-0.128114\pi$
$883$	3.63776e8	+	3.63776e8i	0.528386	+	0.528386i	−0.391705	+	0.920091i	$0.628114\pi$
$884$	−4.49817e8	−	1.19580e8i	−0.651147	−	0.173103i
$885$	1.91080e8	+	1.91080e8i	0.275667	+	0.275667i
$886$	1.56589e8	+	5.82107e8i	0.225144	+	0.836954i
$887$	2.58424e8			0.370307			0.185154	−	0.982710i	$-0.440722\pi$
$887$	2.58424e8			0.370307			0.185154	+	0.982710i	$0.440722\pi$
$888$	−354127.	−	1.20052e8i	−0.000505732	−	0.171447i
$889$		−	9.82841e8i		−	1.39887i
$890$	1.29748e8	+	4.82327e8i	0.184047	+	0.684183i
$891$	−6.21185e7	+	6.21185e7i	−0.0878189	+	0.0878189i
$892$	4.88565e8	−	2.83355e8i	0.688379	−	0.399243i
$893$	3.17520e8	−	3.17520e8i	0.445878	−	0.445878i
$894$	−1.58450e9	−	9.12737e8i	−2.21759	−	1.27742i
$895$		−	4.06192e8i		−	0.566582i
$896$	4.61295e8	−	8.11839e8i	0.641290	−	1.12862i
$897$	−9.47765e8			−1.31318
$898$	3.67432e8	−	6.37859e8i	0.507398	−	0.880838i
$899$	−2.85343e8	−	2.85343e8i	−0.392724	−	0.392724i
$900$	−2.39721e8	−	4.13329e8i	−0.328835	−	0.566981i
$901$	−2.41433e8	−	2.41433e8i	−0.330083	−	0.330083i
$902$	1.83191e8	−	4.92790e7i	0.249623	−	0.0671494i
$903$	2.82987e9			3.84329
$904$	1.20362e9	−	3.55042e6i	1.62924	−	0.00480590i
$905$		−	1.59680e8i		−	0.215429i
$906$	−2.19179e7	+	5.89599e6i	−0.0294724	+	0.00792816i
$907$	−4.74645e8	+	4.74645e8i	−0.636131	+	0.636131i	−0.949599	−	0.313468i	$-0.898509\pi$
$907$	−4.74645e8	+	4.74645e8i	−0.636131	+	0.636131i	0.313468	+	0.949599i	$0.398509\pi$
$908$	−2.35723e8	+	8.86701e8i	−0.314880	+	1.18446i
$909$	−5.30206e8	+	5.30206e8i	−0.705916	+	0.705916i
$910$	4.44204e8	−	7.71135e8i	0.589466	−	1.02331i
$911$			1.18705e9i			1.57006i	0.619460	+	0.785028i	$0.287352\pi$
$911$			1.18705e9i			1.57006i	−0.619460	+	0.785028i	$0.712648\pi$
$912$	−1.94572e9	−	1.11318e9i	−2.56506	−	1.46751i
$913$	3.21410e7			0.0422326
$914$	−1.75429e8	−	1.01054e8i	−0.229754	−	0.132348i
$915$	3.50091e8	+	3.50091e8i	0.457001	+	0.457001i
$916$	9.05996e7	−	3.40802e8i	0.117880	−	0.443420i
$917$	3.80049e8	+	3.80049e8i	0.492869	+	0.492869i
$918$	−1.47109e8	−	5.46867e8i	−0.190157	−	0.706893i
$919$	4.88666e8			0.629602			0.314801	−	0.949158i	$-0.398062\pi$
$919$	4.88666e8			0.629602			0.314801	+	0.949158i	$0.398062\pi$
$920$	−3.00787e8	−	2.99018e8i	−0.386274	−	0.384002i
$921$		−	5.28651e8i		−	0.676691i
$922$	−3.42158e8	−	1.27195e9i	−0.436550	−	1.62284i
$923$	−6.85169e8	+	6.85169e8i	−0.871350	+	0.871350i
$924$	3.31104e8	+	5.70894e8i	0.419710	+	0.723668i
$925$	−2.16234e7	+	2.16234e7i	−0.0273211	+	0.0273211i
$926$	5.45180e8	+	3.14045e8i	0.686605	+	0.395512i
$927$		−	6.36117e8i		−	0.798543i
$928$	−6.20653e8	−	1.63037e8i	−0.776613	−	0.204006i
$929$	8.08216e8			1.00805			0.504023	−	0.863690i	$-0.331853\pi$
$929$	8.08216e8			1.00805			0.504023	+	0.863690i	$0.331853\pi$
$930$	−3.64583e8	+	6.32913e8i	−0.453261	+	0.786856i
$931$	6.96194e8	+	6.96194e8i	0.862743	+	0.862743i
$932$	1.06013e9	−	6.14849e8i	1.30952	−	0.759487i
$933$	−9.17335e8	−	9.17335e8i	−1.12949	−	1.12949i
$934$	1.17894e8	−	3.17139e7i	0.144694	−	0.0389232i
$935$	1.47215e8			0.180102
$936$	1.17208e9	+	1.16518e9i	1.42932	+	1.42091i
$937$		−	9.18312e7i		−	0.111628i	−0.998441	−	0.0558138i	$-0.982225\pi$
$937$		−	9.18312e7i		−	0.111628i	0.998441	−	0.0558138i	$-0.0177753\pi$
$938$	−7.36364e8	+	1.98084e8i	−0.892245	+	0.240017i
$939$	4.58629e8	−	4.58629e8i	0.553942	−	0.553942i
$940$	−2.24860e8	−	5.97774e7i	−0.270725	−	0.0719703i
$941$	1.01549e9	−	1.01549e9i	1.21873	−	1.21873i	0.250652	−	0.968077i	$-0.419355\pi$
$941$	1.01549e9	−	1.01549e9i	1.21873	−	1.21873i	0.968077	−	0.250652i	$-0.0806450\pi$
$942$	7.66606e8	−	1.33082e9i	0.917105	−	1.59209i
$943$			3.84152e8i			0.458108i
$944$	6.56036e7	+	2.41040e8i	0.0779851	+	0.286532i
$945$	1.08278e9			1.28306
$946$	−5.08465e8	−	2.92896e8i	−0.600603	−	0.345971i
$947$	−3.42416e8	−	3.42416e8i	−0.403184	−	0.403184i	0.476169	−	0.879354i	$-0.342025\pi$
$947$	−3.42416e8	−	3.42416e8i	−0.403184	−	0.403184i	−0.879354	+	0.476169i	$0.842025\pi$
$948$	1.05514e9	+	2.80500e8i	1.23847	+	0.329237i
$949$	−1.81635e8	−	1.81635e8i	−0.212521	−	0.212521i
$950$	1.48328e8	+	5.51399e8i	0.173003	+	0.643125i
$951$	−8.69821e8			−1.01132
$952$	−6.56310e8	+	1.93597e6i	−0.760673	+	0.00224382i
$953$			8.02540e8i			0.927231i	0.886037	+	0.463615i	$0.153448\pi$
$953$			8.02540e8i			0.927231i	−0.886037	+	0.463615i	$0.846552\pi$
$954$	3.14941e8	+	1.17077e9i	0.362730	+	1.34842i
$955$	−1.92444e8	+	1.92444e8i	−0.220951	+	0.220951i
$956$	−6.51054e8	+	3.77595e8i	−0.745150	+	0.432168i
$957$	3.20712e8	−	3.20712e8i	0.365914	−	0.365914i
$958$	−9.24392e8	−	5.32487e8i	−1.05138	−	0.605637i
$959$			7.34158e7i			0.0832403i
$960$	6.85236e6	+	1.16149e9i	0.00774509	+	1.31281i
$961$	4.62897e8			0.521572
$962$	5.27962e7	−	9.16537e7i	0.0593031	−	0.102950i
$963$	6.22139e8	+	6.22139e8i	0.696640	+	0.696640i
$964$	1.59489e8	+	2.74993e8i	0.178033	+	0.306966i
$965$	−2.27986e8	−	2.27986e8i	−0.253703	−	0.253703i
$966$	−1.29055e9	+	3.47163e8i	−1.43168	+	0.385126i
$967$	−1.72319e9			−1.90570			−0.952849	−	0.303444i	$-0.901863\pi$
$967$	−1.72319e9			−1.90570			−0.952849	+	0.303444i	$0.901863\pi$
$968$	2.27189e6	+	7.70189e8i	0.00250473	+	0.849124i
$969$			1.57562e9i			1.73173i
$970$	8.08550e8	−	2.17503e8i	0.885915	−	0.238314i
$971$	−1.34281e8	+	1.34281e8i	−0.146675	+	0.146675i	−0.776631	−	0.629956i	$-0.783073\pi$
$971$	−1.34281e8	+	1.34281e8i	−0.146675	+	0.146675i	0.629956	+	0.776631i	$0.283073\pi$
$972$	1.69563e8	−	6.37831e8i	0.184642	−	0.694556i
$973$	−1.37598e9	+	1.37598e9i	−1.49373	+	1.49373i
$974$	9.62746e7	−	1.67132e8i	0.104192	−	0.180877i
$975$		−	6.61143e8i		−	0.713315i
$976$	1.20197e8	+	4.41625e8i	0.129284	+	0.475012i
$977$	−4.47967e8			−0.480355			−0.240177	−	0.970729i	$-0.577206\pi$
$977$	−4.47967e8			−0.480355			−0.240177	+	0.970729i	$0.577206\pi$
$978$	1.36151e9	+	7.84285e8i	1.45548	+	0.838412i
$979$	−2.30763e8	−	2.30763e8i	−0.245933	−	0.245933i
$980$	1.31068e8	−	4.93028e8i	0.139257	−	0.523834i
$981$	−1.47966e9	−	1.47966e9i	−1.56731	−	1.56731i
$982$	2.63576e8	+	9.79825e8i	0.278337	+	1.03470i
$983$	−4.21768e8			−0.444031			−0.222015	−	0.975043i	$-0.571264\pi$
$983$	−4.21768e8			−0.444031			−0.222015	+	0.975043i	$0.571264\pi$
$984$	7.41703e8	−	7.46092e8i	0.778475	−	0.783082i
$985$		−	1.26234e9i		−	1.32089i
$986$	1.17168e8	+	4.35563e8i	0.122230	+	0.454381i
$987$	−5.18413e8	+	5.18413e8i	−0.539168	+	0.539168i
$988$	−9.90871e8	−	1.70847e9i	−1.02742	−	1.77148i
$989$	8.40228e8	−	8.40228e8i	0.868577	−	0.868577i
$990$	−4.52959e8	−	2.60922e8i	−0.466824	−	0.268909i
$991$		−	1.67316e9i		−	1.71916i	−0.511001	−	0.859580i	$-0.670725\pi$
$991$		−	1.67316e9i		−	1.71916i	0.511001	−	0.859580i	$-0.329275\pi$
$992$	−5.83088e8	+	3.40479e8i	−0.597309	+	0.348783i
$993$	−1.13924e9			−1.16351
$994$	−6.82007e8	+	1.18396e9i	−0.694432	+	1.20553i
$995$	3.73235e8	+	3.73235e8i	0.378890	+	0.378890i
$996$	1.54188e8	−	8.94254e7i	0.156054	−	0.0905072i
$997$	−7.73778e8	−	7.73778e8i	−0.780784	−	0.780784i	0.199179	−	0.979963i	$-0.436172\pi$
$997$	−7.73778e8	−	7.73778e8i	−0.780784	−	0.780784i	−0.979963	+	0.199179i	$0.936172\pi$
$998$	9.36442e8	−	2.51906e8i	0.942083	−	0.253424i
$999$	1.28695e8			0.129082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.11.5	yes	22
4.3	odd	2		64.7.f.a.15.1		22
8.3	odd	2		128.7.f.a.31.11		22
8.5	even	2		128.7.f.b.31.1		22
16.3	odd	4	inner	16.7.f.a.3.5	✓	22
16.5	even	4		128.7.f.a.95.11		22
16.11	odd	4		128.7.f.b.95.1		22
16.13	even	4		64.7.f.a.47.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.5	✓	22	16.3	odd	4	inner
16.7.f.a.11.5	yes	22	1.1	even	1	trivial
64.7.f.a.15.1		22	4.3	odd	2
64.7.f.a.47.1		22	16.13	even	4
128.7.f.a.31.11		22	8.3	odd	2
128.7.f.a.95.11		22	16.5	even	4
128.7.f.b.31.1		22	8.5	even	2
128.7.f.b.95.1		22	16.11	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.99319 + 6.93213i) q^{2} +(31.6770 + 31.6770i) q^{3} +(-32.1089 - 55.3626i) q^{4} +(69.9376 + 69.9376i) q^{5} +(-346.081 + 93.0969i) q^{6} -445.243 q^{7} +(511.998 - 1.51028i) q^{8} +1277.86i q^{9} +O(q^{10})\)	\(q+(-3.99319 + 6.93213i) q^{2} +(31.6770 + 31.6770i) q^{3} +(-32.1089 - 55.3626i) q^{4} +(69.9376 + 69.9376i) q^{5} +(-346.081 + 93.0969i) q^{6} -445.243 q^{7} +(511.998 - 1.51028i) q^{8} +1277.86i q^{9} +(-764.090 + 205.543i) q^{10} +(365.568 - 365.568i) q^{11} +(736.605 - 2770.83i) q^{12} +(1786.18 - 1786.18i) q^{13} +(1777.94 - 3086.49i) q^{14} +4430.82i q^{15} +(-2034.03 + 3555.27i) q^{16} +2879.01 q^{17} +(-8858.29 - 5102.73i) q^{18} +(8638.45 + 8638.45i) q^{19} +(1626.30 - 6117.55i) q^{20} +(-14103.9 - 14103.9i) q^{21} +(1074.38 + 3993.95i) q^{22} -8375.32 q^{23} +(16266.4 + 16170.7i) q^{24} -5842.47i q^{25} +(5249.49 + 19514.6i) q^{26} +(-17386.2 + 17386.2i) q^{27} +(14296.3 + 24649.8i) q^{28} +(13847.6 - 13847.6i) q^{29} +(-30715.0 - 17693.1i) q^{30} -20606.0i q^{31} +(-16523.3 - 28297.0i) q^{32} +23160.2 q^{33} +(-11496.4 + 19957.7i) q^{34} +(-31139.2 - 31139.2i) q^{35} +(70745.6 - 41030.7i) q^{36} +(-3701.07 - 3701.07i) q^{37} +(-94377.8 + 25387.9i) q^{38} +113162. q^{39} +(35913.5 + 35702.3i) q^{40} -45867.1i q^{41} +(154090. - 41450.8i) q^{42} +(-100322. + 100322. i) q^{43} +(-31976.8 - 8500.79i) q^{44} +(-89370.4 + 89370.4i) q^{45} +(33444.2 - 58058.8i) q^{46} -36756.6i q^{47} +(-177052. + 48188.1i) q^{48} +80592.5 q^{49} +(40500.8 + 23330.1i) q^{50} +(91198.3 + 91198.3i) q^{51} +(-156240. - 41535.2i) q^{52} +(-83859.8 - 83859.8i) q^{53} +(-51097.1 - 189950. i) q^{54} +51133.9 q^{55} +(-227964. + 672.443i) q^{56} +547279. i q^{57} +(40697.3 + 151289. i) q^{58} +(43125.2 - 43125.2i) q^{59} +(245302. - 142269. i) q^{60} +(79012.6 - 79012.6i) q^{61} +(142843. + 82283.5i) q^{62} -568958. i q^{63} +(262139. - 1546.52i) q^{64} +249842. q^{65} +(-92482.8 + 160549. i) q^{66} +(-151377. - 151377. i) q^{67} +(-92442.0 - 159390. i) q^{68} +(-265305. - 265305. i) q^{69} +(340206. - 91516.6i) q^{70} -383594. q^{71} +(1929.93 + 654261. i) q^{72} -101689. i q^{73} +(40435.4 - 10877.3i) q^{74} +(185072. - 185072. i) q^{75} +(200875. - 755618. i) q^{76} +(-162767. + 162767. i) q^{77} +(-451875. + 784451. i) q^{78} +380802. i q^{79} +(-390902. + 106391. i) q^{80} -169923. q^{81} +(317957. + 183156. i) q^{82} +(43960.4 + 43960.4i) q^{83} +(-327968. + 1.23369e6i) q^{84} +(201351. + 201351. i) q^{85} +(-294841. - 1.09605e6i) q^{86} +877297. q^{87} +(186618. - 187722. i) q^{88} -631244. i q^{89} +(-262655. - 976400. i) q^{90} +(-795285. + 795285. i) q^{91} +(268923. + 463680. i) q^{92} +(652735. - 652735. i) q^{93} +(254801. + 146776. i) q^{94} +1.20830e6i q^{95} +(372955. - 1.41977e6i) q^{96} -1.05819e6 q^{97} +(-321821. + 558678. i) q^{98} +(467144. + 467144. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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