LMFDB - Embedded newform 38.7.d.a.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, 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:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9440 x^{18} + 37579488 x^{16} + 83109028728 x^{14} + 112838424559344 x^{12} + \cdots + 83\!\cdots\!96 $ x^20 + 9440x^18 + 37579488x^16 + 83109028728x^14 + 112838424559344x^12 + 97808951849137728x^10 + 54352282696688610576x^8 + 18825433555812367062720x^6 + 3765133606401310416173376x^4 + 360077534420960567854418432*x^2 + 8303121574870947536327197696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.5
Root			$-50.9515i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.7.d.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(41.4005 + 23.9026i) q^{3} +(16.0000 + 27.7128i) q^{4} +(94.3029 - 163.337i) q^{5} +(-135.214 - 234.197i) q^{6} +72.4666 q^{7} -181.019i q^{8} +(778.168 + 1347.83i) q^{9} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(41.4005 + 23.9026i) q^{3} +(16.0000 + 27.7128i) q^{4} +(94.3029 - 163.337i) q^{5} +(-135.214 - 234.197i) q^{6} +72.4666 q^{7} -181.019i q^{8} +(778.168 + 1347.83i) q^{9} +(-923.976 + 533.458i) q^{10} -1294.78 q^{11} +1529.77i q^{12} +(3271.98 - 1889.08i) q^{13} +(-355.013 - 204.967i) q^{14} +(7808.38 - 4508.17i) q^{15} +(-512.000 + 886.810i) q^{16} +(-2493.43 + 4318.75i) q^{17} -8803.97i q^{18} +(4812.71 - 4887.09i) q^{19} +6035.39 q^{20} +(3000.16 + 1732.14i) q^{21} +(6343.09 + 3662.18i) q^{22} +(7090.50 + 12281.1i) q^{23} +(4326.83 - 7494.29i) q^{24} +(-9973.57 - 17274.7i) q^{25} -21372.5 q^{26} +39551.0i q^{27} +(1159.47 + 2008.25i) q^{28} +(-17848.0 + 10304.5i) q^{29} -51004.1 q^{30} -4270.12i q^{31} +(5016.55 - 2896.31i) q^{32} +(-53604.5 - 30948.5i) q^{33} +(24430.5 - 14105.0i) q^{34} +(6833.81 - 11836.5i) q^{35} +(-24901.4 + 43130.5i) q^{36} +50110.2i q^{37} +(-37400.2 + 10329.3i) q^{38} +180616. q^{39} +(-29567.2 - 17070.6i) q^{40} +(-91608.1 - 52889.9i) q^{41} +(-9798.47 - 16971.4i) q^{42} +(-6033.26 + 10449.9i) q^{43} +(-20716.4 - 35881.9i) q^{44} +293534. q^{45} -80219.8i q^{46} +(-54720.2 - 94778.2i) q^{47} +(-42394.1 + 24476.3i) q^{48} -112398. q^{49} +112838. i q^{50} +(-206459. + 119199. i) q^{51} +(104703. + 60450.6i) q^{52} +(-118645. + 68499.9i) q^{53} +(111867. - 193760. i) q^{54} +(-122101. + 211486. i) q^{55} -13117.9i q^{56} +(316063. - 87291.7i) q^{57} +116583. q^{58} +(18275.2 + 10551.2i) q^{59} +(249868. + 144261. i) q^{60} +(-100136. - 173440. i) q^{61} +(-12077.7 + 20919.2i) q^{62} +(56391.2 + 97672.5i) q^{63} -32768.0 q^{64} -712583. i q^{65} +(175071. + 303233. i) q^{66} +(244318. - 141057. i) q^{67} -159580. q^{68} +677925. i q^{69} +(-66957.4 + 38657.9i) q^{70} +(-179627. - 103707. i) q^{71} +(243983. - 140864. i) q^{72} +(-157608. + 272985. i) q^{73} +(141733. - 245489. i) q^{74} -953577. i q^{75} +(212438. + 55180.4i) q^{76} -93828.2 q^{77} +(-884832. - 510858. i) q^{78} +(-97290.3 - 56170.6i) q^{79} +(96566.2 + 167258. i) q^{80} +(-378087. + 654866. i) q^{81} +(299191. + 518213. i) q^{82} +457611. q^{83} +110857. i q^{84} +(470276. + 814541. i) q^{85} +(59113.7 - 34129.3i) q^{86} -985221. q^{87} +234380. i q^{88} +(-928050. + 535810. i) q^{89} +(-1.43802e6 - 830240. i) q^{90} +(237110. - 136895. i) q^{91} +(-226896. + 392995. i) q^{92} +(102067. - 176785. i) q^{93} +619089. i q^{94} +(-344392. - 1.24696e6i) q^{95} +276917. q^{96} +(849967. + 490729. i) q^{97} +(550633. + 317908. i) q^{98} +(-1.00756e6 - 1.74514e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$3$	41.4005	+	23.9026i	1.53335	+	0.885281i	0.999204	+	0.0398906i	$0.0127010\pi$
$3$	41.4005	+	23.9026i	1.53335	+	0.885281i	0.534148	+	0.845391i	$0.320632\pi$
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	94.3029	−	163.337i	0.754423	−	1.30670i	−0.191237	−	0.981544i	$-0.561250\pi$
$5$	94.3029	−	163.337i	0.754423	−	1.30670i	0.945661	−	0.325155i	$-0.105417\pi$
$6$	−135.214	−	234.197i	−0.625988	−	1.08424i
$7$	72.4666			0.211273			0.105636	−	0.994405i	$-0.466312\pi$
$7$	72.4666			0.211273			0.105636	+	0.994405i	$0.466312\pi$
$8$		−	181.019i		−	0.353553i
$9$	778.168	+	1347.83i	1.06745	+	1.84887i
$10$	−923.976	+	533.458i	−0.923976	+	0.533458i
$11$	−1294.78			−0.972786			−0.486393	−	0.873740i	$-0.661688\pi$
$11$	−1294.78			−0.972786			−0.486393	+	0.873740i	$0.661688\pi$
$12$			1529.77i			0.885281i
$13$	3271.98	−	1889.08i	1.48930	−	0.859845i	0.489370	−	0.872076i	$-0.337227\pi$
$13$	3271.98	−	1889.08i	1.48930	−	0.859845i	0.999925	+	0.0122309i	$0.00389333\pi$
$14$	−355.013	−	204.967i	−0.129378	−	0.0746963i
$15$	7808.38	−	4508.17i	2.31359	−	1.33575i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	−2493.43	+	4318.75i	−0.507517	+	0.879045i	0.492445	+	0.870344i	$0.336103\pi$
$17$	−2493.43	+	4318.75i	−0.507517	+	0.879045i	−0.999962	+	0.00870181i	$0.997230\pi$
$18$		−	8803.97i		−	1.50960i
$19$	4812.71	−	4887.09i	0.701664	−	0.712508i
$19$	4812.71	−	4887.09i	0.701664	−	0.712508i
$20$	6035.39			0.754423
$21$	3000.16	+	1732.14i	0.323956	+	0.187036i
$22$	6343.09	+	3662.18i	0.595707	+	0.343932i
$23$	7090.50	+	12281.1i	0.582765	+	1.00938i	0.995150	+	0.0983684i	$0.0313623\pi$
$23$	7090.50	+	12281.1i	0.582765	+	1.00938i	−0.412386	+	0.911009i	$0.635304\pi$
$24$	4326.83	−	7494.29i	0.312994	−	0.542122i
$25$	−9973.57	−	17274.7i	−0.638309	−	1.10558i
$26$	−21372.5			−1.21600
$27$			39551.0i			2.00940i
$28$	1159.47	+	2008.25i	0.0528182	+	0.0914839i
$29$	−17848.0	+	10304.5i	−0.731805	+	0.422508i	−0.819082	−	0.573676i	$-0.805517\pi$
$29$	−17848.0	+	10304.5i	−0.731805	+	0.422508i	0.0872772	+	0.996184i	$0.472183\pi$
$30$	−51004.1			−1.88904
$31$		−	4270.12i		−	0.143336i	−0.997429	−	0.0716679i	$-0.977168\pi$
$31$		−	4270.12i		−	0.143336i	0.997429	−	0.0716679i	$-0.0228322\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$	−53604.5	−	30948.5i	−1.49162	−	0.861189i
$34$	24430.5	−	14105.0i	0.621579	−	0.358869i
$35$	6833.81	−	11836.5i	0.159389	−	0.276070i
$36$	−24901.4	+	43130.5i	−0.533723	+	0.924436i
$37$			50110.2i			0.989283i	0.869097	+	0.494642i	$0.164701\pi$
$37$			50110.2i			0.989283i	−0.869097	+	0.494642i	$0.835299\pi$
$38$	−37400.2	+	10329.3i	−0.681589	+	0.188244i
$39$	180616.			3.04482
$40$	−29567.2	−	17070.6i	−0.461988	−	0.266729i
$41$	−91608.1	−	52889.9i	−1.32917	−	0.767399i	−0.344003	−	0.938969i	$-0.611783\pi$
$41$	−91608.1	−	52889.9i	−1.32917	−	0.767399i	−0.985172	+	0.171569i	$0.945116\pi$
$42$	−9798.47	−	16971.4i	−0.132254	−	0.229071i
$43$	−6033.26	+	10449.9i	−0.0758834	+	0.131434i	−0.901470	−	0.432841i	$-0.857511\pi$
$43$	−6033.26	+	10449.9i	−0.0758834	+	0.131434i	0.825587	+	0.564275i	$0.190844\pi$
$44$	−20716.4	−	35881.9i	−0.243196	−	0.421229i
$45$	293534.			3.22122
$46$		−	80219.8i		−	0.824154i
$47$	−54720.2	−	94778.2i	−0.527053	−	0.912883i	−0.999503	−	0.0315253i	$-0.989964\pi$
$47$	−54720.2	−	94778.2i	−0.527053	−	0.912883i	0.472450	−	0.881358i	$-0.343370\pi$
$48$	−42394.1	+	24476.3i	−0.383338	+	0.221320i
$49$	−112398.			−0.955364
$50$			112838.i			0.902705i
$51$	−206459.	+	119199.i	−1.55640	+	0.898591i
$52$	104703.	+	60450.6i	0.744648	+	0.429923i
$53$	−118645.	+	68499.9i	−0.796935	+	0.460111i	−0.842398	−	0.538855i	$-0.818857\pi$
$53$	−118645.	+	68499.9i	−0.796935	+	0.460111i	0.0454631	+	0.998966i	$0.485524\pi$
$54$	111867.	−	193760.i	0.710430	−	1.23050i
$55$	−122101.	+	211486.i	−0.733892	+	1.27114i
$56$		−	13117.9i		−	0.0746963i
$57$	316063.	−	87291.7i	1.70667	−	0.471355i
$58$	116583.			0.597516
$59$	18275.2	+	10551.2i	0.0889828	+	0.0513743i	0.543831	−	0.839195i	$-0.316973\pi$
$59$	18275.2	+	10551.2i	0.0889828	+	0.0513743i	−0.454848	+	0.890569i	$0.650307\pi$
$60$	249868.	+	144261.i	1.15680	+	0.667877i
$61$	−100136.	−	173440.i	−0.441164	−	0.764118i	0.556612	−	0.830772i	$-0.312101\pi$
$61$	−100136.	−	173440.i	−0.441164	−	0.764118i	−0.997776	+	0.0666541i	$0.978768\pi$
$62$	−12077.7	+	20919.2i	−0.0506769	+	0.0877749i
$63$	56391.2	+	97672.5i	0.225523	+	0.390617i
$64$	−32768.0			−0.125000
$65$		−	712583.i		−	2.59475i
$66$	175071.	+	303233.i	0.608953	+	1.05474i
$67$	244318.	−	141057.i	0.812328	−	0.468998i	−0.0354357	−	0.999372i	$-0.511282\pi$
$67$	244318.	−	141057.i	0.812328	−	0.468998i	0.847764	+	0.530374i	$0.177949\pi$
$68$	−159580.			−0.507517
$69$			677925.i			2.06364i
$70$	−66957.4	+	38657.9i	−0.195211	+	0.112705i
$71$	−179627.	−	103707.i	−0.501875	−	0.289758i	0.227612	−	0.973752i	$-0.426908\pi$
$71$	−179627.	−	103707.i	−0.501875	−	0.289758i	−0.729488	+	0.683994i	$0.760241\pi$
$72$	243983.	−	140864.i	0.653675	−	0.377399i
$73$	−157608.	+	272985.i	−0.405144	+	0.701729i	−0.994338	−	0.106262i	$-0.966112\pi$
$73$	−157608.	+	272985.i	−0.405144	+	0.701729i	0.589195	+	0.807991i	$0.299445\pi$
$74$	141733.	−	245489.i	0.349764	−	0.605810i
$75$		−	953577.i		−	2.26033i
$76$	212438.	+	55180.4i	0.483941	+	0.125703i
$77$	−93828.2			−0.205523
$78$	−884832.	−	510858.i	−1.86456	−	1.07651i
$79$	−97290.3	−	56170.6i	−0.197328	−	0.113927i	0.398081	−	0.917350i	$-0.369676\pi$
$79$	−97290.3	−	56170.6i	−0.197328	−	0.113927i	−0.595408	+	0.803423i	$0.703010\pi$
$80$	96566.2	+	167258.i	0.188606	+	0.326675i
$81$	−378087.	+	654866.i	−0.711437	+	1.23225i
$82$	299191.	+	518213.i	0.542633	+	0.939868i
$83$	457611.			0.800317			0.400159	−	0.916446i	$-0.368955\pi$
$83$	457611.			0.800317			0.400159	+	0.916446i	$0.368955\pi$
$84$			110857.i			0.187036i
$85$	470276.	+	814541.i	0.765765	+	1.32634i
$86$	59113.7	−	34129.3i	0.0929378	−	0.0536577i
$87$	−985221.			−1.49615
$88$			234380.i			0.343932i
$89$	−928050.	+	535810.i	−1.31644	+	0.760047i	−0.983154	−	0.182778i	$-0.941491\pi$
$89$	−928050.	+	535810.i	−1.31644	+	0.760047i	−0.333287	+	0.942826i	$0.608158\pi$
$90$	−1.43802e6	−	830240.i	−1.97259	−	1.13888i
$91$	237110.	−	136895.i	0.314648	−	0.181662i
$92$	−226896.	+	392995.i	−0.291382	+	0.504689i
$93$	102067.	−	176785.i	0.126893	−	0.219784i
$94$			619089.i			0.745366i
$95$	−344392.	−	1.24696e6i	−0.401682	−	1.45440i
$96$	276917.			0.312994
$97$	849967.	+	490729.i	0.931294	+	0.537683i	0.887221	−	0.461345i	$-0.152633\pi$
$97$	849967.	+	490729.i	0.931294	+	0.537683i	0.0440736	+	0.999028i	$0.485966\pi$
$98$	550633.	+	317908.i	0.585038	+	0.337772i
$99$	−1.00756e6	−	1.74514e6i	−1.03840	−	1.79856i
$100$	319154.	−	552791.i	0.319154	−	0.552791i
$101$	390995.	+	677224.i	0.379496	+	0.657307i	0.990989	−	0.133943i	$-0.0427640\pi$
$101$	390995.	+	677224.i	0.379496	+	0.657307i	−0.611493	+	0.791250i	$0.709431\pi$
$102$	1.34858e6			1.27080
$103$		−	612828.i		−	0.560824i	−0.959880	−	0.280412i	$-0.909529\pi$
$103$		−	612828.i		−	0.560824i	0.959880	−	0.280412i	$-0.0904711\pi$
$104$	−341960.	−	592292.i	−0.304001	−	0.526545i
$105$	565847.	−	326692.i	0.488800	−	0.282209i
$106$	774988.			0.650695
$107$			658832.i			0.537804i	0.963168	+	0.268902i	$0.0866607\pi$
$107$			658832.i			0.537804i	−0.963168	+	0.268902i	$0.913339\pi$
$108$	−1.09607e6	+	632816.i	−0.870095	+	0.502350i
$109$	−935796.	−	540282.i	−0.722606	−	0.417197i	0.0931051	−	0.995656i	$-0.470321\pi$
$109$	−935796.	−	540282.i	−0.722606	−	0.417197i	−0.815711	+	0.578460i	$0.803654\pi$
$110$	1.19634e6	−	690709.i	0.898830	−	0.518940i
$111$	−1.19776e6	+	2.07459e6i	−0.875794	+	1.51692i
$112$	−37102.9	+	64264.1i	−0.0264091	+	0.0457419i
$113$			1.56575e6i			1.08514i	0.840009	+	0.542572i	$0.182550\pi$
$113$			1.56575e6i			1.08514i	−0.840009	+	0.542572i	$0.817450\pi$
$114$	−1.79528e6	−	466321.i	−1.21177	−	0.314753i
$115$	2.67462e6			1.75860
$116$	−571136.	−	329745.i	−0.365902	−	0.211254i
$117$	5.09231e6	+	2.94004e6i	3.17949	+	1.83568i
$118$	−59686.6	−	103380.i	−0.0363271	−	0.0629204i
$119$	−180691.	+	312965.i	−0.107225	+	0.185719i
$120$	−816066.	−	1.41347e6i	−0.472260	−	0.817979i
$121$	−95111.9			−0.0536882
$122$			1.13291e6i			0.623900i
$123$	−2.52841e6	−	4.37934e6i	−1.35873	−	2.35339i
$124$	118337.	−	68321.9i	0.0620663	−	0.0358340i
$125$	−815181.			−0.417373
$126$		−	637994.i		−	0.318937i
$127$	2.36941e6	−	1.36798e6i	1.15672	−	0.667835i	0.206207	−	0.978508i	$-0.433888\pi$
$127$	2.36941e6	−	1.36798e6i	1.15672	−	0.667835i	0.950517	+	0.310673i	$0.100555\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$	−499560.	+	288421.i	−0.232712	+	0.134356i
$130$	−2.01549e6	+	3.49093e6i	−0.917382	+	1.58895i
$131$	1.78978e6	−	3.09998e6i	0.796132	−	1.37894i	−0.125986	−	0.992032i	$-0.540210\pi$
$131$	1.78978e6	−	3.09998e6i	0.796132	−	1.37894i	0.922118	−	0.386909i	$-0.126457\pi$
$132$		−	1.98071e6i		−	0.861189i
$133$	348761.	−	354151.i	0.148243	−	0.150534i
$134$	−1.59588e6			−0.663263
$135$	6.46016e6	+	3.72977e6i	2.62568	+	1.51594i
$136$	781777.	+	451359.i	0.310789	+	0.179434i
$137$	−264588.	−	458280.i	−0.102898	−	0.178225i	0.809979	−	0.586459i	$-0.199478\pi$
$137$	−264588.	−	458280.i	−0.102898	−	0.178225i	−0.912878	+	0.408233i	$0.866145\pi$
$138$	1.91746e6	−	3.32114e6i	0.729608	−	1.26372i
$139$	1.36688e6	+	2.36750e6i	0.508961	+	0.881547i	0.999946	+	0.0103789i	$0.00330376\pi$
$139$	1.36688e6	+	2.36750e6i	0.508961	+	0.881547i	−0.490985	+	0.871168i	$0.663363\pi$
$140$	437364.			0.159389
$141$		−	5.23182e6i		−	1.86636i
$142$	586658.	+	1.01612e6i	0.204890	+	0.354879i
$143$	−4.23649e6	+	2.44594e6i	−1.44877	+	0.836445i
$144$	−1.59369e6			−0.533723
$145$			3.88699e6i			1.27500i
$146$	1.54423e6	−	891564.i	0.496197	−	0.286480i
$147$	−4.65332e6	−	2.68659e6i	−1.46491	−	0.845766i
$148$	−1.38869e6	+	801763.i	−0.428372	+	0.247321i
$149$	2.79088e6	−	4.83395e6i	0.843690	−	1.46131i	−0.0430643	−	0.999072i	$-0.513712\pi$
$149$	2.79088e6	−	4.83395e6i	0.843690	−	1.46131i	0.886754	−	0.462241i	$-0.152955\pi$
$150$	−2.69712e6	+	4.67155e6i	−0.799148	+	1.38416i
$151$			3.72828e6i			1.08287i	0.840742	+	0.541436i	$0.182119\pi$
$151$			3.72828e6i			1.08287i	−0.840742	+	0.541436i	$0.817881\pi$
$152$	−884658.	−	871194.i	−0.251910	−	0.248076i
$153$	−7.76124e6			−2.16699
$154$	459662.	+	265386.i	0.125857	+	0.0726635i
$155$	−697470.	−	402685.i	−0.187297	−	0.108136i
$156$	2.88985e6	+	5.00537e6i	0.761205	+	1.31845i
$157$	−1.85548e6	+	3.21379e6i	−0.479466	+	0.830459i	−0.999723	−	0.0235509i	$-0.992503\pi$
$157$	−1.85548e6	+	3.21379e6i	−0.479466	+	0.830459i	0.520257	+	0.854010i	$0.325836\pi$
$158$	317749.	+	550357.i	0.0805587	+	0.139532i
$159$	−6.54930e6			−1.62931
$160$		−	1.09252e6i		−	0.266729i
$161$	513824.	+	889970.i	0.123122	+	0.213254i
$162$	3.70448e6	−	2.13878e6i	0.871329	−	0.503062i
$163$	−5.09856e6			−1.17729			−0.588647	−	0.808390i	$-0.700339\pi$
$163$	−5.09856e6			−1.17729			−0.588647	+	0.808390i	$0.700339\pi$
$164$		−	3.38496e6i		−	0.767399i
$165$	−1.01101e7	+	5.83708e6i	−2.25063	+	1.29940i
$166$	−2.24183e6	−	1.29432e6i	−0.490092	−	0.282955i
$167$	−287192.	+	165810.i	−0.0616627	+	0.0356010i	−0.530514	−	0.847676i	$-0.678001\pi$
$167$	−287192.	+	165810.i	−0.0616627	+	0.0356010i	0.468852	+	0.883277i	$0.344668\pi$
$168$	313551.	−	543086.i	0.0661272	−	0.114536i
$169$	4.72384e6	−	8.18193e6i	0.978667	−	1.69510i
$170$		−	5.32056e6i		−	1.08296i
$171$	1.03321e7	+	2.68373e6i	2.06632	+	0.536723i
$172$	−386129.			−0.0758834
$173$	−2.12189e6	−	1.22508e6i	−0.409812	−	0.236605i	0.280897	−	0.959738i	$-0.409368\pi$
$173$	−2.12189e6	−	1.22508e6i	−0.409812	−	0.236605i	−0.690709	+	0.723133i	$0.742701\pi$
$174$	4.82658e6	+	2.78663e6i	0.916203	+	0.528970i
$175$	−722751.	−	1.25184e6i	−0.134857	−	0.233580i
$176$	662926.	−	1.14822e6i	0.121598	−	0.210614i
$177$	504402.	+	873650.i	0.0909613	+	0.157550i
$178$	6.06200e6			1.07487
$179$			4.36772e6i			0.761545i	0.924669	+	0.380772i	$0.124342\pi$
$179$			4.36772e6i			0.761545i	−0.924669	+	0.380772i	$0.875658\pi$
$180$	4.69655e6	+	8.13466e6i	0.805306	+	1.39483i
$181$	−1.32298e6	+	763823.i	−0.223109	+	0.128812i	−0.607389	−	0.794404i	$-0.707783\pi$
$181$	−1.32298e6	+	763823.i	−0.223109	+	0.128812i	0.384280	+	0.923217i	$0.374450\pi$
$182$	−1.54879e6			−0.256909
$183$		−	9.57403e6i		−	1.56222i
$184$	2.22312e6	−	1.28352e6i	0.356869	−	0.206038i
$185$	8.18486e6	+	4.72553e6i	1.29270	+	0.746338i
$186$	−1.00005e6	+	577378.i	−0.155411	+	0.0897266i
$187$	3.22844e6	−	5.59182e6i	0.493705	−	0.855123i
$188$	1.75105e6	−	3.03290e6i	0.263527	−	0.456441i
$189$			2.86613e6i			0.424532i
$190$	−1.83978e6	+	7.08293e6i	−0.268228	+	1.03265i
$191$	−7.93208e6			−1.13838			−0.569189	−	0.822206i	$-0.692743\pi$
$191$	−7.93208e6			−1.13838			−0.569189	+	0.822206i	$0.692743\pi$
$192$	−1.35661e6	−	783240.i	−0.191669	−	0.110660i
$193$	−7.56258e6	−	4.36625e6i	−1.05196	−	0.607347i	−0.128760	−	0.991676i	$-0.541100\pi$
$193$	−7.56258e6	−	4.36625e6i	−1.05196	−	0.607347i	−0.923196	+	0.384328i	$0.874433\pi$
$194$	−2.77598e6	−	4.80814e6i	−0.380199	−	0.658525i
$195$	1.70326e7	−	2.95013e7i	2.29708	−	3.97866i
$196$	−1.79836e6	−	3.11485e6i	−0.238841	−	0.413685i
$197$	1.37917e7			1.80393			0.901964	−	0.431811i	$-0.142125\pi$
$197$	1.37917e7			1.80393			0.901964	+	0.431811i	$0.142125\pi$
$198$			1.13992e7i			1.46851i
$199$	3.67351e6	+	6.36271e6i	0.466146	+	0.807389i	0.999252	−	0.0386592i	$-0.0123087\pi$
$199$	3.67351e6	+	6.36271e6i	0.466146	+	0.807389i	−0.533106	+	0.846048i	$0.678975\pi$
$200$	−3.12706e6	+	1.80541e6i	−0.390883	+	0.225676i
$201$	1.34865e7			1.66078
$202$		−	4.42361e6i		−	0.536689i
$203$	−1.29338e6	+	746735.i	−0.154611	+	0.0892645i
$204$	−6.60668e6	−	3.81437e6i	−0.778202	−	0.449295i
$205$	−1.72778e7	+	9.97535e6i	−2.00552	+	1.15789i
$206$	−1.73334e6	+	3.00223e6i	−0.198281	+	0.343433i
$207$	−1.10352e7	+	1.91135e7i	−1.24414	+	2.15491i
$208$			3.86884e6i			0.429923i
$209$	−6.23140e6	+	6.32770e6i	−0.682569	+	0.693117i
$210$	−3.69610e6			−0.399103
$211$	1.32960e7	+	7.67647e6i	1.41539	+	0.817174i	0.995889	−	0.0905831i	$-0.0288731\pi$
$211$	1.32960e7	+	7.67647e6i	1.41539	+	0.817174i	0.419497	+	0.907757i	$0.362206\pi$
$212$	−3.79665e6	−	2.19200e6i	−0.398468	−	0.230055i
$213$	−4.95776e6	−	8.58709e6i	−0.513034	−	0.888601i
$214$	1.86346e6	−	3.22761e6i	0.190142	−	0.329336i
$215$	1.13791e6	+	1.97091e6i	0.114496	+	0.198314i
$216$	7.15950e6			0.710430
$217$		−	309441.i		−	0.0302830i
$218$	3.05630e6	+	5.29366e6i	0.295003	+	0.510960i
$219$	−1.30501e7	+	7.53447e6i	−1.24246	+	0.717332i
$220$	−7.81448e6			−0.733892
$221$			1.88412e7i			1.74554i
$222$	1.17356e7	−	6.77557e6i	1.07262	−	0.619280i
$223$	1.27016e7	+	7.33329e6i	1.14537	+	0.661278i	0.947754	−	0.319002i	$-0.103348\pi$
$223$	1.27016e7	+	7.33329e6i	1.14537	+	0.661278i	0.197613	+	0.980280i	$0.436681\pi$
$224$	363533.	−	209886.i	0.0323444	−	0.0186741i
$225$	1.55222e7	−	2.68853e7i	1.36272	−	2.36030i
$226$	4.42862e6	−	7.67059e6i	0.383657	−	0.664513i
$227$		−	1.22834e7i		−	1.05012i	−0.851064	−	0.525061i	$-0.824042\pi$
$227$		−	1.22834e7i		−	1.05012i	0.851064	−	0.525061i	$-0.175958\pi$
$228$	7.47611e6	+	7.36233e6i	0.630770	+	0.621170i
$229$	4.58805e6			0.382051			0.191026	−	0.981585i	$-0.438819\pi$
$229$	4.58805e6			0.382051			0.191026	+	0.981585i	$0.438819\pi$
$230$	−1.31029e7	−	7.56496e6i	−1.07692	−	0.621760i
$231$	−3.88453e6	−	2.24274e6i	−0.315140	−	0.181946i
$232$	1.86532e6	+	3.23083e6i	0.149379	+	0.258732i
$233$	4.21974e6	−	7.30881e6i	0.333594	−	0.577802i	−0.649620	−	0.760259i	$-0.725072\pi$
$233$	4.21974e6	−	7.30881e6i	0.333594	−	0.577802i	0.983214	+	0.182457i	$0.0584052\pi$
$234$	−1.66314e7	−	2.88064e7i	−1.29802	−	2.24824i
$235$	−2.06411e7			−1.59048
$236$			675276.i			0.0513743i
$237$	−2.68525e6	−	4.65098e6i	−0.201715	−	0.349381i
$238$	1.77040e6	−	1.02214e6i	0.131323	−	0.0758193i
$239$	−4.63684e6			−0.339648			−0.169824	−	0.985474i	$-0.554320\pi$
$239$	−4.63684e6			−0.339648			−0.169824	+	0.985474i	$0.554320\pi$
$240$			9.23273e6i			0.667877i
$241$	1.11493e7	−	6.43706e6i	0.796520	−	0.459871i	−0.0457328	−	0.998954i	$-0.514562\pi$
$241$	1.11493e7	−	6.43706e6i	0.796520	−	0.459871i	0.842253	+	0.539083i	$0.181229\pi$
$242$	465951.	+	269017.i	0.0328772	+	0.0189816i
$243$	−6.33615e6	+	3.65818e6i	−0.441577	+	0.254945i
$244$	3.20435e6	−	5.55009e6i	0.220582	−	0.382059i
$245$	−1.05994e7	+	1.83587e7i	−0.720749	+	1.24837i
$246$			2.86057e7i			1.92153i
$247$	6.51501e6	−	2.50821e7i	0.432339	−	1.66446i
$248$	−772974.			−0.0506769
$249$	1.89453e7	+	1.09381e7i	1.22717	+	0.708506i
$250$	3.99356e6	+	2.30568e6i	0.255588	+	0.147564i
$251$	−44322.5	−	76768.8i	−0.00280287	−	0.00485471i	0.864621	−	0.502425i	$-0.167559\pi$
$251$	−44322.5	−	76768.8i	−0.00280287	−	0.00485471i	−0.867423	+	0.497571i	$0.834226\pi$
$252$	−1.80452e6	+	3.12552e6i	−0.112761	+	0.195308i
$253$	−9.18062e6	−	1.59013e7i	−0.566905	−	0.981908i
$254$	−1.54769e7			−0.944461
$255$			4.49632e7i			2.71167i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.24868e6	+	720927.i	−0.0735619	+	0.0424710i	−0.536330	−	0.844009i	$-0.680190\pi$
$257$	−1.24868e6	+	720927.i	−0.0735619	+	0.0424710i	0.462768	+	0.886479i	$0.346856\pi$
$258$	3.26311e6			0.190009
$259$			3.63131e6i			0.209009i
$260$	1.97477e7	−	1.14013e7i	1.12356	−	0.648687i
$261$	−2.77775e7	−	1.60373e7i	−1.56232	−	0.902009i
$262$	−1.75362e7	+	1.01245e7i	−0.975058	+	0.562950i
$263$	8.79904e6	−	1.52404e7i	0.483691	−	0.837778i	−0.516133	−	0.856508i	$-0.672629\pi$
$263$	8.79904e6	−	1.52404e7i	0.483691	−	0.837778i	0.999825	+	0.0187305i	$0.00596244\pi$
$264$	−5.60229e6	+	9.70344e6i	−0.304476	+	0.527368i
$265$			2.58390e7i			1.38847i
$266$	−2.71026e6	+	748533.i	−0.144001	+	0.0397709i
$267$	−5.12290e7			−2.69142
$268$	7.81818e6	+	4.51383e6i	0.406164	+	0.234499i
$269$	2.22350e7	+	1.28374e7i	1.14230	+	0.659509i	0.947000	−	0.321234i	$-0.104098\pi$
$269$	2.22350e7	+	1.28374e7i	1.14230	+	0.659509i	0.195303	+	0.980743i	$0.437431\pi$
$270$	−2.10988e7	−	3.65442e7i	−1.07193	−	1.85664i
$271$	2.21097e6	−	3.82951e6i	0.111090	−	0.192414i	−0.805120	−	0.593112i	$-0.797899\pi$
$271$	2.21097e6	−	3.82951e6i	0.111090	−	0.192414i	0.916210	+	0.400698i	$0.131232\pi$
$272$	−2.55327e6	−	4.42240e6i	−0.126879	−	0.219761i
$273$	1.30886e7			0.643288
$274$			2.99347e6i			0.145520i
$275$	1.29136e7	+	2.23669e7i	0.620937	+	1.07550i
$276$	−1.87872e7	+	1.08468e7i	−0.893583	+	0.515911i
$277$	1.46321e7			0.688442			0.344221	−	0.938889i	$-0.388143\pi$
$277$	1.46321e7			0.688442			0.344221	+	0.938889i	$0.388143\pi$
$278$		−	1.54644e7i		−	0.719780i
$279$	5.75538e6	−	3.32287e6i	0.265010	−	0.153003i
$280$	−2.14264e6	−	1.23705e6i	−0.0976056	−	0.0563526i
$281$	−7.39051e6	+	4.26691e6i	−0.333085	+	0.192307i	−0.657210	−	0.753708i	$-0.728264\pi$
$281$	−7.39051e6	+	4.26691e6i	−0.333085	+	0.192307i	0.324125	+	0.946014i	$0.394930\pi$
$282$	−1.47978e7	+	2.56306e7i	−0.659859	+	1.14291i
$283$	9.03455e6	−	1.56483e7i	0.398609	−	0.690411i	−0.594946	−	0.803766i	$-0.702826\pi$
$283$	9.03455e6	−	1.56483e7i	0.398609	−	0.690411i	0.993555	+	0.113355i	$0.0361597\pi$
$284$		−	6.63728e6i		−	0.289758i
$285$	1.55477e7	−	5.98568e7i	0.671631	−	2.58570i
$286$	2.76726e7			1.18291
$287$	−6.63853e6	−	3.83276e6i	−0.280819	−	0.162131i
$288$	7.80745e6	+	4.50763e6i	0.326837	+	0.188700i
$289$	−365615.	−	633264.i	−0.0151471	−	0.0262356i
$290$	1.09941e7	−	1.90423e7i	0.450780	−	0.780774i
$291$	2.34594e7	+	4.06328e7i	0.952002	+	1.64892i
$292$	−1.00869e7			−0.405144
$293$		−	8.85882e6i		−	0.352187i	−0.984373	−	0.176093i	$-0.943654\pi$
$293$		−	8.85882e6i		−	0.352187i	0.984373	−	0.176093i	$-0.0563461\pi$
$294$	1.51977e7	+	2.63231e7i	0.598047	+	1.03585i
$295$	3.44681e6	−	1.99002e6i	0.134261	−	0.0775158i
$296$	9.07091e6			0.349764
$297$		−	5.12097e7i		−	1.95471i
$298$	−2.73450e7	+	1.57876e7i	−1.03330	+	0.596579i
$299$	4.64000e7	+	2.67890e7i	1.73582	+	1.00217i
$300$	2.64263e7	−	1.52572e7i	0.978752	−	0.565083i
$301$	−437210.	+	757270.i	−0.0160321	+	0.0277684i
$302$	1.05452e7	−	1.82647e7i	0.382853	−	0.663121i
$303$			3.73832e7i			1.34384i
$304$	1.86981e6	+	6.77015e6i	0.0665544	+	0.240978i
$305$	−3.77724e7			−1.33130
$306$	3.80221e7	+	2.19521e7i	1.32700	+	0.766146i
$307$	2.31462e6	+	1.33635e6i	0.0799954	+	0.0461853i	0.539464	−	0.842009i	$-0.318627\pi$
$307$	2.31462e6	+	1.33635e6i	0.0799954	+	0.0461853i	−0.459469	+	0.888194i	$0.651960\pi$
$308$	−1.50125e6	−	2.60024e6i	−0.0513808	−	0.0889942i
$309$	1.46482e7	−	2.53714e7i	0.496487	−	0.859941i
$310$	2.27793e6	+	3.94549e6i	0.0764636	+	0.132439i
$311$	4.26039e6			0.141634			0.0708171	−	0.997489i	$-0.477439\pi$
$311$	4.26039e6			0.141634			0.0708171	+	0.997489i	$0.477439\pi$
$312$		−	3.26949e7i		−	1.07651i
$313$	−1.35456e7	−	2.34617e7i	−0.441739	−	0.765114i	0.556080	−	0.831129i	$-0.312305\pi$
$313$	−1.35456e7	−	2.34617e7i	−0.441739	−	0.765114i	−0.997819	+	0.0660150i	$0.978971\pi$
$314$	1.81799e7	−	1.04962e7i	0.587223	−	0.339033i
$315$	2.12714e7			0.680558
$316$		−	3.59492e6i		−	0.113927i
$317$	−4.40884e7	+	2.54545e7i	−1.38403	+	0.799072i	−0.992634	−	0.121149i	$-0.961342\pi$
$317$	−4.40884e7	+	2.54545e7i	−1.38403	+	0.799072i	−0.391400	+	0.920221i	$0.628009\pi$
$318$	3.20849e7	+	1.85242e7i	0.997745	+	0.576048i
$319$	2.31092e7	−	1.33421e7i	0.711889	−	0.411009i
$320$	−3.09012e6	+	5.35224e6i	−0.0943029	+	0.163337i
$321$	−1.57478e7	+	2.72760e7i	−0.476107	+	0.824642i
$322$		−	5.81326e6i		−	0.174121i
$323$	9.10595e6	+	3.29705e7i	0.270220	+	0.978404i
$324$	−2.41976e7			−0.711437
$325$	−6.52667e7	−	3.76817e7i	−1.90126	−	1.09769i
$326$	2.49778e7	+	1.44209e7i	0.720942	+	0.416236i
$327$	−2.58283e7	−	4.47359e7i	−0.738673	−	1.27942i
$328$	−9.57410e6	+	1.65828e7i	−0.271317	+	0.469934i
$329$	−3.96539e6	−	6.86826e6i	−0.111352	−	0.192868i
$330$	6.60390e7			1.83763
$331$		−	6.19336e7i		−	1.70782i	−0.520420	−	0.853910i	$-0.674225\pi$
$331$		−	6.19336e7i		−	1.70782i	0.520420	−	0.853910i	$-0.325775\pi$
$332$	7.32177e6	+	1.26817e7i	0.200079	+	0.346547i
$333$	−6.75398e7	+	3.89941e7i	−1.82906	+	1.05601i
$334$	1.87593e6			0.0503474
$335$		−	5.32084e7i		−	1.41529i
$336$	−3.07216e6	+	1.77371e6i	−0.0809890	+	0.0467590i
$337$	−5.80639e7	−	3.35232e7i	−1.51711	−	0.875903i	−0.999798	−	0.0201054i	$-0.993600\pi$
$337$	−5.80639e7	−	3.35232e7i	−1.51711	−	0.875903i	−0.517311	−	0.855798i	$-0.673067\pi$
$338$	−4.62840e7	+	2.67221e7i	−1.19862	+	0.692022i
$339$	−3.74255e7	+	6.48229e7i	−0.960658	+	1.66391i
$340$	−1.50488e7	+	2.60653e7i	−0.382883	+	0.663172i
$341$			5.52885e6i			0.139435i
$342$	−4.30258e7	−	4.23710e7i	−1.07560	−	1.05923i
$343$	−1.66707e7			−0.413116
$344$	1.89164e6	+	1.09214e6i	0.0464689	+	0.0268288i
$345$	1.10731e8	+	6.39303e7i	2.69656	+	1.55686i
$346$	6.93007e6	+	1.20032e7i	0.167305	+	0.289781i
$347$	−1.43380e7	+	2.48341e7i	−0.343163	+	0.594375i	−0.985018	−	0.172451i	$-0.944831\pi$
$347$	−1.43380e7	+	2.48341e7i	−0.343163	+	0.594375i	0.641856	+	0.766825i	$0.278165\pi$
$348$	−1.57635e7	−	2.73033e7i	−0.374038	−	0.647853i
$349$	3.47756e7			0.818086			0.409043	−	0.912515i	$-0.365863\pi$
$349$	3.47756e7			0.818086			0.409043	+	0.912515i	$0.365863\pi$
$350$			8.17700e6i			0.190717i
$351$	7.47150e7	+	1.29410e8i	1.72777	+	2.99259i
$352$	−6.49532e6	+	3.75008e6i	−0.148927	+	0.0859829i
$353$	−4.80897e6			−0.109327			−0.0546636	−	0.998505i	$-0.517409\pi$
$353$	−4.80897e6			−0.109327			−0.0546636	+	0.998505i	$0.517409\pi$
$354$		−	5.70666e6i		−	0.128639i
$355$	−3.38786e7	+	1.95598e7i	−0.757252	+	0.437200i
$356$	−2.96976e7	−	1.71459e7i	−0.658220	−	0.380024i
$357$	−1.49614e7	+	8.63795e6i	−0.328826	+	0.189848i
$358$	1.23538e7	−	2.13974e7i	0.269247	−	0.466349i
$359$	2.08167e7	−	3.60556e7i	0.449913	−	0.779272i	−0.548467	−	0.836172i	$-0.684788\pi$
$359$	2.08167e7	−	3.60556e7i	0.449913	−	0.779272i	0.998380	+	0.0569005i	$0.0181218\pi$
$360$		−	5.31354e7i		−	1.13888i
$361$	−721435.	−	4.70403e7i	−0.0153347	−	0.999882i
$362$	8.64167e6			0.182168
$363$	−3.93768e6	−	2.27342e6i	−0.0823229	−	0.0475292i
$364$	7.58750e6	+	4.38065e6i	0.157324	+	0.0908310i
$365$	2.97257e7	+	5.14865e7i	0.611299	+	1.05880i
$366$	−2.70794e7	+	4.69030e7i	−0.552327	+	0.956659i
$367$	−4.24563e7	−	7.35366e7i	−0.858904	−	1.48766i	−0.872976	−	0.487764i	$-0.837813\pi$
$367$	−4.24563e7	−	7.35366e7i	−0.858904	−	1.48766i	0.0140720	−	0.999901i	$-0.495521\pi$
$368$	−1.45213e7			−0.291382
$369$		−	1.64629e8i		−	3.27663i
$370$	−2.67317e7	−	4.63006e7i	−0.527741	−	0.914074i
$371$	−8.59783e6	+	4.96396e6i	−0.168371	+	0.0972090i
$372$	6.53228e6			0.126893
$373$			1.72962e7i			0.333291i	0.986017	+	0.166646i	$0.0532936\pi$
$373$			1.72962e7i			0.333291i	−0.986017	+	0.166646i	$0.946706\pi$
$374$	−3.16321e7	+	1.82628e7i	−0.604663	+	0.349102i
$375$	−3.37489e7	−	1.94849e7i	−0.639979	−	0.369492i
$376$	−1.71567e7	+	9.90542e6i	−0.322753	+	0.186341i
$377$	−3.89322e7	+	6.74326e7i	−0.726582	+	1.25848i
$378$	8.10663e6	−	1.40411e7i	0.150095	−	0.259972i
$379$			3.74684e7i			0.688251i	0.938924	+	0.344126i	$0.111825\pi$
$379$			3.74684e7i			0.688251i	−0.938924	+	0.344126i	$0.888175\pi$
$380$	2.90466e7	−	2.94955e7i	0.529352	−	0.537532i
$381$	1.30793e8			2.36489
$382$	3.88591e7	+	2.24353e7i	0.697112	+	0.402478i
$383$	3.10003e7	+	1.78980e7i	0.551784	+	0.318573i	0.749841	−	0.661618i	$-0.230130\pi$
$383$	3.10003e7	+	1.78980e7i	0.551784	+	0.318573i	−0.198057	+	0.980191i	$0.563463\pi$
$384$	4.43068e6	+	7.67416e6i	0.0782486	+	0.135530i
$385$	−8.84827e6	+	1.53257e7i	−0.155052	+	0.268557i
$386$	2.46993e7	+	4.27804e7i	0.429459	+	0.743846i
$387$	−1.87796e7			−0.324006
$388$			3.14066e7i			0.537683i
$389$	−7.76595e6	−	1.34510e7i	−0.131931	−	0.228511i	0.792490	−	0.609885i	$-0.208784\pi$
$389$	−7.76595e6	−	1.34510e7i	−0.131931	−	0.228511i	−0.924421	+	0.381374i	$0.875451\pi$
$390$	−1.66885e8	+	9.63508e7i	−2.81334	+	1.62428i
$391$	−7.07187e7			−1.18305
$392$			2.03461e7i			0.337772i
$393$	1.48195e8	−	8.55606e7i	2.44150	−	1.40960i
$394$	−6.75653e7	−	3.90088e7i	−1.10468	−	0.637785i
$395$	−1.83495e7	+	1.05941e7i	−0.297737	+	0.171899i
$396$	3.22418e7	−	5.58444e7i	0.519198	−	0.899278i
$397$	−2.64501e7	+	4.58129e7i	−0.422723	+	0.732177i	−0.996205	−	0.0870410i	$-0.972259\pi$
$397$	−2.64501e7	+	4.58129e7i	−0.422723	+	0.732177i	0.573482	+	0.819218i	$0.305592\pi$
$398$		−	4.15611e7i		−	0.659231i
$399$	2.29040e7	−	6.32573e6i	0.360573	−	0.0995846i
$400$	2.04259e7			0.319154
$401$	2.42849e7	+	1.40209e7i	0.376620	+	0.217442i	0.676347	−	0.736583i	$-0.263562\pi$
$401$	2.42849e7	+	1.40209e7i	0.376620	+	0.217442i	−0.299726	+	0.954025i	$0.596895\pi$
$402$	−6.60702e7	−	3.81457e7i	−1.01702	−	0.587174i
$403$	−8.06660e6	−	1.39718e7i	−0.123247	−	0.213469i
$404$	−1.25118e7	+	2.16712e7i	−0.189748	+	0.328653i
$405$	7.13094e7	+	1.23511e8i	1.07345	+	1.85927i
$406$	8.44835e6			0.126239
$407$		−	6.48815e7i		−	0.962361i
$408$	2.15773e7	+	3.73730e7i	0.317700	+	0.550272i
$409$	−3.26748e7	+	1.88648e7i	−0.477577	+	0.275729i	−0.719406	−	0.694590i	$-0.755586\pi$
$409$	−3.26748e7	+	1.88648e7i	−0.477577	+	0.275729i	0.241829	+	0.970319i	$0.422253\pi$
$410$	1.12858e8			1.63750
$411$		−	2.52974e7i		−	0.364376i
$412$	1.69832e7	−	9.80524e6i	0.242844	−	0.140206i
$413$	1.32434e6	+	764609.i	0.0187997	+	0.0108540i
$414$	1.08122e8	−	6.24245e7i	1.52375	−	0.879740i
$415$	4.31540e7	−	7.47450e7i	0.603778	−	1.04577i
$416$	1.09427e7	−	1.89533e7i	0.152001	−	0.263273i
$417$			1.30688e8i			1.80230i
$418$	4.84249e7	−	1.33742e7i	0.663040	−	0.183121i
$419$	4.39776e7			0.597846			0.298923	−	0.954277i	$-0.403373\pi$
$419$	4.39776e7			0.597846			0.298923	+	0.954277i	$0.403373\pi$
$420$	1.81071e7	+	1.04541e7i	0.244400	+	0.141104i
$421$	5.66538e7	+	3.27091e7i	0.759246	+	0.438351i	0.829025	−	0.559211i	$-0.188896\pi$
$421$	5.66538e7	+	3.27091e7i	0.759246	+	0.438351i	−0.0697788	+	0.997562i	$0.522229\pi$
$422$	−4.34247e7	−	7.52138e7i	−0.577829	−	1.00083i
$423$	8.51631e7	−	1.47507e8i	1.12520	−	1.94891i
$424$	1.23998e7	+	2.14771e7i	0.162674	+	0.281759i
$425$	9.94737e7			1.29581
$426$			5.60906e7i			0.725540i
$427$	−7.25651e6	−	1.25686e7i	−0.0932060	−	0.161438i
$428$	−1.82581e7	+	1.05413e7i	−0.232876	+	0.134451i
$429$	−2.33857e8			−2.96196
$430$		−	1.28740e7i		−	0.161922i
$431$	−6.37711e7	+	3.68182e7i	−0.796511	+	0.459866i	−0.842250	−	0.539088i	$-0.818769\pi$
$431$	−6.37711e7	+	3.68182e7i	−0.796511	+	0.459866i	0.0457386	+	0.998953i	$0.485436\pi$
$432$	−3.50742e7	−	2.02501e7i	−0.435048	−	0.251175i
$433$	2.19074e7	−	1.26483e7i	0.269853	−	0.155800i	−0.358968	−	0.933350i	$-0.616871\pi$
$433$	2.19074e7	−	1.26483e7i	0.269853	−	0.155800i	0.628821	+	0.777550i	$0.283538\pi$
$434$	−875232.	+	1.51595e6i	−0.0107067	+	0.0185445i
$435$	−9.29092e7	+	1.60923e8i	−1.12873	+	1.95502i
$436$		−	3.45780e7i		−	0.417197i
$437$	9.41434e7	+	2.44535e7i	1.12809	+	0.293020i
$438$	8.52428e7			1.01446
$439$	1.10684e7	+	6.39036e6i	0.130826	+	0.0755322i	0.563984	−	0.825785i	$-0.309268\pi$
$439$	1.10684e7	+	6.39036e6i	0.130826	+	0.0755322i	−0.433159	+	0.901318i	$0.642601\pi$
$440$	3.82830e7	+	2.21027e7i	0.449415	+	0.259470i
$441$	−8.74643e7	−	1.51493e8i	−1.01980	−	1.76634i
$442$	5.32909e7	−	9.23025e7i	0.617143	−	1.06892i
$443$	−6.95068e7	−	1.20389e8i	−0.799495	−	1.38477i	−0.919945	−	0.392047i	$-0.871767\pi$
$443$	−6.95068e7	−	1.20389e8i	−0.799495	−	1.38477i	0.120450	−	0.992719i	$-0.461566\pi$
$444$	−7.66568e7			−0.875794
$445$			2.02114e8i			2.29359i
$446$	−4.14834e7	−	7.18513e7i	−0.467594	−	0.809897i
$447$	2.31088e8	−	1.33419e8i	2.58735	−	1.49381i
$448$	−2.37459e6			−0.0264091
$449$		−	8.32115e7i		−	0.919272i	−0.888107	−	0.459636i	$-0.847980\pi$
$449$		−	8.32115e7i		−	0.919272i	0.888107	−	0.459636i	$-0.152020\pi$
$450$	−1.52086e8	+	8.78070e7i	−1.66898	+	0.963589i
$451$	1.18612e8	+	6.84807e7i	1.29300	+	0.746515i
$452$	−4.33914e7	+	2.50520e7i	−0.469881	+	0.271286i
$453$	−8.91155e7	+	1.54353e8i	−0.958647	+	1.66042i
$454$	−3.47426e7	+	6.01760e7i	−0.371274	+	0.643066i
$455$		−	5.16385e7i		−	0.548200i
$456$	−1.58015e7	−	5.72135e7i	−0.166649	−	0.603398i
$457$	9.76140e7			1.02274			0.511368	−	0.859362i	$-0.329139\pi$
$457$	9.76140e7			1.02274			0.511368	+	0.859362i	$0.329139\pi$
$458$	−2.24768e7	−	1.29770e7i	−0.233958	−	0.135076i
$459$	−1.70811e8	−	9.86177e7i	−1.76635	−	1.01980i
$460$	4.27939e7	+	7.41212e7i	0.439651	+	0.761498i
$461$	−5.84310e7	+	1.01205e8i	−0.596404	+	1.03300i	0.396944	+	0.917843i	$0.370071\pi$
$461$	−5.84310e7	+	1.01205e8i	−0.596404	+	1.03300i	−0.993347	+	0.115158i	$0.963262\pi$
$462$	1.26868e7	+	2.19742e7i	0.128655	+	0.222837i
$463$	−8.06477e6			−0.0812548			−0.0406274	−	0.999174i	$-0.512936\pi$
$463$	−8.06477e6			−0.0812548			−0.0406274	+	0.999174i	$0.512936\pi$
$464$		−	2.11037e7i		−	0.211254i
$465$	−1.92504e7	−	3.33427e7i	−0.191461	−	0.331621i
$466$	−4.13449e7	+	2.38705e7i	−0.408568	+	0.235887i
$467$	4.60466e7			0.452113			0.226057	−	0.974114i	$-0.427417\pi$
$467$	4.60466e7			0.452113			0.226057	+	0.974114i	$0.427417\pi$
$468$			1.88163e8i			1.83568i
$469$	1.77049e7	−	1.02219e7i	0.171623	−	0.0990866i
$470$	1.01120e8	+	5.83819e7i	0.973969	+	0.562321i
$471$	−1.53636e8	+	8.87016e7i	−1.47038	+	0.848924i
$472$	1.90997e6	−	3.30816e6i	0.0181635	−	0.0314602i
$473$	7.81173e6	−	1.35303e7i	0.0738183	−	0.127857i
$474$			3.03801e7i			0.285269i
$475$	−1.32423e8	−	3.43966e7i	−1.23561	−	0.320948i
$476$	−1.15642e7			−0.107225
$477$	−1.84652e8	−	1.06609e8i	−1.70137	−	0.982287i
$478$	2.27158e7	+	1.31150e7i	0.207991	+	0.120084i
$479$	2.72002e7	+	4.71121e7i	0.247495	+	0.428673i	0.962830	−	0.270108i	$-0.0870594\pi$
$479$	2.72002e7	+	4.71121e7i	0.247495	+	0.428673i	−0.715335	+	0.698781i	$0.753726\pi$
$480$	2.61141e7	−	4.52309e7i	0.236130	−	0.408989i
$481$	9.46621e7	+	1.63960e8i	0.850630	+	1.47334i
$482$	−7.28270e7			−0.650356
$483$			4.91270e7i			0.435992i
$484$	−1.52179e6	−	2.63582e6i	−0.0134220	−	0.0232477i
$485$	1.60309e8	−	9.25543e7i	1.40518	−	0.811281i
$486$	4.13876e7			0.360546
$487$			8.85732e7i			0.766859i	0.923570	+	0.383429i	$0.125257\pi$
$487$			8.85732e7i			0.766859i	−0.923570	+	0.383429i	$0.874743\pi$
$488$	−3.13961e7	+	1.81265e7i	−0.270157	+	0.155975i
$489$	−2.11083e8	−	1.21869e8i	−1.80521	−	1.04224i
$490$	1.03853e8	−	5.99594e7i	0.882733	−	0.509646i
$491$	7.45783e7	−	1.29173e8i	0.630040	−	1.09126i	−0.357503	−	0.933912i	$-0.616372\pi$
$491$	7.45783e7	−	1.29173e8i	0.630040	−	1.09126i	0.987543	−	0.157349i	$-0.0502949\pi$
$492$	8.09092e7	−	1.40139e8i	0.679364	−	1.17669i
$493$		−	1.02775e8i		−	0.857720i
$494$	−1.02860e8	+	1.04449e8i	−0.853227	+	0.866413i
$495$	−3.80061e8			−3.13356
$496$	3.78678e6	+	2.18630e6i	0.0310331	+	0.0179170i
$497$	−1.30169e7	−	7.51533e6i	−0.106033	−	0.0612180i
$498$	−6.18752e7	−	1.07171e8i	−0.500989	−	0.867739i
$499$	4.24482e7	−	7.35224e7i	0.341631	−	0.591722i	−0.643105	−	0.765778i	$-0.722354\pi$
$499$	4.24482e7	−	7.35224e7i	0.341631	−	0.591722i	0.984736	+	0.174056i	$0.0556874\pi$
$500$	−1.30429e7	−	2.25910e7i	−0.104343	−	0.180728i
$501$	−1.58532e7			−0.126068
$502$			501452.i			0.00396386i
$503$	3.63491e7	+	6.29585e7i	0.285621	+	0.494710i	0.972760	−	0.231817i	$-0.0744669\pi$
$503$	3.63491e7	+	6.29585e7i	0.285621	+	0.494710i	−0.687139	+	0.726526i	$0.741134\pi$
$504$	1.76806e7	−	1.02079e7i	0.138104	−	0.0797343i
$505$	1.47488e8			1.14520
$506$			1.03867e8i			0.801725i
$507$	3.91139e8	−	2.25824e8i	3.00128	−	1.73279i
$508$	7.58212e7	+	4.37754e7i	0.578362	+	0.333917i
$509$	−2.19630e8	+	1.26803e8i	−1.66547	+	0.961561i	−0.695442	+	0.718582i	$0.744791\pi$
$509$	−2.19630e8	+	1.26803e8i	−1.66547	+	0.961561i	−0.970032	+	0.242979i	$0.921875\pi$
$510$	1.27175e8	−	2.20274e8i	0.958720	−	1.66055i
$511$	−1.14213e7	+	1.97823e7i	−0.0855959	+	0.148256i
$512$			5.93164e6i			0.0441942i
$513$	1.93289e8	+	1.90348e8i	1.43171	+	1.40992i
$514$	8.15636e6			0.0600630
$515$	−1.00098e8	−	5.77914e7i	−0.732829	−	0.423099i
$516$	−1.59859e7	−	9.22948e6i	−0.116356	−	0.0671782i
$517$	7.08506e7	+	1.22717e8i	0.512710	+	0.888039i
$518$	1.02709e7	−	1.77897e7i	0.0738958	−	0.127991i
$519$	−5.85650e7	−	1.01437e8i	−0.418925	−	0.725599i
$520$	−1.28991e8			−0.917382
$521$		−	4.68649e7i		−	0.331386i	−0.986177	−	0.165693i	$-0.947014\pi$
$521$		−	4.68649e7i		−	0.331386i	0.986177	−	0.165693i	$-0.0529861\pi$
$522$	9.07209e7	+	1.57133e8i	0.637816	+	1.10473i
$523$	4.43902e7	−	2.56287e7i	0.310300	−	0.179152i	−0.336761	−	0.941590i	$-0.609331\pi$
$523$	4.43902e7	−	2.56287e7i	0.310300	−	0.179152i	0.647061	+	0.762439i	$0.275998\pi$
$524$	1.14546e8			0.796132
$525$		−	6.91025e7i		−	0.477547i
$526$	−8.62127e7	+	4.97749e7i	−0.592398	+	0.342021i
$527$	1.84416e7	+	1.06472e7i	0.125999	+	0.0727454i
$528$	5.48910e7	−	3.16913e7i	0.372906	−	0.215297i
$529$	−2.65323e7	+	4.59553e7i	−0.179229	+	0.310434i
$530$	7.30836e7	−	1.26585e8i	0.490899	−	0.850263i
$531$			3.28424e7i			0.219357i
$532$	1.53947e7	+	3.99874e6i	0.102244	+	0.0265576i
$533$	−3.99653e8			−2.63938
$534$	2.50970e8	+	1.44897e8i	1.64815	+	0.951562i
$535$	1.07612e8	+	6.21298e7i	0.702747	+	0.405731i
$536$	−2.55341e7	−	4.42263e7i	−0.165816	−	0.287201i
$537$	−1.04400e8	+	1.80826e8i	−0.674181	+	1.16772i
$538$	−7.26193e7	−	1.25780e8i	−0.466343	−	0.807730i
$539$	1.45530e8			0.929364
$540$			2.38706e8i			1.51594i
$541$	−5.49324e7	−	9.51456e7i	−0.346926	−	0.600893i	0.638776	−	0.769393i	$-0.279441\pi$
$541$	−5.49324e7	−	9.51456e7i	−0.346926	−	0.600893i	−0.985702	+	0.168500i	$0.946108\pi$
$542$	−2.16630e7	+	1.25071e7i	−0.136057	+	0.0785525i
$543$	−7.30294e7			−0.456140
$544$			2.88870e7i			0.179434i
$545$	−1.76496e8	+	1.01900e8i	−1.09030	+	0.629486i
$546$	−6.41208e7	−	3.70202e7i	−0.393932	−	0.227437i
$547$	−1.54801e8	+	8.93741e7i	−0.945824	+	0.546072i	−0.891781	−	0.452467i	$-0.850544\pi$
$547$	−1.54801e8	+	8.93741e7i	−0.945824	+	0.546072i	−0.0540431	+	0.998539i	$0.517211\pi$
$548$	8.46682e6	−	1.46650e7i	0.0514492	−	0.0891127i
$549$	1.55845e8	−	2.69932e8i	0.941838	−	1.63131i
$550$		−	1.46100e8i		−	0.878138i
$551$	−3.55380e7	+	1.36818e8i	−0.212441	+	0.817875i
$552$	1.22718e8			0.729608
$553$	−7.05030e6	−	4.07049e6i	−0.0416900	−	0.0240698i
$554$	−7.16824e7	−	4.13858e7i	−0.421583	−	0.243401i
$555$	2.25905e8	+	3.91279e8i	1.32144	+	2.28880i
$556$	−4.37400e7	+	7.57600e7i	−0.254481	+	0.440774i
$557$	−1.07443e8	−	1.86097e8i	−0.621748	−	1.07690i	−0.989160	−	0.146841i	$-0.953090\pi$
$557$	−1.07443e8	−	1.86097e8i	−0.621748	−	1.07690i	0.367412	−	0.930058i	$-0.380244\pi$
$558$	−3.75940e7			−0.216379
$559$			4.55893e7i			0.260992i
$560$	6.99782e6	+	1.21206e7i	0.0398473	+	0.0690176i
$561$	2.67318e8	−	1.54336e8i	1.51405	−	0.874136i
$562$	4.82746e7			0.271963
$563$			1.73549e8i			0.972516i	0.873815	+	0.486258i	$0.161638\pi$
$563$			1.73549e8i			0.972516i	−0.873815	+	0.486258i	$0.838362\pi$
$564$	1.44989e8	−	8.37092e7i	0.808158	−	0.466590i
$565$	2.55746e8	+	1.47655e8i	1.41796	+	0.818658i
$566$	−8.85201e7	+	5.11071e7i	−0.488194	+	0.281859i
$567$	−2.73987e7	+	4.74559e7i	−0.150307	+	0.260340i
$568$	−1.87731e7	+	3.25159e7i	−0.102445	+	0.177440i
$569$		−	4.16467e7i		−	0.226070i	−0.993591	−	0.113035i	$-0.963943\pi$
$569$		−	4.16467e7i		−	0.226070i	0.993591	−	0.113035i	$-0.0360573\pi$
$570$	−2.45468e8	+	2.49262e8i	−1.32547	+	1.34596i
$571$	−6.25455e6			−0.0335960			−0.0167980	−	0.999859i	$-0.505347\pi$
$571$	−6.25455e6			−0.0335960			−0.0167980	+	0.999859i	$0.505347\pi$
$572$	−1.35568e8	−	7.82700e7i	−0.724383	−	0.418222i
$573$	−3.28392e8	−	1.89597e8i	−1.74554	−	1.00779i
$574$	2.16813e7	+	3.75532e7i	0.114644	+	0.198569i
$575$	1.41435e8	−	2.44973e8i	0.743967	−	1.28859i
$576$	−2.54990e7	−	4.41656e7i	−0.133431	−	0.231109i
$577$	1.02635e8			0.534277			0.267139	−	0.963658i	$-0.413922\pi$
$577$	1.02635e8			0.534277			0.267139	+	0.963658i	$0.413922\pi$
$578$			4.13646e6i			0.0214213i
$579$	−2.08730e8	−	3.61530e8i	−1.07535	−	1.86256i
$580$	−1.07719e8	+	6.21919e7i	−0.552091	+	0.318750i
$581$	3.31615e7			0.169085
$582$		−	2.65413e8i		−	1.34633i
$583$	1.53619e8	−	8.86922e7i	0.775247	−	0.447589i
$584$	4.94155e7	+	2.85300e7i	0.248099	+	0.143240i
$585$	9.60438e8	−	5.54509e8i	4.79736	−	2.76975i
$586$	−2.50565e7	+	4.33992e7i	−0.124517	+	0.215670i
$587$	3.06586e7	−	5.31023e7i	0.151579	−	0.262542i	−0.780229	−	0.625494i	$-0.784898\pi$
$587$	3.06586e7	−	5.31023e7i	0.151579	−	0.262542i	0.931808	+	0.362952i	$0.118231\pi$
$588$		−	1.71942e8i		−	0.845766i
$589$	−2.08685e7	−	2.05509e7i	−0.102128	−	0.100574i
$590$	−2.25145e7			−0.109624
$591$	5.70984e8	+	3.29658e8i	2.76606	+	1.59698i
$592$	−4.44382e7	−	2.56564e7i	−0.214186	−	0.123660i
$593$	−5.87529e7	−	1.01763e8i	−0.281751	−	0.488007i	0.690065	−	0.723747i	$-0.257582\pi$
$593$	−5.87529e7	−	1.01763e8i	−0.281751	−	0.488007i	−0.971816	+	0.235740i	$0.924248\pi$
$594$	−1.44843e8	+	2.50876e8i	−0.691096	+	1.19701i
$595$	3.40793e7	+	5.90271e7i	0.161786	+	0.280221i
$596$	1.78617e8			0.843690
$597$			3.51226e8i			1.65068i
$598$	−1.51542e8	−	2.62478e8i	−0.708644	−	1.22741i
$599$	1.14457e8	−	6.60817e7i	0.532551	−	0.307468i	−0.209504	−	0.977808i	$-0.567185\pi$
$599$	1.14457e8	−	6.60817e7i	0.532551	−	0.307468i	0.742055	+	0.670339i	$0.233851\pi$
$600$	−1.72616e8			−0.799148
$601$			1.34669e8i			0.620359i	0.950678	+	0.310180i	$0.100389\pi$
$601$			1.34669e8i			0.620359i	−0.950678	+	0.310180i	$0.899611\pi$
$602$	4.28377e6	−	2.47323e6i	0.0196352	−	0.0113364i
$603$	3.80241e8	+	2.19532e8i	1.73423	+	1.00126i
$604$	−1.03321e8	+	5.96524e7i	−0.468897	+	0.270718i
$605$	−8.96933e6	+	1.55353e7i	−0.0405036	+	0.0701543i
$606$	1.05736e8	−	1.83140e8i	0.475120	−	0.822933i
$607$			4.02047e8i			1.79767i	0.438283	+	0.898837i	$0.355587\pi$
$607$			4.02047e8i			1.79767i	−0.438283	+	0.898837i	$0.644413\pi$
$608$	9.98872e6	−	3.84555e7i	0.0444426	−	0.171099i
$609$	−7.13957e7			−0.316097
$610$	1.85046e8	+	1.06836e8i	0.815250	+	0.470685i
$611$	−3.58087e8	−	2.06742e8i	−1.56988	−	0.906368i
$612$	−1.24180e8	−	2.15086e8i	−0.541747	−	0.938334i
$613$	9.35581e7	−	1.62047e8i	0.406163	−	0.703494i	−0.588293	−	0.808647i	$-0.700200\pi$
$613$	9.35581e7	−	1.62047e8i	0.406163	−	0.703494i	0.994456	+	0.105153i	$0.0335333\pi$
$614$	−7.55952e6	−	1.30935e7i	−0.0326580	−	0.0565653i
$615$	−9.53747e8			−4.10023
$616$			1.69847e7i			0.0726635i
$617$	9.93419e7	+	1.72065e8i	0.422938	+	0.732550i	0.996225	−	0.0868041i	$-0.0276654\pi$
$617$	9.93419e7	+	1.72065e8i	0.422938	+	0.732550i	−0.573287	+	0.819354i	$0.694332\pi$
$618$	−1.43522e8	+	8.28626e7i	−0.608070	+	0.351070i
$619$	−2.61032e8			−1.10058			−0.550289	−	0.834974i	$-0.685483\pi$
$619$	−2.61032e8			−1.10058			−0.550289	+	0.834974i	$0.685483\pi$
$620$		−	2.57718e7i		−	0.108136i
$621$	−4.85730e8	+	2.80436e8i	−2.02824	+	1.17101i
$622$	−2.08715e7	−	1.20502e7i	−0.0867328	−	0.0500752i
$623$	−6.72527e7	+	3.88283e7i	−0.278128	+	0.160577i
$624$	−9.24752e7	+	1.60172e8i	−0.380602	+	0.659223i
$625$	7.89631e7	−	1.36768e8i	0.323433	−	0.560202i
$626$			1.53251e8i			0.624713i
$627$	−4.09231e8	+	1.13023e8i	−1.66022	+	0.458528i
$628$	−1.18751e8			−0.479466
$629$	−2.16413e8	−	1.24946e8i	−0.869625	−	0.502078i
$630$	−1.04208e8	−	6.01647e7i	−0.416755	−	0.240614i
$631$	1.68753e8	+	2.92288e8i	0.671680	+	1.16338i	0.977427	+	0.211271i	$0.0677604\pi$
$631$	1.68753e8	+	2.92288e8i	0.671680	+	1.16338i	−0.305747	+	0.952113i	$0.598906\pi$
$632$	−1.01680e7	+	1.76114e7i	−0.0402794	+	0.0697659i
$633$	3.66975e8	+	6.35620e8i	1.44686	+	2.50603i
$634$	2.87984e8			1.13006
$635$		−	5.16019e8i		−	2.01532i
$636$	−1.04789e8	−	1.81500e8i	−0.407328	−	0.705512i
$637$	−3.67763e8	+	2.12328e8i	−1.42282	+	0.821465i
$638$	−1.50949e8			−0.581255
$639$		−	3.22808e8i		−	1.23720i
$640$	3.02768e7	−	1.74803e7i	0.115497	−	0.0666822i
$641$	−1.82889e8	−	1.05591e8i	−0.694404	−	0.400915i	0.110856	−	0.993837i	$-0.464641\pi$
$641$	−1.82889e8	−	1.05591e8i	−0.694404	−	0.400915i	−0.805260	+	0.592922i	$0.797974\pi$
$642$	1.54296e8	−	8.90831e7i	0.583110	−	0.336659i
$643$	1.30732e8	−	2.26434e8i	0.491754	−	0.851743i	−0.508201	−	0.861239i	$-0.669689\pi$
$643$	1.30732e8	−	2.26434e8i	0.491754	−	0.851743i	0.999955	+	0.00949534i	$0.00302250\pi$
$644$	−1.64424e7	+	2.84790e7i	−0.0615612	+	0.106627i
$645$			1.08796e8i			0.405446i
$646$	4.86449e7	−	1.87277e8i	0.180443	−	0.694685i
$647$	3.41445e8			1.26069			0.630344	−	0.776316i	$-0.282914\pi$
$647$	3.41445e8			1.26069			0.630344	+	0.776316i	$0.282914\pi$
$648$	1.18543e8	+	6.84410e7i	0.435664	+	0.251531i
$649$	−2.36623e7	−	1.36614e7i	−0.0865612	−	0.0499761i
$650$	2.13160e8	+	3.69204e8i	0.776186	+	1.34439i
$651$	7.39645e6	−	1.28110e7i	0.0268090	−	0.0464345i
$652$	−8.15770e7	−	1.41296e8i	−0.294324	−	0.509783i
$653$	3.27925e8			1.17770			0.588851	−	0.808242i	$-0.299581\pi$
$653$	3.27925e8			1.17770			0.588851	+	0.808242i	$0.299581\pi$
$654$			2.92214e8i			1.04464i
$655$	−3.37562e8	−	5.84675e8i	−1.20124	−	2.08061i
$656$	9.38066e7	−	5.41593e7i	0.332294	−	0.191850i
$657$	−4.90581e8			−1.72988
$658$			4.48633e7i			0.157476i
$659$	−1.50035e7	+	8.66226e6i	−0.0524247	+	0.0302674i	−0.525983	−	0.850495i	$-0.676303\pi$
$659$	−1.50035e7	+	8.66226e6i	−0.0524247	+	0.0302674i	0.473559	+	0.880762i	$0.342969\pi$
$660$	−3.23524e8	−	1.86786e8i	−1.12532	−	0.649701i
$661$	−8.70906e7	+	5.02818e7i	−0.301555	+	0.174103i	−0.643141	−	0.765747i	$-0.722369\pi$
$661$	−8.70906e7	+	5.02818e7i	−0.301555	+	0.174103i	0.341586	+	0.939850i	$0.389036\pi$
$662$	−1.75175e8	+	3.03411e8i	−0.603806	+	1.04582i
$663$	−4.50353e8	+	7.80034e8i	−1.54530	+	2.67653i
$664$		−	8.28364e7i		−	0.282955i
$665$	−2.49569e7	−	9.03632e7i	−0.0848645	−	0.307275i
$666$	4.41168e8			1.49342
$667$	−2.53102e8	−	1.46129e8i	−0.852940	−	0.492445i
$668$	−9.19014e6	−	5.30593e6i	−0.0308314	−	0.0178005i
$669$	3.50569e8	+	6.07204e8i	1.17083	+	2.02795i
$670$	−1.50496e8	+	2.60667e8i	−0.500381	+	0.866685i
$671$	1.29654e8	+	2.24567e8i	0.429158	+	0.743323i
$672$	2.00673e7			0.0661272
$673$		−	3.57367e8i		−	1.17238i	−0.810173	−	0.586191i	$-0.800627\pi$
$673$		−	3.57367e8i		−	1.17238i	0.810173	−	0.586191i	$-0.199373\pi$
$674$	1.89636e8	+	3.28459e8i	0.619357	+	1.07276i
$675$	6.83233e8	−	3.94465e8i	2.22156	−	1.28262i
$676$	3.02326e8			0.978667
$677$		−	2.67824e8i		−	0.863144i	−0.902078	−	0.431572i	$-0.857959\pi$
$677$		−	2.67824e8i		−	0.863144i	0.902078	−	0.431572i	$-0.142041\pi$
$678$	3.66694e8	−	2.11711e8i	1.17656	−	0.679288i
$679$	6.15943e7	+	3.55615e7i	0.196757	+	0.113598i
$680$	1.47448e8	−	8.51290e7i	0.468934	−	0.270739i
$681$	2.93604e8	−	5.08538e8i	0.929654	−	1.61021i
$682$	1.56380e7	−	2.70857e7i	0.0492977	−	0.0853862i
$683$		−	2.25065e8i		−	0.706392i	−0.935549	−	0.353196i	$-0.885095\pi$
$683$		−	2.25065e8i		−	0.706392i	0.935549	−	0.353196i	$-0.114905\pi$
$684$	9.09393e7	+	3.29270e8i	0.284173	+	1.02893i
$685$	−9.98058e7			−0.310516
$686$	8.16694e7	+	4.71519e7i	0.252981	+	0.146058i
$687$	1.89948e8	+	1.09666e8i	0.585819	+	0.338223i
$688$	−6.17806e6	−	1.07007e7i	−0.0189709	−	0.0328585i
$689$	−2.58804e8	+	4.48261e8i	−0.791248	+	1.37048i
$690$	−3.61644e8	−	6.26386e8i	−1.10087	−	1.90676i
$691$	−4.02368e8			−1.21952			−0.609761	−	0.792585i	$-0.708735\pi$
$691$	−4.02368e8			−1.21952			−0.609761	+	0.792585i	$0.708735\pi$
$692$		−	7.84048e7i		−	0.236605i
$693$	−7.30141e7	−	1.26464e8i	−0.219385	−	0.379986i
$694$	1.40483e8	−	8.11079e7i	0.420287	−	0.242653i
$695$	5.15602e8			1.53589
$696$			1.78344e8i			0.528970i
$697$	4.56837e8	−	2.63755e8i	1.34916	−	0.778937i
$698$	−1.70365e8	−	9.83604e7i	−0.500973	−	0.289237i
$699$	3.49399e8	−	2.01726e8i	1.02303	−	0.590649i
$700$	2.31280e7	−	4.00589e7i	0.0674287	−	0.116790i
$701$	2.26182e8	−	3.91759e8i	0.656605	−	1.13727i	−0.324884	−	0.945754i	$-0.605325\pi$
$701$	2.26182e8	−	3.91759e8i	0.656605	−	1.13727i	0.981489	−	0.191519i	$-0.0613414\pi$
$702$		−	8.45304e8i		−	2.44344i
$703$	2.44893e8	+	2.41166e8i	0.704872	+	0.694145i
$704$	4.24273e7			0.121598
$705$	−8.54553e8	−	4.93376e8i	−2.43877	−	1.40803i
$706$	2.35591e7	+	1.36018e7i	0.0669490	+	0.0386530i
$707$	2.83341e7	+	4.90761e7i	0.0801773	+	0.138871i
$708$	−1.61409e7	+	2.79568e7i	−0.0454807	+	0.0787748i
$709$	1.73371e8	+	3.00288e8i	0.486450	+	0.842556i	0.999879	−	0.0155762i	$-0.00495827\pi$
$709$	1.73371e8	+	3.00288e8i	0.486450	+	0.842556i	−0.513429	+	0.858132i	$0.671625\pi$
$710$	2.21294e8			0.618294
$711$		−	1.74841e8i		−	0.486445i
$712$	9.69920e7	+	1.67995e8i	0.268717	+	0.465432i
$713$	5.24418e7	−	3.02773e7i	0.144680	−	0.0835311i
$714$	9.77272e7			0.268486
$715$			9.22636e8i			2.52413i
$716$	−1.21042e8	+	6.98835e7i	−0.329759	+	0.190386i
$717$	−1.91968e8	−	1.10833e8i	−0.520800	−	0.300684i
$718$	−2.03961e8	+	1.17757e8i	−0.551028	+	0.318136i
$719$	−1.32317e8	+	2.29180e8i	−0.355983	+	0.616580i	−0.987286	−	0.158956i	$-0.949187\pi$
$719$	−1.32317e8	+	2.29180e8i	−0.355983	+	0.616580i	0.631303	+	0.775536i	$0.282520\pi$
$720$	−1.50289e8	+	2.60309e8i	−0.402653	+	0.697416i
$721$		−	4.44096e7i		−	0.118487i
$722$	−1.29516e8	+	2.32490e8i	−0.344121	+	0.617722i
$723$	6.15449e8			1.62846
$724$	−4.23354e7	−	2.44423e7i	−0.111555	−	0.0644061i
$725$	3.56016e8	+	2.05546e8i	0.934235	+	0.539381i
$726$	1.28604e7	+	2.22749e7i	0.0336082	+	0.0582111i
$727$	−1.70602e8	+	2.95491e8i	−0.443997	+	0.769026i	−0.997982	−	0.0635013i	$-0.979773\pi$
$727$	−1.70602e8	+	2.95491e8i	−0.443997	+	0.769026i	0.553985	+	0.832527i	$0.313107\pi$
$728$	−2.47807e7	−	4.29214e7i	−0.0642272	−	0.111245i
$729$	2.01491e8			0.520083
$730$		−	3.36308e8i		−	0.864508i
$731$	−3.00871e7	−	5.21123e7i	−0.0770243	−	0.133410i
$732$	2.65323e8	−	1.53184e8i	0.676460	−	0.390554i
$733$	−5.86587e7			−0.148943			−0.0744716	−	0.997223i	$-0.523727\pi$
$733$	−5.86587e7			−0.148943			−0.0744716	+	0.997223i	$0.523727\pi$
$734$			4.80339e8i			1.21467i
$735$	−8.77643e8	+	5.06707e8i	−2.21032	+	1.27613i
$736$	7.11397e7	+	4.10725e7i	0.178434	+	0.103019i
$737$	−3.16338e8	+	1.82638e8i	−0.790221	+	0.456234i
$738$	−4.65641e8	+	8.06515e8i	−1.15846	+	2.00652i
$739$	2.25741e8	−	3.90995e8i	0.559342	−	0.968809i	−0.438209	−	0.898873i	$-0.644387\pi$
$739$	2.25741e8	−	3.90995e8i	0.559342	−	0.968809i	0.997551	−	0.0699359i	$-0.0222795\pi$
$740$			3.02434e8i			0.746338i
$741$	8.69252e8	−	8.82685e8i	2.13644	−	2.16946i
$742$	5.61608e7			0.137474
$743$	−4.80179e8	−	2.77231e8i	−1.17067	−	0.675890i	−0.216836	−	0.976208i	$-0.569574\pi$
$743$	−4.80179e8	−	2.77231e8i	−1.17067	−	0.675890i	−0.953839	+	0.300319i	$0.902907\pi$
$744$	−3.20015e7	−	1.84761e7i	−0.0777055	−	0.0448633i
$745$	−5.26377e8	−	9.11711e8i	−1.27300	−	2.20490i
$746$	4.89210e7	−	8.47336e7i	0.117836	−	0.204098i
$747$	3.56098e8	+	6.16780e8i	0.854296	+	1.47968i
$748$	2.06620e8			0.493705
$749$			4.77434e7i			0.113623i
$750$	1.10224e8	+	1.90913e8i	0.261271	+	0.452534i
$751$	−4.50843e8	+	2.60294e8i	−1.06440	+	0.614532i	−0.926646	−	0.375934i	$-0.877322\pi$
$751$	−4.50843e8	+	2.60294e8i	−1.06440	+	0.614532i	−0.137754	+	0.990466i	$0.543988\pi$
$752$	1.12067e8			0.263527
$753$		−	4.23769e6i		−	0.00992531i
$754$	3.81456e8	−	2.20234e8i	0.889878	−	0.513771i
$755$	6.08967e8	+	3.51587e8i	1.41499	+	0.816944i
$756$	−7.94285e7	+	4.58580e7i	−0.183828	+	0.106133i
$757$	−2.37481e7	+	4.11329e7i	−0.0547446	+	0.0948205i	−0.892099	−	0.451840i	$-0.850768\pi$
$757$	−2.37481e7	+	4.11329e7i	−0.0547446	+	0.0948205i	0.837354	+	0.546660i	$0.184101\pi$
$758$	1.05977e8	−	1.83557e8i	0.243334	−	0.421466i
$759$		−	8.77762e8i		−	2.00748i
$760$	−2.25724e8	+	6.23416e7i	−0.514207	+	0.142016i
$761$	3.06942e8			0.696470			0.348235	−	0.937407i	$-0.386781\pi$
$761$	3.06942e8			0.696470			0.348235	+	0.937407i	$0.386781\pi$
$762$	−6.40754e8	−	3.69939e8i	−1.44819	−	0.836114i
$763$	−6.78140e7	−	3.91524e7i	−0.152667	−	0.0881424i
$764$	−1.26913e8	−	2.19820e8i	−0.284595	−	0.492932i
$765$	−7.31907e8	+	1.26770e9i	−1.63483	+	2.83160i
$766$	−1.01247e8	−	1.75364e8i	−0.225265	−	0.390170i
$767$	7.97282e7			0.176696
$768$		−	5.01274e7i		−	0.110660i
$769$	−3.44575e8	−	5.96822e8i	−0.757713	−	1.31240i	−0.944014	−	0.329905i	$-0.892983\pi$
$769$	−3.44575e8	−	5.96822e8i	−0.757713	−	1.31240i	0.186301	−	0.982493i	$-0.440350\pi$
$770$	8.66950e7	−	5.00534e7i	0.189899	−	0.109638i
$771$	−6.89281e7			−0.150395
$772$		−	2.79440e8i		−	0.607347i
$773$	−2.41761e8	+	1.39581e8i	−0.523417	+	0.302195i	−0.738331	−	0.674438i	$-0.764386\pi$
$773$	−2.41761e8	+	1.39581e8i	−0.523417	+	0.302195i	0.214915	+	0.976633i	$0.431053\pi$
$774$	9.20008e7	+	5.31167e7i	0.198412	+	0.114553i
$775$	−7.37652e7	+	4.25883e7i	−0.158470	+	0.0914925i
$776$	8.88314e7	−	1.53860e8i	0.190100	−	0.329262i
$777$	−8.67979e7	+	1.50338e8i	−0.185032	+	0.320484i
$778$			8.78617e7i			0.186578i
$779$	−6.99361e8	+	1.93153e8i	−1.47941	+	0.408591i
$780$	1.09009e9			2.29708
$781$	2.32577e8	+	1.34278e8i	0.488217	+	0.281872i
$782$	3.46449e8	+	2.00023e8i	0.724468	+	0.418272i
$783$	−4.07555e8	−	7.05906e8i	−0.848987	−	1.47049i
$784$	5.75476e7	−	9.96753e7i	0.119420	−	0.206842i
$785$	3.49954e8	+	6.06139e8i	0.723440	+	1.25303i
$786$	−9.68008e8			−1.99348
$787$		−	7.82322e8i		−	1.60495i	−0.596686	−	0.802475i	$-0.703516\pi$
$787$		−	7.82322e8i		−	1.60495i	0.596686	−	0.802475i	$-0.296484\pi$
$788$	2.20667e8	+	3.82207e8i	0.450982	+	0.781124i
$789$	7.28570e8	−	4.20640e8i	1.48334	−	0.856406i
$790$	1.19859e8			0.243102
$791$			1.13465e8i			0.229262i
$792$	−3.15903e8	+	1.82387e8i	−0.635885	+	0.367129i
$793$	−6.55285e8	−	3.78329e8i	−1.31405	−	0.758665i
$794$	2.59157e8	−	1.49624e8i	0.517727	−	0.298910i
$795$	−6.17618e8	+	1.06975e9i	−1.22919	+	2.12902i
$796$	−1.17552e8	+	2.03607e8i	−0.233073	+	0.403695i
$797$		−	1.62974e8i		−	0.321916i	−0.986961	−	0.160958i	$-0.948542\pi$
$797$		−	1.62974e8i		−	0.321916i	0.986961	−	0.160958i	$-0.0514584\pi$
$798$	−1.30098e8	−	3.37927e7i	−0.256013	−	0.0664989i
$799$	5.45765e8			1.06995
$800$	−1.00066e8	−	5.77731e7i	−0.195441	−	0.112838i
$801$	−1.44436e9	−	8.33901e8i	−2.81046	−	1.62262i
$802$	−7.93143e7	−	1.37376e8i	−0.153755	−	0.266311i
$803$	2.04067e8	−	3.53454e8i	0.394118	−	0.682632i
$804$	2.15785e8	+	3.73750e8i	0.415195	+	0.719139i
$805$	1.93821e8			0.371546
$806$			9.12631e7i			0.174297i
$807$	6.13695e8	+	1.06295e9i	1.16770	+	2.02252i
$808$	1.22591e8	−	7.07777e7i	0.232393	−	0.134172i
$809$	7.51060e8			1.41850			0.709250	−	0.704957i	$-0.249034\pi$
$809$	7.51060e8			1.41850			0.709250	+	0.704957i	$0.249034\pi$
$810$		−	8.06773e8i		−	1.51809i
$811$	−3.10609e8	+	1.79330e8i	−0.582306	+	0.336194i	−0.762049	−	0.647519i	$-0.775807\pi$
$811$	−3.10609e8	+	1.79330e8i	−0.582306	+	0.336194i	0.179743	+	0.983714i	$0.442473\pi$
$812$	−4.13883e7	−	2.38955e7i	−0.0773053	−	0.0446322i
$813$	1.83071e8	−	1.05696e8i	0.340680	−	0.196692i
$814$	−1.83513e8	+	3.17853e8i	−0.340246	+	0.589323i
$815$	−4.80809e8	+	8.32786e8i	−0.888178	+	1.53837i
$816$		−	2.44119e8i		−	0.449295i
$817$	2.20333e7	+	7.97776e7i	0.0404030	+	0.146290i
$818$	2.13431e8			0.389940
$819$	3.69022e8	+	2.13055e8i	0.671740	+	0.387829i
$820$	−5.52890e8	−	3.19211e8i	−1.00276	−	0.578944i
$821$	1.12783e8	+	1.95345e8i	0.203804	+	0.352999i	0.949751	−	0.313006i	$-0.101336\pi$
$821$	1.12783e8	+	1.95345e8i	0.203804	+	0.352999i	−0.745947	+	0.666005i	$0.768003\pi$
$822$	−7.15518e7	+	1.23931e8i	−0.128827	+	0.223134i
$823$	−1.40351e8	−	2.43094e8i	−0.251776	−	0.436089i	0.712239	−	0.701937i	$-0.247681\pi$
$823$	−1.40351e8	−	2.43094e8i	−0.251776	−	0.436089i	−0.964015	+	0.265848i	$0.914348\pi$
$824$	−1.10934e8			−0.198281
$825$			1.23467e9i			2.19882i
$826$	−4.32528e6	−	7.49161e6i	−0.00767493	−	0.0132934i
$827$	−8.25669e6	+	4.76700e6i	−0.0145979	+	0.00842809i	−0.507281	−	0.861781i	$-0.669349\pi$
$827$	−8.25669e6	+	4.76700e6i	−0.0145979	+	0.00842809i	0.492683	+	0.870209i	$0.336016\pi$
$828$	−7.06253e8			−1.24414
$829$		−	1.05929e8i		−	0.185931i	−0.995669	−	0.0929656i	$-0.970365\pi$
$829$		−	1.05929e8i		−	0.185931i	0.995669	−	0.0929656i	$-0.0296347\pi$
$830$	−4.22821e8	+	2.44116e8i	−0.739474	+	0.426935i
$831$	6.05777e8	+	3.49745e8i	1.05562	+	0.609465i
$832$	−1.07216e8	+	6.19014e7i	−0.186162	+	0.107481i
$833$	2.80256e8	−	4.85417e8i	0.484863	−	0.839808i
$834$	3.69640e8	−	6.40236e8i	0.637208	−	1.10368i
$835$			6.25456e7i			0.107433i
$836$	−2.75061e8	−	7.14464e7i	−0.470771	−	0.122282i
$837$	1.68887e8			0.288019
$838$	−2.15445e8	−	1.24387e8i	−0.366104	−	0.211370i
$839$	7.57663e8	+	4.37437e8i	1.28289	+	0.740678i	0.977376	−	0.211509i	$-0.0678378\pi$
$839$	7.57663e8	+	4.37437e8i	1.28289	+	0.740678i	0.305516	+	0.952187i	$0.401171\pi$
$840$	−5.91375e7	−	1.02429e8i	−0.0997758	−	0.172817i
$841$	−8.50445e7	+	1.47301e8i	−0.142974	+	0.247639i
$842$	−1.85031e8	−	3.20482e8i	−0.309961	−	0.536868i
$843$	−4.07961e8			−0.680983
$844$			4.91294e8i			0.817174i
$845$	−8.90944e8	−	1.54316e9i	−1.47666	−	2.55765i
$846$	−8.34425e8	+	4.81755e8i	−1.37809	+	0.795638i
$847$	−6.89244e6			−0.0113429
$848$		−	1.40288e8i		−	0.230055i
$849$	7.48070e8	−	4.31898e8i	1.22242	−	0.705762i
$850$	−4.87319e8	−	2.81354e8i	−0.793518	−	0.458138i
$851$	−6.15408e8	+	3.55306e8i	−0.998561	+	0.576519i
$852$	1.58648e8	−	2.74787e8i	0.256517	−	0.444301i
$853$	−4.30155e7	+	7.45051e7i	−0.0693071	+	0.120044i	−0.898597	−	0.438776i	$-0.855412\pi$
$853$	−4.30155e7	+	7.45051e7i	−0.0693071	+	0.120044i	0.829289	+	0.558819i	$0.188746\pi$
$854$			8.20980e7i			0.131813i
$855$	1.41270e9	−	1.43453e9i	2.26022	−	2.29515i
$856$	1.19261e8			0.190142
$857$	3.88087e8	+	2.24062e8i	0.616575	+	0.355980i	0.775535	−	0.631305i	$-0.217480\pi$
$857$	3.88087e8	+	2.24062e8i	0.616575	+	0.355980i	−0.158959	+	0.987285i	$0.550814\pi$
$858$	1.14566e9	+	6.61448e8i	1.81382	+	1.04721i
$859$	3.30238e8	+	5.71989e8i	0.521012	+	0.902419i	0.999701	+	0.0244345i	$0.00777851\pi$
$859$	3.30238e8	+	5.71989e8i	0.521012	+	0.902419i	−0.478690	+	0.877984i	$0.658888\pi$
$860$	−3.64131e7	+	6.30693e7i	−0.0572482	+	0.0991568i
$861$	−1.83226e8	−	3.17356e8i	−0.287063	−	0.497207i
$862$	4.16551e8			0.650349
$863$		−	1.04665e9i		−	1.62843i	−0.580562	−	0.814216i	$-0.697167\pi$
$863$		−	1.04665e9i		−	1.62843i	0.580562	−	0.814216i	$-0.302833\pi$
$864$	1.14552e8	+	1.98410e8i	0.177607	+	0.307625i
$865$	−4.00201e8	+	2.31056e8i	−0.618344	+	0.357001i
$866$	−1.43099e8			−0.220334
$867$		−	3.49566e7i		−	0.0536379i
$868$	8.57548e6	−	4.95106e6i	0.0131129	−	0.00757075i
$869$	1.25969e8	+	7.27284e7i	0.191958	+	0.110827i
$870$	9.10321e8	−	5.25574e8i	1.38241	−	0.798134i
$871$	5.32937e8	−	9.23073e8i	0.806531	−	1.39695i
$872$	−9.78015e7	+	1.69397e8i	−0.147501	+	0.255480i
$873$			1.52748e9i			2.29579i
$874$	−3.92041e8	−	3.86075e8i	−0.587216	−	0.578279i
$875$	−5.90734e7			−0.0881796
$876$	−4.17603e8	−	2.41103e8i	−0.621228	−	0.358666i
$877$	3.57753e8	+	2.06549e8i	0.530377	+	0.306213i	0.741170	−	0.671317i	$-0.234271\pi$
$877$	3.57753e8	+	2.06549e8i	0.530377	+	0.306213i	−0.210793	+	0.977531i	$0.567605\pi$
$878$	−3.61493e7	−	6.26125e7i	−0.0534093	−	0.0925076i
$879$	2.11749e8	−	3.66760e8i	0.311785	−	0.540027i
$880$	−1.25032e8	−	2.16561e8i	−0.183473	−	0.317785i
$881$	−3.15072e8			−0.460768			−0.230384	−	0.973100i	$-0.573998\pi$
$881$	−3.15072e8			−0.460768			−0.230384	+	0.973100i	$0.573998\pi$
$882$			9.89545e8i			1.44221i
$883$	3.25358e8	+	5.63536e8i	0.472584	+	0.818540i	0.999508	−	0.0313729i	$-0.00998793\pi$
$883$	3.25358e8	+	5.63536e8i	0.472584	+	0.818540i	−0.526924	+	0.849913i	$0.676655\pi$
$884$	−5.22142e8	+	3.01459e8i	−0.755843	+	0.436386i
$885$	1.90266e8			0.274493
$886$			7.86379e8i			1.13066i
$887$	9.11521e8	−	5.26267e8i	1.30616	−	0.754111i	0.324705	−	0.945815i	$-0.394735\pi$
$887$	9.11521e8	−	5.26267e8i	1.30616	−	0.754111i	0.981453	+	0.191705i	$0.0614016\pi$
$888$	3.75540e8	+	2.16818e8i	0.536312	+	0.309640i
$889$	1.71703e8	−	9.91330e7i	0.244385	−	0.141095i
$890$	5.71664e8	−	9.90151e8i	0.810906	−	1.40453i
$891$	4.89538e8	−	8.47905e8i	0.692076	−	1.19871i
$892$			4.69331e8i			0.661278i
$893$	−7.26543e8	−	1.88718e8i	−1.02025	−	0.265008i
$894$	−1.50946e9			−2.11256
$895$	7.13412e8	+	4.11888e8i	0.995110	+	0.574527i
$896$	1.16331e7	+	6.71635e6i	0.0161722	+	0.00933703i
$897$	1.28065e9	+	2.21816e9i	1.77441	+	3.07337i
$898$	−2.35358e8	+	4.07651e8i	−0.325012	+	0.562937i
$899$	4.40016e7	+	7.62130e7i	0.0605605	+	0.104894i
$900$	9.93423e8			1.36272
$901$		−	6.83199e8i		−	0.934056i
$902$	−3.87385e8	−	6.70971e8i	−0.527866	−	0.914291i
$903$	−3.62015e7	+	2.09009e7i	−0.0491658	+	0.0283859i
$904$	2.83431e8			0.383657
$905$			2.88123e8i			0.388716i
$906$	8.73150e8	−	5.04113e8i	1.17410	−	0.677866i
$907$	3.61896e7	+	2.08941e7i	0.0485023	+	0.0280028i	0.524055	−	0.851684i	$-0.324419\pi$
$907$	3.61896e7	+	2.08941e7i	0.0485023	+	0.0280028i	−0.475553	+	0.879687i	$0.657752\pi$
$908$	3.40407e8	−	1.96534e8i	0.454716	−	0.262531i
$909$	−6.08520e8	+	1.05399e9i	−0.810184	+	1.40328i
$910$	−1.46056e8	+	2.52976e8i	−0.193818	+	0.335703i
$911$		−	5.10593e8i		−	0.675336i	−0.941265	−	0.337668i	$-0.890362\pi$
$911$		−	5.10593e8i		−	0.675336i	0.941265	−	0.337668i	$-0.109638\pi$
$912$	−8.44131e7	+	3.24981e8i	−0.111282	+	0.428424i
$913$	−5.92504e8			−0.778537
$914$	−4.78209e8	−	2.76094e8i	−0.626295	−	0.361592i
$915$	−1.56380e9	−	9.02858e8i	−2.04135	−	1.17857i
$916$	7.34088e7	+	1.27148e8i	0.0955128	+	0.165433i
$917$	1.29699e8	−	2.24645e8i	0.168201	−	0.291333i
$918$	5.57866e8	+	9.66252e8i	0.721110	+	1.24900i
$919$	−1.18343e9			−1.52474			−0.762372	−	0.647139i	$-0.775965\pi$
$919$	−1.18343e9			−1.52474			−0.762372	+	0.647139i	$0.775965\pi$
$920$		−	4.84157e8i		−	0.621760i
$921$	6.38843e7	+	1.10651e8i	0.0817740	+	0.141637i
$922$	5.72504e8	−	3.30535e8i	0.730442	−	0.421721i
$923$	−7.83647e8			−0.996587
$924$		−	1.43535e8i		−	0.181946i
$925$	8.65640e8	−	4.99777e8i	1.09373	−	0.631468i
$926$	3.95092e7	+	2.28106e7i	0.0497582	+	0.0287279i
$927$	8.25986e8	−	4.76883e8i	1.03689	−	0.598650i
$928$	−5.96903e7	+	1.03387e8i	−0.0746895	+	0.129366i
$929$	−6.12008e8	+	1.06003e9i	−0.763326	+	1.32212i	0.177801	+	0.984067i	$0.443102\pi$
$929$	−6.12008e8	+	1.06003e9i	−0.763326	+	1.32212i	−0.941127	+	0.338053i	$0.890232\pi$
$930$			2.17794e8i			0.270767i
$931$	−5.40938e8	+	5.49297e8i	−0.670345	+	0.680704i
$932$	2.70064e8			0.333594
$933$	1.76382e8	+	1.01834e8i	0.217175	+	0.125386i
$934$	−2.25582e8	−	1.30240e8i	−0.276862	−	0.159846i
$935$	−6.08902e8	−	1.05465e9i	−0.744925	−	1.29025i
$936$	5.32205e8	−	9.21806e8i	0.649010	−	1.12412i
$937$	−5.95631e8	−	1.03166e9i	−0.724033	−	1.25406i	−0.959371	−	0.282149i	$-0.908953\pi$
$937$	−5.95631e8	−	1.03166e9i	−0.724033	−	1.25406i	0.235337	−	0.971914i	$-0.424380\pi$
$938$	−1.15648e8			−0.140130
$939$		−	1.29510e9i		−	1.56425i
$940$	−3.30258e8	−	5.72023e8i	−0.397621	−	0.688700i
$941$	−9.46093e8	+	5.46227e8i	−1.13544	+	0.655548i	−0.945298	−	0.326208i	$-0.894229\pi$
$941$	−9.46093e8	+	5.46227e8i	−1.13544	+	0.655548i	−0.190144	+	0.981756i	$0.560896\pi$
$942$	1.00354e9			1.20056
$943$		−	1.50006e9i		−	1.78885i
$944$	−1.87138e7	+	1.08044e7i	−0.0222457	+	0.0128436i
$945$	4.68146e8	+	2.70284e8i	0.554735	+	0.320277i
$946$	−7.65390e7	+	4.41898e7i	−0.0904086	+	0.0521974i
$947$	−6.23014e8	+	1.07909e9i	−0.733580	+	1.27060i	0.221763	+	0.975101i	$0.428819\pi$
$947$	−6.23014e8	+	1.07909e9i	−0.733580	+	1.27060i	−0.955343	+	0.295498i	$0.904515\pi$
$948$	8.59279e7	−	1.48831e8i	0.100858	−	0.174691i
$949$			1.19093e9i			1.39344i
$950$	5.51450e8	+	5.43057e8i	0.643184	+	0.633396i
$951$	−2.43371e9			−2.82962
$952$	5.66528e7	+	3.27085e7i	0.0656614	+	0.0379096i
$953$	7.02985e8	+	4.05869e8i	0.812208	+	0.468929i	0.847722	−	0.530441i	$-0.177973\pi$
$953$	7.02985e8	+	4.05869e8i	0.812208	+	0.468929i	−0.0355139	+	0.999369i	$0.511307\pi$
$954$	6.03071e8	+	1.04455e9i	0.694582	+	1.20305i
$955$	−7.48018e8	+	1.29560e9i	−0.858819	+	1.48752i
$956$	−7.41895e7	−	1.28500e8i	−0.0849119	−	0.147072i
$957$	1.27564e9			1.45544
$958$		−	3.07735e8i		−	0.350010i
$959$	−1.91738e7	−	3.32100e7i	−0.0217397	−	0.0376542i
$960$	−2.55865e8	+	1.47724e8i	−0.289199	+	0.166969i
$961$	8.69270e8			0.979455
$962$		−	1.07098e9i		−	1.20297i
$963$	−8.87992e8	+	5.12683e8i	−0.994330	+	0.574076i
$964$	3.56778e8	+	2.05986e8i	0.398260	+	0.229936i
$965$	−1.42635e9	+	8.23501e8i	−1.58724	+	0.916394i
$966$	1.38952e8	−	2.40672e8i	0.154146	−	0.266989i
$967$	−3.84465e8	+	6.65913e8i	−0.425185	+	0.736441i	−0.996438	−	0.0843327i	$-0.973124\pi$
$967$	−3.84465e8	+	6.65913e8i	−0.425185	+	0.736441i	0.571253	+	0.820774i	$0.306457\pi$
$968$			1.72171e7i			0.0189816i
$969$	−4.11090e8	+	1.58265e9i	−0.451821	+	1.73946i
$970$	−1.04713e9			−1.14732
$971$	8.53754e8	+	4.92915e8i	0.932557	+	0.538412i	0.887619	−	0.460578i	$-0.152358\pi$
$971$	8.53754e8	+	4.92915e8i	0.932557	+	0.538412i	0.0449375	+	0.998990i	$0.485691\pi$
$972$	−2.02757e8	−	1.17062e8i	−0.220789	−	0.127472i
$973$	9.90529e7	+	1.71565e8i	0.107530	+	0.186247i
$974$	2.50523e8	−	4.33918e8i	0.271125	−	0.469603i
$975$	−1.80138e9	−	3.12009e9i	−1.94353	−	3.36630i
$976$	2.05078e8			0.220582
$977$			1.77249e9i			1.90065i	0.311266	+	0.950323i	$0.399247\pi$
$977$			1.77249e9i			1.90065i	−0.311266	+	0.950323i	$0.600753\pi$
$978$	6.89395e8	+	1.19407e9i	0.736973	+	1.27647i
$979$	1.20162e9	−	6.93755e8i	1.28061	−	0.739363i
$980$	−6.78363e8			−0.720749
$981$		−	1.68172e9i		−	1.78134i
$982$	−7.30715e8	+	4.21879e8i	−0.771638	+	0.445506i
$983$	2.25798e8	+	1.30364e8i	0.237716	+	0.137246i	0.614127	−	0.789208i	$-0.289508\pi$
$983$	2.25798e8	+	1.30364e8i	0.237716	+	0.137246i	−0.376410	+	0.926453i	$0.622842\pi$
$984$	−7.92745e8	+	4.57692e8i	−0.832048	+	0.480383i
$985$	1.30060e9	−	2.25270e9i	1.36093	−	2.35719i
$986$	−2.90691e8	+	5.03491e8i	−0.303250	+	0.525244i
$987$		−	3.79133e8i		−	0.394312i
$988$	7.99335e8	−	2.20764e8i	0.828816	−	0.228906i
$989$	−1.71115e8			−0.176889
$990$	1.86191e9	+	1.07498e9i	1.91891	+	1.10788i
$991$	1.45720e9	+	8.41315e8i	1.49726	+	0.864446i	0.999995	−	0.00315115i	$-0.00100304\pi$
$991$	1.45720e9	+	8.41315e8i	1.49726	+	0.864446i	0.497269	+	0.867597i	$0.334336\pi$
$992$	−1.23676e7	−	2.14213e7i	−0.0126692	−	0.0219437i
$993$	1.48037e9	−	2.56408e9i	1.51190	−	2.61869i
$994$	4.25131e7	+	7.36349e7i	0.0432876	+	0.0749764i
$995$	1.38569e9			1.40669
$996$			7.00038e8i			0.708506i
$997$	5.43387e8	+	9.41173e8i	0.548307	+	0.949695i	0.998391	+	0.0567087i	$0.0180606\pi$
$997$	5.43387e8	+	9.41173e8i	0.548307	+	0.949695i	−0.450084	+	0.892986i	$0.648606\pi$
$998$	−4.15905e8	+	2.40123e8i	−0.418411	+	0.241570i
$999$	−1.98191e9			−1.98786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.27.5	✓	20
3.2	odd	2		342.7.m.a.217.7		20
19.12	odd	6	inner	38.7.d.a.31.5	yes	20
57.50	even	6		342.7.m.a.145.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.5	✓	20	1.1	even	1	trivial
38.7.d.a.31.5	yes	20	19.12	odd	6	inner
342.7.m.a.145.7		20	57.50	even	6
342.7.m.a.217.7		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(41.4005 + 23.9026i) q^{3} +(16.0000 + 27.7128i) q^{4} +(94.3029 - 163.337i) q^{5} +(-135.214 - 234.197i) q^{6} +72.4666 q^{7} -181.019i q^{8} +(778.168 + 1347.83i) q^{9} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(41.4005 + 23.9026i) q^{3} +(16.0000 + 27.7128i) q^{4} +(94.3029 - 163.337i) q^{5} +(-135.214 - 234.197i) q^{6} +72.4666 q^{7} -181.019i q^{8} +(778.168 + 1347.83i) q^{9} +(-923.976 + 533.458i) q^{10} -1294.78 q^{11} +1529.77i q^{12} +(3271.98 - 1889.08i) q^{13} +(-355.013 - 204.967i) q^{14} +(7808.38 - 4508.17i) q^{15} +(-512.000 + 886.810i) q^{16} +(-2493.43 + 4318.75i) q^{17} -8803.97i q^{18} +(4812.71 - 4887.09i) q^{19} +6035.39 q^{20} +(3000.16 + 1732.14i) q^{21} +(6343.09 + 3662.18i) q^{22} +(7090.50 + 12281.1i) q^{23} +(4326.83 - 7494.29i) q^{24} +(-9973.57 - 17274.7i) q^{25} -21372.5 q^{26} +39551.0i q^{27} +(1159.47 + 2008.25i) q^{28} +(-17848.0 + 10304.5i) q^{29} -51004.1 q^{30} -4270.12i q^{31} +(5016.55 - 2896.31i) q^{32} +(-53604.5 - 30948.5i) q^{33} +(24430.5 - 14105.0i) q^{34} +(6833.81 - 11836.5i) q^{35} +(-24901.4 + 43130.5i) q^{36} +50110.2i q^{37} +(-37400.2 + 10329.3i) q^{38} +180616. q^{39} +(-29567.2 - 17070.6i) q^{40} +(-91608.1 - 52889.9i) q^{41} +(-9798.47 - 16971.4i) q^{42} +(-6033.26 + 10449.9i) q^{43} +(-20716.4 - 35881.9i) q^{44} +293534. q^{45} -80219.8i q^{46} +(-54720.2 - 94778.2i) q^{47} +(-42394.1 + 24476.3i) q^{48} -112398. q^{49} +112838. i q^{50} +(-206459. + 119199. i) q^{51} +(104703. + 60450.6i) q^{52} +(-118645. + 68499.9i) q^{53} +(111867. - 193760. i) q^{54} +(-122101. + 211486. i) q^{55} -13117.9i q^{56} +(316063. - 87291.7i) q^{57} +116583. q^{58} +(18275.2 + 10551.2i) q^{59} +(249868. + 144261. i) q^{60} +(-100136. - 173440. i) q^{61} +(-12077.7 + 20919.2i) q^{62} +(56391.2 + 97672.5i) q^{63} -32768.0 q^{64} -712583. i q^{65} +(175071. + 303233. i) q^{66} +(244318. - 141057. i) q^{67} -159580. q^{68} +677925. i q^{69} +(-66957.4 + 38657.9i) q^{70} +(-179627. - 103707. i) q^{71} +(243983. - 140864. i) q^{72} +(-157608. + 272985. i) q^{73} +(141733. - 245489. i) q^{74} -953577. i q^{75} +(212438. + 55180.4i) q^{76} -93828.2 q^{77} +(-884832. - 510858. i) q^{78} +(-97290.3 - 56170.6i) q^{79} +(96566.2 + 167258. i) q^{80} +(-378087. + 654866. i) q^{81} +(299191. + 518213. i) q^{82} +457611. q^{83} +110857. i q^{84} +(470276. + 814541. i) q^{85} +(59113.7 - 34129.3i) q^{86} -985221. q^{87} +234380. i q^{88} +(-928050. + 535810. i) q^{89} +(-1.43802e6 - 830240. i) q^{90} +(237110. - 136895. i) q^{91} +(-226896. + 392995. i) q^{92} +(102067. - 176785. i) q^{93} +619089. i q^{94} +(-344392. - 1.24696e6i) q^{95} +276917. q^{96} +(849967. + 490729. i) q^{97} +(550633. + 317908. i) q^{98} +(-1.00756e6 - 1.74514e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Introduction

L-functions

Modular forms

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