LMFDB - Embedded newform 19.8.c.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,8,Mod(7,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("19.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, 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:	$5.93531548420$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - x^{19} + 874 x^{18} + 315 x^{17} + 507687 x^{16} + 417048 x^{15} + 164584585 x^{14} + \cdots + 60\!\cdots\!00 $ x^20 - x^19 + 874x^18 + 315x^17 + 507687x^16 + 417048x^15 + 164584585x^14 + 336973169x^13 + 38490109231x^12 + 77542158000x^11 + 5540115855453x^10 + 9818502731517x^9 + 563374808170270x^8 + 415649022449381x^7 + 28126583892888079x^6 - 39545364418737942x^5 + 937145309501459364x^4 - 592470579641290560x^3 + 8461462975161004800x^2 + 1228956006606336000x + 60946825731287040000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.4
Root			$-4.83664 - 8.37730i$ of defining polynomial
Character	$\chi$	$=$	19.7
Dual form			19.8.c.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.33664 - 9.24333i) q^{2} +(-38.4779 - 66.6457i) q^{3} +(7.04059 - 12.1947i) q^{4} +(-118.331 - 204.955i) q^{5} +(-410.685 + 711.328i) q^{6} +1248.71 q^{7} -1516.47 q^{8} +(-1867.60 + 3234.77i) q^{9} +O(q^{10})$	\(q+(-5.33664 - 9.24333i) q^{2} +(-38.4779 - 66.6457i) q^{3} +(7.04059 - 12.1947i) q^{4} +(-118.331 - 204.955i) q^{5} +(-410.685 + 711.328i) q^{6} +1248.71 q^{7} -1516.47 q^{8} +(-1867.60 + 3234.77i) q^{9} +(-1262.98 + 2187.54i) q^{10} +2949.15 q^{11} -1083.63 q^{12} +(581.336 - 1006.90i) q^{13} +(-6663.90 - 11542.2i) q^{14} +(-9106.24 + 15772.5i) q^{15} +(7191.67 + 12456.3i) q^{16} +(-8772.51 - 15194.4i) q^{17} +39866.8 q^{18} +(27654.9 - 11361.3i) q^{19} -3332.47 q^{20} +(-48047.6 - 83221.0i) q^{21} +(-15738.6 - 27260.0i) q^{22} +(4488.16 - 7773.72i) q^{23} +(58350.6 + 101066. i) q^{24} +(11058.1 - 19153.3i) q^{25} -12409.5 q^{26} +119143. q^{27} +(8791.63 - 15227.6i) q^{28} +(-128667. + 222859. i) q^{29} +194387. q^{30} -308929. q^{31} +(-20295.5 + 35152.9i) q^{32} +(-113477. - 196548. i) q^{33} +(-93631.5 + 162174. i) q^{34} +(-147761. - 255929. i) q^{35} +(26298.0 + 45549.4i) q^{36} +480391. q^{37} +(-252601. - 194992. i) q^{38} -89474.3 q^{39} +(179445. + 310808. i) q^{40} +(-87767.5 - 152018. i) q^{41} +(-512826. + 888240. i) q^{42} +(62920.8 + 108982. i) q^{43} +(20763.7 - 35963.9i) q^{44} +883977. q^{45} -95806.8 q^{46} +(252080. - 436615. i) q^{47} +(553440. - 958587. i) q^{48} +735727. q^{49} -236053. q^{50} +(-675096. + 1.16930e6i) q^{51} +(-8185.89 - 14178.4i) q^{52} +(931595. - 1.61357e6i) q^{53} +(-635821. - 1.10127e6i) q^{54} +(-348975. - 604443. i) q^{55} -1.89363e6 q^{56} +(-1.82129e6 - 1.40592e6i) q^{57} +2.74661e6 q^{58} +(206916. + 358388. i) q^{59} +(128227. + 222095. i) q^{60} +(505660. - 875829. i) q^{61} +(1.64864e6 + 2.85553e6i) q^{62} +(-2.33208e6 + 4.03929e6i) q^{63} +2.27431e6 q^{64} -275160. q^{65} +(-1.21117e6 + 2.09781e6i) q^{66} +(-1.52932e6 + 2.64886e6i) q^{67} -247055. q^{68} -690780. q^{69} +(-1.57709e6 + 2.73160e6i) q^{70} +(-1.82464e6 - 3.16036e6i) q^{71} +(2.83216e6 - 4.90544e6i) q^{72} +(1.32719e6 + 2.29876e6i) q^{73} +(-2.56367e6 - 4.44041e6i) q^{74} -1.70198e6 q^{75} +(56158.8 - 417232. i) q^{76} +3.68263e6 q^{77} +(477492. + 827040. i) q^{78} +(-505050. - 874771. i) q^{79} +(1.70199e6 - 2.94794e6i) q^{80} +(-499922. - 865890. i) q^{81} +(-936767. + 1.62253e6i) q^{82} -2.53474e6 q^{83} -1.35313e6 q^{84} +(-2.07612e6 + 3.59594e6i) q^{85} +(671571. - 1.16320e6i) q^{86} +1.98034e7 q^{87} -4.47230e6 q^{88} +(2.70269e6 - 4.68119e6i) q^{89} +(-4.71747e6 - 8.17089e6i) q^{90} +(725918. - 1.25733e6i) q^{91} +(-63198.6 - 109463. i) q^{92} +(1.18869e7 + 2.05888e7i) q^{93} -5.38103e6 q^{94} +(-5.60099e6 - 4.32360e6i) q^{95} +3.12372e6 q^{96} +(-7.51343e6 - 1.30137e7i) q^{97} +(-3.92631e6 - 6.80057e6i) q^{98} +(-5.50783e6 + 9.53984e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9}+O(q^{10}) $ 20 * q - 9 * q^2 - 68 * q^3 - 475 * q^4 + 545 * q^6 - 1456 * q^7 + 2322 * q^8 - 6052 * q^9	\( 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9} - 1732 q^{10} + 7248 q^{11} + 30354 q^{12} - 12888 q^{13} - 7578 q^{14} - 13244 q^{15} - 1027 q^{16} - 63024 q^{17} - 93132 q^{18} + 72752 q^{19} + 156588 q^{20} - 18148 q^{21} + 23317 q^{22} + 56532 q^{23} - 45783 q^{24} - 86450 q^{25} + 198888 q^{26} - 58424 q^{27} + 287154 q^{28} - 178704 q^{29} - 384728 q^{30} + 292880 q^{31} - 640377 q^{32} - 408506 q^{33} + 262520 q^{34} + 621336 q^{35} + 486770 q^{36} - 1408096 q^{37} + 205086 q^{38} + 815736 q^{39} + 925470 q^{40} - 926994 q^{41} - 936278 q^{42} - 1837988 q^{43} - 511371 q^{44} + 1933888 q^{45} + 5286604 q^{46} + 1416996 q^{47} + 144447 q^{48} + 681652 q^{49} - 4138710 q^{50} - 2505268 q^{51} - 3586666 q^{52} - 356328 q^{53} + 228251 q^{54} + 865080 q^{55} - 3446916 q^{56} + 1706388 q^{57} + 11381072 q^{58} - 2297052 q^{59} - 2670886 q^{60} - 1496632 q^{61} + 1024512 q^{62} - 88344 q^{63} + 1773542 q^{64} + 585816 q^{65} - 2197457 q^{66} - 6475124 q^{67} + 4032876 q^{68} + 6329016 q^{69} - 12864588 q^{70} - 8042868 q^{71} + 9440430 q^{72} - 485798 q^{73} + 6232812 q^{74} + 20769104 q^{75} - 6953413 q^{76} + 8525208 q^{77} - 7305352 q^{78} - 5604964 q^{79} - 448650 q^{80} + 7714382 q^{81} + 2321819 q^{82} - 14535552 q^{83} - 42654252 q^{84} - 12944460 q^{85} + 2747550 q^{86} + 6535176 q^{87} + 18704514 q^{88} + 5024424 q^{89} - 15096092 q^{90} + 28222480 q^{91} - 30094896 q^{92} + 26255544 q^{93} + 51863760 q^{94} - 43373748 q^{95} + 116808910 q^{96} - 12341194 q^{97} + 1851183 q^{98} - 26743912 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 68 * q^3 - 475 * q^4 + 545 * q^6 - 1456 * q^7 + 2322 * q^8 - 6052 * q^9 - 1732 * q^10 + 7248 * q^11 + 30354 * q^12 - 12888 * q^13 - 7578 * q^14 - 13244 * q^15 - 1027 * q^16 - 63024 * q^17 - 93132 * q^18 + 72752 * q^19 + 156588 * q^20 - 18148 * q^21 + 23317 * q^22 + 56532 * q^23 - 45783 * q^24 - 86450 * q^25 + 198888 * q^26 - 58424 * q^27 + 287154 * q^28 - 178704 * q^29 - 384728 * q^30 + 292880 * q^31 - 640377 * q^32 - 408506 * q^33 + 262520 * q^34 + 621336 * q^35 + 486770 * q^36 - 1408096 * q^37 + 205086 * q^38 + 815736 * q^39 + 925470 * q^40 - 926994 * q^41 - 936278 * q^42 - 1837988 * q^43 - 511371 * q^44 + 1933888 * q^45 + 5286604 * q^46 + 1416996 * q^47 + 144447 * q^48 + 681652 * q^49 - 4138710 * q^50 - 2505268 * q^51 - 3586666 * q^52 - 356328 * q^53 + 228251 * q^54 + 865080 * q^55 - 3446916 * q^56 + 1706388 * q^57 + 11381072 * q^58 - 2297052 * q^59 - 2670886 * q^60 - 1496632 * q^61 + 1024512 * q^62 - 88344 * q^63 + 1773542 * q^64 + 585816 * q^65 - 2197457 * q^66 - 6475124 * q^67 + 4032876 * q^68 + 6329016 * q^69 - 12864588 * q^70 - 8042868 * q^71 + 9440430 * q^72 - 485798 * q^73 + 6232812 * q^74 + 20769104 * q^75 - 6953413 * q^76 + 8525208 * q^77 - 7305352 * q^78 - 5604964 * q^79 - 448650 * q^80 + 7714382 * q^81 + 2321819 * q^82 - 14535552 * q^83 - 42654252 * q^84 - 12944460 * q^85 + 2747550 * q^86 + 6535176 * q^87 + 18704514 * q^88 + 5024424 * q^89 - 15096092 * q^90 + 28222480 * q^91 - 30094896 * q^92 + 26255544 * q^93 + 51863760 * q^94 - 43373748 * q^95 + 116808910 * q^96 - 12341194 * q^97 + 1851183 * q^98 - 26743912 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−5.33664	−	9.24333i	−0.471697	−	0.817003i	0.527779	−	0.849382i	$-0.323025\pi$
$2$	−5.33664	−	9.24333i	−0.471697	−	0.817003i	−0.999476	+	0.0323792i	$0.989692\pi$
$3$	−38.4779	−	66.6457i	−0.822786	−	1.42511i	−0.903600	−	0.428378i	$-0.859085\pi$
$3$	−38.4779	−	66.6457i	−0.822786	−	1.42511i	0.0808134	−	0.996729i	$-0.474248\pi$
$4$	7.04059	−	12.1947i	0.0550046	−	0.0952707i
$5$	−118.331	−	204.955i	−0.423353	−	0.733269i	0.572912	−	0.819617i	$-0.305814\pi$
$5$	−118.331	−	204.955i	−0.423353	−	0.733269i	−0.996265	+	0.0863478i	$0.972480\pi$
$6$	−410.685	+	711.328i	−0.776211	+	1.34444i
$7$	1248.71			1.37600			0.687999	−	0.725712i	$-0.258489\pi$
$7$	1248.71			1.37600			0.687999	+	0.725712i	$0.258489\pi$
$8$	−1516.47			−1.04718
$9$	−1867.60	+	3234.77i	−0.853954	+	1.47909i
$10$	−1262.98	+	2187.54i	−0.399389	+	0.691761i
$11$	2949.15			0.668071			0.334036	−	0.942560i	$-0.391589\pi$
$11$	2949.15			0.668071			0.334036	+	0.942560i	$0.391589\pi$
$12$	−1083.63			−0.181028
$13$	581.336	−	1006.90i	0.0733880	−	0.127112i	−0.826996	−	0.562208i	$-0.809952\pi$
$13$	581.336	−	1006.90i	0.0733880	−	0.127112i	0.900384	+	0.435096i	$0.143286\pi$
$14$	−6663.90	−	11542.2i	−0.649053	−	1.12419i
$15$	−9106.24	+	15772.5i	−0.696658	+	1.20665i
$16$	7191.67	+	12456.3i	0.438944	+	0.760274i
$17$	−8772.51	−	15194.4i	−0.433065	−	0.750090i	0.564071	−	0.825727i	$-0.309235\pi$
$17$	−8772.51	−	15194.4i	−0.433065	−	0.750090i	−0.997135	+	0.0756363i	$0.975901\pi$
$18$	39866.8			1.61123
$19$	27654.9	−	11361.3i	0.924983	−	0.380008i
$19$	27654.9	−	11361.3i	0.924983	−	0.380008i
$20$	−3332.47			−0.0931454
$21$	−48047.6	−	83221.0i	−1.13215	−	1.96094i
$22$	−15738.6	−	27260.0i	−0.315127	−	0.545816i
$23$	4488.16	−	7773.72i	0.0769168	−	0.133224i	−0.825001	−	0.565131i	$-0.808826\pi$
$23$	4488.16	−	7773.72i	0.0769168	−	0.133224i	0.901918	+	0.431907i	$0.142159\pi$
$24$	58350.6	+	101066.i	0.861601	+	1.49234i
$25$	11058.1	−	19153.3i	0.141544	−	0.245162i
$26$	−12409.5			−0.138468
$27$	119143.			1.16491
$28$	8791.63	−	15227.6i	0.0756861	−	0.131092i
$29$	−128667.	+	222859.i	−0.979661	+	1.69682i	−0.316053	+	0.948741i	$0.602358\pi$
$29$	−128667.	+	222859.i	−0.979661	+	1.69682i	−0.663608	+	0.748081i	$0.730976\pi$
$30$	194387.			1.31445
$31$	−308929.			−1.86249			−0.931243	−	0.364400i	$-0.881274\pi$
$31$	−308929.			−1.86249			−0.931243	+	0.364400i	$0.881274\pi$
$32$	−20295.5	+	35152.9i	−0.109490	+	0.189643i
$33$	−113477.	−	196548.i	−0.549680	−	0.952073i
$34$	−93631.5	+	162174.i	−0.408550	+	0.707630i
$35$	−147761.	−	255929.i	−0.582533	−	1.00898i
$36$	26298.0	+	45549.4i	0.0939428	+	0.162714i
$37$	480391.			1.55915			0.779577	−	0.626306i	$-0.215434\pi$
$37$	480391.			1.55915			0.779577	+	0.626306i	$0.215434\pi$
$38$	−252601.	−	194992.i	−0.746779	−	0.576465i
$39$	−89474.3			−0.241531
$40$	179445.	+	310808.i	0.443325	+	0.767861i
$41$	−87767.5	−	152018.i	−0.198880	−	0.344470i	0.749286	−	0.662247i	$-0.230397\pi$
$41$	−87767.5	−	152018.i	−0.198880	−	0.344470i	−0.948165	+	0.317777i	$0.897064\pi$
$42$	−512826.	+	888240.i	−1.06806	+	1.84994i
$43$	62920.8	+	108982.i	0.120685	+	0.209033i	0.920038	−	0.391829i	$-0.128157\pi$
$43$	62920.8	+	108982.i	0.120685	+	0.209033i	−0.799353	+	0.600862i	$0.794824\pi$
$44$	20763.7	−	35963.9i	0.0367470	−	0.0636476i
$45$	883977.			1.44610
$46$	−95806.8			−0.145126
$47$	252080.	−	436615.i	0.354156	−	0.613417i	−0.632817	−	0.774302i	$-0.718101\pi$
$47$	252080.	−	436615.i	0.354156	−	0.613417i	0.986973	+	0.160885i	$0.0514347\pi$
$48$	553440.	−	958587.i	0.722315	−	1.25109i
$49$	735727.			0.893369
$50$	−236053.			−0.267064
$51$	−675096.	+	1.16930e6i	−0.712639	+	1.23433i
$52$	−8185.89	−	14178.4i	−0.00807335	−	0.0139835i
$53$	931595.	−	1.61357e6i	0.859531	−	1.48875i	−0.0128450	−	0.999917i	$-0.504089\pi$
$53$	931595.	−	1.61357e6i	0.859531	−	1.48875i	0.872376	−	0.488835i	$-0.162578\pi$
$54$	−635821.	−	1.10127e6i	−0.549486	−	0.951738i
$55$	−348975.	−	604443.i	−0.282830	−	0.489876i
$56$	−1.89363e6			−1.44091
$57$	−1.82129e6	−	1.40592e6i	−1.30262	−	1.00554i
$58$	2.74661e6			1.84841
$59$	206916.	+	358388.i	0.131163	+	0.227181i	0.924125	−	0.382090i	$-0.124796\pi$
$59$	206916.	+	358388.i	0.131163	+	0.227181i	−0.792962	+	0.609271i	$0.791462\pi$
$60$	128227.	+	222095.i	0.0766388	+	0.132742i
$61$	505660.	−	875829.i	0.285236	−	0.494043i	−0.687430	−	0.726250i	$-0.741261\pi$
$61$	505660.	−	875829.i	0.285236	−	0.494043i	0.972666	+	0.232207i	$0.0745947\pi$
$62$	1.64864e6	+	2.85553e6i	0.878528	+	1.52166i
$63$	−2.33208e6	+	4.03929e6i	−1.17504	+	2.03523i
$64$	2.27431e6			1.08447
$65$	−275160.			−0.124276
$66$	−1.21117e6	+	2.09781e6i	−0.518564	+	0.898179i
$67$	−1.52932e6	+	2.64886e6i	−0.621206	+	1.07596i	0.368055	+	0.929804i	$0.380024\pi$
$67$	−1.52932e6	+	2.64886e6i	−0.621206	+	1.07596i	−0.989261	+	0.146157i	$0.953310\pi$
$68$	−247055.			−0.0952822
$69$	−690780.			−0.253144
$70$	−1.57709e6	+	2.73160e6i	−0.549558	+	0.951862i
$71$	−1.82464e6	−	3.16036e6i	−0.605023	−	1.04793i	−0.992048	−	0.125862i	$-0.959830\pi$
$71$	−1.82464e6	−	3.16036e6i	−0.605023	−	1.04793i	0.387025	−	0.922069i	$-0.373503\pi$
$72$	2.83216e6	−	4.90544e6i	0.894240	−	1.54887i
$73$	1.32719e6	+	2.29876e6i	0.399303	+	0.691612i	0.993640	−	0.112603i	$-0.0359190\pi$
$73$	1.32719e6	+	2.29876e6i	0.399303	+	0.691612i	−0.594337	+	0.804216i	$0.702586\pi$
$74$	−2.56367e6	−	4.44041e6i	−0.735448	−	1.27383i
$75$	−1.70198e6			−0.465842
$76$	56158.8	−	417232.i	0.0146747	−	0.109026i
$77$	3.68263e6			0.919264
$78$	477492.	+	827040.i	0.113929	+	0.197331i
$79$	−505050.	−	874771.i	−0.115250	−	0.199618i	0.802630	−	0.596477i	$-0.203433\pi$
$79$	−505050.	−	874771.i	−0.115250	−	0.199618i	−0.917879	+	0.396859i	$0.870100\pi$
$80$	1.70199e6	−	2.94794e6i	0.371657	−	0.643729i
$81$	−499922.	−	865890.i	−0.104521	−	0.181036i
$82$	−936767.	+	1.62253e6i	−0.187622	+	0.324970i
$83$	−2.53474e6			−0.486586			−0.243293	−	0.969953i	$-0.578228\pi$
$83$	−2.53474e6			−0.486586			−0.243293	+	0.969953i	$0.578228\pi$
$84$	−1.35313e6			−0.249094
$85$	−2.07612e6	+	3.59594e6i	−0.366679	+	0.635106i
$86$	671571.	−	1.16320e6i	0.113854	−	0.197200i
$87$	1.98034e7			3.22421
$88$	−4.47230e6			−0.699587
$89$	2.70269e6	−	4.68119e6i	0.406379	−	0.703868i	−0.588102	−	0.808787i	$-0.700125\pi$
$89$	2.70269e6	−	4.68119e6i	0.406379	−	0.703868i	0.994481	+	0.104918i	$0.0334581\pi$
$90$	−4.71747e6	−	8.17089e6i	−0.682119	−	1.18146i
$91$	725918.	−	1.25733e6i	0.100982	−	0.174905i
$92$	−63198.6	−	109463.i	−0.00846155	−	0.0146558i
$93$	1.18869e7	+	2.05888e7i	1.53243	+	2.65424i
$94$	−5.38103e6			−0.668218
$95$	−5.60099e6	−	4.32360e6i	−0.670242	−	0.517384i
$96$	3.12372e6			0.360349
$97$	−7.51343e6	−	1.30137e7i	−0.835868	−	1.44777i	−0.893322	−	0.449417i	$-0.851632\pi$
$97$	−7.51343e6	−	1.30137e7i	−0.835868	−	1.44777i	0.0574546	−	0.998348i	$-0.481702\pi$
$98$	−3.92631e6	−	6.80057e6i	−0.421399	−	0.729884i
$99$	−5.50783e6	+	9.53984e6i	−0.570502	+	0.988138i
$100$	−155712.	−	269700.i	−0.0155712	−	0.0269700i
$101$	1.02502e6	−	1.77539e6i	0.0989939	−	0.171462i	−0.812275	−	0.583275i	$-0.801771\pi$
$101$	1.02502e6	−	1.77539e6i	0.0989939	−	0.171462i	0.911268	+	0.411813i	$0.135104\pi$
$102$	1.44110e7			1.34460
$103$	1.17906e7			1.06318			0.531590	−	0.847002i	$-0.321595\pi$
$103$	1.17906e7			1.06318			0.531590	+	0.847002i	$0.321595\pi$
$104$	−881579.	+	1.52694e6i	−0.0768501	+	0.133108i
$105$	−1.13710e7	+	1.96952e7i	−0.958600	+	1.66034i
$106$	−1.98863e7			−1.62175
$107$	−2.93642e6			−0.231726			−0.115863	−	0.993265i	$-0.536963\pi$
$107$	−2.93642e6			−0.231726			−0.115863	+	0.993265i	$0.536963\pi$
$108$	838834.	−	1.45290e6i	0.0640756	−	0.110982i
$109$	4.28096e6	+	7.41484e6i	0.316627	+	0.548415i	0.979782	−	0.200068i	$-0.0641162\pi$
$109$	4.28096e6	+	7.41484e6i	0.316627	+	0.548415i	−0.663155	+	0.748482i	$0.730783\pi$
$110$	−3.72471e6	+	6.45139e6i	−0.266820	+	0.462146i
$111$	−1.84844e7	−	3.20160e7i	−1.28285	−	2.22196i
$112$	8.98029e6	+	1.55543e7i	0.603986	+	1.04614i
$113$	1.58178e7			1.03127			0.515635	−	0.856808i	$-0.327556\pi$
$113$	1.58178e7			1.03127			0.515635	+	0.856808i	$0.327556\pi$
$114$	−3.27580e6	+	2.43376e7i	−0.207086	+	1.53855i
$115$	−2.12435e6			−0.130252
$116$	1.81179e6	+	3.13811e6i	0.107772	+	0.186666i
$117$	2.17140e6	+	3.76098e6i	0.125340	+	0.217095i
$118$	2.20847e6	−	3.82518e6i	0.123738	−	0.214321i
$119$	−1.09543e7	−	1.89734e7i	−0.595896	−	1.03212i
$120$	1.38094e7	−	2.39185e7i	0.729523	−	1.26357i
$121$	−1.07897e7			−0.553681
$122$	−1.07941e7			−0.538179
$123$	−6.75422e6	+	1.16986e7i	−0.327271	+	0.566849i
$124$	−2.17504e6	+	3.76728e6i	−0.102445	+	0.177440i
$125$	−2.37233e7			−1.08640
$126$	4.97819e7			2.21705
$127$	−1.99712e6	+	3.45912e6i	−0.0865151	+	0.149849i	−0.906036	−	0.423201i	$-0.860906\pi$
$127$	−1.99712e6	+	3.45912e6i	−0.0865151	+	0.149849i	0.819521	+	0.573050i	$0.194240\pi$
$128$	−9.53932e6	−	1.65226e7i	−0.402052	−	0.696375i
$129$	4.84212e6	−	8.38680e6i	0.198596	−	0.343979i
$130$	1.46843e6	+	2.54339e6i	0.0586207	+	0.101534i
$131$	1.02232e7	+	1.77072e7i	0.397319	+	0.688176i	0.993394	−	0.114752i	$-0.0366074\pi$
$131$	1.02232e7	+	1.77072e7i	0.397319	+	0.688176i	−0.596075	+	0.802928i	$0.703274\pi$
$132$	−3.19578e6			−0.120940
$133$	3.45328e7	−	1.41870e7i	1.27277	−	0.522889i
$134$	3.26457e7			1.17208
$135$	−1.40982e7	−	2.44189e7i	−0.493170	−	0.854196i
$136$	1.33033e7	+	2.30419e7i	0.453495	+	0.785476i
$137$	1.65998e6	−	2.87517e6i	0.0551545	−	0.0955304i	−0.837130	−	0.547004i	$-0.815768\pi$
$137$	1.65998e6	−	2.87517e6i	0.0551545	−	0.0955304i	0.892284	+	0.451474i	$0.149102\pi$
$138$	3.68644e6	+	6.38511e6i	0.119407	+	0.206819i
$139$	8.38251e6	−	1.45189e7i	0.264742	−	0.458546i	−0.702754	−	0.711433i	$-0.748047\pi$
$139$	8.38251e6	−	1.45189e7i	0.264742	−	0.458546i	0.967496	+	0.252887i	$0.0813800\pi$
$140$	−4.16128e6			−0.128168
$141$	−3.87980e7			−1.16558
$142$	−1.94748e7	+	3.37314e7i	−0.570775	+	0.988611i
$143$	1.71445e6	−	2.96951e6i	0.0490284	−	0.0849197i
$144$	−5.37246e7			−1.49935
$145$	6.09013e7			1.65897
$146$	1.41654e7	−	2.45353e7i	0.376699	−	0.652463i
$147$	−2.83092e7	−	4.90331e7i	−0.735051	−	1.27315i
$148$	3.38224e6	−	5.85820e6i	0.0857606	−	0.148542i
$149$	−1.04984e6	−	1.81838e6i	−0.0259999	−	0.0450331i	0.852733	−	0.522348i	$-0.174944\pi$
$149$	−1.04984e6	−	1.81838e6i	−0.0259999	−	0.0450331i	−0.878733	+	0.477314i	$0.841610\pi$
$150$	9.08283e6	+	1.57319e7i	0.219736	+	0.380594i
$151$	7.87154e6			0.186055			0.0930273	−	0.995664i	$-0.470346\pi$
$151$	7.87154e6			0.186055			0.0930273	+	0.995664i	$0.470346\pi$
$152$	−4.19378e7	+	1.72292e7i	−0.968620	+	0.397934i
$153$	6.55341e7			1.47927
$154$	−1.96528e7	−	3.40397e7i	−0.433614	−	0.751041i
$155$	3.65558e7	+	6.33166e7i	0.788489	+	1.36570i
$156$	−629951.	+	1.09111e6i	−0.0132853	+	0.0230108i
$157$	−2.97230e7	−	5.14817e7i	−0.612976	−	1.06170i	−0.990736	−	0.135801i	$-0.956639\pi$
$157$	−2.97230e7	−	5.14817e7i	−0.612976	−	1.06170i	0.377761	−	0.925903i	$-0.376694\pi$
$158$	−5.39053e6	+	9.33668e6i	−0.108726	+	0.188318i
$159$	−1.43383e8			−2.82884
$160$	9.60636e6			0.185412
$161$	5.60440e6	−	9.70711e6i	0.105837	−	0.183316i
$162$	−5.33580e6	+	9.24188e6i	−0.0986046	+	0.170788i
$163$	−8.69125e6			−0.157190			−0.0785951	−	0.996907i	$-0.525043\pi$
$163$	−8.69125e6			−0.157190			−0.0785951	+	0.996907i	$0.525043\pi$
$164$	−2.47174e6			−0.0437571
$165$	−2.68557e7	+	4.65154e7i	−0.465417	+	0.806126i
$166$	1.35270e7	+	2.34294e7i	0.229521	+	0.397542i
$167$	5.87884e6	−	1.01824e7i	0.0976751	−	0.169178i	−0.813047	−	0.582198i	$-0.802193\pi$
$167$	5.87884e6	−	1.01824e7i	0.0976751	−	0.169178i	0.910722	+	0.413020i	$0.135526\pi$
$168$	7.28629e7	+	1.26202e8i	1.18556	+	2.05345i
$169$	3.06984e7	+	5.31711e7i	0.489228	+	0.847368i
$170$	4.43180e7			0.691844
$171$	−1.48968e7	+	1.10676e8i	−0.227827	+	1.69264i
$172$	1.77200e6			0.0265530
$173$	5.75849e7	+	9.97399e7i	0.845565	+	1.46456i	0.885129	+	0.465345i	$0.154070\pi$
$173$	5.75849e7	+	9.97399e7i	0.845565	+	1.46456i	−0.0395641	+	0.999217i	$0.512597\pi$
$174$	−1.05684e8	−	1.83049e8i	−1.52085	−	2.63418i
$175$	1.38084e7	−	2.39168e7i	0.194764	−	0.337342i
$176$	2.12093e7	+	3.67356e7i	0.293246	+	0.507917i
$177$	1.59234e7	−	2.75801e7i	0.215838	−	0.373843i
$178$	−5.76931e7			−0.766750
$179$	8.71902e6			0.113627			0.0568136	−	0.998385i	$-0.481906\pi$
$179$	8.71902e6			0.113627			0.0568136	+	0.998385i	$0.481906\pi$
$180$	6.22372e6	−	1.07798e7i	0.0795419	−	0.137771i
$181$	7.01178e7	−	1.21448e8i	0.878929	−	1.52235i	0.0264104	−	0.999651i	$-0.491592\pi$
$181$	7.01178e7	−	1.21448e8i	0.878929	−	1.52235i	0.852518	−	0.522698i	$-0.175074\pi$
$182$	−1.54958e7			−0.190531
$183$	−7.78270e7			−0.938753
$184$	−6.80617e6	+	1.17886e7i	−0.0805453	+	0.139509i
$185$	−5.68451e7	−	9.84586e7i	−0.660073	−	1.14328i
$186$	1.26873e8	−	2.19750e8i	1.44568	−	2.50399i
$187$	−2.58715e7	−	4.48107e7i	−0.289318	−	0.501114i
$188$	−3.54958e6	−	6.14805e6i	−0.0389605	−	0.0674815i
$189$	1.48774e8			1.60292
$190$	−1.00741e7	+	7.48453e7i	−0.106553	+	0.791638i
$191$	−6.04152e7			−0.627378			−0.313689	−	0.949526i	$-0.601565\pi$
$191$	−6.04152e7			−0.627378			−0.313689	+	0.949526i	$0.601565\pi$
$192$	−8.75105e7	−	1.51573e8i	−0.892290	−	1.54549i
$193$	−4.11913e7	−	7.13455e7i	−0.412435	−	0.714358i	0.582721	−	0.812673i	$-0.301988\pi$
$193$	−4.11913e7	−	7.13455e7i	−0.412435	−	0.714358i	−0.995155	+	0.0983146i	$0.968655\pi$
$194$	−8.01930e7	+	1.38898e8i	−0.788552	+	1.36581i
$195$	1.05876e7	+	1.83382e7i	0.102253	+	0.177107i
$196$	5.17995e6	−	8.97194e6i	0.0491394	−	0.0851119i
$197$	1.33881e8			1.24764			0.623818	−	0.781569i	$-0.285580\pi$
$197$	1.33881e8			1.24764			0.623818	+	0.781569i	$0.285580\pi$
$198$	1.17573e8			1.07642
$199$	−2.67913e7	+	4.64039e7i	−0.240995	+	0.417415i	−0.960998	−	0.276556i	$-0.910807\pi$
$199$	−2.67913e7	+	4.64039e7i	−0.240995	+	0.417415i	0.720003	+	0.693971i	$0.244140\pi$
$200$	−1.67694e7	+	2.90454e7i	−0.148222	+	0.256727i
$201$	2.35380e8			2.04448
$202$	−2.18807e7			−0.186780
$203$	−1.60668e8	+	2.78285e8i	−1.34801	+	2.33482i
$204$	9.50614e6	+	1.64651e7i	0.0783969	+	0.135787i
$205$	−2.07712e7	+	3.59768e7i	−0.168393	+	0.291665i
$206$	−6.29223e7	−	1.08985e8i	−0.501498	−	0.868620i
$207$	1.67642e7	+	2.90364e7i	0.131367	+	0.227534i
$208$	1.67231e7			0.128853
$209$	8.15584e7	−	3.35063e7i	0.617955	−	0.253872i
$210$	2.42732e8			1.80867
$211$	6.55664e6	+	1.13564e7i	0.0480499	+	0.0832249i	0.889050	−	0.457810i	$-0.151366\pi$
$211$	6.55664e6	+	1.13564e7i	0.0480499	+	0.0832249i	−0.841000	+	0.541035i	$0.818033\pi$
$212$	−1.31180e7	−	2.27210e7i	−0.0945563	−	0.163776i
$213$	−1.40416e8	+	2.43208e8i	−0.995609	+	1.72445i
$214$	1.56706e7	+	2.71423e7i	0.109304	+	0.189321i
$215$	1.48909e7	−	2.57919e7i	0.102185	−	0.176990i
$216$	−1.80676e8			−1.21987
$217$	−3.85762e8			−2.56277
$218$	4.56919e7	−	7.91407e7i	0.298704	−	0.517371i
$219$	1.02135e8	−	1.76903e8i	0.657081	−	1.13810i
$220$	−9.82797e6			−0.0622278
$221$	−2.03991e7			−0.127127
$222$	−1.97290e8	+	3.41716e8i	−1.21023	+	2.09618i
$223$	−4.99148e7	−	8.64550e7i	−0.301413	−	0.522063i	0.675043	−	0.737778i	$-0.264125\pi$
$223$	−4.99148e7	−	8.64550e7i	−0.301413	−	0.522063i	−0.976456	+	0.215715i	$0.930792\pi$
$224$	−2.53432e7	+	4.38957e7i	−0.150658	+	0.260948i
$225$	4.13043e7	+	7.15412e7i	0.241744	+	0.418714i
$226$	−8.44141e7	−	1.46209e8i	−0.486447	−	0.842550i
$227$	3.37838e8			1.91698			0.958492	−	0.285120i	$-0.0920334\pi$
$227$	3.37838e8			1.91698			0.958492	+	0.285120i	$0.0920334\pi$
$228$	−2.99676e7	+	1.23115e7i	−0.167448	+	0.0687920i
$229$	9.14520e7			0.503233			0.251616	−	0.967827i	$-0.419038\pi$
$229$	9.14520e7			0.503233			0.251616	+	0.967827i	$0.419038\pi$
$230$	1.13369e7	+	1.96361e7i	0.0614393	+	0.106416i
$231$	−1.41700e8	−	2.45431e8i	−0.756358	−	1.31005i
$232$	1.95121e8	−	3.37959e8i	1.02588	−	1.77687i
$233$	9.61422e7	+	1.66523e8i	0.497930	+	0.862440i	0.999997	−	0.00238857i	$-0.000760307\pi$
$233$	9.61422e7	+	1.66523e8i	0.497930	+	0.862440i	−0.502067	+	0.864829i	$0.667427\pi$
$234$	2.31760e7	−	4.01420e7i	0.118245	−	0.204806i
$235$	−1.19315e8			−0.599733
$236$	5.82723e6			0.0288583
$237$	−3.88665e7	+	6.73187e7i	−0.189651	+	0.328486i
$238$	−1.16918e8	+	2.02508e8i	−0.562164	+	0.973697i
$239$	−2.01833e8			−0.956314			−0.478157	−	0.878274i	$-0.658695\pi$
$239$	−2.01833e8			−0.956314			−0.478157	+	0.878274i	$0.658695\pi$
$240$	−2.61956e8			−1.22318
$241$	−8.46448e7	+	1.46609e8i	−0.389530	+	0.674685i	−0.992386	−	0.123164i	$-0.960696\pi$
$241$	−8.46448e7	+	1.46609e8i	−0.389530	+	0.674685i	0.602857	+	0.797850i	$0.294029\pi$
$242$	5.75806e7	+	9.97325e7i	0.261170	+	0.452359i
$243$	9.18106e7	−	1.59021e8i	0.410460	−	0.710937i
$244$	−7.12029e6	−	1.23327e7i	−0.0313786	−	0.0543493i
$245$	−8.70592e7	−	1.50791e8i	−0.378210	−	0.655080i
$246$	1.44179e8			0.617490
$247$	4.63698e6	−	3.44505e7i	0.0195793	−	0.145464i
$248$	4.68482e8			1.95035
$249$	9.75313e7	+	1.68929e8i	0.400356	+	0.693437i
$250$	1.26602e8	+	2.19282e8i	0.512451	+	0.887591i
$251$	−7.45031e7	+	1.29043e8i	−0.297383	+	0.515083i	−0.975536	−	0.219838i	$-0.929447\pi$
$251$	−7.45031e7	+	1.29043e8i	−0.297383	+	0.515083i	0.678153	+	0.734920i	$0.262781\pi$
$252$	3.28385e7	+	5.68779e7i	0.129265	+	0.223894i
$253$	1.32363e7	−	2.29259e7i	0.0513859	−	0.0890029i
$254$	4.26317e7			0.163236
$255$	3.19539e8			1.20679
$256$	4.37398e7	−	7.57596e7i	0.162943	−	0.282226i
$257$	9.57808e7	−	1.65897e8i	0.351975	−	0.609639i	−0.634620	−	0.772824i	$-0.718843\pi$
$257$	9.57808e7	−	1.65897e8i	0.351975	−	0.609639i	0.986595	+	0.163185i	$0.0521767\pi$
$258$	−1.03363e8			−0.374709
$259$	5.99868e8			2.14539
$260$	−1.93728e6	+	3.35548e6i	−0.00683576	+	0.0118399i
$261$	−4.80598e8	−	8.32420e8i	−1.67317	−	2.89802i
$262$	1.09115e8	−	1.88994e8i	0.374828	−	0.649221i
$263$	−5.78101e7	−	1.00130e8i	−0.195956	−	0.339406i	0.751257	−	0.660009i	$-0.229448\pi$
$263$	−5.78101e7	−	1.00130e8i	−0.195956	−	0.339406i	−0.947214	+	0.320603i	$0.896114\pi$
$264$	1.72085e8	+	2.98060e8i	0.575611	+	0.996987i
$265$	−4.40946e8			−1.45554
$266$	−3.15424e8	−	2.43487e8i	−1.02757	−	0.793215i
$267$	−4.15975e8			−1.33745
$268$	2.15346e7	+	3.72990e7i	0.0683384	+	0.118366i
$269$	1.50912e8	+	2.61387e8i	0.472704	+	0.818748i	0.999512	−	0.0312364i	$-0.00994449\pi$
$269$	1.50912e8	+	2.61387e8i	0.472704	+	0.818748i	−0.526808	+	0.849985i	$0.676611\pi$
$270$	−1.50474e8	+	2.60629e8i	−0.465253	+	0.805843i
$271$	4.41198e7	+	7.64177e7i	0.134661	+	0.233239i	0.925468	−	0.378826i	$-0.123672\pi$
$271$	4.41198e7	+	7.64177e7i	0.134661	+	0.233239i	−0.790807	+	0.612065i	$0.790339\pi$
$272$	1.26178e8	−	2.18547e8i	0.380183	−	0.658496i
$273$	−1.11727e8			−0.332345
$274$	−3.54349e7			−0.104065
$275$	3.26121e7	−	5.64859e7i	0.0945616	−	0.163785i
$276$	−4.86350e6	+	8.42382e6i	−0.0139241	+	0.0241172i
$277$	6.92447e6			0.0195753			0.00978763	−	0.999952i	$-0.496884\pi$
$277$	6.92447e6			0.0195753			0.00978763	+	0.999952i	$0.496884\pi$
$278$	−1.78938e8			−0.499511
$279$	5.76955e8	−	9.99316e8i	1.59048	−	2.75479i
$280$	2.24075e8	+	3.88109e8i	0.610014	+	1.05658i
$281$	−5.40408e7	+	9.36014e7i	−0.145295	+	0.251658i	−0.929483	−	0.368865i	$-0.879746\pi$
$281$	−5.40408e7	+	9.36014e7i	−0.145295	+	0.251658i	0.784188	+	0.620523i	$0.213080\pi$
$282$	2.07051e8	+	3.58622e8i	0.549800	+	0.952282i
$283$	2.54549e8	+	4.40892e8i	0.667604	+	1.15632i	0.978572	+	0.205904i	$0.0660134\pi$
$283$	2.54549e8	+	4.40892e8i	0.667604	+	1.15632i	−0.310968	+	0.950420i	$0.600653\pi$
$284$	−5.13860e7			−0.133116
$285$	−7.26353e7	+	5.39645e8i	−0.185862	+	1.38086i
$286$	−3.65975e7			−0.0925061
$287$	−1.09596e8	−	1.89826e8i	−0.273658	−	0.473989i
$288$	−7.58078e7	−	1.31303e8i	−0.186999	−	0.323893i
$289$	5.12553e7	−	8.87768e7i	0.124910	−	0.216350i
$290$	−3.25008e8	−	5.62931e8i	−0.782531	−	1.35538i
$291$	−5.78202e8	+	1.00148e9i	−1.37548	+	2.38240i
$292$	3.73767e7			0.0878539
$293$	1.73278e8			0.402446			0.201223	−	0.979545i	$-0.435508\pi$
$293$	1.73278e8			0.402446			0.201223	+	0.979545i	$0.435508\pi$
$294$	−3.02152e8	+	5.23343e8i	−0.693443	+	1.20108i
$295$	4.89690e7	−	8.48168e7i	0.111057	−	0.192356i
$296$	−7.28500e8			−1.63271
$297$	3.51370e8			0.778245
$298$	−1.12052e7	+	1.94080e7i	−0.0245281	+	0.0424839i
$299$	−5.21826e6	−	9.03828e6i	−0.0112895	−	0.0195541i
$300$	−1.19829e7	+	2.07550e7i	−0.0256235	+	0.0443811i
$301$	7.85697e7	+	1.36087e8i	0.166063	+	0.287629i
$302$	−4.20076e7	−	7.27592e7i	−0.0877613	−	0.152007i
$303$	−1.57763e8			−0.325803
$304$	3.40405e8	+	2.62771e8i	0.694926	+	0.536439i
$305$	−2.39341e8			−0.483022
$306$	−3.49732e8	−	6.05753e8i	−0.697767	−	1.20857i
$307$	1.46536e8	+	2.53807e8i	0.289040	+	0.500633i	0.973581	−	0.228342i	$-0.0733305\pi$
$307$	1.46536e8	+	2.53807e8i	0.289040	+	0.500633i	−0.684541	+	0.728975i	$0.739997\pi$
$308$	2.59279e7	−	4.49084e7i	0.0505637	−	0.0875789i
$309$	−4.53678e8	−	7.85794e8i	−0.874769	−	1.51514i
$310$	3.90170e8	−	6.75795e8i	0.743855	−	1.28840i
$311$	1.74353e8			0.328675			0.164338	−	0.986404i	$-0.447451\pi$
$311$	1.74353e8			0.328675			0.164338	+	0.986404i	$0.447451\pi$
$312$	1.35685e8			0.252925
$313$	3.73727e7	−	6.47315e7i	0.0688890	−	0.119319i	−0.829524	−	0.558472i	$-0.811388\pi$
$313$	3.73727e7	−	6.47315e7i	0.0688890	−	0.119319i	0.898412	+	0.439153i	$0.144721\pi$
$314$	−3.17241e8	+	5.49478e8i	−0.578277	+	1.00161i
$315$	1.10383e9			1.98983
$316$	−1.42234e7			−0.0253570
$317$	1.98038e8	−	3.43011e8i	0.349173	−	0.604785i	−0.636930	−	0.770922i	$-0.719796\pi$
$317$	1.98038e8	−	3.43011e8i	0.349173	−	0.604785i	0.986103	+	0.166137i	$0.0531294\pi$
$318$	7.65185e8	+	1.32534e9i	1.33436	+	2.31117i
$319$	−3.79460e8	+	6.57244e8i	−0.654483	+	1.13360i
$320$	−2.69121e8	−	4.66130e8i	−0.459115	−	0.795211i
$321$	1.12987e8	+	1.95700e8i	0.190661	+	0.330235i
$322$	−1.19635e8			−0.199692
$323$	−4.15232e8	−	3.20533e8i	−0.685618	−	0.529253i
$324$	−1.40790e7			−0.0229966
$325$	−1.28570e7	−	2.22689e7i	−0.0207753	−	0.0359839i
$326$	4.63820e7	+	8.03361e7i	0.0741461	+	0.128425i
$327$	3.29445e8	−	5.70615e8i	0.521033	−	0.902456i
$328$	1.33097e8	+	2.30531e8i	0.208262	+	0.360720i
$329$	3.14774e8	−	5.45204e8i	0.487318	−	0.844060i
$330$	5.73276e8			0.878143
$331$	−7.45816e8			−1.13040			−0.565202	−	0.824953i	$-0.691202\pi$
$331$	−7.45816e8			−1.13040			−0.565202	+	0.824953i	$0.691202\pi$
$332$	−1.78460e7	+	3.09102e7i	−0.0267644	+	0.0463574i
$333$	−8.97178e8	+	1.55396e9i	−1.33145	+	2.30613i
$334$	−1.25493e8			−0.184292
$335$	7.23862e8			1.05196
$336$	6.91085e8	−	1.19699e9i	0.993903	−	1.72149i
$337$	−3.43241e8	−	5.94510e8i	−0.488533	−	0.846165i	0.511380	−	0.859355i	$-0.329135\pi$
$337$	−3.43241e8	−	5.94510e8i	−0.488533	−	0.846165i	−0.999913	+	0.0131903i	$0.995801\pi$
$338$	3.27652e8	−	5.67510e8i	0.461535	−	0.799402i
$339$	−6.08637e8	−	1.05419e9i	−0.848515	−	1.46967i
$340$	2.92342e7	+	5.06351e7i	0.0403380	+	0.0698675i
$341$	−9.11079e8			−1.24427
$342$	1.10251e9	−	4.52940e8i	1.49036	−	0.612279i
$343$	−1.09656e8			−0.146724
$344$	−9.54176e7	−	1.65268e8i	−0.126379	−	0.218894i
$345$	8.17406e7	+	1.41579e8i	0.107169	+	0.185623i
$346$	6.14619e8	−	1.06455e9i	0.797701	−	1.38166i
$347$	3.37836e8	+	5.85149e8i	0.434063	+	0.751819i	0.997219	−	0.0745315i	$-0.0237461\pi$
$347$	3.37836e8	+	5.85149e8i	0.434063	+	0.751819i	−0.563156	+	0.826351i	$0.690413\pi$
$348$	1.39428e8	−	2.41496e8i	0.177346	−	0.307172i
$349$	5.01746e8			0.631822			0.315911	−	0.948789i	$-0.397690\pi$
$349$	5.01746e8			0.631822			0.315911	+	0.948789i	$0.397690\pi$
$350$	−2.94761e8			−0.367479
$351$	6.92618e7	−	1.19965e8i	0.0854908	−	0.148074i
$352$	−5.98546e7	+	1.03671e8i	−0.0731473	+	0.126695i
$353$	−7.57474e7			−0.0916551			−0.0458275	−	0.998949i	$-0.514592\pi$
$353$	−7.57474e7			−0.0916551			−0.0458275	+	0.998949i	$0.514592\pi$
$354$	−3.39909e8			−0.407241
$355$	−4.31821e8	+	7.47936e8i	−0.512277	+	0.887290i
$356$	−3.80570e7	−	6.59167e7i	−0.0447054	−	0.0774320i
$357$	−8.42997e8	+	1.46011e9i	−0.980590	+	1.69843i
$358$	−4.65302e7	−	8.05928e7i	−0.0535975	−	0.0928336i
$359$	6.23283e8	+	1.07956e9i	0.710976	+	1.23145i	0.964491	+	0.264115i	$0.0850797\pi$
$359$	6.23283e8	+	1.07956e9i	0.710976	+	1.23145i	−0.253516	+	0.967331i	$0.581587\pi$
$360$	−1.34053e9			−1.51432
$361$	6.35711e8	−	6.28393e8i	0.711188	−	0.703001i
$362$	−1.49677e9			−1.65835
$363$	4.15164e8	+	7.19085e8i	0.455561	+	0.789055i
$364$	−1.02218e7	−	1.77046e7i	−0.0111089	−	0.0192412i
$365$	3.14094e8	−	5.44027e8i	0.338092	−	0.585593i
$366$	4.15334e8	+	7.19380e8i	0.442807	+	0.766964i
$367$	−4.08148e8	+	7.06933e8i	−0.431009	+	0.746529i	−0.996960	−	0.0779093i	$-0.975176\pi$
$367$	−4.08148e8	+	7.06933e8i	−0.431009	+	0.746529i	0.565952	+	0.824438i	$0.308509\pi$
$368$	1.29109e8			0.135049
$369$	6.55657e8			0.679336
$370$	−6.06723e8	+	1.05088e9i	−0.622708	+	1.07856i
$371$	1.16329e9	−	2.01488e9i	1.18271	−	2.04852i
$372$	3.34764e8			0.337162
$373$	−1.37500e9			−1.37189			−0.685947	−	0.727652i	$-0.740612\pi$
$373$	−1.37500e9			−1.37189			−0.685947	+	0.727652i	$0.740612\pi$
$374$	−2.76133e8	+	4.78277e8i	−0.272941	+	0.472747i
$375$	9.12821e8	+	1.58105e9i	0.893874	+	1.54824i
$376$	−3.82272e8	+	6.62114e8i	−0.370864	+	0.642355i
$377$	1.49598e8	+	2.59111e8i	0.143791	+	0.249053i
$378$	−7.93955e8	−	1.37517e9i	−0.756091	−	1.30959i
$379$	8.95550e8			0.844992			0.422496	−	0.906365i	$-0.361154\pi$
$379$	8.95550e8			0.844992			0.422496	+	0.906365i	$0.361154\pi$
$380$	−9.21591e7	+	3.78614e7i	−0.0861580	+	0.0353960i
$381$	3.07381e8			0.284734
$382$	3.22414e8	+	5.58437e8i	0.295932	+	0.512569i
$383$	8.06893e8	+	1.39758e9i	0.733872	+	1.27110i	0.955217	+	0.295907i	$0.0956220\pi$
$383$	8.06893e8	+	1.39758e9i	0.733872	+	1.27110i	−0.221345	+	0.975196i	$0.571045\pi$
$384$	−7.34106e8	+	1.27151e9i	−0.661606	+	1.14594i
$385$	−4.35768e8	−	7.54773e8i	−0.389173	−	0.674068i
$386$	−4.39647e8	+	7.61490e8i	−0.389088	+	0.673921i
$387$	−4.70043e8			−0.412239
$388$	−2.11596e8			−0.183906
$389$	5.37399e8	−	9.30803e8i	0.462886	−	0.801741i	−0.536218	−	0.844080i	$-0.680147\pi$
$389$	5.37399e8	−	9.30803e8i	0.462886	−	0.801741i	0.999103	+	0.0423384i	$0.0134807\pi$
$390$	1.13004e8	−	1.95729e8i	0.0964645	−	0.167081i
$391$	−1.57490e8			−0.133240
$392$	−1.11571e9			−0.935513
$393$	7.86738e8	−	1.36267e9i	0.653817	−	1.13244i
$394$	−7.14476e8	−	1.23751e9i	−0.588506	−	1.01932i
$395$	−1.19526e8	+	2.07025e8i	−0.0975825	+	0.169018i
$396$	7.75567e7	+	1.34332e8i	0.0627604	+	0.108704i
$397$	−1.01720e9	−	1.76184e9i	−0.815905	−	1.41319i	−0.908677	−	0.417501i	$-0.862906\pi$
$397$	−1.01720e9	−	1.76184e9i	−0.815905	−	1.41319i	0.0927721	−	0.995687i	$-0.470427\pi$
$398$	5.71902e8			0.454706
$399$	−2.27425e9	−	1.75558e9i	−1.79239	−	1.38361i
$400$	3.18106e8			0.248520
$401$	8.12390e8	+	1.40710e9i	0.629157	+	1.08973i	0.987721	+	0.156227i	$0.0499331\pi$
$401$	8.12390e8	+	1.40710e9i	0.629157	+	1.08973i	−0.358564	+	0.933505i	$0.616734\pi$
$402$	−1.25614e9	−	2.17569e9i	−0.964374	−	1.67035i
$403$	−1.79591e8	+	3.11062e8i	−0.136684	+	0.236744i
$404$	−1.44335e7	−	2.49996e7i	−0.0108902	−	0.0188624i
$405$	−1.18312e8	+	2.04923e8i	−0.0884988	+	0.153284i
$406$	3.42971e9			2.54341
$407$	1.41675e9			1.04163
$408$	1.02376e9	−	1.77321e9i	0.746258	−	1.29256i
$409$	5.34619e6	−	9.25988e6i	0.00386379	−	0.00669227i	−0.864087	−	0.503342i	$-0.832103\pi$
$409$	5.34619e6	−	9.25988e6i	0.00386379	−	0.00669227i	0.867951	+	0.496650i	$0.165437\pi$
$410$	4.43393e8			0.317721
$411$	−2.55490e8			−0.181521
$412$	8.30129e7	−	1.43783e8i	0.0584797	−	0.101290i
$413$	2.58377e8	+	4.47522e8i	0.180480	+	0.312600i
$414$	1.78929e8	−	3.09913e8i	0.123931	−	0.214654i
$415$	2.99937e8	+	5.19507e8i	0.205998	+	0.356798i
$416$	2.35970e7	+	4.08713e7i	0.0160706	+	0.0278350i
$417$	−1.29017e9			−0.871303
$418$	−7.44958e8	−	5.75060e8i	−0.498901	−	0.385120i
$419$	−3.65555e8			−0.242775			−0.121387	−	0.992605i	$-0.538734\pi$
$419$	−3.65555e8			−0.242775			−0.121387	+	0.992605i	$0.538734\pi$
$420$	1.60117e8	+	2.77332e8i	0.105455	+	0.182653i
$421$	8.48116e8	+	1.46898e9i	0.553947	+	0.959464i	0.997985	+	0.0634556i	$0.0202121\pi$
$421$	8.48116e8	+	1.46898e9i	0.553947	+	0.959464i	−0.444038	+	0.896008i	$0.646455\pi$
$422$	6.99808e7	−	1.21210e8i	0.0453300	−	0.0785138i
$423$	9.41567e8	+	1.63084e9i	0.604867	+	1.04766i
$424$	−1.41274e9	+	2.44693e9i	−0.900080	+	1.55898i
$425$	−3.88031e8			−0.245191
$426$	2.99740e9			1.87850
$427$	6.31422e8	−	1.09365e9i	0.392484	−	0.679802i
$428$	−2.06741e7	+	3.58086e7i	−0.0127460	+	0.0220767i
$429$	−2.63873e8			−0.161360
$430$	−3.17870e8			−0.192801
$431$	−4.34319e8	+	7.52263e8i	−0.261300	+	0.452584i	−0.966588	−	0.256337i	$-0.917484\pi$
$431$	−4.34319e8	+	7.52263e8i	−0.261300	+	0.452584i	0.705288	+	0.708921i	$0.250818\pi$
$432$	8.56834e8	+	1.48408e9i	0.511333	+	0.885654i
$433$	1.52805e9	−	2.64667e9i	0.904546	−	1.56672i	0.0830214	−	0.996548i	$-0.473543\pi$
$433$	1.52805e9	−	2.64667e9i	0.904546	−	1.56672i	0.821525	−	0.570173i	$-0.193124\pi$
$434$	2.05867e9	+	3.56573e9i	1.20885	+	2.09379i
$435$	−2.34335e9	−	4.05881e9i	−1.36498	−	2.36421i
$436$	1.20562e8			0.0696638
$437$	3.57995e7	−	2.65973e8i	0.0205207	−	0.152459i
$438$	−2.18022e9			−1.23977
$439$	−5.22293e8	−	9.04637e8i	−0.294638	−	0.510327i	0.680263	−	0.732968i	$-0.261866\pi$
$439$	−5.22293e8	−	9.04637e8i	−0.294638	−	0.510327i	−0.974901	+	0.222641i	$0.928532\pi$
$440$	5.29211e8	+	9.16621e8i	0.296173	+	0.512986i
$441$	−1.37404e9	+	2.37991e9i	−0.762896	+	1.32137i
$442$	1.08863e8	+	1.88556e8i	0.0599654	+	0.103863i
$443$	1.11659e9	−	1.93399e9i	0.610213	−	1.05692i	−0.380991	−	0.924579i	$-0.624417\pi$
$443$	1.11659e9	−	1.93399e9i	0.610213	−	1.05692i	0.991204	−	0.132342i	$-0.0422496\pi$
$444$	−5.20565e8			−0.282251
$445$	−1.27924e9			−0.688167
$446$	−5.32755e8	+	9.22758e8i	−0.284351	+	0.492511i
$447$	−8.07913e7	+	1.39935e8i	−0.0427847	+	0.0741052i
$448$	2.83994e9			1.49223
$449$	−9.24074e8			−0.481776			−0.240888	−	0.970553i	$-0.577439\pi$
$449$	−9.24074e8			−0.481776			−0.240888	+	0.970553i	$0.577439\pi$
$450$	4.40852e8	−	7.63579e8i	0.228060	−	0.395012i
$451$	−2.58840e8	−	4.48323e8i	−0.132866	−	0.230130i
$452$	1.11367e8	−	1.92893e8i	0.0567246	−	0.0982499i
$453$	−3.02880e8	−	5.24604e8i	−0.153083	−	0.265148i
$454$	−1.80292e9	−	3.12275e9i	−0.904235	−	1.56618i
$455$	−3.43594e8			−0.171004
$456$	2.76193e9	+	2.13203e9i	1.36407	+	1.05297i
$457$	−2.18962e9			−1.07315			−0.536577	−	0.843851i	$-0.680283\pi$
$457$	−2.18962e9			−1.07315			−0.536577	+	0.843851i	$0.680283\pi$
$458$	−4.88046e8	−	8.45321e8i	−0.237373	−	0.411143i
$459$	−1.04518e9	−	1.81031e9i	−0.504483	−	0.873791i
$460$	−1.49567e7	+	2.59057e7i	−0.00716445	+	0.0124092i
$461$	4.58897e8	+	7.94832e8i	0.218153	+	0.377852i	0.954243	−	0.299031i	$-0.0966634\pi$
$461$	4.58897e8	+	7.94832e8i	0.218153	+	0.377852i	−0.736090	+	0.676883i	$0.763330\pi$
$462$	−1.51240e9	+	2.61955e9i	−0.713543	+	1.23589i
$463$	−3.18304e9			−1.49042			−0.745210	−	0.666830i	$-0.767651\pi$
$463$	−3.18304e9			−1.49042			−0.745210	+	0.666830i	$0.767651\pi$
$464$	−3.70133e9			−1.72007
$465$	2.81318e9	−	4.87258e9i	1.29752	−	2.24736i
$466$	1.02615e9	−	1.77735e9i	0.469744	−	0.813620i
$467$	1.81087e9			0.822770			0.411385	−	0.911462i	$-0.365045\pi$
$467$	1.81087e9			0.822770			0.411385	+	0.911462i	$0.365045\pi$
$468$	6.11518e7			0.0275771
$469$	−1.90967e9	+	3.30765e9i	−0.854778	+	1.48052i
$470$	6.36742e8	+	1.10287e9i	0.282892	+	0.489983i
$471$	−2.28735e9	+	3.96181e9i	−1.00870	+	1.74711i
$472$	−3.13782e8	−	5.43486e8i	−0.137351	−	0.237898i
$473$	1.85563e8	+	3.21404e8i	0.0806264	+	0.139649i
$474$	8.29666e8			0.357832
$475$	8.82045e7	−	6.55316e8i	0.0377627	−	0.280558i
$476$	−3.08499e8			−0.131108
$477$	3.47969e9	+	6.02700e9i	1.46800	+	2.54265i
$478$	1.07711e9	+	1.86561e9i	0.451090	+	0.781311i
$479$	1.28237e9	−	2.22113e9i	0.533137	−	0.923421i	−0.466114	−	0.884725i	$-0.654346\pi$
$479$	1.28237e9	−	2.22113e9i	0.533137	−	0.923421i	0.999251	−	0.0386959i	$-0.0123204\pi$
$480$	−3.69632e8	−	6.40222e8i	−0.152555	−	0.264233i
$481$	2.79269e8	−	4.83707e8i	0.114423	−	0.198187i
$482$	1.80687e9			0.734959
$483$	−8.62582e8			−0.348326
$484$	−7.59657e7	+	1.31576e8i	−0.0304550	+	0.0527496i
$485$	−1.77814e9	+	3.07983e9i	−0.707734	+	1.22583i
$486$	−1.95984e9			−0.774450
$487$	1.11752e9			0.438436			0.219218	−	0.975676i	$-0.429649\pi$
$487$	1.11752e9			0.438436			0.219218	+	0.975676i	$0.429649\pi$
$488$	−7.66819e8	+	1.32817e9i	−0.298692	+	0.517350i
$489$	3.34421e8	+	5.79234e8i	0.129334	+	0.224013i
$490$	−9.29207e8	+	1.60943e9i	−0.356801	+	0.617998i
$491$	−1.55235e8	−	2.68875e8i	−0.0591841	−	0.102510i	0.834915	−	0.550378i	$-0.185517\pi$
$491$	−1.55235e8	−	2.68875e8i	−0.0591841	−	0.102510i	−0.894099	+	0.447869i	$0.852183\pi$
$492$	9.51073e7	+	1.64731e8i	0.0360028	+	0.0623586i
$493$	4.51495e9			1.69703
$494$	−3.43183e8	+	1.40989e8i	−0.128080	+	0.0526187i
$495$	2.60698e9			0.966095
$496$	−2.22171e9	−	3.84812e9i	−0.817528	−	1.41600i
$497$	−2.27844e9	−	3.94637e9i	−0.832510	−	1.44195i
$498$	1.04098e9	−	1.80303e9i	0.377693	−	0.654184i
$499$	1.56410e9	+	2.70910e9i	0.563524	+	0.976052i	0.997185	+	0.0749763i	$0.0238881\pi$
$499$	1.56410e9	+	2.70910e9i	0.563524	+	0.976052i	−0.433661	+	0.901076i	$0.642779\pi$
$500$	−1.67026e8	+	2.89297e8i	−0.0597569	+	0.103502i
$501$	−9.04821e8			−0.321463
$502$	1.59038e9			0.561098
$503$	−8.05201e8	+	1.39465e9i	−0.282109	+	0.488627i	−0.971904	−	0.235378i	$-0.924367\pi$
$503$	−8.05201e8	+	1.39465e9i	−0.282109	+	0.488627i	0.689795	+	0.724005i	$0.257701\pi$
$504$	3.53654e9	−	6.12546e9i	1.23047	−	2.13124i
$505$	−4.85167e8			−0.167638
$506$	−2.82549e8			−0.0969542
$507$	2.36242e9	−	4.09183e9i	0.805061	−	1.39441i
$508$	2.81219e7	+	4.87085e7i	0.00951746	+	0.0164847i
$509$	−1.55384e9	+	2.69132e9i	−0.522267	+	0.904594i	0.477397	+	0.878688i	$0.341580\pi$
$509$	−1.55384e9	+	2.69132e9i	−0.522267	+	0.904594i	−0.999664	+	0.0259059i	$0.991753\pi$
$510$	−1.70526e9	−	2.95360e9i	−0.569240	−	0.985953i
$511$	1.65727e9	+	2.87047e9i	0.549439	+	0.951657i
$512$	−3.37576e9			−1.11154
$513$	3.29487e9	−	1.35362e9i	1.07753	−	0.442676i
$514$	−2.04459e9			−0.664102
$515$	−1.39519e9	−	2.41655e9i	−0.450100	−	0.779597i
$516$	−6.81827e7	−	1.18096e8i	−0.0218474	−	0.0378409i
$517$	7.43421e8	−	1.28764e9i	0.236602	−	0.409806i
$518$	−3.20128e9	−	5.54478e9i	−1.01197	−	1.75279i
$519$	4.43149e9	−	7.67557e9i	1.39144	−	2.41004i
$520$	4.17272e8			0.130139
$521$	5.28452e8			0.163709			0.0818547	−	0.996644i	$-0.473916\pi$
$521$	5.28452e8			0.163709			0.0818547	+	0.996644i	$0.473916\pi$
$522$	−5.12956e9	+	8.88465e9i	−1.57846	+	2.73397i
$523$	2.47009e7	−	4.27831e7i	0.00755016	−	0.0130773i	−0.862226	−	0.506524i	$-0.830930\pi$
$523$	2.47009e7	−	4.27831e7i	0.00755016	−	0.0130773i	0.869776	+	0.493447i	$0.164263\pi$
$524$	2.87910e8			0.0874174
$525$	−2.12527e9			−0.640998
$526$	−6.17024e8	+	1.06872e9i	−0.184864	+	0.320193i
$527$	2.71008e9	+	4.69400e9i	0.806577	+	1.39703i
$528$	1.63218e9	−	2.82702e9i	0.482558	−	0.835814i
$529$	1.66213e9	+	2.87889e9i	0.488168	+	0.845531i
$530$	2.35317e9	+	4.07581e9i	0.686574	+	1.18918i
$531$	−1.54574e9			−0.448029
$532$	7.01259e7	−	5.21001e8i	0.0201924	−	0.150019i
$533$	−2.04089e8			−0.0583815
$534$	2.21991e9	+	3.84499e9i	0.630871	+	1.09270i
$535$	3.47469e8	+	6.01834e8i	0.0981020	+	0.169918i
$536$	2.31917e9	−	4.01691e9i	0.650512	−	1.12672i
$537$	−3.35490e8	−	5.81085e8i	−0.0934908	−	0.161931i
$538$	1.61072e9	−	2.78985e9i	0.445946	−	0.772401i
$539$	2.16977e9			0.596834
$540$	−3.97040e8			−0.108506
$541$	2.04623e9	−	3.54418e9i	0.555603	−	0.962333i	−0.442253	−	0.896890i	$-0.645821\pi$
$541$	2.04623e9	−	3.54418e9i	0.555603	−	0.962333i	0.997856	−	0.0654428i	$-0.0208460\pi$
$542$	4.70902e8	−	8.15627e8i	0.127038	−	0.220036i
$543$	−1.07920e10			−2.89268
$544$	7.12172e8			0.189666
$545$	1.01314e9	−	1.75481e9i	0.268090	−	0.464346i
$546$	5.96248e8	+	1.03273e9i	0.156766	+	0.271527i
$547$	−1.13340e9	+	1.96311e9i	−0.296093	+	0.512848i	−0.975238	−	0.221156i	$-0.929017\pi$
$547$	−1.13340e9	+	1.96311e9i	−0.296093	+	0.512848i	0.679146	+	0.734003i	$0.262350\pi$
$548$	−2.33745e7	−	4.04858e7i	−0.00606750	−	0.0105092i
$549$	1.88874e9	+	3.27139e9i	0.487157	+	0.843781i
$550$	−6.96156e8			−0.178417
$551$	−1.02631e9	+	7.62496e9i	−0.261365	+	1.94181i
$552$	1.04755e9			0.265086
$553$	−6.30659e8	−	1.09233e9i	−0.158583	−	0.274674i
$554$	−3.69534e7	−	6.40052e7i	−0.00923359	−	0.0159930i
$555$	−4.37456e9	+	7.57696e9i	−1.08620	+	1.88135i
$556$	−1.18036e8	−	2.04444e8i	−0.0291240	−	0.0504442i
$557$	1.25724e9	−	2.17761e9i	0.308266	−	0.533932i	−0.669717	−	0.742616i	$-0.733585\pi$
$557$	1.25724e9	−	2.17761e9i	0.308266	−	0.533932i	0.977983	+	0.208684i	$0.0669180\pi$
$558$	−1.23160e10			−3.00089
$559$	1.46312e8			0.0354274
$560$	2.12529e9	−	3.68111e9i	0.511399	−	0.885769i
$561$	−1.99096e9	+	3.44844e9i	−0.476094	+	0.824619i
$562$	1.15359e9			0.274140
$563$	−1.97050e9			−0.465369			−0.232684	−	0.972552i	$-0.574751\pi$
$563$	−1.97050e9			−0.465369			−0.232684	+	0.972552i	$0.574751\pi$
$564$	−2.73160e8	+	4.73128e8i	−0.0641122	+	0.111046i
$565$	−1.87174e9	−	3.24194e9i	−0.436592	−	0.756199i
$566$	2.71687e9	−	4.70576e9i	0.629813	−	1.09087i
$567$	−6.24256e8	−	1.08124e9i	−0.143821	−	0.249105i
$568$	2.76701e9	+	4.79260e9i	0.633565	+	1.09737i
$569$	6.19805e9			1.41046			0.705232	−	0.708976i	$-0.250843\pi$
$569$	6.19805e9			1.41046			0.705232	+	0.708976i	$0.250843\pi$
$570$	5.37574e9	−	2.20850e9i	1.21584	−	0.499499i
$571$	−5.03241e9			−1.13123			−0.565614	−	0.824670i	$-0.691361\pi$
$571$	−5.03241e9			−1.13123			−0.565614	+	0.824670i	$0.691361\pi$
$572$	−2.41414e7	−	4.18142e7i	−0.00539357	−	0.00934194i
$573$	2.32465e9	+	4.02641e9i	0.516198	+	0.894081i
$574$	−1.16975e9	+	2.02606e9i	−0.258167	+	0.447158i
$575$	−9.92614e7	−	1.71926e8i	−0.0217742	−	0.0377141i
$576$	−4.24749e9	+	7.35687e9i	−0.926091	+	1.60404i
$577$	4.54380e9			0.984700			0.492350	−	0.870397i	$-0.336138\pi$
$577$	4.54380e9			0.984700			0.492350	+	0.870397i	$0.336138\pi$
$578$	−1.09412e9			−0.235678
$579$	−3.16991e9	+	5.49045e9i	−0.678691	+	1.17553i
$580$	4.28781e8	−	7.42670e8i	0.0912509	−	0.158051i
$581$	−3.16514e9			−0.669541
$582$	1.23426e10			2.59524
$583$	2.74742e9	−	4.75866e9i	0.574228	−	0.994592i
$584$	−2.01264e9	−	3.48600e9i	−0.418140	−	0.724239i
$585$	5.13888e8	−	8.90079e8i	0.106126	−	0.183816i
$586$	−9.24724e8	−	1.60167e9i	−0.189832	−	0.328799i
$587$	−2.86845e9	−	4.96830e9i	−0.585347	−	1.01385i	−0.994832	−	0.101534i	$-0.967625\pi$
$587$	−2.86845e9	−	4.96830e9i	−0.585347	−	1.01385i	0.409485	−	0.912317i	$-0.365708\pi$
$588$	−7.97255e8			−0.161725
$589$	−8.54339e9	+	3.50985e9i	−1.72277	+	0.707759i
$590$	−1.04532e9			−0.209540
$591$	−5.15147e9	−	8.92261e9i	−1.02654	−	1.77802i
$592$	3.45481e9	+	5.98391e9i	0.684382	+	1.18538i
$593$	2.04348e9	−	3.53942e9i	0.402420	−	0.697012i	−0.591597	−	0.806234i	$-0.701502\pi$
$593$	2.04348e9	−	3.53942e9i	0.402420	−	0.697012i	0.994017	+	0.109222i	$0.0348358\pi$
$594$	−1.87513e9	−	3.24782e9i	−0.367096	−	0.635829i
$595$	−2.59246e9	+	4.49028e9i	−0.504549	+	0.873904i
$596$	−2.95660e7			−0.00572045
$597$	4.12349e9			0.793149
$598$	−5.56959e7	+	9.64681e7i	−0.0106505	+	0.0184472i
$599$	−3.90630e9	+	6.76591e9i	−0.742629	+	1.28627i	0.208666	+	0.977987i	$0.433088\pi$
$599$	−3.90630e9	+	6.76591e9i	−0.742629	+	1.28627i	−0.951294	+	0.308284i	$0.900245\pi$
$600$	2.58100e9			0.487819
$601$	4.50745e9			0.846974			0.423487	−	0.905902i	$-0.360806\pi$
$601$	4.50745e9			0.846974			0.423487	+	0.905902i	$0.360806\pi$
$602$	8.38596e8	−	1.45249e9i	0.156662	−	0.271347i
$603$	−5.71230e9	−	9.89399e9i	−1.06096	−	1.83764i
$604$	5.54202e7	−	9.59907e7i	0.0102339	−	0.0177256i
$605$	1.27675e9	+	2.21140e9i	0.234403	+	0.405997i
$606$	8.41923e8	+	1.45825e9i	0.153680	+	0.266182i
$607$	−2.42624e9			−0.440325			−0.220163	−	0.975463i	$-0.570659\pi$
$607$	−2.42624e9			−0.440325			−0.220163	+	0.975463i	$0.570659\pi$
$608$	−1.61886e8	+	1.20273e9i	−0.0292110	+	0.217024i
$609$	2.47287e10			4.43650
$610$	1.27727e9	+	2.21231e9i	0.227840	+	0.394630i
$611$	−2.93086e8	−	5.07639e8i	−0.0519817	−	0.0900349i
$612$	4.61398e8	−	7.99166e8i	0.0813666	−	0.140931i
$613$	−4.81183e9	−	8.33434e9i	−0.843721	−	1.46137i	−0.886727	−	0.462293i	$-0.847027\pi$
$613$	−4.81183e9	−	8.33434e9i	−0.843721	−	1.46137i	0.0430067	−	0.999075i	$-0.486306\pi$
$614$	1.56401e9	−	2.70895e9i	0.272679	−	0.472294i
$615$	3.19693e9			0.554204
$616$	−5.58460e9			−0.962630
$617$	3.69996e8	−	6.40853e8i	0.0634161	−	0.109840i	−0.832574	−	0.553914i	$-0.813134\pi$
$617$	3.69996e8	−	6.40853e8i	0.0634161	−	0.109840i	0.895990	+	0.444074i	$0.146467\pi$
$618$	−4.84224e9	+	8.38700e9i	−0.825251	+	1.42938i
$619$	5.49903e9			0.931898			0.465949	−	0.884812i	$-0.345713\pi$
$619$	5.49903e9			0.931898			0.465949	+	0.884812i	$0.345713\pi$
$620$	1.02950e9			0.173482
$621$	5.34731e8	−	9.26182e8i	0.0896014	−	0.155194i
$622$	−9.30456e8	−	1.61160e9i	−0.155035	−	0.268528i
$623$	3.37487e9	−	5.84544e9i	0.559176	−	0.968521i
$624$	−6.43469e8	−	1.11452e9i	−0.106019	−	0.183629i
$625$	1.94328e9	+	3.36585e9i	0.318386	+	0.551461i
$626$	−7.97779e8			−0.129979
$627$	−5.37125e9	−	4.14626e9i	−0.870239	−	0.671769i
$628$	−8.37068e8			−0.134866
$629$	−4.21424e9	−	7.29928e9i	−0.675215	−	1.16951i
$630$	−5.89074e9	−	1.02031e10i	−0.938594	−	1.62569i
$631$	−2.39823e9	+	4.15386e9i	−0.380004	+	0.658187i	−0.991062	−	0.133399i	$-0.957411\pi$
$631$	−2.39823e9	+	4.15386e9i	−0.380004	+	0.658187i	0.611058	+	0.791586i	$0.290744\pi$
$632$	7.65893e8	+	1.32657e9i	0.120686	+	0.209035i
$633$	5.04571e8	−	8.73943e8i	0.0790696	−	0.136953i
$634$	−4.22742e9			−0.658814
$635$	9.45285e8			0.146506
$636$	−1.00950e9	+	1.74851e9i	−0.155599	+	0.269506i
$637$	4.27705e8	−	7.40806e8i	0.0655626	−	0.113558i
$638$	8.10016e9			1.23487
$639$	1.36307e10			2.06665
$640$	−2.25759e9	+	3.91026e9i	−0.340420	+	0.589625i
$641$	−9.91591e8	−	1.71749e9i	−0.148706	−	0.257567i	0.782043	−	0.623224i	$-0.214178\pi$
$641$	−9.91591e8	−	1.71749e9i	−0.148706	−	0.257567i	−0.930750	+	0.365657i	$0.880844\pi$
$642$	1.20594e9	−	2.08876e9i	0.179868	−	0.311541i
$643$	−2.48631e8	−	4.30641e8i	−0.0368822	−	0.0638818i	0.846995	−	0.531601i	$-0.178409\pi$
$643$	−2.48631e8	−	4.30641e8i	−0.0368822	−	0.0638818i	−0.883877	+	0.467719i	$0.845076\pi$
$644$	−7.89165e7	−	1.36687e8i	−0.0116431	−	0.0201664i
$645$	−2.29189e9			−0.336306
$646$	−7.46845e8	+	5.54869e9i	−0.108998	+	0.809798i
$647$	−8.53476e9			−1.23887			−0.619436	−	0.785047i	$-0.712639\pi$
$647$	−8.53476e9			−1.23887			−0.619436	+	0.785047i	$0.712639\pi$
$648$	7.58117e8	+	1.31310e9i	0.109452	+	0.189576i
$649$	6.10226e8	+	1.05694e9i	0.0876262	+	0.151773i
$650$	−1.37226e8	+	2.37683e8i	−0.0195993	+	0.0339469i
$651$	1.48433e10	+	2.57094e10i	2.10862	+	3.65223i
$652$	−6.11915e7	+	1.05987e8i	−0.00864618	+	0.0149756i
$653$	−6.94811e8			−0.0976496			−0.0488248	−	0.998807i	$-0.515548\pi$
$653$	−6.94811e8			−0.0976496			−0.0488248	+	0.998807i	$0.515548\pi$
$654$	−7.03251e9			−0.983079
$655$	2.41945e9	−	4.19061e9i	0.336412	−	0.582683i
$656$	1.26239e9	−	2.18652e9i	0.174594	−	0.302406i
$657$	−9.91461e9			−1.36394
$658$	−6.71933e9			−0.919466
$659$	−6.20611e9	+	1.07493e10i	−0.844735	+	1.46312i	0.0411168	+	0.999154i	$0.486908\pi$
$659$	−6.20611e9	+	1.07493e10i	−0.844735	+	1.46312i	−0.885851	+	0.463969i	$0.846425\pi$
$660$	3.78159e8	+	6.54991e8i	0.0512001	+	0.0886813i
$661$	−1.61613e9	+	2.79922e9i	−0.217657	+	0.376992i	−0.954091	−	0.299517i	$-0.903175\pi$
$661$	−1.61613e9	+	2.79922e9i	−0.217657	+	0.376992i	0.736434	+	0.676509i	$0.236508\pi$
$662$	3.98015e9	+	6.89382e9i	0.533208	+	0.923543i
$663$	7.84915e8	+	1.35951e9i	0.104598	+	0.181170i
$664$	3.84386e9			0.509541
$665$	−6.99399e9	−	5.39892e9i	−0.922252	−	0.711920i
$666$	1.91516e10			2.51215
$667$	1.15496e9	+	2.00045e9i	0.150705	+	0.261028i
$668$	−8.27809e7	−	1.43381e8i	−0.0107452	−	0.0186112i
$669$	−3.84123e9	+	6.65321e9i	−0.495997	+	0.859093i
$670$	−3.86299e9	−	6.69089e9i	−0.496205	−	0.859453i
$671$	1.49127e9	−	2.58295e9i	0.190558	−	0.330056i
$672$	3.90061e9			0.495839
$673$	8.63238e9			1.09164			0.545818	−	0.837904i	$-0.316219\pi$
$673$	8.63238e9			1.09164			0.545818	+	0.837904i	$0.316219\pi$
$674$	−3.66350e9	+	6.34537e9i	−0.460879	+	0.798266i
$675$	1.31750e9	−	2.28197e9i	0.164887	−	0.285592i
$676$	8.64538e8			0.107639
$677$	−1.29886e10			−1.60880			−0.804399	−	0.594089i	$-0.797513\pi$
$677$	−1.29886e10			−1.60880			−0.804399	+	0.594089i	$0.797513\pi$
$678$	−6.49615e9	+	1.12517e10i	−0.800483	+	1.38648i
$679$	−9.38208e9	−	1.62502e10i	−1.15015	−	1.99212i
$680$	3.14837e9	−	5.45314e9i	0.383977	−	0.665067i
$681$	−1.29993e10	−	2.25155e10i	−1.57727	−	2.73191i
$682$	4.86210e9	+	8.42140e9i	0.586919	+	1.01657i
$683$	3.19338e9			0.383511			0.191756	−	0.981443i	$-0.438582\pi$
$683$	3.19338e9			0.383511			0.191756	+	0.981443i	$0.438582\pi$
$684$	1.24477e9	+	9.60882e8i	0.148728	+	0.114808i
$685$	−7.85708e8			−0.0933994
$686$	5.85194e8	+	1.01359e9i	0.0692094	+	0.119874i
$687$	−3.51888e9	−	6.09488e9i	−0.414053	−	0.717161i
$688$	−9.05011e8	+	1.56752e9i	−0.105948	+	0.183508i
$689$	−1.08314e9	−	1.87605e9i	−0.126159	−	0.218513i
$690$	8.72440e8	−	1.51111e9i	0.101103	−	0.175115i
$691$	8.63713e9			0.995855			0.497928	−	0.867219i	$-0.334094\pi$
$691$	8.63713e9			0.995855			0.497928	+	0.867219i	$0.334094\pi$
$692$	1.62173e9			0.186040
$693$	−6.87767e9	+	1.19125e10i	−0.785009	+	1.35968i
$694$	3.60582e9	−	6.24546e9i	0.409492	−	0.709261i
$695$	−3.96764e9			−0.448317
$696$	−3.00313e10			−3.37631
$697$	−1.53988e9	+	2.66716e9i	−0.172255	+	0.298355i
$698$	−2.67764e9	−	4.63780e9i	−0.298028	−	0.516200i
$699$	7.39870e9	−	1.28149e10i	0.819380	−	1.41921i
$700$	−1.94438e8	−	3.36777e8i	−0.0214259	−	0.0371107i
$701$	−3.05665e7	−	5.29428e7i	−0.00335145	−	0.00580489i	0.864345	−	0.502900i	$-0.167733\pi$
$701$	−3.05665e7	−	5.29428e7i	−0.00335145	−	0.00580489i	−0.867696	+	0.497095i	$0.834400\pi$
$702$	−1.47850e9			−0.161303
$703$	1.32852e10	−	5.45789e9i	1.44219	−	0.592490i
$704$	6.70727e9			0.724506
$705$	4.59100e9	+	7.95184e9i	0.493452	+	0.854684i
$706$	4.04237e8	+	7.00158e8i	0.0432334	+	0.0748824i
$707$	1.27995e9	−	2.21694e9i	0.136215	−	0.235932i
$708$	−2.24220e8	−	3.88360e8i	−0.0237442	−	0.0411261i
$709$	−6.37733e9	+	1.10459e10i	−0.672012	+	1.16396i	0.305321	+	0.952250i	$0.401236\pi$
$709$	−6.37733e9	+	1.10459e10i	−0.672012	+	1.16396i	−0.977333	+	0.211709i	$0.932097\pi$
$710$	9.21790e9			0.966557
$711$	3.77292e9			0.393671
$712$	−4.09855e9	+	7.09889e9i	−0.425550	+	0.737073i
$713$	−1.38652e9	+	2.40153e9i	−0.143256	+	0.248127i
$714$	1.79951e10			1.85016
$715$	−8.11487e8			−0.0830253
$716$	6.13870e7	−	1.06325e8i	0.00625001	−	0.0108253i
$717$	7.76613e9	+	1.34513e10i	0.786842	+	1.36285i
$718$	6.65247e9	−	1.15224e10i	0.670730	−	1.16174i
$719$	−1.56091e9	−	2.70357e9i	−0.156613	−	0.271261i	0.777032	−	0.629461i	$-0.216724\pi$
$719$	−1.56091e9	−	2.70357e9i	−0.156613	−	0.271261i	−0.933645	+	0.358200i	$0.883391\pi$
$720$	6.35727e9	+	1.10111e10i	0.634756	+	1.09943i
$721$	1.47230e10			1.46293
$722$	−9.20100e9	−	2.52258e9i	−0.909819	−	0.249439i
$723$	1.30278e10			1.28200
$724$	−9.87341e8	−	1.71013e9i	−0.0966902	−	0.167472i
$725$	2.84565e9	+	4.92880e9i	0.277331	+	0.480351i
$726$	4.43116e9	−	7.67500e9i	0.429773	−	0.744389i
$727$	−2.89692e9	−	5.01761e9i	−0.279618	−	0.484313i	0.691672	−	0.722212i	$-0.256875\pi$
$727$	−2.89692e9	−	5.01761e9i	−0.279618	−	0.484313i	−0.971290	+	0.237899i	$0.923541\pi$
$728$	−1.10083e9	+	1.90670e9i	−0.105746	+	0.183157i
$729$	−1.63174e10			−1.55993
$730$	−6.70483e9			−0.637908
$731$	1.10395e9	−	1.91209e9i	0.104529	−	0.181050i
$732$	−5.47947e8	+	9.49073e8i	−0.0516357	+	0.0894357i
$733$	4.98891e9			0.467888			0.233944	−	0.972250i	$-0.424837\pi$
$733$	4.98891e9			0.467888			0.233944	+	0.972250i	$0.424837\pi$
$734$	8.71255e9			0.813222
$735$	−6.69971e9	+	1.16042e10i	−0.622373	+	1.07798i
$736$	1.82179e8	+	3.15544e8i	0.0168433	+	0.0291734i
$737$	−4.51019e9	+	7.81188e9i	−0.415010	+	0.718818i
$738$	−3.49901e9	−	6.06046e9i	−0.320441	−	0.555019i
$739$	5.52310e9	+	9.56629e9i	0.503416	+	0.871943i	0.999992	+	0.00394930i	$0.00125711\pi$
$739$	5.52310e9	+	9.56629e9i	0.503416	+	0.871943i	−0.496576	+	0.867993i	$0.665410\pi$
$740$	−1.60089e9			−0.145228
$741$	−2.47440e9	+	1.01655e9i	−0.223412	+	0.0917835i
$742$	−2.48322e10			−2.23153
$743$	−1.93378e9	−	3.34940e9i	−0.172960	−	0.299576i	0.766493	−	0.642252i	$-0.222000\pi$
$743$	−1.93378e9	−	3.34940e9i	−0.172960	−	0.299576i	−0.939453	+	0.342677i	$0.888667\pi$
$744$	−1.80262e10	−	3.12223e10i	−1.60472	−	2.77946i
$745$	−2.48457e8	+	4.30340e8i	−0.0220143	+	0.0381298i
$746$	7.33786e9	+	1.27095e10i	0.647118	+	1.12084i
$747$	4.73387e9	−	8.19930e9i	0.415522	−	0.719705i
$748$	−7.28601e8			−0.0636553
$749$	−3.66673e9			−0.318854
$750$	9.74279e9	−	1.68750e10i	0.843275	−	1.46059i
$751$	9.53628e9	−	1.65173e10i	0.821560	−	1.42298i	−0.0829605	−	0.996553i	$-0.526438\pi$
$751$	9.53628e9	−	1.65173e10i	0.821560	−	1.42298i	0.904520	−	0.426431i	$-0.140229\pi$
$752$	7.25149e9			0.621820
$753$	1.14669e10			0.978731
$754$	1.59670e9	−	2.76557e9i	0.135651	−	0.234955i
$755$	−9.31446e8	−	1.61331e9i	−0.0787668	−	0.136428i
$756$	1.04746e9	−	1.81425e9i	0.0881679	−	0.152711i
$757$	4.22854e9	+	7.32405e9i	0.354287	+	0.613643i	0.986996	−	0.160747i	$-0.0513903\pi$
$757$	4.22854e9	+	7.32405e9i	0.354287	+	0.613643i	−0.632709	+	0.774390i	$0.718057\pi$
$758$	−4.77922e9	−	8.27786e9i	−0.398580	−	0.690360i
$759$	−2.03721e9			−0.169118
$760$	8.49374e9	+	6.55662e9i	0.701861	+	0.541792i
$761$	1.27844e10			1.05156			0.525779	−	0.850621i	$-0.323774\pi$
$761$	1.27844e10			1.05156			0.525779	+	0.850621i	$0.323774\pi$
$762$	−1.64038e9	−	2.84122e9i	−0.134308	−	0.232628i
$763$	5.34567e9	+	9.25897e9i	0.435678	+	0.754617i
$764$	−4.25358e8	+	7.36742e8i	−0.0345087	+	0.0597708i
$765$	−7.75470e9	−	1.34315e10i	−0.626254	−	1.08470i
$766$	8.61219e9	−	1.49168e10i	0.692330	−	1.19915i
$767$	4.81150e8			0.0385032
$768$	−6.73206e9			−0.536271
$769$	−5.26032e9	+	9.11115e9i	−0.417129	+	0.722488i	−0.995649	−	0.0931795i	$-0.970297\pi$
$769$	−5.26032e9	+	9.11115e9i	−0.417129	+	0.722488i	0.578520	+	0.815668i	$0.303630\pi$
$770$	−4.65108e9	+	8.05590e9i	−0.367143	+	0.635911i
$771$	−1.47418e10			−1.15840
$772$	−1.16004e9			−0.0907432
$773$	−5.35537e9	+	9.27577e9i	−0.417024	+	0.722307i	−0.995639	−	0.0932944i	$-0.970260\pi$
$773$	−5.35537e9	+	9.27577e9i	−0.417024	+	0.722307i	0.578615	+	0.815601i	$0.303594\pi$
$774$	2.50845e9	+	4.34476e9i	0.194452	+	0.336800i
$775$	−3.41618e9	+	5.91700e9i	−0.263624	+	0.456610i
$776$	1.13939e10	+	1.97348e10i	0.875300	+	1.51606i
$777$	−2.30817e10	−	3.99786e10i	−1.76520	−	3.05741i
$778$	−1.14716e10			−0.873366
$779$	−4.15432e9	−	3.20687e9i	−0.314861	−	0.243053i
$780$	2.98171e8			0.0224975
$781$	−5.38113e9	−	9.32039e9i	−0.404198	−	0.700092i
$782$	8.40466e8	+	1.45573e9i	0.0628488	+	0.108857i
$783$	−1.53298e10	+	2.65520e10i	−1.14122	+	1.97665i
$784$	5.29111e9	+	9.16446e9i	0.392139	+	0.679205i
$785$	−7.03428e9	+	1.21837e10i	−0.519010	+	0.898952i
$786$	−1.67941e10			−1.23361
$787$	−2.25617e9			−0.164991			−0.0824953	−	0.996591i	$-0.526289\pi$
$787$	−2.25617e9			−0.164991			−0.0824953	+	0.996591i	$0.526289\pi$
$788$	9.42603e8	−	1.63264e9i	0.0686257	−	0.118863i
$789$	−4.44883e9	+	7.70559e9i	−0.322460	+	0.558517i
$790$	2.55146e9			0.184117
$791$	1.97519e10			1.41903
$792$	8.35246e9	−	1.44669e10i	0.597416	−	1.03475i
$793$	−5.87917e8	−	1.01830e9i	−0.0418658	−	0.0725137i
$794$	−1.08569e10	+	1.88046e10i	−0.769719	+	1.33319i
$795$	1.69667e10	+	2.93871e10i	1.19760	+	2.07430i
$796$	3.77253e8	+	6.53421e8i	0.0265116	+	0.0459195i
$797$	2.48532e10			1.73892			0.869458	−	0.494006i	$-0.164468\pi$
$797$	2.48532e10			1.73892			0.869458	+	0.494006i	$0.164468\pi$
$798$	−4.09052e9	+	3.03906e10i	−0.284950	+	2.11704i
$799$	−8.84549e9			−0.613491
$800$	4.48862e8	+	7.77452e8i	0.0309954	+	0.0536857i
$801$	1.00951e10	+	1.74852e10i	0.694057	+	1.20214i
$802$	8.67086e9	−	1.50184e10i	0.593543	−	1.02805i
$803$	3.91408e9	+	6.77938e9i	0.266763	+	0.462046i
$804$	1.65721e9	−	2.87037e9i	0.112456	−	0.194779i
$805$	−2.65269e9			−0.179226
$806$	3.83366e9			0.257894
$807$	1.16135e10	−	2.01152e10i	0.777869	−	1.34731i
$808$	−1.55442e9	+	2.69233e9i	−0.103664	+	0.179551i
$809$	−1.35434e10			−0.899307			−0.449653	−	0.893203i	$-0.648453\pi$
$809$	−1.35434e10			−0.899307			−0.449653	+	0.893203i	$0.648453\pi$
$810$	2.52556e9			0.166978
$811$	8.00356e9	−	1.38626e10i	0.526878	−	0.912579i	−0.472632	−	0.881260i	$-0.656696\pi$
$811$	8.00356e9	−	1.38626e10i	0.526878	−	0.912579i	0.999509	−	0.0313192i	$-0.00997083\pi$
$812$	2.26239e9	+	3.91858e9i	0.148293	+	0.256852i
$813$	3.39527e9	−	5.88078e9i	0.221594	−	0.383812i
$814$	−7.56066e9	−	1.30955e10i	−0.491331	−	0.851011i
$815$	1.02844e9	+	1.78131e9i	0.0665470	+	0.115263i
$816$	−1.94203e10			−1.25124
$817$	2.97825e9	+	2.29902e9i	0.191066	+	0.147491i
$818$	−1.14123e8			−0.00729014
$819$	2.71145e9	+	4.69636e9i	0.172468	+	0.298722i
$820$	2.92483e8	+	5.06595e8i	0.0185247	+	0.0320858i
$821$	3.32421e9	−	5.75770e9i	0.209646	−	0.363118i	−0.741957	−	0.670448i	$-0.766102\pi$
$821$	3.32421e9	−	5.75770e9i	0.209646	−	0.363118i	0.951603	+	0.307330i	$0.0994354\pi$
$822$	1.36346e9	+	2.36158e9i	0.0856231	+	0.148304i
$823$	−8.35819e9	+	1.44768e10i	−0.522652	+	0.905260i	0.477000	+	0.878903i	$0.341724\pi$
$823$	−8.35819e9	+	1.44768e10i	−0.522652	+	0.905260i	−0.999653	+	0.0263571i	$0.991609\pi$
$824$	−1.78801e10			−1.11333
$825$	−5.01938e9			−0.311216
$826$	2.75773e9	−	4.77653e9i	0.170264	−	0.294905i
$827$	−4.51664e9	+	7.82306e9i	−0.277681	+	0.480958i	−0.970808	−	0.239858i	$-0.922899\pi$
$827$	−4.51664e9	+	7.82306e9i	−0.277681	+	0.480958i	0.693127	+	0.720816i	$0.256233\pi$
$828$	4.72118e8			0.0289031
$829$	7.02008e9			0.427958			0.213979	−	0.976838i	$-0.431358\pi$
$829$	7.02008e9			0.427958			0.213979	+	0.976838i	$0.431358\pi$
$830$	3.20131e9	−	5.54484e9i	0.194337	−	0.336601i
$831$	−2.66439e8	−	4.61486e8i	−0.0161063	−	0.0278969i
$832$	1.32214e9	−	2.29001e9i	0.0795874	−	0.137849i
$833$	−6.45418e9	−	1.11790e10i	−0.386887	−	0.670107i
$834$	6.88514e9	+	1.19254e10i	0.410991	+	0.711857i
$835$	−2.78259e9			−0.165404
$836$	1.65621e8	−	1.23048e9i	0.00980376	−	0.0728371i
$837$	−3.68066e10			−2.16964
$838$	1.95084e9	+	3.37895e9i	0.114516	+	0.198348i
$839$	6.00364e9	+	1.03986e10i	0.350952	+	0.607866i	0.986416	−	0.164264i	$-0.0525247\pi$
$839$	6.00364e9	+	1.03986e10i	0.350952	+	0.607866i	−0.635465	+	0.772130i	$0.719191\pi$
$840$	1.72438e10	−	2.98672e10i	1.00382	−	1.73867i
$841$	−2.44857e10	−	4.24105e10i	−1.41947	−	2.45860i
$842$	9.05217e9	−	1.56788e10i	0.522589	−	0.905151i
$843$	8.31751e9			0.478186
$844$	1.84650e8			0.0105719
$845$	7.26512e9	−	1.25836e10i	0.414233	−	0.717472i
$846$	1.00496e10	−	1.74064e10i	0.570627	−	0.988355i
$847$	−1.34732e10			−0.761864
$848$	2.67989e10			1.50915
$849$	1.95890e10	−	3.39292e10i	1.09859	−	1.90282i
$850$	2.07078e9	+	3.58670e9i	0.115656	+	0.200322i
$851$	2.15607e9	−	3.73443e9i	0.119925	−	0.207716i
$852$	1.97723e9	+	3.42466e9i	0.109526	+	0.189705i
$853$	−1.55631e9	−	2.69560e9i	−0.0858566	−	0.148708i	0.819899	−	0.572508i	$-0.194029\pi$
$853$	−1.55631e9	−	2.69560e9i	−0.0858566	−	0.148708i	−0.905756	+	0.423800i	$0.860696\pi$
$854$	−1.34787e10			−0.740534
$855$	2.44463e10	−	1.00432e10i	1.33762	−	0.549528i
$856$	4.45300e9			0.242658
$857$	9.81822e9	+	1.70057e10i	0.532844	+	0.922912i	0.999264	+	0.0383493i	$0.0122100\pi$
$857$	9.81822e9	+	1.70057e10i	0.532844	+	0.922912i	−0.466421	+	0.884563i	$0.654457\pi$
$858$	1.40820e9	+	2.43907e9i	0.0761128	+	0.131831i
$859$	−1.18919e10	+	2.05974e10i	−0.640140	+	1.10875i	0.345262	+	0.938507i	$0.387790\pi$
$859$	−1.18919e10	+	2.05974e10i	−0.640140	+	1.10875i	−0.985401	+	0.170248i	$0.945543\pi$
$860$	−2.09682e8	−	3.63180e8i	−0.0112413	−	0.0194705i
$861$	−8.43404e9	+	1.46082e10i	−0.450324	+	0.779983i
$862$	9.27122e9			0.493016
$863$	2.46112e10			1.30345			0.651725	−	0.758455i	$-0.274046\pi$
$863$	2.46112e10			1.30345			0.651725	+	0.758455i	$0.274046\pi$
$864$	−2.41806e9	+	4.18821e9i	−0.127547	+	0.220918i
$865$	1.36281e10	−	2.36046e10i	0.715945	−	1.24005i
$866$	−3.26187e10			−1.70669
$867$	−7.88879e9			−0.411096
$868$	−2.71599e9	+	4.70423e9i	−0.140964	+	0.244157i
$869$	−1.48947e9	−	2.57983e9i	−0.0769949	−	0.133359i
$870$	−2.50113e10	+	4.33208e10i	−1.28771	+	2.23038i
$871$	1.77809e9	+	3.07975e9i	0.0911782	+	0.157925i
$872$	−6.49196e9	−	1.12444e10i	−0.331564	−	0.574286i
$873$	5.61283e10			2.85517
$874$	−2.64952e9	+	1.08849e9i	−0.134239	+	0.0551488i
$875$	−2.96234e10			−1.49488
$876$	−1.43818e9	−	2.49100e9i	−0.0722850	−	0.125201i
$877$	1.61497e10	+	2.79721e10i	0.808475	+	1.40032i	0.913920	+	0.405894i	$0.133040\pi$
$877$	1.61497e10	+	2.79721e10i	0.808475	+	1.40032i	−0.105445	+	0.994425i	$0.533627\pi$
$878$	−5.57457e9	+	9.65545e9i	−0.277959	+	0.481439i
$879$	−6.66739e9	−	1.15482e10i	−0.331127	−	0.573529i
$880$	5.01943e9	−	8.69391e9i	0.248293	−	0.430057i
$881$	−1.24565e10			−0.613734			−0.306867	−	0.951752i	$-0.599281\pi$
$881$	−1.24565e10			−0.613734			−0.306867	+	0.951752i	$0.599281\pi$
$882$	2.93311e10			1.43942
$883$	−1.03604e10	+	1.79448e10i	−0.506424	+	0.877153i	0.493548	+	0.869719i	$0.335700\pi$
$883$	−1.03604e10	+	1.79448e10i	−0.506424	+	0.877153i	−0.999972	+	0.00743426i	$0.997634\pi$
$884$	−1.43622e8	+	2.48760e8i	−0.00699257	+	0.0121115i
$885$	−7.53690e9			−0.365503
$886$	−2.38354e10			−1.15134
$887$	−1.56837e9	+	2.71650e9i	−0.0754598	+	0.130700i	−0.901286	−	0.433224i	$-0.857376\pi$
$887$	−1.56837e9	+	2.71650e9i	−0.0754598	+	0.130700i	0.825826	+	0.563925i	$0.190709\pi$
$888$	2.80311e10	+	4.85514e10i	1.34337	+	2.32678i
$889$	−2.49382e9	+	4.31943e9i	−0.119045	+	0.206191i
$890$	6.82687e9	+	1.18245e10i	0.324606	+	0.562234i
$891$	−1.47434e9	−	2.55364e9i	−0.0698276	−	0.120945i
$892$	−1.40572e9			−0.0663164
$893$	2.01070e9	−	1.49385e10i	0.0944857	−	0.701983i
$894$	1.72462e9			0.0807255
$895$	−1.03173e9	−	1.78701e9i	−0.0481044	−	0.0833193i
$896$	−1.19118e10	−	2.06319e10i	−0.553223	−	0.958210i
$897$	−4.01575e8	+	6.95548e8i	−0.0185778	+	0.0321776i
$898$	4.93145e9	+	8.54152e9i	0.227252	+	0.393612i
$899$	3.97491e10	−	6.88475e10i	1.82460	−	3.16031i
$900$	1.16323e9			0.0531882
$901$	−3.26897e10			−1.48893
$902$	−2.76267e9	+	4.78508e9i	−0.125345	+	0.217103i
$903$	6.04639e9	−	1.04727e10i	0.273268	−	0.473314i
$904$	−2.39873e10			−1.07992
$905$	−3.31884e10			−1.48839
$906$	−3.23273e9	+	5.59925e9i	−0.144418	+	0.250139i
$907$	5.73550e9	+	9.93418e9i	0.255238	+	0.442086i	0.964960	−	0.262396i	$-0.0845128\pi$
$907$	5.73550e9	+	9.93418e9i	0.255238	+	0.442086i	−0.709722	+	0.704482i	$0.751179\pi$
$908$	2.37858e9	−	4.11982e9i	0.105443	−	0.182632i
$909$	3.82866e9	+	6.63143e9i	0.169073	+	0.292842i
$910$	1.83364e9	+	3.17595e9i	0.0806619	+	0.139710i
$911$	−1.99860e10			−0.875813			−0.437906	−	0.899021i	$-0.644280\pi$
$911$	−1.99860e10			−0.875813			−0.437906	+	0.899021i	$0.644280\pi$
$912$	4.41448e9	−	3.27974e10i	0.192707	−	1.43172i
$913$	−7.47532e9			−0.325074
$914$	1.16852e10	+	2.02394e10i	0.506203	+	0.876770i
$915$	9.20933e9	+	1.59510e10i	0.397424	+	0.688359i
$916$	6.43876e8	−	1.11523e9i	0.0276801	−	0.0479434i
$917$	1.27658e10	+	2.21111e10i	0.546709	+	0.946928i
$918$	−1.11555e10	+	1.93219e10i	−0.475926	+	0.824328i
$919$	−1.39839e10			−0.594325			−0.297162	−	0.954827i	$-0.596040\pi$
$919$	−1.39839e10			−0.594325			−0.297162	+	0.954827i	$0.596040\pi$
$920$	3.22152e9			0.136396
$921$	1.12768e10	−	1.95319e10i	0.475637	−	0.823827i
$922$	4.89793e9	−	8.48346e9i	0.205804	−	0.356463i
$923$	−4.24290e9			−0.177606
$924$	−3.99060e9			−0.166413
$925$	5.31223e9	−	9.20106e9i	0.220689	−	0.382245i
$926$	1.69867e10	+	2.94219e10i	0.703026	+	1.21768i
$927$	−2.20201e10	+	3.81400e10i	−0.907906	+	1.57254i
$928$	−5.22275e9	−	9.04607e9i	−0.214527	−	0.371571i
$929$	9.50669e9	+	1.64661e10i	0.389022	+	0.673806i	0.992318	−	0.123711i	$-0.0394796\pi$
$929$	9.50669e9	+	1.64661e10i	0.389022	+	0.673806i	−0.603296	+	0.797517i	$0.706146\pi$
$930$	−6.00518e10			−2.44814
$931$	2.03464e10	−	8.35886e9i	0.826351	−	0.339487i
$932$	2.70759e9			0.109554
$933$	−6.70872e9	−	1.16198e10i	−0.270429	−	0.468397i
$934$	−9.66396e9	−	1.67385e10i	−0.388098	−	0.672205i
$935$	−6.12278e9	+	1.06050e10i	−0.244967	+	0.424296i
$936$	−3.29287e9	−	5.70342e9i	−0.131253	−	0.227337i
$937$	−1.87086e10	+	3.24043e10i	−0.742940	+	1.28681i	0.208212	+	0.978084i	$0.433236\pi$
$937$	−1.87086e10	+	3.24043e10i	−0.742940	+	1.28681i	−0.951151	+	0.308725i	$0.900098\pi$
$938$	4.07649e10			1.61278
$939$	−5.75210e9			−0.226724
$940$	−8.40048e8	+	1.45501e9i	−0.0329881	+	0.0571370i
$941$	−2.08385e10	+	3.60933e10i	−0.815271	+	1.41209i	0.0938615	+	0.995585i	$0.470079\pi$
$941$	−2.08385e10	+	3.60933e10i	−0.815271	+	1.41209i	−0.909133	+	0.416506i	$0.863254\pi$
$942$	4.88271e10			1.90319
$943$	−1.57566e9			−0.0611887
$944$	−2.97614e9	+	5.15482e9i	−0.115147	+	0.199440i
$945$	−1.76046e10	−	3.04920e10i	−0.678601	−	1.17537i
$946$	1.98056e9	−	3.43044e9i	0.0760624	−	0.131744i
$947$	−2.29467e10	−	3.97449e10i	−0.878002	−	1.52074i	−0.853530	−	0.521044i	$-0.825543\pi$
$947$	−2.29467e10	−	3.97449e10i	−0.878002	−	1.52074i	−0.0244729	−	0.999700i	$-0.507791\pi$
$948$	5.47286e8	+	9.47927e8i	0.0208634	+	0.0361365i
$949$	3.08616e9			0.117216
$950$	−6.52802e9	+	2.68188e9i	−0.247029	+	0.101486i
$951$	−3.04803e10			−1.14918
$952$	1.66119e10	+	2.87726e10i	0.624007	+	1.08081i
$953$	−1.66290e10	−	2.88023e10i	−0.622360	−	1.07796i	−0.989045	−	0.147614i	$-0.952841\pi$
$953$	−1.66290e10	−	2.88023e10i	−0.622360	−	1.07796i	0.366685	−	0.930345i	$-0.380493\pi$
$954$	3.71397e10	−	6.43279e10i	1.38490	−	2.39872i
$955$	7.14898e9	+	1.23824e10i	0.265603	+	0.460037i
$956$	−1.42103e9	+	2.46129e9i	−0.0526016	+	0.0911087i
$957$	5.84033e10			2.15400
$958$	−2.73742e10			−1.00592
$959$	2.07283e9	−	3.59025e9i	0.0758925	−	0.131450i
$960$	−2.07104e10	+	3.58714e10i	−0.755508	+	1.30858i
$961$	6.79246e10			2.46885
$962$	−5.96142e9			−0.215892
$963$	5.48405e9	−	9.49865e9i	0.197883	−	0.342744i
$964$	1.19190e9	+	2.06443e9i	0.0428518	+	0.0742215i
$965$	−9.74841e9	+	1.68847e10i	−0.349211	+	0.604851i
$966$	4.60329e9	+	7.97313e9i	0.164304	+	0.284583i
$967$	−1.38153e10	−	2.39288e10i	−0.491324	−	0.850998i	0.508626	−	0.860987i	$-0.330153\pi$
$967$	−1.38153e10	−	2.39288e10i	−0.491324	−	0.850998i	−0.999950	+	0.00998972i	$0.996820\pi$
$968$	1.63622e10			0.579801
$969$	−5.38486e9	+	4.00068e10i	−0.190126	+	1.41254i
$970$	3.79572e10			1.33534
$971$	−1.71060e10	−	2.96285e10i	−0.599628	−	1.03859i	−0.992876	−	0.119154i	$-0.961982\pi$
$971$	−1.71060e10	−	2.96285e10i	−0.599628	−	1.03859i	0.393248	−	0.919433i	$-0.371351\pi$
$972$	−1.29280e9	−	2.23920e9i	−0.0451543	−	0.0782096i
$973$	1.04673e10	−	1.81299e10i	0.364284	−	0.630958i
$974$	−5.96383e9	−	1.03296e10i	−0.206809	−	0.358203i
$975$	−9.89419e8	+	1.71372e9i	−0.0341873	+	0.0592141i
$976$	1.45462e10			0.500811
$977$	1.00663e9			0.0345335			0.0172667	−	0.999851i	$-0.494504\pi$
$977$	1.00663e9			0.0345335			0.0172667	+	0.999851i	$0.494504\pi$
$978$	3.56937e9	−	6.18233e9i	0.122013	−	0.211332i
$979$	7.97063e9	−	1.38055e10i	0.271490	−	0.470234i
$980$	−2.45179e9			−0.0832132
$981$	−3.19804e10			−1.08154
$982$	−1.65687e9	+	2.86978e9i	−0.0558338	+	0.0967070i
$983$	4.33075e8	+	7.50109e8i	0.0145421	+	0.0251876i	0.873205	−	0.487353i	$-0.162038\pi$
$983$	4.33075e8	+	7.50109e8i	0.0145421	+	0.0251876i	−0.858663	+	0.512541i	$0.828704\pi$
$984$	1.02426e10	−	1.77407e10i	0.342710	−	0.593591i
$985$	−1.58423e10	−	2.74396e10i	−0.528191	−	0.914854i
$986$	−2.40946e10	−	4.17332e10i	−0.800482	−	1.38647i
$987$	−4.84473e10			−1.60384
$988$	−3.87465e8	−	2.99098e8i	−0.0127815	−	0.00986653i
$989$	1.12959e9			0.0371309
$990$	−1.39125e10	−	2.40972e10i	−0.455704	−	0.789302i
$991$	1.63359e10	+	2.82947e10i	0.533195	+	0.923521i	0.999248	+	0.0387644i	$0.0123422\pi$
$991$	1.63359e10	+	2.82947e10i	0.533195	+	0.923521i	−0.466053	+	0.884757i	$0.654324\pi$
$992$	6.26989e9	−	1.08598e10i	0.203924	−	0.353207i
$993$	2.86974e10	+	4.97054e10i	0.930080	+	1.61095i
$994$	−2.43184e10	+	4.21207e10i	−0.785385	+	1.36033i
$995$	1.26809e10			0.408104
$996$	2.74671e9			0.0880857
$997$	1.65350e9	−	2.86394e9i	0.0528410	−	0.0915232i	−0.838395	−	0.545063i	$-0.816506\pi$
$997$	1.65350e9	−	2.86394e9i	0.0528410	−	0.0915232i	0.891236	+	0.453540i	$0.149839\pi$
$998$	1.66941e10	−	2.89150e10i	0.531625	−	0.920801i
$999$	5.72351e10			1.81628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.8.c.a.7.4	✓	20
19.7	even	3		361.8.a.f.1.7		10
19.11	even	3	inner	19.8.c.a.11.4	yes	20
19.12	odd	6		361.8.a.d.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.8.c.a.7.4	✓	20	1.1	even	1	trivial
19.8.c.a.11.4	yes	20	19.11	even	3	inner
361.8.a.d.1.4		10	19.12	odd	6
361.8.a.f.1.7		10	19.7	even	3

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.33664 - 9.24333i) q^{2} +(-38.4779 - 66.6457i) q^{3} +(7.04059 - 12.1947i) q^{4} +(-118.331 - 204.955i) q^{5} +(-410.685 + 711.328i) q^{6} +1248.71 q^{7} -1516.47 q^{8} +(-1867.60 + 3234.77i) q^{9} +O(q^{10})\)	\(q+(-5.33664 - 9.24333i) q^{2} +(-38.4779 - 66.6457i) q^{3} +(7.04059 - 12.1947i) q^{4} +(-118.331 - 204.955i) q^{5} +(-410.685 + 711.328i) q^{6} +1248.71 q^{7} -1516.47 q^{8} +(-1867.60 + 3234.77i) q^{9} +(-1262.98 + 2187.54i) q^{10} +2949.15 q^{11} -1083.63 q^{12} +(581.336 - 1006.90i) q^{13} +(-6663.90 - 11542.2i) q^{14} +(-9106.24 + 15772.5i) q^{15} +(7191.67 + 12456.3i) q^{16} +(-8772.51 - 15194.4i) q^{17} +39866.8 q^{18} +(27654.9 - 11361.3i) q^{19} -3332.47 q^{20} +(-48047.6 - 83221.0i) q^{21} +(-15738.6 - 27260.0i) q^{22} +(4488.16 - 7773.72i) q^{23} +(58350.6 + 101066. i) q^{24} +(11058.1 - 19153.3i) q^{25} -12409.5 q^{26} +119143. q^{27} +(8791.63 - 15227.6i) q^{28} +(-128667. + 222859. i) q^{29} +194387. q^{30} -308929. q^{31} +(-20295.5 + 35152.9i) q^{32} +(-113477. - 196548. i) q^{33} +(-93631.5 + 162174. i) q^{34} +(-147761. - 255929. i) q^{35} +(26298.0 + 45549.4i) q^{36} +480391. q^{37} +(-252601. - 194992. i) q^{38} -89474.3 q^{39} +(179445. + 310808. i) q^{40} +(-87767.5 - 152018. i) q^{41} +(-512826. + 888240. i) q^{42} +(62920.8 + 108982. i) q^{43} +(20763.7 - 35963.9i) q^{44} +883977. q^{45} -95806.8 q^{46} +(252080. - 436615. i) q^{47} +(553440. - 958587. i) q^{48} +735727. q^{49} -236053. q^{50} +(-675096. + 1.16930e6i) q^{51} +(-8185.89 - 14178.4i) q^{52} +(931595. - 1.61357e6i) q^{53} +(-635821. - 1.10127e6i) q^{54} +(-348975. - 604443. i) q^{55} -1.89363e6 q^{56} +(-1.82129e6 - 1.40592e6i) q^{57} +2.74661e6 q^{58} +(206916. + 358388. i) q^{59} +(128227. + 222095. i) q^{60} +(505660. - 875829. i) q^{61} +(1.64864e6 + 2.85553e6i) q^{62} +(-2.33208e6 + 4.03929e6i) q^{63} +2.27431e6 q^{64} -275160. q^{65} +(-1.21117e6 + 2.09781e6i) q^{66} +(-1.52932e6 + 2.64886e6i) q^{67} -247055. q^{68} -690780. q^{69} +(-1.57709e6 + 2.73160e6i) q^{70} +(-1.82464e6 - 3.16036e6i) q^{71} +(2.83216e6 - 4.90544e6i) q^{72} +(1.32719e6 + 2.29876e6i) q^{73} +(-2.56367e6 - 4.44041e6i) q^{74} -1.70198e6 q^{75} +(56158.8 - 417232. i) q^{76} +3.68263e6 q^{77} +(477492. + 827040. i) q^{78} +(-505050. - 874771. i) q^{79} +(1.70199e6 - 2.94794e6i) q^{80} +(-499922. - 865890. i) q^{81} +(-936767. + 1.62253e6i) q^{82} -2.53474e6 q^{83} -1.35313e6 q^{84} +(-2.07612e6 + 3.59594e6i) q^{85} +(671571. - 1.16320e6i) q^{86} +1.98034e7 q^{87} -4.47230e6 q^{88} +(2.70269e6 - 4.68119e6i) q^{89} +(-4.71747e6 - 8.17089e6i) q^{90} +(725918. - 1.25733e6i) q^{91} +(-63198.6 - 109463. i) q^{92} +(1.18869e7 + 2.05888e7i) q^{93} -5.38103e6 q^{94} +(-5.60099e6 - 4.32360e6i) q^{95} +3.12372e6 q^{96} +(-7.51343e6 - 1.30137e7i) q^{97} +(-3.92631e6 - 6.80057e6i) q^{98} +(-5.50783e6 + 9.53984e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9}+O(q^{10}) \) 20 * q - 9 * q^2 - 68 * q^3 - 475 * q^4 + 545 * q^6 - 1456 * q^7 + 2322 * q^8 - 6052 * q^9	\( 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9} - 1732 q^{10} + 7248 q^{11} + 30354 q^{12} - 12888 q^{13} - 7578 q^{14} - 13244 q^{15} - 1027 q^{16} - 63024 q^{17} - 93132 q^{18} + 72752 q^{19} + 156588 q^{20} - 18148 q^{21} + 23317 q^{22} + 56532 q^{23} - 45783 q^{24} - 86450 q^{25} + 198888 q^{26} - 58424 q^{27} + 287154 q^{28} - 178704 q^{29} - 384728 q^{30} + 292880 q^{31} - 640377 q^{32} - 408506 q^{33} + 262520 q^{34} + 621336 q^{35} + 486770 q^{36} - 1408096 q^{37} + 205086 q^{38} + 815736 q^{39} + 925470 q^{40} - 926994 q^{41} - 936278 q^{42} - 1837988 q^{43} - 511371 q^{44} + 1933888 q^{45} + 5286604 q^{46} + 1416996 q^{47} + 144447 q^{48} + 681652 q^{49} - 4138710 q^{50} - 2505268 q^{51} - 3586666 q^{52} - 356328 q^{53} + 228251 q^{54} + 865080 q^{55} - 3446916 q^{56} + 1706388 q^{57} + 11381072 q^{58} - 2297052 q^{59} - 2670886 q^{60} - 1496632 q^{61} + 1024512 q^{62} - 88344 q^{63} + 1773542 q^{64} + 585816 q^{65} - 2197457 q^{66} - 6475124 q^{67} + 4032876 q^{68} + 6329016 q^{69} - 12864588 q^{70} - 8042868 q^{71} + 9440430 q^{72} - 485798 q^{73} + 6232812 q^{74} + 20769104 q^{75} - 6953413 q^{76} + 8525208 q^{77} - 7305352 q^{78} - 5604964 q^{79} - 448650 q^{80} + 7714382 q^{81} + 2321819 q^{82} - 14535552 q^{83} - 42654252 q^{84} - 12944460 q^{85} + 2747550 q^{86} + 6535176 q^{87} + 18704514 q^{88} + 5024424 q^{89} - 15096092 q^{90} + 28222480 q^{91} - 30094896 q^{92} + 26255544 q^{93} + 51863760 q^{94} - 43373748 q^{95} + 116808910 q^{96} - 12341194 q^{97} + 1851183 q^{98} - 26743912 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 68 * q^3 - 475 * q^4 + 545 * q^6 - 1456 * q^7 + 2322 * q^8 - 6052 * q^9 - 1732 * q^10 + 7248 * q^11 + 30354 * q^12 - 12888 * q^13 - 7578 * q^14 - 13244 * q^15 - 1027 * q^16 - 63024 * q^17 - 93132 * q^18 + 72752 * q^19 + 156588 * q^20 - 18148 * q^21 + 23317 * q^22 + 56532 * q^23 - 45783 * q^24 - 86450 * q^25 + 198888 * q^26 - 58424 * q^27 + 287154 * q^28 - 178704 * q^29 - 384728 * q^30 + 292880 * q^31 - 640377 * q^32 - 408506 * q^33 + 262520 * q^34 + 621336 * q^35 + 486770 * q^36 - 1408096 * q^37 + 205086 * q^38 + 815736 * q^39 + 925470 * q^40 - 926994 * q^41 - 936278 * q^42 - 1837988 * q^43 - 511371 * q^44 + 1933888 * q^45 + 5286604 * q^46 + 1416996 * q^47 + 144447 * q^48 + 681652 * q^49 - 4138710 * q^50 - 2505268 * q^51 - 3586666 * q^52 - 356328 * q^53 + 228251 * q^54 + 865080 * q^55 - 3446916 * q^56 + 1706388 * q^57 + 11381072 * q^58 - 2297052 * q^59 - 2670886 * q^60 - 1496632 * q^61 + 1024512 * q^62 - 88344 * q^63 + 1773542 * q^64 + 585816 * q^65 - 2197457 * q^66 - 6475124 * q^67 + 4032876 * q^68 + 6329016 * q^69 - 12864588 * q^70 - 8042868 * q^71 + 9440430 * q^72 - 485798 * q^73 + 6232812 * q^74 + 20769104 * q^75 - 6953413 * q^76 + 8525208 * q^77 - 7305352 * q^78 - 5604964 * q^79 - 448650 * q^80 + 7714382 * q^81 + 2321819 * q^82 - 14535552 * q^83 - 42654252 * q^84 - 12944460 * q^85 + 2747550 * q^86 + 6535176 * q^87 + 18704514 * q^88 + 5024424 * q^89 - 15096092 * q^90 + 28222480 * q^91 - 30094896 * q^92 + 26255544 * q^93 + 51863760 * q^94 - 43373748 * q^95 + 116808910 * q^96 - 12341194 * q^97 + 1851183 * q^98 - 26743912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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