# Properties

 Label 980.2.k.c.883.1 Level $980$ Weight $2$ Character 980.883 Analytic conductor $7.825$ Analytic rank $0$ Dimension $2$ CM discriminant -4 Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.82533939809$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

## Embedding invariants

 Embedding label 883.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 980.883 Dual form 980.2.k.c.687.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-1.00000 - 3.00000i) q^{10} +(-5.00000 - 5.00000i) q^{13} -4.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +(3.00000 + 3.00000i) q^{18} +(-4.00000 - 2.00000i) q^{20} +(-3.00000 - 4.00000i) q^{25} -10.0000 q^{26} +4.00000i q^{29} +(-4.00000 + 4.00000i) q^{32} -10.0000i q^{34} +6.00000 q^{36} +(7.00000 - 7.00000i) q^{37} +(-6.00000 + 2.00000i) q^{40} -10.0000 q^{41} +(6.00000 + 3.00000i) q^{45} +(-7.00000 - 1.00000i) q^{50} +(-10.0000 + 10.0000i) q^{52} +(9.00000 + 9.00000i) q^{53} +(4.00000 + 4.00000i) q^{58} +10.0000 q^{61} +8.00000i q^{64} +(-15.0000 + 5.00000i) q^{65} +(-10.0000 - 10.0000i) q^{68} +(6.00000 - 6.00000i) q^{72} +(5.00000 + 5.00000i) q^{73} -14.0000i q^{74} +(-4.00000 + 8.00000i) q^{80} -9.00000 q^{81} +(-10.0000 + 10.0000i) q^{82} +(-5.00000 - 15.0000i) q^{85} -10.0000i q^{89} +(9.00000 - 3.00000i) q^{90} +(-5.00000 + 5.00000i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{5} - 4 q^{8} + O(q^{10})$$ $$2 q + 2 q^{2} + 2 q^{5} - 4 q^{8} - 2 q^{10} - 10 q^{13} - 8 q^{16} + 10 q^{17} + 6 q^{18} - 8 q^{20} - 6 q^{25} - 20 q^{26} - 8 q^{32} + 12 q^{36} + 14 q^{37} - 12 q^{40} - 20 q^{41} + 12 q^{45} - 14 q^{50} - 20 q^{52} + 18 q^{53} + 8 q^{58} + 20 q^{61} - 30 q^{65} - 20 q^{68} + 12 q^{72} + 10 q^{73} - 8 q^{80} - 18 q^{81} - 20 q^{82} - 10 q^{85} + 18 q^{90} - 10 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$197$$ $$491$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
<
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000i 0.707107 0.707107i
$$3$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$4$$ 2.00000i 1.00000i
$$5$$ 1.00000 2.00000i 0.447214 0.894427i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 3.00000i 1.00000i
$$10$$ −1.00000 3.00000i −0.316228 0.948683i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ −5.00000 5.00000i −1.38675 1.38675i −0.832050 0.554700i $$-0.812833\pi$$
−0.554700 0.832050i $$-0.687167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 5.00000 5.00000i 1.21268 1.21268i 0.242536 0.970143i $$-0.422021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 3.00000 + 3.00000i 0.707107 + 0.707107i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −4.00000 2.00000i −0.894427 0.447214i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ 0 0
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ −10.0000 −1.96116
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.00000i 0.742781i 0.928477 + 0.371391i $$0.121119\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −4.00000 + 4.00000i −0.707107 + 0.707107i
$$33$$ 0 0
$$34$$ 10.0000i 1.71499i
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ 7.00000 7.00000i 1.15079 1.15079i 0.164399 0.986394i $$-0.447432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −6.00000 + 2.00000i −0.948683 + 0.316228i
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$44$$ 0 0
$$45$$ 6.00000 + 3.00000i 0.894427 + 0.447214i
$$46$$ 0 0
$$47$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −7.00000 1.00000i −0.989949 0.141421i
$$51$$ 0 0
$$52$$ −10.0000 + 10.0000i −1.38675 + 1.38675i
$$53$$ 9.00000 + 9.00000i 1.23625 + 1.23625i 0.961524 + 0.274721i $$0.0885855\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 4.00000 + 4.00000i 0.525226 + 0.525226i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ −15.0000 + 5.00000i −1.86052 + 0.620174i
$$66$$ 0 0
$$67$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$68$$ −10.0000 10.0000i −1.21268 1.21268i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 6.00000 6.00000i 0.707107 0.707107i
$$73$$ 5.00000 + 5.00000i 0.585206 + 0.585206i 0.936329 0.351123i $$-0.114200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 14.0000i 1.62747i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −4.00000 + 8.00000i −0.447214 + 0.894427i
$$81$$ −9.00000 −1.00000
$$82$$ −10.0000 + 10.0000i −1.10432 + 1.10432i
$$83$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$84$$ 0 0
$$85$$ −5.00000 15.0000i −0.542326 1.62698i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.0000i 1.06000i −0.847998 0.529999i $$-0.822192\pi$$
0.847998 0.529999i $$-0.177808\pi$$
$$90$$ 9.00000 3.00000i 0.948683 0.316228i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −5.00000 + 5.00000i −0.507673 + 0.507673i −0.913812 0.406138i $$-0.866875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −8.00000 + 6.00000i −0.800000 + 0.600000i
$$101$$ 20.0000 1.99007 0.995037 0.0995037i $$-0.0317255\pi$$
0.995037 + 0.0995037i $$0.0317255\pi$$
$$102$$ 0 0
$$103$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$104$$ 20.0000i 1.96116i
$$105$$ 0 0
$$106$$ 18.0000 1.74831
$$107$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$108$$ 0 0
$$109$$ 6.00000i 0.574696i −0.957826 0.287348i $$-0.907226\pi$$
0.957826 0.287348i $$-0.0927736\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.00000 1.00000i −0.0940721 0.0940721i 0.658505 0.752577i $$-0.271189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 8.00000 0.742781
$$117$$ 15.0000 15.0000i 1.38675 1.38675i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 10.0000 10.0000i 0.905357 0.905357i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −11.0000 + 2.00000i −0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ 8.00000 + 8.00000i 0.707107 + 0.707107i
$$129$$ 0 0
$$130$$ −10.0000 + 20.0000i −0.877058 + 1.75412i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −20.0000 −1.71499
$$137$$ 7.00000 7.00000i 0.598050 0.598050i −0.341743 0.939793i $$-0.611017\pi$$
0.939793 + 0.341743i $$0.111017\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 12.0000i 1.00000i
$$145$$ 8.00000 + 4.00000i 0.664364 + 0.332182i
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ −14.0000 14.0000i −1.15079 1.15079i
$$149$$ 14.0000i 1.14692i −0.819232 0.573462i $$-0.805600\pi$$
0.819232 0.573462i $$-0.194400\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 15.0000 + 15.0000i 1.21268 + 1.21268i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −5.00000 + 5.00000i −0.399043 + 0.399043i −0.877896 0.478852i $$-0.841053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 4.00000 + 12.0000i 0.316228 + 0.948683i
$$161$$ 0 0
$$162$$ −9.00000 + 9.00000i −0.707107 + 0.707107i
$$163$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$164$$ 20.0000i 1.56174i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$168$$ 0 0
$$169$$ 37.0000i 2.84615i
$$170$$ −20.0000 10.0000i −1.53393 0.766965i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 15.0000 + 15.0000i 1.14043 + 1.14043i 0.988372 + 0.152057i $$0.0485898\pi$$
0.152057 + 0.988372i $$0.451410\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −10.0000 10.0000i −0.749532 0.749532i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 6.00000 12.0000i 0.447214 0.894427i
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −7.00000 21.0000i −0.514650 1.54395i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 19.0000 + 19.0000i 1.36765 + 1.36765i 0.863779 + 0.503871i $$0.168091\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 10.0000i 0.717958i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 13.0000 13.0000i 0.926212 0.926212i −0.0712470 0.997459i $$-0.522698\pi$$
0.997459 + 0.0712470i $$0.0226979\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ −2.00000 + 14.0000i −0.141421 + 0.989949i
$$201$$ 0 0
$$202$$ 20.0000 20.0000i 1.40720 1.40720i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −10.0000 + 20.0000i −0.698430 + 1.39686i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 20.0000 + 20.0000i 1.38675 + 1.38675i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 18.0000 18.0000i 1.23625 1.23625i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −6.00000 6.00000i −0.406371 0.406371i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −50.0000 −3.36336
$$222$$ 0 0
$$223$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 12.0000 9.00000i 0.800000 0.600000i
$$226$$ −2.00000 −0.133038
$$227$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$228$$ 0 0
$$229$$ 30.0000i 1.98246i 0.132164 + 0.991228i $$0.457808\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 8.00000 8.00000i 0.525226 0.525226i
$$233$$ 21.0000 + 21.0000i 1.37576 + 1.37576i 0.851658 + 0.524097i $$0.175597\pi$$
0.524097 + 0.851658i $$0.324403\pi$$
$$234$$ 30.0000i 1.96116i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −30.0000 −1.93247 −0.966235 0.257663i $$-0.917048\pi$$
−0.966235 + 0.257663i $$0.917048\pi$$
$$242$$ 11.0000 11.0000i 0.707107 0.707107i
$$243$$ 0 0
$$244$$ 20.0000i 1.28037i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −9.00000 + 13.0000i −0.569210 + 0.822192i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −15.0000 + 15.0000i −0.935674 + 0.935674i −0.998053 0.0623783i $$-0.980131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 10.0000 + 30.0000i 0.620174 + 1.86052i
$$261$$ −12.0000 −0.742781
$$262$$ 0 0
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 0 0
$$265$$ 27.0000 9.00000i 1.65860 0.552866i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 20.0000i 1.21942i −0.792624 0.609711i $$-0.791286\pi$$
0.792624 0.609711i $$-0.208714\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −20.0000 + 20.0000i −1.21268 + 1.21268i
$$273$$ 0 0
$$274$$ 14.0000i 0.845771i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 23.0000 23.0000i 1.38194 1.38194i 0.540758 0.841178i $$-0.318138\pi$$
0.841178 0.540758i $$-0.181862\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −32.0000 −1.90896 −0.954480 0.298275i $$-0.903589\pi$$
−0.954480 + 0.298275i $$0.903589\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −12.0000 12.0000i −0.707107 0.707107i
$$289$$ 33.0000i 1.94118i
$$290$$ 12.0000 4.00000i 0.704664 0.234888i
$$291$$ 0 0
$$292$$ 10.0000 10.0000i 0.585206 0.585206i
$$293$$ −15.0000 15.0000i −0.876309 0.876309i 0.116841 0.993151i $$-0.462723\pi$$
−0.993151 + 0.116841i $$0.962723\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −28.0000 −1.62747
$$297$$ 0 0
$$298$$ −14.0000 14.0000i −0.810998 0.810998i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 10.0000 20.0000i 0.572598 1.14520i
$$306$$ 30.0000 1.71499
$$307$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −25.0000 25.0000i −1.41308 1.41308i −0.734803 0.678280i $$-0.762726\pi$$
−0.678280 0.734803i $$-0.737274\pi$$
$$314$$ 10.0000i 0.564333i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.00000 3.00000i 0.168497 0.168497i −0.617822 0.786318i $$-0.711985\pi$$
0.786318 + 0.617822i $$0.211985\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 16.0000 + 8.00000i 0.894427 + 0.447214i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 18.0000i 1.00000i
$$325$$ −5.00000 + 35.0000i −0.277350 + 1.94145i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 20.0000 + 20.0000i 1.10432 + 1.10432i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 21.0000 + 21.0000i 1.15079 + 1.15079i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 7.00000 7.00000i 0.381314 0.381314i −0.490261 0.871576i $$-0.663099\pi$$
0.871576 + 0.490261i $$0.163099\pi$$
$$338$$ 37.0000 + 37.0000i 2.01253 + 2.01253i
$$339$$ 0 0
$$340$$ −30.0000 + 10.0000i −1.62698 + 0.542326i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 30.0000 1.61281
$$347$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$348$$ 0 0
$$349$$ 10.0000i 0.535288i 0.963518 + 0.267644i $$0.0862451\pi$$
−0.963518 + 0.267644i $$0.913755\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −25.0000 25.0000i −1.33062 1.33062i −0.904819 0.425797i $$-0.859994\pi$$
−0.425797 0.904819i $$-0.640006\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −20.0000 −1.06000
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ −6.00000 18.0000i −0.316228 0.948683i
$$361$$ −19.0000 −1.00000
$$362$$ 20.0000 20.0000i 1.05118 1.05118i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 15.0000 5.00000i 0.785136 0.261712i
$$366$$ 0 0
$$367$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$368$$ 0 0
$$369$$ 30.0000i 1.56174i
$$370$$ −28.0000 14.0000i −1.45565 0.727825i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −11.0000 11.0000i −0.569558 0.569558i 0.362446 0.932005i $$-0.381942\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 20.0000 20.0000i 1.03005 1.03005i
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 38.0000 1.93415
$$387$$ 0 0
$$388$$ 10.0000 + 10.0000i 0.507673 + 0.507673i
$$389$$ 34.0000i 1.72387i 0.507020 + 0.861934i $$0.330747\pi$$
−0.507020 + 0.861934i $$0.669253\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 26.0000i 1.30986i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −25.0000 + 25.0000i −1.25471 + 1.25471i −0.301131 + 0.953583i $$0.597364\pi$$
−0.953583 + 0.301131i $$0.902636\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 12.0000 + 16.0000i 0.600000 + 0.800000i
$$401$$ −2.00000 −0.0998752 −0.0499376 0.998752i $$-0.515902\pi$$
−0.0499376 + 0.998752i $$0.515902\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 40.0000i 1.99007i
$$405$$ −9.00000 + 18.0000i −0.447214 + 0.894427i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 40.0000i 1.97787i 0.148340 + 0.988936i $$0.452607\pi$$
−0.148340 + 0.988936i $$0.547393\pi$$
$$410$$ 10.0000 + 30.0000i 0.493865 + 1.48159i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 40.0000 1.96116
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −28.0000 −1.36464 −0.682318 0.731055i $$-0.739028\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 36.0000i 1.74831i
$$425$$ −35.0000 5.00000i −1.69775 0.242536i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 5.00000 + 5.00000i 0.240285 + 0.240285i 0.816968 0.576683i $$-0.195653\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −12.0000 −0.574696
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −50.0000 + 50.0000i −2.37826 + 2.37826i
$$443$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$444$$ 0 0
$$445$$ −20.0000 10.0000i −0.948091 0.474045i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 14.0000i 0.660701i −0.943858 0.330350i $$-0.892833\pi$$
0.943858 0.330350i $$-0.107167\pi$$
$$450$$ 3.00000 21.0000i 0.141421 0.989949i
$$451$$ 0 0
$$452$$ −2.00000 + 2.00000i −0.0940721 + 0.0940721i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −17.0000 + 17.0000i −0.795226 + 0.795226i −0.982339 0.187112i $$-0.940087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ 30.0000 + 30.0000i 1.40181 + 1.40181i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −20.0000 −0.931493 −0.465746 0.884918i $$-0.654214\pi$$
−0.465746 + 0.884918i $$0.654214\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ 16.0000i 0.742781i
$$465$$ 0 0
$$466$$ 42.0000 1.94561
$$467$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$468$$ −30.0000 30.0000i −1.38675 1.38675i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −27.0000 + 27.0000i −1.23625 + 1.23625i
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −70.0000 −3.19173
$$482$$ −30.0000 + 30.0000i −1.36646 + 1.36646i
$$483$$ 0 0
$$484$$ 22.0000i 1.00000i
$$485$$ 5.00000 + 15.0000i 0.227038 + 0.681115i
$$486$$ 0 0
$$487$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$488$$ −20.0000 20.0000i −0.905357 0.905357i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 20.0000 + 20.0000i 0.900755 + 0.900755i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 4.00000 + 22.0000i 0.178885 + 0.983870i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$504$$ 0 0
$$505$$ 20.0000 40.0000i 0.889988 1.77998i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 10.0000i 0.443242i 0.975133 + 0.221621i $$0.0711348\pi$$
−0.975133 + 0.221621i $$0.928865\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 0 0
$$514$$ 30.0000i 1.32324i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 40.0000 + 20.0000i 1.75412 + 0.877058i
$$521$$ −40.0000 −1.75243 −0.876216 0.481919i $$-0.839940\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$522$$ −12.0000 + 12.0000i −0.525226 + 0.525226i
$$523$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 23.0000i 1.00000i
$$530$$ 18.0000 36.0000i 0.781870 1.56374i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 50.0000 + 50.0000i 2.16574 + 2.16574i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −20.0000 20.0000i −0.862261 0.862261i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 42.0000 1.80572 0.902861 0.429934i $$-0.141463\pi$$
0.902861 + 0.429934i $$0.141463\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 40.0000i 1.71499i
$$545$$ −12.0000 6.00000i −0.514024 0.257012i
$$546$$ 0 0
$$547$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$548$$ −14.0000 14.0000i −0.598050 0.598050i
$$549$$ 30.0000i 1.28037i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 46.0000i 1.95435i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 33.0000 33.0000i 1.39825 1.39825i 0.593199 0.805056i $$-0.297865\pi$$
0.805056 0.593199i $$-0.202135\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −32.0000 + 32.0000i −1.34984 + 1.34984i
$$563$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$564$$ 0 0
$$565$$ −3.00000 + 1.00000i −0.126211 + 0.0420703i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 26.0000i 1.08998i −0.838444 0.544988i $$-0.816534\pi$$
0.838444 0.544988i $$-0.183466\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −24.0000 −1.00000
$$577$$ −25.0000 + 25.0000i −1.04076 + 1.04076i −0.0416305 + 0.999133i $$0.513255\pi$$
−0.999133 + 0.0416305i $$0.986745\pi$$
$$578$$ −33.0000 33.0000i −1.37262 1.37262i
$$579$$ 0 0
$$580$$ 8.00000 16.0000i 0.332182 0.664364i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 20.0000i 0.827606i
$$585$$ −15.0000 45.0000i −0.620174 1.86052i
$$586$$ −30.0000 −1.23929
$$587$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −28.0000 + 28.0000i −1.15079 + 1.15079i
$$593$$ −15.0000 15.0000i −0.615976 0.615976i 0.328521 0.944497i $$-0.393450\pi$$
−0.944497 + 0.328521i $$0.893450\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −28.0000 −1.14692
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 11.0000 22.0000i 0.447214 0.894427i
$$606$$ 0 0
$$607$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −10.0000 30.0000i −0.404888 1.21466i
$$611$$ 0 0
$$612$$ 30.0000 30.0000i 1.21268 1.21268i
$$613$$ 1.00000 + 1.00000i 0.0403896 + 0.0403896i 0.727013 0.686624i $$-0.240908\pi$$
−0.686624 + 0.727013i $$0.740908\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −3.00000 + 3.00000i −0.120775 + 0.120775i −0.764911 0.644136i $$-0.777217\pi$$
0.644136 + 0.764911i $$0.277217\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −50.0000 −1.99840
$$627$$ 0 0
$$628$$ 10.0000 + 10.0000i 0.399043 + 0.399043i
$$629$$ 70.0000i 2.79108i
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 6.00000i 0.238290i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 24.0000 8.00000i 0.948683 0.316228i
$$641$$ 8.00000 0.315981 0.157991 0.987441i $$-0.449498\pi$$
0.157991 + 0.987441i $$0.449498\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$648$$ 18.0000 + 18.0000i 0.707107 + 0.707107i
$$649$$ 0 0
$$650$$ 30.0000 + 40.0000i 1.17670 + 1.56893i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.00000 9.00000i −0.352197 0.352197i 0.508729 0.860927i $$-0.330115\pi$$
−0.860927 + 0.508729i $$0.830115\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 40.0000 1.56174
$$657$$ −15.0000 + 15.0000i −0.585206 + 0.585206i
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 50.0000 1.94477 0.972387 0.233373i $$-0.0749763\pi$$
0.972387 + 0.233373i $$0.0749763\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 42.0000 1.62747
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 11.0000 + 11.0000i 0.424019 + 0.424019i 0.886585 0.462566i $$-0.153071\pi$$
−0.462566 + 0.886585i $$0.653071\pi$$
$$674$$ 14.0000i 0.539260i
$$675$$ 0 0
$$676$$ 74.0000 2.84615
$$677$$ 25.0000 25.0000i 0.960828 0.960828i −0.0384331 0.999261i $$-0.512237\pi$$
0.999261 + 0.0384331i $$0.0122367\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −20.0000 + 40.0000i −0.766965 + 1.53393i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$684$$ 0 0
$$685$$ −7.00000 21.0000i −0.267456 0.802369i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 90.0000i 3.42873i
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 30.0000 30.0000i 1.14043 1.14043i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −50.0000 + 50.0000i −1.89389 + 1.89389i
$$698$$ 10.0000 + 10.0000i 0.378506 + 0.378506i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −52.0000 −1.96401 −0.982006 0.188847i $$-0.939525\pi$$
−0.982006 + 0.188847i $$0.939525\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −50.0000 −1.88177
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 44.0000i 1.65245i 0.563337 + 0.826227i $$0.309517\pi$$
−0.563337 + 0.826227i $$0.690483\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −20.0000 + 20.0000i −0.749532 + 0.749532i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ −24.0000 12.0000i −0.894427 0.447214i
$$721$$ 0 0
$$722$$ −19.0000 + 19.0000i −0.707107 + 0.707107i
$$723$$ 0 0
$$724$$ 40.0000i 1.48659i
$$725$$ 16.0000 12.0000i 0.594225 0.445669i
$$726$$ 0 0
$$727$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 1.00000i
$$730$$ 10.0000 20.0000i 0.370117 0.740233i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 25.0000 + 25.0000i 0.923396 + 0.923396i 0.997268 0.0738717i $$-0.0235355\pi$$
−0.0738717 + 0.997268i $$0.523536\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −30.0000 30.0000i −1.10432 1.10432i
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ −42.0000 + 14.0000i −1.54395 + 0.514650i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$744$$ 0 0
$$745$$ −28.0000 14.0000i −1.02584 0.512920i
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 40.0000i 1.45671i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 17.0000 17.0000i 0.617876 0.617876i −0.327111 0.944986i $$-0.606075\pi$$
0.944986 + 0.327111i $$0.106075\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 40.0000 1.45000 0.724999 0.688749i $$-0.241840\pi$$
0.724999 + 0.688749i $$0.241840\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 45.0000 15.0000i 1.62698 0.542326i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 50.0000i 1.80305i 0.432731 + 0.901523i $$0.357550\pi$$
−0.432731 + 0.901523i $$0.642450\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 38.0000 38.0000i 1.36765 1.36765i
$$773$$ −5.00000 5.00000i −0.179838 0.179838i 0.611448 0.791285i $$-0.290588\pi$$
−0.791285 + 0.611448i $$0.790588\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 20.0000 0.717958
$$777$$ 0 0
$$778$$ 34.0000 + 34.0000i 1.21896 + 1.21896i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 5.00000 + 15.0000i 0.178458 + 0.535373i
$$786$$ 0 0
$$787$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$788$$ −26.0000 26.0000i −0.926212 0.926212i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −50.0000 50.0000i −1.77555 1.77555i
$$794$$ 50.0000i 1.77443i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −15.0000 + 15.0000i −0.531327 + 0.531327i −0.920967 0.389640i $$-0.872599\pi$$
0.389640 + 0.920967i $$0.372599\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 28.0000 + 4.00000i 0.989949 + 0.141421i
$$801$$ 30.0000 1.06000
$$802$$ −2.00000 + 2.00000i −0.0706225 + 0.0706225i
$$803$$ 0 0
$$804$$