# Properties

 Label 304.7.e.c.113.2 Level $304$ Weight $7$ Character 304.113 Analytic conductor $69.936$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 304.e (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$69.9364414204$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 5090 x^{6} + 8905881 x^{4} + 5831691048 x^{2} + 827887219200$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{8}\cdot 3\cdot 5$$ Twist minimal: no (minimal twist has level 76) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 113.2 Root $$-40.3415i$$ of defining polynomial Character $$\chi$$ $$=$$ 304.113 Dual form 304.7.e.c.113.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-40.3415i q^{3} -186.796 q^{5} -202.293 q^{7} -898.437 q^{9} +O(q^{10})$$ $$q-40.3415i q^{3} -186.796 q^{5} -202.293 q^{7} -898.437 q^{9} +1591.27 q^{11} +143.277i q^{13} +7535.62i q^{15} +4771.21 q^{17} +(1010.48 + 6784.16i) q^{19} +8160.80i q^{21} -7737.11 q^{23} +19267.6 q^{25} +6835.36i q^{27} +8820.72i q^{29} +51550.3i q^{31} -64194.3i q^{33} +37787.4 q^{35} -94640.6i q^{37} +5779.99 q^{39} +78747.2i q^{41} +129047. q^{43} +167824. q^{45} +97220.5 q^{47} -76726.6 q^{49} -192478. i q^{51} -46143.8i q^{53} -297243. q^{55} +(273683. - 40764.1i) q^{57} -61729.4i q^{59} -85634.0 q^{61} +181747. q^{63} -26763.5i q^{65} +49044.4i q^{67} +312127. i q^{69} -408517. i q^{71} -130029. q^{73} -777286. i q^{75} -321903. q^{77} +106942. i q^{79} -379212. q^{81} +12258.3 q^{83} -891242. q^{85} +355841. q^{87} -561920. i q^{89} -28983.8i q^{91} +2.07962e6 q^{93} +(-188753. - 1.26725e6i) q^{95} -851962. i q^{97} -1.42966e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 2q^{5} - 362q^{7} - 4348q^{9} + O(q^{10})$$ $$8q + 2q^{5} - 362q^{7} - 4348q^{9} - 902q^{11} + 1550q^{17} - 6232q^{19} + 18820q^{23} - 12158q^{25} + 101762q^{35} - 167028q^{39} + 335042q^{43} - 57230q^{45} + 570394q^{47} + 448182q^{49} - 1089198q^{55} + 341316q^{57} - 632014q^{61} - 328174q^{63} - 852938q^{73} + 1850530q^{77} - 1819456q^{81} - 441200q^{83} - 1828374q^{85} - 1483380q^{87} + 2131176q^{93} - 627950q^{95} + 865394q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$191$$ $$229$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 40.3415i 1.49413i −0.664751 0.747065i $$-0.731462\pi$$
0.664751 0.747065i $$-0.268538\pi$$
$$4$$ 0 0
$$5$$ −186.796 −1.49437 −0.747183 0.664618i $$-0.768594\pi$$
−0.747183 + 0.664618i $$0.768594\pi$$
$$6$$ 0 0
$$7$$ −202.293 −0.589775 −0.294888 0.955532i $$-0.595282\pi$$
−0.294888 + 0.955532i $$0.595282\pi$$
$$8$$ 0 0
$$9$$ −898.437 −1.23242
$$10$$ 0 0
$$11$$ 1591.27 1.19555 0.597773 0.801666i $$-0.296053\pi$$
0.597773 + 0.801666i $$0.296053\pi$$
$$12$$ 0 0
$$13$$ 143.277i 0.0652146i 0.999468 + 0.0326073i $$0.0103811\pi$$
−0.999468 + 0.0326073i $$0.989619\pi$$
$$14$$ 0 0
$$15$$ 7535.62i 2.23278i
$$16$$ 0 0
$$17$$ 4771.21 0.971141 0.485570 0.874198i $$-0.338612\pi$$
0.485570 + 0.874198i $$0.338612\pi$$
$$18$$ 0 0
$$19$$ 1010.48 + 6784.16i 0.147321 + 0.989089i
$$20$$ 0 0
$$21$$ 8160.80i 0.881201i
$$22$$ 0 0
$$23$$ −7737.11 −0.635910 −0.317955 0.948106i $$-0.602996\pi$$
−0.317955 + 0.948106i $$0.602996\pi$$
$$24$$ 0 0
$$25$$ 19267.6 1.23313
$$26$$ 0 0
$$27$$ 6835.36i 0.347272i
$$28$$ 0 0
$$29$$ 8820.72i 0.361668i 0.983514 + 0.180834i $$0.0578796\pi$$
−0.983514 + 0.180834i $$0.942120\pi$$
$$30$$ 0 0
$$31$$ 51550.3i 1.73040i 0.501428 + 0.865199i $$0.332808\pi$$
−0.501428 + 0.865199i $$0.667192\pi$$
$$32$$ 0 0
$$33$$ 64194.3i 1.78630i
$$34$$ 0 0
$$35$$ 37787.4 0.881340
$$36$$ 0 0
$$37$$ 94640.6i 1.86841i −0.356735 0.934206i $$-0.616110\pi$$
0.356735 0.934206i $$-0.383890\pi$$
$$38$$ 0 0
$$39$$ 5779.99 0.0974392
$$40$$ 0 0
$$41$$ 78747.2i 1.14257i 0.820751 + 0.571286i $$0.193555\pi$$
−0.820751 + 0.571286i $$0.806445\pi$$
$$42$$ 0 0
$$43$$ 129047. 1.62308 0.811542 0.584294i $$-0.198629\pi$$
0.811542 + 0.584294i $$0.198629\pi$$
$$44$$ 0 0
$$45$$ 167824. 1.84169
$$46$$ 0 0
$$47$$ 97220.5 0.936406 0.468203 0.883621i $$-0.344902\pi$$
0.468203 + 0.883621i $$0.344902\pi$$
$$48$$ 0 0
$$49$$ −76726.6 −0.652165
$$50$$ 0 0
$$51$$ 192478.i 1.45101i
$$52$$ 0 0
$$53$$ 46143.8i 0.309946i −0.987919 0.154973i $$-0.950471\pi$$
0.987919 0.154973i $$-0.0495290\pi$$
$$54$$ 0 0
$$55$$ −297243. −1.78658
$$56$$ 0 0
$$57$$ 273683. 40764.1i 1.47783 0.220117i
$$58$$ 0 0
$$59$$ 61729.4i 0.300563i −0.988643 0.150282i $$-0.951982\pi$$
0.988643 0.150282i $$-0.0480181\pi$$
$$60$$ 0 0
$$61$$ −85634.0 −0.377274 −0.188637 0.982047i $$-0.560407\pi$$
−0.188637 + 0.982047i $$0.560407\pi$$
$$62$$ 0 0
$$63$$ 181747. 0.726853
$$64$$ 0 0
$$65$$ 26763.5i 0.0974545i
$$66$$ 0 0
$$67$$ 49044.4i 0.163067i 0.996671 + 0.0815334i $$0.0259817\pi$$
−0.996671 + 0.0815334i $$0.974018\pi$$
$$68$$ 0 0
$$69$$ 312127.i 0.950132i
$$70$$ 0 0
$$71$$ 408517.i 1.14139i −0.821161 0.570696i $$-0.806673\pi$$
0.821161 0.570696i $$-0.193327\pi$$
$$72$$ 0 0
$$73$$ −130029. −0.334250 −0.167125 0.985936i $$-0.553448\pi$$
−0.167125 + 0.985936i $$0.553448\pi$$
$$74$$ 0 0
$$75$$ 777286.i 1.84246i
$$76$$ 0 0
$$77$$ −321903. −0.705103
$$78$$ 0 0
$$79$$ 106942.i 0.216904i 0.994102 + 0.108452i $$0.0345893\pi$$
−0.994102 + 0.108452i $$0.965411\pi$$
$$80$$ 0 0
$$81$$ −379212. −0.713554
$$82$$ 0 0
$$83$$ 12258.3 0.0214386 0.0107193 0.999943i $$-0.496588\pi$$
0.0107193 + 0.999943i $$0.496588\pi$$
$$84$$ 0 0
$$85$$ −891242. −1.45124
$$86$$ 0 0
$$87$$ 355841. 0.540379
$$88$$ 0 0
$$89$$ 561920.i 0.797085i −0.917150 0.398542i $$-0.869516\pi$$
0.917150 0.398542i $$-0.130484\pi$$
$$90$$ 0 0
$$91$$ 28983.8i 0.0384620i
$$92$$ 0 0
$$93$$ 2.07962e6 2.58544
$$94$$ 0 0
$$95$$ −188753. 1.26725e6i −0.220152 1.47806i
$$96$$ 0 0
$$97$$ 851962.i 0.933480i −0.884395 0.466740i $$-0.845428\pi$$
0.884395 0.466740i $$-0.154572\pi$$
$$98$$ 0 0
$$99$$ −1.42966e6 −1.47342
$$100$$ 0 0
$$101$$ −1.73735e6 −1.68625 −0.843127 0.537714i $$-0.819288\pi$$
−0.843127 + 0.537714i $$0.819288\pi$$
$$102$$ 0 0
$$103$$ 1.34950e6i 1.23498i 0.786577 + 0.617492i $$0.211851\pi$$
−0.786577 + 0.617492i $$0.788149\pi$$
$$104$$ 0 0
$$105$$ 1.52440e6i 1.31684i
$$106$$ 0 0
$$107$$ 1.32161e6i 1.07883i 0.842042 + 0.539413i $$0.181354\pi$$
−0.842042 + 0.539413i $$0.818646\pi$$
$$108$$ 0 0
$$109$$ 1.99638e6i 1.54157i 0.637093 + 0.770787i $$0.280137\pi$$
−0.637093 + 0.770787i $$0.719863\pi$$
$$110$$ 0 0
$$111$$ −3.81795e6 −2.79165
$$112$$ 0 0
$$113$$ 1.42114e6i 0.984920i −0.870335 0.492460i $$-0.836098\pi$$
0.870335 0.492460i $$-0.163902\pi$$
$$114$$ 0 0
$$115$$ 1.44526e6 0.950282
$$116$$ 0 0
$$117$$ 128725.i 0.0803721i
$$118$$ 0 0
$$119$$ −965182. −0.572754
$$120$$ 0 0
$$121$$ 760581. 0.429328
$$122$$ 0 0
$$123$$ 3.17678e6 1.70715
$$124$$ 0 0
$$125$$ −680431. −0.348381
$$126$$ 0 0
$$127$$ 3.62081e6i 1.76764i −0.467823 0.883822i $$-0.654961\pi$$
0.467823 0.883822i $$-0.345039\pi$$
$$128$$ 0 0
$$129$$ 5.20593e6i 2.42510i
$$130$$ 0 0
$$131$$ 4.12259e6 1.83382 0.916909 0.399096i $$-0.130676\pi$$
0.916909 + 0.399096i $$0.130676\pi$$
$$132$$ 0 0
$$133$$ −204412. 1.37239e6i −0.0868864 0.583340i
$$134$$ 0 0
$$135$$ 1.27682e6i 0.518952i
$$136$$ 0 0
$$137$$ 3.08355e6 1.19920 0.599598 0.800302i $$-0.295327\pi$$
0.599598 + 0.800302i $$0.295327\pi$$
$$138$$ 0 0
$$139$$ 1.59964e6 0.595631 0.297816 0.954623i $$-0.403742\pi$$
0.297816 + 0.954623i $$0.403742\pi$$
$$140$$ 0 0
$$141$$ 3.92202e6i 1.39911i
$$142$$ 0 0
$$143$$ 227992.i 0.0779671i
$$144$$ 0 0
$$145$$ 1.64767e6i 0.540464i
$$146$$ 0 0
$$147$$ 3.09527e6i 0.974420i
$$148$$ 0 0
$$149$$ 3.38080e6 1.02202 0.511011 0.859574i $$-0.329271\pi$$
0.511011 + 0.859574i $$0.329271\pi$$
$$150$$ 0 0
$$151$$ 3.08302e6i 0.895458i −0.894169 0.447729i $$-0.852233\pi$$
0.894169 0.447729i $$-0.147767\pi$$
$$152$$ 0 0
$$153$$ −4.28664e6 −1.19686
$$154$$ 0 0
$$155$$ 9.62938e6i 2.58585i
$$156$$ 0 0
$$157$$ 3.24712e6 0.839072 0.419536 0.907739i $$-0.362193\pi$$
0.419536 + 0.907739i $$0.362193\pi$$
$$158$$ 0 0
$$159$$ −1.86151e6 −0.463099
$$160$$ 0 0
$$161$$ 1.56516e6 0.375044
$$162$$ 0 0
$$163$$ 2.32461e6 0.536769 0.268385 0.963312i $$-0.413510\pi$$
0.268385 + 0.963312i $$0.413510\pi$$
$$164$$ 0 0
$$165$$ 1.19912e7i 2.66939i
$$166$$ 0 0
$$167$$ 274073.i 0.0588460i 0.999567 + 0.0294230i $$0.00936698\pi$$
−0.999567 + 0.0294230i $$0.990633\pi$$
$$168$$ 0 0
$$169$$ 4.80628e6 0.995747
$$170$$ 0 0
$$171$$ −907850. 6.09514e6i −0.181562 1.21898i
$$172$$ 0 0
$$173$$ 2.32755e6i 0.449532i 0.974413 + 0.224766i $$0.0721617\pi$$
−0.974413 + 0.224766i $$0.927838\pi$$
$$174$$ 0 0
$$175$$ −3.89771e6 −0.727269
$$176$$ 0 0
$$177$$ −2.49026e6 −0.449081
$$178$$ 0 0
$$179$$ 6.83222e6i 1.19125i 0.803263 + 0.595625i $$0.203095\pi$$
−0.803263 + 0.595625i $$0.796905\pi$$
$$180$$ 0 0
$$181$$ 9.40294e6i 1.58573i −0.609400 0.792863i $$-0.708590\pi$$
0.609400 0.792863i $$-0.291410\pi$$
$$182$$ 0 0
$$183$$ 3.45460e6i 0.563696i
$$184$$ 0 0
$$185$$ 1.76785e7i 2.79209i
$$186$$ 0 0
$$187$$ 7.59229e6 1.16104
$$188$$ 0 0
$$189$$ 1.38275e6i 0.204813i
$$190$$ 0 0
$$191$$ 1.12644e7 1.61662 0.808309 0.588759i $$-0.200383\pi$$
0.808309 + 0.588759i $$0.200383\pi$$
$$192$$ 0 0
$$193$$ 1.26456e6i 0.175901i 0.996125 + 0.0879504i $$0.0280317\pi$$
−0.996125 + 0.0879504i $$0.971968\pi$$
$$194$$ 0 0
$$195$$ −1.07968e6 −0.145610
$$196$$ 0 0
$$197$$ −5.92683e6 −0.775218 −0.387609 0.921824i $$-0.626699\pi$$
−0.387609 + 0.921824i $$0.626699\pi$$
$$198$$ 0 0
$$199$$ −5.49979e6 −0.697889 −0.348945 0.937143i $$-0.613460\pi$$
−0.348945 + 0.937143i $$0.613460\pi$$
$$200$$ 0 0
$$201$$ 1.97853e6 0.243643
$$202$$ 0 0
$$203$$ 1.78437e6i 0.213303i
$$204$$ 0 0
$$205$$ 1.47096e7i 1.70742i
$$206$$ 0 0
$$207$$ 6.95131e6 0.783711
$$208$$ 0 0
$$209$$ 1.60794e6 + 1.07954e7i 0.176129 + 1.18250i
$$210$$ 0 0
$$211$$ 1.20580e7i 1.28359i 0.766876 + 0.641795i $$0.221810\pi$$
−0.766876 + 0.641795i $$0.778190\pi$$
$$212$$ 0 0
$$213$$ −1.64802e7 −1.70539
$$214$$ 0 0
$$215$$ −2.41053e7 −2.42548
$$216$$ 0 0
$$217$$ 1.04283e7i 1.02055i
$$218$$ 0 0
$$219$$ 5.24556e6i 0.499412i
$$220$$ 0 0
$$221$$ 683603.i 0.0633326i
$$222$$ 0 0
$$223$$ 1.50611e7i 1.35813i −0.734077 0.679066i $$-0.762385\pi$$
0.734077 0.679066i $$-0.237615\pi$$
$$224$$ 0 0
$$225$$ −1.73108e7 −1.51974
$$226$$ 0 0
$$227$$ 1.46485e7i 1.25232i −0.779694 0.626161i $$-0.784625\pi$$
0.779694 0.626161i $$-0.215375\pi$$
$$228$$ 0 0
$$229$$ 1.69472e7 1.41121 0.705603 0.708607i $$-0.250676\pi$$
0.705603 + 0.708607i $$0.250676\pi$$
$$230$$ 0 0
$$231$$ 1.29860e7i 1.05352i
$$232$$ 0 0
$$233$$ −3.81937e6 −0.301942 −0.150971 0.988538i $$-0.548240\pi$$
−0.150971 + 0.988538i $$0.548240\pi$$
$$234$$ 0 0
$$235$$ −1.81604e7 −1.39933
$$236$$ 0 0
$$237$$ 4.31420e6 0.324082
$$238$$ 0 0
$$239$$ −2.51010e7 −1.83864 −0.919322 0.393507i $$-0.871262\pi$$
−0.919322 + 0.393507i $$0.871262\pi$$
$$240$$ 0 0
$$241$$ 7.55161e6i 0.539496i −0.962931 0.269748i $$-0.913060\pi$$
0.962931 0.269748i $$-0.0869404\pi$$
$$242$$ 0 0
$$243$$ 2.02810e7i 1.41342i
$$244$$ 0 0
$$245$$ 1.43322e7 0.974574
$$246$$ 0 0
$$247$$ −972011. + 144778.i −0.0645031 + 0.00960750i
$$248$$ 0 0
$$249$$ 494519.i 0.0320321i
$$250$$ 0 0
$$251$$ 2.68658e7 1.69894 0.849471 0.527635i $$-0.176921\pi$$
0.849471 + 0.527635i $$0.176921\pi$$
$$252$$ 0 0
$$253$$ −1.23118e7 −0.760259
$$254$$ 0 0
$$255$$ 3.59541e7i 2.16834i
$$256$$ 0 0
$$257$$ 1.72065e7i 1.01366i −0.862046 0.506831i $$-0.830817\pi$$
0.862046 0.506831i $$-0.169183\pi$$
$$258$$ 0 0
$$259$$ 1.91451e7i 1.10194i
$$260$$ 0 0
$$261$$ 7.92486e6i 0.445728i
$$262$$ 0 0
$$263$$ 7.35861e6 0.404510 0.202255 0.979333i $$-0.435173\pi$$
0.202255 + 0.979333i $$0.435173\pi$$
$$264$$ 0 0
$$265$$ 8.61947e6i 0.463173i
$$266$$ 0 0
$$267$$ −2.26687e7 −1.19095
$$268$$ 0 0
$$269$$ 2.68576e7i 1.37978i 0.723913 + 0.689891i $$0.242342\pi$$
−0.723913 + 0.689891i $$0.757658\pi$$
$$270$$ 0 0
$$271$$ 1.84648e6 0.0927762 0.0463881 0.998923i $$-0.485229\pi$$
0.0463881 + 0.998923i $$0.485229\pi$$
$$272$$ 0 0
$$273$$ −1.16925e6 −0.0574672
$$274$$ 0 0
$$275$$ 3.06600e7 1.47426
$$276$$ 0 0
$$277$$ 1.00493e7 0.472819 0.236410 0.971653i $$-0.424029\pi$$
0.236410 + 0.971653i $$0.424029\pi$$
$$278$$ 0 0
$$279$$ 4.63147e7i 2.13259i
$$280$$ 0 0
$$281$$ 1.79351e7i 0.808321i 0.914688 + 0.404160i $$0.132436\pi$$
−0.914688 + 0.404160i $$0.867564\pi$$
$$282$$ 0 0
$$283$$ 3.11035e7 1.37230 0.686151 0.727460i $$-0.259299\pi$$
0.686151 + 0.727460i $$0.259299\pi$$
$$284$$ 0 0
$$285$$ −5.11229e7 + 7.61457e6i −2.20841 + 0.328936i
$$286$$ 0 0
$$287$$ 1.59300e7i 0.673860i
$$288$$ 0 0
$$289$$ −1.37309e6 −0.0568860
$$290$$ 0 0
$$291$$ −3.43694e7 −1.39474
$$292$$ 0 0
$$293$$ 2.91396e7i 1.15846i 0.815165 + 0.579229i $$0.196646\pi$$
−0.815165 + 0.579229i $$0.803354\pi$$
$$294$$ 0 0
$$295$$ 1.15308e7i 0.449152i
$$296$$ 0 0
$$297$$ 1.08769e7i 0.415180i
$$298$$ 0 0
$$299$$ 1.10855e6i 0.0414706i
$$300$$ 0 0
$$301$$ −2.61052e7 −0.957254
$$302$$ 0 0
$$303$$ 7.00873e7i 2.51948i
$$304$$ 0 0
$$305$$ 1.59961e7 0.563785
$$306$$ 0 0
$$307$$ 4.02183e7i 1.38998i −0.719020 0.694989i $$-0.755409\pi$$
0.719020 0.694989i $$-0.244591\pi$$
$$308$$ 0 0
$$309$$ 5.44409e7 1.84523
$$310$$ 0 0
$$311$$ 1.73795e7 0.577771 0.288885 0.957364i $$-0.406715\pi$$
0.288885 + 0.957364i $$0.406715\pi$$
$$312$$ 0 0
$$313$$ 3.25313e7 1.06089 0.530443 0.847721i $$-0.322026\pi$$
0.530443 + 0.847721i $$0.322026\pi$$
$$314$$ 0 0
$$315$$ −3.39497e7 −1.08618
$$316$$ 0 0
$$317$$ 2.86504e7i 0.899400i 0.893180 + 0.449700i $$0.148469\pi$$
−0.893180 + 0.449700i $$0.851531\pi$$
$$318$$ 0 0
$$319$$ 1.40361e7i 0.432390i
$$320$$ 0 0
$$321$$ 5.33156e7 1.61190
$$322$$ 0 0
$$323$$ 4.82120e6 + 3.23687e7i 0.143070 + 0.960544i
$$324$$ 0 0
$$325$$ 2.76060e6i 0.0804181i
$$326$$ 0 0
$$327$$ 8.05371e7 2.30331
$$328$$ 0 0
$$329$$ −1.96670e7 −0.552269
$$330$$ 0 0
$$331$$ 4.74259e7i 1.30777i −0.756594 0.653885i $$-0.773138\pi$$
0.756594 0.653885i $$-0.226862\pi$$
$$332$$ 0 0
$$333$$ 8.50287e7i 2.30268i
$$334$$ 0 0
$$335$$ 9.16129e6i 0.243681i
$$336$$ 0 0
$$337$$ 2.20894e7i 0.577157i −0.957456 0.288579i $$-0.906817\pi$$
0.957456 0.288579i $$-0.0931827\pi$$
$$338$$ 0 0
$$339$$ −5.73309e7 −1.47160
$$340$$ 0 0
$$341$$ 8.20305e7i 2.06877i
$$342$$ 0 0
$$343$$ 3.93208e7 0.974406
$$344$$ 0 0
$$345$$ 5.83039e7i 1.41984i
$$346$$ 0 0
$$347$$ −2.73262e7 −0.654019 −0.327009 0.945021i $$-0.606041\pi$$
−0.327009 + 0.945021i $$0.606041\pi$$
$$348$$ 0 0
$$349$$ 4.12946e7 0.971442 0.485721 0.874114i $$-0.338557\pi$$
0.485721 + 0.874114i $$0.338557\pi$$
$$350$$ 0 0
$$351$$ −979348. −0.0226473
$$352$$ 0 0
$$353$$ −5.44872e7 −1.23871 −0.619356 0.785110i $$-0.712606\pi$$
−0.619356 + 0.785110i $$0.712606\pi$$
$$354$$ 0 0
$$355$$ 7.63092e7i 1.70566i
$$356$$ 0 0
$$357$$ 3.89369e7i 0.855770i
$$358$$ 0 0
$$359$$ 1.80050e7 0.389144 0.194572 0.980888i $$-0.437668\pi$$
0.194572 + 0.980888i $$0.437668\pi$$
$$360$$ 0 0
$$361$$ −4.50038e7 + 1.37105e7i −0.956593 + 0.291428i
$$362$$ 0 0
$$363$$ 3.06830e7i 0.641472i
$$364$$ 0 0
$$365$$ 2.42888e7 0.499491
$$366$$ 0 0
$$367$$ 8.33600e7 1.68640 0.843198 0.537603i $$-0.180670\pi$$
0.843198 + 0.537603i $$0.180670\pi$$
$$368$$ 0 0
$$369$$ 7.07494e7i 1.40813i
$$370$$ 0 0
$$371$$ 9.33456e6i 0.182798i
$$372$$ 0 0
$$373$$ 2.46066e7i 0.474159i −0.971490 0.237080i $$-0.923810\pi$$
0.971490 0.237080i $$-0.0761902\pi$$
$$374$$ 0 0
$$375$$ 2.74496e7i 0.520526i
$$376$$ 0 0
$$377$$ −1.26380e6 −0.0235860
$$378$$ 0 0
$$379$$ 1.80987e7i 0.332452i 0.986088 + 0.166226i $$0.0531581\pi$$
−0.986088 + 0.166226i $$0.946842\pi$$
$$380$$ 0 0
$$381$$ −1.46069e8 −2.64109
$$382$$ 0 0
$$383$$ 4.68217e7i 0.833395i 0.909045 + 0.416697i $$0.136812\pi$$
−0.909045 + 0.416697i $$0.863188\pi$$
$$384$$ 0 0
$$385$$ 6.01300e7 1.05368
$$386$$ 0 0
$$387$$ −1.15940e8 −2.00033
$$388$$ 0 0
$$389$$ −2.49752e7 −0.424288 −0.212144 0.977238i $$-0.568045\pi$$
−0.212144 + 0.977238i $$0.568045\pi$$
$$390$$ 0 0
$$391$$ −3.69154e7 −0.617558
$$392$$ 0 0
$$393$$ 1.66312e8i 2.73996i
$$394$$ 0 0
$$395$$ 1.99763e7i 0.324134i
$$396$$ 0 0
$$397$$ 1.03759e6 0.0165827 0.00829133 0.999966i $$-0.497361\pi$$
0.00829133 + 0.999966i $$0.497361\pi$$
$$398$$ 0 0
$$399$$ −5.53642e7 + 8.24630e6i −0.871586 + 0.129820i
$$400$$ 0 0
$$401$$ 1.02883e8i 1.59555i −0.602953 0.797777i $$-0.706009\pi$$
0.602953 0.797777i $$-0.293991\pi$$
$$402$$ 0 0
$$403$$ −7.38595e6 −0.112847
$$404$$ 0 0
$$405$$ 7.08352e7 1.06631
$$406$$ 0 0
$$407$$ 1.50599e8i 2.23377i
$$408$$ 0 0
$$409$$ 7.78751e7i 1.13823i −0.822259 0.569113i $$-0.807287\pi$$
0.822259 0.569113i $$-0.192713\pi$$
$$410$$ 0 0
$$411$$ 1.24395e8i 1.79175i
$$412$$ 0 0
$$413$$ 1.24874e7i 0.177265i
$$414$$ 0 0
$$415$$ −2.28980e6 −0.0320371
$$416$$ 0 0
$$417$$ 6.45318e7i 0.889950i
$$418$$ 0 0
$$419$$ 1.20628e8 1.63986 0.819932 0.572461i $$-0.194011\pi$$
0.819932 + 0.572461i $$0.194011\pi$$
$$420$$ 0 0
$$421$$ 9.94059e7i 1.33219i −0.745867 0.666095i $$-0.767965\pi$$
0.745867 0.666095i $$-0.232035\pi$$
$$422$$ 0 0
$$423$$ −8.73465e7 −1.15405
$$424$$ 0 0
$$425$$ 9.19301e7 1.19754
$$426$$ 0 0
$$427$$ 1.73231e7 0.222507
$$428$$ 0 0
$$429$$ 9.19753e6 0.116493
$$430$$ 0 0
$$431$$ 3.81811e7i 0.476888i 0.971156 + 0.238444i $$0.0766373\pi$$
−0.971156 + 0.238444i $$0.923363\pi$$
$$432$$ 0 0
$$433$$ 1.37273e8i 1.69091i 0.534043 + 0.845457i $$0.320672\pi$$
−0.534043 + 0.845457i $$0.679328\pi$$
$$434$$ 0 0
$$435$$ −6.64696e7 −0.807524
$$436$$ 0 0
$$437$$ −7.81817e6 5.24898e7i −0.0936830 0.628971i
$$438$$ 0 0
$$439$$ 9.17437e6i 0.108438i −0.998529 0.0542192i $$-0.982733\pi$$
0.998529 0.0542192i $$-0.0172670\pi$$
$$440$$ 0 0
$$441$$ 6.89341e7 0.803745
$$442$$ 0 0
$$443$$ −1.79271e6 −0.0206204 −0.0103102 0.999947i $$-0.503282\pi$$
−0.0103102 + 0.999947i $$0.503282\pi$$
$$444$$ 0 0
$$445$$ 1.04964e8i 1.19114i
$$446$$ 0 0
$$447$$ 1.36387e8i 1.52703i
$$448$$ 0 0
$$449$$ 6.43497e6i 0.0710898i 0.999368 + 0.0355449i $$0.0113167\pi$$
−0.999368 + 0.0355449i $$0.988683\pi$$
$$450$$ 0 0
$$451$$ 1.25308e8i 1.36600i
$$452$$ 0 0
$$453$$ −1.24374e8 −1.33793
$$454$$ 0 0
$$455$$ 5.41406e6i 0.0574763i
$$456$$ 0 0
$$457$$ −1.28044e8 −1.34156 −0.670779 0.741658i $$-0.734040\pi$$
−0.670779 + 0.741658i $$0.734040\pi$$
$$458$$ 0 0
$$459$$ 3.26130e7i 0.337250i
$$460$$ 0 0
$$461$$ 3.10758e7 0.317190 0.158595 0.987344i $$-0.449304\pi$$
0.158595 + 0.987344i $$0.449304\pi$$
$$462$$ 0 0
$$463$$ −8.91490e7 −0.898201 −0.449100 0.893481i $$-0.648255\pi$$
−0.449100 + 0.893481i $$0.648255\pi$$
$$464$$ 0 0
$$465$$ −3.88464e8 −3.86359
$$466$$ 0 0
$$467$$ 2.26320e7 0.222214 0.111107 0.993808i $$-0.464560\pi$$
0.111107 + 0.993808i $$0.464560\pi$$
$$468$$ 0 0
$$469$$ 9.92134e6i 0.0961727i
$$470$$ 0 0
$$471$$ 1.30994e8i 1.25368i
$$472$$ 0 0
$$473$$ 2.05348e8 1.94047
$$474$$ 0 0
$$475$$ 1.94695e7 + 1.30715e8i 0.181666 + 1.21967i
$$476$$ 0 0
$$477$$ 4.14573e7i 0.381985i
$$478$$ 0 0
$$479$$ 1.34746e8 1.22605 0.613026 0.790062i $$-0.289952\pi$$
0.613026 + 0.790062i $$0.289952\pi$$
$$480$$ 0 0
$$481$$ 1.35598e7 0.121848
$$482$$ 0 0
$$483$$ 6.31410e7i 0.560364i
$$484$$ 0 0
$$485$$ 1.59143e8i 1.39496i
$$486$$ 0 0
$$487$$ 4.94767e7i 0.428365i 0.976794 + 0.214182i $$0.0687087\pi$$
−0.976794 + 0.214182i $$0.931291\pi$$
$$488$$ 0 0
$$489$$ 9.37783e7i 0.802003i
$$490$$ 0 0
$$491$$ −1.86984e8 −1.57965 −0.789825 0.613333i $$-0.789828\pi$$
−0.789825 + 0.613333i $$0.789828\pi$$
$$492$$ 0 0
$$493$$ 4.20855e7i 0.351230i
$$494$$ 0 0
$$495$$ 2.67054e8 2.20183
$$496$$ 0 0
$$497$$ 8.26400e7i 0.673165i
$$498$$ 0 0
$$499$$ 6.68560e6 0.0538070 0.0269035 0.999638i $$-0.491435\pi$$
0.0269035 + 0.999638i $$0.491435\pi$$
$$500$$ 0 0
$$501$$ 1.10565e7 0.0879236
$$502$$ 0 0
$$503$$ 1.07046e8 0.841139 0.420570 0.907260i $$-0.361830\pi$$
0.420570 + 0.907260i $$0.361830\pi$$
$$504$$ 0 0
$$505$$ 3.24529e8 2.51988
$$506$$ 0 0
$$507$$ 1.93893e8i 1.48778i
$$508$$ 0 0
$$509$$ 8.78261e7i 0.665994i −0.942928 0.332997i $$-0.891940\pi$$
0.942928 0.332997i $$-0.108060\pi$$
$$510$$ 0 0
$$511$$ 2.63039e7 0.197132
$$512$$ 0 0
$$513$$ −4.63722e7 + 6.90697e6i −0.343483 + 0.0511606i
$$514$$ 0 0
$$515$$ 2.52081e8i 1.84552i
$$516$$ 0 0
$$517$$ 1.54704e8 1.11952
$$518$$ 0 0
$$519$$ 9.38968e7 0.671659
$$520$$ 0 0
$$521$$ 5.29466e7i 0.374391i 0.982323 + 0.187195i $$0.0599397\pi$$
−0.982323 + 0.187195i $$0.940060\pi$$
$$522$$ 0 0
$$523$$ 2.04408e8i 1.42887i −0.699701 0.714436i $$-0.746683\pi$$
0.699701 0.714436i $$-0.253317\pi$$
$$524$$ 0 0
$$525$$ 1.57239e8i 1.08663i
$$526$$ 0 0
$$527$$ 2.45958e8i 1.68046i
$$528$$ 0 0
$$529$$ −8.81730e7 −0.595619
$$530$$ 0 0
$$531$$ 5.54600e7i 0.370422i
$$532$$ 0 0
$$533$$ −1.12826e7 −0.0745124
$$534$$ 0 0
$$535$$ 2.46871e8i 1.61216i
$$536$$ 0 0
$$537$$ 2.75622e8 1.77988
$$538$$ 0 0
$$539$$ −1.22093e8 −0.779693
$$540$$ 0 0
$$541$$ 1.07904e7 0.0681469 0.0340735 0.999419i $$-0.489152\pi$$
0.0340735 + 0.999419i $$0.489152\pi$$
$$542$$ 0 0
$$543$$ −3.79329e8 −2.36928
$$544$$ 0 0
$$545$$ 3.72916e8i 2.30368i
$$546$$ 0 0
$$547$$ 5.89052e7i 0.359908i −0.983675 0.179954i $$-0.942405\pi$$
0.983675 0.179954i $$-0.0575949\pi$$
$$548$$ 0 0
$$549$$ 7.69368e7 0.464961
$$550$$ 0 0
$$551$$ −5.98411e7 + 8.91313e6i −0.357722 + 0.0532814i
$$552$$ 0 0
$$553$$ 2.16336e7i 0.127924i
$$554$$ 0 0
$$555$$ 7.13176e8 4.17175
$$556$$ 0 0
$$557$$ 4.50709e7 0.260814 0.130407 0.991461i $$-0.458372\pi$$
0.130407 + 0.991461i $$0.458372\pi$$
$$558$$ 0 0
$$559$$ 1.84893e7i 0.105849i
$$560$$ 0 0
$$561$$ 3.06285e8i 1.73475i
$$562$$ 0 0
$$563$$ 2.83179e8i 1.58685i 0.608670 + 0.793424i $$0.291703\pi$$
−0.608670 + 0.793424i $$0.708297\pi$$
$$564$$ 0 0
$$565$$ 2.65463e8i 1.47183i
$$566$$ 0 0
$$567$$ 7.67119e7 0.420837
$$568$$ 0 0
$$569$$ 2.97743e8i 1.61624i −0.589021 0.808118i $$-0.700486\pi$$
0.589021 0.808118i $$-0.299514\pi$$
$$570$$ 0 0
$$571$$ −4.51806e7 −0.242685 −0.121343 0.992611i $$-0.538720\pi$$
−0.121343 + 0.992611i $$0.538720\pi$$
$$572$$ 0 0
$$573$$ 4.54422e8i 2.41544i
$$574$$ 0 0
$$575$$ −1.49076e8 −0.784159
$$576$$ 0 0
$$577$$ −1.15048e8 −0.598896 −0.299448 0.954113i $$-0.596802\pi$$
−0.299448 + 0.954113i $$0.596802\pi$$
$$578$$ 0 0
$$579$$ 5.10143e7 0.262819
$$580$$ 0 0
$$581$$ −2.47977e6 −0.0126440
$$582$$ 0 0
$$583$$ 7.34273e7i 0.370554i
$$584$$ 0 0
$$585$$ 2.40453e7i 0.120105i
$$586$$ 0 0
$$587$$ −1.59622e8 −0.789183 −0.394592 0.918857i $$-0.629114\pi$$
−0.394592 + 0.918857i $$0.629114\pi$$
$$588$$ 0 0
$$589$$ −3.49726e8 + 5.20904e7i −1.71152 + 0.254925i
$$590$$ 0 0
$$591$$ 2.39097e8i 1.15828i
$$592$$ 0 0
$$593$$ −6.60997e7 −0.316983 −0.158491 0.987360i $$-0.550663\pi$$
−0.158491 + 0.987360i $$0.550663\pi$$
$$594$$ 0 0
$$595$$ 1.80292e8 0.855905
$$596$$ 0 0
$$597$$ 2.21870e8i 1.04274i
$$598$$ 0 0
$$599$$ 1.30989e8i 0.609475i 0.952436 + 0.304738i $$0.0985688\pi$$
−0.952436 + 0.304738i $$0.901431\pi$$
$$600$$ 0 0
$$601$$ 2.96588e8i 1.36625i 0.730303 + 0.683124i $$0.239379\pi$$
−0.730303 + 0.683124i $$0.760621\pi$$
$$602$$ 0 0
$$603$$ 4.40634e7i 0.200967i
$$604$$ 0 0
$$605$$ −1.42073e8 −0.641573
$$606$$ 0 0
$$607$$ 7.29083e7i 0.325995i −0.986626 0.162997i $$-0.947884\pi$$
0.986626 0.162997i $$-0.0521162\pi$$
$$608$$ 0 0
$$609$$ −7.19841e7 −0.318702
$$610$$ 0 0
$$611$$ 1.39294e7i 0.0610674i
$$612$$ 0 0
$$613$$ 3.92971e8 1.70600 0.853000 0.521910i $$-0.174780\pi$$
0.853000 + 0.521910i $$0.174780\pi$$
$$614$$ 0 0
$$615$$ −5.93409e8 −2.55111
$$616$$ 0 0
$$617$$ −2.27576e8 −0.968884 −0.484442 0.874823i $$-0.660977\pi$$
−0.484442 + 0.874823i $$0.660977\pi$$
$$618$$ 0 0
$$619$$ 1.93252e8 0.814804 0.407402 0.913249i $$-0.366435\pi$$
0.407402 + 0.913249i $$0.366435\pi$$
$$620$$ 0 0
$$621$$ 5.28860e7i 0.220834i
$$622$$ 0 0
$$623$$ 1.13672e8i 0.470101i
$$624$$ 0 0
$$625$$ −1.73955e8 −0.712521
$$626$$ 0 0
$$627$$ 4.35504e8 6.48668e7i 1.76681 0.263160i
$$628$$ 0 0
$$629$$ 4.51551e8i 1.81449i
$$630$$ 0 0
$$631$$ −1.93900e7 −0.0771773 −0.0385887 0.999255i $$-0.512286\pi$$
−0.0385887 + 0.999255i $$0.512286\pi$$
$$632$$ 0 0
$$633$$ 4.86436e8 1.91785
$$634$$ 0 0
$$635$$ 6.76353e8i 2.64151i
$$636$$ 0 0
$$637$$ 1.09931e7i 0.0425307i
$$638$$ 0 0
$$639$$ 3.67027e8i 1.40668i
$$640$$ 0 0
$$641$$ 3.28211e8i 1.24617i 0.782152 + 0.623087i $$0.214122\pi$$
−0.782152 + 0.623087i $$0.785878\pi$$
$$642$$ 0 0
$$643$$ −2.37495e7 −0.0893349 −0.0446675 0.999002i $$-0.514223\pi$$
−0.0446675 + 0.999002i $$0.514223\pi$$
$$644$$ 0 0
$$645$$ 9.72446e8i 3.62398i
$$646$$ 0 0
$$647$$ −1.17583e7 −0.0434143 −0.0217072 0.999764i $$-0.506910\pi$$
−0.0217072 + 0.999764i $$0.506910\pi$$
$$648$$ 0 0
$$649$$ 9.82282e7i 0.359337i
$$650$$ 0 0
$$651$$ −4.20692e8 −1.52483
$$652$$ 0 0
$$653$$ 1.27271e8 0.457079 0.228539 0.973535i $$-0.426605\pi$$
0.228539 + 0.973535i $$0.426605\pi$$
$$654$$ 0 0
$$655$$ −7.70082e8 −2.74040
$$656$$ 0 0
$$657$$ 1.16823e8 0.411937
$$658$$ 0 0
$$659$$ 2.32452e8i 0.812227i −0.913823 0.406114i $$-0.866884\pi$$
0.913823 0.406114i $$-0.133116\pi$$
$$660$$ 0 0
$$661$$ 3.14463e8i 1.08884i −0.838812 0.544421i $$-0.816750\pi$$
0.838812 0.544421i $$-0.183250\pi$$
$$662$$ 0 0
$$663$$ 2.75776e7 0.0946271
$$664$$ 0 0
$$665$$ 3.81833e7 + 2.56356e8i 0.129840 + 0.871723i
$$666$$ 0 0
$$667$$ 6.82469e7i 0.229988i
$$668$$ 0 0
$$669$$ −6.07587e8 −2.02923
$$670$$ 0 0
$$671$$ −1.36267e8 −0.451048
$$672$$ 0 0
$$673$$ 2.76451e8i 0.906929i −0.891274 0.453465i $$-0.850188\pi$$
0.891274 0.453465i $$-0.149812\pi$$
$$674$$ 0 0
$$675$$ 1.31701e8i 0.428232i
$$676$$ 0 0
$$677$$ 4.08200e8i 1.31555i 0.753215 + 0.657775i $$0.228502\pi$$
−0.753215 + 0.657775i $$0.771498\pi$$
$$678$$ 0 0
$$679$$ 1.72346e8i 0.550543i
$$680$$ 0 0
$$681$$ −5.90943e8 −1.87113
$$682$$ 0 0
$$683$$ 3.61070e8i 1.13326i 0.823973 + 0.566630i $$0.191753\pi$$
−0.823973 + 0.566630i $$0.808247\pi$$
$$684$$ 0 0
$$685$$ −5.75995e8 −1.79204
$$686$$ 0 0
$$687$$ 6.83674e8i 2.10853i
$$688$$ 0 0
$$689$$ 6.61133e6 0.0202130
$$690$$ 0 0
$$691$$ −3.47750e8 −1.05398 −0.526991 0.849871i $$-0.676680\pi$$
−0.526991 + 0.849871i $$0.676680\pi$$
$$692$$ 0 0
$$693$$ 2.89209e8 0.868986
$$694$$ 0 0
$$695$$ −2.98806e8 −0.890091
$$696$$ 0 0
$$697$$ 3.75720e8i 1.10960i
$$698$$ 0 0
$$699$$ 1.54079e8i 0.451141i
$$700$$ 0 0
$$701$$ −8.95408e7 −0.259936 −0.129968 0.991518i $$-0.541487\pi$$
−0.129968 + 0.991518i $$0.541487\pi$$
$$702$$ 0 0
$$703$$ 6.42057e8 9.56321e7i 1.84802 0.275257i
$$704$$ 0 0
$$705$$ 7.32617e8i 2.09079i
$$706$$ 0 0
$$707$$ 3.51453e8 0.994511
$$708$$ 0 0
$$709$$ 1.93298e8 0.542362 0.271181 0.962528i $$-0.412586\pi$$
0.271181 + 0.962528i $$0.412586\pi$$
$$710$$ 0 0
$$711$$ 9.60807e7i 0.267317i
$$712$$ 0 0
$$713$$ 3.98851e8i 1.10038i
$$714$$ 0 0
$$715$$ 4.25879e7i 0.116511i
$$716$$ 0 0
$$717$$ 1.01261e9i 2.74717i
$$718$$ 0 0
$$719$$ 3.52698e8 0.948891 0.474445 0.880285i $$-0.342649\pi$$
0.474445 + 0.880285i $$0.342649\pi$$
$$720$$ 0 0
$$721$$ 2.72994e8i 0.728363i
$$722$$ 0 0
$$723$$ −3.04643e8 −0.806077
$$724$$ 0 0
$$725$$ 1.69954e8i 0.445983i
$$726$$ 0 0
$$727$$ 2.02827e8 0.527865 0.263932 0.964541i $$-0.414980\pi$$
0.263932 + 0.964541i $$0.414980\pi$$
$$728$$ 0 0
$$729$$ 5.41719e8 1.39827
$$730$$ 0 0
$$731$$ 6.15709e8 1.57624
$$732$$ 0 0
$$733$$ −4.60785e8 −1.17000 −0.585001 0.811033i $$-0.698906\pi$$
−0.585001 + 0.811033i $$0.698906\pi$$
$$734$$ 0 0
$$735$$ 5.78183e8i 1.45614i
$$736$$ 0 0
$$737$$ 7.80430e7i 0.194954i
$$738$$ 0 0
$$739$$ 2.61415e8 0.647734 0.323867 0.946103i $$-0.395017\pi$$
0.323867 + 0.946103i $$0.395017\pi$$
$$740$$ 0 0
$$741$$ 5.84055e6 + 3.92124e7i 0.0143549 + 0.0963760i
$$742$$ 0 0
$$743$$ 3.25053e8i 0.792480i −0.918147 0.396240i $$-0.870315\pi$$
0.918147 0.396240i $$-0.129685\pi$$
$$744$$ 0 0
$$745$$ −6.31519e8 −1.52728
$$746$$ 0 0
$$747$$ −1.10133e7 −0.0264215
$$748$$ 0 0
$$749$$ 2.67352e8i 0.636264i
$$750$$ 0 0
$$751$$ 2.90899e8i 0.686787i −0.939192 0.343393i $$-0.888424\pi$$
0.939192 0.343393i $$-0.111576\pi$$
$$752$$ 0 0
$$753$$ 1.08381e9i 2.53844i
$$754$$ 0 0
$$755$$ 5.75895e8i 1.33814i
$$756$$ 0 0
$$757$$ 7.60667e8 1.75350 0.876752 0.480943i $$-0.159706\pi$$
0.876752 + 0.480943i $$0.159706\pi$$
$$758$$ 0 0
$$759$$ 4.96678e8i 1.13593i
$$760$$ 0 0
$$761$$ −3.20532e8 −0.727306 −0.363653 0.931534i $$-0.618471\pi$$
−0.363653 + 0.931534i $$0.618471\pi$$
$$762$$ 0 0
$$763$$ 4.03854e8i 0.909182i
$$764$$ 0 0
$$765$$ 8.00726e8 1.78854
$$766$$ 0 0
$$767$$ 8.84438e6 0.0196011
$$768$$ 0 0
$$769$$ 4.20733e8 0.925183 0.462592 0.886571i $$-0.346920\pi$$
0.462592 + 0.886571i $$0.346920\pi$$
$$770$$ 0 0
$$771$$ −6.94136e8 −1.51454
$$772$$ 0 0
$$773$$ 6.21759e8i 1.34612i 0.739588 + 0.673060i $$0.235020\pi$$
−0.739588 + 0.673060i $$0.764980\pi$$
$$774$$ 0 0
$$775$$ 9.93253e8i 2.13381i
$$776$$ 0 0
$$777$$ 7.72343e8 1.64645
$$778$$ 0 0
$$779$$ −5.34233e8 + 7.95722e7i −1.13010 + 0.168325i
$$780$$ 0 0
$$781$$ 6.50061e8i 1.36459i
$$782$$ 0 0
$$783$$ −6.02928e7 −0.125597
$$784$$ 0 0
$$785$$ −6.06548e8 −1.25388
$$786$$ 0 0
$$787$$ 1.97860e7i 0.0405913i −0.999794 0.0202956i $$-0.993539\pi$$
0.999794 0.0202956i $$-0.00646075\pi$$
$$788$$ 0 0
$$789$$ 2.96858e8i 0.604390i
$$790$$ 0 0
$$791$$ 2.87486e8i 0.580881i
$$792$$ 0 0
$$793$$ 1.22693e7i 0.0246038i
$$794$$ 0 0
$$795$$ 3.47722e8 0.692040
$$796$$ 0 0